Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [102,5,Mod(47,102)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(102, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("102.47");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 102 = 2 \cdot 3 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 102.e (of order \(4\), degree \(2\), 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: | \(10.5437362346\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.21 | ||
Character | \(\chi\) | \(=\) | 102.47 |
Dual form | 102.5.e.a.89.21 |
$q$-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 \(\left(\mathbb{Z}/102\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843 | 0.707107 | ||||||||
\(3\) | 4.63353 | − | 7.71559i | 0.514837 | − | 0.857288i | ||||
\(4\) | 8.00000 | 0.500000 | ||||||||
\(5\) | 1.85553 | − | 1.85553i | 0.0742213 | − | 0.0742213i | −0.669022 | − | 0.743243i | \(-0.733287\pi\) |
0.743243 | + | 0.669022i | \(0.233287\pi\) | |||||||
\(6\) | 13.1056 | − | 21.8230i | 0.364045 | − | 0.606194i | ||||
\(7\) | 25.3003 | − | 25.3003i | 0.516332 | − | 0.516332i | −0.400127 | − | 0.916460i | \(-0.631034\pi\) |
0.916460 | + | 0.400127i | \(0.131034\pi\) | |||||||
\(8\) | 22.6274 | 0.353553 | ||||||||
\(9\) | −38.0607 | − | 71.5009i | −0.469886 | − | 0.882727i | ||||
\(10\) | 5.24824 | − | 5.24824i | 0.0524824 | − | 0.0524824i | ||||
\(11\) | 14.3492 | + | 14.3492i | 0.118589 | + | 0.118589i | 0.763911 | − | 0.645322i | \(-0.223277\pi\) |
−0.645322 | + | 0.763911i | \(0.723277\pi\) | |||||||
\(12\) | 37.0683 | − | 61.7247i | 0.257418 | − | 0.428644i | ||||
\(13\) | 33.5484 | 0.198511 | 0.0992557 | − | 0.995062i | \(-0.468354\pi\) | ||||
0.0992557 | + | 0.995062i | \(0.468354\pi\) | |||||||
\(14\) | 71.5600 | − | 71.5600i | 0.365102 | − | 0.365102i | ||||
\(15\) | −5.71886 | − | 22.9142i | −0.0254172 | − | 0.101841i | ||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 1.22203 | − | 288.997i | 0.00422847 | − | 0.999991i | ||||
\(18\) | −107.652 | − | 202.235i | −0.332259 | − | 0.624182i | ||||
\(19\) | 149.755i | 0.414835i | 0.978253 | + | 0.207417i | \(0.0665058\pi\) | ||||
−0.978253 | + | 0.207417i | \(0.933494\pi\) | |||||||
\(20\) | 14.8443 | − | 14.8443i | 0.0371107 | − | 0.0371107i | ||||
\(21\) | −77.9770 | − | 312.436i | −0.176819 | − | 0.708472i | ||||
\(22\) | 40.5858 | + | 40.5858i | 0.0838549 | + | 0.0838549i | ||||
\(23\) | −219.486 | − | 219.486i | −0.414907 | − | 0.414907i | 0.468537 | − | 0.883444i | \(-0.344781\pi\) |
−0.883444 | + | 0.468537i | \(0.844781\pi\) | |||||||
\(24\) | 104.845 | − | 174.584i | 0.182022 | − | 0.303097i | ||||
\(25\) | 618.114i | 0.988982i | ||||||||
\(26\) | 94.8893 | 0.140369 | ||||||||
\(27\) | −728.028 | − | 37.6406i | −0.998666 | − | 0.0516332i | ||||
\(28\) | 202.402 | − | 202.402i | 0.258166 | − | 0.258166i | ||||
\(29\) | 482.493 | − | 482.493i | 0.573713 | − | 0.573713i | −0.359451 | − | 0.933164i | \(-0.617036\pi\) |
0.933164 | + | 0.359451i | \(0.117036\pi\) | |||||||
\(30\) | −16.1754 | − | 64.8112i | −0.0179727 | − | 0.0720124i | ||||
\(31\) | 360.066 | + | 360.066i | 0.374678 | + | 0.374678i | 0.869178 | − | 0.494500i | \(-0.164649\pi\) |
−0.494500 | + | 0.869178i | \(0.664649\pi\) | |||||||
\(32\) | 181.019 | 0.176777 | ||||||||
\(33\) | 177.200 | − | 44.2252i | 0.162719 | − | 0.0406108i | ||||
\(34\) | 3.45642 | − | 817.408i | 0.00298998 | − | 0.707100i | ||||
\(35\) | − | 93.8910i | − | 0.0766457i | ||||||
\(36\) | −304.486 | − | 572.007i | −0.234943 | − | 0.441364i | ||||
\(37\) | 979.187 | + | 979.187i | 0.715257 | + | 0.715257i | 0.967630 | − | 0.252373i | \(-0.0812109\pi\) |
−0.252373 | + | 0.967630i | \(0.581211\pi\) | |||||||
\(38\) | 423.572i | 0.293332i | ||||||||
\(39\) | 155.448 | − | 258.846i | 0.102201 | − | 0.170182i | ||||
\(40\) | 41.9859 | − | 41.9859i | 0.0262412 | − | 0.0262412i | ||||
\(41\) | 733.956 | + | 733.956i | 0.436619 | + | 0.436619i | 0.890872 | − | 0.454254i | \(-0.150094\pi\) |
−0.454254 | + | 0.890872i | \(0.650094\pi\) | |||||||
\(42\) | −220.552 | − | 883.703i | −0.125030 | − | 0.500966i | ||||
\(43\) | 904.929i | 0.489415i | 0.969597 | + | 0.244708i | \(0.0786920\pi\) | ||||
−0.969597 | + | 0.244708i | \(0.921308\pi\) | |||||||
\(44\) | 114.794 | + | 114.794i | 0.0592943 | + | 0.0592943i | ||||
\(45\) | −203.295 | − | 62.0493i | −0.100393 | − | 0.0306416i | ||||
\(46\) | −620.799 | − | 620.799i | −0.293383 | − | 0.293383i | ||||
\(47\) | 2298.28i | 1.04042i | 0.854040 | + | 0.520208i | \(0.174146\pi\) | ||||
−0.854040 | + | 0.520208i | \(0.825854\pi\) | |||||||
\(48\) | 296.546 | − | 493.798i | 0.128709 | − | 0.214322i | ||||
\(49\) | 1120.79i | 0.466802i | ||||||||
\(50\) | 1748.29i | 0.699316i | ||||||||
\(51\) | −2224.12 | − | 1348.51i | −0.855103 | − | 0.518457i | ||||
\(52\) | 268.387 | 0.0992557 | ||||||||
\(53\) | −1523.90 | −0.542507 | −0.271253 | − | 0.962508i | \(-0.587438\pi\) | ||||
−0.271253 | + | 0.962508i | \(0.587438\pi\) | |||||||
\(54\) | −2059.17 | − | 106.464i | −0.706164 | − | 0.0365102i | ||||
\(55\) | 53.2509 | 0.0176036 | ||||||||
\(56\) | 572.480 | − | 572.480i | 0.182551 | − | 0.182551i | ||||
\(57\) | 1155.45 | + | 693.896i | 0.355633 | + | 0.213572i | ||||
\(58\) | 1364.70 | − | 1364.70i | 0.405676 | − | 0.405676i | ||||
\(59\) | −1149.83 | −0.330315 | −0.165157 | − | 0.986267i | \(-0.552813\pi\) | ||||
−0.165157 | + | 0.986267i | \(0.552813\pi\) | |||||||
\(60\) | −45.7509 | − | 183.314i | −0.0127086 | − | 0.0509205i | ||||
\(61\) | −2726.59 | + | 2726.59i | −0.732758 | + | 0.732758i | −0.971165 | − | 0.238407i | \(-0.923375\pi\) |
0.238407 | + | 0.971165i | \(0.423375\pi\) | |||||||
\(62\) | 1018.42 | + | 1018.42i | 0.264937 | + | 0.264937i | ||||
\(63\) | −2771.94 | − | 846.045i | −0.698398 | − | 0.213163i | ||||
\(64\) | 512.000 | 0.125000 | ||||||||
\(65\) | 62.2502 | − | 62.2502i | 0.0147338 | − | 0.0147338i | ||||
\(66\) | 501.199 | − | 125.088i | 0.115059 | − | 0.0287162i | ||||
\(67\) | −423.906 | −0.0944321 | −0.0472161 | − | 0.998885i | \(-0.515035\pi\) | ||||
−0.0472161 | + | 0.998885i | \(0.515035\pi\) | |||||||
\(68\) | 9.77623 | − | 2311.98i | 0.00211424 | − | 0.499996i | ||||
\(69\) | −2710.46 | + | 676.468i | −0.569304 | + | 0.142085i | ||||
\(70\) | − | 265.564i | − | 0.0541967i | ||||||
\(71\) | −2735.55 | + | 2735.55i | −0.542660 | + | 0.542660i | −0.924308 | − | 0.381648i | \(-0.875357\pi\) |
0.381648 | + | 0.924308i | \(0.375357\pi\) | |||||||
\(72\) | −861.216 | − | 1617.88i | −0.166130 | − | 0.312091i | ||||
\(73\) | 6319.99 | + | 6319.99i | 1.18596 | + | 1.18596i | 0.978174 | + | 0.207788i | \(0.0666266\pi\) |
0.207788 | + | 0.978174i | \(0.433373\pi\) | |||||||
\(74\) | 2769.56 | + | 2769.56i | 0.505763 | + | 0.505763i | ||||
\(75\) | 4769.12 | + | 2864.05i | 0.847843 | + | 0.509165i | ||||
\(76\) | 1198.04i | 0.207417i | ||||||||
\(77\) | 726.079 | 0.122462 | ||||||||
\(78\) | 439.673 | − | 732.127i | 0.0722671 | − | 0.120337i | ||||
\(79\) | 2569.72 | − | 2569.72i | 0.411748 | − | 0.411748i | −0.470599 | − | 0.882347i | \(-0.655962\pi\) |
0.882347 | + | 0.470599i | \(0.155962\pi\) | |||||||
\(80\) | 118.754 | − | 118.754i | 0.0185553 | − | 0.0185553i | ||||
\(81\) | −3663.76 | + | 5442.76i | −0.558415 | + | 0.829562i | ||||
\(82\) | 2075.94 | + | 2075.94i | 0.308736 | + | 0.308736i | ||||
\(83\) | −6298.36 | −0.914263 | −0.457132 | − | 0.889399i | \(-0.651123\pi\) | ||||
−0.457132 | + | 0.889399i | \(0.651123\pi\) | |||||||
\(84\) | −623.816 | − | 2499.49i | −0.0884093 | − | 0.354236i | ||||
\(85\) | −533.977 | − | 538.512i | −0.0739068 | − | 0.0745345i | ||||
\(86\) | 2559.52i | 0.346069i | ||||||||
\(87\) | −1487.07 | − | 5958.36i | −0.196469 | − | 0.787206i | ||||
\(88\) | 324.686 | + | 324.686i | 0.0419274 | + | 0.0419274i | ||||
\(89\) | − | 5582.17i | − | 0.704730i | −0.935863 | − | 0.352365i | \(-0.885378\pi\) | ||
0.935863 | − | 0.352365i | \(-0.114622\pi\) | |||||||
\(90\) | −575.006 | − | 175.502i | −0.0709884 | − | 0.0216669i | ||||
\(91\) | 848.785 | − | 848.785i | 0.102498 | − | 0.102498i | ||||
\(92\) | −1755.88 | − | 1755.88i | −0.207453 | − | 0.207453i | ||||
\(93\) | 4446.50 | − | 1109.74i | 0.514105 | − | 0.128309i | ||||
\(94\) | 6500.52i | 0.735685i | ||||||||
\(95\) | 277.876 | + | 277.876i | 0.0307896 | + | 0.0307896i | ||||
\(96\) | 838.759 | − | 1396.67i | 0.0910112 | − | 0.151549i | ||||
\(97\) | 4095.68 | + | 4095.68i | 0.435293 | + | 0.435293i | 0.890424 | − | 0.455131i | \(-0.150408\pi\) |
−0.455131 | + | 0.890424i | \(0.650408\pi\) | |||||||
\(98\) | 3170.08i | 0.330079i | ||||||||
\(99\) | 479.841 | − | 1572.13i | 0.0489583 | − | 0.160405i | ||||
\(100\) | 4944.91i | 0.494491i | ||||||||
\(101\) | − | 18840.5i | − | 1.84693i | −0.383685 | − | 0.923464i | \(-0.625345\pi\) | ||
0.383685 | − | 0.923464i | \(-0.374655\pi\) | |||||||
\(102\) | −6290.77 | − | 3814.16i | −0.604649 | − | 0.366605i | ||||
\(103\) | 5385.67 | 0.507651 | 0.253825 | − | 0.967250i | \(-0.418311\pi\) | ||||
0.253825 | + | 0.967250i | \(0.418311\pi\) | |||||||
\(104\) | 759.114 | 0.0701844 | ||||||||
\(105\) | −724.425 | − | 435.047i | −0.0657075 | − | 0.0394600i | ||||
\(106\) | −4310.24 | −0.383610 | ||||||||
\(107\) | 10933.3 | − | 10933.3i | 0.954956 | − | 0.954956i | −0.0440727 | − | 0.999028i | \(-0.514033\pi\) |
0.999028 | + | 0.0440727i | \(0.0140333\pi\) | |||||||
\(108\) | −5824.22 | − | 301.125i | −0.499333 | − | 0.0258166i | ||||
\(109\) | −5776.43 | + | 5776.43i | −0.486191 | + | 0.486191i | −0.907102 | − | 0.420911i | \(-0.861710\pi\) |
0.420911 | + | 0.907102i | \(0.361710\pi\) | |||||||
\(110\) | 150.616 | 0.0124476 | ||||||||
\(111\) | 12092.1 | − | 3017.91i | 0.981422 | − | 0.244941i | ||||
