Formats: - HTML - YAML - JSON - 2026-10-15T05:46:28.841991
  • lfunc_lfunctions • Show schema
    {'Lhash': '594447924130472204633908739388', 'a10': [0, 0], 'a2': [0, 1024.0], 'a3': [0, 194814.7372440774], 'a4': [-1048576.0, 0], 'a5': [0, 0], 'a6': [-199490290.93793526, 0], 'a7': [0, -963461401.883508], 'a8': [0, -1073741824.0], 'a9': [-27492428644.478916, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 139.73867214353106, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '10.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, -1024.0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 5], 'central_character': '50.49', 'coefficient_field': 'CDF', 'conductor': 50, 'conductor_radical': 10, 'conjugate': '1278186192314119650294936038476', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1024.0]], [[1.0, 0], [0, -194814.7372440774], [-10460353203.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 963461401.883508], [-558545864083284030, 0]], [[1.0, 0], [-61088185393.04714, 0], [7400249944258161000000, 0]], [[1.0, 0], [0, -52538268292.91086], [-247064529073450400000000, 0]], 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'6.21421893882950211177726046440082', '7.34273953035467541447688631624146', '8.498377351967123532740545818640206', '9.378191078775384167874399191673795', '11.39017850972601505305373646038413'], 'prelabel': '2-50-5.4-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.821111290548409, 'root_angle': 0.42620819117478337, 'root_number': '-0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42620819117478337', 'prec': 57}, 'spectral_label': 'c21-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46893672753631565036018035023', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.24326415165762654494283528632', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.39036132116305903645881987980', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 139.73867214353106, 'bad_primes': [2, 5], 'central_character': '5.4', 'conductor': 50, 'conductor_radical': 10, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/22/b/d/49/4'], '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': '2-50-5.4-c21-0-11', 'motivic_weight': 21, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [21], 'order_of_vanishing': 0, 'prelabel': '2-50-5.4-c21-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.821111290548409, 'root_angle': 0.42620819117478337, 'self_dual': False, 'spectral_label': 'c21-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46893672753631565036018035023', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '594447924130472204633908739388', 'Lhash_array': ['594447924130472204633908739388'], 'factors': ['2-50-5.4-c21-0-11'], 'label': '2-50-5.4-c21-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/22/b/d/49/4'}