Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,3,Mod(401,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, 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("600.401");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.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: | \(16.3488158616\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.5 | ||
Root | \(-0.542939 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.401 |
Dual form | 600.3.l.f.401.6 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 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 | \(-0.325040\pi\) | ||||
0.522392 | + | 0.852705i | \(0.325040\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 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 | \(-0.734083\pi\) | ||||
−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 | \(-0.872658\pi\) | ||
0.921039 | − | 0.389471i | \(-0.127342\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 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 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −11.8387 | −0.319965 | −0.159982 | − | 0.987120i | \(-0.551144\pi\) | ||||
−0.159982 | + | 0.987120i | \(0.551144\pi\) | |||||||
\(38\) | 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 | \(-0.283826\pi\) | ||||
0.628117 | + | 0.778119i | \(0.283826\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 43.0955i | 0.916925i | 0.888714 | + | 0.458462i | \(0.151600\pi\) | ||||
−0.888714 | + | 0.458462i | \(0.848400\pi\) | |||||||
\(48\) | 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 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 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 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 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 | \(-0.400911\pi\) | ||||
0.306295 | + | 0.951937i | \(0.400911\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | \(0.335945\pi\) | ||||
−0.492877 | + | 0.870099i | \(0.664055\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 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 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −63.9013 | −0.658776 | −0.329388 | − | 0.944195i | \(-0.606842\pi\) | ||||
−0.329388 | + | 0.944195i | \(0.606842\pi\) | |||||||
\(98\) | 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 | \(-0.571603\pi\) | ||||
−0.223054 | + | 0.974806i | \(0.571603\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 110.249i | 1.03036i | 0.857082 | + | 0.515181i | \(0.172275\pi\) | ||||
−0.857082 | + | 0.515181i | \(0.827725\pi\) | |||||||
\(108\) | 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 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 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 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 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 | \(-0.370139\pi\) | ||||
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 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 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 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −142.755 | −0.909269 | −0.454635 | − | 0.890678i | \(-0.650230\pi\) | ||||
−0.454635 | + | 0.890678i | \(0.650230\pi\) | |||||||
\(158\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.38780i | 0.0382503i | 0.999817 | + | 0.0191251i | \(0.00608809\pi\) | ||||
−0.999817 | + | 0.0191251i | \(0.993912\pi\) | |||||||
\(168\) | 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 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 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 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 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 | \(-0.712959\pi\) | ||||
−0.620227 | + | 0.784422i | \(0.712959\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 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 | \(-0.563175\pi\) | ||||
−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 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 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 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 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 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 115.071i | − | 0.506920i | −0.967346 | − | 0.253460i | \(-0.918431\pi\) | ||
0.967346 | − | 0.253460i | \(-0.0815685\pi\) | |||||||
\(228\) | 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 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 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 | \(0.0335665\pi\) | ||||
−0.994445 | + | 0.105257i | \(0.966433\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 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 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.20416 | −0.0187876 | −0.00939379 | − | 0.999956i | \(-0.502990\pi\) | ||||
−0.00939379 | + | 0.999956i | \(0.502990\pi\) | |||||||
\(278\) | 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 | \(-0.587193\pi\) | ||||
−0.270511 | + | 0.962717i | \(0.587193\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 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 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 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 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 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 | \(-0.237279\pi\) | ||||
0.734794 | + | 0.678290i | \(0.237279\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 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 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 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 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 427.942 | 1.26986 | 0.634929 | − | 0.772571i | \(-0.281030\pi\) | ||||
