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lfunc_lfunctions • Show schema
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{'Lhash': '1928137738064516306136829881437', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.8660254037844386, 0.5], 'a4': [0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.8660254037844386, 0.5], 'a8': [0.0, 0.0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.48658838731717735, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8660254037844386, -0.5]]], [5, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [3, 5, 13], 'central_character': '975.224', 'coefficient_field': 'CDF', 'conductor': 975, 'conductor_radical': 195, 'conjugate': '1536611746796952970084433173395', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 1.0]], 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'4.79055650615339204695599332266938', '6.37849423142537571493175652619962', '6.70155950459184538073384470999716', '7.80075570257638120768927486492699', '8.178405054506312168667966082333992', '9.433451871263119959890824783465851', '10.60469753598795742320014688681198'], 'prelabel': '2-975-195.29-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6975588773122864, 'root_angle': 0.10037543095700005, 'root_number': '0.95069138442480817774633186569384 + 0.31013850386632356189045159219239*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.05018771547850002', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.52103248144036848421848201393', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70705884150658762051221679584', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.32327392488439021590355493003', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.48658838731717735, 'bad_primes': [3, 5, 13], 'central_character': '195.29', 'conductor': 975, 'conductor_radical': 195, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/975/1/y/a/224/1'], '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': '2-975-195.29-c0-0-0', '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': '2-975-195.29-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6975588773122864, 'root_angle': 0.050187715478500025, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.52103248144036848421848201393', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1928137738064516306136829881437', 'Lhash_array': ['1928137738064516306136829881437'], 'label': '2-975-195.29-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/975/1/y/a/224/1'}