Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(161,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.161");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.d (of order \(2\), degree \(1\), 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: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 343 x^{10} - 696 x^{9} + 44406 x^{8} + 179640 x^{7} - 2401691 x^{6} - 15554592 x^{5} + \cdots + 653157349 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{30} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.11 | ||
Root | \(-8.35048 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.161 |
Dual form | 320.6.d.d.161.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 20.6292i | 1.32336i | 0.749786 | + | 0.661680i | \(0.230156\pi\) | ||||
−0.749786 | + | 0.661680i | \(0.769844\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 25.0000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −93.5254 | −0.721414 | −0.360707 | − | 0.932679i | \(-0.617465\pi\) | ||||
−0.360707 | + | 0.932679i | \(0.617465\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −182.562 | −0.751284 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 659.055i | 1.64225i | 0.570747 | + | 0.821126i | \(0.306654\pi\) | ||||
−0.570747 | + | 0.821126i | \(0.693346\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 183.844i | 0.301711i | 0.988556 | + | 0.150855i | \(0.0482027\pi\) | ||||
−0.988556 | + | 0.150855i | \(0.951797\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 515.729 | 0.591825 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −467.075 | −0.391980 | −0.195990 | − | 0.980606i | \(-0.562792\pi\) | ||||
−0.195990 | + | 0.980606i | \(0.562792\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 225.914i | 0.143568i | 0.997420 | + | 0.0717841i | \(0.0228693\pi\) | ||||
−0.997420 | + | 0.0717841i | \(0.977131\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 1929.35i | − 0.954691i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1109.57 | 0.437357 | 0.218678 | − | 0.975797i | \(-0.429825\pi\) | ||||
0.218678 | + | 0.975797i | \(0.429825\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −625.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1246.78i | 0.329141i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 1738.98i | − 0.383972i | −0.981398 | − | 0.191986i | \(-0.938507\pi\) | ||||
0.981398 | − | 0.191986i | \(-0.0614929\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7270.81 | −1.35887 | −0.679436 | − | 0.733735i | \(-0.737775\pi\) | ||||
−0.679436 | + | 0.733735i | \(0.737775\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13595.7 | −2.17329 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2338.14i | 0.322626i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 14229.7i | − 1.70881i | −0.519610 | − | 0.854403i | \(-0.673923\pi\) | ||||
0.519610 | − | 0.854403i | \(-0.326077\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3792.54 | −0.399272 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4929.92 | −0.458015 | −0.229008 | − | 0.973425i | \(-0.573548\pi\) | ||||
−0.229008 | + | 0.973425i | \(0.573548\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12379.7i | 1.02103i | 0.859870 | + | 0.510514i | \(0.170545\pi\) | ||||
−0.859870 | + | 0.510514i | \(0.829455\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4564.05i | 0.335984i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −619.842 | −0.0409295 | −0.0204647 | − | 0.999791i | \(-0.506515\pi\) | ||||
−0.0204647 | + | 0.999791i | \(0.506515\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8060.00 | −0.479562 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 9635.36i | − 0.518731i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 16989.0i | 0.830765i | 0.909647 | + | 0.415382i | \(0.136352\pi\) | ||||
−0.909647 | + | 0.415382i | \(0.863648\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16476.4 | 0.734437 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4660.40 | −0.189993 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 50742.8i | − 1.89777i | −0.315615 | − | 0.948887i | \(-0.602211\pi\) | ||||
0.315615 | − | 0.948887i | \(-0.397789\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 20666.3i | − 0.711111i | −0.934655 | − | 0.355555i | \(-0.884292\pi\) | ||||
0.934655 | − | 0.355555i | \(-0.115708\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 17074.2 | 0.541987 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4596.09 | 0.134929 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 41920.3i | − 1.14087i | −0.821341 | − | 0.570437i | \(-0.806774\pi\) | ||||
0.821341 | − | 0.570437i | \(-0.193226\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 22889.5i | 0.578781i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 54687.7 | 1.28749 | 0.643744 | − | 0.765241i | \(-0.277380\pi\) | ||||
0.643744 | + | 0.765241i | \(0.277380\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −25211.5 | −0.553722 | −0.276861 | − | 0.960910i | \(-0.589294\pi\) | ||||
−0.276861 | + | 0.960910i | \(0.589294\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 12893.2i | − 0.264672i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 61638.4i | − 1.18474i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 29000.4 | 0.522802 | 0.261401 | − | 0.965230i | \(-0.415816\pi\) | ||||
0.261401 | + | 0.965230i | \(0.415816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −70082.7 | −1.18686 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 92679.1i | − 1.47668i | −0.674428 | − | 0.738341i | \(-0.735610\pi\) | ||||
0.674428 | − | 0.738341i | \(-0.264390\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11676.9i | 0.175299i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 35873.7 | 0.508134 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 54644.0 | 0.731253 | 0.365627 | − | 0.930762i | \(-0.380855\pi\) | ||||
0.365627 | + | 0.930762i | \(0.380855\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 17194.1i | − 0.217658i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 149991.i | − 1.79828i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5647.84 | 0.0642056 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 45542.8 | 0.491463 | 0.245731 | − | 0.969338i | \(-0.420972\pi\) | ||||
0.245731 | + | 0.969338i | \(0.420972\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 120318.i | − 1.23380i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 195492.i | 1.90689i | 0.301571 | + | 0.953444i | \(0.402489\pi\) | ||||
−0.301571 | + | 0.953444i | \(0.597511\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −81681.1 | −0.758627 | −0.379314 | − | 0.925268i | \(-0.623840\pi\) | ||||
