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lfunc_lfunctions • Show schema
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{'Lhash': '2596471092004171738750920791587', 'a10': [0.1993245406834079, 2.7049722676437398], 'a2': [-0.6151895712538502, 1.2733977349675567], 'a3': [1.7310778048707458, 0.0580485442012098], 'a4': [-1.2430835828410078, -1.5667620132206306], 'a5': [1.6609415900220987, -0.9589450741075037], 'a6': [-1.138859897289475, 2.1686396967559656], 'a7': [-0.708997817017817, -2.5489845224057306], 'a8': [2.7598432552290197, -0.6190841675950757], 'a9': [2.9932607330322405, 0.20097309294354543], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.0122301309362665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6151895712538502, -1.2733977349675567]]], [3, [[1.0, 0], [-1.7310778048707458, -0.0580485442012098]]], [7, [[1.0, 0], [0.708997817017817, 2.5489845224057306]]]], 'bad_primes': [2, 3, 7], 'central_character': '252.103', 'coefficient_field': 'CDF', 'conductor': 252, 'conductor_radical': 42, 'conjugate': 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['2.04825453601859994534967932625507', '2.81853574809902322475863564909102', '4.19728623422829585146794307271099', '5.88733963270184651885236028626123', '7.34821069622515700626004376619084', '8.440321941246821694424324896070772', '9.219251910563159683275258612329142', '9.958225470915676566435348389579100', '10.76126715542789715279308494599847', '12.21300504968367568991399224311456'], 'prelabel': '2-252-252.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4185309763753016, 'root_angle': -0.06352563991291675, 'root_number': '0.9213942444901445 - 0.38862918858525763*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0635256399129', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04825453601859994534967932626', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81853574809902322475863564909', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.19728623422829585146794307271', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.0122301309362665, 'bad_primes': [2, 3, 7], 'central_character': '252.103', 'conductor': 252, 'conductor_radical': 42, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/252/2/bj/b/103/14'], 'is_instance_Artin': False, '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': '2-252-252.103-c1-0-27', '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': '2-252-252.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4185309763753016, 'root_angle': -0.06352563991291675, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04825453601859994534967932626', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2596471092004171738750920791587', 'Lhash_array': ['2596471092004171738750920791587'], 'factors': ['2-252-252.103-c1-0-27'], 'label': '2-252-252.103-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/252/2/bj/b/103/14'}