Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,4,Mod(269,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("756.269");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.t (of order \(6\), 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: | \(44.6054439643\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 43x^{10} + 1500x^{8} - 13455x^{6} + 88433x^{4} - 270824x^{2} + 602176 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{9}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.5 | ||
Root | \(1.74910 + 1.00984i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.593 |
Dual form | 756.4.t.c.269.5 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.90269 | − | 11.9558i | 0.617395 | − | 1.06936i | −0.372564 | − | 0.928007i | \(-0.621521\pi\) |
0.989959 | − | 0.141353i | \(-0.0451454\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.82127 | + | 16.2845i | 0.476304 | + | 0.879281i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −35.5912 | + | 20.5486i | −0.975558 | + | 0.563239i | −0.900926 | − | 0.433972i | \(-0.857111\pi\) |
−0.0746318 | + | 0.997211i | \(0.523778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 57.5129i | − | 1.22702i | −0.789688 | − | 0.613509i | \(-0.789758\pi\) | ||
0.789688 | − | 0.613509i | \(-0.210242\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 56.4236 | + | 97.7285i | 0.804984 | + | 1.39427i | 0.916302 | + | 0.400489i | \(0.131160\pi\) |
−0.111317 | + | 0.993785i | \(0.535507\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 77.1424 | + | 44.5382i | 0.931457 | + | 0.537777i | 0.887272 | − | 0.461247i | \(-0.152598\pi\) |
0.0441846 | + | 0.999023i | \(0.485931\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −56.2992 | − | 32.5044i | −0.510400 | − | 0.294680i | 0.222598 | − | 0.974910i | \(-0.428546\pi\) |
−0.732998 | + | 0.680231i | \(0.761880\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −32.7942 | − | 56.8013i | −0.262354 | − | 0.454410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 277.651i | 1.77788i | 0.458022 | + | 0.888941i | \(0.348558\pi\) | ||||
−0.458022 | + | 0.888941i | \(0.651442\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 228.040 | − | 131.659i | 1.32120 | − | 0.762794i | 0.337279 | − | 0.941405i | \(-0.390493\pi\) |
0.983920 | + | 0.178610i | \(0.0571602\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 255.585 | + | 6.94153i | 1.23434 | + | 0.0335238i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −144.939 | + | 251.042i | −0.643997 | + | 1.11544i | 0.340535 | + | 0.940232i | \(0.389392\pi\) |
−0.984532 | + | 0.175204i | \(0.943942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −140.955 | −0.536916 | −0.268458 | − | 0.963291i | \(-0.586514\pi\) | ||||
−0.268458 | + | 0.963291i | \(0.586514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 260.465 | 0.923732 | 0.461866 | − | 0.886950i | \(-0.347180\pi\) | ||||
0.461866 | + | 0.886950i | \(0.347180\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 238.298 | − | 412.744i | 0.739559 | − | 1.28095i | −0.213135 | − | 0.977023i | \(-0.568367\pi\) |
0.952694 | − | 0.303932i | \(-0.0982994\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −187.370 | + | 287.300i | −0.546270 | + | 0.837609i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −86.0654 | + | 49.6899i | −0.223056 | + | 0.128782i | −0.607365 | − | 0.794423i | \(-0.707773\pi\) |
0.384308 | + | 0.923205i | \(0.374440\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 567.361i | 1.39096i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −335.121 | − | 580.446i | −0.739475 | − | 1.28081i | −0.952732 | − | 0.303812i | \(-0.901741\pi\) |
0.213257 | − | 0.976996i | \(-0.431593\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 119.160 | + | 68.7970i | 0.250113 | + | 0.144403i | 0.619816 | − | 0.784747i | \(-0.287207\pi\) |
−0.369703 | + | 0.929150i | \(0.620541\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −687.614 | − | 396.994i | −1.31212 | − | 0.757555i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 101.900 | + | 176.496i | 0.185807 | + | 0.321827i | 0.943848 | − | 0.330380i | \(-0.107177\pi\) |
−0.758041 | + | 0.652207i | \(0.773843\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 601.833i | 1.00598i | 0.864293 | + | 0.502989i | \(0.167766\pi\) | ||||
−0.864293 | + | 0.502989i | \(0.832234\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 832.666 | − | 480.740i | 1.33502 | − | 0.770772i | 0.348952 | − | 0.937141i | \(-0.386538\pi\) |
0.986064 | + | 0.166369i | \(0.0532043\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −648.582 | − | 398.320i | −0.959907 | − | 0.589517i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 320.201 | − | 554.604i | 0.456017 | − | 0.789845i | −0.542729 | − | 0.839908i | \(-0.682609\pi\) |
0.998746 | + | 0.0500628i | \(0.0159421\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1372.20 | 1.81468 | 0.907340 | − | 0.420398i | \(-0.138109\pi\) | ||||
0.907340 | + | 0.420398i | \(0.138109\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1557.90 | 1.98797 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 181.813 | − | 314.909i | 0.216541 | − | 0.375060i | −0.737207 | − | 0.675667i | \(-0.763856\pi\) |
0.953748 | + | 0.300607i | \(0.0971892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 936.570 | − | 507.337i | 1.07889 | − | 0.584433i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1064.98 | − | 614.866i | 1.15015 | − | 0.664042i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 828.102i | 0.866815i | 0.901198 | + | 0.433407i | \(0.142689\pi\) | ||||
−0.901198 | + | 0.433407i | \(0.857311\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 709.753 | + | 1229.33i | 0.699239 | + | 1.21112i | 0.968731 | + | 0.248114i | \(0.0798108\pi\) |
−0.269492 | + | 0.963003i | \(0.586856\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1622.12 | + | 936.533i | 1.55177 | + | 0.895916i | 0.997998 | + | 0.0632484i | \(0.0201460\pi\) |
