Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [120,3,Mod(41,120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(120, 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("120.41");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 120 = 2^{3} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 120.l (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: | \(3.26976317232\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.4 | ||
Root | \(-0.542939 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 120.41 |
Dual form | 120.3.l.a.41.3 |
$q$-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 \(\left(\mathbb{Z}/120\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(41\) | \(61\) | \(97\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | \(-0.760255\pi\) | ||||
−0.729517 | + | 0.683963i | \(0.760255\pi\) | |||||||
\(8\) | 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 | \(-0.849629\pi\) | ||
0.890477 | − | 0.455029i | \(-0.150371\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −25.4934 | −1.34176 | −0.670879 | − | 0.741567i | \(-0.734083\pi\) | ||||
−0.670879 | + | 0.741567i | \(0.734083\pi\) | |||||||
\(20\) | 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 | \(0.257780\pi\) | ||||
−0.689615 | + | 0.724177i | \(0.742220\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.4878 | 1.24154 | 0.620771 | − | 0.783992i | \(-0.286820\pi\) | ||||
0.620771 | + | 0.783992i | \(0.286820\pi\) | |||||||
\(32\) | 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 | \(-0.808650\pi\) | ||
0.824689 | − | 0.565587i | \(-0.191350\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −54.0181 | −1.25623 | −0.628117 | − | 0.778119i | \(-0.716174\pi\) | ||||
−0.628117 | + | 0.778119i | \(0.716174\pi\) | |||||||
\(44\) | 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 | \(0.285079\pi\) | ||||
−0.625049 | + | 0.780586i | \(0.714921\pi\) | |||||||
\(54\) | 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 | \(-0.417115\pi\) | ||||
0.257459 | + | 0.966289i | \(0.417115\pi\) | |||||||
\(68\) | 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 | \(-0.523693\pi\) | ||||
−0.0743665 | + | 0.997231i | \(0.523693\pi\) | |||||||
\(80\) | 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 | \(0.116513\pi\) | ||||
−0.933753 | + | 0.357918i | \(0.883487\pi\) | |||||||
\(90\) | 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 | \(-0.918956\pi\) | ||
0.967762 | − | 0.251866i | \(-0.0810441\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 45.9491 | 0.446108 | 0.223054 | − | 0.974806i | \(-0.428397\pi\) | ||||
0.223054 | + | 0.974806i | \(0.428397\pi\) | |||||||
\(104\) | 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 | \(-0.754658\pi\) | ||
0.717379 | − | 0.696683i | \(-0.245342\pi\) | |||||||
\(114\) | 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 | \(-0.678466\pi\) | ||||
−0.531753 | + | 0.846900i | \(0.678466\pi\) | |||||||
\(128\) | 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 | \(0.169472\pi\) | ||||
−0.861585 | + | 0.507613i | \(0.830528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 110.296 | 0.793496 | 0.396748 | − | 0.917928i | \(-0.370139\pi\) | ||||
0.396748 | + | 0.917928i | \(0.370139\pi\) | |||||||
\(140\) | 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 | \(0.0985640\pi\) | ||||
−0.952441 | + | 0.304723i | \(0.901436\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 111.286 | 0.736992 | 0.368496 | − | 0.929629i | \(-0.379873\pi\) | ||||
0.368496 | + | 0.929629i | \(0.379873\pi\) | |||||||
\(152\) | 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 | \(-0.674822\pi\) | ||||
−0.522023 | + | 0.852932i | \(0.674822\pi\) | |||||||
\(164\) | 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 | \(-0.758038\pi\) | ||
0.724736 | − | 0.689027i | \(-0.241962\pi\) | |||||||
