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 | 89.21 | ||
Character | \(\chi\) | \(=\) | 102.89 |
Dual form | 102.5.e.a.47.21 |
$q$-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 \(\left(\mathbb{Z}/102\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | 0.743243 | − | 0.669022i | \(-0.233287\pi\) |
−0.669022 | + | 0.743243i | \(0.733287\pi\) | |||||||
\(6\) | 13.1056 | + | 21.8230i | 0.364045 | + | 0.606194i | ||||
\(7\) | 25.3003 | + | 25.3003i | 0.516332 | + | 0.516332i | 0.916460 | − | 0.400127i | \(-0.131034\pi\) |
−0.400127 | + | 0.916460i | \(0.631034\pi\) | |||||||
\(8\) | 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 | −0.645322 | − | 0.763911i | \(-0.723277\pi\) |
0.763911 | + | 0.645322i | \(0.223277\pi\) | |||||||
\(12\) | 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 | \(-0.933494\pi\) | ||
0.978253 | − | 0.207417i | \(-0.0665058\pi\) | |||||||
\(20\) | 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 | −0.883444 | − | 0.468537i | \(-0.844781\pi\) |
0.468537 | + | 0.883444i | \(0.344781\pi\) | |||||||
\(24\) | 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 | 0.933164 | − | 0.359451i | \(-0.117036\pi\) |
−0.359451 | + | 0.933164i | \(0.617036\pi\) | |||||||
\(30\) | −16.1754 | + | 64.8112i | −0.0179727 | + | 0.0720124i | ||||
\(31\) | 360.066 | − | 360.066i | 0.374678 | − | 0.374678i | −0.494500 | − | 0.869178i | \(-0.664649\pi\) |
0.869178 | + | 0.494500i | \(0.164649\pi\) | |||||||
\(32\) | 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 | −0.252373 | − | 0.967630i | \(-0.581211\pi\) |
0.967630 | + | 0.252373i | \(0.0812109\pi\) | |||||||
\(38\) | − | 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 | −0.454254 | − | 0.890872i | \(-0.650094\pi\) |
0.890872 | + | 0.454254i | \(0.150094\pi\) | |||||||
\(42\) | −220.552 | + | 883.703i | −0.125030 | + | 0.500966i | ||||
\(43\) | − | 904.929i | − | 0.489415i | −0.969597 | − | 0.244708i | \(-0.921308\pi\) | ||
0.969597 | − | 0.244708i | \(-0.0786920\pi\) | |||||||
\(44\) | 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 | \(-0.825854\pi\) | ||
0.854040 | − | 0.520208i | \(-0.174146\pi\) | |||||||
\(48\) | 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 | 0.238407 | − | 0.971165i | \(-0.423375\pi\) |
−0.971165 | + | 0.238407i | \(0.923375\pi\) | |||||||
\(62\) | 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 | 0.381648 | − | 0.924308i | \(-0.375357\pi\) |
−0.924308 | + | 0.381648i | \(0.875357\pi\) | |||||||
\(72\) | −861.216 | + | 1617.88i | −0.166130 | + | 0.312091i | ||||
\(73\) | 6319.99 | − | 6319.99i | 1.18596 | − | 1.18596i | 0.207788 | − | 0.978174i | \(-0.433373\pi\) |
0.978174 | − | 0.207788i | \(-0.0666266\pi\) | |||||||
\(74\) | 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 | 0.882347 | − | 0.470599i | \(-0.155962\pi\) |
−0.470599 | + | 0.882347i | \(0.655962\pi\) | |||||||
\(80\) | 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 | \(0.114622\pi\) | ||||
−0.935863 | + | 0.352365i | \(0.885378\pi\) | |||||||
\(90\) | −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 | −0.455131 | − | 0.890424i | \(-0.650408\pi\) |
0.890424 | + | 0.455131i | \(0.150408\pi\) | |||||||
\(98\) | − | 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 | \(0.374655\pi\) | ||||
−0.383685 | + | 0.923464i | \(0.625345\pi\) | |||||||
\(102\) | −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 | 0.999028 | − | 0.0440727i | \(-0.0140333\pi\) |
−0.0440727 | + | 0.999028i | \(0.514033\pi\) | |||||||
\(108\) | −5824.22 | + | 301.125i | −0.499333 | + | 0.0258166i | ||||
\(109\) | −5776.43 | − | 5776.43i | −0.486191 | − | 0.486191i | 0.420911 | − | 0.907102i | \(-0.361710\pi\) |
