Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(80,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.80");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.p (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 80.2 | ||
Character | \(\chi\) | \(=\) | 441.80 |
Dual form | 441.4.p.d.215.2 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.66169 | + | 2.69143i | −1.64816 | + | 0.951563i | −0.670351 | + | 0.742044i | \(0.733857\pi\) |
−0.977804 | + | 0.209519i | \(0.932810\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 10.4876 | − | 18.1650i | 1.31095 | − | 2.27062i | ||||
\(5\) | 9.16288 | + | 15.8706i | 0.819553 | + | 1.41951i | 0.906012 | + | 0.423252i | \(0.139112\pi\) |
−0.0864589 | + | 0.996255i | \(0.527555\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 69.8432i | 3.08666i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −85.4290 | − | 49.3225i | −2.70150 | − | 1.55971i | ||||
\(11\) | −20.5857 | − | 11.8852i | −0.564256 | − | 0.325773i | 0.190596 | − | 0.981669i | \(-0.438958\pi\) |
−0.754852 | + | 0.655895i | \(0.772291\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 11.7971i | − | 0.251686i | −0.992050 | − | 0.125843i | \(-0.959836\pi\) | ||
0.992050 | − | 0.125843i | \(-0.0401636\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −104.077 | − | 180.267i | −1.62621 | − | 2.81668i | ||||
\(17\) | 48.2099 | − | 83.5020i | 0.687801 | − | 1.19131i | −0.284746 | − | 0.958603i | \(-0.591909\pi\) |
0.972548 | − | 0.232704i | \(-0.0747573\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.1933 | − | 10.5039i | 0.219675 | − | 0.126830i | −0.386125 | − | 0.922447i | \(-0.626187\pi\) |
0.605800 | + | 0.795617i | \(0.292853\pi\) | |||||||
\(20\) | 384.385 | 4.29756 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 127.952 | 1.23998 | ||||||||
\(23\) | −132.203 | + | 76.3277i | −1.19854 | + | 0.691975i | −0.960229 | − | 0.279215i | \(-0.909926\pi\) |
−0.238307 | + | 0.971190i | \(0.576592\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −105.417 | + | 182.587i | −0.843334 | + | 1.46070i | ||||
\(26\) | 31.7509 | + | 54.9943i | 0.239495 | + | 0.414818i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 77.5438i | − | 0.496535i | −0.968691 | − | 0.248268i | \(-0.920139\pi\) | ||
0.968691 | − | 0.248268i | \(-0.0798612\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −172.974 | − | 99.8667i | −1.00216 | − | 0.578600i | −0.0932764 | − | 0.995640i | \(-0.529734\pi\) |
−0.908888 | + | 0.417040i | \(0.863067\pi\) | |||||||
\(32\) | 486.465 | + | 280.861i | 2.68737 | + | 1.55155i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 519.014i | 2.61795i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −82.1957 | − | 142.367i | −0.365213 | − | 0.632568i | 0.623597 | − | 0.781746i | \(-0.285671\pi\) |
−0.988810 | + | 0.149178i | \(0.952337\pi\) | |||||||
\(38\) | −56.5410 | + | 97.9319i | −0.241373 | + | 0.418070i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1108.45 | + | 639.965i | −4.38154 | + | 2.52968i | ||||
\(41\) | −435.473 | −1.65877 | −0.829384 | − | 0.558679i | \(-0.811308\pi\) | ||||
−0.829384 | + | 0.558679i | \(0.811308\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −106.148 | −0.376451 | −0.188226 | − | 0.982126i | \(-0.560274\pi\) | ||||
−0.188226 | + | 0.982126i | \(0.560274\pi\) | |||||||
\(44\) | −431.787 | + | 249.293i | −1.47942 | + | 0.854142i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 410.861 | − | 711.632i | 1.31692 | − | 2.28097i | ||||
\(47\) | −5.52293 | − | 9.56599i | −0.0171405 | − | 0.0296882i | 0.857328 | − | 0.514771i | \(-0.172123\pi\) |
−0.874468 | + | 0.485082i | \(0.838790\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 1134.89i | − | 3.20994i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −214.294 | − | 123.722i | −0.571484 | − | 0.329947i | ||||
\(53\) | 96.0735 | + | 55.4681i | 0.248995 | + | 0.143757i | 0.619304 | − | 0.785151i | \(-0.287415\pi\) |
−0.370309 | + | 0.928909i | \(0.620748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 435.609i | − | 1.06795i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 208.703 | + | 361.485i | 0.472485 | + | 0.818367i | ||||
\(59\) | −414.518 | + | 717.966i | −0.914672 | + | 1.58426i | −0.107291 | + | 0.994228i | \(0.534218\pi\) |
−0.807381 | + | 0.590031i | \(0.799116\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 19.5452 | − | 11.2845i | 0.0410248 | − | 0.0236857i | −0.479347 | − | 0.877625i | \(-0.659127\pi\) |
0.520372 | + | 0.853940i | \(0.325793\pi\) | |||||||
\(62\) | 1075.14 | 2.20230 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1358.43 | −2.65318 | ||||||||
\(65\) | 187.226 | − | 108.095i | 0.357270 | − | 0.206270i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −199.265 | + | 345.137i | −0.363345 | + | 0.629331i | −0.988509 | − | 0.151162i | \(-0.951699\pi\) |
0.625164 | + | 0.780493i | \(0.285032\pi\) | |||||||
\(68\) | −1011.21 | − | 1751.47i | −1.80334 | − | 3.12348i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 228.153i | 0.381363i | 0.981652 | + | 0.190682i | \(0.0610698\pi\) | ||||
−0.981652 | + | 0.190682i | \(0.938930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 231.194 | + | 133.480i | 0.370674 | + | 0.214009i | 0.673753 | − | 0.738957i | \(-0.264681\pi\) |
−0.303079 | + | 0.952966i | \(0.598014\pi\) | |||||||
\(74\) | 766.341 | + | 442.447i | 1.20386 | + | 0.695047i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 440.641i | − | 0.665066i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −460.333 | − | 797.321i | −0.655589 | − | 1.13551i | −0.981746 | − | 0.190198i | \(-0.939087\pi\) |
0.326156 | − | 0.945316i | \(-0.394246\pi\) | |||||||
\(80\) | 1907.30 | − | 3303.54i | 2.66553 | − | 4.61683i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2030.04 | − | 1172.04i | 2.73391 | − | 1.57842i | ||||
\(83\) | −642.787 | −0.850061 | −0.425031 | − | 0.905179i | \(-0.639737\pi\) | ||||
−0.425031 | + | 0.905179i | \(0.639737\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1766.97 | 2.25476 | ||||||||
\(86\) | 494.828 | − | 285.689i | 0.620450 | − | 0.358217i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 830.097 | − | 1437.77i | 1.00555 | − | 1.74167i | ||||
\(89\) | −222.627 | − | 385.601i | −0.265150 | − | 0.459254i | 0.702453 | − | 0.711731i | \(-0.252088\pi\) |
−0.967603 | + | 0.252476i | \(0.918755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3201.97i | 3.62856i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 51.4923 | + | 29.7291i | 0.0565003 | + | 0.0326205i | ||||
\(95\) | 333.406 | + | 192.492i | 0.360071 | + | 0.207887i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1617.57i | − | 1.69319i | −0.532236 | − | 0.846596i | \(-0.678648\pi\) | ||
0.532236 | − | 0.846596i | \(-0.321352\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2211.13 | + | 3829.79i | 2.21113 | + | 3.82979i | ||||
\(101\) | −37.5166 | + | 64.9806i | −0.0369608 | + | 0.0640180i | −0.883914 | − | 0.467649i | \(-0.845101\pi\) |
0.846953 | + | 0.531667i | \(0.178434\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 834.971 | − | 482.071i | 0.798759 | − | 0.461164i | −0.0442780 | − | 0.999019i | \(-0.514099\pi\) |
0.843037 | + | 0.537856i | \(0.180765\pi\) | |||||||
\(104\) | 823.945 | 0.776870 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −597.153 | −0.547176 | ||||||||
\(107\) | 1153.79 | − | 666.138i | 1.04244 | − | 0.601851i | 0.121914 | − | 0.992541i | \(-0.461097\pi\) |
0.920522 | + | 0.390690i | \(0.127764\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 445.080 | − | 770.901i | 0.391110 | − | 0.677422i | −0.601487 | − | 0.798883i | \(-0.705425\pi\) |
0.992596 | + | 0.121461i | \(0.0387580\pi\) | |||||||
