Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,3,Mod(641,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.641");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.l (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: | \(26.1581053786\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 56 x^{14} - 252 x^{13} + 1094 x^{12} - 3652 x^{11} + 5452 x^{10} + 1164 x^{9} - 5879 x^{8} - 15060 x^{7} + 42772 x^{6} - 39536 x^{5} + 64024 x^{4} + \cdots + 20736 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{28}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 480) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.1 | ||
Root | \(2.45733 - 4.45426i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.641 |
Dual form | 960.3.l.j.641.2 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −2.99655 | − | 0.143843i | −0.998850 | − | 0.0479478i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.24307 | 0.320439 | 0.160219 | − | 0.987081i | \(-0.448780\pi\) | ||||
0.160219 | + | 0.987081i | \(0.448780\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.95862 | + | 0.862068i | 0.995402 | + | 0.0957853i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 9.03137i | − | 0.821033i | −0.911853 | − | 0.410517i | \(-0.865348\pi\) | ||
0.911853 | − | 0.410517i | \(-0.134652\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.03098 | −0.617767 | −0.308884 | − | 0.951100i | \(-0.599955\pi\) | ||||
−0.308884 | + | 0.951100i | \(0.599955\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.321644 | − | 6.70049i | 0.0214429 | − | 0.446699i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.34437i | 0.432022i | 0.976391 | + | 0.216011i | \(0.0693047\pi\) | ||||
−0.976391 | + | 0.216011i | \(0.930695\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −14.0089 | −0.737310 | −0.368655 | − | 0.929566i | \(-0.620182\pi\) | ||||
−0.368655 | + | 0.929566i | \(0.620182\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.72147 | − | 0.322651i | −0.320070 | − | 0.0153643i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 12.6041i | − | 0.548006i | −0.961729 | − | 0.274003i | \(-0.911652\pi\) | ||
0.961729 | − | 0.274003i | \(-0.0883478\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −26.7209 | − | 3.87187i | −0.989664 | − | 0.143402i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 38.9853i | 1.34432i | 0.740405 | + | 0.672161i | \(0.234634\pi\) | ||||
−0.740405 | + | 0.672161i | \(0.765366\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 44.0396 | 1.42063 | 0.710316 | − | 0.703883i | \(-0.248552\pi\) | ||||
0.710316 | + | 0.703883i | \(0.248552\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.29910 | + | 27.0629i | −0.0393667 | + | 0.820089i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.01566i | 0.143304i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.3292 | 0.684573 | 0.342286 | − | 0.939596i | \(-0.388799\pi\) | ||||
0.342286 | + | 0.939596i | \(0.388799\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 24.0652 | + | 1.15520i | 0.617057 | + | 0.0296206i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.51074i | 0.207579i | 0.994599 | + | 0.103790i | \(0.0330968\pi\) | ||||
−0.994599 | + | 0.103790i | \(0.966903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −45.9971 | −1.06970 | −0.534850 | − | 0.844947i | \(-0.679632\pi\) | ||||
−0.534850 | + | 0.844947i | \(0.679632\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.92764 | + | 20.0321i | −0.0428365 | + | 0.445157i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 51.7389i | − | 1.10083i | −0.834892 | − | 0.550414i | \(-0.814470\pi\) | ||
0.834892 | − | 0.550414i | \(-0.185530\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −43.9686 | −0.897319 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.05644 | − | 22.0078i | 0.0207145 | − | 0.431525i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 60.6457i | − | 1.14426i | −0.820163 | − | 0.572130i | \(-0.806117\pi\) | ||
0.820163 | − | 0.572130i | \(-0.193883\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20.1947 | 0.367177 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 41.9783 | + | 2.01508i | 0.736462 | + | 0.0353524i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 86.0177i | − | 1.45793i | −0.684552 | − | 0.728964i | \(-0.740002\pi\) | ||
0.684552 | − | 0.728964i | \(-0.259998\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 67.0499 | 1.09918 | 0.549590 | − | 0.835435i | \(-0.314784\pi\) | ||||
0.549590 | + | 0.835435i | \(0.314784\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 20.0948 | + | 1.93368i | 0.318965 | + | 0.0306933i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 17.9578i | − | 0.276274i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.5703 | −0.232392 | −0.116196 | − | 0.993226i | \(-0.537070\pi\) | ||||
−0.116196 | + | 0.993226i | \(0.537070\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.81302 | + | 37.7689i | −0.0262757 | + | 0.547375i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 68.6484i | − | 0.966879i | −0.875378 | − | 0.483440i | \(-0.839387\pi\) | ||
0.875378 | − | 0.483440i | \(-0.160613\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −90.6777 | −1.24216 | −0.621080 | − | 0.783747i | \(-0.713306\pi\) | ||||
−0.621080 | + | 0.783747i | \(0.713306\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.9827 | + | 0.719217i | 0.199770 | + | 0.00958956i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 20.2580i | − | 0.263091i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 31.3181 | 0.396431 | 0.198216 | − | 0.980158i | \(-0.436485\pi\) | ||||
0.198216 | + | 0.980158i | \(0.436485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 79.5137 | + | 15.4459i | 0.981650 | + | 0.190690i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 143.046i | − | 1.72344i | −0.507383 | − | 0.861720i | \(-0.669387\pi\) | ||
0.507383 | − | 0.861720i | \(-0.330613\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.4225 | −0.193206 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.60778 | − | 116.821i | 0.0644572 | − | 1.34278i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 140.581i | − | 1.57956i | −0.613392 | − | 0.789778i | \(-0.710196\pi\) | ||
0.613392 | − | 0.789778i | \(-0.289804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.0140 | −0.197956 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −131.967 | − | 6.33480i | −1.41900 | − | 0.0681161i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 31.3248i | − | 0.329735i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.825684 | 0.00851221 | 0.00425610 | − | 0.999991i | \(-0.498645\pi\) | ||||
0.00425610 | + | 0.999991i | \(0.498645\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.78565 | − | 80.9086i | 0.0786429 | − | 0.817258i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 149.256i | − | 1.47778i | −0.673824 | − | 0.738892i | \(-0.735349\pi\) | ||
0.673824 | − | 0.738892i | \(-0.264651\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −86.3106 | −0.837967 | −0.418984 | − | 0.907994i | \(-0.637613\pi\) | ||||
−0.418984 | + | 0.907994i | \(0.637613\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.721469 | − | 15.0297i | 0.00687113 | − | 0.143140i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 156.269i | 1.46046i | 0.683202 | + | 0.730230i | \(0.260587\pi\) | ||||
