Database - lfunc_search ((description not yet updated on this server))

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Query: /api/lfunc_search/?_offset=0

Column	Type
algebraic	boolean
analytic_conductor	double precision
bad_primes	bigint[]
central_character	text
conductor	numeric
conductor_radical	bigint
degree	smallint
dirichlet_coefficients	numeric[]
euler11	numeric[]
euler13	numeric[]
euler17	numeric[]
euler19	numeric[]
euler2	numeric[]
euler23	numeric[]
euler29	numeric[]
euler3	numeric[]
euler31	numeric[]
euler37	numeric[]
euler41	numeric[]
euler43	numeric[]
euler47	numeric[]
euler5	numeric[]
euler53	numeric[]
euler59	numeric[]
euler61	numeric[]
euler67	numeric[]
euler7	numeric[]
euler71	numeric[]
euler73	numeric[]
euler79	numeric[]
euler83	numeric[]
euler89	numeric[]
euler97	numeric[]
euler_factors	numeric[]
index	smallint
instance_types	text[]
instance_urls	text[]
is_instance_Artin	boolean
is_instance_BMF	boolean
is_instance_CMF	boolean
is_instance_DIR	boolean
is_instance_ECNF	boolean
is_instance_ECQ	boolean
is_instance_G2Q	boolean
is_instance_HMF	boolean
is_instance_MaassGL3	boolean
is_instance_MaassGL4	boolean
is_instance_MaassGSp4	boolean
is_instance_NF	boolean
label	text
motivic_weight	smallint
mu_imag	numeric[]
mu_real	smallint[]
nu_imag	numeric[]
nu_real_doubled	smallint[]
order_of_vanishing	smallint
prelabel	text
primitive	boolean
rational	boolean
root_analytic_conductor	double precision
root_angle	double precision
self_dual	boolean
spectral_label	text
trace_hash	bigint
z1	numeric

0. label: 1-1-1.1-r0-0-0
   {'algebraic': True, 'analytic_conductor': 0.004643980476297358, 'bad_primes': [], 'central_character': '1.1', 'conductor': 1, 'conductor_radical': 1, 'degree': 1, 'dirichlet_coefficients': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'euler11': [1, -1], 'euler13': [1, -1], 'euler17': [1, -1], 'euler19': [1, -1], 'euler2': [1, -1], 'euler23': [1, -1], 'euler29': [1, -1], 'euler3': [1, -1], 'euler31': [1, -1], 'euler37': [1, -1], 'euler41': [1, -1], 'euler43': [1, -1], 'euler47': [1, -1], 'euler5': [1, -1], 'euler53': [1, -1], 'euler59': [1, -1], 'euler61': [1, -1], 'euler67': [1, -1], 'euler7': [1, -1], 'euler71': [1, -1], 'euler73': [1, -1], 'euler79': [1, -1], 'euler83': [1, -1], 'euler89': [1, -1], 'euler97': [1, -1], 'euler_factors': [[1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1]], 'index': 0, 'instance_types': ['NF', 'DIR', 'Artin', 'Artin'], 'instance_urls': ['NumberField/1.1.1.1', 'Character/Dirichlet/1/1', 'ArtinRepresentation/1.1.1t1.a.a', 'ArtinRepresentation/1.1.1t1.a'], 'is_instance_Artin': True, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': True, 'label': '1-1-1.1-r0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1-1.1-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.004643980476297358, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '14.1347251417346937904572519835625', 'prec': 113}}
1. label: 1-5-5.4-r0-0-0
   {'algebraic': True, 'analytic_conductor': 0.02321990238148679, 'bad_primes': [5], 'central_character': '5.4', 'conductor': 5, 'conductor_radical': 5, 'degree': 1, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, -1, 1, 1, 1, 0, 1, 1, 1, -1, 0, 1, -1, 1, 1, 0, 1, 1, 1, -1, 0, -1, 1, -1, 1, 0, 1, 1, -1, 1, 0, -1, 1, 1, -1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, -1, -1, -1, 0, -1, -1, 1, 1, 0, -1, 1, 1, 1, 0, -1, 1, 1, 1, 0, -1, -1, 1, -1, 0, 1, -1, 1, 1, 0, 1, -1, -1, -1, 0, 1, 1, -1, 1, 0, 1, 1, 1, -1, 0], 'euler11': [1, 1], 'euler13': [1, -1], 'euler17': [1, -1], 'euler19': [1, 1], 'euler2': [1, -1], 'euler23': [1, -1], 'euler29': [1, 1], 'euler3': [1, -1], 'euler31': [1, 1], 'euler37': [1, -1], 'euler41': [1, 1], 'euler43': [1, -1], 'euler47': [1, -1], 'euler5': [1, 0], 'euler53': [1, -1], 'euler59': [1, 1], 'euler61': [1, 1], 'euler67': [1, -1], 'euler7': [1, -1], 'euler71': [1, 1], 'euler73': [1, -1], 'euler79': [1, 1], 'euler83': [1, -1], 'euler89': [1, 1], 'euler97': [1, -1], 'euler_factors': [[1, -1], [1, -1], [1, 0], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-5-5.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5-5.4-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.02321990238148679, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '6.64845334473', 'prec': 44}}
2. label: 1-7-7.2-r0-0-0
   {'algebraic': True, 'analytic_conductor': 0.03250786333408151, 'bad_primes': [7], 'central_character': '7.2', 'conductor': 7, 'conductor_radical': 7, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/7/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-7-7.2-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-7-7.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.03250786333408151, 'root_angle': -0.07324685680636028, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.35640162474', 'prec': 44}}
3. label: 1-7-7.4-r0-0-0
   {'algebraic': True, 'analytic_conductor': 0.03250786333408151, 'bad_primes': [7], 'central_character': '7.4', 'conductor': 7, 'conductor_radical': 7, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/7/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-7-7.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-7-7.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.03250786333408151, 'root_angle': 0.07324685680636028, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '6.20123004276', 'prec': 44}}
4. label: 1-2e3-8.5-r0-0-0
   {'algebraic': True, 'analytic_conductor': 0.037151843810378865, 'bad_primes': [2], 'central_character': '8.5', 'conductor': 8, 'conductor_radical': 2, 'degree': 1, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0], 'euler11': [1, -1], 'euler13': [1, -1], 'euler17': [1, 1], 'euler19': [1, -1], 'euler2': [1, 0], 'euler23': [1, 1], 'euler29': [1, -1], 'euler3': [1, -1], 'euler31': [1, 1], 'euler37': [1, -1], 'euler41': [1, 1], 'euler43': [1, -1], 'euler47': [1, 1], 'euler5': [1, -1], 'euler53': [1, -1], 'euler59': [1, -1], 'euler61': [1, -1], 'euler67': [1, -1], 'euler7': [1, 1], 'euler71': [1, 1], 'euler73': [1, 1], 'euler79': [1, 1], 'euler83': [1, -1], 'euler89': [1, 1], 'euler97': [1, 1], 'euler_factors': [[1, 0], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 1], [1, 1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/8/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-2e3-8.5-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2e3-8.5-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.037151843810378865, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.89997399701', 'prec': 44}}
5. label: 1-3e2-9.4-r0-0-0
   {'algebraic': True, 'analytic_conductor': 0.04179582428667622, 'bad_primes': [3], 'central_character': '9.4', 'conductor': 9, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/9/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-3e2-9.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3e2-9.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.04179582428667622, 'root_angle': 0.11111111111111113, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '5.31957512328', 'prec': 44}}
6. label: 1-3e2-9.7-r0-0-0
   {'algebraic': True, 'analytic_conductor': 0.04179582428667622, 'bad_primes': [3], 'central_character': '9.7', 'conductor': 9, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/9/7'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-3e2-9.7-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3e2-9.7-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.04179582428667622, 'root_angle': -0.11111111111111113, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.44409315515', 'prec': 44}}
7. label: 1-11-11.3-r0-0-0
   {'algebraic': True, 'analytic_conductor': 0.05108378523927094, 'bad_primes': [11], 'central_character': '11.3', 'conductor': 11, 'conductor_radical': 11, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/11/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-11-11.3-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-11-11.3-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.05108378523927094, 'root_angle': -0.10378373710217174, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.61004043148', 'prec': 44}}
