Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(35,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.35");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.h (of order \(6\), degree \(2\), not 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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 35.7 | ||
Character | \(\chi\) | \(=\) | 108.35 |
Dual form | 108.6.h.a.71.7 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.95514 | − | 4.04436i | −0.699177 | − | 0.714949i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.713689 | + | 31.9920i | −0.0223028 | + | 0.999751i | ||||
\(5\) | 77.8058 | − | 44.9212i | 1.39183 | − | 0.803575i | 0.398314 | − | 0.917249i | \(-0.369595\pi\) |
0.993518 | + | 0.113675i | \(0.0362621\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 124.034 | + | 71.6112i | 0.956745 | + | 0.552377i | 0.895170 | − | 0.445725i | \(-0.147054\pi\) |
0.0615753 | + | 0.998102i | \(0.480388\pi\) | |||||||
\(8\) | 132.210 | − | 123.647i | 0.730364 | − | 0.683058i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −489.410 | − | 137.005i | −1.54765 | − | 0.433247i | ||||
\(11\) | −278.231 | + | 481.910i | −0.693303 | + | 1.20084i | 0.277446 | + | 0.960741i | \(0.410512\pi\) |
−0.970749 | + | 0.240095i | \(0.922821\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 179.796 | + | 311.416i | 0.295068 | + | 0.511072i | 0.975001 | − | 0.222202i | \(-0.0713245\pi\) |
−0.679933 | + | 0.733274i | \(0.737991\pi\) | |||||||
\(14\) | −200.952 | − | 784.871i | −0.274013 | − | 1.07023i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1022.98 | − | 45.6648i | −0.999005 | − | 0.0445945i | ||||
\(17\) | 1076.42i | 0.903356i | 0.892181 | + | 0.451678i | \(0.149174\pi\) | ||||
−0.892181 | + | 0.451678i | \(0.850826\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 348.135i | 0.221240i | 0.993863 | + | 0.110620i | \(0.0352837\pi\) | ||||
−0.993863 | + | 0.110620i | \(0.964716\pi\) | |||||||
\(20\) | 1381.59 | + | 2521.23i | 0.772333 | + | 1.40941i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3049.46 | − | 780.757i | 1.34328 | − | 0.343921i | ||||
\(23\) | 1469.06 | + | 2544.48i | 0.579054 | + | 1.00295i | 0.995588 | + | 0.0938304i | \(0.0299111\pi\) |
−0.416535 | + | 0.909120i | \(0.636756\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2473.33 | − | 4283.93i | 0.791464 | − | 1.37086i | ||||
\(26\) | 548.358 | − | 1958.85i | 0.159086 | − | 0.568288i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2379.51 | + | 3917.00i | −0.573578 | + | 0.944188i | ||||
\(29\) | −3331.19 | − | 1923.26i | −0.735536 | − | 0.424662i | 0.0849079 | − | 0.996389i | \(-0.472940\pi\) |
−0.820444 | + | 0.571727i | \(0.806274\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2346.41 | − | 1354.70i | 0.438531 | − | 0.253186i | −0.264443 | − | 0.964401i | \(-0.585188\pi\) |
0.702974 | + | 0.711215i | \(0.251855\pi\) | |||||||
\(32\) | 3861.35 | + | 4317.91i | 0.666599 | + | 0.745417i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4353.43 | − | 4257.39i | 0.645853 | − | 0.631606i | ||||
\(35\) | 12867.4 | 1.77550 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1992.90 | −0.239321 | −0.119661 | − | 0.992815i | \(-0.538181\pi\) | ||||
−0.119661 | + | 0.992815i | \(0.538181\pi\) | |||||||
\(38\) | 1407.98 | − | 1376.92i | 0.158175 | − | 0.154686i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4732.35 | − | 15559.5i | 0.467657 | − | 1.53760i | ||||
\(41\) | 13432.0 | − | 7754.99i | 1.24791 | − | 0.720479i | 0.277215 | − | 0.960808i | \(-0.410589\pi\) |
0.970692 | + | 0.240329i | \(0.0772552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12474.1 | + | 7201.91i | 1.02882 | + | 0.593987i | 0.916645 | − | 0.399702i | \(-0.130887\pi\) |
0.112170 | + | 0.993689i | \(0.464220\pi\) | |||||||
\(44\) | −15218.7 | − | 9245.10i | −1.18508 | − | 0.719913i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4480.46 | − | 16005.2i | 0.312197 | − | 1.11523i | ||||
\(47\) | −1232.97 | + | 2135.56i | −0.0814153 | + | 0.141015i | −0.903858 | − | 0.427832i | \(-0.859277\pi\) |
0.822443 | + | 0.568848i | \(0.192611\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1852.82 | + | 3209.17i | 0.110241 | + | 0.190943i | ||||
\(50\) | −27108.1 | + | 6940.52i | −1.53347 | + | 0.392615i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10091.1 | + | 5529.78i | −0.517526 | + | 0.283596i | ||||
\(53\) | − | 13364.2i | − | 0.653514i | −0.945108 | − | 0.326757i | \(-0.894044\pi\) | ||
0.945108 | − | 0.326757i | \(-0.105956\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 49993.8i | 2.22848i | ||||||||
\(56\) | 25253.0 | − | 5868.70i | 1.07608 | − | 0.250076i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5396.96 | + | 21079.3i | 0.210659 | + | 0.822785i | ||||
\(59\) | 19878.8 | + | 34431.1i | 0.743464 | + | 1.28772i | 0.950909 | + | 0.309470i | \(0.100152\pi\) |
−0.207445 | + | 0.978247i | \(0.566515\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −211.489 | + | 366.310i | −0.00727718 | + | 0.0126044i | −0.869641 | − | 0.493685i | \(-0.835650\pi\) |
0.862364 | + | 0.506289i | \(0.168983\pi\) | |||||||
\(62\) | −14759.3 | − | 4131.70i | −0.487626 | − | 0.136505i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2191.00 | − | 32694.7i | 0.0668640 | − | 0.997762i | ||||
\(65\) | 27978.3 | + | 16153.3i | 0.821369 | + | 0.474218i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14018.6 | + | 8093.63i | −0.381520 | + | 0.220271i | −0.678479 | − | 0.734620i | \(-0.737361\pi\) |
0.296960 | + | 0.954890i | \(0.404027\pi\) | |||||||
\(68\) | −34436.8 | − | 768.229i | −0.903132 | − | 0.0201474i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −50892.5 | − | 52040.5i | −1.24139 | − | 1.26939i | ||||
\(71\) | −6902.73 | −0.162508 | −0.0812541 | − | 0.996693i | \(-0.525893\pi\) | ||||
−0.0812541 | + | 0.996693i | \(0.525893\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11089.5 | −0.243558 | −0.121779 | − | 0.992557i | \(-0.538860\pi\) | ||||
−0.121779 | + | 0.992557i | \(0.538860\pi\) | |||||||
\(74\) | 7882.20 | + | 8060.00i | 0.167328 | + | 0.171102i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11137.6 | − | 248.460i | −0.221185 | − | 0.00493427i | ||||
\(77\) | −69020.2 | + | 39848.8i | −1.32663 | + | 0.765930i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64310.3 | − | 37129.6i | −1.15935 | − | 0.669349i | −0.208199 | − | 0.978086i | \(-0.566760\pi\) |
−0.951147 | + | 0.308738i | \(0.900093\pi\) | |||||||
\(80\) | −81645.2 | + | 42400.5i | −1.42628 | + | 0.740707i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −84489.6 | − | 23651.9i | −1.38761 | − | 0.388446i | ||||
\(83\) | 48564.9 | − | 84116.9i | 0.773798 | − | 1.34026i | −0.161670 | − | 0.986845i | \(-0.551688\pi\) |
0.935468 | − | 0.353412i | \(-0.114979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 48354.0 | + | 83751.6i | 0.725914 | + | 1.25732i | ||||
\(86\) | −20209.6 | − | 78934.2i | −0.294654 | − | 1.15085i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 22801.6 | + | 98115.6i | 0.313877 | + | 1.35061i | ||||
\(89\) | − | 74459.8i | − | 0.996430i | −0.867054 | − | 0.498215i | \(-0.833989\pi\) | ||
0.867054 | − | 0.498215i | \(-0.166011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 51501.6i | 0.651954i | ||||||||
\(92\) | −82451.5 | + | 45182.1i | −1.01562 | + | 0.556541i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13513.5 | − | 3459.88i | 0.157743 | − | 0.0403870i | ||||
\(95\) | 15638.6 | + | 27086.9i | 0.177783 | + | 0.307929i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 47958.5 | − | 83066.5i | 0.517530 | − | 0.896389i | −0.482262 | − | 0.876027i | \(-0.660185\pi\) |
0.999793 | − | 0.0203622i | \(-0.00648193\pi\) | |||||||
\(98\) | 5650.89 | − | 20186.2i | 0.0594363 | − | 0.212319i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 135286. | + | 82184.1i | 1.35286 | + | 0.821841i | ||||
\(101\) | 34890.0 | + | 20143.7i | 0.340328 | + | 0.196488i | 0.660417 | − | 0.750899i | \(-0.270380\pi\) |
−0.320089 | + | 0.947387i | \(0.603713\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −42984.3 | + | 24817.0i | −0.399225 | + | 0.230492i | −0.686149 | − | 0.727461i | \(-0.740700\pi\) |
0.286925 | + | 0.957953i | \(0.407367\pi\) | |||||||
\(104\) | 62276.3 | + | 18941.1i | 0.564599 | + | 0.171721i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −54049.8 | + | 52857.5i | −0.467229 | + | 0.456922i | ||||
\(107\) | 14176.4 | 0.119703 | 0.0598517 | − | 0.998207i | \(-0.480937\pi\) | ||||
0.0598517 | + | 0.998207i | \(0.480937\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 21788.2 | 0.175653 | 0.0878264 | − | 0.996136i | \(-0.472008\pi\) | ||||
0.0878264 | + | 0.996136i | \(0.472008\pi\) | |||||||
\(110\) | 202193. | − | 197733.i | 1.59325 | − | 1.55810i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −123615. | − | 78920.9i | −0.931160 | − | 0.594493i | ||||
\(113\) | −129459. | + | 74743.4i | −0.953756 | + | 0.550651i | −0.894246 | − | 0.447577i | \(-0.852287\pi\) |