−0.683202 | + | 0.730230i | \(0.739413\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 26.0810 | 0.239275 | 0.119638 | − | 0.992818i | \(-0.461827\pi\) | ||||
0.119638 | + | 0.992818i | \(0.461827\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −75.9002 | − | 3.64344i | −0.683786 | − | 0.0328238i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 42.8246i | 0.378978i | 0.981883 | + | 0.189489i | \(0.0606832\pi\) | ||||
−0.981883 | + | 0.189489i | \(0.939317\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.1837 | 0.245076 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −71.9465 | − | 6.92324i | −0.614927 | − | 0.0591730i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.4739i | 0.138436i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 39.4344 | 0.325904 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.22421 | − | 25.5029i | 0.00995296 | − | 0.207340i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −98.4145 | −0.774918 | −0.387459 | − | 0.921887i | \(-0.626647\pi\) | ||||
−0.387459 | + | 0.921887i | \(0.626647\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 137.832 | + | 6.61637i | 1.06847 | + | 0.0512897i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 98.5827i | − | 0.752539i | −0.926510 | − | 0.376270i | \(-0.877207\pi\) | ||
0.926510 | − | 0.376270i | \(-0.122793\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −31.4229 | −0.236262 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.65776 | − | 59.7498i | 0.0641315 | − | 0.442591i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 154.756i | − | 1.12961i | −0.825225 | − | 0.564804i | \(-0.808952\pi\) | ||
0.825225 | − | 0.564804i | \(-0.191048\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 227.186 | 1.63443 | 0.817215 | − | 0.576333i | \(-0.195517\pi\) | ||||
0.817215 | + | 0.576333i | \(0.195517\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.44230 | + | 155.038i | −0.0527822 | + | 1.09956i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 72.5307i | 0.507208i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −87.1738 | −0.601199 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 131.754 | + | 6.32460i | 0.896287 | + | 0.0430245i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 104.398i | − | 0.700659i | −0.936627 | − | 0.350330i | \(-0.886070\pi\) | ||
0.936627 | − | 0.350330i | \(-0.113930\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −216.256 | −1.43216 | −0.716079 | − | 0.698020i | \(-0.754065\pi\) | ||||
−0.716079 | + | 0.698020i | \(0.754065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.33134 | + | 65.7954i | −0.0413813 | + | 0.430035i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 98.4755i | 0.635326i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 239.367 | 1.52463 | 0.762316 | − | 0.647205i | \(-0.224062\pi\) | ||||
0.762316 | + | 0.647205i | \(0.224062\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.72349 | + | 181.728i | −0.0548647 | + | 1.14294i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 28.2719i | − | 0.175602i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.8765 | 0.121942 | 0.0609708 | − | 0.998140i | \(-0.480580\pi\) | ||||
0.0609708 | + | 0.998140i | \(0.480580\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −60.5146 | − | 2.90488i | −0.366755 | − | 0.0176053i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 293.172i | − | 1.75552i | −0.479099 | − | 0.877761i | \(-0.659036\pi\) | ||
0.479099 | − | 0.877761i | \(-0.340964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −104.503 | −0.618363 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −125.500 | − | 12.0766i | −0.733919 | − | 0.0706234i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 90.1213i | 0.520932i | 0.965483 | + | 0.260466i | \(0.0838762\pi\) | ||||
−0.965483 | + | 0.260466i | \(0.916124\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.2153 | −0.0640877 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.3731 | + | 257.756i | −0.0699044 | + | 1.45625i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 328.689i | − | 1.83625i | −0.396292 | − | 0.918124i | \(-0.629703\pi\) | ||
0.396292 | − | 0.918124i | \(-0.370297\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 200.100 | 1.10552 | 0.552762 | − | 0.833339i | \(-0.313574\pi\) | ||||
0.552762 | + | 0.833339i | \(0.313574\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −200.918 | − | 9.64469i | −1.09791 | − | 0.0527032i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 56.6378i | 0.306150i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 66.3297 | 0.354704 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −59.9369 | − | 8.68486i | −0.317127 | − | 0.0459517i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 197.777i | 1.03548i | 0.855537 | + | 0.517742i | \(0.173227\pi\) | ||||
−0.855537 | + | 0.517742i | \(0.826773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −212.677 | −1.10195 | −0.550977 | − | 0.834521i | \(-0.685745\pi\) | ||||
−0.550977 | + | 0.834521i | \(0.685745\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.58311 | + | 53.8115i | −0.0132467 | + | 0.275956i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 68.5241i | 0.347838i | 0.984760 | + | 0.173919i | \(0.0556431\pi\) | ||||
−0.984760 | + | 0.173919i | \(0.944357\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 252.252 | 1.26760 | 0.633798 | − | 0.773498i | \(-0.281495\pi\) | ||||
0.633798 | + | 0.773498i | \(0.281495\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 46.6572 | + | 2.23968i | 0.232125 | + | 0.0111427i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 87.4468i | 0.430772i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.0306 | −0.0928322 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.8656 | − | 112.916i | 0.0524909 | − | 0.545486i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 126.519i | 0.605356i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.9653 | 0.0851435 | 0.0425717 | − | 0.999093i | \(-0.486445\pi\) | ||||
0.0425717 | + | 0.999093i | \(0.486445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.87462 | + | 205.708i | −0.0463597 | + | 0.965767i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 102.853i | − | 0.478384i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 98.7838 | 0.455225 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 271.720 | + | 13.0434i | 1.24073 | + | 0.0595589i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 58.9825i | − | 0.266889i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −142.384 | −0.638493 | −0.319246 | − | 0.947672i | \(-0.603430\pi\) | ||||
−0.319246 | + | 0.947672i | \(0.603430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −44.7931 | − | 4.31034i | −0.199080 | − | 0.0191571i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 321.954i | 1.41830i | 0.705059 | + | 0.709149i | \(0.250921\pi\) | ||||
−0.705059 | + | 0.709149i | \(0.749079\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 107.541 | 0.469613 | 0.234806 | − | 0.972042i | \(-0.424554\pi\) | ||||
0.234806 | + | 0.972042i | \(0.424554\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.91398 | + | 60.7040i | −0.0126146 | + | 0.262788i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 291.098i | − | 1.24935i | −0.780885 | − | 0.624675i | \(-0.785232\pi\) | ||
