-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '953067125324309954434323036594', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-5.001716715479061, 1.4081299294089862], 'a4': [0, 0], 'a5': [0, 5.866262100201537], 'a6': [0, 0], 'a7': [0, -5.921489338336924], 'a8': [0, 0], 'a9': [23.034340203805286, -14.086134010982553], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.656733442204406, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [5.001716715479061, -1.4081299294089862]]]], 'bad_primes': [2, 3], 'central_character': '384.383', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '937902315450207899462736249324', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [5.001716715479061, -1.4081299294089862]], [[1.0, 0], [0, -5.866262100201537], [-125.0, 0]], [[1.0, 0], [0, 5.921489338336924], [-343.0, 0]], [[1.0, 0], [27.965242493885324, 0], [1331.0, 0]], [[1.0, 0], [0.0653966772817355, 0], [2197.0, 0]], [[1.0, 0], [0, 36.967529157581076], [-4913.0, 0]], [[1.0, 0], [0, 30.769131903047995], [-6859.0, 0]], [[1.0, 0], [61.28637243610882, 0], [12167.0, 0]], [[1.0, 0], [0, -143.5658991324812], [-24389.0, 0]], [[1.0, 0], [0, 299.56838345619053], [-29791.0, 0]], [[1.0, 0], [-340.5589714810523, 0], [50653.0, 0]], [[1.0, 0], [0, -379.31504755705123], [-68921.0, 0]], [[1.0, 0], [0, -470.92604943856156], [-79507.0, 0]], [[1.0, 0], [-428.59319929911453, 0], [103823.0, 0]], [[1.0, 0], [0, 505.8679349681817], [-148877.0, 0]], [[1.0, 0], [-207.82698544841878, 0], [205379.0, 0]], [[1.0, 0], [-578.2206892335404, 0], [226981.0, 0]], [[1.0, 0], [0, -415.34952652535827], [-300763.0, 0]], [[1.0, 0], [-547.6688419995514, 0], [357911.0, 0]], [[1.0, 0], [-194.57160625731805, 0], [389017.0, 0]], [[1.0, 0], [0, 308.3743246090643], [-493039.0, 0]], [[1.0, 0], [62.30188302023228, 0], [571787.0, 0]], [[1.0, 0], [0, -1065.0125918741478], [-704969.0, 0]], [[1.0, 0], [-703.292790998324, 0], [912673.0, 0]], [[1.0, 0], [0, 942.5528653537306], [-1030301.0, 0]], [[1.0, 0], [0, 86.03164940971239], [-1092727.0, 0]], [[1.0, 0], [-688.0815008953562, 0], [1225043.0, 0]], [[1.0, 0], [1849.9371855669801, 0], [1295029.0, 0]], [[1.0, 0], [0, 1054.5411179471648], [-1442897.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 17, 'label': '2-384-12.11-c3-0-17', 'leading_term': '1.1718782103518244894644142558278401949153347109265236268', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/384/4/c/c/383/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 20}, 'plot_values': [1.1718782103518244, 1.1579400166281573, 1.1263732589225115, 1.0776278057539432, 1.012273500915185, 0.9310055078971698, 0.8346513279322234, 0.7241789693566137, 0.6007056557149082, 0.4655063902241866, 0.3200216467609393, 0.16586343354800007, 0.004818975650757973, -0.16114871387266877, -0.3299040573405036, -0.4991465441746821, -0.6664232942943547, -0.8291469661288013, -0.9846192936130115, -1.130060391533107, -1.2626438093083983, -1.379537142208863, -1.4779478290057955, -1.5551735795038015, -1.6086566881704434, -1.6360413055383147, -1.6352325620543435, -1.6044562748603013, -1.5423178221930691, -1.4478586484666156, -1.3206087714379997, -1.1606336068005159, -0.9685734103469019, -0.7456736681627614, -0.4938048449711403, -0.21547003251641247, 0.08620077477219765, 0.4074708106670306, 0.7440318175649814, 1.0910548801346154, 1.4432568334540405, 1.7949818486050138, 2.1402973536226426, 2.4731029867549212, 2.7872508146429253, 3.0766745941155547, 3.335525427646583, 3.5583107746161193, 3.7400334489907063, 3.8763269741804756, 3.9635834920481967, 3.9990703482641785, 3.9810315113021377, 3.908770135615589, 3.7827088560354136, 3.604424801682589, 3.3766568411872537, 3.103283209953582, 2.789268413379034, 2.4405791316499563, 2.0640697520217848, 1.6673390994048385, 1.2585608981878882, 0.8462914472965658, 0.43925889426752207, 0.04613931937089007, -0.324674445638025, -0.6653047696133654, -0.9686150534826111, -1.2284223512520744, -1.4396897115863911, -1.5986914255271196, -1.7031448614252593, -1.7523033039689702, -1.7470051810312714, -1.6896762417831355, -1.5842826150450013, -1.4362341925301871, -1.2522394039074443, -1.0401141290451021, -0.8085491714680453, -0.5668423362307181, -0.32460265352073325, -0.0914356051510619, 0.12338071383653562, 0.311217785351894, 0.4644060563228283, 0.5765203061847848, 0.6426301113099665, 0.6595052711710467, 0.6257672154832389, 0.5419789533389124, 0.4106680186095422, 0.23627905917730224, 0.025055144779027892, -0.21515054967061356, -0.4751283812166281, -0.7446242776641704, -1.0127007789543256, -1.2681354388169876, -1.499843037480614, -1.6973065771837497, -1.851001060926072, -1.9527936554692538, -1.9963040569784276, -1.9772097346243165, -1.89348222226724, -1.745542733568923, -1.5363280379435489, -1.2712606746564188, -0.9581210974876233, -0.6068231093895179, -0.22909782544627585, 