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lfunc_lfunctions • Show schema
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{'Lhash': '771213558987530317089757194453', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.42736734647120733, 1.678498481134302], 'a4': [0.0, 0.0], 'a5': [-0.045817439058354476, 0.17099301043846965], 'a6': [0.0, 0.0], 'a7': [-1.1743150761490875, 2.033973375984335], 'a8': [0.0, 0.0], 'a9': [-2.634714302340318, 1.434670883876637], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.599383156425752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.42736734647120733, -1.678498481134302]]]], 'bad_primes': [2, 3], 'central_character': '576.47', 'coefficient_field': 'CDF', 'conductor': 576, 'conductor_radical': 6, 'conjugate': '2840918939594565524965705666510', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.42736734647120733, -1.678498481134302]], [[1.0, 0], [0.045817439058354476, -0.17099301043846965], [-4.330127018922194, -2.5]], [[1.0, 0], [1.1743150761490875, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-24e2-144.83-c1-0-5', '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/576/2/y/a/47/14', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.1438925093289625, 0.9199121392390571, 0.6949630526220119, 0.4631935714109408, 0.22040812388102615, -0.03454282680007341, -0.2989060372756172, -0.5657124443546986, -0.8239583549306961, -1.0592351475627586, -1.254779266120749, -1.3929139151193908, -1.4568277923595474, -1.4325902156885921, -1.3112468791924343, -1.090787945092265, -0.7777415905988774, -0.38813175776989933, 0.052442977331484245, 0.5097965994814508, 0.9433016900904032, 1.30915890043721, 1.5646033070996948, 1.6727036122018404, 1.607267601599759, 1.3572632958424315, 0.9301226835735463, 0.3533321574842308, 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'8.802891343242643251780061542309278', '9.138598027866464519197536854825555', '10.61197271101100922520693985045780'], 'prelabel': '2-24e2-144.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.144617251731822, 'root_angle': -0.7794506274778723, 'root_number': '-0.7694119626934557 - 0.638752872137734*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.389725313739', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60838022626162135068420152669', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23556737363903290752247014418', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44166959473636057192440469997', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.599383156425752, 'bad_primes': [2, 3], 'central_character': '144.83', 'conductor': 576, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/576/2/y/a/47/14'], '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': '2-24e2-144.83-c1-0-5', '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': '2-24e2-144.83-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.144617251731822, 'root_angle': -0.38972531373893615, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60838022626162135068420152669', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '771213558987530317089757194453', 'Lhash_array': ['771213558987530317089757194453'], 'label': '2-24e2-144.83-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/576/2/y/a/47/14'}