−0.0595101 | + | 0.998228i | \(0.518954\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 228602. | + | 131983.i | 1.61189 | + | 0.930625i | ||||
\(116\) | 63906.5 | − | 105199.i | 0.440961 | − | 0.725882i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 60628.2 | − | 216577.i | 0.400839 | − | 1.43188i | ||||
\(119\) | −77083.6 | + | 133513.i | −0.498993 | + | 0.864282i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −74299.1 | − | 128690.i | −0.461339 | − | 0.799062i | ||||
\(122\) | 2317.96 | − | 593.470i | 0.0140996 | − | 0.00360993i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 41665.1 | + | 76033.4i | 0.243343 | + | 0.444069i | ||||
\(125\) | − | 163661.i | − | 0.936853i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 257349.i | − | 1.41584i | −0.706293 | − | 0.707919i | \(-0.749634\pi\) | ||
0.706293 | − | 0.707919i | \(-0.250366\pi\) | |||||||
\(128\) | −140895. | + | 120451.i | −0.760098 | + | 0.649808i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −45328.5 | − | 177043.i | −0.235241 | − | 0.918799i | ||||
\(131\) | 3161.94 | + | 5476.65i | 0.0160982 | + | 0.0278828i | 0.873962 | − | 0.485994i | \(-0.161542\pi\) |
−0.857864 | + | 0.513877i | \(0.828209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24930.4 | + | 43180.7i | −0.122208 | + | 0.211670i | ||||
\(134\) | 88179.0 | + | 24684.7i | 0.424232 | + | 0.118759i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 133096. | + | 142313.i | 0.617045 | + | 0.659779i | ||||
\(137\) | 250464. | + | 144606.i | 1.14010 | + | 0.658239i | 0.946456 | − | 0.322832i | \(-0.104635\pi\) |
0.193647 | + | 0.981071i | \(0.437968\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 86135.1 | − | 49730.1i | 0.378132 | − | 0.218315i | −0.298873 | − | 0.954293i | \(-0.596611\pi\) |
0.677005 | + | 0.735978i | \(0.263277\pi\) | |||||||
\(140\) | −9183.35 | + | 411655.i | −0.0395987 | + | 1.77506i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 27301.3 | + | 27917.1i | 0.113622 | + | 0.116185i | ||||
\(143\) | −200099. | −0.818285 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −345581. | −1.36499 | ||||||||
\(146\) | 43860.4 | + | 44849.7i | 0.170290 | + | 0.174132i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1422.31 | − | 63756.9i | 0.00533753 | − | 0.239262i | ||||
\(149\) | 323359. | − | 186691.i | 1.19322 | − | 0.688904i | 0.234182 | − | 0.972193i | \(-0.424759\pi\) |
0.959035 | + | 0.283289i | \(0.0914255\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −320356. | − | 184958.i | −1.14338 | − | 0.660131i | −0.196115 | − | 0.980581i | \(-0.562833\pi\) |
−0.947266 | + | 0.320450i | \(0.896166\pi\) | |||||||
\(152\) | 43045.8 | + | 46027.0i | 0.151120 | + | 0.161586i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 434148. | + | 121535.i | 1.47515 | + | 0.412951i | ||||
\(155\) | 121710. | − | 210807.i | 0.406908 | − | 0.704785i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 196653. | + | 340613.i | 0.636724 | + | 1.10284i | 0.986147 | + | 0.165873i | \(0.0530442\pi\) |
−0.349423 | + | 0.936965i | \(0.613622\pi\) | |||||||
\(158\) | 104191. | + | 406947.i | 0.332038 | + | 1.29687i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 494401. | + | 162502.i | 1.52679 | + | 0.501833i | ||||
\(161\) | 420803.i | 1.27942i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 154747.i | − | 0.456198i | −0.973638 | − | 0.228099i | \(-0.926749\pi\) | ||
0.973638 | − | 0.228099i | \(-0.0732509\pi\) | |||||||
\(164\) | 238512. | + | 435253.i | 0.692468 | + | 1.26367i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −532280. | + | 136280.i | −1.49924 | + | 0.383852i | ||||
\(167\) | −98410.6 | − | 170452.i | −0.273055 | − | 0.472946i | 0.696587 | − | 0.717472i | \(-0.254701\pi\) |
−0.969643 | + | 0.244526i | \(0.921368\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 120993. | − | 209567.i | 0.325870 | − | 0.564424i | ||||
\(170\) | 147475. | − | 526811.i | 0.391377 | − | 1.39808i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −239306. | + | 393931.i | −0.616784 | + | 1.01531i | ||||
\(173\) | −583484. | − | 336874.i | −1.48222 | − | 0.855762i | −0.482426 | − | 0.875937i | \(-0.660244\pi\) |
−0.999796 | + | 0.0201751i | \(0.993578\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 613554. | − | 354235.i | 1.51446 | − | 0.874373i | ||||
\(176\) | 306631. | − | 480279.i | 0.746164 | − | 1.16872i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −301142. | + | 294499.i | −0.712396 | + | 0.696681i | ||||
\(179\) | −583842. | −1.36196 | −0.680978 | − | 0.732304i | \(-0.738445\pi\) | ||||
−0.680978 | + | 0.732304i | \(0.738445\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −623067. | −1.41364 | −0.706819 | − | 0.707395i | \(-0.749870\pi\) | ||||
−0.706819 | + | 0.707395i | \(0.749870\pi\) | |||||||
\(182\) | 208291. | − | 203696.i | 0.466114 | − | 0.455831i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 508840. | + | 154762.i | 1.10799 | + | 0.336992i | ||||
\(185\) | −155059. | + | 89523.4i | −0.333095 | + | 0.192312i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −518737. | − | 299493.i | −1.08478 | − | 0.626300i | ||||
\(188\) | −67440.9 | − | 40969.2i | −0.139165 | − | 0.0845401i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 47696.2 | − | 170381.i | 0.0958517 | − | 0.342403i | ||||
\(191\) | −92566.8 | + | 160330.i | −0.183600 | + | 0.318004i | −0.943104 | − | 0.332499i | \(-0.892108\pi\) |
0.759504 | + | 0.650502i | \(0.225442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 145169. | + | 251439.i | 0.280530 | + | 0.485892i | 0.971515 | − | 0.236977i | \(-0.0761565\pi\) |
−0.690985 | + | 0.722869i | \(0.742823\pi\) | |||||||
\(194\) | −525633. | + | 134579.i | −1.00272 | + | 0.256727i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −103990. | + | 56985.0i | −0.193354 | + | 0.105955i | ||||
\(197\) | 232595.i | 0.427007i | 0.976942 | + | 0.213504i | \(0.0684875\pi\) | ||||
−0.976942 | + | 0.213504i | \(0.931512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 524007.i | 0.938004i | 0.883197 | + | 0.469002i | \(0.155386\pi\) | ||||
−0.883197 | + | 0.469002i | \(0.844614\pi\) | |||||||
\(200\) | −202695. | − | 872197.i | −0.358317 | − | 1.54184i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −56526.3 | − | 220779.i | −0.0974703 | − | 0.380697i | ||||
\(203\) | −275454. | − | 477100.i | −0.469147 | − | 0.812587i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 696727. | − | 1.20677e6i | 1.15792 | − | 2.00557i | ||||
\(206\) | 270378. | + | 75689.3i | 0.443919 | + | 0.124270i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −169707. | − | 326783.i | −0.271983 | − | 0.523722i | ||||
\(209\) | −167770. | − | 96861.9i | −0.265673 | − | 0.153386i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −389705. | + | 224996.i | −0.602601 | + | 0.347912i | −0.770064 | − | 0.637967i | \(-0.779776\pi\) |
0.167463 | + | 0.985878i | \(0.446442\pi\) | |||||||
\(212\) | 427549. | + | 9537.92i | 0.653351 | + | 0.0145752i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −56069.7 | − | 57334.5i | −0.0836939 | − | 0.0855818i | ||||
\(215\) | 1.29407e6 | 1.90925 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 388047. | 0.559416 | ||||||||
\(218\) | −86175.4 | − | 88119.3i | −0.122812 | − | 0.125583i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.59940e6 | − | 35680.0i | −2.22793 | − | 0.0497014i | ||||
\(221\) | −335214. | + | 193536.i | −0.461680 | + | 0.266551i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 33442.0 | + | 19307.7i | 0.0450329 | + | 0.0259998i | 0.522347 | − | 0.852733i | \(-0.325056\pi\) |
−0.477315 | + | 0.878733i | \(0.658390\pi\) | |||||||
\(224\) | 169729. | + | 812085.i | 0.226014 | + | 1.08139i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 814319. | + | 227959.i | 1.06053 | + | 0.296884i | ||||
\(227\) | −447303. | + | 774752.i | −0.576152 | + | 0.997925i | 0.419763 | + | 0.907634i | \(0.362113\pi\) |
−0.995915 | + | 0.0902911i | \(0.971220\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 714088. | + | 1.23684e6i | 0.899836 | + | 1.55856i | 0.827703 | + | 0.561166i | \(0.189647\pi\) |
0.0721321 | + | 0.997395i | \(0.477020\pi\) | |||||||
\(230\) | −370365. | − | 1.44656e6i | −0.461648 | − | 1.80309i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −678221. | + | 157616.i | −0.827278 | + | 0.192256i | ||||
\(233\) | 379913.i | 0.458453i | 0.973373 | + | 0.229226i | \(0.0736196\pi\) | ||||
−0.973373 | + | 0.229226i | \(0.926380\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 221545.i | 0.261693i | ||||||||
\(236\) | −1.11571e6 | + | 611390.i | −1.30398 | + | 0.714559i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 844850. | − | 216308.i | 0.966802 | − | 0.247531i | ||||
\(239\) | −379157. | − | 656720.i | −0.429363 | − | 0.743679i | 0.567454 | − | 0.823405i | \(-0.307929\pi\) |