\(112\) | 1619.22 | − | 1619.22i | 0.129083 | − | 0.129083i | ||||
\(113\) | −8823.98 | − | 8823.98i | −0.691047 | − | 0.691047i | 0.271415 | − | 0.962462i | \(-0.412508\pi\) |
−0.962462 | + | 0.271415i | \(0.912508\pi\) | |||||||
\(114\) | 3268.11 | + | 1962.63i | 0.251470 | + | 0.151018i | ||||
\(115\) | −814.525 | −0.0615898 | ||||||||
\(116\) | 3859.94 | − | 3859.94i | 0.286857 | − | 0.286857i | ||||
\(117\) | −1276.88 | − | 2398.74i | −0.0932777 | − | 0.175231i | ||||
\(118\) | −3252.20 | −0.233568 | ||||||||
\(119\) | −7280.80 | − | 7342.63i | −0.514144 | − | 0.518511i | ||||
\(120\) | −129.403 | − | 518.489i | −0.00898633 | − | 0.0360062i | ||||
\(121\) | − | 14229.2i | − | 0.971873i | ||||||
\(122\) | −7711.97 | + | 7711.97i | −0.518138 | + | 0.518138i | ||||
\(123\) | 9063.72 | − | 2262.10i | 0.599096 | − | 0.149521i | ||||
\(124\) | 2880.53 | + | 2880.53i | 0.187339 | + | 0.187339i | ||||
\(125\) | 2306.64 | + | 2306.64i | 0.147625 | + | 0.147625i | ||||
\(126\) | −7840.23 | − | 2392.98i | −0.493842 | − | 0.150729i | ||||
\(127\) | − | 21588.5i | − | 1.33849i | −0.743041 | − | 0.669246i | \(-0.766617\pi\) | ||
0.743041 | − | 0.669246i | \(-0.233383\pi\) | |||||||
\(128\) | 1448.15 | 0.0883883 | ||||||||
\(129\) | 6982.06 | + | 4193.02i | 0.419570 | + | 0.251969i | ||||
\(130\) | 176.070 | − | 176.070i | 0.0104184 | − | 0.0104184i | ||||
\(131\) | 9790.41 | − | 9790.41i | 0.570503 | − | 0.570503i | −0.361766 | − | 0.932269i | \(-0.617826\pi\) |
0.932269 | + | 0.361766i | \(0.117826\pi\) | |||||||
\(132\) | 1417.60 | − | 353.801i | 0.0813593 | − | 0.0203054i | ||||
\(133\) | 3788.85 | + | 3788.85i | 0.214192 | + | 0.214192i | ||||
\(134\) | −1198.99 | −0.0667736 | ||||||||
\(135\) | −1420.72 | + | 1281.04i | −0.0779546 | + | 0.0702900i | ||||
\(136\) | 27.6513 | − | 6539.27i | 0.00149499 | − | 0.353550i | ||||
\(137\) | 16451.9i | 0.876546i | 0.898842 | + | 0.438273i | \(0.144410\pi\) | ||||
−0.898842 | + | 0.438273i | \(0.855590\pi\) | |||||||
\(138\) | −7666.33 | + | 1913.34i | −0.402559 | + | 0.100469i | ||||
\(139\) | −10892.5 | − | 10892.5i | −0.563765 | − | 0.563765i | 0.366610 | − | 0.930375i | \(-0.380518\pi\) |
−0.930375 | + | 0.366610i | \(0.880518\pi\) | |||||||
\(140\) | − | 751.128i | − | 0.0383229i | ||||||
\(141\) | 17732.6 | + | 10649.2i | 0.891936 | + | 0.535645i | ||||
\(142\) | −7737.30 | + | 7737.30i | −0.383719 | + | 0.383719i | ||||
\(143\) | 481.394 | + | 481.394i | 0.0235412 | + | 0.0235412i | ||||
\(144\) | −2435.89 | − | 4576.06i | −0.117471 | − | 0.220682i | ||||
\(145\) | − | 1790.56i | − | 0.0851635i | ||||||
\(146\) | 17875.6 | + | 17875.6i | 0.838602 | + | 0.838602i | ||||
\(147\) | 8647.57 | + | 5193.23i | 0.400184 | + | 0.240327i | ||||
\(148\) | 7833.50 | + | 7833.50i | 0.357629 | + | 0.357629i | ||||
\(149\) | 27226.1i | 1.22635i | 0.789948 | + | 0.613174i | \(0.210107\pi\) | ||||
−0.789948 | + | 0.613174i | \(0.789893\pi\) | |||||||
\(150\) | 13489.1 | + | 8100.76i | 0.599515 | + | 0.360034i | ||||
\(151\) | − | 36111.8i | − | 1.58378i | −0.610662 | − | 0.791891i | \(-0.709097\pi\) | ||
0.610662 | − | 0.791891i | \(-0.290903\pi\) | |||||||
\(152\) | 3388.58i | 0.146666i | ||||||||
\(153\) | −20710.1 | + | 10912.1i | −0.884706 | + | 0.466149i | ||||
\(154\) | 2053.66 | 0.0865939 | ||||||||
\(155\) | 1336.23 | 0.0556182 | ||||||||
\(156\) | 1243.58 | − | 2070.77i | 0.0511005 | − | 0.0850908i | ||||
\(157\) | 6867.43 | 0.278609 | 0.139304 | − | 0.990250i | \(-0.455513\pi\) | ||||
0.139304 | + | 0.990250i | \(0.455513\pi\) | |||||||
\(158\) | 7268.27 | − | 7268.27i | 0.291150 | − | 0.291150i | ||||
\(159\) | −7061.05 | + | 11757.8i | −0.279303 | + | 0.465085i | ||||
\(160\) | 335.887 | − | 335.887i | 0.0131206 | − | 0.0131206i | ||||
\(161\) | −11106.1 | −0.428459 | ||||||||
\(162\) | −10362.7 | + | 15394.4i | −0.394859 | + | 0.586589i | ||||
\(163\) | −8462.94 | + | 8462.94i | −0.318527 | + | 0.318527i | −0.848201 | − | 0.529674i | \(-0.822314\pi\) |
0.529674 | + | 0.848201i | \(0.322314\pi\) | |||||||
\(164\) | 5871.65 | + | 5871.65i | 0.218309 | + | 0.218309i | ||||
\(165\) | 246.740 | − | 410.863i | 0.00906299 | − | 0.0150914i | ||||
\(166\) | −17814.5 | −0.646482 | ||||||||
\(167\) | −9743.62 | + | 9743.62i | −0.349372 | + | 0.349372i | −0.859875 | − | 0.510504i | \(-0.829459\pi\) |
0.510504 | + | 0.859875i | \(0.329459\pi\) | |||||||
\(168\) | −1764.42 | − | 7069.63i | −0.0625148 | − | 0.250483i | ||||
\(169\) | −27435.5 | −0.960593 | ||||||||
\(170\) | −1510.31 | − | 1523.14i | −0.0522600 | − | 0.0527038i | ||||
\(171\) | 10707.6 | − | 5699.80i | 0.366186 | − | 0.194925i | ||||
\(172\) | 7239.43i | 0.244708i | ||||||||
\(173\) | −34837.9 | + | 34837.9i | −1.16402 | + | 1.16402i | −0.180432 | + | 0.983587i | \(0.557750\pi\) |
−0.983587 | + | 0.180432i | \(0.942250\pi\) | |||||||
\(174\) | −4206.07 | − | 16852.8i | −0.138924 | − | 0.556639i | ||||
\(175\) | 15638.5 | + | 15638.5i | 0.510643 | + | 0.510643i | ||||
\(176\) | 918.351 | + | 918.351i | 0.0296472 | + | 0.0296472i | ||||
\(177\) | −5327.75 | + | 8871.59i | −0.170058 | + | 0.283175i | ||||
\(178\) | − | 15788.8i | − | 0.498319i | ||||||
\(179\) | 26730.0 | 0.834245 | 0.417122 | − | 0.908850i | \(-0.363039\pi\) | ||||
0.417122 | + | 0.908850i | \(0.363039\pi\) | |||||||
\(180\) | −1626.36 | − | 496.395i | −0.0501964 | − | 0.0153208i | ||||
\(181\) | −32190.8 | + | 32190.8i | −0.982596 | + | 0.982596i | −0.999851 | − | 0.0172553i | \(-0.994507\pi\) |
0.0172553 | + | 0.999851i | \(0.494507\pi\) | |||||||
\(182\) | 2400.73 | − | 2400.73i | 0.0724769 | − | 0.0724769i | ||||
\(183\) | 8403.52 | + | 33671.0i | 0.250934 | + | 1.00544i | ||||
\(184\) | −4966.39 | − | 4966.39i | −0.146692 | − | 0.146692i | ||||
\(185\) | 3633.83 | 0.106175 | ||||||||
\(186\) | 12576.6 | − | 3138.83i | 0.363527 | − | 0.0907281i | ||||
\(187\) | 4164.43 | − | 4129.36i | 0.119089 | − | 0.118086i | ||||
\(188\) | 18386.2i | 0.520208i | ||||||||
\(189\) | −19371.6 | + | 17467.0i | −0.542303 | + | 0.488984i | ||||
\(190\) | 785.952 | + | 785.952i | 0.0217715 | + | 0.0217715i | ||||
\(191\) | − | 2609.70i | − | 0.0715359i | −0.999360 | − | 0.0357680i | \(-0.988612\pi\) | ||
0.999360 | − | 0.0357680i | \(-0.0113877\pi\) | |||||||
\(192\) | 2372.37 | − | 3950.38i | 0.0643546 | − | 0.107161i | ||||
\(193\) | −28794.9 | + | 28794.9i | −0.773039 | + | 0.773039i | −0.978637 | − | 0.205598i | \(-0.934086\pi\) |
0.205598 | + | 0.978637i | \(0.434086\pi\) | |||||||
\(194\) | 11584.3 | + | 11584.3i | 0.307799 | + | 0.307799i | ||||
\(195\) | −191.859 | − | 768.736i | −0.00504560 | − | 0.0202166i | ||||
\(196\) | 8966.33i | 0.233401i | ||||||||
\(197\) | −9426.16 | − | 9426.16i | −0.242886 | − | 0.242886i | 0.575157 | − | 0.818043i | \(-0.304941\pi\) |
−0.818043 | + | 0.575157i | \(0.804941\pi\) | |||||||
\(198\) | 1357.19 | − | 4446.64i | 0.0346188 | − | 0.113423i | ||||
\(199\) | −26218.0 | − | 26218.0i | −0.662053 | − | 0.662053i | 0.293811 | − | 0.955864i | \(-0.405076\pi\) |
−0.955864 | + | 0.293811i | \(0.905076\pi\) | |||||||
\(200\) | 13986.3i | 0.349658i | ||||||||
\(201\) | −1964.18 | + | 3270.68i | −0.0486171 | + | 0.0809555i | ||||
\(202\) | − | 53289.0i | − | 1.30598i | ||||||
\(203\) | − | 24414.4i | − | 0.592453i | ||||||
\(204\) | −17793.0 | − | 10788.1i | −0.427552 | − | 0.259229i | ||||
\(205\) | 2723.76 | 0.0648129 | ||||||||
\(206\) | 15233.0 | 0.358963 | ||||||||
\(207\) | −7339.63 | + | 24047.2i | −0.171291 | + | 0.561208i | ||||
\(208\) | 2147.10 | 0.0496279 | ||||||||
\(209\) | −2148.87 | + | 2148.87i | −0.0491947 | + | 0.0491947i | ||||
\(210\) | −2048.98 | − | 1230.50i | −0.0464622 | − | 0.0279025i | ||||
\(211\) | 33732.8 | − | 33732.8i | 0.757684 | − | 0.757684i | −0.218217 | − | 0.975900i | \(-0.570024\pi\) |
0.975900 | + | 0.218217i | \(0.0700240\pi\) | |||||||
\(212\) | −12191.2 | −0.271253 | ||||||||
\(213\) | 8431.13 | + | 33781.7i | 0.185835 | + | 0.744598i | ||||
\(214\) | 30924.0 | − | 30924.0i | 0.675256 | − | 0.675256i | ||||
\(215\) | 1679.12 | + | 1679.12i | 0.0363250 | + | 0.0363250i | ||||
\(216\) | −16473.4 | − | 851.709i | −0.353082 | − | 0.0182551i | ||||
\(217\) | 18219.5 | 0.386917 | ||||||||
\(218\) | −16338.2 | + | 16338.2i | −0.343789 | + | 0.343789i | ||||
\(219\) | 78046.4 | − | 19478.6i | 1.62729 | − | 0.406134i | ||||
\(220\) | 426.007 | 0.00880181 | ||||||||
\(221\) | 40.9971 | − | 9695.41i | 0.000839400 | − | 0.198510i | ||||
\(222\) | 34201.6 | − | 8535.95i | 0.693970 | − | 0.173199i | ||||
\(223\) | − | 17396.1i | − | 0.349818i | −0.984585 | − | 0.174909i | \(-0.944037\pi\) | ||
0.984585 | − | 0.174909i | \(-0.0559631\pi\) | |||||||
\(224\) | 4579.84 | − | 4579.84i | 0.0912755 | − | 0.0912755i | ||||
\(225\) | 44195.7 | − | 23525.9i | 0.873002 | − | 0.464709i | ||||
\(226\) | −24958.0 | − | 24958.0i | −0.488644 | − | 0.488644i | ||||
\(227\) | −18325.1 | − | 18325.1i | −0.355627 | − | 0.355627i | 0.506571 | − | 0.862198i | \(-0.330913\pi\) |
−0.862198 | + | 0.506571i | \(0.830913\pi\) | |||||||
\(228\) | 9243.61 | + | 5551.17i | 0.177816 | + | 0.106786i | ||||
\(229\) | 7235.68i | 0.137978i | 0.997617 | + | 0.0689888i | \(0.0219773\pi\) | ||||
−0.997617 | + | 0.0689888i | \(0.978023\pi\) | |||||||
\(230\) | −2303.83 | −0.0435506 | ||||||||
\(231\) | 3364.31 | − | 5602.13i | 0.0630481 | − | 0.104985i | ||||
\(232\) | 10917.6 | − | 10917.6i | 0.202838 | − | 0.202838i | ||||
\(233\) | 57194.5 | − | 57194.5i | 1.05352 | − | 1.05352i | 0.0550346 | − | 0.998484i | \(-0.482473\pi\) |
0.998484 | − | 0.0550346i | \(-0.0175269\pi\) | |||||||
\(234\) | −3611.56 | − | 6784.67i | −0.0659573 | − | 0.123907i | ||||
\(235\) | 4264.53 | + | 4264.53i | 0.0772211 | + | 0.0772211i | ||||