\(110\) | 1172.41 | + | 2030.67i | 1.01623 | + | 1.76016i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1240.25i | − | 1.03251i | −0.856436 | − | 0.516253i | \(-0.827326\pi\) | ||
0.856436 | − | 0.516253i | \(-0.172674\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2422.73 | − | 1398.76i | −1.96453 | − | 1.13422i | ||||
\(116\) | −1408.58 | − | 813.245i | −1.12744 | − | 0.650930i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 4462.58i | − | 3.48147i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −382.986 | − | 663.352i | −0.287743 | − | 0.498386i | ||||
\(122\) | −60.7426 | + | 105.209i | −0.0450768 | + | 0.0780754i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3628.16 | + | 2094.72i | −2.62756 | + | 1.51703i | ||||
\(125\) | −1572.97 | −1.12552 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1338.38 | 0.935137 | 0.467569 | − | 0.883957i | \(-0.345130\pi\) | ||||
0.467569 | + | 0.883957i | \(0.345130\pi\) | |||||||
\(128\) | 2440.84 | − | 1409.22i | 1.68548 | − | 0.973114i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −581.860 | + | 1007.81i | −0.392558 | + | 0.679930i | ||||
\(131\) | −1156.91 | − | 2003.82i | −0.771597 | − | 1.33645i | −0.936687 | − | 0.350167i | \(-0.886125\pi\) |
0.165090 | − | 0.986279i | \(-0.447209\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 2145.23i | − | 1.38298i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5832.05 | + | 3367.13i | 3.67716 | + | 2.12301i | ||||
\(137\) | −1915.10 | − | 1105.68i | −1.19429 | − | 0.689524i | −0.235014 | − | 0.971992i | \(-0.575514\pi\) |
−0.959277 | + | 0.282468i | \(0.908847\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2718.66i | 1.65895i | 0.558545 | + | 0.829474i | \(0.311360\pi\) | ||||
−0.558545 | + | 0.829474i | \(0.688640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −614.058 | − | 1063.58i | −0.362891 | − | 0.628546i | ||||
\(143\) | −140.210 | + | 242.851i | −0.0819926 | + | 0.142015i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1230.66 | − | 710.524i | 0.704835 | − | 0.406937i | ||||
\(146\) | −1437.01 | −0.814572 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3448.13 | −1.91510 | ||||||||
\(149\) | −1589.86 | + | 917.904i | −0.874135 | + | 0.504682i | −0.868720 | − | 0.495303i | \(-0.835057\pi\) |
−0.00541480 | + | 0.999985i | \(0.501724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1446.78 | + | 2505.90i | −0.779718 | + | 1.35051i | 0.152386 | + | 0.988321i | \(0.451304\pi\) |
−0.932104 | + | 0.362190i | \(0.882029\pi\) | |||||||
\(152\) | 733.626 | + | 1270.68i | 0.391480 | + | 0.678063i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3660.27i | − | 1.89677i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1479.73 | − | 854.325i | −0.752201 | − | 0.434284i | 0.0742874 | − | 0.997237i | \(-0.476332\pi\) |
−0.826489 | + | 0.562953i | \(0.809665\pi\) | |||||||
\(158\) | 4291.86 | + | 2477.91i | 2.16103 | + | 1.24767i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10294.0i | 5.08631i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1519.04 | + | 2631.05i | 0.729941 | + | 1.26429i | 0.956908 | + | 0.290392i | \(0.0937858\pi\) |
−0.226967 | + | 0.973903i | \(0.572881\pi\) | |||||||
\(164\) | −4567.05 | + | 7910.36i | −2.17455 | + | 3.76644i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2996.47 | − | 1730.02i | 1.40103 | − | 0.808887i | ||||
\(167\) | −702.416 | −0.325477 | −0.162738 | − | 0.986669i | \(-0.552033\pi\) | ||||
−0.162738 | + | 0.986669i | \(0.552033\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2057.83 | 0.936654 | ||||||||
\(170\) | −8237.05 | + | 4755.66i | −3.71619 | + | 2.14555i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1113.23 | + | 1928.17i | −0.493507 | + | 0.854779i | ||||
\(173\) | −740.395 | − | 1282.40i | −0.325383 | − | 0.563579i | 0.656207 | − | 0.754581i | \(-0.272160\pi\) |
−0.981590 | + | 0.191002i | \(0.938826\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4947.90i | 2.11910i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2075.63 | + | 1198.37i | 0.874019 | + | 0.504615i | ||||
\(179\) | 829.096 | + | 478.679i | 0.346199 | + | 0.199878i | 0.663010 | − | 0.748611i | \(-0.269279\pi\) |
−0.316811 | + | 0.948489i | \(0.602612\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 505.013i | 0.207389i | 0.994609 | + | 0.103694i | \(0.0330664\pi\) | ||||
−0.994609 | + | 0.103694i | \(0.966934\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5330.97 | − | 9233.51i | −2.13589 | − | 3.69948i | ||||
\(185\) | 1506.30 | − | 2608.99i | 0.598623 | − | 1.03685i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1984.87 | + | 1145.96i | −0.776192 | + | 0.448135i | ||||
\(188\) | −231.688 | −0.0898808 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2072.31 | −0.791271 | ||||||||
\(191\) | 2019.91 | − | 1166.20i | 0.765214 | − | 0.441796i | −0.0659508 | − | 0.997823i | \(-0.521008\pi\) |
0.831165 | + | 0.556027i | \(0.187675\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1962.92 | − | 3399.89i | 0.732095 | − | 1.26803i | −0.223891 | − | 0.974614i | \(-0.571876\pi\) |
0.955986 | − | 0.293412i | \(-0.0947908\pi\) | |||||||
\(194\) | 4353.58 | + | 7540.62i | 1.61118 | + | 2.79064i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1429.05i | − | 0.516831i | −0.966034 | − | 0.258416i | \(-0.916800\pi\) | ||
0.966034 | − | 0.258416i | \(-0.0832004\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4276.35 | − | 2468.95i | −1.52333 | − | 0.879494i | −0.999619 | − | 0.0275964i | \(-0.991215\pi\) |
−0.523709 | − | 0.851897i | \(-0.675452\pi\) | |||||||
\(200\) | −12752.5 | − | 7362.65i | −4.50868 | − | 2.60309i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 403.893i | − | 0.140682i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3990.19 | − | 6911.21i | −1.35945 | − | 2.35463i | ||||
\(206\) | −2594.92 | + | 4494.53i | −0.877653 | + | 1.52014i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2126.63 | + | 1227.81i | −0.708918 | + | 0.409294i | ||||
\(209\) | −499.362 | −0.165271 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1803.90 | 0.588557 | 0.294279 | − | 0.955720i | \(-0.404921\pi\) | ||||
0.294279 | + | 0.955720i | \(0.404921\pi\) | |||||||
\(212\) | 2015.15 | − | 1163.45i | 0.652836 | − | 0.376915i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3585.73 | + | 6210.66i | −1.14540 | + | 1.98389i | ||||
\(215\) | −972.620 | − | 1684.63i | −0.308522 | − | 0.534375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4791.60i | 1.48866i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7912.83 | − | 4568.48i | −2.42492 | − | 1.40003i | ||||
\(221\) | −985.079 | − | 568.736i | −0.299835 | − | 0.173110i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2540.18i | − | 0.762795i | −0.924411 | − | 0.381397i | \(-0.875443\pi\) | ||
0.924411 | − | 0.381397i | \(-0.124557\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3338.05 | + | 5781.67i | 0.982495 | + | 1.70173i | ||||
\(227\) | −1989.54 | + | 3445.98i | −0.581719 | + | 1.00757i | 0.413557 | + | 0.910478i | \(0.364286\pi\) |
−0.995276 | + | 0.0970885i | \(0.969047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1917.78 | + | 1107.23i | −0.553407 | + | 0.319510i | −0.750495 | − | 0.660876i | \(-0.770185\pi\) |
0.197088 | + | 0.980386i | \(0.436852\pi\) | |||||||
\(230\) | 15058.7 | 4.31713 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5415.91 | 1.53264 | ||||||||
\(233\) | 4060.10 | − | 2344.10i | 1.14157 | − | 0.659087i | 0.194752 | − | 0.980852i | \(-0.437610\pi\) |
0.946819 | + | 0.321766i | \(0.104276\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 101.212 | − | 175.304i | 0.0280950 | − | 0.0486620i | ||||
