Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,3,Mod(161,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.l (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.53952634465\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.681615360000.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 2x^{6} + 20x^{5} + 49x^{4} - 136x^{3} + 168x^{2} - 96x + 864 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.6 | ||
Root | \(-0.542939 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.161 |
Dual form | 240.3.l.d.161.5 |
$q$-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 \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.40140 | + | 1.79813i | 0.800467 | + | 0.599377i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.2132 | 1.45903 | 0.729517 | − | 0.683963i | \(-0.239745\pi\) | ||||
0.729517 | + | 0.683963i | \(0.239745\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.53346 | + | 8.63606i | 0.281496 | + | 0.959563i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 8.19300i | − | 0.744818i | −0.928069 | − | 0.372409i | \(-0.878532\pi\) | ||
0.928069 | − | 0.372409i | \(-0.121468\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.5822 | −1.04478 | −0.522392 | − | 0.852705i | \(-0.674960\pi\) | ||||
−0.522392 | + | 0.852705i | \(0.674960\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.02074 | + | 5.36970i | −0.268049 | + | 0.357980i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.4710i | 0.910058i | 0.890477 | + | 0.455029i | \(0.150371\pi\) | ||||
−0.890477 | + | 0.455029i | \(0.849629\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.4934 | 1.34176 | 0.670879 | − | 0.741567i | \(-0.265917\pi\) | ||||
0.670879 | + | 0.741567i | \(0.265917\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 24.5261 | + | 18.3647i | 1.16791 | + | 0.874511i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 17.9156i | 0.778941i | 0.921039 | + | 0.389471i | \(0.127342\pi\) | ||||
−0.921039 | + | 0.389471i | \(0.872658\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.44491 | + | 25.2941i | −0.349811 | + | 0.936820i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 42.0022i | − | 1.44835i | −0.689615 | − | 0.724177i | \(-0.742220\pi\) | ||
0.689615 | − | 0.724177i | \(-0.257780\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −38.4878 | −1.24154 | −0.620771 | − | 0.783992i | \(-0.713180\pi\) | ||||
−0.620771 | + | 0.783992i | \(0.713180\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.7321 | − | 19.6747i | 0.446426 | − | 0.596202i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 22.8375i | 0.652500i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.8387 | 0.319965 | 0.159982 | − | 0.987120i | \(-0.448856\pi\) | ||||
0.159982 | + | 0.987120i | \(0.448856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −32.6163 | − | 24.4225i | −0.836315 | − | 0.626219i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 46.3781i | 1.13117i | 0.824689 | + | 0.565587i | \(0.191350\pi\) | ||||
−0.824689 | + | 0.565587i | \(0.808650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 54.0181 | 1.25623 | 0.628117 | − | 0.778119i | \(-0.283826\pi\) | ||||
0.628117 | + | 0.778119i | \(0.283826\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −19.3108 | + | 5.66499i | −0.429129 | + | 0.125889i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 43.0955i | − | 0.916925i | −0.888714 | − | 0.458462i | \(-0.848400\pi\) | ||
0.888714 | − | 0.458462i | \(-0.151600\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 55.3102 | 1.12878 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −27.8188 | + | 37.1521i | −0.545468 | + | 0.728472i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 82.7421i | − | 1.56117i | −0.625049 | − | 0.780586i | \(-0.714921\pi\) | ||
0.625049 | − | 0.780586i | \(-0.285079\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.3201 | 0.333093 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 61.2199 | + | 45.8404i | 1.07403 | + | 0.804218i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 45.8928i | − | 0.777844i | −0.921271 | − | 0.388922i | \(-0.872848\pi\) | ||
0.921271 | − | 0.388922i | \(-0.127152\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −93.6873 | −1.53586 | −0.767929 | − | 0.640535i | \(-0.778713\pi\) | ||||
−0.767929 | + | 0.640535i | \(0.778713\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 25.8748 | + | 88.2022i | 0.410712 | + | 1.40003i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 30.3707i | − | 0.467242i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −34.4995 | −0.514917 | −0.257459 | − | 0.966289i | \(-0.582885\pi\) | ||||
−0.257459 | + | 0.966289i | \(0.582885\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −32.2147 | + | 43.0227i | −0.466879 | + | 0.623517i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 68.0061i | − | 0.957832i | −0.877861 | − | 0.478916i | \(-0.841030\pi\) | ||
0.877861 | − | 0.478916i | \(-0.158970\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −44.7191 | −0.612591 | −0.306295 | − | 0.951937i | \(-0.599089\pi\) | ||||
−0.306295 | + | 0.951937i | \(0.599089\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.0070 | − | 8.99065i | −0.160093 | − | 0.119875i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 83.6770i | − | 1.08671i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.7499 | 0.148733 | 0.0743665 | − | 0.997231i | \(-0.476307\pi\) | ||||
0.0743665 | + | 0.997231i | \(0.476307\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −68.1632 | + | 43.7582i | −0.841521 | + | 0.540225i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 144.436i | − | 1.74020i | −0.492877 | − | 0.870099i | \(-0.664055\pi\) | ||
0.492877 | − | 0.870099i | \(-0.335945\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −34.5942 | −0.406990 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 75.5255 | − | 100.864i | 0.868109 | − | 1.15936i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 63.7094i | − | 0.715836i | −0.933753 | − | 0.357918i | \(-0.883487\pi\) | ||
0.933753 | − | 0.357918i | \(-0.116513\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −138.718 | −1.52438 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −92.4247 | − | 69.2061i | −0.993814 | − | 0.744151i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 57.0050i | 0.600052i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 63.9013 | 0.658776 | 0.329388 | − | 0.944195i | \(-0.393158\pi\) | ||||
0.329388 | + | 0.944195i | \(0.393158\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 70.7552 | − | 20.7566i | 0.714699 | − | 0.209663i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 50.8769i | 0.503731i | 0.967762 | + | 0.251866i | \(0.0810441\pi\) | ||||
−0.967762 | + | 0.251866i | \(0.918956\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −45.9491 | −0.446108 | −0.223054 | − | 0.974806i | \(-0.571603\pi\) | ||||
−0.223054 | + | 0.974806i | \(0.571603\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −41.0648 | + | 54.8420i | −0.391093 | + | 0.522305i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 110.249i | − | 1.03036i | −0.857082 | − | 0.515181i | \(-0.827725\pi\) | ||
0.857082 | − | 0.515181i | \(-0.172275\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −49.2797 | −0.452107 | −0.226054 | − | 0.974115i | \(-0.572582\pi\) | ||||