−0.379314 | + | 0.925268i | \(0.623840\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −48233.8 | −0.426951 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 107507.i | − 0.907775i | −0.891059 | − | 0.453888i | \(-0.850037\pi\) | ||||
0.891059 | − | 0.453888i | \(-0.149963\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 170366.i | − 1.37346i | −0.726912 | − | 0.686731i | \(-0.759045\pi\) | ||||
0.726912 | − | 0.686731i | \(-0.240955\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 293548. | 2.26137 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −81363.4 | −0.599423 | −0.299711 | − | 0.954030i | \(-0.596890\pi\) | ||||
−0.299711 | + | 0.954030i | \(0.596890\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 27739.3i | − 0.195592i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 33562.9i | − 0.226670i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 43683.4 | 0.282780 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −273302. | −1.69699 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 101700.i | − 0.606119i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −291463. | −1.60352 | −0.801759 | − | 0.597647i | \(-0.796102\pi\) | ||||
−0.801759 | + | 0.597647i | \(0.796102\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −255382. | −1.35119 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 276390.i | 1.40716i | 0.710616 | + | 0.703580i | \(0.248416\pi\) | ||||
−0.710616 | + | 0.703580i | \(0.751584\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 21128.7i | − 0.103572i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 31169.6 | 0.147196 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −366347. | −1.66760 | −0.833798 | − | 0.552069i | \(-0.813839\pi\) | ||||
−0.833798 | + | 0.552069i | \(0.813839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 162496.i | 0.713353i | 0.934228 | + | 0.356676i | \(0.116090\pi\) | ||||
−0.934228 | + | 0.356676i | \(0.883910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 12786.8i | − 0.0541645i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −121163. | −0.495485 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −43474.5 | −0.171718 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 166271.i | − 0.634633i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 301589.i | − 1.11288i | −0.830887 | − | 0.556441i | \(-0.812166\pi\) | ||||
0.830887 | − | 0.556441i | \(-0.187834\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 375519. | 1.34026 | 0.670131 | − | 0.742243i | \(-0.266238\pi\) | ||||
0.670131 | + | 0.742243i | \(0.266238\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 85270.1 | 0.294488 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 181770.i | 0.607706i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 548149.i | − 1.77480i | −0.460999 | − | 0.887400i | \(-0.652509\pi\) | ||||
0.460999 | − | 0.887400i | \(-0.347491\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −350469. | −1.09940 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −103773. | −0.315515 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 19042.7i | − 0.0561383i | −0.999606 | − | 0.0280692i | \(-0.991064\pi\) | ||||
0.999606 | − | 0.0280692i | \(-0.00893587\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 339894.i | 0.971926i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −287366. | −0.797340 | −0.398670 | − | 0.917094i | \(-0.630528\pi\) | ||||
−0.398670 | + | 0.917094i | \(0.630528\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 337494. | 0.908971 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 41243.2i | − 0.107860i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 352199.i | 0.894692i | 0.894361 | + | 0.447346i | \(0.147631\pi\) | ||||
−0.894361 | + | 0.447346i | \(0.852369\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 58453.4 | 0.144283 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.04678e6 | 2.51144 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 87611.7i | 0.204376i | 0.994765 | + | 0.102188i | \(0.0325843\pi\) | ||||
−0.994765 | + | 0.102188i | \(0.967416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 534314.i | 1.21227i | 0.795361 | + | 0.606136i | \(0.207281\pi\) | ||||
−0.795361 | + | 0.606136i | \(0.792719\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 426328. | 0.941056 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −355744. | −0.764202 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 307828.i | − 0.643730i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 116606.i | − 0.237447i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 45622.1 | 0.0904882 | 0.0452441 | − | 0.998976i | \(-0.485593\pi\) | ||||
0.0452441 | + | 0.998976i | \(0.485593\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26392.3 | −0.0510017 | −0.0255009 | − | 0.999675i | \(-0.508118\pi\) | ||||
−0.0255009 | + | 0.999675i | \(0.508118\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 94813.5i | 0.178560i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 483767.i | − 0.888119i | −0.895997 | − | 0.444059i | \(-0.853538\pi\) | ||||
0.895997 | − | 0.444059i | \(-0.146462\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −51497.1 | −0.0921828 | −0.0460914 | − | 0.998937i | \(-0.514677\pi\) | ||||
−0.0460914 | + | 0.998937i | \(0.514677\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 864781. | 1.50979 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 162639.i | 0.277003i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 123248.i | 0.204831i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −202566. | −0.328579 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −148889. | −0.235775 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 716759.i | 1.10833i | 0.832408 | + | 0.554163i | \(0.186961\pi\) | ||||
−0.832408 | + | 0.554163i | \(0.813039\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.12816e6i | 1.70381i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 309491. | 0.456617 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 680005. | 0.980309 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 520092.i | − 0.732774i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 85868.8i | − 0.118265i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −747997. | −1.00725 | −0.503625 | − | 0.863922i | \(-0.668001\pi\) | ||||
−0.503625 | + | 0.863922i | \(0.668001\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 114101. | 0.150257 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 598186.i | 0.770498i | 0.922813 | + | 0.385249i | \(0.125884\pi\) | ||||
−0.922813 | + | 0.385249i | \(0.874116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 655203.i | 0.825633i | 0.910814 | + | 0.412816i | \(0.135455\pi\) | ||||