\(236\) | 8694.57 | + | 15059.4i | 2.39817 | + | 4.15375i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6575.90i | 1.77975i | 0.456207 | + | 0.889874i | \(0.349208\pi\) | ||||
−0.456207 | + | 0.889874i | \(0.650792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3358.45 | + | 1939.00i | 0.897662 | + | 0.518265i | 0.876441 | − | 0.481510i | \(-0.159911\pi\) |
0.0212209 | + | 0.999775i | \(0.493245\pi\) | |||||||
\(242\) | 3570.73 | + | 2061.56i | 0.948492 | + | 0.547612i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 473.386i | − | 0.124202i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −123.915 | − | 214.628i | −0.0319212 | − | 0.0552892i | ||||
\(248\) | 6975.01 | − | 12081.1i | 1.78594 | − | 3.09334i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7332.68 | − | 4233.53i | 1.85504 | − | 1.07101i | ||||
\(251\) | −2789.25 | −0.701418 | −0.350709 | − | 0.936484i | \(-0.614059\pi\) | ||||
−0.350709 | + | 0.936484i | \(0.614059\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3628.66 | 0.901708 | ||||||||
\(254\) | −6239.13 | + | 3602.16i | −1.54125 | + | 0.889842i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2151.92 | + | 3727.24i | −0.525371 | + | 0.909970i | ||||
\(257\) | −1502.32 | − | 2602.09i | −0.364638 | − | 0.631572i | 0.624080 | − | 0.781361i | \(-0.285474\pi\) |
−0.988718 | + | 0.149789i | \(0.952141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 4534.62i | − | 1.08163i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10786.3 | + | 6227.45i | 2.54343 | + | 1.46845i | ||||
\(263\) | 3452.66 | + | 1993.39i | 0.809506 | + | 0.467368i | 0.846784 | − | 0.531937i | \(-0.178536\pi\) |
−0.0372784 | + | 0.999305i | \(0.511869\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2032.99i | 0.471266i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4179.61 | + | 7239.29i | 0.952650 | + | 1.65004i | ||||
\(269\) | 2608.45 | − | 4517.97i | 0.591227 | − | 1.02403i | −0.402841 | − | 0.915270i | \(-0.631977\pi\) |
0.994068 | − | 0.108765i | \(-0.0346895\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 232.269 | − | 134.101i | 0.0520640 | − | 0.0300591i | −0.473742 | − | 0.880664i | \(-0.657097\pi\) |
0.525806 | + | 0.850604i | \(0.323764\pi\) | |||||||
\(272\) | −20070.3 | −4.47404 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11903.5 | 2.62450 | ||||||||
\(275\) | 4340.16 | − | 2505.79i | 0.951713 | − | 0.549472i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1859.88 | + | 3221.41i | −0.403427 | + | 0.698756i | −0.994137 | − | 0.108128i | \(-0.965514\pi\) |
0.590710 | + | 0.806884i | \(0.298848\pi\) | |||||||
\(278\) | −7317.08 | − | 12673.6i | −1.57859 | − | 2.73421i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4360.92i | 0.925802i | 0.886410 | + | 0.462901i | \(0.153191\pi\) | ||||
−0.886410 | + | 0.462901i | \(0.846809\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2540.70 | + | 1466.87i | 0.533671 | + | 0.308115i | 0.742510 | − | 0.669835i | \(-0.233635\pi\) |
−0.208839 | + | 0.977950i | \(0.566968\pi\) | |||||||
\(284\) | 4144.40 | + | 2392.77i | 0.865933 | + | 0.499946i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1509.46i | − | 0.312085i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2191.89 | − | 3796.47i | −0.446141 | − | 0.772739i | ||||
\(290\) | −3824.65 | + | 6624.49i | −0.774452 | + | 1.34139i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4849.33 | − | 2799.76i | 0.971868 | − | 0.561108i | ||||
\(293\) | −1081.19 | −0.215577 | −0.107789 | − | 0.994174i | \(-0.534377\pi\) | ||||
−0.107789 | + | 0.994174i | \(0.534377\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15192.7 | −2.99849 | ||||||||
\(296\) | 9943.37 | − | 5740.81i | 1.95252 | − | 1.12729i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4940.94 | − | 8557.97i | 0.960474 | − | 1.66359i | ||||
\(299\) | 900.443 | + | 1559.61i | 0.174160 | + | 0.301655i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 15575.6i | − | 2.96780i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3787.02 | − | 2186.44i | −0.714476 | − | 0.412503i | ||||
\(305\) | 358.182 | + | 206.796i | 0.0672440 | + | 0.0388233i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4327.83i | 0.804567i | 0.915515 | + | 0.402284i | \(0.131783\pi\) | ||||
−0.915515 | + | 0.402284i | \(0.868217\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9851.35 | + | 17063.0i | 1.80490 | + | 3.12618i | ||||
\(311\) | −762.084 | + | 1319.97i | −0.138951 | + | 0.240671i | −0.927100 | − | 0.374814i | \(-0.877706\pi\) |
0.788149 | + | 0.615485i | \(0.211040\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5520.33 | + | 3187.16i | −0.996893 | + | 0.575556i | −0.907327 | − | 0.420425i | \(-0.861881\pi\) |
−0.0895652 | + | 0.995981i | \(0.528548\pi\) | |||||||
\(314\) | 9197.41 | 1.65299 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19311.1 | −3.43777 | ||||||||
\(317\) | −809.520 | + | 467.377i | −0.143430 | + | 0.0828091i | −0.569998 | − | 0.821646i | \(-0.693056\pi\) |
0.426568 | + | 0.904456i | \(0.359723\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −921.620 | + | 1596.29i | −0.161758 | + | 0.280173i | ||||
\(320\) | −12447.1 | − | 21559.0i | −2.17442 | − | 3.76620i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2025.57i | − | 0.348934i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2153.99 | + | 1243.61i | 0.367637 | + | 0.212255i | ||||
\(326\) | −14162.6 | − | 8176.77i | −2.40611 | − | 1.38917i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 30414.8i | − | 5.12006i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2488.04 | + | 4309.41i | 0.413157 | + | 0.715609i | 0.995233 | − | 0.0975255i | \(-0.0310928\pi\) |
−0.582076 | + | 0.813134i | \(0.697759\pi\) | |||||||
\(332\) | −6741.27 | + | 11676.2i | −1.11438 | + | 1.93017i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3274.45 | − | 1890.50i | 0.536436 | − | 0.309712i | ||||
\(335\) | −7303.37 | −1.19112 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5127.06 | −0.828750 | −0.414375 | − | 0.910106i | \(-0.636000\pi\) | ||||
−0.414375 | + | 0.910106i | \(0.636000\pi\) | |||||||
\(338\) | −9592.96 | + | 5538.50i | −1.54375 | + | 0.891286i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18531.2 | − | 32096.9i | 2.95587 | − | 5.11971i | ||||
\(341\) | 2373.86 | + | 4111.65i | 0.376985 | + | 0.652957i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 7413.71i | − | 1.16198i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6902.98 | + | 3985.44i | 1.07256 | + | 0.619244i | ||||
\(347\) | −4466.14 | − | 2578.52i | −0.690936 | − | 0.398912i | 0.113027 | − | 0.993592i | \(-0.463945\pi\) |
−0.803963 | + | 0.594680i | \(0.797279\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2961.44i | − | 0.454218i | −0.973869 | − | 0.227109i | \(-0.927073\pi\) | ||
0.973869 | − | 0.227109i | \(-0.0729274\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6676.15 | − | 11563.4i | −1.01091 | − | 1.75094i | ||||
\(353\) | 5649.11 | − | 9784.54i | 0.851761 | − | 1.47529i | −0.0278569 | − | 0.999612i | \(-0.508868\pi\) |
0.879618 | − | 0.475681i | \(-0.157798\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3620.92 | + | 2090.54i | −0.541348 | + | 0.312547i | ||||
\(356\) | −9339.25 | −1.39039 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5153.32 | −0.760786 | ||||||||
\(359\) | 2275.44 | − | 1313.72i | 0.334521 | − | 0.193136i | −0.323326 | − | 0.946288i | \(-0.604801\pi\) |
0.657847 | + | 0.753152i | \(0.271468\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3208.84 | + | 5557.87i | −0.467829 | + | 0.810303i | ||||
\(362\) | −1359.21 | − | 2354.21i | −0.197343 | − | 0.341809i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4892.25i | 0.701567i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2320.20 | + | 1339.57i | 0.330009 | + | 0.190531i | 0.655845 | − | 0.754895i | \(-0.272312\pi\) |
