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 | 5.9 | ||
Character | \(\chi\) | \(=\) | 33.5 |
Dual form | 33.5.h.a.20.9 |
$q$-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 | −0.0614026 | − | 0.998113i | \(-0.519557\pi\) |
0.537000 | + | 0.843582i | \(0.319557\pi\) | |||||||
\(3\) | −7.92936 | + | 4.25737i | −0.881040 | + | 0.473041i | ||||
\(4\) | −9.70726 | + | 7.05274i | −0.606704 | + | 0.440796i | ||||
\(5\) | 8.40855 | + | 2.73210i | 0.336342 | + | 0.109284i | 0.472319 | − | 0.881428i | \(-0.343417\pi\) |
−0.135977 | + | 0.990712i | \(0.543417\pi\) | |||||||
\(6\) | −12.4532 | + | 13.0005i | −0.345921 | + | 0.361125i | ||||
\(7\) | −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 | ||||
\(9\) | 44.7496 | − | 67.5164i | 0.552465 | − | 0.833536i | ||||
\(10\) | 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 | ||||
\(15\) | −78.3061 | + | 14.1344i | −0.348027 | + | 0.0628198i | ||||
\(16\) | 24.7069 | − | 76.0400i | 0.0965113 | − | 0.297031i | ||||
\(17\) | −186.116 | − | 60.4726i | −0.643999 | − | 0.209248i | −0.0312325 | − | 0.999512i | \(-0.509943\pi\) |
−0.612766 | + | 0.790264i | \(0.709943\pi\) | |||||||
\(18\) | 43.3978 | − | 156.104i | 0.133944 | − | 0.481801i | ||||
\(19\) | 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 | \(0.129524\pi\) | ||||
−0.918348 | + | 0.395774i | \(0.870476\pi\) | |||||||
\(24\) | 68.1300 | − | 499.427i | 0.118281 | − | 0.867061i | ||||
\(25\) | −442.396 | − | 321.420i | −0.707834 | − | 0.514272i | ||||
\(26\) | −56.7450 | − | 78.1028i | −0.0839424 | − | 0.115537i | ||||
\(27\) | −67.3939 | + | 725.878i | −0.0924471 | + | 0.995718i | ||||
\(28\) | 283.883 | − | 873.703i | 0.362096 | − | 1.11442i | ||||
\(29\) | 798.795 | + | 1099.45i | 0.949816 | + | 1.30731i | 0.951609 | + | 0.307311i | \(0.0994291\pi\) |
−0.00179349 | + | 0.999998i | \(0.500571\pi\) | |||||||
\(30\) | −140.232 | + | 75.2921i | −0.155813 | + | 0.0836579i | ||||
\(31\) | 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 | ||||||
\(33\) | −1085.87 | + | 82.4586i | −0.997129 | + | 0.0757196i | ||||
\(34\) | −391.444 | −0.338620 | ||||||||
\(35\) | −643.784 | + | 209.178i | −0.525538 | + | 0.170758i | ||||
\(36\) | 41.7793 | + | 971.007i | 0.0322371 | + | 0.749234i | ||||
\(37\) | −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 | ||||
\(39\) | 313.677 | + | 300.471i | 0.206231 | + | 0.197548i | ||||
\(40\) | −400.595 | + | 291.050i | −0.250372 | + | 0.181906i | ||||
\(41\) | −565.214 | + | 777.950i | −0.336237 | + | 0.462790i | −0.943338 | − | 0.331835i | \(-0.892332\pi\) |
0.607101 | + | 0.794625i | \(0.292332\pi\) | |||||||
\(42\) | 186.302 | − | 1365.69i | 0.105613 | − | 0.774199i | ||||
\(43\) | 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 | −0.680319 | − | 0.732916i | \(-0.738159\pi\) |
0.907275 | + | 0.420538i | \(0.138159\pi\) | |||||||
\(48\) | 127.820 | + | 708.135i | 0.0554776 | + | 0.307350i | ||||
\(49\) | 1069.47 | − | 3291.50i | 0.445428 | − | 1.37089i | ||||
\(50\) | −1040.29 | − | 338.010i | −0.416115 | − | 0.135204i | ||||
\(51\) | 1733.23 | − | 312.853i | 0.666372 | − | 0.120282i | ||||
\(52\) | 468.503 | + | 340.387i | 0.173263 | + | 0.125883i | ||||
\(53\) | 4402.93 | − | 1430.60i | 1.56744 | − | 0.509292i | 0.608656 | − | 0.793434i | \(-0.291709\pi\) |
0.958782 | + | 0.284143i | \(0.0917089\pi\) | |||||||
\(54\) | 320.473 | + | 1422.56i | 0.109902 | + | 0.487847i | ||||
\(55\) | 796.394 | + | 714.295i | 0.263271 | + | 0.236130i | ||||
\(56\) | − | 4287.97i | − | 1.36734i | ||||||
\(57\) | −3286.84 | − | 448.379i | −1.01165 | − | 0.138005i | ||||
\(58\) | 2199.22 | + | 1597.82i | 0.653750 | + | 0.474977i | ||||
\(59\) | −2859.96 | − | 3936.40i | −0.821591 | − | 1.13082i | −0.989430 | − | 0.145009i | \(-0.953679\pi\) |
0.167839 | − | 0.985814i | \(-0.446321\pi\) | |||||||
\(60\) | 660.450 | − | 689.479i | 0.183458 | − | 0.191522i | ||||
\(61\) | 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 | ||||
\(63\) | 266.588 | + | 6195.87i | 0.0671676 | + | 1.56107i | ||||
\(64\) | −257.443 | − | 792.330i | −0.0628524 | − | 0.193440i | ||||
\(65\) | − | 426.708i | − | 0.100996i | ||||||
\(66\) | −2014.79 | + | 828.074i | −0.462531 | + | 0.190100i | ||||
\(67\) | −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 | ||||
\(69\) | −1782.68 | − | 3320.26i | −0.374435 | − | 0.697386i | ||||
\(70\) | −1095.43 | + | 795.877i | −0.223557 | + | 0.162424i | ||||
\(71\) | 2773.95 | + | 901.311i | 0.550278 | + | 0.178796i | 0.570942 | − | 0.820990i | \(-0.306578\pi\) |
−0.0206643 | + | 0.999786i | \(0.506578\pi\) | |||||||
\(72\) | 1586.02 | + | 4250.19i | 0.305945 | + | 0.819868i | ||||
\(73\) | 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 | ||||
\(75\) | 4876.32 | + | 665.210i | 0.866902 | + | 0.118260i | ||||
\(76\) | −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 | ||||
\(81\) | −2555.94 | − | 6042.67i | −0.389565 | − | 0.920999i | ||||
\(82\) | −594.388 | + | 1829.34i | −0.0883980 | + | 0.272061i | ||||
\(83\) | 7327.31 | + | 2380.79i | 1.06362 | + | 0.345592i | 0.788001 | − | 0.615673i | \(-0.211116\pi\) |
0.275623 | + | 0.961266i | \(0.411116\pi\) | |||||||
\(84\) | 1468.66 | + | 8136.51i | 0.208144 | + | 1.15313i | ||||
\(85\) | −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 | \(0.178087\pi\) | ||||
−0.847533 | + | 0.530743i | \(0.821913\pi\) | |||||||
\(90\) | 791.404 | − | 1194.04i | 0.0977041 | − | 0.147412i | ||||
\(91\) | 2989.46 | + | 2171.97i | 0.361002 | + | 0.262283i | ||||
\(92\) | −2953.19 | − | 4064.71i | −0.348911 | − | 0.480235i | ||||
\(93\) | −3911.82 | − | 3747.13i | −0.452286 | − | 0.433244i | ||||
\(94\) | 527.223 | − | 1622.63i | 0.0596676 | − | 0.183638i | ||||
\(95\) | 1915.46 | + | 2636.41i | 0.212240 | + | 0.292123i | ||||
\(96\) | 4495.88 | + | 8373.59i | 0.487834 | + | 0.908593i | ||||
\(97\) | −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 | ||||||
\(99\) | 8259.23 | − | 5276.81i | 0.842693 | − | 0.538395i | ||||
\(100\) | 6561.34 | 0.656134 | ||||||||
\(101\) | 3450.32 | − | 1121.08i | 0.338234 | − | 0.109899i | −0.134975 | − | 0.990849i | \(-0.543096\pi\) |
0.473209 | + | 0.880950i | \(0.343096\pi\) | |||||||
\(102\) | 3103.90 | − | 1666.52i | 0.298338 | − | 0.160181i | ||||
\(103\) | −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 | ||||
\(105\) | 4214.25 | − | 4399.47i | 0.382245 | − | 0.399045i | ||||
\(106\) | 7491.81 | − | 5443.12i | 0.666769 | − | 0.484436i | ||||
\(107\) | −7150.63 | + | 9842.00i | −0.624564 | + | 0.859639i | −0.997675 | − | 0.0681480i | \(-0.978291\pi\) |
0.373111 | + | 0.927787i | \(0.378291\pi\) | |||||||
\(108\) | −4465.22 | − | 7521.60i | −0.382820 | − | 0.644856i | ||||
\(109\) | 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 | \(0.426534\pi\) |
−0.996528 | + | 0.0832631i | \(0.973466\pi\) | |||||||
\(114\) | −6530.01 | + | 1178.68i | −0.502463 | + | 0.0906959i | ||||
\(115\) | −1144.01 | + | 3520.91i | −0.0865037 | + | 0.266231i | ||||
\(116\) | −15508.2 | − | 5038.93i | −1.15251 | − | 0.374474i | ||||
\(117\) | −3766.47 | − | 1047.10i | −0.275146 | − | 0.0764923i | ||||
\(118\) | −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 | ||||||
\(123\) | 1169.77 | − | 8574.98i | 0.0773195 | − | 0.566791i | ||||