0.16190475865869505, 0.552083874514278, 0.926909761837771, 1.271980340484921, 1.5735918574581742, 1.8193012199232754, 1.998457205115221, 2.1026781304318414, 2.1262548962658014, 2.0664605660842614, 1.9237507690339146, 1.701843106580258, 1.4076682856448275, 1.0511907220638737, 0.6451016675487686, 0.2043932972043462, -0.25417257317698855, -0.7126826200603626, -1.1527542291868325, -1.5562555954612562, -1.9060350606239285, -2.1866297351563517, -2.384923378287521, -2.4907247234627836, -2.4972399316535157, -2.4014165698804395, -2.2041413290384577, -1.9102794414439361, -1.5285502140018983, -1.071239996612428, -0.5537609662559783, 0.005928984243976023, 0.5880235216387865, 1.1716549096872235, 1.73573878736039, 2.2598413424499846, 2.725031698437103, 3.1146821139127994, 3.4151800542805675, 3.6165193200973667, 3.7127421125903246, 3.702210015580872, 3.5876891339246035, 3.3762427487446556, 3.078933475845678, 2.710345656935043, 2.287947166700316, 1.831317576192331, 1.3612762884642522, 0.8989495098246635, 0.4648184510290205, 0.07779275277966846, -0.24564732858072294, -0.4921989878501147, -0.6523387721727952, -0.7207483184482223, -0.6965419331088655, -0.583283257602805, -0.3887883099706776, -0.12472257459433364, 0.1939899770045678, 0.5499185229176702, 0.9240019192219623, 1.2965076200410657, 1.648025753246879, 1.9604486642768386, 2.2178862524357075, 2.407469957482641, 2.5200032401482337, 2.550423641670107, 2.498050686191586, 2.3666045789047017, 2.163992335187844, 1.901870068981657, 1.5950020522067396, 1.2604482050673498, 0.9166212901726618, 0.582262721116881, 0.2753911073822096, 0.01228010693547163, -0.1934783523911396, -0.3317729379632012, -0.3965877288360462, -0.38639588165322397, -0.30430628209837685, -0.1579502134936617, 0.040891025283379505, 0.27690243901914924, 0.5320667763513417, 0.786669805559209, 1.0204276135380663, 1.2136761535015503, 1.348558370498975, 1.4101427502996555, 1.3874092371999927, 1.2740441292254547, 1.0689945686977012, 0.776745196370466, 0.40729384978513455, -0.02418086313101132, -0.4979505301562455, -0.9906401989902357, -1.4763620592465605, -1.9280239294063657, -2.3187459165270434, -2.6233109879235994, -2.8195714636279785, -2.889733910121078, -2.8214496675850103, -2.608647116216507, -2.2520543894814002, -1.759376962895398, -1.1451125856904165, -0.43000542975678246, 0.35983894408645367, 1.1941372508468153, 2.039853122993131, 2.862790817386077, 3.6292755219362514, 4.307831614493509, 4.870768852707856, 5.295590081137294, 5.566142524729442, 5.673447710399896, 5.61616187126426, 5.400638459022435, 5.040586049859171, 4.556337279327318, 3.9737662203150026, 3.322911572403776, 2.6363799894449884, 1.947616815366772, 1.28913962067582, 0.6908326941909535, 0.17839780937416286, -0.22795176187901411, -0.5144804629260679, -0.6745472012414192, -0.7088151717010046, -0.6250437211073179, -0.4374754924650842, -0.16585577998914414, 0.16585727196307257, 0.5310145948995656], 'positive_zeros': ['0.75183739521972265520206074724686', '2.23258448020362551157766563034282', '4.07004975284969874845031916624699', '5.21330710773585461855209515368343', '5.88184649021317030496040757136820', '7.03673534725833083465586113198767', '8.028015519472578053772530532435709', '8.999354639095324571942889949856742', '10.26387055605048900766538799612907', '10.77556881635364858922387987692698'], 'prelabel': '2-384-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.759908974151124, 'root_angle': -0.08735259846669806, 'root_number': '0.9625808306973621771283817337969266022150702552755090938 - 0.2709947312660823171155987949429690948763245468123257602*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.04367629923334903', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.75183739521972265520206074725', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23258448020362551157766563034', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07004975284969874845031916625', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 22.656733442204406, 'bad_primes': [2, 3], 'central_character': '12.11', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/4/c/c/383/2'], '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': '2-384-12.11-c3-0-17', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-384-12.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.759908974151124, 'root_angle': -0.04367629923334903, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.75183739521972265520206074725', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '953067125324309954434323036594', 'Lhash_array': ['953067125324309954434323036594'], 'label': '2-384-12.11-c3-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/4/c/c/383/2'}