−0.325836 | + | 0.945426i | \(0.605646\pi\) | |||||||
\(368\) | 27518.8 | + | 15888.0i | 3.89814 | + | 2.25059i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 16216.4i | 2.27851i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2593.86 | + | 4492.70i | 0.360068 | + | 0.623655i | 0.987972 | − | 0.154636i | \(-0.0494203\pi\) |
−0.627904 | + | 0.778291i | \(0.716087\pi\) | |||||||
\(374\) | 6168.56 | − | 10684.3i | 0.852857 | − | 1.47719i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 668.119 | − | 385.739i | 0.0916373 | − | 0.0529068i | ||||
\(377\) | −914.789 | −0.124971 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2469.97 | −0.334760 | −0.167380 | − | 0.985892i | \(-0.553531\pi\) | ||||
−0.167380 | + | 0.985892i | \(0.553531\pi\) | |||||||
\(380\) | 6993.23 | − | 4037.54i | 0.944067 | − | 0.545057i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6277.47 | + | 10872.9i | −0.840794 | + | 1.45630i | ||||
\(383\) | −5632.62 | − | 9755.99i | −0.751472 | − | 1.30159i | −0.947109 | − | 0.320911i | \(-0.896011\pi\) |
0.195638 | − | 0.980676i | \(-0.437322\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21132.3i | 2.78654i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −29383.2 | − | 16964.4i | −3.84460 | − | 2.21968i | ||||
\(389\) | −6658.54 | − | 3844.31i | −0.867870 | − | 0.501065i | −0.00122995 | − | 0.999999i | \(-0.500392\pi\) |
−0.866640 | + | 0.498934i | \(0.833725\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14719.0i | 1.90376i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3846.19 | + | 6661.80i | 0.491798 | + | 0.851819i | ||||
\(395\) | 8435.96 | − | 14611.5i | 1.07458 | − | 1.86123i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −700.905 | + | 404.668i | −0.0886081 | + | 0.0511579i | −0.543649 | − | 0.839312i | \(-0.682958\pi\) |
0.455041 | + | 0.890470i | \(0.349625\pi\) | |||||||
\(398\) | 26580.0 | 3.34758 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 43886.0 | 5.48575 | ||||||||
\(401\) | −3813.91 | + | 2201.96i | −0.474956 | + | 0.274216i | −0.718312 | − | 0.695721i | \(-0.755085\pi\) |
0.243356 | + | 0.969937i | \(0.421752\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1178.13 | + | 2040.59i | −0.145625 | + | 0.252231i | ||||
\(404\) | 786.915 | + | 1362.98i | 0.0969072 | + | 0.167848i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3907.63i | 0.475907i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −50.4345 | − | 29.1184i | −0.00609737 | − | 0.00352032i | 0.496948 | − | 0.867780i | \(-0.334454\pi\) |
−0.503046 | + | 0.864260i | \(0.667787\pi\) | |||||||
\(410\) | 37202.0 | + | 21478.6i | 4.48116 | + | 2.58720i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 20223.0i | − | 2.41824i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5889.78 | − | 10201.4i | −0.696670 | − | 1.20667i | ||||
\(416\) | 3313.33 | − | 5738.86i | 0.390504 | − | 0.676372i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2327.87 | − | 1344.00i | 0.272392 | − | 0.157266i | ||||
\(419\) | 6309.98 | 0.735711 | 0.367855 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367855 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 939.246 | 0.108732 | 0.0543658 | − | 0.998521i | \(-0.482686\pi\) | ||||
0.0543658 | + | 0.998521i | \(0.482686\pi\) | |||||||
\(422\) | −8409.22 | + | 4855.07i | −0.970034 | + | 0.560050i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3874.07 | + | 6710.08i | −0.443730 | + | 0.768562i | ||||
\(425\) | 10164.3 | + | 17605.0i | 1.16009 | + | 2.00934i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 27944.7i | − | 3.15597i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9068.11 | + | 5235.47i | 1.01698 | + | 0.587156i | ||||
\(431\) | −8233.84 | − | 4753.81i | −0.920209 | − | 0.531283i | −0.0365070 | − | 0.999333i | \(-0.511623\pi\) |
−0.883702 | + | 0.468051i | \(0.844956\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9603.12i | 1.06581i | 0.846175 | + | 0.532906i | \(0.178900\pi\) | ||||
−0.846175 | + | 0.532906i | \(0.821100\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9335.61 | − | 16169.8i | −1.02545 | − | 1.77613i | ||||
\(437\) | −1603.48 | + | 2777.30i | −0.175526 | + | 0.304019i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 756.045 | − | 436.503i | 0.0821960 | − | 0.0474559i | −0.458339 | − | 0.888778i | \(-0.651555\pi\) |
0.540535 | + | 0.841322i | \(0.318222\pi\) | |||||||
\(440\) | 30424.3 | 3.29642 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6122.84 | 0.658900 | ||||||||
\(443\) | 696.335 | − | 402.029i | 0.0746815 | − | 0.0431174i | −0.462194 | − | 0.886779i | \(-0.652938\pi\) |
0.536876 | + | 0.843661i | \(0.319604\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4079.81 | − | 7066.43i | 0.434610 | − | 0.752766i | ||||
\(446\) | 6836.72 | + | 11841.5i | 0.725847 | + | 1.25720i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12649.5i | 1.32955i | 0.747046 | + | 0.664773i | \(0.231472\pi\) | ||||
−0.747046 | + | 0.664773i | \(0.768528\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8964.51 | + | 5175.66i | 0.935970 | + | 0.540383i | ||||
\(452\) | −22529.2 | − | 13007.2i | −2.34443 | − | 1.35356i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 21418.8i | − | 2.21417i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3813.36 | + | 6604.93i | 0.390331 | + | 0.676073i | 0.992493 | − | 0.122301i | \(-0.0390272\pi\) |
−0.602162 | + | 0.798374i | \(0.705694\pi\) | |||||||
\(458\) | 5960.05 | − | 10323.1i | 0.608067 | − | 1.05320i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −50817.0 | + | 29339.2i | −5.15078 | + | 2.97380i | ||||
\(461\) | 15305.4 | 1.54630 | 0.773148 | − | 0.634226i | \(-0.218681\pi\) | ||||
0.773148 | + | 0.634226i | \(0.218681\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9675.77 | −0.971212 | −0.485606 | − | 0.874178i | \(-0.661401\pi\) | ||||
−0.485606 | + | 0.874178i | \(0.661401\pi\) | |||||||
\(464\) | −13978.6 | + | 8070.56i | −1.39858 | + | 0.807470i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12618.0 | + | 21854.9i | −1.25433 | + | 2.17256i | ||||
\(467\) | 1743.83 | + | 3020.40i | 0.172794 | + | 0.299288i | 0.939396 | − | 0.342835i | \(-0.111387\pi\) |
−0.766602 | + | 0.642123i | \(0.778054\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1089.62i | 0.106937i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −50145.1 | − | 28951.3i | −4.89007 | − | 2.82328i | ||||
\(473\) | 2185.13 | + | 1261.58i | 0.212415 | + | 0.122638i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4429.15i | 0.427839i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17698.6 | − | 30654.8i | −1.69354 | − | 2.93330i | ||||
\(479\) | −9087.22 | + | 15739.5i | −0.866818 | + | 1.50137i | −0.00158646 | + | 0.999999i | \(0.500505\pi\) |
−0.865231 | + | 0.501373i | \(0.832828\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1679.51 | + | 969.668i | −0.159208 | + | 0.0919190i | ||||
\(482\) | −20874.7 | −1.97265 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16066.4 | −1.50886 | ||||||||
\(485\) | 25671.8 | − | 14821.6i | 2.40350 | − | 1.38766i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7405.34 | − | 12826.4i | 0.689052 | − | 1.19347i | −0.283094 | − | 0.959092i | \(-0.591361\pi\) |
0.972145 | − | 0.234380i | \(-0.0753060\pi\) | |||||||
\(488\) | 788.142 | + | 1365.10i | 0.0731097 | + | 0.126630i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5187.59i | − | 0.476808i | −0.971166 | − | 0.238404i | \(-0.923376\pi\) | ||
0.971166 | − | 0.238404i | \(-0.0766242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6475.06 | − | 3738.38i | −0.591526 | − | 0.341517i | ||||
