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lfunc_lfunctions • Show schema
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{'Lhash': '1619055579677798731877951661402', 'a10': [0.16640380509173866, -0.28821984499168], 'a2': [-0.8660254037844386, -0.5], 'a3': [0.5, -0.8660254037844386], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, 0.3328076101834773], 'a6': [-0.8660254037844386, 0.5], 'a7': [-0.8660254037844386, 0.5], 'a8': [0.0, -1.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [0.8660254037844386, -0.5]]], [13, [[1.0, 0], [-3.41140175370102, -1.1671923898165226]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.43', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': '1382463282299526536939055418546', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8660254037844386, 0.5]], [[1.0, 0], [-0.5, 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'9.839699141875592161504024291141864', '10.83355609530452157101228701211977'], 'prelabel': '2-546-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.2675186558125451, 'root_number': '0.6671391082900575 + 0.7449331582027658*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.133759327906', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27720965018775831276361634425', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.14060414376862508795376117042', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15570252696066319005374244641', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '13.4', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/s/e/43/1'], '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': '2-546-13.4-c1-0-5', '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': '2-546-13.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.13375932790627254, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27720965018775831276361634425', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1619055579677798731877951661402', 'Lhash_array': ['1619055579677798731877951661402'], 'label': '2-546-13.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/s/e/43/1'}