−0.996817 | + | 0.0797266i | \(0.974595\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −595565. | + | 1.03155e6i | −0.660520 | + | 1.14405i | 0.319959 | + | 0.947432i | \(0.396331\pi\) |
−0.980479 | + | 0.196623i | \(0.937002\pi\) | |||||||
\(242\) | −226604. | + | 809479.i | −0.248731 | + | 0.888520i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11568.1 | − | 7027.40i | −0.0124390 | − | 0.00755649i | ||||
\(245\) | 288320. | + | 166461.i | 0.306873 | + | 0.177173i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −108415. | + | 62593.3i | −0.113070 | + | 0.0652808i | ||||
\(248\) | 142715. | − | 469231.i | 0.147347 | − | 0.484460i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −661906. | + | 647305.i | −0.669802 | + | 0.655026i | ||||
\(251\) | −705353. | −0.706679 | −0.353340 | − | 0.935495i | \(-0.614954\pi\) | ||||
−0.353340 | + | 0.935495i | \(0.614954\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.63495e6 | −1.60584 | ||||||||
\(254\) | −1.04081e6 | + | 1.01785e6i | −1.01225 | + | 0.989922i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.04441e6 | + | 93428.4i | 0.996023 | + | 0.0891003i | ||||
\(257\) | 1.11396e6 | − | 643145.i | 1.05205 | − | 0.607402i | 0.128828 | − | 0.991667i | \(-0.458878\pi\) |
0.923223 | + | 0.384265i | \(0.125545\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −247188. | − | 142714.i | −0.228969 | − | 0.132196i | ||||
\(260\) | −536745. | + | 883555.i | −0.492418 | + | 0.810588i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9643.59 | − | 34449.0i | 0.00867932 | − | 0.0310044i | ||||
\(263\) | 812371. | − | 1.40707e6i | 0.724211 | − | 1.25437i | −0.235087 | − | 0.971974i | \(-0.575537\pi\) |
0.959298 | − | 0.282396i | \(-0.0911292\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −600338. | − | 1.03982e6i | −0.525147 | − | 0.909581i | ||||
\(266\) | 273241. | − | 69958.3i | 0.236778 | − | 0.0606227i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −248927. | − | 454259.i | −0.211707 | − | 0.386337i | ||||
\(269\) | − | 1.30693e6i | − | 1.10121i | −0.834766 | − | 0.550605i | \(-0.814397\pi\) | ||
0.834766 | − | 0.550605i | \(-0.185603\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 109448.i | 0.0905280i | 0.998975 | + | 0.0452640i | \(0.0144129\pi\) | ||||
−0.998975 | + | 0.0452640i | \(0.985587\pi\) | |||||||
\(272\) | 49154.4 | − | 1.10116e6i | 0.0402847 | − | 0.902458i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −405785. | − | 1.58490e6i | −0.326527 | − | 1.27534i | ||||
\(275\) | 1.37631e6 | + | 2.38384e6i | 1.09745 | + | 1.90084i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 377853. | − | 654461.i | 0.295885 | − | 0.512488i | −0.679305 | − | 0.733856i | \(-0.737719\pi\) |
0.975190 | + | 0.221368i | \(0.0710520\pi\) | |||||||
\(278\) | −541803. | − | 151672.i | −0.420465 | − | 0.117704i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.70120e6 | − | 1.59102e6i | 1.29677 | − | 1.21277i | ||||
\(281\) | 133655. | + | 77165.9i | 0.100977 | + | 0.0582988i | 0.549638 | − | 0.835403i | \(-0.314766\pi\) |
−0.448661 | + | 0.893702i | \(0.648099\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −921332. | + | 531931.i | −0.683833 | + | 0.394811i | −0.801298 | − | 0.598266i | \(-0.795857\pi\) |
0.117465 | + | 0.993077i | \(0.462523\pi\) | |||||||
\(284\) | 4926.41 | − | 220833.i | 0.00362439 | − | 0.162468i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 791420. | + | 809272.i | 0.572126 | + | 0.585032i | ||||
\(287\) | 2.22137e6 | 1.59190 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 261179. | 0.183947 | ||||||||
\(290\) | 1.36682e6 | + | 1.39765e6i | 0.954370 | + | 0.975898i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7914.43 | − | 354774.i | 0.00543203 | − | 0.243498i | ||||
\(293\) | 519996. | − | 300220.i | 0.353860 | − | 0.204301i | −0.312524 | − | 0.949910i | \(-0.601175\pi\) |
0.666384 | + | 0.745609i | \(0.267841\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.09337e6 | + | 1.78596e6i | 2.06955 | + | 1.19486i | ||||
\(296\) | −263481. | + | 246415.i | −0.174792 | + | 0.163470i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.03398e6 | − | 569389.i | −1.32680 | − | 0.371423i | ||||
\(299\) | −528261. | + | 914974.i | −0.341720 | + | 0.591876i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.03147e6 | + | 1.78657e6i | 0.656209 | + | 1.13659i | ||||
\(302\) | 519019. | + | 2.02717e6i | 0.327466 | + | 1.27901i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15897.5 | − | 356136.i | 0.00986609 | − | 0.221020i | ||||
\(305\) | 38001.3i | 0.0233910i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.78186e6i | 1.68457i | 0.539031 | + | 0.842286i | \(0.318791\pi\) | ||||
−0.539031 | + | 0.842286i | \(0.681209\pi\) | |||||||
\(308\) | −1.22559e6 | − | 2.23654e6i | −0.736152 | − | 1.34338i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.33396e6 | + | 341535.i | −0.788385 | + | 0.201851i | ||||
\(311\) | 1.14667e6 | + | 1.98609e6i | 0.672262 | + | 1.16439i | 0.977261 | + | 0.212039i | \(0.0680104\pi\) |
−0.304999 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.41302e6 | − | 2.44742e6i | 0.815244 | − | 1.41204i | −0.0939092 | − | 0.995581i | \(-0.529936\pi\) |
0.909153 | − | 0.416463i | \(-0.136730\pi\) | |||||||
\(314\) | 599770. | − | 2.14251e6i | 0.343290 | − | 1.22630i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.23375e6 | − | 2.03092e6i | 0.695039 | − | 1.14413i | ||||
\(317\) | 185665. | + | 107194.i | 0.103773 | + | 0.0599132i | 0.550988 | − | 0.834513i | \(-0.314251\pi\) |
−0.447215 | + | 0.894426i | \(0.647584\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.85368e6 | − | 1.07022e6i | 1.01990 | − | 0.588839i | ||||
\(320\) | −1.29821e6 | − | 2.64226e6i | −0.708713 | − | 1.44245i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.70188e6 | − | 1.66434e6i | 0.914722 | − | 0.894544i | ||||
\(323\) | −374739. | −0.199859 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.77878e6 | 0.934142 | ||||||||
\(326\) | −625852. | + | 612046.i | −0.326158 | + | 0.318963i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 816971. | − | 2.68611e6i | 0.419298 | − | 1.37860i | ||||
\(329\) | −305860. | + | 176588.i | −0.155787 | + | 0.0899439i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −352745. | − | 203658.i | −0.176967 | − | 0.102172i | 0.408900 | − | 0.912579i | \(-0.365912\pi\) |
−0.585867 | + | 0.810407i | \(0.699246\pi\) | |||||||
\(332\) | 2.65641e6 | + | 1.61372e6i | 1.32267 | + | 0.803497i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −300142. | + | 1.07217e6i | −0.147218 | + | 0.525893i | ||||
\(335\) | −727151. | + | 1.25946e6i | −0.354008 | + | 0.613159i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.44822e6 | − | 2.50838e6i | −0.694638 | − | 1.20315i | −0.970302 | − | 0.241895i | \(-0.922231\pi\) |
0.275664 | − | 0.961254i | \(-0.411102\pi\) | |||||||
\(338\) | −1.32611e6 | + | 339525.i | −0.631375 | + | 0.161652i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.71390e6 | + | 1.48717e6i | −1.27320 | + | 0.697692i | ||||
\(341\) | 1.50768e6i | 0.702139i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.87641e6i | − | 0.861176i | ||||||
\(344\) | 2.53969e6 | − | 590213.i | 1.15714 | − | 0.268914i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 945320. | + | 3.69220e6i | 0.424511 | + | 1.65804i | ||||
\(347\) | −1.79724e6 | − | 3.11291e6i | −0.801275 | − | 1.38785i | −0.918777 | − | 0.394777i | \(-0.870822\pi\) |
0.117502 | − | 0.993073i | \(-0.462512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −956981. | + | 1.65754e6i | −0.420571 | + | 0.728451i | −0.995995 | − | 0.0894044i | \(-0.971504\pi\) |
0.575424 | + | 0.817855i | \(0.304837\pi\) | |||||||
\(350\) | −3.85935e6 | − | 1.08038e6i | −1.68401 | − | 0.471418i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.15519e6 | + | 659447.i | −1.35728 | + | 0.283676i | ||||
\(353\) | −2.21063e6 | − | 1.27631e6i | −0.944232 | − | 0.545152i | −0.0529474 | − | 0.998597i | \(-0.516862\pi\) |
−0.891284 | + | 0.453445i | \(0.850195\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −537073. | + | 310079.i | −0.226184 | + | 0.130587i | ||||
\(356\) | 2.38212e6 | + | 53141.1i | 0.996182 | + | 0.0222232i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.30918e6 | + | 2.36127e6i | 0.952248 | + | 0.973728i | ||||
\(359\) | 2.70497e6 | 1.10771 | 0.553856 | − | 0.832612i | \(-0.313156\pi\) | ||||
0.553856 | + | 0.832612i | \(0.313156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.35490e6 | 0.951053 | ||||||||
\(362\) | 2.46432e6 | + | 2.51991e6i | 0.988383 | + | 1.01068i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.64764e6 | − | 36756.1i | −0.651792 | − | 0.0145404i | ||||
\(365\) | −862824. | + | 498151.i | −0.338992 | + | 0.195717i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.78493e6 | − | 2.18523e6i | −1.46687 | − | 0.846900i | −0.467561 | − | 0.883961i | \(-0.654867\pi\) |
−0.999313 | + | 0.0370602i | \(0.988201\pi\) | |||||||
