Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(37,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.i (of order \(9\), degree \(6\), 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: | \(19.1166188419\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Character | \(\chi\) | \(=\) | 324.37 |
Dual form | 324.4.i.a.289.4 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{7}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.21695 | + | 1.89881i | −0.466618 | + | 0.169835i | −0.564620 | − | 0.825351i | \(-0.690977\pi\) |
0.0980017 | + | 0.995186i | \(0.468755\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.58868 | + | 9.00985i | 0.0857806 | + | 0.486486i | 0.997185 | + | 0.0749750i | \(0.0238877\pi\) |
−0.911405 | + | 0.411511i | \(0.865001\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 67.4972 | + | 24.5670i | 1.85011 | + | 0.673384i | 0.985189 | + | 0.171472i | \(0.0548522\pi\) |
0.864918 | + | 0.501912i | \(0.167370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −63.1985 | − | 53.0298i | −1.34832 | − | 1.13137i | −0.979405 | − | 0.201907i | \(-0.935286\pi\) |
−0.368911 | − | 0.929465i | \(-0.620269\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −21.0212 | + | 36.4097i | −0.299905 | + | 0.519450i | −0.976114 | − | 0.217259i | \(-0.930288\pi\) |
0.676209 | + | 0.736710i | \(0.263622\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −22.5218 | − | 39.0089i | −0.271940 | − | 0.471013i | 0.697419 | − | 0.716664i | \(-0.254332\pi\) |
−0.969358 | + | 0.245650i | \(0.920998\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −12.1174 | + | 68.7214i | −0.109855 | + | 0.623018i | 0.879315 | + | 0.476241i | \(0.158001\pi\) |
−0.989170 | + | 0.146777i | \(0.953110\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −72.1445 | + | 60.5364i | −0.577156 | + | 0.484291i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −142.727 | + | 119.762i | −0.913924 | + | 0.766873i | −0.972861 | − | 0.231388i | \(-0.925673\pi\) |
0.0589376 | + | 0.998262i | \(0.481229\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.3221 | + | 262.706i | −0.268377 | + | 1.52204i | 0.490866 | + | 0.871235i | \(0.336680\pi\) |
−0.759243 | + | 0.650807i | \(0.774431\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −25.3961 | − | 43.9873i | −0.122649 | − | 0.212435i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −40.4209 | + | 70.0111i | −0.179599 | + | 0.311074i | −0.941743 | − | 0.336333i | \(-0.890813\pi\) |
0.762144 | + | 0.647407i | \(0.224147\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 216.792 | + | 181.910i | 0.825787 | + | 0.692918i | 0.954320 | − | 0.298788i | \(-0.0965822\pi\) |
−0.128533 | + | 0.991705i | \(0.541027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −249.820 | − | 90.9271i | −0.885982 | − | 0.322471i | −0.141361 | − | 0.989958i | \(-0.545148\pi\) |
−0.744621 | + | 0.667487i | \(0.767370\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.5496 | + | 59.8299i | 0.0327409 | + | 0.185683i | 0.996792 | − | 0.0800335i | \(-0.0255027\pi\) |
−0.964051 | + | 0.265716i | \(0.914392\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 243.661 | − | 88.6854i | 0.710382 | − | 0.258558i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −206.241 | −0.534517 | −0.267258 | − | 0.963625i | \(-0.586118\pi\) | ||||
−0.267258 | + | 0.963625i | \(0.586118\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −398.778 | −0.977658 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −558.381 | + | 203.234i | −1.23212 | + | 0.448455i | −0.874323 | − | 0.485345i | \(-0.838694\pi\) |
−0.357797 | + | 0.933800i | \(0.616472\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 124.554 | + | 706.379i | 0.261434 | + | 1.48266i | 0.779002 | + | 0.627022i | \(0.215726\pi\) |
−0.517568 | + | 0.855642i | \(0.673163\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 430.397 | + | 156.652i | 0.821295 | + | 0.298927i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 23.6459 | + | 19.8412i | 0.0431164 | + | 0.0361790i | 0.664091 | − | 0.747652i | \(-0.268819\pi\) |
−0.620975 | + | 0.783831i | \(0.713263\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −155.414 | + | 269.185i | −0.259779 | + | 0.449950i | −0.966182 | − | 0.257859i | \(-0.916983\pi\) |
0.706404 | + | 0.707809i | \(0.250316\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −263.889 | − | 457.070i | −0.423094 | − | 0.732821i | 0.573146 | − | 0.819453i | \(-0.305723\pi\) |
−0.996240 | + | 0.0866322i | \(0.972389\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −114.113 | + | 647.169i | −0.168889 | + | 0.957815i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −500.648 | + | 420.094i | −0.713004 | + | 0.598281i | −0.925440 | − | 0.378893i | \(-0.876305\pi\) |
0.212436 | + | 0.977175i | \(0.431860\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 883.108 | − | 741.015i | 1.16788 | − | 0.979964i | 0.167893 | − | 0.985805i | \(-0.446304\pi\) |
0.999983 | + | 0.00584137i | \(0.00185938\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 40.5310 | − | 229.863i | 0.0517201 | − | 0.293319i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −240.988 | − | 417.404i | −0.287019 | − | 0.497132i | 0.686078 | − | 0.727528i | \(-0.259331\pi\) |
−0.973097 | + | 0.230397i | \(0.925998\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 377.389 | − | 653.656i | 0.434737 | − | 0.752987i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 191.566 | + | 160.743i | 0.206887 | + | 0.173598i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −858.230 | − | 312.370i | −0.898351 | − | 0.326973i | −0.148759 | − | 0.988873i | \(-0.547528\pi\) |
−0.749592 | + | 0.661901i | \(0.769750\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 92.4446 | + | 524.279i | 0.0910750 | + | 0.516512i | 0.995880 | + | 0.0906852i | \(0.0289057\pi\) |
−0.904805 | + | 0.425827i | \(0.859983\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 303.355 | − | 110.412i | 0.290199 | − | 0.105624i | −0.192819 | − | 0.981234i | \(-0.561763\pi\) |
