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lfunc_lfunctions • Show schema
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{'Lhash': '1616224335268932228884442896122', 'a10': [0, 1.4142135623730951], 'a2': [1.0, 0], 'a3': [0, -1.4142135623730951], 'a4': [1.0, 0], 'a5': [0, 1.4142135623730951], 'a6': [0, -1.4142135623730951], 'a7': [0, 0], 'a8': [1.0, 0], 'a9': [1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.017990645468853, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-3.0, -2.8284271247461903]]], [59, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 17, 59], 'central_character': '2006.237', 'coefficient_field': 'CDF', 'conductor': 2006, 'conductor_radical': 2006, 'conjugate': '1308543982743998047755379585664', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-3.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-5.0, 0]], [[1.0, 0], [0, 0], [-7.0, 0]], [[1.0, 0], [0, 2.8284271247461903], [-11.0, 0]], [[1.0, 0], [-2.0, 0], [13.0, 0]], [[1.0, 0], [-3.0, 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'5.68658250302459622809080923318822', '6.92697351519564258103361389146841', '7.52795155958275918945649534277670', '8.570973083145581782998812872989482', '9.433574081830349060915977396449892'], 'prelabel': '2-2006-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.002248198883829, 'root_angle': 0.24063253699046142, 'root_number': '0.72760687510899892055671938634836653384950574565416831195 + 0.6859943405700353495146062208877156560613409805748202300*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1203162684952307', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27497619216047795474960636252', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53256842118922009663334651894', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86382045219950488255191986257', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.017990645468853, 'bad_primes': [2, 17, 59], 'central_character': '17.16', 'conductor': 2006, 'conductor_radical': 2006, 'degree': 2, 'index': 55, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2006/2/b/c/237/1'], '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': '2-2006-17.16-c1-0-55', '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': '2-2006-17.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.002248198883829, 'root_angle': 0.12031626849523071, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27497619216047795474960636252', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1616224335268932228884442896122', 'Lhash_array': ['1616224335268932228884442896122'], 'label': '2-2006-17.16-c1-0-55', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2006/2/b/c/237/1'}