0.553774 | + | 0.832667i | \(0.313187\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1337.23 | − | 772.053i | −1.20818 | − | 0.697543i | −0.245819 | − | 0.969316i | \(-0.579057\pi\) |
−0.962362 | + | 0.271772i | \(0.912390\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 58.6482 | + | 101.582i | 0.0515365 | + | 0.0892639i | 0.890643 | − | 0.454704i | \(-0.150255\pi\) |
−0.839106 | + | 0.543967i | \(0.816921\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 972.690i | 0.809761i | 0.914370 | + | 0.404881i | \(0.132687\pi\) | ||||
−0.914370 | + | 0.404881i | \(0.867313\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −777.232 | + | 448.735i | −0.630237 | + | 0.363868i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1093.73 | + | 1780.92i | −0.842541 | + | 1.37190i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 178.987 | − | 310.015i | 0.134476 | − | 0.232919i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 820.199 | 0.586886 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 232.704 | 0.162592 | 0.0812958 | − | 0.996690i | \(-0.474094\pi\) | ||||
0.0812958 | + | 0.996690i | \(0.474094\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −305.933 | + | 529.891i | −0.204042 | + | 0.353410i | −0.949827 | − | 0.312776i | \(-0.898741\pi\) |
0.745785 | + | 0.666186i | \(0.232074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −44.7888 | + | 1649.11i | −0.0292006 | + | 1.07516i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1648.39 | + | 951.696i | −1.02796 | + | 0.593495i | −0.916401 | − | 0.400262i | \(-0.868919\pi\) |
−0.111563 | + | 0.993757i | \(0.535586\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 597.088i | − | 0.364348i | −0.983266 | − | 0.182174i | \(-0.941687\pi\) | ||
0.983266 | − | 0.182174i | \(-0.0583134\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1181.81 | + | 2046.95i | 0.691103 | + | 1.19703i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3319.55 | + | 1916.54i | 1.90120 | + | 1.09766i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −543.947 | − | 314.048i | −0.299073 | − | 0.172670i | 0.342954 | − | 0.939352i | \(-0.388573\pi\) |
−0.642026 | + | 0.766683i | \(0.721906\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 939.284 | + | 1626.89i | 0.506211 | + | 0.876783i | 0.999974 | + | 0.00718665i | \(0.00228760\pi\) |
−0.493763 | + | 0.869596i | \(0.664379\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3635.20i | − | 1.88378i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 160.799 | − | 92.8375i | 0.0817400 | − | 0.0471926i | −0.458573 | − | 0.888657i | \(-0.651639\pi\) |
0.540313 | + | 0.841464i | \(0.318306\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.6873 | − | 1203.54i | 0.0160007 | − | 0.589142i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 731.972 | − | 1267.81i | 0.351733 | − | 0.609219i | −0.634820 | − | 0.772660i | \(-0.718926\pi\) |
0.986553 | + | 0.163441i | \(0.0522592\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1283.16 | 0.594572 | 0.297286 | − | 0.954788i | \(-0.403919\pi\) | ||||
0.297286 | + | 0.954788i | \(0.403919\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1110.74 | −0.505571 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1539.71 | − | 2666.86i | 0.676660 | − | 1.17201i | −0.299321 | − | 0.954152i | \(-0.596760\pi\) |
0.975981 | − | 0.217856i | \(-0.0699064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 635.694 | − | 1035.10i | 0.274594 | − | 0.447120i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1251.05 | + | 722.292i | −0.522389 | + | 0.301601i | −0.737911 | − | 0.674898i | \(-0.764188\pi\) |
0.215523 | + | 0.976499i | \(0.430854\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2205.51i | − | 0.905714i | −0.891583 | − | 0.452857i | \(-0.850405\pi\) | ||
0.891583 | − | 0.452857i | \(-0.149595\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2000.94 | + | 3465.74i | 0.795202 | + | 1.37733i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4016.36 | − | 2318.85i | −1.57062 | − | 0.906797i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1349.66 | + | 779.228i | 0.511299 | + | 0.295199i | 0.733368 | − | 0.679832i | \(-0.237947\pi\) |
−0.222068 | + | 0.975031i | \(0.571281\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1926.18 | + | 3336.24i | 0.718390 | + | 1.24429i | 0.961637 | + | 0.274324i | \(0.0884539\pi\) |
−0.243248 | + | 0.969964i | \(0.578213\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 457.056i | − | 0.165299i | −0.996579 | − | 0.0826494i | \(-0.973662\pi\) | ||
0.996579 | − | 0.0826494i | \(-0.0263382\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2047.48 | + | 1182.11i | −0.729356 | + | 0.421094i | −0.818187 | − | 0.574953i | \(-0.805020\pi\) |
0.0888304 | + | 0.996047i | \(0.471687\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4521.42 | + | 2449.24i | −1.56326 | + | 0.846811i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −972.972 | + | 1685.24i | −0.331489 | + | 0.574156i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3660.78 | −1.21159 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5393.44 | 1.75971 | 0.879857 | − | 0.475239i | \(-0.157638\pi\) | ||||
0.879857 | + | 0.475239i | \(0.157638\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1797.91 | − | 3114.06i | 0.570308 | − | 0.987802i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4155.60 | + | 2552.12i | 1.30000 | + | 0.798383i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5620.66 | − | 3245.09i | 1.71080 | − | 0.987729i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 882.724i | − | 0.265074i | −0.991178 | − | 0.132537i | \(-0.957688\pi\) | ||
0.991178 | − | 0.132537i | \(-0.0423124\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2766.99 | − | 4792.56i | −0.809037 | − | 1.40129i | −0.913532 | − | 0.406768i | \(-0.866656\pi\) |
