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lfunc_lfunctions • Show schema
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{'Lhash': '1477482677716522348506692597986', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-10.1459462447276, 0.0], 'a4': [0.0, 0.0], 'a5': [8.699953721425512, 0.0], 'a6': [0.0, 0.0], 'a7': [7.0, 0.0], 'a8': [0.0, 0.0], 'a9': [75.9402252009021, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.69035312707247, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-7.0, 0]]], [11, [[1.0, 0], [-11.0, 0]]]], 'bad_primes': [2, 7, 11], 'central_character': '1232.1', 'coefficient_field': 'CDF', 'conductor': 1232, 'conductor_radical': 154, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [10.1459462447276, 0], [27.0, 0]], [[1.0, 0], [-8.699953721425512, 0], [125.0, 0]], [[1.0, 0], [-7.0, 0]], [[1.0, 0], [-11.0, 0]], [[1.0, 0], [76.3572264144797, 0], [2197.0, 0]], [[1.0, 0], [-39.72784594608682, 0], [4913.0, 0]], [[1.0, 0], [-27.987612870033477, 0], [6859.0, 0]], [[1.0, 0], 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'4.97986559769831821620795053815148', '5.51448642916635854182502317375597', '6.24664216259771538233751562328332', '7.08985415769147355126255954122870', '7.78520653904640543621688212872106', '9.331365291576990630597634661955310'], 'prelabel': '2-1232-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.525863776009588, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.16552832259182026736239862710', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22255664627633354396678006536', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06157890309676685964490331456', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 72.69035312707247, 'bad_primes': [2, 7, 11], 'central_character': '1.1', 'conductor': 1232, 'conductor_radical': 154, 'degree': 2, 'index': 58, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1232/4/a/s/1/1'], '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': '2-1232-1.1-c3-0-58', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1232-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.525863776009588, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.16552832259182026736239862710', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1477482677716522348506692597986', 'Lhash_array': ['1477482677716522348506692597986'], 'label': '2-1232-1.1-c3-0-58', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1232/4/a/s/1/1'}