Database - modlgal_reps (mod-ell Galois reps)

Formats: - HTML - YAML - JSON - 2026-04-20T08:07:00.855508 - next page

Query: /api/modlgal_reps/?_offset=0

Column	Type
algebraic_group	text
bad_prime_list	jsonb
base_ring_characteristic	integer
base_ring_is_field	boolean
base_ring_order	integer
conductor	integer
conductor_is_squarefree	boolean
conductor_num_primes	integer
conductor_primes	integer[]
cyclotomic_exponent	integer
determinant_label	text
dimension	integer
dual_pair_of_algebras	jsonb
frobenius_matrices	integer[]
generating_primes	integer[]
good_prime_list	jsonb
image_index	integer
image_label	text
image_order	integer
image_type	text
is_absolutely_irreducible	boolean
is_irreducible	boolean
is_solvable	boolean
is_surjective	boolean
kernel_polynomial	integer[]
label	text
num	integer
projective_is_surjective	boolean
projective_kernel_polynomial	integer[]
projective_type	text
related_objects	text[]
top_slope_rational	text
top_slope_real	real
weight	integer

0. label: 2.1.1.1
   {'algebraic_group': 'GL', 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 1, 'conductor_is_squarefree': True, 'conductor_num_primes': 0, 'conductor_primes': [], 'cyclotomic_exponent': 1, 'determinant_label': '2.1.1.1', 'dimension': 1, 'frobenius_matrices': [[1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1], [1]], 'generating_primes': [], 'good_prime_list': [[3, [1]], [5, [1]], [7, [1]], [11, [1]], [13, [1]], [17, [1]], [19, [1]], [23, [1]], [29, [1]], [31, [1]], [37, [1]], [41, [1]], [43, [1]], [47, [1]], [53, [1]], [59, [1]], [61, [1]], [67, [1]], [71, [1]], [73, [1]], [79, [1]], [83, [1]], [89, [1]], [97, [1]]], 'image_index': 1, 'image_label': '1.1.1', 'image_order': 1, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [0, 1], 'label': '2.1.1.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [0, 1], 'projective_type': 'big', 'related_objects': [['Dirichlet', '2.1']], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
1. label: 2.2.11.1
   {'algebraic_group': 'GL', 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 11, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [11], 'cyclotomic_exponent': 1, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [1, 1, -1, 1]], [[0, 1], [1, 1, -1, 1]], [4, [[1, 3, 1, -1], [3, -3, -1, 1], [1, -1, -3, -9], [-1, 1, -9, -11]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [1, 0, 0, 1]], [53, [1, 0, 0, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [1, 1, -1, 1], 'label': '2.2.11.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [1, 1, -1, 1], 'projective_type': 'big', 'related_objects': [['ECQ', '11.a1'], ['MF', '11.2.a.a']], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
2. label: 2.2.13.1
   {'algebraic_group': 'GL', 'bad_prime_list': [[13, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 13, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [13], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, -1, 0, 1]], [[0, 1], [-2, -1, 0, 1]], [4, [[1, 3, 0, 2], [3, -3, 0, -2], [0, 0, 4, 12], [2, -2, 12, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 11], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [1, 0, 0, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, -1, 0, 1], 'label': '2.2.13.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, -1, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
3. label: 2.2.19.1
   {'algebraic_group': 'GL', 'bad_prime_list': [[19, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 19, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [19], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, -2, 0, 1]], [[0, 1], [-2, -2, 0, 1]], [4, [[1, 3, 0, 4], [3, -3, 0, -4], [0, 0, 8, 12], [4, -4, 12, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [23, [1, 0, 0, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [1, 0, 0, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, -2, 0, 1], 'label': '2.2.19.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, -2, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
4. label: 2.2.19.2
   {'algebraic_group': 'GL', 'bad_prime_list': [[19, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 19, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [19], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, -2, -1, 1]], [[0, 1], [-2, -2, -1, 1]], [4, [[1, 3, 1, 5], [3, -3, -1, -5], [1, -1, 9, 21], [5, -5, 21, 25]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [1, 0, 0, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [1, 0, 0, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, -2, -1, 1], 'label': '2.2.19.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, -2, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
5. label: 2.2.23.1
   {'algebraic_group': 'GL', 'bad_prime_list': [[23, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 23, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [23], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [1, 0, -1, 1]], [[0, 1], [1, 0, -1, 1]], [4, [[1, 3, 1, 1], [3, -3, -1, -1], [1, -1, 1, -5], [1, -1, -5, -7]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [1, 0, -1, 1], 'label': '2.2.23.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [1, 0, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
6. label: 2.2.25.1
   {'algebraic_group': 'GL', 'bad_prime_list': [[5, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 25, 'conductor_is_squarefree': False, 'conductor_num_primes': 1, 'conductor_primes': [5], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [2, 2, -1, 1]], [[0, 1], [2, 2, -1, 1]], [4, [[1, 3, 1, -3], [3, -3, -1, 3], [1, -1, -7, -19], [-3, 3, -19, -23]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [1, 0, 0, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 1]], [97, [1, 0, 0, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [2, 2, -1, 1], 'label': '2.2.25.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [2, 2, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
7. label: 2.2.27.1
   {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 27, 'conductor_is_squarefree': False, 'conductor_num_primes': 1, 'conductor_primes': [3], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, 0, 0, 1]], [[0, 1], [-2, 0, 0, 1]], [4, [[1, 3, 0, 0], [3, -3, 0, 0], [0, 0, 0, 12], [0, 0, 12, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [5, 7], 'good_prime_list': [[5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [1, 0, 0, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [1, 0, 0, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, 0, 0, 1], 'label': '2.2.27.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, 0, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
8. label: 2.2.27.2
   {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 27, 'conductor_is_squarefree': False, 'conductor_num_primes': 1, 'conductor_primes': [3], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, 3, 0, 1]], [[0, 1], [-2, 3, 0, 1]], [4, [[1, 3, 0, -6], [3, -3, 0, 6], [0, 0, -12, 12], [-6, 6, 12, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [5, 13], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [1, 0, 0, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [1, 0, 0, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, 3, 0, 1], 'label': '2.2.27.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, 3, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
9. label: 2.2.29.1
   {'algebraic_group': 'GL', 'bad_prime_list': [[29, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 29, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [29], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, 0, -1, 1]], [[0, 1], [-2, 0, -1, 1]], [4, [[1, 3, 1, 1], [3, -3, -1, -1], [1, -1, 1, 13], [1, -1, 13, 17]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [1, 0, 0, 1]], [23, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, 0, -1, 1], 'label': '2.2.29.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, 0, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
10. label: 2.2.31.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[31, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 31, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [31], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-1, 1, 0, 1]], [[0, 1], [-1, 1, 0, 1]], [4, [[1, 3, 0, -2], [3, -3, 0, 2], [0, 0, -4, 6], [-2, 2, 6, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [1, 0, 0, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-1, 1, 0, 1], 'label': '2.2.31.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-1, 1, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
11. label: 2.2.35.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[5, '', '', '', ''], [7, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 35, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [5, 7], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, 2, 0, 1]], [[0, 1], [-2, 2, 0, 1]], [4, [[1, 3, 0, -4], [3, -3, 0, 4], [0, 0, -8, 12], [-4, 4, 12, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [3, 19], 'good_prime_list': [[3, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [1, 0, 0, 1]], [73, [1, 0, 0, 1]], [79, [0, 1, 1, 1]], [83, [1, 0, 0, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, 2, 0, 1], 'label': '2.2.35.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, 2, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
