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lfunc_lfunctions • Show schema
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{'Lhash': '1692022232659275094371104480381', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-11.135528725660043, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [122.49081598226049, 0.0], 'a8': [0.0, 0.0], 'a9': [-119.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.15352792519226, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '400.1', 'coefficient_field': 'CDF', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [11.135528725660043, 0], [243.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-122.49081598226049, 0], [16807.0, 0]], [[1.0, 0], [-100.0, 0], [161051.0, 0]], [[1.0, 0], [734.944895893563, 0], [371293.0, 0]], [[1.0, 0], [-979.9265278580839, 0], [1419857.0, 0]], [[1.0, 0], [-2244.0, 0], [2476099.0, 0]], [[1.0, 0], [3418.6073187776333, 0], [6436343.0, 0]], 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'7.35675809772460653499090833221763', '7.922428708031892592764370896945710', '9.211491275119775273157434754492774', '10.06476433693374402781690937415008'], 'prelabel': '2-20e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009589747620803, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33477019010967319602636011112', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.72629607185546027503657036339', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.22229360111555653389876517937', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.15352792519226, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/6/a/s/1/1'], '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': '2-20e2-1.1-c5-0-31', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-20e2-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.009589747620803, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33477019010967319602636011112', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1692022232659275094371104480381', 'Lhash_array': ['1692022232659275094371104480381'], 'factors': ['2-20e2-1.1-c5-0-31'], 'label': '2-20e2-1.1-c5-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/6/a/s/1/1'}