Formats: - HTML - YAML - JSON - 2026-10-12T22:58:53.320327
  • lfunc_lfunctions • Show schema
    {'Lhash': '2154458898410256452634912658392', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.33987688662318255, 0], 'a4': [0, 0], 'a5': [0, 1.0], 'a6': [0, 0], 'a7': [0, -3.8844837019393323], 'a8': [0, 0], 'a9': [-2.8844837019393323, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.304441810213165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, -1.0]]], [13, [[1.0, 0], [-3.5446068153161496, -0.6601231133768174]]]], 'bad_primes': [2, 5, 13], 'central_character': '1040.961', 'coefficient_field': 'CDF', 'conductor': 1040, 'conductor_radical': 130, 'conjugate': '660290265166598155996998987627', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.33987688662318255, 0], [3.0, 0]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0, 3.8844837019393323], [-7.0, 0]], [[1.0, 0], [0, 1.5446068153161499], [-11.0, 0]], [[1.0, 0], [-3.5446068153161496, -0.6601231133768174]], [[1.0, 0], [0, 0], [17.0, 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'3.85488805321423240665942762690616', '5.22012886994153803640302637605604', '5.75462949637089191171937094613125', '6.60244552089941096674829127559365', '8.148569020855830695057358092831716', '8.373611855646889178885669053964284', '9.213573656538685710974718380341825', '9.973649897576247350732512345453349'], 'prelabel': '2-1040-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.881742842484937, 'root_angle': 0.27930421225946594, 'root_number': '-0.1830852102614649046637088585593014854438358845904199466 + 0.9830970479985763775661667155326375796162350427697048103*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.27930421225946594', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69956839686137881733068151461', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.79196807006025048337080165198', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.85488805321423240665942762691', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 8.304441810213165, 'bad_primes': [2, 5, 13], 'central_character': '13.12', 'conductor': 1040, 'conductor_radical': 130, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1040/2/k/c/961/4'], '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': '2-1040-13.12-c1-0-19', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1040-13.12-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.881742842484937, 'root_angle': 0.27930421225946594, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.69956839686137881733068151461', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2154458898410256452634912658392', 'Lhash_array': ['2154458898410256452634912658392'], 'factors': ['2-1040-13.12-c1-0-19'], 'label': '2-1040-13.12-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1040/2/k/c/961/4'}