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  • lfunc_lfunctions • Show schema
    {'Lhash': '1931377980870142561561646181231,3133064319433832105157566557013', 'a10': -8, 'a2': 2, 'a3': -6, 'a4': 3, 'a5': -4, 'a6': -12, 'a7': 0, 'a8': 4, 'a9': 21, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 24.03759182669148, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1, -2, 1]], [307, [1, 16, 307]]], 'bad_primes': [2, 307], 'central_character': '614.1', 'coefficient_field': '1.1.1.1', 'conductor': 376996, 'conductor_radical': 614, 'degree': 4, 'euler_factors': [[1, -2, 1], [1, 6, 15, 18, 9], [1, 4, 11, 20, 25], [1, 0, -7, 0, 49], [1, 3, -2, 33, 121], [1, -6, 23, -78, 169], [1, 14, 83, 238, 289], [1, 8, 54, 152, 361], [1, 4, -7, 92, 529], [1, -6, 7, -174, 841], [1, 10, 69, 310, 961], [1, -6, -1, -222, 1369], [1, -7, 8, -287, 1681], [1, 11, 78, 473, 1849], [1, 6, -11, 282, 2209], [1, -4, -37, -212, 2809], [1, 1, -58, 59, 3481], [1, -2, -57, -122, 3721], [1, 1, -66, 67, 4489], [1, 6, -35, 426, 5041], [1, 11, 48, 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2]], [[[1, -3, -98, -321, 11449], 1]], [[[1, 14, 87, 1526, 11881], 1]], [[[1, 13, 113], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-614e2-1.1-c1e2-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/614/2/c/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 10}, 'plot_values': [3.888893035993413e-123, -0.013215605320890987, -0.05306926581075279, -0.12009964132343758, -0.2150190415995218, -0.3386291688762591, -0.49138048415553653, -0.6731840856648319, -0.8828490650739099, -1.117969319932991, -1.3741957302976864, -1.645263273009797, -1.922363924784158, -2.1943958234261234, -2.4476233501709967, -2.6662220855332333, -2.8324818910337957, -2.927651323525256, -2.9328534394870376, -2.830130005287061, -2.6041034320116627, -2.2429782112460215, -1.7407546094262203, -1.097816657203191, -0.3232481760148965, 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'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1454658459753923052, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52358858231315068307710758304', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.47155195514422608380179301057', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.88729562333261088718551048360', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 24.03759182669148, 'bad_primes': [2, 307], 'central_character': '1.1', 'conductor': 376996, 'conductor_radical': 614, 'degree': 4, 'dirichlet_coefficients': [1, 2, -6, 3, -4, -12, 0, 4, 21, -8, -3, -18, 6, 0, 24, 5, -14, 42, -8, -12, 0, -6, -4, -24, 5, 12, -54, 0, 6, 48, -10, 6, 18, -28, 0, 63, 6, -16, -36, -16, 7, 0, -11, -9, -84, -8, -6, -30, 7, 10, 84, 18, 4, -108, 12, 0, 48, 12, -1, 72, 2, -20, 0, 7, -24, 36, -1, -42, 24, 0, -6, 84, -11, 12, -30, -24, 0, -72, -8, -20, 108, 14, -8, 0, 56, -22, -36, -12, -6, -168, 0, -12, 60, -12, 32, -36, 2, 14, -63, 15], 'euler11': [1, 3, -2, 33, 121], 'euler13': [1, -6, 23, -78, 169], 'euler17': [1, 14, 83, 238, 289], 'euler19': [1, 8, 54, 152, 361], 'euler2': [1, -2, 1, 0, 0], 'euler23': [1, 4, -7, 92, 529], 'euler29': [1, -6, 7, -174, 841], 'euler3': [1, 6, 15, 18, 9], 'euler31': [1, 10, 69, 310, 961], 'euler37': [1, -6, -1, -222, 1369], 'euler41': [1, -7, 8, -287, 1681], 'euler43': [1, 11, 78, 473, 1849], 'euler47': [1, 6, -11, 282, 2209], 'euler5': [1, 4, 11, 20, 25], 'euler53': [1, -4, -37, -212, 2809], 'euler59': [1, 1, -58, 59, 3481], 'euler61': [1, -2, -57, -122, 3721], 'euler67': [1, 1, -66, 67, 4489], 'euler7': [1, 0, -7, 0, 49], 'euler71': [1, 6, -35, 426, 5041], 'euler73': [1, 11, 48, 803, 5329], 'euler79': [1, 8, 174, 632, 6241], 'euler83': [1, 8, -19, 664, 6889], 'euler89': [1, 6, -53, 534, 7921], 'euler97': [1, -2, 195, -194, 9409], 'euler_factors': [[1, -2, 1, 0, 0], [1, 6, 15, 18, 9], [1, 4, 11, 20, 25], [1, 0, -7, 0, 49], [1, 3, -2, 33, 121], [1, -6, 23, -78, 169], [1, 14, 83, 238, 289], [1, 8, 54, 152, 361], [1, 4, -7, 92, 529], [1, -6, 7, -174, 841], [1, 10, 69, 310, 961], [1, -6, -1, -222, 1369], [1, -7, 8, -287, 1681], [1, 11, 78, 473, 1849], [1, 6, -11, 282, 2209], [1, -4, -37, -212, 2809], [1, 1, -58, 59, 3481], [1, -2, -57, -122, 3721], [1, 1, -66, 67, 4489], [1, 6, -35, 426, 5041], [1, 11, 48, 803, 5329], [1, 8, 174, 632, 6241], [1, 8, -19, 664, 6889], [1, 6, -53, 534, 7921], [1, -2, 195, -194, 9409]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/614/2/c/a'], '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': '4-614e2-1.1-c1e2-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 2, 'prelabel': '4-614e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 2.214230043176774, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1454658459753923052, 'z1': {'__RealLiteral__': 0, 'data': '1.52358858231315068307710758304', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1931377980870142561561646181231,3133064319433832105157566557013', 'Lhash_array': ['1931377980870142561561646181231', '3133064319433832105157566557013'], 'factors': ['2-614-307.17-c1-0-15', '2-614-307.289-c1-0-26'], 'label': '4-614e2-1.1-c1e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/614/2/c/a'}