\(174\) | 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 | \(-0.773258\pi\) | ||
0.756840 | − | 0.653600i | \(-0.226742\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −78.4735 | −0.394339 | −0.197170 | − | 0.980369i | \(-0.563175\pi\) | ||||
−0.197170 | + | 0.980369i | \(0.563175\pi\) | |||||||
\(200\) | 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 | \(-0.586072\pi\) | ||||
−0.267119 | + | 0.963664i | \(0.586072\pi\) | |||||||
\(212\) | 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 | \(-0.651769\pi\) | ||||
−0.458936 | + | 0.888469i | \(0.651769\pi\) | |||||||
\(224\) | 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 | \(-0.819632\pi\) | ||
0.843708 | − | 0.536803i | \(-0.180368\pi\) | |||||||
\(234\) | 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 | \(-0.930203\pi\) | ||
0.976056 | − | 0.217520i | \(-0.0697969\pi\) | |||||||
\(258\) | 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 | \(-0.804947\pi\) | ||
0.818053 | − | 0.575142i | \(-0.195053\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −194.062 | −0.716096 | −0.358048 | − | 0.933703i | \(-0.616558\pi\) | ||||
−0.358048 | + | 0.933703i | \(0.616558\pi\) | |||||||
\(272\) | 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 | \(0.140448\pi\) | ||||
−0.904227 | + | 0.427053i | \(0.859552\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 153.109 | 0.541022 | 0.270511 | − | 0.962717i | \(-0.412807\pi\) | ||||
0.270511 | + | 0.962717i | \(0.412807\pi\) | |||||||
\(284\) | 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 | \(0.0932651\pi\) | ||||
−0.957381 | + | 0.288827i | \(0.906735\pi\) | |||||||
\(294\) | 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 | \(-0.319137\pi\) | ||||
0.538113 | + | 0.842873i | \(0.319137\pi\) | |||||||
\(308\) | 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 | \(0.155843\pi\) | ||||
−0.882524 | + | 0.470268i | \(0.844157\pi\) | |||||||
\(318\) | 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 | \(-0.294927\pi\) | ||||
0.600602 | + | 0.799548i | \(0.294927\pi\) | |||||||
\(332\) | 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 | \(0.0647487\pi\) | ||||
−0.979383 | + | 0.202014i | \(0.935251\pi\) | |||||||
\(354\) | 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 | \(-0.668207\pi\) | ||||
−0.504186 | + | 0.863595i | \(0.668207\pi\) | |||||||
\(368\) | 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 | \(-0.667177\pi\) | ||||
−0.501387 | + | 0.865223i | \(0.667177\pi\) | |||||||
\(380\) | 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 | \(-0.742687\pi\) | ||
0.690676 | − | 0.723164i | \(-0.257313\pi\) | |||||||
\(390\) | 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 | \(-0.990678\pi\) | ||
0.999571 | − | 0.0292807i | \(-0.00932166\pi\) | |||||||
\(402\) | 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 | \(-0.345611\pi\) | ||||
0.466234 | + | 0.884661i | \(0.345611\pi\) | |||||||
\(440\) | 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 | \(-0.893591\pi\) | ||
0.944642 | − | 0.328103i | \(-0.106409\pi\) | |||||||
\(450\) | 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 | \(0.0147412\pi\) | ||||
−0.998928 | + | 0.0462942i | \(0.985259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −422.582 | −0.912705 | −0.456352 | − | 0.889799i | \(-0.650844\pi\) | ||||
−0.456352 | + | 0.889799i | \(0.650844\pi\) | |||||||
\(464\) | 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 | \(-0.454084\pi\) | ||||
0.143750 | + | 0.989614i | \(0.454084\pi\) | |||||||
\(488\) | 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 | \(-0.484300\pi\) | ||||
0.0493037 | + | 0.998784i | \(0.484300\pi\) | |||||||
\(500\) | 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 | \(-0.777362\pi\) | ||
0.765205 | − | 0.643787i | \(-0.222638\pi\) | |||||||
\(510\) | 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 | \(0.132013\pi\) | ||||
