Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,5,Mod(5,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 4]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.h (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.41120878177\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 5.6 | ||
Character | \(\chi\) | \(=\) | 33.5 |
Dual form | 33.5.h.a.20.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90239 | + | 0.618124i | −0.475598 | + | 0.154531i | −0.537000 | − | 0.843582i | \(-0.680443\pi\) |
0.0614026 | + | 0.998113i | \(0.480443\pi\) | |||||||
\(3\) | 1.59869 | − | 8.85687i | 0.177632 | − | 0.984097i | ||||
\(4\) | −9.70726 | + | 7.05274i | −0.606704 | + | 0.440796i | ||||
\(5\) | −8.40855 | − | 2.73210i | −0.336342 | − | 0.109284i | 0.135977 | − | 0.990712i | \(-0.456583\pi\) |
−0.472319 | + | 0.881428i | \(0.656583\pi\) | |||||||
\(6\) | 2.43332 | + | 17.8374i | 0.0675921 | + | 0.495484i | ||||
\(7\) | −61.9407 | + | 45.0026i | −1.26410 | + | 0.918420i | −0.998951 | − | 0.0457884i | \(-0.985420\pi\) |
−0.265146 | + | 0.964208i | \(0.585420\pi\) | |||||||
\(8\) | 32.9194 | − | 45.3097i | 0.514366 | − | 0.707964i | ||||
\(9\) | −75.8884 | − | 28.3188i | −0.936894 | − | 0.349614i | ||||
\(10\) | 17.6851 | 0.176851 | ||||||||
\(11\) | −110.634 | − | 49.0015i | −0.914330 | − | 0.404971i | ||||
\(12\) | 46.9463 | + | 97.2511i | 0.326016 | + | 0.675355i | ||||
\(13\) | −14.9141 | − | 45.9010i | −0.0882493 | − | 0.271603i | 0.897186 | − | 0.441652i | \(-0.145607\pi\) |
−0.985436 | + | 0.170049i | \(0.945607\pi\) | |||||||
\(14\) | 90.0183 | − | 123.900i | 0.459277 | − | 0.632141i | ||||
\(15\) | −37.6406 | + | 70.1057i | −0.167291 | + | 0.311581i | ||||
\(16\) | 24.7069 | − | 76.0400i | 0.0965113 | − | 0.297031i | ||||
\(17\) | 186.116 | + | 60.4726i | 0.643999 | + | 0.209248i | 0.612766 | − | 0.790264i | \(-0.290057\pi\) |
0.0312325 | + | 0.999512i | \(0.490057\pi\) | |||||||
\(18\) | 161.874 | + | 6.96491i | 0.499611 | + | 0.0214966i | ||||
\(19\) | 298.193 | + | 216.650i | 0.826020 | + | 0.600139i | 0.918430 | − | 0.395582i | \(-0.129457\pi\) |
−0.0924106 | + | 0.995721i | \(0.529457\pi\) | |||||||
\(20\) | 100.893 | − | 32.7821i | 0.252232 | − | 0.0819551i | ||||
\(21\) | 299.558 | + | 620.546i | 0.679270 | + | 1.40713i | ||||
\(22\) | 240.758 | + | 24.8345i | 0.497434 | + | 0.0513109i | ||||
\(23\) | − | 418.729i | − | 0.791548i | −0.918348 | − | 0.395774i | \(-0.870476\pi\) | ||
0.918348 | − | 0.395774i | \(-0.129524\pi\) | |||||||
\(24\) | −348.674 | − | 363.999i | −0.605337 | − | 0.631943i | ||||
\(25\) | −442.396 | − | 321.420i | −0.707834 | − | 0.514272i | ||||
\(26\) | 56.7450 | + | 78.1028i | 0.0839424 | + | 0.115537i | ||||
\(27\) | −372.138 | + | 626.861i | −0.510477 | + | 0.859891i | ||||
\(28\) | 283.883 | − | 873.703i | 0.362096 | − | 1.11442i | ||||
\(29\) | −798.795 | − | 1099.45i | −0.949816 | − | 1.30731i | −0.951609 | − | 0.307311i | \(-0.900571\pi\) |
0.00179349 | − | 0.999998i | \(-0.499429\pi\) | |||||||
\(30\) | 28.2730 | − | 156.635i | 0.0314145 | − | 0.174039i | ||||
\(31\) | 185.992 | + | 572.425i | 0.193540 | + | 0.595656i | 0.999991 | + | 0.00435377i | \(0.00138585\pi\) |
−0.806450 | + | 0.591302i | \(0.798614\pi\) | |||||||
\(32\) | 1056.02i | 1.03127i | ||||||||
\(33\) | −610.869 | + | 901.532i | −0.560945 | + | 0.827853i | ||||
\(34\) | −391.444 | −0.338620 | ||||||||
\(35\) | 643.784 | − | 209.178i | 0.525538 | − | 0.170758i | ||||
\(36\) | 936.393 | − | 260.323i | 0.722525 | − | 0.200867i | ||||
\(37\) | −1482.41 | + | 1077.03i | −1.08284 | + | 0.786728i | −0.978176 | − | 0.207779i | \(-0.933376\pi\) |
−0.104663 | + | 0.994508i | \(0.533376\pi\) | |||||||
\(38\) | −701.197 | − | 227.833i | −0.485593 | − | 0.157779i | ||||
\(39\) | −430.382 | + | 58.7112i | −0.282960 | + | 0.0386004i | ||||
\(40\) | −400.595 | + | 291.050i | −0.250372 | + | 0.181906i | ||||
\(41\) | 565.214 | − | 777.950i | 0.336237 | − | 0.462790i | −0.607101 | − | 0.794625i | \(-0.707668\pi\) |
0.943338 | + | 0.331835i | \(0.107668\pi\) | |||||||
\(42\) | −953.452 | − | 995.358i | −0.540505 | − | 0.564262i | ||||
\(43\) | 435.575 | 0.235573 | 0.117787 | − | 0.993039i | \(-0.462420\pi\) | ||||
0.117787 | + | 0.993039i | \(0.462420\pi\) | |||||||
\(44\) | 1419.55 | − | 304.602i | 0.733237 | − | 0.157336i | ||||
\(45\) | 560.742 | + | 445.455i | 0.276909 | + | 0.219978i | ||||
\(46\) | 258.827 | + | 796.587i | 0.122319 | + | 0.376459i | ||||
\(47\) | −501.345 | + | 690.043i | −0.226956 | + | 0.312378i | −0.907275 | − | 0.420538i | \(-0.861841\pi\) |
0.680319 | + | 0.732916i | \(0.261841\pi\) | |||||||
\(48\) | −633.978 | − | 340.390i | −0.275164 | − | 0.147739i | ||||
\(49\) | 1069.47 | − | 3291.50i | 0.445428 | − | 1.37089i | ||||
\(50\) | 1040.29 | + | 338.010i | 0.416115 | + | 0.135204i | ||||
\(51\) | 833.139 | − | 1551.73i | 0.320315 | − | 0.596588i | ||||
\(52\) | 468.503 | + | 340.387i | 0.173263 | + | 0.125883i | ||||
\(53\) | −4402.93 | + | 1430.60i | −1.56744 | + | 0.509292i | −0.958782 | − | 0.284143i | \(-0.908291\pi\) |
−0.608656 | + | 0.793434i | \(0.708291\pi\) | |||||||
\(54\) | 320.473 | − | 1422.56i | 0.109902 | − | 0.487847i | ||||
\(55\) | 796.394 | + | 714.295i | 0.263271 | + | 0.236130i | ||||
\(56\) | 4287.97i | 1.36734i | ||||||||
\(57\) | 2395.56 | − | 2294.70i | 0.737322 | − | 0.706280i | ||||
\(58\) | 2199.22 | + | 1597.82i | 0.653750 | + | 0.474977i | ||||
\(59\) | 2859.96 | + | 3936.40i | 0.821591 | + | 1.13082i | 0.989430 | + | 0.145009i | \(0.0463211\pi\) |
−0.167839 | + | 0.985814i | \(0.553679\pi\) | |||||||
\(60\) | −129.050 | − | 946.003i | −0.0358473 | − | 0.262779i | ||||
\(61\) | 25.0943 | − | 77.2324i | 0.00674398 | − | 0.0207558i | −0.947628 | − | 0.319377i | \(-0.896527\pi\) |
0.954372 | + | 0.298621i | \(0.0965265\pi\) | |||||||
\(62\) | −707.660 | − | 974.010i | −0.184095 | − | 0.253385i | ||||
\(63\) | 5975.00 | − | 1661.09i | 1.50542 | − | 0.418515i | ||||
\(64\) | −257.443 | − | 792.330i | −0.0628524 | − | 0.193440i | ||||
\(65\) | 426.708i | 0.100996i | ||||||||
\(66\) | 604.853 | − | 2092.66i | 0.138855 | − | 0.480409i | ||||
\(67\) | −4752.88 | −1.05878 | −0.529392 | − | 0.848377i | \(-0.677580\pi\) | ||||
−0.529392 | + | 0.848377i | \(0.677580\pi\) | |||||||
\(68\) | −2233.17 | + | 725.601i | −0.482952 | + | 0.156921i | ||||
\(69\) | −3708.63 | − | 669.418i | −0.778960 | − | 0.140604i | ||||
\(70\) | −1095.43 | + | 795.877i | −0.223557 | + | 0.162424i | ||||
\(71\) | −2773.95 | − | 901.311i | −0.550278 | − | 0.178796i | 0.0206643 | − | 0.999786i | \(-0.493422\pi\) |
−0.570942 | + | 0.820990i | \(0.693422\pi\) | |||||||
\(72\) | −3781.32 | + | 2506.24i | −0.729420 | + | 0.483457i | ||||
\(73\) | 5417.24 | − | 3935.86i | 1.01656 | − | 0.738573i | 0.0509845 | − | 0.998699i | \(-0.483764\pi\) |
0.965575 | + | 0.260126i | \(0.0837641\pi\) | |||||||
\(74\) | 2154.38 | − | 2965.25i | 0.393422 | − | 0.541499i | ||||
\(75\) | −3554.03 | + | 3404.40i | −0.631827 | + | 0.605226i | ||||
\(76\) | −4422.61 | −0.765688 | ||||||||
\(77\) | 9057.94 | − | 1943.62i | 1.52773 | − | 0.327816i | ||||
\(78\) | 782.465 | − | 377.721i | 0.128610 | − | 0.0620844i | ||||
\(79\) | 1039.38 | + | 3198.89i | 0.166541 | + | 0.512561i | 0.999147 | − | 0.0413058i | \(-0.0131518\pi\) |
−0.832605 | + | 0.553867i | \(0.813152\pi\) | |||||||
\(80\) | −415.498 | + | 571.885i | −0.0649216 | + | 0.0893570i | ||||
\(81\) | 4957.09 | + | 4298.13i | 0.755540 | + | 0.655103i | ||||
\(82\) | −594.388 | + | 1829.34i | −0.0883980 | + | 0.272061i | ||||
\(83\) | −7327.31 | − | 2380.79i | −1.06362 | − | 0.345592i | −0.275623 | − | 0.961266i | \(-0.588884\pi\) |
−0.788001 | + | 0.615673i | \(0.788884\pi\) | |||||||
\(84\) | −7284.44 | − | 3911.10i | −1.03237 | − | 0.554294i | ||||
\(85\) | −1399.75 | − | 1016.97i | −0.193736 | − | 0.140758i | ||||
\(86\) | −828.634 | + | 269.240i | −0.112038 | + | 0.0364034i | ||||
\(87\) | −11014.7 | + | 5317.15i | −1.45524 | + | 0.702491i | ||||
\(88\) | −5862.24 | + | 3399.69i | −0.757005 | + | 0.439009i | ||||
\(89\) | − | 8408.03i | − | 1.06149i | −0.847533 | − | 0.530743i | \(-0.821913\pi\) | ||
0.847533 | − | 0.530743i | \(-0.178087\pi\) | |||||||
\(90\) | −1342.10 | − | 500.821i | −0.165691 | − | 0.0618298i | ||||
\(91\) | 2989.46 | + | 2171.97i | 0.361002 | + | 0.262283i | ||||
\(92\) | 2953.19 | + | 4064.71i | 0.348911 | + | 0.480235i | ||||
\(93\) | 5367.24 | − | 732.180i | 0.620562 | − | 0.0846548i | ||||
\(94\) | 527.223 | − | 1622.63i | 0.0596676 | − | 0.183638i | ||||
\(95\) | −1915.46 | − | 2636.41i | −0.212240 | − | 0.292123i | ||||
\(96\) | 9353.06 | + | 1688.25i | 1.01487 | + | 0.183187i | ||||
\(97\) | −3234.39 | − | 9954.42i | −0.343755 | − | 1.05797i | −0.962247 | − | 0.272177i | \(-0.912256\pi\) |
0.618493 | − | 0.785791i | \(-0.287744\pi\) | |||||||
\(98\) | 6922.79i | 0.720823i | ||||||||
\(99\) | 7008.17 | + | 6851.66i | 0.715046 | + | 0.699077i | ||||
\(100\) | 6561.34 | 0.656134 | ||||||||
\(101\) | −3450.32 | + | 1121.08i | −0.338234 | + | 0.109899i | −0.473209 | − | 0.880950i | \(-0.656904\pi\) |
0.134975 | + | 0.990849i | \(0.456904\pi\) | |||||||
\(102\) | −625.798 | + | 3466.97i | −0.0601497 | + | 0.333235i | ||||
\(103\) | −81.4085 | + | 59.1467i | −0.00767353 | + | 0.00557515i | −0.591615 | − | 0.806220i | \(-0.701510\pi\) |
0.583942 | + | 0.811795i | \(0.301510\pi\) | |||||||
\(104\) | −2570.72 | − | 835.279i | −0.237678 | − | 0.0772262i | ||||
\(105\) | −823.453 | − | 6036.32i | −0.0746896 | − | 0.547512i | ||||
\(106\) | 7491.81 | − | 5443.12i | 0.666769 | − | 0.484436i | ||||
\(107\) | 7150.63 | − | 9842.00i | 0.624564 | − | 0.859639i | −0.373111 | − | 0.927787i | \(-0.621709\pi\) |
0.997675 | + | 0.0681480i | \(0.0217090\pi\) | |||||||
\(108\) | −808.648 | − | 8709.69i | −0.0693285 | − | 0.746715i | ||||
\(109\) | 8190.72 | 0.689396 | 0.344698 | − | 0.938714i | \(-0.387981\pi\) | ||||
0.344698 | + | 0.938714i | \(0.387981\pi\) | |||||||
\(110\) | −1956.58 | − | 866.598i | −0.161700 | − | 0.0716196i | ||||
\(111\) | 7169.22 | + | 14851.3i | 0.581870 | + | 1.20537i | ||||
\(112\) | 1891.63 | + | 5821.85i | 0.150800 | + | 0.464114i | ||||
\(113\) | 9803.67 | − | 13493.6i | 0.767772 | − | 1.05675i | −0.228756 | − | 0.973484i | \(-0.573466\pi\) |
