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lfunc_lfunctions • Show schema
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{'Lhash': '4357966635231217007139382573307', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.5, -0.8660254037844386], 'a3': [0.5, -0.8660254037844386], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.5, -0.8660254037844386], 'a6': [-1.0, 0.0], 'a7': [-0.5, 0.8660254037844386], 'a8': [1.0, 3.9689140359382235e-80], 'a9': [-4.582907173931562e-80, -2.6459426907612794e-80], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.06986910176862034, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, 0.8660254037844386]]], [5, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0.5, -0.8660254037844386]]]], 'bad_primes': [2, 5, 7], 'central_character': '140.39', 'coefficient_field': 'CDF', 'conductor': 140, 'conductor_radical': 70, 'conjugate': '2342602250330984828983461175679', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], 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4.863740065947309, 3.947756052412444, 2.898555337671491, 1.800084980589715, 0.7383714838199635, -0.20627047379825492], 'positive_zeros': ['3.43782950479146480647989201128876', '4.57530209214505313204504732398203', '6.41661967871024913557960236053121', '7.26104126294525014046992686963354', '8.416143973274795439126093561837327', '9.614591293890291152644650722769997', '10.27748392754102519390547451999084', '11.16716525752643526132281201911720', '12.96999685799762280518674606496397', '14.17587321847294524728955915446102'], 'prelabel': '2-140-140.39-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2643276409470268, 'root_angle': 0.5201729530539461, 'root_number': '-0.063332786104344676563637747749200 + 0.99799246400173850503495435029375*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2600864765269731', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.43782950479146480647989201129', 'prec': 103}, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.06986910176862034, 'bad_primes': [2, 5, 7], 'central_character': '140.39', 'conductor': 140, 'conductor_radical': 70, 'degree': 2, 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/140/1/p/a/39/1', 'ArtinRepresentation/2.140.6t5.a.b'], 'is_instance_Artin': True, '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': '2-140-140.39-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': '2-140-140.39-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.2643276409470268, 'root_angle': 0.26008647652697303, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '3.43782950479146480647989201129', 'prec': 103}}
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lfunc_instances • Show schema
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id: 24596415
{'Lhash': '4357966635231217007139382573307', 'Lhash_array': ['4357966635231217007139382573307'], 'label': '2-140-140.39-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.140.6t5.a.b'}
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id: 19810410
{'Lhash': '4357966635231217007139382573307', 'Lhash_array': ['4357966635231217007139382573307'], 'label': '2-140-140.39-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/140/1/p/a/39/1'}