−0.910814 | + | 0.412816i | \(0.864545\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.27155e6 | 1.56784 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 170801. | 0.206111 | 0.103055 | − | 0.994676i | \(-0.467138\pi\) | ||||
0.103055 | + | 0.994676i | \(0.467138\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15496.0i | 0.0183042i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 598255.i | 0.691855i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.26920e6 | −1.43726 | −0.718629 | − | 0.695393i | \(-0.755230\pi\) | ||||
−0.718629 | + | 0.695393i | \(0.755230\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 274289. | 0.304205 | 0.152103 | − | 0.988365i | \(-0.451396\pi\) | ||||
0.152103 | + | 0.988365i | \(0.451396\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1.14278e6i | − 1.24150i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 201500.i | 0.214467i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −41532.8 | −0.0433160 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.91189e6 | 1.95418 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 861371.i | 0.862990i | 0.902115 | + | 0.431495i | \(0.142014\pi\) | ||||
−0.902115 | + | 0.431495i | \(0.857986\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 731268.i | 0.718250i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −240884. | −0.231984 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 524792. | 0.495626 | 0.247813 | − | 0.968808i | \(-0.420288\pi\) | ||||
0.247813 | + | 0.968808i | \(0.420288\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.33084e6i | 1.23276i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 317472.i | 0.288472i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.03635e6 | −1.81536 | −0.907680 | − | 0.419664i | \(-0.862148\pi\) | ||||
−0.907680 | + | 0.419664i | \(0.862148\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 424725. | 0.371529 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.12726e6i | 0.967712i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 477001.i | 0.401919i | 0.979600 | + | 0.200960i | \(0.0644060\pi\) | ||||
−0.979600 | + | 0.200960i | \(0.935594\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −350310. | −0.289754 | −0.144877 | − | 0.989450i | \(-0.546279\pi\) | ||||
−0.144877 | + | 0.989450i | \(0.546279\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 354699. | 0.288040 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 411909.i | − 0.328450i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.08816e6i | − 1.63518i | −0.575804 | − | 0.817588i | \(-0.695311\pi\) | ||||
0.575804 | − | 0.817588i | \(-0.304689\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.32737e6 | 1.02090 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.24077e6 | −0.937399 | −0.468699 | − | 0.883358i | \(-0.655277\pi\) | ||||
−0.468699 | + | 0.883358i | \(0.655277\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.85643e6i | 1.37788i | 0.724818 | + | 0.688940i | \(0.241924\pi\) | ||||
−0.724818 | + | 0.688940i | \(0.758076\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 116510.i | 0.0849672i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 461072. | 0.330419 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.20170e6 | −0.846352 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 939510.i | 0.650383i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.64126e6i | − 1.11689i | −0.829543 | − | 0.558443i | \(-0.811399\pi\) | ||||
0.829543 | − | 0.558443i | \(-0.188601\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.26857e6 | −0.848711 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −821699. | −0.540532 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 203988.i | 0.131955i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.15781e6i | − 0.736583i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.03283e6 | −2.52350 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −516657. | −0.318018 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.40107e6i | 0.848423i | 0.905563 | + | 0.424212i | \(0.139449\pi\) | ||||
−0.905563 | + | 0.424212i | \(0.860551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 1.68501e6i | − 1.00394i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.24137e6 | 0.727783 | 0.363891 | − | 0.931441i | \(-0.381448\pi\) | ||||
0.363891 | + | 0.931441i | \(0.381448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.66880e6 | −1.53977 | −0.769885 | − | 0.638183i | \(-0.779686\pi\) | ||||
−0.769885 | + | 0.638183i | \(0.779686\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 426855.i | − 0.242384i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.96026e6i | 1.65456i | 0.561793 | + | 0.827278i | \(0.310112\pi\) | ||||
−0.561793 | + | 0.827278i | \(0.689888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.14608e6 | 0.630579 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.21778e6 | 1.20131 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 105518.i | − 0.0562759i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 114902.i | − 0.0603421i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.51450e6 | 1.81758 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 57971.0 | 0.0295271 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.50180e6i | 0.753430i | 0.926329 | + | 0.376715i | \(0.122946\pi\) | ||||
−0.926329 | + | 0.376715i | \(0.877054\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.59781e6i | 1.28380i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.04801e6 | −0.510214 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.61150e6 | −0.772957 | −0.386478 | − | 0.922298i | \(-0.626309\pi\) | ||||
−0.386478 | + | 0.922298i | \(0.626309\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.67846e6i | − 0.793253i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 4.79186e6i | − 2.23161i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.32570e6 | 1.06738 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 572238. | 0.258839 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 497865.i | − 0.221967i | −0.993822 | − | 0.110983i | \(-0.964600\pi\) | ||||
0.993822 | − | 0.110983i | \(-0.0354001\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.24174e6i | 1.42467i | 0.701839 | + | 0.712335i | \(0.252362\pi\) | ||||
−0.701839 | + | 0.712335i | \(0.747638\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −229214. | −0.0993053 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −436867. | −0.186600 | −0.0933001 | − | 0.995638i | \(-0.529742\pi\) | ||||