\(124\) | −5842.64 | − | 4244.92i | −0.379984 | − | 0.276075i | ||||
\(125\) | −6089.74 | − | 8381.81i | −0.389744 | − | 0.536436i | ||||
\(126\) | 4336.97 | + | 11622.2i | 0.273178 | + | 0.732060i | ||||
\(127\) | −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 | ||||
\(129\) | −3453.83 | + | 1854.40i | −0.207550 | + | 0.111436i | ||||
\(130\) | −263.759 | − | 811.765i | −0.0156070 | − | 0.0480335i | ||||
\(131\) | 5121.14i | 0.298417i | 0.988806 | + | 0.149209i | \(0.0476726\pi\) | ||||
−0.988806 | + | 0.149209i | \(0.952327\pi\) | |||||||
\(132\) | 9959.30 | − | 8458.83i | 0.571585 | − | 0.485470i | ||||
\(133\) | −28220.1 | −1.59535 | ||||||||
\(134\) | −9041.84 | + | 2937.87i | −0.503555 | + | 0.163615i | ||||
\(135\) | −2549.86 | + | 5919.46i | −0.139910 | + | 0.324799i | ||||
\(136\) | 8866.81 | − | 6442.12i | 0.479391 | − | 0.348298i | ||||
\(137\) | 23223.8 | + | 7545.87i | 1.23735 | + | 0.402039i | 0.853371 | − | 0.521303i | \(-0.174554\pi\) |
0.383977 | + | 0.923342i | \(0.374554\pi\) | |||||||
\(138\) | −5443.69 | − | 5214.51i | −0.285848 | − | 0.273814i | ||||
\(139\) | −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 | ||||
\(141\) | −1037.58 | + | 7606.01i | −0.0521898 | + | 0.382577i | ||||
\(142\) | 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 | ||||
\(147\) | 5532.88 | + | 30652.6i | 0.256045 | + | 1.41851i | ||||
\(148\) | 6794.08 | − | 20910.0i | 0.310175 | − | 0.954622i | ||||
\(149\) | −4470.47 | − | 1452.54i | −0.201363 | − | 0.0654270i | 0.206599 | − | 0.978426i | \(-0.433761\pi\) |
−0.407962 | + | 0.912999i | \(0.633761\pi\) | |||||||
\(150\) | 9687.86 | − | 1748.68i | 0.430571 | − | 0.0777193i | ||||
\(151\) | 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 | ||||||||
\(156\) | −5164.08 | − | 704.466i | −0.212199 | − | 0.0289475i | ||||
\(157\) | −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 | ||||
\(159\) | −28821.9 | + | 30088.7i | −1.14006 | + | 1.19017i | ||||
\(160\) | 2885.17 | − | 8879.63i | 0.112702 | − | 0.346860i | ||||
\(161\) | −18843.9 | − | 25936.4i | −0.726974 | − | 1.00059i | ||||
\(162\) | −8597.52 | − | 9915.64i | −0.327599 | − | 0.377825i | ||||
\(163\) | 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 | ||||||
\(165\) | −9355.91 | − | 2273.36i | −0.343651 | − | 0.0835028i | ||||
\(166\) | 15411.0 | 0.559262 | ||||||||
\(167\) | −7682.69 | + | 2496.26i | −0.275474 | + | 0.0895069i | −0.443496 | − | 0.896276i | \(-0.646262\pi\) |
0.168022 | + | 0.985783i | \(0.446262\pi\) | |||||||
\(168\) | 18255.5 | + | 34000.9i | 0.646807 | + | 1.20468i | ||||
\(169\) | 21221.9 | − | 15418.6i | 0.743036 | − | 0.539848i | ||||
\(170\) | −3291.48 | − | 1069.47i | −0.113892 | − | 0.0370058i | ||||
\(171\) | 27971.5 | − | 10437.9i | 0.956584 | − | 0.356962i | ||||
\(172\) | −4228.24 | + | 3072.00i | −0.142923 | + | 0.103840i | ||||
\(173\) | 34883.7 | − | 48013.2i | 1.16555 | − | 1.60424i | 0.477354 | − | 0.878711i | \(-0.341596\pi\) |
0.688194 | − | 0.725527i | \(-0.258404\pi\) | |||||||
\(174\) | −24240.9 | − | 3306.86i | −0.800664 | − | 0.109224i | ||||
\(175\) | 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 | −0.311470 | − | 0.950256i | \(-0.600821\pi\) |
0.999997 | + | 0.00258020i | \(0.000821302\pi\) | |||||||
\(180\) | −2301.59 | + | 8278.91i | −0.0710367 | + | 0.255522i | ||||
\(181\) | 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 | ||||
\(183\) | 129.825 | + | 719.240i | 0.00387664 | + | 0.0214769i | ||||
\(184\) | −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 | ||||||||
\(189\) | −28492.0 | − | 47994.3i | −0.797625 | − | 1.34359i | ||||
\(190\) | 5273.59 | + | 3831.49i | 0.146083 | + | 0.106135i | ||||
\(191\) | 9331.90 | + | 12844.3i | 0.255802 | + | 0.352081i | 0.917533 | − | 0.397661i | \(-0.130178\pi\) |
−0.661731 | + | 0.749741i | \(0.730178\pi\) | |||||||
\(192\) | 5414.60 | + | 5186.64i | 0.146880 | + | 0.140697i | ||||
\(193\) | −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 | ||||
\(195\) | 1816.65 | + | 3383.52i | 0.0477752 | + | 0.0889815i | ||||
\(196\) | 12832.4 | + | 39494.1i | 0.334039 | + | 1.02806i | ||||
\(197\) | 50990.1i | 1.31387i | 0.753946 | + | 0.656937i | \(0.228148\pi\) | ||||
−0.753946 | + | 0.656937i | \(0.771852\pi\) | |||||||
\(198\) | 12450.6 | − | 15143.8i | 0.317584 | − | 0.386282i | ||||
\(199\) | −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 | ||||
\(201\) | 37687.3 | − | 20234.8i | 0.932832 | − | 0.500848i | ||||
\(202\) | 5870.89 | − | 4265.45i | 0.143880 | − | 0.104535i | ||||
\(203\) | −98955.9 | − | 32152.7i | −2.40132 | − | 0.780235i | ||||
\(204\) | −14618.5 | + | 15261.0i | −0.351270 | + | 0.366709i | ||||
\(205\) | −6878.07 | + | 4997.21i | −0.163666 | + | 0.118910i | ||||
\(206\) | −118.311 | + | 162.841i | −0.00278798 | + | 0.00383733i | ||||
\(207\) | 28271.1 | + | 18738.0i | 0.659784 | + | 0.437303i | ||||
\(208\) | −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 | ||||
\(213\) | −25832.9 | + | 4662.90i | −0.569395 | + | 0.102777i | ||||
\(214\) | −7519.72 | + | 23143.3i | −0.164200 | + | 0.505357i | ||||
\(215\) | 3662.56 | + | 1190.04i | 0.0792332 | + | 0.0257444i | ||||
\(216\) | −30670.7 | − | 26949.1i | −0.657380 | − | 0.577612i | ||||
\(217\) | −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 | ||||||||
\(222\) | 4458.70 | − | 32684.5i | 0.0904695 | − | 0.663187i | ||||
\(223\) | 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 | ||||
\(225\) | −41498.2 | + | 15485.6i | −0.819717 | + | 0.305888i | ||||
\(226\) | −10309.7 | + | 31730.0i | −0.201850 | + | 0.621231i | ||||
\(227\) | −27590.5 | − | 37975.1i | −0.535437 | − | 0.736966i | 0.452510 | − | 0.891759i | \(-0.350529\pi\) |
−0.987947 | + | 0.154794i | \(0.950529\pi\) | |||||||
\(228\) | 35068.5 | − | 18828.7i | 0.674602 | − | 0.362202i | ||||
\(229\) | −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 | ||||||||
\(231\) | 63549.0 | − | 53974.7i | 1.19093 | − | 1.01150i | ||||
\(232\) | −76111.5 | −1.41408 | ||||||||
\(233\) | 29024.2 | − | 9430.53i | 0.534624 | − | 0.173710i | −0.0292480 | − | 0.999572i | \(-0.509311\pi\) |
0.563872 | + | 0.825862i | \(0.309311\pi\) | |||||||
\(234\) | −7812.55 | + | 336.149i | −0.142679 | + | 0.00613903i | ||||
\(235\) | 6100.86 | − | 4432.53i | 0.110473 | − | 0.0802632i | ||||
\(236\) | 55524.7 | + | 18041.1i | 0.996925 | + | 0.323920i | ||||
\(237\) | −21860.5 | − | 20940.1i | −0.389192 | − | 0.372806i | ||||
\(238\) | 24246.4 | − | 17616.0i | 0.428048 | − | 0.310995i | ||||
\(239\) | 4803.61 | − | 6611.60i | 0.0840954 | − | 0.115747i | −0.764897 | − | 0.644153i | \(-0.777210\pi\) |
0.848992 | + | 0.528406i | \(0.177210\pi\) | |||||||
\(240\) | −859.916 | + | 6303.61i | −0.0149291 | + | 0.109438i | ||||
\(241\) | 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 | ||||
\(246\) | −3075.05 | − | 17036.0i | −0.0508138 | − | 0.281513i | ||||
\(247\) | 5497.16 | − | 16918.5i | 0.0901040 | − | 0.277312i | ||||
\(248\) | −32059.2 | − | 10416.7i | −0.521253 | − | 0.169365i | ||||
\(249\) | −68236.8 | + | 12316.9i | −1.10058 | + | 0.198657i | ||||
\(250\) | −16766.1 | − | 12181.3i | −0.268257 | − | 0.194900i | ||||
\(251\) | −90729.5 | + | 29479.8i | −1.44013 | + | 0.467926i | −0.921937 | − | 0.387339i | \(-0.873394\pi\) |
