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lfunc_lfunctions • Show schema
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{'Lhash': '3303861397029721767140186794754', 'a10': [0.6689841613707391, -1.1587145569529769], 'a2': [0.5, 0.8660254037844386], 'a3': [-1.077434651784375, -0.6220571862419395], 'a4': [-0.5, 0.8660254037844386], 'a5': [-0.6689841613707391, -1.1587145569529769], 'a6': [-1.2304707631208883e-61, -1.244114372483879], 'a7': [-2.0953592982900484, 1.6153852206422579], 'a8': [-1.0, 0.0], 'a9': [-0.7260897140895219, -1.2576242756562117], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, -0.8660254037844386]]], [7, [[1.0, 0], [2.0953592982900484, -1.6153852206422579]]], [23, [[1.0, 0], [1.356753574852645, 4.599915188036032]]]], 'bad_primes': [2, 7, 23], 'central_character': '322.45', 'coefficient_field': 'CDF', 'conductor': 322, 'conductor_radical': 322, 'conjugate': '47518118488110072930734300647', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 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'9.832095011808870847606288443594479', '10.41669762110185673632389061015246', '10.80512695685898586069122698938058', '11.93964580860079001427594358595885'], 'prelabel': '2-322-161.45-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6034908621770283, 'root_angle': 0.8259685422071702, 'root_number': '-0.8542260552423042 + 0.5199017662454819*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.412984271104', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.60628709238562299731206157607', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.67821495906757859919396709099', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.08467736981552967891785917407', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.5711829450852295, 'bad_primes': [2, 7, 23], 'central_character': '161.45', 'conductor': 322, 'conductor_radical': 322, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/322/2/g/b/45/3'], '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': '2-322-161.45-c1-0-14', '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': '2-322-161.45-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.6034908621770283, 'root_angle': 0.4129842711035851, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.60628709238562299731206157607', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3303861397029721767140186794754', 'Lhash_array': ['3303861397029721767140186794754'], 'label': '2-322-161.45-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/322/2/g/b/45/3'}