Newspace parameters
Level: | \( N \) | \(=\) | \( 352 = 2^{5} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 352.m (of order \(5\), degree \(4\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(2.81073415115\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
|
|
Defining polynomial: |
\( x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} + \cdots + 25 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 257.3 | ||
Root | \(-1.36475 + 0.991547i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 352.257 |
Dual form | 352.2.m.f.289.3 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/352\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(287\) | \(321\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 | ||||||||
\(3\) | 0.212270 | − | 0.653300i | 0.122554 | − | 0.377183i | −0.870893 | − | 0.491472i | \(-0.836459\pi\) |
0.993448 | + | 0.114289i | \(0.0364590\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.607036 | + | 0.441038i | −0.271475 | + | 0.197238i | −0.715190 | − | 0.698930i | \(-0.753660\pi\) |
0.443716 | + | 0.896168i | \(0.353660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.944137 | + | 2.90576i | 0.356850 | + | 1.09827i | 0.954929 | + | 0.296835i | \(0.0959311\pi\) |
−0.598079 | + | 0.801438i | \(0.704069\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.04531 | + | 1.48600i | 0.681770 | + | 0.495335i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.27718 | − | 0.510019i | −0.988106 | − | 0.153777i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.02345 | + | 3.64975i | 1.39325 | + | 1.01226i | 0.995499 | + | 0.0947671i | \(0.0302106\pi\) |
0.397755 | + | 0.917492i | \(0.369789\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.159274 | + | 0.490196i | 0.0411244 | + | 0.126568i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.49320 | − | 1.81142i | 0.604691 | − | 0.439333i | −0.242850 | − | 0.970064i | \(-0.578082\pi\) |
0.847541 | + | 0.530730i | \(0.178082\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.30894 | − | 4.02849i | 0.300290 | − | 0.924199i | −0.681103 | − | 0.732188i | \(-0.738499\pi\) |
0.981393 | − | 0.192011i | \(-0.0615008\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.09874 | 0.457983 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.264608 | −0.0551745 | −0.0275873 | − | 0.999619i | \(-0.508782\pi\) | ||||
−0.0275873 | + | 0.999619i | \(0.508782\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.37111 | + | 4.21983i | −0.274221 | + | 0.843966i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.07215 | − | 2.23205i | 0.591236 | − | 0.429558i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.513105 | − | 1.57918i | −0.0952813 | − | 0.293246i | 0.892046 | − | 0.451945i | \(-0.149270\pi\) |
−0.987327 | + | 0.158700i | \(0.949270\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.39534 | + | 2.46686i | 0.609821 | + | 0.443061i | 0.849351 | − | 0.527828i | \(-0.176993\pi\) |
−0.239530 | + | 0.970889i | \(0.576993\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.02884 | + | 2.03272i | −0.179098 | + | 0.353851i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.85467 | − | 1.34750i | −0.313497 | − | 0.227769i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.730823 | − | 2.24924i | −0.120147 | − | 0.369773i | 0.872839 | − | 0.488008i | \(-0.162276\pi\) |
−0.992986 | + | 0.118235i | \(0.962276\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.45071 | − | 2.50709i | 0.552556 | − | 0.401455i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.75476 | − | 5.40060i | 0.274048 | − | 0.843432i | −0.715422 | − | 0.698693i | \(-0.753765\pi\) |
0.989470 | − | 0.144740i | \(-0.0462345\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.90575 | −1.51061 | −0.755306 | − | 0.655372i | \(-0.772512\pi\) | ||||
−0.755306 | + | 0.655372i | \(0.772512\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.89696 | −0.282782 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.56217 | + | 10.9632i | −0.519596 | + | 1.59915i | 0.255165 | + | 0.966898i | \(0.417870\pi\) |
−0.774761 | + | 0.632255i | \(0.782130\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.88890 | + | 1.37237i | −0.269843 | + | 0.196052i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.654167 | − | 2.01332i | −0.0916017 | − | 0.281921i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.56561 | − | 2.59057i | −0.489775 | − | 0.355842i | 0.315323 | − | 0.948984i | \(-0.397887\pi\) |
−0.805098 | + | 0.593142i | \(0.797887\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.21430 | − | 1.13576i | 0.298576 | − | 0.153146i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.35396 | − | 1.71025i | −0.311790 | − | 0.226529i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.258400 | − | 0.795272i | −0.0336407 | − | 0.103536i | 0.932826 | − | 0.360327i | \(-0.117335\pi\) |
−0.966467 | + | 0.256791i | \(0.917335\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.06629 | + | 3.68088i | −0.648672 | + | 0.471288i | −0.862819 | − | 0.505514i | \(-0.831303\pi\) |