8. label: 1-11-11.4-r0-0-0
   {'algebraic': True, 'analytic_conductor': 0.05108378523927094, 'bad_primes': [11], 'central_character': '11.4', 'conductor': 11, 'conductor_radical': 11, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/11/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-11-11.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-11-11.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.05108378523927094, 'root_angle': 0.10378373710217174, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '5.13369962695', 'prec': 44}}
9. label: 1-11-11.5-r0-0-0
   {'algebraic': True, 'analytic_conductor': 0.05108378523927094, 'bad_primes': [11], 'central_character': '11.5', 'conductor': 11, 'conductor_radical': 11, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/11/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-11-11.5-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-11-11.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.05108378523927094, 'root_angle': 0.14271713006960676, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.62935366251', 'prec': 44}}
10. label: 1-11-11.9-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.05108378523927094, 'bad_primes': [11], 'central_character': '11.9', 'conductor': 11, 'conductor_radical': 11, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/11/9'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-11-11.9-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-11-11.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.05108378523927094, 'root_angle': -0.14271713006960676, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.69600408487', 'prec': 44}}
11. label: 1-12-12.11-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.0557277657155683, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 12, 'conductor_radical': 6, 'degree': 1, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0], 'euler11': [1, 1], 'euler13': [1, 1], 'euler17': [1, -1], 'euler19': [1, -1], 'euler2': [1, 0], 'euler23': [1, 1], 'euler29': [1, -1], 'euler3': [1, 0], 'euler31': [1, -1], 'euler37': [1, 1], 'euler41': [1, -1], 'euler43': [1, -1], 'euler47': [1, 1], 'euler5': [1, -1], 'euler53': [1, -1], 'euler59': [1, 1], 'euler61': [1, 1], 'euler67': [1, -1], 'euler7': [1, -1], 'euler71': [1, 1], 'euler73': [1, 1], 'euler79': [1, -1], 'euler83': [1, 1], 'euler89': [1, -1], 'euler97': [1, 1], 'euler_factors': [[1, 0], [1, 0], [1, -1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/12/11'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-12-12.11-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-12-12.11-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.0557277657155683, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.80462763305', 'prec': 44}}
12. label: 1-13-13.9-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.06037174619186565, 'bad_primes': [13], 'central_character': '13.9', 'conductor': 13, 'conductor_radical': 13, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/13/9'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-13-13.9-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-13-13.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.06037174619186565, 'root_angle': -0.20935380902961667, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.27313120101', 'prec': 44}}
13. label: 1-13-13.10-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.06037174619186565, 'bad_primes': [13], 'central_character': '13.10', 'conductor': 13, 'conductor_radical': 13, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/13/10'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-13-13.10-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-13-13.10-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.06037174619186565, 'root_angle': -0.08537428472590003, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.66097464838', 'prec': 44}}
14. label: 1-13-13.12-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.06037174619186565, 'bad_primes': [13], 'central_character': '13.12', 'conductor': 13, 'conductor_radical': 13, 'degree': 1, 'dirichlet_coefficients': [1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 0, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 0, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 0, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 0, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 0, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 0, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 0, -1, -1, 1, 1, -1, 1, 1, 1, 1], 'euler11': [1, -1], 'euler13': [1, 0], 'euler17': [1, 1], 'euler19': [1, -1], 'euler2': [1, -1], 'euler23': [1, 1], 'euler29': [1, 1], 'euler3': [1, 1], 'euler31': [1, -1], 'euler37': [1, -1], 'euler41': [1, -1], 'euler43': [1, 1], 'euler47': [1, -1], 'euler5': [1, -1], 'euler53': [1, 1], 'euler59': [1, -1], 'euler61': [1, 1], 'euler67': [1, -1], 'euler7': [1, -1], 'euler71': [1, -1], 'euler73': [1, -1], 'euler79': [1, 1], 'euler83': [1, -1], 'euler89': [1, -1], 'euler97': [1, -1], 'euler_factors': [[1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 0], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/13/12'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-13-13.12-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-13-13.12-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.06037174619186565, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.11934147901', 'prec': 44}}
15. label: 1-13-13.3-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.06037174619186565, 'bad_primes': [13], 'central_character': '13.3', 'conductor': 13, 'conductor_radical': 13, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/13/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-13-13.3-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-13-13.3-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.06037174619186565, 'root_angle': 0.20935380902961667, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.93859080846', 'prec': 44}}
16. label: 1-13-13.4-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.06037174619186565, 'bad_primes': [13], 'central_character': '13.4', 'conductor': 13, 'conductor_radical': 13, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/13/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-13-13.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-13-13.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.06037174619186565, 'root_angle': 0.08537428472590003, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.45485391156', 'prec': 44}}
17. label: 1-15-15.2-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.06965970714446038, 'bad_primes': [3, 5], 'central_character': '15.2', 'conductor': 15, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/15/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-15-15.2-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-15-15.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.06965970714446038, 'root_angle': -0.16189590441260832, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.73460370912', 'prec': 44}}
18. label: 1-15-15.8-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.06965970714446038, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 15, 'conductor_radical': 15, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/15/8'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-15-15.8-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-15-15.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.06965970714446038, 'root_angle': 0.16189590441260832, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.4067002398', 'prec': 40}}
