Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(97,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.f (of order \(2\), degree \(1\), 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: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.3 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.97 |
Dual form | 2352.3.f.e.97.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.43488i | − 0.286976i | −0.989652 | − | 0.143488i | \(-0.954168\pi\) | ||||
0.989652 | − | 0.143488i | \(-0.0458318\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.00000 | −0.545455 | −0.272727 | − | 0.962091i | \(-0.587926\pi\) | ||||
−0.272727 | + | 0.962091i | \(0.587926\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 21.3280i | − 1.64061i | −0.571924 | − | 0.820306i | \(-0.693803\pi\) | ||||
0.571924 | − | 0.820306i | \(-0.306197\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.48528 | 0.165685 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.95743i | 0.526907i | 0.964672 | + | 0.263454i | \(0.0848616\pi\) | ||||
−0.964672 | + | 0.263454i | \(0.915138\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.22538i | 0.380283i | 0.981757 | + | 0.190141i | \(0.0608947\pi\) | ||||
−0.981757 | + | 0.190141i | \(0.939105\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 37.4558 | 1.62851 | 0.814257 | − | 0.580504i | \(-0.197144\pi\) | ||||
0.814257 | + | 0.580504i | \(0.197144\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 22.9411 | 0.917645 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −33.9411 | −1.17038 | −0.585192 | − | 0.810895i | \(-0.698981\pi\) | ||||
−0.585192 | + | 0.810895i | \(0.698981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.1418i | 1.42393i | 0.702215 | + | 0.711965i | \(0.252194\pi\) | ||||
−0.702215 | + | 0.711965i | \(0.747806\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 10.3923i | − 0.314918i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −27.9706 | −0.755961 | −0.377981 | − | 0.925814i | \(-0.623381\pi\) | ||||
−0.377981 | + | 0.925814i | \(0.623381\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 36.9411 | 0.947208 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 54.8313i | − 1.33735i | −0.743556 | − | 0.668674i | \(-0.766862\pi\) | ||||
0.743556 | − | 0.668674i | \(-0.233138\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.48528 | 0.0345414 | 0.0172707 | − | 0.999851i | \(-0.494502\pi\) | ||||
0.0172707 | + | 0.999851i | \(0.494502\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.30463i | 0.0956585i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 43.0041i | 0.914981i | 0.889215 | + | 0.457490i | \(0.151252\pi\) | ||||
−0.889215 | + | 0.457490i | \(0.848748\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.5147 | −0.304210 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −85.4558 | −1.61237 | −0.806187 | − | 0.591661i | \(-0.798473\pi\) | ||||
−0.806187 | + | 0.591661i | \(0.798473\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.60927i | 0.156532i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.5147 | −0.219556 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 41.2211i | − 0.698662i | −0.936999 | − | 0.349331i | \(-0.886409\pi\) | ||||
0.936999 | − | 0.349331i | \(-0.113591\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.18869i | − 0.0194867i | −0.999953 | − | 0.00974337i | \(-0.996899\pi\) | ||||
0.999953 | − | 0.00974337i | \(-0.00310146\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −30.6030 | −0.470816 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.39697 | −0.0656264 | −0.0328132 | − | 0.999462i | \(-0.510447\pi\) | ||||
−0.0328132 | + | 0.999462i | \(0.510447\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 64.8754i | 0.940224i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −137.397 | −1.93517 | −0.967584 | − | 0.252548i | \(-0.918731\pi\) | ||||
−0.967584 | + | 0.252548i | \(0.918731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 78.9270i | − 1.08119i | −0.841282 | − | 0.540596i | \(-0.818199\pi\) | ||||
0.841282 | − | 0.540596i | \(-0.181801\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 39.7352i | 0.529803i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −98.3381 | −1.24479 | −0.622393 | − | 0.782705i | \(-0.713839\pi\) | ||||
−0.622393 | + | 0.782705i | \(0.713839\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 110.401i | − 1.33013i | −0.746784 | − | 0.665067i | \(-0.768403\pi\) | ||||
0.746784 | − | 0.665067i | \(-0.231597\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.8528 | 0.151210 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 58.7878i | − 0.675721i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 20.7846i | − 0.233535i | −0.993159 | − | 0.116767i | \(-0.962747\pi\) | ||||
0.993159 | − | 0.116767i | \(-0.0372532\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −76.4558 | −0.822106 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.3675 | 0.109132 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 10.9867i | − 0.113264i | −0.998395 | − | 0.0566322i | \(-0.981964\pi\) | ||||
0.998395 | − | 0.0566322i | \(-0.0180362\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.0000 | 0.181818 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 107.183i | 1.06122i | 0.847616 | + | 0.530610i | \(0.178037\pi\) | ||||
−0.847616 | + | 0.530610i | \(0.821963\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 105.205i | − 1.02141i | −0.859757 | − | 0.510704i | \(-0.829385\pi\) | ||||
0.859757 | − | 0.510704i | \(-0.170615\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −118.544 | −1.10789 | −0.553945 | − | 0.832553i | \(-0.686878\pi\) | ||||
−0.553945 | + | 0.832553i | \(0.686878\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 111.059 | 1.01889 | 0.509444 | − | 0.860504i | \(-0.329851\pi\) | ||||
0.509444 | + | 0.860504i | \(0.329851\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 48.4464i | − 0.436454i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 101.397 | 0.897318 | 0.448659 | − | 0.893703i | \(-0.351902\pi\) | ||||