−0.907102 | + | 0.420911i | \(0.861710\pi\) | |||||||
\(110\) | 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 | −0.962462 | − | 0.271415i | \(-0.912508\pi\) |
0.271415 | + | 0.962462i | \(0.412508\pi\) | |||||||
\(114\) | 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 | \(0.233383\pi\) | ||||
−0.743041 | + | 0.669246i | \(0.766617\pi\) | |||||||
\(128\) | 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 | 0.932269 | − | 0.361766i | \(-0.117826\pi\) |
−0.361766 | + | 0.932269i | \(0.617826\pi\) | |||||||
\(132\) | 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 | \(-0.855590\pi\) | ||
0.898842 | − | 0.438273i | \(-0.144410\pi\) | |||||||
\(138\) | −7666.33 | − | 1913.34i | −0.402559 | − | 0.100469i | ||||
\(139\) | −10892.5 | + | 10892.5i | −0.563765 | + | 0.563765i | −0.930375 | − | 0.366610i | \(-0.880518\pi\) |
0.366610 | + | 0.930375i | \(0.380518\pi\) | |||||||
\(140\) | 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 | \(-0.789893\pi\) | ||
0.789948 | − | 0.613174i | \(-0.210107\pi\) | |||||||
\(150\) | 13489.1 | − | 8100.76i | 0.599515 | − | 0.360034i | ||||
\(151\) | 36111.8i | 1.58378i | 0.610662 | + | 0.791891i | \(0.290903\pi\) | ||||
−0.610662 | + | 0.791891i | \(0.709097\pi\) | |||||||
\(152\) | − | 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 | 0.529674 | − | 0.848201i | \(-0.322314\pi\) |
−0.848201 | + | 0.529674i | \(0.822314\pi\) | |||||||
\(164\) | 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 | 0.510504 | − | 0.859875i | \(-0.329459\pi\) |
−0.859875 | + | 0.510504i | \(0.829459\pi\) | |||||||
\(168\) | −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 | −0.983587 | − | 0.180432i | \(-0.942250\pi\) |
−0.180432 | − | 0.983587i | \(-0.557750\pi\) | |||||||
\(174\) | −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 | 0.0172553 | − | 0.999851i | \(-0.494507\pi\) |
−0.999851 | + | 0.0172553i | \(0.994507\pi\) | |||||||
\(182\) | 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 | \(0.0113877\pi\) | ||||
−0.999360 | + | 0.0357680i | \(0.988612\pi\) | |||||||
\(192\) | 2372.37 | + | 3950.38i | 0.0643546 | + | 0.107161i | ||||
\(193\) | −28794.9 | − | 28794.9i | −0.773039 | − | 0.773039i | 0.205598 | − | 0.978637i | \(-0.434086\pi\) |
−0.978637 | + | 0.205598i | \(0.934086\pi\) | |||||||
\(194\) | 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 | −0.818043 | − | 0.575157i | \(-0.804941\pi\) |
0.575157 | + | 0.818043i | \(0.304941\pi\) | |||||||
\(198\) | 1357.19 | + | 4446.64i | 0.0346188 | + | 0.113423i | ||||
\(199\) | −26218.0 | + | 26218.0i | −0.662053 | + | 0.662053i | −0.955864 | − | 0.293811i | \(-0.905076\pi\) |
0.293811 | + | 0.955864i | \(0.405076\pi\) | |||||||
\(200\) | − | 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 | 0.975900 | − | 0.218217i | \(-0.0700240\pi\) |
−0.218217 | + | 0.975900i | \(0.570024\pi\) | |||||||
\(212\) | −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 | \(0.0559631\pi\) | ||||
−0.984585 | + | 0.174909i | \(0.944037\pi\) | |||||||
\(224\) | 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 | −0.862198 | − | 0.506571i | \(-0.830913\pi\) |
0.506571 | + | 0.862198i | \(0.330913\pi\) | |||||||
\(228\) | 9243.61 | − | 5551.17i | 0.177816 | − | 0.106786i | ||||
\(229\) | − | 7235.68i | − | 0.137978i | −0.997617 | − | 0.0689888i | \(-0.978023\pi\) | ||
0.997617 | − | 0.0689888i | \(-0.0219773\pi\) | |||||||
\(230\) | −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 | 0.998484 | + | 0.0550346i | \(0.0175269\pi\) |
0.0550346 | + | 0.998484i | \(0.482473\pi\) | |||||||
\(234\) | −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 | \(0.110534\pi\) | ||||
−0.940311 | + | 0.340317i | \(0.889466\pi\) | |||||||