0.214147 | + | 0.976802i | \(0.431303\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.38691 | + | 7.34616i | −0.300723 | + | 0.925529i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.65909 | −0.577889 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.76323 | 0.948430 | 0.474215 | − | 0.880409i | \(-0.342732\pi\) | ||||
0.474215 | + | 0.880409i | \(0.342732\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0561683 | + | 0.172868i | −0.00676187 | + | 0.0208109i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.38148 | − | 6.08950i | 0.994699 | − | 0.722691i | 0.0337539 | − | 0.999430i | \(-0.489254\pi\) |
0.960945 | + | 0.276739i | \(0.0892538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.61683 | − | 8.05376i | −0.306276 | − | 0.942621i | −0.979198 | − | 0.202908i | \(-0.934961\pi\) |
0.672922 | − | 0.739714i | \(-0.265039\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.46577 | + | 1.79149i | 0.284723 | + | 0.206863i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.61211 | − | 10.0042i | −0.183717 | − | 1.14008i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9096 | − | 8.65285i | −1.33994 | − | 0.973521i | −0.999446 | − | 0.0332737i | \(-0.989407\pi\) |
−0.340491 | − | 0.940248i | \(-0.610593\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.53764 | + | 4.73238i | 0.170849 | + | 0.525820i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.89570 | − | 6.46311i | 0.976430 | − | 0.709418i | 0.0195224 | − | 0.999809i | \(-0.493785\pi\) |
0.956908 | + | 0.290391i | \(0.0937854\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.714561 | + | 2.19919i | −0.0775050 | + | 0.238536i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.14059 | −0.122284 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.9492 | −1.69061 | −0.845306 | − | 0.534282i | \(-0.820582\pi\) | ||||
−0.845306 | + | 0.534282i | \(0.820582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.86246 | + | 18.0428i | −0.614552 | + | 1.89140i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.33233 | − | 1.69454i | 0.241851 | − | 0.175715i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.982144 | + | 3.02273i | 0.100766 | + | 0.310125i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.712979 | + | 0.518009i | 0.0723920 | + | 0.0525959i | 0.623393 | − | 0.781909i | \(-0.285754\pi\) |
−0.551001 | + | 0.834505i | \(0.685754\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.94495 | − | 5.91304i | −0.597489 | − | 0.594283i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.30209 | − | 6.75837i | −0.925593 | − | 0.672483i | 0.0193169 | − | 0.999813i | \(-0.493851\pi\) |
−0.944910 | + | 0.327331i | \(0.893851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.37708 | − | 10.3936i | −0.332753 | − | 1.02411i | −0.967818 | − | 0.251651i | \(-0.919027\pi\) |
0.635065 | − | 0.772459i | \(-0.280973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.27401 | + | 0.925624i | −0.124331 | + | 0.0903317i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.645212 | + | 1.98576i | −0.0623750 | + | 0.191970i | −0.977388 | − | 0.211454i | \(-0.932180\pi\) |
0.915013 | + | 0.403424i | \(0.132180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.88713 | −0.372320 | −0.186160 | − | 0.982519i | \(-0.559604\pi\) | ||||
−0.186160 | + | 0.982519i | \(0.559604\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.62456 | −0.154197 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.20708 | − | 12.9481i | 0.395769 | − | 1.21805i | −0.532592 | − | 0.846372i | \(-0.678782\pi\) |
0.928361 | − | 0.371679i | \(-0.121218\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.160626 | − | 0.116702i | 0.0149785 | − | 0.0108825i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.85096 | + | 14.9297i | 0.448472 | + | 1.38025i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.61746 | + | 5.53441i | 0.698292 | + | 0.507339i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4798 | + | 3.34284i | 0.952706 | + | 0.303895i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.15573 | − | 2.29277i | −0.284543 | − | 0.206732i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.18813 | − | 6.73437i | −0.195712 | − | 0.602340i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.61306 | − | 4.80467i | 0.586814 | − | 0.426345i | −0.254360 | − | 0.967110i | \(-0.581865\pi\) |
0.841174 | + | 0.540764i | \(0.181865\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.10269 | + | 6.47143i | −0.185132 | + | 0.569777i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.90996 | 0.516356 | 0.258178 | − | 0.966097i | \(-0.416878\pi\) | ||||
0.258178 | + | 0.966097i | \(0.416878\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.9416 | 1.12218 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.880490 | + | 2.70987i | −0.0757806 | + | 0.233229i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.71184 | − | 4.87644i | 0.573431 | − | 0.416622i | −0.262919 | − | 0.964818i | \(-0.584685\pi\) |
0.836350 | + | 0.548196i | \(0.184685\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.62320 | + | 17.3064i | 0.476953 | + | 1.46791i | 0.843305 | + | 0.537435i | \(0.180607\pi\) |
