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lfunc_lfunctions • Show schema
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{'Lhash': '3462440170404700179259639352364', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, -1.0], 'a4': [0.8660254037844386, -0.5], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.5, 0.8660254037844386], 'a8': [0.0, 0.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [7, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [0.8660254037844386, -0.5]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.206', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '2419167407462199615848636746541', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0, 1.0]], [[1.0, 0], [0.8660254037844386, -0.5]], [[1.0, 0], [0, 0], [0.5, 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['2.73138368709904615285565722031969', '3.75303998144454337047904639609941', '4.99547877614419799826341225902575', '6.40346037199099792192881583171090', '7.34422395005505103383706224488783', '8.430785080488699196297846898803082', '9.616580360163929324624946920287184', '10.53110970486695897649286361158173', '11.04032795834345718993695084373335', '12.21970123440303917988899681681636'], 'prelabel': '2-273-273.206-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.28069628826070836, 'root_number': '0.63573700373060376509821731310281 + 0.77190573393882383729925904721391*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.14034814413035415', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.73138368709904615285565722032', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.75303998144454337047904639610', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.99547877614419799826341225903', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.13624474844880965, 'bad_primes': [3, 7, 13], 'central_character': '273.206', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/1/ch/a/206/1'], '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': '2-273-273.206-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': '2-273-273.206-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.3691134628387451, 'root_angle': 0.14034814413035418, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.73138368709904615285565722032', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3462440170404700179259639352364', 'Lhash_array': ['3462440170404700179259639352364'], 'label': '2-273-273.206-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/1/ch/a/206/1'}