0.780885 | − | 0.624675i | \(-0.214768\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 115.692 | 0.492305 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −93.8461 | − | 4.50490i | −0.395975 | − | 0.0190080i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 452.505i | 1.89333i | 0.322223 | + | 0.946664i | \(0.395570\pi\) | ||||
−0.322223 | + | 0.946664i | \(0.604430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 62.6968 | 0.260153 | 0.130076 | − | 0.991504i | \(-0.458478\pi\) | ||||
0.130076 | + | 0.991504i | \(0.458478\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −236.045 | − | 57.7218i | −0.971378 | − | 0.237538i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 98.3169i | − | 0.401293i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 112.505 | 0.455486 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.5762 | + | 428.643i | −0.0826352 | + | 1.72146i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 242.908i | 0.967759i | 0.875135 | + | 0.483880i | \(0.160773\pi\) | ||||
−0.875135 | + | 0.483880i | \(0.839227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −113.833 | −0.449931 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 49.2109 | + | 2.36227i | 0.192984 | + | 0.00926380i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 258.831i | − | 1.00712i | −0.863959 | − | 0.503562i | \(-0.832022\pi\) | ||
0.863959 | − | 0.503562i | \(-0.167978\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 56.8152 | 0.219364 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −33.6080 | + | 349.255i | −0.128766 | + | 1.33814i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 205.895i | 0.782869i | 0.920206 | + | 0.391435i | \(0.128021\pi\) | ||||
−0.920206 | + | 0.391435i | \(0.871979\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 135.608 | 0.511728 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.2216 | + | 421.257i | −0.0757363 | + | 1.57774i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 200.612i | − | 0.745768i | −0.927878 | − | 0.372884i | \(-0.878369\pi\) | ||
0.927878 | − | 0.372884i | \(-0.121631\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 46.0058 | 0.169763 | 0.0848816 | − | 0.996391i | \(-0.472949\pi\) | ||||
0.0848816 | + | 0.996391i | \(0.472949\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 53.9800 | + | 2.59120i | 0.197729 | + | 0.00949158i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 45.1568i | 0.164207i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −256.932 | −0.927551 | −0.463776 | − | 0.885953i | \(-0.653506\pi\) | ||||
−0.463776 | + | 0.885953i | \(0.653506\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 394.534 | + | 37.9651i | 1.41410 | + | 0.136076i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 42.9617i | 0.152889i | 0.997074 | + | 0.0764444i | \(0.0243568\pi\) | ||||
−0.997074 | + | 0.0764444i | \(0.975643\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −519.170 | −1.83452 | −0.917261 | − | 0.398287i | \(-0.869605\pi\) | ||||
−0.917261 | + | 0.398287i | \(0.869605\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.50587 | + | 93.8664i | −0.0158101 | + | 0.329356i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 19.0902i | 0.0665163i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 235.060 | 0.813357 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.47420 | − | 0.118769i | −0.00850242 | − | 0.000408142i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 88.7773i | − | 0.302994i | −0.988458 | − | 0.151497i | \(-0.951591\pi\) | ||
0.988458 | − | 0.151497i | \(-0.0484094\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 192.341 | 0.652005 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −34.9682 | + | 241.327i | −0.117738 | + | 0.812547i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 101.223i | 0.338540i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −103.175 | −0.342773 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.4695 | + | 447.254i | −0.0708565 | + | 1.47608i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 149.928i | 0.491568i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −345.304 | −1.12477 | −0.562385 | − | 0.826876i | \(-0.690116\pi\) | ||||
−0.562385 | + | 0.826876i | \(0.690116\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 258.634 | + | 12.4152i | 0.837003 | + | 0.0401787i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 65.2492i | − | 0.209804i | −0.994483 | − | 0.104902i | \(-0.966547\pi\) | ||
0.994483 | − | 0.104902i | \(-0.0334529\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 114.858 | 0.366959 | 0.183480 | − | 0.983023i | \(-0.441264\pi\) | ||||
0.183480 | + | 0.983023i | \(0.441264\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.32383 | + | 44.9333i | −0.0137265 | + | 0.142646i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.0703i | − | 0.0317675i | −0.999874 | − | 0.0158837i | \(-0.994944\pi\) | ||
0.999874 | − | 0.0158837i | \(-0.00505616\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 352.091 | 1.10373 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.4783 | − | 468.268i | 0.0700258 | − | 1.45878i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 102.886i | − | 0.318534i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 40.1549 | 0.123553 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −78.1530 | − | 3.75158i | −0.239000 | − | 0.0114727i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 116.054i | − | 0.352748i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −365.387 | −1.10389 | −0.551944 | − | 0.833881i | \(-0.686114\pi\) | ||||
−0.551944 | + | 0.833881i | \(0.686114\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 226.915 | + | 21.8355i | 0.681425 | + | 0.0655720i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 34.8162i | − | 0.103929i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −103.132 | −0.306028 | −0.153014 | − | 0.988224i | \(-0.548898\pi\) | ||||
−0.153014 | + | 0.988224i | \(0.548898\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.16003 | − | 128.326i | 0.0181712 | − | 0.378543i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 397.738i | − | 1.16639i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −208.535 | −0.607974 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −84.4538 | − | 4.05404i | −0.244794 | − | 0.0117508i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 411.888i | 1.18700i | 0.804836 | + | 0.593498i | \(0.202253\pi\) | ||||
−0.804836 | + | 0.593498i | \(0.797747\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −492.648 | −1.41160 | −0.705800 | − | 0.708411i | \(-0.749412\pi\) | ||||
−0.705800 | + | 0.708411i | \(0.749412\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 214.595 | + | 31.0949i | 0.611382 | + | 0.0885894i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 444.692i | − | 1.25975i | −0.776697 | − | 0.629875i | \(-0.783106\pi\) | ||
0.776697 | − | 0.629875i | \(-0.216894\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 153.503 | 0.432402 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.36967 | − | 49.3650i | 0.00663772 | − | 0.138277i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 137.546i | 0.383136i | 0.981479 | + | 0.191568i | \(0.0613572\pi\) | ||||