−0.915224 | + | 0.402945i | \(0.867987\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 146.678 | 0.280454 | 0.140227 | − | 0.990119i | \(-0.455217\pi\) | ||||
0.140227 | + | 0.990119i | \(0.455217\pi\) | |||||||
\(524\) | 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 | \(-0.498990\pi\) | ||||
0.00317180 | + | 0.999995i | \(0.498990\pi\) | |||||||
\(548\) | 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 | \(0.199885\pi\) | ||||
−0.809230 | + | 0.587493i | \(0.800115\pi\) | |||||||
\(558\) | 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 | \(0.227844\pi\) | ||||
−0.754573 | + | 0.656216i | \(0.772156\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −230.358 | −0.403430 | −0.201715 | − | 0.979444i | \(-0.564651\pi\) | ||||
−0.201715 | + | 0.979444i | \(0.564651\pi\) | |||||||
\(572\) | 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 | \(-0.586108\pi\) | ||
0.267230 | − | 0.963633i | \(-0.413892\pi\) | |||||||
\(594\) | 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 | \(-0.702087\pi\) | ||||
−0.593077 | + | 0.805146i | \(0.702087\pi\) | |||||||
\(608\) | 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 | \(-0.940010\pi\) | ||
0.982293 | − | 0.187350i | \(-0.0599900\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −689.633 | −1.11411 | −0.557054 | − | 0.830476i | \(-0.688068\pi\) | ||||
−0.557054 | + | 0.830476i | \(0.688068\pi\) | |||||||
\(620\) | 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 | \(-0.662596\pi\) | ||||
−0.488885 | + | 0.872348i | \(0.662596\pi\) | |||||||
\(632\) | 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 | \(-0.655601\pi\) | ||
0.469598 | − | 0.882880i | \(-0.344399\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −637.481 | −0.991418 | −0.495709 | − | 0.868489i | \(-0.665092\pi\) | ||||
−0.495709 | + | 0.868489i | \(0.665092\pi\) | |||||||
\(644\) | 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 | \(0.0770835\pi\) | ||||
−0.970821 | + | 0.239805i | \(0.922916\pi\) | |||||||
\(654\) | 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 | \(0.0993047\pi\) | ||||
−0.951729 | + | 0.306939i | \(0.900695\pi\) | |||||||
\(678\) | 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 | \(-0.538473\pi\) | ||||
−0.120572 | + | 0.992705i | \(0.538473\pi\) | |||||||
\(692\) | 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 | \(0.0566833\pi\) | ||||
−0.984186 | + | 0.177136i | \(0.943317\pi\) | |||||||
\(702\) | 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 | \(-0.601299\pi\) | ||||
−0.312895 | + | 0.949788i | \(0.601299\pi\) | |||||||
\(728\) | 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 | \(-0.253487\pi\) | ||||
0.699319 | + | 0.714810i | \(0.253487\pi\) | |||||||
\(740\) | 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 | \(-0.392798\pi\) | ||||
0.330455 | + | 0.943822i | \(0.392798\pi\) | |||||||
\(752\) | 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 | \(-0.967119\pi\) | ||
0.994669 | − | 0.103115i | \(-0.0328808\pi\) | |||||||
\(762\) | 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 | \(-0.789286\pi\) | ||
0.788779 | − | 0.614677i | \(-0.210714\pi\) | |||||||
\(774\) | 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 | \(-0.265743\pi\) | ||||
0.671284 | + | 0.741200i | \(0.265743\pi\) | |||||||
\(788\) | 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 | \(0.0157247\pi\) | ||||
−0.998780 | + | 0.0493806i | \(0.984275\pi\) | |||||||
\(798\) | 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 | \(-0.965267\pi\) | ||
0.994053 | − | 0.108899i | \(-0.0347327\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1103.89 | 1.36115 | 0.680574 | − | 0.732679i | \(-0.261730\pi\) | ||||
0.680574 | + | 0.732679i | \(0.261730\pi\) | |||||||
\(812\) | 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 | \(-0.702325\pi\) | ||
