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lfunc_lfunctions • Show schema
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{'Lhash': '583959036166384795486279997843', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -24.545828035942403], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 49.0], 'a8': [0, 0], 'a9': [-359.49767397005604, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 112.26867386908647, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, -49.0]]]], 'bad_primes': [2, 5, 7], 'central_character': '700.449', 'coefficient_field': 'CDF', 'conductor': 700, 'conductor_radical': 70, 'conjugate': '979011985713664402667266846404', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 24.545828035942403], [-243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -49.0]], [[1.0, 0], [-90.2355746050224, 0], [161051.0, 0]], [[1.0, 0], [0, -14.44130311343681], [-371293.0, 0]], [[1.0, 0], [0, -407.3836015335264], [-1419857.0, 0]], [[1.0, 0], [2289.1917723287506, 0], [2476099.0, 0]], [[1.0, 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'positive_zeros': ['0.46066245388220388121517235430151', '2.22978328907376025874699502391889', '3.51771690953161198621399785380550', '4.20926557938158378355747168224325', '5.00130387518343635566408852654283', '6.01067446598911200335893954307363', '7.09060921472928119391075572202273', '8.300874914641278507343318921864043', '9.087424324715515881122258648355825', '9.747993255194303500347523712151316'], 'prelabel': '2-700-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.59569128792862, 'root_angle': 0.14758361765043326, 'root_number': '0.8944271909999158785636694674925104941762473438446102897 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07379180882521663', 'prec': 64}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46066245388220388121517235430', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.22978328907376025874699502392', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51771690953161198621399785381', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 112.26867386908647, 'bad_primes': [2, 5, 7], 'central_character': '5.4', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/6/e/g/449/1'], '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': '2-700-5.4-c5-0-13', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-700-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.59569128792862, 'root_angle': 0.07379180882521663, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46066245388220388121517235430', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '583959036166384795486279997843', 'Lhash_array': ['583959036166384795486279997843'], 'label': '2-700-5.4-c5-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/6/e/g/449/1'}