-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1366593326984005036163648134543', 'a10': [-1.9208171880489648, 2.4635841003080876], 'a2': [-0.805572188010694, -2.4057540843743834], 'a3': [-0.15338331332198687, 0.08617294625947135], 'a4': [-3.5419915164321414, 2.671649140886162], 'a5': [-0.6803935473612767, -1.026257555891125], 'a6': [0.33087224874342025, 0.2995840036336754], 'a7': [1.034750234492019, 2.283337591618397], 'a8': [5.0969784873238115, 3.497856910405316], 'a9': [-1.544433486877594, 2.5357385392704788], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.849294518691866, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[983, [[1.0, 0], [-15.776830732919153, 27.094125046305106]]]], 'bad_primes': [983], 'central_character': '983.492', 'coefficient_field': 'CDF', 'conductor': 983, 'conductor_radical': 983, 'conjugate': '735887525483999716642617249796', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.805572188010694, 2.4057540843743834], [-1.5967146479555487, 1.2043680222441095]], [[1.0, 0], [0.15338331332198687, -0.08617294625947135], [1.560534151016187, -2.5621735233024694]], [[1.0, 0], [0.6803935473612767, 1.026257555891125], [-1.9466184226935204, 4.605505044664503]], [[1.0, 0], [-1.034750234492019, -2.283337591618397], [-4.6147191278294235, 5.26349383691529]], [[1.0, 0], [2.2993824981890456, -0.14732376896675645], [10.910057136717617, -1.4037995845408218]], [[1.0, 0], [-3.7341831946561066, 4.314545468037396], [-1.8650610942190307, -12.865517755412354]], [[1.0, 0], [-0.9752056188432826, -0.43070505666004844], [11.450461518245792, 12.56530664246489]], [[1.0, 0], [-0.8537924874892974, 0.6526101564448638], [4.986026180986206, -18.334108729974307]], [[1.0, 0], [0.3103451252742688, -2.928700077515952], [-22.489202943353245, -4.820347598739293]], [[1.0, 0], [2.972079305522514, 4.3012704166527875], [-10.256845295719327, 27.125580631199036]], [[1.0, 0], [-4.909839080110965, 7.303750851505164], [-11.702657041690953, -28.706233089079472]], [[1.0, 0], [-1.222240408726, -0.3031702310842904], [32.71095255068839, 17.291430919001844]], [[1.0, 0], [8.485233416402584, -0.7621211036732446], [40.34378708135564, -7.306082666808616]], [[1.0, 0], [-3.517136738891321, 4.82143412250374], [-13.13063512083356, -40.94614049362323]], [[1.0, 0], [-1.4036400831131433, 4.684443760788255], [-39.255681998055486, -25.84553019126407]], [[1.0, 0], [-1.185013747357161, -1.0868340843524755], [4.572332766481506, 52.80240309940978]], [[1.0, 0], [-8.339949197696166, 0.6416048329586951], [58.305731160038945, -9.024506296372325]], [[1.0, 0], [-1.43961153236026, 1.2219971018787832], [9.908543565782079, -60.18987260665202]], [[1.0, 0], [-3.8684876550542096, -3.3265392058293366], [10.036293422665729, 66.24403984008038]], [[1.0, 0], [3.4811641269365654, 2.8418066417602517], [14.213236951203863, 69.56280540180171]], [[1.0, 0], [3.8734879991751385, -2.7690651411696257], [23.621665701313056, -69.0725481613022]], [[1.0, 0], [-9.824313163385662, -1.4562954195117814], [75.60287033116114, 22.91737327203171]], [[1.0, 0], [2.8978100574094956, 0.8986929106691226], [68.43504363720105, 46.96429284439816]], [[1.0, 0], [2.231277761669643, -1.4690499265096313], [35.17361942307715, -81.75461147042734]], [[1.0, 0], [-2.473417389463371, -0.12671712377532254], [96.49214569927949, 9.91291169884105]], [[1.0, 0], [-0.7675123284234917, 0.55613112831565], [31.45645593962514, -95.97651473000269]], [[1.0, 0], [0.35890503054405787, -0.1396623354859595], [75.90863912349604, -69.61952676095153]], [[1.0, 0], [-0.797802899586187, -3.7811163571406254], [-97.8788768178778, 43.2287574754434]], [[1.0, 0], [-8.454739876785023, 