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lfunc_lfunctions • Show schema
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{'Lhash': '1447686609048845636459940842974', 'a10': [-2.7637727822750784, 1.088529407486269], 'a2': [1.0881679556158201, 0.7619434053604462], 'a3': [0.0, 0.0], 'a4': [-0.08048853999449702, -0.22114044615975084], 'a5': [-1.2342560170984447, 1.8645675327690021], 'a6': [0.0, 0.0], 'a7': [0.8273884845538622, 1.7743403310756733], 'a8': [0.7685459252567244, -2.8682524410081283], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.233941281861857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.2342560170984447, -1.8645675327690021]]]], 'bad_primes': [3, 5], 'central_character': '405.152', 'coefficient_field': 'CDF', 'conductor': 405, 'conductor_radical': 15, 'conjugate': '2518699847735197523915872306343', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0881679556158201, -0.7619434053604462], [0.6840402866513374, 1.8793852415718169]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21835077454212939836865229133', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.95152895229891668958609516138', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.233941281861857, 'bad_primes': [3, 5], 'central_character': '135.122', 'conductor': 405, 'conductor_radical': 15, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/405/2/r/a/152/11'], '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': '2-405-135.122-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': '2-405-135.122-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7983162352216746, 'root_angle': -0.21301380592006733, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14202336889060938911935856744', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1447686609048845636459940842974', 'Lhash_array': ['1447686609048845636459940842974'], 'label': '2-405-135.122-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/405/2/r/a/152/11'}