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lfunc_lfunctions • Show schema
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{'Lhash': '3264565511024333975848008664601', 'a10': [0.14424252076967078, 0.1338375004895442], 'a2': [-0.07473009358642425, -0.9972037971811801], 'a3': [1.5287040236839473, 0.47154274210735203], 'a4': [-0.9888308262251285, 0.14904226617617444], 'a5': [-0.14424252076967078, 0.1338375004895442], 'a6': [0.3559840182068327, -1.5596678904314625], 'a7': [2.4477483565010836, -1.0042549393686069], 'a8': [0.2225209339563144, 0.9749279121818236], 'a9': [-0.3641328885546149, -0.24826159979392431], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7825339398085481, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.07473009358642425, 0.9972037971811801]]], [7, [[1.0, 0], [-2.4477483565010836, 1.0042549393686069]]]], 'bad_primes': [2, 7], 'central_character': '98.81', 'coefficient_field': 'CDF', 'conductor': 98, 'conductor_radical': 14, 'conjugate': '2903250254729560821083858047284', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[[1.0, 0], [-5.115593217430945, 2.4635398536586863], [51.749653554274886, -64.89201304484648]], [[1.0, 0], [-11.077676054987705, -7.552631651391219], [32.51535116860916, 82.84776362933418]], [[1.0, 0], [14.831312821081049, 0], [97.0, 0]], [[1.0, 0], [-11.609014348010119, -3.580906685672491], [83.45011620591548, 56.89532586442582]], [[1.0, 0], [-10.728349934721988, 9.954454012441708], [7.697199639401698, -102.71199110966155]], [[1.0, 0], [12.269668379536984, 8.365318257672042], [39.09148960720427, 99.60349110492986]], [[1.0, 0], [2.652538451090102, -1.8084700945208836], [39.822171655937055, -101.46523860221826]], [[1.0, 0], [15.117348195103746, -7.280131194437768], [70.45434761003689, -88.34695751888736]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 2, 'label': '2-98-49.32-c1-0-2', '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, 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'0.7941348552737136 + 0.607741582944098*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.103962175672', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.57528810417995109468605858266', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.65819487938708336282582912873', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.99140668536068573652854551172', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7825339398085481, 'bad_primes': [2, 7], 'central_character': '49.32', 'conductor': 98, 'conductor_radical': 14, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/98/2/g/a/81/2'], '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': '2-98-49.32-c1-0-2', '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': '2-98-49.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8846094843537164, 'root_angle': 0.10396217567202325, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.57528810417995109468605858266', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3264565511024333975848008664601', 'Lhash_array': ['3264565511024333975848008664601'], 'label': '2-98-49.32-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/98/2/g/a/81/2'}