Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(337,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.c (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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.1362828.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 23x^{2} + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.4 | ||
Root | \(-4.54739i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.337 |
Dual form | 624.4.c.c.337.1 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.9118i | 1.15487i | 0.816437 | + | 0.577434i | \(0.195946\pi\) | ||||
−0.816437 | + | 0.577434i | \(0.804054\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.7289i | 0.903273i | 0.892202 | + | 0.451637i | \(0.149160\pi\) | ||||
−0.892202 | + | 0.451637i | \(0.850840\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24.9280i | 0.683280i | 0.939831 | + | 0.341640i | \(0.110982\pi\) | ||||
−0.939831 | + | 0.341640i | \(0.889018\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 33.7151 | + | 32.5621i | 0.719299 | + | 0.694700i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 38.7355i | − | 0.666764i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 134.145 | 1.91383 | 0.956913 | − | 0.290376i | \(-0.0937804\pi\) | ||||
0.956913 | + | 0.290376i | \(0.0937804\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.9376i | 0.180365i | 0.995925 | + | 0.0901824i | \(0.0287450\pi\) | ||||
−0.995925 | + | 0.0901824i | \(0.971255\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 50.1866i | − | 0.521505i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 72.0000 | 0.652741 | 0.326370 | − | 0.945242i | \(-0.394174\pi\) | ||||
0.326370 | + | 0.945242i | \(0.394174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −41.7151 | −0.333721 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −206.145 | −1.32001 | −0.660004 | − | 0.751262i | \(-0.729445\pi\) | ||||
−0.660004 | + | 0.751262i | \(0.729445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 249.142i | 1.44346i | 0.692176 | + | 0.721728i | \(0.256652\pi\) | ||||
−0.692176 | + | 0.721728i | \(0.743348\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 74.7841i | − | 0.394492i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −216.000 | −1.04316 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 293.955i | − | 1.30610i | −0.757313 | − | 0.653052i | \(-0.773488\pi\) | ||
0.757313 | − | 0.653052i | \(-0.226512\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −101.145 | − | 97.6863i | −0.415288 | − | 0.401085i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 250.506i | 0.954208i | 0.878847 | + | 0.477104i | \(0.158314\pi\) | ||||
−0.878847 | + | 0.477104i | \(0.841686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 432.145 | 1.53259 | 0.766297 | − | 0.642486i | \(-0.222097\pi\) | ||||
0.766297 | + | 0.642486i | \(0.222097\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 116.206i | 0.384956i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 159.889i | − | 0.496217i | −0.968732 | − | 0.248109i | \(-0.920191\pi\) | ||
0.968732 | − | 0.248109i | \(-0.0798090\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 63.1454 | 0.184097 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −402.436 | −1.10495 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −194.581 | −0.504298 | −0.252149 | − | 0.967688i | \(-0.581137\pi\) | ||||
−0.252149 | + | 0.967688i | \(0.581137\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −321.866 | −0.789099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 44.8129i | − | 0.104134i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 232.647i | 0.513358i | 0.966497 | + | 0.256679i | \(0.0826283\pi\) | ||||
−0.966497 | + | 0.256679i | \(0.917372\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −185.006 | −0.388321 | −0.194160 | − | 0.980970i | \(-0.562198\pi\) | ||||
−0.194160 | + | 0.980970i | \(0.562198\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 150.560i | 0.301091i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −420.436 | + | 435.324i | −0.802287 | + | 0.830696i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 39.4393i | 0.0719145i | 0.999353 | + | 0.0359573i | \(0.0114480\pi\) | ||||
−0.999353 | + | 0.0359573i | \(0.988552\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 920.460i | − | 1.53857i | −0.638905 | − | 0.769286i | \(-0.720612\pi\) | ||
0.638905 | − | 0.769286i | \(-0.279388\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 549.078i | 0.880338i | 0.897915 | + | 0.440169i | \(0.145082\pi\) | ||||
−0.897915 | + | 0.440169i | \(0.854918\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 125.145 | 0.192674 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −417.018 | −0.617189 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −933.140 | −1.32894 | −0.664471 | − | 0.747314i | \(-0.731343\pi\) | ||||
−0.664471 | + | 0.747314i | \(0.731343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1095.38i | 1.44860i | 0.689484 | + | 0.724301i | \(0.257837\pi\) | ||||
−0.689484 | + | 0.724301i | \(0.742163\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1732.06i | 2.21022i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 618.436 | 0.762107 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 532.114i | 0.633753i | 0.948467 | + | 0.316876i | \(0.102634\pi\) | ||||
−0.948467 | + | 0.316876i | \(0.897366\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −544.727 | + | 564.015i | −0.627504 | + | 0.649724i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 747.425i | − | 0.833380i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −192.872 | −0.208298 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 362.661i | − | 0.379615i | −0.981821 | − | 0.189808i | \(-0.939214\pi\) | ||
0.981821 | − | 0.189808i | \(-0.0607864\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 224.352i | 0.227760i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1490.58 | −1.46850 | −0.734249 | − | 0.678880i | \(-0.762466\pi\) | ||||
−0.734249 | + | 0.678880i | \(0.762466\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 628.436 | 0.601181 | 0.300591 | − | 0.953753i | \(-0.402816\pi\) | ||||
0.300591 | + | 0.953753i | \(0.402816\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 648.000 | 0.602270 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −477.454 | −0.431376 | −0.215688 | − | 0.976462i | \(-0.569199\pi\) | ||||
−0.215688 | + | 0.976462i | \(0.569199\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 378.207i | − | 0.332345i | −0.986097 | − | 0.166173i | \(-0.946859\pi\) | ||
0.986097 | − | 0.166173i | \(-0.0531409\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 881.864i | 0.754079i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.2732 | 0.0110499 | 0.00552495 | − | 0.999985i | \(-0.498241\pi\) | ||||