12. label: 2.2.37.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[37, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 37, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [37], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [1, -3, -1, 1]], [[0, 1], [1, -3, -1, 1]], [4, [[1, 3, 1, 7], [3, -3, -1, -7], [1, -1, 13, 7], [7, -7, 7, 5]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [1, -3, -1, 1], 'label': '2.2.37.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [1, -3, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
13. label: 2.2.43.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[43, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 43, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [43], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [3, -1, -1, 1]], [[0, 1], [3, -1, -1, 1]], [4, [[1, 3, 1, 3], [3, -3, -1, -3], [1, -1, 5, -13], [3, -3, -13, -19]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [3, 11], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [47, [1, 0, 0, 1]], [53, [0, 1, 1, 1]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [1, 0, 0, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [3, -1, -1, 1], 'label': '2.2.43.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [3, -1, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
14. label: 2.2.49.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[7, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 49, 'conductor_is_squarefree': False, 'conductor_num_primes': 1, 'conductor_primes': [7], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'frobenius_matrices': [[0, 1, 1, 1], [1, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 1, 1, 0], [1, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [1, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 1, 1, 0], [1, 0, 0, 1], [1, 1, 1, 0], [1, 0, 0, 1]], 'generating_primes': [3], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [1, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [1, 0, 0, 1]], [17, [0, 1, 1, 1]], [19, [1, 1, 1, 0]], [23, [1, 1, 1, 0]], [29, [1, 0, 0, 1]], [31, [0, 1, 1, 1]], [37, [1, 1, 1, 0]], [41, [1, 0, 0, 1]], [43, [1, 0, 0, 1]], [47, [1, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [1, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [1, 0, 0, 1]], [73, [0, 1, 1, 1]], [79, [1, 1, 1, 0]], [83, [1, 0, 0, 1]], [89, [1, 1, 1, 0]], [97, [1, 0, 0, 1]]], 'image_index': 2, 'image_label': '2Cn', 'image_order': 3, 'image_type': 'cyclic', 'is_absolutely_irreducible': False, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': False, 'kernel_polynomial': [1, -2, -1, 1], 'label': '2.2.49.1', 'num': 1, 'projective_is_surjective': False, 'projective_kernel_polynomial': [1, -2, -1, 1], 'projective_type': 'cyclic', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0}
15. label: 2.2.51.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [17, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 51, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 17], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-3, 1, -1, 1]], [[0, 1], [-3, 1, -1, 1]], [4, [[1, 3, 1, -1], [3, -3, -1, 1], [1, -1, -3, 15], [-1, 1, 15, 21]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [5, 7], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [1, 0, 0, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [1, 0, 0, 1]], [71, [1, 0, 0, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-3, 1, -1, 1], 'label': '2.2.51.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-3, 1, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
16. label: 2.2.53.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[53, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 53, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [53], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, 4, -1, 1]], [[0, 1], [-2, 4, -1, 1]], [4, [[1, 3, 1, -7], [3, -3, -1, 7], [1, -1, -15, -3], [-7, 7, -3, 1]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [1, 0, 0, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [1, 0, 0, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, 4, -1, 1], 'label': '2.2.53.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, 4, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
17. label: 2.2.53.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[53, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 53, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [53], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [8, 0, -1, 1]], [[0, 1], [8, 0, -1, 1]], [4, [[1, 3, 1, 1], [3, -3, -1, -1], [1, -1, 1, -47], [1, -1, -47, -63]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 0]], [71, [1, 0, 0, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [8, 0, -1, 1], 'label': '2.2.53.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [8, 0, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
18. label: 2.2.55.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[5, '', '', '', ''], [11, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 55, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [5, 11], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-8, 2, 0, 1]], [[0, 1], [-8, 2, 0, 1]], [4, [[1, 3, 0, -4], [3, -3, 0, 4], [0, 0, -8, 48], [-4, 4, 48, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 13], 'good_prime_list': [[3, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 1]], [73, [1, 0, 0, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-8, 2, 0, 1], 'label': '2.2.55.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-8, 2, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
19. label: 2.2.59.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[59, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 59, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [59], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-1, 2, 0, 1]], [[0, 1], [-1, 2, 0, 1]], [4, [[1, 3, 0, -4], [3, -3, 0, 4], [0, 0, -8, 6], [-4, 4, 6, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 11], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [1, 0, 0, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [1, 0, 0, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-1, 2, 0, 1], 'label': '2.2.59.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-1, 2, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
20. label: 2.2.59.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[59, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 59, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [59], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-6, -5, 0, 1]], [[0, 1], [-6, -5, 0, 1]], [4, [[1, 3, 0, 10], [3, -3, 0, -10], [0, 0, 20, 36], [10, -10, 36, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [61, [1, 0, 0, 1]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-6, -5, 0, 1], 'label': '2.2.59.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-6, -5, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
21. label: 2.2.61.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[61, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 61, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [61], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-6, 1, 0, 1]], [[0, 1], [-6, 1, 0, 1]], [4, [[1, 3, 0, -2], [3, -3, 0, 2], [0, 0, -4, 36], [-2, 2, 36, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [1, 0, 0, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [1, 0, 0, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [67, [0, 1, 1, 1]], [71, [1, 0, 0, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [1, 0, 0, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-6, 1, 0, 1], 'label': '2.2.61.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-6, 1, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
22. label: 2.2.67.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[67, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 67, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [67], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [5, -3, -1, 1]], [[0, 1], [5, -3, -1, 1]], [4, [[1, 3, 1, 7], [3, -3, -1, -7], [1, -1, 13, -17], [7, -7, -17, -27]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 17], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [71, [1, 0, 0, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [1, 0, 0, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [5, -3, -1, 1], 'label': '2.2.67.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [5, -3, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
23. label: 2.2.71.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[71, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 71, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [71], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, -6, -1, 1]], [[0, 1], [-2, -6, -1, 1]], [4, [[1, 3, 1, 13], [3, -3, -1, -13], [1, -1, 25, 37], [13, -13, 37, 41]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [1, 0, 0, 1]], [59, [0, 1, 1, 0]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [1, 0, 0, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, -6, -1, 1], 'label': '2.2.71.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, -6, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
24. label: 2.2.75.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [5, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 75, 'conductor_is_squarefree': False, 'conductor_num_primes': 2, 'conductor_primes': [3, 5], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-3, -3, -1, 1]], [[0, 1], [-3, -3, -1, 1]], [4, [[1, 3, 1, 7], [3, -3, -1, -7], [1, -1, 13, 31], [7, -7, 31, 37]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [7, 11], 'good_prime_list': [[7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [1, 0, 0, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [1, 0, 0, 1]], [79, [1, 0, 0, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-3, -3, -1, 1], 'label': '2.2.75.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-3, -3, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
