Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(97,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 588) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(1.60021 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.97 |
Dual form | 2352.3.f.j.97.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.73205i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 5.37964i | − 1.07593i | −0.842968 | − | 0.537964i | \(-0.819194\pi\) | ||||
0.842968 | − | 0.537964i | \(-0.180806\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.59159 | 0.781054 | 0.390527 | − | 0.920592i | \(-0.372293\pi\) | ||||
0.390527 | + | 0.920592i | \(0.372293\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 21.0158i | 1.61660i | 0.588769 | + | 0.808301i | \(0.299613\pi\) | ||||
−0.588769 | + | 0.808301i | \(0.700387\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.31781 | −0.621187 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.48622i | 0.322719i | 0.986896 | + | 0.161359i | \(0.0515878\pi\) | ||||
−0.986896 | + | 0.161359i | \(0.948412\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 7.24098i | − 0.381104i | −0.981677 | − | 0.190552i | \(-0.938972\pi\) | ||||
0.981677 | − | 0.190552i | \(-0.0610278\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −28.0556 | −1.21981 | −0.609905 | − | 0.792474i | \(-0.708792\pi\) | ||||
−0.609905 | + | 0.792474i | \(0.708792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.94054 | −0.157621 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 40.3447 | 1.39120 | 0.695599 | − | 0.718431i | \(-0.255139\pi\) | ||||
0.695599 | + | 0.718431i | \(0.255139\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 40.5101i | − 1.30678i | −0.757023 | − | 0.653388i | \(-0.773347\pi\) | ||||
0.757023 | − | 0.653388i | \(-0.226653\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 14.8811i | − 0.450941i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 66.6370 | 1.80100 | 0.900500 | − | 0.434856i | \(-0.143201\pi\) | ||||
0.900500 | + | 0.434856i | \(0.143201\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 36.4005 | 0.933346 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 33.6357i | − 0.820383i | −0.911999 | − | 0.410191i | \(-0.865462\pi\) | ||||
0.911999 | − | 0.410191i | \(-0.134538\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.932907 | −0.0216955 | −0.0108478 | − | 0.999941i | \(-0.503453\pi\) | ||||
−0.0108478 | + | 0.999941i | \(0.503453\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 16.1389i | 0.358643i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 85.6544i | − 1.82243i | −0.411927 | − | 0.911217i | \(-0.635144\pi\) | ||||
0.411927 | − | 0.911217i | \(-0.364856\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.50241 | 0.186322 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −44.5954 | −0.841422 | −0.420711 | − | 0.907195i | \(-0.638219\pi\) | ||||
−0.420711 | + | 0.907195i | \(0.638219\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 46.2197i | − 0.840358i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.5418 | −0.220031 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 63.6950i | − 1.07958i | −0.841801 | − | 0.539788i | \(-0.818504\pi\) | ||||
0.841801 | − | 0.539788i | \(-0.181496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 32.0084i | − 0.524727i | −0.964969 | − | 0.262364i | \(-0.915498\pi\) | ||||
0.964969 | − | 0.262364i | \(-0.0845020\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 113.058 | 1.73935 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 47.7341 | 0.712450 | 0.356225 | − | 0.934400i | \(-0.384064\pi\) | ||||
0.356225 | + | 0.934400i | \(0.384064\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 48.5938i | 0.704258i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.9676 | −0.210811 | −0.105405 | − | 0.994429i | \(-0.533614\pi\) | ||||
−0.105405 | + | 0.994429i | \(0.533614\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 140.298i | 1.92188i | 0.276750 | + | 0.960942i | \(0.410742\pi\) | ||||
−0.276750 | + | 0.960942i | \(0.589258\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.82521i | 0.0910028i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 122.307 | 1.54820 | 0.774098 | − | 0.633066i | \(-0.218204\pi\) | ||||
0.774098 | + | 0.633066i | \(0.218204\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 33.1852i | 0.399822i | 0.979814 | + | 0.199911i | \(0.0640652\pi\) | ||||
−0.979814 | + | 0.199911i | \(0.935935\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29.5139 | 0.347222 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 69.8791i | − 0.803208i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 36.1246i | − 0.405894i | −0.979190 | − | 0.202947i | \(-0.934948\pi\) | ||||
0.979190 | − | 0.202947i | \(-0.0650519\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −70.1655 | −0.754468 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −38.9539 | −0.410041 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 16.2175i | − 0.167191i | −0.996500 | − | 0.0835956i | \(-0.973360\pi\) | ||||
0.996500 | − | 0.0835956i | \(-0.0266404\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −25.7748 | −0.260351 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 119.464i | − 1.18281i | −0.806373 | − | 0.591407i | \(-0.798573\pi\) | ||||
0.806373 | − | 0.591407i | \(-0.201427\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 8.93188i | − 0.0867173i | −0.999060 | − | 0.0433586i | \(-0.986194\pi\) | ||||
0.999060 | − | 0.0433586i | \(-0.0138058\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −173.856 | −1.62482 | −0.812410 | − | 0.583086i | \(-0.801845\pi\) | ||||
−0.812410 | + | 0.583086i | \(0.801845\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −160.315 | −1.47078 | −0.735388 | − | 0.677646i | \(-0.763000\pi\) | ||||
−0.735388 | + | 0.677646i | \(0.763000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 115.419i | − 1.03981i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −81.4420 | −0.720725 | −0.360363 | − | 0.932812i | \(-0.617347\pi\) | ||||