0.996528 | − | 0.0832631i | \(-0.0265342\pi\) | |||||||
\(114\) | −3138.88 | + | 5846.18i | −0.241527 | + | 0.449844i | ||||
\(115\) | −1144.01 | + | 3520.91i | −0.0865037 | + | 0.266231i | ||||
\(116\) | 15508.2 | + | 5038.93i | 1.15251 | + | 0.374474i | ||||
\(117\) | −168.050 | + | 3905.70i | −0.0122763 | + | 0.285317i | ||||
\(118\) | −7873.94 | − | 5720.75i | −0.565494 | − | 0.410856i | ||||
\(119\) | −14249.6 | + | 4629.96i | −1.00625 | + | 0.326952i | ||||
\(120\) | 1937.36 | + | 4013.32i | 0.134539 | + | 0.278703i | ||||
\(121\) | 9838.71 | + | 10842.4i | 0.671997 | + | 0.740554i | ||||
\(122\) | 162.438i | 0.0109136i | ||||||||
\(123\) | −5986.61 | − | 6249.73i | −0.395704 | − | 0.413096i | ||||
\(124\) | −5842.64 | − | 4244.92i | −0.379984 | − | 0.276075i | ||||
\(125\) | 6089.74 | + | 8381.81i | 0.389744 | + | 0.536436i | ||||
\(126\) | −10340.0 | + | 6853.33i | −0.651299 | + | 0.431679i | ||||
\(127\) | −2258.08 | + | 6949.67i | −0.140001 | + | 0.430880i | −0.996334 | − | 0.0855440i | \(-0.972737\pi\) |
0.856333 | + | 0.516424i | \(0.172737\pi\) | |||||||
\(128\) | −8951.92 | − | 12321.3i | −0.546382 | − | 0.752030i | ||||
\(129\) | 696.349 | − | 3857.83i | 0.0418454 | − | 0.231827i | ||||
\(130\) | −263.759 | − | 811.765i | −0.0156070 | − | 0.0480335i | ||||
\(131\) | − | 5121.14i | − | 0.298417i | −0.988806 | − | 0.149209i | \(-0.952327\pi\) | ||
0.988806 | − | 0.149209i | \(-0.0476726\pi\) | |||||||
\(132\) | −428.406 | − | 13059.7i | −0.0245871 | − | 0.749524i | ||||
\(133\) | −28220.1 | −1.59535 | ||||||||
\(134\) | 9041.84 | − | 2937.87i | 0.503555 | − | 0.163615i | ||||
\(135\) | 4841.79 | − | 4254.27i | 0.265667 | − | 0.233431i | ||||
\(136\) | 8866.81 | − | 6442.12i | 0.479391 | − | 0.348298i | ||||
\(137\) | −23223.8 | − | 7545.87i | −1.23735 | − | 0.402039i | −0.383977 | − | 0.923342i | \(-0.625446\pi\) |
−0.853371 | + | 0.521303i | \(0.825446\pi\) | |||||||
\(138\) | 7469.05 | − | 1018.90i | 0.392200 | − | 0.0535025i | ||||
\(139\) | −15222.8 | + | 11060.0i | −0.787886 | + | 0.572433i | −0.907335 | − | 0.420407i | \(-0.861887\pi\) |
0.119449 | + | 0.992840i | \(0.461887\pi\) | |||||||
\(140\) | −4774.10 | + | 6570.98i | −0.243576 | + | 0.335254i | ||||
\(141\) | 5310.13 | + | 5543.52i | 0.267096 | + | 0.278835i | ||||
\(142\) | 5834.26 | 0.289340 | ||||||||
\(143\) | −599.207 | + | 5809.02i | −0.0293025 | + | 0.284074i | ||||
\(144\) | −4028.33 | + | 5070.88i | −0.194267 | + | 0.244545i | ||||
\(145\) | 3712.91 | + | 11427.1i | 0.176595 | + | 0.543503i | ||||
\(146\) | −7872.87 | + | 10836.1i | −0.369341 | + | 0.508354i | ||||
\(147\) | −27442.6 | − | 14734.3i | −1.26996 | − | 0.681858i | ||||
\(148\) | 6794.08 | − | 20910.0i | 0.310175 | − | 0.954622i | ||||
\(149\) | 4470.47 | + | 1452.54i | 0.201363 | + | 0.0654270i | 0.407962 | − | 0.912999i | \(-0.366239\pi\) |
−0.206599 | + | 0.978426i | \(0.566239\pi\) | |||||||
\(150\) | 4656.81 | − | 8673.33i | 0.206969 | − | 0.385481i | ||||
\(151\) | 17521.9 | + | 12730.4i | 0.768472 | + | 0.558327i | 0.901497 | − | 0.432785i | \(-0.142469\pi\) |
−0.133025 | + | 0.991113i | \(0.542469\pi\) | |||||||
\(152\) | 19632.7 | − | 6379.05i | 0.849753 | − | 0.276101i | ||||
\(153\) | −12411.5 | − | 9859.74i | −0.530202 | − | 0.421194i | ||||
\(154\) | −16030.3 | + | 9296.46i | −0.675929 | + | 0.391991i | ||||
\(155\) | − | 5321.42i | − | 0.221495i | ||||||
\(156\) | 3763.76 | − | 3605.30i | 0.154658 | − | 0.148147i | ||||
\(157\) | −31060.1 | − | 22566.5i | −1.26010 | − | 0.915515i | −0.261335 | − | 0.965248i | \(-0.584163\pi\) |
−0.998763 | + | 0.0497336i | \(0.984163\pi\) | |||||||
\(158\) | −3954.63 | − | 5443.08i | −0.158413 | − | 0.218037i | ||||
\(159\) | 5631.72 | + | 41283.3i | 0.222765 | + | 1.63298i | ||||
\(160\) | 2885.17 | − | 8879.63i | 0.112702 | − | 0.346860i | ||||
\(161\) | 18843.9 | + | 25936.4i | 0.726974 | + | 1.00059i | ||||
\(162\) | −12087.1 | − | 5112.63i | −0.460567 | − | 0.194811i | ||||
\(163\) | 4852.05 | + | 14933.1i | 0.182621 | + | 0.562048i | 0.999899 | − | 0.0141943i | \(-0.00451834\pi\) |
−0.817279 | + | 0.576243i | \(0.804518\pi\) | |||||||
\(164\) | 11538.1i | 0.428988i | ||||||||
\(165\) | 7599.60 | − | 5911.62i | 0.279141 | − | 0.217140i | ||||
\(166\) | 15411.0 | 0.559262 | ||||||||
\(167\) | 7682.69 | − | 2496.26i | 0.275474 | − | 0.0895069i | −0.168022 | − | 0.985783i | \(-0.553738\pi\) |
0.443496 | + | 0.896276i | \(0.353738\pi\) | |||||||
\(168\) | 37978.0 | + | 6855.14i | 1.34559 | + | 0.242883i | ||||
\(169\) | 21221.9 | − | 15418.6i | 0.743036 | − | 0.539848i | ||||
\(170\) | 3291.48 | + | 1069.47i | 0.113892 | + | 0.0370058i | ||||
\(171\) | −16494.1 | − | 24885.7i | −0.564076 | − | 0.851055i | ||||
\(172\) | −4228.24 | + | 3072.00i | −0.142923 | + | 0.103840i | ||||
\(173\) | −34883.7 | + | 48013.2i | −1.16555 | + | 1.60424i | −0.477354 | + | 0.878711i | \(0.658404\pi\) |
−0.688194 | + | 0.725527i | \(0.741596\pi\) | |||||||
\(174\) | 17667.6 | − | 16923.8i | 0.583551 | − | 0.558982i | ||||
\(175\) | 41867.1 | 1.36709 | ||||||||
\(176\) | −6459.49 | + | 7201.93i | −0.208532 | + | 0.232500i | ||||
\(177\) | 39436.3 | − | 19037.2i | 1.25878 | − | 0.607655i | ||||
\(178\) | 5197.21 | + | 15995.4i | 0.164033 | + | 0.504840i | ||||
\(179\) | −22061.1 | + | 30364.5i | −0.688527 | + | 0.947676i | −0.999997 | − | 0.00258020i | \(-0.999179\pi\) |
0.311470 | + | 0.950256i | \(0.399179\pi\) | |||||||
\(180\) | −8584.94 | − | 369.382i | −0.264967 | − | 0.0114007i | ||||
\(181\) | 17565.3 | − | 54060.5i | 0.536165 | − | 1.65015i | −0.204952 | − | 0.978772i | \(-0.565704\pi\) |
0.741117 | − | 0.671375i | \(-0.234296\pi\) | |||||||
\(182\) | −7029.66 | − | 2284.07i | −0.212223 | − | 0.0689553i | ||||
\(183\) | −643.920 | − | 345.728i | −0.0192278 | − | 0.0103236i | ||||
\(184\) | −18972.5 | − | 13784.3i | −0.560388 | − | 0.407145i | ||||
\(185\) | 15407.5 | − | 5006.18i | 0.450181 | − | 0.146273i | ||||
\(186\) | −9758.01 | + | 4710.51i | −0.282056 | + | 0.136158i | ||||
\(187\) | −17627.4 | − | 15810.3i | −0.504088 | − | 0.452122i | ||||
\(188\) | − | 10234.3i | − | 0.289562i | ||||||
\(189\) | −5159.88 | − | 55575.4i | −0.144449 | − | 1.55582i | ||||
\(190\) | 5273.59 | + | 3831.49i | 0.146083 | + | 0.106135i | ||||
\(191\) | −9331.90 | − | 12844.3i | −0.255802 | − | 0.352081i | 0.661731 | − | 0.749741i | \(-0.269822\pi\) |
−0.917533 | + | 0.397661i | \(0.869822\pi\) | |||||||
\(192\) | −7429.13 | + | 1013.46i | −0.201528 | + | 0.0274917i | ||||
\(193\) | −12545.1 | + | 38610.0i | −0.336791 | + | 1.03654i | 0.629042 | + | 0.777372i | \(0.283447\pi\) |
−0.965833 | + | 0.259165i | \(0.916553\pi\) | |||||||
\(194\) | 12306.1 | + | 16937.9i | 0.326978 | + | 0.450046i | ||||
\(195\) | 3779.30 | + | 682.173i | 0.0993898 | + | 0.0179401i | ||||
\(196\) | 12832.4 | + | 39494.1i | 0.334039 | + | 1.02806i | ||||
\(197\) | − | 50990.1i | − | 1.31387i | −0.753946 | − | 0.656937i | \(-0.771852\pi\) | ||
0.753946 | − | 0.656937i | \(-0.228148\pi\) | |||||||
\(198\) | −17567.5 | − | 8702.62i | −0.448104 | − | 0.221983i | ||||
\(199\) | −21330.1 | −0.538626 | −0.269313 | − | 0.963053i | \(-0.586797\pi\) | ||||
−0.269313 | + | 0.963053i | \(0.586797\pi\) | |||||||
\(200\) | −29126.8 | + | 9463.89i | −0.728171 | + | 0.236597i | ||||
\(201\) | −7598.38 | + | 42095.7i | −0.188074 | + | 1.04195i | ||||
\(202\) | 5870.89 | − | 4265.45i | 0.143880 | − | 0.104535i | ||||
\(203\) | 98955.9 | + | 32152.7i | 2.40132 | + | 0.780235i | ||||
\(204\) | 2856.41 | + | 20938.9i | 0.0686373 | + | 0.503146i | ||||
\(205\) | −6878.07 | + | 4997.21i | −0.163666 | + | 0.118910i | ||||
\(206\) | 118.311 | − | 162.841i | 0.00278798 | − | 0.00383733i | ||||
\(207\) | −11857.9 | + | 31776.7i | −0.276737 | + | 0.741597i | ||||
\(208\) | −3858.79 | −0.0891918 | ||||||||
\(209\) | −22374.1 | − | 38580.7i | −0.512216 | − | 0.883238i | ||||
\(210\) | 5297.73 | + | 10974.4i | 0.120130 | + | 0.248854i | ||||
\(211\) | 4989.98 | + | 15357.6i | 0.112082 | + | 0.344951i | 0.991327 | − | 0.131417i | \(-0.0419528\pi\) |
−0.879246 | + | 0.476369i | \(0.841953\pi\) | |||||||
\(212\) | 32650.8 | − | 44939.9i | 0.726477 | − | 0.999909i | ||||
\(213\) | −12417.5 | + | 23127.6i | −0.273700 | + | 0.509767i | ||||
\(214\) | −7519.72 | + | 23143.3i | −0.164200 | + | 0.505357i | ||||
\(215\) | −3662.56 | − | 1190.04i | −0.0792332 | − | 0.0257444i | ||||
\(216\) | 16152.3 | + | 37497.3i | 0.346200 | + | 0.803698i | ||||
\(217\) | −37281.1 | − | 27086.3i | −0.791716 | − | 0.575215i | ||||
\(218\) | −15582.0 | + | 5062.88i | −0.327875 | + | 0.106533i | ||||
\(219\) | −26198.9 | − | 54272.1i | −0.546254 | − | 1.13159i | ||||
\(220\) | −12768.5 | − | 1317.09i | −0.263813 | − | 0.0272126i | ||||
\(221\) | − | 9444.79i | − | 0.193378i | ||||||
\(222\) | −22818.6 | − | 23821.6i | −0.463003 | − | 0.483353i | ||||
\(223\) | 5124.27 | + | 3723.00i | 0.103044 | + | 0.0748657i | 0.638114 | − | 0.769942i | \(-0.279715\pi\) |
−0.535070 | + | 0.844808i | \(0.679715\pi\) | |||||||
\(224\) | −47523.8 | − | 65410.9i | −0.947142 | − | 1.30363i | ||||
\(225\) | 24470.5 | + | 36920.1i | 0.483368 | + | 0.729287i | ||||
\(226\) | −10309.7 | + | 31730.0i | −0.201850 | + | 0.621231i | ||||
\(227\) | 27590.5 | + | 37975.1i | 0.535437 | + | 0.736966i | 0.987947 | − | 0.154794i | \(-0.0494713\pi\) |
−0.452510 | + | 0.891759i | \(0.649471\pi\) | |||||||
\(228\) | −7070.38 | + | 39170.5i | −0.136011 | + | 0.753511i | ||||
\(229\) | −1507.91 | − | 4640.88i | −0.0287545 | − | 0.0884972i | 0.935649 | − | 0.352931i | \(-0.114815\pi\) |
−0.964404 | + | 0.264434i | \(0.914815\pi\) | |||||||
\(230\) | − | 7405.28i | − | 0.139986i | ||||||
\(231\) | −2733.60 | − | 83332.2i | −0.0512284 | − | 1.56167i | ||||
\(232\) | −76111.5 | −1.41408 | ||||||||
\(233\) | −29024.2 | + | 9430.53i | −0.534624 | + | 0.173710i | −0.563872 | − | 0.825862i | \(-0.690689\pi\) |
0.0292480 | + | 0.999572i | \(0.490689\pi\) | |||||||
\(234\) | −2094.51 | − | 7534.05i | −0.0382518 | − | 0.137593i | ||||
\(235\) | 6100.86 | − | 4432.53i | 0.110473 | − | 0.0802632i | ||||
\(236\) | −55524.7 | − | 18041.1i | −0.996925 | − | 0.323920i | ||||
\(237\) | 29993.8 | − | 4091.65i | 0.533993 | − | 0.0728453i | ||||
\(238\) | 24246.4 | − | 17616.0i | 0.428048 | − | 0.310995i | ||||