\(236\) | −9198.60 | −0.165157 | ||||||||
\(237\) | −7920.03 | − | 31733.8i | −0.141004 | − | 0.564970i | ||||
\(238\) | −20593.2 | − | 20768.1i | −0.363555 | − | 0.366643i | ||||
\(239\) | − | 38878.5i | − | 0.680634i | −0.940311 | − | 0.340317i | \(-0.889466\pi\) | ||
0.940311 | − | 0.340317i | \(-0.110534\pi\) | |||||||
\(240\) | −366.007 | − | 1466.51i | −0.00635429 | − | 0.0254602i | ||||
\(241\) | 18484.7 | + | 18484.7i | 0.318257 | + | 0.318257i | 0.848097 | − | 0.529840i | \(-0.177748\pi\) |
−0.529840 | + | 0.848097i | \(0.677748\pi\) | |||||||
\(242\) | − | 40246.3i | − | 0.687218i | ||||||
\(243\) | 25017.9 | + | 53487.3i | 0.423681 | + | 0.905811i | ||||
\(244\) | −21812.7 | + | 21812.7i | −0.366379 | + | 0.366379i | ||||
\(245\) | 2079.67 | + | 2079.67i | 0.0346467 | + | 0.0346467i | ||||
\(246\) | 25636.1 | − | 6398.18i | 0.423625 | − | 0.105727i | ||||
\(247\) | 5024.06i | 0.0823494i | ||||||||
\(248\) | 8147.36 | + | 8147.36i | 0.132469 | + | 0.132469i | ||||
\(249\) | −29183.7 | + | 48595.6i | −0.470697 | + | 0.783787i | ||||
\(250\) | 6524.16 | + | 6524.16i | 0.104387 | + | 0.104387i | ||||
\(251\) | − | 34887.2i | − | 0.553756i | −0.960905 | − | 0.276878i | \(-0.910700\pi\) | ||
0.960905 | − | 0.276878i | \(-0.0892998\pi\) | |||||||
\(252\) | −22175.5 | − | 6768.36i | −0.349199 | − | 0.106582i | ||||
\(253\) | − | 6298.90i | − | 0.0984065i | ||||||
\(254\) | − | 61061.6i | − | 0.946457i | ||||||
\(255\) | −6629.14 | + | 1624.73i | −0.101947 | + | 0.0249863i | ||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | −4375.85 | −0.0662516 | −0.0331258 | − | 0.999451i | \(-0.510546\pi\) | ||||
−0.0331258 | + | 0.999451i | \(0.510546\pi\) | |||||||
\(258\) | 19748.2 | + | 11859.6i | 0.296681 | + | 0.178169i | ||||
\(259\) | 49547.4 | 0.738621 | ||||||||
\(260\) | 498.002 | − | 498.002i | 0.00736689 | − | 0.00736689i | ||||
\(261\) | −52862.7 | − | 16134.6i | −0.776012 | − | 0.236853i | ||||
\(262\) | 27691.5 | − | 27691.5i | 0.403407 | − | 0.403407i | ||||
\(263\) | −88830.3 | −1.28425 | −0.642125 | − | 0.766600i | \(-0.721947\pi\) | ||||
−0.642125 | + | 0.766600i | \(0.721947\pi\) | |||||||
\(264\) | 4009.59 | − | 1000.70i | 0.0575297 | − | 0.0143581i | ||||
\(265\) | −2827.65 | + | 2827.65i | −0.0402656 | + | 0.0402656i | ||||
\(266\) | 10716.5 | + | 10716.5i | 0.151457 | + | 0.151457i | ||||
\(267\) | −43069.7 | − | 25865.2i | −0.604157 | − | 0.362821i | ||||
\(268\) | −3391.25 | −0.0472161 | ||||||||
\(269\) | 15906.0 | − | 15906.0i | 0.219815 | − | 0.219815i | −0.588605 | − | 0.808420i | \(-0.700323\pi\) |
0.808420 | + | 0.588605i | \(0.200323\pi\) | |||||||
\(270\) | −4018.41 | + | 3623.32i | −0.0551222 | + | 0.0497026i | ||||
\(271\) | −116793. | −1.59030 | −0.795149 | − | 0.606414i | \(-0.792608\pi\) | ||||
−0.795149 | + | 0.606414i | \(0.792608\pi\) | |||||||
\(272\) | 78.2098 | − | 18495.8i | 0.00105712 | − | 0.249998i | ||||
\(273\) | −2616.01 | − | 10481.8i | −0.0351005 | − | 0.140640i | ||||
\(274\) | 46533.0i | 0.619812i | ||||||||
\(275\) | −8869.46 | + | 8869.46i | −0.117282 | + | 0.117282i | ||||
\(276\) | −21683.6 | + | 5411.74i | −0.284652 | + | 0.0710426i | ||||
\(277\) | 101912. | + | 101912.i | 1.32821 | + | 1.32821i | 0.906928 | + | 0.421285i | \(0.138421\pi\) |
0.421285 | + | 0.906928i | \(0.361579\pi\) | |||||||
\(278\) | −30808.6 | − | 30808.6i | −0.398642 | − | 0.398642i | ||||
\(279\) | 12040.7 | − | 39449.4i | 0.154683 | − | 0.506794i | ||||
\(280\) | − | 2124.51i | − | 0.0270984i | ||||||
\(281\) | −6557.95 | −0.0830530 | −0.0415265 | − | 0.999137i | \(-0.513222\pi\) | ||||
−0.0415265 | + | 0.999137i | \(0.513222\pi\) | |||||||
\(282\) | 50155.3 | + | 30120.4i | 0.630694 | + | 0.378758i | ||||
\(283\) | −80337.4 | + | 80337.4i | −1.00310 | + | 1.00310i | −0.00310644 | + | 0.999995i | \(0.500989\pi\) |
−0.999995 | + | 0.00310644i | \(0.999011\pi\) | |||||||
\(284\) | −21884.4 | + | 21884.4i | −0.271330 | + | 0.271330i | ||||
\(285\) | 3431.52 | − | 856.430i | 0.0422471 | − | 0.0105439i | ||||
\(286\) | 1361.59 | + | 1361.59i | 0.0166462 | + | 0.0166462i | ||||
\(287\) | 37138.6 | 0.450881 | ||||||||
\(288\) | −6889.73 | − | 12943.0i | −0.0830648 | − | 0.156046i | ||||
\(289\) | −83518.0 | − | 706.326i | −0.999964 | − | 0.00845687i | ||||
\(290\) | − | 5064.47i | − | 0.0602197i | ||||||
\(291\) | 50578.0 | − | 12623.1i | 0.597277 | − | 0.149067i | ||||
\(292\) | 50559.9 | + | 50559.9i | 0.592981 | + | 0.592981i | ||||
\(293\) | 60800.7i | 0.708229i | 0.935202 | + | 0.354114i | \(0.115218\pi\) | ||||
−0.935202 | + | 0.354114i | \(0.884782\pi\) | |||||||
\(294\) | 24459.0 | + | 14688.7i | 0.282973 | + | 0.169937i | ||||
\(295\) | −2133.54 | + | 2133.54i | −0.0245164 | + | 0.0245164i | ||||
\(296\) | 22156.5 | + | 22156.5i | 0.252882 | + | 0.252882i | ||||
\(297\) | −9906.52 | − | 10986.7i | −0.112307 | − | 0.124554i | ||||
\(298\) | 77007.1i | 0.867158i | ||||||||
\(299\) | −7363.40 | − | 7363.40i | −0.0823637 | − | 0.0823637i | ||||
\(300\) | 38152.9 | + | 22912.4i | 0.423921 | + | 0.254582i | ||||
\(301\) | 22894.9 | + | 22894.9i | 0.252701 | + | 0.252701i | ||||
\(302\) | − | 102140.i | − | 1.11990i | ||||||
\(303\) | −145366. | − | 87298.1i | −1.58335 | − | 0.950867i | ||||
\(304\) | 9584.34i | 0.103709i | ||||||||
\(305\) | 10118.6i | 0.108773i | ||||||||
\(306\) | −58577.0 | + | 30864.0i | −0.625582 | + | 0.329617i | ||||
\(307\) | 124362. | 1.31950 | 0.659750 | − | 0.751485i | \(-0.270662\pi\) | ||||
0.659750 | + | 0.751485i | \(0.270662\pi\) | |||||||
\(308\) | 5808.63 | 0.0612312 | ||||||||
\(309\) | 24954.7 | − | 41553.6i | 0.261357 | − | 0.435203i | ||||
\(310\) | 3779.42 | 0.0393280 | ||||||||
\(311\) | −117113. | + | 117113.i | −1.21083 | + | 1.21083i | −0.240079 | + | 0.970753i | \(0.577173\pi\) |
−0.970753 | + | 0.240079i | \(0.922827\pi\) | |||||||
\(312\) | 3517.38 | − | 5857.02i | 0.0361335 | − | 0.0601683i | ||||
\(313\) | 111563. | − | 111563.i | 1.13876 | − | 1.13876i | 0.150083 | − | 0.988673i | \(-0.452046\pi\) |
0.988673 | − | 0.150083i | \(-0.0479540\pi\) | |||||||
\(314\) | 19424.0 | 0.197006 | ||||||||
\(315\) | −6713.29 | + | 3573.56i | −0.0676573 | + | 0.0360147i | ||||
\(316\) | 20557.8 | − | 20557.8i | 0.205874 | − | 0.205874i | ||||
\(317\) | 91274.3 | + | 91274.3i | 0.908301 | + | 0.908301i | 0.996135 | − | 0.0878337i | \(-0.0279944\pi\) |
−0.0878337 | + | 0.996135i | \(0.527994\pi\) | |||||||
\(318\) | −19971.7 | + | 33256.1i | −0.197497 | + | 0.328864i | ||||
\(319\) | 13846.8 | 0.136072 | ||||||||
\(320\) | 950.033 | − | 950.033i | 0.00927766 | − | 0.00927766i | ||||
\(321\) | −33697.0 | − | 135017.i | −0.327026 | − | 1.31032i | ||||
\(322\) | −31412.8 | −0.302966 | ||||||||
\(323\) | 43278.9 | + | 183.005i | 0.414831 | + | 0.00175412i | ||||
\(324\) | −29310.1 | + | 43542.0i | −0.279207 | + | 0.414781i | ||||
\(325\) | 20736.8i | 0.196324i | ||||||||
\(326\) | −23936.8 | + | 23936.8i | −0.225233 | + | 0.225233i | ||||
\(327\) | 17803.3 | + | 71333.9i | 0.166496 | + | 0.667114i | ||||
\(328\) | 16607.5 | + | 16607.5i | 0.154368 | + | 0.154368i | ||||
\(329\) | 58147.1 | + | 58147.1i | 0.537200 | + | 0.537200i | ||||
\(330\) | 697.886 | − | 1162.09i | 0.00640850 | − | 0.0106712i | ||||
\(331\) | − | 201966.i | − | 1.84341i | −0.387893 | − | 0.921705i | \(-0.626797\pi\) | ||
0.387893 | − | 0.921705i | \(-0.373203\pi\) | |||||||
\(332\) | −50386.9 | −0.457132 | ||||||||
\(333\) | 32744.2 | − | 107281.i | 0.295288 | − | 0.967466i | ||||
\(334\) | −27559.1 | + | 27559.1i | −0.247043 | + | 0.247043i | ||||
\(335\) | −786.571 | + | 786.571i | −0.00700888 | + | 0.00700888i | ||||
\(336\) | −4990.53 | − | 19995.9i | −0.0442046 | − | 0.177118i | ||||
\(337\) | −7733.40 | − | 7733.40i | −0.0680943 | − | 0.0680943i | 0.672239 | − | 0.740334i | \(-0.265333\pi\) |
−0.740334 | + | 0.672239i | \(0.765333\pi\) | |||||||
\(338\) | −77599.3 | −0.679242 | ||||||||
\(339\) | −108968. | + | 27196.0i | −0.948203 | + | 0.236650i | ||||
\(340\) | −4271.81 | − | 4308.09i | −0.0369534 | − | 0.0372672i | ||||
\(341\) | 10333.3i | 0.0888652i | ||||||||
\(342\) | 30285.8 | − | 16121.5i | 0.258932 | − | 0.137833i | ||||
\(343\) | 89102.3 | + | 89102.3i | 0.757357 | + | 0.757357i | ||||
\(344\) | 20476.2i | 0.173034i | ||||||||
\(345\) | −3774.13 | + | 6284.55i | −0.0317087 | + | 0.0528002i | ||||
\(346\) | −98536.6 | + | 98536.6i | −0.823086 | + | 0.823086i | ||||
\(347\) | 62366.0 | + | 62366.0i | 0.517951 | + | 0.517951i | 0.916951 | − | 0.399000i | \(-0.130643\pi\) |
−0.399000 | + | 0.916951i | \(0.630643\pi\) | |||||||
\(348\) | −11896.6 | − | 47666.9i | −0.0982343 | − | 0.393603i | ||||
\(349\) | − | 25887.9i | − | 0.212543i | −0.994337 | − | 0.106271i | \(-0.966109\pi\) | ||
0.994337 | − | 0.106271i | \(-0.0338912\pi\) | |||||||
\(350\) | 44232.2 | + | 44232.2i | 0.361079 | + | 0.361079i | ||||
\(351\) | −24424.2 | − | 1262.78i | −0.198247 | − | 0.0102498i | ||||
\(352\) | 2597.49 | + | 2597.49i | 0.0209637 | + | 0.0209637i | ||||
\(353\) | 74256.9i | 0.595919i | 0.954578 | + | 0.297960i | \(0.0963061\pi\) | ||||
−0.954578 | + | 0.297960i | \(0.903694\pi\) | |||||||
\(354\) | −15069.2 | + | 25092.6i | −0.120249 | + | 0.200235i | ||||
\(355\) | 10151.8i | 0.0805539i | ||||||||
\(356\) | − | 44657.3i | − | 0.352365i | ||||||
\(357\) | −90388.6 | + | 22153.3i | −0.709214 | + | 0.173821i | ||||
\(358\) | 75604.0 | 0.589900 | ||||||||
\(359\) | 211033. | 1.63743 | 0.818714 | − | 0.574201i | \(-0.194687\pi\) | ||||
0.818714 | + | 0.574201i | \(0.194687\pi\) | |||||||
\(360\) | −4600.05 | − | 1404.02i | −0.0354942 | − | 0.0108335i | ||||
\(361\) | 107894. | 0.827912 | ||||||||
\(362\) | −91049.4 | + | 91049.4i | −0.694800 | + | 0.694800i | ||||
