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lfunc_lfunctions • Show schema
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{'Lhash': '1246266260074045602457021947442', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.215510220317541, 0.0], 'a4': [0.0, 0.0], 'a5': [3.5966927482342452, 0.0], 'a6': [0.0, 0.0], 'a7': [5.064792110834649, 0.0], 'a8': [0.0, 0.0], 'a9': [1.90848553633148, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 53.691410319108954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [41, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 41], 'central_character': '6724.1', 'coefficient_field': 'CDF', 'conductor': 6724, 'conductor_radical': 82, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.215510220317541, 0], [3.0, 0]], [[1.0, 0], [-3.5966927482342452, 0], [5.0, 0]], [[1.0, 0], [-5.064792110834649, 0], [7.0, 0]], [[1.0, 0], [-2.5596138262689236, 0], [11.0, 0]], [[1.0, 0], [-4.936198725200808, 0], [13.0, 0]], [[1.0, 0], [2.6882072119027653, 0], [17.0, 0]], [[1.0, 0], [4.720688504883267, 0], [19.0, 0]], 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'5.21971392893576506600918901737344', '5.92921898557324499568839671136694', '6.32686793550529663790725564068206', '6.93538673515830858185224155073045', '8.193336753382257660749269551140177'], 'prelabel': '2-82e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.327442276750391, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.983130730068416537128204228536', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.66649080093027739177911646094', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.29014701559842378351435942418', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 53.691410319108954, 'bad_primes': [2, 41], 'central_character': '1.1', 'conductor': 6724, 'conductor_radical': 82, 'degree': 2, 'index': 65, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6724/2/a/c/1/2'], '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': '2-82e2-1.1-c1-0-65', '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': '2-82e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.327442276750391, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.983130730068416537128204228536', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1246266260074045602457021947442', 'Lhash_array': ['1246266260074045602457021947442'], 'label': '2-82e2-1.1-c1-0-65', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6724/2/a/c/1/2'}