0.00552495 | + | 0.999985i | \(0.498241\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 929.651i | 0.753830i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 303.436 | + | 293.059i | 0.239766 | + | 0.231567i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2244.10i | 1.72871i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 709.593 | 0.533128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 751.519i | − | 0.550912i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1075.36i | 0.769465i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 145.988 | 0.102003 | 0.0510015 | − | 0.998699i | \(-0.483759\pi\) | ||||
0.0510015 | + | 0.998699i | \(0.483759\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1296.44 | −0.884844 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −317.163 | −0.211532 | −0.105766 | − | 0.994391i | \(-0.533729\pi\) | ||||
−0.105766 | + | 0.994391i | \(0.533729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −249.890 | −0.162919 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 348.619i | − | 0.222255i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 443.149i | − | 0.276356i | −0.990407 | − | 0.138178i | \(-0.955875\pi\) | ||
0.990407 | − | 0.138178i | \(-0.0441247\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −785.018 | −0.479024 | −0.239512 | − | 0.970893i | \(-0.576987\pi\) | ||||
−0.239512 | + | 0.970893i | \(0.576987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 479.667i | 0.286491i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −811.709 | + | 840.452i | −0.474675 | + | 0.491483i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2661.71i | − | 1.52444i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −189.436 | −0.106289 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 135.420i | 0.0744566i | 0.999307 | + | 0.0372283i | \(0.0118529\pi\) | ||||
−0.999307 | + | 0.0372283i | \(0.988147\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2373.74i | − | 1.27929i | −0.768672 | − | 0.639643i | \(-0.779082\pi\) | ||
0.768672 | − | 0.639643i | \(-0.220918\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1207.31 | 0.637942 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3216.87 | −1.66700 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1166.73 | −0.593089 | −0.296544 | − | 0.955019i | \(-0.595834\pi\) | ||||
−0.296544 | + | 0.955019i | \(0.595834\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 583.744 | 0.291157 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1204.48i | 0.589603i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2309.19i | − | 1.10963i | −0.831974 | − | 0.554815i | \(-0.812789\pi\) | ||
0.831974 | − | 0.554815i | \(-0.187211\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 965.599 | 0.455587 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 600.788i | − | 0.278386i | −0.990265 | − | 0.139193i | \(-0.955549\pi\) | ||
0.990265 | − | 0.139193i | \(-0.0444508\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 76.4186 | + | 2195.67i | 0.0347831 | + | 0.999395i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 134.439i | 0.0601216i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3430.36 | −1.50755 | −0.753773 | − | 0.657135i | \(-0.771768\pi\) | ||||
−0.753773 | + | 0.657135i | \(0.771768\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 697.846i | − | 0.301441i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 697.942i | − | 0.296387i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 978.837 | 0.408725 | 0.204362 | − | 0.978895i | \(-0.434488\pi\) | ||||
0.204362 | + | 0.978895i | \(0.434488\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3839.09 | 1.57656 | 0.788279 | − | 0.615318i | \(-0.210972\pi\) | ||||
0.788279 | + | 0.615318i | \(0.210972\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 555.018 | 0.224197 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3795.49 | 1.50838 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3343.98i | 1.30768i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 451.679i | − | 0.173835i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 487.709 | 0.184761 | 0.0923806 | − | 0.995724i | \(-0.470552\pi\) | ||||
0.0923806 | + | 0.995724i | \(0.470552\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4245.61i | − | 1.58345i | −0.610878 | − | 0.791725i | \(-0.709183\pi\) | ||
0.610878 | − | 0.791725i | \(-0.290817\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1261.31 | − | 1305.97i | 0.463201 | − | 0.479603i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2712.71i | − | 0.981079i | −0.871419 | − | 0.490539i | \(-0.836800\pi\) | ||
0.871419 | − | 0.490539i | \(-0.163200\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3116.90 | 1.11031 | 0.555153 | − | 0.831748i | \(-0.312660\pi\) | ||||
0.555153 | + | 0.831748i | \(0.312660\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 118.318i | − | 0.0415199i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 3448.58i | − | 1.19233i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3234.49 | −1.10198 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 648.000 | 0.217580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −372.366 | −0.123240 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1051.22 | 0.342981 | 0.171491 | − | 0.985186i | \(-0.445142\pi\) | ||||
0.171491 | + | 0.985186i | \(0.445142\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2761.38i | 0.888294i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5579.78i | 1.76994i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4167.85 | −1.30384 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1647.23i | − | 0.508264i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4522.73 | + | 4368.06i | 1.37661 | + | 1.32953i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5496.12i | − | 1.65044i | −0.564814 | − | 0.825218i | \(-0.691052\pi\) | ||
0.564814 | − | 0.825218i | \(-0.308948\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −375.436 | −0.111240 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 921.570i | 0.269457i | 0.990883 | + | 0.134729i | \(0.0430162\pi\) | ||||
−0.990883 | + | 0.134729i | \(0.956984\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 192.941i | − | 0.0556764i | −0.999612 | − | 0.0278382i | \(-0.991138\pi\) | ||
0.999612 | − | 0.0278382i | \(-0.00886232\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1251.05 | 0.356334 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −913.779 | −0.256926 | −0.128463 | − | 0.991714i | \(-0.541004\pi\) | ||||
−0.128463 | + | 0.991714i | \(0.541004\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2064.46 | 0.573066 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2799.42 | 0.767265 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1976.86i | 0.535032i | 0.963553 | + | 0.267516i | \(0.0862028\pi\) | ||||
