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lfunc_lfunctions • Show schema
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{'Lhash': '509543240255328544130884339167', 'a10': [-27074.3118704652, -177475.57677287835], 'a2': [-36.459863569055216, -26.8081768967209], 'a3': [-475.97635960363834, 475.97635960363834], 'a4': [610.6433029482394, 1954.8449443790842], 'a5': [2805.1378779287634, 2805.1378779287634], 'a6': [30114.091580155797, -4593.97468633264], 'a7': [0.0, 76033.60021024726], 'a8': [30141.857559724962, -87643.61365695308], 'a9': [0.0, -275959.9898030641], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.293490888953425, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '5.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [36.459863569055216, 26.8081768967209]]]], 'bad_primes': [2], 'central_character': '16.5', 'coefficient_field': 'CDF', 'conductor': 16, 'conductor_radical': 2, 'conjugate': '2934365197387795323503235014852', 'degree': 2, 'euler_factors': [[[1.0, 0], [36.459863569055216, 26.8081768967209]], [[1.0, 0], [475.97635960363834, -475.97635960363834], [0, -177147.0]], [[1.0, 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0], [38358611506121120000000, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-2e4-16.5-c11-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/16/12/e/a/5/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.5405007693293411, 0.2792275226955977, 0.05488455974858266, -0.11421869955422928, -0.21197822731140475, -0.22526595149637033, -0.14461993234228054, 0.03517149825564708, 0.31461922264736103, 0.6892452473850113, 1.1494856746503577, 1.6808112026468787, 2.2640868773837224, 2.8761850721505207, 3.4908547113367088, 4.07983565299388, 4.6141903137342455, 5.065805858580154, 5.40900078321655, 5.622151056695879, 5.689235044651127, 5.601185260166825, 5.3569306758291395, 4.9640177688018445, 4.43871311791319, 3.805515991689797, 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'11.27000732313250356815578449649181', '12.96061883975486308706455032505994', '14.24207702201509748812870975467925', '16.49472197970787008278510620163022'], 'prelabel': '2-2e4-16.5-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.506207479450328, 'root_angle': 0.9322504156507742, 'root_number': '-0.9774346079686452 + 0.21123822368402165*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.466125207825', 'prec': 47}, 'spectral_label': 'c11-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40195874175706597785959418791', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.20262085526861008207412444628', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.35879920151058858872709998089', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.293490888953425, 'bad_primes': [2], 'central_character': '16.5', 'conductor': 16, 'conductor_radical': 2, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/16/12/e/a/5/4'], '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': '2-2e4-16.5-c11-0-2', 'motivic_weight': 11, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [11], 'order_of_vanishing': 0, 'prelabel': '2-2e4-16.5-c11-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.506207479450328, 'root_angle': 0.4661252078253871, 'self_dual': False, 'spectral_label': 'c11-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40195874175706597785959418791', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '509543240255328544130884339167', 'Lhash_array': ['509543240255328544130884339167'], 'label': '2-2e4-16.5-c11-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/16/12/e/a/5/4'}