0.448659 | + | 0.893703i | \(0.351902\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 53.7446i | − 0.467344i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 63.9839i | 0.546871i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −85.0000 | −0.702479 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 94.9706 | 0.772118 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 68.7897i | − 0.550317i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −82.5736 | −0.650186 | −0.325093 | − | 0.945682i | \(-0.605396\pi\) | ||||
−0.325093 | + | 0.945682i | \(0.605396\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.57258i | 0.0199425i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 60.5708i | 0.462372i | 0.972910 | + | 0.231186i | \(0.0742607\pi\) | ||||
−0.972910 | + | 0.231186i | \(0.925739\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.45584 | −0.0552285 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 67.0294 | 0.489266 | 0.244633 | − | 0.969616i | \(-0.421333\pi\) | ||||
0.244633 | + | 0.969616i | \(0.421333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 91.5525i | − 0.658651i | −0.944216 | − | 0.329326i | \(-0.893179\pi\) | ||||
0.944216 | − | 0.329326i | \(-0.106821\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −74.4853 | −0.528264 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 127.968i | 0.894880i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 48.7014i | 0.335872i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 81.0883 | 0.544217 | 0.272108 | − | 0.962267i | \(-0.412279\pi\) | ||||
0.272108 | + | 0.962267i | \(0.412279\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 51.2061 | 0.339113 | 0.169556 | − | 0.985520i | \(-0.445766\pi\) | ||||
0.169556 | + | 0.985520i | \(0.445766\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 26.8723i | − 0.175636i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 63.3381 | 0.408633 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 187.061i | − 1.19147i | −0.803179 | − | 0.595737i | \(-0.796860\pi\) | ||||
0.803179 | − | 0.595737i | \(-0.203140\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 148.014i | − 0.930905i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −83.9411 | −0.514976 | −0.257488 | − | 0.966281i | \(-0.582895\pi\) | ||||
−0.257488 | + | 0.966281i | \(0.582895\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14.9117 | −0.0903739 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 127.620i | 0.764190i | 0.924123 | + | 0.382095i | \(0.124797\pi\) | ||||
−0.924123 | + | 0.382095i | \(0.875203\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −285.882 | −1.69161 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 21.6761i | − 0.126761i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 142.971i | − 0.826420i | −0.910636 | − | 0.413210i | \(-0.864408\pi\) | ||||
0.910636 | − | 0.413210i | \(-0.135592\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 71.3970 | 0.403373 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −169.279 | −0.945694 | −0.472847 | − | 0.881145i | \(-0.656774\pi\) | ||||
−0.472847 | + | 0.881145i | \(0.656774\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 209.969i | − 1.16005i | −0.814600 | − | 0.580024i | \(-0.803043\pi\) | ||||
0.814600 | − | 0.580024i | \(-0.196957\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.05887 | 0.0112507 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 40.1343i | 0.216942i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 53.7446i | − 0.287404i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −66.6030 | −0.348707 | −0.174353 | − | 0.984683i | \(-0.555784\pi\) | ||||
−0.174353 | + | 0.984683i | \(0.555784\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.79394 | −0.0507458 | −0.0253729 | − | 0.999678i | \(-0.508077\pi\) | ||||
−0.0253729 | + | 0.999678i | \(0.508077\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 53.0060i | − 0.271826i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −267.161 | −1.35615 | −0.678075 | − | 0.734993i | \(-0.737185\pi\) | ||||
−0.678075 | + | 0.734993i | \(0.737185\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 130.940i | − 0.657988i | −0.944332 | − | 0.328994i | \(-0.893290\pi\) | ||||
0.944332 | − | 0.328994i | \(-0.106710\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 7.61577i | − 0.0378894i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −78.6762 | −0.383786 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −112.368 | −0.542838 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 43.3523i | − 0.207427i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0883 | 0.109423 | 0.0547116 | − | 0.998502i | \(-0.482576\pi\) | ||||
0.0547116 | + | 0.998502i | \(0.482576\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 237.979i | − 1.11727i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 2.13120i | − 0.00991255i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 136.706 | 0.624227 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 191.044 | 0.864451 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 228.631i | − 1.02525i | −0.858613 | − | 0.512625i | \(-0.828673\pi\) | ||||
0.858613 | − | 0.512625i | \(-0.171327\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −68.8234 | −0.305882 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 65.6140i | 0.289048i | 0.989501 | + | 0.144524i | \(0.0461652\pi\) | ||||
−0.989501 | + | 0.144524i | \(0.953835\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 93.4798i | 0.408209i | 0.978949 | + | 0.204104i | \(0.0654282\pi\) | ||||
−0.978949 | + | 0.204104i | \(0.934572\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −237.515 | −1.01938 | −0.509688 | − | 0.860359i | \(-0.670239\pi\) | ||||
−0.509688 | + | 0.860359i | \(0.670239\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 61.7056 | 0.262577 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 170.327i | − 0.718678i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −366.853 | −1.53495 | −0.767475 | − | 0.641079i | \(-0.778487\pi\) | ||||
−0.767475 | + | 0.641079i | \(0.778487\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 421.024i | 1.74699i | 0.486836 | + | 0.873493i | \(0.338151\pi\) | ||||