\(368\) | −1.38662e6 | − | 2.67004e6i | −0.533751 | − | 1.02778i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 975346. | + | 273037.i | 0.370386 | + | 0.103685i | ||||
\(371\) | 957029. | − | 1.65762e6i | 0.360986 | − | 0.625246i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.08643e6 | − | 1.88176e6i | −0.404325 | − | 0.700312i | 0.589917 | − | 0.807464i | \(-0.299160\pi\) |
−0.994243 | + | 0.107152i | \(0.965827\pi\) | |||||||
\(374\) | 840421. | + | 3.28249e6i | 0.310683 | + | 1.21346i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 101044. | + | 434794.i | 0.0368589 | + | 0.158604i | ||||
\(377\) | − | 1.38318e6i | − | 0.501216i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 872712.i | − | 0.312085i | −0.987750 | − | 0.156043i | \(-0.950126\pi\) | ||
0.987750 | − | 0.156043i | \(-0.0498737\pi\) | |||||||
\(380\) | −877727. | + | 480980.i | −0.311818 | + | 0.170871i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.01455e6 | − | 259756.i | 0.355725 | − | 0.0910767i | ||||
\(383\) | −817267. | − | 1.41555e6i | −0.284687 | − | 0.493092i | 0.687846 | − | 0.725856i | \(-0.258556\pi\) |
−0.972533 | + | 0.232764i | \(0.925223\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.58011e6 | + | 6.20094e6i | −1.23096 | + | 2.13209i | ||||
\(386\) | 442748. | − | 1.58159e6i | 0.151248 | − | 0.540289i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.62324e6 | + | 1.59357e6i | 0.884624 | + | 0.537394i | ||||
\(389\) | 89924.7 | + | 51918.0i | 0.0301304 | + | 0.0173958i | 0.514990 | − | 0.857196i | \(-0.327796\pi\) |
−0.484859 | + | 0.874592i | \(0.661129\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.73893e6 | + | 1.58132e6i | −0.906021 | + | 0.523092i | ||||
\(392\) | 641764. | + | 195190.i | 0.210941 | + | 0.0641568i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 940699. | − | 919948.i | 0.305288 | − | 0.298554i | ||||
\(395\) | −6.67162e6 | −2.15149 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.33523e6 | −1.06206 | −0.531031 | − | 0.847352i | \(-0.678195\pi\) | ||||
−0.531031 | + | 0.847352i | \(0.678195\pi\) | |||||||
\(398\) | 2.11927e6 | − | 2.07252e6i | 0.670625 | − | 0.655831i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.72579e6 | + | 4.26943e6i | −0.851810 | + | 1.33420i | ||||
\(401\) | −144161. | + | 83231.6i | −0.0447701 | + | 0.0258480i | −0.522218 | − | 0.852812i | \(-0.674895\pi\) |
0.477448 | + | 0.878660i | \(0.341562\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 843751. | + | 487140.i | 0.258793 | + | 0.149414i | ||||
\(404\) | −669340. | + | 1.10183e6i | −0.204030 | + | 0.335861i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −840105. | + | 3.00104e6i | −0.252941 | + | 0.903558i | ||||
\(407\) | 554486. | − | 960398.i | 0.165922 | − | 0.287386i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.56963e6 | + | 4.45073e6i | 0.759560 | + | 1.31560i | 0.943075 | + | 0.332580i | \(0.107919\pi\) |
−0.183515 | + | 0.983017i | \(0.558748\pi\) | |||||||
\(410\) | −7.63625e6 | + | 1.95512e6i | −2.24347 | + | 0.574399i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −763270. | − | 1.39287e6i | −0.221531 | − | 0.404266i | ||||
\(413\) | 5.69417e6i | 1.64269i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.72638e6i | − | 2.48722i | ||||||
\(416\) | −650411. | + | 1.97883e6i | −0.184270 | + | 0.560628i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 271809. | + | 1.06162e6i | 0.0760892 | + | 0.297187i | ||||
\(419\) | −1.65720e6 | − | 2.87035e6i | −0.461146 | − | 0.798729i | 0.537872 | − | 0.843027i | \(-0.319228\pi\) |
−0.999018 | + | 0.0442975i | \(0.985895\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.80550e6 | − | 3.12721e6i | 0.496468 | − | 0.859908i | −0.503524 | − | 0.863981i | \(-0.667963\pi\) |
0.999992 | + | 0.00407351i | \(0.00129664\pi\) | |||||||
\(422\) | 2.45130e6 | + | 686214.i | 0.670064 | + | 0.187577i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.65244e6 | − | 1.76689e6i | −0.446388 | − | 0.477303i | ||||
\(425\) | 4.61130e6 | + | 2.66234e6i | 1.23837 | + | 0.714974i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −52463.7 | + | 30289.9i | −0.0139248 | + | 0.00803950i | ||||
\(428\) | −10117.5 | + | 453532.i | −0.00266972 | + | 0.119674i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.11825e6 | − | 5.23370e6i | −1.33490 | − | 1.36502i | ||||
\(431\) | −7.53077e6 | −1.95275 | −0.976374 | − | 0.216090i | \(-0.930670\pi\) | ||||
−0.976374 | + | 0.216090i | \(0.930670\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.24585e6 | 0.575653 | 0.287827 | − | 0.957683i | \(-0.407067\pi\) | ||||
0.287827 | + | 0.957683i | \(0.407067\pi\) | |||||||
\(434\) | −1.53478e6 | − | 1.56940e6i | −0.391131 | − | 0.399954i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15550.0 | + | 697049.i | −0.00391755 | + | 0.175609i | ||||
\(437\) | −885823. | + | 511430.i | −0.221893 | + | 0.128110i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −925006. | − | 534052.i | −0.229078 | − | 0.132258i | 0.381069 | − | 0.924547i | \(-0.375556\pi\) |
−0.610147 | + | 0.792289i | \(0.708889\pi\) | |||||||
\(440\) | 6.18157e6 | + | 6.60968e6i | 1.52218 | + | 1.62760i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.10855e6 | + | 590263.i | 0.513367 | + | 0.143711i | ||||
\(443\) | −149436. | + | 258831.i | −0.0361781 | + | 0.0626623i | −0.883548 | − | 0.468342i | \(-0.844852\pi\) |
0.847369 | + | 0.531004i | \(0.178185\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.34482e6 | − | 5.79340e6i | −0.800705 | − | 1.38686i | ||||
\(446\) | −54180.4 | − | 211616.i | −0.0128975 | − | 0.0503747i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.61306e6 | − | 3.89836e6i | 0.615113 | − | 0.917670i | ||||
\(449\) | − | 8.39456e6i | − | 1.96509i | −0.186028 | − | 0.982544i | \(-0.559561\pi\) | ||
0.186028 | − | 0.982544i | \(-0.440439\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.63070e6i | 1.99804i | ||||||||
\(452\) | −2.29880e6 | − | 4.19501e6i | −0.529243 | − | 0.965800i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.90252e6 | − | 1.25520e6i | 1.11630 | − | 0.285807i | ||||
\(455\) | 2.31351e6 | + | 4.00712e6i | 0.523894 | + | 0.907411i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.98648e6 | + | 3.44069e6i | −0.444933 | + | 0.770646i | −0.998048 | − | 0.0624588i | \(-0.980106\pi\) |
0.553115 | + | 0.833105i | \(0.313439\pi\) | |||||||
\(458\) | 2.17789e6 | − | 7.77990e6i | 0.485146 | − | 1.73305i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.38557e6 | + | 7.21925e6i | −0.966344 | + | 1.59073i | ||||
\(461\) | 2.12064e6 | + | 1.22435e6i | 0.464744 | + | 0.268320i | 0.714037 | − | 0.700108i | \(-0.246865\pi\) |
−0.249293 | + | 0.968428i | \(0.580198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.77486e6 | − | 3.33412e6i | 1.25196 | − | 0.722817i | 0.280459 | − | 0.959866i | \(-0.409513\pi\) |
0.971498 | + | 0.237049i | \(0.0761801\pi\) | |||||||
\(464\) | 3.31992e6 | + | 2.11958e6i | 0.715867 | + | 0.457040i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.53651e6 | − | 1.50261e6i | 0.327770 | − | 0.320540i | ||||
\(467\) | 3.34371e6 | 0.709474 | 0.354737 | − | 0.934966i | \(-0.384570\pi\) | ||||
0.354737 | + | 0.934966i | \(0.384570\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.31838e6 | −0.486689 | ||||||||
\(470\) | 896008. | − | 876242.i | 0.187097 | − | 0.182970i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.88546e6 | + | 2.09419e6i | 1.42258 | + | 0.432674i | ||||
\(473\) | −6.94134e6 | + | 4.00759e6i | −1.42656 | + | 0.823626i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.49139e6 | + | 861052.i | 0.303288 | + | 0.175104i | ||||
\(476\) | −4.21633e6 | − | 2.56135e6i | −0.852938 | − | 0.518145i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.15639e6 | + | 4.13087e6i | −0.231491 | + | 0.826936i | ||||
\(479\) | 2.32045e6 | − | 4.01914e6i | 0.462097 | − | 0.800376i | −0.536968 | − | 0.843603i | \(-0.680430\pi\) |
0.999065 | + | 0.0432268i | \(0.0137638\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −358315. | − | 620620.i | −0.0706159 | − | 0.122310i | ||||
\(482\) | 6.52749e6 | − | 1.67124e6i | 1.27976 | − | 0.327659i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.17008e6 | − | 2.28513e6i | 0.809153 | − | 0.443403i | ||||
\(485\) | − | 8.61740e6i | − | 1.66350i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.91616e6i | − | 0.939299i | −0.882853 | − | 0.469650i | \(-0.844380\pi\) | ||
0.882853 | − | 0.469650i | \(-0.155620\pi\) | |||||||
\(488\) | 17332.0 | + | 74579.7i | 0.00329457 | + | 0.0141766i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −467115. | − | 1.82445e6i | −0.0878889 | − | 0.343274i | ||||
\(491\) | −346602. | − | 600332.i | −0.0648824 | − | 0.112380i | 0.831759 | − | 0.555136i | \(-0.187334\pi\) |
−0.896642 | + | 0.442757i | \(0.854001\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.07024e6 | − | 3.58575e6i | 0.383621 | − | 0.664451i | ||||