\(239\) | −4803.61 | + | 6611.60i | −0.0840954 | + | 0.115747i | −0.848992 | − | 0.528406i | \(-0.822790\pi\) |
0.764897 | + | 0.644153i | \(0.222790\pi\) | |||||||
\(240\) | 4400.86 | + | 4594.28i | 0.0764038 | + | 0.0797619i | ||||
\(241\) | 71328.7 | 1.22809 | 0.614045 | − | 0.789271i | \(-0.289541\pi\) | ||||
0.614045 | + | 0.789271i | \(0.289541\pi\) | |||||||
\(242\) | −25419.1 | − | 14545.0i | −0.434039 | − | 0.248361i | ||||
\(243\) | 45992.9 | − | 37033.0i | 0.778893 | − | 0.627157i | ||||
\(244\) | 301.103 | + | 926.699i | 0.00505749 | + | 0.0155653i | ||||
\(245\) | −17985.4 | + | 24754.8i | −0.299633 | + | 0.412409i | ||||
\(246\) | 15252.0 | + | 8188.96i | 0.252032 | + | 0.135319i | ||||
\(247\) | 5497.16 | − | 16918.5i | 0.0901040 | − | 0.277312i | ||||
\(248\) | 32059.2 | + | 10416.7i | 0.521253 | + | 0.169365i | ||||
\(249\) | −32800.4 | + | 61090.9i | −0.529030 | + | 0.985321i | ||||
\(250\) | −16766.1 | − | 12181.3i | −0.268257 | − | 0.194900i | ||||
\(251\) | 90729.5 | − | 29479.8i | 1.44013 | − | 0.467926i | 0.518191 | − | 0.855265i | \(-0.326606\pi\) |
0.921937 | + | 0.387339i | \(0.126606\pi\) | |||||||
\(252\) | −46285.7 | + | 58264.7i | −0.728862 | + | 0.917497i | ||||
\(253\) | −20518.3 | + | 46325.6i | −0.320554 | + | 0.723736i | ||||
\(254\) | − | 14616.8i | − | 0.226560i | ||||||
\(255\) | −11245.0 | + | 10771.5i | −0.172933 | + | 0.165652i | ||||
\(256\) | 35430.1 | + | 25741.5i | 0.540620 | + | 0.392783i | ||||
\(257\) | 6159.31 | + | 8477.57i | 0.0932537 | + | 0.128353i | 0.853094 | − | 0.521757i | \(-0.174723\pi\) |
−0.759841 | + | 0.650109i | \(0.774723\pi\) | |||||||
\(258\) | 1059.89 | + | 7769.54i | 0.0159229 | + | 0.116723i | ||||
\(259\) | 43352.2 | − | 133424.i | 0.646266 | − | 1.98900i | ||||
\(260\) | −3009.46 | − | 4142.16i | −0.0445186 | − | 0.0612746i | ||||
\(261\) | 29484.3 | + | 106056.i | 0.432822 | + | 1.55688i | ||||
\(262\) | 3165.50 | + | 9742.41i | 0.0461148 | + | 0.141927i | ||||
\(263\) | − | 30267.6i | − | 0.437589i | −0.975771 | − | 0.218795i | \(-0.929788\pi\) | ||
0.975771 | − | 0.218795i | \(-0.0702124\pi\) | |||||||
\(264\) | 20738.7 | + | 57356.2i | 0.297559 | + | 0.822948i | ||||
\(265\) | 40930.8 | 0.582853 | ||||||||
\(266\) | 53685.7 | − | 17443.5i | 0.758744 | − | 0.246531i | ||||
\(267\) | −74468.9 | − | 13441.8i | −1.04461 | − | 0.188554i | ||||
\(268\) | 46137.4 | − | 33520.8i | 0.642368 | − | 0.466708i | ||||
\(269\) | 16179.4 | + | 5257.01i | 0.223593 | + | 0.0726498i | 0.418671 | − | 0.908138i | \(-0.362496\pi\) |
−0.195078 | + | 0.980788i | \(0.562496\pi\) | |||||||
\(270\) | −6581.31 | + | 11086.1i | −0.0902785 | + | 0.152073i | ||||
\(271\) | −7999.25 | + | 5811.79i | −0.108921 | + | 0.0791355i | −0.640912 | − | 0.767614i | \(-0.721444\pi\) |
0.531992 | + | 0.846750i | \(0.321444\pi\) | |||||||
\(272\) | 9196.68 | − | 12658.1i | 0.124306 | − | 0.171093i | ||||
\(273\) | 24016.0 | − | 23004.9i | 0.322238 | − | 0.308671i | ||||
\(274\) | 48845.0 | 0.650608 | ||||||||
\(275\) | 33194.0 | + | 57238.0i | 0.438929 | + | 0.756866i | ||||
\(276\) | 40721.9 | − | 19657.8i | 0.534576 | − | 0.258057i | ||||
\(277\) | 41862.4 | + | 128839.i | 0.545588 | + | 1.67915i | 0.719587 | + | 0.694402i | \(0.244331\pi\) |
−0.173999 | + | 0.984746i | \(0.555669\pi\) | |||||||
\(278\) | 22123.2 | − | 30450.0i | 0.286258 | − | 0.394001i | ||||
\(279\) | 2095.73 | − | 48707.5i | 0.0269232 | − | 0.625731i | ||||
\(280\) | 11715.2 | − | 36055.7i | 0.149428 | − | 0.459894i | ||||
\(281\) | −74585.3 | − | 24234.2i | −0.944584 | − | 0.306914i | −0.204071 | − | 0.978956i | \(-0.565417\pi\) |
−0.740513 | + | 0.672042i | \(0.765417\pi\) | |||||||
\(282\) | −13528.5 | − | 7263.62i | −0.170119 | − | 0.0913387i | ||||
\(283\) | −123739. | − | 89901.9i | −1.54502 | − | 1.12253i | −0.947085 | − | 0.320983i | \(-0.895987\pi\) |
−0.597938 | − | 0.801542i | \(-0.704013\pi\) | |||||||
\(284\) | 33284.2 | − | 10814.7i | 0.412668 | − | 0.134084i | ||||
\(285\) | −26412.6 | + | 12750.2i | −0.325178 | + | 0.156974i | ||||
\(286\) | −2450.77 | − | 11421.4i | −0.0299620 | − | 0.139633i | ||||
\(287\) | 73622.9i | 0.893818i | ||||||||
\(288\) | 29905.3 | − | 80139.9i | 0.360548 | − | 0.966193i | ||||
\(289\) | −36587.8 | − | 26582.6i | −0.438067 | − | 0.318275i | ||||
\(290\) | −14126.8 | − | 19443.9i | −0.167976 | − | 0.231199i | ||||
\(291\) | −93335.8 | + | 12732.5i | −1.10220 | + | 0.150359i | ||||
\(292\) | −24828.0 | + | 76412.8i | −0.291190 | + | 0.896190i | ||||
\(293\) | −54108.1 | − | 74473.4i | −0.630271 | − | 0.867493i | 0.367779 | − | 0.929913i | \(-0.380118\pi\) |
−0.998050 | + | 0.0624198i | \(0.980118\pi\) | |||||||
\(294\) | 61314.2 | + | 11067.4i | 0.709360 | + | 0.128041i | ||||
\(295\) | −13293.5 | − | 40913.1i | −0.152755 | − | 0.470130i | ||||
\(296\) | 102623.i | 1.17128i | ||||||||
\(297\) | 71888.1 | − | 51116.8i | 0.814975 | − | 0.579496i | ||||
\(298\) | −9402.44 | −0.105879 | ||||||||
\(299\) | −19220.1 | + | 6244.98i | −0.214987 | + | 0.0698536i | ||||
\(300\) | 10489.5 | − | 58113.0i | 0.116550 | − | 0.645700i | ||||
\(301\) | −26979.8 | + | 19602.0i | −0.297787 | + | 0.216355i | ||||
\(302\) | −41202.5 | − | 13387.5i | −0.451762 | − | 0.146786i | ||||
\(303\) | 4413.25 | + | 32351.3i | 0.0480699 | + | 0.352376i | ||||
\(304\) | 23841.5 | − | 17321.9i | 0.257980 | − | 0.187434i | ||||
\(305\) | −422.014 | + | 580.852i | −0.00453657 | + | 0.00624405i | ||||
\(306\) | 29706.1 | + | 11085.2i | 0.317251 | + | 0.118386i | ||||
\(307\) | 7448.66 | 0.0790317 | 0.0395158 | − | 0.999219i | \(-0.487418\pi\) | ||||
0.0395158 | + | 0.999219i | \(0.487418\pi\) | |||||||
\(308\) | −74219.9 | + | 82750.5i | −0.782382 | + | 0.872306i | ||||
\(309\) | 393.708 | + | 815.582i | 0.00412342 | + | 0.00854182i | ||||
\(310\) | 3289.30 | + | 10123.4i | 0.0342279 | + | 0.105343i | ||||
\(311\) | −28270.6 | + | 38911.1i | −0.292290 | + | 0.402302i | −0.929756 | − | 0.368176i | \(-0.879982\pi\) |
0.637466 | + | 0.770478i | \(0.279982\pi\) | |||||||
\(312\) | −11507.7 | + | 21433.2i | −0.118217 | + | 0.220180i | ||||
\(313\) | −29513.7 | + | 90833.7i | −0.301255 | + | 0.927168i | 0.679793 | + | 0.733404i | \(0.262070\pi\) |
−0.981048 | + | 0.193764i | \(0.937930\pi\) | |||||||
\(314\) | 73037.5 | + | 23731.3i | 0.740775 | + | 0.240692i | ||||
\(315\) | −54779.4 | − | 2356.98i | −0.552072 | − | 0.0237539i | ||||
\(316\) | −32650.5 | − | 23722.0i | −0.326976 | − | 0.237562i | ||||
\(317\) | −69953.7 | + | 22729.3i | −0.696132 | + | 0.226187i | −0.635645 | − | 0.771982i | \(-0.719266\pi\) |
−0.0604878 | + | 0.998169i | \(0.519266\pi\) | |||||||
\(318\) | −36232.0 | − | 75055.9i | −0.358292 | − | 0.742216i | ||||
\(319\) | 34499.3 | + | 160778.i | 0.339023 | + | 1.57996i | ||||
\(320\) | 7365.71i | 0.0719307i | ||||||||
\(321\) | −75737.7 | − | 79066.6i | −0.735025 | − | 0.767331i | ||||
\(322\) | −51880.4 | − | 37693.3i | −0.500370 | − | 0.363540i | ||||
\(323\) | 42397.0 | + | 58354.5i | 0.406378 | + | 0.559331i | ||||
\(324\) | −78433.4 | − | 6761.99i | −0.747155 | − | 0.0644146i | ||||
\(325\) | −8155.52 | + | 25100.1i | −0.0772121 | + | 0.237634i | ||||
\(326\) | −18461.0 | − | 25409.4i | −0.173708 | − | 0.239088i | ||||
\(327\) | 13094.4 | − | 72544.2i | 0.122459 | − | 0.678433i | ||||
\(328\) | −16642.2 | − | 51219.3i | −0.154690 | − | 0.476087i | ||||
\(329\) | − | 65303.6i | − | 0.603317i | ||||||
\(330\) | −10803.3 | + | 15943.7i | −0.0992039 | + | 0.146407i | ||||
\(331\) | −157185. | −1.43468 | −0.717338 | − | 0.696725i | \(-0.754640\pi\) | ||||
−0.717338 | + | 0.696725i | \(0.754640\pi\) | |||||||
\(332\) | 87919.1 | − | 28566.7i | 0.797640 | − | 0.259169i | ||||
\(333\) | 142998. | − | 39754.2i | 1.28956 | − | 0.358505i | ||||
\(334\) | −13072.5 | + | 9497.72i | −0.117183 | + | 0.0851385i | ||||
\(335\) | 39964.9 | + | 12985.4i | 0.356114 | + | 0.115708i | ||||
\(336\) | 54587.5 | − | 7446.63i | 0.483520 | − | 0.0659601i | ||||
\(337\) | 28576.2 | − | 20761.8i | 0.251620 | − | 0.182812i | −0.454825 | − | 0.890581i | \(-0.650298\pi\) |
0.706444 | + | 0.707769i | \(0.250298\pi\) | |||||||
\(338\) | −30841.7 | + | 42449.9i | −0.269963 | + | 0.371573i | ||||
\(339\) | −103838. | − | 108402.i | −0.903561 | − | 0.943274i | ||||
\(340\) | 20760.1 | 0.179586 | ||||||||
\(341\) | 7472.63 | − | 72443.5i | 0.0642636 | − | 0.623004i | ||||
\(342\) | 46760.8 | + | 37146.9i | 0.399788 | + | 0.317592i | ||||
\(343\) | 25076.2 | + | 77176.5i | 0.213144 | + | 0.655989i | ||||
\(344\) | 14338.9 | − | 19735.8i | 0.121171 | − | 0.166777i | ||||
\(345\) | 29355.3 | + | 15761.2i | 0.246631 | + | 0.132419i | ||||
\(346\) | 36684.2 | − | 112902.i | 0.306427 | − | 0.943086i | ||||
\(347\) | −50710.8 | − | 16476.9i | −0.421155 | − | 0.136841i | 0.0907698 | − | 0.995872i | \(-0.471067\pi\) |
−0.511925 | + | 0.859030i | \(0.671067\pi\) | |||||||
\(348\) | 69421.9 | − | 129299.i | 0.573242 | − | 1.06767i | ||||
\(349\) | 177310. | + | 128823.i | 1.45573 | + | 1.05765i | 0.984449 | + | 0.175669i | \(0.0562087\pi\) |
0.471282 | + | 0.881982i | \(0.343791\pi\) | |||||||
\(350\) | −79647.5 | + | 25879.1i | −0.650184 | + | 0.211258i | ||||
\(351\) | 34323.6 | + | 7732.40i | 0.278599 | + | 0.0627625i | ||||
\(352\) | 51746.7 | − | 116832.i | 0.417635 | − | 0.942923i | ||||
\(353\) | 129570.i | 1.03981i | 0.854223 | + | 0.519907i | \(0.174033\pi\) | ||||
−0.854223 | + | 0.519907i | \(0.825967\pi\) | |||||||
\(354\) | −63256.0 | + | 60592.8i | −0.504772 | + | 0.483520i | ||||
\(355\) | 20862.4 | + | 15157.4i | 0.165542 | + | 0.120273i | ||||
\(356\) | 59299.6 | + | 81618.9i | 0.467899 | + | 0.644007i | ||||
\(357\) | 18226.4 | + | 133608.i | 0.143009 | + | 1.04833i | ||||
\(358\) | 23199.8 | − | 71401.6i | 0.181016 | − | 0.557111i | ||||
\(359\) | 55233.2 | + | 76022.0i | 0.428560 | + | 0.589862i | 0.967622 | − | 0.252404i | \(-0.0812212\pi\) |
−0.539062 | + | 0.842266i | \(0.681221\pi\) | |||||||
\(360\) | 38642.7 | − | 10742.9i | 0.298169 | − | 0.0828929i | ||||
\(361\) | 1710.54 | + | 5264.50i | 0.0131256 | + | 0.0403964i | ||||
\(362\) | 113702.i | 0.867661i | ||||||||
\(363\) | 111759. | − | 69806.5i | 0.848145 | − | 0.529764i | ||||
\(364\) | −44337.7 | −0.334634 | ||||||||
\(365\) | −56304.4 | + | 18294.4i | −0.422626 | + | 0.137320i | ||||