−0.486836 | + | 0.873493i | \(0.661849\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 154.103 | 0.623897 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 191.220 | 0.767953 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 146.621i | 0.584148i | 0.956396 | + | 0.292074i | \(0.0943454\pi\) | ||||
−0.956396 | + | 0.292074i | \(0.905655\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −224.735 | −0.888281 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 22.2617i | 0.0873009i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.0892i | 0.0976235i | 0.998808 | + | 0.0488118i | \(0.0155434\pi\) | ||||
−0.998808 | + | 0.0488118i | \(0.984457\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 101.823 | 0.390128 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 90.6762 | 0.344776 | 0.172388 | − | 0.985029i | \(-0.444852\pi\) | ||||
0.172388 | + | 0.985029i | \(0.444852\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 122.619i | 0.462712i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 36.0000 | 0.134831 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 68.3993i | 0.254272i | 0.991885 | + | 0.127136i | \(0.0405785\pi\) | ||||
−0.991885 | + | 0.127136i | \(0.959421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 123.519i | 0.455790i | 0.973686 | + | 0.227895i | \(0.0731842\pi\) | ||||
−0.973686 | + | 0.227895i | \(0.926816\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −137.647 | −0.500534 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −272.882 | −0.985134 | −0.492567 | − | 0.870274i | \(-0.663941\pi\) | ||||
−0.492567 | + | 0.870274i | \(0.663941\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 132.425i | − 0.474643i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 133.103 | 0.473675 | 0.236837 | − | 0.971549i | \(-0.423889\pi\) | ||||
0.236837 | + | 0.971549i | \(0.423889\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 128.757i | − 0.454973i | −0.973781 | − | 0.227486i | \(-0.926949\pi\) | ||||
0.973781 | − | 0.227486i | \(-0.0730508\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.9571i | 0.0630073i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 208.765 | 0.722369 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.0294 | 0.0653933 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 308.984i | − 1.05455i | −0.849694 | − | 0.527276i | \(-0.823213\pi\) | ||||
0.849694 | − | 0.527276i | \(-0.176787\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −59.1472 | −0.200499 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 31.1769i | 0.104973i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 798.857i | − 2.67176i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −185.647 | −0.612696 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.70563 | −0.00559222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 606.090i | − 1.97423i | −0.160003 | − | 0.987117i | \(-0.551150\pi\) | ||||
0.160003 | − | 0.987117i | \(-0.448850\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 182.220 | 0.589710 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 203.278i | − 0.653626i | −0.945089 | − | 0.326813i | \(-0.894025\pi\) | ||||
0.945089 | − | 0.326813i | \(-0.105975\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 405.639i | − 1.29597i | −0.761652 | − | 0.647986i | \(-0.775611\pi\) | ||||
0.761652 | − | 0.647986i | \(-0.224389\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.0589 | −0.0822047 | −0.0411023 | − | 0.999155i | \(-0.513087\pi\) | ||||
−0.0411023 | + | 0.999155i | \(0.513087\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 203.647 | 0.638391 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 205.325i | − 0.639640i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −64.7208 | −0.200374 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 489.288i | − 1.50550i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 192.360i | 0.588256i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 108.632 | 0.328195 | 0.164097 | − | 0.986444i | \(-0.447529\pi\) | ||||
0.164097 | + | 0.986444i | \(0.447529\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 83.9117 | 0.251987 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.30911i | 0.0188332i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 441.735 | 1.31079 | 0.655393 | − | 0.755288i | \(-0.272503\pi\) | ||||
0.655393 | + | 0.755288i | \(0.272503\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 175.625i | 0.518067i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 264.851i | − 0.776689i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 93.0883 | 0.269821 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.1909 | −0.0985329 | −0.0492664 | − | 0.998786i | \(-0.515688\pi\) | ||||
−0.0492664 | + | 0.998786i | \(0.515688\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 221.787i | 0.635493i | 0.948176 | + | 0.317746i | \(0.102926\pi\) | ||||
−0.948176 | + | 0.317746i | \(0.897074\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −110.823 | −0.315736 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 447.386i | − 1.26738i | −0.773586 | − | 0.633692i | \(-0.781539\pi\) | ||||
0.773586 | − | 0.633692i | \(-0.218461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 197.148i | 0.555346i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −291.765 | −0.812714 | −0.406357 | − | 0.913714i | \(-0.633201\pi\) | ||||
−0.406357 | + | 0.913714i | \(0.633201\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 308.794 | 0.855385 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 147.224i | − 0.405577i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −113.251 | −0.310276 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 419.351i | − 1.14265i | −0.820725 | − | 0.571324i | \(-0.806430\pi\) | ||||
0.820725 | − | 0.571324i | \(-0.193570\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 164.494i | 0.445783i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.3818 | 0.0841336 | 0.0420668 | − | 0.999115i | \(-0.486606\pi\) | ||||
