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lfunc_lfunctions • Show schema
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{'Lhash': '2002614459336245119662675267287', 'a10': [0.24426131172014454, -1.3852747363944298], 'a2': [-1.8178593375849845, 1.1956248950938677], 'a3': [0.0, 0.0], 'a4': [1.0829341493983826, -2.5105235458303614], 'a5': [-0.44365089668412294, 0.470242478014728], 'a6': [0.0, 0.0], 'a7': [1.8169698973364783, 0.2123733226928159], 'a8': [0.2773730249616682, 1.573060593717478], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.28', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '318774288879274669095313012157', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8178593375849845, -1.1956248950938677], [0.7921595320783137, -1.836432213760548]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.44365089668412294, -0.470242478014728], [-0.29072414455237916, 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'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57978425520067746160046752005', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.37210293768974581516236167295', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.04202759163170981427389325392', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '81.67', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/g/c/28/1'], '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': '2-3e6-81.67-c1-0-21', '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': '2-3e6-81.67-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.2205588254060444, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57978425520067746160046752005', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2002614459336245119662675267287', 'Lhash_array': ['2002614459336245119662675267287'], 'label': '2-3e6-81.67-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/g/c/28/1'}