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lfunc_lfunctions • Show schema
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{'Lhash': '2040419396108905938612544948137', 'a10': [0.0, 0.0], 'a2': [0.8660254037844386, -0.5], 'a3': [-1.0, 0.0], 'a4': [4.582907174201562e-80, -2.6459426906140066e-80], 'a5': [0.0, 0.0], 'a6': [-0.8660254037844386, 0.5], 'a7': [0.0, -1.0], 'a8': [1.3229713455367871e-80, 1.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.3458520537546707, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [0, 1.0]]], [11, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7, 11], 'central_character': '693.142', 'coefficient_field': 'CDF', 'conductor': 693, 'conductor_radical': 231, 'conjugate': '1776071095521805963357672829002', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-0.8660254037844386, 0.5], [0.5, -0.8660254037844386]], 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'0.10102463458413805', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60960709184498179182490488074', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.73714501775804461804290552566', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.42711058102940267492558436630', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.3458520537546707, 'bad_primes': [3, 7, 11], 'central_character': '693.142', 'conductor': 693, 'conductor_radical': 231, 'degree': 2, 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/693/1/bl/a/142/2', 'ArtinRepresentation/2.693.16t60.a.a'], 'is_instance_Artin': True, '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': '2-693-693.142-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-693-693.142-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5880918752666718, 'root_angle': 0.10102463458413806, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60960709184498179182490488074', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24603542
{'Lhash': '2040419396108905938612544948137', 'Lhash_array': ['2040419396108905938612544948137'], 'label': '2-693-693.142-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.693.16t60.a.a'}
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id: 19803506
{'Lhash': '2040419396108905938612544948137', 'Lhash_array': ['2040419396108905938612544948137'], 'label': '2-693-693.142-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/693/1/bl/a/142/2'}