Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,4,Mod(145,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.145");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.d (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: | \(16.9925500817\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 145.2 | ||
Root | \(0.500000 - 1.32288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 288.145 |
Dual form | 288.4.d.a.145.1 |
$q$-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 \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.5830i | 0.946573i | 0.880909 | + | 0.473286i | \(0.156932\pi\) | ||||
−0.880909 | + | 0.473286i | \(0.843068\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.00000 | 0.431959 | 0.215980 | − | 0.976398i | \(-0.430705\pi\) | ||||
0.215980 | + | 0.976398i | \(0.430705\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 15.8745i | − 0.435122i | −0.976047 | − | 0.217561i | \(-0.930190\pi\) | ||||
0.976047 | − | 0.217561i | \(-0.0698101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 52.9150i | 1.12892i | 0.825460 | + | 0.564461i | \(0.190916\pi\) | ||||
−0.825460 | + | 0.564461i | \(0.809084\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.0000 | 0.199735 | 0.0998676 | − | 0.995001i | \(-0.468158\pi\) | ||||
0.0998676 | + | 0.995001i | \(0.468158\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 37.0405i | 0.447246i | 0.974676 | + | 0.223623i | \(0.0717885\pi\) | ||||
−0.974676 | + | 0.223623i | \(0.928212\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −152.000 | −1.37801 | −0.689004 | − | 0.724757i | \(-0.741952\pi\) | ||||
−0.689004 | + | 0.724757i | \(0.741952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.0000 | 0.104000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 158.745i | 1.01649i | 0.861212 | + | 0.508245i | \(0.169706\pi\) | ||||
−0.861212 | + | 0.508245i | \(0.830294\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −224.000 | −1.29779 | −0.648897 | − | 0.760877i | \(-0.724769\pi\) | ||||
−0.648897 | + | 0.760877i | \(0.724769\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 84.6640i | 0.408881i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 243.409i | 1.08152i | 0.841177 | + | 0.540760i | \(0.181863\pi\) | ||||
−0.841177 | + | 0.540760i | \(0.818137\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 70.0000 | 0.266638 | 0.133319 | − | 0.991073i | \(-0.457436\pi\) | ||||
0.133319 | + | 0.991073i | \(0.457436\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 439.195i | 1.55759i | 0.627276 | + | 0.778797i | \(0.284170\pi\) | ||||
−0.627276 | + | 0.778797i | \(0.715830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 336.000 | 1.04278 | 0.521390 | − | 0.853319i | \(-0.325414\pi\) | ||||
0.521390 | + | 0.853319i | \(0.325414\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −279.000 | −0.813411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 31.7490i | − 0.0822842i | −0.999153 | − | 0.0411421i | \(-0.986900\pi\) | ||||
0.999153 | − | 0.0411421i | \(-0.0130996\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 168.000 | 0.411875 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 534.442i | 1.17929i | 0.807661 | + | 0.589647i | \(0.200733\pi\) | ||||
−0.807661 | + | 0.589647i | \(0.799267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 95.2470i | 0.199920i | 0.994991 | + | 0.0999601i | \(0.0318715\pi\) | ||||
−0.994991 | + | 0.0999601i | \(0.968128\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −560.000 | −1.06861 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 174.620i | − 0.318406i | −0.987246 | − | 0.159203i | \(-0.949108\pi\) | ||||
0.987246 | − | 0.159203i | \(-0.0508924\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −72.0000 | −0.120350 | −0.0601748 | − | 0.998188i | \(-0.519166\pi\) | ||||
−0.0601748 | + | 0.998188i | \(0.519166\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −294.000 | −0.471371 | −0.235686 | − | 0.971829i | \(-0.575734\pi\) | ||||
−0.235686 | + | 0.971829i | \(0.575734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 126.996i | − 0.187955i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 464.000 | 0.660811 | 0.330406 | − | 0.943839i | \(-0.392814\pi\) | ||||
0.330406 | + | 0.943839i | \(0.392814\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 545.025i | − 0.720774i | −0.932803 | − | 0.360387i | \(-0.882645\pi\) | ||||
0.932803 | − | 0.360387i | \(-0.117355\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 148.162i | 0.189064i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −266.000 | −0.316808 | −0.158404 | − | 0.987374i | \(-0.550635\pi\) | ||||
−0.158404 | + | 0.987374i | \(0.550635\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 423.320i | 0.487649i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −392.000 | −0.423351 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 994.000 | 1.04047 | 0.520234 | − | 0.854024i | \(-0.325845\pi\) | ||||
0.520234 | + | 0.854024i | \(0.325845\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 751.393i | − 0.740262i | −0.928980 | − | 0.370131i | \(-0.879313\pi\) | ||||
0.928980 | − | 0.370131i | \(-0.120687\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1176.00 | −1.12500 | −0.562499 | − | 0.826798i | \(-0.690160\pi\) | ||||