−0.360363 | + | 0.932812i | \(0.617347\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 150.929i | 1.31243i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 63.0475i | − 0.538867i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −47.1846 | −0.389955 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −58.2587 | −0.473648 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 113.292i | − 0.906339i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −117.172 | −0.922613 | −0.461307 | − | 0.887241i | \(-0.652619\pi\) | ||||
−0.461307 | + | 0.887241i | \(0.652619\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.61584i | 0.0125259i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 244.150i | − 1.86374i | −0.362795 | − | 0.931869i | \(-0.618177\pi\) | ||||
0.362795 | − | 0.931869i | \(-0.381823\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 27.9534 | 0.207062 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 245.412 | 1.79133 | 0.895663 | − | 0.444733i | \(-0.146701\pi\) | ||||
0.895663 | + | 0.444733i | \(0.146701\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 17.1371i | − 0.123288i | −0.998098 | − | 0.0616441i | \(-0.980366\pi\) | ||||
0.998098 | − | 0.0616441i | \(-0.0196344\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −148.358 | −1.05218 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 180.559i | 1.26265i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 217.040i | − 1.49683i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 134.242 | 0.900952 | 0.450476 | − | 0.892789i | \(-0.351254\pi\) | ||||
0.450476 | + | 0.892789i | \(0.351254\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −199.009 | −1.31794 | −0.658971 | − | 0.752168i | \(-0.729008\pi\) | ||||
−0.658971 | + | 0.752168i | \(0.729008\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 16.4587i | − 0.107573i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −217.930 | −1.40600 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 77.0189i | − 0.490566i | −0.969451 | − | 0.245283i | \(-0.921119\pi\) | ||||
0.969451 | − | 0.245283i | \(-0.0788810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 77.2415i | 0.485795i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 230.379 | 1.41337 | 0.706684 | − | 0.707529i | \(-0.250190\pi\) | ||||
0.706684 | + | 0.707529i | \(0.250190\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −80.0548 | −0.485181 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 229.231i | 1.37264i | 0.727298 | + | 0.686321i | \(0.240776\pi\) | ||||
−0.727298 | + | 0.686321i | \(0.759224\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −272.665 | −1.61340 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21.7230i | 0.127035i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 112.473i | 0.650133i | 0.945691 | + | 0.325066i | \(0.105387\pi\) | ||||
−0.945691 | + | 0.325066i | \(0.894613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −110.323 | −0.623293 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −105.494 | −0.589352 | −0.294676 | − | 0.955597i | \(-0.595212\pi\) | ||||
−0.294676 | + | 0.955597i | \(0.595212\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 15.2683i | − 0.0843553i | −0.999110 | − | 0.0421776i | \(-0.986570\pi\) | ||||
0.999110 | − | 0.0421776i | \(-0.0134295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −55.4401 | −0.302951 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 358.483i | − 1.93775i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 47.1353i | 0.252061i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 306.186 | 1.60307 | 0.801534 | − | 0.597950i | \(-0.204018\pi\) | ||||
0.801534 | + | 0.597950i | \(0.204018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.84100 | −0.00953885 | −0.00476943 | − | 0.999989i | \(-0.501518\pi\) | ||||
−0.00476943 | + | 0.999989i | \(0.501518\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 195.822i | − 1.00421i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −255.334 | −1.29611 | −0.648056 | − | 0.761593i | \(-0.724418\pi\) | ||||
−0.648056 | + | 0.761593i | \(0.724418\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 36.6483i | − 0.184162i | −0.995752 | − | 0.0920812i | \(-0.970648\pi\) | ||||
0.995752 | − | 0.0920812i | \(-0.0293519\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 82.6779i | − 0.411333i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −180.948 | −0.882673 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 84.1669 | 0.406603 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 62.2116i | − 0.297663i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 126.571 | 0.599862 | 0.299931 | − | 0.953961i | \(-0.403036\pi\) | ||||
0.299931 | + | 0.953961i | \(0.403036\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 25.9246i | 0.121712i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.01871i | 0.0233428i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 243.002 | 1.10960 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −115.297 | −0.521708 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 212.193i | − 0.951536i | −0.879571 | − | 0.475768i | \(-0.842170\pi\) | ||||
0.879571 | − | 0.475768i | \(-0.157830\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.8216 | 0.0525405 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 105.489i | − 0.464708i | −0.972631 | − | 0.232354i | \(-0.925357\pi\) | ||||
0.972631 | − | 0.232354i | \(-0.0746428\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 6.99086i | − 0.0305278i | −0.999884 | − | 0.0152639i | \(-0.995141\pi\) | ||||
0.999884 | − | 0.0152639i | \(-0.00485883\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 336.046 | 1.44226 | 0.721128 | − | 0.692801i | \(-0.243624\pi\) | ||||
0.721128 | + | 0.692801i | \(0.243624\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −460.790 | −1.96081 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 211.843i | − 0.893851i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 232.382 | 0.972309 | 0.486155 | − | 0.873873i | \(-0.338399\pi\) | ||||