\(366\) | 1438.69 | + | 259.687i | 0.0107400 | + | 0.00193860i | ||||
\(367\) | 37721.7 | − | 27406.4i | 0.280065 | − | 0.203479i | −0.438881 | − | 0.898545i | \(-0.644625\pi\) |
0.718946 | + | 0.695066i | \(0.244625\pi\) | |||||||
\(368\) | −31840.2 | − | 10345.5i | −0.235115 | − | 0.0763934i | ||||
\(369\) | −64923.8 | + | 43031.2i | −0.476816 | + | 0.316032i | ||||
\(370\) | −26216.6 | + | 19047.4i | −0.191502 | + | 0.139134i | ||||
\(371\) | 208340. | − | 286756.i | 1.51365 | − | 2.08336i | ||||
\(372\) | −46937.3 | + | 44961.2i | −0.339182 | + | 0.324902i | ||||
\(373\) | −68598.7 | −0.493059 | −0.246529 | − | 0.969135i | \(-0.579290\pi\) | ||||
−0.246529 | + | 0.969135i | \(0.579290\pi\) | |||||||
\(374\) | 43307.0 | + | 19181.3i | 0.309610 | + | 0.137131i | ||||
\(375\) | 83972.2 | − | 40536.2i | 0.597136 | − | 0.288257i | ||||
\(376\) | 14761.6 | + | 45431.6i | 0.104414 | + | 0.321353i | ||||
\(377\) | −38552.4 | + | 53062.8i | −0.271249 | + | 0.373342i | ||||
\(378\) | 44168.6 | + | 102537.i | 0.309122 | + | 0.717622i | ||||
\(379\) | 74805.3 | − | 230227.i | 0.520779 | − | 1.60279i | −0.251735 | − | 0.967796i | \(-0.581001\pi\) |
0.772514 | − | 0.634998i | \(-0.218999\pi\) | |||||||
\(380\) | 37187.8 | + | 12083.0i | 0.257533 | + | 0.0836776i | ||||
\(381\) | 57942.3 | + | 31109.9i | 0.399159 | + | 0.214313i | ||||
\(382\) | 25692.3 | + | 18666.5i | 0.176066 | + | 0.127920i | ||||
\(383\) | −189408. | + | 61542.4i | −1.29122 | + | 0.419543i | −0.872519 | − | 0.488580i | \(-0.837515\pi\) |
−0.418702 | + | 0.908124i | \(0.637515\pi\) | |||||||
\(384\) | −123439. | + | 59588.2i | −0.837126 | + | 0.404108i | ||||
\(385\) | −81474.3 | − | 8404.17i | −0.549667 | − | 0.0566987i | ||||
\(386\) | − | 81205.7i | − | 0.545019i | ||||||
\(387\) | −33055.1 | − | 12334.9i | −0.220707 | − | 0.0823598i | ||||
\(388\) | 101603. | + | 73818.8i | 0.674905 | + | 0.490347i | ||||
\(389\) | 50459.2 | + | 69451.1i | 0.333458 | + | 0.458965i | 0.942516 | − | 0.334160i | \(-0.108453\pi\) |
−0.609059 | + | 0.793125i | \(0.708453\pi\) | |||||||
\(390\) | −7611.37 | + | 1038.32i | −0.0500419 | + | 0.00682653i | ||||
\(391\) | 25321.7 | − | 77932.0i | 0.165630 | − | 0.509756i | ||||
\(392\) | −113930. | − | 156812.i | −0.741425 | − | 1.02048i | ||||
\(393\) | −45357.3 | − | 8187.11i | −0.293672 | − | 0.0530085i | ||||
\(394\) | 31518.2 | + | 97003.2i | 0.203034 | + | 0.624875i | ||||
\(395\) | − | 29737.8i | − | 0.190596i | ||||||
\(396\) | −116353. | − | 17084.1i | −0.741971 | − | 0.108943i | ||||
\(397\) | 86041.5 | 0.545917 | 0.272959 | − | 0.962026i | \(-0.411998\pi\) | ||||
0.272959 | + | 0.962026i | \(0.411998\pi\) | |||||||
\(398\) | 40578.3 | − | 13184.7i | 0.256169 | − | 0.0832345i | ||||
\(399\) | −45115.2 | + | 249942.i | −0.283385 | + | 1.56998i | ||||
\(400\) | −35371.0 | + | 25698.5i | −0.221069 | + | 0.160616i | ||||
\(401\) | 32573.5 | + | 10583.8i | 0.202571 | + | 0.0658192i | 0.408545 | − | 0.912738i | \(-0.366036\pi\) |
−0.205974 | + | 0.978557i | \(0.566036\pi\) | |||||||
\(402\) | −11565.3 | − | 84779.2i | −0.0715655 | − | 0.524611i | ||||
\(403\) | 23501.0 | − | 17074.5i | 0.144702 | − | 0.105132i | ||||
\(404\) | 25586.5 | − | 35216.8i | 0.156765 | − | 0.215768i | ||||
\(405\) | −29939.1 | − | 49684.4i | −0.182527 | − | 0.302907i | ||||
\(406\) | −208127. | −1.26263 | ||||||||
\(407\) | 216780. | − | 46516.1i | 1.30867 | − | 0.280811i | ||||
\(408\) | −42881.7 | − | 88831.2i | −0.257604 | − | 0.533636i | ||||
\(409\) | −48365.8 | − | 148854.i | −0.289129 | − | 0.889847i | −0.985131 | − | 0.171807i | \(-0.945039\pi\) |
0.696002 | − | 0.718040i | \(-0.254961\pi\) | |||||||
\(410\) | 9995.89 | − | 13758.2i | 0.0594639 | − | 0.0818451i | ||||
\(411\) | −103960. | + | 193627.i | −0.615438 | + | 1.14626i | ||||
\(412\) | 373.107 | − | 1148.30i | 0.00219806 | − | 0.00676492i | ||||
\(413\) | −354296. | − | 115118.i | −2.07714 | − | 0.674904i | ||||
\(414\) | 2916.41 | − | 67781.3i | 0.0170156 | − | 0.395466i | ||||
\(415\) | 55107.5 | + | 40037.9i | 0.319974 | + | 0.232475i | ||||
\(416\) | 48472.5 | − | 15749.7i | 0.280097 | − | 0.0910091i | ||||
\(417\) | 73620.4 | + | 152507.i | 0.423376 | + | 0.877039i | ||||
\(418\) | 66412.0 | + | 59565.7i | 0.380097 | + | 0.340913i | ||||
\(419\) | − | 182960.i | − | 1.04215i | −0.853512 | − | 0.521074i | \(-0.825532\pi\) | ||
0.853512 | − | 0.521074i | \(-0.174468\pi\) | |||||||
\(420\) | 50566.0 | + | 52788.5i | 0.286656 | + | 0.299255i | ||||
\(421\) | −171519. | − | 124616.i | −0.967714 | − | 0.703085i | −0.0127844 | − | 0.999918i | \(-0.504070\pi\) |
−0.954929 | + | 0.296833i | \(0.904070\pi\) | |||||||
\(422\) | −18985.8 | − | 26131.7i | −0.106611 | − | 0.146738i | ||||
\(423\) | 57587.5 | − | 38168.8i | 0.321845 | − | 0.213318i | ||||
\(424\) | −80122.0 | + | 246590.i | −0.445677 | + | 1.37165i | ||||
\(425\) | −62899.8 | − | 86574.1i | −0.348234 | − | 0.479303i | ||||
\(426\) | 9327.17 | − | 51673.3i | 0.0513961 | − | 0.284739i | ||||
\(427\) | 1921.30 | + | 5913.14i | 0.0105375 | + | 0.0324312i | ||||
\(428\) | 145970.i | 0.796851i | ||||||||
\(429\) | 50491.8 | + | 14593.9i | 0.274351 | + | 0.0792971i | ||||
\(430\) | 7703.21 | 0.0416615 | ||||||||
\(431\) | 1120.42 | − | 364.046i | 0.00603150 | − | 0.00195975i | −0.306000 | − | 0.952032i | \(-0.598991\pi\) |
0.312031 | + | 0.950072i | \(0.398991\pi\) | |||||||
\(432\) | 38472.1 | + | 43785.1i | 0.206148 | + | 0.234617i | ||||
\(433\) | −114896. | + | 83476.7i | −0.612813 | + | 0.445235i | −0.850404 | − | 0.526130i | \(-0.823642\pi\) |
0.237590 | + | 0.971365i | \(0.423642\pi\) | |||||||
\(434\) | 87666.0 | + | 28484.4i | 0.465427 | + | 0.151226i | ||||
\(435\) | 107145. | − | 14616.3i | 0.566229 | − | 0.0772429i | ||||
\(436\) | −79509.4 | + | 57767.0i | −0.418259 | + | 0.303883i | ||||
\(437\) | 90717.7 | − | 124862.i | 0.475039 | − | 0.653835i | ||||
\(438\) | 83387.4 | + | 87052.5i | 0.434663 | + | 0.453767i | ||||
\(439\) | 32159.2 | 0.166869 | 0.0834345 | − | 0.996513i | \(-0.473411\pi\) | ||||
0.0834345 | + | 0.996513i | \(0.473411\pi\) | |||||||
\(440\) | 58581.3 | − | 12570.2i | 0.302589 | − | 0.0649286i | ||||
\(441\) | −174372. | + | 219500.i | −0.896601 | + | 1.12865i | ||||
\(442\) | 5838.05 | + | 17967.7i | 0.0298830 | + | 0.0919703i | ||||
\(443\) | 42413.4 | − | 58377.1i | 0.216120 | − | 0.297464i | −0.687168 | − | 0.726499i | \(-0.741146\pi\) |
0.903288 | + | 0.429035i | \(0.141146\pi\) | |||||||
\(444\) | −174336. | − | 93603.0i | −0.884343 | − | 0.474814i | ||||
\(445\) | −22971.6 | + | 70699.4i | −0.116004 | + | 0.357022i | ||||
\(446\) | −12049.6 | − | 3915.16i | −0.0605765 | − | 0.0196825i | ||||
\(447\) | 20011.9 | − | 37272.2i | 0.100155 | − | 0.186539i | ||||
\(448\) | 51603.1 | + | 37491.9i | 0.257111 | + | 0.186802i | ||||
\(449\) | 15527.1 | − | 5045.05i | 0.0770188 | − | 0.0250249i | −0.270254 | − | 0.962789i | \(-0.587108\pi\) |
0.347273 | + | 0.937764i | \(0.387108\pi\) | |||||||
\(450\) | −69373.8 | − | 55110.7i | −0.342586 | − | 0.272152i | ||||
\(451\) | −100653. | + | 58371.4i | −0.494848 | + | 0.286977i | ||||
\(452\) | 200129.i | 0.979563i | ||||||||
\(453\) | 140764. | − | 134837.i | 0.685953 | − | 0.657074i | ||||
\(454\) | −75961.3 | − | 55189.1i | −0.368537 | − | 0.267758i | ||||
\(455\) | −19203.0 | − | 26430.6i | −0.0927567 | − | 0.127669i | ||||
\(456\) | −25111.8 | − | 184082.i | −0.120767 | − | 0.885284i | ||||
\(457\) | 4962.48 | − | 15272.9i | 0.0237611 | − | 0.0731291i | −0.938473 | − | 0.345353i | \(-0.887759\pi\) |
0.962234 | + | 0.272224i | \(0.0877592\pi\) | |||||||
\(458\) | 5737.28 | + | 7896.69i | 0.0273511 | + | 0.0376456i | ||||
\(459\) | −107169. | + | 94164.5i | −0.508677 | + | 0.446953i | ||||
\(460\) | −13726.8 | − | 42246.8i | −0.0648715 | − | 0.199654i | ||||
\(461\) | − | 131582.i | − | 0.619150i | −0.950875 | − | 0.309575i | \(-0.899813\pi\) | ||
0.950875 | − | 0.309575i | \(-0.100187\pi\) | |||||||
\(462\) | 56710.1 | + | 156841.i | 0.265691 | + | 0.734810i | ||||
\(463\) | 84383.7 | 0.393638 | 0.196819 | − | 0.980440i | \(-0.436939\pi\) | ||||
0.196819 | + | 0.980440i | \(0.436939\pi\) | |||||||
\(464\) | −103338. | + | 33576.5i | −0.479980 | + | 0.155955i | ||||
\(465\) | −47131.1 | − | 8507.29i | −0.217973 | − | 0.0393446i | ||||
\(466\) | 49386.1 | − | 35881.1i | 0.227422 | − | 0.165232i | ||||
\(467\) | −214194. | − | 69595.9i | −0.982140 | − | 0.319117i | −0.226433 | − | 0.974027i | \(-0.572707\pi\) |
−0.755707 | + | 0.654910i | \(0.772707\pi\) | |||||||
\(468\) | −25914.6 | − | 39098.9i | −0.118318 | − | 0.178514i | ||||
\(469\) | 294397. | − | 213892.i | 1.33841 | − | 0.972409i | ||||
\(470\) | −8866.36 | + | 12203.5i | −0.0401375 | + | 0.0552445i | ||||
\(471\) | −249524. | + | 239019.i | −1.12479 | + | 1.07743i | ||||
\(472\) | 272505. | 1.22318 | ||||||||
\(473\) | −48189.4 | − | 21343.8i | −0.215392 | − | 0.0954003i | ||||
\(474\) | −54530.8 | + | 26323.8i | −0.242709 | + | 0.117164i | ||||
\(475\) | −62284.0 | − | 191690.i | −0.276051 | − | 0.849597i | ||||
\(476\) | 105670. | − | 145443.i | 0.466379 | − | 0.641916i | ||||
\(477\) | 374644. | + | 16119.7i | 1.64658 | + | 0.0708470i | ||||
\(478\) | 5051.55 | − | 15547.1i | 0.0221090 | − | 0.0680445i | ||||
\(479\) | 408867. | + | 132849.i | 1.78201 | + | 0.579012i | 0.999072 | − | 0.0430814i | \(-0.0137175\pi\) |
0.782943 | + | 0.622093i | \(0.213717\pi\) | |||||||
\(480\) | −74033.3 | − | 39749.3i | −0.321325 | − | 0.172523i | ||||
\(481\) | 71545.6 | + | 51980.9i | 0.309238 | + | 0.224675i | ||||
\(482\) | −135695. | + | 44090.0i | −0.584077 | + | 0.189778i | ||||
\(483\) | 259841. | − | 125434.i | 1.11382 | − | 0.537675i | ||||
\(484\) | −171976. | − | 35860.6i | −0.734136 | − | 0.153083i | ||||
\(485\) | 92538.9i | 0.393406i | ||||||||
\(486\) | −64605.4 | + | 98880.5i | −0.273525 | + | 0.418638i | ||||
\(487\) | 257205. | + | 186870.i | 1.08448 | + | 0.787921i | 0.978459 | − | 0.206443i | \(-0.0661889\pi\) |
0.106021 | + | 0.994364i | \(0.466189\pi\) | |||||||
\(488\) | −2673.29 | − | 3679.46i | −0.0112255 | − | 0.0154506i | ||||
\(489\) | 140017. | − | 19100.6i | 0.585549 | − | 0.0798785i | ||||
\(490\) | 18913.8 | − | 58210.6i | 0.0787746 | − | 0.242443i | ||||