−0.0933001 | + | 0.995638i | \(0.529742\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.36719e6i | − 0.575783i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 901151.i | 0.374220i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.67096e6 | 0.684274 | 0.342137 | − | 0.939650i | \(-0.388849\pi\) | ||||
0.342137 | + | 0.939650i | \(0.388849\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.42506e6 | 0.979388 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 5.63799e6i | − 2.24573i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 630288.i | 0.247632i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.06532e6 | −1.18799 | −0.593993 | − | 0.804471i | \(-0.702449\pi\) | ||||
−0.593993 | + | 0.804471i | \(0.702449\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 900015. | 0.344099 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.58890e6i | − 0.599325i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.45643e6i | 1.28634i | 0.765724 | + | 0.643169i | \(0.222381\pi\) | ||||
−0.765724 | + | 0.643169i | \(0.777619\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −322331. | −0.118365 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 319701. | 0.115849 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.61905e6i | 0.578979i | 0.957181 | + | 0.289489i | \(0.0934855\pi\) | ||||
−0.957181 | + | 0.289489i | \(0.906514\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 6.01263e6i | − 2.12203i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 151934. | 0.0529248 | 0.0264624 | − | 0.999650i | \(-0.491576\pi\) | ||||
0.0264624 | + | 0.999650i | \(0.491576\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.54096e6 | −0.529833 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 2.26005e6i | − 0.767081i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 2.83414e6i | − 0.949615i | −0.880090 | − | 0.474807i | \(-0.842518\pi\) | ||||
0.880090 | − | 0.474807i | \(-0.157482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −518253. | −0.171435 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.70168e6 | −1.86218 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 725011.i | − 0.233804i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.66354e6i | − 0.529732i | −0.964285 | − | 0.264866i | \(-0.914672\pi\) | ||||
0.964285 | − | 0.264866i | \(-0.0853277\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 435866. | 0.137063 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.72720e6 | 1.15750 | 0.578751 | − | 0.815504i | \(-0.303540\pi\) | ||||
0.578751 | + | 0.815504i | \(0.303540\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.33669e6i | − 0.409986i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.75207e6i | 0.530778i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.37818e6 | 2.80629 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.06547e6 | −0.610536 | −0.305268 | − | 0.952267i | \(-0.598746\pi\) | ||||
−0.305268 | + | 0.952267i | \(0.598746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 7.55743e6i | − 2.20683i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.74574e6i | 1.36908i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.31698e6 | −0.660392 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.35215e6 | −0.944023 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 2.02283e6i | − 0.562892i | −0.959577 | − | 0.281446i | \(-0.909186\pi\) | ||||
0.959577 | − | 0.281446i | \(-0.0908141\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 4.21007e6i | − 1.15767i | −0.815445 | − | 0.578834i | \(-0.803508\pi\) | ||||
0.815445 | − | 0.578834i | \(-0.196492\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 113160. | 0.0307497 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 291922. | 0.0783960 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.93282e6i | 0.513005i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 2.49949e6i | − 0.655705i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.35990e6 | −0.871231 | −0.435616 | − | 0.900133i | \(-0.643469\pi\) | ||||
−0.435616 | + | 0.900133i | \(0.643469\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.98488e6 | 0.508762 | 0.254381 | − | 0.967104i | \(-0.418128\pi\) | ||||
0.254381 | + | 0.967104i | \(0.418128\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 896843.i | − 0.227244i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 250667.i | 0.0627905i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.52991e6 | 1.36948 | 0.684741 | − | 0.728786i | \(-0.259915\pi\) | ||||
0.684741 | + | 0.728786i | \(0.259915\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.47145e6 | 0.360287 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2.55974e6i | − 0.619708i | −0.950784 | − | 0.309854i | \(-0.899720\pi\) | ||||
0.950784 | − | 0.309854i | \(-0.100280\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 1.36610e6i | − 0.327026i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.22152e6 | 1.47275 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.29746e6 | −1.47418 | −0.737088 | − | 0.675796i | \(-0.763800\pi\) | ||||
−0.737088 | + | 0.675796i | \(0.763800\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 3.24908e6i | − 0.752176i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.74664e6i | 1.77365i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −429852. | −0.0973397 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.50464e6 | 1.00895 | 0.504475 | − | 0.863426i | \(-0.331686\pi\) | ||||
0.504475 | + | 0.863426i | \(0.331686\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 582341.i | − 0.129017i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 8.91962e6i | − 1.95476i | −0.211486 | − | 0.977381i | \(-0.567830\pi\) | ||||
0.211486 | − | 0.977381i | \(-0.432170\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.68162e6 | −1.66533 | −0.832665 | − | 0.553778i | \(-0.813186\pi\) | ||||
−0.832665 | + | 0.553778i | \(0.813186\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.74977e6 | −0.804214 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.20606e6i | 0.255903i | 0.991780 | + | 0.127951i | \(0.0408402\pi\) | ||||
−0.991780 | + | 0.127951i | \(0.959160\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.92062e6i | 0.823042i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.13079e7 | 2.34870 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.15887e6 | −1.67678 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 141196.i | − 0.0287136i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 3.10155e6i | − 0.624140i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.89691e6 | −0.377753 | −0.188876 | − | 0.982001i | \(-0.560485\pi\) | ||||