0.486155 | + | 0.873873i | \(0.338399\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 63.7346i | 0.264459i | 0.991219 | + | 0.132229i | \(0.0422136\pi\) | ||||
−0.991219 | + | 0.132229i | \(0.957786\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 152.175 | 0.616094 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 57.4784 | 0.230837 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 415.450i | 1.65518i | 0.561334 | + | 0.827589i | \(0.310288\pi\) | ||||
−0.561334 | + | 0.827589i | \(0.689712\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −241.043 | −0.952737 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 51.1196i | − 0.200469i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 265.598i | − 1.03345i | −0.856150 | − | 0.516727i | \(-0.827150\pi\) | ||||
0.856150 | − | 0.516727i | \(-0.172850\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −121.034 | −0.463732 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −156.373 | −0.594575 | −0.297288 | − | 0.954788i | \(-0.596082\pi\) | ||||
−0.297288 | + | 0.954788i | \(0.596082\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 239.907i | 0.905310i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −62.5696 | −0.234343 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 332.861i | − 1.23740i | −0.785626 | − | 0.618701i | \(-0.787659\pi\) | ||||
0.785626 | − | 0.618701i | \(-0.212341\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 209.089i | − 0.771546i | −0.922594 | − | 0.385773i | \(-0.873935\pi\) | ||||
0.922594 | − | 0.385773i | \(-0.126065\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −33.8555 | −0.123111 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −263.231 | −0.950293 | −0.475146 | − | 0.879907i | \(-0.657605\pi\) | ||||
−0.475146 | + | 0.879907i | \(0.657605\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 121.530i | 0.435592i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 391.519 | 1.39331 | 0.696653 | − | 0.717408i | \(-0.254672\pi\) | ||||
0.696653 | + | 0.717408i | \(0.254672\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 109.394i | 0.386550i | 0.981145 | + | 0.193275i | \(0.0619109\pi\) | ||||
−0.981145 | + | 0.193275i | \(0.938089\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 67.4701i | 0.236737i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 258.901 | 0.895853 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.0896 | −0.0965278 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 35.3685i | − 0.120712i | −0.998177 | − | 0.0603558i | \(-0.980776\pi\) | ||||
0.998177 | − | 0.0603558i | \(-0.0192235\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −342.656 | −1.16155 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 44.6432i | 0.150314i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 589.613i | − 1.97195i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −206.918 | −0.682898 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −172.194 | −0.564569 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 125.621i | 0.409189i | 0.978847 | + | 0.204594i | \(0.0655875\pi\) | ||||
−0.978847 | + | 0.204594i | \(0.934412\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.4705 | −0.0500662 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 315.735i | − 1.01523i | −0.861585 | − | 0.507613i | \(-0.830528\pi\) | ||||
0.861585 | − | 0.507613i | \(-0.169472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 51.6046i | 0.164871i | 0.996596 | + | 0.0824355i | \(0.0262698\pi\) | ||||
−0.996596 | + | 0.0824355i | \(0.973730\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.99391 | −0.0157537 | −0.00787683 | − | 0.999969i | \(-0.502507\pi\) | ||||
−0.00787683 | + | 0.999969i | \(0.502507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 346.625 | 1.08660 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 301.127i | 0.938091i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.7256 | 0.122990 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 82.8137i | − 0.254811i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 277.673i | 0.849153i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −454.780 | −1.37396 | −0.686980 | − | 0.726677i | \(-0.741064\pi\) | ||||
−0.686980 | + | 0.726677i | \(0.741064\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −199.911 | −0.600333 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 256.792i | − 0.766545i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −183.824 | −0.545471 | −0.272736 | − | 0.962089i | \(-0.587928\pi\) | ||||
−0.272736 | + | 0.962089i | \(0.587928\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 141.062i | 0.416111i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 348.046i | − 1.02066i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 261.417 | 0.757731 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −144.776 | −0.417223 | −0.208611 | − | 0.977999i | \(-0.566894\pi\) | ||||
−0.208611 | + | 0.977999i | \(0.566894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 187.069i | − 0.536015i | −0.963417 | − | 0.268007i | \(-0.913635\pi\) | ||||
0.963417 | − | 0.268007i | \(-0.0863651\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −109.201 | −0.311115 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 222.601i | 0.630597i | 0.948993 | + | 0.315299i | \(0.102105\pi\) | ||||
−0.948993 | + | 0.315299i | \(0.897895\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 80.5201i | 0.226817i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −62.9856 | −0.175447 | −0.0877237 | − | 0.996145i | \(-0.527959\pi\) | ||||
−0.0877237 | + | 0.996145i | \(0.527959\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 308.568 | 0.854759 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 81.7261i | 0.225141i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 754.750 | 2.06781 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 547.100i | − 1.49074i | −0.666653 | − | 0.745368i | \(-0.732274\pi\) | ||||
