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lfunc_lfunctions • Show schema
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{'Lhash': '1569832828986588914040154447544', 'a10': [-0.7071067811865476, -0.7071067811865476], 'a2': [0.0, 1.0], 'a3': [0.0, 0.0], 'a4': [-1.0, 0.0], 'a5': [-0.7071067811865476, 0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [1.4142135623730951, 0.0], 'a8': [0.0, -1.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0779804272872853, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]]], 'bad_primes': [2, 3, 5], 'central_character': '2160.1349', 'coefficient_field': 'CDF', 'conductor': 2160, 'conductor_radical': 30, 'conjugate': '1379338871837775442193661349512', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476], [0, -1.0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476], [0, 1.0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 1.0], [0, -1.0]], [[1.0, 0], [0, -1.0], [-1.0, 0]], [[1.0, 0], [0.7071067811865476, 0.7071067811865476], [0, 1.0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.7071067811865476, -0.7071067811865476], [0, -1.0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [-1.0, -1.0], [0, 1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, -1.0]], [[1.0, 0], [-1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476], [0, -1.0]], [[1.0, 0], [1.4142135623730951, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [1.0, -1.0], [0, -1.0]], [[1.0, 0], [1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 4, 'label': '2-2160-240.149-c0-0-4', 'leading_term': '1.1455106770324414940714383703571', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/2160/1/bn/b/1349/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.1455106770324415, 1.1357184183700288, 1.133815520348435, 1.1379551689157723, 1.1455692728991187, 1.1537068384196938, 1.1593386917368371, 1.1595889346749624, 1.1518895379684164, 1.1340743578923105, 1.1044333508206894, 1.0617439367394295, 1.005290349728218, 0.9348764470608344, 0.8508336975179431, 0.7540238077438629, 0.6458342749340948, 0.5281647055555989, 0.4034017488841072, 0.2743807921813918, 0.14433304888599388, 0.01681727982598405, -0.10436392054097982, -0.21526259589661856, -0.31189720958066003, 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'5.48244397069680638827321513553025', '7.04612737900362720761430417232413', '7.893110472461591857894419402662479', '8.357204361920694281803123970729513', '9.208712827412928105776574307955566'], 'prelabel': '2-2160-240.149-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.038258362493308, 'root_angle': -0.1875, 'root_number': '0.38268343236508977172845998403043 - 0.92387953251128675612818318939698*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1875', 'prec': 24}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.23837974652002235132161079893', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.94436799820489478805099549287', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.40287507272241670787520641834', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0779804272872853, 'bad_primes': [2, 3, 5], 'central_character': '240.149', 'conductor': 2160, 'conductor_radical': 30, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2160/1/bn/b/1349/1'], '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': '2-2160-240.149-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': '2-2160-240.149-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.038258362493308, 'root_angle': -0.1875, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.23837974652002235132161079893', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1569832828986588914040154447544', 'Lhash_array': ['1569832828986588914040154447544'], 'factors': ['2-2160-240.149-c0-0-4'], 'label': '2-2160-240.149-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2160/1/bn/b/1349/1'}