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lfunc_lfunctions • Show schema
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{'Lhash': '390729046461045404818012599766', 'a10': [65.99034433798349, -3.642466031441887e-60], 'a2': [-5.111590092630059, 2.9511779159669884], 'a3': [1.2817566014058777, -8.908260212564093], 'a4': [9.418902183382514, -16.314017133139945], 'a5': [-9.682458365518542, -5.5901699437494745], 'a6': [19.73804646409708, 49.31806642082709], 'a7': [36.16059224581622, 62.63198300153487], 'a8': [0.0, 16.749731154063262], 'a9': [-77.71420002950491, -22.836442668990706], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.651648338772996, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.2817566014058777, 8.908260212564093]]], [5, [[1.0, 0], [9.682458365518542, 5.5901699437494745]]]], 'bad_primes': [3, 5], 'central_character': '45.41', 'coefficient_field': 'CDF', 'conductor': 45, 'conductor_radical': 15, 'conjugate': '2512226552904021368544689159813', 'degree': 2, 'euler_factors': [[[1.0, 0], [5.111590092630059, 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'2.95563001276716921979149465173005', '4.86803610415363232916164563438379', '7.67117330883457323544373159754359', '8.533976346241133951651813090954091', '10.04235872072942208106835133409842', '10.79197708333819447927190397678812', '11.38550788631049605707302285860726', '13.52871654487031555551272591285717', '14.75795122060604920358096204132788'], 'prelabel': '2-45-9.5-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.156768030821348, 'root_angle': -0.39895691657191806, 'root_number': '-0.8051473691766564 - 0.5930747962170615*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.398956916572', 'prec': 50}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.30823086928740305727598759657', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95563001276716921979149465173', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.86803610415363232916164563438', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.651648338772996, 'bad_primes': [3, 5], 'central_character': '9.5', 'conductor': 45, 'conductor_radical': 15, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/45/5/i/a/41/3'], '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': '2-45-9.5-c4-0-1', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-45-9.5-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.156768030821348, 'root_angle': -0.39895691657191806, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '0.30823086928740305727598759657', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '390729046461045404818012599766', 'Lhash_array': ['390729046461045404818012599766'], 'factors': ['2-45-9.5-c4-0-1'], 'label': '2-45-9.5-c4-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/45/5/i/a/41/3'}