0.666653 | − | 0.745368i | \(-0.267726\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 100.907i | 0.273461i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.4417 | −0.0869750 | −0.0434875 | − | 0.999054i | \(-0.513847\pi\) | ||||
−0.0434875 | + | 0.999054i | \(0.513847\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −196.228 | −0.523275 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 847.878i | 2.24901i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −508.859 | −1.34263 | −0.671317 | − | 0.741170i | \(-0.734271\pi\) | ||||
−0.671317 | + | 0.741170i | \(0.734271\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 202.948i | 0.532671i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.2839i | 0.0686263i | 0.999411 | + | 0.0343131i | \(0.0109244\pi\) | ||||
−0.999411 | + | 0.0343131i | \(0.989076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.79872 | 0.00723184 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −360.128 | −0.925779 | −0.462890 | − | 0.886416i | \(-0.653187\pi\) | ||||
−0.462890 | + | 0.886416i | \(0.653187\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 153.919i | − 0.393656i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −422.880 | −1.07603 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 657.970i | − 1.66575i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 570.992i | − 1.43827i | −0.694872 | − | 0.719134i | \(-0.744539\pi\) | ||||
0.694872 | − | 0.719134i | \(-0.255461\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 68.4014 | 0.170577 | 0.0852885 | − | 0.996356i | \(-0.472819\pi\) | ||||
0.0852885 | + | 0.996356i | \(0.472819\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 851.353 | 2.11254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 48.4168i | − 0.119548i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 572.518 | 1.40668 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.3649i | 0.0375671i | 0.999824 | + | 0.0187835i | \(0.00597934\pi\) | ||||
−0.999824 | + | 0.0187835i | \(0.994021\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 425.066i | − 1.03422i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 178.524 | 0.430179 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.6823 | −0.0711805 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 366.079i | − 0.873696i | −0.899535 | − | 0.436848i | \(-0.856095\pi\) | ||||
0.899535 | − | 0.436848i | \(-0.143905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 607.135 | 1.44213 | 0.721063 | − | 0.692870i | \(-0.243654\pi\) | ||||
0.721063 | + | 0.692870i | \(0.243654\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 256.963i | 0.607478i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 21.6186i | − 0.0508674i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 312.738 | 0.728993 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 586.353 | 1.36045 | 0.680224 | − | 0.733004i | \(-0.261882\pi\) | ||||
0.680224 | + | 0.733004i | \(0.261882\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 518.769i | − 1.19808i | −0.800719 | − | 0.599040i | \(-0.795549\pi\) | ||||
0.800719 | − | 0.599040i | \(-0.204451\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −375.924 | −0.864194 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 203.150i | 0.464875i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 221.524i | − 0.504610i | −0.967648 | − | 0.252305i | \(-0.918811\pi\) | ||||
0.967648 | − | 0.252305i | \(-0.0811886\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 226.415 | 0.511095 | 0.255548 | − | 0.966796i | \(-0.417744\pi\) | ||||
0.255548 | + | 0.966796i | \(0.417744\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −194.337 | −0.436713 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 232.514i | − 0.520165i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −378.422 | −0.842810 | −0.421405 | − | 0.906873i | \(-0.638463\pi\) | ||||
−0.421405 | + | 0.906873i | \(0.638463\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 288.984i | − 0.640763i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 344.694i | 0.760914i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 438.153 | 0.958760 | 0.479380 | − | 0.877607i | \(-0.340862\pi\) | ||||
0.479380 | + | 0.877607i | \(0.340862\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −28.5072 | −0.0621073 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 46.3981i | − 0.100647i | −0.998733 | − | 0.0503234i | \(-0.983975\pi\) | ||||
0.998733 | − | 0.0503234i | \(-0.0160252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −367.455 | −0.793639 | −0.396820 | − | 0.917897i | \(-0.629886\pi\) | ||||
−0.396820 | + | 0.917897i | \(0.629886\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 377.465i | 0.811753i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 529.465i | 1.13376i | 0.823801 | + | 0.566879i | \(0.191849\pi\) | ||||
−0.823801 | + | 0.566879i | \(0.808151\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −133.401 | −0.283229 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.01516 | −0.0169454 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.5334i | 0.0600702i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 133.786 | 0.280474 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 289.761i | − 0.604928i | −0.953161 | − | 0.302464i | \(-0.902191\pi\) | ||||
0.953161 | − | 0.302464i | \(-0.0978093\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1400.43i | 2.91150i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −87.2445 | −0.179886 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −439.636 | −0.902744 | −0.451372 | − | 0.892336i | \(-0.649065\pi\) | ||||
−0.451372 | + | 0.892336i | \(0.649065\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 399.028i | − 0.816009i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 320.561 | 0.652874 | 0.326437 | − | 0.945219i | \(-0.394152\pi\) | ||||
