Formats: - HTML - YAML - JSON - 2026-10-16T09:04:30.868344
  • lfunc_lfunctions • Show schema
    {'Lhash': '1023992374733708755947755071453', 'a10': 0, 'a2': -1, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': -1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21.1284163748308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '2646.1', 'coefficient_field': '1.1.1.1', 'conductor': 2646, 'conductor_radical': 42, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 0, 5], [1], [1, -6, 11], [1, 5, 13], [1, 6, 17], [1, -4, 19], [1, -6, 23], [1, -6, 29], [1, -1, 31], [1, 1, 37], [1, -6, 41], [1, 1, 43], [1, -6, 47], [1, 6, 53], [1, -6, 59], [1, -1, 61], [1, 1, 67], [1, -12, 71], [1, 2, 73], [1, 1, 79], [1, 6, 83], [1, 0, 89], [1, 17, 97], [1, 12, 101], [1, -19, 103], [1, -18, 107], [1, -5, 109], [1, -12, 113]], 'euler_factors_factorization': [[[[1, 1], 1]], [1], [[[1, 0, 5], 1]], [1], [[[1, -6, 11], 1]], [[[1, 5, 13], 1]], [[[1, 6, 17], 1]], [[[1, -4, 19], 1]], [[[1, -6, 23], 1]], [[[1, -6, 29], 1]], [[[1, -1, 31], 1]], [[[1, 1, 37], 1]], [[[1, -6, 41], 1]], [[[1, 1, 43], 1]], [[[1, -6, 47], 1]], [[[1, 6, 53], 1]], [[[1, -6, 59], 1]], [[[1, -1, 61], 1]], [[[1, 1, 67], 1]], [[[1, -12, 71], 1]], [[[1, 2, 73], 1]], [[[1, 1, 79], 1]], [[[1, 6, 83], 1]], [[[1, 0, 89], 1]], [[[1, 17, 97], 1]], [[[1, 12, 101], 1]], [[[1, -19, 103], 1]], [[[1, -18, 107], 1]], [[[1, -5, 109], 1]], [[[1, -12, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 8, 'label': '2-2646-1.1-c1-0-8', 'leading_term': '1.306615511421958192372629475374000000000000000000000000000000000000000000000000000000000000', '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/2646/2/a/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [1.3066155114219582, 1.300051307523405, 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1.05122345910109, 1.700412635303641, 2.322081364048841, 2.865893543232775, 3.288576024555401, 3.5570810880406167, 3.6509532694388005, 3.5637256194383355, 3.303244020999377, 2.890899679962232, 2.3598331225957], 'positive_zeros': ['0.807787551671847026691110476190694', '1.97786137008912495989390313193606', '2.95453084311476587817392272475930', '4.09964776417661011092906723802288', '4.87602663790637391350842024268919', '5.99293789071915916490293453418478', '6.86373819824463860920029366769671', '7.17756521662208616357912102378248', '8.213222746268842791227564813952801', '9.057732301440674521981200930485855'], 'prelabel': '2-2646-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.596565715273828, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1622472768785807444, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.807787551671847026691110476191', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.97786137008912495989390313194', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.95453084311476587817392272476', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 21.1284163748308, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 2646, 'conductor_radical': 42, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, 0, -1, 0, 0, 6, 0, -5, 0, 0, 1, -6, 0, 4, 0, 0, -6, 6, 0, -5, 5, 0, 0, 6, 0, 1, -1, 0, 6, 0, 0, -1, -4, 0, 0, 6, 0, -1, 6, 0, -6, 6, 0, 0, 5, 0, -5, -6, 0, 0, 0, 0, -6, 6, 0, 1, -1, 0, 1, 0, 0, -1, -6, 0, 0, 12, 0, -2, 1, 0, 4, 0, 0, -1, 0, 0, -6, -6, 0, 0, 1, 0, -6, 0, 0, 0, 6, 0, -6, 0, 0, -17, 0, 0, -5], 'euler11': [1, -6, 11], 'euler13': [1, 5, 13], 'euler17': [1, 6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, -6, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -1, 31], 'euler37': [1, 1, 37], 'euler41': [1, -6, 41], 'euler43': [1, 1, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 5], 'euler53': [1, 6, 53], 'euler59': [1, -6, 59], 'euler61': [1, -1, 61], 'euler67': [1, 1, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, 2, 73], 'euler79': [1, 1, 79], 'euler83': [1, 6, 83], 'euler89': [1, 0, 89], 'euler97': [1, 17, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 0, 5], [1, 0, 0], [1, -6, 11], [1, 5, 13], [1, 6, 17], [1, -4, 19], [1, -6, 23], [1, -6, 29], [1, -1, 31], [1, 1, 37], [1, -6, 41], [1, 1, 43], [1, -6, 47], [1, 6, 53], [1, -6, 59], [1, -1, 61], [1, 1, 67], [1, -12, 71], [1, 2, 73], [1, 1, 79], [1, 6, 83], [1, 0, 89], [1, 17, 97]], 'index': 8, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2646/g', 'ModularForm/GL2/Q/holomorphic/2646/2/a/g/1/1', 'ModularForm/GL2/Q/holomorphic/2646/2/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': '2-2646-1.1-c1-0-8', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2646-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.596565715273828, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1622472768785807444, 'z1': {'__RealLiteral__': 0, 'data': '0.807787551671847026691110476191', 'prec': 100}}
  • lfunc_instances • Show schema
    • id: 24919
      {'Lhash': '1622472768785807444', 'Lhash_array': ['1622472768785807444'], 'factors': ['2-2646-1.1-c1-0-8'], 'label': '2-2646-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2646/g'}
    • id: 20307865
      {'Lhash': '1023992374733708755947755071453', 'Lhash_array': ['1023992374733708755947755071453'], 'factors': ['2-2646-1.1-c1-0-8'], 'label': '2-2646-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2646/2/a/g'}
    • id: 24558102
      {'Lhash': '1023992374733708755947755071453', 'Lhash_array': ['1023992374733708755947755071453'], 'factors': ['2-2646-1.1-c1-0-8'], 'label': '2-2646-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2646/2/a/g/1/1'}