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lfunc_lfunctions • Show schema
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{'Lhash': '3975536459540312649402092482966', 'a10': [-1.7071067811865475, 0.7071067811865476], 'a2': [1.3065629648763766, -1.3065629648763766], 'a3': [0.0, 0.0], 'a4': [0.0, -2.414213562373095], 'a5': [-0.9238795325112867, -0.3826834323650898], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-1.8477590650225735, -1.8477590650225735], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2919530323903064, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.9238795325112867, 0.3826834323650898]]], [13, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [3, 5, 13], 'central_character': '585.532', 'coefficient_field': 'CDF', 'conductor': 585, 'conductor_radical': 195, 'conjugate': '1922931279084336890651573287952', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3065629648763766, 1.3065629648763766], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.9238795325112867, 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'6.49936911497139519509939936503648', '7.46539072737060528135118735332949', '8.299254130005556637255294869504171', '8.873055399219407593816508098265645', '10.74190454206365760751838209807573', '11.51698535593075887418137425205091'], 'prelabel': '2-585-65.12-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5403267829659255, 'root_angle': 0.6987918088252166, 'root_number': '-0.58471028466376494325476189408372 + 0.81124218517556085398167691672200*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3493959044126083', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.13614529021210741099343827663', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.73894123633339661424945036085', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.75563794454157060964909283617', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2919530323903064, 'bad_primes': [3, 5, 13], 'central_character': '65.12', 'conductor': 585, 'conductor_radical': 195, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/585/1/o/a/532/4'], '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': '2-585-65.12-c0-0-3', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-585-65.12-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5403267829659255, 'root_angle': 0.3493959044126083, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.13614529021210741099343827663', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3975536459540312649402092482966', 'Lhash_array': ['3975536459540312649402092482966'], 'label': '2-585-65.12-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/585/1/o/a/532/4'}