−0.963553 | + | 0.267516i | \(0.913797\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3904.45i | − | 1.04360i | −0.853068 | − | 0.521800i | \(-0.825261\pi\) | ||
0.853068 | − | 0.521800i | \(-0.174739\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 815.322i | 0.212608i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −486.401 | + | 503.624i | −0.125299 | + | 0.129736i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3286.15i | − | 0.836350i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −942.035 | −0.236895 | −0.118448 | − | 0.992960i | \(-0.537792\pi\) | ||||
−0.118448 | + | 0.992960i | \(0.537792\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1794.82i | 0.446005i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 5196.18i | − | 1.27607i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 812.616 | 0.197236 | 0.0986179 | − | 0.995125i | \(-0.468558\pi\) | ||||
0.0986179 | + | 0.995125i | \(0.468558\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4917.52 | 1.17977 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1855.31 | −0.440003 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2608.29 | 0.611536 | 0.305768 | − | 0.952106i | \(-0.401087\pi\) | ||||
0.305768 | + | 0.952106i | \(0.401087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2512.40i | − | 0.582398i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1596.34i | − | 0.365897i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4791.02 | −1.08592 | −0.542962 | − | 0.839757i | \(-0.682697\pi\) | ||||
−0.542962 | + | 0.839757i | \(0.682697\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3663.62i | − | 0.821214i | −0.911812 | − | 0.410607i | \(-0.865317\pi\) | ||
0.911812 | − | 0.410607i | \(-0.134683\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1634.18 | − | 1692.05i | 0.362290 | − | 0.375118i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 1039.88i | − | 0.228025i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 624.326 | 0.135423 | 0.0677114 | − | 0.997705i | \(-0.478430\pi\) | ||||
0.0677114 | + | 0.997705i | \(0.478430\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2242.27i | 0.481152i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 5535.12i | − | 1.17508i | −0.809195 | − | 0.587540i | \(-0.800096\pi\) | ||
0.809195 | − | 0.587540i | \(-0.199904\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 175.151 | 0.0367903 | 0.0183952 | − | 0.999831i | \(-0.494144\pi\) | ||||
0.0183952 | + | 0.999831i | \(0.494144\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 578.616 | 0.120261 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4190.69 | −0.861911 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13082.0 | 2.66273 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1087.98i | 0.219171i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7774.33i | 1.55011i | 0.631895 | + | 0.775054i | \(0.282277\pi\) | ||||
−0.631895 | + | 0.775054i | \(0.717723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3003.90 | −0.592861 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 673.057i | − | 0.131497i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2427.49 | + | 2344.47i | 0.469516 | + | 0.453459i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7229.30i | 1.38435i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4471.74 | 0.847838 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2388.76i | − | 0.448459i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8022.85i | 1.49149i | 0.666230 | + | 0.745746i | \(0.267907\pi\) | ||||
−0.666230 | + | 0.745746i | \(0.732093\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1885.31 | −0.347092 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9264.87 | −1.68927 | −0.844635 | − | 0.535343i | \(-0.820182\pi\) | ||||
−0.844635 | + | 0.535343i | \(0.820182\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7423.57 | 1.34059 | 0.670296 | − | 0.742094i | \(-0.266167\pi\) | ||||
0.670296 | + | 0.742094i | \(0.266167\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1944.00 | −0.347721 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2641.04i | 0.467935i | 0.972244 | + | 0.233968i | \(0.0751710\pi\) | ||||
−0.972244 | + | 0.233968i | \(0.924829\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5138.80i | − | 0.901936i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1432.36 | 0.249055 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2003.82i | 0.345187i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1406.43 | − | 1358.33i | −0.240045 | − | 0.231836i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1134.62i | 0.191880i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2674.76 | 0.448220 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10779.5i | − | 1.79001i | −0.446052 | − | 0.895007i | \(-0.647170\pi\) | ||
0.446052 | − | 0.895007i | \(-0.352830\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2645.59i | − | 0.435368i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −509.233 | −0.0830518 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 313.465 | 0.0506693 | 0.0253346 | − | 0.999679i | \(-0.491935\pi\) | ||||
0.0253346 | + | 0.999679i | \(0.491935\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −39.8196 | −0.00637966 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6210.61 | −0.986286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6794.35i | 1.06956i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 2788.95i | − | 0.435224i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2849.23 | 0.440792 | 0.220396 | − | 0.975410i | \(-0.429265\pi\) | ||||
0.220396 | + | 0.975410i | \(0.429265\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6466.94i | − | 0.991883i | −0.868356 | − | 0.495941i | \(-0.834823\pi\) | ||
0.868356 | − | 0.495941i | \(-0.165177\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −910.308 | − | 879.177i | −0.138429 | − | 0.133695i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2773.10i | − | 0.418122i | −0.977903 | − | 0.209061i | \(-0.932959\pi\) | ||
0.977903 | − | 0.209061i | \(-0.0670408\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11884.8 | 1.77685 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 6732.30i | − | 0.998070i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1467.11i | − | 0.215685i | −0.994168 | − | 0.107843i | \(-0.965606\pi\) | ||
0.994168 | − | 0.107843i | \(-0.0343942\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6635.87 | 0.967469 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2128.78 | −0.307801 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7089.59 | −1.01667 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4648.22 | −0.661130 | −0.330565 | − | 0.943783i | \(-0.607239\pi\) | ||||
