Formats: - HTML - YAML - JSON - 2026-10-06T16:25:39.426364
  • lfunc_lfunctions • Show schema
    {'Lhash': '974247737917911027167355095116', 'a10': 0, 'a2': -1, 'a3': 1, 'a4': -1, 'a5': 0, 'a6': -1, 'a7': -4, 'a8': 3, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.37868228803246, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [1, -1]], [5, [1]], [19, [1, 1]]], 'bad_primes': [3, 5, 19], 'central_character': '1425.1', 'coefficient_field': '1.1.1.1', 'conductor': 1425, 'conductor_radical': 285, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, -1], [1], [1, 4, 7], [1, -4, 11], [1, 2, 13], [1, 2, 17], [1, 1], [1, -4, 23], [1, 2, 29], [1, 0, 31], [1, -6, 37], [1, 6, 41], [1, 8, 43], [1, -12, 47], [1, -14, 53], [1, -4, 59], [1, -14, 61], [1, -4, 67], [1, 0, 71], [1, -14, 73], [1, -16, 79], [1, 0, 83], [1, 6, 89], [1, -10, 97], [1, 10, 101], [1, 16, 103], [1, 12, 107], [1, 2, 109], [1, -10, 113]], 'euler_factors_factorization': [[[[1, 1, 2], 1]], [[[1, -1], 1]], [1], [[[1, 4, 7], 1]], [[[1, -4, 11], 1]], [[[1, 2, 13], 1]], [[[1, 2, 17], 1]], [[[1, 1], 1]], [[[1, -4, 23], 1]], [[[1, 2, 29], 1]], [[[1, 0, 31], 1]], [[[1, -6, 37], 1]], [[[1, 6, 41], 1]], [[[1, 8, 43], 1]], [[[1, -12, 47], 1]], [[[1, -14, 53], 1]], [[[1, -4, 59], 1]], [[[1, -14, 61], 1]], [[[1, -4, 67], 1]], [[[1, 0, 71], 1]], [[[1, -14, 73], 1]], [[[1, -16, 79], 1]], [[[1, 0, 83], 1]], [[[1, 6, 89], 1]], [[[1, -10, 97], 1]], [[[1, 10, 101], 1]], [[[1, 16, 103], 1]], [[[1, 12, 107], 1]], [[[1, 2, 109], 1]], [[[1, -10, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-1425-1.1-c1-0-6', 'leading_term': '0.970065103371171255530586309980830000000000000000000000000000000000000000000000000000000000', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1425/2/a/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [0.9700651033711712, 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'0.76854595244344636007624940810', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.29629701215321469443462239002', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.54490000396289616314690825839', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 11.37868228803246, 'bad_primes': [3, 5, 19], 'central_character': '1.1', 'conductor': 1425, 'conductor_radical': 285, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, -1, 0, -1, -4, 3, 1, 0, 4, -1, -2, 4, 0, -1, -2, -1, -1, 0, -4, -4, 4, 3, 0, 2, 1, 4, -2, 0, 0, -5, 4, 2, 0, -1, 6, 1, -2, 0, -6, 4, -8, -4, 0, -4, 12, -1, 9, 0, -2, 2, 14, -1, 0, -12, -1, 2, 4, 0, 14, 0, -4, 7, 0, -4, 4, 2, 4, 0, 0, 3, 14, -6, 0, 1, -16, 2, 16, 0, 1, 6, 0, 4, 0, 8, -2, 12, -6, 0, 8, -4, 0, -12, 0, -5, 10, -9, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, 2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 1, 0], 'euler2': [1, 1, 2], 'euler23': [1, -4, 23], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, 8, 43], 'euler47': [1, -12, 47], 'euler5': [1, 0, 0], 'euler53': [1, -14, 53], 'euler59': [1, -4, 59], 'euler61': [1, -14, 61], 'euler67': [1, -4, 67], 'euler7': [1, 4, 7], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, -16, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 1, 2], [1, -1, 0], [1, 0, 0], [1, 4, 7], [1, -4, 11], [1, 2, 13], [1, 2, 17], [1, 1, 0], [1, -4, 23], [1, 2, 29], [1, 0, 31], [1, -6, 37], [1, 6, 41], [1, 8, 43], [1, -12, 47], [1, -14, 53], [1, -4, 59], [1, -14, 61], [1, -4, 67], [1, 0, 71], [1, -14, 73], [1, -16, 79], [1, 0, 83], [1, 6, 89], [1, -10, 97]], 'index': 6, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1425/c', 'ModularForm/GL2/Q/holomorphic/1425/2/a/c/1/1', 'ModularForm/GL2/Q/holomorphic/1425/2/a/c'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-1425-1.1-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1425-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.3732302453334637, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 383746192666252305, 'z1': {'__RealLiteral__': 0, 'data': '0.76854595244344636007624940810', 'prec': 97}}
  • lfunc_instances • Show schema
    • id: 32092
      {'Lhash': '383746192666252305', 'Lhash_array': ['383746192666252305'], 'factors': ['2-1425-1.1-c1-0-6'], 'label': '2-1425-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1425/c'}
    • id: 20615313
      {'Lhash': '974247737917911027167355095116', 'Lhash_array': ['974247737917911027167355095116'], 'factors': ['2-1425-1.1-c1-0-6'], 'label': '2-1425-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1425/2/a/c'}
    • id: 24553071
      {'Lhash': '974247737917911027167355095116', 'Lhash_array': ['974247737917911027167355095116'], 'factors': ['2-1425-1.1-c1-0-6'], 'label': '2-1425-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1425/2/a/c/1/1'}