−0.562499 | + | 0.826798i | \(0.690160\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 269.867i | − 0.243822i | −0.992541 | − | 0.121911i | \(-0.961098\pi\) | ||||
0.992541 | − | 0.121911i | \(-0.0389023\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1894.36i | − 1.66465i | −0.554290 | − | 0.832324i | \(-0.687010\pi\) | ||||
0.554290 | − | 0.832324i | \(-0.312990\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1710.00 | 1.42357 | 0.711784 | − | 0.702398i | \(-0.247887\pi\) | ||||
0.711784 | + | 0.702398i | \(0.247887\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1608.62i | − 1.30439i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 112.000 | 0.0862775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1079.00 | 0.810669 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1460.45i | 1.04502i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1664.00 | 1.16265 | 0.581323 | − | 0.813673i | \(-0.302535\pi\) | ||||
0.581323 | + | 0.813673i | \(0.302535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 672.021i | − 0.448204i | −0.974566 | − | 0.224102i | \(-0.928055\pi\) | ||||
0.974566 | − | 0.224102i | \(-0.0719449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 296.324i | 0.193192i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1062.00 | 0.662283 | 0.331142 | − | 0.943581i | \(-0.392566\pi\) | ||||
0.331142 | + | 0.943581i | \(0.392566\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2693.37i | − 1.64352i | −0.569835 | − | 0.821759i | \(-0.692993\pi\) | ||||
0.569835 | − | 0.821759i | \(-0.307007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 840.000 | 0.491219 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1680.00 | −0.962182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 793.725i | − 0.436406i | −0.975903 | − | 0.218203i | \(-0.929980\pi\) | ||||
0.975903 | − | 0.218203i | \(-0.0700195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −744.000 | −0.400966 | −0.200483 | − | 0.979697i | \(-0.564251\pi\) | ||||
−0.200483 | + | 0.979697i | \(0.564251\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2370.59i | − 1.22846i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 179.911i | 0.0914552i | 0.998954 | + | 0.0457276i | \(0.0145606\pi\) | ||||
−0.998954 | + | 0.0457276i | \(0.985439\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1216.00 | −0.595244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1772.65i | 0.851809i | 0.904768 | + | 0.425905i | \(0.140044\pi\) | ||||
−0.904768 | + | 0.425905i | \(0.859956\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1960.00 | −0.908200 | −0.454100 | − | 0.890951i | \(-0.650039\pi\) | ||||
−0.454100 | + | 0.890951i | \(0.650039\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −603.000 | −0.274465 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 2000.19i | − 0.879026i | −0.898236 | − | 0.439513i | \(-0.855151\pi\) | ||||
0.898236 | − | 0.439513i | \(-0.144849\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 104.000 | 0.0449238 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3264.86i | 1.36328i | 0.731688 | + | 0.681639i | \(0.238733\pi\) | ||||
−0.731688 | + | 0.681639i | \(0.761267\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2338.84i | − 0.960469i | −0.877140 | − | 0.480235i | \(-0.840552\pi\) | ||||
0.877140 | − | 0.480235i | \(-0.159448\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2576.00 | −1.02374 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 222.243i | − 0.0869092i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3904.00 | 1.47897 | 0.739486 | − | 0.673172i | \(-0.235069\pi\) | ||||
0.739486 | + | 0.673172i | \(0.235069\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3330.00 | 1.24196 | 0.620981 | − | 0.783826i | \(-0.286734\pi\) | ||||
0.620981 | + | 0.783826i | \(0.286734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1195.88i | 0.432502i | 0.976338 | + | 0.216251i | \(0.0693829\pi\) | ||||
−0.976338 | + | 0.216251i | \(0.930617\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1736.00 | 0.618401 | 0.309200 | − | 0.950997i | \(-0.399939\pi\) | ||||
0.309200 | + | 0.950997i | \(0.399939\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1269.96i | 0.439083i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 740.810i | 0.252392i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 588.000 | 0.194607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2915.62i | 0.951277i | 0.879641 | + | 0.475638i | \(0.157783\pi\) | ||||
−0.879641 | + | 0.475638i | \(0.842217\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4648.00 | −1.47438 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1792.00 | −0.560594 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 740.810i | 0.225486i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1568.00 | −0.470857 | −0.235428 | − | 0.971892i | \(-0.575649\pi\) | ||||
−0.235428 | + | 0.971892i | \(0.575649\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1264.67i | − 0.369775i | −0.982760 | − | 0.184888i | \(-0.940808\pi\) | ||||
0.982760 | − | 0.184888i | \(-0.0591922\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5153.92i | 1.48725i | 0.668595 | + | 0.743626i | \(0.266896\pi\) | ||||
−0.668595 | + | 0.743626i | \(0.733104\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 838.000 | 0.235619 | 0.117809 | − | 0.993036i | \(-0.462413\pi\) | ||||