−0.226054 | + | 0.974115i | \(0.572582\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28.4295 | + | 21.2875i | 0.256121 | + | 0.191779i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 157.450i | 1.39337i | 0.717379 | + | 0.696683i | \(0.245342\pi\) | ||||
−0.717379 | + | 0.696683i | \(0.754658\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −40.0606 | −0.348353 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −34.4099 | − | 117.297i | −0.294102 | − | 1.00254i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 158.009i | 1.32781i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 53.8748 | 0.445246 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −83.3939 | + | 111.373i | −0.677999 | + | 0.905468i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 135.065 | 1.06351 | 0.531753 | − | 0.846900i | \(-0.321534\pi\) | ||||
0.531753 | + | 0.846900i | \(0.321534\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 129.719 | + | 97.1315i | 1.00557 | + | 0.752957i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 150.653i | 1.15002i | 0.818146 | + | 0.575010i | \(0.195002\pi\) | ||||
−0.818146 | + | 0.575010i | \(0.804998\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 260.370 | 1.95767 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −56.5594 | − | 21.1195i | −0.418959 | − | 0.156440i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 139.086i | − | 1.01523i | −0.861585 | − | 0.507613i | \(-0.830528\pi\) | ||
0.861585 | − | 0.507613i | \(-0.169472\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −110.296 | −0.793496 | −0.396748 | − | 0.917928i | \(-0.629861\pi\) | ||||
−0.396748 | + | 0.917928i | \(0.629861\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 77.4912 | − | 103.490i | 0.549583 | − | 0.733968i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 111.279i | 0.778174i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 93.9199 | 0.647723 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 132.822 | + | 99.4549i | 0.903551 | + | 0.676564i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 90.8076i | − | 0.609447i | −0.952441 | − | 0.304723i | \(-0.901436\pi\) | ||
0.952441 | − | 0.304723i | \(-0.0985640\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −111.286 | −0.736992 | −0.368496 | − | 0.929629i | \(-0.620127\pi\) | ||||
−0.368496 | + | 0.929629i | \(0.620127\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −133.608 | + | 39.1951i | −0.873258 | + | 0.256177i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 86.0614i | − | 0.555235i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 142.755 | 0.909269 | 0.454635 | − | 0.890678i | \(-0.349770\pi\) | ||||
0.454635 | + | 0.890678i | \(0.349770\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 148.781 | − | 198.697i | 0.935730 | − | 1.24967i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 182.977i | 1.13650i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 170.179 | 1.04405 | 0.522023 | − | 0.852932i | \(-0.325178\pi\) | ||||
0.522023 | + | 0.852932i | \(0.325178\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 43.9939 | + | 32.9419i | 0.266630 | + | 0.199648i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.38780i | − | 0.0382503i | −0.999817 | − | 0.0191251i | \(-0.993912\pi\) | ||
0.999817 | − | 0.0191251i | \(-0.00608809\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.4759 | 0.0915734 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 64.5865 | + | 220.163i | 0.377699 | + | 1.28750i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 238.403i | 1.37805i | 0.724736 | + | 0.689027i | \(0.241962\pi\) | ||||
−0.724736 | + | 0.689027i | \(0.758038\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −51.0662 | −0.291807 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 82.5212 | − | 110.207i | 0.466221 | − | 0.622638i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 243.541i | 1.36057i | 0.732950 | + | 0.680283i | \(0.238143\pi\) | ||||
−0.732950 | + | 0.680283i | \(0.761857\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −325.449 | −1.79806 | −0.899030 | − | 0.437887i | \(-0.855727\pi\) | ||||
−0.899030 | + | 0.437887i | \(0.855727\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −224.981 | − | 168.462i | −1.22940 | − | 0.920557i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 26.4721i | 0.143093i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 126.754 | 0.677828 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −96.4631 | + | 258.335i | −0.510387 | + | 1.36685i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 166.001i | 0.869113i | 0.900645 | + | 0.434556i | \(0.143095\pi\) | ||||
−0.900645 | + | 0.434556i | \(0.856905\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 239.408 | 1.24045 | 0.620227 | − | 0.784422i | \(-0.287041\pi\) | ||||
0.620227 | + | 0.784422i | \(0.287041\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 54.6105 | − | 72.9323i | 0.280054 | − | 0.374012i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 257.518i | 1.30720i | 0.756840 | + | 0.653600i | \(0.226742\pi\) | ||||
−0.756840 | + | 0.653600i | \(0.773258\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 78.4735 | 0.394339 | 0.197170 | − | 0.980369i | \(-0.436825\pi\) | ||||
0.197170 | + | 0.980369i | \(0.436825\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −82.8471 | − | 62.0345i | −0.412174 | − | 0.308629i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 428.979i | − | 2.11320i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −103.705 | −0.505876 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −154.721 | + | 45.3886i | −0.747443 | + | 0.219268i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 208.867i | − | 0.999365i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 112.724 | 0.534237 | 0.267119 | − | 0.963664i | \(-0.413928\pi\) | ||||
0.267119 | + | 0.963664i | \(0.413928\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 122.284 | − | 163.310i | 0.574102 | − | 0.766713i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 120.788i | 0.561805i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −393.085 | −1.81145 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −107.389 | − | 80.4108i | −0.490359 | − | 0.367172i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 210.130i | − | 0.950814i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 204.686 | 0.917872 | 0.458936 | − | 0.888469i | \(-0.348231\pi\) | ||||
0.458936 | + | 0.888469i | \(0.348231\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.6673 | − | 43.1803i | −0.0562991 | − | 0.191913i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 115.071i | 0.506920i | 0.967346 | + | 0.253460i | \(0.0815685\pi\) | ||||
−0.967346 | + | 0.253460i | \(0.918431\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −129.458 | −0.565317 | −0.282659 | − | 0.959221i | \(-0.591216\pi\) | ||||
−0.282659 | + | 0.959221i | \(0.591216\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 150.462 | − | 200.942i | 0.651351 | − | 0.869879i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 250.150i | 1.07361i | 0.843708 | + | 0.536803i | \(0.180368\pi\) | ||||
−0.843708 | + | 0.536803i | \(0.819632\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 96.3644 | 0.410061 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 28.2162 | + | 21.1278i | 0.119056 | + | 0.0891470i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 49.2556i | 0.206090i | 0.994677 | + | 0.103045i | \(0.0328586\pi\) | ||||