25. label: 2.2.79.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[79, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 79, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [79], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [2, -4, -1, 1]], [[0, 1], [2, -4, -1, 1]], [4, [[1, 3, 1, 9], [3, -3, -1, -9], [1, -1, 17, 5], [9, -9, 5, 1]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1]], 'generating_primes': [3, 11], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [1, 0, 0, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [1, 0, 0, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [2, -4, -1, 1], 'label': '2.2.79.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [2, -4, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
26. label: 2.2.81.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 81, 'conductor_is_squarefree': False, 'conductor_num_primes': 1, 'conductor_primes': [3], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-4, -3, 0, 1]], [[0, 1], [-4, -3, 0, 1]], [4, [[1, 3, 0, 6], [3, -3, 0, -6], [0, 0, 12, 24], [6, -6, 24, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1]], 'generating_primes': [5, 7], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [1, 0, 0, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [1, 0, 0, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [1, 0, 0, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-4, -3, 0, 1], 'label': '2.2.81.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-4, -3, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
27. label: 2.2.81.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 81, 'conductor_is_squarefree': False, 'conductor_num_primes': 1, 'conductor_primes': [3], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-10, -3, 0, 1]], [[0, 1], [-10, -3, 0, 1]], [4, [[1, 3, 0, 6], [3, -3, 0, -6], [0, 0, 12, 60], [6, -6, 60, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 1]], 'generating_primes': [5, 11], 'good_prime_list': [[5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [1, 0, 0, 1]], [89, [1, 0, 0, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-10, -3, 0, 1], 'label': '2.2.81.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-10, -3, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
28. label: 2.2.81.3
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 81, 'conductor_is_squarefree': False, 'conductor_num_primes': 1, 'conductor_primes': [3], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'frobenius_matrices': [[1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1]], 'generating_primes': [], 'good_prime_list': [[5, [1, 0, 0, 1]], [7, [1, 0, 0, 1]], [11, [1, 0, 0, 1]], [13, [1, 0, 0, 1]], [17, [1, 0, 0, 1]], [19, [1, 0, 0, 1]], [23, [1, 0, 0, 1]], [29, [1, 0, 0, 1]], [31, [1, 0, 0, 1]], [37, [1, 0, 0, 1]], [41, [1, 0, 0, 1]], [43, [1, 0, 0, 1]], [47, [1, 0, 0, 1]], [53, [1, 0, 0, 1]], [59, [1, 0, 0, 1]], [61, [1, 0, 0, 1]], [67, [1, 0, 0, 1]], [71, [1, 0, 0, 1]], [73, [1, 0, 0, 1]], [79, [1, 0, 0, 1]], [83, [1, 0, 0, 1]], [89, [1, 0, 0, 1]], [97, [1, 0, 0, 1]]], 'image_index': 2, 'image_label': '2Cn', 'image_order': 3, 'image_type': 'cyclic', 'is_absolutely_irreducible': False, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': False, 'kernel_polynomial': [-1, -3, 0, 1], 'label': '2.2.81.3', 'num': 3, 'projective_is_surjective': False, 'projective_kernel_polynomial': [-1, -3, 0, 1], 'projective_type': 'cyclic', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0}
29. label: 2.2.83.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[83, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 83, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [83], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, 1, -1, 1]], [[0, 1], [-2, 1, -1, 1]], [4, [[1, 3, 1, -1], [3, -3, -1, 1], [1, -1, -3, 9], [-1, 1, 9, 13]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [1, 0, 0, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 1]], [41, [1, 0, 0, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, 1, -1, 1], 'label': '2.2.83.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, 1, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
30. label: 2.2.85.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[5, '', '', '', ''], [17, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 85, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [5, 17], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [10, -6, -1, 1]], [[0, 1], [10, -6, -1, 1]], [4, [[1, 3, 1, 13], [3, -3, -1, -13], [1, -1, 25, -35], [13, -13, -35, -55]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [1, 0, 0, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [10, -6, -1, 1], 'label': '2.2.85.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [10, -6, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
31. label: 2.2.87.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [29, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 87, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 29], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [1, 2, -1, 1]], [[0, 1], [1, 2, -1, 1]], [4, [[1, 3, 1, -3], [3, -3, -1, 3], [1, -1, -7, -13], [-3, 3, -13, -15]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [5, 7], 'good_prime_list': [[5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [1, 0, 0, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [1, 2, -1, 1], 'label': '2.2.87.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [1, 2, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
32. label: 2.2.87.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [29, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 87, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 29], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [6, -2, -1, 1]], [[0, 1], [6, -2, -1, 1]], [4, [[1, 3, 1, 5], [3, -3, -1, -5], [1, -1, 9, -27], [5, -5, -27, -39]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 0]], 'generating_primes': [5, 11], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [1, 0, 0, 1]], [59, [0, 1, 1, 1]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [1, 0, 0, 1]], [89, [1, 0, 0, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [6, -2, -1, 1], 'label': '2.2.87.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [6, -2, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
33. label: 2.2.89.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[89, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 89, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [89], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [7, 1, -1, 1]], [[0, 1], [7, 1, -1, 1]], [4, [[1, 3, 1, -1], [3, -3, -1, 1], [1, -1, -3, -45], [-1, 1, -45, -59]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1]], 'generating_primes': [3, 11], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 1]], [7, [1, 0, 0, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [1, 0, 0, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [7, 1, -1, 1], 'label': '2.2.89.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [7, 1, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
34. label: 2.2.91.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[7, '', '', '', ''], [13, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 91, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [7, 13], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, 4, 0, 1]], [[0, 1], [-2, 4, 0, 1]], [4, [[1, 3, 0, -8], [3, -3, 0, 8], [0, 0, -16, 12], [-8, 8, 12, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [1, 0, 0, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, 4, 0, 1], 'label': '2.2.91.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, 4, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
35. label: 2.2.91.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[7, '', '', '', ''], [13, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 91, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [7, 13], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, 6, -1, 1]], [[0, 1], [-2, 6, -1, 1]], [4, [[1, 3, 1, -11], [3, -3, -1, 11], [1, -1, -23, -11], [-11, 11, -11, -7]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [1, 0, 0, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, 6, -1, 1], 'label': '2.2.91.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, 6, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
36. label: 2.2.93.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [31, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 93, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 31], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-6, -6, -1, 1]], [[0, 1], [-6, -6, -1, 1]], [4, [[1, 3, 1, 13], [3, -3, -1, -13], [1, -1, 25, 61], [13, -13, 61, 73]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1]], 'generating_primes': [5, 7], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [37, [1, 0, 0, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [1, 0, 0, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-6, -6, -1, 1], 'label': '2.2.93.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-6, -6, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