19. label: 1-2e4-16.13-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.07430368762075773, 'bad_primes': [2], 'central_character': '16.13', 'conductor': 16, 'conductor_radical': 2, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/16/13'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-2e4-16.13-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2e4-16.13-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.07430368762075773, 'root_angle': 0.06250000000000001, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.77219663607', 'prec': 44}}
20. label: 1-2e4-16.5-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.07430368762075773, 'bad_primes': [2], 'central_character': '16.5', 'conductor': 16, 'conductor_radical': 2, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/16/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-2e4-16.5-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2e4-16.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.07430368762075773, 'root_angle': -0.06250000000000001, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.84244102408', 'prec': 44}}
21. label: 1-17-17.8-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'bad_primes': [17], 'central_character': '17.8', 'conductor': 17, 'conductor_radical': 17, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/17/8'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-17-17.8-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-17-17.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.07894766809705508, 'root_angle': -0.23791074295044418, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.12217010146', 'prec': 44}}
22. label: 1-17-17.9-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'bad_primes': [17], 'central_character': '17.9', 'conductor': 17, 'conductor_radical': 17, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/17/9'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-17-17.9-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-17-17.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.07894766809705508, 'root_angle': -0.11759447445521348, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.03085021754', 'prec': 44}}
23. label: 1-17-17.13-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'bad_primes': [17], 'central_character': '17.13', 'conductor': 17, 'conductor_radical': 17, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/17/13'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-17-17.13-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-17-17.13-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.07894766809705508, 'root_angle': 0.14449478259434237, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.3876430198', 'prec': 40}}
24. label: 1-17-17.15-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'bad_primes': [17], 'central_character': '17.15', 'conductor': 17, 'conductor_radical': 17, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/17/15'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-17-17.15-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-17-17.15-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.07894766809705508, 'root_angle': 0.23791074295044418, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.85147420421', 'prec': 44}}
25. label: 1-17-17.16-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'bad_primes': [17], 'central_character': '17.16', 'conductor': 17, 'conductor_radical': 17, 'degree': 1, 'dirichlet_coefficients': [1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 0, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 0, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 0, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 0, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 0, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1], 'euler11': [1, -1], 'euler13': [1, 1], 'euler17': [1, 0], 'euler19': [1, 1], 'euler2': [1, 1], 'euler23': [1, -1], 'euler29': [1, -1], 'euler3': [1, -1], 'euler31': [1, -1], 'euler37': [1, -1], 'euler41': [1, -1], 'euler43': [1, 1], 'euler47': [1, 1], 'euler5': [1, -1], 'euler53': [1, 1], 'euler59': [1, 1], 'euler61': [1, -1], 'euler67': [1, 1], 'euler7': [1, -1], 'euler71': [1, -1], 'euler73': [1, -1], 'euler79': [1, -1], 'euler83': [1, 1], 'euler89': [1, 1], 'euler97': [1, -1], 'euler_factors': [[1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [1, 0], [1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 1], [1, 1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/17/16'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-17-17.16-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-17-17.16-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.07894766809705508, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.72814208504', 'prec': 44}}
26. label: 1-17-17.2-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'bad_primes': [17], 'central_character': '17.2', 'conductor': 17, 'conductor_radical': 17, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/17/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-17-17.2-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-17-17.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.07894766809705508, 'root_angle': 0.11759447445521348, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.73234531397', 'prec': 44}}
27. label: 1-17-17.4-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.07894766809705508, 'bad_primes': [17], 'central_character': '17.4', 'conductor': 17, 'conductor_radical': 17, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/17/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-17-17.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-17-17.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.07894766809705508, 'root_angle': -0.14449478259434237, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89456288884', 'prec': 44}}
28. label: 1-19-19.11-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'bad_primes': [19], 'central_character': '19.11', 'conductor': 19, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/19/11'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-19-19.11-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-19-19.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': -0.29945668930219493, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57320808455', 'prec': 44}}
29. label: 1-19-19.16-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'bad_primes': [19], 'central_character': '19.16', 'conductor': 19, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/19/16'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-19-19.16-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-19-19.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': 0.11352277336167924, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.63715141027', 'prec': 44}}
30. label: 1-19-19.17-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'bad_primes': [19], 'central_character': '19.17', 'conductor': 19, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/19/17'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-19-19.17-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-19-19.17-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': 0.05304001234598393, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.87454712438', 'prec': 44}}
31. label: 1-19-19.4-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'bad_primes': [19], 'central_character': '19.4', 'conductor': 19, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/19/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-19-19.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-19-19.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': 0.1326861416765248, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.27062371722', 'prec': 44}}
32. label: 1-19-19.5-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'bad_primes': [19], 'central_character': '19.5', 'conductor': 19, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/19/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-19-19.5-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-19-19.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': -0.1326861416765248, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.7332750435', 'prec': 40}}