\(491\) | 75938.8 | + | 104521.i | 0.314993 | + | 0.433550i | 0.936930 | − | 0.349517i | \(-0.113654\pi\) |
−0.621937 | + | 0.783067i | \(0.713654\pi\) | |||||||
\(492\) | 102191. | + | 18445.8i | 0.422166 | + | 0.0762021i | ||||
\(493\) | −82181.8 | − | 252930.i | −0.338128 | − | 1.04065i | ||||
\(494\) | 35583.6i | 0.145813i | ||||||||
\(495\) | −40209.1 | − | 76759.6i | −0.164102 | − | 0.313272i | ||||
\(496\) | 48122.5 | 0.195607 | ||||||||
\(497\) | 212382. | − | 69007.0i | 0.859814 | − | 0.279371i | ||||
\(498\) | 24637.4 | − | 136494.i | 0.0993429 | − | 0.550368i | ||||
\(499\) | −143629. | + | 104352.i | −0.576819 | + | 0.419084i | −0.837576 | − | 0.546321i | \(-0.816028\pi\) |
0.260757 | + | 0.965405i | \(0.416028\pi\) | |||||||
\(500\) | −118229. | − | 38415.1i | −0.472918 | − | 0.153660i | ||||
\(501\) | −9826.80 | − | 72035.3i | −0.0391504 | − | 0.286992i | ||||
\(502\) | −154381. | + | 112164.i | −0.612613 | + | 0.445089i | ||||
\(503\) | −223986. | + | 308290.i | −0.885288 | + | 1.21849i | 0.0896398 | + | 0.995974i | \(0.471428\pi\) |
−0.974928 | + | 0.222520i | \(0.928572\pi\) | |||||||
\(504\) | 121430. | − | 325407.i | 0.478041 | − | 1.28105i | ||||
\(505\) | 32075.1 | 0.125772 | ||||||||
\(506\) | 10398.9 | − | 100812.i | 0.0406150 | − | 0.393743i | ||||
\(507\) | −102633. | − | 212609.i | −0.399275 | − | 0.827114i | ||||
\(508\) | −27094.4 | − | 83387.9i | −0.104991 | − | 0.323129i | ||||
\(509\) | −72166.4 | + | 99328.5i | −0.278548 | + | 0.383388i | −0.925252 | − | 0.379353i | \(-0.876147\pi\) |
0.646705 | + | 0.762741i | \(0.276147\pi\) | |||||||
\(510\) | 14734.2 | − | 27442.5i | 0.0566482 | − | 0.105507i | ||||
\(511\) | −158424. | + | 487580.i | −0.606708 | + | 1.86726i | ||||
\(512\) | 148439. | + | 48230.7i | 0.566250 | + | 0.183986i | ||||
\(513\) | −246778. | + | 106302.i | −0.937718 | + | 0.403931i | ||||
\(514\) | −16957.6 | − | 12320.4i | −0.0641857 | − | 0.0466337i | ||||
\(515\) | 846.123 | − | 274.922i | 0.00319021 | − | 0.00103656i | ||||
\(516\) | 20448.6 | + | 42360.1i | 0.0768007 | + | 0.159096i | ||||
\(517\) | 89278.9 | − | 51775.5i | 0.334016 | − | 0.193706i | ||||
\(518\) | 280622.i | 1.04583i | ||||||||
\(519\) | 369479. | + | 385718.i | 1.37169 | + | 1.43198i | ||||
\(520\) | 19334.0 | + | 14047.0i | 0.0715015 | + | 0.0519489i | ||||
\(521\) | −16951.2 | − | 23331.3i | −0.0624489 | − | 0.0859536i | 0.776650 | − | 0.629932i | \(-0.216917\pi\) |
−0.839099 | + | 0.543979i | \(0.816917\pi\) | |||||||
\(522\) | −121647. | − | 183535.i | −0.446436 | − | 0.673564i | ||||
\(523\) | −3336.85 | + | 10269.8i | −0.0121993 | + | 0.0375455i | −0.956971 | − | 0.290184i | \(-0.906283\pi\) |
0.944772 | + | 0.327730i | \(0.106283\pi\) | |||||||
\(524\) | 36118.1 | + | 49712.2i | 0.131541 | + | 0.181051i | ||||
\(525\) | 66932.4 | − | 370811.i | 0.242839 | − | 1.34535i | ||||
\(526\) | 18709.1 | + | 57580.8i | 0.0676211 | + | 0.208116i | ||||
\(527\) | 117785.i | 0.424099i | ||||||||
\(528\) | 53459.8 | + | 68724.5i | 0.191761 | + | 0.246515i | ||||
\(529\) | 104507. | 0.373451 | ||||||||
\(530\) | −77866.5 | + | 25300.4i | −0.277204 | + | 0.0900689i | ||||
\(531\) | −105564. | − | 379717.i | −0.374391 | − | 1.34670i | ||||
\(532\) | 273940. | − | 199029.i | 0.967904 | − | 0.703223i | ||||
\(533\) | −44138.4 | − | 14341.4i | −0.155368 | − | 0.0504822i | ||||
\(534\) | 149978. | − | 20459.4i | 0.525949 | − | 0.0717481i | ||||
\(535\) | −87015.9 | + | 63220.7i | −0.304012 | + | 0.220878i | ||||
\(536\) | −156462. | + | 215352.i | −0.544602 | + | 0.749581i | ||||
\(537\) | 233666. | + | 243936.i | 0.810300 | + | 0.845915i | ||||
\(538\) | −34029.1 | −0.117567 | ||||||||
\(539\) | −279608. | + | 311746.i | −0.962437 | + | 1.07306i | ||||
\(540\) | −16996.2 | + | 75445.2i | −0.0582861 | + | 0.258728i | ||||
\(541\) | −45629.7 | − | 140434.i | −0.155902 | − | 0.479818i | 0.842349 | − | 0.538933i | \(-0.181172\pi\) |
−0.998251 | + | 0.0591144i | \(0.981172\pi\) | |||||||
\(542\) | 11625.3 | − | 16000.8i | 0.0395736 | − | 0.0544683i | ||||
\(543\) | −450725. | − | 242000.i | −1.52866 | − | 0.820758i | ||||
\(544\) | −63860.5 | + | 196542.i | −0.215792 | + | 0.664138i | ||||
\(545\) | −68872.1 | − | 22377.9i | −0.231873 | − | 0.0753401i | ||||
\(546\) | −31468.0 | + | 58609.3i | −0.105556 | + | 0.196599i | ||||
\(547\) | −125515. | − | 91192.0i | −0.419489 | − | 0.304777i | 0.357943 | − | 0.933743i | \(-0.383478\pi\) |
−0.777432 | + | 0.628967i | \(0.783478\pi\) | |||||||
\(548\) | 278658. | − | 90541.6i | 0.927921 | − | 0.301500i | ||||
\(549\) | −4091.50 | + | 5150.40i | −0.0135749 | + | 0.0170882i | ||||
\(550\) | −98528.1 | − | 88371.0i | −0.325713 | − | 0.292136i | ||||
\(551\) | − | 500907.i | − | 1.64988i | ||||||
\(552\) | −152417. | + | 146000.i | −0.500213 | + | 0.479154i | ||||
\(553\) | −208339. | − | 151367.i | −0.681270 | − | 0.494972i | ||||
\(554\) | −159277. | − | 219227.i | −0.518961 | − | 0.714289i | ||||
\(555\) | −19707.4 | − | 144465.i | −0.0639799 | − | 0.469005i | ||||
\(556\) | 69768.1 | − | 214724.i | 0.225687 | − | 0.694594i | ||||
\(557\) | −47684.5 | − | 65632.0i | −0.153697 | − | 0.211546i | 0.725224 | − | 0.688513i | \(-0.241736\pi\) |
−0.878921 | + | 0.476967i | \(0.841736\pi\) | |||||||
\(558\) | 26120.4 | + | 93956.1i | 0.0838902 | + | 0.301757i | ||||
\(559\) | −6496.23 | − | 19993.3i | −0.0207892 | − | 0.0639825i | ||||
\(560\) | − | 54121.5i | − | 0.172581i | ||||||
\(561\) | −168210. | + | 130848.i | −0.534474 | + | 0.415760i | ||||
\(562\) | 156870. | 0.496670 | ||||||||
\(563\) | −198354. | + | 64449.1i | −0.625783 | + | 0.203329i | −0.604706 | − | 0.796448i | \(-0.706710\pi\) |
−0.0210771 | + | 0.999778i | \(0.506710\pi\) | |||||||
\(564\) | −90643.7 | − | 16361.4i | −0.284957 | − | 0.0514355i | ||||
\(565\) | −119301. | + | 86677.0i | −0.373720 | + | 0.271523i | ||||
\(566\) | 290971. | + | 94542.3i | 0.908275 | + | 0.295116i | ||||
\(567\) | −500473. | − | 43147.4i | −1.55673 | − | 0.134211i | ||||
\(568\) | −132155. | + | 96016.2i | −0.409625 | + | 0.297610i | ||||
\(569\) | −140127. | + | 192868.i | −0.432810 | + | 0.595712i | −0.968595 | − | 0.248642i | \(-0.920016\pi\) |
0.535785 | + | 0.844354i | \(0.320016\pi\) | |||||||
\(570\) | 42365.8 | − | 40582.1i | 0.130396 | − | 0.124907i | ||||
\(571\) | −382582. | −1.17342 | −0.586709 | − | 0.809798i | \(-0.699577\pi\) | ||||
−0.586709 | + | 0.809798i | \(0.699577\pi\) | |||||||
\(572\) | −35152.8 | − | 60615.7i | −0.107441 | − | 0.185265i | ||||
\(573\) | −128679. | + | 62117.5i | −0.391920 | + | 0.189193i | ||||
\(574\) | −45508.1 | − | 140060.i | −0.138123 | − | 0.425098i | ||||
\(575\) | −134588. | + | 185244.i | −0.407071 | + | 0.560285i | ||||
\(576\) | −2900.83 | + | 67419.1i | −0.00874333 | + | 0.203207i | ||||
\(577\) | −44023.4 | + | 135490.i | −0.132231 | + | 0.406964i | −0.995149 | − | 0.0983794i | \(-0.968634\pi\) |
0.862918 | + | 0.505343i | \(0.168634\pi\) | |||||||
\(578\) | 86035.7 | + | 27954.7i | 0.257527 | + | 0.0836757i | ||||
\(579\) | 321908. | + | 172836.i | 0.960228 | + | 0.515558i | ||||
\(580\) | −116635. | − | 84740.1i | −0.346715 | − | 0.251903i | ||||
\(581\) | 561000. | − | 182280.i | 1.66192 | − | 0.539992i | ||||
\(582\) | 169691. | − | 81915.4i | 0.500971 | − | 0.241835i | ||||
\(583\) | 557215. | + | 57477.4i | 1.63940 | + | 0.169106i | ||||
\(584\) | − | 375020.i | − | 1.09958i | ||||||
\(585\) | 12083.8 | − | 32382.2i | 0.0353096 | − | 0.0946225i | ||||
\(586\) | 148969. | + | 108232.i | 0.433810 | + | 0.315182i | ||||
\(587\) | 177598. | + | 244442.i | 0.515420 | + | 0.709414i | 0.984821 | − | 0.173570i | \(-0.0555304\pi\) |
−0.469402 | + | 0.882985i | \(0.655530\pi\) | |||||||
\(588\) | 370310. | − | 50516.3i | 1.07105 | − | 0.146109i | ||||
\(589\) | −68554.3 | + | 210989.i | −0.197608 | + | 0.608174i | ||||
\(590\) | 50578.8 | + | 69615.7i | 0.145300 | + | 0.199988i | ||||
\(591\) | −451613. | − | 81517.3i | −1.29298 | − | 0.233386i | ||||
\(592\) | 45271.8 | + | 139332.i | 0.129177 | + | 0.397565i | ||||
\(593\) | − | 101060.i | − | 0.287389i | −0.989622 | − | 0.143694i | \(-0.954102\pi\) | ||
0.989622 | − | 0.143694i | \(-0.0458982\pi\) | |||||||
\(594\) | −105163. | + | 141680.i | −0.298050 | + | 0.401546i | ||||
\(595\) | 132468. | 0.374176 | ||||||||
\(596\) | −53640.4 | + | 17428.8i | −0.151008 | + | 0.0490654i | ||||
\(597\) | −34100.3 | + | 188918.i | −0.0956773 | + | 0.530060i | ||||
\(598\) | 32703.9 | − | 23760.8i | 0.0914529 | − | 0.0664445i | ||||
\(599\) | −73845.5 | − | 23993.9i | −0.205812 | − | 0.0668724i | 0.204297 | − | 0.978909i | \(-0.434509\pi\) |
−0.410109 | + | 0.912037i | \(0.634509\pi\) | |||||||
\(600\) | 37255.7 | + | 273103.i | 0.103488 | + | 0.758618i | ||||
\(601\) | 9866.79 | − | 7168.64i | 0.0273166 | − | 0.0198467i | −0.574043 | − | 0.818825i | \(-0.694626\pi\) |
0.601360 | + | 0.798978i | \(0.294626\pi\) | |||||||
\(602\) | 39209.7 | − | 53967.6i | 0.108193 | − | 0.148916i | ||||
\(603\) | 360689. | + | 134596.i | 0.991968 | + | 0.370166i | ||||
\(604\) | −259874. | −0.712343 | ||||||||
\(605\) | −53106.6 | − | 118050.i | −0.145090 | − | 0.322518i | ||||
\(606\) | −28392.9 | − | 58816.9i | −0.0773150 | − | 0.160161i | ||||
\(607\) | −28504.3 | − | 87727.3i | −0.0773630 | − | 0.238099i | 0.904895 | − | 0.425636i | \(-0.139950\pi\) |
−0.982258 | + | 0.187537i | \(0.939950\pi\) | |||||||
\(608\) | −228788. | + | 314899.i | −0.618907 | + | 0.851852i | ||||
\(609\) | 442972. | − | 825038.i | 1.19438 | − | 2.22453i | ||||
\(610\) | 443.797 | − | 1365.87i | 0.00119268 | − | 0.00367070i | ||||
\(611\) | 39150.8 | + | 12720.9i | 0.104872 | + | 0.0340749i | ||||
\(612\) | 190020. | + | 8175.94i | 0.507336 | + | 0.0218290i | ||||
\(613\) | 83039.3 | + | 60331.6i | 0.220985 | + | 0.160555i | 0.692770 | − | 0.721159i | \(-0.256390\pi\) |
−0.471785 | + | 0.881714i | \(0.656390\pi\) | |||||||
\(614\) | −14170.3 | + | 4604.20i | −0.0375873 | + | 0.0122129i | ||||
\(615\) | 33263.8 | + | 68907.2i | 0.0879471 | + | 0.182186i | ||||
\(616\) | 210117. | − | 474395.i | 0.553732 | − | 1.25020i | ||||
\(617\) | − | 19530.9i | − | 0.0513040i | −0.999671 | − | 0.0256520i | \(-0.991834\pi\) | ||
0.999671 | − | 0.0256520i | \(-0.00816618\pi\) | |||||||