\(240\) | −366.007 | + | 1466.51i | −0.00635429 | + | 0.0254602i | ||||
\(241\) | 18484.7 | − | 18484.7i | 0.318257 | − | 0.318257i | −0.529840 | − | 0.848097i | \(-0.677748\pi\) |
0.848097 | + | 0.529840i | \(0.177748\pi\) | |||||||
\(242\) | 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 | \(0.0892998\pi\) | ||||
−0.960905 | + | 0.276878i | \(0.910700\pi\) | |||||||
\(252\) | −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 | 0.808420 | − | 0.588605i | \(-0.200323\pi\) |
−0.588605 | + | 0.808420i | \(0.700323\pi\) | |||||||
\(270\) | −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 | 0.421285 | − | 0.906928i | \(-0.361579\pi\) |
0.906928 | − | 0.421285i | \(-0.138421\pi\) | |||||||
\(278\) | −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 | −0.999995 | − | 0.00310644i | \(-0.999011\pi\) |
−0.00310644 | − | 0.999995i | \(-0.500989\pi\) | |||||||
\(284\) | −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 | \(-0.884782\pi\) | ||
0.935202 | − | 0.354114i | \(-0.115218\pi\) | |||||||
\(294\) | 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 | −0.970753 | − | 0.240079i | \(-0.922827\pi\) |
−0.240079 | − | 0.970753i | \(-0.577173\pi\) | |||||||
\(312\) | 3517.38 | + | 5857.02i | 0.0361335 | + | 0.0601683i | ||||
\(313\) | 111563. | + | 111563.i | 1.13876 | + | 1.13876i | 0.988673 | + | 0.150083i | \(0.0479540\pi\) |
0.150083 | + | 0.988673i | \(0.452046\pi\) | |||||||
\(314\) | 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 | −0.0878337 | − | 0.996135i | \(-0.527994\pi\) |
0.996135 | + | 0.0878337i | \(0.0279944\pi\) | |||||||
\(318\) | −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 | \(0.373203\pi\) | ||||
−0.387893 | + | 0.921705i | \(0.626797\pi\) | |||||||
\(332\) | −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 | −0.740334 | − | 0.672239i | \(-0.765333\pi\) |
0.672239 | + | 0.740334i | \(0.265333\pi\) | |||||||
\(338\) | −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 | −0.399000 | − | 0.916951i | \(-0.630643\pi\) |
0.916951 | + | 0.399000i | \(0.130643\pi\) | |||||||
\(348\) | −11896.6 | + | 47666.9i | −0.0982343 | + | 0.393603i | ||||
\(349\) | 25887.9i | 0.212543i | 0.994337 | + | 0.106271i | \(0.0338912\pi\) | ||||
−0.994337 | + | 0.106271i | \(0.966109\pi\) | |||||||
\(350\) | 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 | \(-0.903694\pi\) | ||
0.954578 | − | 0.297960i | \(-0.0963061\pi\) | |||||||
\(354\) | −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 | 0.686954 | − | 0.726701i | \(-0.258947\pi\) |
−0.726701 | + | 0.686954i | \(0.758947\pi\) | |||||||
\(368\) | −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 | −0.397891 | − | 0.917433i | \(-0.630258\pi\) |
0.917433 | + | 0.397891i | \(0.130258\pi\) | |||||||
\(380\) | 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 | 0.360335 | − | 0.932823i | \(-0.382662\pi\) |
−0.932823 | + | 0.360335i | \(0.882662\pi\) | |||||||
\(398\) | −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 | −0.856640 | − | 0.515915i | \(-0.827452\pi\) |
0.515915 | + | 0.856640i | \(0.327452\pi\) | |||||||
\(402\) | −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 | −0.820323 | − | 0.571900i | \(-0.806206\pi\) |
0.571900 | + | 0.820323i | \(0.306206\pi\) | |||||||
\(420\) | −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 | −0.996256 | − | 0.0864491i | \(-0.972448\pi\) |
0.0864491 | + | 0.996256i | \(0.472448\pi\) | |||||||
\(432\) | −46593.8 | + | 2409.00i | −0.249667 | + | 0.0129083i | ||||
\(433\) | 308901.i | 1.64757i | 0.566903 | + | 0.823785i | \(0.308142\pi\) | ||||
−0.566903 | + | 0.823785i | \(0.691858\pi\) | |||||||
\(434\) | 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 | −0.356957 | − | 0.934121i | \(-0.616186\pi\) |