−0.518191 | + | 0.855265i | \(0.673394\pi\) | |||||||
\(252\) | −46285.7 | − | 58264.7i | −0.728862 | − | 0.917497i | ||||
\(253\) | −20518.3 | + | 46325.6i | −0.320554 | + | 0.723736i | ||||
\(254\) | 14616.8i | 0.226560i | ||||||||
\(255\) | 15428.7 | + | 2104.73i | 0.237274 | + | 0.0323680i | ||||
\(256\) | 35430.1 | + | 25741.5i | 0.540620 | + | 0.392783i | ||||
\(257\) | −6159.31 | − | 8477.57i | −0.0932537 | − | 0.128353i | 0.759841 | − | 0.650109i | \(-0.225277\pi\) |
−0.853094 | + | 0.521757i | \(0.825277\pi\) | |||||||
\(258\) | −5424.29 | + | 5662.70i | −0.0814899 | + | 0.0850715i | ||||
\(259\) | 43352.2 | − | 133424.i | 0.646266 | − | 1.98900i | ||||
\(260\) | 3009.46 | + | 4142.16i | 0.0445186 | + | 0.0612746i | ||||
\(261\) | 109977. | − | 4731.94i | 1.61443 | − | 0.0694637i | ||||
\(262\) | 3165.50 | + | 9742.41i | 0.0461148 | + | 0.141927i | ||||
\(263\) | 30267.6i | 0.437589i | 0.975771 | + | 0.218795i | \(0.0702124\pi\) | ||||
−0.975771 | + | 0.218795i | \(0.929788\pi\) | |||||||
\(264\) | 32010.1 | − | 51915.1i | 0.459282 | − | 0.744879i | ||||
\(265\) | 40930.8 | 0.582853 | ||||||||
\(266\) | −53685.7 | + | 17443.5i | −0.758744 | + | 0.246531i | ||||
\(267\) | −35796.1 | − | 66670.3i | −0.502126 | − | 0.935212i | ||||
\(268\) | 46137.4 | − | 33520.8i | 0.642368 | − | 0.466708i | ||||
\(269\) | −16179.4 | − | 5257.01i | −0.223593 | − | 0.0726498i | 0.195078 | − | 0.980788i | \(-0.437504\pi\) |
−0.418671 | + | 0.908138i | \(0.637504\pi\) | |||||||
\(270\) | −1191.87 | + | 12837.3i | −0.0163494 | + | 0.176094i | ||||
\(271\) | −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 | ||||
\(273\) | −32951.3 | − | 4495.10i | −0.442128 | − | 0.0603135i | ||||
\(274\) | 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 | ||||
\(279\) | 46971.2 | + | 13058.3i | 0.603425 | + | 0.167756i | ||||
\(280\) | 11715.2 | − | 36055.7i | 0.149428 | − | 0.459894i | ||||
\(281\) | 74585.3 | + | 24234.2i | 0.944584 | + | 0.306914i | 0.740513 | − | 0.672042i | \(-0.234583\pi\) |
0.204071 | + | 0.978956i | \(0.434583\pi\) | |||||||
\(282\) | 2727.57 | + | 15111.0i | 0.0342987 | + | 0.190018i | ||||
\(283\) | −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 | ||||||
\(288\) | −71298.9 | − | 47256.7i | −0.859603 | − | 0.569742i | ||||
\(289\) | −36587.8 | − | 26582.6i | −0.438067 | − | 0.318275i | ||||
\(290\) | 14126.8 | + | 19443.9i | 0.167976 | + | 0.231199i | ||||
\(291\) | 68026.2 | + | 65162.2i | 0.803324 | + | 0.769502i | ||||
\(292\) | −24828.0 | + | 76412.8i | −0.291190 | + | 0.896190i | ||||
\(293\) | 54108.1 | + | 74473.4i | 0.630271 | + | 0.867493i | 0.998050 | − | 0.0624198i | \(-0.0198818\pi\) |
−0.367779 | + | 0.929913i | \(0.619882\pi\) | |||||||
\(294\) | 29472.9 | + | 54893.3i | 0.340979 | + | 0.635075i | ||||
\(295\) | −13293.5 | − | 40913.1i | −0.152755 | − | 0.470130i | ||||
\(296\) | − | 102623.i | − | 1.17128i | ||||||
\(297\) | −43025.1 | + | 77004.3i | −0.487764 | + | 0.872976i | ||||
\(298\) | −9402.44 | −0.105879 | ||||||||
\(299\) | 19220.1 | − | 6244.98i | 0.214987 | − | 0.0698536i | ||||
\(300\) | −52027.3 | + | 27934.0i | −0.578081 | + | 0.310378i | ||||
\(301\) | −26979.8 | + | 19602.0i | −0.297787 | + | 0.216355i | ||||
\(302\) | 41202.5 | + | 13387.5i | 0.451762 | + | 0.146786i | ||||
\(303\) | −22586.0 | + | 23578.7i | −0.246011 | + | 0.256824i | ||||
\(304\) | 23841.5 | − | 17321.9i | 0.257980 | − | 0.187434i | ||||
\(305\) | 422.014 | − | 580.852i | 0.00453657 | − | 0.00624405i | ||||
\(306\) | −17517.0 | + | 26428.9i | −0.187075 | + | 0.282252i | ||||
\(307\) | 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 | −0.637466 | − | 0.770478i | \(-0.720018\pi\) |
0.929756 | + | 0.368176i | \(0.120018\pi\) | |||||||
\(312\) | −23940.3 | + | 4321.29i | −0.245935 | + | 0.0443919i | ||||
\(313\) | −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 | ||||
\(315\) | −14686.1 | + | 52826.6i | −0.148008 | + | 0.532392i | ||||
\(316\) | −32650.5 | − | 23722.0i | −0.326976 | − | 0.237562i | ||||
\(317\) | 69953.7 | − | 22729.3i | 0.696132 | − | 0.226187i | 0.0604878 | − | 0.998169i | \(-0.480734\pi\) |
0.635645 | + | 0.771982i | \(0.280734\pi\) | |||||||
\(318\) | −36232.0 | + | 75055.9i | −0.358292 | + | 0.742216i | ||||
\(319\) | 34499.3 | + | 160778.i | 0.339023 | + | 1.57996i | ||||
\(320\) | − | 7365.71i | − | 0.0719307i | ||||||
\(321\) | 14799.0 | − | 108484.i | 0.143622 | − | 1.05282i | ||||
\(322\) | −51880.4 | − | 37693.3i | −0.500370 | − | 0.363540i | ||||
\(323\) | −42397.0 | − | 58354.5i | −0.406378 | − | 0.559331i | ||||
\(324\) | 67428.5 | + | 40631.4i | 0.642323 | + | 0.387054i | ||||
\(325\) | −8155.52 | + | 25100.1i | −0.0772121 | + | 0.237634i | ||||
\(326\) | 18461.0 | + | 25409.4i | 0.173708 | + | 0.239088i | ||||
\(327\) | −64947.2 | + | 34870.9i | −0.607386 | + | 0.326113i | ||||
\(328\) | −16642.2 | − | 51219.3i | −0.154690 | − | 0.476087i | ||||
\(329\) | 65303.6i | 0.603317i | ||||||||
\(330\) | −19203.8 | + | 1458.29i | −0.176344 | + | 0.0133911i | ||||
\(331\) | −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 | ||||
\(333\) | 6380.16 | + | 148284.i | 0.0575365 | + | 1.33723i | ||||
\(334\) | −13072.5 | + | 9497.72i | −0.117183 | + | 0.0851385i | ||||
\(335\) | −39964.9 | − | 12985.4i | −0.356114 | − | 0.115708i | ||||
\(336\) | −39785.2 | − | 38110.2i | −0.352406 | − | 0.337569i | ||||
\(337\) | 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 | ||||
\(339\) | 20289.7 | − | 148734.i | 0.176553 | − | 1.29422i | ||||
\(340\) | 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 | ||||
\(345\) | −5918.51 | − | 32789.0i | −0.0497249 | − | 0.275480i | ||||
\(346\) | 36684.2 | − | 112902.i | 0.306427 | − | 0.943086i | ||||
\(347\) | 50710.8 | + | 16476.9i | 0.421155 | + | 0.136841i | 0.511925 | − | 0.859030i | \(-0.328933\pi\) |
−0.0907698 | + | 0.995872i | \(0.528933\pi\) | |||||||
\(348\) | 144423. | − | 26068.7i | 1.19255 | − | 0.215259i | ||||
\(349\) | 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 | \(-0.825967\pi\) | ||
0.854223 | − | 0.519907i | \(-0.174033\pi\) | |||||||
\(354\) | 86790.7 | + | 11839.7i | 0.692575 | + | 0.0944786i | ||||
\(355\) | 20862.4 | + | 15157.4i | 0.165542 | + | 0.120273i | ||||
\(356\) | −59299.6 | − | 81618.9i | −0.467899 | − | 0.644007i | ||||
\(357\) | −93278.5 | + | 97378.3i | −0.731889 | + | 0.764057i | ||||
\(358\) | 23199.8 | − | 71401.6i | 0.181016 | − | 0.557111i | ||||
\(359\) | −55233.2 | − | 76022.0i | −0.428560 | − | 0.589862i | 0.539062 | − | 0.842266i | \(-0.318779\pi\) |
−0.967622 | + | 0.252404i | \(0.918779\pi\) | |||||||
\(360\) | 1724.13 | + | 40071.1i | 0.0133035 | + | 0.309191i | ||||
\(361\) | 1710.54 | + | 5264.50i | 0.0131256 | + | 0.0403964i | ||||
\(362\) | − | 113702.i | − | 0.867661i | ||||||
\(363\) | −124175. | − | 44086.7i | −0.942369 | − | 0.334576i | ||||
\(364\) | −44337.7 | −0.334634 | ||||||||
\(365\) | 56304.4 | − | 18294.4i | 0.422626 | − | 0.137320i | ||||
\(366\) | 691.557 | + | 1288.03i | 0.00516257 | + | 0.00961530i | ||||
\(367\) | 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 | ||||
\(369\) | 27231.3 | + | 72974.2i | 0.199993 | + | 0.535941i | ||||
\(370\) | −26216.6 | + | 19047.4i | −0.191502 | + | 0.139134i | ||||
\(371\) | −208340. | + | 286756.i | −1.51365 | + | 2.08336i | ||||
