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lfunc_lfunctions • Show schema
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{'Lhash': '948892372241763530639601508144', 'a10': [0, 0], 'a2': [0, -1.0], 'a3': [0, 1.0], 'a4': [-1.0, 0], 'a5': [0, 0], 'a6': [1.0, 0], 'a7': [0, -2.0], 'a8': [0, 1.0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.548388697341746, '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]]], [23, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '3450.2899', 'coefficient_field': 'CDF', 'conductor': 3450, 'conductor_radical': 690, 'conjugate': '988273934808052437382384947528', '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, 2.0], [-7.0, 0]], [[1.0, 0], [-2.0, 0], [11.0, 0]], [[1.0, 0], [0, -2.0], [-13.0, 0]], [[1.0, 0], [0, 0], [-17.0, 0]], [[1.0, 0], [8.0, 0], [19.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [-10.0, 0], [29.0, 0]], [[1.0, 0], [-8.0, 0], 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0.14758361765043326, 'root_number': '0.8944271909999158785636694674925104941762473438446102897 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07379180882521663', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74854409572395087390692142387', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11006488667088853878591070086', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99801721752752521504811295188', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 27.548388697341746, 'bad_primes': [2, 3, 5, 23], 'central_character': '5.4', 'conductor': 3450, 'conductor_radical': 690, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3450/2/d/q/2899/1'], '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': '2-3450-5.4-c1-0-30', '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': '2-3450-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.248655894354453, 'root_angle': 0.07379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74854409572395087390692142387', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '948892372241763530639601508144', 'Lhash_array': ['948892372241763530639601508144'], 'label': '2-3450-5.4-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3450/2/d/q/2899/1'}