37. label: 2.2.101.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[101, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 101, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [101], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-1, -5, -1, 1]], [[0, 1], [-1, -5, -1, 1]], [4, [[1, 3, 1, 11], [3, -3, -1, -11], [1, -1, 21, 27], [11, -11, 27, 29]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [1, 0, 0, 1]], [41, [0, 1, 1, 0]], [43, [1, 0, 0, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [1, 0, 0, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-1, -5, -1, 1], 'label': '2.2.101.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-1, -5, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
38. label: 2.2.101.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[101, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 101, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [101], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-6, 2, -1, 1]], [[0, 1], [-6, 2, -1, 1]], [4, [[1, 3, 1, -3], [3, -3, -1, 3], [1, -1, -7, 29], [-3, 3, 29, 41]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-6, 2, -1, 1], 'label': '2.2.101.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-6, 2, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
39. label: 2.2.107.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[107, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 107, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [107], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, 3, -1, 1]], [[0, 1], [-2, 3, -1, 1]], [4, [[1, 3, 1, -5], [3, -3, -1, 5], [1, -1, -11, 1], [-5, 5, 1, 5]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [1, 0, 0, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [1, 0, 0, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [1, 0, 0, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, 3, -1, 1], 'label': '2.2.107.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, 3, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
40. label: 2.2.107.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[107, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 107, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [107], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [11, 1, -1, 1]], [[0, 1], [11, 1, -1, 1]], [4, [[1, 3, 1, -1], [3, -3, -1, 1], [1, -1, -3, -69], [-1, 1, -69, -91]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [11, 1, -1, 1], 'label': '2.2.107.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [11, 1, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
41. label: 2.2.109.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[109, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 109, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [109], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-4, 1, 0, 1]], [[0, 1], [-4, 1, 0, 1]], [4, [[1, 3, 0, -2], [3, -3, 0, 2], [0, 0, -4, 24], [-2, 2, 24, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 1]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [1, 0, 0, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-4, 1, 0, 1], 'label': '2.2.109.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-4, 1, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
42. label: 2.2.111.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [37, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 111, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 37], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [3, 9, -1, 1]], [[0, 1], [3, 9, -1, 1]], [4, [[1, 3, 1, -17], [3, -3, -1, 17], [1, -1, -35, -53], [-17, 17, -53, -59]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [5, 7], 'good_prime_list': [[5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [1, 0, 0, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [3, 9, -1, 1], 'label': '2.2.111.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [3, 9, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
43. label: 2.2.115.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[5, '', '', '', ''], [23, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 115, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [5, 23], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-3, 5, -1, 1]], [[0, 1], [-3, 5, -1, 1]], [4, [[1, 3, 1, -9], [3, -3, -1, 9], [1, -1, -19, -1], [-9, 9, -1, 5]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [1, 0, 0, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [1, 0, 0, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-3, 5, -1, 1], 'label': '2.2.115.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-3, 5, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
44. label: 2.2.121.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[11, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 121, 'conductor_is_squarefree': False, 'conductor_num_primes': 1, 'conductor_primes': [11], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [2, 4, -1, 1]], [[0, 1], [2, 4, -1, 1]], [4, [[1, 3, 1, -7], [3, -3, -1, 7], [1, -1, -15, -27], [-7, 7, -27, -31]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [1, 0, 0, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [2, 4, -1, 1], 'label': '2.2.121.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [2, 4, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
45. label: 2.2.123.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [41, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 123, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 41], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [3, 3, -1, 1]], [[0, 1], [3, 3, -1, 1]], [4, [[1, 3, 1, -5], [3, -3, -1, 5], [1, -1, -11, -29], [-5, 5, -29, -35]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0]], 'generating_primes': [5, 11], 'good_prime_list': [[5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [1, 0, 0, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [1, 0, 0, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [3, 3, -1, 1], 'label': '2.2.123.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [3, 3, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
46. label: 2.2.123.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [41, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 123, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 41], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-12, 0, -1, 1]], [[0, 1], [-12, 0, -1, 1]], [4, [[1, 3, 1, 1], [3, -3, -1, -1], [1, -1, 1, 73], [1, -1, 73, 97]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [5, 7], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [1, 0, 0, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-12, 0, -1, 1], 'label': '2.2.123.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-12, 0, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
47. label: 2.2.127.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[127, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 127, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [127], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [2, -6, -1, 1]], [[0, 1], [2, -6, -1, 1]], [4, [[1, 3, 1, 13], [3, -3, -1, -13], [1, -1, 25, 13], [13, -13, 13, 9]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [1, 0, 0, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [1, 0, 0, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [2, -6, -1, 1], 'label': '2.2.127.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [2, -6, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
48. label: 2.2.129.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [43, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 129, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 43], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-9, 1, -1, 1]], [[0, 1], [-9, 1, -1, 1]], [4, [[1, 3, 1, -1], [3, -3, -1, 1], [1, -1, -3, 51], [-1, 1, 51, 69]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1]], 'generating_primes': [5, 17], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [1, 0, 0, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [1, 0, 0, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-9, 1, -1, 1], 'label': '2.2.129.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-9, 1, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
49. label: 2.2.131.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[131, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 131, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [131], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-5, 3, -1, 1]], [[0, 1], [-5, 3, -1, 1]], [4, [[1, 3, 1, -5], [3, -3, -1, 5], [1, -1, -11, 19], [-5, 5, 19, 29]]]], 'frobenius_matrices': [[0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 17], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [1, 0, 0, 1]], [7, [0, 1, 1, 1]], [11, [1, 0, 0, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-5, 3, -1, 1], 'label': '2.2.131.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-5, 3, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
50. label: 2.2.131.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[131, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 131, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [131], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-12, 8, -1, 1]], [[0, 1], [-12, 8, -1, 1]], [4, [[1, 3, 1, -15], [3, -3, -1, 15], [1, -1, -31, 41], [-15, 15, 41, 65]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-12, 8, -1, 1], 'label': '2.2.131.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-12, 8, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
