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lfunc_lfunctions • Show schema
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{'Lhash': '711908385035248117885155369418', 'a10': [-5.767038248899697, 0.0], 'a2': [1.4839876851428622, 0.0], 'a3': [1.0898632378315798, 0.0], 'a4': [0.20221944965567093, 0.0], 'a5': [-3.8861766217045854, 0.0], 'a6': [1.6173436234319907, 0.0], 'a7': [2.4406904856715586, 0.0], 'a8': [-2.6678841973003418, 0.0], 'a9': [-1.8121981228232655, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [43, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.4839876851428622, 0], [2.0, 0]], [[1.0, 0], [-1.0898632378315798, 0], [3.0, 0]], [[1.0, 0], [3.8861766217045854, 0], [5.0, 0]], [[1.0, 0], [-2.4406904856715586, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], 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'2.98504025436348885875524585707953', '3.73482034268868646020035134858983', '4.18685098676032372855966566441748', '4.74520630314494731069583131412696', '5.56817012438211196551338416098606', '6.31543814664365657642658070588511', '7.33981934492647753266893796296255', '7.83604349161059480832574464462872'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56159669305333444463881854392', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.15253787351089487682494582116', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.98504025436348885875524585708', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 134, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/57'], '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': '2-8041-1.1-c1-0-134', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56159669305333444463881854392', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '711908385035248117885155369418', 'Lhash_array': ['711908385035248117885155369418'], 'label': '2-8041-1.1-c1-0-134', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/j/1/57'}