−0.994677 | + | 0.103045i | \(0.967141\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −457.672 | −1.89905 | −0.949526 | − | 0.313688i | \(-0.898435\pi\) | ||||
−0.949526 | + | 0.313688i | \(0.898435\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −242.370 | − | 17.4851i | −0.997408 | − | 0.0719551i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 123.677i | 0.504806i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −346.256 | −1.40185 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 259.715 | − | 346.850i | 1.04303 | − | 1.39297i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 119.717i | − | 0.476959i | −0.971148 | − | 0.238479i | \(-0.923351\pi\) | ||
0.971148 | − | 0.238479i | \(-0.0766489\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 146.783 | 0.580169 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −83.0745 | − | 62.2048i | −0.325782 | − | 0.243940i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 111.805i | 0.435041i | 0.976056 | + | 0.217520i | \(0.0697969\pi\) | ||||
−0.976056 | + | 0.217520i | \(0.930203\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 120.911 | 0.466839 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 362.734 | − | 106.411i | 1.38979 | − | 0.407705i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 55.3652i | − | 0.210514i | −0.994445 | − | 0.105257i | \(-0.966433\pi\) | ||
0.994445 | − | 0.105257i | \(-0.0335665\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 185.017 | 0.698177 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 114.558 | − | 152.992i | 0.429055 | − | 0.573003i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 309.427i | 1.15028i | 0.818053 | + | 0.575142i | \(0.195053\pi\) | ||||
−0.818053 | + | 0.575142i | \(0.804947\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 194.062 | 0.716096 | 0.358048 | − | 0.933703i | \(-0.383442\pi\) | ||||
0.358048 | + | 0.933703i | \(0.383442\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −333.118 | − | 249.433i | −1.22021 | − | 0.913675i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 40.9650i | 0.148964i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.20416 | 0.0187876 | 0.00939379 | − | 0.999956i | \(-0.497010\pi\) | ||||
0.00939379 | + | 0.999956i | \(0.497010\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −97.5073 | − | 332.383i | −0.349489 | − | 1.19134i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 240.004i | − | 0.854105i | −0.904227 | − | 0.427053i | \(-0.859552\pi\) | ||
0.904227 | − | 0.427053i | \(-0.140448\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −153.109 | −0.541022 | −0.270511 | − | 0.962717i | \(-0.587193\pi\) | ||||
−0.270511 | + | 0.962717i | \(0.587193\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −102.502 | + | 136.892i | −0.359657 | + | 0.480322i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 473.671i | 1.65042i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 49.6485 | 0.171794 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 153.453 | + | 114.903i | 0.527329 | + | 0.394855i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 169.252i | − | 0.577653i | −0.957381 | − | 0.288827i | \(-0.906735\pi\) | ||
0.957381 | − | 0.288827i | \(-0.0932651\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 102.619 | 0.347862 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 207.235 | + | 77.3821i | 0.697760 | + | 0.260546i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 243.334i | − | 0.813825i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 551.699 | 1.83289 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −91.4832 | + | 122.176i | −0.301925 | + | 0.403220i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 209.491i | − | 0.686857i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −330.401 | −1.07623 | −0.538113 | − | 0.842873i | \(-0.680863\pi\) | ||||
−0.538113 | + | 0.842873i | \(0.680863\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −110.342 | − | 82.6224i | −0.357095 | − | 0.267387i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 133.596i | − | 0.429570i | −0.976661 | − | 0.214785i | \(-0.931095\pi\) | ||
0.976661 | − | 0.214785i | \(-0.0689050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −459.981 | −1.46959 | −0.734794 | − | 0.678290i | \(-0.762721\pi\) | ||||
−0.734794 | + | 0.678290i | \(0.762721\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −197.226 | + | 57.8579i | −0.626114 | + | 0.183676i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 298.150i | − | 0.940536i | −0.882524 | − | 0.470268i | \(-0.844157\pi\) | ||
0.882524 | − | 0.470268i | \(-0.155843\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −344.124 | −1.07876 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 198.241 | − | 264.751i | 0.617574 | − | 0.824771i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 394.408i | 1.22108i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 67.9110 | 0.208957 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −118.340 | − | 88.6112i | −0.361897 | − | 0.270982i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 440.144i | − | 1.33782i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −397.599 | −1.20120 | −0.600602 | − | 0.799548i | \(-0.705073\pi\) | ||||
−0.600602 | + | 0.799548i | \(0.705073\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 29.9929 | + | 102.240i | 0.0900687 | + | 0.307026i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 77.1432i | − | 0.230278i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −427.942 | −1.26986 | −0.634929 | − | 0.772571i | \(-0.718970\pi\) | ||||
−0.634929 | + | 0.772571i | \(0.718970\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −283.116 | + | 378.101i | −0.835151 | + | 1.11534i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 315.331i | 0.924723i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 64.4477 | 0.187894 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −96.2016 | − | 72.0342i | −0.278845 | − | 0.208795i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 138.137i | − | 0.398090i | −0.979990 | − | 0.199045i | \(-0.936216\pi\) | ||
0.979990 | − | 0.199045i | \(-0.0637840\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −301.421 | −0.863669 | −0.431835 | − | 0.901953i | \(-0.642134\pi\) | ||||
−0.431835 | + | 0.901953i | \(0.642134\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 128.283 | − | 343.550i | 0.365477 | − | 0.978775i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 142.622i | − | 0.404028i | −0.979383 | − | 0.202014i | \(-0.935251\pi\) | ||
0.979383 | − | 0.202014i | \(-0.0647487\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 152.066 | 0.428356 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −284.120 | + | 379.443i | −0.795856 | + | 1.06286i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.05663i | 0.00851429i | 0.999991 | + | 0.00425715i | \(0.00135510\pi\) | ||||
−0.999991 | + | 0.00425715i | \(0.998645\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 288.913 | 0.800313 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 129.375 | + | 96.8739i | 0.356405 | + | 0.266870i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 99.9950i | − | 0.273959i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 370.072 | 1.00837 | 0.504186 | − | 0.863595i | \(-0.331793\pi\) | ||||