0.117809 | + | 0.993036i | \(0.462413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3555.89i | 0.987067i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6288.00 | 1.70183 | 0.850914 | − | 0.525305i | \(-0.176049\pi\) | ||||
0.850914 | + | 0.525305i | \(0.176049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2926.00 | −0.782076 | −0.391038 | − | 0.920375i | \(-0.627884\pi\) | ||||
−0.391038 | + | 0.920375i | \(0.627884\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2952.66i | − 0.769953i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1960.00 | −0.504906 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5444.96i | 1.36925i | 0.728894 | + | 0.684627i | \(0.240035\pi\) | ||||
−0.728894 | + | 0.684627i | \(0.759965\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2412.93i | 0.599602i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2562.00 | −0.621841 | −0.310921 | − | 0.950436i | \(-0.600637\pi\) | ||||
−0.310921 | + | 0.950436i | \(0.600637\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1947.27i | 0.467172i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5896.00 | −1.38237 | −0.691184 | − | 0.722679i | \(-0.742911\pi\) | ||||
−0.691184 | + | 0.722679i | \(0.742911\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 336.000 | 0.0778880 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5365.58i | 1.21615i | 0.793878 | + | 0.608077i | \(0.208059\pi\) | ||||
−0.793878 | + | 0.608077i | \(0.791941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1680.00 | 0.376578 | 0.188289 | − | 0.982114i | \(-0.439706\pi\) | ||||
0.188289 | + | 0.982114i | \(0.439706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 206.369i | − 0.0452527i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1576.87i | − 0.342039i | −0.985268 | − | 0.171019i | \(-0.945294\pi\) | ||||
0.985268 | − | 0.171019i | \(-0.0547061\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2742.00 | 0.582114 | 0.291057 | − | 0.956706i | \(-0.405993\pi\) | ||||
0.291057 | + | 0.956706i | \(0.405993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2989.70i | − 0.627983i | −0.949426 | − | 0.313991i | \(-0.898334\pi\) | ||||
0.949426 | − | 0.313991i | \(-0.101666\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 560.000 | 0.115177 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4717.00 | −0.960106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9238.96i | 1.84214i | 0.389401 | + | 0.921068i | \(0.372682\pi\) | ||||
−0.389401 | + | 0.921068i | \(0.627318\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5656.00 | −1.11629 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 8043.08i | − 1.55566i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3513.56i | 0.672818i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1008.00 | −0.189239 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2587.54i | − 0.481039i | −0.970644 | − | 0.240520i | \(-0.922682\pi\) | ||||
0.970644 | − | 0.240520i | \(-0.0773178\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2744.00 | −0.500315 | −0.250157 | − | 0.968205i | \(-0.580482\pi\) | ||||
−0.250157 | + | 0.968205i | \(0.580482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2282.00 | 0.412097 | 0.206048 | − | 0.978542i | \(-0.433940\pi\) | ||||
0.206048 | + | 0.978542i | \(0.433940\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 9577.62i | − 1.69695i | −0.529237 | − | 0.848474i | \(-0.677522\pi\) | ||||
0.529237 | − | 0.848474i | \(-0.322478\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2520.00 | 0.442298 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 518.567i | 0.0893308i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 687.895i | 0.117408i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2688.00 | 0.450438 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4249.08i | 0.705590i | 0.935701 | + | 0.352795i | \(0.114769\pi\) | ||||
−0.935701 | + | 0.352795i | \(0.885231\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1848.00 | 0.301394 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6130.00 | 0.990868 | 0.495434 | − | 0.868646i | \(-0.335009\pi\) | ||||
0.495434 | + | 0.868646i | \(0.335009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3555.89i | 0.564699i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4976.00 | −0.783320 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2481.71i | 0.383935i | 0.981401 | + | 0.191967i | \(0.0614868\pi\) | ||||
−0.981401 | + | 0.191967i | \(0.938513\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 328.073i | − 0.0503191i | −0.999683 | − | 0.0251595i | \(-0.991991\pi\) | ||||
0.999683 | − | 0.0251595i | \(-0.00800937\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10206.0 | 1.53884 | 0.769420 | − | 0.638743i | \(-0.220545\pi\) | ||||
0.769420 | + | 0.638743i | \(0.220545\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 761.976i | − 0.113920i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3176.00 | −0.466916 | −0.233458 | − | 0.972367i | \(-0.575004\pi\) | ||||
−0.233458 | + | 0.972367i | \(0.575004\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5487.00 | 0.799971 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 3111.40i | − 0.446187i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11760.0 | 1.67266 | 0.836331 | − | 0.548225i | \(-0.184696\pi\) | ||||