10.025200484903921], [-18.39322167366047, -107.43690891152625]], [[1.0, 0], [-11.592859369021104, 5.661358620046525], [69.48108558498774, -89.11441379446767]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 35, 'label': '2-983-983.492-c1-0-35', '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/983/2/c/a/492/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.8100110076556409, 0.936405670862905, 1.0386547860872493, 1.107120326395221, 1.127215965413495, 1.0799574632601858, 0.9433973683712985, 0.6947658814479567, 0.31314611411315507, -0.21748897028084768, -0.9050911835140465, -1.7464868065276005, -2.724817804508146, -3.8078791162468635, -4.947757760493262, -6.082118944592921, -7.137355625466848, -8.033624512142195, -8.691547877795621, -9.04009262202224, -9.024881408946701, -8.615987230807999, -7.814154931718506, -6.654417323598839, -5.206252025713545, -3.569760031866928, -1.8678151003600754, -0.23468496885012974, 1.197811197418265, 2.3150569239044083, 3.033429266788375, 3.311170797782151, 3.1545966473825993, 2.618396761570053, 1.7995532722204242, 0.8253129490618827, -0.1633989250308315, -1.030920866334572, -1.6654194814677, -1.9942163861992774, -1.9933639331743382, -1.689758005884068, -1.1552351753465118, -0.49344085373761243, 0.1784543633102182, 0.7501143753392864, 1.1369020734663313, 1.293819127552454, 1.2218916892582719, 0.9657238286485987, 0.6026149670593502, 0.22532174324242946, -0.07810395677698381, -0.24325316327040902, -0.2430401513872611, -0.09306760533512076, 0.15269074819587225, 0.415172181540377, 0.6097053222410185, 0.6673711059920416, 0.5532602865072501, 0.27708240631373593, -0.10688874472862496, -0.5111947687511685, -0.8358665578639243, -0.993938543729253, -0.9357970890769225, -0.6661263153801251, -0.24848388869173182, 0.2048573562708073, 0.5567329191492605, 0.6779992266545691, 0.48222854187536623, -0.04632793085724263, -0.839255735162821, -1.7499630700860258, -2.579856339777858, -3.120528775255936, -3.203402501482119, -2.745521114109099, -1.7799245335209255, -0.46156479241062337, 0.9552990405088495, 2.1658301775133655, 2.880563139664738, 2.894686565111873, 2.144666817575449, 0.7377534618065439, -1.0549721464245336, -2.8435718493341113, -4.195049233069813, -4.72504091349581, -4.185707516976163, -2.5296882151925764, 0.06574854710404178, 3.2219737126878614, 6.42681133631017, 9.133688082222971, 10.87121569699422, 11.339218859500827, 10.4696749574179, 8.438634623221358, 5.62626699591762, 2.53412779573303, -0.32131284414653666, -2.5143942571465745, -3.791194275533377, -4.10790110151889, -3.6194573524497553, -2.6235481043780413, -1.4757884075639216, -0.4985353783765017, 0.09356105539290877, 0.23346530055500034, -0.000851383633127754, -0.42784761983549885, -0.828690130884619, -1.0182370342140887, -0.9002281195769879, -0.49161180657969195, 0.08948270372392214, 0.6667101304184319, 1.0649479672156144, 1.167208196225816, 0.9512944616019055, 0.49513530538584316, -0.050286397086291526, -0.511242629044313, -0.7483189168445257, -0.7016338181867858, -0.4094571048672618, 0.005933839442985538, 0.3806279359890914, 0.5657798042331056, 0.47974445603394, 0.1378976060863699, -0.3505392883001834, -0.8184927300503678, -1.0984906767062392, -1.0824234623430105, -0.7628151212877937, -0.2401646950130864, 0.3081588083460918, 0.6888635698061886, 0.7639068224331791, 0.507235131675388, 0.02549281252852522, -0.46819342567867034, -0.7229163095412837, -0.54158513740843, 0.13405100954515828, 1.1752813857693387, 2.276322683978352, 3.0262126290295486, 3.0266263681357843, 2.0227964224693475, 0.007027339070732504, -2.7411108537814046, -5.697411137636962, -8.214011289894632, -9.68971026831691, -9.743111033437478, -8.337583817049651, -5.817781926995017, -2.841052549682075, -0.21708214345894072, 