0.504186 | + | 0.863595i | \(0.331793\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −400.525 | + | 117.497i | −1.08543 | + | 0.318420i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 845.065i | − | 2.27780i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 455.556 | 1.22133 | 0.610665 | − | 0.791889i | \(-0.290902\pi\) | ||||
0.610665 | + | 0.791889i | \(0.290902\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.1037 | − | 26.8485i | 0.0536099 | − | 0.0715960i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 570.482i | 1.51322i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 380.051 | 1.00277 | 0.501387 | − | 0.865223i | \(-0.332823\pi\) | ||||
0.501387 | + | 0.865223i | \(0.332823\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 324.346 | + | 242.865i | 0.851301 | + | 0.637440i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 164.078i | 0.428402i | 0.976790 | + | 0.214201i | \(0.0687147\pi\) | ||||
−0.976790 | + | 0.214201i | \(0.931285\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 187.108 | 0.485994 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 136.853 | + | 466.503i | 0.353624 | + | 1.20544i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 562.622i | 1.44633i | 0.690676 | + | 0.723164i | \(0.257313\pi\) | ||||
−0.690676 | + | 0.723164i | \(0.742687\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −277.173 | −0.708882 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −270.893 | + | 361.778i | −0.689295 | + | 0.920553i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 26.2736i | 0.0665154i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −93.4668 | −0.235433 | −0.117716 | − | 0.993047i | \(-0.537557\pi\) | ||||
−0.117716 | + | 0.993047i | \(0.537557\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 625.253 | + | 468.179i | 1.56705 | + | 1.17338i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.4831i | 0.0585613i | 0.999571 | + | 0.0292807i | \(0.00932166\pi\) | ||||
−0.999571 | + | 0.0292807i | \(0.990678\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 522.749 | 1.29714 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −97.8464 | − | 152.417i | −0.241596 | − | 0.376339i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 96.9944i | − | 0.238316i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 697.472 | 1.70531 | 0.852655 | − | 0.522474i | \(-0.174991\pi\) | ||||
0.852655 | + | 0.522474i | \(0.174991\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 250.095 | − | 334.001i | 0.608503 | − | 0.812656i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 468.714i | − | 1.13490i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 322.970 | 0.778240 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −264.865 | − | 198.326i | −0.635167 | − | 0.475603i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 115.537i | − | 0.275744i | −0.990450 | − | 0.137872i | \(-0.955974\pi\) | ||
0.990450 | − | 0.137872i | \(-0.0440262\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 117.396 | 0.278850 | 0.139425 | − | 0.990233i | \(-0.455475\pi\) | ||||
0.139425 | + | 0.990233i | \(0.455475\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 372.175 | − | 109.181i | 0.879847 | − | 0.258110i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 77.3549i | − | 0.182012i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −956.851 | −2.24087 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −200.094 | + | 267.225i | −0.466419 | + | 0.622903i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 673.123i | 1.56177i | 0.624675 | + | 0.780885i | \(0.285232\pi\) | ||||
−0.624675 | + | 0.780885i | \(0.714768\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −392.655 | −0.906824 | −0.453412 | − | 0.891301i | \(-0.649793\pi\) | ||||
−0.453412 | + | 0.891301i | \(0.649793\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 225.539 | + | 168.880i | 0.518481 | + | 0.388230i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 456.731i | 1.04515i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −409.353 | −0.932468 | −0.466234 | − | 0.884661i | \(-0.654389\pi\) | ||||
−0.466234 | + | 0.884661i | \(0.654389\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 140.126 | + | 477.662i | 0.317746 | + | 1.08313i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 355.935i | 0.803464i | 0.915757 | + | 0.401732i | \(0.131592\pi\) | ||||
−0.915757 | + | 0.401732i | \(0.868408\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 142.459 | 0.320132 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 163.284 | − | 218.065i | 0.365288 | − | 0.487842i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 294.636i | 0.656205i | 0.944642 | + | 0.328103i | \(0.106409\pi\) | ||||
−0.944642 | + | 0.328103i | \(0.893591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 379.976 | 0.842519 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −267.242 | − | 200.106i | −0.589938 | − | 0.441736i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 310.183i | − | 0.681721i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 491.814 | 1.07618 | 0.538090 | − | 0.842887i | \(-0.319146\pi\) | ||||
0.538090 | + | 0.842887i | \(0.319146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −391.325 | − | 146.122i | −0.852561 | − | 0.318349i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 42.6832i | − | 0.0925883i | −0.998928 | − | 0.0462942i | \(-0.985259\pi\) | ||
0.998928 | − | 0.0462942i | \(-0.0147412\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 422.582 | 0.912705 | 0.456352 | − | 0.889799i | \(-0.349156\pi\) | ||||
0.456352 | + | 0.889799i | \(0.349156\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 154.749 | − | 206.668i | 0.332795 | − | 0.444447i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 203.497i | − | 0.435754i | −0.975976 | − | 0.217877i | \(-0.930087\pi\) | ||
0.975976 | − | 0.217877i | \(-0.0699131\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −352.351 | −0.751282 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 342.813 | + | 256.693i | 0.727840 | + | 0.544995i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 442.570i | − | 0.935666i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −127.467 | −0.268352 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 714.566 | − | 209.624i | 1.49804 | − | 0.439463i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 485.253i | 1.01305i | 0.862224 | + | 0.506527i | \(0.169071\pi\) | ||||
−0.862224 | + | 0.506527i | \(0.830929\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −160.795 | −0.334294 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −329.016 | + | 439.401i | −0.681192 | + | 0.909732i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 142.888i | 0.294614i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −140.013 | −0.287500 | −0.143750 | − | 0.989614i | \(-0.545916\pi\) | ||||
−0.143750 | + | 0.989614i | \(0.545916\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 408.669 | + | 306.005i | 0.835724 | + | 0.625776i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 20.4450i | − | 0.0416396i | −0.999783 | − | 0.0208198i | \(-0.993372\pi\) | ||
0.999783 | − | 0.0208198i | \(-0.00662763\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 649.816 | 1.31809 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 46.4132 | + | 158.214i | 0.0937641 | + | 0.319623i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 694.562i | − | 1.39751i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −49.2051 | −0.0986074 | −0.0493037 | − | 0.998784i | \(-0.515700\pi\) | ||||
