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lfunc_lfunctions • Show schema
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{'Lhash': '1967225633120275928125975801120', 'a10': [0.0, 3.509934698477231], 'a2': [-2.301274014280787, 0.0], 'a3': [-0.22034246794408555, 1.7179782294372388], 'a4': [3.2958620888040073, 0.0], 'a5': [0.0, -1.5252137193119895], 'a6': [0.5070683957222214, -3.953538656504033], 'a7': [0.0, -1.0], 'a8': [-2.982133751056283, 0.0], 'a9': [-2.902898393640619, -0.7570871258968233], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8445442866915778, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.22034246794408555, -1.7179782294372388]]], [7, [[1.0, 0], [0, 1.0]]], [11, [[1.0, 0], [2.5611159802148418, 2.1072932723966473]]]], 'bad_primes': [3, 7, 11], 'central_character': '231.197', 'coefficient_field': 'CDF', 'conductor': 231, 'conductor_radical': 231, 'conjugate': '856375704499344874310862630008', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.301274014280787, 0], [2.0, 0]], [[1.0, 0], [0.22034246794408555, 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2.801523178381307, 3.9954200570249294, 3.88063223713016, 2.2226211817874835, -0.8958299840745623], 'positive_zeros': ['1.55186739371723893133931517696493', '2.86864163341020050304143253074709', '5.52708560573349056551571786506615', '6.78116645425318942014598867159514', '7.54693815214865434660498024768232', '8.188156822289942633156755394874182', '9.434171310713313440747474918362641', '10.22311241412225200923223631444278', '11.26312503636567398111773599708445', '11.96591874983502679371032075030431'], 'prelabel': '2-231-33.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3581400099737795, 'root_angle': 0.2597573148651243, 'root_number': '0.6851026856018138 + 0.728446504680462*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.129878657433', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55186739371723893133931517696', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86864163341020050304143253075', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.52708560573349056551571786507', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8445442866915778, 'bad_primes': [3, 7, 11], 'central_character': '33.32', 'conductor': 231, 'conductor_radical': 231, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/231/2/g/a/197/4'], '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': '2-231-33.32-c1-0-10', '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': '2-231-33.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3581400099737795, 'root_angle': 0.12987865743256216, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55186739371723893133931517696', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1967225633120275928125975801120', 'Lhash_array': ['1967225633120275928125975801120'], 'label': '2-231-33.32-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/231/2/g/a/197/4'}