Formats: - HTML - YAML - JSON - 2026-09-15T02:48:16.663339
  • lfunc_lfunctions • Show schema
    {'Lhash': '1439040608764482859543598418292', 'a10': [-1.1535195440555088, 0.0], 'a2': [-0.5239763970818659, 0.0], 'a3': [0.0, 0.0], 'a4': [-1.7254487353011068, 0.0], 'a5': [2.201472338219241, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [1.9520472058362681, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.5275177946066, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 7], 'central_character': '567.1', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'conjugate': '1439040608764482859543598418292', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5239763970818659, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.201472338219241, 0], [5.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [5.201472338219241, 0], [11.0, 0]], [[1.0, 0], [-3.153519544055509, 0], [13.0, 0]], [[1.0, 0], [-3.2494251323829726, 0], [17.0, 0]], [[1.0, 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[13.748275397148918, 0], [109.0, 0]], [[1.0, 0], [19.901794941204425, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-567-1.1-c1-0-6', '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/567/2/a/e/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.2235028884275108, 1.215502760778146, 1.1897764170195553, 1.14151840408759, 1.0638503089574574, 0.9492027524865642, 0.7908106959179123, 0.5841442414439892, 0.3281765046245898, 0.026421358223118835, -0.31233369955079876, -0.6736933924802716, -1.0378220026857239, -1.3802025307229635, -1.6730408548746591, -1.8873078000744086, -1.995333817021995, -1.9737830335918343, -1.8067466961434722, -1.4886234018389408, -1.026408749926288, -0.4410128587301721, 0.2327297121326575, 0.9475922834746188, 1.6471124165872317, 2.270260200724286, 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'7.55962259273529413884355354640267', '8.049930774046966205195793375803150', '9.117042056171947074786138601113314', '9.908266084003225308963323680640037', '10.38957458617619065232339124584305'], 'prelabel': '2-567-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.13520287727974584344038223712', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.70814742136531414936084382173', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.17067308450487679386062782940', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.5275177946066, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/2/a/e/1/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, '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': '2-567-1.1-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-567-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1277964645629526, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.13520287727974584344038223712', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1439040608764482859543598418292', 'Lhash_array': ['1439040608764482859543598418292'], 'factors': ['2-567-1.1-c1-0-6'], 'label': '2-567-1.1-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/2/a/e/1/2'}