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lfunc_lfunctions • Show schema
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{'Lhash': '2433406325887047797996577894670', 'a10': [0.0, 0.0], 'a2': [0.38855124275036584, 1.359789664527991], 'a3': [-1.0399699894938719, -1.0399699894938719], 'a4': [-1.6980558635142926, 1.056695928062908], 'a5': [0.0, 0.0], 'a6': [1.0100588112921214, -1.818222074973979], 'a7': [-1.4966818145567138, 0.0], 'a8': [-2.0966659175567797, -1.8984182969397938], '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], [-0.38855124275036584, -1.359789664527991]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '400.149', 'coefficient_field': 'CDF', 'conductor': 400, 'conductor_radical': 10, 'conjugate': '494496837932302799231670199329', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.38855124275036584, -1.359789664527991]], [[1.0, 0], [1.0399699894938719, 1.0399699894938719], [0, 3.0]], [[1.0, 0], [0, 0]], 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47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91961911700979297909045518016', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51758888813181010888687561482', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.41401080368300183379709686599', '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': '80.69', 'conductor': 400, 'conductor_radical': 10, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/2/q/f/149/4'], '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': '2-20e2-80.69-c1-0-21', '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': '2-20e2-80.69-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7871810431098514, 'root_angle': 0.20910346868868748, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91961911700979297909045518016', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2433406325887047797996577894670', 'Lhash_array': ['2433406325887047797996577894670'], 'label': '2-20e2-80.69-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/2/q/f/149/4'}