33. label: 1-19-19.6-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'bad_primes': [19], 'central_character': '19.6', 'conductor': 19, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/19/6'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-19-19.6-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-19-19.6-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': -0.11352277336167924, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.09878079652', 'prec': 44}}
34. label: 1-19-19.7-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'bad_primes': [19], 'central_character': '19.7', 'conductor': 19, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/19/7'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-19-19.7-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-19-19.7-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': 0.29945668930219493, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.40883445096', 'prec': 44}}
35. label: 1-19-19.9-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.08823562904964981, 'bad_primes': [19], 'central_character': '19.9', 'conductor': 19, 'conductor_radical': 19, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/19/9'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-19-19.9-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-19-19.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.08823562904964981, 'root_angle': -0.05304001234598393, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.13818063441', 'prec': 44}}
36. label: 1-20-20.3-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.09287960952594716, 'bad_primes': [2, 5], 'central_character': '20.3', 'conductor': 20, 'conductor_radical': 10, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/20/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-20-20.3-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-20-20.3-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.09287960952594716, 'root_angle': -0.0881040955873917, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.43970471075', 'prec': 44}}
37. label: 1-20-20.7-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.09287960952594716, 'bad_primes': [2, 5], 'central_character': '20.7', 'conductor': 20, 'conductor_radical': 10, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/20/7'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-20-20.7-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-20-20.7-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.09287960952594716, 'root_angle': 0.0881040955873917, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.53109568391', 'prec': 44}}
38. label: 1-21-21.17-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.09752359000224452, 'bad_primes': [3, 7], 'central_character': '21.17', 'conductor': 21, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/21/17'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-21-21.17-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-21-21.17-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.09752359000224452, 'root_angle': -0.14649371361272054, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.71366105453', 'prec': 44}}
39. label: 1-21-21.20-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.09752359000224452, 'bad_primes': [3, 7], 'central_character': '21.20', 'conductor': 21, 'conductor_radical': 21, 'degree': 1, 'dirichlet_coefficients': [1, 1, 0, 1, -1, 0, 0, 1, 0, -1, 1, 0, 1, 0, 0, 1, -1, 0, 1, -1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, -1, 0, 0, -1, 1, 0, -1, -1, 0, -1, 1, 0, 1, -1, 0, 0, 1, 0, 1, 1, 0, -1, 0, 0, 1, -1, 0, 1, 1, 0, 1, -1, 0, -1, -1, 0, 0, 1, 0, 1, -1, 0, 1, 0, 0, -1, -1, 0, -1, -1, 0, 1, -1, 0, 1, -1, 0, 0, 1, 0, -1, -1, 0, 1, 0, 0, 1], 'euler11': [1, -1], 'euler13': [1, -1], 'euler17': [1, 1], 'euler19': [1, -1], 'euler2': [1, -1], 'euler23': [1, -1], 'euler29': [1, -1], 'euler3': [1, 0], 'euler31': [1, -1], 'euler37': [1, 1], 'euler41': [1, 1], 'euler43': [1, 1], 'euler47': [1, 1], 'euler5': [1, 1], 'euler53': [1, -1], 'euler59': [1, 1], 'euler61': [1, -1], 'euler67': [1, 1], 'euler7': [1, 0], 'euler71': [1, -1], 'euler73': [1, -1], 'euler79': [1, 1], 'euler83': [1, 1], 'euler89': [1, 1], 'euler97': [1, -1], 'euler_factors': [[1, -1], [1, 0], [1, 1], [1, 0], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/21/20'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-21-21.20-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-21-21.20-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.09752359000224452, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.3151870643', 'prec': 40}}
40. label: 1-21-21.5-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.09752359000224452, 'bad_primes': [3, 7], 'central_character': '21.5', 'conductor': 21, 'conductor_radical': 21, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/21/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-21-21.5-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-21-21.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.09752359000224452, 'root_angle': 0.14649371361272054, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.9367913196', 'prec': 40}}
41. label: 1-23-23.12-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'bad_primes': [23], 'central_character': '23.12', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/12'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-23-23.12-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23-23.12-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': -0.2337159910286797, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.96977154105', 'prec': 44}}
42. label: 1-23-23.13-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'bad_primes': [23], 'central_character': '23.13', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/13'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-23-23.13-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23-23.13-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': 0.24812572185883944, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.12168134698', 'prec': 44}}
43. label: 1-23-23.16-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'bad_primes': [23], 'central_character': '23.16', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/16'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-23-23.16-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23-23.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': -0.24812572185883944, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04476223592', 'prec': 44}}
44. label: 1-23-23.18-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'bad_primes': [23], 'central_character': '23.18', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/18'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-23-23.18-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23-23.18-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': 0.026399097906712733, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.18006776084', 'prec': 44}}
45. label: 1-23-23.2-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'bad_primes': [23], 'central_character': '23.2', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-23-23.2-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23-23.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': 0.2337159910286797, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.10757637345', 'prec': 44}}
46. label: 1-23-23.3-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'bad_primes': [23], 'central_character': '23.3', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-23-23.3-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23-23.3-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': -0.18767132286184093, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27653878245', 'prec': 44}}
