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lfunc_lfunctions • Show schema
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{'Lhash': '4039141457283802800332941005025', 'a10': [2.1694888502255923e-59, -68.58166728518603], 'a2': [1.0188846739768997, 1.402374444306971], 'a3': [-1.6056994039789048, -4.941834621277992], 'a4': [4.015743806818887, -12.35918860375997], 'a5': [-32.00805902564843, -23.255216121039417], 'a6': [5.294280067143725, -7.286951366327534], 'a7': [27.31160724657664, 8.874079130190125], 'a8': [47.80123059944402, -15.531561325930458], 'a9': [-21.843458848123582, 15.870201811896775], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.411208781766864, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.6056994039789048, 4.941834621277992]]], [11, [[1.0, 0], [-30.602678890427992, 117.06611826113205]]]], 'bad_primes': [3, 11], 'central_character': '33.19', 'coefficient_field': 'CDF', 'conductor': 33, 'conductor_radical': 33, 'conjugate': '1321509539085046587371292549964', 'degree': 2, 'euler_factors': [[[1.0, 0], 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.18632078630861746469983171388', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.46432870592376678894658199071', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.11399508949871954293759246724', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.411208781766864, 'bad_primes': [3, 11], 'central_character': '11.8', 'conductor': 33, 'conductor_radical': 33, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/33/5/g/a/19/6'], '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': '2-33-11.8-c4-0-4', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-33-11.8-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8469457982753212, 'root_angle': 0.22962799432443237, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '3.18632078630861746469983171388', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4039141457283802800332941005025', 'Lhash_array': ['4039141457283802800332941005025'], 'label': '2-33-11.8-c4-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/33/5/g/a/19/6'}