0.483017 | + | 0.875611i | \(0.339541\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 209.423 | 0.189212 | 0.0946062 | − | 0.995515i | \(-0.469841\pi\) | ||||
0.0946062 | + | 0.995515i | \(0.469841\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −196.115 | −0.172334 | −0.0861672 | − | 0.996281i | \(-0.527462\pi\) | ||||
−0.0861672 | + | 0.996281i | \(0.527462\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −203.446 | + | 74.0482i | −0.169368 | + | 0.0616448i | −0.425312 | − | 0.905047i | \(-0.639836\pi\) |
0.255945 | + | 0.966691i | \(0.417614\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −67.2731 | − | 381.525i | −0.0545500 | − | 0.309368i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −361.442 | − | 131.554i | −0.278431 | − | 0.101341i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2932.73 | + | 2460.86i | 2.20341 | + | 1.84888i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 608.412 | − | 1053.80i | 0.435344 | − | 0.754038i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −611.723 | − | 1059.53i | −0.427414 | − | 0.740303i | 0.569228 | − | 0.822180i | \(-0.307242\pi\) |
−0.996642 | + | 0.0818763i | \(0.973909\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −194.741 | + | 1104.43i | −0.129882 | + | 0.736599i | 0.848405 | + | 0.529347i | \(0.177563\pi\) |
−0.978288 | + | 0.207252i | \(0.933548\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 315.684 | − | 264.891i | 0.205814 | − | 0.172699i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1967.06 | − | 1650.56i | 1.22670 | − | 1.02932i | 0.228252 | − | 0.973602i | \(-0.426699\pi\) |
0.998446 | − | 0.0557200i | \(-0.0177454\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 434.934 | − | 2466.63i | 0.265400 | − | 1.50516i | −0.502494 | − | 0.864581i | \(-0.667584\pi\) |
0.767894 | − | 0.640577i | \(-0.221305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2962.94 | − | 5131.96i | −1.73268 | − | 3.00109i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 517.194 | − | 895.807i | 0.296211 | − | 0.513053i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −88.5089 | − | 74.2678i | −0.0486640 | − | 0.0408339i | 0.618131 | − | 0.786075i | \(-0.287890\pi\) |
−0.666795 | + | 0.745241i | \(0.732334\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1464.39 | + | 532.995i | 0.789209 | + | 0.287249i | 0.705007 | − | 0.709200i | \(-0.250944\pi\) |
0.0842019 | + | 0.996449i | \(0.473166\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −257.169 | − | 1458.48i | −0.133267 | − | 0.755792i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1712.19 | − | 623.186i | 0.870367 | − | 0.316788i | 0.132052 | − | 0.991243i | \(-0.457844\pi\) |
0.738316 | + | 0.674455i | \(0.235621\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −638.420 | −0.312513 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1785.32 | 0.857897 | 0.428948 | − | 0.903329i | \(-0.358884\pi\) | ||||
0.428948 | + | 0.903329i | \(0.358884\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1097.06 | + | 399.298i | −0.508343 | + | 0.185022i | −0.583442 | − | 0.812154i | \(-0.698295\pi\) |
0.0751000 | + | 0.997176i | \(0.476072\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 800.382 | + | 4539.19i | 0.364307 | + | 2.06609i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3928.51 | + | 1429.86i | 1.72647 | + | 0.628383i | 0.998369 | − | 0.0570873i | \(-0.0181813\pi\) |
0.728100 | + | 0.685471i | \(0.240404\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −660.038 | − | 553.838i | −0.285110 | − | 0.239235i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −918.530 | + | 1590.94i | −0.383543 | + | 0.664316i | −0.991566 | − | 0.129604i | \(-0.958629\pi\) |
0.608023 | + | 0.793919i | \(0.291963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1157.45 | − | 2004.76i | −0.475318 | − | 0.823275i | 0.524282 | − | 0.851544i | \(-0.324334\pi\) |
−0.999600 | + | 0.0282697i | \(0.991000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 77.9358 | − | 441.996i | 0.0309727 | − | 0.175655i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2313.35 | + | 1941.13i | −0.904646 | + | 0.759088i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1309.35 | + | 1098.67i | −0.496027 | + | 0.416216i | −0.856180 | − | 0.516677i | \(-0.827169\pi\) |
0.360153 | + | 0.932893i | \(0.382724\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −538.413 | + | 3053.49i | −0.200808 | + | 1.13884i | 0.703095 | + | 0.711096i | \(0.251801\pi\) |
−0.903902 | + | 0.427740i | \(0.859310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 269.298 | + | 466.438i | 0.0973943 | + | 0.168692i | 0.910605 | − | 0.413277i | \(-0.135616\pi\) |
−0.813211 | + | 0.581969i | \(0.802283\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1847.26 | − | 3199.55i | 0.658035 | − | 1.13975i | −0.323089 | − | 0.946369i | \(-0.604721\pi\) |
0.981124 | − | 0.193381i | \(-0.0619454\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1305.79 | − | 1095.69i | −0.451470 | − | 0.378828i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1476.41 | − | 537.369i | −0.503009 | − | 0.183080i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −561.828 | − | 3186.28i | −0.185945 | − | 1.05455i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3344.47 | − | 1217.29i | 1.09120 | − | 0.397164i | 0.267134 | − | 0.963660i | \(-0.413924\pi\) |
0.824065 | + | 0.566496i | \(0.191701\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1475.95 | 0.468182 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2440.53 | −0.763474 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3259.31 | − | 1186.29i | 0.992058 | − | 0.361080i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −932.642 | − | 5289.28i | −0.280064 | − | 1.58832i | −0.722401 | − | 0.691474i | \(-0.756962\pi\) |
0.442337 | − | 0.896849i | \(-0.354150\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1788.67 | + | 651.023i | 0.522988 | + | 0.190352i | 0.590005 | − | 0.807400i | \(-0.299126\pi\) |
−0.0670166 | + | 0.997752i | \(0.521348\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1969.18 | − | 1652.34i | −0.568240 | − | 0.476810i | 0.312821 | − | 0.949812i | \(-0.398726\pi\) |