47. label: 1-23-23.4-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'bad_primes': [23], 'central_character': '23.4', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-23-23.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23-23.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': 0.08692076689710643, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.69506368546', 'prec': 44}}
48. label: 1-23-23.6-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'bad_primes': [23], 'central_character': '23.6', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/6'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-23-23.6-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23-23.6-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': -0.08692076689710643, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.47039178967', 'prec': 44}}
49. label: 1-23-23.8-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'bad_primes': [23], 'central_character': '23.8', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/8'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-23-23.8-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23-23.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': 0.18767132286184093, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.0119744257', 'prec': 40}}
50. label: 1-23-23.9-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.10681155095483924, 'bad_primes': [23], 'central_character': '23.9', 'conductor': 23, 'conductor_radical': 23, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/23/9'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-23-23.9-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-23-23.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.10681155095483924, 'root_angle': -0.026399097906712733, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.46109369894', 'prec': 44}}
51. label: 2-23-23.22-c0-0-0
    {'algebraic': True, 'analytic_conductor': 0.011478495290559056, 'bad_primes': [23], 'central_character': '23.22', 'conductor': 23, 'conductor_radical': 23, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, -1, 1, 1, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, -1, 1, 1, -1, 0, 0, 0, -1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, -1, 0, 0], 'euler11': [1, 0, -1], 'euler13': [1, 1, 1], 'euler17': [1, 0, -1], 'euler19': [1, 0, -1], 'euler2': [1, 1, 1], 'euler23': [1, -1, 0], 'euler29': [1, 1, 1], 'euler3': [1, 1, 1], 'euler31': [1, 1, 1], 'euler37': [1, 0, -1], 'euler41': [1, 1, 1], 'euler43': [1, 0, -1], 'euler47': [1, 1, 1], 'euler5': [1, 0, -1], 'euler53': [1, 0, -1], 'euler59': [1, -2, 1], 'euler61': [1, 0, -1], 'euler67': [1, 0, -1], 'euler7': [1, 0, -1], 'euler71': [1, 1, 1], 'euler73': [1, 1, 1], 'euler79': [1, 0, -1], 'euler83': [1, 0, -1], 'euler89': [1, 0, -1], 'euler97': [1, 0, -1], 'euler_factors': [[1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, -1, 0], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, -2, 1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1]], 'index': 0, 'instance_types': ['CMF', 'CMF', 'Artin', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/23/1/b/a/22/1', 'ModularForm/GL2/Q/holomorphic/23/1/b/a', 'ArtinRepresentation/2.23.3t2.b.a', 'ArtinRepresentation/2.23.3t2.b'], 'is_instance_Artin': True, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-23-23.22-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-23-23.22-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.10713773980516415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'trace_hash': 426797760822574538, 'z1': {'__RealLiteral__': 0, 'data': '5.11568332881511759855335642038', 'prec': 103}}
52. label: 1-24-24.11-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1114555314311366, 'bad_primes': [2, 3], 'central_character': '24.11', 'conductor': 24, 'conductor_radical': 6, 'degree': 1, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 0, 0], 'euler11': [1, -1], 'euler13': [1, -1], 'euler17': [1, -1], 'euler19': [1, 1], 'euler2': [1, 0], 'euler23': [1, 1], 'euler29': [1, 1], 'euler3': [1, 0], 'euler31': [1, -1], 'euler37': [1, -1], 'euler41': [1, -1], 'euler43': [1, 1], 'euler47': [1, 1], 'euler5': [1, 1], 'euler53': [1, 1], 'euler59': [1, -1], 'euler61': [1, -1], 'euler67': [1, 1], 'euler7': [1, -1], 'euler71': [1, 1], 'euler73': [1, 1], 'euler79': [1, -1], 'euler83': [1, -1], 'euler89': [1, -1], 'euler97': [1, 1], 'euler_factors': [[1, 0], [1, 0], [1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/24/11'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-24-24.11-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-24-24.11-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.1114555314311366, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.68865813247', 'prec': 44}}
53. label: 1-5e2-25.11-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.11609951190743395, 'bad_primes': [5], 'central_character': '25.11', 'conductor': 25, 'conductor_radical': 5, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/25/11'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-5e2-25.11-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5e2-25.11-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.11609951190743395, 'root_angle': -0.28, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.73898283151', 'prec': 44}}
54. label: 1-5e2-25.14-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.11609951190743395, 'bad_primes': [5], 'central_character': '25.14', 'conductor': 25, 'conductor_radical': 5, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/25/14'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-5e2-25.14-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5e2-25.14-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.11609951190743395, 'root_angle': 0.22, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.56286301216', 'prec': 44}}
55. label: 1-5e2-25.16-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.11609951190743395, 'bad_primes': [5], 'central_character': '25.16', 'conductor': 25, 'conductor_radical': 5, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/25/16'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-5e2-25.16-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5e2-25.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.11609951190743395, 'root_angle': 0.28, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.28610390947', 'prec': 44}}
56. label: 1-5e2-25.19-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.11609951190743395, 'bad_primes': [5], 'central_character': '25.19', 'conductor': 25, 'conductor_radical': 5, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/25/19'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-5e2-25.19-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5e2-25.19-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.11609951190743395, 'root_angle': -0.04, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.12335403532', 'prec': 44}}
57. label: 1-5e2-25.21-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.11609951190743395, 'bad_primes': [5], 'central_character': '25.21', 'conductor': 25, 'conductor_radical': 5, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/25/21'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-5e2-25.21-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5e2-25.21-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.11609951190743395, 'root_angle': 0.04, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.68355491112', 'prec': 44}}
58. label: 1-5e2-25.4-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.11609951190743395, 'bad_primes': [5], 'central_character': '25.4', 'conductor': 25, 'conductor_radical': 5, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/25/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-5e2-25.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5e2-25.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.11609951190743395, 'root_angle': 0.04, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.06516421169', 'prec': 44}}