−0.330565 | + | 0.943783i | \(0.607239\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2254.56i | 0.318069i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3255.12i | − | 0.455519i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1763.72 | 0.244831 | 0.122416 | − | 0.992479i | \(-0.460936\pi\) | ||||
0.122416 | + | 0.992479i | \(0.460936\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 3226.08i | − | 0.444251i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6950.22 | − | 6712.53i | −0.949481 | − | 0.917010i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1930.47i | − | 0.261640i | −0.991406 | − | 0.130820i | \(-0.958239\pi\) | ||
0.991406 | − | 0.130820i | \(-0.0417611\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −437.965 | −0.0588914 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8845.93i | 1.18017i | 0.807340 | + | 0.590086i | \(0.200906\pi\) | ||||
−0.807340 | + | 0.590086i | \(0.799094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 5384.46i | − | 0.712772i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3889.31 | 0.510865 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1598.08 | 0.208292 | 0.104146 | − | 0.994562i | \(-0.466789\pi\) | ||||
0.104146 | + | 0.994562i | \(0.466789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9658.47 | 1.24923 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 951.489 | 0.122128 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 12048.5i | − | 1.53475i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3578.82i | − | 0.452433i | −0.974077 | − | 0.226217i | \(-0.927364\pi\) | ||
0.974077 | − | 0.226217i | \(-0.0726357\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 749.669 | 0.0940611 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3485.99i | 0.434120i | 0.976158 | + | 0.217060i | \(0.0696467\pi\) | ||||
−0.976158 | + | 0.217060i | \(0.930353\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8112.58 | + | 8399.84i | −1.00277 | + | 1.03828i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1045.86i | 0.128319i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7327.71 | 0.892435 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14709.1i | 1.77828i | 0.457637 | + | 0.889139i | \(0.348696\pi\) | ||||
−0.457637 | + | 0.889139i | \(0.651304\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1329.45i | 0.159554i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3891.92 | −0.463702 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14143.4 | −1.67294 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2355.05 | 0.276565 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3709.01 | −0.432451 | −0.216226 | − | 0.976343i | \(-0.569375\pi\) | ||||
−0.216226 | + | 0.976343i | \(0.569375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 794.029i | 0.0919207i | 0.998943 | + | 0.0459603i | \(0.0146348\pi\) | ||||
−0.998943 | + | 0.0459603i | \(0.985365\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1439.00i | − | 0.165406i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5595.89 | −0.638684 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3094.94i | − | 0.350760i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2435.13 | − | 2521.35i | 0.274054 | − | 0.283758i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 2891.52i | − | 0.323155i | −0.986860 | − | 0.161577i | \(-0.948342\pi\) | ||
0.986860 | − | 0.161577i | \(-0.0516582\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5560.94 | −0.617186 | −0.308593 | − | 0.951194i | \(-0.599858\pi\) | ||||
−0.308593 | + | 0.951194i | \(0.599858\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7985.14i | 0.880133i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1075.51i | 0.117731i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15127.2 | 1.64460 | 0.822302 | − | 0.569051i | \(-0.192689\pi\) | ||||
0.822302 | + | 0.569051i | \(0.192689\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 568.308 | 0.0613658 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2357.89 | −0.252883 | −0.126441 | − | 0.991974i | \(-0.540356\pi\) | ||||
−0.126441 | + | 0.991974i | \(0.540356\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6870.56 | −0.731901 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 406.260i | − | 0.0429876i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7165.06i | 0.753096i | 0.926397 | + | 0.376548i | \(0.122889\pi\) | ||||
−0.926397 | + | 0.376548i | \(0.877111\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6244.63 | −0.651992 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7121.22i | 0.738596i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7282.47 | − | 7033.41i | −0.750346 | − | 0.724685i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8020.96i | 0.821017i | 0.911857 | + | 0.410508i | \(0.134649\pi\) | ||||
−0.911857 | + | 0.410508i | \(0.865351\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3621.92 | −0.368316 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4146.59i | − | 0.418928i | −0.977816 | − | 0.209464i | \(-0.932828\pi\) | ||
0.977816 | − | 0.209464i | \(-0.0671720\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7118.21i | 0.714495i | 0.934010 | + | 0.357248i | \(0.116285\pi\) | ||||
−0.934010 | + | 0.357248i | \(0.883715\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9650.62 | 0.962444 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2128.22 | −0.210883 | −0.105441 | − | 0.994426i | \(-0.533626\pi\) | ||||
−0.105441 | + | 0.994426i | \(0.533626\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −659.774 | −0.0649585 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3500.18 | 0.342420 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10772.5i | 1.04719i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 623.125i | − | 0.0601915i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1751.23 | −0.168099 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 3715.30i | − | 0.354397i | −0.984175 | − | 0.177199i | \(-0.943296\pi\) | ||
0.984175 | − | 0.177199i | \(-0.0567035\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9571.78 | − | 9910.71i | 0.907350 | − | 0.939479i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 3613.43i | − | 0.340408i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4682.62 | 0.438405 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8139.28i | 0.757343i | 0.925531 | + | 0.378671i | \(0.123619\pi\) | ||||
−0.925531 | + | 0.378671i | \(0.876381\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6927.57i | 0.640645i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18081.7 | 1.66194 | 0.830972 | − | 0.556315i | \(-0.187785\pi\) | ||||