\(618\) | −1253.12 | − | 1308.19i | −0.00328107 | − | 0.00342528i | ||||
\(619\) | 288970. | + | 209949.i | 0.754175 | + | 0.547940i | 0.897118 | − | 0.441791i | \(-0.145657\pi\) |
−0.142943 | + | 0.989731i | \(0.545657\pi\) | |||||||
\(620\) | 37530.5 | + | 51656.4i | 0.0976341 | + | 0.134382i | ||||
\(621\) | 262485. | + | 155825.i | 0.680646 | + | 0.404067i | ||||
\(622\) | 29729.8 | − | 91498.8i | 0.0768441 | − | 0.236502i | ||||
\(623\) | 378383. | + | 520800.i | 0.974890 | + | 1.34182i | ||||
\(624\) | −6169.01 | + | 34176.8i | −0.0158433 | + | 0.0877734i | ||||
\(625\) | 77306.8 | + | 237926.i | 0.197905 | + | 0.609090i | ||||
\(626\) | − | 191044.i | − | 0.487512i | ||||||
\(627\) | −377474. | + | 136486.i | −0.960178 | + | 0.347179i | ||||
\(628\) | 460664. | 1.16806 | ||||||||
\(629\) | −341030. | + | 110807.i | −0.861968 | + | 0.280070i | ||||
\(630\) | 105669. | − | 29376.6i | 0.266235 | − | 0.0740150i | ||||
\(631\) | 79978.8 | − | 58108.0i | 0.200870 | − | 0.145941i | −0.482803 | − | 0.875729i | \(-0.660381\pi\) |
0.683673 | + | 0.729788i | \(0.260381\pi\) | |||||||
\(632\) | 179157. | + | 58211.5i | 0.448538 | + | 0.145739i | ||||
\(633\) | 143998. | − | 19643.6i | 0.359375 | − | 0.0490246i | ||||
\(634\) | 119030. | − | 86480.1i | 0.296126 | − | 0.215148i | ||||
\(635\) | 37974.4 | − | 52267.3i | 0.0941768 | − | 0.129623i | ||||
\(636\) | −345829. | − | 361029.i | −0.854962 | − | 0.892539i | ||||
\(637\) | −167033. | −0.411646 | ||||||||
\(638\) | −165012. | − | 284538.i | −0.405391 | − | 0.699036i | ||||
\(639\) | 184987. | + | 146954.i | 0.453042 | + | 0.359898i | ||||
\(640\) | 41609.7 | + | 128062.i | 0.101586 | + | 0.312650i | ||||
\(641\) | 338508. | − | 465917.i | 0.823860 | − | 1.13395i | −0.165175 | − | 0.986264i | \(-0.552819\pi\) |
0.989035 | − | 0.147681i | \(-0.0471810\pi\) | |||||||
\(642\) | 192956. | + | 103600.i | 0.468153 | + | 0.251357i | ||||
\(643\) | 13470.3 | − | 41457.2i | 0.0325803 | − | 0.100272i | −0.933444 | − | 0.358723i | \(-0.883212\pi\) |
0.966024 | + | 0.258451i | \(0.0832122\pi\) | |||||||
\(644\) | −365845. | − | 118870.i | −0.882115 | − | 0.286617i | ||||
\(645\) | −16395.3 | + | 30536.3i | −0.0394094 | + | 0.0734001i | ||||
\(646\) | −116726. | − | 84806.4i | −0.279707 | − | 0.203219i | ||||
\(647\) | −310659. | + | 100939.i | −0.742122 | + | 0.241130i | −0.655588 | − | 0.755119i | \(-0.727579\pi\) |
−0.0865342 | + | 0.996249i | \(0.527579\pi\) | |||||||
\(648\) | 357932. | − | 83112.4i | 0.852413 | − | 0.197932i | ||||
\(649\) | −123519. | − | 575641.i | −0.293255 | − | 1.36667i | ||||
\(650\) | − | 52791.4i | − | 0.124950i | ||||||
\(651\) | −299501. | + | 286891.i | −0.706702 | + | 0.676948i | ||||
\(652\) | −152419. | − | 110739.i | −0.358545 | − | 0.260498i | ||||
\(653\) | −119068. | − | 163883.i | −0.279234 | − | 0.384333i | 0.646246 | − | 0.763129i | \(-0.276338\pi\) |
−0.925480 | + | 0.378796i | \(0.876338\pi\) | |||||||
\(654\) | 19930.6 | + | 146101.i | 0.0465978 | + | 0.341585i | ||||
\(655\) | −13991.5 | + | 43061.4i | −0.0326123 | + | 0.100370i | ||||
\(656\) | −45190.7 | − | 62199.6i | −0.105013 | − | 0.144537i | ||||
\(657\) | −522565. | + | 145276.i | −1.21062 | + | 0.336561i | ||||
\(658\) | 40365.7 | + | 124233.i | 0.0932312 | + | 0.286936i | ||||
\(659\) | − | 664955.i | − | 1.53116i | −0.643339 | − | 0.765581i | \(-0.722451\pi\) | ||
0.643339 | − | 0.765581i | \(-0.277549\pi\) | |||||||
\(660\) | −32078.2 | + | 110984.i | −0.0736414 | + | 0.254783i | ||||
\(661\) | −356233. | −0.815325 | −0.407662 | − | 0.913133i | \(-0.633656\pi\) | ||||
−0.407662 | + | 0.913133i | \(0.633656\pi\) | |||||||
\(662\) | 299026. | − | 97159.6i | 0.682329 | − | 0.221702i | ||||
\(663\) | −83651.3 | − | 15099.3i | −0.190303 | − | 0.0343502i | ||||
\(664\) | −349083. | + | 253624.i | −0.791759 | + | 0.575247i | ||||
\(665\) | 237290. | + | 77100.3i | 0.536583 | + | 0.174346i | ||||
\(666\) | −247464. | + | 164018.i | −0.557910 | + | 0.369781i | ||||
\(667\) | −460370. | + | 334479.i | −1.03480 | + | 0.751825i | ||||
\(668\) | −56972.4 | + | 78415.8i | −0.127677 | + | 0.175732i | ||||
\(669\) | 41166.2 | − | 39433.1i | 0.0919790 | − | 0.0881065i | ||||
\(670\) | −84055.4 | −0.187247 | ||||||||
\(671\) | −6560.78 | + | 7314.86i | −0.0145717 | + | 0.0162465i | ||||
\(672\) | −655311. | + | 316340.i | −1.45114 | + | 0.700513i | ||||
\(673\) | 3413.22 | + | 10504.8i | 0.00753589 | + | 0.0231931i | 0.954754 | − | 0.297397i | \(-0.0961186\pi\) |
−0.947218 | + | 0.320591i | \(0.896119\pi\) | |||||||
\(674\) | −41529.7 | + | 57160.8i | −0.0914196 | + | 0.125828i | ||||
\(675\) | 366118. | − | 157709.i | 0.803551 | − | 0.346137i | ||||
\(676\) | −97262.9 | + | 299344.i | −0.212840 | + | 0.655055i | ||||
\(677\) | 505292. | + | 164179.i | 1.10247 | + | 0.358213i | 0.803051 | − | 0.595910i | \(-0.203209\pi\) |
0.299415 | + | 0.954123i | \(0.403209\pi\) | |||||||
\(678\) | 264547. | + | 142038.i | 0.575497 | + | 0.308991i | ||||
\(679\) | 648315. | + | 471028.i | 1.40620 | + | 1.02166i | ||||
\(680\) | −92157.6 | + | 29943.8i | −0.199303 | + | 0.0647574i | ||||
\(681\) | 380449. | − | 183655.i | 0.820356 | − | 0.396013i | ||||
\(682\) | 30563.2 | + | 142435.i | 0.0657099 | + | 0.306230i | ||||
\(683\) | − | 63990.3i | − | 0.137174i | −0.997645 | − | 0.0685871i | \(-0.978151\pi\) | ||
0.997645 | − | 0.0685871i | \(-0.0218491\pi\) | |||||||
\(684\) | 335625. | + | 125243.i | 0.717368 | + | 0.267696i | ||||
\(685\) | 174662. | + | 126900.i | 0.372236 | + | 0.270445i | ||||
\(686\) | −95409.3 | − | 131320.i | −0.202741 | − | 0.279050i | ||||
\(687\) | −43514.4 | + | 5936.07i | −0.0921975 | + | 0.0125773i | ||||
\(688\) | 10761.7 | − | 33121.1i | 0.0227355 | − | 0.0699726i | ||||
\(689\) | 131332. | + | 180763.i | 0.276651 | + | 0.380777i | ||||
\(690\) | −65587.6 | − | 11838.7i | −0.137760 | − | 0.0248661i | ||||
\(691\) | −147361. | − | 453529.i | −0.308621 | − | 0.949838i | −0.978301 | − | 0.207188i | \(-0.933569\pi\) |
0.669680 | − | 0.742650i | \(-0.266431\pi\) | |||||||
\(692\) | − | 712102.i | − | 1.48707i | ||||||
\(693\) | −742433. | − | 109011.i | −1.54593 | − | 0.226989i | ||||
\(694\) | 106657. | 0.221447 | ||||||||
\(695\) | 158218. | − | 51408.2i | 0.327557 | − | 0.106430i | ||||
\(696\) | −121679. | + | 674110.i | −0.251186 | + | 1.39159i | ||||
\(697\) | 152240. | − | 110609.i | 0.313374 | − | 0.227679i | ||||
\(698\) | −416941. | − | 135472.i | −0.855783 | − | 0.278061i | ||||
\(699\) | 37124.4 | + | 272140.i | 0.0759809 | + | 0.556978i | ||||
\(700\) | −406414. | + | 295277.i | −0.829417 | + | 0.602607i | ||||
\(701\) | −385381. | + | 530432.i | −0.784250 | + | 1.07943i | 0.210550 | + | 0.977583i | \(0.432474\pi\) |
−0.994800 | + | 0.101844i | \(0.967526\pi\) | |||||||
\(702\) | −70076.6 | + | 6506.24i | −0.142200 | + | 0.0132025i | ||||
\(703\) | −675382. | −1.36659 | ||||||||
\(704\) | −10343.3 | + | 100274.i | −0.0208697 | + | 0.202321i | ||||
\(705\) | −29505.0 | − | 61120.8i | −0.0593632 | − | 0.122973i | ||||
\(706\) | −80090.5 | − | 246493.i | −0.160684 | − | 0.494533i | ||||
\(707\) | 163264. | − | 224714.i | 0.326627 | − | 0.449563i | ||||
\(708\) | −248554. | + | 462933.i | −0.495855 | + | 0.923532i | ||||
\(709\) | 199394. | − | 613672.i | 0.396661 | − | 1.22080i | −0.530999 | − | 0.847372i | \(-0.678183\pi\) |
0.927660 | − | 0.373425i | \(-0.121817\pi\) | |||||||
\(710\) | −49057.7 | − | 15939.8i | −0.0973174 | − | 0.0316203i | ||||
\(711\) | 11711.6 | − | 272193.i | 0.0231673 | − | 0.538440i | ||||
\(712\) | −380965. | − | 276787.i | −0.751494 | − | 0.545992i | ||||
\(713\) | 239691. | − | 77880.4i | 0.471490 | − | 0.153197i | ||||
\(714\) | −117260. | − | 242909.i | −0.230014 | − | 0.476483i | ||||
\(715\) | 20909.3 | − | 47208.3i | 0.0409004 | − | 0.0923436i | ||||
\(716\) | − | 450347.i | − | 0.878458i | ||||||
\(717\) | 50878.7 | + | 53114.9i | 0.0989686 | + | 0.103318i | ||||
\(718\) | −152066. | − | 110483.i | −0.294974 | − | 0.214311i | ||||
\(719\) | −386426. | − | 531870.i | −0.747496 | − | 1.02884i | −0.998152 | − | 0.0607636i | \(-0.980646\pi\) |
0.250656 | − | 0.968076i | \(-0.419354\pi\) | |||||||
\(720\) | 47726.6 | − | 31633.0i | 0.0920652 | − | 0.0610204i | ||||
\(721\) | 2380.75 | − | 7327.18i | 0.00457976 | − | 0.0140950i | ||||
\(722\) | −6508.23 | − | 8957.81i | −0.0124850 | − | 0.0171841i | ||||
\(723\) | 114032. | − | 631749.i | 0.218148 | − | 1.20856i | ||||
\(724\) | 210763. | + | 648663.i | 0.402085 | + | 1.23749i | ||||
\(725\) | 743140.i | 1.41382i | ||||||||
\(726\) | −169461. | + | 201880.i | −0.321511 | + | 0.383020i | ||||
\(727\) | 418622. | 0.792051 | 0.396026 | − | 0.918239i | \(-0.370389\pi\) | ||||
0.396026 | + | 0.918239i | \(0.370389\pi\) | |||||||
\(728\) | 196822. | − | 63951.4i | 0.371374 | − | 0.120667i | ||||
\(729\) | −254468. | − | 466557.i | −0.478827 | − | 0.877909i | ||||
\(730\) | 95804.7 | − | 69606.2i | 0.179780 | − | 0.130618i | ||||
\(731\) | 81067.3 | + | 26340.4i | 0.151709 | + | 0.0492932i | ||||
\(732\) | 8689.02 | − | 1185.32i | 0.0162162 | − | 0.00221215i | ||||
\(733\) | 421157. | − | 305988.i | 0.783855 | − | 0.569504i | −0.122278 | − | 0.992496i | \(-0.539020\pi\) |
0.906134 | + | 0.422992i | \(0.139020\pi\) | |||||||
\(734\) | −54820.8 | + | 75454.4i | −0.101754 | + | 0.140053i | ||||
\(735\) | 190497. | + | 198870.i | 0.352626 | + | 0.368124i | ||||
\(736\) | 442188. | 0.816302 | ||||||||
\(737\) | 525830. | + | 232898.i | 0.968078 | + | 0.428777i | ||||
\(738\) | 96911.8 | − | 121993.i | 0.177936 | − | 0.223987i | ||||
\(739\) | −106662. | − | 328271.i | −0.195308 | − | 0.601097i | −0.999973 | − | 0.00736713i | \(-0.997655\pi\) |
0.804665 | − | 0.593729i | \(-0.202345\pi\) | |||||||
\(740\) | −114257. | + | 157261.i | −0.208650 | + | 0.287182i | ||||
\(741\) | −141057. | − | 75735.1i | −0.256896 | − | 0.137931i | ||||
\(742\) | −219094. | + | 674302.i | −0.397945 | + | 1.22475i | ||||
\(743\) | −361533. | − | 117469.i | −0.654893 | − | 0.212787i | −0.0373224 | − | 0.999303i | \(-0.511883\pi\) |
−0.617570 | + | 0.786516i | \(0.711883\pi\) | |||||||
\(744\) | 143512. | − | 267291.i | 0.259263 | − | 0.482879i | ||||
\(745\) | −33621.7 | − | 24427.6i | −0.0605769 | − | 0.0440117i | ||||
\(746\) | 130502. | − | 42402.6i | 0.234498 | − | 0.0761929i | ||||
