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lfunc_lfunctions • Show schema
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{'Lhash': '852501272301863228412757506189', 'a10': [0.860404070192127, 0.0], 'a2': [0.6295093837420657, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.6037179357806848, 0.0], 'a5': [1.3667851384160903, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5879942136606989, 0.0], 'a8': [-2.268574256933528, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 78.26137902105694, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '9801.1', 'coefficient_field': 'CDF', 'conductor': 9801, 'conductor_radical': 33, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6295093837420657, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.3667851384160903, 0], [5.0, 0]], [[1.0, 0], [0.5879942136606989, 0], [7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.799910218401867, 0], [13.0, 0]], [[1.0, 0], [-0.19349310929449012, 0], [17.0, 0]], [[1.0, 0], [1.945784996073631, 0], [19.0, 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[109.0, 0]], [[1.0, 0], [2.885444508821854, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 126, 'label': '2-99e2-1.1-c1-0-126', 'leading_term': '2.16983559619887986362935351884', '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/9801/2/a/cr/1/15', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [2.16983559619888, 2.158539831144909, 2.12465588112398, 2.068201480710041, 1.9892312984368976, 1.887872719539816, 1.7643723516516845, 1.6191500469298121, 1.4528567975642803, 1.2664326837479107, 1.0611611096575126, 0.8387158113112222, 0.6011975107118802, 0.3511575760561341, 0.0916065888443914, -0.17399371289827611, -0.44175606837876563, -0.7074112806863985, -0.9663695603293287, -1.2137988654981893, -1.4447189252429258, -1.654109093141398, 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'4.33144422519519376759696083714518', '4.76921881969619706437673565119497', '5.76634117962301350832988744536908', '6.12654972778909408252675534103165', '6.68423294580760467160495173639747', '7.907275000355748871313180026090434'], 'prelabel': '2-99e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846546163393764, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.67250492537011210485914002260', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.70074557685441949057307697874', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.81314934475870088078020577669', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 78.26137902105694, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 9801, 'conductor_radical': 33, 'degree': 2, 'index': 126, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9801/2/a/cr/1/15'], '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': '2-99e2-1.1-c1-0-126', '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': '2-99e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.846546163393764, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.67250492537011210485914002260', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '852501272301863228412757506189', 'Lhash_array': ['852501272301863228412757506189'], 'label': '2-99e2-1.1-c1-0-126', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9801/2/a/cr/1/15'}