0.830972 | + | 0.556315i | \(0.187785\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27653.4 | −2.52626 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2896.80 | −0.263033 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15398.3 | 1.38975 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 11031.5i | − | 0.989659i | −0.868990 | − | 0.494829i | \(-0.835231\pi\) | ||
0.868990 | − | 0.494829i | \(-0.164769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1802.37i | 0.160726i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8016.14 | −0.710581 | −0.355290 | − | 0.934756i | \(-0.615618\pi\) | ||||
−0.355290 | + | 0.934756i | \(0.615618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 19246.1i | − | 1.69592i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −229.256 | − | 6587.01i | −0.0200821 | − | 0.577001i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20173.9i | 1.75676i | 0.477959 | + | 0.878382i | \(0.341377\pi\) | ||||
−0.477959 | + | 0.878382i | \(0.658623\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9185.44 | −0.795186 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 403.316i | − | 0.0347112i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8114.25i | 0.694285i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3985.72 | 0.339056 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10291.1 | 0.870382 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9746.95 | 0.819619 | 0.409810 | − | 0.912171i | \(-0.365595\pi\) | ||||
0.409810 | + | 0.912171i | \(0.365595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18929.3 | 1.58264 | 0.791320 | − | 0.611402i | \(-0.209394\pi\) | ||||
0.791320 | + | 0.611402i | \(0.209394\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2093.54i | 0.174037i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33421.2i | 2.76252i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2093.83i | 0.171119i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8157.02 | + | 8445.85i | −0.662889 | + | 0.686361i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 6164.80i | − | 0.498182i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2936.51 | −0.235977 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1574.09i | 0.125790i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11366.8i | 0.903321i | 0.892190 | + | 0.451661i | \(0.149168\pi\) | ||||
−0.892190 | + | 0.451661i | \(0.850832\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11517.3 | −0.910227 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4883.34 | 0.383815 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17495.4 | −1.36755 | −0.683775 | − | 0.729693i | \(-0.739663\pi\) | ||||
−0.683775 | + | 0.729693i | \(0.739663\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1665.05 | −0.129440 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3079.33i | − | 0.238083i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15610.4i | − | 1.20040i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11386.5 | −0.870862 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11873.1i | 0.903192i | 0.892223 | + | 0.451596i | \(0.149145\pi\) | ||||
−0.892223 | + | 0.451596i | \(0.850855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14569.8 | + | 14071.6i | 1.10239 | + | 1.06469i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 10031.9i | − | 0.754989i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2829.31 | −0.211796 | −0.105898 | − | 0.994377i | \(-0.533772\pi\) | ||||
−0.105898 | + | 0.994377i | \(0.533772\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 171.381i | 0.0127612i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1355.04i | 0.100364i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16136.8 | −1.18891 | −0.594453 | − | 0.804130i | \(-0.702632\pi\) | ||||
−0.594453 | + | 0.804130i | \(0.702632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17840.5 | −1.30754 | −0.653769 | − | 0.756695i | \(-0.726813\pi\) | ||||
−0.653769 | + | 0.756695i | \(0.726813\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1463.13 | −0.106672 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3003.49 | −0.217833 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8516.17i | 0.614442i | 0.951638 | + | 0.307221i | \(0.0993990\pi\) | ||||
−0.951638 | + | 0.307221i | \(0.900601\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12736.8i | 0.914205i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18324.5 | −1.30848 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4850.53i | − | 0.344577i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3783.92 | + | 3917.91i | −0.267429 | + | 0.276899i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20688.3i | 1.45468i | 0.686277 | + | 0.727340i | \(0.259244\pi\) | ||||
−0.686277 | + | 0.727340i | \(0.740756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3721.59 | −0.260349 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8138.13i | 0.566426i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11435.9i | − | 0.791933i | −0.918265 | − | 0.395966i | \(-0.870410\pi\) | ||
0.918265 | − | 0.395966i | \(-0.129590\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28975.4 | −1.99643 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9350.69 | −0.641035 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1260.80 | −0.0860016 | −0.0430008 | − | 0.999075i | \(-0.513692\pi\) | ||||
−0.0430008 | + | 0.999075i | \(0.513692\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6261.10 | 0.424951 | 0.212476 | − | 0.977166i | \(-0.431847\pi\) | ||||
0.212476 | + | 0.977166i | \(0.431847\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 354.954i | 0.0239715i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9162.14i | 0.615692i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3230.33 | −0.216005 | −0.108003 | − | 0.994151i | \(-0.534445\pi\) | ||||
−0.108003 | + | 0.994151i | \(0.534445\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10345.7i | 0.688391i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5206.33 | − | 5390.68i | 0.344722 | − | 0.356929i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14868.5i | 0.979660i | 0.871818 | + | 0.489830i | \(0.162941\pi\) | ||||
−0.871818 | + | 0.489830i | \(0.837059\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9703.48 | 0.636231 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 19952.8i | − | 1.30190i | −0.759121 | − | 0.650949i | \(-0.774371\pi\) | ||
0.759121 | − | 0.650949i | \(-0.225629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8316.48i | 0.540012i | 0.962859 | + | 0.270006i | \(0.0870257\pi\) | ||||
