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lfunc_lfunctions • Show schema
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{'Lhash': '1333543535308437398728564333209', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-8.729030325852962, 0.0], 'a4': [0.0, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [5.162191127167216, 0.0], 'a8': [0.0, 0.0], 'a9': [49.19597042966066, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 108.56351441056277, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-5.0, 0]]], [23, [[1.0, 0], [-23.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '1840.1', 'coefficient_field': 'CDF', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [8.729030325852962, 0], [27.0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [-5.162191127167216, 0], [343.0, 0]], [[1.0, 0], [38.009840566160996, 0], [1331.0, 0]], [[1.0, 0], [-39.84629875258414, 0], [2197.0, 0]], [[1.0, 0], [52.16002731369075, 0], [4913.0, 0]], [[1.0, 0], [-35.31336256417937, 0], [6859.0, 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'4.80175773628930691825307024559215', '5.25478621854143859432528327276514', '6.01430378890785619014079496748826', '6.69441064506753449746860711157131', '7.49787879898458228388849350466329', '8.509939931272652761467408599722158'], 'prelabel': '2-1840-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.419381671220359, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05198036041504224483051805700', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.14631043315500016280924519100', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58710645965383676301006644124', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 108.56351441056277, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 1840, 'conductor_radical': 230, 'degree': 2, 'index': 78, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1840/4/a/t/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': '2-1840-1.1-c3-0-78', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1840-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.419381671220359, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05198036041504224483051805700', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1333543535308437398728564333209', 'Lhash_array': ['1333543535308437398728564333209'], 'label': '2-1840-1.1-c3-0-78', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1840/4/a/t/1/1'}