−0.881061 | + | 0.473002i | \(0.843170\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1769.64 | + | 3065.11i | −0.497567 | + | 0.861811i | −0.999996 | − | 0.00280750i | \(-0.999106\pi\) |
0.502429 | + | 0.864618i | \(0.332440\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −168.643 | − | 292.098i | −0.0468129 | − | 0.0810823i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1060.55 | + | 6014.68i | −0.287035 | + | 1.62786i | 0.410890 | + | 0.911685i | \(0.365218\pi\) |
−0.697925 | + | 0.716171i | \(0.745893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2459.06 | + | 2063.40i | −0.657270 | + | 0.551515i | −0.909267 | − | 0.416213i | \(-0.863357\pi\) |
0.251997 | + | 0.967728i | \(0.418913\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1102.77 | + | 925.334i | −0.287565 | + | 0.241296i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −645.292 | + | 3659.63i | −0.166230 | + | 0.942740i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1804.49 | − | 3125.47i | −0.453778 | − | 0.785967i | 0.544839 | − | 0.838541i | \(-0.316591\pi\) |
−0.998617 | + | 0.0525736i | \(0.983258\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2506.17 | + | 4340.82i | −0.622773 | + | 1.07868i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4944.99 | + | 4149.34i | 1.20023 | + | 1.00712i | 0.999623 | + | 0.0274439i | \(0.00873676\pi\) |
0.200610 | + | 0.979671i | \(0.435708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −695.005 | − | 252.961i | −0.166739 | − | 0.0606882i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1324.95 | + | 7514.17i | 0.310646 | + | 1.76176i | 0.595657 | + | 0.803239i | \(0.296892\pi\) |
−0.285011 | + | 0.958524i | \(0.591997\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1075.95 | − | 391.613i | 0.249415 | − | 0.0907797i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7418.04 | 1.68136 | 0.840681 | − | 0.541531i | \(-0.182155\pi\) | ||||
0.840681 | + | 0.541531i | \(0.182155\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5946.94 | −1.33303 | −0.666515 | − | 0.745492i | \(-0.732215\pi\) | ||||
−0.666515 | + | 0.745492i | \(0.732215\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6356.75 | + | 2313.67i | −1.39391 | + | 0.507343i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 105.510 | + | 598.379i | 0.0228863 | + | 0.129795i | 0.994110 | − | 0.108373i | \(-0.0345642\pi\) |
−0.971224 | + | 0.238168i | \(0.923453\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6387.32 | − | 2324.79i | −1.35600 | − | 0.493543i | −0.441184 | − | 0.897417i | \(-0.645441\pi\) |
−0.914815 | + | 0.403874i | \(0.867664\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −56.9781 | − | 47.8103i | −0.0119682 | − | 0.0100425i | 0.636784 | − | 0.771042i | \(-0.280264\pi\) |
−0.648752 | + | 0.761000i | \(0.724709\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1294.57 | + | 2242.26i | −0.266258 | + | 0.461173i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1572.72 | + | 2724.03i | 0.320114 | + | 0.554454i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.3041 | − | 98.1364i | 0.00345023 | − | 0.0195672i | −0.983034 | − | 0.183423i | \(-0.941282\pi\) |
0.986484 | + | 0.163856i | \(0.0523932\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2527.14 | − | 2120.52i | 0.498766 | − | 0.418514i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4410.09 | − | 3700.50i | 0.852983 | − | 0.715738i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 422.355 | − | 2395.30i | 0.0808776 | − | 0.458680i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1991.07 | − | 3448.64i | −0.373798 | − | 0.647437i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2496.99 | + | 4324.91i | −0.464204 | + | 0.804024i | −0.999165 | − | 0.0408521i | \(-0.986993\pi\) |
0.534962 | + | 0.844876i | \(0.320326\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5733.38 | − | 4810.88i | −1.04537 | − | 0.877170i | −0.0527712 | − | 0.998607i | \(-0.516805\pi\) |
−0.992599 | + | 0.121437i | \(0.961250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4171.87 | + | 1518.44i | 0.753380 | + | 0.274208i | 0.690027 | − | 0.723783i | \(-0.257599\pi\) |
0.0633524 | + | 0.997991i | \(0.479821\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 299.891 | + | 1700.77i | 0.0531342 | + | 0.301339i | 0.999781 | − | 0.0209343i | \(-0.00666407\pi\) |
−0.946647 | + | 0.322273i | \(0.895553\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12575.9 | + | 4577.25i | −2.20726 | + | 0.803376i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1893.74 | 0.326224 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7769.66 | 1.32610 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −522.298 | + | 190.101i | −0.0875235 | + | 0.0318559i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −146.572 | − | 831.251i | −0.0243393 | − | 0.138035i | 0.970217 | − | 0.242239i | \(-0.0778818\pi\) |
−0.994556 | + | 0.104204i | \(0.966771\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −161.034 | − | 58.6116i | −0.0262634 | − | 0.00955908i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.8927 | + | 21.7265i | 0.00418536 | + | 0.00351193i | 0.644878 | − | 0.764286i | \(-0.276908\pi\) |
−0.640693 | + | 0.767798i | \(0.721353\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9580.49 | + | 16593.9i | −1.52145 | + | 2.63522i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2755.17 | + | 4772.09i | 0.433717 | + | 0.751220i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1785.27 | − | 10124.8i | 0.276191 | − | 1.56636i | −0.458963 | − | 0.888455i | \(-0.651779\pi\) |
0.735154 | − | 0.677900i | \(-0.237110\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5099.40 | + | 4278.91i | −0.782134 | + | 0.656289i | −0.943785 | − | 0.330559i | \(-0.892763\pi\) |
0.161651 | + | 0.986848i | \(0.448318\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6159.61 | + | 5168.53i | −0.928734 | + | 0.779300i | −0.975590 | − | 0.219601i | \(-0.929524\pi\) |