0.0420668 | + | 0.999115i | \(0.486606\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 119.147 | 0.317726 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 723.895i | 1.92015i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −206.779 | −0.545590 | −0.272795 | − | 0.962072i | \(-0.587948\pi\) | ||||
−0.272795 | + | 0.962072i | \(0.587948\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 143.022i | − 0.375385i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 498.567i | 1.30174i | 0.759189 | + | 0.650871i | \(0.225596\pi\) | ||||
−0.759189 | + | 0.650871i | \(0.774404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.45584 | −0.0115138 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −648.426 | −1.66691 | −0.833453 | − | 0.552590i | \(-0.813639\pi\) | ||||
−0.833453 | + | 0.552590i | \(0.813639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 335.508i | 0.858077i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −104.912 | −0.266951 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 141.103i | 0.357223i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 75.7514i | 0.190809i | 0.995439 | + | 0.0954047i | \(0.0304145\pi\) | ||||
−0.995439 | + | 0.0954047i | \(0.969585\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −564.250 | −1.40711 | −0.703553 | − | 0.710642i | \(-0.748404\pi\) | ||||
−0.703553 | + | 0.710642i | \(0.748404\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 941.455 | 2.33612 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 12.9139i | − 0.0318862i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 167.823 | 0.412342 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 357.448i | 0.873955i | 0.899472 | + | 0.436978i | \(0.143951\pi\) | ||||
−0.899472 | + | 0.436978i | \(0.856049\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 116.098i | 0.282478i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −158.412 | −0.381716 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 158.574 | 0.380272 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 502.175i | 1.19851i | 0.800559 | + | 0.599254i | \(0.204536\pi\) | ||||
−0.800559 | + | 0.599254i | \(0.795464\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.7939 | 0.0802706 | 0.0401353 | − | 0.999194i | \(-0.487221\pi\) | ||||
0.0401353 | + | 0.999194i | \(0.487221\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 129.012i | − 0.304994i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 205.493i | 0.483514i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −221.647 | −0.516659 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −503.720 | −1.16872 | −0.584362 | − | 0.811493i | \(-0.698655\pi\) | ||||
−0.584362 | + | 0.811493i | \(0.698655\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 837.548i | − 1.93429i | −0.254224 | − | 0.967145i | \(-0.581820\pi\) | ||||
0.254224 | − | 0.967145i | \(-0.418180\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −84.3532 | −0.193916 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 270.633i | 0.619296i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 190.016i | 0.432838i | 0.976301 | + | 0.216419i | \(0.0694377\pi\) | ||||
−0.976301 | + | 0.216419i | \(0.930562\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 169.456 | 0.382519 | 0.191259 | − | 0.981540i | \(-0.438743\pi\) | ||||
0.191259 | + | 0.981540i | \(0.438743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.8234 | −0.0670188 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 140.449i | 0.314204i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.1035 | 0.0403195 | 0.0201598 | − | 0.999797i | \(-0.493583\pi\) | ||||
0.0201598 | + | 0.999797i | \(0.493583\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 328.988i | 0.729463i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 88.6915i | 0.195787i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −328.823 | −0.719526 | −0.359763 | − | 0.933044i | \(-0.617142\pi\) | ||||
−0.359763 | + | 0.933044i | \(0.617142\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 46.5442 | 0.101403 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 794.331i | 1.72306i | 0.507706 | + | 0.861530i | \(0.330494\pi\) | ||||
−0.507706 | + | 0.861530i | \(0.669506\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 403.396 | 0.871266 | 0.435633 | − | 0.900124i | \(-0.356525\pi\) | ||||
0.435633 | + | 0.900124i | \(0.356525\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 109.705i | 0.235924i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.82752i | 0.00605464i | 0.999995 | + | 0.00302732i | \(0.000963627\pi\) | ||||
−0.999995 | + | 0.00302732i | \(0.999036\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 324.000 | 0.687898 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.91169 | −0.0188408 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 165.758i | 0.348965i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 256.368 | 0.537458 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 379.514i | 0.792305i | 0.918185 | + | 0.396153i | \(0.129655\pi\) | ||||
−0.918185 | + | 0.396153i | \(0.870345\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 596.555i | 1.24024i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.7645 | −0.0325041 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −575.514 | −1.18175 | −0.590877 | − | 0.806762i | \(-0.701218\pi\) | ||||
−0.590877 | + | 0.806762i | \(0.701218\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 145.390i | − 0.297322i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −238.441 | −0.485623 | −0.242811 | − | 0.970074i | \(-0.578070\pi\) | ||||
−0.242811 | + | 0.970074i | \(0.578070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 304.025i | − 0.616684i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 25.8278i | − 0.0521774i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 286.574 | 0.574296 | 0.287148 | − | 0.957886i | \(-0.407293\pi\) | ||||
0.287148 | + | 0.957886i | \(0.407293\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −221.044 | −0.441205 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.4374i | 0.0505714i | 0.999680 | + | 0.0252857i | \(0.00804954\pi\) | ||||
