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lfunc_lfunctions • Show schema
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{'Lhash': '2588512712971410433004905398128', 'a10': [0.0, 0.0], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [-0.25881904510252074, -0.9659258262890683], 'a4': [0.0, 1.0], 'a5': [0.0, 0.0], 'a6': [-0.5, 0.8660254037844386], 'a7': [0.0, 0.0], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [-0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.29943900757980146, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [0.25881904510252074, 0.9659258262890683]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.443', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '1006730843082854129362620287718', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0.25881904510252074, 0.9659258262890683]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'5.83560833343820260372064453634980', '6.77921109451525082756886939279399', '7.75401124315300017862988597835852', '8.754694289198534238840156128672717', '9.514677351899863268037575824303470', '10.22457150227953432869521154792780', '10.77632476075205934241087032853754'], 'prelabel': '2-600-120.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5472102041992651, 'root_angle': 0.8108277494169627, 'root_number': '-0.82853944668138905356607855401919 + 0.55993069686604758036114566502623*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4054138747084813', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.04197648193072394133171450053', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.00331564109542064884171016440', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.85792538980520456859987723705', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.29943900757980146, 'bad_primes': [2, 3, 5], 'central_character': '120.83', 'conductor': 600, 'conductor_radical': 30, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/600/1/q/b/443/1'], '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': '2-600-120.83-c0-0-4', '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': '2-600-120.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5472102041992651, 'root_angle': 0.40541387470848134, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.04197648193072394133171450053', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2588512712971410433004905398128', 'Lhash_array': ['2588512712971410433004905398128'], 'label': '2-600-120.83-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/600/1/q/b/443/1'}