0.0468557 | + | 0.998902i | \(0.485080\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 299.655 | − | 1699.43i | 0.0448001 | − | 0.254074i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1712.40 | + | 2965.97i | 0.251747 | + | 0.436039i | 0.964007 | − | 0.265877i | \(-0.0856615\pi\) |
−0.712260 | + | 0.701916i | \(0.752328\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2415.04 | − | 4182.97i | 0.352098 | − | 0.609851i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2244.59 | + | 1883.43i | 0.321882 | + | 0.270091i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3402.99 | − | 1238.59i | −0.484018 | − | 0.176168i | 0.0884742 | − | 0.996078i | \(-0.471801\pi\) |
−0.572492 | + | 0.819910i | \(0.694023\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −327.651 | − | 1858.20i | −0.0458512 | − | 0.260035i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1812.31 | + | 659.627i | −0.251576 | + | 0.0915662i | −0.464730 | − | 0.885452i | \(-0.653849\pi\) |
0.213154 | + | 0.977019i | \(0.431626\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15371.1 | 2.09988 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4403.13 | 0.596763 | 0.298382 | − | 0.954447i | \(-0.403553\pi\) | ||||
0.298382 | + | 0.954447i | \(0.403553\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10231.3 | − | 3723.88i | 1.36500 | − | 0.496819i | 0.447402 | − | 0.894333i | \(-0.352349\pi\) |
0.917596 | + | 0.397515i | \(0.130127\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −633.530 | − | 3592.93i | −0.0838641 | − | 0.475617i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7053.47 | − | 2567.25i | −0.919345 | − | 0.334614i | −0.161367 | − | 0.986894i | \(-0.551590\pi\) |
−0.757978 | + | 0.652280i | \(0.773813\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2247.41 | − | 1885.80i | −0.290681 | − | 0.243910i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1814.18 | − | 3142.25i | 0.231091 | − | 0.400262i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3635.79 | − | 6297.37i | −0.459635 | − | 0.796111i | 0.539307 | − | 0.842110i | \(-0.318686\pi\) |
−0.998942 | + | 0.0459984i | \(0.985353\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2014.16 | − | 11422.9i | 0.250828 | − | 1.42252i | −0.555729 | − | 0.831363i | \(-0.687561\pi\) |
0.806558 | − | 0.591155i | \(-0.201328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16858.7 | − | 14146.1i | 2.08385 | − | 1.74856i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4448.26 | + | 3732.53i | −0.541750 | + | 0.454582i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1420.37 | − | 8055.31i | 0.171718 | − | 0.973862i | −0.770146 | − | 0.637868i | \(-0.779817\pi\) |
0.941864 | − | 0.335994i | \(-0.109072\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2718.20 | − | 4708.06i | −0.323859 | − | 0.560940i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3200.08 | + | 5542.70i | −0.378520 | + | 0.655615i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6454.20 | + | 5415.71i | 0.752525 | + | 0.631444i | 0.936169 | − | 0.351549i | \(-0.114345\pi\) |
−0.183644 | + | 0.982993i | \(0.558789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4401.68 | + | 1602.08i | 0.509560 | + | 0.185465i | 0.583989 | − | 0.811762i | \(-0.301491\pi\) |
−0.0744290 | + | 0.997226i | \(0.523713\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −687.553 | − | 3899.31i | −0.0784735 | − | 0.445045i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6166.49 | + | 2244.42i | −0.698869 | + | 0.254368i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8784.41 | 0.981740 | 0.490870 | − | 0.871233i | \(-0.336679\pi\) | ||||
0.490870 | + | 0.871233i | \(0.336679\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6469.85 | −0.718063 | −0.359031 | − | 0.933325i | \(-0.616893\pi\) | ||||
−0.359031 | + | 0.933325i | \(0.616893\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2953.65 | − | 1075.04i | 0.323323 | − | 0.117680i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −148.990 | − | 844.963i | −0.0161979 | − | 0.0918631i | 0.975637 | − | 0.219391i | \(-0.0704070\pi\) |
−0.991835 | + | 0.127528i | \(0.959296\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −412.777 | − | 150.239i | −0.0442701 | − | 0.0161130i | 0.319790 | − | 0.947488i | \(-0.396388\pi\) |
−0.364060 | + | 0.931375i | \(0.618610\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2049.80 | + | 1719.98i | 0.218359 | + | 0.183225i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1510.09 | + | 2615.54i | −0.158720 | + | 0.274911i | −0.934407 | − | 0.356206i | \(-0.884070\pi\) |
0.775687 | + | 0.631117i | \(0.217403\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10163.9 | + | 17604.4i | 1.06120 | + | 1.83804i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −727.645 | + | 4126.68i | −0.0749726 | + | 0.425191i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5728.39 | − | 4806.69i | 0.586352 | − | 0.492008i | −0.300674 | − | 0.953727i | \(-0.597212\pi\) |
0.887026 | + | 0.461719i | \(0.152767\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4559.80 | + | 3826.13i | −0.460675 | + | 0.386552i | −0.843379 | − | 0.537319i | \(-0.819437\pi\) |
0.382705 | + | 0.923871i | \(0.374993\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 299.450 | − | 1698.27i | 0.0300575 | − | 0.170465i | −0.966084 | − | 0.258229i | \(-0.916861\pi\) |
0.996141 | + | 0.0877642i | \(0.0279722\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7069.94 | − | 12245.5i | −0.700552 | − | 1.21339i | −0.968273 | − | 0.249895i | \(-0.919604\pi\) |
0.267721 | − | 0.963496i | \(-0.413729\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −141.201 | + | 244.567i | −0.0139020 | + | 0.0240790i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −14628.4 | − | 12274.7i | −1.42202 | − | 1.19321i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3986.28 | + | 1450.89i | 0.385059 | + | 0.140150i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −467.551 | − | 2651.62i | −0.0445991 | − | 0.252934i | 0.954354 | − | 0.298677i | \(-0.0965455\pi\) |
