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lfunc_lfunctions • Show schema
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{'Lhash': '2031837921514086847177750773491', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 28.74614472766095, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]]], 'bad_primes': [2, 3, 5], 'central_character': '3600.1', 'coefficient_field': '1.1.1.1', 'conductor': 3600, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, -2, 7], [1, -2, 11], [1, 4, 13], [1, 2, 17], [1, 4, 19], [1, 8, 23], [1, -10, 29], [1, 4, 31], [1, 0, 37], [1, 0, 41], [1, 8, 43], [1, 8, 47], [1, -6, 53], [1, 14, 59], [1, 14, 61], [1, 4, 67], [1, -12, 71], [1, 6, 73], [1, -12, 79], [1, 4, 83], [1, -12, 89], [1, -14, 97], [1, 6, 101], [1, 14, 103], [1, -12, 107], [1, -2, 109], [1, -18, 113]], 'euler_factors_factorization': [[1], [1], [1], [[[1, -2, 7], 1]], [[[1, -2, 11], 1]], [[[1, 4, 13], 1]], [[[1, 2, 17], 1]], [[[1, 4, 19], 1]], [[[1, 8, 23], 1]], [[[1, -10, 29], 1]], [[[1, 4, 31], 1]], [[[1, 0, 37], 1]], [[[1, 0, 41], 1]], [[[1, 8, 43], 1]], [[[1, 8, 47], 1]], [[[1, -6, 53], 1]], [[[1, 14, 59], 1]], [[[1, 14, 61], 1]], [[[1, 4, 67], 1]], [[[1, -12, 71], 1]], [[[1, 6, 73], 1]], [[[1, -12, 79], 1]], [[[1, 4, 83], 1]], [[[1, -12, 89], 1]], [[[1, -14, 97], 1]], [[[1, 6, 101], 1]], [[[1, 14, 103], 1]], [[[1, -12, 107], 1]], [[[1, -2, 109], 1]], [[[1, -18, 113], 1]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 43, 'label': '2-60e2-1.1-c1-0-43', '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/3600/2/a/bh', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-8.781501051278662e-61, 0.18770271628411378, 0.37480567855165686, 0.5606580381499103, 0.7445102197531467, 0.9254729352375864, 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-2.307282892157557, -2.13391396002518, -1.834823997598529, -1.4172678710765163, -0.8953795749521023, -0.28948991865133517, 0.37492560625024984, 1.0686113193125302, 1.7601315575513508], 'positive_zeros': ['1.60283750202798168785107955037423', '2.35505983147355055980691824518513', '3.51328020901121211794442097242069', '4.57113923904869265275559722907794', '4.85336813856523536332818646018192', '6.10737883281255681448901758144253', '6.59511445118676575363387732511134', '7.56375687578774005336898856196444', '8.167988003130550779122029197988971'], 'prelabel': '2-60e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.361543129329554, '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': 1272963104990716533, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60283750202798168785107955037', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.35505983147355055980691824519', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.51328020901121211794442097242', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 28.74614472766095, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 3600, 'conductor_radical': 30, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -4, 0, 0, 0, -2, 0, -4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 10, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, -3, 0, 0, 0, 6, 0, 0, 0, 0, 0, -14, 0, -14, 0, 0, 0, 0, 0, -4, 0, 0, 0, 12, 0, -6, 0, 0, 0, 4, 0, 12, 0, 0, 0, -4, 0, 0, 0, 0, 0, 12, 0, -8, 0, 0, 0, 0, 0, 14, 0, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, 4, 13], 'euler17': [1, 2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 0, 37], 'euler41': [1, 0, 41], 'euler43': [1, 8, 43], 'euler47': [1, 8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 14, 59], 'euler61': [1, 14, 61], 'euler67': [1, 4, 67], 'euler7': [1, -2, 7], 'euler71': [1, -12, 71], 'euler73': [1, 6, 73], 'euler79': [1, -12, 79], 'euler83': [1, 4, 83], 'euler89': [1, -12, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -2, 7], [1, -2, 11], [1, 4, 13], [1, 2, 17], [1, 4, 19], [1, 8, 23], [1, -10, 29], [1, 4, 31], [1, 0, 37], [1, 0, 41], [1, 8, 43], [1, 8, 47], [1, -6, 53], [1, 14, 59], [1, 14, 61], [1, 4, 67], [1, -12, 71], [1, 6, 73], [1, -12, 79], [1, 4, 83], [1, -12, 89], [1, -14, 97]], 'index': 43, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/3600/bh', 'ModularForm/GL2/Q/holomorphic/3600/2/a/bh/1/1', 'ModularForm/GL2/Q/holomorphic/3600/2/a/bh'], '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': '2-60e2-1.1-c1-0-43', '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': '2-60e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 5.361543129329554, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1272963104990716533, 'z1': {'__RealLiteral__': 0, 'data': '1.60283750202798168785107955037', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20546692
{'Lhash': '2031837921514086847177750773491', 'Lhash_array': ['2031837921514086847177750773491'], 'label': '2-60e2-1.1-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3600/2/a/bh'}
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id: 24562266
{'Lhash': '2031837921514086847177750773491', 'Lhash_array': ['2031837921514086847177750773491'], 'label': '2-60e2-1.1-c1-0-43', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3600/2/a/bh/1/1'}
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id: 23389
{'Lhash': '1272963104990716533', 'Lhash_array': ['1272963104990716533'], 'label': '2-60e2-1.1-c1-0-43', 'type': 'ECQ', 'url': 'EllipticCurve/Q/3600/bh'}