\(494\) | 1155.31 | + | 667.018i | 0.105222 | + | 0.0607501i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 41575.5i | 3.76370i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2292.61 | + | 3970.91i | 0.205674 | + | 0.356238i | 0.950347 | − | 0.311192i | \(-0.100728\pi\) |
−0.744673 | + | 0.667429i | \(0.767395\pi\) | |||||||
\(500\) | −16496.6 | + | 28572.9i | −1.47550 | + | 2.55564i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13002.6 | − | 7507.06i | 1.15605 | − | 0.667444i | ||||
\(503\) | −2600.54 | −0.230521 | −0.115261 | − | 0.993335i | \(-0.536770\pi\) | ||||
−0.115261 | + | 0.993335i | \(0.536770\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1375.04 | −0.121165 | ||||||||
\(506\) | −16915.7 | + | 9766.29i | −1.48616 | + | 0.858032i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14036.4 | − | 24311.7i | 1.22591 | − | 2.12334i | ||||
\(509\) | −5759.80 | − | 9976.27i | −0.501569 | − | 0.868743i | −0.999998 | − | 0.00181295i | \(-0.999423\pi\) |
0.498429 | − | 0.866930i | \(-0.333910\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 619.438i | − | 0.0534678i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14006.7 | + | 8086.76i | 1.20196 | + | 0.693953i | ||||
\(515\) | 15301.5 | + | 8834.32i | 1.30925 | + | 0.755896i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 262.563i | 0.0223356i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7549.71 | + | 13076.5i | 0.636686 | + | 1.10277i | ||||
\(521\) | −3361.14 | + | 5821.67i | −0.282638 | + | 0.489543i | −0.972034 | − | 0.234842i | \(-0.924543\pi\) |
0.689396 | + | 0.724385i | \(0.257876\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19252.8 | + | 11115.6i | −1.60969 | + | 0.929352i | −0.620246 | + | 0.784407i | \(0.712967\pi\) |
−0.989440 | + | 0.144945i | \(0.953700\pi\) | |||||||
\(524\) | −48532.5 | −4.04609 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21460.3 | −1.77892 | ||||||||
\(527\) | −16678.1 | + | 9629.13i | −1.37858 | + | 0.795923i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5568.33 | − | 9644.63i | 0.457659 | − | 0.792688i | ||||
\(530\) | −5471.64 | − | 9477.16i | −0.448440 | − | 0.776720i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5137.31i | 0.417489i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21144.0 | + | 12207.5i | 1.70866 | + | 0.986497i | ||||
\(536\) | −24105.5 | − | 13917.3i | −1.94253 | − | 1.12152i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 28081.8i | 2.25036i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2578.35 | + | 4465.84i | 0.204902 | + | 0.354901i | 0.950102 | − | 0.311941i | \(-0.100979\pi\) |
−0.745199 | + | 0.666842i | \(0.767646\pi\) | |||||||
\(542\) | −721.844 | + | 1250.27i | −0.0572064 | + | 0.0990843i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 46904.9 | − | 27080.5i | 3.69675 | − | 2.13432i | ||||
\(545\) | 16312.9 | 1.28214 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22545.5 | 1.76230 | 0.881149 | − | 0.472839i | \(-0.156771\pi\) | ||||
0.881149 | + | 0.472839i | \(0.156771\pi\) | |||||||
\(548\) | −40169.4 | + | 23191.8i | −3.13130 | + | 1.80786i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −13488.3 | + | 23362.4i | −1.04571 | + | 1.81123i | ||||
\(551\) | −814.512 | − | 1410.78i | −0.0629753 | − | 0.109076i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 20022.9i | − | 1.53555i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 49384.5 | + | 28512.1i | 3.76685 | + | 2.17479i | ||||
\(557\) | 8246.05 | + | 4760.86i | 0.627282 | + | 0.362162i | 0.779699 | − | 0.626155i | \(-0.215372\pi\) |
−0.152417 | + | 0.988316i | \(0.548706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1252.23i | 0.0947475i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11737.1 | − | 20329.2i | −0.880959 | − | 1.52587i | ||||
\(563\) | −2761.09 | + | 4782.34i | −0.206689 | + | 0.357996i | −0.950670 | − | 0.310205i | \(-0.899602\pi\) |
0.743981 | + | 0.668201i | \(0.232935\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19683.5 | − | 11364.3i | 1.46565 | − | 0.846194i | ||||
\(566\) | −15791.9 | −1.17276 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15934.9 | −1.17714 | ||||||||
\(569\) | 2537.61 | − | 1465.09i | 0.186963 | − | 0.107943i | −0.403597 | − | 0.914937i | \(-0.632240\pi\) |
0.590560 | + | 0.806994i | \(0.298907\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4359.17 | + | 7550.30i | −0.319484 | + | 0.553363i | −0.980381 | − | 0.197114i | \(-0.936843\pi\) |
0.660896 | + | 0.750477i | \(0.270176\pi\) | |||||||
\(572\) | 2940.92 | + | 5093.82i | 0.214976 | + | 0.372349i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 32184.9i | − | 2.33427i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14243.4 | − | 8223.43i | −1.02766 | − | 0.593320i | −0.111347 | − | 0.993782i | \(-0.535517\pi\) |
−0.916314 | + | 0.400461i | \(0.868850\pi\) | |||||||
\(578\) | 20435.8 | + | 11798.6i | 1.47062 | + | 0.849063i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 29806.7i | − | 2.13389i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1318.49 | − | 2283.70i | −0.0936645 | − | 0.162232i | ||||
\(584\) | −9322.67 | + | 16147.3i | −0.660574 | + | 1.14415i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5040.19 | − | 2909.96i | 0.355305 | − | 0.205135i | ||||
\(587\) | −2346.72 | −0.165008 | −0.0825040 | − | 0.996591i | \(-0.526292\pi\) | ||||
−0.0825040 | + | 0.996591i | \(0.526292\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4195.96 | −0.293534 | ||||||||
\(590\) | 70823.7 | − | 40890.1i | 4.94198 | − | 2.85325i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17109.4 | + | 29634.4i | −1.18783 | + | 2.05738i | ||||
\(593\) | −7971.40 | − | 13806.9i | −0.552017 | − | 0.956122i | −0.998129 | − | 0.0611443i | \(-0.980525\pi\) |
0.446112 | − | 0.894977i | \(-0.352808\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 38506.3i | 2.64644i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8395.17 | − | 4846.95i | −0.574087 | − | 0.331449i | ||||
\(599\) | −17836.6 | − | 10298.0i | −1.21667 | − | 0.702445i | −0.252466 | − | 0.967606i | \(-0.581242\pi\) |
−0.964204 | + | 0.265161i | \(0.914575\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 662.921i | 0.0449935i | 0.999747 | + | 0.0224968i | \(0.00716154\pi\) | ||||
−0.999747 | + | 0.0224968i | \(0.992838\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 30346.4 | + | 52561.5i | 2.04434 | + | 3.54089i | ||||
\(605\) | 7018.52 | − | 12156.4i | 0.471642 | − | 0.816908i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11688.2 | − | 6748.21i | 0.781567 | − | 0.451238i | −0.0554186 | − | 0.998463i | \(-0.517649\pi\) |
0.836985 | + | 0.547226i | \(0.184316\pi\) | |||||||
\(608\) | 11800.5 | 0.787130 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2226.31 | −0.147771 | ||||||||
\(611\) | −112.851 | + | 65.1543i | −0.00747209 | + | 0.00431401i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10037.0 | + | 17384.6i | −0.661322 | + | 1.14544i | 0.318946 | + | 0.947773i | \(0.396671\pi\) |
−0.980268 | + | 0.197671i | \(0.936662\pi\) | |||||||
\(614\) | −11648.0 | − | 20175.0i | −0.765597 | − | 1.32605i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21664.4i | 1.41358i | 0.707425 | + | 0.706788i | \(0.249857\pi\) | ||||
−0.707425 | + | 0.706788i | \(0.750143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1881.89 | + | 1086.51i | 0.122196 | + | 0.0705501i | 0.559852 | − | 0.828592i | \(-0.310858\pi\) |
−0.437656 | + | 0.899143i | \(0.644191\pi\) | |||||||
\(620\) | −66488.7 | − | 38387.3i | −4.30686 | − | 2.48657i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 8204.38i | − | 0.528884i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1235.81 | − | 2140.48i | −0.0790916 | − | 0.136991i | ||||