59. label: 1-5e2-25.6-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.11609951190743395, 'bad_primes': [5], 'central_character': '25.6', 'conductor': 25, 'conductor_radical': 5, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/25/6'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-5e2-25.6-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5e2-25.6-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.11609951190743395, 'root_angle': -0.04, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91294097474', 'prec': 44}}
60. label: 1-5e2-25.9-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.11609951190743395, 'bad_primes': [5], 'central_character': '25.9', 'conductor': 25, 'conductor_radical': 5, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/25/9'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-5e2-25.9-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5e2-25.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.11609951190743395, 'root_angle': -0.22, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.13858987186', 'prec': 44}}
61. label: 2-31-31.30-c0-0-0
    {'algebraic': True, 'analytic_conductor': 0.015471015391623075, 'bad_primes': [31], 'central_character': '31.30', 'conductor': 31, 'conductor_radical': 31, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 0, -1, 0, -1, 1, 1, 1, 0, 0, 0, 1, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, -1, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, -1, -1, 1, 0, 0, 2, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 1, 0, -1, 0, 0, 0], 'euler11': [1, 0, -1], 'euler13': [1, 0, -1], 'euler17': [1, 0, -1], 'euler19': [1, 1, 1], 'euler2': [1, 1, 1], 'euler23': [1, 0, -1], 'euler29': [1, 0, -1], 'euler3': [1, 0, -1], 'euler31': [1, -1, 0], 'euler37': [1, 0, -1], 'euler41': [1, 1, 1], 'euler43': [1, 0, -1], 'euler47': [1, -2, 1], 'euler5': [1, 1, 1], 'euler53': [1, 0, -1], 'euler59': [1, 1, 1], 'euler61': [1, 0, -1], 'euler67': [1, -2, 1], 'euler7': [1, 1, 1], 'euler71': [1, 1, 1], 'euler73': [1, 0, -1], 'euler79': [1, 0, -1], 'euler83': [1, 0, -1], 'euler89': [1, 0, -1], 'euler97': [1, 1, 1], 'euler_factors': [[1, 1, 1], [1, 0, -1], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, -1, 0], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, -2, 1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, -2, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 1, 1]], 'index': 0, 'instance_types': ['CMF', 'CMF', 'Artin', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/31/1/b/a/30/1', 'ModularForm/GL2/Q/holomorphic/31/1/b/a', 'ArtinRepresentation/2.31.3t2.b.a', 'ArtinRepresentation/2.31.3t2.b'], 'is_instance_Artin': True, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-31-31.30-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-31-31.30-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.12438253652190517, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'trace_hash': 58047233262006326, 'z1': {'__RealLiteral__': 0, 'data': '4.16621475268391289462455833400', 'prec': 103}}
62. label: 1-3e3-27.4-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.12538747286002866, 'bad_primes': [3], 'central_character': '27.4', 'conductor': 27, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/27/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-3e3-27.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3e3-27.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.12538747286002866, 'root_angle': 0.12037037037037036, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.58950910323', 'prec': 44}}
63. label: 1-3e3-27.7-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.12538747286002866, 'bad_primes': [3], 'central_character': '27.7', 'conductor': 27, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/27/7'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-3e3-27.7-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3e3-27.7-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.12538747286002866, 'root_angle': -0.12037037037037036, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.65531742487', 'prec': 44}}
64. label: 1-3e3-27.13-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.12538747286002866, 'bad_primes': [3], 'central_character': '27.13', 'conductor': 27, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/27/13'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-3e3-27.13-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3e3-27.13-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.12538747286002866, 'root_angle': 0.12037037037037036, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.46476458252', 'prec': 44}}
65. label: 1-3e3-27.16-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.12538747286002866, 'bad_primes': [3], 'central_character': '27.16', 'conductor': 27, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/27/16'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-3e3-27.16-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3e3-27.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.12538747286002866, 'root_angle': 0.21296296296296297, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.51591294159', 'prec': 44}}
66. label: 1-3e3-27.22-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.12538747286002866, 'bad_primes': [3], 'central_character': '27.22', 'conductor': 27, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/27/22'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-3e3-27.22-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3e3-27.22-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.12538747286002866, 'root_angle': -0.21296296296296297, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.06798021117', 'prec': 44}}
67. label: 1-3e3-27.25-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.12538747286002866, 'bad_primes': [3], 'central_character': '27.25', 'conductor': 27, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/27/25'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-3e3-27.25-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-3e3-27.25-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.12538747286002866, 'root_angle': -0.12037037037037036, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.74993694859', 'prec': 44}}
68. label: 1-28-28.19-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.13003145333632604, 'bad_primes': [2, 7], 'central_character': '28.19', 'conductor': 28, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/28/19'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-28-28.19-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-28-28.19-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.13003145333632604, 'root_angle': 0.14649371361272054, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.16874276814', 'prec': 44}}
69. label: 1-28-28.27-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.13003145333632604, 'bad_primes': [2, 7], 'central_character': '28.27', 'conductor': 28, 'conductor_radical': 14, 'degree': 1, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 1, 0], 'euler11': [1, -1], 'euler13': [1, -1], 'euler17': [1, -1], 'euler19': [1, 1], 'euler2': [1, 0], 'euler23': [1, -1], 'euler29': [1, 1], 'euler3': [1, 1], 'euler31': [1, 1], 'euler37': [1, 1], 'euler41': [1, -1], 'euler43': [1, -1], 'euler47': [1, 1], 'euler5': [1, -1], 'euler53': [1, 1], 'euler59': [1, 1], 'euler61': [1, -1], 'euler67': [1, -1], 'euler7': [1, 0], 'euler71': [1, -1], 'euler73': [1, -1], 'euler79': [1, -1], 'euler83': [1, 1], 'euler89': [1, -1], 'euler97': [1, -1], 'euler_factors': [[1, 0], [1, 1], [1, -1], [1, 0], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/28/27'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-28-28.27-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-28-28.27-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.13003145333632604, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.77728324208', 'prec': 44}}