−0.962859 | + | 0.270006i | \(0.912974\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1944.00 | −0.125620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8901.66 | −0.572452 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19099.2 | −1.22235 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1117.10 | 0.0711525 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 39432.6i | − | 2.49965i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12605.9i | − | 0.795299i | −0.917537 | − | 0.397649i | \(-0.869826\pi\) | ||
0.917537 | − | 0.397649i | \(-0.130174\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3153.66 | −0.198020 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1884.98i | 0.117800i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2128.95 | + | 2056.15i | 0.132421 | + | 0.127892i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 8284.14i | − | 0.512857i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9224.04 | 0.568374 | 0.284187 | − | 0.958769i | \(-0.408276\pi\) | ||||
0.284187 | + | 0.958769i | \(0.408276\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 4439.16i | − | 0.272260i | −0.990691 | − | 0.136130i | \(-0.956533\pi\) | ||
0.990691 | − | 0.136130i | \(-0.0434665\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 16739.4i | − | 1.02188i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9601.15 | −0.583401 | −0.291700 | − | 0.956510i | \(-0.594221\pi\) | ||||
−0.291700 | + | 0.956510i | \(0.594221\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5799.44 | −0.350767 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12503.6 | 0.752770 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27112.8 | 1.62482 | 0.812410 | − | 0.583087i | \(-0.198155\pi\) | ||||
0.812410 | + | 0.583087i | \(0.198155\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4095.15i | − | 0.244291i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4941.70i | 0.293446i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5587.26 | −0.330271 | −0.165136 | − | 0.986271i | \(-0.552806\pi\) | ||||
−0.165136 | + | 0.986271i | \(0.552806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3060.13i | 0.180069i | 0.995939 | + | 0.0900343i | \(0.0286977\pi\) | ||||
−0.995939 | + | 0.0900343i | \(0.971302\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13568.2 | − | 13104.2i | −0.794788 | − | 0.767607i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 3226.53i | − | 0.188150i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14842.5 | −0.861623 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16488.4i | 0.952880i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4611.83i | − | 0.265332i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4121.55 | −0.236069 | −0.118034 | − | 0.993010i | \(-0.537659\pi\) | ||||
−0.118034 | + | 0.993010i | \(0.537659\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1126.31 | 0.0642246 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22889.5 | 1.29943 | 0.649715 | − | 0.760178i | \(-0.274888\pi\) | ||||
0.649715 | + | 0.760178i | \(0.274888\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6066.91 | 0.342896 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 2764.71i | − | 0.155571i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 19297.9i | − | 1.08113i | −0.841301 | − | 0.540566i | \(-0.818210\pi\) | ||
0.841301 | − | 0.540566i | \(-0.181790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5721.87 | 0.319155 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 578.823i | 0.0321448i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6560.34 | − | 6335.98i | −0.362742 | − | 0.350336i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30317.8i | 1.66910i | 0.550935 | + | 0.834548i | \(0.314271\pi\) | ||||
−0.550935 | + | 0.834548i | \(0.685729\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3753.16 | −0.205730 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 10136.0i | − | 0.553210i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33604.3i | 1.82619i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2741.34 | 0.148336 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9606.16 | −0.517574 | −0.258787 | − | 0.965934i | \(-0.583323\pi\) | ||||
−0.258787 | + | 0.965934i | \(0.583323\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4390.99 | 0.235575 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6193.38 | −0.330860 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 24935.7i | − | 1.32646i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23398.8i | 1.23944i | 0.784825 | + | 0.619718i | \(0.212753\pi\) | ||||
−0.784825 | + | 0.619718i | \(0.787247\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8398.26 | −0.442981 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17938.2i | 0.942203i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10851.8 | − | 10480.6i | −0.567598 | − | 0.548187i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 5930.59i | − | 0.308901i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23588.7 | −1.22352 | −0.611758 | − | 0.791045i | \(-0.709537\pi\) | ||||
−0.611758 | + | 0.791045i | \(0.709537\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10513.0i | 0.543031i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11713.3i | 0.602522i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8599.38 | 0.440514 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15733.5 | 0.802644 | 0.401322 | − | 0.915937i | \(-0.368551\pi\) | ||||
0.401322 | + | 0.915937i | \(0.368551\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 57970.3 | 2.93312 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 17297.1i | − | 0.871598i | −0.900044 | − | 0.435799i | \(-0.856466\pi\) | ||
0.900044 | − | 0.435799i | \(-0.143534\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 2445.96i | − | 0.122749i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −983.144 | −0.0491378 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38749.2i | 1.92884i | 0.264377 | + | 0.964419i | \(0.414834\pi\) | ||||
−0.264377 | + | 0.964419i | \(0.585166\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1459.20 | − | 1510.87i | 0.0723417 | − | 0.0749033i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3139.76i | 0.155029i | 0.996991 | + | 0.0775144i | \(0.0246984\pi\) | ||||
−0.996991 | + | 0.0775144i | \(0.975302\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1748.52 | −0.0859876 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9858.45i | 0.482867i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 7987.25i | − | 0.389650i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40628.6 | 1.97411 | 0.987055 | − | 0.160380i | \(-0.0512721\pi\) | ||||
0.987055 | + | 0.160380i | \(0.0512721\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2826.11 | 0.136772 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30649.3 | 1.47741 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24004.9 | 1.15254 | 0.576271 | − | 0.817259i | \(-0.304507\pi\) | ||||
