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lfunc_lfunctions • Show schema
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{'Lhash': '2433773496022571931442812886387', 'a10': [0, 0], 'a2': [0.8660254037844386, -1.118033988749895], 'a3': [0, 0], 'a4': [-0.5, -1.9364916731037085], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 0], 'a8': [-2.598076211353316, -1.118033988749895], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 14.373072363830476, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, 1.118033988749895]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.901', 'coefficient_field': 'CDF', 'conductor': 1800, 'conductor_radical': 30, 'conjugate': '373007995591707422494505156572', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 1.118033988749895]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [7.0, 0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [0, 0], [-13.0, 0]], [[1.0, 0], [6.928203230275509, 0], [17.0, 0]], [[1.0, 0], [0, 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'8.782163323088016888889263595809885', '9.444246884475609162091025842247475'], 'prelabel': '2-1800-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7911835043730706, 'root_angle': -0.8706459348827494, 'root_number': '-0.91855865354369178682398152801470927198723030524625129816 - 0.3952847075210474164998616930540898167149443924156521034*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.4353229674413747', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91990876317527266858473834235', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.18447596422298736151619903959', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05169193048543115347778490065', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 14.373072363830476, 'bad_primes': [2, 3, 5], 'central_character': '8.5', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'index': 88, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/2/k/l/901/3'], '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': '2-1800-8.5-c1-0-88', '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': '2-1800-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.7911835043730706, 'root_angle': -0.4353229674413747, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91990876317527266858473834235', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2433773496022571931442812886387', 'Lhash_array': ['2433773496022571931442812886387'], 'label': '2-1800-8.5-c1-0-88', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/2/k/l/901/3'}