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  • lfunc_lfunctions • Show schema
    {'Lhash': '774663806132044161965181103632', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 2.0], 'a6': [0, 0], 'a7': [-4.0, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.697224203915887, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '2592.1297', 'coefficient_field': 'CDF', 'conductor': 2592, 'conductor_radical': 6, 'conjugate': '1084470483376523599930707172216', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -2.0], [-5.0, 0]], [[1.0, 0], [4.0, 0], [7.0, 0]], [[1.0, 0], [0, 3.0], [-11.0, 0]], [[1.0, 0], [0, 2.0], [-13.0, 0]], [[1.0, 0], [-5.0, 0], [17.0, 0]], [[1.0, 0], [0, -1.0], [-19.0, 0]], [[1.0, 0], [2.0, 0], [23.0, 0]], [[1.0, 0], [0, 0], [-29.0, 0]], [[1.0, 0], [-4.0, 0], [31.0, 0]], [[1.0, 0], [0, 2.0], [-37.0, 0]], [[1.0, 0], [5.0, 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0.28467951804364344, 0.21738722028301138, 0.09711453661715609, -0.05676676279747969, -0.22353080189526717, -0.38238430030873105, -0.5137485637362661, -0.6004635606583357, -0.6288447664692184, -0.5895312733963646, -0.47807503144211166, -0.29523541284732463, -0.046959815560659056, 0.25595116050963806, 0.5984773049985953, 0.9622770851220029, 1.3268008588766333], 'positive_zeros': ['0.61110199134727875348818370995092', '1.94371899044137482646927338356248', '3.12776852230276948505832194139704', '3.95713403100406123580054285921117', '4.87014942433607626347001482681120', '5.64813379326229438411499386793481', '6.58081543741336949721027823851221', '7.12344649649113331973845811093007', '8.114126714555162090223280194443052', '8.877039115066084812017234753564313'], 'prelabel': '2-2592-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.549420205247685, 'root_angle': -0.125, 'root_number': '0.707106781186547524400844362104849039284835937688474037 - 0.707106781186547524400844362104849039284835937688474037*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.125', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61110199134727875348818370995', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.94371899044137482646927338356', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.12776852230276948505832194140', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 20.697224203915887, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 2592, 'conductor_radical': 6, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2592/2/d/b/1297/2'], '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': '2-2592-8.5-c1-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-2592-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.549420205247685, 'root_angle': -0.125, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.61110199134727875348818370995', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '774663806132044161965181103632', 'Lhash_array': ['774663806132044161965181103632'], 'factors': ['2-2592-8.5-c1-0-15'], 'label': '2-2592-8.5-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2592/2/d/b/1297/2'}