−0.366352 | + | 0.930476i | \(0.619393\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.40614 | + | 4.65433i | 0.539494 | + | 0.391966i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.6013 | − | 14.5229i | −1.22102 | − | 1.21447i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.00795 | + | 0.732318i | 0.0837057 | + | 0.0608157i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.495610 | + | 1.52533i | 0.0408773 | + | 0.125807i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.89158 | + | 6.46011i | −0.728426 | + | 0.529233i | −0.889065 | − | 0.457781i | \(-0.848645\pi\) |
0.160639 | + | 0.987013i | \(0.448645\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.42468 | − | 16.6955i | 0.441454 | − | 1.35866i | −0.444871 | − | 0.895594i | \(-0.646751\pi\) |
0.886326 | − | 0.463062i | \(-0.153249\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.79114 | 0.629877 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.14907 | −0.252940 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.09117 | + | 12.5913i | −0.326511 | + | 1.00490i | 0.644243 | + | 0.764821i | \(0.277173\pi\) |
−0.970754 | + | 0.240077i | \(0.922827\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.44929 | + | 1.77952i | −0.194242 | + | 0.141125i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.249826 | − | 0.768885i | −0.0196890 | − | 0.0605967i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.2756 | + | 13.2780i | 1.43146 | + | 1.04001i | 0.989743 | + | 0.142859i | \(0.0456295\pi\) |
0.441714 | + | 0.897156i | \(0.354371\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.271961 | − | 1.68769i | −0.0211721 | − | 0.131387i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.0270 | − | 9.46466i | −1.00806 | − | 0.732397i | −0.0442572 | − | 0.999020i | \(-0.514092\pi\) |
−0.963801 | + | 0.266623i | \(0.914092\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.89716 | + | 24.3050i | 0.607474 | + | 1.86961i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.66352 | − | 6.29442i | 0.662516 | − | 0.481346i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.66741 | − | 8.20943i | 0.202799 | − | 0.624151i | −0.796998 | − | 0.603983i | \(-0.793580\pi\) |
0.999797 | − | 0.0201688i | \(-0.00642035\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.5563 | −1.02476 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.574402 | −0.0431747 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.17100 | + | 12.8370i | −0.311755 | + | 0.959483i | 0.665315 | + | 0.746563i | \(0.268297\pi\) |
−0.977070 | + | 0.212920i | \(0.931703\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.62903 | − | 4.81627i | 0.492732 | − | 0.357991i | −0.313502 | − | 0.949588i | \(-0.601502\pi\) |
0.806234 | + | 0.591597i | \(0.201502\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.32929 | + | 4.09115i | 0.0982643 | + | 0.302426i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.43564 | + | 1.04305i | 0.105550 | + | 0.0766866i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.09452 | + | 4.66475i | −0.665057 | + | 0.341121i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.38633 | + | 6.81957i | 0.682755 | + | 0.496051i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.08452 | + | 18.7262i | 0.440260 | + | 1.35498i | 0.887599 | + | 0.460617i | \(0.152372\pi\) |
−0.447339 | + | 0.894364i | \(0.647628\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.3032 | − | 14.0246i | 1.38948 | − | 1.00951i | 0.393556 | − | 0.919301i | \(-0.371245\pi\) |
0.995922 | − | 0.0902141i | \(-0.0287551\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.988986 | + | 3.04379i | −0.0708228 | + | 0.217970i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.9000 | 1.34657 | 0.673283 | − | 0.739385i | \(-0.264884\pi\) | ||||
0.673283 | + | 0.739385i | \(0.264884\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.81826 | 0.695998 | 0.347999 | − | 0.937495i | \(-0.386861\pi\) | ||||
0.347999 | + | 0.937495i | \(0.386861\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.64790 | − | 5.07172i | 0.116234 | − | 0.357732i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.10426 | − | 2.98192i | 0.288062 | − | 0.209290i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.31666 | + | 4.05228i | 0.0919598 | + | 0.283023i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.541204 | − | 0.393208i | −0.0376163 | − | 0.0273298i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.34422 | + | 12.5345i | −0.438839 | + | 0.867028i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.5325 | − | 7.65227i | −0.725084 | − | 0.526804i | 0.162921 | − | 0.986639i | \(-0.447909\pi\) |
−0.888004 | + | 0.459835i | \(0.847909\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.19914 | − | 6.76824i | −0.150682 | − | 0.463752i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.01315 | − | 4.36881i | 0.410093 | − | 0.297950i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.96242 | + | 12.1951i | −0.268987 | + | 0.827857i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.81700 | −0.393076 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.1357 | 1.28721 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.08063 | + | 3.32583i | −0.0723642 | + | 0.222714i | −0.980697 | − | 0.195534i | \(-0.937356\pi\) |
