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lfunc_lfunctions • Show schema
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{'Lhash': '2815786413421700483094808555202', 'a10': [0.0, 0.0], 'a2': [1.359789664527991, -0.38855124275036584], 'a3': [1.0399699894938719, -1.0399699894938719], 'a4': [1.6980558635142926, -1.056695928062908], 'a5': [0.0, 0.0], 'a6': [1.0100588112921214, -1.818222074973979], 'a7': [0.0, 1.4966818145567138], 'a8': [1.8984182969397938, -2.0966659175567797], 'a9': [0.0, 0.8369248419042326], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.194016080851217, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.359789664527991, 0.38855124275036584]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '400.101', 'coefficient_field': 'CDF', 'conductor': 400, 'conductor_radical': 10, 'conjugate': '2341449651447838701855088797235', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.359789664527991, 0.38855124275036584]], [[1.0, 0], [-1.0399699894938719, 1.0399699894938719], [0, -3.0]], [[1.0, 0], [0, 0]], [[1.0, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.22126381900086882861725382774', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.80020830423017680902026643815', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.08487245027669400888291316243', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.194016080851217, 'bad_primes': [2, 5], 'central_character': '16.5', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'index': 27, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/2/l/g/101/6'], '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': '2-20e2-16.5-c1-0-27', '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': '2-20e2-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7871810431098514, 'root_angle': 0.13531165986347082, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.22126381900086882861725382774', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2815786413421700483094808555202', 'Lhash_array': ['2815786413421700483094808555202'], 'label': '2-20e2-16.5-c1-0-27', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/2/l/g/101/6'}