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  • lfunc_lfunctions • Show schema
    {'Lhash': '1409787842482565922355298975151', 'a10': [261958202.43638283, 0], 'a2': [-670.61299823714, 0], 'a3': [-6561.0, 0], 'a4': [318649.79340460635, 0], 'a5': [-390625.0, 0], 'a6': [4399891.881433875, 0], 'a7': [-27080419.853429858, 0], 'a8': [-125792106.4377699, 0], 'a9': [43046721.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.48331310168397, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [6561.0, 0]]], [5, [[1.0, 0], [390625.0, 0]]]], 'bad_primes': [3, 5], 'central_character': '15.1', 'coefficient_field': 'CDF', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'euler_factors': [[[1.0, 0], [670.61299823714, 0], [131072.0, 0]], [[1.0, 0], [6561.0, 0]], [[1.0, 0], [390625.0, 0]], [[1.0, 0], [27080419.853429858, 0], [232630513987207.0, 0]], [[1.0, 0], [-1016437517.8280613, 0], [505447028499293760, 0]], [[1.0, 0], [1048341692.8712277, 0], [8650415919381338000, 0]], [[1.0, 0], 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'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c17-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11212651359037415654593838235', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.21676616608390694558560197309', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.34020726083234593095457565294', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 27.48331310168397, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/18/a/b/1/1'], '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': '2-15-1.1-c17-0-5', 'motivic_weight': 17, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [17], 'order_of_vanishing': 1, 'prelabel': '2-15-1.1-c17-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.242452966091729, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c17-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11212651359037415654593838235', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '1409787842482565922355298975151', 'Lhash_array': ['1409787842482565922355298975151'], 'factors': ['2-15-1.1-c17-0-5'], 'label': '2-15-1.1-c17-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/18/a/b/1/1'}