Formats: - HTML - YAML - JSON - 2026-07-18T21:29:27.563243
  • lfunc_lfunctions • Show schema
    {'Lhash': '1010667028228164787635191293557', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0.5176380902050415], 'a6': [0, 0], 'a7': [0, 2.9216259830550255], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.394448407831774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '5184.5183', 'coefficient_field': 'CDF', 'conductor': 5184, 'conductor_radical': 6, 'conjugate': '800902612315765374481899009430', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -0.5176380902050415], [-5.0, 0]], [[1.0, 0], [0, -2.9216259830550255], [-7.0, 0]], [[1.0, 0], [5.6441479835800745, 0], [11.0, 0]], [[1.0, 0], [-4.464101615137754, 0], [13.0, 0]], [[1.0, 0], [0, 2.3107890345411484], [-17.0, 0]], [[1.0, 0], [0, 5.060404643364672], [-19.0, 0]], [[1.0, 0], 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[109.0, 0]], [[1.0, 0], [0, 12.108748005673862], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 46, 'label': '2-72e2-12.11-c1-0-46', 'leading_term': '1.7133317126079907743222750205043237413726699829178230310', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5184/2/c/k/5183/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.7133317126079908, 1.7262115410486165, 1.7212940979470446, 1.6986348118252896, 1.65823912211353, 1.6000991780631388, 1.5242425148762417, 1.43078933572698, 1.320014612911516, 1.1924110990041834, 1.0487494641495299, 0.890132084035038, 0.7180374281753867, 0.5343524837969287, 0.34139115740194786, 0.14189710191210322, -0.06097008574064336, -0.26366586209677606, -0.4623090070963673, -0.652746750932609, -0.8306358410465169, 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'3.66171535558394259181555704757011', '4.56189579245298916169170775440245', '5.23650988726559740201079683088856', '6.09217171359985984726576402692551', '6.75560389567321960486190357927763', '7.67383241047183906725797287929317', '8.156008792882300851463587321524714'], 'prelabel': '2-72e2-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.797275706765099965441842950747', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.73872165070198527161729450710', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01894209429748805524953379396', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 41.394448407831774, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 5184, 'conductor_radical': 6, 'degree': 2, 'index': 46, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5184/2/c/k/5183/6'], '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': '2-72e2-12.11-c1-0-46', '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': '2-72e2-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.433851755195466, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.797275706765099965441842950747', 'prec': 107}}
  • lfunc_instances • Show schema
    {'Lhash': '1010667028228164787635191293557', 'Lhash_array': ['1010667028228164787635191293557'], 'factors': ['2-72e2-12.11-c1-0-46'], 'label': '2-72e2-12.11-c1-0-46', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5184/2/c/k/5183/6'}