Formats: - HTML - YAML - JSON - 2026-08-25T14:02:02.662289
  • lfunc_lfunctions • Show schema
    {'A10': 0, 'A2': 0, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 0, 'Lhash': '1213267560017124334287611977848', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.4577260512502574, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1, 0, -1]], [3, [1]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '116964.1', 'coefficient_field': '1.1.1.1', 'conductor': 116964, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1, 0, -1], [1], [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, 0, -23, 0, 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, 0, 25, 0, 2809], [1, 0, 109, 0, 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['0.957099345670396971730515506954339', '2.08653099113308129105484111705235', '2.94051047602386801244437832636374', '3.38667134184301674532306741577094', '4.02570731207988655165226312934003', '4.95882909759922539371601914551919', '5.35196356144638793869165345130023', '5.93839100089462174116444512665802', '6.63629908732757091523076348265479', '6.82772899016339717101170695807512', '7.50259449898580288804945304688990', '7.917561078639665250780088901621917', '8.432395833356932333111491246682498', '9.099664708448324668905021423621096', '9.605407065703912343416851780161705'], 'prelabel': '4-342e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.6525385771980605, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1363892045729493062, 'z1': {'__RealLiteral__': 0, 'data': '0.957099345670396971730515506954339', 'prec': 110}, 'z2': {'__RealLiteral__': 0, 'data': '2.08653099113308129105484111705235', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '2.94051047602386801244437832636374', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 7.4577260512502574, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 116964, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 8, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2], '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, 0, -1, 0, 0], 'euler23': [1, 0, 19, 0, 529], 'euler29': [1, 0, -23, 0, 841], 'euler3': [1, 0, 0, 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, 0, 25, 0, 2809], 'euler59': [1, 0, 109, 0, 3481], 'euler61': [1, -16, 186, -976, 3721], 'euler67': [1, 0, -59, 0, 4489], 'euler7': [1, 2, 15, 14, 49], 'euler71': [1, 0, -2, 0, 5041], 'euler73': [1, -22, 267, -1606, 5329], 'euler79': [1, 0, -110, 0, 6241], 'euler83': [1, 0, 58, 0, 6889], 'euler89': [1, 0, 142, 0, 7921], 'euler97': [1, 0, -2, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 0], [1, 0, 0, 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, 0, -23, 0, 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, 0, 25, 0, 2809], [1, 0, 109, 0, 3481], [1, -16, 186, -976, 3721], [1, 0, -59, 0, 4489], [1, 0, -2, 0, 5041], [1, -22, 267, -1606, 5329], [1, 0, -110, 0, 6241], [1, 0, 58, 0, 6889], [1, 0, 142, 0, 7921], [1, 0, -2, 0, 9409]], 'index': 5, 'instance_types': ['HMF', 'HMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-36.1-f', 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-36.1-b', 'EllipticCurve/2.2.57.1/36.1/f', 'EllipticCurve/2.2.57.1/36.1/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, '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': '4-342e2-1.1-c1e2-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-342e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.6525385771980605, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1363892045729493062, 'z1': {'__RealLiteral__': 0, 'data': '0.957099345670396971730515506954339', 'prec': 110}}
  • lfunc_instances • Show schema
    • id: 9488545
      {'Lhash': '1213267560017124334287611977848', 'Lhash_array': ['1213267560017124334287611977848'], 'factors': ['4-342e2-1.1-c1e2-0-5'], 'label': '4-342e2-1.1-c1e2-0-5', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-36.1-f'}
    • id: 9488650
      {'Lhash': '1213267560017124334287611977848', 'Lhash_array': ['1213267560017124334287611977848'], 'factors': ['4-342e2-1.1-c1e2-0-5'], 'label': '4-342e2-1.1-c1e2-0-5', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-36.1-b'}
    • id: 9488652
      {'Lhash': '1213267560017124334287611977848', 'Lhash_array': ['1213267560017124334287611977848'], 'factors': ['4-342e2-1.1-c1e2-0-5'], 'label': '4-342e2-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.57.1/36.1/f'}
    • id: 9488997
      {'Lhash': '1213267560017124334287611977848', 'Lhash_array': ['1213267560017124334287611977848'], 'factors': ['4-342e2-1.1-c1e2-0-5'], 'label': '4-342e2-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.57.1/36.1/b'}