−0.981479 | + | 0.191568i | \(0.938643\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −164.751 | −0.456375 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −118.167 | − | 5.67238i | −0.325530 | − | 0.0156264i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 202.762i | − | 0.555511i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −122.989 | −0.335119 | −0.167559 | − | 0.985862i | \(-0.553589\pi\) | ||||
−0.167559 | + | 0.985862i | \(0.553589\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.33683 | + | 76.2445i | −0.0198830 | + | 0.206625i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 136.033i | − | 0.366665i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.5537 | 0.0470609 | 0.0235305 | − | 0.999723i | \(-0.492509\pi\) | ||||
0.0235305 | + | 0.999723i | \(0.492509\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.60822 | + | 33.5024i | −0.00428858 | + | 0.0893398i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 313.090i | − | 0.830478i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 295.437 | 0.779517 | 0.389759 | − | 0.920917i | \(-0.372558\pi\) | ||||
0.389759 | + | 0.920917i | \(0.372558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 294.904 | + | 14.1563i | 0.774026 | + | 0.0371556i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 249.327i | 0.650984i | 0.945545 | + | 0.325492i | \(0.105530\pi\) | ||||
−0.945545 | + | 0.325492i | \(0.894470\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 45.2982 | 0.117658 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −412.070 | − | 39.6526i | −1.06478 | − | 0.102461i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 100.365i | 0.258008i | 0.991644 | + | 0.129004i | \(0.0411780\pi\) | ||||
−0.991644 | + | 0.129004i | \(0.958822\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 92.5694 | 0.236750 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.1805 | + | 295.408i | −0.0360826 | + | 0.751674i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 70.0293i | 0.177289i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 420.402 | 1.05895 | 0.529473 | − | 0.848327i | \(-0.322390\pi\) | ||||
0.529473 | + | 0.848327i | \(0.322390\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 94.1603 | + | 4.51998i | 0.235991 | + | 0.0113283i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 465.360i | 1.16050i | 0.814439 | + | 0.580249i | \(0.197045\pi\) | ||||
−0.814439 | + | 0.580249i | \(0.802955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −353.681 | −0.877620 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −34.5380 | + | 177.798i | −0.0852790 | + | 0.439007i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 228.757i | − | 0.562057i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −441.627 | −1.07977 | −0.539886 | − | 0.841738i | \(-0.681533\pi\) | ||||
−0.539886 | + | 0.841738i | \(0.681533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.2607 | + | 463.735i | −0.0541622 | + | 1.12831i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 192.944i | − | 0.467176i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 319.860 | 0.770746 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −680.773 | − | 32.6792i | −1.63255 | − | 0.0783673i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 133.888i | 0.319542i | 0.987154 | + | 0.159771i | \(0.0510756\pi\) | ||||
−0.987154 | + | 0.159771i | \(0.948924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −659.449 | −1.56639 | −0.783193 | − | 0.621778i | \(-0.786411\pi\) | ||||
−0.783193 | + | 0.621778i | \(0.786411\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 44.6024 | − | 463.509i | 0.105443 | − | 1.09577i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 36.7219i | − | 0.0864044i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 150.398 | 0.352219 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.4331 | − | 217.342i | 0.0243195 | − | 0.506624i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 464.823i | 1.07848i | 0.842153 | + | 0.539238i | \(0.181288\pi\) | ||||
−0.842153 | + | 0.539238i | \(0.818712\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 393.188 | 0.908055 | 0.454028 | − | 0.890988i | \(-0.349987\pi\) | ||||
0.454028 | + | 0.890988i | \(0.349987\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 261.221 | + | 12.5394i | 0.600507 | + | 0.0288262i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 176.570i | 0.404050i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 406.911 | 0.926904 | 0.463452 | − | 0.886122i | \(-0.346611\pi\) | ||||
0.463452 | + | 0.886122i | \(0.346611\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −393.898 | − | 37.9039i | −0.893193 | − | 0.0859500i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 531.885i | 1.20064i | 0.799758 | + | 0.600322i | \(0.204961\pi\) | ||||
−0.799758 | + | 0.600322i | \(0.795039\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 314.348 | 0.706399 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.0170 | + | 312.834i | −0.0335951 | + | 0.699853i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 690.916i | − | 1.53879i | −0.638774 | − | 0.769394i | \(-0.720558\pi\) | ||
0.638774 | − | 0.769394i | \(-0.279442\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 76.8636 | 0.170429 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 648.021 | + | 31.1070i | 1.43051 | + | 0.0686688i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 40.2806i | − | 0.0885288i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 885.218 | 1.93702 | 0.968510 | − | 0.248974i | \(-0.0800934\pi\) | ||||
0.968510 | + | 0.248974i | \(0.0800934\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.4364 | − | 196.248i | 0.0619530 | − | 0.427557i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 516.543i | − | 1.12048i | −0.828329 | − | 0.560242i | \(-0.810708\pi\) | ||
0.828329 | − | 0.560242i | \(-0.189292\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −465.526 | −1.00546 | −0.502728 | − | 0.864445i | \(-0.667670\pi\) | ||||
−0.502728 | + | 0.864445i | \(0.667670\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 14.1650 | − | 295.087i | 0.0304625 | − | 0.634595i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 646.351i | − | 1.38405i | −0.721874 | − | 0.692025i | \(-0.756719\pi\) | ||
0.721874 | − | 0.692025i | \(-0.243281\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.9253 | −0.0744675 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −717.275 | − | 34.4314i | −1.52288 | − | 0.0731027i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 415.416i | 0.878258i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 70.0444 | 0.147462 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 52.2807 | − | 543.302i | 0.109603 | − | 1.13900i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 55.5045i | 0.115876i | 0.998320 | + | 0.0579379i | \(0.0184526\pi\) | ||||
−0.998320 | + | 0.0579379i | \(0.981547\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −203.418 | −0.422907 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.06673 | + | 84.7183i | −0.00841973 | + | 0.175400i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.84629i | 0.00380678i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −188.411 | −0.386880 | −0.193440 | − | 0.981112i | \(-0.561964\pi\) | ||||