−0.998953 | + | 0.0457434i | \(0.985434\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6267.22 | − | 2281.08i | 0.594097 | − | 0.216234i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5070.47 | 0.474718 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12687.7 | 1.18056 | 0.590280 | − | 0.807199i | \(-0.299017\pi\) | ||||
0.590280 | + | 0.807199i | \(0.299017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5094.55 | − | 1854.26i | 0.468256 | − | 0.170431i | −0.0971061 | − | 0.995274i | \(-0.530959\pi\) |
0.565362 | + | 0.824843i | \(0.308736\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1360.22 | − | 7714.21i | −0.124262 | − | 0.704727i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2672.22 | − | 972.609i | −0.241178 | − | 0.0877817i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10451.5 | − | 8769.82i | −0.937619 | − | 0.786756i | 0.0395506 | − | 0.999218i | \(-0.487407\pi\) |
−0.977169 | + | 0.212462i | \(0.931852\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3966.78 | + | 6870.66i | −0.351630 | + | 0.609041i | −0.986535 | − | 0.163549i | \(-0.947706\pi\) |
0.634905 | + | 0.772590i | \(0.281039\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1477.79 | − | 2559.60i | −0.130219 | − | 0.225546i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3183.90 | − | 18056.8i | 0.277257 | − | 1.57240i | −0.454443 | − | 0.890776i | \(-0.650162\pi\) |
0.731700 | − | 0.681627i | \(-0.238727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3698.89 | − | 3103.74i | 0.320214 | − | 0.268691i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1372.94 | + | 1152.03i | −0.117473 | + | 0.0985718i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −757.769 | + | 4297.52i | −0.0644616 | + | 0.365580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3020.36 | + | 5231.43i | 0.253982 | + | 0.439910i | 0.964618 | − | 0.263650i | \(-0.0849263\pi\) |
−0.710637 | + | 0.703559i | \(0.751593\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2909.21 | − | 5038.90i | 0.243233 | − | 0.421292i | −0.718400 | − | 0.695630i | \(-0.755125\pi\) |
0.961633 | + | 0.274338i | \(0.0884586\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8591.29 | − | 7208.95i | −0.710138 | − | 0.595876i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6857.44 | + | 2495.90i | 0.563610 | + | 0.205137i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4054.27 | − | 22992.9i | −0.329475 | − | 1.86854i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1092.55 | + | 397.656i | −0.0882899 | + | 0.0321349i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18625.2 | 1.48839 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6742.32 | 0.535813 | 0.267907 | − | 0.963445i | \(-0.413668\pi\) | ||||
0.267907 | + | 0.963445i | \(0.413668\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1023.12 | − | 372.387i | 0.0804144 | − | 0.0292684i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 996.065 | + | 5648.96i | 0.0778586 | + | 0.441558i | 0.998670 | + | 0.0515507i | \(0.0164164\pi\) |
−0.920812 | + | 0.390007i | \(0.872473\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7886.27 | + | 2870.37i | 0.609740 | + | 0.221927i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4580.35 | − | 3843.37i | −0.352217 | − | 0.295546i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11916.4 | + | 20639.9i | −0.906492 | + | 1.57009i | −0.0875890 | + | 0.996157i | \(0.527916\pi\) |
−0.818902 | + | 0.573933i | \(0.805417\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10966.4 | + | 18994.4i | 0.829749 | + | 1.43717i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −143.937 | + | 816.308i | −0.0107748 | + | 0.0611070i | −0.989721 | − | 0.143011i | \(-0.954322\pi\) |
0.978946 | + | 0.204118i | \(0.0654327\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 920.762 | − | 772.611i | 0.0685606 | − | 0.0575292i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −809.884 | + | 679.573i | −0.0596698 | + | 0.0500689i | −0.672135 | − | 0.740429i | \(-0.734622\pi\) |
0.612465 | + | 0.790498i | \(0.290178\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4496.33 | + | 25499.9i | −0.329537 | + | 1.86890i | 0.146124 | + | 0.989266i | \(0.453320\pi\) |
−0.475661 | + | 0.879629i | \(0.657791\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3285.94 | − | 5691.42i | −0.238319 | − | 0.412780i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1489.92 | + | 2580.62i | −0.107498 | + | 0.186192i | −0.914756 | − | 0.404007i | \(-0.867617\pi\) |
0.807258 | + | 0.590199i | \(0.200951\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8079.41 | + | 6779.43i | 0.576920 | + | 0.484093i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13920.7 | − | 5066.72i | −0.988913 | − | 0.359935i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3085.89 | + | 17501.0i | 0.216982 | + | 1.23057i | 0.877434 | + | 0.479698i | \(0.159254\pi\) |
−0.660452 | + | 0.750868i | \(0.729635\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11291.1 | − | 4109.63i | 0.789884 | − | 0.287494i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3329.70 | 0.230581 | 0.115290 | − | 0.993332i | \(-0.463220\pi\) | ||||
0.115290 | + | 0.993332i | \(0.463220\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2135.42 | 0.147132 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12799.7 | + | 4658.71i | −0.873090 | + | 0.317779i | −0.739418 | − | 0.673247i | \(-0.764899\pi\) |
−0.133672 | + | 0.991026i | \(0.542677\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 447.186 | + | 2536.12i | 0.0303513 | + | 0.172131i | 0.996215 | − | 0.0869185i | \(-0.0277020\pi\) |
−0.965864 | + | 0.259049i | \(0.916591\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19972.6 | − | 7269.45i | −1.34215 | − | 0.488504i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8011.80 | − | 6722.70i | −0.535731 | − | 0.449532i | 0.334344 | − | 0.942451i | \(-0.391485\pi\) |
−0.870075 | + | 0.492919i | \(0.835930\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2506.05 | − | 4340.60i | 0.165931 | − | 0.287401i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12357.4 | − | 21403.7i | −0.814211 | − | 1.41025i | −0.909893 | − | 0.414842i | \(-0.863837\pi\) |