\(747\) | 488637. | + | 388174.i | 0.875679 | + | 0.695642i | ||||
\(748\) | 282620. | + | 29152.6i | 0.505126 | + | 0.0521043i | ||||
\(749\) | 931418.i | 1.66028i | ||||||||
\(750\) | −134692. | + | 129021.i | −0.239452 | + | 0.229371i | ||||
\(751\) | 219104. | + | 159188.i | 0.388482 | + | 0.282249i | 0.764833 | − | 0.644228i | \(-0.222821\pi\) |
−0.376351 | + | 0.926477i | \(0.622821\pi\) | |||||||
\(752\) | 40084.2 | + | 55171.1i | 0.0708822 | + | 0.0975610i | ||||
\(753\) | −116051. | − | 850709.i | −0.204672 | − | 1.50034i | ||||
\(754\) | 40542.3 | − | 124776.i | 0.0713125 | − | 0.219477i | ||||
\(755\) | −112553. | − | 154916.i | −0.197453 | − | 0.271771i | ||||
\(756\) | 442047. | + | 503093.i | 0.773436 | + | 0.880248i | ||||
\(757\) | 53681.0 | + | 165213.i | 0.0936761 | + | 0.288305i | 0.986906 | − | 0.161294i | \(-0.0515667\pi\) |
−0.893230 | + | 0.449599i | \(0.851567\pi\) | |||||||
\(758\) | 484221.i | 0.842762i | ||||||||
\(759\) | 377498. | + | 255789.i | 0.655286 | + | 0.444015i | ||||
\(760\) | −182511. | −0.315981 | ||||||||
\(761\) | −139733. | + | 45401.8i | −0.241284 | + | 0.0783979i | −0.427163 | − | 0.904175i | \(-0.640487\pi\) |
0.185879 | + | 0.982573i | \(0.440487\pi\) | |||||||
\(762\) | −129459. | − | 23367.6i | −0.222957 | − | 0.0402444i | ||||
\(763\) | −507339. | + | 368604.i | −0.871464 | + | 0.633156i | ||||
\(764\) | 181174. | + | 58867.1i | 0.310392 | + | 0.100852i | ||||
\(765\) | 77425.0 | + | 116816.i | 0.132299 | + | 0.199608i | ||||
\(766\) | 322287. | − | 234155.i | 0.549270 | − | 0.399068i | ||||
\(767\) | 138031. | − | 189983.i | 0.234631 | − | 0.322941i | ||||
\(768\) | 284630. | − | 272647.i | 0.482568 | − | 0.462251i | ||||
\(769\) | 314651. | 0.532080 | 0.266040 | − | 0.963962i | \(-0.414285\pi\) | ||||
0.266040 | + | 0.963962i | \(0.414285\pi\) | |||||||
\(770\) | 160191. | − | 34373.2i | 0.270182 | − | 0.0579748i | ||||
\(771\) | 84931.5 | − | 40999.2i | 0.142876 | − | 0.0689711i | ||||
\(772\) | −150527. | − | 463274.i | −0.252569 | − | 0.777327i | ||||
\(773\) | −168410. | + | 231796.i | −0.281844 | + | 0.387924i | −0.926343 | − | 0.376680i | \(-0.877066\pi\) |
0.644500 | + | 0.764604i | \(0.277066\pi\) | |||||||
\(774\) | 70508.2 | + | 3033.74i | 0.117695 | + | 0.00506404i | ||||
\(775\) | 101706. | − | 313020.i | 0.169334 | − | 0.521158i | ||||
\(776\) | −557506. | − | 181145.i | −0.925818 | − | 0.300817i | ||||
\(777\) | −1.11241e6 | − | 597268.i | −1.84257 | − | 0.989299i | ||||
\(778\) | −138923. | − | 100933.i | −0.229516 | − | 0.166753i | ||||
\(779\) | 337086. | − | 109526.i | 0.555477 | − | 0.180485i | ||||
\(780\) | −41497.8 | + | 20032.4i | −0.0682081 | + | 0.0329263i | ||||
\(781\) | 262727. | + | 235643.i | 0.430728 | + | 0.386325i | ||||
\(782\) | 163909.i | 0.268034i | ||||||||
\(783\) | 986462. | − | 91587.7i | 1.60900 | − | 0.149387i | ||||
\(784\) | −223862. | − | 162645.i | −0.364207 | − | 0.264612i | ||||
\(785\) | 199517. | + | 274611.i | 0.323773 | + | 0.445635i | ||||
\(786\) | 91348.0 | − | 12461.4i | 0.147861 | − | 0.0201707i | ||||
\(787\) | 239761. | − | 737907.i | 0.387104 | − | 1.19139i | −0.547838 | − | 0.836585i | \(-0.684549\pi\) |
0.934942 | − | 0.354800i | \(-0.115451\pi\) | |||||||
\(788\) | 359620. | + | 494974.i | 0.579150 | + | 0.797132i | ||||
\(789\) | −268076. | − | 48388.5i | −0.430630 | − | 0.0777299i | ||||
\(790\) | 18381.6 | + | 56572.8i | 0.0294530 | + | 0.0906471i | ||||
\(791\) | 1.27699e6i | 2.04097i | ||||||||
\(792\) | 541151. | − | 91985.2i | 0.862717 | − | 0.146645i | ||||
\(793\) | −3919.30 | −0.00623250 | ||||||||
\(794\) | −163685. | + | 53184.3i | −0.259637 | + | 0.0843612i | ||||
\(795\) | 65435.7 | − | 362519.i | 0.103533 | − | 0.573584i | ||||
\(796\) | 207057. | − | 150436.i | 0.326786 | − | 0.237424i | ||||
\(797\) | −591897. | − | 192319.i | −0.931815 | − | 0.302765i | −0.196510 | − | 0.980502i | \(-0.562961\pi\) |
−0.735305 | + | 0.677737i | \(0.762961\pi\) | |||||||
\(798\) | −68668.5 | − | 503374.i | −0.107833 | − | 0.790470i | ||||
\(799\) | −135037. | + | 98110.1i | −0.211524 | + | 0.153681i | ||||
\(800\) | 339427. | − | 467181.i | 0.530354 | − | 0.729970i | ||||
\(801\) | −238105. | + | 638072.i | −0.371111 | + | 0.994500i | ||||
\(802\) | −68509.7 | −0.106513 | ||||||||
\(803\) | −792194. | + | 169986.i | −1.22857 | + | 0.263623i | ||||
\(804\) | −223130. | − | 462223.i | −0.345180 | − | 0.715055i | ||||
\(805\) | −87588.9 | − | 269571.i | −0.135163 | − | 0.415989i | ||||
\(806\) | −34153.9 | + | 47008.8i | −0.0525739 | + | 0.0723618i | ||||
\(807\) | 72426.5 | − | 134895.i | 0.111212 | − | 0.207132i | ||||
\(808\) | −62786.9 | + | 193238.i | −0.0961714 | + | 0.295985i | ||||
\(809\) | 968591. | + | 314714.i | 1.47994 | + | 0.480861i | 0.934094 | − | 0.357027i | \(-0.116209\pi\) |
0.545843 | + | 0.837887i | \(0.316209\pi\) | |||||||
\(810\) | 87666.9 | + | 76013.0i | 0.133618 | + | 0.115856i | ||||
\(811\) | 1.00976e6 | + | 733632.i | 1.53524 | + | 1.11541i | 0.953236 | + | 0.302227i | \(0.0977299\pi\) |
0.582001 | + | 0.813188i | \(0.302270\pi\) | |||||||
\(812\) | −1.18736e6 | + | 385795.i | −1.80081 | + | 0.585120i | ||||
\(813\) | 38686.0 | + | 80139.5i | 0.0585292 | + | 0.121246i | ||||
\(814\) | −383649. | + | 222489.i | −0.579008 | + | 0.335784i | ||||
\(815\) | − | 138822.i | − | 0.208998i | ||||||
\(816\) | −97408.9 | − | 101690.i | −0.146291 | − | 0.152721i | ||||
\(817\) | 129886. | + | 94367.4i | 0.194588 | + | 0.141377i | ||||
\(818\) | 184021. | + | 253283.i | 0.275018 | + | 0.378530i | ||||
\(819\) | −165358. | − | 249485.i | −0.246522 | − | 0.371943i | ||||
\(820\) | 31523.2 | − | 97018.5i | 0.0468816 | − | 0.144287i | ||||
\(821\) | −764095. | − | 1.05169e6i | −1.13360 | − | 1.56027i | −0.781039 | − | 0.624483i | \(-0.785310\pi\) |
−0.352564 | − | 0.935788i | \(-0.614690\pi\) | |||||||
\(822\) | 78088.0 | − | 432614.i | 0.115569 | − | 0.640261i | ||||
\(823\) | −283649. | − | 872983.i | −0.418776 | − | 1.28886i | −0.908829 | − | 0.417169i | \(-0.863022\pi\) |
0.490053 | − | 0.871693i | \(-0.336978\pi\) | |||||||
\(824\) | 5635.67i | 0.00830025i | ||||||||
\(825\) | 560016. | − | 202489.i | 0.822797 | − | 0.297505i | ||||
\(826\) | 745167. | 1.09218 | ||||||||
\(827\) | 234133. | − | 76074.4i | 0.342335 | − | 0.111231i | −0.132803 | − | 0.991142i | \(-0.542398\pi\) |
0.475139 | + | 0.879911i | \(0.342398\pi\) | |||||||
\(828\) | −109005. | − | 392095.i | −0.158996 | − | 0.571914i | ||||
\(829\) | −1.08292e6 | + | 786787.i | −1.57575 | + | 1.14485i | −0.654377 | + | 0.756169i | \(0.727069\pi\) |
−0.921373 | + | 0.388680i | \(0.872931\pi\) | |||||||
\(830\) | −129584. | − | 42104.5i | −0.188103 | − | 0.0611185i | ||||
\(831\) | 1.20804e6 | − | 164796.i | 1.74936 | − | 0.238641i | ||||
\(832\) | −32529.2 | + | 23633.8i | −0.0469923 | + | 0.0341419i | ||||
\(833\) | 398091. | − | 547926.i | 0.573710 | − | 0.789645i | ||||
\(834\) | −234323. | − | 244622.i | −0.336886 | − | 0.351693i | ||||
\(835\) | −71420.3 | −0.102435 | ||||||||
\(836\) | 489291. | + | 216715.i | 0.700091 | + | 0.310081i | ||||
\(837\) | −428046. | − | 96429.7i | −0.610997 | − | 0.137645i | ||||
\(838\) | 113092. | + | 348062.i | 0.161044 | + | 0.495643i | ||||
\(839\) | 372044. | − | 512075.i | 0.528532 | − | 0.727461i | −0.458374 | − | 0.888759i | \(-0.651568\pi\) |
0.986906 | + | 0.161298i | \(0.0515680\pi\) | |||||||
\(840\) | −300611. | − | 161402.i | −0.426037 | − | 0.228744i | ||||
\(841\) | −352148. | + | 1.08380e6i | −0.497890 | + | 1.53235i | ||||
\(842\) | 403323. | + | 131048.i | 0.568891 | + | 0.184844i | ||||
\(843\) | −333878. | + | 621849.i | −0.469821 | + | 0.875044i | ||||
\(844\) | −156752. | − | 113887.i | −0.220053 | − | 0.159878i | ||||
\(845\) | −220570. | + | 71667.7i | −0.308911 | + | 0.100371i | ||||
\(846\) | −85960.8 | + | 108208.i | −0.120105 | + | 0.151189i | ||||
\(847\) | −1.09736e6 | − | 228822.i | −1.52961 | − | 0.318956i | ||||
\(848\) | 370145.i | 0.514731i | ||||||||
\(849\) | −994071. | + | 952219.i | −1.37912 | + | 1.32106i | ||||
\(850\) | 173174. | + | 125818.i | 0.239687 | + | 0.174142i | ||||
\(851\) | 450984. | + | 620727.i | 0.622734 | + | 0.857119i | ||||
\(852\) | −42573.2 | − | 312083.i | −0.0586485 | − | 0.429923i | ||||
\(853\) | −334163. | + | 1.02845e6i | −0.459261 | + | 1.41346i | 0.406798 | + | 0.913518i | \(0.366645\pi\) |
−0.866059 | + | 0.499942i | \(0.833355\pi\) | |||||||
\(854\) | −7310.12 | − | 10061.5i | −0.0100232 | − | 0.0137958i | ||||
\(855\) | 70701.5 | + | 254316.i | 0.0967156 | + | 0.347890i | ||||
\(856\) | −210543. | − | 647986.i | −0.287339 | − | 0.884337i | ||||
\(857\) | − | 281404.i | − | 0.383150i | −0.981478 | − | 0.191575i | \(-0.938641\pi\) | ||
0.981478 | − | 0.191575i | \(-0.0613594\pi\) | |||||||
\(858\) | −105076. | + | 3446.88i | −0.142735 | + | 0.00468221i | ||||
\(859\) | −883353. | −1.19715 | −0.598574 | − | 0.801067i | \(-0.704266\pi\) | ||||
−0.598574 | + | 0.801067i | \(0.704266\pi\) | |||||||
\(860\) | 43946.4 | − | 14279.0i | 0.0594191 | − | 0.0193064i | ||||
\(861\) | 652069. | + | 117700.i | 0.879604 | + | 0.158771i | ||||
\(862\) | −1906.45 | + | 1385.11i | −0.00256573 | + | 0.00186411i | ||||
\(863\) | −166527. | − | 54107.8i | −0.223595 | − | 0.0726505i | 0.195077 | − | 0.980788i | \(-0.437504\pi\) |
−0.418672 | + | 0.908137i | \(0.637504\pi\) | |||||||
\(864\) | −661980. | − | 392986.i | −0.886783 | − | 0.526441i | ||||
\(865\) | 424498. | − | 308416.i | 0.567341 | − | 0.412197i | ||||
\(866\) | 166978. | − | 229825.i | 0.222650 | − | 0.306452i | ||||
\(867\) | −293931. | + | 281556.i | −0.391028 | + | 0.374565i | ||||
\(868\) | 552930. | 0.733889 | ||||||||
\(869\) | 41759.4 | − | 404837.i | 0.0552987 | − | 0.536094i | ||||
\(870\) | −194796. | + | 94034.6i | −0.257361 | + | 0.124236i | ||||
\(871\) | 70885.1 | + | 218162.i | 0.0934370 | + | 0.287569i | ||||
\(872\) | 269634. | − | 371119.i | 0.354602 | − | 0.488068i | ||||
\(873\) | −36444.5 | + | 847019.i | −0.0478193 | + | 1.11138i | ||||
\(874\) | −95400.2 | + | 293612.i | −0.124890 | + | 0.384371i | ||||
\(875\) | −754406. | − | 245121.i | −0.985347 | − | 0.320159i | ||||
\(876\) | 637086. | + | 342059.i | 0.830214 | + | 0.445751i | ||||