0.836331 | + | 0.548225i | \(0.184696\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 253.992i | − 0.0355434i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 10974.6i | − 1.52344i | −0.647908 | − | 0.761719i | \(-0.724356\pi\) | ||||
0.647908 | − | 0.761719i | \(-0.275644\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8400.00 | −1.14754 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3074.36i | − 0.416674i | −0.978057 | − | 0.208337i | \(-0.933195\pi\) | ||||
0.978057 | − | 0.208337i | \(-0.0668051\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2688.00 | 0.358617 | 0.179309 | − | 0.983793i | \(-0.442614\pi\) | ||||
0.179309 | + | 0.983793i | \(0.442614\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1344.00 | 0.177913 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 10487.8i | − 1.36697i | −0.729966 | − | 0.683484i | \(-0.760464\pi\) | ||||
0.729966 | − | 0.683484i | \(-0.239536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2128.00 | −0.275237 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4910.51i | 0.625506i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5704.24i | − 0.721127i | −0.932735 | − | 0.360564i | \(-0.882584\pi\) | ||||
0.932735 | − | 0.360564i | \(-0.117416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12402.0 | −1.54445 | −0.772227 | − | 0.635346i | \(-0.780857\pi\) | ||||
−0.772227 | + | 0.635346i | \(0.780857\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 11853.0i | − 1.46511i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3864.00 | 0.470593 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12278.0 | −1.48437 | −0.742186 | − | 0.670194i | \(-0.766211\pi\) | ||||
−0.742186 | + | 0.670194i | \(0.766211\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4275.53i | 0.509407i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5768.00 | 0.682265 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 8207.12i | − 0.956907i | −0.878113 | − | 0.478454i | \(-0.841198\pi\) | ||||
0.878113 | − | 0.478454i | \(-0.158802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1449.87i | − 0.167844i | −0.996472 | − | 0.0839221i | \(-0.973255\pi\) | ||||
0.996472 | − | 0.0839221i | \(-0.0267447\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 182.000 | 0.0207725 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 761.976i | 0.0863574i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7632.00 | 0.852948 | 0.426474 | − | 0.904500i | \(-0.359756\pi\) | ||||
0.426474 | + | 0.904500i | \(0.359756\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3794.00 | 0.421081 | 0.210540 | − | 0.977585i | \(-0.432478\pi\) | ||||
0.210540 | + | 0.977585i | \(0.432478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 5630.16i | − 0.616309i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1848.00 | 0.200912 | 0.100456 | − | 0.994942i | \(-0.467970\pi\) | ||||
0.100456 | + | 0.994942i | \(0.467970\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 12334.5i | − 1.32287i | −0.750004 | − | 0.661433i | \(-0.769949\pi\) | ||||
0.750004 | − | 0.661433i | \(-0.230051\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2815.08i | − 0.299882i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3582.00 | 0.376492 | 0.188246 | − | 0.982122i | \(-0.439720\pi\) | ||||
0.188246 | + | 0.982122i | \(0.439720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1111.22i | − 0.116020i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4480.00 | −0.461595 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2714.00 | 0.277802 | 0.138901 | − | 0.990306i | \(-0.455643\pi\) | ||||
0.138901 | + | 0.990306i | \(0.455643\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 8349.99i | − 0.843596i | −0.906690 | − | 0.421798i | \(-0.861399\pi\) | ||||
0.906690 | − | 0.421798i | \(-0.138601\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2224.00 | −0.223236 | −0.111618 | − | 0.993751i | \(-0.535603\pi\) | ||||
−0.111618 | + | 0.993751i | \(0.535603\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10292.0i | 1.01982i | 0.860228 | + | 0.509910i | \(0.170321\pi\) | ||||
−0.860228 | + | 0.509910i | \(0.829679\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1396.96i | − 0.137538i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6972.00 | 0.677744 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 481.527i | 0.0465136i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17696.0 | 1.68800 | 0.843999 | − | 0.536345i | \(-0.180195\pi\) | ||||
0.843999 | + | 0.536345i | \(0.180195\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12880.0 | −1.22095 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10519.5i | 0.984879i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1304.00 | −0.121334 | −0.0606672 | − | 0.998158i | \(-0.519323\pi\) | ||||
−0.0606672 | + | 0.998158i | \(0.519323\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16662.9i | 1.53154i | 0.643112 | + | 0.765772i | \(0.277643\pi\) | ||||
−0.643112 | + | 0.765772i | \(0.722357\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2222.43i | 0.203029i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −576.000 | −0.0519862 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 3095.53i | − 0.277705i | −0.990313 | − | 0.138853i | \(-0.955659\pi\) | ||||
0.990313 | − | 0.138853i | \(-0.0443414\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19320.0 | −1.71260 | −0.856298 | − | 0.516481i | \(-0.827242\pi\) | ||||
