Formats: - HTML - YAML - JSON - 2026-09-10T00:41:09.403120
  • lfunc_lfunctions • Show schema
    {'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1354515936124802321121739947217', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 37.05679574373166, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 3]], [1009, [1, 45, 963, -1009]]], 'bad_primes': [2, 3, 1009], 'central_character': '581184.1', 'coefficient_field': '1.1.1.1', 'conductor': 581184, 'conductor_radical': 6054, 'degree': 4, 'euler_factors': [[1], [1, 2, 3], [1, 0, -1, 0, 25], [1, 0, 10, 0, 49], [1, 0, -10, 0, 121], [1, -1, 26, -13, 169], [1, 0, -4, 0, 289], [1, -1, 36, -19, 361], [1, 0, 2, 0, 529], [1, 0, -47, 0, 841], [1, 4, 62, 124, 961], [1, 7, 56, 259, 1369], [1, 0, -43, 0, 1681], [1, -17, 152, -731, 1849], [1, 0, 82, 0, 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['1.06852466750769776448809655922890', '1.84658378022775822430616002877711', '2.75231051843497608569693497474093', '3.29395055167982143092190391451660', '3.95854169351807564784346778354622', '4.60068441561639828402739528966493', '4.90063822383271781452146519359820', '5.57742035985541333610868371286848', '5.89741473052595736606368755125652', '6.20966919235154791869497646246674', '6.81557315012418195084836739172812', '7.29509030229603541832274632713431', '7.58114537532604372124805893614838', '8.202741108228490129597075796040386'], 'prelabel': '4-581184-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4672716351177817, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 205278350410187957, 'z1': {'__RealLiteral__': 0, 'data': '1.06852466750769776448809655922890', 'prec': 110}, 'z2': {'__RealLiteral__': 0, 'data': '1.84658378022775822430616002877711', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '2.75231051843497608569693497474093', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 37.05679574373166, 'bad_primes': [2, 3, 1009], 'central_character': '1.1', 'conductor': 581184, 'conductor_radical': 6054, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, -7, 0, -2, 0, 0, 0, 17, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, -7, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, -7, 0, -2, 0, 0, 0, -7, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 15, 0, 0, 0], 'euler11': [1, 0, -10, 0, 121], 'euler13': [1, -1, 26, -13, 169], 'euler17': [1, 0, -4, 0, 289], 'euler19': [1, -1, 36, -19, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 2, 0, 529], 'euler29': [1, 0, -47, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 4, 62, 124, 961], 'euler37': [1, 7, 56, 259, 1369], 'euler41': [1, 0, -43, 0, 1681], 'euler43': [1, -17, 152, -731, 1849], 'euler47': [1, 0, 82, 0, 2209], 'euler5': [1, 0, -1, 0, 25], 'euler53': [1, 0, 32, 0, 2809], 'euler59': [1, 0, -40, 0, 3481], 'euler61': [1, 7, 44, 427, 3721], 'euler67': [1, 12, 161, 804, 4489], 'euler7': [1, 0, 10, 0, 49], 'euler71': [1, 0, 74, 0, 5041], 'euler73': [1, 7, 156, 511, 5329], 'euler79': [1, 7, 150, 553, 6241], 'euler83': [1, 0, 110, 0, 6889], 'euler89': [1, 0, 100, 0, 7921], 'euler97': [1, -15, 178, -1455, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 2, 3, 0, 0], [1, 0, -1, 0, 25], [1, 0, 10, 0, 49], [1, 0, -10, 0, 121], [1, -1, 26, -13, 169], [1, 0, -4, 0, 289], [1, -1, 36, -19, 361], [1, 0, 2, 0, 529], [1, 0, -47, 0, 841], [1, 4, 62, 124, 961], [1, 7, 56, 259, 1369], [1, 0, -43, 0, 1681], [1, -17, 152, -731, 1849], [1, 0, 82, 0, 2209], [1, 0, 32, 0, 2809], [1, 0, -40, 0, 3481], [1, 7, 44, 427, 3721], [1, 12, 161, 804, 4489], [1, 0, 74, 0, 5041], [1, 7, 156, 511, 5329], [1, 7, 150, 553, 6241], [1, 0, 110, 0, 6889], [1, 0, 100, 0, 7921], [1, -15, 178, -1455, 9409]], 'index': 1, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.3.1/64576.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/64576.2/a', 'EllipticCurve/2.0.3.1/64576.2/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/64576.1/a'], 'is_instance_Artin': False, 'is_instance_BMF': True, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, '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': '4-581184-1.1-c1e2-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-581184-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.4672716351177817, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 205278350410187957, 'z1': {'__RealLiteral__': 0, 'data': '1.06852466750769776448809655922890', 'prec': 110}}
  • lfunc_instances • Show schema
    • id: 9791035
      {'Lhash': '1354515936124802321121739947217', 'Lhash_array': ['1354515936124802321121739947217'], 'factors': ['4-581184-1.1-c1e2-0-1'], 'label': '4-581184-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/64576.1/a'}
    • id: 9791405
      {'Lhash': '1354515936124802321121739947217', 'Lhash_array': ['1354515936124802321121739947217'], 'factors': ['4-581184-1.1-c1e2-0-1'], 'label': '4-581184-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/64576.2/a'}
    • id: 9791538
      {'Lhash': '1354515936124802321121739947217', 'Lhash_array': ['1354515936124802321121739947217'], 'factors': ['4-581184-1.1-c1e2-0-1'], 'label': '4-581184-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.3.1/64576.2/a'}
    • id: 9791611
      {'Lhash': '1354515936124802321121739947217', 'Lhash_array': ['1354515936124802321121739947217'], 'factors': ['4-581184-1.1-c1e2-0-1'], 'label': '4-581184-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.3.1/64576.1/a'}