Formats: - HTML - YAML - JSON - 2026-07-26T16:50:07.281071
  • lfunc_lfunctions • Show schema
    {'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '977207988480830855066607966897', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896257, 0], 'a4': [0.0, 0], 'a5': [0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.524520684314037, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -1]], [13, [1, 0, 12, 13]]], 'bad_primes': [2, 5, 13], 'central_character': '416000.1', 'coefficient_field': '1.1.1.1', 'conductor': 416000, 'conductor_radical': 130, 'degree': 4, 'euler_factors': [[1], [1, -1, 4, -3, 9], [1, -1], [1, 0, -5, 0, 49], [1, 0, -20, 0, 121], [1, 0, 12, 13], [1, 0, -2, 0, 289], [1, 0, 28, 0, 361], [1, 0, -2, 0, 529], [1, 0, 34, 0, 841], [1, 5, 66, 155, 961], [1, -14, 114, -518, 1369], [1, 3, 82, 123, 1681], [1, -8, 102, -344, 1849], [1, 0, 37, 0, 2209], [1, 9, 70, 477, 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-0.8000550354271891, -0.22163242541877318, 0.08627603220229836, 0.1081578503812412], 'positive_zeros': ['0.77088117838219230527668027430463', '1.92479522432444201826489410957389', '2.48911703396987557234828169689549', '2.98212283208671920725303181409058', '3.63238644278741619632373268736866', '4.15926715015460879204798328299112', '4.88065411300981315104598920778905', '5.33178396974182342337405072548574', '5.87762842983473907520289444940990', '6.26514125671461671021940770725503', '6.68090479383506612086531062741402', '7.46138896248954653094546129347552', '7.76513424888821708258199154210759', '8.136130804916435083548943140734388', '8.744366244332160258213147604362377'], 'prelabel': '4-416000-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.2694043666139754, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1789550132533737417, 'z1': {'__RealLiteral__': 0, 'data': '0.77088117838219230527668027430463', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.92479522432444201826489410957389', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.48911703396987557234828169689549', 'prec': 113}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 26.524520684314037, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 416000, 'conductor_radical': 130, 'degree': 4, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 0, 0, -3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, -5, 0, 0, 0, 0, 0, 14, 0, 0, 0, -3, 0, 8, 0, -3, 0, 0, 0, 5, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 25, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, -20, 0, 121], 'euler13': [1, 0, 12, 13, 0], 'euler17': [1, 0, -2, 0, 289], 'euler19': [1, 0, 28, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -2, 0, 529], 'euler29': [1, 0, 34, 0, 841], 'euler3': [1, -1, 4, -3, 9], 'euler31': [1, 5, 66, 155, 961], 'euler37': [1, -14, 114, -518, 1369], 'euler41': [1, 3, 82, 123, 1681], 'euler43': [1, -8, 102, -344, 1849], 'euler47': [1, 0, 37, 0, 2209], 'euler5': [1, -1, 0, 0, 0], 'euler53': [1, 9, 70, 477, 2809], 'euler59': [1, 0, -116, 0, 3481], 'euler61': [1, 0, -89, 0, 3721], 'euler67': [1, -8, 69, -536, 4489], 'euler7': [1, 0, -5, 0, 49], 'euler71': [1, -3, -38, -213, 5041], 'euler73': [1, 0, -71, 0, 5329], 'euler79': [1, -25, 294, -1975, 6241], 'euler83': [1, 0, 130, 0, 6889], 'euler89': [1, -3, 70, -267, 7921], 'euler97': [1, 0, 19, 0, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, -1, 4, -3, 9], [1, -1, 0, 0, 0], [1, 0, -5, 0, 49], [1, 0, -20, 0, 121], [1, 0, 12, 13, 0], [1, 0, -2, 0, 289], [1, 0, 28, 0, 361], [1, 0, -2, 0, 529], [1, 0, 34, 0, 841], [1, 5, 66, 155, 961], [1, -14, 114, -518, 1369], [1, 3, 82, 123, 1681], [1, -8, 102, -344, 1849], [1, 0, 37, 0, 2209], [1, 9, 70, 477, 2809], [1, 0, -116, 0, 3481], [1, 0, -89, 0, 3721], [1, -8, 69, -536, 4489], [1, -3, -38, -213, 5041], [1, 0, -71, 0, 5329], [1, -25, 294, -1975, 6241], [1, 0, 130, 0, 6889], [1, -3, 70, -267, 7921], [1, 0, 19, 0, 9409]], 'index': 5, 'instance_types': ['HMF', 'HMF', 'ECNF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-260.1-b', 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-260.2-b', 'EllipticCurve/2.2.40.1/260.1/b', 'EllipticCurve/2.2.40.1/260.2/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': '4-416000-1.1-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': '4-416000-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.2694043666139754, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1789550132533737417, 'z1': {'__RealLiteral__': 0, 'data': '0.77088117838219230527668027430463', 'prec': 113}}
  • lfunc_instances • Show schema
    • id: 9495517
      {'Lhash': '977207988480830855066607966897', 'Lhash_array': ['977207988480830855066607966897'], 'factors': ['4-416000-1.1-c1e2-0-5'], 'label': '4-416000-1.1-c1e2-0-5', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-260.1-b'}
    • id: 9495521
      {'Lhash': '977207988480830855066607966897', 'Lhash_array': ['977207988480830855066607966897'], 'factors': ['4-416000-1.1-c1e2-0-5'], 'label': '4-416000-1.1-c1e2-0-5', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.40.1/holomorphic/2.2.40.1-260.2-b'}
    • id: 9495849
      {'Lhash': '977207988480830855066607966897', 'Lhash_array': ['977207988480830855066607966897'], 'factors': ['4-416000-1.1-c1e2-0-5'], 'label': '4-416000-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/260.1/b'}
    • id: 9495980
      {'Lhash': '977207988480830855066607966897', 'Lhash_array': ['977207988480830855066607966897'], 'factors': ['4-416000-1.1-c1e2-0-5'], 'label': '4-416000-1.1-c1e2-0-5', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.40.1/260.2/b'}