\(494\) | 681946. | + | 190903.i | 0.125728 | + | 0.0351961i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.46220e6 | + | 1.27869e6i | −0.449385 | + | 0.233378i | ||||
\(497\) | −856175. | − | 494313.i | −0.155479 | − | 0.0897658i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −400079. | + | 230986.i | −0.0719274 | + | 0.0415273i | −0.535532 | − | 0.844515i | \(-0.679889\pi\) |
0.463605 | + | 0.886042i | \(0.346556\pi\) | |||||||
\(500\) | 5.23587e6 | + | 116803.i | 0.936620 | + | 0.0208944i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.78977e6 | + | 2.85270e6i | 0.494094 | + | 0.505239i | ||||
\(503\) | 3.22518e6 | 0.568373 | 0.284187 | − | 0.958769i | \(-0.408276\pi\) | ||||
0.284187 | + | 0.958769i | \(0.408276\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.61952e6 | 0.631572 | ||||||||
\(506\) | 6.46644e6 | + | 6.61231e6i | 1.12277 | + | 1.14809i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.23313e6 | + | 183667.i | 1.41549 | + | 0.0315772i | ||||
\(509\) | 213328. | − | 123165.i | 0.0364967 | − | 0.0210714i | −0.481641 | − | 0.876369i | \(-0.659959\pi\) |
0.518137 | + | 0.855297i | \(0.326626\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.37547e6 | − | 794129.i | −0.233023 | − | 0.134536i | ||||
\(512\) | −3.75291e6 | − | 4.59347e6i | −0.632694 | − | 0.774402i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.00698e6 | − | 1.96152e6i | −1.16983 | − | 0.327481i | ||||
\(515\) | −2.22962e6 | + | 3.86181e6i | −0.370436 | + | 0.641613i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −686097. | − | 1.18836e6i | −0.112891 | − | 0.195533i | ||||
\(518\) | 400476. | + | 1.56417e6i | 0.0655771 | + | 0.256129i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.69632e6 | − | 1.32380e6i | 0.923817 | − | 0.214691i | ||||
\(521\) | 5.09612e6i | 0.822519i | 0.911518 | + | 0.411259i | \(0.134911\pi\) | ||||
−0.911518 | + | 0.411259i | \(0.865089\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5.13482e6i | − | 0.820863i | −0.911891 | − | 0.410432i | \(-0.865378\pi\) | ||
0.911891 | − | 0.410432i | \(-0.134622\pi\) | |||||||
\(524\) | −177466. | + | 97248.4i | −0.0282349 | + | 0.0154723i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.90373e6 | + | 2.27963e6i | −1.40316 | + | 0.359253i | ||||
\(527\) | 1.45823e6 | + | 2.52572e6i | 0.228717 | + | 0.396150i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.09808e6 | + | 1.90193e6i | −0.170606 | + | 0.295498i | ||||
\(530\) | −1.83097e6 | + | 6.54060e6i | −0.283133 | + | 1.01141i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.36364e6 | − | 828391.i | −0.208892 | − | 0.126898i | ||||
\(533\) | 4.83005e6 | + | 2.78863e6i | 0.736434 | + | 0.425180i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.10301e6 | − | 636821.i | 0.166607 | − | 0.0961906i | ||||
\(536\) | −852647. | + | 2.80341e6i | −0.128191 | + | 0.421478i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.28568e6 | + | 5.16908e6i | −0.787309 | + | 0.769941i | ||||
\(539\) | −2.06204e6 | −0.305721 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.10092e7 | 1.61720 | 0.808601 | − | 0.588357i | \(-0.200225\pi\) | ||||
0.808601 | + | 0.588357i | \(0.200225\pi\) | |||||||
\(542\) | 442645. | − | 432881.i | 0.0647229 | − | 0.0632951i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.64789e6 | + | 4.15643e6i | −0.673377 | + | 0.602176i | ||||
\(545\) | 1.69525e6 | − | 978751.i | 0.244479 | − | 0.141150i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.43955e6 | + | 1.98583e6i | 0.491511 | + | 0.283774i | 0.725201 | − | 0.688537i | \(-0.241747\pi\) |
−0.233690 | + | 0.972311i | \(0.575080\pi\) | |||||||
\(548\) | −4.80498e6 | + | 7.90966e6i | −0.683503 | + | 1.12514i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.19760e6 | − | 1.49947e7i | 0.591690 | − | 2.11364i | ||||
\(551\) | 669555. | − | 1.15970e6i | 0.0939523 | − | 0.162730i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.31779e6 | − | 9.21068e6i | −0.739466 | − | 1.28079i | ||||
\(554\) | −4.14134e6 | + | 1.06031e6i | −0.573279 | + | 0.146777i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.52949e6 | + | 2.79113e6i | 0.209827 | + | 0.382907i | ||||
\(557\) | 9.38422e6i | 1.28162i | 0.767698 | + | 0.640812i | \(0.221402\pi\) | ||||
−0.767698 | + | 0.640812i | \(0.778598\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.17950e6i | 0.701065i | ||||||||
\(560\) | −1.31631e7 | − | 587588.i | −1.77374 | − | 0.0791777i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −216539. | − | 845753.i | −0.0289198 | − | 0.112954i | ||||
\(563\) | 2.54261e6 | + | 4.40393e6i | 0.338072 | + | 0.585558i | 0.984070 | − | 0.177781i | \(-0.0568919\pi\) |
−0.645998 | + | 0.763339i | \(0.723559\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.71512e6 | + | 1.16309e7i | −0.884978 | + | 1.53283i | ||||
\(566\) | 5.79532e6 | + | 1.62233e6i | 0.760390 | + | 0.212863i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −912611. | + | 853500.i | −0.118690 | + | 0.111002i | ||||
\(569\) | −7.59213e6 | − | 4.38332e6i | −0.983067 | − | 0.567574i | −0.0798721 | − | 0.996805i | \(-0.525451\pi\) |
−0.903195 | + | 0.429231i | \(0.858785\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.07595e7 | + | 6.21203e6i | −1.38103 | + | 0.797339i | −0.992282 | − | 0.124004i | \(-0.960426\pi\) |
−0.388750 | + | 0.921343i | \(0.627093\pi\) | |||||||
\(572\) | 142809. | − | 6.40157e6i | 0.0182500 | − | 0.818082i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.78585e6 | − | 8.98404e6i | −1.11302 | − | 1.13813i | ||||
\(575\) | 1.45338e7 | 1.83320 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.43597e6 | 1.17990 | 0.589952 | − | 0.807438i | \(-0.299146\pi\) | ||||
0.589952 | + | 0.807438i | \(0.299146\pi\) | |||||||
\(578\) | −1.03300e6 | − | 1.05630e6i | −0.128612 | − | 0.131513i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 246637. | − | 1.10558e7i | 0.0304431 | − | 1.36465i | ||||
\(581\) | 1.20474e7 | − | 6.95558e6i | 1.48065 | − | 0.854856i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.44036e6 | + | 3.71834e6i | 0.784763 | + | 0.453083i | ||||
\(584\) | −1.46614e6 | + | 1.37117e6i | −0.177886 | + | 0.166364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.27086e6 | − | 915639.i | −0.393475 | − | 0.110149i | ||||
\(587\) | −6.76932e6 | + | 1.17248e7i | −0.810868 | + | 1.40446i | 0.101390 | + | 0.994847i | \(0.467671\pi\) |
−0.912258 | + | 0.409617i | \(0.865662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 471619. | + | 816869.i | 0.0560149 | + | 0.0970206i | ||||
\(590\) | −5.01166e6 | − | 1.95744e7i | −0.592723 | − | 2.31504i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.03870e6 | + | 91005.3i | 0.239083 | + | 0.0106724i | ||||
\(593\) | 1.76321e6i | 0.205905i | 0.994686 | + | 0.102952i | \(0.0328289\pi\) | ||||
−0.994686 | + | 0.102952i | \(0.967171\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.38508e7i | 1.60391i | ||||||||
\(596\) | 5.74186e6 | + | 1.04782e7i | 0.662120 | + | 1.20828i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.78983e6 | − | 1.48238e6i | 0.662084 | − | 0.169514i | ||||
\(599\) | 3.59905e6 | + | 6.23374e6i | 0.409846 | + | 0.709875i | 0.994872 | − | 0.101140i | \(-0.0322489\pi\) |
−0.585026 | + | 0.811015i | \(0.698916\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.35517e6 | − | 2.34722e6i | 0.153041 | − | 0.265075i | −0.779303 | − | 0.626647i | \(-0.784427\pi\) |
0.932344 | + | 0.361573i | \(0.117760\pi\) | |||||||
\(602\) | 3.14589e6 | − | 1.12378e7i | 0.353795 | − | 1.26383i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.14581e6 | − | 1.01168e7i | 0.685467 | − | 1.12837i | ||||
\(605\) | −1.15618e7 | − | 6.67521e6i | −1.28421 | − | 0.741440i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.91340e6 | − | 1.10470e6i | 0.210782 | − | 0.121695i | −0.390893 | − | 0.920436i | \(-0.627834\pi\) |
0.601675 | + | 0.798741i | \(0.294500\pi\) | |||||||
\(608\) | −1.50322e6 | + | 1.34427e6i | −0.164916 | + | 0.147478i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 153691. | − | 150301.i | 0.0167234 | − | 0.0163545i | ||||
\(611\) | −886728. | −0.0960921 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.95842e6 | −0.532957 | −0.266478 | − | 0.963841i | \(-0.585860\pi\) | ||||
−0.266478 | + | 0.963841i | \(0.585860\pi\) | |||||||
\(614\) | 1.12508e7 | − | 1.10027e7i | 1.20438 | − | 1.17781i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.19799e6 | + | 1.38025e7i | −0.445748 | + | 1.46557i | ||||
\(617\) | 6.51356e6 | − | 3.76060e6i | 0.688819 | − | 0.397690i | −0.114350 | − | 0.993440i | \(-0.536479\pi\) |
0.803170 | + | 0.595750i | \(0.203145\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.79004e6 | + | 2.18818e6i | 0.397573 | + | 0.229539i | 0.685436 | − | 0.728133i | \(-0.259612\pi\) |
−0.287863 | + | 0.957671i | \(0.592945\pi\) | |||||||
\(620\) | 6.65729e6 | + | 4.04419e6i | 0.695534 | + | 0.422525i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.49723e6 | − | 1.24928e7i | 0.362450 | − | 1.29475i | ||||