51. label: 2.2.135.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [5, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 135, 'conductor_is_squarefree': False, 'conductor_num_primes': 2, 'conductor_primes': [3, 5], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-1, 3, 0, 1]], [[0, 1], [-1, 3, 0, 1]], [4, [[1, 3, 0, -6], [3, -3, 0, 6], [0, 0, -12, 6], [-6, 6, 6, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [7, 17], 'good_prime_list': [[7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [1, 0, 0, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-1, 3, 0, 1], 'label': '2.2.135.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-1, 3, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
52. label: 2.2.135.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [5, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 135, 'conductor_is_squarefree': False, 'conductor_num_primes': 2, 'conductor_primes': [3, 5], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-6, 3, 0, 1]], [[0, 1], [-6, 3, 0, 1]], [4, [[1, 3, 0, -6], [3, -3, 0, 6], [0, 0, -12, 36], [-6, 6, 36, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [7, 11], 'good_prime_list': [[7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [1, 0, 0, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 0]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-6, 3, 0, 1], 'label': '2.2.135.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-6, 3, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
53. label: 2.2.137.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[137, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 137, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [137], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-13, 1, -1, 1]], [[0, 1], [-13, 1, -1, 1]], [4, [[1, 3, 1, -1], [3, -3, -1, 1], [1, -1, -3, 75], [-1, 1, 75, 101]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [1, 0, 0, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [1, 0, 0, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-13, 1, -1, 1], 'label': '2.2.137.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-13, 1, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
54. label: 2.2.139.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[139, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 139, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [139], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [2, 1, -1, 1]], [[0, 1], [2, 1, -1, 1]], [4, [[1, 3, 1, -1], [3, -3, -1, 1], [1, -1, -3, -15], [-1, 1, -15, -19]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [1, 0, 0, 1]], [41, [1, 0, 0, 1]], [43, [0, 1, 1, 0]], [47, [1, 0, 0, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [2, 1, -1, 1], 'label': '2.2.139.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [2, 1, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
55. label: 2.2.141.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [47, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 141, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 47], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [3, -5, -1, 1]], [[0, 1], [3, -5, -1, 1]], [4, [[1, 3, 1, 11], [3, -3, -1, -11], [1, -1, 21, 3], [11, -11, 3, -3]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [5, 13], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [1, 0, 0, 1]], [43, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [3, -5, -1, 1], 'label': '2.2.141.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [3, -5, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
56. label: 2.2.143.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[11, '', '', '', ''], [13, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 143, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [11, 13], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [2, 6, -1, 1]], [[0, 1], [2, 6, -1, 1]], [4, [[1, 3, 1, -11], [3, -3, -1, 11], [1, -1, -23, -35], [-11, 11, -35, -39]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [1, 0, 0, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [2, 6, -1, 1], 'label': '2.2.143.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [2, 6, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
57. label: 2.2.147.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [7, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 147, 'conductor_is_squarefree': False, 'conductor_num_primes': 2, 'conductor_primes': [3, 7], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [1, 5, -1, 1]], [[0, 1], [1, 5, -1, 1]], [4, [[1, 3, 1, -9], [3, -3, -1, 9], [1, -1, -19, -25], [-9, 9, -25, -27]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1]], 'generating_primes': [5, 13], 'good_prime_list': [[5, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [1, 0, 0, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [1, 5, -1, 1], 'label': '2.2.147.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [1, 5, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
58. label: 2.2.147.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [7, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 147, 'conductor_is_squarefree': False, 'conductor_num_primes': 2, 'conductor_primes': [3, 7], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-6, -2, -1, 1]], [[0, 1], [-6, -2, -1, 1]], [4, [[1, 3, 1, 5], [3, -3, -1, -5], [1, -1, 9, 45], [5, -5, 45, 57]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [5, 13], 'good_prime_list': [[5, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [1, 0, 0, 1]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-6, -2, -1, 1], 'label': '2.2.147.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-6, -2, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
59. label: 2.2.149.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[149, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 149, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [149], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [6, 2, -1, 1]], [[0, 1], [6, 2, -1, 1]], [4, [[1, 3, 1, -3], [3, -3, -1, 3], [1, -1, -7, -43], [-3, 3, -43, -55]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 13], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [6, 2, -1, 1], 'label': '2.2.149.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [6, 2, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
60. label: 2.2.151.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[151, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 151, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [151], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [8, 8, -1, 1]], [[0, 1], [8, 8, -1, 1]], [4, [[1, 3, 1, -15], [3, -3, -1, 15], [1, -1, -31, -79], [-15, 15, -79, -95]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [1, 0, 0, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [8, 8, -1, 1], 'label': '2.2.151.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [8, 8, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
61. label: 2.2.155.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[5, '', '', '', ''], [31, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 155, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [5, 31], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-5, -5, -1, 1]], [[0, 1], [-5, -5, -1, 1]], [4, [[1, 3, 1, 11], [3, -3, -1, -11], [1, -1, 21, 51], [11, -11, 51, 61]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [1, 0, 0, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [1, 0, 0, 1]], [29, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-5, -5, -1, 1], 'label': '2.2.155.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-5, -5, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
62. label: 2.2.157.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[157, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 157, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [157], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [8, 4, -1, 1]], [[0, 1], [8, 4, -1, 1]], [4, [[1, 3, 1, -7], [3, -3, -1, 7], [1, -1, -15, -63], [-7, 7, -63, -79]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [1, 0, 0, 1]], [83, [1, 0, 0, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [8, 4, -1, 1], 'label': '2.2.157.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [8, 4, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
63. label: 2.2.159.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [53, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 159, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 53], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [15, -3, -1, 1]], [[0, 1], [15, -3, -1, 1]], [4, [[1, 3, 1, 7], [3, -3, -1, -7], [1, -1, 13, -77], [7, -7, -77, -107]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [5, 7], 'good_prime_list': [[5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [15, -3, -1, 1], 'label': '2.2.159.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [15, -3, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
64. label: 2.2.163.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[163, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 163, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [163], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [5, 7, -1, 1]], [[0, 1], [5, 7, -1, 1]], [4, [[1, 3, 1, -13], [3, -3, -1, 13], [1, -1, -27, -57], [-13, 13, -57, -67]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [3, 41], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [5, 7, -1, 1], 'label': '2.2.163.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [5, 7, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