0.104495 | − | 0.994525i | \(-0.466677\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2099.57 | − | 1212.19i | −0.605868 | − | 0.349798i | 0.165479 | − | 0.986213i | \(-0.447083\pi\) |
−0.771347 | + | 0.636415i | \(0.780416\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5052.62 | − | 2917.13i | −1.42064 | − | 0.820204i | −0.424282 | − | 0.905530i | \(-0.639474\pi\) |
−0.996353 | + | 0.0853257i | \(0.972807\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3289.79 | − | 5698.08i | −0.913201 | − | 1.58171i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2431.96i | 0.658202i | 0.944295 | + | 0.329101i | \(0.106746\pi\) | ||||
−0.944295 | + | 0.329101i | \(0.893254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3899.69 | + | 2251.49i | −1.04233 | + | 0.601788i | −0.920492 | − | 0.390762i | \(-0.872212\pi\) |
−0.121836 | + | 0.992550i | \(0.538878\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2141.54 | + | 4223.31i | 0.558442 | + | 1.10130i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2561.52 | − | 4436.69i | 0.659861 | − | 1.14291i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 623.293 | 0.156741 | 0.0783704 | − | 0.996924i | \(-0.475028\pi\) | ||||
0.0783704 | + | 0.996924i | \(0.475028\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2671.67 | 0.663900 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2314.84 | − | 4009.42i | 0.561852 | − | 0.973156i | −0.435483 | − | 0.900197i | \(-0.643422\pi\) |
0.997335 | − | 0.0729589i | \(-0.0232442\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5366.65 | − | 145.755i | −1.28752 | − | 0.0349682i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1073.98 | − | 620.062i | 0.251804 | − | 0.145379i | −0.368786 | − | 0.929514i | \(-0.620227\pi\) |
0.620590 | + | 0.784135i | \(0.286893\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1371.98i | 0.318037i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −194.109 | − | 336.207i | −0.0439965 | − | 0.0762041i | 0.843189 | − | 0.537618i | \(-0.180676\pi\) |
−0.887185 | + | 0.461414i | \(0.847342\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 99.8873 | + | 57.6700i | 0.0223901 | + | 0.0129269i | 0.511153 | − | 0.859490i | \(-0.329218\pi\) |
−0.488763 | + | 0.872417i | \(0.662552\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2334.37 | + | 1347.75i | 0.511883 | + | 0.295536i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4188.29 | − | 7254.34i | −0.908484 | − | 1.57354i | −0.816171 | − | 0.577811i | \(-0.803907\pi\) |
−0.0923135 | − | 0.995730i | \(-0.529426\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2525.53i | 0.536157i | 0.963397 | + | 0.268079i | \(0.0863887\pi\) | ||||
−0.963397 | + | 0.268079i | \(0.913611\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 781.546 | − | 451.226i | 0.164163 | − | 0.0947794i | −0.415668 | − | 0.909517i | \(-0.636452\pi\) |
0.579831 | + | 0.814737i | \(0.303119\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1243.41 | − | 2295.39i | −0.255735 | − | 0.472100i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3910.74 | + | 6773.61i | −0.795999 | + | 1.37871i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9361.31 | −1.86653 | −0.933266 | − | 0.359187i | \(-0.883054\pi\) | ||||
−0.933266 | + | 0.359187i | \(0.883054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9252.94 | −1.82619 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1869.42 | + | 3237.93i | −0.361577 | + | 0.626269i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2297.63 | + | 4241.54i | 0.439977 | + | 0.812220i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1645.05 | − | 949.769i | 0.308837 | − | 0.178307i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2174.87i | − | 0.404321i | −0.979352 | − | 0.202161i | \(-0.935204\pi\) | ||
0.979352 | − | 0.202161i | \(-0.0647963\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1441.27 | + | 2496.35i | 0.262787 | + | 0.455161i | 0.966982 | − | 0.254846i | \(-0.0820249\pi\) |
−0.704194 | + | 0.710007i | \(0.748692\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4723.23 | − | 2726.96i | −0.852948 | − | 0.492450i | 0.00869669 | − | 0.999962i | \(-0.497232\pi\) |
−0.861644 | + | 0.507513i | \(0.830565\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6327.02 | + | 3652.91i | 1.12101 | + | 0.647217i | 0.941659 | − | 0.336568i | \(-0.109266\pi\) |
0.179353 | + | 0.983785i | \(0.442599\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5705.34 | − | 9881.93i | −1.00137 | − | 1.73443i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10052.0i | 1.73161i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3266.81 | + | 1886.09i | −0.557569 | + | 0.321913i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8823.42 | + | 239.638i | 1.47857 | + | 0.0401571i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −751.986 | + | 1302.48i | −0.124873 | + | 0.216286i | −0.921683 | − | 0.387943i | \(-0.873186\pi\) |
0.796810 | + | 0.604229i | \(0.206519\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2813.53 | 0.458865 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5276.54 | −0.852913 | −0.426456 | − | 0.904508i | \(-0.640238\pi\) | ||||
−0.426456 | + | 0.904508i | \(0.640238\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5410.80 | + | 9371.78i | −0.859271 | + | 1.48830i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6331.38 | − | 516.886i | −0.996684 | − | 0.0813680i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7507.70 | + | 4334.57i | −1.16148 | + | 0.670582i | −0.951659 | − | 0.307157i | \(-0.900622\pi\) |
−0.209823 | + | 0.977739i | \(0.567289\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2809.46i | 0.430908i | 0.976514 | + | 0.215454i | \(0.0691232\pi\) | ||||
−0.976514 | + | 0.215454i | \(0.930877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 222.247 | + | 384.944i | 0.0335100 | + | 0.0580411i | 0.882294 | − | 0.470699i | \(-0.155998\pi\) |