−0.193440 | + | 0.981112i | \(0.561964\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −59.5608 | − | 2.85910i | −0.121801 | − | 0.00584683i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 154.621i | − | 0.314910i | −0.987526 | − | 0.157455i | \(-0.949671\pi\) | ||
0.987526 | − | 0.157455i | \(-0.0503290\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −286.323 | −0.580776 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 180.917 | + | 17.4092i | 0.365489 | + | 0.0351702i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 153.983i | − | 0.309825i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 961.012 | 1.92588 | 0.962938 | − | 0.269722i | \(-0.0869318\pi\) | ||||
0.962938 | + | 0.269722i | \(0.0869318\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −42.1709 | + | 878.505i | −0.0841734 | + | 1.75350i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 435.850i | − | 0.866500i | −0.901274 | − | 0.433250i | \(-0.857367\pi\) | ||
0.901274 | − | 0.433250i | \(-0.142633\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 333.747 | 0.660885 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 313.150 | + | 15.0321i | 0.617652 | + | 0.0296492i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 748.589i | 1.47070i | 0.677685 | + | 0.735352i | \(0.262983\pi\) | ||||
−0.677685 | + | 0.735352i | \(0.737017\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −203.396 | −0.398036 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 374.330 | + | 54.2405i | 0.729689 | + | 0.105732i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 192.996i | − | 0.374750i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −467.273 | −0.903816 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.9633 | − | 270.053i | 0.0249775 | − | 0.520333i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 331.457i | 0.636193i | 0.948058 | + | 0.318097i | \(0.103044\pi\) | ||||
−0.948058 | + | 0.318097i | \(0.896956\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 223.173 | 0.426717 | 0.213359 | − | 0.976974i | \(-0.431560\pi\) | ||||
0.213359 | + | 0.976974i | \(0.431560\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 33.6073 | + | 1.61325i | 0.0640140 | + | 0.00307286i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 323.443i | 0.613744i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 370.136 | 0.699690 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 74.1531 | − | 770.600i | 0.139648 | − | 1.45122i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 68.3495i | − | 0.128236i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −349.428 | −0.653137 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −47.2797 | + | 984.931i | −0.0880441 | + | 1.83414i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 397.097i | 0.736729i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −674.035 | −1.24591 | −0.622953 | − | 0.782259i | \(-0.714067\pi\) | ||||
−0.622953 | + | 0.782259i | \(0.714067\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −599.609 | − | 28.7830i | −1.10425 | − | 0.0530074i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 58.3189i | 0.107007i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 205.195 | 0.375128 | 0.187564 | − | 0.982252i | \(-0.439941\pi\) | ||||
0.187564 | + | 0.982252i | \(0.439941\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 600.675 | + | 57.8016i | 1.09413 | + | 0.105285i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 546.141i | − | 0.991181i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 70.2486 | 0.127032 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.14697 | − | 169.718i | 0.0146792 | − | 0.305798i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 886.612i | 1.59176i | 0.605453 | + | 0.795881i | \(0.292992\pi\) | ||||
−0.605453 | + | 0.795881i | \(0.707008\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 369.401 | 0.660825 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −198.760 | − | 9.54109i | −0.354296 | − | 0.0170073i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 453.686i | − | 0.805836i | −0.915236 | − | 0.402918i | \(-0.867996\pi\) | ||
0.915236 | − | 0.402918i | \(-0.132004\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −95.7586 | −0.169484 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 178.355 | + | 34.6462i | 0.314559 | + | 0.0611043i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 313.662i | − | 0.551251i | −0.961265 | − | 0.275625i | \(-0.911115\pi\) | ||
0.961265 | − | 0.275625i | \(-0.0888849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −418.596 | −0.733092 | −0.366546 | − | 0.930400i | \(-0.619460\pi\) | ||||
−0.366546 | + | 0.930400i | \(0.619460\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.4490 | − | 592.650i | 0.0496492 | − | 1.03429i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 63.0207i | 0.109601i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.7107 | −0.0324276 | −0.0162138 | − | 0.999869i | \(-0.505161\pi\) | ||||
−0.0162138 | + | 0.999869i | \(0.505161\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 637.297 | + | 30.5922i | 1.10069 | + | 0.0528362i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 320.861i | − | 0.552257i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −547.714 | −0.939475 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.4808 | − | 160.877i | 0.0264630 | − | 0.275004i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 937.505i | − | 1.59711i | −0.601920 | − | 0.798556i | \(-0.705597\pi\) | ||
0.601920 | − | 0.798556i | \(-0.294403\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −616.945 | −1.04745 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.85674 | − | 205.336i | 0.0166781 | − | 0.347438i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 902.817i | 1.52246i | 0.648484 | + | 0.761228i | \(0.275403\pi\) | ||||
−0.648484 | + | 0.761228i | \(0.724597\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.8368 | −0.0619106 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −755.885 | − | 36.2847i | −1.26614 | − | 0.0607784i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 991.033i | − | 1.65448i | −0.561849 | − | 0.827240i | \(-0.689910\pi\) | ||
0.561849 | − | 0.827240i | \(-0.310090\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 218.484 | 0.363534 | 0.181767 | − | 0.983342i | \(-0.441818\pi\) | ||||
0.181767 | + | 0.983342i | \(0.441818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −139.488 | − | 13.4226i | −0.231324 | − | 0.0222598i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 88.1781i | 0.145749i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −438.702 | −0.722738 | −0.361369 | − | 0.932423i | \(-0.617690\pi\) | ||||
−0.361369 | + | 0.932423i | \(0.617690\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.5786 | − | 262.039i | 0.0206546 | − | 0.430277i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 415.514i | 0.680055i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 597.090 | 0.974046 | 0.487023 | − | 0.873389i | \(-0.338083\pi\) | ||||
0.487023 | + | 0.873389i | \(0.338083\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 57.0261 | + | 2.73742i | 0.0927254 | + | 0.00445110i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 321.463i | − | 0.521010i | −0.965473 | − | 0.260505i | \(-0.916111\pi\) | ||
