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lfunc_lfunctions • Show schema
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{'Lhash': '2318434136896327880323687679257', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': 1, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.635718998299005, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [37, [1, -1]]], 'bad_primes': [2, 5, 37], 'central_character': '2960.1', 'coefficient_field': '1.1.1.1', 'conductor': 2960, 'conductor_radical': 370, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 1], [1, -1, 7], [1, 3, 11], [1, 4, 13], [1, -3, 17], [1, 2, 19], [1, 6, 23], [1, -3, 29], [1, 5, 31], [1, -1], [1, -3, 41], [1, -1, 43], [1, 12, 47], [1, -3, 53], [1, 0, 59], [1, 1, 61], [1, -4, 67], [1, 6, 71], [1, 16, 73], [1, 8, 79], [1, -12, 83], [1, 6, 89], [1, -17, 97], [1, 6, 101], [1, -4, 103], [1, 6, 107], [1, -11, 109], [1, -9, 113]], 'euler_factors_factorization': [[1], [[[1, -2, 3], 1]], [[[1, 1], 1]], [[[1, -1, 7], 1]], [[[1, 3, 11], 1]], [[[1, 4, 13], 1]], [[[1, -3, 17], 1]], [[[1, 2, 19], 1]], [[[1, 6, 23], 1]], [[[1, -3, 29], 1]], [[[1, 5, 31], 1]], [[[1, -1], 1]], [[[1, -3, 41], 1]], [[[1, -1, 43], 1]], [[[1, 12, 47], 1]], [[[1, -3, 53], 1]], [[[1, 0, 59], 1]], [[[1, 1, 61], 1]], [[[1, -4, 67], 1]], [[[1, 6, 71], 1]], [[[1, 16, 73], 1]], [[[1, 8, 79], 1]], [[[1, -12, 83], 1]], [[[1, 6, 89], 1]], [[[1, -17, 97], 1]], [[[1, 6, 101], 1]], [[[1, -4, 103], 1]], [[[1, 6, 107], 1]], [[[1, -11, 109], 1]], [[[1, -9, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 67, 'label': '2-2960-1.1-c1-0-67', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/2960/2/a/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.362500024703582e-60, 0.21529902466655065, 0.4303589981413271, 0.644885259199672, 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0.8099762201096409, 0.2955081320409708, -0.20116824738703318, -0.65236906280906, -1.0332493910619664, -1.3231463958239629, -1.5066813012912978, -1.5745593113709029, -1.5240236368878284], 'positive_zeros': ['1.82892205192733241717251603918515', '2.65209192124627030493117144784032', '3.40211614659968515387465276613925', '4.35398309815315781351355776418575', '5.14462937098489056863036116363313', '6.05862458218504358555244114858253', '7.25190206823653094417112473387062', '7.80191348675256968137318821157438', '8.213079647180113859147339692981058'], 'prelabel': '2-2960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.861658050325938, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1349961653163959782, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.82892205192733241717251603919', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.65209192124627030493117144784', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40211614659968515387465276614', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 23.635718998299005, 'bad_primes': [2, 5, 37], 'central_character': '1.1', 'conductor': 2960, 'conductor_radical': 370, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, -1, 0, 1, 0, 1, 0, -3, 0, -4, 0, -2, 0, 3, 0, -2, 0, 2, 0, -6, 0, 1, 0, -4, 0, 3, 0, -5, 0, -6, 0, -1, 0, 1, 0, -8, 0, 3, 0, 1, 0, -1, 0, -12, 0, -6, 0, 6, 0, 3, 0, 3, 0, -4, 0, 0, 0, -1, 0, 1, 0, 4, 0, 4, 0, -12, 0, -6, 0, -16, 0, 2, 0, -3, 0, -8, 0, -11, 0, 12, 0, -3, 0, 6, 0, -6, 0, -4, 0, -10, 0, 2, 0, 17, 0, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, 4, 13], 'euler17': [1, -3, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -3, 29], 'euler3': [1, -2, 3], 'euler31': [1, 5, 31], 'euler37': [1, -1, 0], 'euler41': [1, -3, 41], 'euler43': [1, -1, 43], 'euler47': [1, 12, 47], 'euler5': [1, 1, 0], 'euler53': [1, -3, 53], 'euler59': [1, 0, 59], 'euler61': [1, 1, 61], 'euler67': [1, -4, 67], 'euler7': [1, -1, 7], 'euler71': [1, 6, 71], 'euler73': [1, 16, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 6, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 1, 0], [1, -1, 7], [1, 3, 11], [1, 4, 13], [1, -3, 17], [1, 2, 19], [1, 6, 23], [1, -3, 29], [1, 5, 31], [1, -1, 0], [1, -3, 41], [1, -1, 43], [1, 12, 47], [1, -3, 53], [1, 0, 59], [1, 1, 61], [1, -4, 67], [1, 6, 71], [1, 16, 73], [1, 8, 79], [1, -12, 83], [1, 6, 89], [1, -17, 97]], 'index': 67, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/2960/j', 'ModularForm/GL2/Q/holomorphic/2960/2/a/j/1/1', 'ModularForm/GL2/Q/holomorphic/2960/2/a/j'], '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': '2-2960-1.1-c1-0-67', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-2960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.861658050325938, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1349961653163959782, 'z1': {'__RealLiteral__': 0, 'data': '1.82892205192733241717251603919', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20301921
{'Lhash': '2318434136896327880323687679257', 'Lhash_array': ['2318434136896327880323687679257'], 'label': '2-2960-1.1-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2960/2/a/j'}
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id: 24559545
{'Lhash': '2318434136896327880323687679257', 'Lhash_array': ['2318434136896327880323687679257'], 'label': '2-2960-1.1-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2960/2/a/j/1/1'}
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id: 40527
{'Lhash': '1349961653163959782', 'Lhash_array': ['1349961653163959782'], 'label': '2-2960-1.1-c1-0-67', 'type': 'ECQ', 'url': 'EllipticCurve/Q/2960/j'}