−0.999680 | + | 0.0252857i | \(0.991950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 153.795 | 0.304544 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 495.163i | − 0.976652i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 805.852i | − 1.58321i | −0.611035 | − | 0.791603i | \(-0.709247\pi\) | ||||
0.611035 | − | 0.791603i | \(-0.290753\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 37.5442 | 0.0731855 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −150.956 | −0.293119 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 258.025i | − 0.499080i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 247.632 | 0.477134 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 764.072i | 1.46655i | 0.679933 | + | 0.733274i | \(0.262009\pi\) | ||||
−0.679933 | + | 0.733274i | \(0.737991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 176.780i | 0.338011i | 0.985615 | + | 0.169006i | \(0.0540556\pi\) | ||||
−0.985615 | + | 0.169006i | \(0.945944\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −395.397 | −0.750279 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 873.940 | 1.65206 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 123.663i | 0.232887i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1169.44 | −2.19407 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 170.096i | 0.317937i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 293.200i | − 0.545997i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.1766 | 0.0317498 | 0.0158749 | − | 0.999874i | \(-0.494947\pi\) | ||||
0.0158749 | + | 0.999874i | \(0.494947\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 363.676 | 0.669754 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 159.356i | − 0.292396i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −212.676 | −0.388805 | −0.194402 | − | 0.980922i | \(-0.562277\pi\) | ||||
−0.194402 | + | 0.980922i | \(0.562277\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.56608i | 0.00649558i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 245.237i | − 0.445077i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −69.5147 | −0.125252 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −881.647 | −1.58285 | −0.791424 | − | 0.611267i | \(-0.790660\pi\) | ||||
−0.791424 | + | 0.611267i | \(0.790660\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 31.6780i | − 0.0566691i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 93.0883 | 0.165933 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 767.068i | 1.36247i | 0.732067 | + | 0.681233i | \(0.238556\pi\) | ||||
−0.732067 | + | 0.681233i | \(0.761444\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 145.492i | − 0.257508i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.2935 | −0.0514824 | −0.0257412 | − | 0.999669i | \(-0.508195\pi\) | ||||
−0.0257412 | + | 0.999669i | \(0.508195\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −965.043 | −1.69009 | −0.845046 | − | 0.534693i | \(-0.820427\pi\) | ||||
−0.845046 | + | 0.534693i | \(0.820427\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 115.360i | − 0.201326i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 859.279 | 1.49440 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 263.136i | − 0.456042i | −0.973656 | − | 0.228021i | \(-0.926775\pi\) | ||||
0.973656 | − | 0.228021i | \(-0.0732255\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 16.9636i | − 0.0292981i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 512.735 | 0.879477 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 91.8091 | 0.156939 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 436.477i | − 0.743572i | −0.928318 | − | 0.371786i | \(-0.878746\pi\) | ||||
0.928318 | − | 0.371786i | \(-0.121254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −318.941 | −0.541496 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 462.737i | − 0.782973i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 696.981i | 1.17535i | 0.809098 | + | 0.587673i | \(0.199956\pi\) | ||||
−0.809098 | + | 0.587673i | \(0.800044\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 226.794 | 0.379889 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −398.412 | −0.665129 | −0.332564 | − | 0.943081i | \(-0.607914\pi\) | ||||
−0.332564 | + | 0.943081i | \(0.607914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.1691i | 0.0601816i | 0.999547 | + | 0.0300908i | \(0.00957964\pi\) | ||||
−0.999547 | + | 0.0300908i | \(0.990420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.1909 | 0.0218755 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 121.965i | 0.201594i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 31.5761i | − 0.0520199i | −0.999662 | − | 0.0260099i | \(-0.991720\pi\) | ||||
0.999662 | − | 0.0260099i | \(-0.00828015\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 917.190 | 1.50113 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −409.265 | −0.667643 | −0.333821 | − | 0.942636i | \(-0.608338\pi\) | ||||
−0.333821 | + | 0.942636i | \(0.608338\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 136.271i | − 0.221579i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1227.38 | 1.98927 | 0.994636 | − | 0.103436i | \(-0.0329837\pi\) | ||||
0.994636 | + | 0.103436i | \(0.0329837\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 475.762i | 0.768598i | 0.923209 | + | 0.384299i | \(0.125557\pi\) | ||||
−0.923209 | + | 0.384299i | \(0.874443\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 194.626i | − 0.313408i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 474.823 | 0.759717 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 75.0883 | 0.119758 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 250.544i | − 0.398322i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 54.9420 | 0.0870713 | 0.0435357 | − | 0.999052i | \(-0.486138\pi\) | ||||
0.0435357 | + | 0.999052i | \(0.486138\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 39.9901i | 0.0631756i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 118.483i | 0.186587i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 412.191 | 0.645056 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −229.103 | −0.357414 | −0.178707 | − | 0.983902i | \(-0.557191\pi\) | ||||