−0.188876 | + | 0.982001i | \(0.560485\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.61605e6 | 0.515565 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.14075e6i | − 0.417540i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.13857e6i | − 0.219789i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.24462e6 | −0.428864 | −0.214432 | − | 0.976739i | \(-0.568790\pi\) | ||||
−0.214432 | + | 0.976739i | \(0.568790\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 392835. | 0.0742913 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.45333e6i | 1.76962i | 0.465948 | + | 0.884812i | \(0.345714\pi\) | ||||
−0.465948 | + | 0.884812i | \(0.654286\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 812234.i | 0.150510i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.00796e6 | −0.551771 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.11469e6 | −0.928812 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.68957e6i | 1.74202i | 0.491265 | + | 0.871010i | \(0.336535\pi\) | ||||
−0.491265 | + | 0.871010i | \(0.663465\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 5.92811e6i | − 1.05517i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.98436e6 | −0.878394 | −0.439197 | − | 0.898391i | \(-0.644737\pi\) | ||||
−0.439197 | + | 0.898391i | \(0.644737\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.88729e6 | 0.852786 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.96223e6i | 1.20290i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 3.72859e6i | − 0.637896i | −0.947772 | − | 0.318948i | \(-0.896670\pi\) | ||||
0.947772 | − | 0.318948i | \(-0.103330\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.35792e6 | 0.399463 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −281665. | −0.0472542 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.04203e6i | 0.339268i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 408510.i | − 0.0672165i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.26558e6 | −1.18400 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.50570e6 | −1.21143 | −0.605713 | − | 0.795683i | \(-0.707112\pi\) | ||||
−0.605713 | + | 0.795683i | \(0.707112\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 8.28837e6i | − 1.32500i | −0.749063 | − | 0.662498i | \(-0.769496\pi\) | ||||
0.749063 | − | 0.662498i | \(-0.230504\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.20584e6i | 0.190938i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.39601e6 | 0.532651 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.20519e6 | −0.808719 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.26371e6i | 1.42577i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 906334.i | − 0.138188i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.68768e6 | −0.405970 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.80735e6 | −0.270463 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.31198e6i | − 0.787561i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.42308e6i | 0.649728i | 0.945761 | + | 0.324864i | \(0.105318\pi\) | ||||
−0.945761 | + | 0.324864i | \(0.894682\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.10224e7 | −1.60427 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.25915e6 | −0.614231 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.60000e6i | 0.228640i | 0.993444 | + | 0.114320i | \(0.0364689\pi\) | ||||
−0.993444 | + | 0.114320i | \(0.963531\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.77287e6i | 0.534246i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 392859. | 0.0551262 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.71228e6 | −0.377156 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 7.33869e6i | − 1.01131i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5.33213e6i | − 0.728220i | −0.931356 | − | 0.364110i | \(-0.881373\pi\) | ||||
0.931356 | − | 0.364110i | \(-0.118627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.27592e6 | −0.308055 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.35023e6 | 0.851887 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 5.39829e6i | − 0.717770i | −0.933382 | − | 0.358885i | \(-0.883157\pi\) | ||||
0.933382 | − | 0.358885i | \(-0.116843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.03409e6i | 0.268070i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.55451e6 | 0.856215 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.34873e7 | 1.74641 | 0.873204 | − | 0.487355i | \(-0.162038\pi\) | ||||
0.873204 | + | 0.487355i | \(0.162038\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.16933e6i | 0.791859i | 0.918281 | + | 0.395929i | \(0.129578\pi\) | ||||
−0.918281 | + | 0.395929i | \(0.870422\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 941145.i | 0.119748i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −693482. | −0.0874713 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.47140e7 | 1.83989 | 0.919943 | − | 0.392052i | \(-0.128235\pi\) | ||||
0.919943 | + | 0.392052i | \(0.128235\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 544452.i | − 0.0674937i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.66786e6i | 1.06530i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.11967e7 | −1.36432 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −839072. | −0.101370 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.19357e6i | 0.142972i | 0.997442 | + | 0.0714860i | \(0.0227741\pi\) | ||||
−0.997442 | + | 0.0714860i | \(0.977226\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 1.64257e6i | − 0.195091i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.97971e6 | 1.17530 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.29056e6 | 1.08494 | 0.542469 | − | 0.840076i | \(-0.317490\pi\) | ||||
0.542469 | + | 0.840076i | \(0.317490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.09208e6i | − 0.126463i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.06234e6i | − 0.121991i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.60680e7 | 1.82976 | 0.914880 | − | 0.403725i | \(-0.132285\pi\) | ||||
0.914880 | + | 0.403725i | \(0.132285\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.28035e7 | 1.44591 | 0.722957 | − | 0.690893i | \(-0.242782\pi\) | ||||
0.722957 | + | 0.690893i | \(0.242782\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.65306e6i | 0.857120i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.83255e6i | 0.758918i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.81825e6 | −0.971428 | −0.485714 | − | 0.874118i | \(-0.661440\pi\) | ||||
−0.485714 | + | 0.874118i | \(0.661440\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.35510e6 | −0.366575 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 113954.i | − 0.0123489i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.50578e7i | 1.61849i | 0.587468 | + | 0.809247i | \(0.300125\pi\) | ||||