0.934121 | + | 0.356957i | \(0.116186\pi\) | |||||||
\(440\) | 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 | \(0.186259\pi\) | ||||
−0.833629 | + | 0.552325i | \(0.813741\pi\) | |||||||
\(444\) | 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 | 0.0259193 | − | 0.999664i | \(-0.491749\pi\) |
0.999664 | − | 0.0259193i | \(-0.00825131\pi\) | |||||||
\(450\) | 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 | \(0.324565\pi\) | ||||
−0.523662 | + | 0.851926i | \(0.675435\pi\) | |||||||
\(458\) | − | 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 | 0.821018 | − | 0.570903i | \(-0.193407\pi\) |
−0.570903 | + | 0.821018i | \(0.693407\pi\) | |||||||
\(480\) | −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 | 0.562626 | − | 0.826712i | \(-0.309791\pi\) |
−0.826712 | + | 0.562626i | \(0.809791\pi\) | |||||||
\(488\) | −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 | −0.917114 | − | 0.398626i | \(-0.869487\pi\) |
−0.398626 | − | 0.917114i | \(-0.630513\pi\) | |||||||
\(500\) | 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 | −0.151729 | + | 0.988422i | \(0.548484\pi\) |
−0.988422 | + | 0.151729i | \(0.951516\pi\) | |||||||
\(504\) | −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 | \(-0.862037\pi\) | ||
0.907533 | − | 0.419981i | \(-0.137963\pi\) | |||||||
\(510\) | −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 | −0.850506 | − | 0.525966i | \(-0.823704\pi\) |
0.525966 | + | 0.850506i | \(0.323704\pi\) | |||||||
\(522\) | −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 | −0.194241 | − | 0.980954i | \(-0.562224\pi\) |
0.980954 | + | 0.194241i | \(0.0622245\pi\) | |||||||
\(542\) | −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 | −0.569457 | − | 0.822021i | \(-0.692846\pi\) |
0.822021 | + | 0.569457i | \(0.192846\pi\) | |||||||
\(548\) | − | 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 | \(-0.826827\pi\) | ||
0.855625 | − | 0.517596i | \(-0.173173\pi\) | |||||||
\(558\) | 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 | 0.710721 | − | 0.703474i | \(-0.248369\pi\) |
−0.703474 | + | 0.710721i | \(0.748369\pi\) | |||||||
\(572\) | 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 | \(-0.979304\pi\) | ||
0.997887 | − | 0.0649741i | \(-0.0206965\pi\) | |||||||
\(600\) | 107913. | − | 64806.1i | 0.299758 | − | 0.180017i | ||||
\(601\) | 252512. | + | 252512.i | 0.699091 | + | 0.699091i | 0.964215 | − | 0.265123i | \(-0.0854126\pi\) |
−0.265123 | + | 0.964215i | \(0.585413\pi\) | |||||||
\(602\) | 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 | −0.594800 | − | 0.803874i | \(-0.702769\pi\) |
0.803874 | + | 0.594800i | \(0.202769\pi\) | |||||||
\(608\) | − | 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 | 0.912751 | − | 0.408516i | \(-0.133954\pi\) |
−0.408516 | + | 0.912751i | \(0.633954\pi\) | |||||||
\(618\) | 70582.5 | + | 117531.i | 0.184808 | + | 0.307735i | ||||
\(619\) | 418394. | + | 418394.i | 1.09195 | + | 1.09195i | 0.995320 | + | 0.0966325i | \(0.0308071\pi\) |
0.0966325 | + | 0.995320i | \(0.469193\pi\) | |||||||
\(620\) | 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 | \(0.0959805\pi\) | ||||
−0.954883 | + | 0.296983i | \(0.904020\pi\) | |||||||
\(632\) | 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 | 0.602095 | − | 0.798424i | \(-0.294333\pi\) |
−0.798424 | + | 0.602095i | \(0.794333\pi\) | |||||||
\(642\) | −95309.6 | + | 381884.i | −0.231242 | + | 0.926535i | ||||
\(643\) | −132413. | + | 132413.i | −0.320264 | + | 0.320264i | −0.848868 | − | 0.528604i | \(-0.822716\pi\) |
0.528604 | + | 0.848868i | \(0.322716\pi\) | |||||||
\(644\) | −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 | \(0.154649\pi\) | ||||