\(363\) | −109787. | − | 65931.5i | −0.833176 | − | 0.500356i | ||||
\(364\) | 6790.28 | − | 6790.28i | 0.0512489 | − | 0.0512489i | ||||
\(365\) | 23453.9 | 0.176047 | ||||||||
\(366\) | 23768.8 | + | 95236.1i | 0.177437 | + | 0.710951i | ||||
\(367\) | −5353.48 | + | 5353.48i | −0.0397470 | + | 0.0397470i | −0.726701 | − | 0.686954i | \(-0.758947\pi\) |
0.686954 | + | 0.726701i | \(0.258947\pi\) | |||||||
\(368\) | −14047.1 | − | 14047.1i | −0.103727 | − | 0.103727i | ||||
\(369\) | 24543.6 | − | 80413.5i | 0.180254 | − | 0.590576i | ||||
\(370\) | 10278.0 | 0.0750768 | ||||||||
\(371\) | −38555.1 | + | 38555.1i | −0.280114 | + | 0.280114i | ||||
\(372\) | 35572.0 | − | 8877.95i | 0.257053 | − | 0.0641545i | ||||
\(373\) | −272198. | −1.95644 | −0.978222 | − | 0.207561i | \(-0.933447\pi\) | ||||
−0.978222 | + | 0.207561i | \(0.933447\pi\) | |||||||
\(374\) | 11778.8 | − | 11679.6i | 0.0842087 | − | 0.0834995i | ||||
\(375\) | 28485.0 | − | 7109.20i | 0.202560 | − | 0.0505543i | ||||
\(376\) | 52004.1i | 0.367843i | ||||||||
\(377\) | 16186.9 | − | 16186.9i | 0.113889 | − | 0.113889i | ||||
\(378\) | −54791.2 | + | 49404.1i | −0.383466 | + | 0.345764i | ||||
\(379\) | 74627.5 | + | 74627.5i | 0.519542 | + | 0.519542i | 0.917433 | − | 0.397891i | \(-0.130258\pi\) |
−0.397891 | + | 0.917433i | \(0.630258\pi\) | |||||||
\(380\) | 2223.01 | + | 2223.01i | 0.0153948 | + | 0.0153948i | ||||
\(381\) | −166568. | − | 100031.i | −1.14747 | − | 0.689105i | ||||
\(382\) | − | 7381.35i | − | 0.0505835i | ||||||
\(383\) | −151922. | −1.03568 | −0.517838 | − | 0.855479i | \(-0.673263\pi\) | ||||
−0.517838 | + | 0.855479i | \(0.673263\pi\) | |||||||
\(384\) | 6710.07 | − | 11173.4i | 0.0455056 | − | 0.0757743i | ||||
\(385\) | 1347.26 | − | 1347.26i | 0.00908931 | − | 0.00908931i | ||||
\(386\) | −81444.3 | + | 81444.3i | −0.546621 | + | 0.546621i | ||||
\(387\) | 64703.2 | − | 34442.3i | 0.432020 | − | 0.229969i | ||||
\(388\) | 32765.4 | + | 32765.4i | 0.217647 | + | 0.217647i | ||||
\(389\) | 174510. | 1.15324 | 0.576621 | − | 0.817012i | \(-0.304371\pi\) | ||||
0.576621 | + | 0.817012i | \(0.304371\pi\) | |||||||
\(390\) | −542.659 | − | 2174.31i | −0.00356778 | − | 0.0142953i | ||||
\(391\) | −63699.0 | + | 63162.6i | −0.416657 | + | 0.413148i | ||||
\(392\) | 25360.6i | 0.165039i | ||||||||
\(393\) | −30174.6 | − | 120903.i | −0.195369 | − | 0.782802i | ||||
\(394\) | −26661.2 | − | 26661.2i | −0.171746 | − | 0.171746i | ||||
\(395\) | − | 9536.40i | − | 0.0611210i | ||||||
\(396\) | 3838.72 | − | 12577.0i | 0.0244792 | − | 0.0802023i | ||||
\(397\) | −90229.2 | + | 90229.2i | −0.572487 | + | 0.572487i | −0.932823 | − | 0.360335i | \(-0.882662\pi\) |
0.360335 | + | 0.932823i | \(0.382662\pi\) | |||||||
\(398\) | −74155.6 | − | 74155.6i | −0.468142 | − | 0.468142i | ||||
\(399\) | 46789.0 | − | 11677.5i | 0.293899 | − | 0.0733505i | ||||
\(400\) | 39559.3i | 0.247246i | ||||||||
\(401\) | −54788.9 | − | 54788.9i | −0.340725 | − | 0.340725i | 0.515915 | − | 0.856640i | \(-0.327452\pi\) |
−0.856640 | + | 0.515915i | \(0.827452\pi\) | |||||||
\(402\) | −5555.54 | + | 9250.89i | −0.0343775 | + | 0.0572442i | ||||
\(403\) | 12079.6 | + | 12079.6i | 0.0743779 | + | 0.0743779i | ||||
\(404\) | − | 150724.i | − | 0.923464i | ||||||
\(405\) | 3300.99 | + | 16897.4i | 0.0201249 | + | 0.103017i | ||||
\(406\) | − | 69054.3i | − | 0.418928i | ||||||
\(407\) | 28101.2i | 0.169643i | ||||||||
\(408\) | −50326.2 | − | 30513.2i | −0.302325 | − | 0.183302i | ||||
\(409\) | 43883.7 | 0.262335 | 0.131168 | − | 0.991360i | \(-0.458127\pi\) | ||||
0.131168 | + | 0.991360i | \(0.458127\pi\) | |||||||
\(410\) | 7703.96 | 0.0458296 | ||||||||
\(411\) | 126936. | + | 76230.4i | 0.751452 | + | 0.451278i | ||||
\(412\) | 43085.4 | 0.253825 | ||||||||
\(413\) | −29090.9 | + | 29090.9i | −0.170552 | + | 0.170552i | ||||
\(414\) | −20759.6 | + | 68015.8i | −0.121121 | + | 0.396834i | ||||
\(415\) | −11686.8 | + | 11686.8i | −0.0678578 | + | 0.0678578i | ||||
\(416\) | 6072.92 | 0.0350922 | ||||||||
\(417\) | −134513. | + | 33571.3i | −0.773556 | + | 0.193062i | ||||
\(418\) | −6077.93 | + | 6077.93i | −0.0347859 | + | 0.0347859i | ||||
\(419\) | −43613.3 | − | 43613.3i | −0.248423 | − | 0.248423i | 0.571900 | − | 0.820323i | \(-0.306206\pi\) |
−0.820323 | + | 0.571900i | \(0.806206\pi\) | |||||||
\(420\) | −5795.40 | − | 3480.38i | −0.0328537 | − | 0.0197300i | ||||
\(421\) | 222802. | 1.25706 | 0.628529 | − | 0.777787i | \(-0.283658\pi\) | ||||
0.628529 | + | 0.777787i | \(0.283658\pi\) | |||||||
\(422\) | 95410.9 | − | 95410.9i | 0.535763 | − | 0.535763i | ||||
\(423\) | 164329. | − | 87474.2i | 0.918404 | − | 0.488877i | ||||
\(424\) | −34482.0 | −0.191805 | ||||||||
\(425\) | 178633. | + | 755.353i | 0.988974 | + | 0.00418188i | ||||
\(426\) | 23846.8 | + | 95548.9i | 0.131405 | + | 0.526510i | ||||
\(427\) | 137967.i | 0.756693i | ||||||||
\(428\) | 87466.3 | − | 87466.3i | 0.477478 | − | 0.477478i | ||||
\(429\) | 5944.80 | − | 1483.69i | 0.0323015 | − | 0.00806171i | ||||
\(430\) | 4749.28 | + | 4749.28i | 0.0256857 | + | 0.0256857i | ||||
\(431\) | −169007. | − | 169007.i | −0.909807 | − | 0.909807i | 0.0864491 | − | 0.996256i | \(-0.472448\pi\) |
−0.996256 | + | 0.0864491i | \(0.972448\pi\) | |||||||
\(432\) | −46593.8 | − | 2409.00i | −0.249667 | − | 0.0129083i | ||||
\(433\) | − | 308901.i | − | 1.64757i | −0.566903 | − | 0.823785i | \(-0.691858\pi\) | ||
0.566903 | − | 0.823785i | \(-0.308142\pi\) | |||||||
\(434\) | 51532.6 | 0.273591 | ||||||||
\(435\) | −13815.2 | − | 8296.63i | −0.0730096 | − | 0.0438453i | ||||
\(436\) | −46211.4 | + | 46211.4i | −0.243095 | + | 0.243095i | ||||
\(437\) | 32869.1 | − | 32869.1i | 0.172118 | − | 0.172118i | ||||
\(438\) | 220749. | − | 55093.8i | 1.15067 | − | 0.287180i | ||||
\(439\) | 111232. | + | 111232.i | 0.577163 | + | 0.577163i | 0.934121 | − | 0.356957i | \(-0.116186\pi\) |
−0.356957 | + | 0.934121i | \(0.616186\pi\) | |||||||
\(440\) | 1204.93 | 0.00622382 | ||||||||
\(441\) | 80137.6 | − | 42658.2i | 0.412059 | − | 0.219344i | ||||
\(442\) | 115.957 | − | 27422.8i | 0.000593545 | − | 0.140368i | ||||
\(443\) | − | 216786.i | − | 1.10465i | −0.833629 | − | 0.552325i | \(-0.813741\pi\) | ||
0.833629 | − | 0.552325i | \(-0.186259\pi\) | |||||||
\(444\) | 96736.8 | − | 24143.3i | 0.490711 | − | 0.122470i | ||||
\(445\) | −10357.9 | − | 10357.9i | −0.0523060 | − | 0.0523060i | ||||
\(446\) | − | 49203.6i | − | 0.247359i | ||||||
\(447\) | 210066. | + | 126153.i | 1.05133 | + | 0.631369i | ||||
\(448\) | 12953.7 | − | 12953.7i | 0.0645415 | − | 0.0645415i | ||||
\(449\) | 206759. | + | 206759.i | 1.02558 | + | 1.02558i | 0.999664 | + | 0.0259193i | \(0.00825131\pi\) |
0.0259193 | + | 0.999664i | \(0.491749\pi\) | |||||||
\(450\) | 125004. | − | 66541.2i | 0.617305 | − | 0.328599i | ||||
\(451\) | 21063.4i | 0.103556i | ||||||||
\(452\) | −70591.9 | − | 70591.9i | −0.345524 | − | 0.345524i | ||||
\(453\) | −278624. | − | 167325.i | −1.35776 | − | 0.815390i | ||||
\(454\) | −51831.2 | − | 51831.2i | −0.251466 | − | 0.251466i | ||||
\(455\) | − | 3149.90i | − | 0.0152151i | ||||||
\(456\) | 26144.9 | + | 15701.1i | 0.125735 | + | 0.0755092i | ||||
\(457\) | − | 355848.i | − | 1.70385i | −0.523662 | − | 0.851926i | \(-0.675435\pi\) | ||
0.523662 | − | 0.851926i | \(-0.324565\pi\) | |||||||
\(458\) | 20465.6i | 0.0975649i | ||||||||
\(459\) | −11767.7 | + | 210352.i | −0.0558556 | + | 0.998439i | ||||
\(460\) | −6516.20 | −0.0307949 | ||||||||
\(461\) | −365968. | −1.72203 | −0.861016 | − | 0.508577i | \(-0.830172\pi\) | ||||
−0.861016 | + | 0.508577i | \(0.830172\pi\) | |||||||
\(462\) | 9515.71 | − | 15845.2i | 0.0445818 | − | 0.0742359i | ||||
\(463\) | −167944. | −0.783434 | −0.391717 | − | 0.920086i | \(-0.628119\pi\) | ||||
−0.391717 | + | 0.920086i | \(0.628119\pi\) | |||||||
\(464\) | 30879.5 | − | 30879.5i | 0.143428 | − | 0.143428i | ||||
\(465\) | 6191.45 | − | 10309.8i | 0.0286343 | − | 0.0476808i | ||||
\(466\) | 161770. | − | 161770.i | 0.744950 | − | 0.744950i | ||||
\(467\) | 122248. | 0.560540 | 0.280270 | − | 0.959921i | \(-0.409576\pi\) | ||||
0.280270 | + | 0.959921i | \(0.409576\pi\) | |||||||
\(468\) | −10215.0 | − | 19189.9i | −0.0466389 | − | 0.0876157i | ||||
\(469\) | −10724.9 | + | 10724.9i | −0.0487583 | + | 0.0487583i | ||||
\(470\) | 12061.9 | + | 12061.9i | 0.0546035 | + | 0.0546035i | ||||
\(471\) | 31820.5 | − | 52986.3i | 0.143438 | − | 0.238848i | ||||
\(472\) | −26017.6 | −0.116784 | ||||||||
\(473\) | −12985.0 | + | 12985.0i | −0.0580391 | + | 0.0580391i | ||||
\(474\) | −22401.2 | − | 89756.7i | −0.0997046 | − | 0.399494i | ||||
\(475\) | −92565.9 | −0.410264 | ||||||||
\(476\) | −58246.4 | − | 58741.1i | −0.257072 | − | 0.259255i | ||||
\(477\) | 58000.8 | + | 108960.i | 0.254916 | + | 0.478886i | ||||
\(478\) | − | 109965.i | − | 0.481281i | ||||||
\(479\) | 57386.6 | − | 57386.6i | 0.250115 | − | 0.250115i | −0.570903 | − | 0.821018i | \(-0.693407\pi\) |
0.821018 | + | 0.570903i | \(0.193407\pi\) | |||||||
\(480\) | −1035.22 | − | 4147.91i | −0.00449316 | − | 0.0180031i | ||||
\(481\) | 32850.2 | + | 32850.2i | 0.141987 | + | 0.141987i | ||||
\(482\) | 52282.6 | + | 52282.6i | 0.225042 | + | 0.225042i | ||||
\(483\) | −51460.5 | + | 85690.1i | −0.220587 | + | 0.367313i | ||||
\(484\) | − | 113834.i | − | 0.485937i | ||||||
\(485\) | 15199.3 | 0.0646161 | ||||||||
\(486\) | 70761.4 | + | 151285.i | 0.299588 | + | 0.640505i | ||||
\(487\) | −62632.9 | + | 62632.9i | −0.264085 | + | 0.264085i | −0.826712 | − | 0.562626i | \(-0.809791\pi\) |
0.562626 | + | 0.826712i | \(0.309791\pi\) | |||||||
\(488\) | −61695.8 | + | 61695.8i | −0.259069 | + | 0.259069i | ||||