0.965473 | − | 0.260505i | \(-0.0838890\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 511.960 | 0.827076 | 0.413538 | − | 0.910487i | \(-0.364293\pi\) | ||||
0.413538 | + | 0.910487i | \(0.364293\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −48.8015 | + | 336.794i | −0.0785854 | + | 0.542342i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 315.332i | − | 0.506151i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.1990 | − | 379.121i | 0.0290255 | − | 0.604659i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 186.027i | 0.295750i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1070.42 | −1.69639 | −0.848195 | − | 0.529684i | \(-0.822311\pi\) | ||||
−0.848195 | + | 0.529684i | \(0.822311\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −53.8338 | − | 2.58418i | −0.0850455 | − | 0.00408244i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 220.062i | − | 0.346554i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 353.111 | 0.554335 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 59.1796 | − | 614.995i | 0.0926128 | − | 0.962434i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 865.824i | 1.35074i | 0.737479 | + | 0.675370i | \(0.236016\pi\) | ||||
−0.737479 | + | 0.675370i | \(0.763984\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −731.670 | −1.13790 | −0.568950 | − | 0.822372i | \(-0.692650\pi\) | ||||
−0.568950 | + | 0.822372i | \(0.692650\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.7947 | + | 308.203i | −0.0229375 | + | 0.477834i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 230.583i | 0.356388i | 0.983995 | + | 0.178194i | \(0.0570254\pi\) | ||||
−0.983995 | + | 0.178194i | \(0.942975\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −776.857 | −1.19701 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −296.011 | − | 14.2094i | −0.454701 | − | 0.0218270i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 617.718i | 0.945970i | 0.881070 | + | 0.472985i | \(0.156824\pi\) | ||||
−0.881070 | + | 0.472985i | \(0.843176\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 220.438 | 0.336546 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −812.347 | − | 78.1703i | −1.23645 | − | 0.118981i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 265.710i | − | 0.403202i | −0.979468 | − | 0.201601i | \(-0.935386\pi\) | ||
0.979468 | − | 0.201601i | \(-0.0646145\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 987.246 | 1.49356 | 0.746782 | − | 0.665069i | \(-0.231598\pi\) | ||||
0.746782 | + | 0.665069i | \(0.231598\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.48424 | + | 176.744i | −0.0127967 | + | 0.266582i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 70.2637i | − | 0.105660i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 491.376 | 0.736696 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 426.660 | + | 20.4810i | 0.637758 | + | 0.0306143i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 605.552i | − | 0.902463i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 587.447 | 0.872878 | 0.436439 | − | 0.899734i | \(-0.356240\pi\) | ||||
0.436439 | + | 0.899734i | \(0.356240\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 133.605 | + | 19.3593i | 0.197933 | + | 0.0286805i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 168.689i | − | 0.249172i | −0.992209 | − | 0.124586i | \(-0.960240\pi\) | ||
0.992209 | − | 0.124586i | \(-0.0397602\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.85207 | 0.00272764 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 46.3109 | − | 964.750i | 0.0680043 | − | 1.41667i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 363.184i | − | 0.531749i | −0.964008 | − | 0.265874i | \(-0.914339\pi\) | ||
0.964008 | − | 0.265874i | \(-0.0856606\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 346.045 | 0.505176 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −322.253 | − | 15.4691i | −0.469073 | − | 0.0225169i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 487.044i | 0.706886i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 395.111 | 0.571795 | 0.285898 | − | 0.958260i | \(-0.407708\pi\) | ||||
0.285898 | + | 0.958260i | \(0.407708\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.4637 | − | 181.484i | 0.0252002 | − | 0.261881i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 508.003i | 0.730939i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −62.5060 | −0.0896787 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −41.8726 | + | 872.291i | −0.0599035 | + | 1.24791i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 473.115i | − | 0.674914i | −0.941341 | − | 0.337457i | \(-0.890433\pi\) | ||
0.941341 | − | 0.337457i | \(-0.109567\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −354.834 | −0.504742 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −346.676 | − | 16.6415i | −0.491739 | − | 0.0236049i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 334.792i | − | 0.473539i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −441.603 | −0.622853 | −0.311427 | − | 0.950270i | \(-0.600807\pi\) | ||||
−0.311427 | + | 0.950270i | \(0.600807\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 280.567 | + | 26.9983i | 0.394608 | + | 0.0379723i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 555.081i | − | 0.778514i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −162.184 | −0.226830 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 65.0899 | − | 1355.95i | 0.0907809 | − | 1.89115i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1096.09i | − | 1.52446i | −0.647307 | − | 0.762229i | \(-0.724105\pi\) | ||
0.647307 | − | 0.762229i | \(-0.275895\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −193.601 | −0.268517 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −187.874 | − | 9.01852i | −0.259853 | − | 0.0124737i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 194.927i | − | 0.268864i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1331.47 | 1.83146 | 0.915731 | − | 0.401791i | \(-0.131612\pi\) | ||||
0.915731 | + | 0.401791i | \(0.131612\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 699.017 | + | 206.920i | 0.958871 | + | 0.283841i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 337.819i | − | 0.462133i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 295.464 | 0.403089 | 0.201545 | − | 0.979479i | \(-0.435404\pi\) | ||||
0.201545 | + | 0.979479i | \(0.435404\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14.1422 | + | 294.611i | −0.0192411 | + | 0.400832i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 140.621i | 0.190802i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −512.085 | −0.692943 | −0.346471 | − | 0.938061i | \(-0.612620\pi\) | ||||
−0.346471 | + | 0.938061i | \(0.612620\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −337.127 | − | 16.1831i | −0.454962 | − | 0.0218395i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 117.627i | − | 0.158313i | −0.996862 | − | 0.0791567i | \(-0.974777\pi\) | ||
0.996862 | − | 0.0791567i | \(-0.0252227\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 233.441 | 0.313344 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 123.315 | − | 1281.49i | 0.165080 | − | 1.71552i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 350.523i | 0.467987i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 313.995 | 0.418103 | 0.209051 | − | 0.977905i | \(-0.432962\pi\) | ||||
