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lfunc_lfunctions • Show schema
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{'Lhash': '227110883820544153273517109827', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.1112533734198565, 2.9979364047462216], 'a4': [0.0, 0.0], 'a5': [-2.1837848861528224, 2.6025334835255642], 'a6': [0.0, 0.0], 'a7': [-6.994357798306969, -2.5457380463914268], 'a8': [0.0, 0.0], 'a9': [-8.975245373805404, 0.6670610766524269], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.885573710182413, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.1112533734198565, -2.9979364047462216]]]], 'bad_primes': [2, 3], 'central_character': '216.41', 'coefficient_field': 'CDF', 'conductor': 216, 'conductor_radical': 6, 'conjugate': '3782416417779057132699153923649', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.1112533734198565, -2.9979364047462216]], [[1.0, 0], [2.1837848861528224, -2.6025334835255642], [-4.341204441673259, -24.6201938253052]], [[1.0, 0], [6.994357798306969, 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103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69950333349919039522776770137', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.885573710182413, 'bad_primes': [2, 3], 'central_character': '27.14', 'conductor': 216, 'conductor_radical': 6, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/216/3/u/a/41/9'], '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': '2-6e3-27.14-c2-0-1', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-6e3-27.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4260201380414, 'root_angle': 0.4452523776302009, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '0.17915889739621850480563721754', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '227110883820544153273517109827', 'Lhash_array': ['227110883820544153273517109827'], 'label': '2-6e3-27.14-c2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/216/3/u/a/41/9'}