−0.856298 | + | 0.516481i | \(0.827242\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7952.00 | 0.700712 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4476.61i | 0.389828i | 0.980820 | + | 0.194914i | \(0.0624427\pi\) | ||||
−0.980820 | + | 0.194914i | \(0.937557\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2352.00 | −0.203613 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 12445.6i | − 1.06489i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 5333.83i | − 0.453737i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2982.00 | 0.250756 | 0.125378 | − | 0.992109i | \(-0.459986\pi\) | ||||
0.125378 | + | 0.992109i | \(0.459986\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2016.06i | − 0.168559i | −0.996442 | − | 0.0842794i | \(-0.973141\pi\) | ||||
0.996442 | − | 0.0842794i | \(-0.0268588\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3136.00 | −0.259215 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10937.0 | 0.898907 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3704.05i | 0.301014i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2856.00 | 0.230796 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4428.99i | 0.353933i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15419.4i | 1.22539i | 0.790321 | + | 0.612693i | \(0.209914\pi\) | ||||
−0.790321 | + | 0.612693i | \(0.790086\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20048.0 | 1.57571 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12609.7i | 0.985649i | 0.870129 | + | 0.492824i | \(0.164035\pi\) | ||||
−0.870129 | + | 0.492824i | \(0.835965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5880.00 | −0.454621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3712.00 | 0.285444 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7143.53i | 0.543413i | 0.962380 | + | 0.271706i | \(0.0875880\pi\) | ||||
−0.962380 | + | 0.271706i | \(0.912412\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23240.0 | −1.75840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 7572.14i | − 0.566834i | −0.958997 | − | 0.283417i | \(-0.908532\pi\) | ||||
0.958997 | − | 0.283417i | \(-0.0914681\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18096.9i | 1.34751i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15594.0 | −1.14892 | −0.574459 | − | 0.818533i | \(-0.694788\pi\) | ||||
−0.574459 | + | 0.818533i | \(0.694788\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16737.0i | 1.22666i | 0.789827 | + | 0.613330i | \(0.210170\pi\) | ||||
−0.789827 | + | 0.613330i | \(0.789830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1976.00 | −0.143313 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6594.00 | 0.475757 | 0.237879 | − | 0.971295i | \(-0.423548\pi\) | ||||
0.237879 | + | 0.971295i | \(0.423548\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 4360.20i | − 0.311345i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −504.000 | −0.0358037 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 23213.8i | − 1.63226i | −0.577868 | − | 0.816130i | \(-0.696115\pi\) | ||||
0.577868 | − | 0.816130i | \(-0.303885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 8297.08i | − 0.580433i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14322.0 | −0.991794 | −0.495897 | − | 0.868381i | \(-0.665161\pi\) | ||||
−0.495897 | + | 0.868381i | \(0.665161\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1185.30i | 0.0816679i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16088.0 | −1.09739 | −0.548696 | − | 0.836022i | \(-0.684876\pi\) | ||||
−0.548696 | + | 0.836022i | \(0.684876\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21238.0 | −1.44146 | −0.720729 | − | 0.693217i | \(-0.756193\pi\) | ||||
−0.720729 | + | 0.693217i | \(0.756193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11419.1i | 0.767357i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13664.0 | 0.913681 | 0.456841 | − | 0.889549i | \(-0.348981\pi\) | ||||
0.456841 | + | 0.889549i | \(0.348981\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17779.4i | 1.17722i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20393.5i | 1.34369i | 0.740690 | + | 0.671846i | \(0.234499\pi\) | ||||
−0.740690 | + | 0.671846i | \(0.765501\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3782.00 | 0.246771 | 0.123385 | − | 0.992359i | \(-0.460625\pi\) | ||||
0.123385 | + | 0.992359i | \(0.460625\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5825.94i | − 0.378295i | −0.981949 | − | 0.189147i | \(-0.939428\pi\) | ||||
0.981949 | − | 0.189147i | \(-0.0605724\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2128.00 | −0.136848 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13831.0 | −0.885184 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3407.73i | 0.216017i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2056.00 | −0.129712 | −0.0648558 | − | 0.997895i | \(-0.520659\pi\) | ||||
−0.0648558 | + | 0.997895i | \(0.520659\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17610.1i | 1.10053i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 14763.3i | − 0.918278i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11842.0 | −0.729689 | −0.364845 | − | 0.931068i | \(-0.618878\pi\) | ||||
−0.364845 | + | 0.931068i | \(0.618878\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16250.2i | 0.996649i | 0.866991 | + | 0.498325i | \(0.166051\pi\) | ||||