1.3032951216458128, 1.2324922279338222, -0.5141818444662983, -3.5847895595891868, -7.274738047681241, -10.706738421173535, -13.057341911686986, -13.76715453933273, -12.676728632930025, -10.052030837261261, -6.495700311806076, -2.773237854526513, 0.39315926295232745, 2.5031910864639695, 3.3805585385949923, 3.175021886238211, 2.2722799252396593, 1.146976754660324, 0.20908687117566527, -0.3078867476755147, -0.3857362799375451, -0.18261719943332297, 0.06206196424202185, 0.13987227133425506, -0.039391780340409716, -0.41576626592436366, -0.8108398072537781, -1.0075671241907709, -0.8452668863280718, -0.29224061780633775, 0.5321571773535675, 1.3944680421505196, 2.0290150672002856, 2.2336521487713052, 1.9431669642520784, 1.252692333878348, 0.38247189956138355, -0.40244679958247137, -0.8869861075329853, -0.9793399187509194, -0.735329890908361, -0.3254474902976874, 0.04133687835820834, 0.20582678408876265, 0.1228084389763302, -0.12546647930983473, -0.37278990775933357, -0.4521679871630534, -0.2839019952463701, 0.07011956687221295, 0.4128111487594814, 0.4821688910214015, 0.061897716522777514, -0.9103812781967386, -2.283535328561549, -3.7131442684549527, -4.763817871062166, -5.0632499021169375, -4.4537985967265525, -3.082332832131541, -1.386400703160654, 0.03024847163366818, 0.5988972612355051, -0.0019213962865816591, -1.6992964895212446, -4.003252535282332, -6.128247640597549, -7.228925314107236, -6.677726585962727, -4.292387252163546, -0.4329184667708068, 4.072085575552509, 8.153885044003857, 10.817927346784996, 11.4440560581527, 9.974675976195806, 6.928446361065813, 3.2343474543264206, -0.05945408570041633, -2.1061823724875595, -2.5059763984392887, -1.398703510419488, 0.6206970180609416, 2.7287879085055935, 4.159956327336392, 4.45340109824772, 3.5796950976388495, 1.9114001358383468, 0.058312616308521276, -1.3658287417833506, -1.9581612436438793], 'positive_zeros': ['1.07805204899359639181296886453292', '3.39407473027739473009204536156262', '4.47870626924605759569453517856500', '5.46575203723212707818724853320848', '6.46281297064172369942425721067979', '6.92613331026135332422894836649513', '7.71714034074771098854512785861846', '8.567387225408221882524206994428709', '9.116353407926264915270726703086836', '10.16541340910437683774813942535913'], 'prelabel': '2-983-983.492-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8016592438574444, 'root_angle': 0.8649338811123425, 'root_number': '-0.9113177777826158 + 0.4117036651492853*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.432466940556', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07805204899359639181296886453', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.39407473027739473009204536156', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.47870626924605759569453517857', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.849294518691866, 'bad_primes': [983], 'central_character': '983.492', 'conductor': 983, 'conductor_radical': 983, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/983/2/c/a/492/6'], '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': '2-983-983.492-c1-0-35', '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': '2-983-983.492-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8016592438574444, 'root_angle': 0.43246694055617124, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07805204899359639181296886453', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1366593326984005036163648134543', 'Lhash_array': ['1366593326984005036163648134543'], 'label': '2-983-983.492-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/983/2/c/a/492/6'}