Formats: - HTML - YAML - JSON - 2026-10-11T03:22:53.669027
  • lfunc_lfunctions • Show schema
    {'A10': 1, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 1, 'A9': 0, 'Lhash': '1360658641406989112416057248902', 'a10': [0.316227766016838, 0], 'a2': [0.7071067811865476, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.447213595499958, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.3535533905932738, 0], 'a9': [0.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.742430877147186, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1, -1, 5, -5]], [13, [1, 3, 9, -13]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '168480.1', 'coefficient_field': '1.1.1.1', 'conductor': 168480, 'conductor_radical': 390, 'degree': 4, 'euler_factors': [[1, -1], [1], [1, -1, 5, -5], [1, 0, -14, 0, 49], [1, 0, 4, 0, 121], [1, 3, 9, -13], [1, -6, 34, -102, 289], [1, 0, 16, 0, 361], [1, 0, 10, 0, 529], [1, -6, 58, -174, 841], [1, 0, -26, 0, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 0, 76, 0, 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-0.43172472598884704, -0.27310412820208646, 0.03039978926059537, 0.40309109101285095], 'positive_zeros': ['1.07337040755710952743210609151719', '2.15208911038553247046831385072566', '2.70583544879978146447085120519728', '3.42856705058392951499862656907437', '4.03144326619956465039150001296695', '4.70579199748302297626620176053163', '5.18149554716019271725491985200055', '5.73695515141950226267871118173515', '6.09962680495509908804233627573788', '6.67924072818607010840500599450572', '7.33351741478492979478258572485457', '7.64145340943707910190665727819358', '8.103057818740215840301437151270995', '8.763077774724861816648258036874334', '9.273929926966407120703243088012688'], 'prelabel': '4-168480-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8104045897208219, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1963128803094981706, 'z1': {'__RealLiteral__': 0, 'data': '1.07337040755710952743210609151719', 'prec': 110}, 'z2': {'__RealLiteral__': 0, 'data': '2.15208911038553247046831385072566', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '2.70583544879978146447085120519728', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 10.742430877147186, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 168480, 'conductor_radical': 390, 'degree': 4, 'dirichlet_coefficients': [1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, -3, 0, 0, 1, 6, 0, 0, 1, 0, 0, 0, 0, -4, -3, 0, 0, 6, 0, 0, 1, 0, 6, 0, 0, 4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 14, -4, 0, -3, 0, 0, 0, 0, 0, 6, 0, 0, -2, 0, 0, 1, -3, 0, 0, 6, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 6, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 16, 14, 0, -4], 'euler11': [1, 0, 4, 0, 121], 'euler13': [1, 3, 9, -13, 0], 'euler17': [1, -6, 34, -102, 289], 'euler19': [1, 0, 16, 0, 361], 'euler2': [1, -1, 0, 0, 0], 'euler23': [1, 0, 10, 0, 529], 'euler29': [1, -6, 58, -174, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 0, -26, 0, 961], 'euler37': [1, -4, 78, -148, 1369], 'euler41': [1, 0, 46, 0, 1681], 'euler43': [1, 0, 76, 0, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, -1, 5, -5, 0], 'euler53': [1, 0, 70, 0, 2809], 'euler59': [1, 0, -80, 0, 3481], 'euler61': [1, 2, 42, 122, 3721], 'euler67': [1, 0, -26, 0, 4489], 'euler7': [1, 0, -14, 0, 49], 'euler71': [1, 0, 106, 0, 5041], 'euler73': [1, -4, 150, -292, 5329], 'euler79': [1, 0, -14, 0, 6241], 'euler83': [1, 0, 58, 0, 6889], 'euler89': [1, 6, 106, 534, 7921], 'euler97': [1, -16, 258, -1552, 9409], 'euler_factors': [[1, -1, 0, 0, 0], [1, 0, 0, 0, 0], [1, -1, 5, -5, 0], [1, 0, -14, 0, 49], [1, 0, 4, 0, 121], [1, 3, 9, -13, 0], [1, -6, 34, -102, 289], [1, 0, 16, 0, 361], [1, 0, 10, 0, 529], [1, -6, 58, -174, 841], [1, 0, -26, 0, 961], [1, -4, 78, -148, 1369], [1, 0, 46, 0, 1681], [1, 0, 76, 0, 1849], [1, 0, -50, 0, 2209], [1, 0, 70, 0, 2809], [1, 0, -80, 0, 3481], [1, 2, 42, 122, 3721], [1, 0, -26, 0, 4489], [1, 0, 106, 0, 5041], [1, -4, 150, -292, 5329], [1, 0, -14, 0, 6241], [1, 0, 58, 0, 6889], [1, 6, 106, 534, 7921], [1, -16, 258, -1552, 9409]], 'index': 1, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.4.1/10530.1/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/10530.1/a', 'EllipticCurve/2.0.4.1/10530.4/a', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/10530.4/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': '4-168480-1.1-c1e2-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-168480-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 1.8104045897208219, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1963128803094981706, 'z1': {'__RealLiteral__': 0, 'data': '1.07337040755710952743210609151719', 'prec': 110}}
  • lfunc_instances • Show schema
    • id: 9648481
      {'Lhash': '1360658641406989112416057248902', 'Lhash_array': ['1360658641406989112416057248902'], 'factors': ['4-168480-1.1-c1e2-0-1'], 'label': '4-168480-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/10530.1/a'}
    • id: 9648698
      {'Lhash': '1360658641406989112416057248902', 'Lhash_array': ['1360658641406989112416057248902'], 'factors': ['4-168480-1.1-c1e2-0-1'], 'label': '4-168480-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/10530.1/a'}
    • id: 9648699
      {'Lhash': '1360658641406989112416057248902', 'Lhash_array': ['1360658641406989112416057248902'], 'factors': ['4-168480-1.1-c1e2-0-1'], 'label': '4-168480-1.1-c1e2-0-1', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/10530.4/a'}
    • id: 9648971
      {'Lhash': '1360658641406989112416057248902', 'Lhash_array': ['1360658641406989112416057248902'], 'factors': ['4-168480-1.1-c1e2-0-1'], 'label': '4-168480-1.1-c1e2-0-1', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/10530.4/a'}