−0.178707 | + | 0.983902i | \(0.557191\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 854.640i | 1.32914i | 0.747224 | + | 0.664572i | \(0.231386\pi\) | ||||
−0.747224 | + | 0.664572i | \(0.768614\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.69134 | 0.00572301 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1003.01i | 1.55025i | 0.631809 | + | 0.775124i | \(0.282313\pi\) | ||||
−0.631809 | + | 0.775124i | \(0.717687\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 247.326i | 0.381088i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1270.76 | 1.94604 | 0.973020 | − | 0.230722i | \(-0.0741089\pi\) | ||||
0.973020 | + | 0.230722i | \(0.0741089\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 86.9117 | 0.132690 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 236.781i | 0.360397i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 783.308 | 1.18863 | 0.594315 | − | 0.804232i | \(-0.297423\pi\) | ||||
0.594315 | + | 0.804232i | \(0.297423\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 83.7838i | − 0.126753i | −0.997990 | − | 0.0633765i | \(-0.979813\pi\) | ||||
0.997990 | − | 0.0633765i | \(-0.0201869\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 330.897i | 0.499091i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1271.29 | −1.90599 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 396.000 | 0.591928 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.13215i | 0.0106291i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 415.676 | 0.617647 | 0.308823 | − | 0.951119i | \(-0.400065\pi\) | ||||
0.308823 | + | 0.951119i | \(0.400065\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 119.206i | − 0.176601i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 791.292i | 1.16882i | 0.811458 | + | 0.584411i | \(0.198674\pi\) | ||||
−0.811458 | + | 0.584411i | \(0.801326\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −113.647 | −0.166882 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 328.161 | 0.480469 | 0.240235 | − | 0.970715i | \(-0.422776\pi\) | ||||
0.240235 | + | 0.970715i | \(0.422776\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 96.1791i | − 0.140407i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −161.912 | −0.235679 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1822.60i | 2.64528i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1010.57i | − 1.46248i | −0.682120 | − | 0.731240i | \(-0.738942\pi\) | ||||
0.682120 | − | 0.731240i | \(-0.261058\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −131.367 | −0.189017 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 491.147 | 0.704659 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 411.388i | − 0.588537i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.103464 | −0.000147594 0 | −7.37972e−5 | − | 1.00000i | \(-0.500023\pi\) | ||||
−7.37972e−5 | 1.00000i | \(0.500023\pi\) | ||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 202.098i | − 0.287479i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 106.877i | 0.151599i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1205.18 | 1.69982 | 0.849912 | − | 0.526924i | \(-0.176655\pi\) | ||||
0.849912 | + | 0.526924i | \(0.176655\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 295.014 | 0.414929 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1653.37i | 2.31889i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 183.618 | 0.256809 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 635.408i | − 0.886203i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 982.564i | − 1.36657i | −0.730152 | − | 0.683285i | \(-0.760551\pi\) | ||||
0.730152 | − | 0.683285i | \(-0.239449\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −729.235 | −1.00862 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −778.648 | −1.07400 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 630.440i | 0.867181i | 0.901110 | + | 0.433590i | \(0.142753\pi\) | ||||
−0.901110 | + | 0.433590i | \(0.857247\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.3043i | 0.0182001i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 298.474i | 0.407195i | 0.979055 | + | 0.203597i | \(0.0652633\pi\) | ||||
−0.979055 | + | 0.203597i | \(0.934737\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.3818 | 0.0357962 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −345.368 | −0.467344 | −0.233672 | − | 0.972315i | \(-0.575074\pi\) | ||||
−0.233672 | + | 0.972315i | \(0.575074\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 266.914i | 0.360207i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −683.616 | −0.920076 | −0.460038 | − | 0.887899i | \(-0.652164\pi\) | ||||
−0.460038 | + | 0.887899i | \(0.652164\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 116.352i | − 0.156177i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 331.203i | 0.443378i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 578.338 | 0.770091 | 0.385045 | − | 0.922898i | \(-0.374186\pi\) | ||||
0.385045 | + | 0.922898i | \(0.374186\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −253.955 | −0.337258 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 73.4744i | − 0.0973171i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1204.82 | 1.59158 | 0.795788 | − | 0.605576i | \(-0.207057\pi\) | ||||
0.795788 | + | 0.605576i | \(0.207057\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 389.253i | − 0.512849i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 234.022i | − 0.307519i | −0.988108 | − | 0.153760i | \(-0.950862\pi\) | ||||
0.988108 | − | 0.153760i | \(-0.0491381\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −38.5584 | −0.0504032 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −879.161 | −1.14623 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1290.16i | 1.67771i | 0.544358 | + | 0.838853i | \(0.316774\pi\) | ||||
−0.544358 | + | 0.838853i | \(0.683226\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.4558 | −0.0563630 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 399.117i | − 0.516323i | −0.966102 | − | 0.258161i | \(-0.916883\pi\) | ||||