−0.0493037 | + | 0.998784i | \(0.515700\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.4861 | − | 15.3397i | 0.0229263 | − | 0.0306181i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 149.060i | 0.296343i | 0.988962 | + | 0.148171i | \(0.0473387\pi\) | ||||
−0.988962 | + | 0.148171i | \(0.952661\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −113.764 | −0.225275 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.1639 | + | 27.8277i | 0.0733015 | + | 0.0548870i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 655.375i | 1.28757i | 0.765205 | + | 0.643787i | \(0.222638\pi\) | ||||
−0.765205 | + | 0.643787i | \(0.777362\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −456.727 | −0.893790 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −240.783 | + | 644.834i | −0.469362 | + | 1.25699i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 102.745i | − | 0.199505i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −353.081 | −0.682942 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −428.680 | + | 572.502i | −0.825973 | + | 1.10309i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 419.868i | − | 0.805890i | −0.915224 | − | 0.402945i | \(-0.867987\pi\) | ||
0.915224 | − | 0.402945i | \(-0.132013\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −146.678 | −0.280454 | −0.140227 | − | 0.990119i | \(-0.544783\pi\) | ||||
−0.140227 | + | 0.990119i | \(0.544783\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −122.630 | − | 91.8236i | −0.233582 | − | 0.174902i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 595.444i | − | 1.12988i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 208.030 | 0.393251 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 396.333 | − | 116.268i | 0.746390 | − | 0.218960i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 629.917i | − | 1.18183i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 246.524 | 0.460792 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −437.919 | + | 584.840i | −0.815491 | + | 1.08909i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 453.156i | − | 0.840735i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.07300 | 0.0130739 | 0.00653697 | − | 0.999979i | \(-0.497919\pi\) | ||||
0.00653697 | + | 0.999979i | \(0.497919\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −781.534 | − | 585.199i | −1.43929 | − | 1.07772i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 110.193i | − | 0.202188i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.46995 | −0.00634360 | −0.00317180 | − | 0.999995i | \(-0.501010\pi\) | ||||
−0.00317180 | + | 0.999995i | \(0.501010\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −237.353 | − | 809.090i | −0.432337 | − | 1.47375i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1070.78i | − | 1.94334i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 120.005 | 0.217006 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −47.6003 | + | 63.5702i | −0.0857663 | + | 0.114541i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 654.467i | − | 1.17499i | −0.809230 | − | 0.587493i | \(-0.800115\pi\) | ||
0.809230 | − | 0.587493i | \(-0.199885\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −733.684 | −1.31249 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 304.387 | + | 227.920i | 0.542579 | + | 0.406274i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 546.529i | 0.970745i | 0.874307 | + | 0.485373i | \(0.161316\pi\) | ||||
−0.874307 | + | 0.485373i | \(0.838684\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −352.070 | −0.623132 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −696.167 | + | 446.913i | −1.22781 | + | 0.788207i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 746.774i | − | 1.31243i | −0.754573 | − | 0.656216i | \(-0.772156\pi\) | ||
0.754573 | − | 0.656216i | \(-0.227844\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 230.358 | 0.403430 | 0.201715 | − | 0.979444i | \(-0.435349\pi\) | ||||
0.201715 | + | 0.979444i | \(0.435349\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −298.491 | + | 398.634i | −0.520926 | + | 0.695696i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 89.5782i | − | 0.155788i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 525.585 | 0.910893 | 0.455446 | − | 0.890263i | \(-0.349480\pi\) | ||||
0.455446 | + | 0.890263i | \(0.349480\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 574.914 | + | 430.486i | 0.992943 | + | 0.743499i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 1475.16i | − | 2.53901i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −677.906 | −1.16279 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 262.283 | − | 76.9430i | 0.448348 | − | 0.131526i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 75.3619i | 0.128385i | 0.997938 | + | 0.0641924i | \(0.0204471\pi\) | ||||
−0.997938 | + | 0.0641924i | \(0.979553\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −981.185 | −1.66585 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −463.051 | + | 618.405i | −0.783505 | + | 1.04637i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1142.87i | 1.92727i | 0.267230 | + | 0.963633i | \(0.413892\pi\) | ||||
−0.267230 | + | 0.963633i | \(0.586108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −353.319 | −0.593813 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 188.446 | + | 141.106i | 0.315656 | + | 0.236358i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1060.02i | − | 1.76965i | −0.465927 | − | 0.884823i | \(-0.654279\pi\) | ||
0.465927 | − | 0.884823i | \(-0.345721\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −530.900 | −0.883361 | −0.441681 | − | 0.897172i | \(-0.645618\pi\) | ||||
−0.441681 | + | 0.897172i | \(0.645618\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −87.4030 | − | 297.940i | −0.144947 | − | 0.494095i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 120.468i | 0.199120i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 719.995 | 1.18615 | 0.593077 | − | 0.805146i | \(-0.297913\pi\) | ||||
0.593077 | + | 0.805146i | \(0.297913\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 771.360 | − | 1030.15i | 1.26660 | − | 1.69154i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 585.331i | 0.957988i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −216.348 | −0.352932 | −0.176466 | − | 0.984307i | \(-0.556467\pi\) | ||||
−0.176466 | + | 0.984307i | \(0.556467\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −249.037 | − | 186.474i | −0.404938 | − | 0.303210i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 231.190i | 0.374701i | 0.982293 | + | 0.187350i | \(0.0599900\pi\) | ||||
−0.982293 | + | 0.187350i | \(0.940010\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 689.633 | 1.11411 | 0.557054 | − | 0.830476i | \(-0.311932\pi\) | ||||
0.557054 | + | 0.830476i | \(0.311932\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −453.161 | − | 169.212i | −0.729728 | − | 0.272482i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 650.679i | − | 1.04443i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 375.570 | − | 501.574i | 0.598996 | − | 0.799959i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 183.156i | 0.291187i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 616.973 | 0.977770 | 0.488885 | − | 0.872348i | \(-0.337404\pi\) | ||||