70. label: 1-28-28.3-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.13003145333632604, 'bad_primes': [2, 7], 'central_character': '28.3', 'conductor': 28, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/28/3'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-28-28.3-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-28-28.3-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.13003145333632604, 'root_angle': -0.14649371361272054, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.791040603', 'prec': 37}}
71. label: 1-29-29.5-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.5', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.5-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.19185652886442398, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.49079792248', 'prec': 44}}
72. label: 1-29-29.6-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.6', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/6'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.6-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.6-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': 0.19185652886442398, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.60892371717', 'prec': 44}}
73. label: 1-29-29.7-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.7', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/7'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.7-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.7-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': 0.2136681182021348, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.9602220809', 'prec': 40}}
74. label: 1-29-29.9-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.9', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/9'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.9-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.03441040005183911, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79704209862', 'prec': 44}}
75. label: 1-29-29.13-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.13', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/13'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.13-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.13-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': 0.03441040005183911, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.69742322738', 'prec': 44}}
76. label: 1-29-29.16-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.16', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/16'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.16-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': 0.08663515346759294, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.9533960079', 'prec': 40}}
77. label: 1-29-29.20-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.20', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/20'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.20-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.20-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.08663515346759294, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.61651033358', 'prec': 44}}
78. label: 1-29-29.22-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.22', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/22'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.22-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.22-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.15744612881258488, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26652633877', 'prec': 44}}
79. label: 1-29-29.23-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.23', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/23'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.23-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.23-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.4067598392337177, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00015516298', 'prec': 44}}
80. label: 1-29-29.24-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.24', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/24'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.24-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.24-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': 0.4067598392337177, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '4.08081536102', 'prec': 44}}
81. label: 1-29-29.25-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.25', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/25'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.25-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.25-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': -0.2136681182021348, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61214558537', 'prec': 44}}
82. label: 1-29-29.28-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.28', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'dirichlet_coefficients': [1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 0, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 0, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 0, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1], 'euler11': [1, -1], 'euler13': [1, 1], 'euler17': [1, -1], 'euler19': [1, -1], 'euler2': [1, -1], 'euler23': [1, 1], 'euler29': [1, 0], 'euler3': [1, -1], 'euler31': [1, -1], 'euler37': [1, -1], 'euler41': [1, -1], 'euler43': [1, -1], 'euler47': [1, -1], 'euler5': [1, 1], 'euler53': [1, 1], 'euler59': [1, 1], 'euler61': [1, -1], 'euler67': [1, 1], 'euler7': [1, 1], 'euler71': [1, 1], 'euler73': [1, -1], 'euler79': [1, -1], 'euler83': [1, 1], 'euler89': [1, -1], 'euler97': [1, -1], 'euler_factors': [[1, -1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, 0], [1, -1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [1, 1], [1, -1], [1, 1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/28'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.28-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.28-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79380926972', 'prec': 44}}
83. label: 1-29-29.4-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1346754338126234, 'bad_primes': [29], 'central_character': '29.4', 'conductor': 29, 'conductor_radical': 29, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/29/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-29-29.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-29-29.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1346754338126234, 'root_angle': 0.15744612881258488, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.89565228478', 'prec': 44}}
84. label: 2-39-39.38-c0-0-0
    {'algebraic': True, 'analytic_conductor': 0.019463535492687093, 'bad_primes': [3, 13], 'central_character': '39.38', 'conductor': 39, 'conductor_radical': 39, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, -1, 0, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler11': [1, 0, 1], 'euler13': [1, 1, 0], 'euler17': [1, 0, -1], 'euler19': [1, 0, -1], 'euler2': [1, 0, 1], 'euler23': [1, 0, -1], 'euler29': [1, 0, -1], 'euler3': [1, 1, 0], 'euler31': [1, 0, -1], 'euler37': [1, 0, -1], 'euler41': [1, 0, 1], 'euler43': [1, -2, 1], 'euler47': [1, 0, 1], 'euler5': [1, 0, 1], 'euler53': [1, 0, -1], 'euler59': [1, 0, 1], 'euler61': [1, 2, 1], 'euler67': [1, 0, -1], 'euler7': [1, 0, -1], 'euler71': [1, 0, 1], 'euler73': [1, 0, -1], 'euler79': [1, 2, 1], 'euler83': [1, 0, 1], 'euler89': [1, 0, 1], 'euler97': [1, 0, -1], 'euler_factors': [[1, 0, 1], [1, 1, 0], [1, 0, 1], [1, 0, -1], [1, 0, 1], [1, 1, 0], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 0, 1], [1, -2, 1], [1, 0, 1], [1, 0, -1], [1, 0, 1], [1, 2, 1], [1, 0, -1], [1, 0, 1], [1, 0, -1], [1, 2, 1], [1, 0, 1], [1, 0, 1], [1, 0, -1]], 'index': 0, 'instance_types': ['CMF', 'CMF', 'Artin', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/39/1/d/a/38/1', 'ModularForm/GL2/Q/holomorphic/39/1/d/a', 'ArtinRepresentation/2.39.4t3.a.a', 'ArtinRepresentation/2.39.4t3.a'], 'is_instance_Artin': True, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-39-39.38-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-39-39.38-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.13951177546245727, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'trace_hash': 701519358932584307, 'z1': {'__RealLiteral__': 0, 'data': '4.39582175376675801531882680457', 'prec': 103}}
