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lfunc_lfunctions • Show schema
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{'Lhash': '1932659216311411447615698513889', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [18.82382583591484, 0.0], 'a8': [0.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 81.42263580792209, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-3.0, 0]]], [5, [[1.0, 0], [5.0, 0]]], [23, [[1.0, 0], [-23.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.1', 'coefficient_field': 'CDF', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [-18.82382583591484, 0], [343.0, 0]], [[1.0, 0], [3.1258124247014085, 0], [1331.0, 0]], [[1.0, 0], [76.28744900441909, 0], [2197.0, 0]], [[1.0, 0], [-66.68850128067338, 0], [4913.0, 0]], [[1.0, 0], [79.20263541162409, 0], [6859.0, 0]], [[1.0, 0], [-23.0, 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[1530.9567133930786, 0], [1295029.0, 0]], [[1.0, 0], [-494.3097254446193, 0], [1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 40, 'label': '2-1380-1.1-c3-0-40', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/1380/4/a/g/1/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-1.4366414176624745e-60, 0.26301651806883863, 0.5232885098762795, 0.778091661770814, 1.024742361353905, 1.2606187179006902, 1.4831823305114973, 1.6900009621916545, 1.878772204560228, 2.047348131465605, 2.193760843731288, 2.316248705215639, 2.413282966213576, 2.4835943679188124, 2.5261992251367533, 2.5404243974875955, 2.525930485528643, 2.482732530798649, 2.4112174606002355, 2.312157501795395, 2.1867187948996616, 2.036464471683878, 1.8633515171062787, 1.6697208198617794, 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'5.13460142230385892843409861158941', '6.49825663918346621628170197789674', '7.46947879294443984171645352362470', '7.965680267748825956546449984224325', '8.616071613117737171594430048196897'], 'prelabel': '2-1380-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.023449219002792, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52459929886315129903608151432', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.50188468471346285714917185979', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54856510142997798029708154288', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 81.42263580792209, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 1380, 'conductor_radical': 690, 'degree': 2, 'index': 40, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1380/4/a/g/1/5'], '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': '2-1380-1.1-c3-0-40', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1380-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.023449219002792, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52459929886315129903608151432', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1932659216311411447615698513889', 'Lhash_array': ['1932659216311411447615698513889'], 'label': '2-1380-1.1-c3-0-40', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/4/a/g/1/5'}