−0.587468 | + | 0.809247i | \(0.699875\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.54250e6 | −0.271065 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.92373e6 | 0.626445 | 0.313222 | − | 0.949680i | \(-0.398592\pi\) | ||||
0.313222 | + | 0.949680i | \(0.398592\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.67289e6i | 0.175485i | 0.996143 | + | 0.0877426i | \(0.0279653\pi\) | ||||
−0.996143 | + | 0.0877426i | \(0.972035\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.38340e6i | 0.143952i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.11061e6 | −0.527536 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 3.07146e6i | − 0.312016i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.64636e6i | 0.669818i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.34503e7 | 1.34480 | 0.672402 | − | 0.740186i | \(-0.265263\pi\) | ||||
0.672402 | + | 0.740186i | \(0.265263\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.47861e7 | −1.46671 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.28657e6i | 0.717115i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.48178e6i | − 0.144689i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.98389e6 | −0.967270 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.66915e6 | 0.448841 | 0.224421 | − | 0.974492i | \(-0.427951\pi\) | ||||
0.224421 | + | 0.974492i | \(0.427951\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.53466e7i | 1.46381i | 0.681405 | + | 0.731906i | \(0.261369\pi\) | ||||
−0.681405 | + | 0.731906i | \(0.738631\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.38454e6i | 0.604269i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.28923e7 | −1.21079 | −0.605395 | − | 0.795925i | \(-0.706985\pi\) | ||||
−0.605395 | + | 0.795925i | \(0.706985\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.34423e7 | 3.11662 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.40279e7i | 1.29730i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.98908e6i | 0.641412i | 0.947179 | + | 0.320706i | \(0.103920\pi\) | ||||
−0.947179 | + | 0.320706i | \(0.896080\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.90974e6 | 0.629301 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.60267e6 | 0.416003 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 5.92616e6i | − 0.531569i | −0.964032 | − | 0.265785i | \(-0.914369\pi\) | ||||
0.964032 | − | 0.265785i | \(-0.0856310\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 6.41040e6i | − 0.570665i | −0.958429 | − | 0.285333i | \(-0.907896\pi\) | ||||
0.958429 | − | 0.285333i | \(-0.0921040\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.77140e6 | 0.156507 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −528216. | −0.0463188 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.92952e6i | − 0.167933i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 1.54305e7i | − 1.33296i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.36202e7 | 1.16782 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.44237e7 | 1.22755 | 0.613775 | − | 0.789481i | \(-0.289650\pi\) | ||||
0.613775 | + | 0.789481i | \(0.289650\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 779240.i | − 0.0658282i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.61864e6i | 0.219585i | 0.993955 | + | 0.109793i | \(0.0350187\pi\) | ||||
−0.993955 | + | 0.109793i | \(0.964981\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.25941e6 | −0.354548 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.23401e7 | −1.01965 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.73254e7i | − 1.42112i | −0.703635 | − | 0.710561i | \(-0.748441\pi\) | ||||
0.703635 | − | 0.710561i | \(-0.251559\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.15867e6i | 0.745772i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.35163e7 | −1.09261 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.12332e6 | −0.250650 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.93677e6i | 0.791681i | 0.918319 | + | 0.395840i | \(0.129547\pi\) | ||||
−0.918319 | + | 0.395840i | \(0.870453\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.12528e7i | 0.890079i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.06239e6 | 0.319021 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.30264e6 | 0.179533 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.52348e6i | 0.272759i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 2.70085e6i | − 0.207590i | −0.994599 | − | 0.103795i | \(-0.966901\pi\) | ||||
0.994599 | − | 0.103795i | \(-0.0330985\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.21469e6 | 0.245330 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −319670. | −0.0242231 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.82835e7i | − 1.37566i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 1.98847e6i | − 0.148561i | −0.997237 | − | 0.0742804i | \(-0.976334\pi\) | ||||
0.997237 | − | 0.0742804i | \(-0.0236660\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.29438e6 | −0.392773 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.06748e6 | −0.594312 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.02908e6i | 0.221587i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.61825e7i | − 1.90201i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.01212e6 | 0.361576 | 0.180788 | − | 0.983522i | \(-0.442135\pi\) | ||||
0.180788 | + | 0.983522i | \(0.442135\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.63926e6 | 0.547284 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.65836e6i | 0.402573i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.08686e6i | 0.0767945i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.08406e7 | −0.760709 | −0.380355 | − | 0.924841i | \(-0.624198\pi\) | ||||
−0.380355 | + | 0.924841i | \(0.624198\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.54445e6 | 0.456094 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 5.78222e6i | − 0.400222i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.18857e6i | 0.631667i | 0.948815 | + | 0.315833i | \(0.102284\pi\) | ||||
−0.948815 | + | 0.315833i | \(0.897716\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.15677e6 | −0.283817 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.76278e7 | 1.87360 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.19968e6i | 0.417598i | 0.977959 | + | 0.208799i | \(0.0669554\pi\) | ||||
−0.977959 | + | 0.208799i | \(0.933045\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 856786.i | − 0.0573227i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.11862e6 | −0.473068 | −0.236534 | − | 0.971623i | \(-0.576012\pi\) | ||||
