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lfunc_lfunctions • Show schema
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{'Lhash': '1438701831530915895942996448439', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [0, 0], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -1.7015621187164243], 'a8': [0, 1.0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.71248518244905, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '5850.5149', 'coefficient_field': 'CDF', 'conductor': 5850, 'conductor_radical': 390, 'conjugate': '528070090480488343115390030139', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.7015621187164243], [-7.0, 0]], [[1.0, 0], [-1.7015621187164243, 0], [11.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 5.701562118716424], [-17.0, 0]], [[1.0, 0], [4.701562118716424, 0], [19.0, 0]], [[1.0, 0], [0, 0], [-23.0, 0]], 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 75, 'label': '2-5850-5.4-c1-0-75', 'leading_term': '1.437443015359111636583391108352363552169318820403146556', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5850/2/e/bi/5149/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.4374430153591116, 1.5940555589472734, 1.7419728722098091, 1.8796612458836495, 2.0054287283878605, 2.1174098962806647, 2.2135680055331917, 2.291715451189896, 2.3495523271613785, 2.384721871594451, 2.394880760998789, 2.377781593596733, 2.3313644648877827, 2.253854255028614, 2.14386008278239, 2.0004733037197586, 1.8233604200283624, 1.612847315652897, 1.3699913331020095, 1.0966378735512134, 0.7954584399889695, 0.4699673650124243, 0.12451487973409207, -0.23574530612288644, 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'5.90275190404228325288598588795241', '6.14818877053540847696121274571964', '6.83373480038600671653915133028142', '7.85516538328857580197310743645729', '8.311353571195392780725234288229216'], 'prelabel': '2-5850-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.834653259855181, 'root_angle': 0.8524163823495667, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42620819117478337', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13493562916460593838828628316', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.27973483301547936810215092228', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.24933086278471458165605094752', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 46.71248518244905, 'bad_primes': [2, 3, 5, 13], 'central_character': '5.4', 'conductor': 5850, 'conductor_radical': 390, 'degree': 2, 'index': 75, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5850/2/e/bi/5149/1'], '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': '2-5850-5.4-c1-0-75', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-5850-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.834653259855181, 'root_angle': 0.42620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13493562916460593838828628316', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1438701831530915895942996448439', 'Lhash_array': ['1438701831530915895942996448439'], 'label': '2-5850-5.4-c1-0-75', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5850/2/e/bi/5149/1'}