0.488885 | + | 0.872348i | \(0.337404\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 270.696 | + | 202.692i | 0.427639 | + | 0.320209i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 302.015i | 0.475614i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −751.234 | −1.17933 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 587.305 | − | 172.291i | 0.919100 | − | 0.269626i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1131.85i | 1.76576i | 0.469598 | + | 0.882880i | \(0.344399\pi\) | ||||
−0.469598 | + | 0.882880i | \(0.655601\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 637.481 | 0.991418 | 0.495709 | − | 0.868489i | \(-0.334908\pi\) | ||||
0.495709 | + | 0.868489i | \(0.334908\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −217.193 | + | 290.061i | −0.336733 | + | 0.449706i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 800.782i | 1.23769i | 0.785515 | + | 0.618843i | \(0.212398\pi\) | ||||
−0.785515 | + | 0.618843i | \(0.787602\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −375.999 | −0.579352 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −943.955 | − | 706.818i | −1.45001 | − | 1.08574i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 313.185i | − | 0.479610i | −0.970821 | − | 0.239805i | \(-0.922916\pi\) | ||
0.970821 | − | 0.239805i | \(-0.0770835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −336.870 | −0.514305 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −113.294 | − | 386.197i | −0.172442 | − | 0.587819i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 878.311i | − | 1.33279i | −0.745597 | − | 0.666397i | \(-0.767836\pi\) | ||
0.745597 | − | 0.666397i | \(-0.232164\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 200.421 | 0.303208 | 0.151604 | − | 0.988441i | \(-0.451556\pi\) | ||||
0.151604 | + | 0.988441i | \(0.451556\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 377.841 | − | 504.606i | 0.569896 | − | 0.761096i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 582.205i | 0.875497i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 752.497 | 1.12818 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 491.532 | + | 368.051i | 0.734727 | + | 0.550151i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 767.580i | 1.14393i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −60.8622 | −0.0904341 | −0.0452171 | − | 0.998977i | \(-0.514398\pi\) | ||||
−0.0452171 | + | 0.998977i | \(0.514398\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 47.2245 | − | 126.471i | 0.0699623 | − | 0.187364i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 415.595i | − | 0.613877i | −0.951729 | − | 0.306939i | \(-0.900695\pi\) | ||
0.951729 | − | 0.306939i | \(-0.0993047\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 652.639 | 0.961177 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −206.912 | + | 276.331i | −0.303836 | + | 0.405772i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 434.504i | − | 0.636170i | −0.948062 | − | 0.318085i | \(-0.896960\pi\) | ||
0.948062 | − | 0.318085i | \(-0.103040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 311.006 | 0.454023 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −310.880 | − | 232.782i | −0.452518 | − | 0.338838i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1123.82i | 1.63109i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 166.630 | 0.241144 | 0.120572 | − | 0.992705i | \(-0.461527\pi\) | ||||
0.120572 | + | 0.992705i | \(0.461527\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 722.640 | − | 211.992i | 1.04277 | − | 0.305905i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 246.629i | − | 0.354862i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −717.516 | −1.02943 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −449.802 | + | 600.711i | −0.643494 | + | 0.859386i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 248.345i | − | 0.354272i | −0.984186 | − | 0.177136i | \(-0.943317\pi\) | ||
0.984186 | − | 0.177136i | \(-0.0566833\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 301.809 | 0.429315 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 231.410 | + | 173.276i | 0.328241 | + | 0.245781i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 519.617i | 0.734961i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.1911 | −0.0341200 | −0.0170600 | − | 0.999854i | \(-0.505431\pi\) | ||||
−0.0170600 | + | 0.999854i | \(0.505431\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.7679 | + | 101.473i | 0.0418677 | + | 0.142719i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 689.534i | − | 0.967088i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −248.827 | −0.348010 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −88.5679 | + | 118.282i | −0.123526 | + | 0.164969i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 323.584i | − | 0.450048i | −0.974353 | − | 0.225024i | \(-0.927754\pi\) | ||
0.974353 | − | 0.225024i | \(-0.0722460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −469.289 | −0.650886 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1099.05 | − | 822.953i | −1.52013 | − | 1.13825i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 210.011i | 0.289671i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 454.949 | 0.625789 | 0.312895 | − | 0.949788i | \(-0.398701\pi\) | ||||
0.312895 | + | 0.949788i | \(0.398701\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −550.588 | − | 477.802i | −0.755264 | − | 0.655421i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 835.713i | 1.14325i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 131.588 | 0.179520 | 0.0897600 | − | 0.995963i | \(-0.471390\pi\) | ||||
0.0897600 | + | 0.995963i | \(0.471390\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −222.388 | + | 296.999i | −0.302569 | + | 0.404080i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 282.654i | 0.383520i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1033.59 | −1.39864 | −0.699319 | − | 0.714810i | \(-0.746513\pi\) | ||||
−0.699319 | + | 0.714810i | \(0.746513\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −831.500 | − | 622.613i | −1.12213 | − | 0.840234i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 439.535i | − | 0.591569i | −0.955255 | − | 0.295784i | \(-0.904419\pi\) | ||
0.955255 | − | 0.295784i | \(-0.0955810\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 203.052 | 0.272553 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1247.36 | − | 365.924i | 1.66983 | − | 0.489858i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1126.00i | − | 1.50333i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −496.343 | −0.660909 | −0.330455 | − | 0.943822i | \(-0.607202\pi\) | ||||
−0.330455 | + | 0.943822i | \(0.607202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 215.266 | − | 287.488i | 0.285878 | − | 0.381790i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 248.843i | − | 0.329593i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 468.694 | 0.619147 | 0.309574 | − | 0.950875i | \(-0.399814\pi\) | ||||
0.309574 | + | 0.950875i | \(0.399814\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 352.485 | + | 263.935i | 0.464406 | + | 0.347740i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 156.940i | 0.206229i | 0.994669 | + | 0.103115i | \(0.0328808\pi\) | ||||