−0.236534 | + | 0.971623i | \(0.576012\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.53972e6 | −0.497696 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.69197e7i | 1.10941i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.00547e7i | 0.654882i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.67860e6 | −0.496801 | −0.248400 | − | 0.968657i | \(-0.579905\pi\) | ||||
−0.248400 | + | 0.968657i | \(0.579905\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.77694e7 | −1.14205 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 9.38797e6i | − 0.599383i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 5.96101e6i | − 0.378077i | −0.981970 | − | 0.189039i | \(-0.939463\pi\) | ||||
0.981970 | − | 0.189039i | \(-0.0605371\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.50854e7 | −0.950504 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.00820e7 | −1.25703 | −0.628513 | − | 0.777799i | \(-0.716336\pi\) | ||||
−0.628513 | + | 0.777799i | \(0.716336\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.59335e7i | 0.990834i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 2.13175e6i | − 0.131699i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.32875e6 | 0.572579 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.98669e7 | −1.82127 | −0.910635 | − | 0.413212i | \(-0.864407\pi\) | ||||
−0.910635 | + | 0.413212i | \(0.864407\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.08260e7i | 0.655892i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1.24588e7i | − 0.749944i | −0.927036 | − | 0.374972i | \(-0.877652\pi\) | ||||
0.927036 | − | 0.374972i | \(-0.122348\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.54425e6 | 0.271774 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.74542e7 | −1.63138 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1.11373e6i | − 0.0657564i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.60422e7i | 2.11438i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.16813e6 | 0.126381 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.37037e7 | −0.793715 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.73472e7i | 0.998372i | 0.866495 | + | 0.499186i | \(0.166368\pi\) | ||||
−0.866495 | + | 0.499186i | \(0.833632\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 4.20081e7i | − 2.40238i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.60955e6 | 0.432432 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.79936e6 | 0.214550 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.76172e6i | 0.491667i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 6.44517e6i | − 0.359408i | −0.983721 | − | 0.179704i | \(-0.942486\pi\) | ||||
0.983721 | − | 0.179704i | \(-0.0575141\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 289512. | 0.0160435 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.97592e6 | −0.549379 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.66158e7i | − 0.909351i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.59433e6i | 0.141103i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.84013e6 | −0.531884 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.85411e6 | 0.0996010 | 0.0498005 | − | 0.998759i | \(-0.484141\pi\) | ||||
0.0498005 | + | 0.998759i | \(0.484141\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.23842e7i | 0.661176i | 0.943775 | + | 0.330588i | \(0.107247\pi\) | ||||
−0.943775 | + | 0.330588i | \(0.892753\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7.22659e6i | − 0.383449i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −476067. | −0.0251058 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.79673e6 | −0.146587 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.13898e6i | 0.163523i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 1.24225e7i | − 0.643207i | −0.946874 | − | 0.321603i | \(-0.895778\pi\) | ||||
0.946874 | − | 0.321603i | \(-0.104222\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.32448e7 | −1.19626 | −0.598132 | − | 0.801398i | \(-0.704090\pi\) | ||||
−0.598132 | + | 0.801398i | \(0.704090\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.49734e6 | 0.434658 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 2.28900e7i | − 1.16381i | −0.813257 | − | 0.581904i | \(-0.802308\pi\) | ||||
0.813257 | − | 0.581904i | \(-0.197692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.27454e7i | 1.65487i | 0.561562 | + | 0.827435i | \(0.310201\pi\) | ||||
−0.561562 | + | 0.827435i | \(0.689799\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.30770e7 | 2.16393 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.76462e6 | 0.187979 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.18414e6i | 0.356581i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 9.06513e6i | − 0.447260i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.43580e7 | −1.19464 | −0.597319 | − | 0.802003i | \(-0.703768\pi\) | ||||
−0.597319 | + | 0.802003i | \(0.703768\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.74871e7 | 0.852565 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.55960e7i | − 1.24052i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 8.43736e6i | − 0.406504i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.55607e7 | 1.22423 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.82965e7 | −1.82343 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1.57889e7i | − 0.747358i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 4.14097e7i | − 1.94863i | −0.225192 | − | 0.974314i | \(-0.572301\pi\) | ||||
0.225192 | − | 0.974314i | \(-0.427699\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.03108e6 | −0.0482367 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.65781e6 | −0.309656 | −0.154828 | − | 0.987941i | \(-0.549482\pi\) | ||||
−0.154828 | + | 0.987941i | \(0.549482\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1.99635e7i | − 0.923111i | −0.887111 | − | 0.461555i | \(-0.847292\pi\) | ||||
0.887111 | − | 0.461555i | \(-0.152708\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.51153e6i | 0.437263i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.53117e7 | 1.15690 | 0.578448 | − | 0.815719i | \(-0.303659\pi\) | ||||
0.578448 | + | 0.815719i | \(0.303659\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.80498e6 | 0.400118 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2.47900e7i | − 1.12003i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.91129e7i | 0.858572i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.70679e6 | 0.344214 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.31439e6 | −0.369228 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.46133e6i | − 0.0645252i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.34243e7i | 1.46745i | 0.679446 | + | 0.733726i | \(0.262220\pi\) | ||||