0.634929 | + | 0.772571i | \(0.281030\pi\) | |||||||
\(338\) | 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 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 138.137i | 0.398090i | 0.979990 | + | 0.199045i | \(0.0637840\pi\) | ||||
−0.979990 | + | 0.199045i | \(0.936216\pi\) | |||||||
\(348\) | 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 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 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 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 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 | \(-0.709098\pi\) | ||||
−0.610665 | + | 0.791889i | \(0.709098\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | \(-0.931285\pi\) | ||
0.976790 | − | 0.214201i | \(-0.0687147\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 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 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 93.4668 | 0.235433 | 0.117716 | − | 0.993047i | \(-0.462443\pi\) | ||||
0.117716 | + | 0.993047i | \(0.462443\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 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 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 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 | \(-0.350207\pi\) | ||||
0.453412 | + | 0.891301i | \(0.350207\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | \(-0.868408\pi\) | ||
0.915757 | − | 0.401732i | \(-0.131592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −491.814 | −1.07618 | −0.538090 | − | 0.842887i | \(-0.680854\pi\) | ||||
−0.538090 | + | 0.842887i | \(0.680854\pi\) | |||||||
\(458\) | 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 | \(-0.349156\pi\) | ||||
0.456352 | + | 0.889799i | \(0.349156\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 203.497i | 0.435754i | 0.975976 | + | 0.217877i | \(0.0699131\pi\) | ||||
−0.975976 | + | 0.217877i | \(0.930087\pi\) | |||||||
\(468\) | 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 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 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 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 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 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 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 | \(-0.952661\pi\) | ||
0.988962 | − | 0.148171i | \(-0.0473387\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 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 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 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 | \(-0.544783\pi\) | ||||
−0.140227 | + | 0.990119i | \(0.544783\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 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 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 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 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 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 | \(-0.838684\pi\) | ||
0.874307 | − | 0.485373i | \(-0.161316\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 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 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −525.585 | −0.910893 | −0.455446 | − | 0.890263i | \(-0.650520\pi\) | ||||
−0.455446 | + | 0.890263i | \(0.650520\pi\) | |||||||
\(578\) | 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 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 75.3619i | − | 0.128385i | −0.997938 | − | 0.0641924i | \(-0.979553\pi\) | ||
0.997938 | − | 0.0641924i | \(-0.0204471\pi\) | |||||||
\(588\) | 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 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 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 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 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 | \(-0.443533\pi\) | ||||
0.176466 | + | 0.984307i | \(0.443533\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 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 | \(-0.688068\pi\) | ||||
−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 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 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 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 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 | \(-0.334908\pi\) | ||||
0.495709 | + | 0.868489i | \(0.334908\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 800.782i | − | 1.23769i | −0.785515 | − | 0.618843i | \(-0.787602\pi\) | ||
0.785515 | − | 0.618843i | \(-0.212398\pi\) | |||||||
\(648\) | 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 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 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 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | \(-0.485602\pi\) | ||||
0.0452171 | + | 0.998977i | \(0.485602\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 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 | \(0.103040\pi\) | ||||
−0.948062 | + | 0.318085i | \(0.896960\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 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 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 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 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 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 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 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 | \(-0.528610\pi\) | ||||
