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lfunc_lfunctions • Show schema
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{'Lhash': '2296561868362018571151571438245', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -2.9575869857265658], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -3.9575869857265658], 'a8': [0, 0], 'a9': [-5.747320778139154, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.731184929788995, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, -1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '4600.4049', 'coefficient_field': 'CDF', 'conductor': 4600, 'conductor_radical': 230, 'conjugate': '547815703811790066483956346169', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 2.9575869857265658], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.9575869857265658], [-7.0, 0]], [[1.0, 0], [0.9575869857265659, 0], [11.0, 0]], [[1.0, 0], [0, 2.7473207781391538], [-13.0, 0]], [[1.0, 0], [0, 5.747320778139154], [-17.0, 0]], [[1.0, 0], [-6.747320778139154, 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'4.30356250060874856613590651342245', '5.27805928863159772762486076728345', '5.53390656996627086922856834109625', '6.33377654175968675279954334907314', '7.50487884450880196741006073595857', '8.461226086453458510116896568625619', '8.932785431146564220040795085506625'], 'prelabel': '2-4600-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.06062578697852, 'root_angle': -0.6475836176504333, 'root_number': '-0.4472135954999579392818347337462552470881236719223051449 - 0.89442719099991587856366946749251049417624734384461028971*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.32379180882521663', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.81166787437212012243185777794', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.83631217822550075622880749205', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.58146424281946542996058199995', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.731184929788995, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 4600, 'conductor_radical': 230, 'degree': 2, 'index': 96, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4600/2/e/p/4049/2'], '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': '2-4600-5.4-c1-0-96', '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': '2-4600-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.06062578697852, 'root_angle': -0.32379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81166787437212012243185777794', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2296561868362018571151571438245', 'Lhash_array': ['2296561868362018571151571438245'], 'label': '2-4600-5.4-c1-0-96', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4600/2/e/p/4049/2'}