\(626\) | 17156.0 | − | 29715.1i | 1.09536 | − | 1.89721i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −31037.6 | + | 17919.6i | −1.97219 | + | 1.13864i | ||||
\(629\) | −15850.6 | −1.00478 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7823.69 | −0.493591 | −0.246796 | − | 0.969068i | \(-0.579378\pi\) | ||||
−0.246796 | + | 0.969068i | \(0.579378\pi\) | |||||||
\(632\) | 55687.5 | − | 32151.2i | 3.50495 | − | 2.02358i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2515.82 | − | 4357.53i | 0.157596 | − | 0.272965i | ||||
\(635\) | 12263.5 | + | 21240.9i | 0.766395 | + | 1.32743i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 9921.89i | − | 0.615692i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 44730.3 | + | 25825.0i | 2.76269 | + | 1.59504i | ||||
\(641\) | −268.735 | − | 155.154i | −0.0165591 | − | 0.00956040i | 0.491698 | − | 0.870766i | \(-0.336377\pi\) |
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 28064.5i | − | 1.72124i | −0.509250 | − | 0.860618i | \(-0.670077\pi\) | ||
0.509250 | − | 0.860618i | \(-0.329923\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5451.67 | + | 9442.57i | 0.332033 | + | 0.575098i | ||||
\(647\) | 4219.67 | − | 7308.68i | 0.256402 | − | 0.444101i | −0.708873 | − | 0.705336i | \(-0.750796\pi\) |
0.965275 | + | 0.261234i | \(0.0841295\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17066.3 | − | 9853.22i | 1.03222 | − | 0.595952i | ||||
\(650\) | −13388.3 | −0.807898 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 63724.1 | 3.82765 | ||||||||
\(653\) | −22966.4 | + | 13259.6i | −1.37633 | + | 0.794624i | −0.991716 | − | 0.128453i | \(-0.958999\pi\) |
−0.384614 | + | 0.923077i | \(0.625665\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21201.2 | − | 36721.5i | 1.26473 | − | 2.19058i | ||||
\(656\) | 45322.9 | + | 78501.6i | 2.69750 | + | 4.67221i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 29625.1i | − | 1.75118i | −0.483054 | − | 0.875591i | \(-0.660473\pi\) | ||
0.483054 | − | 0.875591i | \(-0.339527\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18868.3 | − | 10893.6i | −1.11027 | − | 0.641018i | −0.171374 | − | 0.985206i | \(-0.554821\pi\) |
−0.938901 | + | 0.344188i | \(0.888154\pi\) | |||||||
\(662\) | −23196.9 | − | 13392.7i | −1.36189 | − | 0.786290i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 44894.3i | − | 2.62385i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5918.74 | + | 10251.6i | 0.343590 | + | 0.595115i | ||||
\(668\) | −7366.63 | + | 12759.4i | −0.426682 | + | 0.739035i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 34046.0 | − | 19656.5i | 1.96315 | − | 1.13343i | ||||
\(671\) | −536.470 | −0.0308647 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14551.5 | 0.833462 | 0.416731 | − | 0.909030i | \(-0.363176\pi\) | ||||
0.416731 | + | 0.909030i | \(0.363176\pi\) | |||||||
\(674\) | 23900.8 | − | 13799.1i | 1.36591 | − | 0.788608i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21581.6 | − | 37380.4i | 1.22790 | − | 2.12679i | ||||
\(677\) | 6158.05 | + | 10666.0i | 0.349591 | + | 0.605509i | 0.986177 | − | 0.165697i | \(-0.0529873\pi\) |
−0.636586 | + | 0.771206i | \(0.719654\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 123411.i | 6.95968i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22132.4 | − | 12778.2i | −1.24266 | − | 0.717450i | ||||
\(683\) | 9488.46 | + | 5478.16i | 0.531575 | + | 0.306905i | 0.741658 | − | 0.670779i | \(-0.234040\pi\) |
−0.210083 | + | 0.977684i | \(0.567373\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 40524.9i | − | 2.26041i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11047.6 | + | 19135.0i | 0.612188 | + | 1.06034i | ||||
\(689\) | 654.361 | − | 1133.39i | 0.0361816 | − | 0.0626684i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20240.0 | + | 11685.6i | −1.11428 | + | 0.643328i | −0.939934 | − | 0.341357i | \(-0.889113\pi\) |
−0.174343 | + | 0.984685i | \(0.555780\pi\) | |||||||
\(692\) | −31059.7 | −1.70623 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27759.6 | 1.51836 | ||||||||
\(695\) | −43146.7 | + | 24910.8i | −2.35489 | + | 1.35960i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20994.1 | + | 36362.9i | −1.14090 | + | 1.97610i | ||||
\(698\) | 7970.49 | + | 13805.3i | 0.432217 | + | 0.748622i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13644.5i | 0.735160i | 0.929992 | + | 0.367580i | \(0.119814\pi\) | ||||
−0.929992 | + | 0.367580i | \(0.880186\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2990.82 | − | 1726.75i | −0.160457 | − | 0.0926396i | ||||
\(704\) | 27964.1 | + | 16145.1i | 1.49707 | + | 0.864335i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 60816.6i | 3.24202i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11964.6 | + | 20723.3i | 0.633767 | + | 1.09772i | 0.986775 | + | 0.162096i | \(0.0518256\pi\) |
−0.353008 | + | 0.935620i | \(0.614841\pi\) | |||||||
\(710\) | 11253.1 | − | 19490.9i | 0.594817 | − | 1.03025i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 26931.6 | − | 15549.0i | 1.41756 | − | 0.818430i | ||||
\(713\) | 30490.4 | 1.60151 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5138.91 | −0.268789 | ||||||||
\(716\) | 17390.4 | − | 10040.3i | 0.907695 | − | 0.524058i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7071.59 | + | 12248.4i | −0.367562 | + | 0.636636i | ||||
\(719\) | −14781.6 | − | 25602.4i | −0.766703 | − | 1.32797i | −0.939341 | − | 0.342984i | \(-0.888562\pi\) |
0.172638 | − | 0.984985i | \(-0.444771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 34545.4i | − | 1.78067i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9173.56 | + | 5296.36i | 0.470902 | + | 0.271875i | ||||
\(725\) | 14158.5 | + | 8174.42i | 0.725288 | + | 0.418745i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3335.51i | 0.170161i | 0.996374 | + | 0.0850805i | \(0.0271148\pi\) | ||||
−0.996374 | + | 0.0850805i | \(0.972885\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13167.1 | − | 22806.1i | −0.667585 | − | 1.15629i | ||||
\(731\) | −5117.38 | + | 8863.56i | −0.258924 | + | 0.448469i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10582.6 | − | 6109.89i | 0.533258 | − | 0.307877i | −0.209084 | − | 0.977898i | \(-0.567048\pi\) |
0.742342 | + | 0.670021i | \(0.233715\pi\) | |||||||
\(734\) | −14421.4 | −0.725209 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −85749.8 | −4.29454 | ||||||||
\(737\) | 8204.01 | − | 4736.59i | 0.410039 | − | 0.236736i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8879.68 | + | 15380.1i | −0.442009 | + | 0.765581i | −0.997838 | − | 0.0657148i | \(-0.979067\pi\) |
0.555830 | + | 0.831296i | \(0.312401\pi\) | |||||||
\(740\) | −31594.8 | − | 54723.8i | −1.56952 | − | 2.71850i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5371.15i | − | 0.265207i | −0.991169 | − | 0.132603i | \(-0.957666\pi\) | ||
0.991169 | − | 0.132603i | \(-0.0423336\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29135.3 | − | 16821.3i | −1.43280 | − | 0.827227i | ||||
\(746\) | −24183.6 | − | 13962.4i | −1.18689 | − | 0.685254i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 48073.5i | 2.34992i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11636.4 | − | 20154.8i | −0.565403 | − | 0.979306i | −0.997012 | − | 0.0772457i | \(-0.975387\pi\) |
0.431609 | − | 0.902061i | \(-0.357946\pi\) | |||||||
\(752\) | −1149.62 | + | 1991.21i | −0.0557480 | + | 0.0965583i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4264.46 | − | 2462.09i | 0.205972 | − | 0.118918i | ||||
