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lfunc_lfunctions • Show schema
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{'Lhash': '2853586318079816295591576396972', 'a10': [-0.7540553187891937, -0.23259526187784946], 'a2': [0.4459387216780912, 0.3040358724346746], 'a3': [0.7594702435073364, 0.704685404448228], 'a4': [-0.6242585169680137, -1.5905847606928045], 'a5': [-1.3971196311868728, 0.4309543323855832], 'a6': [0.12442754780881167, 0.5451527065177793], 'a7': [-2.5234154159379236, -0.7952198680911062], 'a8': [0.44541238617128204, -1.9514791709221555], 'a9': [-0.1439767492285427, -1.9212362001188172], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [2.5234154159379236, 0.7952198680911062]]], [13, [[1.0, 0], [0.9009688679024191, -0.4338837391175581]]]], 'bad_primes': [7, 13], 'central_character': '637.53', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '335546656813682522709108093691', 'degree': 2, 'euler_factors': [[[1.0, 0], 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0.7320407394522582*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.369284026739', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.25108268600673800923114580110', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.30317694165815289322668432492', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07859724118526021010132319922', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '49.4', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 52, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/bl/b/53/18'], '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': '2-637-49.4-c1-0-52', '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': '2-637-49.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.3692840267387409, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.25108268600673800923114580110', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2853586318079816295591576396972', 'Lhash_array': ['2853586318079816295591576396972'], 'label': '2-637-49.4-c1-0-52', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/bl/b/53/18'}