\(372\) | 64400.6 | + | 8785.30i | 0.465376 | + | 0.0634849i | ||||
\(373\) | −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 | ||||
\(378\) | −83869.3 | − | 73692.4i | −0.586975 | − | 0.515750i | ||||
\(379\) | 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 | ||||
\(381\) | −11682.1 | − | 64719.9i | −0.0804770 | − | 0.445849i | ||||
\(382\) | 25692.3 | + | 18666.5i | 0.176066 | + | 0.127920i | ||||
\(383\) | 189408. | − | 61542.4i | 1.29122 | − | 0.419543i | 0.418702 | − | 0.908124i | \(-0.362485\pi\) |
0.872519 | + | 0.488580i | \(0.162485\pi\) | |||||||
\(384\) | −123439. | − | 59588.2i | −0.837126 | − | 0.404108i | ||||
\(385\) | −81474.3 | − | 8404.17i | −0.549667 | − | 0.0566987i | ||||
\(386\) | 81205.7i | 0.545019i | ||||||||
\(387\) | 19491.8 | − | 29408.5i | 0.130146 | − | 0.196359i | ||||
\(388\) | 101603. | + | 73818.8i | 0.674905 | + | 0.490347i | ||||
\(389\) | −50459.2 | − | 69451.1i | −0.333458 | − | 0.458965i | 0.609059 | − | 0.793125i | \(-0.291547\pi\) |
−0.942516 | + | 0.334160i | \(0.891547\pi\) | |||||||
\(390\) | 5547.42 | + | 5313.87i | 0.0364722 | + | 0.0349367i | ||||
\(391\) | 25321.7 | − | 77932.0i | 0.165630 | − | 0.509756i | ||||
\(392\) | 113930. | + | 156812.i | 0.741425 | + | 1.02048i | ||||
\(393\) | −21802.6 | − | 40607.4i | −0.141164 | − | 0.262918i | ||||
\(394\) | 31518.2 | + | 97003.2i | 0.203034 | + | 0.624875i | ||||
\(395\) | 29737.8i | 0.190596i | ||||||||
\(396\) | −42958.6 | + | 109474.i | −0.273942 | + | 0.698102i | ||||
\(397\) | 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 | ||||
\(399\) | 223768. | − | 120143.i | 1.40557 | − | 0.754665i | ||||
\(400\) | −35371.0 | + | 25698.5i | −0.221069 | + | 0.160616i | ||||
\(401\) | −32573.5 | − | 10583.8i | −0.202571 | − | 0.0658192i | 0.205974 | − | 0.978557i | \(-0.433964\pi\) |
−0.408545 | + | 0.912738i | \(0.633964\pi\) | |||||||
\(402\) | 59188.4 | − | 61789.9i | 0.366256 | − | 0.382354i | ||||
\(403\) | 23501.0 | − | 17074.5i | 0.144702 | − | 0.105132i | ||||
\(404\) | −25586.5 | + | 35216.8i | −0.156765 | + | 0.215768i | ||||
\(405\) | −4982.54 | − | 57793.2i | −0.0303767 | − | 0.352344i | ||||
\(406\) | −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 | ||||
\(411\) | −216276. | + | 39038.3i | −1.28034 | + | 0.231104i | ||||
\(412\) | 373.107 | − | 1148.30i | 0.00219806 | − | 0.00676492i | ||||
\(413\) | 354296. | + | 115118.i | 2.07714 | + | 0.674904i | ||||
\(414\) | 65365.1 | + | 18171.9i | 0.381369 | + | 0.106023i | ||||
\(415\) | 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 | \(0.174468\pi\) | ||||
−0.853512 | + | 0.521074i | \(0.825532\pi\) | |||||||
\(420\) | −9880.47 | + | 72428.8i | −0.0560118 | + | 0.410594i | ||||
\(421\) | −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 | ||||
\(423\) | −24154.2 | − | 64728.2i | −0.134993 | − | 0.361754i | ||||
\(424\) | −80122.0 | + | 246590.i | −0.445677 | + | 1.37165i | ||||
\(425\) | 62899.8 | + | 86574.1i | 0.348234 | + | 0.479303i | ||||
\(426\) | −46262.0 | + | 24838.6i | −0.254921 | + | 0.136870i | ||||
\(427\) | 1921.30 | + | 5913.14i | 0.0105375 | + | 0.0324312i | ||||
\(428\) | − | 145970.i | − | 0.796851i | ||||||
\(429\) | 19979.8 | + | 48612.9i | 0.108562 | + | 0.264142i | ||||
\(430\) | 7703.21 | 0.0416615 | ||||||||
\(431\) | −1120.42 | + | 364.046i | −0.00603150 | + | 0.00195975i | −0.312031 | − | 0.950072i | \(-0.601009\pi\) |
0.306000 | + | 0.952032i | \(0.401009\pi\) | |||||||
\(432\) | 53530.7 | + | 23058.8i | 0.286837 | + | 0.123558i | ||||
\(433\) | −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 | ||||
\(435\) | −78090.6 | − | 74802.8i | −0.412686 | − | 0.395312i | ||||
\(436\) | −79509.4 | + | 57767.0i | −0.418259 | + | 0.303883i | ||||
\(437\) | −90717.7 | + | 124862.i | −0.475039 | + | 0.653835i | ||||
\(438\) | −16293.7 | + | 119441.i | −0.0849320 | + | 0.622594i | ||||
\(439\) | 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 | −0.903288 | − | 0.429035i | \(-0.858854\pi\) |
0.687168 | + | 0.726499i | \(0.258854\pi\) | |||||||
\(444\) | 35149.0 | + | 194728.i | 0.178298 | + | 0.987786i | ||||
\(445\) | −22971.6 | + | 70699.4i | −0.116004 | + | 0.357022i | ||||
\(446\) | 12049.6 | + | 3915.16i | 0.0605765 | + | 0.0196825i | ||||
\(447\) | 41632.0 | − | 7514.69i | 0.208359 | − | 0.0376093i | ||||
\(448\) | 51603.1 | + | 37491.9i | 0.257111 | + | 0.186802i | ||||
\(449\) | −15527.1 | + | 5045.05i | −0.0770188 | + | 0.0250249i | −0.347273 | − | 0.937764i | \(-0.612892\pi\) |
0.270254 | + | 0.962789i | \(0.412892\pi\) | |||||||
\(450\) | −69373.8 | + | 55110.7i | −0.342586 | + | 0.272152i | ||||
\(451\) | −100653. | + | 58371.4i | −0.494848 | + | 0.286977i | ||||
\(452\) | − | 200129.i | − | 0.979563i | ||||||
\(453\) | −193136. | − | 26346.9i | −0.941166 | − | 0.128390i | ||||
\(454\) | −75961.3 | − | 55189.1i | −0.368537 | − | 0.267758i | ||||
\(455\) | 19203.0 | + | 26430.6i | 0.0927567 | + | 0.127669i | ||||
\(456\) | 128517. | − | 134165.i | 0.618059 | − | 0.645224i | ||||
\(457\) | 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 | ||||
\(459\) | 56438.8 | − | 131022.i | 0.267888 | − | 0.621896i | ||||
\(460\) | −13726.8 | − | 42246.8i | −0.0648715 | − | 0.199654i | ||||
\(461\) | 131582.i | 0.619150i | 0.950875 | + | 0.309575i | \(0.100187\pi\) | ||||
−0.950875 | + | 0.309575i | \(0.899813\pi\) | |||||||
\(462\) | 87531.9 | − | 141962.i | 0.410093 | − | 0.665102i | ||||
\(463\) | 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 | ||||
\(465\) | −22655.2 | − | 42195.5i | −0.104776 | − | 0.195146i | ||||
\(466\) | 49386.1 | − | 35881.1i | 0.227422 | − | 0.165232i | ||||
\(467\) | 214194. | + | 69595.9i | 0.982140 | + | 0.319117i | 0.755707 | − | 0.654910i | \(-0.227293\pi\) |
0.226433 | + | 0.974027i | \(0.427293\pi\) | |||||||
\(468\) | 43947.1 | − | 16399.4i | 0.200650 | − | 0.0748751i | ||||
\(469\) | 294397. | − | 213892.i | 1.33841 | − | 0.972409i | ||||
\(470\) | 8866.36 | − | 12203.5i | 0.0401375 | − | 0.0552445i | ||||
\(471\) | 342361. | + | 46703.7i | 1.54327 | + | 0.210528i | ||||
\(472\) | 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 | ||||
\(477\) | 100441. | − | 361289.i | 0.441441 | − | 1.58788i | ||||
\(478\) | 5051.55 | − | 15547.1i | 0.0221090 | − | 0.0680445i | ||||
\(479\) | −408867. | − | 132849.i | −1.78201 | − | 0.579012i | −0.782943 | − | 0.622093i | \(-0.786283\pi\) |
−0.999072 | + | 0.0430814i | \(0.986283\pi\) | |||||||
\(480\) | 14926.3 | + | 82693.0i | 0.0647843 | + | 0.358911i | ||||
\(481\) | 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 | ||||||
\(486\) | 110387. | + | 42021.9i | 0.467355 | + | 0.177911i | ||||
\(487\) | 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 | ||||
\(489\) | −102049. | − | 97752.7i | −0.426768 | − | 0.408800i | ||||
\(490\) | 18913.8 | − | 58210.6i | 0.0787746 | − | 0.242443i | ||||
\(491\) | −75938.8 | − | 104521.i | −0.314993 | − | 0.433550i | 0.621937 | − | 0.783067i | \(-0.286346\pi\) |
−0.936930 | + | 0.349517i | \(0.886346\pi\) | |||||||
\(492\) | 49121.8 | + | 91489.6i | 0.202929 | + | 0.377956i | ||||
\(493\) | −82181.8 | − | 252930.i | −0.338128 | − | 1.04065i | ||||
\(494\) | − | 35583.6i | − | 0.145813i | ||||||
\(495\) | 83865.0 | − | 21805.2i | 0.342271 | − | 0.0889919i | ||||
