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lfunc_lfunctions • Show schema
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{'Lhash': '2578077067691855962227555953741', 'a10': [2.4319554631212563, -2.2565249050644676], 'a2': [0.9195269693930399, -0.44282084976869523], 'a3': [1.709593805126199, -0.2780090312815826], 'a4': [-0.5975400612661879, 0.7492915369923417], 'a5': [3.1062042195865445, -0.9581371099681807], 'a6': [1.4489094150453268, -1.012680583543529], 'a7': [-2.220349355939097, -1.4387663943743048], 'a8': [-0.6718610995080215, 2.943615808965342], 'a9': [2.845421957051752, -0.9505650352962587], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.709593805126199, 0.2780090312815826]]], [7, [[1.0, 0], [2.220349355939097, 1.4387663943743048]]]], 'bad_primes': [3, 7], 'central_character': '441.121', 'coefficient_field': 'CDF', 'conductor': 441, 'conductor_radical': 21, 'conjugate': '2227354958032195039279586160508', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[-4.509413245821634, 3.074465893436264], [32.51535116860916, -82.84776362933418]], [[1.0, 0], [2.0279408165007635, 3.5124965289220356], [-48.5, 84.00446416709055]], [[1.0, 0], [-10.148642712301413, -9.41656431632084], [7.54773945222885, 100.7175835152992]], [[1.0, 0], [-0.627086159669328, 0.19343046311571557], [85.10259375454747, -58.02196598055307]], [[1.0, 0], [7.213222359084284, -4.917891733547652], [39.09148960720427, -99.60349110492986]], [[1.0, 0], [-8.445737635408706, -5.758206420543739], [39.822171655937055, 101.46523860221826]], [[1.0, 0], [9.566174411286712, -6.522107279791995], [41.28353575340264, -105.18873359679507]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 44, 'label': '2-21e2-441.121-c1-0-44', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/441/2/y/a/121/38', 'plot_delta': 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'0.0784145538822', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.03374420934892922271362784789', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07217683519181341848771199874', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.45351354204459166877725673454', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5214027291384666, 'bad_primes': [3, 7], 'central_character': '441.121', 'conductor': 441, 'conductor_radical': 21, 'degree': 2, 'index': 44, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/441/2/y/a/121/38'], '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': '2-21e2-441.121-c1-0-44', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-21e2-441.121-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.8765400952653442, 'root_angle': 0.07841455388215944, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.03374420934892922271362784789', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2578077067691855962227555953741', 'Lhash_array': ['2578077067691855962227555953741'], 'label': '2-21e2-441.121-c1-0-44', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/441/2/y/a/121/38'}