−0.848784 | + | 0.528740i | \(0.822665\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7195.40 | + | 4154.27i | 1.07575 | + | 0.621086i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −219.665 | − | 126.824i | −0.0322938 | − | 0.0186448i | 0.483766 | − | 0.875197i | \(-0.339269\pi\) |
−0.516060 | + | 0.856552i | \(0.672602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 537.797 | + | 931.492i | 0.0784075 | + | 0.135806i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 13273.6i | − | 1.90348i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11543.5 | + | 6664.65i | −1.64187 | + | 0.947934i | −0.661702 | + | 0.749767i | \(0.730166\pi\) |
−0.980168 | + | 0.198168i | \(0.936501\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1568.38 | − | 963.205i | −0.219478 | − | 0.134790i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4284.06 | − | 7420.21i | 0.594692 | − | 1.03004i | −0.398898 | − | 0.916995i | \(-0.630607\pi\) |
0.993590 | − | 0.113042i | \(-0.0360594\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15968.5 | 2.18149 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5015.67 | 0.679783 | 0.339892 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339892 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2374.05 | + | 4111.98i | −0.316732 | + | 0.548596i | −0.979804 | − | 0.199960i | \(-0.935919\pi\) |
0.663072 | + | 0.748556i | \(0.269252\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9239.20 | + | 5004.85i | −1.22305 | + | 0.662521i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4157.27 | + | 2400.20i | −0.541856 | + | 0.312841i | −0.745831 | − | 0.666135i | \(-0.767947\pi\) |
0.203975 | + | 0.978976i | \(0.434614\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7336.05i | − | 0.948850i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4420.49 | − | 7656.51i | −0.563086 | − | 0.975294i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2411.67 | − | 1392.38i | −0.304883 | − | 0.176024i | 0.339752 | − | 0.940515i | \(-0.389657\pi\) |
−0.644634 | + | 0.764491i | \(0.722990\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8763.27 | − | 5059.48i | −1.09131 | − | 0.630070i | −0.157388 | − | 0.987537i | \(-0.550307\pi\) |
−0.933926 | + | 0.357467i | \(0.883641\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7572.09 | − | 13115.2i | −0.935962 | − | 1.62113i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 11913.2i | − | 1.45090i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1342.22 | + | 774.928i | −0.162270 | + | 0.0936864i | −0.578936 | − | 0.815373i | \(-0.696532\pi\) |
0.416666 | + | 0.909060i | \(0.363198\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6496.09 | − | 10577.5i | 0.773975 | − | 1.26026i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9471.87 | − | 16405.8i | 1.12037 | − | 1.94055i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −401.529 | −0.0468161 | −0.0234081 | − | 0.999726i | \(-0.507452\pi\) | ||||
−0.0234081 | + | 0.999726i | \(0.507452\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4507.73 | 0.521836 | 0.260918 | − | 0.965361i | \(-0.415975\pi\) | ||||
0.260918 | + | 0.965361i | \(0.415975\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3700.74 | − | 6409.87i | 0.422382 | − | 0.731586i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −69.1841 | + | 2547.34i | −0.00784088 | + | 0.288699i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1239.54 | + | 715.647i | −0.138530 | + | 0.0799803i | −0.567663 | − | 0.823261i | \(-0.692152\pi\) |
0.429133 | + | 0.903241i | \(0.358819\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1115.14i | 0.123765i | 0.998083 | + | 0.0618826i | \(0.0197104\pi\) | ||||
−0.998083 | + | 0.0618826i | \(0.980290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2895.37 | − | 5014.93i | −0.316944 | − | 0.548962i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4322.17 | − | 2495.41i | −0.469900 | − | 0.271297i | 0.246298 | − | 0.969194i | \(-0.420786\pi\) |
−0.716198 | + | 0.697897i | \(0.754119\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2006.48 | + | 1158.44i | 0.215193 | + | 0.124242i | 0.603723 | − | 0.797194i | \(-0.293683\pi\) |
−0.388529 | + | 0.921436i | \(0.627017\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2510.00 | − | 4347.44i | −0.267383 | − | 0.463120i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14186.0i | 1.49104i | 0.666481 | + | 0.745522i | \(0.267800\pi\) | ||||
−0.666481 | + | 0.745522i | \(0.732200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5016.77 | − | 2896.43i | 0.523792 | − | 0.302412i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 399.228 | − | 14699.4i | 0.0411342 | − | 1.51455i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6577.70 | + | 11392.9i | −0.673286 | + | 1.16617i | 0.303680 | + | 0.952774i | \(0.401785\pi\) |
−0.976967 | + | 0.213392i | \(0.931549\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14004.0 | −1.41482 | −0.707409 | − | 0.706804i | \(-0.750136\pi\) | ||||
−0.707409 | + | 0.706804i | \(0.750136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7911.37 | 0.794109 | 0.397054 | − | 0.917795i | \(-0.370032\pi\) | ||||
0.397054 | + | 0.917795i | \(0.370032\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6052.64 | + | 10483.5i | −0.599749 | + | 1.03880i | 0.393108 | + | 0.919492i | \(0.371400\pi\) |
−0.992858 | + | 0.119304i | \(0.961934\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1975.26 | + | 3216.31i | −0.194476 | + | 0.316664i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9270.24 | + | 5352.17i | −0.901154 | + | 0.520282i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5842.38i | − | 0.564351i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4454.29 | + | 7715.05i | 0.424889 | + | 0.735929i | 0.996410 | − | 0.0846585i | \(-0.0269799\pi\) |