\(623\) | 5.33215e6 | − | 9.23555e6i | 0.550405 | − | 0.953329i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 377275. | + | 653459.i | 0.0386329 | + | 0.0669142i | ||||
\(626\) | −1.54870e7 | + | 3.96514e6i | −1.57954 | + | 0.404411i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.10372e7 | + | 6.04824e6i | −1.11676 | + | 0.611969i | ||||
\(629\) | − | 2.14520e6i | − | 0.216192i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.79597e6i | 0.279549i | 0.990183 | + | 0.139775i | \(0.0446378\pi\) | ||||
−0.990183 | + | 0.139775i | \(0.955362\pi\) | |||||||
\(632\) | −1.30934e7 | + | 3.04285e6i | −1.30395 | + | 0.303032i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −300802. | − | 1.17487e6i | −0.0297206 | − | 0.116082i | ||||
\(635\) | −1.15604e7 | − | 2.00233e7i | −1.13773 | − | 1.97061i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −666257. | + | 1.15399e6i | −0.0650569 | + | 0.112682i | ||||
\(638\) | −1.16599e7 | − | 3.26406e6i | −1.13408 | − | 0.317473i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.55163e6 | + | 1.57009e7i | −0.535760 | + | 1.51522i | ||||
\(641\) | 4.59173e6 | + | 2.65104e6i | 0.441399 | + | 0.254842i | 0.704191 | − | 0.710011i | \(-0.251310\pi\) |
−0.262792 | + | 0.964853i | \(0.584643\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.45248e7 | + | 8.38588e6i | −1.38542 | + | 0.799873i | −0.992795 | − | 0.119825i | \(-0.961767\pi\) |
−0.392626 | + | 0.919698i | \(0.628433\pi\) | |||||||
\(644\) | −1.34624e7 | − | 300323.i | −1.27911 | − | 0.0285347i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.48215e6 | + | 1.51558e6i | 0.139737 | + | 0.142889i | ||||
\(647\) | 8.06422e6 | 0.757359 | 0.378679 | − | 0.925528i | \(-0.376378\pi\) | ||||
0.378679 | + | 0.925528i | \(0.376378\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.21235e7 | −2.06178 | ||||||||
\(650\) | −7.03531e6 | − | 7.19401e6i | −0.653130 | − | 0.667863i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.95067e6 | + | 110441.i | 0.456084 | + | 0.0101745i | ||||
\(653\) | 620058. | − | 357991.i | 0.0569049 | − | 0.0328540i | −0.471278 | − | 0.881985i | \(-0.656207\pi\) |
0.528183 | + | 0.849131i | \(0.322874\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 492035. | + | 284077.i | 0.0448118 | + | 0.0258721i | ||||
\(656\) | −1.40948e7 | + | 7.31984e6i | −1.27879 | + | 0.664113i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.92390e6 | + | 538575.i | 0.173228 | + | 0.0484933i | ||||
\(659\) | 15687.4 | − | 27171.4i | 0.00140714 | − | 0.00243724i | −0.865321 | − | 0.501218i | \(-0.832885\pi\) |
0.866728 | + | 0.498781i | \(0.166219\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.41600e6 | + | 7.64875e6i | 0.393121 | + | 0.680905i | 0.992859 | − | 0.119291i | \(-0.0380621\pi\) |
−0.599739 | + | 0.800196i | \(0.704729\pi\) | |||||||
\(662\) | 571493. | + | 2.23212e6i | 0.0506834 | + | 0.197958i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.98001e6 | − | 1.71260e7i | −0.350319 | − | 1.50742i | ||||
\(665\) | 4.47961e6i | 0.392813i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.13015e7i | − | 0.983608i | ||||||
\(668\) | 5.52335e6 | − | 3.02671e6i | 0.478918 | − | 0.262439i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.96970e6 | − | 2.04049e6i | 0.685891 | − | 0.175610i | ||||
\(671\) | −117685. | − | 203837.i | −0.0100906 | − | 0.0174774i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.33892e6 | − | 5.78318e6i | 0.284163 | − | 0.492186i | −0.688242 | − | 0.725481i | \(-0.741617\pi\) |
0.972406 | + | 0.233295i | \(0.0749508\pi\) | |||||||
\(674\) | −4.41691e6 | + | 1.57781e7i | −0.374514 | + | 1.33784i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.61811e6 | + | 4.02039e6i | 0.557016 | + | 0.338377i | ||||
\(677\) | −1.26099e7 | − | 7.28033e6i | −1.05740 | − | 0.610491i | −0.132689 | − | 0.991158i | \(-0.542361\pi\) |
−0.924712 | + | 0.380667i | \(0.875694\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.18970e7 | − | 6.86872e6i | 0.990289 | − | 0.571744i | ||||
\(680\) | 1.67485e7 | + | 5.09399e6i | 1.38900 | + | 0.422460i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.09760e6 | − | 5.96308e6i | 0.501993 | − | 0.490919i | ||||
\(683\) | −5.63380e6 | −0.462114 | −0.231057 | − | 0.972940i | \(-0.574218\pi\) | ||||
−0.231057 | + | 0.972940i | \(0.574218\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.59834e7 | 2.11578 | ||||||||
\(686\) | −7.58887e6 | + | 7.42146e6i | −0.615697 | + | 0.602115i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.24319e7 | − | 7.93705e6i | −1.00130 | − | 0.639275i | ||||
\(689\) | 4.16183e6 | − | 2.40284e6i | 0.333993 | − | 0.192831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.00873e6 | − | 5.20119e6i | −0.717742 | − | 0.414389i | 0.0961788 | − | 0.995364i | \(-0.469338\pi\) |
−0.813921 | + | 0.580975i | \(0.802671\pi\) | |||||||
\(692\) | 1.11937e7 | − | 1.84264e7i | 0.888606 | − | 1.46277i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.48138e6 | + | 1.95807e7i | −0.432008 | + | 1.54322i | ||||
\(695\) | 4.46787e6 | − | 7.73858e6i | 0.350864 | − | 0.607714i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.34762e6 | + | 1.44585e7i | 0.650850 | + | 1.12730i | ||||
\(698\) | 1.04887e7 | − | 2.68543e6i | 0.814859 | − | 0.208629i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.08948e7 | + | 1.98817e7i | 0.840379 | + | 1.53358i | ||||
\(701\) | 1.19679e7i | 0.919862i | 0.887955 | + | 0.459931i | \(0.152126\pi\) | ||||
−0.887955 | + | 0.459931i | \(0.847874\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 693798.i | − | 0.0529474i | ||||||
\(704\) | 1.51463e7 | + | 1.01525e7i | 1.15179 | + | 0.772044i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.58150e6 | + | 1.39885e7i | 0.270429 | + | 1.05624i | ||||
\(707\) | 2.88503e6 | + | 4.99702e6i | 0.217071 | + | 0.375978i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.72698e6 | + | 6.45531e6i | −0.278446 | + | 0.482283i | −0.970999 | − | 0.239084i | \(-0.923153\pi\) |
0.692553 | + | 0.721367i | \(0.256486\pi\) | |||||||
\(710\) | 3.37827e6 | + | 945708.i | 0.251506 | + | 0.0704062i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.20670e6 | − | 9.84433e6i | −0.680619 | − | 0.727757i | ||||
\(713\) | 6.89402e6 | + | 3.98027e6i | 0.507866 | + | 0.293216i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.55689e7 | + | 8.98868e6i | −1.13892 | + | 0.657553i | ||||
\(716\) | 416682. | − | 1.86783e7i | 0.0303754 | − | 1.36162i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.06986e7 | − | 1.09399e7i | −0.774487 | − | 0.791957i | ||||
\(719\) | 1.53936e7 | 1.11050 | 0.555248 | − | 0.831685i | \(-0.312623\pi\) | ||||
0.555248 | + | 0.831685i | \(0.312623\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.10870e6 | −0.509275 | ||||||||
\(722\) | −9.31397e6 | − | 9.52407e6i | −0.664954 | − | 0.679954i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 444676. | − | 1.99332e7i | 0.0315281 | − | 1.41329i | ||||
\(725\) | −1.64782e7 | + | 9.51371e6i | −1.16430 | + | 0.672210i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.42385e6 | − | 4.28616e6i | −0.520946 | − | 0.300768i | 0.216375 | − | 0.976310i | \(-0.430576\pi\) |
−0.737322 | + | 0.675542i | \(0.763910\pi\) | |||||||
\(728\) | 6.36800e6 | + | 6.80903e6i | 0.445322 | + | 0.476164i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.42729e6 | + | 1.51931e6i | 0.376943 | + | 0.105521i | ||||
\(731\) | −7.75228e6 | + | 1.34273e7i | −0.536582 | + | 0.929387i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.79172e6 | − | 1.52277e7i | −0.604386 | − | 1.04683i | −0.992148 | − | 0.125067i | \(-0.960085\pi\) |
0.387763 | − | 0.921759i | \(-0.373248\pi\) | |||||||
\(734\) | 6.13209e6 | + | 2.39505e7i | 0.420115 | + | 1.64087i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.31430e6 | + | 1.61684e7i | −0.361619 | + | 1.10020i | ||||
\(737\) | − | 9.00758e6i | − | 0.610857i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 186950.i | 0.0125926i | 0.999980 | + | 0.00629629i | \(0.00200418\pi\) | ||||
−0.999980 | + | 0.00629629i | \(0.997996\pi\) | |||||||
\(740\) | −2.75337e6 | − | 5.02455e6i | −0.184836 | − | 0.337301i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.04892e7 | + | 2.68557e6i | −0.699412 | + | 0.179071i | ||||
\(743\) | 3.19316e6 | + | 5.53072e6i | 0.212202 | + | 0.367544i | 0.952403 | − | 0.304841i | \(-0.0986033\pi\) |
−0.740202 | + | 0.672385i | \(0.765270\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.67728e7 | − | 2.90513e7i | 1.10717 | − | 1.91768i | ||||
\(746\) | −3.31351e6 | + | 1.18365e7i | −0.217992 | + | 0.778714i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.95160e6 | − | 1.63817e7i | 0.650338 | − | 1.07055i | ||||
\(749\) | 1.75836e6 | + | 1.01519e6i | 0.114526 | + | 0.0661214i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.55553e7 | − | 1.47544e7i | 1.65341 | − | 0.954598i | 0.677757 | − | 0.735286i | \(-0.262952\pi\) |
0.975655 | − | 0.219312i | \(-0.0703814\pi\) | |||||||
