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lfunc_lfunctions • Show schema
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{'Lhash': '1349197849508338004587990318370', 'a10': [1.4142135623730951, 0.0], 'a2': [-0.6180339887498949, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.618033988749895, 0.0], 'a5': [-2.288245611270737, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [2.23606797749979, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.6926245622462, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '3969.1', 'coefficient_field': 'CDF', 'conductor': 3969, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6180339887498949, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.288245611270737, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0], [11.0, 0]], [[1.0, 0], [4.576491222541474, 0], [13.0, 0]], [[1.0, 0], [-3.1622776601683795, 0], [17.0, 0]], [[1.0, 0], [-4.036309709066021, 0], [19.0, 0]], [[1.0, 0], [7.23606797749979, 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'6.93654511565299587938198312838814', '7.61366586905601631214974495888209', '8.015404085966748123152822807833946'], 'prelabel': '2-63e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.629620285796032, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06432943688538997592263563449', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47215739719307441325815145112', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.67858528210579546848526599244', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.6926245622462, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 3969, 'conductor_radical': 21, 'degree': 2, 'index': 80, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3969/2/a/y/1/1'], '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': '2-63e2-1.1-c1-0-80', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-63e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.629620285796032, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06432943688538997592263563449', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1349197849508338004587990318370', 'Lhash_array': ['1349197849508338004587990318370'], 'label': '2-63e2-1.1-c1-0-80', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3969/2/a/y/1/1'}