0.576271 | + | 0.817259i | \(0.304507\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 5384.46i | − | 0.257501i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 29540.1i | − | 1.40713i | −0.710630 | − | 0.703566i | \(-0.751590\pi\) | ||
0.710630 | − | 0.703566i | \(-0.248410\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6326.97 | 0.300199 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15588.5i | 0.736739i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7575.49 | + | 7843.73i | −0.356630 | + | 0.369258i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7585.63i | 0.355715i | 0.984056 | + | 0.177857i | \(0.0569166\pi\) | ||||
−0.984056 | + | 0.177857i | \(0.943083\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2437.85 | −0.113874 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3284.29i | 0.152817i | 0.997077 | + | 0.0764086i | \(0.0243453\pi\) | ||||
−0.997077 | + | 0.0764086i | \(0.975655\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10393.0i | − | 0.481712i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14752.6 | −0.681140 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3741.98 | −0.172106 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22945.3 | 1.05128 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5565.92 | 0.254036 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 15064.6i | − | 0.684939i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 41624.1i | − | 1.88531i | −0.333772 | − | 0.942654i | \(-0.608321\pi\) | ||
0.333772 | − | 0.942654i | \(-0.391679\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7824.87 | −0.353071 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 222.046i | 0.00998108i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6237.49 | − | 6024.18i | −0.279319 | − | 0.269767i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7537.20i | 0.336248i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30333.3 | 1.34813 | 0.674066 | − | 0.738671i | \(-0.264546\pi\) | ||||
0.674066 | + | 0.738671i | \(0.264546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 21448.4i | − | 0.949674i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4789.03i | 0.211251i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13687.4 | −0.601518 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15552.0 | −0.680914 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14373.1 | 0.626958 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24853.9 | −1.08012 | −0.540060 | − | 0.841627i | \(-0.681598\pi\) | ||||
−0.540060 | + | 0.841627i | \(0.681598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17383.5i | 0.752674i | 0.926483 | + | 0.376337i | \(0.122816\pi\) | ||||
−0.926483 | + | 0.376337i | \(0.877184\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10990.9i | 0.474128i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29815.8 | 1.28148 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6455.23i | 0.276426i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4902.54 | + | 5076.14i | −0.209168 | + | 0.216575i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 31169.4i | − | 1.32499i | −0.749065 | − | 0.662496i | \(-0.769497\pi\) | ||
0.749065 | − | 0.662496i | \(-0.230503\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5512.79 | 0.233492 | 0.116746 | − | 0.993162i | \(-0.462754\pi\) | ||||
0.116746 | + | 0.993162i | \(0.462754\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3119.63i | 0.131650i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13335.8i | − | 0.560738i | −0.959892 | − | 0.280369i | \(-0.909543\pi\) | ||
0.959892 | − | 0.280369i | \(-0.0904568\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28338.5 | 1.18726 | 0.593628 | − | 0.804739i | \(-0.297695\pi\) | ||||
0.593628 | + | 0.804739i | \(0.297695\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1872.98 | −0.0781864 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8470.66 | 0.352330 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7757.27 | 0.321499 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 6726.82i | − | 0.277793i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 27149.5i | − | 1.11717i | −0.829447 | − | 0.558585i | \(-0.811344\pi\) | ||
0.829447 | − | 0.558585i | \(-0.188656\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18106.9 | 0.742421 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16605.4i | 0.678433i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28350.1 | + | 986.703i | −1.15417 | + | 0.0401700i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11870.7i | 0.481560i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −525.454 | −0.0212409 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 21164.7i | − | 0.852547i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 7978.22i | − | 0.320245i | −0.987097 | − | 0.160123i | \(-0.948811\pi\) | ||
0.987097 | − | 0.160123i | \(-0.0511889\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1735.85 | −0.0694325 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13614.4 | 0.542657 | 0.271329 | − | 0.962487i | \(-0.412537\pi\) | ||||
0.271329 | + | 0.962487i | \(0.412537\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35007.7 | 1.39051 | 0.695255 | − | 0.718763i | \(-0.255291\pi\) | ||||
0.695255 | + | 0.718763i | \(0.255291\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12572.1 | 0.497624 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24461.5i | 0.964867i | 0.875933 | + | 0.482434i | \(0.160247\pi\) | ||||
−0.875933 | + | 0.482434i | \(0.839753\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 44292.2i | − | 1.74102i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −39245.9 | −1.53733 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 23261.3i | − | 0.908040i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1284.23 | + | 1329.70i | −0.0499591 | + | 0.0517281i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3263.95i | − | 0.126538i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −17989.5 | −0.695037 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 43121.6i | − | 1.66034i | −0.557514 | − | 0.830168i | \(-0.688245\pi\) | ||
0.557514 | − | 0.830168i | \(-0.311755\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 23323.0i | − | 0.894955i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40824.5 | 1.56120 | 0.780598 | − | 0.625034i | \(-0.214915\pi\) | ||||
0.780598 | + | 0.625034i | \(0.214915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8262.14 | 0.314885 | 0.157442 | − | 0.987528i | \(-0.449675\pi\) | ||||