−0.994669 | + | 0.103115i | \(0.967119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −503.305 | −0.659640 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −87.6430 | − | 298.758i | −0.114566 | − | 0.390533i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 623.325i | 0.812679i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1188.63 | 1.54569 | 0.772844 | − | 0.634596i | \(-0.218834\pi\) | ||||
0.772844 | + | 0.634596i | \(0.218834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −201.041 | + | 268.490i | −0.260753 | + | 0.348236i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 950.291i | 1.22935i | 0.788779 | + | 0.614677i | \(0.210714\pi\) | ||||
−0.788779 | + | 0.614677i | \(0.789286\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 192.439 | 0.248308 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 290.357 | + | 217.414i | 0.373690 | + | 0.279813i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1182.34i | 1.51776i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −557.174 | −0.713411 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1062.41 | + | 396.707i | 1.35685 | + | 0.506650i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 319.211i | 0.406638i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1056.60 | −1.34257 | −0.671284 | − | 0.741200i | \(-0.734257\pi\) | ||||
−0.671284 | + | 0.741200i | \(0.734257\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 99.5538 | − | 132.954i | 0.126177 | − | 0.168510i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1608.08i | 2.03297i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1272.48 | 1.60464 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 444.300 | + | 332.684i | 0.558868 | + | 0.418471i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 78.7126i | − | 0.0987612i | −0.998780 | − | 0.0493806i | \(-0.984275\pi\) | ||
0.998780 | − | 0.0493806i | \(-0.0157247\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 666.730 | 0.834455 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 550.198 | − | 161.405i | 0.686889 | − | 0.201505i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 366.384i | 0.456268i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −409.148 | −0.508259 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −556.389 | + | 743.058i | −0.689454 | + | 0.920765i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 176.199i | 0.217799i | 0.994053 | + | 0.108899i | \(0.0347327\pi\) | ||||
−0.994053 | + | 0.108899i | \(0.965267\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1103.89 | −1.36115 | −0.680574 | − | 0.732679i | \(-0.738270\pi\) | ||||
−0.680574 | + | 0.732679i | \(0.738270\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 466.021 | + | 348.949i | 0.573211 | + | 0.429211i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 380.533i | 0.466911i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1377.10 | 1.68556 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −351.437 | − | 1197.98i | −0.429105 | − | 1.46273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1321.32i | 1.60940i | 0.593679 | + | 0.804702i | \(0.297675\pi\) | ||||
−0.593679 | + | 0.804702i | \(0.702325\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −760.814 | −0.924439 | −0.462220 | − | 0.886765i | \(-0.652947\pi\) | ||||
−0.462220 | + | 0.886765i | \(0.652947\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −73.6604 | + | 98.3734i | −0.0892853 | + | 0.119240i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 610.599i | − | 0.738331i | −0.929364 | − | 0.369165i | \(-0.879644\pi\) | ||
0.929364 | − | 0.369165i | \(-0.120356\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 265.766 | 0.320586 | 0.160293 | − | 0.987069i | \(-0.448756\pi\) | ||||
0.160293 | + | 0.987069i | \(0.448756\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.4973 | + | 9.35776i | 0.0150388 | + | 0.0112608i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 855.704i | 1.02726i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.2836 | 0.0171061 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 363.514 | − | 973.516i | 0.434306 | − | 1.16310i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 48.5299i | − | 0.0578425i | −0.999582 | − | 0.0289213i | \(-0.990793\pi\) | ||
0.999582 | − | 0.0289213i | \(-0.00920721\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −923.188 | −1.09773 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 431.558 | − | 576.345i | 0.511931 | − | 0.683683i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34.6052i | 0.0409529i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 550.236 | 0.649629 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −367.677 | − | 275.310i | −0.433071 | − | 0.324276i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 212.098i | 0.249234i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −331.180 | −0.388253 | −0.194127 | − | 0.980976i | \(-0.562187\pi\) | ||||
−0.194127 | + | 0.980976i | \(0.562187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −492.298 | + | 144.420i | −0.575788 | + | 0.168912i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 159.395i | 0.185992i | 0.995666 | + | 0.0929961i | \(0.0296444\pi\) | ||||
−0.995666 | + | 0.0929961i | \(0.970356\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1635.01 | 1.90339 | 0.951694 | − | 0.307049i | \(-0.0993416\pi\) | ||||
0.951694 | + | 0.307049i | \(0.0993416\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −851.722 | + | 1137.47i | −0.989224 | + | 1.32111i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 152.237i | 0.176405i | 0.996103 | + | 0.0882025i | \(0.0281123\pi\) | ||||
−0.996103 | + | 0.0882025i | \(0.971888\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −533.086 | −0.616284 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 119.226 | + | 89.2744i | 0.137516 | + | 0.102969i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 96.2669i | − | 0.110779i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 468.578 | 0.537977 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 161.891 | + | 551.856i | 0.185443 | + | 0.632137i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 114.187i | − | 0.130500i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 521.588 | 0.594742 | 0.297371 | − | 0.954762i | \(-0.403890\pi\) | ||||
0.297371 | + | 0.954762i | \(0.403890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 304.338 | − | 406.443i | 0.346232 | − | 0.462392i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 821.701i | − | 0.932692i | −0.884603 | − | 0.466346i | \(-0.845570\pi\) | ||
0.884603 | − | 0.466346i | \(-0.154430\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −747.791 | −0.846876 | −0.423438 | − | 0.905925i | \(-0.639177\pi\) | ||||
−0.423438 | + | 0.905925i | \(0.639177\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 246.430 | + | 184.523i | 0.278452 | + | 0.208501i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1160.21i | − | 1.30801i | −0.756490 | − | 0.654006i | \(-0.773087\pi\) | ||
0.756490 | − | 0.654006i | \(-0.226913\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1379.45 | 1.55169 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 358.511 | + | 558.461i | 0.402369 | + | 0.626780i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1098.65i | − | 1.23029i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −544.575 | −0.608463 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 437.546 | − | 584.342i | 0.487788 | − | 0.651440i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1616.57i | 1.79819i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1280.10 | 1.42076 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1324.85 | + | 992.027i | 1.46717 | + | 1.09859i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 727.726i | − | 0.804117i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 354.207 | 0.390526 | 0.195263 | − | 0.980751i | \(-0.437444\pi\) | ||||