\(489\) | 26083.3 | + | 104510.i | 0.109080 | + | 0.437059i | ||||
\(490\) | 5882.18 | + | 5882.18i | 0.0244989 | + | 0.0244989i | ||||
\(491\) | −86353.0 | −0.358191 | −0.179095 | − | 0.983832i | \(-0.557317\pi\) | ||||
−0.179095 | + | 0.983832i | \(0.557317\pi\) | |||||||
\(492\) | 72509.8 | − | 18096.8i | 0.299548 | − | 0.0747603i | ||||
\(493\) | −138850. | − | 140029.i | −0.571282 | − | 0.576134i | ||||
\(494\) | 14210.2i | 0.0582298i | ||||||||
\(495\) | −2026.77 | − | 3807.49i | −0.00827169 | − | 0.0155392i | ||||
\(496\) | 23044.2 | + | 23044.2i | 0.0936695 | + | 0.0936695i | ||||
\(497\) | 138420.i | 0.560386i | ||||||||
\(498\) | −82543.9 | + | 137449.i | −0.332833 | + | 0.554221i | ||||
\(499\) | −327620. | + | 327620.i | −1.31574 | + | 1.31574i | −0.398626 | + | 0.917114i | \(0.630513\pi\) |
−0.917114 | + | 0.398626i | \(0.869487\pi\) | |||||||
\(500\) | 18453.1 | + | 18453.1i | 0.0738124 | + | 0.0738124i | ||||
\(501\) | 30030.4 | + | 120325.i | 0.119643 | + | 0.479381i | ||||
\(502\) | − | 98675.9i | − | 0.391565i | ||||||
\(503\) | −288469. | − | 288469.i | −1.14015 | − | 1.14015i | −0.988422 | − | 0.151729i | \(-0.951516\pi\) |
−0.151729 | − | 0.988422i | \(-0.548484\pi\) | |||||||
\(504\) | −62721.8 | − | 19143.8i | −0.246921 | − | 0.0753646i | ||||
\(505\) | −34959.2 | − | 34959.2i | −0.137081 | − | 0.137081i | ||||
\(506\) | − | 17816.0i | − | 0.0695839i | ||||||
\(507\) | −127123. | + | 211681.i | −0.494549 | + | 0.823505i | ||||
\(508\) | − | 172708.i | − | 0.669246i | ||||||
\(509\) | 217618.i | 0.839962i | 0.907533 | + | 0.419981i | \(0.137963\pi\) | ||||
−0.907533 | + | 0.419981i | \(0.862037\pi\) | |||||||
\(510\) | −18750.0 | + | 4595.44i | −0.0720878 | + | 0.0176680i | ||||
\(511\) | 319795. | 1.22470 | ||||||||
\(512\) | 11585.2 | 0.0441942 | ||||||||
\(513\) | 5636.88 | − | 109026.i | 0.0214192 | − | 0.414281i | ||||
\(514\) | −12376.8 | −0.0468470 | ||||||||
\(515\) | 9993.29 | − | 9993.29i | 0.0376785 | − | 0.0376785i | ||||
\(516\) | 55856.5 | + | 33544.1i | 0.209785 | + | 0.125985i | ||||
\(517\) | −32978.5 | + | 32978.5i | −0.123382 | + | 0.123382i | ||||
\(518\) | 140141. | 0.522284 | ||||||||
\(519\) | 107373. | + | 430218.i | 0.398620 | + | 1.59718i | ||||
\(520\) | 1408.56 | − | 1408.56i | 0.00520918 | − | 0.00520918i | ||||
\(521\) | −88093.5 | − | 88093.5i | −0.324540 | − | 0.324540i | 0.525966 | − | 0.850506i | \(-0.323704\pi\) |
−0.850506 | + | 0.525966i | \(0.823704\pi\) | |||||||
\(522\) | −149518. | − | 45635.6i | −0.548723 | − | 0.167480i | ||||
\(523\) | −275699. | −1.00793 | −0.503967 | − | 0.863723i | \(-0.668127\pi\) | ||||
−0.503967 | + | 0.863723i | \(0.668127\pi\) | |||||||
\(524\) | 78323.3 | − | 78323.3i | 0.285252 | − | 0.285252i | ||||
\(525\) | 193121. | − | 48198.7i | 0.700667 | − | 0.174870i | ||||
\(526\) | −251250. | −0.908102 | ||||||||
\(527\) | 104498. | − | 103618.i | 0.376259 | − | 0.373090i | ||||
\(528\) | 11340.8 | − | 2830.41i | 0.0406796 | − | 0.0101527i | ||||
\(529\) | − | 183493.i | − | 0.655705i | ||||||
\(530\) | −7997.80 | + | 7997.80i | −0.0284721 | + | 0.0284721i | ||||
\(531\) | 43763.2 | + | 82213.6i | 0.155210 | + | 0.291578i | ||||
\(532\) | 30310.8 | + | 30310.8i | 0.107096 | + | 0.107096i | ||||
\(533\) | 24623.1 | + | 24623.1i | 0.0866739 | + | 0.0866739i | ||||
\(534\) | −121820. | − | 73157.7i | −0.427203 | − | 0.256553i | ||||
\(535\) | − | 40574.1i | − | 0.141756i | ||||||
\(536\) | −9591.89 | −0.0333868 | ||||||||
\(537\) | 123855. | − | 206238.i | 0.429500 | − | 0.715188i | ||||
\(538\) | 44989.1 | − | 44989.1i | 0.155433 | − | 0.155433i | ||||
\(539\) | −16082.5 | + | 16082.5i | −0.0553574 | + | 0.0553574i | ||||
\(540\) | −11365.8 | + | 10248.3i | −0.0389773 | + | 0.0351450i | ||||
\(541\) | 230256. | + | 230256.i | 0.786712 | + | 0.786712i | 0.980954 | − | 0.194241i | \(-0.0622245\pi\) |
−0.194241 | + | 0.980954i | \(0.562224\pi\) | |||||||
\(542\) | −330341. | −1.12451 | ||||||||
\(543\) | 99214.0 | + | 397529.i | 0.336491 | + | 1.34824i | ||||
\(544\) | 221.211 | − | 52314.1i | 0.000747495 | − | 0.176775i | ||||
\(545\) | 21436.7i | 0.0721714i | ||||||||
\(546\) | −7399.18 | − | 29646.9i | −0.0248198 | − | 0.0994474i | ||||
\(547\) | 75569.7 | + | 75569.7i | 0.252565 | + | 0.252565i | 0.822021 | − | 0.569457i | \(-0.192846\pi\) |
−0.569457 | + | 0.822021i | \(0.692846\pi\) | |||||||
\(548\) | 131615.i | 0.438273i | ||||||||
\(549\) | 298730. | + | 91177.7i | 0.991138 | + | 0.302513i | ||||
\(550\) | −25086.6 | + | 25086.6i | −0.0829310 | + | 0.0829310i | ||||
\(551\) | 72255.8 | + | 72255.8i | 0.237996 | + | 0.237996i | ||||
\(552\) | −61330.6 | + | 15306.7i | −0.201279 | + | 0.0502347i | ||||
\(553\) | − | 130029.i | − | 0.425198i | ||||||
\(554\) | 288252. | + | 288252.i | 0.939189 | + | 0.939189i | ||||
\(555\) | 16837.5 | − | 28037.1i | 0.0546626 | − | 0.0910223i | ||||
\(556\) | −87140.0 | − | 87140.0i | −0.281882 | − | 0.281882i | ||||
\(557\) | 321167.i | 1.03519i | 0.855625 | + | 0.517596i | \(0.173173\pi\) | ||||
−0.855625 | + | 0.517596i | \(0.826827\pi\) | |||||||
\(558\) | 34056.1 | − | 111580.i | 0.109377 | − | 0.358358i | ||||
\(559\) | 30358.9i | 0.0971545i | ||||||||
\(560\) | − | 6009.02i | − | 0.0191614i | ||||||
\(561\) | −12564.4 | − | 51264.5i | −0.0399224 | − | 0.162889i | ||||
\(562\) | −18548.7 | −0.0587274 | ||||||||
\(563\) | −346905. | −1.09445 | −0.547223 | − | 0.836987i | \(-0.684315\pi\) | ||||
−0.547223 | + | 0.836987i | \(0.684315\pi\) | |||||||
\(564\) | 141861. | + | 85193.2i | 0.445968 | + | 0.267822i | ||||
\(565\) | −32746.4 | −0.102581 | ||||||||
\(566\) | −227228. | + | 227228.i | −0.709300 | + | 0.709300i | ||||
\(567\) | 45009.1 | + | 230397.i | 0.140002 | + | 0.716657i | ||||
\(568\) | −61898.4 | + | 61898.4i | −0.191859 | + | 0.191859i | ||||
\(569\) | 442202. | 1.36583 | 0.682914 | − | 0.730499i | \(-0.260713\pi\) | ||||
0.682914 | + | 0.730499i | \(0.260713\pi\) | |||||||
\(570\) | 9705.82 | − | 2422.35i | 0.0298732 | − | 0.00745568i | ||||
\(571\) | 2362.57 | − | 2362.57i | 0.00724623 | − | 0.00724623i | −0.703474 | − | 0.710721i | \(-0.748369\pi\) |
0.710721 | + | 0.703474i | \(0.248369\pi\) | |||||||
\(572\) | 3851.15 | + | 3851.15i | 0.0117706 | + | 0.0117706i | ||||
\(573\) | −20135.4 | − | 12092.1i | −0.0613269 | − | 0.0368293i | ||||
\(574\) | 105044. | 0.318821 | ||||||||
\(575\) | 135667. | − | 135667.i | 0.410335 | − | 0.410335i | ||||
\(576\) | −19487.1 | − | 36608.5i | −0.0587357 | − | 0.110341i | ||||
\(577\) | −506106. | −1.52016 | −0.760081 | − | 0.649828i | \(-0.774841\pi\) | ||||
−0.760081 | + | 0.649828i | \(0.774841\pi\) | |||||||
\(578\) | −236225. | − | 1997.79i | −0.707081 | − | 0.00597991i | ||||
\(579\) | 88747.7 | + | 355592.i | 0.264728 | + | 1.06071i | ||||
\(580\) | − | 14324.5i | − | 0.0425817i | ||||||
\(581\) | −159350. | + | 159350.i | −0.472064 | + | 0.472064i | ||||
\(582\) | 143056. | − | 35703.6i | 0.422339 | − | 0.105406i | ||||
\(583\) | −21866.8 | − | 21866.8i | −0.0643352 | − | 0.0643352i | ||||
\(584\) | 143005. | + | 143005.i | 0.419301 | + | 0.419301i | ||||
\(585\) | −6820.24 | − | 2081.66i | −0.0199291 | − | 0.00608272i | ||||
\(586\) | 171970.i | 0.500793i | ||||||||
\(587\) | −344806. | −1.00069 | −0.500344 | − | 0.865827i | \(-0.666793\pi\) | ||||
−0.500344 | + | 0.865827i | \(0.666793\pi\) | |||||||
\(588\) | 69180.6 | + | 41545.8i | 0.200092 | + | 0.120163i | ||||
\(589\) | −53921.7 | + | 53921.7i | −0.155429 | + | 0.155429i | ||||
\(590\) | −6034.56 | + | 6034.56i | −0.0173357 | + | 0.0173357i | ||||
\(591\) | −116405. | + | 29052.0i | −0.333270 | + | 0.0831765i | ||||
\(592\) | 62668.0 | + | 62668.0i | 0.178814 | + | 0.178814i | ||||
\(593\) | −61748.7 | −0.175598 | −0.0877988 | − | 0.996138i | \(-0.527983\pi\) | ||||
−0.0877988 | + | 0.996138i | \(0.527983\pi\) | |||||||
\(594\) | −28019.9 | − | 31075.2i | −0.0794133 | − | 0.0880727i | ||||
\(595\) | −27134.3 | − | 114.737i | −0.0766450 | − | 0.000324094i | ||||
\(596\) | 217809.i | 0.613174i | ||||||||
\(597\) | −323769. | + | 80805.3i | −0.908419 | + | 0.226721i | ||||
\(598\) | −20826.8 | − | 20826.8i | −0.0582399 | − | 0.0582399i | ||||
\(599\) | 46625.6i | 0.129948i | 0.997887 | + | 0.0649741i | \(0.0206965\pi\) | ||||
−0.997887 | + | 0.0649741i | \(0.979304\pi\) | |||||||
\(600\) | 107913. | + | 64806.1i | 0.299758 | + | 0.180017i | ||||
\(601\) | 252512. | − | 252512.i | 0.699091 | − | 0.699091i | −0.265123 | − | 0.964215i | \(-0.585413\pi\) |
0.964215 | + | 0.265123i | \(0.0854126\pi\) | |||||||
\(602\) | 64756.7 | + | 64756.7i | 0.178686 | + | 0.178686i | ||||
\(603\) | 16134.2 | + | 30309.6i | 0.0443723 | + | 0.0833578i | ||||
\(604\) | − | 288895.i | − | 0.791891i | ||||||
\(605\) | −26402.7 | − | 26402.7i | −0.0721337 | − | 0.0721337i | ||||
\(606\) | −411156. | − | 246916.i | −1.11960 | − | 0.672365i | ||||
\(607\) | 77033.1 | + | 77033.1i | 0.209074 | + | 0.209074i | 0.803874 | − | 0.594800i | \(-0.202769\pi\) |
−0.594800 | + | 0.803874i | \(0.702769\pi\) | |||||||
\(608\) | 27108.6i | 0.0733331i | ||||||||
\(609\) | −188372. | − | 113125.i | −0.507903 | − | 0.305017i | ||||
\(610\) | 28619.6i | 0.0769138i | ||||||||
\(611\) | 77103.7i | 0.206535i | ||||||||
\(612\) | −165681. | + | 87296.6i | −0.442353 | + | 0.233074i | ||||
\(613\) | −71441.3 | −0.190120 | −0.0950602 | − | 0.995472i | \(-0.530304\pi\) | ||||
−0.0950602 | + | 0.995472i | \(0.530304\pi\) | |||||||
\(614\) | 351748. | 0.933027 | ||||||||
\(615\) | 12620.6 | − | 21015.4i | 0.0333681 | − | 0.0555633i | ||||
\(616\) | 16429.3 | 0.0432970 | ||||||||
\(617\) | 191957. | − | 191957.i | 0.504235 | − | 0.504235i | −0.408516 | − | 0.912751i | \(-0.633954\pi\) |