0.593679 | − | 0.804702i | \(-0.297675\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 760.814 | 0.924439 | 0.462220 | − | 0.886765i | \(-0.347053\pi\) | ||||
0.462220 | + | 0.886765i | \(0.347053\pi\) | |||||||
\(824\) | 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 | \(-0.970356\pi\) | ||
0.995666 | − | 0.0929961i | \(-0.0296444\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1635.01 | −1.90339 | −0.951694 | − | 0.307049i | \(-0.900658\pi\) | ||||
−0.951694 | + | 0.307049i | \(0.900658\pi\) | |||||||
\(860\) | 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 | \(0.154430\pi\) | ||||
−0.884603 | + | 0.466346i | \(0.845570\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 747.791 | 0.846876 | 0.423438 | − | 0.905925i | \(-0.360823\pi\) | ||||
0.423438 | + | 0.905925i | \(0.360823\pi\) | |||||||
\(884\) | 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 | \(-0.562556\pi\) | ||||
−0.195263 | + | 0.980751i | \(0.562556\pi\) | |||||||
\(908\) | 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 | \(-0.394131\pi\) | ||||
0.326499 | + | 0.945198i | \(0.394131\pi\) | |||||||
\(920\) | 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 | \(-0.958107\pi\) | ||
0.991352 | − | 0.131231i | \(-0.0418930\pi\) | |||||||
\(930\) | 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 | \(-0.898084\pi\) | ||
0.949179 | − | 0.314737i | \(-0.101916\pi\) | |||||||
\(942\) | 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 | \(0.0195781\pi\) | ||||
−0.998109 | + | 0.0614678i | \(0.980422\pi\) | |||||||
\(954\) | 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 | \(-0.637791\pi\) | ||||
−0.419490 | + | 0.907760i | \(0.637791\pi\) | |||||||
\(968\) | 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 | \(0.139795\pi\) | ||||
−0.905102 | + | 0.425195i | \(0.860205\pi\) | |||||||
\(978\) | 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 | \(-0.202937\pi\) | ||||
0.803559 | + | 0.595225i | \(0.202937\pi\) | |||||||
\(992\) | 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 | 120.3.l.a.41.4 | yes | 8 | |
3.2 | odd | 2 | inner | 120.3.l.a.41.3 | ✓ | 8 | |
4.3 | odd | 2 | 240.3.l.d.161.5 | 8 | |||
5.2 | odd | 4 | 600.3.c.d.449.14 | 16 | |||
5.3 | odd | 4 | 600.3.c.d.449.3 | 16 | |||
5.4 | even | 2 | 600.3.l.f.401.5 | 8 | |||
8.3 | odd | 2 | 960.3.l.g.641.4 | 8 | |||
8.5 | even | 2 | 960.3.l.h.641.5 | 8 | |||
12.11 | even | 2 | 240.3.l.d.161.6 | 8 | |||
15.2 | even | 4 | 600.3.c.d.449.4 | 16 | |||
15.8 | even | 4 | 600.3.c.d.449.13 | 16 | |||
15.14 | odd | 2 | 600.3.l.f.401.6 | 8 | |||
20.3 | even | 4 | 1200.3.c.m.449.14 | 16 | |||
20.7 | even | 4 | 1200.3.c.m.449.3 | 16 | |||
20.19 | odd | 2 | 1200.3.l.x.401.4 | 8 | |||
24.5 | odd | 2 | 960.3.l.h.641.6 | 8 | |||
24.11 | even | 2 | 960.3.l.g.641.3 | 8 | |||
60.23 | odd | 4 | 1200.3.c.m.449.4 | 16 | |||
60.47 | odd | 4 | 1200.3.c.m.449.13 | 16 | |||
60.59 | even | 2 | 1200.3.l.x.401.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.l.a.41.3 | ✓ | 8 | 3.2 | odd | 2 | inner | |
120.3.l.a.41.4 | yes | 8 | 1.1 | even | 1 | trivial | |
240.3.l.d.161.5 | 8 | 4.3 | odd | 2 | |||
240.3.l.d.161.6 | 8 | 12.11 | even | 2 | |||
600.3.c.d.449.3 | 16 | 5.3 | odd | 4 | |||
600.3.c.d.449.4 | 16 | 15.2 | even | 4 | |||
600.3.c.d.449.13 | 16 | 15.8 | even | 4 | |||
600.3.c.d.449.14 | 16 | 5.2 | odd | 4 | |||
600.3.l.f.401.5 | 8 | 5.4 | even | 2 | |||
600.3.l.f.401.6 | 8 | 15.14 | odd | 2 | |||
960.3.l.g.641.3 | 8 | 24.11 | even | 2 | |||
960.3.l.g.641.4 | 8 | 8.3 | odd | 2 | |||
960.3.l.h.641.5 | 8 | 8.5 | even | 2 | |||
960.3.l.h.641.6 | 8 | 24.5 | odd | 2 | |||
1200.3.c.m.449.3 | 16 | 20.7 | even | 4 | |||
1200.3.c.m.449.4 | 16 | 60.23 | odd | 4 | |||
1200.3.c.m.449.13 | 16 | 60.47 | odd | 4 | |||
1200.3.c.m.449.14 | 16 | 20.3 | even | 4 | |||
1200.3.l.x.401.3 | 8 | 60.59 | even | 2 | |||
1200.3.l.x.401.4 | 8 | 20.19 | odd | 2 |