0.326437 | + | 0.945219i | \(0.394152\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 221.340i | 0.448965i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 138.659i | 0.280119i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −771.973 | −1.54704 | −0.773520 | − | 0.633772i | \(-0.781506\pi\) | ||||
−0.773520 | + | 0.633772i | \(0.781506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 397.040 | 0.792496 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 101.632i | 0.202052i | 0.994884 | + | 0.101026i | \(0.0322126\pi\) | ||||
−0.994884 | + | 0.101026i | \(0.967787\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −642.675 | −1.27262 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 472.270i | 0.931499i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 605.407i | − 1.18941i | −0.803946 | − | 0.594703i | \(-0.797270\pi\) | ||||
0.803946 | − | 0.594703i | \(-0.202730\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 37.6253 | 0.0733436 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −48.0503 | −0.0933016 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 735.907i | − 1.42342i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 194.809 | 0.375354 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 383.293i | 0.735688i | 0.929888 | + | 0.367844i | \(0.119904\pi\) | ||||
−0.929888 | + | 0.367844i | \(0.880096\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 448.095i | 0.856777i | 0.903595 | + | 0.428389i | \(0.140919\pi\) | ||||
−0.903595 | + | 0.428389i | \(0.859081\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 222.247 | 0.421721 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 258.119 | 0.487937 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 191.085i | 0.359859i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 706.882 | 1.32623 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 935.282i | 1.74819i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 182.721i | 0.340262i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −271.258 | −0.501400 | −0.250700 | − | 0.968065i | \(-0.580661\pi\) | ||||
−0.250700 | + | 0.968065i | \(0.580661\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.4455 | −0.0487025 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 862.435i | 1.58245i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 590.544 | 1.07961 | 0.539803 | − | 0.841791i | \(-0.318499\pi\) | ||||
0.539803 | + | 0.841791i | \(0.318499\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 96.0251i | 0.174909i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 292.135i | − 0.530191i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −620.911 | −1.11876 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 188.295 | 0.338051 | 0.169026 | − | 0.985612i | \(-0.445938\pi\) | ||||
0.169026 | + | 0.985612i | \(0.445938\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 19.6058i | − 0.0350730i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 81.6408 | 0.145527 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 204.157i | 0.362623i | 0.983426 | + | 0.181312i | \(0.0580342\pi\) | ||||
−0.983426 | + | 0.181312i | \(0.941966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 438.129i | 0.775449i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −660.913 | −1.16153 | −0.580767 | − | 0.814070i | \(-0.697247\pi\) | ||||
−0.580767 | + | 0.814070i | \(0.697247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 533.978 | 0.935162 | 0.467581 | − | 0.883950i | \(-0.345126\pi\) | ||||
0.467581 | + | 0.883950i | \(0.345126\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 530.329i | − 0.925531i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 110.554 | 0.192268 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 53.4337i | 0.0926062i | 0.998927 | + | 0.0463031i | \(0.0147440\pi\) | ||||
−0.998927 | + | 0.0463031i | \(0.985256\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.18870i | 0.00550726i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −383.145 | −0.657196 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −339.173 | −0.579783 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 413.063i | 0.703684i | 0.936059 | + | 0.351842i | \(0.114445\pi\) | ||||
−0.936059 | + | 0.351842i | \(0.885555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −293.333 | −0.498018 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 442.252i | 0.748311i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 122.452i | 0.206496i | 0.994656 | + | 0.103248i | \(0.0329235\pi\) | ||||
−0.994656 | + | 0.103248i | \(0.967076\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −63.4768 | −0.106326 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 645.136 | 1.07702 | 0.538511 | − | 0.842619i | \(-0.318987\pi\) | ||||
0.538511 | + | 0.842619i | \(0.318987\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 683.488i | 1.13725i | 0.822596 | + | 0.568626i | \(0.192525\pi\) | ||||
−0.822596 | + | 0.568626i | \(0.807475\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −143.202 | −0.237483 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 253.836i | 0.419564i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 257.253i | 0.423811i | 0.977290 | + | 0.211905i | \(0.0679669\pi\) | ||||
−0.977290 | + | 0.211905i | \(0.932033\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1800.10 | 2.94615 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 885.713 | 1.44488 | 0.722441 | − | 0.691433i | \(-0.243020\pi\) | ||||
0.722441 | + | 0.691433i | \(0.243020\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 313.411i | 0.509612i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 46.0724 | 0.0746717 | 0.0373358 | − | 0.999303i | \(-0.488113\pi\) | ||||
0.0373358 | + | 0.999303i | \(0.488113\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1096.33i | 1.77112i | 0.464522 | + | 0.885562i | \(0.346226\pi\) | ||||
−0.464522 | + | 0.885562i | \(0.653774\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 145.781i | − 0.234753i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −707.986 | −1.13278 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −107.754 | −0.171856 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 365.585i | 0.581217i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −606.319 | −0.960886 | −0.480443 | − | 0.877026i | \(-0.659524\pi\) | ||||