\(496\) | 48122.5 | 0.195607 | ||||||||
\(497\) | −212382. | + | 69007.0i | −0.859814 | + | 0.279371i | ||||
\(498\) | −122200. | + | 65610.4i | −0.492733 | + | 0.264554i | ||||
\(499\) | −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 | ||||
\(501\) | 50291.4 | − | 52501.8i | 0.200363 | − | 0.209170i | ||||
\(502\) | −154381. | + | 112164.i | −0.612613 | + | 0.445089i | ||||
\(503\) | 223986. | − | 308290.i | 0.885288 | − | 1.21849i | −0.0896398 | − | 0.995974i | \(-0.528572\pi\) |
0.974928 | − | 0.222520i | \(-0.0714284\pi\) | |||||||
\(504\) | −289509. | − | 191885.i | −1.13973 | − | 0.755406i | ||||
\(505\) | 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 | −0.646705 | − | 0.762741i | \(-0.723853\pi\) |
0.925252 | + | 0.379353i | \(0.123853\pi\) | |||||||
\(510\) | 30652.5 | − | 5532.85i | 0.117849 | − | 0.0212720i | ||||
\(511\) | −158424. | + | 487580.i | −0.606708 | + | 1.86726i | ||||
\(512\) | −148439. | − | 48230.7i | −0.566250 | − | 0.183986i | ||||
\(513\) | −177358. | + | 201851.i | −0.673932 | + | 0.767002i | ||||
\(514\) | −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 | ||||||
\(519\) | −72195.3 | + | 529227.i | −0.268024 | + | 1.96475i | ||||
\(520\) | 19334.0 | + | 14047.0i | 0.0715015 | + | 0.0519489i | ||||
\(521\) | 16951.2 | + | 23331.3i | 0.0624489 | + | 0.0859536i | 0.839099 | − | 0.543979i | \(-0.183083\pi\) |
−0.776650 | + | 0.629932i | \(0.783083\pi\) | |||||||
\(522\) | 206293. | − | 76981.2i | 0.757085 | − | 0.282516i | ||||
\(523\) | −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 | ||||
\(525\) | −331979. | + | 178243.i | −1.20446 | + | 0.646688i | ||||
\(526\) | 18709.1 | + | 57580.8i | 0.0676211 | + | 0.208116i | ||||
\(527\) | − | 117785.i | − | 0.424099i | ||||||
\(528\) | −20558.4 | + | 84607.1i | −0.0737432 | + | 0.303486i | ||||
\(529\) | 104507. | 0.373451 | ||||||||
\(530\) | 77866.5 | − | 25300.4i | 0.277204 | − | 0.0900689i | ||||
\(531\) | −393754. | + | 16941.9i | −1.39648 | + | 0.0600861i | ||||
\(532\) | 273940. | − | 199029.i | 0.967904 | − | 0.703223i | ||||
\(533\) | 44138.4 | + | 14341.4i | 0.155368 | + | 0.0504822i | ||||
\(534\) | −109309. | − | 104707.i | −0.383330 | − | 0.367191i | ||||
\(535\) | −87015.9 | + | 63220.7i | −0.304012 | + | 0.220878i | ||||
\(536\) | 156462. | − | 215352.i | 0.544602 | − | 0.749581i | ||||
\(537\) | −45657.6 | + | 334693.i | −0.158331 | + | 1.16064i | ||||
\(538\) | −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 | ||||
\(543\) | 90873.6 | + | 503447.i | 0.308204 | + | 1.70747i | ||||
\(544\) | −63860.5 | + | 196542.i | −0.215792 | + | 0.664138i | ||||
\(545\) | 68872.1 | + | 22377.9i | 0.231873 | + | 0.0753401i | ||||
\(546\) | −65464.9 | + | 11816.6i | −0.219595 | + | 0.0396375i | ||||
\(547\) | −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 | ||||||||
\(552\) | 209125. | + | 28528.0i | 0.686321 | + | 0.0936254i | ||||
\(553\) | −208339. | − | 151367.i | −0.681270 | − | 0.494972i | ||||
\(554\) | 159277. | + | 219227.i | 0.518961 | + | 0.714289i | ||||
\(555\) | 100858. | − | 105291.i | 0.327435 | − | 0.341826i | ||||
\(556\) | 69768.1 | − | 214724.i | 0.225687 | − | 0.694594i | ||||
\(557\) | 47684.5 | + | 65632.0i | 0.153697 | + | 0.211546i | 0.878921 | − | 0.476967i | \(-0.158264\pi\) |
−0.725224 | + | 0.688513i | \(0.758264\pi\) | |||||||
\(558\) | 97429.2 | − | 4192.07i | 0.312911 | − | 0.0134636i | ||||
\(559\) | −6496.23 | − | 19993.3i | −0.0207892 | − | 0.0639825i | ||||
\(560\) | 54121.5i | 0.172581i | ||||||||
\(561\) | 207085. | + | 50318.8i | 0.657994 | + | 0.159884i | ||||
\(562\) | 156870. | 0.496670 | ||||||||
\(563\) | 198354. | − | 64449.1i | 0.625783 | − | 0.203329i | 0.0210771 | − | 0.999778i | \(-0.493290\pi\) |
0.604706 | + | 0.796448i | \(0.293290\pi\) | |||||||
\(564\) | −43571.1 | − | 81151.3i | −0.136975 | − | 0.255116i | ||||
\(565\) | −119301. | + | 86677.0i | −0.373720 | + | 0.271523i | ||||
\(566\) | −290971. | − | 94542.3i | −0.908275 | − | 0.295116i | ||||
\(567\) | 430253. | + | 259264.i | 1.33831 | + | 0.806447i | ||||
\(568\) | −132155. | + | 96016.2i | −0.409625 | + | 0.297610i | ||||
\(569\) | 140127. | − | 192868.i | 0.432810 | − | 0.595712i | −0.535785 | − | 0.844354i | \(-0.679984\pi\) |
0.968595 | + | 0.248642i | \(0.0799844\pi\) | |||||||
\(570\) | −58128.2 | − | 7929.65i | −0.178911 | − | 0.0244064i | ||||
\(571\) | −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 | ||||
\(576\) | −65015.8 | − | 18074.8i | −0.195963 | − | 0.0544789i | ||||
\(577\) | −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 | ||||
\(579\) | −64901.8 | − | 359562.i | −0.193598 | − | 1.07255i | ||||
\(580\) | −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 | ||||||||
\(585\) | −28809.8 | − | 19095.0i | −0.0841838 | − | 0.0557967i | ||||
\(586\) | 148969. | + | 108232.i | 0.433810 | + | 0.315182i | ||||
\(587\) | −177598. | − | 244442.i | −0.515420 | − | 0.709414i | 0.469402 | − | 0.882985i | \(-0.344470\pi\) |
−0.984821 | + | 0.173570i | \(0.944470\pi\) | |||||||
\(588\) | −269894. | − | 258531.i | −0.780618 | − | 0.747753i | ||||
\(589\) | −68554.3 | + | 210989.i | −0.197608 | + | 0.608174i | ||||
\(590\) | −50578.8 | − | 69615.7i | −0.145300 | − | 0.199988i | ||||
\(591\) | −217084. | − | 404319.i | −0.621516 | − | 1.15758i | ||||
\(592\) | 45271.8 | + | 139332.i | 0.129177 | + | 0.397565i | ||||
\(593\) | 101060.i | 0.287389i | 0.989622 | + | 0.143694i | \(0.0458982\pi\) | ||||
−0.989622 | + | 0.143694i | \(0.954102\pi\) | |||||||
\(594\) | −34252.4 | + | 173087.i | −0.0970774 | + | 0.490560i | ||||
\(595\) | 132468. | 0.374176 | ||||||||
\(596\) | 53640.4 | − | 17428.8i | 0.151008 | − | 0.0490654i | ||||
\(597\) | 169134. | − | 90810.2i | 0.474551 | − | 0.254792i | ||||
\(598\) | 32703.9 | − | 23760.8i | 0.0914529 | − | 0.0664445i | ||||
\(599\) | 73845.5 | + | 23993.9i | 0.205812 | + | 0.0668724i | 0.410109 | − | 0.912037i | \(-0.365491\pi\) |
−0.204297 | + | 0.978909i | \(0.565491\pi\) | |||||||
\(600\) | −190666. | + | 199046.i | −0.529628 | + | 0.552906i | ||||
\(601\) | 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 | ||||
\(603\) | −212690. | + | 320898.i | −0.584941 | + | 0.882535i | ||||
\(604\) | −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 | ||||
\(609\) | 921543. | − | 166341.i | 2.48474 | − | 0.448502i | ||||
\(610\) | 443.797 | − | 1365.87i | 0.00119268 | − | 0.00367070i | ||||
\(611\) | −39150.8 | − | 12720.9i | −0.104872 | − | 0.0340749i | ||||
\(612\) | 50943.6 | − | 183246.i | 0.136015 | − | 0.489251i | ||||
\(613\) | 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 | \(0.00816618\pi\) | ||||
−0.999671 | + | 0.0256520i | \(0.991834\pi\) | |||||||
\(618\) | 244.856 | − | 1794.92i | 0.000641112 | − | 0.00469967i | ||||
\(619\) | 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 | ||||
\(621\) | −303946. | − | 28219.8i | −0.788159 | − | 0.0731763i | ||||
\(622\) | 29729.8 | − | 91498.8i | 0.0768441 | − | 0.236502i | ||||
\(623\) | −378383. | − | 520800.i | −0.974890 | − | 1.34182i | ||||
\(624\) | 30597.8 | − | 16428.3i | 0.0785816 | − | 0.0421914i | ||||
\(625\) | 77306.8 | + | 237926.i | 0.197905 | + | 0.609090i | ||||
\(626\) | 191044.i | 0.487512i | ||||||||