−0.866991 | + | 0.498325i | \(0.833949\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19320.0 | 1.17395 | 0.586976 | − | 0.809604i | \(-0.300318\pi\) | ||||
0.586976 | + | 0.809604i | \(0.300318\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8484.00 | 0.513137 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2317.68i | 0.138894i | 0.997586 | + | 0.0694470i | \(0.0221235\pi\) | ||||
−0.997586 | + | 0.0694470i | \(0.977877\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7112.00 | 0.424258 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27732.8i | 1.63932i | 0.572847 | + | 0.819662i | \(0.305839\pi\) | ||||
−0.572847 | + | 0.819662i | \(0.694161\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22467.7i | 1.32208i | 0.750352 | + | 0.661039i | \(0.229884\pi\) | ||||
−0.750352 | + | 0.661039i | \(0.770116\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3136.00 | −0.182870 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 24129.3i | − 1.40073i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1512.00 | 0.0869897 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10078.0 | −0.577234 | −0.288617 | − | 0.957445i | \(-0.593195\pi\) | ||||
−0.288617 | + | 0.957445i | \(0.593195\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 16160.2i | − 0.917413i | −0.888588 | − | 0.458707i | \(-0.848313\pi\) | ||||
0.888588 | − | 0.458707i | \(-0.151687\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7952.00 | 0.449440 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 16356.0i | − 0.916320i | −0.888870 | − | 0.458160i | \(-0.848509\pi\) | ||||
0.888870 | − | 0.458160i | \(-0.151491\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11239.2i | 0.626899i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1680.00 | 0.0928925 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29246.1i | 1.61009i | 0.593211 | + | 0.805047i | \(0.297860\pi\) | ||||
−0.593211 | + | 0.805047i | \(0.702140\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28504.0 | 1.55571 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 980.000 | 0.0532570 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 2465.84i | − 0.132858i | −0.997791 | − | 0.0664290i | \(-0.978839\pi\) | ||||
0.997791 | − | 0.0664290i | \(-0.0211606\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9016.00 | −0.483705 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 6011.15i | − 0.319763i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 31674.9i | − 1.67782i | −0.544267 | − | 0.838912i | \(-0.683192\pi\) | ||||
0.544267 | − | 0.838912i | \(-0.316808\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 34048.0 | 1.78837 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8889.72i | 0.464975i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9296.00 | −0.482173 | −0.241086 | − | 0.970504i | \(-0.577504\pi\) | ||||
−0.241086 | + | 0.970504i | \(0.577504\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9408.00 | −0.485953 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2063.69i | 0.105715i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21672.0 | −1.10560 | −0.552799 | − | 0.833315i | \(-0.686440\pi\) | ||||
−0.552799 | + | 0.833315i | \(0.686440\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6148.73i | 0.311106i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 9471.79i | − 0.477283i | −0.971108 | − | 0.238642i | \(-0.923298\pi\) | ||||
0.971108 | − | 0.238642i | \(-0.0767021\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2772.00 | −0.138545 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 6863.08i | − 0.341627i | −0.985303 | − | 0.170814i | \(-0.945360\pi\) | ||||
0.985303 | − | 0.170814i | \(-0.0546396\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17432.0 | 0.860724 | 0.430362 | − | 0.902656i | \(-0.358386\pi\) | ||||
0.430362 | + | 0.902656i | \(0.358386\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8400.00 | 0.413090 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 2158.93i | − 0.105321i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11632.0 | 0.565190 | 0.282595 | − | 0.959239i | \(-0.408805\pi\) | ||||
0.282595 | + | 0.959239i | \(0.408805\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 7873.76i | − 0.379543i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 16731.7i | − 0.803336i | −0.915785 | − | 0.401668i | \(-0.868431\pi\) | ||||
0.915785 | − | 0.401668i | \(-0.131569\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39466.0 | −1.87995 | −0.939975 | − | 0.341244i | \(-0.889152\pi\) | ||||
−0.939975 | + | 0.341244i | \(0.889152\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 15154.9i | − 0.719060i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −28280.0 | −1.33133 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35266.0 | 1.65374 | 0.826869 | − | 0.562395i | \(-0.190120\pi\) | ||||
0.826869 | + | 0.562395i | \(0.190120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 16244.9i | − 0.755872i | −0.925832 | − | 0.377936i | \(-0.876634\pi\) | ||||
0.925832 | − | 0.377936i | \(-0.123366\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2912.00 | −0.134970 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2592.84i | 0.119253i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1142.96i | 0.0523668i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1904.00 | −0.0865690 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34844.5i | − 1.57824i | −0.614240 | − | 0.789119i | \(-0.710537\pi\) | ||||
