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lfunc_lfunctions • Show schema
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{'Lhash': '677565607802140677092611904783', 'a10': [0, 0], 'a2': [-2.2693452091957607, 5.181705541759417], 'a3': [-10.82401264448558, 0], 'a4': [-21.700144643000495, -23.518157293309713], 'a5': [0, 0], 'a6': [24.563421239037687, -56.08684630400493], 'a7': [0, 163.70607496888653], 'a8': [171.1092852631608, -59.07294217093185], 'a9': [-125.84075027201628, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.07676396259613, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.2693452091957607, -5.181705541759417]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '200.149', 'coefficient_field': 'CDF', 'conductor': 200, 'conductor_radical': 10, 'conjugate': '864781011901997365021128337536', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2693452091957607, -5.181705541759417]], [[1.0, 0], [10.82401264448558, 0], [243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -163.70607496888653], [-16807.0, 0]], [[1.0, 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'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.53450501871742175373383690551', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.90508697466420051823660322468', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66644819728538982814396477458', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.07676396259613, 'bad_primes': [2, 5], 'central_character': '40.29', 'conductor': 200, 'conductor_radical': 10, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/200/6/f/b/149/8'], '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': '2-200-40.29-c5-0-28', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-200-40.29-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.663635225064917, 'root_angle': -0.22911506406101034, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.53450501871742175373383690551', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '677565607802140677092611904783', 'Lhash_array': ['677565607802140677092611904783'], 'label': '2-200-40.29-c5-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/200/6/f/b/149/8'}