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lfunc_lfunctions • Show schema
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{'Lhash': '1064462555877142553995560295145', 'a10': [-867.019181115198, 1501.7212728282852], 'a2': [-4.0, -6.928203230275509], 'a3': [10.438698819699873, -18.080356720629453], 'a4': [-32.0, 55.42562584220407], 'a5': [-108.37739763939975, -187.71515910353565], 'a6': [-167.01918111519797, 0], 'a7': [0, 0], 'a8': [512.0, 0], 'a9': [875.5671339031929, 1516.5267613577926], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 30.613732497443944, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [4.0, 6.928203230275509]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 7], 'central_character': '98.67', 'coefficient_field': 'CDF', 'conductor': 98, 'conductor_radical': 14, 'conjugate': '1155043197571821029741751474614', 'degree': 2, 'euler_factors': [[[1.0, 0], [4.0, 6.928203230275509]], [[1.0, 0], [-10.438698819699873, 18.080356720629453], [-1093.5, -1893.9975580765674]], [[1.0, 0], [108.37739763939975, 187.71515910353565], 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['0.839712895403114535226539335439564', '3.06311944136038810762847482503947', '4.34971298843738378503423515941227', '6.05376208239756697813627763977473', '7.02111091202473304749395803292520', '8.304672243564300997024962273162498', '9.253527346906432173796067547198335', '10.47247144179597299579000513882216', '11.30475441028285365174074463272812', '12.81866737486288740412256522852236'], 'prelabel': '2-98-7.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.532967783879095, 'root_angle': 0.14649371361272054, 'root_number': '0.6054643436493674 + 0.7958724323465669*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.14649371361272054', 'prec': 64}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.839712895403114535226539335439564', 'prec': 117}, 'z2': {'__RealLiteral__': 0, 'data': '3.06311944136038810762847482503947', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '4.34971298843738378503423515941227', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 30.613732497443944, 'bad_primes': [2, 7], 'central_character': '7.4', 'conductor': 98, 'conductor_radical': 14, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/98/8/c/h/67/2'], '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': '2-98-7.4-c7-0-11', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-98-7.4-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.532967783879095, 'root_angle': 0.14649371361272054, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.839712895403114535226539335439564', 'prec': 117}}
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lfunc_instances • Show schema
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{'Lhash': '1064462555877142553995560295145', 'Lhash_array': ['1064462555877142553995560295145'], 'factors': ['2-98-7.4-c7-0-11'], 'label': '2-98-7.4-c7-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/98/8/c/h/67/2'}