Formats: - HTML - YAML - JSON - 2026-10-24T13:41:15.920178
  • lfunc_lfunctions • Show schema
    {'A10': 1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': -1, 'Lhash': '1449374882733526552802747408736', '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': [-0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 43.102346112010316, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1, 1]], [5, [1, 1]], [13, [1, -2, 13]]], 'bad_primes': [2, 5, 13], 'central_character': '676000.1', 'coefficient_field': '1.1.1.1', 'conductor': 676000, 'conductor_radical': 130, 'degree': 4, 'euler_factors': [[1, 1], [1, 0, 1, 0, 9], [1, 1], [1, 0, -5, 0, 49], [1, 0, -1, 0, 121], [1, -2, 13], [1, -3, 34, -51, 289], [1, 0, 29, 0, 361], [1, 0, -16, 0, 529], [1, -3, 58, -87, 841], [1, 0, 26, 0, 961], [1, 7, 84, 259, 1369], [1, -3, 64, -123, 1681], [1, 0, 17, 0, 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0.618093554732199, -0.06451449412937597], 'positive_zeros': ['1.14335518199776758983685468581703', '1.77528514736944221016048597945534', '2.69942176364012743511866030438704', '3.23021728427081232010672472120106', '3.58741430792992342794029026612444', '4.46722529202266215215785044728827', '4.72946633360835778285371042856562', '5.55069658304606360009438427803132', '5.91891950258160904250663824116024', '6.30679328627392989362577619247977', '6.91672182871210589798164049597155', '7.32405764960486285969670034765015', '7.75500375629573116937004093273307', '8.105630465279676568065200103399131'], 'prelabel': '4-676000-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.562271980909001, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1471479737321853625, 'z1': {'__RealLiteral__': 0, 'data': '1.14335518199776758983685468581703', 'prec': 110}, 'z2': {'__RealLiteral__': 0, 'data': '1.77528514736944221016048597945534', 'prec': 110}, 'z3': {'__RealLiteral__': 0, 'data': '2.69942176364012743511866030438704', 'prec': 110}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 43.102346112010316, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 676000, 'conductor_radical': 130, 'degree': 4, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, 0, -1, -1, 1, 0, 0, 2, 0, 0, 1, 3, 1, 0, -1, 0, 0, 0, 0, 1, -2, 0, 0, 3, 0, 0, -1, 0, -3, 0, -1, -7, 0, 0, 1, 3, 0, 0, 0, 1, 0, 0, 0, 5, -1, 0, 2, -12, 0, 0, 0, 0, -3, 0, 0, -28, 0, 0, 1, -2, 0, 0, 3, 0, 0, 0, 1, 2, 7, 0, 0, 0, 0, 0, -1, -8, -3, 0, 0, -3, 0, 0, 0, -18, -1, 0, 0, 0, 0, 0, 0, 4, -5, 0, 1], 'euler11': [1, 0, -1, 0, 121], 'euler13': [1, -2, 13, 0, 0], 'euler17': [1, -3, 34, -51, 289], 'euler19': [1, 0, 29, 0, 361], 'euler2': [1, 1, 0, 0, 0], 'euler23': [1, 0, -16, 0, 529], 'euler29': [1, -3, 58, -87, 841], 'euler3': [1, 0, 1, 0, 9], 'euler31': [1, 0, 26, 0, 961], 'euler37': [1, 7, 84, 259, 1369], 'euler41': [1, -3, 64, -123, 1681], 'euler43': [1, 0, 17, 0, 1849], 'euler47': [1, 0, 49, 0, 2209], 'euler5': [1, 1, 0, 0, 0], 'euler53': [1, 12, 133, 636, 2809], 'euler59': [1, 0, 17, 0, 3481], 'euler61': [1, 28, 318, 1708, 3721], 'euler67': [1, 0, -14, 0, 4489], 'euler7': [1, 0, -5, 0, 49], 'euler71': [1, 0, 116, 0, 5041], 'euler73': [1, -2, 138, -146, 5329], 'euler79': [1, 0, -65, 0, 6241], 'euler83': [1, 0, 40, 0, 6889], 'euler89': [1, 18, 250, 1602, 7921], 'euler97': [1, -4, 117, -388, 9409], 'euler_factors': [[1, 1, 0, 0, 0], [1, 0, 1, 0, 9], [1, 1, 0, 0, 0], [1, 0, -5, 0, 49], [1, 0, -1, 0, 121], [1, -2, 13, 0, 0], [1, -3, 34, -51, 289], [1, 0, 29, 0, 361], [1, 0, -16, 0, 529], [1, -3, 58, -87, 841], [1, 0, 26, 0, 961], [1, 7, 84, 259, 1369], [1, -3, 64, -123, 1681], [1, 0, 17, 0, 1849], [1, 0, 49, 0, 2209], [1, 12, 133, 636, 2809], [1, 0, 17, 0, 3481], [1, 28, 318, 1708, 3721], [1, 0, -14, 0, 4489], [1, 0, 116, 0, 5041], [1, -2, 138, -146, 5329], [1, 0, -65, 0, 6241], [1, 0, 40, 0, 6889], [1, 18, 250, 1602, 7921], [1, -4, 117, -388, 9409]], 'index': 25, 'instance_types': ['ECNF', 'BMF', 'ECNF', 'BMF'], 'instance_urls': ['EllipticCurve/2.0.4.1/42250.6/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/42250.7/b', 'EllipticCurve/2.0.4.1/42250.7/b', 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/42250.6/b'], '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': '4-676000-1.1-c1e2-0-25', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 1, 'prelabel': '4-676000-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.562271980909001, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1471479737321853625, 'z1': {'__RealLiteral__': 0, 'data': '1.14335518199776758983685468581703', 'prec': 110}}
  • lfunc_instances • Show schema
    • id: 9681532
      {'Lhash': '1449374882733526552802747408736', 'Lhash_array': ['1449374882733526552802747408736'], 'factors': ['4-676000-1.1-c1e2-0-25'], 'label': '4-676000-1.1-c1e2-0-25', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/42250.6/b'}
    • id: 9681883
      {'Lhash': '1449374882733526552802747408736', 'Lhash_array': ['1449374882733526552802747408736'], 'factors': ['4-676000-1.1-c1e2-0-25'], 'label': '4-676000-1.1-c1e2-0-25', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/42250.7/b'}
    • id: 9681911
      {'Lhash': '1449374882733526552802747408736', 'Lhash_array': ['1449374882733526552802747408736'], 'factors': ['4-676000-1.1-c1e2-0-25'], 'label': '4-676000-1.1-c1e2-0-25', 'type': 'ECNF', 'url': 'EllipticCurve/2.0.4.1/42250.7/b'}
    • id: 9682186
      {'Lhash': '1449374882733526552802747408736', 'Lhash_array': ['1449374882733526552802747408736'], 'factors': ['4-676000-1.1-c1e2-0-25'], 'label': '4-676000-1.1-c1e2-0-25', 'type': 'BMF', 'url': 'ModularForm/GL2/ImaginaryQuadratic/2.0.4.1/42250.6/b'}