0.966102 | − | 0.258161i | \(-0.0831166\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1012.66i | 1.30666i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 396.177 | 0.508571 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 824.382 | 1.05555 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 176.363i | 0.225240i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −268.410 | −0.341924 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1556.72i | − 1.97805i | −0.147763 | − | 0.989023i | \(-0.547207\pi\) | ||||
0.147763 | − | 0.989023i | \(-0.452793\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 157.056i | 0.199057i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.3524 | −0.0319702 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −212.382 | −0.267147 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 600.232i | 0.753114i | 0.926393 | + | 0.376557i | \(0.122892\pi\) | ||||
−0.926393 | + | 0.376557i | \(0.877108\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −385.206 | −0.482110 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 62.3538i | 0.0778450i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 473.562i | 0.589741i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −118.471 | −0.146804 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −229.279 | −0.283411 | −0.141705 | − | 0.989909i | \(-0.545259\pi\) | ||||
−0.141705 | + | 0.989909i | \(0.545259\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 529.955i | − 0.653459i | −0.945118 | − | 0.326729i | \(-0.894053\pi\) | ||||
0.945118 | − | 0.326729i | \(-0.105947\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −213.941 | −0.263150 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 120.445i | 0.147786i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.7317i | 0.0131355i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −303.338 | −0.369474 | −0.184737 | − | 0.982788i | \(-0.559143\pi\) | ||||
−0.184737 | + | 0.982788i | \(0.559143\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1129.91 | 1.37292 | 0.686459 | − | 0.727169i | \(-0.259164\pi\) | ||||
0.686459 | + | 0.727169i | \(0.259164\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 238.411i | − 0.288983i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 161.604 | 0.195410 | 0.0977049 | − | 0.995215i | \(-0.468850\pi\) | ||||
0.0977049 | + | 0.995215i | \(0.468850\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1530.35i | − 1.84602i | −0.384776 | − | 0.923010i | \(-0.625721\pi\) | ||||
0.384776 | − | 0.923010i | \(-0.374279\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 472.646i | − 0.568768i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 183.119 | 0.219304 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 229.368 | 0.274035 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 218.629i | 0.260583i | 0.991476 | + | 0.130291i | \(0.0415913\pi\) | ||||
−0.991476 | + | 0.130291i | \(0.958409\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 311.000 | 0.369798 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 230.540i | 0.273476i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 410.206i | 0.485451i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 223.014 | 0.262679 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1047.66 | −1.23109 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 762.730i | 0.894174i | 0.894491 | + | 0.447087i | \(0.147539\pi\) | ||||
−0.894491 | + | 0.447087i | \(0.852461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −31.1026 | −0.0363773 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 918.004i | 1.07118i | 0.844477 | + | 0.535592i | \(0.179911\pi\) | ||||
−0.844477 | + | 0.535592i | \(0.820089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 879.150i | 1.02346i | 0.859147 | + | 0.511729i | \(0.170995\pi\) | ||||
−0.859147 | + | 0.511729i | \(0.829005\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −350.589 | −0.406244 | −0.203122 | − | 0.979153i | \(-0.565109\pi\) | ||||
−0.203122 | + | 0.979153i | \(0.565109\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −205.145 | −0.237162 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 361.591i | 0.417060i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 590.029 | 0.678974 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 93.7784i | 0.107668i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 32.9600i | 0.0377548i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.55931 | 0.00405850 | 0.00202925 | − | 0.999998i | \(-0.499354\pi\) | ||||
0.00202925 | + | 0.999998i | \(0.499354\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 535.176 | 0.608846 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 488.565i | − 0.554557i | −0.960790 | − | 0.277279i | \(-0.910567\pi\) | ||||
0.960790 | − | 0.277279i | \(-0.0894325\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1162.16 | 1.31615 | 0.658075 | − | 0.752953i | \(-0.271371\pi\) | ||||
0.658075 | + | 0.752953i | \(0.271371\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 102.446i | − 0.115758i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 86.9260i | − 0.0980000i | −0.998799 | − | 0.0490000i | \(-0.984397\pi\) | ||||
0.998799 | − | 0.0490000i | \(-0.0156034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −54.0000 | −0.0606061 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −310.721 | −0.347952 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 242.895i | 0.271391i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1383.66 | 1.54254 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1498.22i | − 1.66654i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 765.464i | − 0.849572i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −301.279 | −0.332905 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 460.897 | 0.508155 | 0.254077 | − | 0.967184i | \(-0.418228\pi\) | ||||
0.254077 | + | 0.967184i | \(0.418228\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 321.550i | − 0.353740i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1184.28 | 1.29998 | 0.649988 | − | 0.759944i | \(-0.274774\pi\) | ||||
