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lfunc_lfunctions • Show schema
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{'Lhash': '1866842829239861112817295242934', 'a10': [8.315804065108486, 0.0], 'a2': [2.687909725150971, 0.0], 'a3': [-2.909853368696051, 0.0], 'a4': [5.2248586905611685, 0.0], 'a5': [3.093781010313289, 0.0], 'a6': [-7.82142316848143, 0.0], 'a7': [1.7039671259009506, 0.0], 'a8': [8.668129036596989, 0.0], 'a9': [5.467246627311757, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.84418973575603, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 13], 'central_character': '1859.1', 'coefficient_field': 'CDF', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.687909725150971, 0], [2.0, 0]], [[1.0, 0], [2.909853368696051, 0], [3.0, 0]], [[1.0, 0], [-3.093781010313289, 0], [5.0, 0]], [[1.0, 0], [-1.7039671259009506, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0423681876441444, 0], [17.0, 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'4.63227471385997061686226447431136', '5.42272911170412415053760104482653', '5.64426390390831888795870701639070', '6.49125098078374360340142930800626', '6.88764644847844978180949146411809', '8.121508448975128849023689160899140', '9.827592375266782604554463777180847'], 'prelabel': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.47267932417951160364159962718', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22389768627036907976256747365', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75233532098444110936882463897', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.84418973575603, 'bad_primes': [11, 13], 'central_character': '1.1', 'conductor': 1859, 'conductor_radical': 143, 'degree': 2, 'index': 80, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1859/2/a/t/1/21'], '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': '2-1859-1.1-c1-0-80', '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': '2-1859-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8528158190803814, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.47267932417951160364159962718', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1866842829239861112817295242934', 'Lhash_array': ['1866842829239861112817295242934'], 'label': '2-1859-1.1-c1-0-80', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1859/2/a/t/1/21'}