−0.884281 | + | 0.466955i | \(0.845351\pi\) | |||||||
\(648\) | −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 | −0.698144 | − | 0.715958i | \(-0.745990\pi\) |
0.715958 | + | 0.698144i | \(0.245990\pi\) | |||||||
\(654\) | 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 | \(-0.960646\pi\) | ||
0.992367 | − | 0.123319i | \(-0.0393540\pi\) | |||||||
\(660\) | 1973.92 | + | 3286.90i | 0.00453150 | + | 0.00754568i | ||||
\(661\) | − | 348318.i | − | 0.797210i | −0.917123 | − | 0.398605i | \(-0.869495\pi\) | ||
0.917123 | − | 0.398605i | \(-0.130505\pi\) | |||||||
\(662\) | 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 | 0.968535 | + | 0.248879i | \(0.0800620\pi\) |
0.248879 | + | 0.968535i | \(0.419938\pi\) | |||||||
\(674\) | −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 | 0.992855 | + | 0.119328i | \(0.0380739\pi\) |
0.119328 | + | 0.992855i | \(0.461926\pi\) | |||||||
\(678\) | −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 | 0.0106031 | − | 0.999944i | \(-0.496625\pi\) |
−0.999944 | + | 0.0106031i | \(0.996625\pi\) | |||||||
\(684\) | 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 | 0.900362 | − | 0.435142i | \(-0.143302\pi\) |
−0.435142 | + | 0.900362i | \(0.643302\pi\) | |||||||
\(692\) | −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 | \(-0.908016\pi\) | ||
0.958536 | − | 0.284971i | \(-0.0919839\pi\) | |||||||
\(702\) | −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 | 0.114760 | − | 0.993393i | \(-0.463390\pi\) |
0.993393 | − | 0.114760i | \(-0.0366098\pi\) | |||||||
\(710\) | − | 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 | 0.993577 | + | 0.113156i | \(0.0360960\pi\) |
0.113156 | + | 0.993577i | \(0.463904\pi\) | |||||||
\(720\) | −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 | \(-0.719534\pi\) | ||
0.636296 | − | 0.771445i | \(-0.280466\pi\) | |||||||
\(734\) | −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 | \(-0.905894\pi\) | ||
0.956615 | − | 0.291356i | \(-0.0941063\pi\) | |||||||
\(740\) | 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 | 0.888514 | − | 0.458850i | \(-0.151738\pi\) |
−0.458850 | + | 0.888514i | \(0.651738\pi\) | |||||||
\(744\) | 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 | −0.519247 | − | 0.854624i | \(-0.673788\pi\) |
0.854624 | + | 0.519247i | \(0.173788\pi\) | |||||||
\(752\) | − | 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 | \(-0.836593\pi\) | ||
0.871100 | − | 0.491106i | \(-0.163407\pi\) | |||||||
\(758\) | 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 | \(-0.671554\pi\) | ||
0.513239 | − | 0.858246i | \(-0.328446\pi\) | |||||||
\(762\) | −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 | −0.236599 | + | 0.971607i | \(0.576033\pi\) |
−0.971607 | + | 0.236599i | \(0.923967\pi\) | |||||||
\(788\) | −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 | −0.738636 | − | 0.674104i | \(-0.764530\pi\) |
0.674104 | + | 0.738636i | \(0.264530\pi\) | |||||||
\(810\) | 9336.60 | − | 47793.2i | 0.0142304 | − | 0.0728443i | ||||
\(811\) | 260693. | − | 260693.i | 0.396358 | − | 0.396358i | −0.480589 | − | 0.876946i | \(-0.659577\pi\) |
0.876946 | + | 0.480589i | \(0.159577\pi\) | |||||||
\(812\) | 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 | 0.812482 | − | 0.582987i | \(-0.198116\pi\) |
−0.582987 | + | 0.812482i | \(0.698116\pi\) | |||||||
\(822\) | 359029. | − | 215612.i | 0.531357 | − | 0.319102i | ||||
\(823\) | −133830. | − | 133830.i | −0.197585 | − | 0.197585i | 0.601379 | − | 0.798964i | \(-0.294618\pi\) |
−0.798964 | + | 0.601379i | \(0.794618\pi\) | |||||||
\(824\) | 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 | 0.208377 | − | 0.978049i | \(-0.433182\pi\) |