65. label: 2.2.163.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[163, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 163, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [163], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, -11, 0, 1]], [[0, 1], [-2, -11, 0, 1]], [4, [[1, 3, 0, 22], [3, -3, 0, -22], [0, 0, 44, 12], [22, -22, 12, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [1, 0, 0, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [1, 0, 0, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, -11, 0, 1], 'label': '2.2.163.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, -11, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
66. label: 2.2.167.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[167, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 167, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [167], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-13, 9, -1, 1]], [[0, 1], [-13, 9, -1, 1]], [4, [[1, 3, 1, -17], [3, -3, -1, 17], [1, -1, -35, 43], [-17, 17, 43, 69]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [1, 0, 0, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [1, 0, 0, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-13, 9, -1, 1], 'label': '2.2.167.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-13, 9, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
67. label: 2.2.169.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[13, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 169, 'conductor_is_squarefree': False, 'conductor_num_primes': 1, 'conductor_primes': [13], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [12, -4, -1, 1]], [[0, 1], [12, -4, -1, 1]], [4, [[1, 3, 1, 9], [3, -3, -1, -9], [1, -1, 17, -55], [9, -9, -55, -79]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [1, 0, 0, 1]], [97, [1, 0, 0, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [12, -4, -1, 1], 'label': '2.2.169.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [12, -4, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
68. label: 2.2.169.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[13, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 169, 'conductor_is_squarefree': False, 'conductor_num_primes': 1, 'conductor_primes': [13], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'frobenius_matrices': [[0, 1, 1, 1], [1, 0, 0, 1], [1, 1, 1, 0], [0, 1, 1, 1], [1, 1, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [1, 1, 1, 0], [1, 1, 1, 0], [0, 1, 1, 1], [1, 1, 1, 0], [1, 0, 0, 1], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 1, 1, 0]], 'generating_primes': [3], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [1, 0, 0, 1]], [7, [1, 1, 1, 0]], [11, [0, 1, 1, 1]], [17, [1, 1, 1, 0]], [19, [1, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [1, 0, 0, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [1, 1, 1, 0]], [47, [1, 0, 0, 1]], [53, [1, 0, 0, 1]], [59, [1, 1, 1, 0]], [61, [1, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [1, 1, 1, 0]], [73, [1, 0, 0, 1]], [79, [1, 0, 0, 1]], [83, [1, 0, 0, 1]], [89, [0, 1, 1, 1]], [97, [1, 1, 1, 0]]], 'image_index': 2, 'image_label': '2Cn', 'image_order': 3, 'image_type': 'cyclic', 'is_absolutely_irreducible': False, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': False, 'kernel_polynomial': [-1, -4, -1, 1], 'label': '2.2.169.2', 'num': 2, 'projective_is_surjective': False, 'projective_kernel_polynomial': [-1, -4, -1, 1], 'projective_type': 'cyclic', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0}
69. label: 2.2.173.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[173, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 173, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [173], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [14, -10, -1, 1]], [[0, 1], [14, -10, -1, 1]], [4, [[1, 3, 1, 21], [3, -3, -1, -21], [1, -1, 41, -43], [21, -21, -43, -71]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [1, 0, 0, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [1, 0, 0, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [14, -10, -1, 1], 'label': '2.2.173.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [14, -10, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
70. label: 2.2.175.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[5, '', '', '', ''], [7, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 175, 'conductor_is_squarefree': False, 'conductor_num_primes': 2, 'conductor_primes': [5, 7], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-3, 2, -1, 1]], [[0, 1], [-3, 2, -1, 1]], [4, [[1, 3, 1, -3], [3, -3, -1, 3], [1, -1, -7, 11], [-3, 3, 11, 17]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 11], 'good_prime_list': [[3, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [1, 0, 0, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-3, 2, -1, 1], 'label': '2.2.175.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-3, 2, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
71. label: 2.2.179.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[179, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 179, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [179], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-6, -4, 0, 1]], [[0, 1], [-6, -4, 0, 1]], [4, [[1, 3, 0, 8], [3, -3, 0, -8], [0, 0, 16, 36], [8, -8, 36, 0]]]], 'frobenius_matrices': [[1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [5, 7], 'good_prime_list': [[3, [1, 0, 0, 1]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [1, 0, 0, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-6, -4, 0, 1], 'label': '2.2.179.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-6, -4, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
72. label: 2.2.179.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[179, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 179, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [179], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-8, 10, 0, 1]], [[0, 1], [-8, 10, 0, 1]], [4, [[1, 3, 0, -20], [3, -3, 0, 20], [0, 0, -40, 48], [-20, 20, 48, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 11], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-8, 10, 0, 1], 'label': '2.2.179.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-8, 10, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
73. label: 2.2.181.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[181, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 181, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [181], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-14, 5, 0, 1]], [[0, 1], [-14, 5, 0, 1]], [4, [[1, 3, 0, -10], [3, -3, 0, 10], [0, 0, -20, 84], [-10, 10, 84, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [7, [1, 0, 0, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [1, 0, 0, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 1]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-14, 5, 0, 1], 'label': '2.2.181.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-14, 5, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
74. label: 2.2.183.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [61, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 183, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 61], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [19, -7, -1, 1]], [[0, 1], [19, -7, -1, 1]], [4, [[1, 3, 1, 15], [3, -3, -1, -15], [1, -1, 29, -85], [15, -15, -85, -123]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1]], 'generating_primes': [5, 7], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [19, -7, -1, 1], 'label': '2.2.183.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [19, -7, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
75. label: 2.2.185.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[5, '', '', '', ''], [37, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 185, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [5, 37], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, 7, 0, 1]], [[0, 1], [-2, 7, 0, 1]], [4, [[1, 3, 0, -14], [3, -3, 0, 14], [0, 0, -28, 12], [-14, 14, 12, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [1, 0, 0, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [1, 0, 0, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, 7, 0, 1], 'label': '2.2.185.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, 7, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
76. label: 2.2.187.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[11, '', '', '', ''], [17, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 187, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [11, 17], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [5, 1, -1, 1]], [[0, 1], [5, 1, -1, 1]], [4, [[1, 3, 1, -1], [3, -3, -1, 1], [1, -1, -3, -33], [-1, 1, -33, -43]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [1, 0, 0, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [5, 1, -1, 1], 'label': '2.2.187.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [5, 1, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
77. label: 2.2.189.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [7, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 189, 'conductor_is_squarefree': False, 'conductor_num_primes': 2, 'conductor_primes': [3, 7], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-2, -6, 0, 1]], [[0, 1], [-2, -6, 0, 1]], [4, [[1, 3, 0, 12], [3, -3, 0, -12], [0, 0, 24, 12], [12, -12, 12, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0]], 'generating_primes': [5, 11], 'good_prime_list': [[5, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [1, 0, 0, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-2, -6, 0, 1], 'label': '2.2.189.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-2, -6, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
