Formats: - HTML - YAML - JSON - 2026-08-26T06:47:10.884107
  • lfunc_lfunctions • Show schema
    {'A10': 0, 'A2': 1, 'A3': 3, 'A4': 1, 'A5': 0, 'A6': 3, 'A7': 0, 'A8': 1, 'A9': 6, 'Lhash': '1613917649352271711409544602184', 'a10': [0.0, 0], 'a2': [0.7071067811865476, 0], 'a3': [1.7320508075688772, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [1.224744871391589, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [2.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.51635929333425, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -3, 3]], [19, [1, -8, 19]]], 'bad_primes': [2, 3, 19], 'central_character': '415872.1', 'coefficient_field': '1.1.1.1', 'conductor': 415872, 'conductor_radical': 114, 'degree': 4, 'euler_factors': [[1, -1], [1, -3, 3], [1, 0, -2, 0, 25], [1, 0, 13, 0, 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, 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'positive_zeros': ['1.27315653782020057953763083055818', '1.89788314102936140312185908888429', '2.70678198949014858718396855564003', '3.21870034436397941270835984621615', '3.42171154743551676241609849178001', '4.13862501481106319527729444194541', '4.78938031771961950710214108675064', '5.03978044028836672994308230391187', '5.85532409349730578043944208088651', '6.29468661547540970579688800445592', '6.97049407956336384207438784156040', '7.38891725579909033971910904855058', '7.62904025825301046186028084803579', '8.134822752393194998575286471881646', '8.650006878665126244618813702580862'], 'prelabel': '4-415872-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.2692297769010543, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1388208850131029622, 'z1': {'__RealLiteral__': 0, 'data': '1.27315653782020057953763083055818', 'prec': 110}, 'z2': {'__RealLiteral__': 0, 'data': '1.89788314102936140312185908888429', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '2.70678198949014858718396855564003', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 26.51635929333425, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 415872, 'conductor_radical': 114, 'degree': 4, 'dirichlet_coefficients': [1, 1, 3, 1, 0, 3, 0, 1, 6, 0, 0, 3, 0, 0, 0, 1, 0, 6, 8, 0, 0, 0, 0, 3, 2, 0, 9, 0, 0, 0, 0, 1, 0, 0, 0, 6, 0, 8, 0, 0, 0, 0, -4, 0, 0, 0, 0, 3, -13, 2, 0, 0, 0, 9, 0, 0, 24, 0, -6, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 6, -22, 0, 6, 8, 0, 0, 0, 0, 9, 0, 0, 0, 0, -4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 3, 0, -13, 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, -1, 0, 0, 0], 'euler23': [1, 0, 19, 0, 529], 'euler29': [1, 0, -23, 0, 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, 0, 25, 0, 2809], 'euler59': [1, 6, 127, 354, 3481], 'euler61': [1, 0, 58, 0, 3721], 'euler67': [1, 0, -59, 0, 4489], 'euler7': [1, 0, 13, 0, 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, -12, 214, -1068, 7921], 'euler97': [1, 0, -2, 0, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, -3, 3, 0, 0], [1, 0, -2, 0, 25], [1, 0, 13, 0, 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, 6, 127, 354, 3481], [1, 0, 58, 0, 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, -12, 214, -1068, 7921], [1, 0, -2, 0, 9409]], 'index': 33, 'instance_types': ['HMF', 'ECNF', 'HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-128.5-c', 'EllipticCurve/2.2.57.1/128.6/c', 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-128.6-c', 'EllipticCurve/2.2.57.1/128.5/c'], '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': '4-415872-1.1-c1e2-0-33', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-415872-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.2692297769010543, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1388208850131029622, 'z1': {'__RealLiteral__': 0, 'data': '1.27315653782020057953763083055818', 'prec': 110}}
  • lfunc_instances • Show schema
    • id: 9487005
      {'Lhash': '1613917649352271711409544602184', 'Lhash_array': ['1613917649352271711409544602184'], 'factors': ['4-415872-1.1-c1e2-0-33'], 'label': '4-415872-1.1-c1e2-0-33', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-128.5-c'}
    • id: 9487260
      {'Lhash': '1613917649352271711409544602184', 'Lhash_array': ['1613917649352271711409544602184'], 'factors': ['4-415872-1.1-c1e2-0-33'], 'label': '4-415872-1.1-c1e2-0-33', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.57.1/128.6/c'}
    • id: 9487386
      {'Lhash': '1613917649352271711409544602184', 'Lhash_array': ['1613917649352271711409544602184'], 'factors': ['4-415872-1.1-c1e2-0-33'], 'label': '4-415872-1.1-c1e2-0-33', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.57.1/holomorphic/2.2.57.1-128.6-c'}
    • id: 9487420
      {'Lhash': '1613917649352271711409544602184', 'Lhash_array': ['1613917649352271711409544602184'], 'factors': ['4-415872-1.1-c1e2-0-33'], 'label': '4-415872-1.1-c1e2-0-33', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.57.1/128.5/c'}