−0.571521 | + | 0.820587i | \(0.693647\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14438.2 | + | 8335.89i | 1.36866 | + | 0.790195i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9900.63 | + | 5716.13i | 0.926937 | + | 0.535167i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3029.89 | − | 5247.93i | −0.281925 | − | 0.488309i | 0.689934 | − | 0.723873i | \(-0.257640\pi\) |
−0.971859 | + | 0.235564i | \(0.924306\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 13210.0i | − | 1.21418i | −0.794634 | − | 0.607089i | \(-0.792337\pi\) | ||
0.794634 | − | 0.607089i | \(-0.207663\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27134.5 | + | 15666.1i | −2.47885 | + | 1.43117i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9800.56 | + | 5308.93i | −0.884538 | + | 0.479151i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1741.82 | − | 3016.91i | 0.156261 | − | 0.270653i | −0.777256 | − | 0.629184i | \(-0.783389\pi\) |
0.933518 | + | 0.358532i | \(0.116722\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16902.6 | 1.49831 | 0.749154 | − | 0.662396i | \(-0.230461\pi\) | ||||
0.749154 | + | 0.662396i | \(0.230461\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19596.8 | 1.72683 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4357.87 | + | 7548.04i | −0.379487 | + | 0.657291i | −0.990988 | − | 0.133953i | \(-0.957233\pi\) |
0.611501 | + | 0.791244i | \(0.290566\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15173.8 | + | 9318.82i | 1.31360 | + | 0.806732i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22394.0 | − | 12929.2i | 1.91611 | − | 1.10627i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19586.7i | 1.66619i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11287.1 | − | 19549.9i | −0.949132 | − | 1.64394i | −0.747259 | − | 0.664533i | \(-0.768631\pi\) |
−0.201873 | − | 0.979412i | \(-0.564703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12790.3 | − | 7384.48i | −1.06937 | − | 0.617401i | −0.141361 | − | 0.989958i | \(-0.545148\pi\) |
−0.928009 | + | 0.372557i | \(0.878481\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25733.7 | + | 14857.3i | 2.12709 | + | 1.22808i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3970.43 | − | 6876.99i | −0.326328 | − | 0.565216i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8106.76i | 0.658805i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18461.0 | + | 10658.5i | −1.49185 | + | 0.861320i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 765.130 | − | 14075.5i | 0.0611437 | − | 1.12482i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2903.12 | + | 5028.35i | −0.230711 | + | 0.399604i | −0.958018 | − | 0.286709i | \(-0.907439\pi\) |
0.727306 | + | 0.686313i | \(0.240772\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1619.32 | 0.127274 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1466.05 | 0.114595 | 0.0572977 | − | 0.998357i | \(-0.481752\pi\) | ||||
0.0572977 | + | 0.998357i | \(0.481752\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12366.1 | + | 21418.7i | −0.956103 | + | 1.65602i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11856.0 | + | 322.002i | 0.911699 | + | 0.0247612i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16685.6 | + | 9633.41i | −1.26928 | + | 0.732820i | −0.974852 | − | 0.222853i | \(-0.928463\pi\) |
−0.294429 | + | 0.955673i | \(0.595130\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 14980.1i | − | 1.13343i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1960.15 | − | 3395.08i | −0.146732 | − | 0.254148i | 0.783286 | − | 0.621662i | \(-0.213542\pi\) |
−0.930018 | + | 0.367514i | \(0.880209\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11629.3 | + | 6714.18i | 0.865926 | + | 0.499943i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8741.34 | + | 5046.82i | 0.644035 | + | 0.371834i | 0.786167 | − | 0.618014i | \(-0.212062\pi\) |
−0.142132 | + | 0.989848i | \(0.545396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −326.600 | − | 565.687i | −0.0239365 | − | 0.0414593i | 0.853809 | − | 0.520586i | \(-0.174287\pi\) |
−0.877746 | + | 0.479127i | \(0.840953\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4263.82i | 0.309241i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1603.38 | + | 925.713i | −0.115684 | + | 0.0667902i | −0.556725 | − | 0.830697i | \(-0.687942\pi\) |
0.441042 | + | 0.897487i | \(0.354609\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12104.5 | + | 22345.6i | 0.864339 | + | 1.59561i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2042.11 | − | 3537.04i | 0.145070 | − | 0.251268i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12502.1 | −0.879075 | −0.439537 | − | 0.898224i | \(-0.644858\pi\) | ||||
−0.439537 | + | 0.898224i | \(0.644858\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23455.4 | 1.64085 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4196.37 | − | 7268.33i | 0.290598 | − | 0.503330i | −0.683354 | − | 0.730088i | \(-0.739479\pi\) |
0.973951 | + | 0.226758i | \(0.0728126\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13742.6 | + | 25369.6i | 0.946879 | + | 1.74799i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1190.12 | − | 687.119i | 0.0811806 | − | 0.0468696i | −0.458860 | − | 0.888508i | \(-0.651742\pi\) |
0.540041 | + | 0.841639i | \(0.318409\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 18277.0i | − | 1.24049i | −0.784408 | − | 0.620245i | \(-0.787033\pi\) | ||
0.784408 | − | 0.620245i | \(-0.212967\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2470.98 | − | 4279.87i | −0.166049 | − | 0.287606i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 780.950 | + | 450.882i | 0.0522204 | + | 0.0301495i | 0.525883 | − | 0.850557i | \(-0.323735\pi\) |
−0.473663 | + | 0.880706i | \(0.657068\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23738.1 | − | 13705.2i | −1.57175 | − | 0.907452i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8361.05 | + | 14481.8i | 0.550896 | + | 0.954181i | 0.998210 | + | 0.0598035i | \(0.0190474\pi\) |