0.978049 | − | 0.208377i | \(-0.0668180\pi\) | |||||||
\(828\) | −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 | −0.925586 | − | 0.378538i | \(-0.876427\pi\) |
0.378538 | + | 0.925586i | \(0.376427\pi\) | |||||||
\(840\) | −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 | −0.817255 | − | 0.576276i | \(-0.804505\pi\) |
0.576276 | + | 0.817255i | \(0.304505\pi\) | |||||||
\(854\) | − | 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 | −0.744198 | − | 0.667960i | \(-0.767168\pi\) |
0.667960 | + | 0.744198i | \(0.267168\pi\) | |||||||
\(858\) | 16814.4 | + | 4196.50i | 0.0228406 | + | 0.00570049i | ||||
\(859\) | 714142.i | 0.967828i | 0.875116 | + | 0.483914i | \(0.160785\pi\) | ||||
−0.875116 | + | 0.483914i | \(0.839215\pi\) | |||||||
\(860\) | 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 | \(-0.884141\pi\) | ||
0.934487 | − | 0.355997i | \(-0.115859\pi\) | |||||||
\(864\) | −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 | 0.313055 | − | 0.949735i | \(-0.398648\pi\) |
−0.949735 | + | 0.313055i | \(0.898648\pi\) | |||||||
\(878\) | 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 | 0.232076 | − | 0.972698i | \(-0.425448\pi\) |
−0.972698 | + | 0.232076i | \(0.925448\pi\) | |||||||
\(882\) | 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 | 0.331664 | − | 0.943398i | \(-0.392390\pi\) |
−0.943398 | + | 0.331664i | \(0.892390\pi\) | |||||||
\(888\) | 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 | 0.984855 | − | 0.173381i | \(-0.0554691\pi\) |
−0.173381 | + | 0.984855i | \(0.555469\pi\) | |||||||
\(908\) | −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 | −0.962049 | − | 0.272878i | \(-0.912024\pi\) |
0.272878 | + | 0.962049i | \(0.412024\pi\) | |||||||
\(912\) | 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 | 0.247751 | − | 0.968824i | \(-0.420309\pi\) |
0.968824 | − | 0.247751i | \(-0.0796915\pi\) | |||||||
\(930\) | 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 | \(-0.688420\pi\) | ||
0.557970 | − | 0.829861i | \(-0.311580\pi\) | |||||||
\(938\) | −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 | −0.885043 | − | 0.465509i | \(-0.845871\pi\) |
0.465509 | + | 0.885043i | \(0.345871\pi\) | |||||||
\(942\) | 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 | 0.998901 | + | 0.0468659i | \(0.0149233\pi\) |
0.0468659 | + | 0.998901i | \(0.485077\pi\) | |||||||
\(948\) | −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 | \(0.310303\pi\) | ||||
−0.561295 | + | 0.827616i | \(0.689697\pi\) | |||||||
\(954\) | 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 | \(-0.704848\pi\) | ||
0.600039 | − | 0.799970i | \(-0.295152\pi\) | |||||||
\(968\) | 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 | 0.876323 | − | 0.481724i | \(-0.159989\pi\) |
−0.481724 | + | 0.876323i | \(0.659989\pi\) | |||||||
\(984\) | 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 | −0.0555356 | + | 0.998457i | \(0.517687\pi\) |
−0.998457 | + | 0.0555356i | \(0.982313\pi\) | |||||||
\(992\) | 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 | 0.603013 | − | 0.797731i | \(-0.293967\pi\) |
−0.797731 | + | 0.603013i | \(0.793967\pi\) | |||||||
\(998\) | −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.89.21 | yes | 48 | |
3.2 | odd | 2 | inner | 102.5.e.a.89.3 | yes | 48 | |
17.13 | even | 4 | inner | 102.5.e.a.47.3 | ✓ | 48 | |
51.47 | odd | 4 | inner | 102.5.e.a.47.21 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
102.5.e.a.47.3 | ✓ | 48 | 17.13 | even | 4 | inner | |
102.5.e.a.47.21 | yes | 48 | 51.47 | odd | 4 | inner | |
102.5.e.a.89.3 | yes | 48 | 3.2 | odd | 2 | inner | |
102.5.e.a.89.21 | yes | 48 | 1.1 | even | 1 | trivial |