\(627\) | −341665. | − | 210666.i | −0.869091 | − | 0.535870i | ||||
\(628\) | 460664. | 1.16806 | ||||||||
\(629\) | 341030. | − | 110807.i | 0.861968 | − | 0.280070i | ||||
\(630\) | 4714.65 | + | 109575.i | 0.0118787 | + | 0.276077i | ||||
\(631\) | 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 | ||||
\(633\) | −104950. | − | 100532.i | −0.261924 | − | 0.250897i | ||||
\(634\) | 119030. | − | 86480.1i | 0.296126 | − | 0.215148i | ||||
\(635\) | −37974.4 | + | 52267.3i | −0.0941768 | + | 0.129623i | ||||
\(636\) | 67574.0 | − | 495351.i | 0.167057 | − | 1.22461i | ||||
\(637\) | −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 | \(0.447181\pi\) |
−0.989035 | + | 0.147681i | \(0.952819\pi\) | |||||||
\(642\) | −38903.0 | − | 215526.i | −0.0943872 | − | 0.522913i | ||||
\(643\) | 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 | ||||
\(645\) | −34108.2 | + | 6156.61i | −0.0819859 | + | 0.0147987i | ||||
\(646\) | −116726. | − | 84806.4i | −0.279707 | − | 0.203219i | ||||
\(647\) | 310659. | − | 100939.i | 0.742122 | − | 0.241130i | 0.0865342 | − | 0.996249i | \(-0.472421\pi\) |
0.655588 | + | 0.755119i | \(0.272421\pi\) | |||||||
\(648\) | 357932. | + | 83112.4i | 0.852413 | + | 0.197932i | ||||
\(649\) | −123519. | − | 575641.i | −0.293255 | − | 1.36667i | ||||
\(650\) | 52791.4i | 0.124950i | ||||||||
\(651\) | 410932. | + | 56057.8i | 0.969634 | + | 0.132274i | ||||
\(652\) | −152419. | − | 110739.i | −0.358545 | − | 0.260498i | ||||
\(653\) | 119068. | + | 163883.i | 0.279234 | + | 0.384333i | 0.925480 | − | 0.378796i | \(-0.123662\pi\) |
−0.646246 | + | 0.763129i | \(0.723662\pi\) | |||||||
\(654\) | −102000. | + | 106484.i | −0.238477 | + | 0.248959i | ||||
\(655\) | −13991.5 | + | 43061.4i | −0.0326123 | + | 0.100370i | ||||
\(656\) | 45190.7 | + | 62199.6i | 0.105013 | + | 0.144537i | ||||
\(657\) | −23315.4 | − | 541881.i | −0.0540147 | − | 1.25537i | ||||
\(658\) | 40365.7 | + | 124233.i | 0.0932312 | + | 0.286936i | ||||
\(659\) | 664955.i | 1.53116i | 0.643339 | + | 0.765581i | \(0.277549\pi\) | ||||
−0.643339 | + | 0.765581i | \(0.722451\pi\) | |||||||
\(660\) | 106854. | − | 43916.7i | 0.245302 | − | 0.100819i | ||||
\(661\) | −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 | ||||
\(663\) | −40209.9 | − | 74891.2i | −0.0914758 | − | 0.170374i | ||||
\(664\) | −349083. | + | 253624.i | −0.791759 | + | 0.575247i | ||||
\(665\) | −237290. | − | 77100.3i | −0.536583 | − | 0.174346i | ||||
\(666\) | 103795. | + | 278150.i | 0.234007 | + | 0.627090i | ||||
\(667\) | −460370. | + | 334479.i | −1.03480 | + | 0.751825i | ||||
\(668\) | 56972.4 | − | 78415.8i | 0.127677 | − | 0.175732i | ||||
\(669\) | −56482.3 | − | 7705.12i | −0.126200 | − | 0.0172158i | ||||
\(670\) | −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 | ||||
\(675\) | 263126. | − | 299464.i | 0.577506 | − | 0.657260i | ||||
\(676\) | −97262.9 | + | 299344.i | −0.212840 | + | 0.655055i | ||||
\(677\) | −505292. | − | 164179.i | −1.10247 | − | 0.358213i | −0.299415 | − | 0.954123i | \(-0.596791\pi\) |
−0.803051 | + | 0.595910i | \(0.796791\pi\) | |||||||
\(678\) | −53336.9 | − | 295491.i | −0.116029 | − | 0.642813i | ||||
\(679\) | 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 | \(0.0218491\pi\) | ||||
−0.997645 | + | 0.0685871i | \(0.978151\pi\) | |||||||
\(684\) | −197910. | + | 298599.i | −0.423016 | + | 0.638229i | ||||
\(685\) | 174662. | + | 126900.i | 0.372236 | + | 0.270445i | ||||
\(686\) | 95409.3 | + | 131320.i | 0.202741 | + | 0.279050i | ||||
\(687\) | 31714.7 | + | 30379.5i | 0.0671966 | + | 0.0643676i | ||||
\(688\) | 10761.7 | − | 33121.1i | 0.0227355 | − | 0.0699726i | ||||
\(689\) | −131332. | − | 180763.i | −0.276651 | − | 0.380777i | ||||
\(690\) | −31527.0 | − | 58719.2i | −0.0662193 | − | 0.123334i | ||||
\(691\) | −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 | ||||||||
\(693\) | −274113. | + | 698536.i | −0.570772 | + | 1.45453i | ||||
\(694\) | 106657. | 0.221447 | ||||||||
\(695\) | −158218. | + | 51408.2i | −0.327557 | + | 0.106430i | ||||
\(696\) | 603516. | − | 324034.i | 1.24586 | − | 0.668918i | ||||
\(697\) | 152240. | − | 110609.i | 0.313374 | − | 0.227679i | ||||
\(698\) | 416941. | + | 135472.i | 0.855783 | + | 0.278061i | ||||
\(699\) | −189994. | + | 198345.i | −0.388853 | + | 0.405944i | ||||
\(700\) | −406414. | + | 295277.i | −0.829417 | + | 0.602607i | ||||
\(701\) | 385381. | − | 530432.i | 0.784250 | − | 1.07943i | −0.210550 | − | 0.977583i | \(-0.567526\pi\) |
0.994800 | − | 0.101844i | \(-0.0324744\pi\) | |||||||
\(702\) | 60517.4 | − | 35926.3i | 0.122802 | − | 0.0729019i | ||||
\(703\) | −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 | ||||
\(708\) | −517083. | + | 93334.9i | −1.03156 | + | 0.186199i | ||||
\(709\) | 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 | ||||
\(711\) | 262490. | + | 72973.8i | 0.519246 | + | 0.144354i | ||||
\(712\) | −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 | ||||||||
\(717\) | −9941.56 | + | 72876.6i | −0.0193382 | + | 0.141759i | ||||
\(718\) | −152066. | − | 110483.i | −0.294974 | − | 0.214311i | ||||
\(719\) | 386426. | + | 531870.i | 0.747496 | + | 1.02884i | 0.998152 | + | 0.0607636i | \(0.0193536\pi\) |
−0.250656 | + | 0.968076i | \(0.580646\pi\) | |||||||
\(720\) | −20018.2 | − | 53644.6i | −0.0386154 | − | 0.103481i | ||||
\(721\) | 2380.75 | − | 7327.18i | 0.00457976 | − | 0.0140950i | ||||
\(722\) | 6508.23 | + | 8957.81i | 0.0124850 | + | 0.0171841i | ||||
\(723\) | −565591. | + | 303672.i | −1.08200 | + | 0.580937i | ||||
\(724\) | 210763. | + | 648663.i | 0.402085 | + | 1.23749i | ||||
\(725\) | − | 743140.i | − | 1.41382i | ||||||
\(726\) | −263481. | − | 7114.51i | −0.499891 | − | 0.0134981i | ||||
\(727\) | 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 | ||||
\(729\) | −522357. | − | 97839.5i | −0.982907 | − | 0.184102i | ||||
\(730\) | 95804.7 | − | 69606.2i | 0.179780 | − | 0.130618i | ||||
\(731\) | −81067.3 | − | 26340.4i | −0.151709 | − | 0.0492932i | ||||
\(732\) | −6332.85 | − | 6066.23i | −0.0118189 | − | 0.0113213i | ||||
\(733\) | 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 | ||||
\(735\) | −37222.7 | + | 272861.i | −0.0689022 | + | 0.505087i | ||||
\(736\) | 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 | ||||
\(741\) | 28439.4 | + | 157556.i | 0.0517945 | + | 0.286946i | ||||
\(742\) | −219094. | + | 674302.i | −0.397945 | + | 1.22475i | ||||
\(743\) | 361533. | + | 117469.i | 0.654893 | + | 0.212787i | 0.617570 | − | 0.786516i | \(-0.288117\pi\) |
0.0373224 | + | 0.999303i | \(0.488117\pi\) | |||||||
\(744\) | 298556. | − | 53890.2i | 0.539362 | − | 0.0973563i | ||||
\(745\) | −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 | ||||||
\(750\) | 184804. | + | 25210.4i | 0.328541 | + | 0.0448184i | ||||
\(751\) | 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 | ||||
\(753\) | 593921. | − | 620025.i | 1.04746 | − | 1.09350i | ||||
\(754\) | 40542.3 | − | 124776.i | 0.0713125 | − | 0.219477i | ||||
\(755\) | 112553. | + | 154916.i | 0.197453 | + | 0.271771i | ||||
\(756\) | 615070. | + | 264947.i | 1.07617 | + | 0.463570i | ||||
\(757\) | 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 | ||||||