−0.447314 | + | 0.894377i | \(0.647619\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18190.2i | 1.18689i | 0.804875 | + | 0.593444i | \(0.202232\pi\) | ||||
−0.804875 | + | 0.593444i | \(0.797768\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22572.0 | − | 13031.9i | 1.46566 | − | 0.846200i | 0.466399 | − | 0.884575i | \(-0.345551\pi\) |
0.999263 | + | 0.0383743i | \(0.0122179\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6731.97 | + | 182.836i | 0.432922 | + | 0.0117579i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9760.86 | − | 16906.3i | 0.624695 | − | 1.08200i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −32712.0 | −2.07363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −371.934 | −0.0234650 | −0.0117325 | − | 0.999931i | \(-0.503735\pi\) | ||||
−0.0117325 | + | 0.999931i | \(0.503735\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1606.28 | − | 2782.16i | 0.100383 | − | 0.173869i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16523.5 | + | 10776.2i | 1.02776 | + | 0.670282i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10616.1 | − | 6129.20i | 0.654150 | − | 0.377673i | −0.135895 | − | 0.990723i | \(-0.543391\pi\) |
0.790044 | + | 0.613050i | \(0.210058\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 23619.7i | − | 1.44863i | −0.689469 | − | 0.724315i | \(-0.742156\pi\) | ||
0.689469 | − | 0.724315i | \(-0.257844\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6707.48 | + | 11617.7i | 0.407571 | + | 0.705933i | 0.994617 | − | 0.103620i | \(-0.0330426\pi\) |
−0.587046 | + | 0.809554i | \(0.699709\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 23854.7 | + | 13772.5i | 1.44280 | + | 0.833002i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8873.40 | + | 5123.06i | 0.531766 | + | 0.307015i | 0.741735 | − | 0.670693i | \(-0.234003\pi\) |
−0.209969 | + | 0.977708i | \(0.567336\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4223.52 | + | 7315.34i | 0.251949 | + | 0.436388i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 27958.0i | − | 1.65264i | −0.563203 | − | 0.826318i | \(-0.690431\pi\) | ||
0.563203 | − | 0.826318i | \(-0.309569\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6982.19 | + | 4031.17i | −0.410856 | + | 0.237208i | −0.691157 | − | 0.722704i | \(-0.742899\pi\) |
0.280301 | + | 0.959912i | \(0.409566\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19407.3 | + | 11918.8i | 1.13170 | + | 0.695023i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9024.88 | − | 15631.6i | 0.523905 | − | 0.907431i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5654.72 | −0.325333 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10696.6 | 0.612668 | 0.306334 | − | 0.951924i | \(-0.400898\pi\) | ||||
0.306334 | + | 0.951924i | \(0.400898\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14294.5 | − | 24758.8i | 0.811495 | − | 1.40555i | −0.100323 | − | 0.994955i | \(-0.531987\pi\) |
0.911818 | − | 0.410596i | \(-0.134679\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13485.2 | + | 7304.91i | −0.762173 | + | 0.412867i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1675.51 | − | 967.357i | 0.0938677 | − | 0.0541945i | −0.452331 | − | 0.891850i | \(-0.649408\pi\) |
0.546199 | + | 0.837655i | \(0.316074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26277.0i | 1.46568i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2857.81 | + | 4949.87i | 0.158017 | + | 0.273694i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11556.5 | + | 6672.18i | 0.636226 | + | 0.367325i | 0.783159 | − | 0.621821i | \(-0.213607\pi\) |
−0.146934 | + | 0.989146i | \(0.546940\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7138.67 | − | 4121.51i | −0.389619 | − | 0.224947i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7953.21 | − | 13775.4i | −0.432209 | − | 0.748607i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1011.59i | − | 0.0545040i | −0.999629 | − | 0.0272520i | \(-0.991324\pi\) | ||
0.999629 | − | 0.0272520i | \(-0.00867566\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22361.9 | + | 12910.7i | −1.19971 | + | 0.692653i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13758.1 | + | 22402.2i | −0.731862 | + | 1.19169i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6697.92 | − | 11601.1i | 0.354789 | − | 0.614513i | −0.632293 | − | 0.774730i | \(-0.717886\pi\) |
0.987082 | + | 0.160217i | \(0.0512193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17118.0 | −0.899120 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32630.6 | 1.70674 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12849.9 | − | 22256.6i | 0.666509 | − | 1.15443i | −0.312365 | − | 0.949962i | \(-0.601121\pi\) |
0.978874 | − | 0.204465i | \(-0.0655454\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −941.802 | + | 34676.9i | −0.0486471 | + | 1.79117i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15771.0 | − | 9105.36i | 0.807888 | − | 0.466434i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19526.6i | 0.996149i | 0.867134 | + | 0.498074i | \(0.165959\pi\) | ||||
−0.867134 | + | 0.498074i | \(0.834041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14696.3 | + | 25454.8i | 0.743590 | + | 1.28794i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23713.8 | + | 13691.2i | 1.19494 | + | 0.689897i | 0.959422 | − | 0.281974i | \(-0.0909893\pi\) |
0.235514 | + | 0.971871i | \(0.424323\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7253.47 | − | 4187.79i | −0.362531 | − | 0.209307i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19235.8 | − | 33317.4i | −0.957512 | − | 1.65846i | −0.728511 | − | 0.685034i | \(-0.759787\pi\) |
−0.229001 | − | 0.973426i | \(-0.573546\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 14729.9i | − | 0.727304i | −0.931535 | − | 0.363652i | \(-0.881530\pi\) | ||