0.157442 | + | 0.987528i | \(0.449675\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9011.70 | 0.342288 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 40858.6 | 1.54667 | 0.773336 | − | 0.633997i | \(-0.218587\pi\) | ||||
0.773336 | + | 0.633997i | \(0.218587\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2442.22i | 0.0921365i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2019.17i | 0.0759201i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2388.37 | 0.0895001 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12638.6i | 0.472023i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7282.47 | − | 7033.41i | −0.271075 | − | 0.261805i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 51359.4i | − | 1.90537i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26102.2 | −0.965139 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 21687.9i | − | 0.799256i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 49569.6i | 1.82072i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32729.3 | −1.19819 | −0.599095 | − | 0.800678i | \(-0.704473\pi\) | ||||
−0.599095 | + | 0.800678i | \(0.704473\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13415.2 | −0.489500 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11065.9 | −0.402447 | −0.201223 | − | 0.979545i | \(-0.564492\pi\) | ||||
−0.201223 | + | 0.979545i | \(0.564492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27305.7 | −0.989801 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7166.29i | 0.258918i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 5305.77i | − | 0.191071i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50682.2 | −1.81921 | −0.909604 | − | 0.415477i | \(-0.863615\pi\) | ||||
−0.909604 | + | 0.415477i | \(0.863615\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 24068.5i | − | 0.861114i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29972.1 | − | 31033.4i | 1.06885 | − | 1.10669i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12262.3i | 0.435874i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5655.92 | 0.200394 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 41045.5i | 1.44958i | 0.688970 | + | 0.724790i | \(0.258063\pi\) | ||||
−0.688970 | + | 0.724790i | \(0.741937\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 943.243i | 0.0332047i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27794.6 | 0.975300 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −43176.9 | −1.51020 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −788.985 | −0.0275080 | −0.0137540 | − | 0.999905i | \(-0.504378\pi\) | ||||
−0.0137540 | + | 0.999905i | \(0.504378\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22270.7 | −0.773991 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 25676.2i | − | 0.889499i | −0.895655 | − | 0.444750i | \(-0.853293\pi\) | ||
0.895655 | − | 0.444750i | \(-0.146707\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18036.5i | 0.622851i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5832.00 | 0.200757 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 679.352i | − | 0.0233115i | −0.999932 | − | 0.0116557i | \(-0.996290\pi\) | ||
0.999932 | − | 0.0116557i | \(-0.00371022\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17879.1 | + | 18512.2i | −0.611571 | + | 0.633227i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 7923.12i | − | 0.270163i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20238.4 | 0.687917 | 0.343958 | − | 0.938985i | \(-0.388232\pi\) | ||||
0.343958 | + | 0.938985i | \(0.388232\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6297.21i | 0.213375i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15416.4i | 0.520733i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7413.38 | 0.249625 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −32280.6 | −1.08357 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4297.08 | −0.143792 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 54818.6 | 1.82868 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6161.63i | 0.204906i | 0.994738 | + | 0.102453i | \(0.0326692\pi\) | ||||
−0.994738 | + | 0.102453i | \(0.967331\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 6011.45i | − | 0.199294i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48569.5 | 1.60522 | 0.802610 | − | 0.596504i | \(-0.203444\pi\) | ||||
0.802610 | + | 0.596504i | \(0.203444\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 13132.4i | − | 0.432689i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4219.29 | + | 4075.00i | 0.138590 | + | 0.133851i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 44595.8i | − | 1.46033i | −0.683269 | − | 0.730167i | \(-0.739442\pi\) | ||
0.683269 | − | 0.730167i | \(-0.260558\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13264.6 | −0.433031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 3403.86i | − | 0.110782i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 29599.0i | − | 0.960389i | −0.877162 | − | 0.480195i | \(-0.840566\pi\) | ||
0.877162 | − | 0.480195i | \(-0.159434\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 35026.0 | 1.13302 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8024.29 | −0.258780 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31114.5 | 1.00039 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5718.45 | −0.183302 | −0.0916511 | − | 0.995791i | \(-0.529214\pi\) | ||||
−0.0916511 | + | 0.995791i | \(0.529214\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32338.5i | 1.03347i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40244.8i | 1.28226i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1491.44 | −0.0473766 | −0.0236883 | − | 0.999719i | \(-0.507541\pi\) | ||||
−0.0236883 | + | 0.999719i | \(0.507541\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7936.77i | 0.251360i |
(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 | 624.4.c.c.337.4 | 4 | ||
4.3 | odd | 2 | 39.4.b.b.25.4 | yes | 4 | ||
12.11 | even | 2 | 117.4.b.e.64.1 | 4 | |||
13.12 | even | 2 | inner | 624.4.c.c.337.1 | 4 | ||
52.31 | even | 4 | 507.4.a.l.1.4 | 4 | |||
52.47 | even | 4 | 507.4.a.l.1.1 | 4 | |||
52.51 | odd | 2 | 39.4.b.b.25.1 | ✓ | 4 | ||
156.47 | odd | 4 | 1521.4.a.w.1.4 | 4 | |||
156.83 | odd | 4 | 1521.4.a.w.1.1 | 4 | |||
156.155 | even | 2 | 117.4.b.e.64.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.b.b.25.1 | ✓ | 4 | 52.51 | odd | 2 | ||
39.4.b.b.25.4 | yes | 4 | 4.3 | odd | 2 | ||
117.4.b.e.64.1 | 4 | 12.11 | even | 2 | |||
117.4.b.e.64.4 | 4 | 156.155 | even | 2 | |||
507.4.a.l.1.1 | 4 | 52.47 | even | 4 | |||
507.4.a.l.1.4 | 4 | 52.31 | even | 4 | |||
624.4.c.c.337.1 | 4 | 13.12 | even | 2 | inner | ||
624.4.c.c.337.4 | 4 | 1.1 | even | 1 | trivial | ||
1521.4.a.w.1.1 | 4 | 156.83 | odd | 4 | |||
1521.4.a.w.1.4 | 4 | 156.47 | odd | 4 |