Formats: - HTML - YAML - JSON - 2026-10-25T11:01:12.129811
  • lfunc_lfunctions • Show schema
    {'Lhash': '966286576989713656050920394532', 'a10': -3, 'a2': -1, 'a3': -1, 'a4': 1, 'a5': 3, 'a6': 1, 'a7': 0, 'a8': -1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 25.82362001368209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [7, [1]], [11, [1, 1]]], 'bad_primes': [2, 3, 7, 11], 'central_character': '3234.1', 'coefficient_field': '1.1.1.1', 'conductor': 3234, 'conductor_radical': 462, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, -3, 5], [1], [1, 1], [1, 2, 13], [1, 3, 17], [1, 2, 19], [1, -3, 23], [1, 6, 29], [1, -4, 31], [1, -2, 37], [1, -3, 41], [1, -2, 43], [1, -9, 47], [1, -6, 53], [1, -12, 59], [1, 5, 61], [1, -5, 67], [1, -12, 71], [1, -16, 73], [1, -17, 79], [1, 9, 83], [1, -6, 89], [1, 17, 97], [1, 12, 101], [1, 14, 103], [1, -3, 107], [1, -11, 109], [1, 6, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [[[1, 1], 1]], [[[1, -3, 5], 1]], [1], [[[1, 1], 1]], [[[1, 2, 13], 1]], [[[1, 3, 17], 1]], [[[1, 2, 19], 1]], [[[1, -3, 23], 1]], [[[1, 6, 29], 1]], [[[1, -4, 31], 1]], [[[1, -2, 37], 1]], [[[1, -3, 41], 1]], [[[1, -2, 43], 1]], [[[1, -9, 47], 1]], [[[1, -6, 53], 1]], [[[1, -12, 59], 1]], [[[1, 5, 61], 1]], [[[1, -5, 67], 1]], [[[1, -12, 71], 1]], [[[1, -16, 73], 1]], [[[1, -17, 79], 1]], [[[1, 9, 83], 1]], [[[1, -6, 89], 1]], [[[1, 17, 97], 1]], [[[1, 12, 101], 1]], [[[1, 14, 103], 1]], [[[1, -3, 107], 1]], [[[1, -11, 109], 1]], [[[1, 6, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 12, 'label': '2-3234-1.1-c1-0-12', 'leading_term': '1.257285605158439554987759941229200000000000000000000000000000000000000000000000000000000000', '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/3234/2/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': 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'0.76226570382701843132880365607', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.02572365669600761750685686373', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.56485651029984601868018839076', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 25.82362001368209, 'bad_primes': [2, 3, 7, 11], 'central_character': '1.1', 'conductor': 3234, 'conductor_radical': 462, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 3, 1, 0, -1, 1, -3, -1, -1, -2, 0, -3, 1, -3, -1, -2, 3, 0, 1, 3, 1, 4, 2, -1, 0, -6, 3, 4, -1, 1, 3, 0, 1, 2, 2, 2, -3, 3, 0, 2, -1, 3, -3, 9, -1, 0, -4, 3, -2, 6, 1, -3, 0, 2, 6, 12, -3, -5, -4, 0, 1, -6, -1, 5, -3, -3, 0, 12, -1, 16, -2, -4, -2, 0, -2, 17, 3, 1, -3, -9, 0, -9, -2, 6, 1, 6, -3, 0, 3, -4, -9, -6, 1, -17, 0, -1, 4], 'euler11': [1, 1, 0], 'euler13': [1, 2, 13], 'euler17': [1, 3, 17], 'euler19': [1, 2, 19], 'euler2': [1, 1, 0], 'euler23': [1, -3, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -3, 41], 'euler43': [1, -2, 43], 'euler47': [1, -9, 47], 'euler5': [1, -3, 5], 'euler53': [1, -6, 53], 'euler59': [1, -12, 59], 'euler61': [1, 5, 61], 'euler67': [1, -5, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, -16, 73], 'euler79': [1, -17, 79], 'euler83': [1, 9, 83], 'euler89': [1, -6, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, -3, 5], [1, 0, 0], [1, 1, 0], [1, 2, 13], [1, 3, 17], [1, 2, 19], [1, -3, 23], [1, 6, 29], [1, -4, 31], [1, -2, 37], [1, -3, 41], [1, -2, 43], [1, -9, 47], [1, -6, 53], [1, -12, 59], [1, 5, 61], [1, -5, 67], [1, -12, 71], [1, -16, 73], [1, -17, 79], [1, 9, 83], [1, -6, 89], [1, 17, 97]], 'index': 12, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3234/g', 'ModularForm/GL2/Q/holomorphic/3234/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/3234/2/a/g'], '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': '2-3234-1.1-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-3234-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.081694600591626, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 831760922750147911, 'z1': {'__RealLiteral__': 0, 'data': '0.76226570382701843132880365607', 'prec': 97}}
  • lfunc_instances • Show schema
    • id: 103100
      {'Lhash': '831760922750147911', 'Lhash_array': ['831760922750147911'], 'factors': ['2-3234-1.1-c1-0-12'], 'label': '2-3234-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3234/g'}
    • id: 20140277
      {'Lhash': '966286576989713656050920394532', 'Lhash_array': ['966286576989713656050920394532'], 'factors': ['2-3234-1.1-c1-0-12'], 'label': '2-3234-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3234/2/a/g'}
    • id: 24560682
      {'Lhash': '966286576989713656050920394532', 'Lhash_array': ['966286576989713656050920394532'], 'factors': ['2-3234-1.1-c1-0-12'], 'label': '2-3234-1.1-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3234/2/a/g/1/1'}