−0.480443 | + | 0.877026i | \(0.659524\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 219.227i | − 0.346330i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 630.343i | 0.992666i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 44.9027 | 0.0702702 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 939.184 | 1.46519 | 0.732593 | − | 0.680667i | \(-0.238310\pi\) | ||||
0.732593 | + | 0.680667i | \(0.238310\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 992.960i | − 1.54426i | −0.635464 | − | 0.772131i | \(-0.719191\pi\) | ||||
0.635464 | − | 0.772131i | \(-0.280809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.69266 | 0.0134770 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 265.184i | 0.409867i | 0.978776 | + | 0.204933i | \(0.0656978\pi\) | ||||
−0.978776 | + | 0.204933i | \(0.934302\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 547.241i | − 0.843206i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1134.14 | −1.73682 | −0.868409 | − | 0.495849i | \(-0.834857\pi\) | ||||
−0.868409 | + | 0.495849i | \(0.834857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1313.44 | −2.00525 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 420.893i | − 0.640628i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 924.147 | 1.40235 | 0.701174 | − | 0.712990i | \(-0.252660\pi\) | ||||
0.701174 | + | 0.712990i | \(0.252660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 234.367i | − 0.354564i | −0.984160 | − | 0.177282i | \(-0.943269\pi\) | ||||
0.984160 | − | 0.177282i | \(-0.0567305\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 199.701i | 0.301208i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1131.90 | −1.69700 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −367.528 | −0.549370 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 275.003i | − 0.409840i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −465.127 | −0.691125 | −0.345563 | − | 0.938396i | \(-0.612312\pi\) | ||||
−0.345563 | + | 0.938396i | \(0.612312\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 20.4756i | − 0.0303343i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1295.93i | − 1.91422i | −0.289724 | − | 0.957110i | \(-0.593563\pi\) | ||||
0.289724 | − | 0.957110i | \(-0.406437\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −182.712 | −0.268300 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.2612 | −0.0238085 | −0.0119042 | − | 0.999929i | \(-0.503789\pi\) | ||||
−0.0119042 | + | 0.999929i | \(0.503789\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1320.23i | − 1.92734i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −12.1085 | −0.0176252 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 937.209i | − 1.36025i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 68.5364i | − 0.0991843i | −0.998770 | − | 0.0495922i | \(-0.984208\pi\) | ||||
0.998770 | − | 0.0495922i | \(-0.0157922\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −92.1912 | −0.132649 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 184.533 | 0.264753 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 582.048i | − 0.832687i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 923.360 | 1.31720 | 0.658602 | − | 0.752491i | \(-0.271148\pi\) | ||||
0.658602 | + | 0.752491i | \(0.271148\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 482.518i | − 0.686369i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 798.111i | 1.13207i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −912.863 | −1.28754 | −0.643768 | − | 0.765221i | \(-0.722630\pi\) | ||||
−0.643768 | + | 0.765221i | \(0.722630\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −366.922 | −0.516065 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1136.54i | 1.59402i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 971.345 | 1.35852 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 402.497i | − 0.561363i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 545.020i | 0.758025i | 0.925391 | + | 0.379013i | \(0.123736\pi\) | ||||
−0.925391 | + | 0.379013i | \(0.876264\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 110.392 | 0.152685 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −158.980 | −0.219283 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 750.292i | 1.03204i | 0.856577 | + | 0.516019i | \(0.172587\pi\) | ||||
−0.856577 | + | 0.516019i | \(0.827413\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 5.11813i | − 0.00700155i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 926.599i | 1.26412i | 0.774920 | + | 0.632059i | \(0.217790\pi\) | ||||
−0.774920 | + | 0.632059i | \(0.782210\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 410.112 | 0.556461 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −488.147 | −0.660551 | −0.330275 | − | 0.943885i | \(-0.607142\pi\) | ||||
−0.330275 | + | 0.943885i | \(0.607142\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 263.575i | − 0.355702i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1091.72 | 1.46935 | 0.734674 | − | 0.678421i | \(-0.237335\pi\) | ||||
0.734674 | + | 0.678421i | \(0.237335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 722.173i | − 0.969360i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 99.5556i | − 0.133274i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 480.443 | 0.639738 | 0.319869 | − | 0.947462i | \(-0.396361\pi\) | ||||
0.319869 | + | 0.947462i | \(0.396361\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 719.580 | 0.955618 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1070.60i | 1.41801i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 941.400 | 1.24359 | 0.621796 | − | 0.783179i | \(-0.286403\pi\) | ||||
0.621796 | + | 0.783179i | \(0.286403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 417.498i | 0.550063i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1192.34i | 1.56681i | 0.621509 | + | 0.783407i | \(0.286520\pi\) | ||||