−0.0897600 | + | 0.995963i | \(0.528610\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | \(0.0955810\pi\) | ||||
−0.955255 | + | 0.295784i | \(0.904419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 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 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −468.694 | −0.619147 | −0.309574 | − | 0.950875i | \(-0.600186\pi\) | ||||
−0.309574 | + | 0.950875i | \(0.600186\pi\) | |||||||
\(758\) | 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 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 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 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 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 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 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 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 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 | \(-0.652947\pi\) | ||||
−0.462220 | + | 0.886765i | \(0.652947\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 610.599i | 0.738331i | 0.929364 | + | 0.369165i | \(0.120356\pi\) | ||||
−0.929364 | + | 0.369165i | \(0.879644\pi\) | |||||||
\(828\) | 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 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 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 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 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 | \(-0.437813\pi\) | ||||
0.194127 | + | 0.980976i | \(0.437813\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 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 | \(-0.900658\pi\) | ||||
−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 | \(-0.971888\pi\) | ||
0.996103 | − | 0.0882025i | \(-0.0281123\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −521.588 | −0.594742 | −0.297371 | − | 0.954762i | \(-0.596110\pi\) | ||||
−0.297371 | + | 0.954762i | \(0.596110\pi\) | |||||||
\(878\) | 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 | \(-0.639177\pi\) | ||||
−0.423438 | + | 0.905925i | \(0.639177\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1160.21i | 1.30801i | 0.756490 | + | 0.654006i | \(0.226913\pi\) | ||||
−0.756490 | + | 0.654006i | \(0.773087\pi\) | |||||||
\(888\) | 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 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 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 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 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 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 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 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −894.637 | −0.954789 | −0.477395 | − | 0.878689i | \(-0.658419\pi\) | ||||
−0.477395 | + | 0.878689i | \(0.658419\pi\) | |||||||
\(938\) | 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 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 526.526i | − | 0.555994i | −0.960582 | − | 0.277997i | \(-0.910330\pi\) | ||
0.960582 | − | 0.277997i | \(-0.0896705\pi\) | |||||||
\(948\) | 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 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 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 | \(-0.819451\pi\) | ||
0.843402 | − | 0.537283i | \(-0.180549\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 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 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −978.023 | −0.980966 | −0.490483 | − | 0.871451i | \(-0.663180\pi\) | ||||
−0.490483 | + | 0.871451i | \(0.663180\pi\) | |||||||
\(998\) | 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 | 600.3.l.f.401.5 | 8 | ||
3.2 | odd | 2 | inner | 600.3.l.f.401.6 | 8 | ||
4.3 | odd | 2 | 1200.3.l.x.401.4 | 8 | |||
5.2 | odd | 4 | 600.3.c.d.449.3 | 16 | |||
5.3 | odd | 4 | 600.3.c.d.449.14 | 16 | |||
5.4 | even | 2 | 120.3.l.a.41.4 | yes | 8 | ||
12.11 | even | 2 | 1200.3.l.x.401.3 | 8 | |||
15.2 | even | 4 | 600.3.c.d.449.13 | 16 | |||
15.8 | even | 4 | 600.3.c.d.449.4 | 16 | |||
15.14 | odd | 2 | 120.3.l.a.41.3 | ✓ | 8 | ||
20.3 | even | 4 | 1200.3.c.m.449.3 | 16 | |||
20.7 | even | 4 | 1200.3.c.m.449.14 | 16 | |||
20.19 | odd | 2 | 240.3.l.d.161.5 | 8 | |||
40.19 | odd | 2 | 960.3.l.g.641.4 | 8 | |||
40.29 | even | 2 | 960.3.l.h.641.5 | 8 | |||
60.23 | odd | 4 | 1200.3.c.m.449.13 | 16 | |||
60.47 | odd | 4 | 1200.3.c.m.449.4 | 16 | |||
60.59 | even | 2 | 240.3.l.d.161.6 | 8 | |||
120.29 | odd | 2 | 960.3.l.h.641.6 | 8 | |||
120.59 | even | 2 | 960.3.l.g.641.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.l.a.41.3 | ✓ | 8 | 15.14 | odd | 2 | ||
120.3.l.a.41.4 | yes | 8 | 5.4 | even | 2 | ||
240.3.l.d.161.5 | 8 | 20.19 | odd | 2 | |||
240.3.l.d.161.6 | 8 | 60.59 | even | 2 | |||
600.3.c.d.449.3 | 16 | 5.2 | odd | 4 | |||
600.3.c.d.449.4 | 16 | 15.8 | even | 4 | |||
600.3.c.d.449.13 | 16 | 15.2 | even | 4 | |||
600.3.c.d.449.14 | 16 | 5.3 | odd | 4 | |||
600.3.l.f.401.5 | 8 | 1.1 | even | 1 | trivial | ||
600.3.l.f.401.6 | 8 | 3.2 | odd | 2 | inner | ||
960.3.l.g.641.3 | 8 | 120.59 | even | 2 | |||
960.3.l.g.641.4 | 8 | 40.19 | odd | 2 | |||
960.3.l.h.641.5 | 8 | 40.29 | even | 2 | |||
960.3.l.h.641.6 | 8 | 120.29 | odd | 2 | |||
1200.3.c.m.449.3 | 16 | 20.3 | even | 4 | |||
1200.3.c.m.449.4 | 16 | 60.47 | odd | 4 | |||
1200.3.c.m.449.13 | 16 | 60.23 | odd | 4 | |||
1200.3.c.m.449.14 | 16 | 20.7 | even | 4 | |||
1200.3.l.x.401.3 | 8 | 12.11 | even | 2 | |||
1200.3.l.x.401.4 | 8 | 4.3 | odd | 2 |