78. label: 2.2.189.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [7, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 189, 'conductor_is_squarefree': False, 'conductor_num_primes': 2, 'conductor_primes': [3, 7], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-12, -6, 0, 1]], [[0, 1], [-12, -6, 0, 1]], [4, [[1, 3, 0, 12], [3, -3, 0, -12], [0, 0, 24, 72], [12, -12, 72, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [5, 13], 'good_prime_list': [[5, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [1, 0, 0, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-12, -6, 0, 1], 'label': '2.2.189.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-12, -6, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
79. label: 2.2.189.3
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [7, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 189, 'conductor_is_squarefree': False, 'conductor_num_primes': 2, 'conductor_primes': [3, 7], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-16, -6, 0, 1]], [[0, 1], [-16, -6, 0, 1]], [4, [[1, 3, 0, 12], [3, -3, 0, -12], [0, 0, 24, 96], [12, -12, 96, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [5, 13], 'good_prime_list': [[5, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [1, 0, 0, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [1, 0, 0, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-16, -6, 0, 1], 'label': '2.2.189.3', 'num': 3, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-16, -6, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
80. label: 2.2.195.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [5, '', '', '', ''], [13, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 195, 'conductor_is_squarefree': True, 'conductor_num_primes': 3, 'conductor_primes': [3, 5, 13], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-5, -1, -1, 1]], [[0, 1], [-5, -1, -1, 1]], [4, [[1, 3, 1, 3], [3, -3, -1, -3], [1, -1, 5, 35], [3, -3, 35, 45]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1]], 'generating_primes': [7, 19], 'good_prime_list': [[7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 1]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 1]], [73, [1, 0, 0, 1]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-5, -1, -1, 1], 'label': '2.2.195.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-5, -1, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
81. label: 2.2.197.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[197, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 197, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [197], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-3, -7, -1, 1]], [[0, 1], [-3, -7, -1, 1]], [4, [[1, 3, 1, 15], [3, -3, -1, -15], [1, -1, 29, 47], [15, -15, 47, 53]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [1, 0, 0, 1]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [1, 0, 0, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-3, -7, -1, 1], 'label': '2.2.197.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-3, -7, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
82. label: 2.2.199.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[199, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 199, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [199], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-1, 4, -1, 1]], [[0, 1], [-1, 4, -1, 1]], [4, [[1, 3, 1, -7], [3, -3, -1, 7], [1, -1, -15, -9], [-7, 7, -9, -7]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [1, 0, 0, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [1, 0, 0, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-1, 4, -1, 1], 'label': '2.2.199.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-1, 4, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
83. label: 2.2.201.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [67, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 201, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 67], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-6, 4, -1, 1]], [[0, 1], [-6, 4, -1, 1]], [4, [[1, 3, 1, -7], [3, -3, -1, 7], [1, -1, -15, 21], [-7, 7, 21, 33]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [5, 11], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [1, 0, 0, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [71, [1, 0, 0, 1]], [73, [0, 1, 1, 1]], [79, [1, 0, 0, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-6, 4, -1, 1], 'label': '2.2.201.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-6, 4, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
84. label: 2.2.203.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[7, '', '', '', ''], [29, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 203, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [7, 29], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-7, -7, -1, 1]], [[0, 1], [-7, -7, -1, 1]], [4, [[1, 3, 1, 15], [3, -3, -1, -15], [1, -1, 29, 71], [15, -15, 71, 85]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [1, 0, 0, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [31, [1, 0, 0, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-7, -7, -1, 1], 'label': '2.2.203.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-7, -7, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
85. label: 2.2.211.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[211, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 211, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [211], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-3, -2, 0, 1]], [[0, 1], [-3, -2, 0, 1]], [4, [[1, 3, 0, 4], [3, -3, 0, -4], [0, 0, 8, 18], [4, -4, 18, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [1, 0, 0, 1]], [59, [1, 0, 0, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [1, 0, 0, 1]], [79, [0, 1, 1, 1]], [83, [1, 0, 0, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-3, -2, 0, 1], 'label': '2.2.211.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-3, -2, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
86. label: 2.2.213.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [71, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 213, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 71], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-17, 5, -1, 1]], [[0, 1], [-17, 5, -1, 1]], [4, [[1, 3, 1, -9], [3, -3, -1, 9], [1, -1, -19, 83], [-9, 9, 83, 117]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [5, 23], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [1, 0, 0, 1]], [17, [1, 0, 0, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-17, 5, -1, 1], 'label': '2.2.213.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-17, 5, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
87. label: 2.2.215.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[5, '', '', '', ''], [43, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 215, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [5, 43], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-16, -2, 0, 1]], [[0, 1], [-16, -2, 0, 1]], [4, [[1, 3, 0, 4], [3, -3, 0, -4], [0, 0, 8, 96], [4, -4, 96, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [1, 0, 0, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 1]], [83, [1, 0, 0, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-16, -2, 0, 1], 'label': '2.2.215.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-16, -2, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
88. label: 2.2.217.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[7, '', '', '', ''], [31, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 217, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [7, 31], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-16, 2, 0, 1]], [[0, 1], [-16, 2, 0, 1]], [4, [[1, 3, 0, -4], [3, -3, 0, 4], [0, 0, -8, 96], [-4, 4, 96, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 11], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 1]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 0]], [17, [1, 0, 0, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [37, [1, 0, 0, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [1, 0, 0, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-16, 2, 0, 1], 'label': '2.2.217.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-16, 2, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '3', 'top_slope_real': 3.0, 'weight': 0}
89. label: 2.2.219.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [73, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 219, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 73], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-11, -1, -1, 1]], [[0, 1], [-11, -1, -1, 1]], [4, [[1, 3, 1, 3], [3, -3, -1, -3], [1, -1, 5, 71], [3, -3, 71, 93]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [5, 7], 'good_prime_list': [[5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [1, 0, 0, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [1, 0, 0, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-11, -1, -1, 1], 'label': '2.2.219.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-11, -1, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