−0.621509 | + | 0.783407i | \(0.713480\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −88.5417 | −0.115741 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1338.60 | 1.74524 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 908.294i | 1.18114i | 0.806988 | + | 0.590568i | \(0.201096\pi\) | ||||
−0.806988 | + | 0.590568i | \(0.798904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −460.029 | −0.596665 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1189.38i | − 1.53866i | −0.638854 | − | 0.769328i | \(-0.720591\pi\) | ||||
0.638854 | − | 0.769328i | \(-0.279409\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 159.632i | 0.205976i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −243.556 | −0.312652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −128.595 | −0.164654 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 209.637i | 0.267736i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −414.334 | −0.527814 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1057.12i | 1.34323i | 0.740902 | + | 0.671613i | \(0.234398\pi\) | ||||
−0.740902 | + | 0.671613i | \(0.765602\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 270.846i | 0.343278i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 672.682 | 0.848275 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 415.531 | 0.522681 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1037.94i | − 1.30231i | −0.758945 | − | 0.651154i | \(-0.774285\pi\) | ||||
0.758945 | − | 0.651154i | \(-0.225715\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 469.919 | 0.588133 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 108.374i | 0.135298i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1205.38i | 1.50109i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −576.533 | −0.714415 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1087.36 | 1.34408 | 0.672041 | − | 0.740514i | \(-0.265418\pi\) | ||||
0.672041 | + | 0.740514i | \(0.265418\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 926.995i | 1.14303i | 0.820593 | + | 0.571514i | \(0.193644\pi\) | ||||
−0.820593 | + | 0.571514i | \(0.806356\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −362.153 | −0.445452 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1239.36i | − 1.52068i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.75517i | 0.00826826i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −430.300 | −0.524117 | −0.262058 | − | 0.965052i | \(-0.584401\pi\) | ||||
−0.262058 | + | 0.965052i | \(0.584401\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1044.74 | 1.26942 | 0.634712 | − | 0.772749i | \(-0.281119\pi\) | ||||
0.634712 | + | 0.772749i | \(0.281119\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 58.6394i | 0.0710781i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 610.313 | 0.737984 | 0.368992 | − | 0.929433i | \(-0.379703\pi\) | ||||
0.368992 | + | 0.929433i | \(0.379703\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1413.90i | 1.70555i | 0.522279 | + | 0.852775i | \(0.325082\pi\) | ||||
−0.522279 | + | 0.852775i | \(0.674918\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 455.930i | 0.548652i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1233.18 | 1.47687 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 210.497 | 0.251489 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.3303i | 0.0552209i | 0.999619 | + | 0.0276105i | \(0.00878980\pi\) | ||||
−0.999619 | + | 0.0276105i | \(0.991210\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 786.696 | 0.935430 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 678.131i | − 0.804426i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1466.84i | 1.73591i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 189.475 | 0.223175 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1869.54 | −2.19688 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 773.111i | − 0.906343i | −0.891423 | − | 0.453172i | \(-0.850292\pi\) | ||||
0.891423 | − | 0.453172i | \(-0.149708\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 116.862 | 0.136680 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 438.159i | − 0.511271i | −0.966773 | − | 0.255636i | \(-0.917715\pi\) | ||||
0.966773 | − | 0.255636i | \(-0.0822847\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 72.3419i | 0.0842164i | 0.999113 | + | 0.0421082i | \(0.0134074\pi\) | ||||
−0.999113 | + | 0.0421082i | \(0.986593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −426.495 | −0.494200 | −0.247100 | − | 0.968990i | \(-0.579478\pi\) | ||||
−0.247100 | + | 0.968990i | \(0.579478\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 605.064 | 0.699496 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 448.430i | − 0.517221i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1050.82 | 1.20922 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1003.17i | 1.15175i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 48.6526i | 0.0557304i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 416.485 | 0.474898 | 0.237449 | − | 0.971400i | \(-0.423689\pi\) | ||||
0.237449 | + | 0.971400i | \(0.423689\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −61.2600 | −0.0696929 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1249.01i | 1.41771i | 0.705353 | + | 0.708857i | \(0.250789\pi\) | ||||
−0.705353 | + | 0.708857i | \(0.749211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −81.5906 | −0.0924016 | −0.0462008 | − | 0.998932i | \(-0.514711\pi\) | ||||
−0.0462008 | + | 0.998932i | \(0.514711\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 593.498i | 0.670619i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 917.730i | − 1.03464i | −0.855791 | − | 0.517322i | \(-0.826929\pi\) | ||||