0.912751 | + | 0.408516i | \(0.133954\pi\) | |||||||
\(618\) | 70582.5 | − | 117531.i | 0.184808 | − | 0.307735i | ||||
\(619\) | 418394. | − | 418394.i | 1.09195 | − | 1.09195i | 0.0966325 | − | 0.995320i | \(-0.469193\pi\) |
0.995320 | − | 0.0966325i | \(-0.0308071\pi\) | |||||||
\(620\) | 10689.8 | 0.0278091 | ||||||||
\(621\) | 151530. | + | 168053.i | 0.392930 | + | 0.435776i | ||||
\(622\) | −331245. | + | 331245.i | −0.856188 | + | 0.856188i | ||||
\(623\) | −141230. | − | 141230.i | −0.363875 | − | 0.363875i | ||||
\(624\) | 9948.66 | − | 16566.1i | 0.0255503 | − | 0.0425454i | ||||
\(625\) | −377761. | −0.967069 | ||||||||
\(626\) | 315547. | − | 315547.i | 0.805222 | − | 0.805222i | ||||
\(627\) | 6622.96 | + | 26536.7i | 0.0168468 | + | 0.0675013i | ||||
\(628\) | 54939.4 | 0.139304 | ||||||||
\(629\) | 284179. | − | 281786.i | 0.718275 | − | 0.712226i | ||||
\(630\) | −18988.1 | + | 10107.6i | −0.0478409 | + | 0.0254663i | ||||
\(631\) | − | 236494.i | − | 0.593966i | −0.954883 | − | 0.296983i | \(-0.904020\pi\) | ||
0.954883 | − | 0.296983i | \(-0.0959805\pi\) | |||||||
\(632\) | 58146.1 | − | 58146.1i | 0.145575 | − | 0.145575i | ||||
\(633\) | −103967. | − | 416571.i | −0.259470 | − | 1.03964i | ||||
\(634\) | 258163. | + | 258163.i | 0.642266 | + | 0.642266i | ||||
\(635\) | −40058.2 | − | 40058.2i | −0.0993447 | − | 0.0993447i | ||||
\(636\) | −56488.4 | + | 94062.4i | −0.139651 | + | 0.232542i | ||||
\(637\) | 37600.8i | 0.0926656i | ||||||||
\(638\) | 39164.7 | 0.0962173 | ||||||||
\(639\) | 299711. | + | 91477.2i | 0.734009 | + | 0.224033i | ||||
\(640\) | 2687.10 | − | 2687.10i | 0.00656030 | − | 0.00656030i | ||||
\(641\) | −80667.7 | + | 80667.7i | −0.196329 | + | 0.196329i | −0.798424 | − | 0.602095i | \(-0.794333\pi\) |
0.602095 | + | 0.798424i | \(0.294333\pi\) | |||||||
\(642\) | −95309.6 | − | 381884.i | −0.231242 | − | 0.926535i | ||||
\(643\) | −132413. | − | 132413.i | −0.320264 | − | 0.320264i | 0.528604 | − | 0.848868i | \(-0.322716\pi\) |
−0.848868 | + | 0.528604i | \(0.822716\pi\) | |||||||
\(644\) | −88848.7 | −0.214230 | ||||||||
\(645\) | 20735.7 | − | 5175.16i | 0.0498425 | − | 0.0124395i | ||||
\(646\) | 122411. | + | 517.617i | 0.293330 | + | 0.00124035i | ||||
\(647\) | − | 390943.i | − | 0.933910i | −0.884281 | − | 0.466955i | \(-0.845351\pi\) | ||
0.884281 | − | 0.466955i | \(-0.154649\pi\) | |||||||
\(648\) | −82901.4 | + | 123155.i | −0.197429 | + | 0.293294i | ||||
\(649\) | −16499.1 | − | 16499.1i | −0.0391716 | − | 0.0391716i | ||||
\(650\) | 58652.4i | 0.138822i | ||||||||
\(651\) | 84420.8 | − | 140574.i | 0.199199 | − | 0.331699i | ||||
\(652\) | −67703.5 | + | 67703.5i | −0.159263 | + | 0.159263i | ||||
\(653\) | 7596.15 | + | 7596.15i | 0.0178142 | + | 0.0178142i | 0.715958 | − | 0.698144i | \(-0.245990\pi\) |
−0.698144 | + | 0.715958i | \(0.745990\pi\) | |||||||
\(654\) | 50355.3 | + | 201763.i | 0.117731 | + | 0.471721i | ||||
\(655\) | − | 36332.8i | − | 0.0846870i | ||||||
\(656\) | 46973.2 | + | 46973.2i | 0.109155 | + | 0.109155i | ||||
\(657\) | 211342. | − | 692429.i | 0.489614 | − | 1.60415i | ||||
\(658\) | 164465. | + | 164465.i | 0.379858 | + | 0.379858i | ||||
\(659\) | 107111.i | 0.246639i | 0.992367 | + | 0.123319i | \(0.0393540\pi\) | ||||
−0.992367 | + | 0.123319i | \(0.960646\pi\) | |||||||
\(660\) | 1973.92 | − | 3286.90i | 0.00453150 | − | 0.00754568i | ||||
\(661\) | 348318.i | 0.797210i | 0.917123 | + | 0.398605i | \(0.130505\pi\) | ||||
−0.917123 | + | 0.398605i | \(0.869495\pi\) | |||||||
\(662\) | − | 571245.i | − | 1.30349i | ||||||
\(663\) | −74615.9 | − | 45240.3i | −0.169748 | − | 0.102920i | ||||
\(664\) | −142516. | −0.323241 | ||||||||
\(665\) | 14060.7 | 0.0317953 | ||||||||
\(666\) | 92614.5 | − | 303438.i | 0.208800 | − | 0.684102i | ||||
\(667\) | −211800. | −0.476075 | ||||||||
\(668\) | −77949.0 | + | 77949.0i | −0.174686 | + | 0.174686i | ||||
\(669\) | −134221. | − | 80605.4i | −0.299895 | − | 0.180099i | ||||
\(670\) | −2224.76 | + | 2224.76i | −0.00495602 | + | 0.00495602i | ||||
\(671\) | −78249.0 | −0.173794 | ||||||||
\(672\) | −14115.3 | − | 56557.0i | −0.0312574 | − | 0.125241i | ||||
\(673\) | 551402. | − | 551402.i | 1.21741 | − | 1.21741i | 0.248879 | − | 0.968535i | \(-0.419938\pi\) |
0.968535 | − | 0.248879i | \(-0.0800620\pi\) | |||||||
\(674\) | −21873.4 | − | 21873.4i | −0.0481499 | − | 0.0481499i | ||||
\(675\) | 23266.2 | − | 450004.i | 0.0510643 | − | 0.987663i | ||||
\(676\) | −219484. | −0.480297 | ||||||||
\(677\) | 509746. | − | 509746.i | 1.11218 | − | 1.11218i | 0.119328 | − | 0.992855i | \(-0.461926\pi\) |
0.992855 | − | 0.119328i | \(-0.0380739\pi\) | |||||||
\(678\) | −308209. | + | 76922.0i | −0.670481 | + | 0.167337i | ||||
\(679\) | 207243. | 0.449512 | ||||||||
\(680\) | −12082.5 | − | 12185.1i | −0.0261300 | − | 0.0263519i | ||||
\(681\) | −226299. | + | 56479.0i | −0.487964 | + | 0.121785i | ||||
\(682\) | 29227.1i | 0.0628372i | ||||||||
\(683\) | −461517. | + | 461517.i | −0.989341 | + | 0.989341i | −0.999944 | − | 0.0106031i | \(-0.996625\pi\) |
0.0106031 | + | 0.999944i | \(0.496625\pi\) | |||||||
\(684\) | 85661.1 | − | 45598.4i | 0.183093 | − | 0.0974624i | ||||
\(685\) | 30527.0 | + | 30527.0i | 0.0650584 | + | 0.0650584i | ||||
\(686\) | 252019. | + | 252019.i | 0.535532 | + | 0.535532i | ||||
\(687\) | 55827.6 | + | 33526.8i | 0.118287 | + | 0.0710360i | ||||
\(688\) | 57915.4i | 0.122354i | ||||||||
\(689\) | −51124.5 | −0.107694 | ||||||||
\(690\) | −10674.9 | + | 17775.4i | −0.0224215 | + | 0.0373354i | ||||
\(691\) | 222134. | − | 222134.i | 0.465220 | − | 0.465220i | −0.435142 | − | 0.900362i | \(-0.643302\pi\) |
0.900362 | + | 0.435142i | \(0.143302\pi\) | |||||||
\(692\) | −278704. | + | 278704.i | −0.582010 | + | 0.582010i | ||||
\(693\) | −27635.1 | − | 51915.3i | −0.0575433 | − | 0.108101i | ||||
\(694\) | 176398. | + | 176398.i | 0.366247 | + | 0.366247i | ||||
\(695\) | −40422.8 | −0.0836867 | ||||||||
\(696\) | −33648.6 | − | 134822.i | −0.0694622 | − | 0.278319i | ||||
\(697\) | 213008. | − | 211215.i | 0.438461 | − | 0.434769i | ||||
\(698\) | − | 73222.0i | − | 0.150290i | ||||||
\(699\) | −176277. | − | 706302.i | −0.360779 | − | 1.44556i | ||||
\(700\) | 125108. | + | 125108.i | 0.255322 | + | 0.255322i | ||||
\(701\) | 280070.i | 0.569942i | 0.958536 | + | 0.284971i | \(0.0919839\pi\) | ||||
−0.958536 | + | 0.284971i | \(0.908016\pi\) | |||||||
\(702\) | −69082.0 | − | 3571.69i | −0.140182 | − | 0.00724769i | ||||
\(703\) | −146638. | + | 146638.i | −0.296713 | + | 0.296713i | ||||
\(704\) | 7346.81 | + | 7346.81i | 0.0148236 | + | 0.0148236i | ||||
\(705\) | 52663.3 | − | 13143.5i | 0.105957 | − | 0.0264444i | ||||
\(706\) | 210030.i | 0.421378i | ||||||||
\(707\) | −476670. | − | 476670.i | −0.953629 | − | 0.953629i | ||||
\(708\) | −42622.0 | + | 70972.7i | −0.0850291 | + | 0.141587i | ||||
\(709\) | 557047. | + | 557047.i | 1.10815 | + | 1.10815i | 0.993393 | + | 0.114760i | \(0.0366098\pi\) |
0.114760 | + | 0.993393i | \(0.463390\pi\) | |||||||
\(710\) | 28713.6i | 0.0569602i | ||||||||
\(711\) | −281543. | − | 85931.9i | −0.556936 | − | 0.169987i | ||||
\(712\) | − | 126310.i | − | 0.249160i | ||||||
\(713\) | − | 158058.i | − | 0.310913i | ||||||
\(714\) | −255658. | + | 62659.1i | −0.501490 | + | 0.122910i | ||||
\(715\) | 1786.49 | 0.00349452 | ||||||||
\(716\) | 213840. | 0.417122 | ||||||||
\(717\) | −299971. | − | 180145.i | −0.583500 | − | 0.350416i | ||||
\(718\) | 596893. | 1.15784 | ||||||||
\(719\) | 572138. | − | 572138.i | 1.10673 | − | 1.10673i | 0.113156 | − | 0.993577i | \(-0.463904\pi\) |
0.993577 | − | 0.113156i | \(-0.0360960\pi\) | |||||||
\(720\) | −13010.9 | − | 3971.16i | −0.0250982 | − | 0.00766041i | ||||
\(721\) | 136259. | − | 136259.i | 0.262117 | − | 0.262117i | ||||
\(722\) | 305171. | 0.585422 | ||||||||
\(723\) | 228270. | − | 56970.9i | 0.436688 | − | 0.108987i | ||||
\(724\) | −257527. | + | 257527.i | −0.491298 | + | 0.491298i | ||||
\(725\) | 298235. | + | 298235.i | 0.567392 | + | 0.567392i | ||||
\(726\) | −310524. | − | 186482.i | −0.589144 | − | 0.353805i | ||||
\(727\) | −36669.3 | −0.0693800 | −0.0346900 | − | 0.999398i | \(-0.511044\pi\) | ||||
−0.0346900 | + | 0.999398i | \(0.511044\pi\) | |||||||
\(728\) | 19205.8 | − | 19205.8i | 0.0362385 | − | 0.0362385i | ||||
\(729\) | 528607. | + | 54806.8i | 0.994668 | + | 0.103129i | ||||
\(730\) | 66337.7 | 0.124484 | ||||||||
\(731\) | 261522. | + | 1105.85i | 0.489411 | + | 0.00206948i | ||||
\(732\) | 67228.2 | + | 269368.i | 0.125467 | + | 0.502718i | ||||
\(733\) | 828977.i | 1.54289i | 0.636296 | + | 0.771445i | \(0.280466\pi\) | ||||
−0.636296 | + | 0.771445i | \(0.719534\pi\) | |||||||
\(734\) | −15141.9 | + | 15141.9i | −0.0281054 | + | 0.0281054i | ||||
\(735\) | 25682.1 | − | 6409.66i | 0.0475396 | − | 0.0118648i | ||||
\(736\) | −39731.1 | − | 39731.1i | −0.0733458 | − | 0.0733458i | ||||
\(737\) | −6082.72 | − | 6082.72i | −0.0111986 | − | 0.0111986i | ||||
\(738\) | 69419.8 | − | 227444.i | 0.127459 | − | 0.417601i | ||||
\(739\) | 318231.i | 0.582712i | 0.956615 | + | 0.291356i | \(0.0941063\pi\) | ||||
−0.956615 | + | 0.291356i | \(0.905894\pi\) | |||||||
\(740\) | 29070.6 | 0.0530873 | ||||||||
\(741\) | 38763.6 | + | 23279.1i | 0.0705972 | + | 0.0423965i | ||||
\(742\) | −109050. | + | 109050.i | −0.198070 | + | 0.198070i | ||||
\(743\) | 237196. | − | 237196.i | 0.429664 | − | 0.429664i | −0.458850 | − | 0.888514i | \(-0.651738\pi\) |
0.888514 | + | 0.458850i | \(0.151738\pi\) | |||||||
\(744\) | 100613. | − | 25110.6i | 0.181764 | − | 0.0453641i | ||||
\(745\) | 50519.0 | + | 50519.0i | 0.0910211 | + | 0.0910211i | ||||
\(746\) | −769893. | −1.38341 | ||||||||