\(755\) | −53026.8 | −2.55608 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16172.1 | 0.776465 | 0.388233 | − | 0.921561i | \(-0.373086\pi\) | ||||
0.388233 | + | 0.921561i | \(0.373086\pi\) | |||||||
\(758\) | 11514.2 | − | 6647.76i | 0.551737 | − | 0.318545i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13444.3 | + | 23286.1i | −0.641677 | + | 1.11142i | ||||
\(761\) | 9460.31 | + | 16385.7i | 0.450639 | + | 0.780529i | 0.998426 | − | 0.0560887i | \(-0.0178630\pi\) |
−0.547787 | + | 0.836618i | \(0.684530\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 48922.3i | − | 2.31668i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 52515.1 | + | 30319.6i | 2.47709 | + | 1.43015i | ||||
\(767\) | 8469.90 | + | 4890.10i | 0.398736 | + | 0.230210i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 33747.4i | − | 1.58253i | −0.611475 | − | 0.791264i | \(-0.709423\pi\) | ||
0.611475 | − | 0.791264i | \(-0.290577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −41172.6 | − | 71313.0i | −1.91947 | − | 3.32463i | ||||
\(773\) | −10806.4 | + | 18717.2i | −0.502817 | + | 0.870905i | 0.497178 | + | 0.867649i | \(0.334370\pi\) |
−0.999995 | + | 0.00325584i | \(0.998964\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36468.8 | − | 21055.3i | 1.69032 | − | 0.975906i | ||||
\(776\) | 112976. | 5.22631 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 41386.7 | 1.90718 | ||||||||
\(779\) | −7922.69 | + | 4574.17i | −0.364390 | + | 0.210381i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2711.63 | − | 4696.69i | 0.124238 | − | 0.215187i | ||||
\(782\) | −39615.1 | − | 68615.4i | −1.81155 | − | 3.13770i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 31312.3i | − | 1.42367i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21260.3 | + | 12274.6i | 0.962957 | + | 0.555963i | 0.897082 | − | 0.441865i | \(-0.145683\pi\) |
0.0658748 | + | 0.997828i | \(0.479016\pi\) | |||||||
\(788\) | −25958.7 | − | 14987.3i | −1.17353 | − | 0.677538i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 90819.1i | 4.09013i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −133.123 | − | 230.577i | −0.00596135 | − | 0.0103254i | ||||
\(794\) | 2178.27 | − | 3772.87i | 0.0973600 | − | 0.168632i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −89696.9 | + | 51786.5i | −3.99400 | + | 2.30594i | ||||
\(797\) | 12323.1 | 0.547687 | 0.273844 | − | 0.961774i | \(-0.411705\pi\) | ||||
0.273844 | + | 0.961774i | \(0.411705\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1065.04 | −0.0471569 | ||||||||
\(800\) | −102563. | + | 59214.9i | −4.53270 | + | 2.61695i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11852.8 | − | 20529.7i | 0.521868 | − | 0.903901i | ||||
\(803\) | −3172.86 | − | 5495.56i | −0.139437 | − | 0.241512i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 12683.5i | − | 0.554287i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4538.46 | − | 2620.28i | −0.197602 | − | 0.114086i | ||||
\(809\) | 3177.11 | + | 1834.31i | 0.138073 | + | 0.0797167i | 0.567445 | − | 0.823411i | \(-0.307932\pi\) |
−0.429372 | + | 0.903128i | \(0.641265\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24967.7i | − | 1.08105i | −0.841327 | − | 0.540527i | \(-0.818225\pi\) | ||
0.841327 | − | 0.540527i | \(-0.181775\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10517.1 | − | 18216.2i | −0.452856 | − | 0.784369i | ||||
\(815\) | −27837.6 | + | 48216.1i | −1.19645 | + | 2.07231i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1931.18 | + | 1114.97i | −0.0826970 | + | 0.0477451i | ||||
\(818\) | 313.480 | 0.0133992 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −167389. | −7.12865 | ||||||||
\(821\) | −5425.51 | + | 3132.42i | −0.230635 | + | 0.133157i | −0.610865 | − | 0.791735i | \(-0.709178\pi\) |
0.380230 | + | 0.924892i | \(0.375845\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1666.86 | + | 2887.08i | −0.0705990 | + | 0.122281i | −0.899164 | − | 0.437612i | \(-0.855824\pi\) |
0.828565 | + | 0.559893i | \(0.189158\pi\) | |||||||
\(824\) | 33669.4 | + | 58317.1i | 1.42346 | + | 2.46550i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 27785.4i | − | 1.16831i | −0.811643 | − | 0.584154i | \(-0.801426\pi\) | ||
0.811643 | − | 0.584154i | \(-0.198574\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7667.54 | − | 4426.86i | −0.321236 | − | 0.185466i | 0.330707 | − | 0.943733i | \(-0.392713\pi\) |
−0.651943 | + | 0.758268i | \(0.726046\pi\) | |||||||
\(830\) | 54912.7 | + | 31703.8i | 2.29644 | + | 1.32585i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16025.4i | 0.667767i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6436.16 | − | 11147.8i | −0.266745 | − | 0.462017i | ||||
\(836\) | −5237.09 | + | 9070.91i | −0.216661 | + | 0.375268i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −29415.2 | + | 16982.9i | −1.21257 | + | 0.700075i | ||||
\(839\) | 92.8332 | 0.00381997 | 0.00190999 | − | 0.999998i | \(-0.499392\pi\) | ||||
0.00190999 | + | 0.999998i | \(0.499392\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18376.0 | 0.753453 | ||||||||
\(842\) | −4378.47 | + | 2527.91i | −0.179207 | + | 0.103465i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18918.5 | − | 32767.8i | 0.771566 | − | 1.33639i | ||||
\(845\) | 18855.6 | + | 32658.9i | 0.767638 | + | 1.32959i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 23091.9i | − | 0.935116i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −94765.3 | − | 54712.8i | −3.82403 | − | 2.20780i | ||||
\(851\) | 21733.1 | + | 12547.6i | 0.875442 | + | 0.505437i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8509.71i | 0.341579i | 0.985308 | + | 0.170790i | \(0.0546318\pi\) | ||||
−0.985308 | + | 0.170790i | \(0.945368\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 46525.2 | + | 80584.1i | 1.85771 | + | 3.21765i | ||||
\(857\) | −19517.2 | + | 33804.9i | −0.777942 | + | 1.34744i | 0.155184 | + | 0.987886i | \(0.450403\pi\) |
−0.933126 | + | 0.359550i | \(0.882930\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30440.2 | + | 17574.7i | −1.20909 | + | 0.698067i | −0.962560 | − | 0.271069i | \(-0.912623\pi\) |
−0.246527 | + | 0.969136i | \(0.579290\pi\) | |||||||
\(860\) | −40801.7 | −1.61782 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 51178.1 | 2.02220 | ||||||||
\(863\) | 13889.2 | − | 8018.96i | 0.547851 | − | 0.316302i | −0.200404 | − | 0.979713i | \(-0.564225\pi\) |
0.748255 | + | 0.663411i | \(0.230892\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13568.3 | − | 23501.0i | 0.533336 | − | 0.923766i | ||||
\(866\) | −25846.1 | − | 44766.7i | −1.01419 | − | 1.75662i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21884.5i | 0.854295i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4071.60 | + | 2350.74i | 0.158394 | + | 0.0914488i | ||||
\(872\) | 53842.2 | + | 31085.8i | 2.09097 | + | 1.20722i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 17262.6i | − | 0.668095i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11223.0 | − | 19438.8i | −0.432126 | − | 0.748464i | 0.564930 | − | 0.825139i | \(-0.308903\pi\) |
−0.997056 | + | 0.0766749i | \(0.975570\pi\) | |||||||
\(878\) | −2349.63 | + | 4069.68i | −0.0903146 | + | 0.156429i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −78526.1 | + | 45337.1i | −3.00808 | + | 1.73672i | ||||
\(881\) | 4544.20 | 0.173778 | 0.0868888 | − | 0.996218i | \(-0.472308\pi\) | ||||
0.0868888 | + | 0.996218i | \(0.472308\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18749.1 | 0.714561 | 0.357280 | − | 0.933997i | \(-0.383704\pi\) | ||||
0.357280 | + | 0.933997i | \(0.383704\pi\) | |||||||
\(884\) | −20662.2 | + | 11929.3i | −0.786135 | + | 0.453875i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2164.07 | + | 3748.27i | −0.0820578 | + | 0.142128i | ||||
