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lfunc_lfunctions • Show schema
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{'Lhash': '2293504221932565156529065643250', 'a10': [350.3987322494556, 0.0], 'a2': [8.938473489547206, 0.0], 'a3': [-9.0, 0.0], 'a4': [47.8963083233382, 0.0], 'a5': [39.20118269178932, 0.0], 'a6': [-80.44626140592484, 0.0], 'a7': [-156.56283866132918, 0.0], 'a8': [142.08873052982707, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 75.5407791319139, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [157, [[1.0, 0], [24649.0, 0]]]], 'bad_primes': [3, 157], 'central_character': '471.1', 'coefficient_field': 'CDF', 'conductor': 471, 'conductor_radical': 471, 'degree': 2, 'euler_factors': [[[1.0, 0], [-8.938473489547206, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [-39.20118269178932, 0], [3125.0, 0]], [[1.0, 0], [156.56283866132918, 0], [16807.0, 0]], [[1.0, 0], [13.141003763751486, 0], [161051.0, 0]], [[1.0, 0], [-140.73713296562912, 0], [371293.0, 0]], [[1.0, 0], 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0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.80925581664193570715972339843', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.11320076684392116113878205954', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.90839272610548554775365153113', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 75.5407791319139, 'bad_primes': [3, 157], 'central_character': '1.1', 'conductor': 471, 'conductor_radical': 471, 'degree': 2, 'index': 118, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/471/6/a/b/1/26'], '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': '2-471-1.1-c5-0-118', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-471-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.691419857072486, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.80925581664193570715972339843', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2293504221932565156529065643250', 'Lhash_array': ['2293504221932565156529065643250'], 'label': '2-471-1.1-c5-0-118', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/471/6/a/b/1/26'}