0.0956826 | − | 0.995412i | \(-0.469497\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1578.77 | + | 8953.67i | −0.103013 | + | 0.584216i | 0.888982 | + | 0.457942i | \(0.151413\pi\) |
−0.991995 | + | 0.126274i | \(0.959698\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7255.84 | − | 6088.37i | 0.471142 | − | 0.395335i | −0.376069 | − | 0.926592i | \(-0.622725\pi\) |
0.847211 | + | 0.531257i | \(0.178280\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3377.89 | − | 2834.39i | 0.217227 | − | 0.182275i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 871.146 | − | 4940.52i | 0.0557534 | − | 0.316193i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1699.39 | − | 2943.43i | −0.107725 | − | 0.186585i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7345.25 | + | 12722.3i | −0.463407 | + | 0.802644i | −0.999128 | − | 0.0417505i | \(-0.986707\pi\) |
0.535721 | + | 0.844395i | \(0.320040\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5203.19 | + | 4365.99i | 0.325169 | + | 0.272849i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20102.0 | − | 7316.53i | −1.25035 | − | 0.455088i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4526.38 | + | 25670.4i | 0.278910 | + | 1.58178i | 0.726261 | + | 0.687419i | \(0.241256\pi\) |
−0.447351 | + | 0.894359i | \(0.647632\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2079.34 | − | 756.817i | 0.127529 | − | 0.0464167i | −0.277467 | − | 0.960735i | \(-0.589495\pi\) |
0.404996 | + | 0.914318i | \(0.367273\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13758.7 | 0.836027 | 0.418013 | − | 0.908441i | \(-0.362727\pi\) | ||||
0.418013 | + | 0.908441i | \(0.362727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −42682.0 | −2.58154 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15288.2 | − | 5564.44i | 0.916191 | − | 0.333466i | 0.159469 | − | 0.987203i | \(-0.449022\pi\) |
0.756722 | + | 0.653737i | \(0.226800\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1081.15 | − | 6131.53i | −0.0644949 | − | 0.365769i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10222.0 | + | 3720.52i | 0.604240 | + | 0.219925i | 0.625981 | − | 0.779838i | \(-0.284699\pi\) |
−0.0217411 | + | 0.999764i | \(0.506921\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 316.290 | + | 265.399i | 0.0186116 | + | 0.0156170i | 0.652046 | − | 0.758179i | \(-0.273911\pi\) |
−0.633434 | + | 0.773796i | \(0.718355\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1143.93 | + | 1981.35i | −0.0667063 | + | 0.115539i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6500.75 | − | 11259.6i | −0.377377 | − | 0.653635i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8946.57 | + | 50738.5i | −0.514722 | + | 2.91913i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18608.4 | + | 15614.3i | −1.06582 | + | 0.894333i | −0.994668 | − | 0.103133i | \(-0.967113\pi\) |
−0.0711564 | + | 0.997465i | \(0.522669\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8328.43 | − | 6988.38i | 0.472803 | − | 0.396729i | −0.375013 | − | 0.927020i | \(-0.622362\pi\) |
0.847816 | + | 0.530291i | \(0.177917\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1450.95 | − | 8228.77i | 0.0820067 | − | 0.465083i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6279.52 | − | 10876.5i | −0.351800 | − | 0.609335i | 0.634765 | − | 0.772705i | \(-0.281097\pi\) |
−0.986565 | + | 0.163370i | \(0.947764\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7127.96 | + | 12346.0i | −0.397585 | + | 0.688637i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13034.1 | + | 10936.9i | 0.720698 | + | 0.604737i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16718.3 | + | 6084.96i | 0.920396 | + | 0.334997i | 0.758396 | − | 0.651794i | \(-0.225983\pi\) |
0.162000 | + | 0.986791i | \(0.448206\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2414.65 | + | 13694.2i | 0.131788 | + | 0.747408i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11180.5 | + | 4069.38i | −0.607594 | + | 0.221146i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21646.4 | −1.16629 | −0.583147 | − | 0.812367i | \(-0.698179\pi\) | ||||
−0.583147 | + | 0.812367i | \(0.698179\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3641.41 | 0.195360 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4576.81 | + | 1665.82i | −0.243463 | + | 0.0886135i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3459.28 | + | 19618.5i | 0.183238 | + | 1.03920i | 0.928198 | + | 0.372086i | \(0.121357\pi\) |
−0.744960 | + | 0.667109i | \(0.767532\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17492.2 | − | 6366.64i | −0.918777 | − | 0.334407i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25202.2 | + | 21147.1i | 1.31819 | + | 1.10609i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10932.0 | + | 18934.8i | −0.567031 | + | 0.982126i | 0.429827 | + | 0.902911i | \(0.358575\pi\) |
−0.996858 | + | 0.0792148i | \(0.974759\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1476.73 | + | 2557.77i | 0.0762779 | + | 0.132117i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3047.00 | − | 17280.4i | 0.156087 | − | 0.885211i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25330.4 | + | 21254.7i | −1.29223 | + | 1.08431i | −0.300799 | + | 0.953688i | \(0.597253\pi\) |
−0.991432 | + | 0.130623i | \(0.958302\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8562.15 | − | 7184.49i | 0.433218 | − | 0.363513i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2985.32 | − | 16930.6i | 0.150430 | − | 0.853131i | −0.812416 | − | 0.583079i | \(-0.801848\pi\) |
0.962846 | − | 0.270052i | \(-0.0870410\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1108.59 | + | 1920.14i | 0.0554077 | + | 0.0959689i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9649.35 | − | 16713.2i | 0.480321 | − | 0.831940i | −0.519424 | − | 0.854516i | \(-0.673854\pi\) |
0.999745 | + | 0.0225766i | \(0.00718696\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20573.9 | − | 17263.5i | −1.01586 | − | 0.852405i | −0.0267555 | − | 0.999642i | \(-0.508518\pi\) |