\(752\) | 1.35882e6 | − | 2.12833e6i | 0.0876228 | − | 0.137245i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.59407e6 | + | 5.47067e6i | −0.358344 | + | 0.350439i | ||||
\(755\) | −3.32341e7 | −2.12186 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.98899e7 | −1.89576 | −0.947882 | − | 0.318621i | \(-0.896780\pi\) | ||||
−0.947882 | + | 0.318621i | \(0.896780\pi\) | |||||||
\(758\) | −3.52956e6 | + | 3.45170e6i | −0.223125 | + | 0.218203i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.41679e6 | + | 1.64750e6i | 0.340180 | + | 0.103464i | ||||
\(761\) | −1.12672e7 | + | 6.50513e6i | −0.705269 | + | 0.407187i | −0.809307 | − | 0.587386i | \(-0.800157\pi\) |
0.104038 | + | 0.994573i | \(0.466824\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.70248e6 | + | 1.56028e6i | 0.168055 | + | 0.0970265i | ||||
\(764\) | −5.06323e6 | − | 3.07583e6i | −0.313830 | − | 0.190646i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.49258e6 | + | 8.90402e6i | −0.153489 | + | 0.548295i | ||||
\(767\) | −7.14825e6 | + | 1.23811e7i | −0.438744 | + | 0.759927i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.45635e6 | − | 2.52248e6i | −0.0888077 | − | 0.153819i | 0.818200 | − | 0.574934i | \(-0.194972\pi\) |
−0.907007 | + | 0.421115i | \(0.861639\pi\) | |||||||
\(770\) | 3.92387e7 | − | 1.00463e7i | 2.38500 | − | 0.610634i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.14766e6 | + | 4.46479e6i | −0.492028 | + | 0.269623i | ||||
\(773\) | − | 6.84734e6i | − | 0.412167i | −0.978534 | − | 0.206084i | \(-0.933928\pi\) | ||
0.978534 | − | 0.206084i | \(-0.0660719\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.34025e7i | − | 0.801551i | ||||||
\(776\) | −3.93030e6 | − | 1.69121e7i | −0.234300 | − | 1.00819i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −145690. | − | 569031.i | −0.00862939 | − | 0.0337044i | ||||
\(779\) | 2.69978e6 | + | 4.67616e6i | 0.159399 | + | 0.276087i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.92055e6 | − | 3.32649e6i | 0.112667 | − | 0.195146i | ||||
\(782\) | 1.72283e7 | + | 4.82286e6i | 1.00745 | + | 0.282025i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.74885e6 | − | 3.36753e6i | −0.101616 | − | 0.195669i | ||||
\(785\) | 3.06015e7 | + | 1.76678e7i | 1.77243 | + | 1.02331i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.80432e7 | − | 1.61907e7i | 1.61395 | − | 0.931814i | 0.625507 | − | 0.780218i | \(-0.284892\pi\) |
0.988443 | − | 0.151596i | \(-0.0484413\pi\) | |||||||
\(788\) | −7.44120e6 | − | 166001.i | −0.426901 | − | 0.00952346i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.63872e7 | + | 2.69824e7i | 1.50427 | + | 1.53820i | ||||
\(791\) | −2.14098e7 | −1.21667 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −152099. | −0.00858904 | ||||||||
\(794\) | 1.31913e7 | + | 1.34889e7i | 0.742570 | + | 0.759320i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.67641e7 | − | 373979.i | −0.937771 | − | 0.0209201i | ||||
\(797\) | 4.17052e6 | − | 2.40785e6i | 0.232565 | − | 0.134271i | −0.379190 | − | 0.925319i | \(-0.623797\pi\) |
0.611755 | + | 0.791047i | \(0.290464\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.29876e6 | − | 1.32719e6i | −0.127387 | − | 0.0735471i | ||||
\(800\) | 2.80480e7 | − | 5.86214e6i | 1.54945 | − | 0.323840i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 906797. | + | 253847.i | 0.0497822 | + | 0.0139360i | ||||
\(803\) | 3.08543e6 | − | 5.34411e6i | 0.168860 | − | 0.292474i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.89030e7 | + | 3.27409e7i | 1.02811 | + | 1.78074i | ||||
\(806\) | −1.36699e6 | − | 5.33914e6i | −0.0741185 | − | 0.289490i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.10351e6 | − | 1.65083e6i | 0.382776 | − | 0.0889555i | ||||
\(809\) | − | 7.74333e6i | − | 0.415965i | −0.978133 | − | 0.207982i | \(-0.933310\pi\) | ||
0.978133 | − | 0.207982i | \(-0.0666897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.68630e7i | 1.43417i | 0.696984 | + | 0.717087i | \(0.254525\pi\) | ||||
−0.696984 | + | 0.717087i | \(0.745475\pi\) | |||||||
\(812\) | 1.54600e7 | − | 8.47183e6i | 0.822848 | − | 0.450907i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.07726e6 | + | 1.55597e6i | −0.321475 | + | 0.0823076i | ||||
\(815\) | −6.95142e6 | − | 1.20402e7i | −0.366589 | − | 0.634951i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.50724e6 | + | 4.34267e6i | −0.131414 | + | 0.227615i | ||||
\(818\) | 7.83709e6 | − | 2.79958e7i | 0.409517 | − | 1.46288i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.81097e7 | + | 2.31510e7i | 1.97925 | + | 1.20236i | ||||
\(821\) | −1.13361e7 | − | 6.54492e6i | −0.586958 | − | 0.338881i | 0.176936 | − | 0.984222i | \(-0.443382\pi\) |
−0.763894 | + | 0.645342i | \(0.776715\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.45404e6 | + | 3.14889e6i | −0.280684 | + | 0.162053i | −0.633733 | − | 0.773552i | \(-0.718478\pi\) |
0.353049 | + | 0.935605i | \(0.385145\pi\) | |||||||
\(824\) | −2.61442e6 | + | 8.59593e6i | −0.134140 | + | 0.441037i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.30293e7 | − | 2.25213e7i | 1.17444 | − | 1.14853i | ||||
\(827\) | 1.03982e7 | 0.528680 | 0.264340 | − | 0.964430i | \(-0.414846\pi\) | ||||
0.264340 | + | 0.964430i | \(0.414846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.24354e6 | 0.366070 | 0.183035 | − | 0.983106i | \(-0.441408\pi\) | ||||
0.183035 | + | 0.983106i | \(0.441408\pi\) | |||||||
\(830\) | −3.52926e7 | + | 3.45141e7i | −1.77823 | + | 1.73901i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.05756e7 | − | 5.19606e6i | 0.529658 | − | 0.260235i | ||||
\(833\) | −3.45441e6 | + | 1.99441e6i | −0.172489 | + | 0.0995867i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.53138e7 | − | 8.84144e6i | −0.760094 | − | 0.438841i | ||||
\(836\) | 3.21854e6 | − | 5.29816e6i | 0.159274 | − | 0.262186i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.05427e6 | + | 1.80549e7i | −0.248627 | + | 0.888149i | ||||
\(839\) | 1.22662e7 | − | 2.12456e7i | 0.601595 | − | 1.04199i | −0.390985 | − | 0.920397i | \(-0.627866\pi\) |
0.992580 | − | 0.121596i | \(-0.0388011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.85770e6 | − | 4.94968e6i | −0.139324 | − | 0.241317i | ||||
\(842\) | −1.97886e7 | + | 5.06649e6i | −0.961909 | + | 0.246279i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.91996e6 | − | 1.26280e7i | −0.334385 | − | 0.610210i | ||||
\(845\) | − | 2.17407e7i | − | 1.04744i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.12826e7i | − | 1.01933i | ||||||
\(848\) | −610275. | + | 1.36714e7i | −0.0291431 | + | 0.652864i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.47091e6 | − | 2.91797e7i | −0.354671 | − | 1.38527i | ||||
\(851\) | −2.92768e6 | − | 5.07089e6i | −0.138580 | − | 0.240027i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.26783e6 | + | 3.92799e6i | −0.106718 | + | 0.184841i | −0.914439 | − | 0.404724i | \(-0.867368\pi\) |
0.807721 | + | 0.589565i | \(0.200701\pi\) | |||||||
\(854\) | 330005. | + | 92381.1i | 0.0154837 | + | 0.00433449i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.87426e6 | − | 1.75287e6i | 0.0874271 | − | 0.0817644i | ||||
\(857\) | −4.32468e6 | − | 2.49686e6i | −0.201142 | − | 0.116129i | 0.396046 | − | 0.918231i | \(-0.370382\pi\) |
−0.597188 | + | 0.802101i | \(0.703715\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.79301e7 | − | 1.61254e7i | 1.29149 | − | 0.745640i | 0.312568 | − | 0.949895i | \(-0.398811\pi\) |
0.978918 | + | 0.204256i | \(0.0654774\pi\) | |||||||
\(860\) | −923567. | + | 4.14001e7i | −0.0425816 | + | 1.90878i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.97853e7 | + | 3.04571e7i | 1.36532 | + | 1.39611i | ||||
\(863\) | 2.09873e7 | 0.959247 | 0.479624 | − | 0.877474i | \(-0.340773\pi\) | ||||
0.479624 | + | 0.877474i | \(0.340773\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.05312e7 | −2.75067 | ||||||||
\(866\) | −8.88266e6 | − | 9.08302e6i | −0.402483 | − | 0.411562i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −276945. | + | 1.24144e7i | −0.0124766 | + | 0.559277i | ||||
\(869\) | 3.57862e7 | − | 2.06612e7i | 1.60756 | − | 0.928123i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.04097e6 | − | 2.91040e6i | −0.225148 | − | 0.129989i | ||||
\(872\) | 2.88062e6 | − | 2.69404e6i | 0.128290 | − | 0.119981i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.57196e6 | + | 1.55981e6i | 0.246734 | + | 0.0690705i | ||||
\(875\) | 1.17200e7 | − | 2.02996e7i | 0.517496 | − | 0.896330i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.12204e7 | − | 1.94343e7i | −0.492616 | − | 0.853236i | 0.507348 | − | 0.861742i | \(-0.330626\pi\) |
−0.999964 | + | 0.00850516i | \(0.997293\pi\) | |||||||
\(878\) | 1.49863e6 | + | 5.85331e6i | 0.0656082 | + | 0.256251i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.28296e6 | − | 5.11427e7i | 0.0993781 | − | 2.22627i | ||||
\(881\) | 2.46288e7i | 1.06906i | 0.845149 | + | 0.534531i | \(0.179512\pi\) | ||||