0.614240 | − | 0.789119i | \(-0.289463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13680.0 | 0.614924 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5040.00 | −0.225694 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 2550.50i | − 0.113354i | −0.998393 | − | 0.0566772i | \(-0.981949\pi\) | ||||
0.998393 | − | 0.0566772i | \(-0.0180506\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4704.00 | 0.208280 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4667.11i | 0.205104i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 12868.9i | − 0.563441i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24390.0 | 1.05996 | 0.529979 | − | 0.848010i | \(-0.322200\pi\) | ||||
0.529979 | + | 0.848010i | \(0.322200\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9582.91i | 0.414922i | 0.978243 | + | 0.207461i | \(0.0665200\pi\) | ||||
−0.978243 | + | 0.207461i | \(0.933480\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18760.0 | −0.806300 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16268.0 | −0.696628 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8773.31i | 0.372948i | 0.982460 | + | 0.186474i | \(0.0597061\pi\) | ||||
−0.982460 | + | 0.186474i | \(0.940294\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21688.0 | 0.918586 | 0.459293 | − | 0.888285i | \(-0.348103\pi\) | ||||
0.459293 | + | 0.888285i | \(0.348103\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 19446.3i | − 0.817670i | −0.912608 | − | 0.408835i | \(-0.865935\pi\) | ||||
0.912608 | − | 0.408835i | \(-0.134065\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 19546.8i | − 0.818925i | −0.912327 | − | 0.409462i | \(-0.865716\pi\) | ||||
0.912327 | − | 0.409462i | \(-0.134284\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3906.00 | −0.162467 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 20742.7i | − 0.859677i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18760.0 | −0.771951 | −0.385976 | − | 0.922509i | \(-0.626135\pi\) | ||||
−0.385976 | + | 0.922509i | \(0.626135\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −811.000 | −0.0332527 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 6381.55i | − 0.259801i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8632.00 | 0.350176 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 36998.2i | − 1.49034i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28732.9i | 1.15333i | 0.816979 | + | 0.576667i | \(0.195647\pi\) | ||||
−0.816979 | + | 0.576667i | \(0.804353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8778.00 | −0.349884 | −0.174942 | − | 0.984579i | \(-0.555974\pi\) | ||||
−0.174942 | + | 0.984579i | \(0.555974\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5646.03i | 0.224261i | 0.993693 | + | 0.112130i | \(0.0357675\pi\) | ||||
−0.993693 | + | 0.112130i | \(0.964233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9312.00 | −0.367305 | −0.183652 | − | 0.982991i | \(-0.558792\pi\) | ||||
−0.183652 | + | 0.982991i | \(0.558792\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21168.0 | 0.832062 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 7365.77i | − 0.287534i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9240.00 | 0.359455 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11683.6i | 0.451405i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 137.579i | 0.00529728i | 0.999996 | + | 0.00264864i | \(0.000843089\pi\) | ||||
−0.999996 | + | 0.00264864i | \(0.999157\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31150.0 | 1.19123 | 0.595613 | − | 0.803272i | \(-0.296909\pi\) | ||||
0.595613 | + | 0.803272i | \(0.296909\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 12577.9i | − 0.479366i | −0.970851 | − | 0.239683i | \(-0.922957\pi\) | ||||
0.970851 | − | 0.239683i | \(-0.0770435\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37128.0 | 1.40545 | 0.702726 | − | 0.711460i | \(-0.251966\pi\) | ||||
0.702726 | + | 0.711460i | \(0.251966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13312.0 | 0.502216 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12445.6i | 0.466379i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34552.0 | −1.29044 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 35558.9i | − 1.31919i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 444.486i | − 0.0164351i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24752.0 | 0.909154 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 35204.4i | − 1.28880i | −0.764688 | − | 0.644400i | \(-0.777107\pi\) | ||||
0.764688 | − | 0.644400i | \(-0.222893\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10512.0 | −0.382303 | −0.191152 | − | 0.981561i | \(-0.561222\pi\) | ||||
−0.191152 | + | 0.981561i | \(0.561222\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8652.00 | −0.313625 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 5376.17i | − 0.193606i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46104.0 | 1.65488 | 0.827438 | − | 0.561557i | \(-0.189798\pi\) | ||||
0.827438 | + | 0.561557i | \(0.189798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3809.88i | − 0.135865i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3164.32i | 0.112478i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5726.00 | 0.202222 | 0.101111 | − | 0.994875i | \(-0.467760\pi\) | ||||