85. label: 1-31-31.10-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.10', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/10'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.10-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.10-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': 0.3332196959897036, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.95325943908', 'prec': 44}}
86. label: 1-31-31.14-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.14', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/14'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.14-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.14-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': -0.3532937361824128, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.10014849249', 'prec': 44}}
87. label: 1-31-31.16-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.16', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/16'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.16-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.16-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': -0.09764150081108221, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.58899933972', 'prec': 44}}
88. label: 1-31-31.18-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.18', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/18'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.18-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.18-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': -0.22514457281149072, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.26173985233', 'prec': 44}}
89. label: 1-31-31.19-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.19', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/19'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.19-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.19-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': 0.22514457281149072, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.85538862', 'prec': 34}}
90. label: 1-31-31.2-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.2', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.2-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.2-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': 0.09764150081108221, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.75999348976', 'prec': 44}}
91. label: 1-31-31.20-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.20', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/20'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.20-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.20-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': 0.3532937361824128, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.41870484484', 'prec': 44}}
92. label: 1-31-31.25-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.25', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/25'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.25-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.25-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': 0.06384099589317323, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.29454214027', 'prec': 44}}
93. label: 1-31-31.28-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.28', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/28'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.28-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.28-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': -0.3332196959897036, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.32588585235', 'prec': 44}}
94. label: 1-31-31.4-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.4', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/4'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.4-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.4-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': -0.05600576961227646, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46574756997', 'prec': 44}}
95. label: 1-31-31.5-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.5', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/5'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.5-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.5-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': -0.06384099589317323, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.59082007421', 'prec': 44}}
96. label: 1-31-31.7-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.7', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/7'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.7-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.7-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': 0.0003535342409458859, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98829132602', 'prec': 44}}
97. label: 1-31-31.8-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.8', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/8'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.8-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.8-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': 0.05600576961227646, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.2307377015', 'prec': 40}}
98. label: 1-31-31.9-r0-0-0
    {'algebraic': True, 'analytic_conductor': 0.1439633947652181, 'bad_primes': [31], 'central_character': '31.9', 'conductor': 31, 'conductor_radical': 31, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/31/9'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-31-31.9-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-31-31.9-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.1439633947652181, 'root_angle': 0.0003535342409458859, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.5337554983', 'prec': 40}}
99. label: 2-44-11.10-c0-0-0
    {'algebraic': True, 'analytic_conductor': 0.021958860555852108, 'bad_primes': [2, 11], 'central_character': '11.10', 'conductor': 44, 'conductor_radical': 22, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, 0, -1], 'euler17': [1, 0, -1], 'euler19': [1, 0, -1], 'euler2': [1, 0, 0], 'euler23': [1, 1, 1], 'euler29': [1, 0, -1], 'euler3': [1, 1, 1], 'euler31': [1, 1, 1], 'euler37': [1, 1, 1], 'euler41': [1, 0, -1], 'euler43': [1, 0, -1], 'euler47': [1, -2, 1], 'euler5': [1, 1, 1], 'euler53': [1, -2, 1], 'euler59': [1, 1, 1], 'euler61': [1, 0, -1], 'euler67': [1, 1, 1], 'euler7': [1, 0, -1], 'euler71': [1, 1, 1], 'euler73': [1, 0, -1], 'euler79': [1, 0, -1], 'euler83': [1, 0, -1], 'euler89': [1, 1, 1], 'euler97': [1, 1, 1], 'euler_factors': [[1, 0, 0], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, -1, 0], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, -2, 1], [1, -2, 1], [1, 1, 1], [1, 0, -1], [1, 1, 1], [1, 1, 1], [1, 0, -1], [1, 0, -1], [1, 0, -1], [1, 1, 1], [1, 1, 1]], 'index': 0, 'instance_types': ['CMF', 'CMF', 'Artin', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/44/1/d/a/21/1', 'ModularForm/GL2/Q/holomorphic/44/1/d/a', 'ArtinRepresentation/2.44.3t2.b.a', 'ArtinRepresentation/2.44.3t2.b'], 'is_instance_Artin': True, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-44-11.10-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-44-11.10-c0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 0.14818522381078386, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'trace_hash': 912108308855815057, 'z1': {'__RealLiteral__': 0, 'data': '4.04199480857272067821281564908', 'prec': 103}}