−0.679446 | + | 0.733726i | \(0.737780\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.38578e7 | 1.47804 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.99218e7 | −0.864745 | −0.432373 | − | 0.901695i | \(-0.642323\pi\) | ||||
−0.432373 | + | 0.901695i | \(0.642323\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3.47030e7i | − 1.49784i | −0.662661 | − | 0.748920i | \(-0.730573\pi\) | ||||
0.662661 | − | 0.748920i | \(-0.269427\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 2.61695e7i | − 1.12315i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.55960e7 | 0.665586 | 0.332793 | − | 0.943000i | \(-0.392009\pi\) | ||||
0.332793 | + | 0.943000i | \(0.392009\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.72592e7 | 1.15680 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 4.61883e7i | − 1.94912i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 140031.i | − 0.00587617i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.19029e6 | 0.0913996 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.20810e6 | −0.174624 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.26438e7i | 0.521769i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 7.93513e6i | − 0.325643i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.38847e7 | 0.974765 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.33578e7 | 0.542144 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.98603e7i | 0.801620i | 0.916161 | + | 0.400810i | \(0.131271\pi\) | ||||
−0.916161 | + | 0.400810i | \(0.868729\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 3.56894e7i | − 1.43261i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.26907e7 | −0.506627 | −0.253313 | − | 0.967384i | \(-0.581520\pi\) | ||||
−0.253313 | + | 0.967384i | \(0.581520\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.10806e7 | 2.42508 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 1.06582e7i | − 0.420853i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 2.58494e7i | − 1.01514i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.26560e7 | −0.494318 | −0.247159 | − | 0.968975i | \(-0.579497\pi\) | ||||
−0.247159 | + | 0.968975i | \(0.579497\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.89028e7 | −1.12277 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.00540e7i | 0.388449i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.89359e6i | 0.341761i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.49119e7 | 0.569944 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.77116e7 | −1.43363 | −0.716813 | − | 0.697265i | \(-0.754400\pi\) | ||||
−0.716813 | + | 0.697265i | \(0.754400\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.82086e6i | − 0.0688498i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.56085e7i | 0.963119i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.69569e6 | −0.287885 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.13200e7 | −0.421208 | −0.210604 | − | 0.977572i | \(-0.567543\pi\) | ||||
−0.210604 | + | 0.977572i | \(0.567543\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 5.50551e7i | − 2.03767i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1.30012e7i | − 0.478641i | −0.970941 | − | 0.239320i | \(-0.923075\pi\) | ||||
0.970941 | − | 0.239320i | \(-0.0769246\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.47009e6 | −0.200316 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.91515e6 | −0.106189 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.89411e7i | − 1.04867i | −0.851511 | − | 0.524337i | \(-0.824313\pi\) | ||||
0.851511 | − | 0.524337i | \(-0.175687\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 4.63498e6i | − 0.167064i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.10676e7 | −2.18957 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.70255e6 | −0.0963922 | −0.0481961 | − | 0.998838i | \(-0.515347\pi\) | ||||
−0.0481961 | + | 0.998838i | \(0.515347\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.14055e6i | − 0.0404675i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.36427e7i | 0.834484i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.42627e7 | 1.20303 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.42355e7 | 0.846532 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.96267e7i | 0.681997i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 659809.i | 0.0228087i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.39559e7 | 0.823847 | 0.411923 | − | 0.911218i | \(-0.364857\pi\) | ||||
0.411923 | + | 0.911218i | \(0.364857\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.17676e6 | 0.0744733 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.62085e7i | − 0.551689i | −0.961202 | − | 0.275844i | \(-0.911043\pi\) | ||||
0.961202 | − | 0.275844i | \(-0.0889574\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.51975e7i | − 0.514623i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.37034e6 | 0.0798544 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.57236e7 | −0.862175 | −0.431087 | − | 0.902310i | \(-0.641870\pi\) | ||||
−0.431087 | + | 0.902310i | \(0.641870\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.60134e7i | 1.20090i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.11023e7i | 1.03186i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.83343e6 | 0.192548 | 0.0962742 | − | 0.995355i | \(-0.469307\pi\) | ||||
0.0962742 | + | 0.995355i | \(0.469307\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.20942e7 | −0.397179 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.19589e6i | 0.0390750i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.37361e7i | 0.446553i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.31418e7 | −1.39545 | −0.697725 | − | 0.716366i | \(-0.745804\pi\) | ||||
−0.697725 | + | 0.716366i | \(0.745804\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.09809e7 | −0.997059 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.28743e6i | 0.0412254i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.95272e7i | 1.57800i | 0.614396 | + | 0.788998i | \(0.289400\pi\) | ||||
−0.614396 | + | 0.788998i | \(0.710600\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.77414e7 | 0.562438 |
(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 | 320.6.d.d.161.11 | yes | 12 | |
4.3 | odd | 2 | 320.6.d.c.161.2 | ✓ | 12 | ||
8.3 | odd | 2 | 320.6.d.c.161.11 | yes | 12 | ||
8.5 | even | 2 | inner | 320.6.d.d.161.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.d.c.161.2 | ✓ | 12 | 4.3 | odd | 2 | ||
320.6.d.c.161.11 | yes | 12 | 8.3 | odd | 2 | ||
320.6.d.d.161.2 | yes | 12 | 8.5 | even | 2 | inner | |
320.6.d.d.161.11 | yes | 12 | 1.1 | even | 1 | trivial |