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lfunc_lfunctions • Show schema
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{'Lhash': '2022561021552295142258720812336', 'a10': [-3.4641016151377544, 1.020788829390789e-60], 'a2': [-0.25881904510252074, -0.9659258262890683], 'a3': [0.0, 0.0], 'a4': [-0.8660254037844386, 0.5], 'a5': [0.8965754721680536, -3.3460652149512318], 'a6': [0.0, 0.0], 'a7': [0.5, 0.8660254037844386], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.318036774617276, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25881904510252074, 0.9659258262890683]]], [3, [[1.0, 0], [0, 0]]], [37, [[1.0, 0], [-6.0, 1.0]]]], 'bad_primes': [2, 3, 37], 'central_character': '666.125', 'coefficient_field': 'CDF', 'conductor': 666, 'conductor_radical': 222, 'conjugate': '1310906640348538178357706594716', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.25881904510252074, 0.9659258262890683]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8965754721680536, 3.3460652149512318], 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'9.971861232235404984582057468381609', '10.70811600348675740690534102785244'], 'prelabel': '2-666-111.14-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.5643117622104553, 'root_number': '-0.20066958387840397 + 0.9796589805162143*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.282155881105', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59551931832647791367798104305', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.32007312215929481981711908625', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.13305128061001138629158340862', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.318036774617276, 'bad_primes': [2, 3, 37], 'central_character': '111.14', 'conductor': 666, 'conductor_radical': 222, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/666/2/be/b/125/1'], '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': '2-666-111.14-c1-0-6', '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': '2-666-111.14-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3060868965885213, 'root_angle': 0.28215588110522766, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59551931832647791367798104305', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2022561021552295142258720812336', 'Lhash_array': ['2022561021552295142258720812336'], 'label': '2-666-111.14-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/666/2/be/b/125/1'}