0.209051 | + | 0.977905i | \(0.432962\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 34.9406 | − | 727.884i | 0.0464019 | − | 0.966646i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 483.563i | − | 0.640480i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 880.421 | 1.16304 | 0.581520 | − | 0.813532i | \(-0.302458\pi\) | ||||
0.581520 | + | 0.813532i | \(0.302458\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 341.105 | + | 16.3741i | 0.449413 | + | 0.0215732i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 177.647i | 0.233439i | 0.993165 | + | 0.116720i | \(0.0372379\pi\) | ||||
−0.993165 | + | 0.116720i | \(0.962762\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 58.5015 | 0.0766730 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −147.123 | − | 14.1573i | −0.192318 | − | 0.0185063i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 690.806i | 0.900660i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −539.556 | −0.701633 | −0.350816 | − | 0.936444i | \(-0.614096\pi\) | ||||
−0.350816 | + | 0.936444i | \(0.614096\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −37.2311 | + | 775.600i | −0.0482894 | + | 1.00597i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 648.160i | − | 0.838499i | −0.907871 | − | 0.419250i | \(-0.862293\pi\) | ||
0.907871 | − | 0.419250i | \(-0.137707\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −220.198 | −0.284126 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −170.249 | − | 8.17248i | −0.219111 | − | 0.0105180i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 119.226i | − | 0.153050i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −619.989 | −0.793840 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 150.946 | − | 1041.72i | 0.192779 | − | 1.33043i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 535.241i | 0.681836i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1149.99 | −1.46123 | −0.730615 | − | 0.682789i | \(-0.760767\pi\) | ||||
−0.730615 | + | 0.682789i | \(0.760767\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.6166 | − | 616.973i | 0.0375368 | − | 0.781969i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 96.0585i | 0.121439i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −538.476 | −0.679037 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −406.356 | − | 19.5063i | −0.511140 | − | 0.0245362i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1436.14i | 1.80194i | 0.433884 | + | 0.900969i | \(0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 379.990 | 0.475581 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 121.190 | − | 1259.41i | 0.151298 | − | 1.57229i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 818.944i | 1.01986i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 63.2180 | 0.0785317 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28.8567 | + | 601.143i | −0.0357579 | + | 0.744910i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 9.50158i | − | 0.0117449i | −0.999983 | − | 0.00587243i | \(-0.998131\pi\) | ||
0.999983 | − | 0.00587243i | \(-0.00186926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −938.529 | −1.15725 | −0.578624 | − | 0.815594i | \(-0.696410\pi\) | ||||
−0.578624 | + | 0.815594i | \(0.696410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −137.859 | − | 6.61763i | −0.169568 | − | 0.00813977i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 44.4451i | 0.0545339i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 644.367 | 0.788699 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −161.381 | − | 15.5293i | −0.197046 | − | 0.0189613i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 469.104i | − | 0.571381i | −0.958322 | − | 0.285691i | \(-0.907777\pi\) | ||
0.958322 | − | 0.285691i | \(-0.0922230\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1016.98 | 1.23570 | 0.617852 | − | 0.786294i | \(-0.288003\pi\) | ||||
0.617852 | + | 0.786294i | \(0.288003\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.49551 | − | 135.315i | 0.00787335 | − | 0.164018i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 460.051i | − | 0.556289i | −0.960539 | − | 0.278145i | \(-0.910281\pi\) | ||
0.960539 | − | 0.278145i | \(-0.0897194\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.7992 | −0.0226770 | −0.0113385 | − | 0.999936i | \(-0.503609\pi\) | ||||
−0.0113385 | + | 0.999936i | \(0.503609\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 769.909 | + | 36.9579i | 0.926484 | + | 0.0444740i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 322.922i | − | 0.387661i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 655.553 | 0.785093 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1176.78 | − | 170.515i | −1.40595 | − | 0.203722i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 496.989i | − | 0.592359i | −0.955132 | − | 0.296179i | \(-0.904287\pi\) | ||
0.955132 | − | 0.296179i | \(-0.0957126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −678.856 | −0.807200 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.17976 | − | 128.737i | 0.00733068 | − | 0.152713i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 233.677i | − | 0.276541i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 88.4542 | 0.104432 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1555.72 | + | 74.6791i | 1.83241 | + | 0.0879613i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 319.253i | − | 0.375150i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1432.68 | −1.67958 | −0.839791 | − | 0.542911i | \(-0.817322\pi\) | ||||
−0.839791 | + | 0.542911i | \(0.817322\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 27.0041 | − | 280.627i | 0.0315837 | − | 0.328219i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1211.90i | − | 1.41412i | −0.707154 | − | 0.707060i | \(-0.750021\pi\) | ||
0.707154 | − | 0.707060i | \(-0.249979\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.5883 | −0.0216394 | −0.0108197 | − | 0.999941i | \(-0.503444\pi\) | ||||
−0.0108197 | + | 0.999941i | \(0.503444\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.74600 | − | 57.2047i | 0.00318931 | − | 0.0664398i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 936.142i | − | 1.08475i | −0.840135 | − | 0.542377i | \(-0.817525\pi\) | ||
0.840135 | − | 0.542377i | \(-0.182475\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −201.517 | −0.232968 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −704.370 | − | 33.8119i | −0.812422 | − | 0.0389987i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 282.845i | − | 0.325483i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 125.045 | 0.143564 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.39699 | + | 0.711796i | 0.00847307 | + | 0.000815344i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 25.0783i | − | 0.0286609i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 873.860 | 0.996419 | 0.498210 | − | 0.867057i | \(-0.333991\pi\) | ||||
0.498210 | + | 0.867057i | \(0.333991\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.7700 | + | 266.025i | −0.0145279 | + | 0.302646i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 808.376i | 0.917566i | 0.888548 | + | 0.458783i | \(0.151714\pi\) | ||||
