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lfunc_lfunctions • Show schema
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{'Lhash': '1261246133918536233422990373646', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.10452846326765347, 0.9945218953682733], 'a5': [0.6691306063588582, -0.7431448254773942], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.630445396272019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.3016', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'conjugate': '1608500714955092066134214713962', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.10452846326765347, -0.9945218953682733]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.6691306063588582, 0.7431448254773942], [-0.10452846326765347, -0.9945218953682733]], [[1.0, 0], [0, 0], [-0.6691306063588582, 0.7431448254773942]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], 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'8.946658968489712595620682824371762'], 'prelabel': '2-3267-99.79-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.19234351763856422, 'root_number': '0.82291992579150579174134709459091 - 0.56815736881193629452374548306040*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09617175881928211', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.994947766909477974499249911054', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.26549419501268866170171849637', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.88127019819479572893797242291', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.630445396272019, 'bad_primes': [3, 11], 'central_character': '99.79', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/w/a/3016/1'], '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': '2-3267-99.79-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3267-99.79-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.09617175881928211, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.994947766909477974499249911054', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1261246133918536233422990373646', 'Lhash_array': ['1261246133918536233422990373646'], 'label': '2-3267-99.79-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/w/a/3016/1'}