−0.989101 | + | 0.147237i | \(0.952962\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 602.767 | + | 219.389i | 0.0296425 | + | 0.0107890i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 332.707 | + | 1886.87i | 0.0162308 | + | 0.0920492i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27645.8 | + | 10062.2i | −1.34329 | + | 0.488916i | −0.910846 | − | 0.412746i | \(-0.864570\pi\) |
−0.432440 | + | 0.901663i | \(0.642347\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8651.72 | −0.417044 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24191.8 | 1.16151 | 0.580756 | − | 0.814077i | \(-0.302757\pi\) | ||||
0.580756 | + | 0.814077i | \(0.302757\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12610.5 | + | 4589.85i | −0.600698 | + | 0.218636i | −0.624428 | − | 0.781082i | \(-0.714668\pi\) |
0.0237304 | + | 0.999718i | \(0.492446\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −311.565 | − | 1766.97i | −0.0147830 | − | 0.0838383i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 46066.3 | + | 16766.8i | 2.16866 | + | 0.789326i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16690.9 | + | 14005.3i | 0.782689 | + | 0.656754i | 0.943924 | − | 0.330162i | \(-0.107103\pi\) |
−0.161235 | + | 0.986916i | \(0.551548\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 670.497 | − | 1161.34i | 0.0311981 | − | 0.0540367i | −0.850005 | − | 0.526775i | \(-0.823401\pi\) |
0.881203 | + | 0.472738i | \(0.156734\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12561.4 | − | 21756.9i | −0.582216 | − | 1.00843i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2213.57 | − | 12553.8i | 0.101809 | − | 0.577389i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17103.1 | + | 14351.2i | −0.783607 | + | 0.657524i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7749.10 | + | 6502.26i | −0.352327 | + | 0.295638i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −508.621 | + | 2884.53i | −0.0230373 | + | 0.130651i | −0.994157 | − | 0.107940i | \(-0.965575\pi\) |
0.971120 | + | 0.238591i | \(0.0766856\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −990.373 | − | 1715.38i | −0.0445178 | − | 0.0771071i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29587.5 | − | 51247.1i | 1.32495 | − | 2.29488i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21377.1 | + | 17937.5i | 0.950082 | + | 0.797213i | 0.979311 | − | 0.202359i | \(-0.0648609\pi\) |
−0.0292296 | + | 0.999573i | \(0.509305\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2400.15 | − | 873.585i | −0.106272 | − | 0.0386799i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6582.97 | − | 37333.9i | −0.289300 | − | 1.64070i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3330.61 | − | 1212.24i | 0.145824 | − | 0.0530756i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12704.1 | −0.552104 | −0.276052 | − | 0.961143i | \(-0.589026\pi\) | ||||
−0.276052 | + | 0.961143i | \(0.589026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5012.10 | 0.217014 | 0.108507 | − | 0.994096i | \(-0.465393\pi\) | ||||
0.108507 | + | 0.994096i | \(0.465393\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9313.93 | + | 3389.99i | −0.400310 | + | 0.145701i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2079.43 | + | 11793.1i | 0.0890455 | + | 0.505002i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13568.4 | + | 4938.51i | 0.576787 | + | 0.209933i | 0.613908 | − | 0.789378i | \(-0.289597\pi\) |
−0.0371213 | + | 0.999311i | \(0.511819\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 677.888 | + | 568.816i | 0.0287117 | + | 0.0240919i | 0.657031 | − | 0.753864i | \(-0.271812\pi\) |
−0.628319 | + | 0.777956i | \(0.716257\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16997.2 | − | 29440.1i | 0.714693 | − | 1.23789i | −0.248384 | − | 0.968662i | \(-0.579900\pi\) |
0.963078 | − | 0.269224i | \(-0.0867671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2235.23 | + | 3871.54i | 0.0936463 | + | 0.162200i | 0.909043 | − | 0.416703i | \(-0.136814\pi\) |
−0.815397 | + | 0.578903i | \(0.803481\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1893.03 | + | 10735.9i | −0.0787390 | + | 0.446551i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4965.12 | − | 4166.23i | 0.205779 | − | 0.172669i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4716.06 | − | 3957.24i | 0.194060 | − | 0.162836i | −0.540580 | − | 0.841292i | \(-0.681795\pi\) |
0.734640 | + | 0.678457i | \(0.237351\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1792.94 | − | 10168.3i | 0.0735142 | − | 0.416920i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12794.6 | − | 22160.9i | −0.520886 | − | 0.902201i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17512.8 | + | 30333.0i | −0.710444 | + | 1.23052i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4321.46 | − | 3626.14i | −0.174075 | − | 0.146066i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8837.84 | + | 3216.71i | 0.354750 | + | 0.129119i | 0.513247 | − | 0.858241i | \(-0.328442\pi\) |
−0.158497 | + | 0.987360i | \(0.550665\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2250.77 | − | 12764.8i | −0.0897141 | − | 0.508794i | −0.996239 | − | 0.0866426i | \(-0.972386\pi\) |
0.906525 | − | 0.422151i | \(-0.138725\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22836.3 | − | 8311.73i | 0.907059 | − | 0.330143i | 0.153981 | − | 0.988074i | \(-0.450791\pi\) |
0.753078 | + | 0.657931i | \(0.228568\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21125.6 | −0.833285 | −0.416643 | − | 0.909070i | \(-0.636793\pi\) | ||||
−0.416643 | + | 0.909070i | \(0.636793\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23209.9 | −0.912323 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −44112.8 | + | 16055.7i | −1.72201 | + | 0.626759i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −442.205 | − | 2507.87i | −0.0172027 | − | 0.0975614i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10461.1 | + | 3807.55i | 0.404173 | + | 0.147107i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22826.9 | + | 19154.0i | 0.878915 | + | 0.737498i | 0.965956 | − | 0.258707i | \(-0.0832965\pi\) |
