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lfunc_lfunctions • Show schema
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{'Lhash': '1620346611451683212281263050651', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [2.5, -1.6583123951777], 'a4': [4.0, 0.0], 'a5': [0.0, 9.9498743710662], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [3.5, -8.2915619758885], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.89103359627878, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-2.5, 1.6583123951777]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '363.122', 'coefficient_field': 'CDF', 'conductor': 363, 'conductor_radical': 33, 'conjugate': '2426696131562941221514338257633', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-4.0, 0]], [[1.0, 0], [-2.5, 1.6583123951777]], [[1.0, 0], [0, -9.9498743710662], [-25.0, 0]], [[1.0, 0], [0, 0], [49.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [169.0, 0]], [[1.0, 0], [0, 0], [-289.0, 0]], [[1.0, 0], [0, 0], [361.0, 0]], [[1.0, 0], [0, -29.8496231131986], [-529.0, 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'root_analytic_conductor': 3.145001366657697, 'root_angle': -0.18642949867733727, 'root_number': '0.8333333333333334 - 0.5527707983925666*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0932147493387', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27822809468157391260321744731', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61752170669671940248949119837', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16676985653622901857812369999', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 9.89103359627878, 'bad_primes': [3, 11], 'central_character': '3.2', 'conductor': 363, 'conductor_radical': 33, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/363/3/b/c/122/1'], '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': '2-363-3.2-c2-0-32', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-363-3.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.145001366657697, 'root_angle': -0.09321474933866863, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27822809468157391260321744731', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1620346611451683212281263050651', 'Lhash_array': ['1620346611451683212281263050651'], 'label': '2-363-3.2-c2-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/363/3/b/c/122/1'}