\(759\) | −34527.8 | − | 454687.i | −0.0599357 | − | 0.789276i | ||||
\(760\) | −182511. | −0.315981 | ||||||||
\(761\) | 139733. | − | 45401.8i | 0.241284 | − | 0.0783979i | −0.185879 | − | 0.982573i | \(-0.559513\pi\) |
0.427163 | + | 0.904175i | \(0.359513\pi\) | |||||||
\(762\) | −62228.9 | − | 115902.i | −0.107172 | − | 0.199609i | ||||
\(763\) | −507339. | + | 368604.i | −0.871464 | + | 0.633156i | ||||
\(764\) | −181174. | − | 58867.1i | −0.310392 | − | 0.100852i | ||||
\(765\) | −131301. | + | 48996.6i | −0.224359 | + | 0.0837226i | ||||
\(766\) | 322287. | − | 234155.i | 0.549270 | − | 0.399068i | ||||
\(767\) | −138031. | + | 189983.i | −0.234631 | + | 0.322941i | ||||
\(768\) | −390529. | − | 53274.5i | −0.662111 | − | 0.0903227i | ||||
\(769\) | 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 | −0.644500 | − | 0.764604i | \(-0.722934\pi\) |
0.926343 | + | 0.376680i | \(0.122934\pi\) | |||||||
\(774\) | 18903.0 | − | 67994.8i | 0.0315536 | − | 0.113499i | ||||
\(775\) | 101706. | − | 313020.i | 0.169334 | − | 0.521158i | ||||
\(776\) | 557506. | + | 181145.i | 0.925818 | + | 0.300817i | ||||
\(777\) | 224281. | + | 1.24254e6i | 0.371493 | + | 2.05810i | ||||
\(778\) | −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 | ||||||
\(783\) | −851898. | + | 505732.i | −1.38952 | + | 0.824891i | ||||
\(784\) | −223862. | − | 162645.i | −0.364207 | − | 0.264612i | ||||
\(785\) | −199517. | − | 274611.i | −0.323773 | − | 0.445635i | ||||
\(786\) | −66577.5 | − | 63774.5i | −0.107766 | − | 0.103229i | ||||
\(787\) | 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 | ||||
\(789\) | −128860. | − | 240003.i | −0.206997 | − | 0.385534i | ||||
\(790\) | 18381.6 | + | 56572.8i | 0.0294530 | + | 0.0906471i | ||||
\(791\) | − | 1.27699e6i | − | 2.04097i | ||||||
\(792\) | −32798.5 | + | 547933.i | −0.0522883 | + | 0.873528i | ||||
\(793\) | −3919.30 | −0.00623250 | ||||||||
\(794\) | 163685. | − | 53184.3i | 0.259637 | − | 0.0843612i | ||||
\(795\) | −324556. | + | 174258.i | −0.513517 | + | 0.275713i | ||||
\(796\) | 207057. | − | 150436.i | 0.326786 | − | 0.237424i | ||||
\(797\) | 591897. | + | 192319.i | 0.931815 | + | 0.302765i | 0.735305 | − | 0.677737i | \(-0.237039\pi\) |
0.196510 | + | 0.980502i | \(0.437039\pi\) | |||||||
\(798\) | 351430. | − | 366876.i | 0.551865 | − | 0.576121i | ||||
\(799\) | −135037. | + | 98110.1i | −0.211524 | + | 0.153681i | ||||
\(800\) | −339427. | + | 467181.i | −0.530354 | + | 0.729970i | ||||
\(801\) | 567680. | + | 376256.i | 0.884787 | + | 0.586434i | ||||
\(802\) | −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 | ||||
\(807\) | 150673. | − | 27197.0i | 0.231361 | − | 0.0417612i | ||||
\(808\) | −62786.9 | + | 193238.i | −0.0961714 | + | 0.295985i | ||||
\(809\) | −968591. | − | 314714.i | −1.47994 | − | 0.480861i | −0.545843 | − | 0.837887i | \(-0.683791\pi\) |
−0.934094 | + | 0.357027i | \(0.883791\pi\) | |||||||
\(810\) | −45202.1 | − | 106866.i | −0.0688952 | − | 0.162880i | ||||
\(811\) | 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 | ||||||||
\(816\) | 19033.5 | − | 139525.i | 0.0285849 | − | 0.209542i | ||||
\(817\) | 129886. | + | 94367.4i | 0.194588 | + | 0.141377i | ||||
\(818\) | −184021. | − | 253283.i | −0.275018 | − | 0.378530i | ||||
\(819\) | 280421. | − | 104643.i | 0.418063 | − | 0.156006i | ||||
\(820\) | 31523.2 | − | 97018.5i | 0.0468816 | − | 0.144287i | ||||
\(821\) | 764095. | + | 1.05169e6i | 1.13360 | + | 1.56027i | 0.781039 | + | 0.624483i | \(0.214690\pi\) |
0.352564 | + | 0.935788i | \(0.385310\pi\) | |||||||
\(822\) | −387310. | + | 207951.i | −0.573212 | + | 0.307764i | ||||
\(823\) | −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 | ||||||
\(825\) | 506890. | + | 312542.i | 0.744742 | + | 0.459198i | ||||
\(826\) | 745167. | 1.09218 | ||||||||
\(827\) | −234133. | + | 76074.4i | −0.342335 | + | 0.111231i | −0.475139 | − | 0.879911i | \(-0.657602\pi\) |
0.132803 | + | 0.991142i | \(0.457602\pi\) | |||||||
\(828\) | −406589. | + | 17494.2i | −0.593055 | + | 0.0255172i | ||||
\(829\) | −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 | ||||
\(831\) | −880459. | − | 843390.i | −1.27499 | − | 1.22131i | ||||
\(832\) | −32529.2 | + | 23633.8i | −0.0469923 | + | 0.0341419i | ||||
\(833\) | −398091. | + | 547926.i | −0.573710 | + | 0.789645i | ||||
\(834\) | 45786.2 | − | 335635.i | 0.0658267 | − | 0.482542i | ||||
\(835\) | −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 | −0.986906 | − | 0.161298i | \(-0.948432\pi\) |
0.458374 | + | 0.888759i | \(0.348432\pi\) | |||||||
\(840\) | 60608.1 | + | 335774.i | 0.0858959 | + | 0.475871i | ||||
\(841\) | −352148. | + | 1.08380e6i | −0.497890 | + | 1.53235i | ||||
\(842\) | −403323. | − | 131048.i | −0.568891 | − | 0.184844i | ||||
\(843\) | −694588. | + | 125375.i | −0.977399 | + | 0.176423i | ||||
\(844\) | −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 | ||||||
\(849\) | 1.36392e6 | + | 186061.i | 1.89223 | + | 0.258131i | ||||
\(850\) | 173174. | + | 125818.i | 0.239687 | + | 0.174142i | ||||
\(851\) | −450984. | − | 620727.i | −0.622734 | − | 0.857119i | ||||
\(852\) | 217880. | − | 227456.i | 0.300150 | − | 0.313342i | ||||
\(853\) | −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 | ||||
\(855\) | 263717. | − | 11346.9i | 0.360750 | − | 0.0155219i | ||||
\(856\) | −210543. | − | 647986.i | −0.287339 | − | 0.884337i | ||||
\(857\) | 281404.i | 0.383150i | 0.981478 | + | 0.191575i | \(0.0613594\pi\) | ||||
−0.981478 | + | 0.191575i | \(0.938641\pi\) | |||||||
\(858\) | 68058.2 | + | 80130.7i | 0.0924498 | + | 0.108849i | ||||
\(859\) | −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 | ||||
\(861\) | 313440. | + | 583783.i | 0.422813 | + | 0.787490i | ||||
\(862\) | −1906.45 | + | 1385.11i | −0.00256573 | + | 0.00186411i | ||||
\(863\) | 166527. | + | 54107.8i | 0.223595 | + | 0.0726505i | 0.418672 | − | 0.908137i | \(-0.362496\pi\) |
−0.195077 | + | 0.980788i | \(0.562496\pi\) | |||||||
\(864\) | 766544. | + | 71169.5i | 1.02686 | + | 0.0953381i | ||||
\(865\) | 424498. | − | 308416.i | 0.567341 | − | 0.412197i | ||||
\(866\) | −166978. | + | 229825.i | −0.222650 | + | 0.306452i | ||||
\(867\) | 403290. | + | 55015.4i | 0.536512 | + | 0.0731890i | ||||
\(868\) | 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 | ||||
\(873\) | −816824. | − | 227082.i | −1.07177 | − | 0.297958i | ||||
\(874\) | −95400.2 | + | 293612.i | −0.124890 | + | 0.384371i | ||||
\(875\) | 754406. | + | 245121.i | 0.985347 | + | 0.320159i | ||||
\(876\) | −128447. | − | 711607.i | −0.167385 | − | 0.927325i | ||||
\(877\) | 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 | \(-0.992090\pi\) | ||
0.999691 | − | 0.0248478i | \(-0.00791012\pi\) | |||||||
\(882\) | −467402. | − | 309792.i | −0.600832 | − | 0.398229i | ||||
\(883\) | 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 | ||||
\(885\) | 279591. | + | 267820.i | 0.356974 | + | 0.341945i | ||||
\(886\) | −44602.6 | + | 137273.i | −0.0568189 | + | 0.174871i | ||||
\(887\) | 800439. | + | 1.10171e6i | 1.01737 | + | 1.40030i | 0.914028 | + | 0.405651i | \(0.132955\pi\) |
0.103346 | + | 0.994645i | \(0.467045\pi\) | |||||||
\(888\) | 436902. | + | 813732.i | 0.554062 | + | 1.03194i | ||||