90. label: 2.2.223.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[223, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 223, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [223], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [10, -8, -1, 1]], [[0, 1], [10, -8, -1, 1]], [4, [[1, 3, 1, 17], [3, -3, -1, -17], [1, -1, 33, -27], [17, -17, -27, -47]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [1, 0, 0, 1]], [73, [0, 1, 1, 1]], [79, [1, 0, 0, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [10, -8, -1, 1], 'label': '2.2.223.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [10, -8, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
91. label: 2.2.227.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[227, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 227, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [227], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-12, -4, 0, 1]], [[0, 1], [-12, -4, 0, 1]], [4, [[1, 3, 0, 8], [3, -3, 0, -8], [0, 0, 16, 72], [8, -8, 72, 0]]]], 'frobenius_matrices': [[1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1]], 'generating_primes': [5, 7], 'good_prime_list': [[3, [1, 0, 0, 1]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [1, 0, 0, 1]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [1, 0, 0, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [1, 0, 0, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-12, -4, 0, 1], 'label': '2.2.227.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-12, -4, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
92. label: 2.2.229.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[229, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 229, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [229], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-1, -4, 0, 1]], [[0, 1], [-1, -4, 0, 1]], [4, [[1, 3, 0, 8], [3, -3, 0, -8], [0, 0, 16, 6], [8, -8, 6, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [3, 7], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [1, 0, 0, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [1, 0, 0, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-1, -4, 0, 1], 'label': '2.2.229.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-1, -4, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
93. label: 2.2.231.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [7, '', '', '', ''], [11, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 231, 'conductor_is_squarefree': True, 'conductor_num_primes': 3, 'conductor_primes': [3, 7, 11], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [3, 0, -1, 1]], [[0, 1], [3, 0, -1, 1]], [4, [[1, 3, 1, 1], [3, -3, -1, -1], [1, -1, 1, -17], [1, -1, -17, -23]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0]], 'generating_primes': [5, 17], 'good_prime_list': [[5, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [1, 0, 0, 1]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [1, 0, 0, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [3, 0, -1, 1], 'label': '2.2.231.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [3, 0, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
94. label: 2.2.233.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[233, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 233, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [233], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-4, 5, 0, 1]], [[0, 1], [-4, 5, 0, 1]], [4, [[1, 3, 0, -10], [3, -3, 0, 10], [0, 0, -20, 24], [-10, 10, 24, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 1]], [5, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [1, 0, 0, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 1]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 1]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-4, 5, 0, 1], 'label': '2.2.233.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-4, 5, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
95. label: 2.2.235.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[5, '', '', '', ''], [47, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 235, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [5, 47], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-6, -2, 0, 1]], [[0, 1], [-6, -2, 0, 1]], [4, [[1, 3, 0, 4], [3, -3, 0, -4], [0, 0, 8, 36], [4, -4, 36, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0]], 'generating_primes': [3, 13], 'good_prime_list': [[3, [0, 1, 1, 0]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 0]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 1]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 1]], [61, [0, 1, 1, 1]], [67, [1, 0, 0, 1]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 1]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-6, -2, 0, 1], 'label': '2.2.235.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-6, -2, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '1', 'top_slope_real': 1.0, 'weight': 0}
96. label: 2.2.235.2
    {'algebraic_group': 'GL', 'bad_prime_list': [[5, '', '', '', ''], [47, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 235, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [5, 47], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-4, -7, 0, 1]], [[0, 1], [-4, -7, 0, 1]], [4, [[1, 3, 0, 14], [3, -3, 0, -14], [0, 0, 28, 24], [14, -14, 24, 0]]]], 'frobenius_matrices': [[0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0]], 'generating_primes': [3, 17], 'good_prime_list': [[3, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 0]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [1, 0, 0, 1]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-4, -7, 0, 1], 'label': '2.2.235.2', 'num': 2, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-4, -7, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
97. label: 2.2.237.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[3, '', '', '', ''], [79, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 237, 'conductor_is_squarefree': True, 'conductor_num_primes': 2, 'conductor_primes': [3, 79], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [6, 0, -1, 1]], [[0, 1], [6, 0, -1, 1]], [4, [[1, 3, 1, 1], [3, -3, -1, -1], [1, -1, 1, -35], [1, -1, -35, -47]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [5, 7], 'good_prime_list': [[5, [0, 1, 1, 0]], [7, [0, 1, 1, 1]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 1]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 0]], [37, [0, 1, 1, 0]], [41, [1, 0, 0, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [1, 0, 0, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 0]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 0]], [73, [0, 1, 1, 1]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [6, 0, -1, 1], 'label': '2.2.237.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [6, 0, -1, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}
98. label: 2.2.239.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[239, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 239, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [239], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-3, -1, 0, 1]], [[0, 1], [-3, -1, 0, 1]], [4, [[1, 3, 0, 2], [3, -3, 0, -2], [0, 0, 4, 18], [2, -2, 18, 0]]]], 'frobenius_matrices': [[1, 0, 0, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0]], 'generating_primes': [5, 7], 'good_prime_list': [[3, [1, 0, 0, 1]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 0]], [11, [0, 1, 1, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 1]], [19, [0, 1, 1, 0]], [23, [0, 1, 1, 0]], [29, [0, 1, 1, 1]], [31, [0, 1, 1, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 0]], [43, [0, 1, 1, 0]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 0]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 1]], [71, [1, 0, 0, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 1]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 0]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-3, -1, 0, 1], 'label': '2.2.239.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-3, -1, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '0', 'top_slope_real': 0.0, 'weight': 0}
99. label: 2.2.241.1
    {'algebraic_group': 'GL', 'bad_prime_list': [[241, '', '', '', '']], 'base_ring_characteristic': 2, 'base_ring_is_field': True, 'base_ring_order': 2, 'conductor': 241, 'conductor_is_squarefree': True, 'conductor_num_primes': 1, 'conductor_primes': [241], 'cyclotomic_exponent': 0, 'determinant_label': '2.1.1.1', 'dimension': 2, 'dual_pair_of_algebras': [[[0, 1], [-12, -2, 0, 1]], [[0, 1], [-12, -2, 0, 1]], [4, [[1, 3, 0, 4], [3, -3, 0, -4], [0, 0, 8, 72], [4, -4, 72, 0]]]], 'frobenius_matrices': [[0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 1], [1, 0, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 1], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 0], [0, 1, 1, 1]], 'generating_primes': [3, 5], 'good_prime_list': [[3, [0, 1, 1, 0]], [5, [0, 1, 1, 1]], [7, [0, 1, 1, 1]], [11, [1, 0, 0, 1]], [13, [0, 1, 1, 0]], [17, [0, 1, 1, 0]], [19, [0, 1, 1, 1]], [23, [0, 1, 1, 1]], [29, [0, 1, 1, 1]], [31, [1, 0, 0, 1]], [37, [0, 1, 1, 0]], [41, [0, 1, 1, 1]], [43, [0, 1, 1, 1]], [47, [0, 1, 1, 0]], [53, [0, 1, 1, 1]], [59, [0, 1, 1, 0]], [61, [0, 1, 1, 1]], [67, [0, 1, 1, 0]], [71, [0, 1, 1, 1]], [73, [0, 1, 1, 0]], [79, [0, 1, 1, 0]], [83, [0, 1, 1, 0]], [89, [0, 1, 1, 0]], [97, [0, 1, 1, 1]]], 'image_index': 1, 'image_label': '2G', 'image_order': 6, 'image_type': 'big', 'is_absolutely_irreducible': True, 'is_irreducible': True, 'is_solvable': True, 'is_surjective': True, 'kernel_polynomial': [-12, -2, 0, 1], 'label': '2.2.241.1', 'num': 1, 'projective_is_surjective': True, 'projective_kernel_polynomial': [-12, -2, 0, 1], 'projective_type': 'big', 'related_objects': [], 'top_slope_rational': '2', 'top_slope_real': 2.0, 'weight': 0}