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lfunc_lfunctions • Show schema
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{'Lhash': '1200040075767102067167960317122', 'a10': 0, 'a2': 0, 'a3': 1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.40869910383263, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [31, [1, -1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '7440.1', 'coefficient_field': '1.1.1.1', 'conductor': 7440, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, -2, 7], [1, 0, 11], [1, -4, 13], [1, -6, 17], [1, 0, 19], [1, 0, 23], [1, -8, 29], [1, -1], [1, -4, 37], [1, -10, 41], [1, 8, 43], [1, -4, 47], [1, 14, 53], [1, 14, 59], [1, 6, 61], [1, -10, 67], [1, 6, 71], [1, 8, 73], [1, 8, 79], [1, -12, 83], [1, -16, 89], [1, 10, 97], [1, 6, 101], [1, -6, 103], [1, 8, 107], [1, -18, 109], [1, -14, 113]], 'euler_factors_factorization': [[1], [[[1, -1], 1]], [[[1, 1], 1]], [[[1, -2, 7], 1]], [[[1, 0, 11], 1]], [[[1, -4, 13], 1]], [[[1, -6, 17], 1]], [[[1, 0, 19], 1]], [[[1, 0, 23], 1]], [[[1, -8, 29], 1]], [[[1, -1], 1]], [[[1, -4, 37], 1]], [[[1, -10, 41], 1]], [[[1, 8, 43], 1]], [[[1, -4, 47], 1]], [[[1, 14, 53], 1]], [[[1, 14, 59], 1]], [[[1, 6, 61], 1]], [[[1, -10, 67], 1]], [[[1, 6, 71], 1]], [[[1, 8, 73], 1]], [[[1, 8, 79], 1]], [[[1, -12, 83], 1]], [[[1, -16, 89], 1]], [[[1, 10, 97], 1]], [[[1, 6, 101], 1]], [[[1, -6, 103], 1]], [[[1, 8, 107], 1]], [[[1, -18, 109], 1]], [[[1, -14, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 55, 'label': '2-7440-1.1-c1-0-55', 'leading_term': '3.12572372034786531168014515615430000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/7440/2/a/u', 'plot_delta': {'__RealLiteral__': 0, 'data': 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-2.3639349504053317, -2.384283828513359, -2.2868250417180187, -2.075828467820536, -1.7619593413700532, -1.3617182470914038, -0.896550585640423, -0.3916724051347462, 0.12532415217153314, 0.6260095468500212, 1.0827145898756005, 1.4700979887781345, 1.7665952685998023, 1.9556664749115793], 'positive_zeros': ['0.946664700471127729645202728930405', '1.66543491238490246529369513530615', '2.90951403003388796725691476457359', '3.41546735722577944204540536845699', '4.35753299899360647882796770061842', '4.87649587064915316027668833441607', '5.90043500550419334803503618108183', '6.46193266592321770928633568409942', '7.51756058099746396838226247290091', '7.929051861249934832356481311560034'], 'prelabel': '2-7440-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.7077038801339945, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 350706137010428653, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.946664700471127729645202728930', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.66543491238490246529369513531', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.90951403003388796725691476457', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 59.40869910383263, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 7440, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 2, 0, 1, 0, 0, 0, 4, 0, -1, 0, 6, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 8, 0, 1, 0, 0, 0, -2, 0, 4, 0, 4, 0, 10, 0, -8, 0, -1, 0, 4, 0, -3, 0, 6, 0, -14, 0, 0, 0, 0, 0, -14, 0, -6, 0, 2, 0, -4, 0, 10, 0, 0, 0, -6, 0, -8, 0, 1, 0, 0, 0, -8, 0, 1, 0, 12, 0, -6, 0, 8, 0, 16, 0, 8, 0, 1, 0, 0, 0, -10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -4, 13], 'euler17': [1, -6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -8, 29], 'euler3': [1, -1, 0], 'euler31': [1, -1, 0], 'euler37': [1, -4, 37], 'euler41': [1, -10, 41], 'euler43': [1, 8, 43], 'euler47': [1, -4, 47], 'euler5': [1, 1, 0], 'euler53': [1, 14, 53], 'euler59': [1, 14, 59], 'euler61': [1, 6, 61], 'euler67': [1, -10, 67], 'euler7': [1, -2, 7], 'euler71': [1, 6, 71], 'euler73': [1, 8, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -16, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, -2, 7], [1, 0, 11], [1, -4, 13], [1, -6, 17], [1, 0, 19], [1, 0, 23], [1, -8, 29], [1, -1, 0], [1, -4, 37], [1, -10, 41], [1, 8, 43], [1, -4, 47], [1, 14, 53], [1, 14, 59], [1, 6, 61], [1, -10, 67], [1, 6, 71], [1, 8, 73], [1, 8, 79], [1, -12, 83], [1, -16, 89], [1, 10, 97]], 'index': 55, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7440/u', 'ModularForm/GL2/Q/holomorphic/7440/2/a/u/1/1', 'ModularForm/GL2/Q/holomorphic/7440/2/a/u'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-7440-1.1-c1-0-55', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-7440-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.7077038801339945, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 350706137010428653, 'z1': {'__RealLiteral__': 0, 'data': '0.946664700471127729645202728930', 'prec': 107}}
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lfunc_instances • Show schema
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id: 22217499
{'Lhash': '1200040075767102067167960317122', 'Lhash_array': ['1200040075767102067167960317122'], 'label': '2-7440-1.1-c1-0-55', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7440/2/a/u'}
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id: 24579634
{'Lhash': '1200040075767102067167960317122', 'Lhash_array': ['1200040075767102067167960317122'], 'label': '2-7440-1.1-c1-0-55', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7440/2/a/u/1/1'}
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id: 34359
{'Lhash': '350706137010428653', 'Lhash_array': ['350706137010428653'], 'label': '2-7440-1.1-c1-0-55', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7440/u'}