−0.888548 | + | 0.458783i | \(0.848286\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −177.913 | −0.201487 | −0.100743 | − | 0.994912i | \(-0.532122\pi\) | ||||
−0.100743 | + | 0.994912i | \(0.532122\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −576.361 | − | 27.6670i | −0.651255 | − | 0.0312622i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1157.53i | 1.30500i | 0.757789 | + | 0.652499i | \(0.226279\pi\) | ||||
−0.757789 | + | 0.652499i | \(0.773721\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −220.751 | −0.248313 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 139.497 | − | 718.117i | 0.156563 | − | 0.805968i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 724.804i | 0.811651i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 734.970 | 0.821195 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.5603 | − | 303.321i | 0.0162322 | − | 0.338151i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1716.90i | 1.90979i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 445.405 | 0.494345 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 309.168 | + | 14.8410i | 0.342379 | + | 0.0164352i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 447.437i | 0.494405i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −89.1205 | −0.0982586 | −0.0491293 | − | 0.998792i | \(-0.515645\pi\) | ||||
−0.0491293 | + | 0.998792i | \(0.515645\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 128.669 | − | 1337.13i | 0.141550 | − | 1.47099i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 280.274i | − | 0.307655i | −0.988098 | − | 0.153827i | \(-0.950840\pi\) | ||
0.988098 | − | 0.153827i | \(-0.0491600\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1291.90 | −1.41500 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.5662 | − | 449.267i | 0.0235696 | − | 0.491002i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 221.128i | − | 0.241143i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 240.880 | 0.262111 | 0.131056 | − | 0.991375i | \(-0.458163\pi\) | ||||
0.131056 | + | 0.991375i | \(0.458163\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1034.72 | + | 49.6697i | 1.12348 | + | 0.0539302i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 551.314i | 0.597307i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −126.646 | −0.136915 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −773.224 | − | 74.4056i | −0.834114 | − | 0.0802649i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1119.74i | 1.20531i | 0.798001 | + | 0.602657i | \(0.205891\pi\) | ||||
−0.798001 | + | 0.602657i | \(0.794109\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 615.951 | 0.661602 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.38566 | + | 195.522i | −0.0100597 | + | 0.209563i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 148.318i | 0.158629i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 771.901 | 0.823800 | 0.411900 | − | 0.911229i | \(-0.364865\pi\) | ||||
0.411900 | + | 0.911229i | \(0.364865\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −344.179 | − | 16.5216i | −0.366537 | − | 0.0175949i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1423.21i | 1.51245i | 0.654313 | + | 0.756223i | \(0.272958\pi\) | ||||
−0.654313 | + | 0.756223i | \(0.727042\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 107.270 | 0.113754 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 19.4199 | − | 134.023i | 0.0205502 | − | 0.141823i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 492.999i | − | 0.520590i | −0.965529 | − | 0.260295i | \(-0.916180\pi\) | ||
0.965529 | − | 0.260295i | \(-0.0838199\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 728.231 | 0.767366 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.44854 | + | 30.1761i | −0.00152318 | + | 0.0317309i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1076.66i | − | 1.12976i | −0.825173 | − | 0.564880i | \(-0.808922\pi\) | ||
0.825173 | − | 0.564880i | \(-0.191078\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −442.244 | −0.463082 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1055.06 | − | 50.6459i | −1.10246 | − | 0.0529215i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 347.129i | − | 0.361970i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 978.485 | 1.01819 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −134.715 | + | 1399.96i | −0.139891 | + | 1.45374i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 475.560i | − | 0.492808i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.16082 | −0.00740519 | −0.00370260 | − | 0.999993i | \(-0.501179\pi\) | ||||
−0.00370260 | + | 0.999993i | \(0.501179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.7995 | + | 308.304i | −0.0152730 | + | 0.318167i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 161.099i | 0.165911i | 0.996553 | + | 0.0829554i | \(0.0264359\pi\) | ||||
−0.996553 | + | 0.0829554i | \(0.973564\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 509.593 | 0.523734 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −120.326 | − | 5.77601i | −0.123411 | − | 0.00592412i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1311.58i | 1.34246i | 0.741248 | + | 0.671231i | \(0.234234\pi\) | ||||
−0.741248 | + | 0.671231i | \(0.765766\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1269.63 | −1.29687 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 233.650 | + | 22.4836i | 0.238175 | + | 0.0229190i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 674.305i | 0.685966i | 0.939342 | + | 0.342983i | \(0.111437\pi\) | ||||
−0.939342 | + | 0.342983i | \(0.888563\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −153.225 | −0.155558 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.6936 | + | 347.761i | −0.0169135 | + | 0.352342i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 579.753i | 0.586201i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1291.05 | 1.30277 | 0.651386 | − | 0.758746i | \(-0.274188\pi\) | ||||
0.651386 | + | 0.758746i | \(0.274188\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1094.90 | + | 52.5584i | 1.10262 | + | 0.0529289i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 564.052i | 0.566886i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 409.552 | 0.410784 | 0.205392 | − | 0.978680i | \(-0.434153\pi\) | ||||
0.205392 | + | 0.978680i | \(0.434153\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −676.820 | − | 98.0713i | −0.677497 | − | 0.0981694i |
(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 | 960.3.l.j.641.1 | 16 | ||
3.2 | odd | 2 | inner | 960.3.l.j.641.2 | 16 | ||
4.3 | odd | 2 | inner | 960.3.l.j.641.16 | 16 | ||
8.3 | odd | 2 | 480.3.l.b.161.1 | ✓ | 16 | ||
8.5 | even | 2 | 480.3.l.b.161.16 | yes | 16 | ||
12.11 | even | 2 | inner | 960.3.l.j.641.15 | 16 | ||
24.5 | odd | 2 | 480.3.l.b.161.15 | yes | 16 | ||
24.11 | even | 2 | 480.3.l.b.161.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.3.l.b.161.1 | ✓ | 16 | 8.3 | odd | 2 | ||
480.3.l.b.161.2 | yes | 16 | 24.11 | even | 2 | ||
480.3.l.b.161.15 | yes | 16 | 24.5 | odd | 2 | ||
480.3.l.b.161.16 | yes | 16 | 8.5 | even | 2 | ||
960.3.l.j.641.1 | 16 | 1.1 | even | 1 | trivial | ||
960.3.l.j.641.2 | 16 | 3.2 | odd | 2 | inner | ||
960.3.l.j.641.15 | 16 | 12.11 | even | 2 | inner | ||
960.3.l.j.641.16 | 16 | 4.3 | odd | 2 | inner |