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lfunc_lfunctions • Show schema
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{'Lhash': '2083634513329348070736626838973,3791082860209497353818338744255', 'a10': 0, 'a2': 2, 'a3': -3, 'a4': 3, 'a5': 0, 'a6': -6, 'a7': 2, 'a8': 4, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8286362279166953, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 1]], [3, [1, 3, 3]], [19, [1, 8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '114.1', 'coefficient_field': '1.1.1.1', 'conductor': 12996, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 3, 3], [1, 0, 2, 0, 25], [1, -2, 15, -14, 49], [1, 0, -10, 0, 121], [1, 0, -23, 0, 169], [1, 0, -31, 0, 289], [1, 8, 19], [1, 0, -19, 0, 529], [1, -18, 139, -522, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, -82, 0, 2209], [1, 18, 187, 954, 2809], [1, 6, 127, 354, 3481], [1, 16, 186, 976, 3721], [1, 0, -59, 0, 4489], [1, 24, 286, 1704, 5041], [1, -22, 267, -1606, 5329], [1, 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-2.2997098528784616], 'positive_zeros': ['1.64369780833473190775040709017309', '2.99063705687272663952860070260190', '4.36832954540764876987581180628100', '4.58512735759355047775599264373289', '5.07148813490284239032473666909335', '5.99522944989182225075727631749579', '6.53910247390834776155477036816474', '6.54564424096198188129094551059523', '7.76232100624168519610049007081187', '8.112262278083392832402569165284373', '9.118119754959359622108277338484358', '10.11430042684651296706286539675128', '10.58246001556314574441209511666508', '10.82738199385273632155144207713571', '11.43843241121292595298890662751771', '11.86405326257156272124322486984335', '12.38098109882178152909384304627679', '12.61561510748546313828220353693467', '13.15489901751515059955542535017165', '13.93865406482178534730604431979094'], 'prelabel': '4-114e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e2-0', 'trace_hash': 369474799736995269, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.64369780833473190775040709017', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99063705687272663952860070260', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.36832954540764876987581180628', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8286362279166953, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 12996, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 2, -3, 3, 0, -6, 2, 4, 6, 0, 0, -9, 0, 4, 0, 5, 0, 12, -8, 0, -6, 0, 0, -12, -2, 0, -9, 6, 18, 0, 0, 6, 0, 0, 0, 18, 0, -16, 0, 0, 0, -12, 4, 0, 0, 0, 0, -15, -11, -4, 0, 0, -18, -18, 0, 8, 24, 36, -6, 0, -16, 0, 12, 7, 0, 0, 0, 0, 0, 0, -24, 24, 22, 0, 6, -24, 0, 0, 0, 0, 9, 0, 0, -18, 0, 8, -54, 0, 12, 0, 0, 0, 0, 0, 0, -18, 0, -22, 0, -6], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, 0, -23, 0, 169], 'euler17': [1, 0, -31, 0, 289], 'euler19': [1, 8, 19, 0, 0], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 0, -19, 0, 529], 'euler29': [1, -18, 139, -522, 841], 'euler3': [1, 3, 3, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 0, -26, 0, 1369], 'euler41': [1, 0, 82, 0, 1681], 'euler43': [1, -4, 90, -172, 1849], 'euler47': [1, 0, -82, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 18, 187, 954, 2809], 'euler59': [1, 6, 127, 354, 3481], 'euler61': [1, 16, 186, 976, 3721], 'euler67': [1, 0, -59, 0, 4489], 'euler7': [1, -2, 15, -14, 49], 'euler71': [1, 24, 286, 1704, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, 0, -110, 0, 6241], 'euler83': [1, 0, -58, 0, 6889], 'euler89': [1, -12, 214, -1068, 7921], 'euler97': [1, 0, -2, 0, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 3, 3, 0, 0], [1, 0, 2, 0, 25], [1, -2, 15, -14, 49], [1, 0, -10, 0, 121], [1, 0, -23, 0, 169], [1, 0, -31, 0, 289], [1, 8, 19, 0, 0], [1, 0, -19, 0, 529], [1, -18, 139, -522, 841], [1, 0, 46, 0, 961], [1, 0, -26, 0, 1369], [1, 0, 82, 0, 1681], [1, -4, 90, -172, 1849], [1, 0, -82, 0, 2209], [1, 18, 187, 954, 2809], [1, 6, 127, 354, 3481], [1, 16, 186, 976, 3721], [1, 0, -59, 0, 4489], [1, 24, 286, 1704, 5041], [1, -22, 267, -1606, 5329], [1, 0, -110, 0, 6241], [1, 0, -58, 0, 6889], [1, -12, 214, -1068, 7921], [1, 0, -2, 0, 9409]], 'index': 5, 'instance_types': ['HMF', 'ECNF', 'CMF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-4.1-d', 'EllipticCurve/2.2.57.1/4.1/d', 'ModularForm/GL2/Q/holomorphic/114/2/b/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-114e2-1.1-c1e2-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-114e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 369474799736995269, 'z1': {'__RealLiteral__': 0, 'data': '1.64369780833473190775040709017', 'prec': 103}}
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lfunc_instances • Show schema
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id: 9969099
{'Lhash': '2083634513329348070736626838973,3791082860209497353818338744255', 'Lhash_array': ['2083634513329348070736626838973', '3791082860209497353818338744255'], 'label': '4-114e2-1.1-c1e2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/b/c'}
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id: 9488999
{'Lhash': '_2083634513329348070736626838973', 'Lhash_array': ['_2083634513329348070736626838973'], 'label': '4-114e2-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.57.1/4.1/d'}
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id: 9488547
{'Lhash': '_2083634513329348070736626838973', 'Lhash_array': ['_2083634513329348070736626838973'], 'label': '4-114e2-1.1-c1e2-0-5', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-4.1-d'}