0.649988 | + | 0.759944i | \(0.274774\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 662.407i | 0.725528i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 2.95423i | − 0.00322867i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 541.839 | 0.589596 | 0.294798 | − | 0.955560i | \(-0.404748\pi\) | ||||
0.294798 | + | 0.955560i | \(0.404748\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1049.78 | 1.13982 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2930.40i | 3.17486i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −641.676 | −0.693704 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 315.615i | 0.340469i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 900.216i | − 0.969016i | −0.874787 | − | 0.484508i | \(-0.838999\pi\) | ||||
0.874787 | − | 0.484508i | \(-0.161001\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 352.087 | 0.377371 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −77.1169 | −0.0824779 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 233.964i | 0.249695i | 0.992176 | + | 0.124847i | \(0.0398441\pi\) | ||||
−0.992176 | + | 0.124847i | \(0.960156\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 702.588 | 0.748230 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1307.69i | − 1.38968i | −0.719164 | − | 0.694840i | \(-0.755475\pi\) | ||||
0.719164 | − | 0.694840i | \(-0.244525\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 2053.75i | − 2.17789i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1127.76 | 1.19088 | 0.595440 | − | 0.803400i | \(-0.296978\pi\) | ||||
0.595440 | + | 0.803400i | \(0.296978\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1683.35 | −1.77382 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 45.1353i | − 0.0474609i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −91.4255 | −0.0959345 | −0.0479672 | − | 0.998849i | \(-0.515274\pi\) | ||||
−0.0479672 | + | 0.998849i | \(0.515274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 95.5672i | 0.100070i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 352.727i | 0.368575i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −987.499 | −1.02757 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 355.632 | 0.369296 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.0531i | 0.0145628i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1098.19 | 1.13567 | 0.567834 | − | 0.823143i | \(-0.307782\pi\) | ||||
0.567834 | + | 0.823143i | \(0.307782\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 112.100i | − 0.115686i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 132.103i | − 0.136049i | −0.997684 | − | 0.0680245i | \(-0.978330\pi\) | ||||
0.997684 | − | 0.0680245i | \(-0.0216696\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 847.471 | 0.869201 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 448.234 | 0.458786 | 0.229393 | − | 0.973334i | \(-0.426326\pi\) | ||||
0.229393 | + | 0.973334i | \(0.426326\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 124.708i | 0.127383i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −333.177 | −0.339630 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1646.76i | 1.67524i | 0.546251 | + | 0.837621i | \(0.316054\pi\) | ||||
−0.546251 | + | 0.837621i | \(0.683946\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 383.344i | 0.389182i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.6325 | 0.0562512 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 628.897 | 0.634608 | 0.317304 | − | 0.948324i | \(-0.397222\pi\) | ||||
0.317304 | + | 0.948324i | \(0.397222\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 188.157i | 0.189483i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −187.882 | −0.188826 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1004.18i | 1.00720i | 0.863936 | + | 0.503601i | \(0.167992\pi\) | ||||
−0.863936 | + | 0.503601i | \(0.832008\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 145.339i | 0.145485i |
(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 | 2352.3.f.e.97.3 | 4 | ||
4.3 | odd | 2 | 294.3.c.a.97.1 | 4 | |||
7.2 | even | 3 | 336.3.bh.e.241.1 | 4 | |||
7.3 | odd | 6 | 336.3.bh.e.145.1 | 4 | |||
7.6 | odd | 2 | inner | 2352.3.f.e.97.2 | 4 | ||
12.11 | even | 2 | 882.3.c.b.685.4 | 4 | |||
21.2 | odd | 6 | 1008.3.cg.h.577.2 | 4 | |||
21.17 | even | 6 | 1008.3.cg.h.145.2 | 4 | |||
28.3 | even | 6 | 42.3.g.a.19.2 | ✓ | 4 | ||
28.11 | odd | 6 | 294.3.g.a.19.2 | 4 | |||
28.19 | even | 6 | 294.3.g.a.31.2 | 4 | |||
28.23 | odd | 6 | 42.3.g.a.31.2 | yes | 4 | ||
28.27 | even | 2 | 294.3.c.a.97.2 | 4 | |||
84.11 | even | 6 | 882.3.n.e.19.1 | 4 | |||
84.23 | even | 6 | 126.3.n.a.73.1 | 4 | |||
84.47 | odd | 6 | 882.3.n.e.325.1 | 4 | |||
84.59 | odd | 6 | 126.3.n.a.19.1 | 4 | |||
84.83 | odd | 2 | 882.3.c.b.685.3 | 4 | |||
140.3 | odd | 12 | 1050.3.q.a.649.2 | 8 | |||
140.23 | even | 12 | 1050.3.q.a.199.3 | 8 | |||
140.59 | even | 6 | 1050.3.p.a.901.1 | 4 | |||
140.79 | odd | 6 | 1050.3.p.a.451.1 | 4 | |||
140.87 | odd | 12 | 1050.3.q.a.649.3 | 8 | |||
140.107 | even | 12 | 1050.3.q.a.199.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.g.a.19.2 | ✓ | 4 | 28.3 | even | 6 | ||
42.3.g.a.31.2 | yes | 4 | 28.23 | odd | 6 | ||
126.3.n.a.19.1 | 4 | 84.59 | odd | 6 | |||
126.3.n.a.73.1 | 4 | 84.23 | even | 6 | |||
294.3.c.a.97.1 | 4 | 4.3 | odd | 2 | |||
294.3.c.a.97.2 | 4 | 28.27 | even | 2 | |||
294.3.g.a.19.2 | 4 | 28.11 | odd | 6 | |||
294.3.g.a.31.2 | 4 | 28.19 | even | 6 | |||
336.3.bh.e.145.1 | 4 | 7.3 | odd | 6 | |||
336.3.bh.e.241.1 | 4 | 7.2 | even | 3 | |||
882.3.c.b.685.3 | 4 | 84.83 | odd | 2 | |||
882.3.c.b.685.4 | 4 | 12.11 | even | 2 | |||
882.3.n.e.19.1 | 4 | 84.11 | even | 6 | |||
882.3.n.e.325.1 | 4 | 84.47 | odd | 6 | |||
1008.3.cg.h.145.2 | 4 | 21.17 | even | 6 | |||
1008.3.cg.h.577.2 | 4 | 21.2 | odd | 6 | |||
1050.3.p.a.451.1 | 4 | 140.79 | odd | 6 | |||
1050.3.p.a.901.1 | 4 | 140.59 | even | 6 | |||
1050.3.q.a.199.2 | 8 | 140.107 | even | 12 | |||
1050.3.q.a.199.3 | 8 | 140.23 | even | 12 | |||
1050.3.q.a.649.2 | 8 | 140.3 | odd | 12 | |||
1050.3.q.a.649.3 | 8 | 140.87 | odd | 12 | |||
2352.3.f.e.97.2 | 4 | 7.6 | odd | 2 | inner | ||
2352.3.f.e.97.3 | 4 | 1.1 | even | 1 | trivial |