0.101111 | + | 0.994875i | \(0.467760\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 10334.3i | − 0.363795i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2352.00 | 0.0822659 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1274.00 | 0.0444181 | 0.0222091 | − | 0.999753i | \(-0.492930\pi\) | ||||
0.0222091 | + | 0.999753i | \(0.492930\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26446.9i | 0.916201i | 0.888900 | + | 0.458101i | \(0.151470\pi\) | ||||
−0.888900 | + | 0.458101i | \(0.848530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10640.0 | −0.367430 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23922.9i | 0.820897i | 0.911884 | + | 0.410448i | \(0.134628\pi\) | ||||
−0.911884 | + | 0.410448i | \(0.865372\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 15557.0i | − 0.532141i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38250.0 | −1.30015 | −0.650073 | − | 0.759872i | \(-0.725262\pi\) | ||||
−0.650073 | + | 0.759872i | \(0.725262\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41316.1i | 1.39995i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8496.00 | 0.286079 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20385.0 | 0.684267 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 35241.4i | 1.17561i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4664.00 | −0.155103 | −0.0775513 | − | 0.996988i | \(-0.524710\pi\) | ||||
−0.0775513 | + | 0.996988i | \(0.524710\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30971.2i | 1.02360i | 0.859106 | + | 0.511798i | \(0.171020\pi\) | ||||
−0.859106 | + | 0.511798i | \(0.828980\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 21547.0i | − 0.709933i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4814.00 | 0.157639 | 0.0788196 | − | 0.996889i | \(-0.474885\pi\) | ||||
0.0788196 | + | 0.996889i | \(0.474885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4222.62i | 0.137850i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12376.0 | −0.401560 | −0.200780 | − | 0.979636i | \(-0.564348\pi\) | ||||
−0.200780 | + | 0.979636i | \(0.564348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12656.0 | −0.409395 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 66757.6i | − 2.14638i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45344.0 | −1.45348 | −0.726740 | − | 0.686912i | \(-0.758966\pi\) | ||||
−0.726740 | + | 0.686912i | \(0.758966\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18372.1i | 0.585361i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 26002.4i | − 0.825984i | −0.910735 | − | 0.412992i | \(-0.864484\pi\) | ||||
0.910735 | − | 0.412992i | \(-0.135516\pi\) | |||||||
\(998\) | 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 | 288.4.d.a.145.2 | 2 | ||
3.2 | odd | 2 | 32.4.b.a.17.1 | 2 | |||
4.3 | odd | 2 | 72.4.d.b.37.2 | 2 | |||
8.3 | odd | 2 | 72.4.d.b.37.1 | 2 | |||
8.5 | even | 2 | inner | 288.4.d.a.145.1 | 2 | ||
12.11 | even | 2 | 8.4.b.a.5.1 | ✓ | 2 | ||
15.2 | even | 4 | 800.4.f.a.49.2 | 4 | |||
15.8 | even | 4 | 800.4.f.a.49.3 | 4 | |||
15.14 | odd | 2 | 800.4.d.a.401.2 | 2 | |||
16.3 | odd | 4 | 2304.4.a.bn.1.2 | 2 | |||
16.5 | even | 4 | 2304.4.a.v.1.1 | 2 | |||
16.11 | odd | 4 | 2304.4.a.bn.1.1 | 2 | |||
16.13 | even | 4 | 2304.4.a.v.1.2 | 2 | |||
24.5 | odd | 2 | 32.4.b.a.17.2 | 2 | |||
24.11 | even | 2 | 8.4.b.a.5.2 | yes | 2 | ||
48.5 | odd | 4 | 256.4.a.j.1.1 | 2 | |||
48.11 | even | 4 | 256.4.a.l.1.2 | 2 | |||
48.29 | odd | 4 | 256.4.a.j.1.2 | 2 | |||
48.35 | even | 4 | 256.4.a.l.1.1 | 2 | |||
60.23 | odd | 4 | 200.4.f.a.149.2 | 4 | |||
60.47 | odd | 4 | 200.4.f.a.149.3 | 4 | |||
60.59 | even | 2 | 200.4.d.a.101.2 | 2 | |||
120.29 | odd | 2 | 800.4.d.a.401.1 | 2 | |||
120.53 | even | 4 | 800.4.f.a.49.1 | 4 | |||
120.59 | even | 2 | 200.4.d.a.101.1 | 2 | |||
120.77 | even | 4 | 800.4.f.a.49.4 | 4 | |||
120.83 | odd | 4 | 200.4.f.a.149.4 | 4 | |||
120.107 | odd | 4 | 200.4.f.a.149.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.4.b.a.5.1 | ✓ | 2 | 12.11 | even | 2 | ||
8.4.b.a.5.2 | yes | 2 | 24.11 | even | 2 | ||
32.4.b.a.17.1 | 2 | 3.2 | odd | 2 | |||
32.4.b.a.17.2 | 2 | 24.5 | odd | 2 | |||
72.4.d.b.37.1 | 2 | 8.3 | odd | 2 | |||
72.4.d.b.37.2 | 2 | 4.3 | odd | 2 | |||
200.4.d.a.101.1 | 2 | 120.59 | even | 2 | |||
200.4.d.a.101.2 | 2 | 60.59 | even | 2 | |||
200.4.f.a.149.1 | 4 | 120.107 | odd | 4 | |||
200.4.f.a.149.2 | 4 | 60.23 | odd | 4 | |||
200.4.f.a.149.3 | 4 | 60.47 | odd | 4 | |||
200.4.f.a.149.4 | 4 | 120.83 | odd | 4 | |||
256.4.a.j.1.1 | 2 | 48.5 | odd | 4 | |||
256.4.a.j.1.2 | 2 | 48.29 | odd | 4 | |||
256.4.a.l.1.1 | 2 | 48.35 | even | 4 | |||
256.4.a.l.1.2 | 2 | 48.11 | even | 4 | |||
288.4.d.a.145.1 | 2 | 8.5 | even | 2 | inner | ||
288.4.d.a.145.2 | 2 | 1.1 | even | 1 | trivial | ||
800.4.d.a.401.1 | 2 | 120.29 | odd | 2 | |||
800.4.d.a.401.2 | 2 | 15.14 | odd | 2 | |||
800.4.f.a.49.1 | 4 | 120.53 | even | 4 | |||
800.4.f.a.49.2 | 4 | 15.2 | even | 4 | |||
800.4.f.a.49.3 | 4 | 15.8 | even | 4 | |||
800.4.f.a.49.4 | 4 | 120.77 | even | 4 | |||
2304.4.a.v.1.1 | 2 | 16.5 | even | 4 | |||
2304.4.a.v.1.2 | 2 | 16.13 | even | 4 | |||
2304.4.a.bn.1.1 | 2 | 16.11 | odd | 4 | |||
2304.4.a.bn.1.2 | 2 | 16.3 | odd | 4 |