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lfunc_lfunctions • Show schema
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{'Lhash': '2520157775206865144676442689236', 'a10': [0.0, 0.0], 'a2': [-0.25881904510252074, 0.9659258262890683], 'a3': [0.0, 0.0], 'a4': [-0.8660254037844386, -0.5], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.7071067811865476, -0.7071067811865476], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.34934550884310167, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25881904510252074, -0.9659258262890683]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]]], 'bad_primes': [2, 5, 7], 'central_character': '700.643', 'coefficient_field': 'CDF', 'conductor': 700, 'conductor_radical': 70, 'conjugate': '1020368939824152128288023072158', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.25881904510252074, -0.9659258262890683]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, 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'6.23578288166587369387614805734385', '7.51444128250068842465806506959159', '8.214114294649035784754420745721208', '9.328888631941133333912872975829494', '9.889744785430964022676723467244681', '10.54801336012114048920984632332344'], 'prelabel': '2-700-140.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5910545734897089, 'root_angle': 0.06246098313296875, 'root_number': '0.92397331967055129062313806981359 + 0.38245693161058178870336896159674*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.062460983132968745', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.98805394384945882006328897110', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.73231768835505107283855656580', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.23334257377945410391829502847', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.34934550884310167, 'bad_primes': [2, 5, 7], 'central_character': '140.83', 'conductor': 700, 'conductor_radical': 70, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/700/1/j/b/643/2'], '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': '2-700-140.83-c0-0-3', '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': '2-700-140.83-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5910545734897089, 'root_angle': 0.06246098313296875, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.98805394384945882006328897110', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2520157775206865144676442689236', 'Lhash_array': ['2520157775206865144676442689236'], 'factors': ['2-700-140.83-c0-0-3'], 'label': '2-700-140.83-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/700/1/j/b/643/2'}