−0.845149 | + | 0.534531i | \(0.820488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.33073e7i | − | 0.574365i | −0.957876 | − | 0.287183i | \(-0.907281\pi\) | ||
0.957876 | − | 0.287183i | \(-0.0927187\pi\) | |||||||
\(884\) | −5.95237e6 | − | 1.08623e7i | −0.256188 | − | 0.467510i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.63784e6 | − | 419339.i | 0.0700952 | − | 0.0179466i | ||||
\(887\) | −1.14459e7 | − | 1.98249e7i | −0.488474 | − | 0.846062i | 0.511438 | − | 0.859320i | \(-0.329113\pi\) |
−0.999912 | + | 0.0132580i | \(0.995780\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.84291e7 | − | 3.19201e7i | 0.782077 | − | 1.35460i | ||||
\(890\) | −1.02013e7 | + | 3.64414e7i | −0.431700 | + | 1.54213i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −641561. | + | 1.05610e6i | −0.0269977 | + | 0.0444418i | ||||
\(893\) | −743463. | − | 429239.i | −0.0311983 | − | 0.0180123i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.54263e7 | + | 2.62269e7i | −1.89561 | + | 1.09443i | ||||
\(896\) | −2.61014e7 | + | 4.85039e6i | −1.08616 | + | 0.201840i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.39506e7 | + | 3.32017e7i | −1.40494 | + | 1.37395i | ||||
\(899\) | −1.04218e7 | −0.430074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.43855e7 | 0.590356 | ||||||||
\(902\) | 3.49057e7 | − | 3.41357e7i | 1.42850 | − | 1.39699i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.87405e6 | + | 2.58890e7i | −0.320463 | + | 1.05365i | ||||
\(905\) | −4.84782e7 | + | 2.79889e7i | −1.96755 | + | 1.13596i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.40173e7 | − | 1.38664e7i | −0.969407 | − | 0.559688i | −0.0703518 | − | 0.997522i | \(-0.522412\pi\) |
−0.899055 | + | 0.437835i | \(0.855746\pi\) | |||||||
\(908\) | −2.44666e7 | − | 1.48631e7i | −0.984827 | − | 0.598265i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.05596e6 | − | 2.52054e7i | 0.282457 | − | 1.00900i | ||||
\(911\) | −1.93415e7 | + | 3.35005e7i | −0.772138 | + | 1.33738i | 0.164250 | + | 0.986419i | \(0.447479\pi\) |
−0.936389 | + | 0.350964i | \(0.885854\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.70245e7 | + | 4.68078e7i | 1.07295 | + | 1.85841i | ||||
\(914\) | 2.17722e7 | − | 5.57437e6i | 0.862059 | − | 0.220714i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.00786e7 | + | 2.19624e7i | −1.57824 | + | 0.864851i | ||||
\(917\) | 905722.i | 0.0355690i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.70205e6i | 0.0664790i | 0.999447 | + | 0.0332395i | \(0.0105824\pi\) | ||||
−0.999447 | + | 0.0332395i | \(0.989418\pi\) | |||||||
\(920\) | 4.65428e7 | − | 1.08163e7i | 1.81294 | − | 0.421319i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.43571e6 | − | 1.34191e7i | −0.133103 | − | 0.519871i | ||||
\(923\) | −1.24108e6 | − | 2.14962e6i | −0.0479509 | − | 0.0830534i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.92909e6 | + | 8.53743e6i | −0.189414 | + | 0.328075i | ||||
\(926\) | −3.63248e7 | − | 1.01687e7i | −1.39212 | − | 0.389707i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.55841e6 | − | 2.18102e7i | −0.173757 | − | 0.831360i | ||||
\(929\) | −2.05945e6 | − | 1.18902e6i | −0.0782908 | − | 0.0452012i | 0.460344 | − | 0.887741i | \(-0.347726\pi\) |
−0.538634 | + | 0.842540i | \(0.681060\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.11723e6 | + | 645030.i | −0.0422441 | + | 0.0243897i | ||||
\(932\) | −1.21542e7 | − | 271140.i | −0.458339 | − | 0.0102248i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.32249e7 | − | 1.35232e7i | −0.496048 | − | 0.507237i | ||||
\(935\) | −5.38143e7 | −2.01311 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.36658e6 | −0.0508495 | −0.0254248 | − | 0.999677i | \(-0.508094\pi\) | ||||
−0.0254248 | + | 0.999677i | \(0.508094\pi\) | |||||||
\(938\) | 9.16951e6 | + | 9.37635e6i | 0.340282 | + | 0.347958i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.08768e6 | − | 158114.i | −0.261628 | − | 0.00583649i | ||||
\(941\) | −1.57768e7 | + | 9.10873e6i | −0.580824 | + | 0.335339i | −0.761461 | − | 0.648211i | \(-0.775517\pi\) |
0.180637 | + | 0.983550i | \(0.442184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.94648e7 | + | 2.27850e7i | 1.44521 | + | 0.834392i | ||||
\(944\) | −1.87633e7 | − | 3.61301e7i | −0.685299 | − | 1.31959i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.36621e7 | + | 1.22227e7i | 1.58627 | + | 0.444058i | ||||
\(947\) | 1.49933e6 | − | 2.59692e6i | 0.0543279 | − | 0.0940987i | −0.837582 | − | 0.546311i | \(-0.816032\pi\) |
0.891910 | + | 0.452212i | \(0.149365\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.99384e6 | − | 3.45343e6i | −0.0718662 | − | 0.124476i | ||||
\(950\) | −2.41624e6 | − | 9.43728e6i | −0.0868622 | − | 0.339264i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.31718e6 | + | 2.71829e7i | 0.225908 | + | 0.972082i | ||||
\(953\) | − | 5.86700e6i | − | 0.209259i | −0.994511 | − | 0.104629i | \(-0.966634\pi\) | ||
0.994511 | − | 0.104629i | \(-0.0333656\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.66328e7i | 0.590144i | ||||||||
\(956\) | 2.12804e7 | − | 1.16613e7i | 0.753070 | − | 0.412670i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.54325e7 | + | 6.51153e6i | −0.895315 | + | 0.229229i | ||||
\(959\) | 2.07107e7 | + | 3.58721e7i | 0.727192 | + | 1.25953i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.06441e7 | + | 1.84362e7i | −0.371794 | + | 0.643966i | ||||
\(962\) | −1.09282e6 | + | 3.90380e6i | −0.0380726 | + | 0.136003i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.25763e7 | − | 1.97895e7i | −1.12904 | − | 0.685872i | ||||
\(965\) | 2.25899e7 | + | 1.30423e7i | 0.780901 | + | 0.450853i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.39133e7 | + | 1.38063e7i | −0.822381 | + | 0.474802i | −0.851237 | − | 0.524782i | \(-0.824147\pi\) |
0.0288561 | + | 0.999584i | \(0.490814\pi\) | |||||||
\(968\) | −2.57351e7 | − | 7.82725e6i | −0.882751 | − | 0.268485i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.48519e7 | + | 3.40831e7i | −1.18932 | + | 1.16308i | ||||
\(971\) | 3.42357e7 | 1.16528 | 0.582642 | − | 0.812729i | \(-0.302019\pi\) | ||||
0.582642 | + | 0.812729i | \(0.302019\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.42449e7 | 0.482368 | ||||||||
\(974\) | −1.98827e7 | + | 1.94441e7i | −0.671551 | + | 0.656737i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 233077. | − | 365070.i | 0.00783203 | − | 0.0122674i | ||||
\(977\) | 2.71573e7 | − | 1.56793e7i | 0.910229 | − | 0.525521i | 0.0297244 | − | 0.999558i | \(-0.490537\pi\) |
0.880505 | + | 0.474037i | \(0.157204\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.58829e7 | + | 2.07170e7i | 1.19655 | + | 0.690828i | ||||
\(980\) | −5.53121e6 | + | 9.10513e6i | −0.183973 | + | 0.302845i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.05710e6 | + | 3.77618e6i | −0.0349814 | + | 0.124961i | ||||
\(983\) | −3.01652e6 | + | 5.22477e6i | −0.0995686 | + | 0.172458i | −0.911506 | − | 0.411286i | \(-0.865080\pi\) |
0.811938 | + | 0.583744i | \(0.198413\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.04485e7 | + | 1.80973e7i | 0.343132 | + | 0.594322i | ||||
\(986\) | −2.26902e7 | + | 5.80939e6i | −0.743268 | + | 0.190300i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.92511e6 | − | 3.51308e6i | −0.0627428 | − | 0.114497i | ||||
\(989\) | 4.23200e7i | 1.37580i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.95516e7i | 1.27932i | 0.768657 | + | 0.639661i | \(0.220925\pi\) | ||||
−0.768657 | + | 0.639661i | \(0.779075\pi\) | |||||||
\(992\) | 1.49098e7 | + | 4.90063e6i | 0.481053 | + | 0.158115i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.38712e6 | + | 5.41776e6i | 0.0445294 | + | 0.173922i | ||||
\(995\) | 2.35390e7 | + | 4.07708e7i | 0.753756 | + | 1.30554i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.17737e6 | − | 1.41636e7i | 0.260541 | − | 0.451270i | −0.705845 | − | 0.708366i | \(-0.749432\pi\) |
0.966386 | + | 0.257096i | \(0.0827658\pi\) | |||||||
\(998\) | 2.51656e6 | + | 704482.i | 0.0799799 | + | 0.0223894i | ||||
\(999\) | 0 | 0 |
(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 | 108.6.h.a.35.7 | 56 | ||
3.2 | odd | 2 | 36.6.h.a.11.22 | ✓ | 56 | ||
4.3 | odd | 2 | inner | 108.6.h.a.35.3 | 56 | ||
9.4 | even | 3 | 36.6.h.a.23.26 | yes | 56 | ||
9.5 | odd | 6 | inner | 108.6.h.a.71.3 | 56 | ||
12.11 | even | 2 | 36.6.h.a.11.26 | yes | 56 | ||
36.23 | even | 6 | inner | 108.6.h.a.71.7 | 56 | ||
36.31 | odd | 6 | 36.6.h.a.23.22 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.6.h.a.11.22 | ✓ | 56 | 3.2 | odd | 2 | ||
36.6.h.a.11.26 | yes | 56 | 12.11 | even | 2 | ||
36.6.h.a.23.22 | yes | 56 | 36.31 | odd | 6 | ||
36.6.h.a.23.26 | yes | 56 | 9.4 | even | 3 | ||
108.6.h.a.35.3 | 56 | 4.3 | odd | 2 | inner | ||
108.6.h.a.35.7 | 56 | 1.1 | even | 1 | trivial | ||
108.6.h.a.71.3 | 56 | 9.5 | odd | 6 | inner | ||
108.6.h.a.71.7 | 56 | 36.23 | even | 6 | inner |