\(747\) | 239720. | + | 450338.i | 0.429599 | + | 0.807045i | ||||
\(748\) | 33315.4 | − | 33034.8i | 0.0595445 | − | 0.0590431i | ||||
\(749\) | − | 553230.i | − | 0.986149i | ||||||
\(750\) | 80567.7 | − | 20107.9i | 0.143231 | − | 0.0357473i | ||||
\(751\) | 189153. | + | 189153.i | 0.335377 | + | 0.335377i | 0.854624 | − | 0.519247i | \(-0.173788\pi\) |
−0.519247 | + | 0.854624i | \(0.673788\pi\) | |||||||
\(752\) | 147090.i | 0.260104i | ||||||||
\(753\) | −269175. | − | 161651.i | −0.474729 | − | 0.285094i | ||||
\(754\) | 45783.4 | − | 45783.4i | 0.0805314 | − | 0.0805314i | ||||
\(755\) | −67006.7 | − | 67006.7i | −0.117550 | − | 0.117550i | ||||
\(756\) | −154973. | + | 139736.i | −0.271152 | + | 0.244492i | ||||
\(757\) | 562855.i | 0.982211i | 0.871100 | + | 0.491106i | \(0.163407\pi\) | ||||
−0.871100 | + | 0.491106i | \(0.836593\pi\) | |||||||
\(758\) | 211078. | + | 211078.i | 0.367372 | + | 0.367372i | ||||
\(759\) | −48599.7 | − | 29186.2i | −0.0843627 | − | 0.0506633i | ||||
\(760\) | 6287.61 | + | 6287.61i | 0.0108858 | + | 0.0108858i | ||||
\(761\) | 994056.i | 1.71649i | 0.513239 | + | 0.858246i | \(0.328446\pi\) | ||||
−0.513239 | + | 0.858246i | \(0.671554\pi\) | |||||||
\(762\) | −471127. | − | 282931.i | −0.811386 | − | 0.487271i | ||||
\(763\) | 292291.i | 0.502072i | ||||||||
\(764\) | − | 20877.6i | − | 0.0357680i | ||||||
\(765\) | −18180.5 | + | 58676.0i | −0.0310659 | + | 0.100262i | ||||
\(766\) | −429701. | −0.732334 | ||||||||
\(767\) | −38574.9 | −0.0655713 | ||||||||
\(768\) | 18979.0 | − | 31603.1i | 0.0321773 | − | 0.0535805i | ||||
\(769\) | 244827. | 0.414007 | 0.207003 | − | 0.978340i | \(-0.433629\pi\) | ||||
0.207003 | + | 0.978340i | \(0.433629\pi\) | |||||||
\(770\) | 3810.64 | − | 3810.64i | 0.00642712 | − | 0.00642712i | ||||
\(771\) | −20275.7 | + | 33762.3i | −0.0341088 | + | 0.0567967i | ||||
\(772\) | −230359. | + | 230359.i | −0.386519 | + | 0.386519i | ||||
\(773\) | −926714. | −1.55091 | −0.775455 | − | 0.631402i | \(-0.782480\pi\) | ||||
−0.775455 | + | 0.631402i | \(0.782480\pi\) | |||||||
\(774\) | 183008. | − | 97417.4i | 0.305484 | − | 0.162613i | ||||
\(775\) | −222562. | + | 222562.i | −0.370550 | + | 0.370550i | ||||
\(776\) | 92674.6 | + | 92674.6i | 0.153899 | + | 0.153899i | ||||
\(777\) | 229580. | − | 382288.i | 0.380269 | − | 0.633211i | ||||
\(778\) | 493588. | 0.815465 | ||||||||
\(779\) | −109914. | + | 109914.i | −0.181125 | + | 0.181125i | ||||
\(780\) | −1534.87 | − | 6149.89i | −0.00252280 | − | 0.0101083i | ||||
\(781\) | −78506.1 | −0.128707 | ||||||||
\(782\) | −180168. | + | 178651.i | −0.294621 | + | 0.292140i | ||||
\(783\) | −369429. | + | 333107.i | −0.602570 | + | 0.543325i | ||||
\(784\) | 71730.7i | 0.116701i | ||||||||
\(785\) | 12742.7 | − | 12742.7i | 0.0206787 | − | 0.0206787i | ||||
\(786\) | −85346.7 | − | 341965.i | −0.138147 | − | 0.553525i | ||||
\(787\) | −748326. | − | 748326.i | −1.20821 | − | 1.20821i | −0.971607 | − | 0.236599i | \(-0.923967\pi\) |
−0.236599 | − | 0.971607i | \(-0.576033\pi\) | |||||||
\(788\) | −75409.2 | − | 75409.2i | −0.121443 | − | 0.121443i | ||||
\(789\) | −411598. | + | 685379.i | −0.661180 | + | 1.10097i | ||||
\(790\) | − | 26973.0i | − | 0.0432191i | ||||||
\(791\) | −446498. | −0.713620 | ||||||||
\(792\) | 10857.6 | − | 35573.1i | 0.0173094 | − | 0.0567116i | ||||
\(793\) | −91472.9 | + | 91472.9i | −0.145461 | + | 0.145461i | ||||
\(794\) | −255207. | + | 255207.i | −0.404810 | + | 0.404810i | ||||
\(795\) | 8714.98 | + | 34919.0i | 0.0137890 | + | 0.0552494i | ||||
\(796\) | −209744. | − | 209744.i | −0.331026 | − | 0.331026i | ||||
\(797\) | −485836. | −0.764844 | −0.382422 | − | 0.923988i | \(-0.624910\pi\) | ||||
−0.382422 | + | 0.923988i | \(0.624910\pi\) | |||||||
\(798\) | 132339. | − | 33028.9i | 0.207818 | − | 0.0518666i | ||||
\(799\) | 664197. | + | 2808.56i | 1.04041 | + | 0.00439937i | ||||
\(800\) | 111891.i | 0.174829i | ||||||||
\(801\) | −399130. | + | 212461.i | −0.622084 | + | 0.331143i | ||||
\(802\) | −154966. | − | 154966.i | −0.240929 | − | 0.240929i | ||||
\(803\) | 181374.i | 0.281283i | ||||||||
\(804\) | −15713.5 | + | 26165.5i | −0.0243086 | + | 0.0404778i | ||||
\(805\) | −20607.7 | + | 20607.7i | −0.0318008 | + | 0.0318008i | ||||
\(806\) | 34166.4 | + | 34166.4i | 0.0525931 | + | 0.0525931i | ||||
\(807\) | −49023.4 | − | 196426.i | −0.0752759 | − | 0.301614i | ||||
\(808\) | − | 426312.i | − | 0.652988i | ||||||
\(809\) | −42234.8 | − | 42234.8i | −0.0645318 | − | 0.0645318i | 0.674104 | − | 0.738636i | \(-0.264530\pi\) |
−0.738636 | + | 0.674104i | \(0.764530\pi\) | |||||||
\(810\) | 9336.60 | + | 47793.2i | 0.0142304 | + | 0.0728443i | ||||
\(811\) | 260693. | + | 260693.i | 0.396358 | + | 0.396358i | 0.876946 | − | 0.480589i | \(-0.159577\pi\) |
−0.480589 | + | 0.876946i | \(0.659577\pi\) | |||||||
\(812\) | − | 195315.i | − | 0.296227i | ||||||
\(813\) | −541165. | + | 901128.i | −0.818745 | + | 1.36334i | ||||
\(814\) | 79482.1i | 0.119956i | ||||||||
\(815\) | 31406.5i | 0.0472830i | ||||||||
\(816\) | −142344. | − | 86304.5i | −0.213776 | − | 0.129614i | ||||
\(817\) | −135518. | −0.203026 | ||||||||
\(818\) | 124122. | 0.185499 | ||||||||
\(819\) | −92994.3 | − | 28383.5i | −0.138640 | − | 0.0423154i | ||||
\(820\) | 21790.1 | 0.0324064 | ||||||||
\(821\) | 154689. | − | 154689.i | 0.229495 | − | 0.229495i | −0.582987 | − | 0.812482i | \(-0.698116\pi\) |
0.812482 | + | 0.582987i | \(0.198116\pi\) | |||||||
\(822\) | 359029. | + | 215612.i | 0.531357 | + | 0.319102i | ||||
\(823\) | −133830. | + | 133830.i | −0.197585 | + | 0.197585i | −0.798964 | − | 0.601379i | \(-0.794618\pi\) |
0.601379 | + | 0.798964i | \(0.294618\pi\) | |||||||
\(824\) | 121864. | 0.179482 | ||||||||
\(825\) | 27336.2 | + | 109530.i | 0.0401634 | + | 0.160926i | ||||
\(826\) | −82281.5 | + | 82281.5i | −0.120599 | + | 0.120599i | ||||
\(827\) | 811431. | + | 811431.i | 1.18643 | + | 1.18643i | 0.978049 | + | 0.208377i | \(0.0668180\pi\) |
0.208377 | + | 0.978049i | \(0.433182\pi\) | |||||||
\(828\) | −58717.1 | + | 192378.i | −0.0856453 | + | 0.280604i | ||||
\(829\) | −193545. | −0.281627 | −0.140813 | − | 0.990036i | \(-0.544972\pi\) | ||||
−0.140813 | + | 0.990036i | \(0.544972\pi\) | |||||||
\(830\) | −33055.3 | + | 33055.3i | −0.0479827 | + | 0.0479827i | ||||
\(831\) | 1.25853e6 | − | 314100.i | 1.82248 | − | 0.454848i | ||||
\(832\) | 17176.8 | 0.0248139 | ||||||||
\(833\) | 323906. | + | 1369.64i | 0.466798 | + | 0.00197386i | ||||
\(834\) | −380460. | + | 94954.1i | −0.546986 | + | 0.136515i | ||||
\(835\) | 36159.2i | 0.0518616i | ||||||||
\(836\) | −17191.0 | + | 17191.0i | −0.0245973 | + | 0.0245973i | ||||
\(837\) | −248585. | − | 275691.i | −0.354832 | − | 0.393524i | ||||
\(838\) | −123357. | − | 123357.i | −0.175661 | − | 0.175661i | ||||
\(839\) | −385079. | − | 385079.i | −0.547048 | − | 0.547048i | 0.378538 | − | 0.925586i | \(-0.376427\pi\) |
−0.925586 | + | 0.378538i | \(0.876427\pi\) | |||||||
\(840\) | −16391.9 | − | 9843.99i | −0.0232311 | − | 0.0139512i | ||||
\(841\) | 241683.i | 0.341707i | ||||||||
\(842\) | 630179. | 0.888874 | ||||||||
\(843\) | −30386.5 | + | 50598.5i | −0.0427588 | + | 0.0712004i | ||||
\(844\) | 269863. | − | 269863.i | 0.378842 | − | 0.378842i | ||||
\(845\) | −50907.5 | + | 50907.5i | −0.0712965 | + | 0.0712965i | ||||
\(846\) | 464793. | − | 247414.i | 0.649410 | − | 0.345688i | ||||
\(847\) | −360003. | − | 360003.i | −0.501810 | − | 0.501810i | ||||
\(848\) | −97529.7 | −0.135627 | ||||||||
\(849\) | 247605. | + | 992097.i | 0.343513 | + | 1.37638i | ||||
\(850\) | 505251. | + | 2136.46i | 0.699310 | + | 0.00295704i | ||||
\(851\) | − | 429835.i | − | 0.593530i | ||||||
\(852\) | 67449.0 | + | 270253.i | 0.0929173 | + | 0.372299i | ||||
\(853\) | −175339. | − | 175339.i | −0.240980 | − | 0.240980i | 0.576276 | − | 0.817255i | \(-0.304505\pi\) |
−0.817255 | + | 0.576276i | \(0.804505\pi\) | |||||||
\(854\) | 390230.i | 0.535063i | ||||||||
\(855\) | 9292.21 | − | 30444.5i | 0.0127112 | − | 0.0416464i | ||||
\(856\) | 247392. | − | 247392.i | 0.337628 | − | 0.337628i | ||||
\(857\) | −55993.0 | − | 55993.0i | −0.0762381 | − | 0.0762381i | 0.667960 | − | 0.744198i | \(-0.267168\pi\) |
−0.744198 | + | 0.667960i | \(0.767168\pi\) | |||||||
\(858\) | 16814.4 | − | 4196.50i | 0.0228406 | − | 0.00570049i | ||||
\(859\) | − | 714142.i | − | 0.967828i | −0.875116 | − | 0.483914i | \(-0.839215\pi\) | ||
0.875116 | − | 0.483914i | \(-0.160785\pi\) | |||||||
\(860\) | 13433.0 | + | 13433.0i | 0.0181625 | + | 0.0181625i | ||||
\(861\) | 172083. | − | 286546.i | 0.232130 | − | 0.386535i | ||||
\(862\) | −478023. | − | 478023.i | −0.643331 | − | 0.643331i | ||||
\(863\) | 530271.i | 0.711994i | 0.934487 | + | 0.355997i | \(0.115859\pi\) | ||||
−0.934487 | + | 0.355997i | \(0.884141\pi\) | |||||||
\(864\) | −131787. | − | 6813.68i | −0.176541 | − | 0.00912754i | ||||
\(865\) | 129286.i | 0.172790i | ||||||||
\(866\) | − | 873704.i | − | 1.16501i | ||||||
\(867\) | −392433. | + | 641118.i | −0.522069 | + | 0.852904i | ||||
\(868\) | 145756. | 0.193458 | ||||||||
\(869\) | 73747.0 | 0.0976573 | ||||||||
\(870\) | −39075.4 | − | 23466.4i | −0.0516256 | − | 0.0310033i | ||||
\(871\) | −14221.4 | −0.0187459 | ||||||||
\(872\) | −130706. | + | 130706.i | −0.171894 | + | 0.171894i | ||||
\(873\) | 136960. | − | 448729.i | 0.179707 | − | 0.588784i | ||||
\(874\) | 92967.9 | − | 92967.9i | 0.121706 | − | 0.121706i | ||||
\(875\) | 116717. | 0.152447 | ||||||||
\(876\) | 624371. | − | 155829.i | 0.813644 | − | 0.203067i | ||||
\(877\) | −489689. | + | 489689.i | −0.636680 | + | 0.636680i | −0.949735 | − | 0.313055i | \(-0.898648\pi\) |