0.195263 | + | 0.980751i | \(0.437444\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −439.376 | + | 128.894i | −0.483362 | + | 0.141798i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1461.82i | − | 1.60463i | −0.596900 | − | 0.802316i | \(-0.703601\pi\) | ||
0.596900 | − | 0.802316i | \(-0.296399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1183.37 | −1.29613 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 376.692 | − | 503.073i | 0.411686 | − | 0.549806i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1538.65i | 1.67792i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −600.104 | −0.652997 | −0.326499 | − | 0.945198i | \(-0.605869\pi\) | ||||
−0.326499 | + | 0.945198i | \(0.605869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −793.427 | − | 594.105i | −0.861484 | − | 0.645065i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 923.672i | 1.00073i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −59.1935 | −0.0639930 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −116.410 | − | 396.819i | −0.125577 | − | 0.428068i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 243.828i | 0.262462i | 0.991352 | + | 0.131231i | \(0.0418930\pi\) | ||||
−0.991352 | + | 0.131231i | \(0.958107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1410.05 | 1.51455 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 240.223 | − | 320.818i | 0.257474 | − | 0.343856i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 283.430i | 0.303134i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 894.637 | 0.954789 | 0.477395 | − | 0.878689i | \(-0.341581\pi\) | ||||
0.477395 | + | 0.878689i | \(0.341581\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1104.60 | − | 827.105i | −1.17636 | − | 0.880837i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 592.336i | 0.629475i | 0.949179 | + | 0.314737i | \(0.101916\pi\) | ||||
−0.949179 | + | 0.314737i | \(0.898084\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −830.894 | −0.881118 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −577.655 | − | 215.698i | −0.611275 | − | 0.228252i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 526.526i | 0.555994i | 0.960582 | + | 0.277997i | \(0.0896705\pi\) | ||||
−0.960582 | + | 0.277997i | \(0.910330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 607.383 | 0.640025 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 536.112 | − | 715.977i | 0.563735 | − | 0.752868i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 117.158i | − | 0.122936i | −0.998109 | − | 0.0614678i | \(-0.980422\pi\) | ||
0.998109 | − | 0.0614678i | \(-0.0195781\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −371.189 | −0.388679 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −826.381 | − | 618.780i | −0.863512 | − | 0.646583i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1420.52i | − | 1.48125i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 520.311 | 0.541427 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 952.114 | − | 279.311i | 0.988696 | − | 0.290042i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 535.332i | 0.554748i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 811.294 | 0.838981 | 0.419490 | − | 0.907760i | \(-0.362209\pi\) | ||||
0.419490 | + | 0.907760i | \(0.362209\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −709.197 | + | 947.132i | −0.731885 | + | 0.977432i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1052.66i | 1.08410i | 0.840346 | + | 0.542050i | \(0.182352\pi\) | ||||
−0.840346 | + | 0.542050i | \(0.817648\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1126.48 | −1.15774 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 163.081 | + | 122.113i | 0.167263 | + | 0.125244i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 830.832i | − | 0.850391i | −0.905102 | − | 0.425195i | \(-0.860205\pi\) | ||
0.905102 | − | 0.425195i | \(-0.139795\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −521.971 | −0.533167 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −124.848 | − | 425.582i | −0.127266 | − | 0.433825i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1056.30i | 1.07457i | 0.843402 | + | 0.537283i | \(0.180549\pi\) | ||||
−0.843402 | + | 0.537283i | \(0.819451\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −575.829 | −0.584598 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 791.436 | − | 1056.96i | 0.801861 | − | 1.07088i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 967.768i | 0.978532i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1592.65 | −1.60712 | −0.803559 | − | 0.595225i | \(-0.797063\pi\) | ||||
−0.803559 | + | 0.595225i | \(0.797063\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −954.795 | − | 714.934i | −0.961525 | − | 0.719974i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 175.472i | 0.176354i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 978.023 | 0.980966 | 0.490483 | − | 0.871451i | \(-0.336820\pi\) | ||||
0.490483 | + | 0.871451i | \(0.336820\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −111.815 | + | 299.450i | −0.111927 | + | 0.299749i |
(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 | 240.3.l.d.161.6 | 8 | ||
3.2 | odd | 2 | inner | 240.3.l.d.161.5 | 8 | ||
4.3 | odd | 2 | 120.3.l.a.41.3 | ✓ | 8 | ||
5.2 | odd | 4 | 1200.3.c.m.449.13 | 16 | |||
5.3 | odd | 4 | 1200.3.c.m.449.4 | 16 | |||
5.4 | even | 2 | 1200.3.l.x.401.3 | 8 | |||
8.3 | odd | 2 | 960.3.l.h.641.6 | 8 | |||
8.5 | even | 2 | 960.3.l.g.641.3 | 8 | |||
12.11 | even | 2 | 120.3.l.a.41.4 | yes | 8 | ||
15.2 | even | 4 | 1200.3.c.m.449.3 | 16 | |||
15.8 | even | 4 | 1200.3.c.m.449.14 | 16 | |||
15.14 | odd | 2 | 1200.3.l.x.401.4 | 8 | |||
20.3 | even | 4 | 600.3.c.d.449.13 | 16 | |||
20.7 | even | 4 | 600.3.c.d.449.4 | 16 | |||
20.19 | odd | 2 | 600.3.l.f.401.6 | 8 | |||
24.5 | odd | 2 | 960.3.l.g.641.4 | 8 | |||
24.11 | even | 2 | 960.3.l.h.641.5 | 8 | |||
60.23 | odd | 4 | 600.3.c.d.449.3 | 16 | |||
60.47 | odd | 4 | 600.3.c.d.449.14 | 16 | |||
60.59 | even | 2 | 600.3.l.f.401.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.l.a.41.3 | ✓ | 8 | 4.3 | odd | 2 | ||
120.3.l.a.41.4 | yes | 8 | 12.11 | even | 2 | ||
240.3.l.d.161.5 | 8 | 3.2 | odd | 2 | inner | ||
240.3.l.d.161.6 | 8 | 1.1 | even | 1 | trivial | ||
600.3.c.d.449.3 | 16 | 60.23 | odd | 4 | |||
600.3.c.d.449.4 | 16 | 20.7 | even | 4 | |||
600.3.c.d.449.13 | 16 | 20.3 | even | 4 | |||
600.3.c.d.449.14 | 16 | 60.47 | odd | 4 | |||
600.3.l.f.401.5 | 8 | 60.59 | even | 2 | |||
600.3.l.f.401.6 | 8 | 20.19 | odd | 2 | |||
960.3.l.g.641.3 | 8 | 8.5 | even | 2 | |||
960.3.l.g.641.4 | 8 | 24.5 | odd | 2 | |||
960.3.l.h.641.5 | 8 | 24.11 | even | 2 | |||
960.3.l.h.641.6 | 8 | 8.3 | odd | 2 | |||
1200.3.c.m.449.3 | 16 | 15.2 | even | 4 | |||
1200.3.c.m.449.4 | 16 | 5.3 | odd | 4 | |||
1200.3.c.m.449.13 | 16 | 5.2 | odd | 4 | |||
1200.3.c.m.449.14 | 16 | 15.8 | even | 4 | |||
1200.3.l.x.401.3 | 8 | 5.4 | even | 2 | |||
1200.3.l.x.401.4 | 8 | 15.14 | odd | 2 |