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lfunc_lfunctions • Show schema
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{'Lhash': '1945970864243298557336310994092', 'a10': [0.32851096180678385, 0.07785852820986944], 'a2': [0.12917676871884481, 0.03595881123693554], 'a3': [0.0, 0.0], 'a4': [-1.6969401975894647, -1.0241086562186095], 'a5': [2.51593468566391, -0.09762972368372963], 'a6': [0.0, 0.0], 'a7': [4.084532615793282, 0.6388092441545307], 'a8': [-0.3664134784023655, -0.38837559745676187], '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': '729.685', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '1407954254018799083063230061202', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.12917676871884481, -0.03595881123693554], [1.712333799060533, 1.0333987423037259]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.51593468566391, 0.09762972368372963], [4.98496470583896, 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'data': '0.108905958993', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53510033750068317411054984549', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68778828665969101427304520475', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50665261944917320018404642480', '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': '243.103', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/i/a/685/14'], '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': '2-3e6-243.103-c1-0-13', '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': '2-3e6-243.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.10890595899336074, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53510033750068317411054984549', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1945970864243298557336310994092', 'Lhash_array': ['1945970864243298557336310994092'], 'label': '2-3e6-243.103-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/i/a/685/14'}