0.855791 | − | 0.517322i | \(-0.173071\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 77.3243 | 0.0867837 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −620.222 | −0.694537 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 567.520i | 0.634100i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1021.24 | −1.13850 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1634.37i | − 1.81798i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 244.660i | − 0.271543i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −82.1380 | −0.0907602 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1451.40 | 1.60022 | 0.800110 | − | 0.599853i | \(-0.204774\pi\) | ||||
0.800110 | + | 0.599853i | \(0.204774\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 358.393i | 0.394272i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 562.064 | 0.616975 | 0.308487 | − | 0.951228i | \(-0.400177\pi\) | ||||
0.308487 | + | 0.951228i | \(0.400177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 285.114i | 0.312282i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 298.248i | 0.325954i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −538.158 | −0.585591 | −0.292795 | − | 0.956175i | \(-0.594586\pi\) | ||||
−0.292795 | + | 0.956175i | \(0.594586\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 217.582 | 0.236245 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 314.556i | − 0.340797i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −262.586 | −0.283876 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 26.7956i | 0.0289058i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 827.080i | − 0.890291i | −0.895458 | − | 0.445145i | \(-0.853152\pi\) | ||||
0.895458 | − | 0.445145i | \(-0.146848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −546.869 | −0.586141 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 253.571 | 0.271199 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1501.10i | 1.60203i | 0.598644 | + | 0.801016i | \(0.295707\pi\) | ||||
−0.598644 | + | 0.801016i | \(0.704293\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 89.3818 | 0.0951883 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 766.672i | 0.814742i | 0.913263 | + | 0.407371i | \(0.133554\pi\) | ||||
−0.913263 | + | 0.407371i | \(0.866446\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 943.671i | 1.00071i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1362.23 | −1.43847 | −0.719237 | − | 0.694765i | \(-0.755508\pi\) | ||||
−0.719237 | + | 0.694765i | \(0.755508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2948.47 | −3.10692 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.64971i | 0.00909538i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1431.37 | 1.50196 | 0.750980 | − | 0.660325i | \(-0.229581\pi\) | ||||
0.750980 | + | 0.660325i | \(0.229581\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1647.17i | − 1.72479i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 600.373i | − 0.627348i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −680.067 | −0.707666 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 521.567 | 0.541607 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.90391i | 0.0102631i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 426.276 | 0.440823 | 0.220411 | − | 0.975407i | \(-0.429260\pi\) | ||||
0.220411 | + | 0.975407i | \(0.429260\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 68.8068i | − 0.0710080i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1728.41i | − 1.78003i | −0.455934 | − | 0.890013i | \(-0.650695\pi\) | ||||
0.455934 | − | 0.890013i | \(-0.349305\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −143.437 | −0.147115 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −712.320 | −0.729089 | −0.364545 | − | 0.931186i | \(-0.618775\pi\) | ||||
−0.364545 | + | 0.931186i | \(0.618775\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 310.368i | − 0.317025i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 480.944 | 0.490259 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1042.56i | 1.06059i | 0.847812 | + | 0.530297i | \(0.177920\pi\) | ||||
−0.847812 | + | 0.530297i | \(0.822080\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1373.61i | 1.39452i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 26.1733 | 0.0264644 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1397.41 | −1.41010 | −0.705052 | − | 0.709156i | \(-0.749076\pi\) | ||||
−0.705052 | + | 0.709156i | \(0.749076\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 787.703i | 0.793256i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −197.155 | −0.198146 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 717.962i | 0.720122i | 0.932929 | + | 0.360061i | \(0.117244\pi\) | ||||
−0.932929 | + | 0.360061i | \(0.882756\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 346.256i | 0.346603i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2352.3.f.j.97.1 | 8 | ||
4.3 | odd | 2 | 588.3.d.c.97.5 | yes | 8 | ||
7.6 | odd | 2 | inner | 2352.3.f.j.97.8 | 8 | ||
12.11 | even | 2 | 1764.3.d.h.685.7 | 8 | |||
28.3 | even | 6 | 588.3.m.e.313.1 | 8 | |||
28.11 | odd | 6 | 588.3.m.f.313.4 | 8 | |||
28.19 | even | 6 | 588.3.m.f.325.4 | 8 | |||
28.23 | odd | 6 | 588.3.m.e.325.1 | 8 | |||
28.27 | even | 2 | 588.3.d.c.97.4 | ✓ | 8 | ||
84.11 | even | 6 | 1764.3.z.l.901.1 | 8 | |||
84.23 | even | 6 | 1764.3.z.m.325.4 | 8 | |||
84.47 | odd | 6 | 1764.3.z.l.325.1 | 8 | |||
84.59 | odd | 6 | 1764.3.z.m.901.4 | 8 | |||
84.83 | odd | 2 | 1764.3.d.h.685.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.3.d.c.97.4 | ✓ | 8 | 28.27 | even | 2 | ||
588.3.d.c.97.5 | yes | 8 | 4.3 | odd | 2 | ||
588.3.m.e.313.1 | 8 | 28.3 | even | 6 | |||
588.3.m.e.325.1 | 8 | 28.23 | odd | 6 | |||
588.3.m.f.313.4 | 8 | 28.11 | odd | 6 | |||
588.3.m.f.325.4 | 8 | 28.19 | even | 6 | |||
1764.3.d.h.685.2 | 8 | 84.83 | odd | 2 | |||
1764.3.d.h.685.7 | 8 | 12.11 | even | 2 | |||
1764.3.z.l.325.1 | 8 | 84.47 | odd | 6 | |||
1764.3.z.l.901.1 | 8 | 84.11 | even | 6 | |||
1764.3.z.m.325.4 | 8 | 84.23 | even | 6 | |||
1764.3.z.m.901.4 | 8 | 84.59 | odd | 6 | |||
2352.3.f.j.97.1 | 8 | 1.1 | even | 1 | trivial | ||
2352.3.f.j.97.8 | 8 | 7.6 | odd | 2 | inner |