0.931535 | − | 0.363652i | \(-0.118470\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7509.39 | + | 4335.55i | −0.369292 | + | 0.213211i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 776.397 | − | 28586.7i | 0.0378757 | − | 1.39457i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3886.66 | + | 6731.89i | −0.188850 | + | 0.327098i | −0.944867 | − | 0.327454i | \(-0.893809\pi\) |
0.756017 | + | 0.654552i | \(0.227143\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25934.3 | 1.25013 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33391.2 | 1.60320 | 0.801601 | − | 0.597860i | \(-0.203982\pi\) | ||||
0.801601 | + | 0.597860i | \(0.203982\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10098.8 | − | 17491.7i | 0.481053 | − | 0.833209i | −0.518710 | − | 0.854950i | \(-0.673588\pi\) |
0.999764 | + | 0.0217412i | \(0.00692097\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1136.86 | + | 1851.14i | −0.0539410 | + | 0.0878318i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33383.2 | + | 19273.8i | −1.57157 | + | 0.907348i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3862.66i | 0.181133i | 0.995890 | + | 0.0905665i | \(0.0288678\pi\) | ||||
−0.995890 | + | 0.0905665i | \(0.971132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8478.71 | − | 14685.6i | −0.394512 | − | 0.683315i | 0.598527 | − | 0.801103i | \(-0.295753\pi\) |
−0.993039 | + | 0.117788i | \(0.962420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14956.8 | − | 8635.30i | −0.693243 | − | 0.400244i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10873.6 | − | 6277.90i | −0.500114 | − | 0.288741i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12366.8 | − | 21419.9i | −0.566606 | − | 0.981390i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2563.31i | − | 0.116546i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24154.2 | + | 13945.4i | −1.09403 | + | 0.631640i | −0.934647 | − | 0.355576i | \(-0.884285\pi\) |
−0.159385 | + | 0.987216i | \(0.550951\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15839.8 | + | 8580.36i | −0.712008 | + | 0.385692i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3956.72 | − | 6853.24i | 0.177184 | − | 0.306893i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6934.09 | 0.308178 | 0.154089 | − | 0.988057i | \(-0.450756\pi\) | ||||
0.154089 | + | 0.988057i | \(0.450756\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 53782.5 | 2.38133 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19757.0 | + | 34220.2i | −0.868257 | + | 1.50386i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14163.6 | − | 8698.43i | −0.620126 | − | 0.380844i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13288.6 | − | 7672.20i | 0.577507 | − | 0.333424i | −0.182635 | − | 0.983181i | \(-0.558463\pi\) |
0.760142 | + | 0.649757i | \(0.225129\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6315.36i | − | 0.273443i | −0.990610 | − | 0.136721i | \(-0.956343\pi\) | ||
0.990610 | − | 0.136721i | \(-0.0436565\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10105.2 | − | 17502.6i | −0.434317 | − | 0.752258i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20092.9 | + | 11600.6i | 0.860416 | + | 0.496762i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5211.61 | + | 3008.92i | 0.221542 | + | 0.127908i | 0.606664 | − | 0.794958i | \(-0.292507\pi\) |
−0.385122 | + | 0.922866i | \(0.625841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6811.63 | + | 11798.1i | 0.288504 | + | 0.499703i | 0.973453 | − | 0.228888i | \(-0.0735089\pi\) |
−0.684949 | + | 0.728591i | \(0.740176\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 14214.7i | − | 0.597694i | −0.954301 | − | 0.298847i | \(-0.903398\pi\) | ||
0.954301 | − | 0.298847i | \(-0.0966020\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18508.4 | + | 10685.8i | −0.775418 | + | 0.447688i | −0.834804 | − | 0.550547i | \(-0.814419\pi\) |
0.0593859 | + | 0.998235i | \(0.481086\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38649.5 | − | 2100.94i | −1.60760 | − | 0.0873870i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8857.22 | − | 15341.2i | 0.367086 | − | 0.635812i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14814.1 | −0.609583 | −0.304791 | − | 0.952419i | \(-0.598587\pi\) | ||||
−0.304791 | + | 0.952419i | \(0.598587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −52701.3 | −2.16086 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7667.09 | + | 13279.8i | −0.312137 | + | 0.540637i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6627.33 | + | 179.994i | 0.268852 | + | 0.00730185i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16320.0 | − | 9422.33i | 0.657392 | − | 0.379546i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 72.2930i | 0.00290183i | 0.999999 | + | 0.00145092i | \(0.000461841\pi\) | ||||
−0.999999 | + | 0.00145092i | \(0.999538\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1544.70 | + | 2675.50i | 0.0615705 | + | 0.106643i | 0.895168 | − | 0.445730i | \(-0.147056\pi\) |
−0.833597 | + | 0.552373i | \(0.813722\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17965.2 | + | 10372.2i | 0.713581 | + | 0.411986i | 0.812386 | − | 0.583121i | \(-0.198168\pi\) |
−0.0988044 | + | 0.995107i | \(0.531502\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3404.77 | + | 1965.75i | 0.134299 | + | 0.0775374i | 0.565644 | − | 0.824649i | \(-0.308628\pi\) |
−0.431345 | + | 0.902187i | \(0.641961\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21256.3 | − | 36817.0i | −0.835533 | − | 1.44719i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26318.6i | 1.02739i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10150.8 | − | 5860.57i | 0.394887 | − | 0.227988i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7235.19 | + | 13356.5i | 0.279536 | + | 0.516038i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5314.79 | + | 9205.49i | −0.204638 | + | 0.354444i | −0.950017 | − | 0.312197i | \(-0.898935\pi\) |