0.313055 | + | 0.949735i | \(0.398648\pi\) | |||||||
\(878\) | 314610. | + | 314610.i | 0.408116 | + | 0.408116i | ||||
\(879\) | 469114. | + | 281722.i | 0.607156 | + | 0.364622i | ||||
\(880\) | 3408.06 | 0.00440090 | ||||||||
\(881\) | −574842. | + | 574842.i | −0.740622 | + | 0.740622i | −0.972698 | − | 0.232076i | \(-0.925448\pi\) |
0.232076 | + | 0.972698i | \(0.425448\pi\) | |||||||
\(882\) | 226663. | − | 120656.i | 0.291370 | − | 0.155099i | ||||
\(883\) | 1.14202e6 | 1.46471 | 0.732354 | − | 0.680924i | \(-0.238422\pi\) | ||||
0.732354 | + | 0.680924i | \(0.238422\pi\) | |||||||
\(884\) | 327.977 | − | 77563.3i | 0.000419700 | − | 0.0992548i | ||||
\(885\) | 6575.70 | + | 26347.3i | 0.00839567 | + | 0.0336396i | ||||
\(886\) | − | 613164.i | − | 0.781105i | ||||||
\(887\) | −481293. | + | 481293.i | −0.611734 | + | 0.611734i | −0.943398 | − | 0.331664i | \(-0.892390\pi\) |
0.331664 | + | 0.943398i | \(0.392390\pi\) | |||||||
\(888\) | 273613. | − | 68287.6i | 0.346985 | − | 0.0865996i | ||||
\(889\) | −546196. | − | 546196.i | −0.691107 | − | 0.691107i | ||||
\(890\) | −29296.5 | − | 29296.5i | −0.0369859 | − | 0.0369859i | ||||
\(891\) | −130671. | + | 25527.2i | −0.164598 | + | 0.0321550i | ||||
\(892\) | − | 139169.i | − | 0.174909i | ||||||
\(893\) | −344180. | −0.431601 | ||||||||
\(894\) | 594156. | + | 356815.i | 0.743404 | + | 0.446445i | ||||
\(895\) | 49598.5 | − | 49598.5i | 0.0619188 | − | 0.0619188i | ||||
\(896\) | 36638.7 | − | 36638.7i | 0.0456378 | − | 0.0456378i | ||||
\(897\) | −90931.5 | + | 22694.4i | −0.113013 | + | 0.0282055i | ||||
\(898\) | 584802. | + | 584802.i | 0.725197 | + | 0.725197i | ||||
\(899\) | 347458. | 0.429915 | ||||||||
\(900\) | 353566. | − | 188207.i | 0.436501 | − | 0.232354i | ||||
\(901\) | −1862.25 | + | 440404.i | −0.00229397 | + | 0.542502i | ||||
\(902\) | 59576.3i | 0.0732252i | ||||||||
\(903\) | 282733. | − | 70563.6i | 0.346737 | − | 0.0865377i | ||||
\(904\) | −199664. | − | 199664.i | −0.244322 | − | 0.244322i | ||||
\(905\) | 119462.i | 0.145859i | ||||||||
\(906\) | −788068. | − | 473267.i | −0.960080 | − | 0.576568i | ||||
\(907\) | 667558. | − | 667558.i | 0.811474 | − | 0.811474i | −0.173381 | − | 0.984855i | \(-0.555469\pi\) |
0.984855 | + | 0.173381i | \(0.0554691\pi\) | |||||||
\(908\) | −146601. | − | 146601.i | −0.177813 | − | 0.177813i | ||||
\(909\) | −1.34711e6 | + | 717084.i | −1.63033 | + | 0.867845i | ||||
\(910\) | − | 8909.25i | − | 0.0107587i | ||||||
\(911\) | −571957. | − | 571957.i | −0.689170 | − | 0.689170i | 0.272878 | − | 0.962049i | \(-0.412024\pi\) |
−0.962049 | + | 0.272878i | \(0.912024\pi\) | |||||||
\(912\) | 73948.9 | + | 44409.4i | 0.0889082 | + | 0.0533931i | ||||
\(913\) | −90376.6 | − | 90376.6i | −0.108421 | − | 0.108421i | ||||
\(914\) | − | 1.00649e6i | − | 1.20481i | ||||||
\(915\) | 78070.7 | + | 46884.7i | 0.0932494 | + | 0.0560001i | ||||
\(916\) | 57885.5i | 0.0689888i | ||||||||
\(917\) | − | 495400.i | − | 0.589138i | ||||||
\(918\) | −33284.1 | + | 594966.i | −0.0394958 | + | 0.706003i | ||||
\(919\) | −272540. | −0.322701 | −0.161350 | − | 0.986897i | \(-0.551585\pi\) | ||||
−0.161350 | + | 0.986897i | \(0.551585\pi\) | |||||||
\(920\) | −18430.6 | −0.0217753 | ||||||||
\(921\) | 576233. | − | 959523.i | 0.679327 | − | 1.13119i | ||||
\(922\) | −1.03511e6 | −1.21766 | ||||||||
\(923\) | −91773.4 | + | 91773.4i | −0.107724 | + | 0.107724i | ||||
\(924\) | 26914.5 | − | 44817.0i | 0.0315241 | − | 0.0524927i | ||||
\(925\) | −605249. | + | 605249.i | −0.707377 | + | 0.707377i | ||||
\(926\) | −475017. | −0.553971 | ||||||||
\(927\) | −204983. | − | 385080.i | −0.238538 | − | 0.448117i | ||||
\(928\) | 87340.5 | − | 87340.5i | 0.101419 | − | 0.101419i | ||||
\(929\) | 1.04995e6 | + | 1.04995e6i | 1.21657 | + | 1.21657i | 0.968824 | + | 0.247751i | \(0.0796915\pi\) |
0.247751 | + | 0.968824i | \(0.420309\pi\) | |||||||
\(930\) | 17512.1 | − | 29160.5i | 0.0202475 | − | 0.0337154i | ||||
\(931\) | −167845. | −0.193646 | ||||||||
\(932\) | 457556. | − | 457556.i | 0.526760 | − | 0.526760i | ||||
\(933\) | 360949. | + | 1.44624e6i | 0.414651 | + | 1.66141i | ||||
\(934\) | 345769. | 0.396362 | ||||||||
\(935\) | 65.0742 | − | 15389.4i | 7.44364e−5 | − | 0.0176035i | ||||
\(936\) | −28892.5 | − | 54277.4i | −0.0329786 | − | 0.0619537i | ||||
\(937\) | 1.45718e6i | 1.65972i | 0.557970 | + | 0.829861i | \(0.311580\pi\) | ||||
−0.557970 | + | 0.829861i | \(0.688420\pi\) | |||||||
\(938\) | −30334.7 | + | 30334.7i | −0.0344774 | + | 0.0344774i | ||||
\(939\) | −343843. | − | 1.37770e6i | −0.389968 | − | 1.56252i | ||||
\(940\) | 34116.3 | + | 34116.3i | 0.0386105 | + | 0.0386105i | ||||
\(941\) | −371489. | − | 371489.i | −0.419534 | − | 0.419534i | 0.465509 | − | 0.885043i | \(-0.345871\pi\) |
−0.885043 | + | 0.465509i | \(0.845871\pi\) | |||||||
\(942\) | 90001.8 | − | 149868.i | 0.101426 | − | 0.168891i | ||||
\(943\) | − | 322186.i | − | 0.362312i | ||||||
\(944\) | −73588.8 | −0.0825787 | ||||||||
\(945\) | −3534.11 | + | 68355.2i | −0.00395746 | + | 0.0765435i | ||||
\(946\) | −36727.2 | + | 36727.2i | −0.0410398 | + | 0.0410398i | ||||
\(947\) | 937853. | − | 937853.i | 1.04577 | − | 1.04577i | 0.0468659 | − | 0.998901i | \(-0.485077\pi\) |
0.998901 | − | 0.0468659i | \(-0.0149233\pi\) | |||||||
\(948\) | −63360.2 | − | 253870.i | −0.0705018 | − | 0.282485i | ||||
\(949\) | 212026. | + | 212026.i | 0.235427 | + | 0.235427i | ||||
\(950\) | −261816. | −0.290101 | ||||||||
\(951\) | 1.12716e6 | − | 281313.i | 1.24630 | − | 0.311049i | ||||
\(952\) | −164746. | − | 166145.i | −0.181777 | − | 0.183321i | ||||
\(953\) | − | 1.50330e6i | − | 1.65523i | −0.561295 | − | 0.827616i | \(-0.689697\pi\) | ||
0.561295 | − | 0.827616i | \(-0.310303\pi\) | |||||||
\(954\) | 164051. | + | 308186.i | 0.180253 | + | 0.338623i | ||||
\(955\) | −4842.39 | − | 4842.39i | −0.00530949 | − | 0.00530949i | ||||
\(956\) | − | 311028.i | − | 0.340317i | ||||||
\(957\) | 64159.6 | − | 106836.i | 0.0700548 | − | 0.116653i | ||||
\(958\) | 162314. | − | 162314.i | 0.176858 | − | 0.176858i | ||||
\(959\) | 416237. | + | 416237.i | 0.452589 | + | 0.452589i | ||||
\(960\) | −2928.06 | − | 11732.1i | −0.00317715 | − | 0.0127301i | ||||
\(961\) | − | 664226.i | − | 0.719233i | ||||||
\(962\) | 92914.4 | + | 92914.4i | 0.100400 | + | 0.100400i | ||||
\(963\) | −1.19787e6 | − | 365611.i | −1.29169 | − | 0.394245i | ||||
\(964\) | 147877. | + | 147877.i | 0.159128 | + | 0.159128i | ||||
\(965\) | 106860.i | 0.114752i | ||||||||
\(966\) | −145552. | + | 242368.i | −0.155978 | + | 0.259730i | ||||
\(967\) | 1.49609e6i | 1.59994i | 0.600039 | + | 0.799970i | \(0.295152\pi\) | ||||
−0.600039 | + | 0.799970i | \(0.704848\pi\) | |||||||
\(968\) | − | 321970.i | − | 0.343609i | ||||||
\(969\) | 201946. | − | 333074.i | 0.215074 | − | 0.354727i | ||||
\(970\) | 42990.2 | 0.0456905 | ||||||||
\(971\) | 1.00846e6 | 1.06960 | 0.534798 | − | 0.844980i | \(-0.320388\pi\) | ||||
0.534798 | + | 0.844980i | \(0.320388\pi\) | |||||||
\(972\) | 200143. | + | 427898.i | 0.211840 | + | 0.452906i | ||||
\(973\) | −551166. | −0.582180 | ||||||||
\(974\) | −177153. | + | 177153.i | −0.186737 | + | 0.186737i | ||||
\(975\) | 159996. | + | 96084.5i | 0.168307 | + | 0.101075i | ||||
\(976\) | −174502. | + | 174502.i | −0.183190 | + | 0.183190i | ||||
\(977\) | −807334. | −0.845793 | −0.422896 | − | 0.906178i | \(-0.638987\pi\) | ||||
−0.422896 | + | 0.906178i | \(0.638987\pi\) | |||||||
\(978\) | 73774.7 | + | 295599.i | 0.0771311 | + | 0.309047i | ||||
\(979\) | 80099.8 | − | 80099.8i | 0.0835730 | − | 0.0835730i | ||||
\(980\) | 16637.3 | + | 16637.3i | 0.0173233 | + | 0.0173233i | ||||
\(981\) | 632875. | + | 193165.i | 0.657628 | + | 0.200720i | ||||
\(982\) | −244243. | −0.253279 | ||||||||
\(983\) | 381297. | − | 381297.i | 0.394599 | − | 0.394599i | −0.481724 | − | 0.876323i | \(-0.659989\pi\) |
0.876323 | + | 0.481724i | \(0.159989\pi\) | |||||||
\(984\) | 205089. | − | 51185.4i | 0.211812 | − | 0.0528635i | ||||
\(985\) | −34981.1 | −0.0360546 | ||||||||
\(986\) | −392726. | − | 396061.i | −0.403957 | − | 0.407388i | ||||
\(987\) | 718066. | − | 179213.i | 0.737106 | − | 0.183965i | ||||
\(988\) | 40192.5i | 0.0411747i | ||||||||
\(989\) | 198619. | − | 198619.i | 0.203062 | − | 0.203062i | ||||
\(990\) | −5732.57 | − | 10769.2i | −0.00584897 | − | 0.0109879i | ||||
\(991\) | −1.03511e6 | − | 1.03511e6i | −1.05399 | − | 1.05399i | −0.998457 | − | 0.0555356i | \(-0.982313\pi\) |
−0.0555356 | − | 0.998457i | \(-0.517687\pi\) | |||||||
\(992\) | 65178.8 | + | 65178.8i | 0.0662344 | + | 0.0662344i | ||||
\(993\) | −1.55829e6 | − | 935815.i | −1.58033 | − | 0.949055i | ||||
\(994\) | 391512.i | 0.396253i | ||||||||
\(995\) | −97296.5 | −0.0982769 | ||||||||
\(996\) | −233469. | + | 388765.i | −0.235348 | + | 0.391894i | ||||
\(997\) | −193552. | + | 193552.i | −0.194718 | + | 0.194718i | −0.797731 | − | 0.603013i | \(-0.793967\pi\) |
0.603013 | + | 0.797731i | \(0.293967\pi\) | |||||||
\(998\) | −926651. | + | 926651.i | −0.930368 | + | 0.930368i | ||||
\(999\) | −676018. | − | 749732.i | −0.677372 | − | 0.751234i |
(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 | 102.5.e.a.47.21 | yes | 48 | |
3.2 | odd | 2 | inner | 102.5.e.a.47.3 | ✓ | 48 | |
17.4 | even | 4 | inner | 102.5.e.a.89.3 | yes | 48 | |
51.38 | odd | 4 | inner | 102.5.e.a.89.21 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
102.5.e.a.47.3 | ✓ | 48 | 3.2 | odd | 2 | inner | |
102.5.e.a.47.21 | yes | 48 | 1.1 | even | 1 | trivial | |
102.5.e.a.89.3 | yes | 48 | 17.4 | even | 4 | inner | |
102.5.e.a.89.21 | yes | 48 | 51.38 | odd | 4 | inner |