\(889\) | −172886. | − | 532087.i | −0.218754 | − | 0.673254i | ||||
\(890\) | 148697.i | 0.187725i | ||||||||
\(891\) | 13326.4 | − | 793769.i | 0.0167863 | − | 0.999859i | ||||
\(892\) | −75999.9 | −0.0955175 | ||||||||
\(893\) | 298996. | − | 97149.6i | 0.374940 | − | 0.121825i | ||||
\(894\) | 74555.3 | − | 40029.6i | 0.0932833 | − | 0.0500849i | ||||
\(895\) | 268461. | − | 195048.i | 0.335147 | − | 0.243498i | ||||
\(896\) | −1.10898e6 | − | 360329.i | −1.38136 | − | 0.448831i | ||||
\(897\) | −125816. | + | 131346.i | −0.156369 | + | 0.163242i | ||||
\(898\) | −26420.1 | + | 19195.3i | −0.0327628 | + | 0.0238036i | ||||
\(899\) | −480781. | + | 661739.i | −0.594879 | + | 0.818780i | ||||
\(900\) | 293618. | − | 442998.i | 0.362491 | − | 0.546912i | ||||
\(901\) | −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 | ||||
\(906\) | −383705. | + | 69259.8i | −0.467457 | + | 0.0843772i | ||||
\(907\) | 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 | ||||
\(909\) | 78709.5 | − | 283121.i | 0.0952575 | − | 0.342645i | ||||
\(910\) | 52868.9 | + | 38411.5i | 0.0638437 | + | 0.0463851i | ||||
\(911\) | 1.11225e6 | − | 361393.i | 1.34019 | − | 0.435455i | 0.450811 | − | 0.892620i | \(-0.351135\pi\) |
0.889382 | + | 0.457164i | \(0.151135\pi\) | |||||||
\(912\) | −115302. | + | 238853.i | −0.138627 | + | 0.287172i | ||||
\(913\) | 693986. | + | 622444.i | 0.832548 | + | 0.746722i | ||||
\(914\) | − | 32122.6i | − | 0.0384519i | ||||||
\(915\) | −873.401 | + | 6402.46i | −0.00104321 | + | 0.00764724i | ||||
\(916\) | 47368.6 | + | 34415.3i | 0.0564546 | + | 0.0410167i | ||||
\(917\) | −230465. | − | 317207.i | −0.274073 | − | 0.377228i | ||||
\(918\) | 26381.0 | − | 284141.i | 0.0313044 | − | 0.337170i | ||||
\(919\) | 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 | ||||
\(921\) | −59063.1 | + | 31711.7i | −0.0696301 | + | 0.0373852i | ||||
\(922\) | 81334.2 | + | 250321.i | 0.0956779 | + | 0.294466i | ||||
\(923\) | − | 140769.i | − | 0.165236i | ||||||
\(924\) | −236217. | + | 972140.i | −0.276673 | + | 1.13864i | ||||
\(925\) | 1.00199e6 | 1.17106 | ||||||||
\(926\) | 160531. | − | 52159.6i | 0.187213 | − | 0.0608293i | ||||
\(927\) | 350.376 | + | 8143.21i | 0.000407732 | + | 0.00947624i | ||||
\(928\) | 1.16104e6 | − | 843546.i | 1.34819 | − | 0.979519i | ||||
\(929\) | 312484. | + | 101532.i | 0.362073 | + | 0.117645i | 0.484403 | − | 0.874845i | \(-0.339037\pi\) |
−0.122331 | + | 0.992489i | \(0.539037\pi\) | |||||||
\(930\) | −69181.2 | − | 66268.5i | −0.0799875 | − | 0.0766199i | ||||
\(931\) | 1.03201e6 | − | 749801.i | 1.19065 | − | 0.865061i | ||||
\(932\) | −215234. | + | 296244.i | −0.247787 | + | 0.341050i | ||||
\(933\) | −58508.8 | + | 428898.i | −0.0672137 | + | 0.492710i | ||||
\(934\) | 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 | ||||
\(939\) | −152688. | − | 845904.i | −0.173170 | − | 0.959378i | ||||
\(940\) | −27961.1 | + | 86055.5i | −0.0316445 | + | 0.0973919i | ||||
\(941\) | −456702. | − | 148392.i | −0.515767 | − | 0.167583i | 0.0395563 | − | 0.999217i | \(-0.487406\pi\) |
−0.555324 | + | 0.831634i | \(0.687406\pi\) | |||||||
\(942\) | 680174. | − | 122773.i | 0.766510 | − | 0.138357i | ||||
\(943\) | −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 | \(-0.912263\pi\) | ||
0.962253 | − | 0.272158i | \(-0.0877372\pi\) | |||||||
\(948\) | 359891. | + | 49095.0i | 0.400455 | + | 0.0546287i | ||||
\(949\) | −261453. | − | 189957.i | −0.290310 | − | 0.210922i | ||||
\(950\) | −236977. | − | 326171.i | −0.262578 | − | 0.361408i | ||||
\(951\) | −457921. | + | 478048.i | −0.506325 | + | 0.528579i | ||||
\(952\) | −259305. | + | 798059.i | −0.286113 | + | 0.880564i | ||||
\(953\) | 669623. | + | 921658.i | 0.737301 | + | 1.01481i | 0.998769 | + | 0.0495957i | \(0.0157933\pi\) |
−0.261468 | + | 0.965212i | \(0.584207\pi\) | |||||||
\(954\) | −32244.2 | − | 749398.i | −0.0354287 | − | 0.823410i | ||||
\(955\) | 43375.9 | + | 133497.i | 0.0475600 | + | 0.146375i | ||||
\(956\) | 98059.1i | 0.107293i | ||||||||
\(957\) | −958049. | − | 1.12799e6i | −1.04608 | − | 1.23164i | ||||
\(958\) | −859943. | −0.936998 | ||||||||
\(959\) | −1.77808e6 | + | 577734.i | −1.93337 | + | 0.628190i | ||||
\(960\) | 31358.5 | + | 58405.4i | 0.0340262 | + | 0.0633739i | ||||
\(961\) | 454067. | − | 329899.i | 0.491669 | − | 0.357219i | ||||
\(962\) | 168238. | + | 54664.0i | 0.181792 | + | 0.0590678i | ||||
\(963\) | 344509. | + | 923211.i | 0.371490 | + | 0.995517i | ||||
\(964\) | −692406. | + | 503062.i | −0.745087 | + | 0.541337i | ||||
\(965\) | −210973. | + | 290379.i | −0.226554 | + | 0.311825i | ||||
\(966\) | 571853. | + | 78010.1i | 0.612816 | + | 0.0835981i | ||||
\(967\) | −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 | −0.932551 | − | 0.361037i | \(-0.882423\pi\) |
0.631541 | + | 0.775343i | \(0.282423\pi\) | |||||||
\(972\) | −707648. | − | 35113.3i | −0.749005 | − | 0.0371654i | ||||
\(973\) | 445181. | − | 1.37013e6i | 0.470231 | − | 1.44722i | ||||
\(974\) | 604814. | + | 196516.i | 0.637534 | + | 0.207147i | ||||
\(975\) | −42192.3 | − | 233749.i | −0.0443838 | − | 0.245890i | ||||
\(976\) | −5252.75 | − | 3816.35i | −0.00551426 | − | 0.00400634i | ||||
\(977\) | −1.43049e6 | + | 464795.i | −1.49864 | + | 0.486937i | −0.939620 | − | 0.342219i | \(-0.888822\pi\) |
−0.559018 | + | 0.829156i | \(0.688822\pi\) | |||||||
\(978\) | −254561. | − | 122885.i | −0.266142 | − | 0.128476i | ||||
\(979\) | −412006. | + | 930213.i | −0.429871 | + | 0.970548i | ||||
\(980\) | 367148.i | 0.382287i | ||||||||
\(981\) | 366532. | − | 553008.i | 0.380867 | − | 0.574637i | ||||
\(982\) | −209072. | − | 151900.i | −0.216807 | − | 0.157519i | ||||
\(983\) | 648995. | + | 893265.i | 0.671636 | + | 0.924428i | 0.999796 | − | 0.0201942i | \(-0.00642844\pi\) |
−0.328160 | + | 0.944622i | \(0.606428\pi\) | |||||||
\(984\) | 350021. | + | 335285.i | 0.361497 | + | 0.346277i | ||||
\(985\) | −139310. | + | 428753.i | −0.143586 | + | 0.441911i | ||||
\(986\) | −312684. | − | 430372.i | −0.321626 | − | 0.442681i | ||||
\(987\) | −278021. | − | 517816.i | −0.285393 | − | 0.531546i | ||||
\(988\) | 65959.5 | + | 203002.i | 0.0675714 | + | 0.207964i | ||||
\(989\) | 182388.i | 0.186468i | ||||||||
\(990\) | 146066. | − | 93321.1i | 0.149031 | − | 0.0952159i | ||||
\(991\) | 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 | ||||
\(993\) | 1.24637e6 | − | 669192.i | 1.26401 | − | 0.678660i | ||||
\(994\) | −361378. | + | 262557.i | −0.365754 | + | 0.265736i | ||||
\(995\) | −179356. | − | 58276.2i | −0.181163 | − | 0.0588633i | ||||
\(996\) | 575524. | − | 600819.i | 0.580156 | − | 0.605655i | ||||
\(997\) | −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 | ||||
\(999\) | −681888. | − | 1.14863e6i | −0.683254 | − | 1.15093i |
(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.5.9 | yes | 56 | |
3.2 | odd | 2 | inner | 33.5.h.a.5.6 | ✓ | 56 | |
11.9 | even | 5 | inner | 33.5.h.a.20.6 | yes | 56 | |
33.20 | odd | 10 | inner | 33.5.h.a.20.9 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.5.h.a.5.6 | ✓ | 56 | 3.2 | odd | 2 | inner | |
33.5.h.a.5.9 | yes | 56 | 1.1 | even | 1 | trivial | |
33.5.h.a.20.6 | yes | 56 | 11.9 | even | 5 | inner | |
33.5.h.a.20.9 | yes | 56 | 33.20 | odd | 10 | inner |