−0.0870404 | + | 0.996205i | \(0.527741\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13196.2 | − | 22856.4i | 0.504643 | − | 0.874066i | −0.495343 | − | 0.868697i | \(-0.664958\pi\) |
0.999986 | − | 0.00536903i | \(-0.00170903\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8184.93 | + | 14176.7i | 0.311942 | + | 0.540299i | 0.978783 | − | 0.204901i | \(-0.0656872\pi\) |
−0.666841 | + | 0.745200i | \(0.732354\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4816.38 | + | 27315.0i | −0.182320 | + | 1.03399i | 0.747030 | + | 0.664791i | \(0.231479\pi\) |
−0.929350 | + | 0.369200i | \(0.879632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8574.42 | − | 7194.79i | 0.323483 | − | 0.271435i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2096.30 | − | 1759.01i | 0.0785555 | − | 0.0659159i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1771.02 | − | 10044.0i | 0.0661439 | − | 0.375121i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24850.8 | − | 43042.9i | −0.921937 | − | 1.59684i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4335.43 | − | 7509.18i | 0.160304 | − | 0.277655i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9845.02 | + | 8260.96i | 0.361613 | + | 0.303429i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15389.5 | + | 5601.34i | 0.563397 | + | 0.205060i | 0.607989 | − | 0.793945i | \(-0.291976\pi\) |
−0.0445917 | + | 0.999005i | \(0.514199\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1424.52 | − | 8078.83i | −0.0518071 | − | 0.293813i | 0.947885 | − | 0.318612i | \(-0.103217\pi\) |
−0.999692 | + | 0.0247988i | \(0.992105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 77811.8 | − | 28321.2i | 2.82059 | − | 1.02661i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10260.1 | −0.369486 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33771.8 | −1.21222 | −0.606109 | − | 0.795381i | \(-0.707271\pi\) | ||||
−0.606109 | + | 0.795381i | \(0.707271\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 24096.8 | − | 8770.52i | 0.859324 | − | 0.312768i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1322.07 | − | 7497.85i | −0.0469941 | − | 0.266517i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45473.2 | + | 16550.9i | 1.60595 | + | 0.584518i | 0.980633 | − | 0.195853i | \(-0.0627475\pi\) |
0.625317 | + | 0.780371i | \(0.284970\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8947.20 | − | 7507.60i | −0.314965 | − | 0.264287i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8382.77 | − | 14519.4i | 0.293204 | − | 0.507845i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20974.0 | − | 36328.0i | −0.731258 | − | 1.26658i | −0.956346 | − | 0.292238i | \(-0.905600\pi\) |
0.225087 | − | 0.974339i | \(-0.427733\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2249.89 | − | 12759.8i | 0.0779431 | − | 0.442037i | −0.920714 | − | 0.390237i | \(-0.872393\pi\) |
0.998657 | − | 0.0518001i | \(-0.0164959\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15128.1 | + | 12694.0i | −0.522417 | + | 0.438360i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16485.1 | − | 13832.7i | 0.565675 | − | 0.474658i | −0.314532 | − | 0.949247i | \(-0.601848\pi\) |
0.880208 | + | 0.474589i | \(0.157403\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7560.92 | + | 42880.1i | −0.258628 | + | 1.46675i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17377.4 | + | 30098.5i | 0.590669 | + | 1.02307i | 0.994142 | + | 0.108078i | \(0.0344695\pi\) |
−0.403473 | + | 0.914991i | \(0.632197\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4744.63 | − | 8217.94i | 0.160767 | − | 0.278457i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17996.4 | + | 15100.7i | 0.605978 | + | 0.508476i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −38874.1 | − | 14149.0i | −1.30489 | − | 0.474942i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2989.14 | − | 16952.3i | −0.0997139 | − | 0.565506i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17056.1 | − | 6207.92i | 0.567205 | − | 0.206446i | −0.0424690 | − | 0.999098i | \(-0.513522\pi\) |
0.609675 | + | 0.792652i | \(0.291300\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32473.1 | 1.07324 | 0.536618 | − | 0.843825i | \(-0.319702\pi\) | ||||
0.536618 | + | 0.843825i | \(0.319702\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22914.9 | 0.755005 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2618.73 | + | 953.139i | −0.0857529 | + | 0.0312115i | −0.384540 | − | 0.923108i | \(-0.625640\pi\) |
0.298787 | + | 0.954320i | \(0.403418\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6011.69 | − | 34094.0i | −0.196256 | − | 1.11302i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54587.2 | − | 19868.1i | −1.77117 | − | 0.644654i | −0.999967 | − | 0.00806713i | \(-0.997432\pi\) |
−0.771205 | − | 0.636587i | \(-0.780346\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2290.59 | − | 1922.04i | −0.0740958 | − | 0.0621737i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9275.82 | − | 16066.2i | 0.298235 | − | 0.516557i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16680.9 | − | 28892.1i | −0.534698 | − | 0.926124i | −0.999178 | − | 0.0405401i | \(-0.987092\pi\) |
0.464480 | − | 0.885584i | \(-0.346241\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3561.72 | + | 20199.5i | −0.113481 | + | 0.643585i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21033.1 | − | 17648.8i | 0.668128 | − | 0.560626i | −0.244383 | − | 0.969679i | \(-0.578585\pi\) |
0.912511 | + | 0.409053i | \(0.134141\pi\) | |||||||
\(998\) | 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 | 324.4.i.a.37.4 | 54 | ||
3.2 | odd | 2 | 108.4.i.a.49.1 | ✓ | 54 | ||
27.11 | odd | 18 | 108.4.i.a.97.1 | yes | 54 | ||
27.16 | even | 9 | inner | 324.4.i.a.289.4 | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.i.a.49.1 | ✓ | 54 | 3.2 | odd | 2 | ||
108.4.i.a.97.1 | yes | 54 | 27.11 | odd | 18 | ||
324.4.i.a.37.4 | 54 | 1.1 | even | 1 | trivial | ||
324.4.i.a.289.4 | 54 | 27.16 | even | 9 | inner |