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lfunc_lfunctions • Show schema
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{'Lhash': '803149786562936901934090755811', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [0, -1.0], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [-1.0, 0], 'a7': [0, 1.5615528128088303], 'a8': [0, 1.0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.1304369398954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 1.0]]], [3, [[1.0, 0], [0, 1.0]]], [5, [[1.0, 0], [0, 0]]], [31, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '4650.3349', 'coefficient_field': 'CDF', 'conductor': 4650, 'conductor_radical': 930, 'conjugate': '843025216356106610182540708875', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -1.5615528128088303], [-7.0, 0]], [[1.0, 0], [1.5615528128088303, 0], [11.0, 0]], [[1.0, 0], [0, -2.0], [-13.0, 0]], [[1.0, 0], [0, 5.123105625617661], [-17.0, 0]], [[1.0, 0], [4.68465843842649, 0], [19.0, 0]], [[1.0, 0], 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0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 34, 'label': '2-4650-5.4-c1-0-34', 'leading_term': '1.429001531645377939648123631037576782062357671126903562', '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/4650/2/d/bd/3349/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.429001531645378, 1.4350648528031893, 1.4231581636243684, 1.39242531191172, 1.3419252593242041, 1.2706630934422338, 1.1776353970453701, 1.0618878283544546, 0.922582144408148, 0.7590695159288825, 0.5709668151071501, 0.35823256415519344, 0.12123936089647377, -0.13916019883429834, -0.4215768385686474, -0.7240396316843647, -1.0439649427254, -1.3781411868940003, -1.7227310016271784, -2.0732920776026753, -2.4248175076988283, -2.771796075291432, -3.1082924159515826, -3.428046451966218, 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'5.51142217494776852550288840647328', '6.36047602896710365436997528561029', '6.81047621081432969713266473774905', '7.984165673191744371984755480426097', '8.237833960591208022785014882874239'], 'prelabel': '2-4650-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.093474947835217, 'root_angle': 0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 + 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.17620819117478337', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63357346765610082826194222411', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.16597438457862505212061249361', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.30929073167262113917873258344', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 37.1304369398954, 'bad_primes': [2, 3, 5, 31], 'central_character': '5.4', 'conductor': 4650, 'conductor_radical': 930, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4650/2/d/bd/3349/2'], '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': '2-4650-5.4-c1-0-34', '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': '2-4650-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.093474947835217, 'root_angle': 0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63357346765610082826194222411', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '803149786562936901934090755811', 'Lhash_array': ['803149786562936901934090755811'], 'label': '2-4650-5.4-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4650/2/d/bd/3349/2'}