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lfunc_lfunctions • Show schema
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{'Lhash': '504710530888708720406515619895', 'a10': [0.0, 0.0], 'a2': [-10.909390040409567, 0.0], 'a3': [-9.0, 0.0], 'a4': [87.01479105378746, 0.0], 'a5': [0.0, 0.0], 'a6': [98.1845103636861, 0.0], 'a7': [-180.63471826791246, 0.0], 'a8': [-600.1778135974023, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.31665134570906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [10.909390040409567, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [180.63471826791246, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [61.0567486606111, 0], [371293.0, 0]], [[1.0, 0], [-133.45037182974906, 0], [1419857.0, 0]], [[1.0, 0], [-1994.8048232733781, 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['0.39814640627144420110330139098921', '1.36491137688305928849167539965593', '2.63940337959941905672016699195700', '3.65015341551642388709726777097059', '5.65254537854282210002724126772370', '6.25038527125330992484175365293603', '7.25453050776198457455515806196572', '7.60239947188951337672814212809706', '9.040675710715031379748582113691797', '9.434312417697342521076101141520464'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39814640627144420110330139099', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.36491137688305928849167539966', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.63940337959941905672016699196', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.31665134570906, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/u/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': '2-825-1.1-c5-0-16', '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': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39814640627144420110330139099', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '504710530888708720406515619895', 'Lhash_array': ['504710530888708720406515619895'], 'label': '2-825-1.1-c5-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/u/1/1'}