\(887\) | −12553.5 | − | 21743.4i | −0.475205 | − | 0.823079i | 0.524392 | − | 0.851477i | \(-0.324293\pi\) |
−0.999597 | + | 0.0283981i | \(0.990959\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 43922.0i | 1.65423i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −46142.4 | − | 26640.3i | −1.73202 | − | 0.999982i | ||||
\(893\) | −200.960 | − | 116.025i | −0.00753067 | − | 0.00434783i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17544.3i | 0.655242i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −34045.1 | − | 58967.9i | −1.26515 | − | 2.19130i | ||||
\(899\) | −7744.04 | + | 13413.1i | −0.287295 | + | 0.497610i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9263.39 | − | 5348.22i | 0.342518 | − | 0.197753i | ||||
\(902\) | −55719.7 | −2.05683 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 86623.3 | 3.18700 | ||||||||
\(905\) | −8014.85 | + | 4627.38i | −0.294390 | + | 0.169966i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5098.56 | − | 8830.96i | 0.186654 | − | 0.323293i | −0.757479 | − | 0.652860i | \(-0.773569\pi\) |
0.944132 | + | 0.329566i | \(0.106902\pi\) | |||||||
\(908\) | 41730.8 | + | 72279.8i | 1.52520 | + | 2.64173i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27309.8i | 0.993208i | 0.867977 | + | 0.496604i | \(0.165420\pi\) | ||||
−0.867977 | + | 0.496604i | \(0.834580\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13232.2 | + | 7639.62i | 0.479652 | + | 0.276927i | ||||
\(914\) | −35553.4 | − | 20526.7i | −1.28665 | − | 0.742849i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 46448.5i | 1.67544i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 117.243 | + | 203.071i | 0.00420837 | + | 0.00728911i | 0.868122 | − | 0.496351i | \(-0.165327\pi\) |
−0.863914 | + | 0.503640i | \(0.831994\pi\) | |||||||
\(920\) | 97694.1 | − | 169211.i | 3.50096 | − | 6.06383i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −71348.9 | + | 41193.3i | −2.54854 | + | 1.47140i | ||||
\(923\) | 2691.54 | 0.0959838 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34659.2 | 1.23199 | ||||||||
\(926\) | 45105.4 | − | 26041.6i | 1.60071 | − | 0.924169i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 21779.0 | − | 37722.3i | 0.770400 | − | 1.33437i | ||||
\(929\) | 12740.7 | + | 22067.6i | 0.449956 | + | 0.779347i | 0.998383 | − | 0.0568516i | \(-0.0181062\pi\) |
−0.548426 | + | 0.836199i | \(0.684773\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 98335.6i | − | 3.45611i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16258.4 | − | 9386.76i | −0.569582 | − | 0.328848i | ||||
\(935\) | −36374.2 | − | 21000.7i | −1.27226 | − | 0.734541i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36561.0i | − | 1.27470i | −0.770574 | − | 0.637350i | \(-0.780031\pi\) | ||
0.770574 | − | 0.637350i | \(-0.219969\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2122.93 | − | 3677.02i | −0.0736621 | − | 0.127587i | ||||
\(941\) | 17521.1 | − | 30347.4i | 0.606984 | − | 1.05133i | −0.384751 | − | 0.923020i | \(-0.625713\pi\) |
0.991735 | − | 0.128306i | \(-0.0409540\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57571.0 | − | 33238.7i | 1.98809 | − | 1.14783i | ||||
\(944\) | 172568. | 5.94979 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13581.8 | −0.466790 | ||||||||
\(947\) | −30868.9 | + | 17822.1i | −1.05924 | + | 0.611554i | −0.925223 | − | 0.379424i | \(-0.876122\pi\) |
−0.134020 | + | 0.990979i | \(0.542789\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1574.67 | − | 2727.41i | 0.0538631 | − | 0.0932936i | ||||
\(950\) | −11920.7 | − | 20647.3i | −0.407116 | − | 0.705145i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35376.7i | 1.20248i | 0.799068 | + | 0.601240i | \(0.205327\pi\) | ||||
−0.799068 | + | 0.601240i | \(0.794673\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37016.5 | + | 21371.5i | 1.25427 | + | 0.724151i | ||||
\(956\) | 119451. | + | 68965.2i | 4.04114 | + | 2.33315i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 97830.3i | − | 3.29933i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5051.23 | + | 8748.98i | 0.169556 | + | 0.293679i | ||||
\(962\) | 5219.58 | − | 9040.58i | 0.174934 | − | 0.302994i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 70443.8 | − | 40670.8i | 2.35357 | − | 1.35883i | ||||
\(965\) | 71944.2 | 2.39996 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27697.2 | −0.921078 | −0.460539 | − | 0.887640i | \(-0.652344\pi\) | ||||
−0.460539 | + | 0.887640i | \(0.652344\pi\) | |||||||
\(968\) | 46330.6 | − | 26749.0i | 1.53835 | − | 0.888166i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −79782.7 | + | 138188.i | −2.64089 | + | 4.57416i | ||||
\(971\) | −15880.0 | − | 27505.0i | −0.524834 | − | 0.909040i | −0.999582 | − | 0.0289176i | \(-0.990794\pi\) |
0.474747 | − | 0.880122i | \(-0.342539\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 79723.8i | 2.62270i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4068.44 | − | 2348.91i | −0.133430 | − | 0.0770357i | ||||
\(977\) | −989.925 | − | 571.533i | −0.0324161 | − | 0.0187154i | 0.483704 | − | 0.875231i | \(-0.339291\pi\) |
−0.516120 | + | 0.856516i | \(0.672624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10583.8i | 0.345516i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13962.0 | + | 24182.9i | 0.453713 | + | 0.785853i | ||||
\(983\) | −6695.23 | + | 11596.5i | −0.217238 | + | 0.376267i | −0.953962 | − | 0.299926i | \(-0.903038\pi\) |
0.736725 | + | 0.676193i | \(0.236371\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22679.9 | − | 13094.2i | 0.733646 | − | 0.423571i | ||||
\(986\) | 40246.3 | 1.29990 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5198.28 | −0.167388 | ||||||||
\(989\) | 14033.1 | − | 8102.02i | 0.451190 | − | 0.260495i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8007.84 | + | 13870.0i | −0.256688 | + | 0.444596i | −0.965353 | − | 0.260949i | \(-0.915964\pi\) |
0.708665 | + | 0.705545i | \(0.249298\pi\) | |||||||
\(992\) | −56097.3 | − | 97163.4i | −1.79545 | − | 3.10982i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 90490.8i | − | 2.88317i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25588.5 | − | 14773.6i | −0.812836 | − | 0.469291i | 0.0351038 | − | 0.999384i | \(-0.488824\pi\) |
−0.847940 | + | 0.530093i | \(0.822157\pi\) | |||||||
\(998\) | −21374.9 | − | 12340.8i | −0.677965 | − | 0.391423i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.4.p.d.80.2 | 48 | ||
3.2 | odd | 2 | inner | 441.4.p.d.80.23 | 48 | ||
7.2 | even | 3 | inner | 441.4.p.d.215.24 | 48 | ||
7.3 | odd | 6 | 441.4.c.b.440.1 | ✓ | 24 | ||
7.4 | even | 3 | 441.4.c.b.440.23 | yes | 24 | ||
7.5 | odd | 6 | inner | 441.4.p.d.215.23 | 48 | ||
7.6 | odd | 2 | inner | 441.4.p.d.80.1 | 48 | ||
21.2 | odd | 6 | inner | 441.4.p.d.215.1 | 48 | ||
21.5 | even | 6 | inner | 441.4.p.d.215.2 | 48 | ||
21.11 | odd | 6 | 441.4.c.b.440.2 | yes | 24 | ||
21.17 | even | 6 | 441.4.c.b.440.24 | yes | 24 | ||
21.20 | even | 2 | inner | 441.4.p.d.80.24 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.4.c.b.440.1 | ✓ | 24 | 7.3 | odd | 6 | ||
441.4.c.b.440.2 | yes | 24 | 21.11 | odd | 6 | ||
441.4.c.b.440.23 | yes | 24 | 7.4 | even | 3 | ||
441.4.c.b.440.24 | yes | 24 | 21.17 | even | 6 | ||
441.4.p.d.80.1 | 48 | 7.6 | odd | 2 | inner | ||
441.4.p.d.80.2 | 48 | 1.1 | even | 1 | trivial | ||
441.4.p.d.80.23 | 48 | 3.2 | odd | 2 | inner | ||
441.4.p.d.80.24 | 48 | 21.20 | even | 2 | inner | ||
441.4.p.d.215.1 | 48 | 21.2 | odd | 6 | inner | ||
441.4.p.d.215.2 | 48 | 21.5 | even | 6 | inner | ||
441.4.p.d.215.23 | 48 | 7.5 | odd | 6 | inner | ||
441.4.p.d.215.24 | 48 | 7.2 | even | 3 | inner |