0.745379 | + | 0.666641i | \(0.232268\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41443.8 | 1.58488 | 0.792438 | − | 0.609952i | \(-0.208811\pi\) | ||||
0.792438 | + | 0.609952i | \(0.208811\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6698.61 | 0.255296 | 0.127648 | − | 0.991820i | \(-0.459257\pi\) | ||||
0.127648 | + | 0.991820i | \(0.459257\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8864.70 | − | 15354.1i | 0.335567 | − | 0.581219i | −0.648027 | − | 0.761618i | \(-0.724406\pi\) |
0.983594 | + | 0.180399i | \(0.0577389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2052.74 | + | 3789.47i | 0.0774429 | + | 0.142964i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 36765.7 | − | 21226.7i | 1.37773 | − | 0.795436i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19943.0i | 0.744829i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36555.3 | + | 63315.6i | 1.35616 | + | 2.34893i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9712.24 | − | 5607.36i | −0.359114 | − | 0.207334i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26368.6 | − | 15223.9i | −0.968534 | − | 0.559183i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7415.53 | − | 12844.1i | −0.271476 | − | 0.470210i | 0.697764 | − | 0.716328i | \(-0.254178\pi\) |
−0.969240 | + | 0.246118i | \(0.920845\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23039.0i | 0.837887i | 0.908012 | + | 0.418943i | \(0.137599\pi\) | ||||
−0.908012 | + | 0.418943i | \(0.862401\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48838.2 | + | 28196.7i | −1.77033 | + | 1.02210i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11327.7 | − | 307.654i | −0.407933 | − | 0.0110792i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20275.1 | + | 35117.5i | −0.727762 | + | 1.26052i | 0.230066 | + | 0.973175i | \(0.426106\pi\) |
−0.957827 | + | 0.287345i | \(0.907227\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34613.2 | 1.23435 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19012.7 | 0.675821 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11232.2 | − | 19454.7i | 0.396680 | − | 0.687069i | −0.596634 | − | 0.802513i | \(-0.703496\pi\) |
0.993314 | + | 0.115444i | \(0.0368291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27250.0 | + | 13817.9i | −0.959273 | + | 0.486426i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −55447.4 | + | 32012.6i | −1.93938 | + | 1.11970i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28667.9i | − | 0.999509i | −0.866167 | − | 0.499755i | \(-0.833424\pi\) | ||
0.866167 | − | 0.499755i | \(-0.166576\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3897.91 | + | 6751.38i | 0.135035 | + | 0.233888i | 0.925611 | − | 0.378476i | \(-0.123552\pi\) |
−0.790576 | + | 0.612365i | \(0.790218\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7935.68 | + | 4581.67i | 0.274042 | + | 0.158218i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4880.63 | + | 2817.83i | 0.167475 | + | 0.0966919i | 0.581395 | − | 0.813622i | \(-0.302507\pi\) |
−0.413920 | + | 0.910313i | \(0.635841\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27648.8 | − | 47889.0i | −0.945750 | − | 1.63809i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28590.4i | 0.971808i | 0.874012 | + | 0.485904i | \(0.161510\pi\) | ||||
−0.874012 | + | 0.485904i | \(0.838490\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18632.6 | − | 10757.5i | 0.631347 | − | 0.364509i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30038.7 | − | 18448.0i | −1.01147 | − | 0.621185i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19772.6 | − | 34247.2i | 0.663711 | − | 1.14958i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 53183.2 | 1.77412 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6507.00 | 0.216392 | 0.108196 | − | 0.994130i | \(-0.465493\pi\) | ||||
0.108196 | + | 0.994130i | \(0.465493\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3949.43 | − | 6840.61i | 0.130528 | − | 0.226082i | −0.793352 | − | 0.608763i | \(-0.791666\pi\) |
0.923880 | + | 0.382681i | \(0.124999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9723.28 | − | 5267.07i | 0.320364 | − | 0.173540i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −23212.0 | + | 13401.5i | −0.760101 | + | 0.438845i | −0.829332 | − | 0.558756i | \(-0.811279\pi\) |
0.0692308 | + | 0.997601i | \(0.477946\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14944.0i | 0.487857i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4616.33 | − | 7995.71i | −0.149784 | − | 0.259434i | 0.781363 | − | 0.624076i | \(-0.214525\pi\) |
−0.931148 | + | 0.364642i | \(0.881191\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5464.47 | − | 3154.91i | −0.176764 | − | 0.102055i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14664.0 | − | 8466.24i | −0.471473 | − | 0.272205i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26268.9 | − | 45499.0i | −0.842037 | − | 1.45845i | −0.888170 | − | 0.459516i | \(-0.848023\pi\) |
0.0461326 | − | 0.998935i | \(-0.485310\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32639.0i | 1.03993i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20043.6 | − | 11572.2i | 0.636696 | − | 0.367597i | −0.146645 | − | 0.989189i | \(-0.546847\pi\) |
0.783341 | + | 0.621593i | \(0.213514\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 756.4.t.c.593.5 | yes | 12 | |
3.2 | odd | 2 | inner | 756.4.t.c.593.2 | yes | 12 | |
7.3 | odd | 6 | inner | 756.4.t.c.269.2 | ✓ | 12 | |
21.17 | even | 6 | inner | 756.4.t.c.269.5 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.4.t.c.269.2 | ✓ | 12 | 7.3 | odd | 6 | inner | |
756.4.t.c.269.5 | yes | 12 | 21.17 | even | 6 | inner | |
756.4.t.c.593.2 | yes | 12 | 3.2 | odd | 2 | inner | |
756.4.t.c.593.5 | yes | 12 | 1.1 | even | 1 | trivial |