\(877\) | 119038. | + | 86486.5i | 0.154770 | + | 0.112447i | 0.662475 | − | 0.749084i | \(-0.269506\pi\) |
−0.507705 | + | 0.861531i | \(0.669506\pi\) | |||||||
\(878\) | −61179.3 | + | 19878.4i | −0.0793625 | + | 0.0257865i | ||||
\(879\) | −746104. | + | 360169.i | −0.965654 | + | 0.466153i | ||||
\(880\) | 73991.4 | − | 42909.8i | 0.0955467 | − | 0.0554104i | ||||
\(881\) | 38571.8i | 0.0496956i | 0.999691 | + | 0.0248478i | \(0.00791012\pi\) | ||||
−0.999691 | + | 0.0248478i | \(0.992090\pi\) | |||||||
\(882\) | 196045. | − | 525359.i | 0.252010 | − | 0.675335i | ||||
\(883\) | 78163.6 | + | 56789.2i | 0.100250 | + | 0.0728357i | 0.636781 | − | 0.771045i | \(-0.280266\pi\) |
−0.536531 | + | 0.843881i | \(0.680266\pi\) | |||||||
\(884\) | 66611.6 | + | 91683.0i | 0.0852404 | + | 0.117323i | ||||
\(885\) | −383614. | + | 52331.3i | −0.489788 | + | 0.0668151i | ||||
\(886\) | −44602.6 | + | 137273.i | −0.0568189 | + | 0.174871i | ||||
\(887\) | −800439. | − | 1.10171e6i | −1.01737 | − | 1.40030i | −0.914028 | − | 0.405651i | \(-0.867045\pi\) |
−0.103346 | − | 0.994645i | \(-0.532955\pi\) | |||||||
\(888\) | 908915. | + | 164062.i | 1.15265 | + | 0.208056i | ||||
\(889\) | −172886. | − | 532087.i | −0.218754 | − | 0.673254i | ||||
\(890\) | − | 148697.i | − | 0.187725i | ||||||
\(891\) | −337808. | − | 718424.i | −0.425515 | − | 0.904952i | ||||
\(892\) | −75999.9 | −0.0955175 | ||||||||
\(893\) | −298996. | + | 97149.6i | −0.374940 | + | 0.121825i | ||||
\(894\) | −15031.6 | + | 83276.2i | −0.0188074 | + | 0.104195i | ||||
\(895\) | 268461. | − | 195048.i | 0.335147 | − | 0.243498i | ||||
\(896\) | 1.10898e6 | + | 360329.i | 1.38136 | + | 0.448831i | ||||
\(897\) | 24584.1 | + | 180214.i | 0.0305541 | + | 0.223977i | ||||
\(898\) | −26420.1 | + | 19195.3i | −0.0327628 | + | 0.0238036i | ||||
\(899\) | 480781. | − | 661739.i | 0.594879 | − | 0.818780i | ||||
\(900\) | −497930. | − | 185809.i | −0.614728 | − | 0.229394i | ||||
\(901\) | −905967. | −1.11600 | ||||||||
\(902\) | 155400. | − | 173261.i | 0.191002 | − | 0.212955i | ||||
\(903\) | 130480. | + | 270295.i | 0.160018 | + | 0.331483i | ||||
\(904\) | −288660. | − | 888403.i | −0.353223 | − | 1.08711i | ||||
\(905\) | −295398. | + | 406580.i | −0.360670 | + | 0.496420i | ||||
\(906\) | −184442. | + | 343523.i | −0.224700 | + | 0.418504i | ||||
\(907\) | 324321. | − | 998158.i | 0.394240 | − | 1.21335i | −0.535312 | − | 0.844655i | \(-0.679806\pi\) |
0.929552 | − | 0.368692i | \(-0.120194\pi\) | |||||||
\(908\) | −535657. | − | 174045.i | −0.649703 | − | 0.211101i | ||||
\(909\) | 293587. | + | 12632.1i | 0.355311 | + | 0.0152879i | ||||
\(910\) | 52868.9 | + | 38411.5i | 0.0638437 | + | 0.0463851i | ||||
\(911\) | −1.11225e6 | + | 361393.i | −1.34019 | + | 0.435455i | −0.889382 | − | 0.457164i | \(-0.848865\pi\) |
−0.450811 | + | 0.892620i | \(0.648865\pi\) | |||||||
\(912\) | −115302. | − | 238853.i | −0.138627 | − | 0.287172i | ||||
\(913\) | 693986. | + | 622444.i | 0.832548 | + | 0.746722i | ||||
\(914\) | 32122.6i | 0.0384519i | ||||||||
\(915\) | 4469.87 | + | 4666.33i | 0.00533891 | + | 0.00557356i | ||||
\(916\) | 47368.6 | + | 34415.3i | 0.0564546 | + | 0.0410167i | ||||
\(917\) | 230465. | + | 317207.i | 0.274073 | + | 0.377228i | ||||
\(918\) | 145671. | − | 245381.i | 0.172858 | − | 0.291176i | ||||
\(919\) | 115377. | − | 355094.i | 0.136612 | − | 0.420448i | −0.859225 | − | 0.511597i | \(-0.829054\pi\) |
0.995837 | + | 0.0911494i | \(0.0290541\pi\) | |||||||
\(920\) | 121871. | + | 167741.i | 0.143987 | + | 0.198182i | ||||
\(921\) | 11908.1 | − | 65971.8i | 0.0140386 | − | 0.0777748i | ||||
\(922\) | 81334.2 | + | 250321.i | 0.0956779 | + | 0.294466i | ||||
\(923\) | 140769.i | 0.165236i | ||||||||
\(924\) | 614256. | + | 789648.i | 0.719458 | + | 0.924889i | ||||
\(925\) | 1.00199e6 | 1.17106 | ||||||||
\(926\) | −160531. | + | 52159.6i | −0.187213 | + | 0.0608293i | ||||
\(927\) | 7852.92 | − | 2183.16i | 0.00913843 | − | 0.00254054i | ||||
\(928\) | 1.16104e6 | − | 843546.i | 1.34819 | − | 0.979519i | ||||
\(929\) | −312484. | − | 101532.i | −0.362073 | − | 0.117645i | 0.122331 | − | 0.992489i | \(-0.460963\pi\) |
−0.484403 | + | 0.874845i | \(0.660963\pi\) | |||||||
\(930\) | 94920.4 | − | 12948.7i | 0.109747 | − | 0.0149713i | ||||
\(931\) | 1.03201e6 | − | 749801.i | 1.19065 | − | 0.865061i | ||||
\(932\) | 215234. | − | 296244.i | 0.247787 | − | 0.341050i | ||||
\(933\) | 299435. | + | 312595.i | 0.343984 | + | 0.359103i | ||||
\(934\) | 450500. | 0.516417 | ||||||||
\(935\) | 105026. | + | 181101.i | 0.120136 | + | 0.207157i | ||||
\(936\) | 171434. | + | 136188.i | 0.195679 | + | 0.155448i | ||||
\(937\) | 242994. | + | 747859.i | 0.276769 | + | 0.851806i | 0.988746 | + | 0.149604i | \(0.0477998\pi\) |
−0.711978 | + | 0.702202i | \(0.752200\pi\) | |||||||
\(938\) | −427846. | + | 588880.i | −0.486275 | + | 0.669301i | ||||
\(939\) | 757319. | + | 406614.i | 0.858911 | + | 0.461159i | ||||
\(940\) | −27961.1 | + | 86055.5i | −0.0316445 | + | 0.0973919i | ||||
\(941\) | 456702. | + | 148392.i | 0.515767 | + | 0.167583i | 0.555324 | − | 0.831634i | \(-0.312594\pi\) |
−0.0395563 | + | 0.999217i | \(0.512594\pi\) | |||||||
\(942\) | 326949. | − | 608945.i | 0.368450 | − | 0.686240i | ||||
\(943\) | −325750. | − | 236672.i | −0.366321 | − | 0.266148i | ||||
\(944\) | 369984. | − | 120215.i | 0.415183 | − | 0.134901i | ||||
\(945\) | −108451. | + | 481406.i | −0.121442 | + | 0.539073i | ||||
\(946\) | 104868. | + | 10817.3i | 0.117182 | + | 0.0120875i | ||||
\(947\) | 488147.i | 0.544315i | 0.962253 | + | 0.272158i | \(0.0877372\pi\) | ||||
−0.962253 | + | 0.272158i | \(0.912263\pi\) | |||||||
\(948\) | −262300. | + | 251257.i | −0.291865 | + | 0.279577i | ||||
\(949\) | −261453. | − | 189957.i | −0.290310 | − | 0.210922i | ||||
\(950\) | 236977. | + | 326171.i | 0.262578 | + | 0.361408i | ||||
\(951\) | 89476.6 | + | 655908.i | 0.0989346 | + | 0.725240i | ||||
\(952\) | −259305. | + | 798059.i | −0.286113 | + | 0.880564i | ||||
\(953\) | −669623. | − | 921658.i | −0.737301 | − | 1.01481i | −0.998769 | − | 0.0495957i | \(-0.984207\pi\) |
0.261468 | − | 0.965212i | \(-0.415793\pi\) | |||||||
\(954\) | −722684. | + | 200911.i | −0.794057 | + | 0.220753i | ||||
\(955\) | 43375.9 | + | 133497.i | 0.0475600 | + | 0.146375i | ||||
\(956\) | − | 98059.1i | − | 0.107293i | ||||||
\(957\) | 1.47915e6 | − | 48521.4i | 1.61505 | − | 0.0529797i | ||||
\(958\) | −859943. | −0.936998 | ||||||||
\(959\) | 1.77808e6 | − | 577734.i | 1.93337 | − | 0.628190i | ||||
\(960\) | 65237.1 | + | 11775.5i | 0.0707868 | + | 0.0127772i | ||||
\(961\) | 454067. | − | 329899.i | 0.491669 | − | 0.357219i | ||||
\(962\) | −168238. | − | 54664.0i | −0.181792 | − | 0.0590678i | ||||
\(963\) | −821363. | + | 544397.i | −0.885692 | + | 0.587033i | ||||
\(964\) | −692406. | + | 503062.i | −0.745087 | + | 0.541337i | ||||
\(965\) | 210973. | − | 290379.i | 0.226554 | − | 0.311825i | ||||
\(966\) | −416785. | + | 399238.i | −0.446641 | + | 0.427836i | ||||
\(967\) | −784279. | −0.838721 | −0.419361 | − | 0.907820i | \(-0.637746\pi\) | ||||
−0.419361 | + | 0.907820i | \(0.637746\pi\) | |||||||
\(968\) | 815152. | − | 88862.0i | 0.869938 | − | 0.0948343i | ||||
\(969\) | 584618. | − | 282214.i | 0.622622 | − | 0.300560i | ||||
\(970\) | −57200.6 | − | 176045.i | −0.0607935 | − | 0.187103i | ||||
\(971\) | 283805. | − | 390624.i | 0.301011 | − | 0.414306i | −0.631541 | − | 0.775343i | \(-0.717577\pi\) |
0.932551 | + | 0.361037i | \(0.117577\pi\) | |||||||
\(972\) | −185281. | + | 683864.i | −0.196109 | + | 0.723831i | ||||
\(973\) | 445181. | − | 1.37013e6i | 0.470231 | − | 1.44722i | ||||
\(974\) | −604814. | − | 196516.i | −0.637534 | − | 0.207147i | ||||
\(975\) | 209270. | + | 112360.i | 0.220140 | + | 0.118196i | ||||
\(976\) | −5252.75 | − | 3816.35i | −0.00551426 | − | 0.00400634i | ||||
\(977\) | 1.43049e6 | − | 464795.i | 1.49864 | − | 0.486937i | 0.559018 | − | 0.829156i | \(-0.311178\pi\) |
0.939620 | + | 0.342219i | \(0.111178\pi\) | |||||||
\(978\) | −254561. | + | 122885.i | −0.266142 | + | 0.128476i | ||||
\(979\) | −412006. | + | 930213.i | −0.429871 | + | 0.970548i | ||||
\(980\) | − | 367148.i | − | 0.382287i | ||||||
\(981\) | −621580. | − | 231951.i | −0.645891 | − | 0.241023i | ||||
\(982\) | −209072. | − | 151900.i | −0.216807 | − | 0.157519i | ||||
\(983\) | −648995. | − | 893265.i | −0.671636 | − | 0.924428i | 0.328160 | − | 0.944622i | \(-0.393572\pi\) |
−0.999796 | + | 0.0201942i | \(0.993572\pi\) | |||||||
\(984\) | −480249. | + | 65513.8i | −0.495994 | + | 0.0676617i | ||||
\(985\) | −139310. | + | 428753.i | −0.143586 | + | 0.441911i | ||||
\(986\) | 312684. | + | 430372.i | 0.321626 | + | 0.442681i | ||||
\(987\) | −578386. | − | 104400.i | −0.593722 | − | 0.107168i | ||||
\(988\) | 65959.5 | + | 203002.i | 0.0675714 | + | 0.207964i | ||||
\(989\) | − | 182388.i | − | 0.186468i | ||||||
\(990\) | 123940. | + | 121173.i | 0.126457 | + | 0.123633i | ||||
\(991\) | 324901. | 0.330829 | 0.165414 | − | 0.986224i | \(-0.447104\pi\) | ||||
0.165414 | + | 0.986224i | \(0.447104\pi\) | |||||||
\(992\) | −604494. | + | 196412.i | −0.614284 | + | 0.199593i | ||||
\(993\) | −251289. | + | 1.39216e6i | −0.254845 | + | 1.41186i | ||||
\(994\) | −361378. | + | 262557.i | −0.365754 | + | 0.265736i | ||||
\(995\) | 179356. | + | 58276.2i | 0.181163 | + | 0.0588633i | ||||
\(996\) | −112456. | − | 824358.i | −0.113361 | − | 0.830992i | ||||
\(997\) | −14244.7 | + | 10349.4i | −0.0143306 | + | 0.0104118i | −0.594927 | − | 0.803779i | \(-0.702819\pi\) |
0.580597 | + | 0.814191i | \(0.302819\pi\) | |||||||
\(998\) | 208735. | − | 287299.i | 0.209573 | − | 0.288452i | ||||
\(999\) | −123490. | − | 1.33007e6i | −0.123737 | − | 1.33273i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 33.5.h.a.5.6 | ✓ | 56 | |
3.2 | odd | 2 | inner | 33.5.h.a.5.9 | yes | 56 | |
11.9 | even | 5 | inner | 33.5.h.a.20.9 | yes | 56 | |
33.20 | odd | 10 | inner | 33.5.h.a.20.6 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.5.h.a.5.6 | ✓ | 56 | 1.1 | even | 1 | trivial | |
33.5.h.a.5.9 | yes | 56 | 3.2 | odd | 2 | inner | |
33.5.h.a.20.6 | yes | 56 | 33.20 | odd | 10 | inner | |
33.5.h.a.20.9 | yes | 56 | 11.9 | even | 5 | inner |