0.908333 | + | 0.418248i | \(0.137356\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.07502 | + | 6.59339i | −0.605001 | + | 0.439559i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.37711 | − | 10.3937i | −0.224147 | − | 0.689852i | −0.998377 | − | 0.0569486i | \(-0.981863\pi\) |
0.774231 | − | 0.632904i | \(-0.218137\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.45596 | − | 6.87016i | −0.624868 | − | 0.453993i | 0.229751 | − | 0.973250i | \(-0.426209\pi\) |
−0.854618 | + | 0.519257i | \(0.826209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.87795 | − | 1.07040i | −0.452536 | − | 0.0704271i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.81746 | − | 2.77354i | −0.250090 | − | 0.181701i | 0.455677 | − | 0.890145i | \(-0.349397\pi\) |
−0.705767 | + | 0.708444i | \(0.749397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.67283 | − | 8.22613i | −0.174356 | − | 0.536614i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.18096 | + | 5.94382i | −0.531411 | + | 0.386092i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.374310 | + | 1.15201i | −0.0242121 | + | 0.0745172i | −0.962432 | − | 0.271521i | \(-0.912473\pi\) |
0.938220 | + | 0.346038i | \(0.112473\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.6151 | −1.13469 | −0.567344 | − | 0.823481i | \(-0.692029\pi\) | ||||
−0.567344 | + | 0.823481i | \(0.692029\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8102 | 0.950077 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.541366 | − | 1.66615i | 0.0345866 | − | 0.106447i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.2783 | − | 15.4596i | 1.35391 | − | 0.983672i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.33406 | − | 7.18349i | −0.147915 | − | 0.455235i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.644281 | + | 0.468097i | 0.0406666 | + | 0.0295460i | 0.607933 | − | 0.793988i | \(-0.291999\pi\) |
−0.567266 | + | 0.823534i | \(0.691999\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.867166 | + | 0.134955i | 0.0545183 | + | 0.00848455i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.28505 | + | 0.933645i | 0.0804731 | + | 0.0584671i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.76394 | − | 14.6619i | −0.297166 | − | 0.914584i | −0.982485 | − | 0.186341i | \(-0.940337\pi\) |
0.685319 | − | 0.728243i | \(-0.259663\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.84575 | − | 4.24718i | 0.363237 | − | 0.263907i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.29720 | − | 3.99238i | 0.0802948 | − | 0.247122i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.1291 | −1.42620 | −0.713101 | − | 0.701062i | \(-0.752710\pi\) | ||||
−0.713101 | + | 0.701062i | \(0.752710\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.30700 | 0.203147 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.38554 | + | 10.4196i | −0.207192 | + | 0.637670i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.5180 | + | 14.1807i | −1.19004 | + | 0.864612i | −0.993268 | − | 0.115838i | \(-0.963045\pi\) |
−0.196768 | + | 0.980450i | \(0.563045\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.56539 | − | 4.81777i | −0.0950905 | − | 0.292658i | 0.892187 | − | 0.451667i | \(-0.149170\pi\) |
−0.987277 | + | 0.159008i | \(0.949170\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.5429 | + | 7.65989i | 0.638087 | + | 0.463597i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.64555 | − | 13.1298i | 0.400742 | − | 0.791759i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.74659 | + | 3.44860i | 0.285195 | + | 0.207206i | 0.721180 | − | 0.692748i | \(-0.243600\pi\) |
−0.435985 | + | 0.899954i | \(0.643600\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.27876 | + | 10.0910i | 0.196294 | + | 0.604131i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.6389 | − | 16.4481i | 1.35052 | − | 0.981212i | 0.351538 | − | 0.936174i | \(-0.385659\pi\) |
0.998985 | − | 0.0450385i | \(-0.0143411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.34921 | + | 7.23013i | −0.139646 | + | 0.429786i | −0.996284 | − | 0.0861321i | \(-0.972549\pi\) |
0.856638 | + | 0.515919i | \(0.172549\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.18323 | 0.129323 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.3496 | 1.02411 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.31846 | + | 7.13550i | −0.136380 | + | 0.419735i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.489760 | − | 0.355831i | 0.0287102 | − | 0.0208592i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.21793 | + | 3.74840i | 0.0711522 | + | 0.218984i | 0.980309 | − | 0.197470i | \(-0.0632726\pi\) |
−0.909157 | + | 0.416454i | \(0.863273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.507603 | + | 0.368795i | 0.0295538 | + | 0.0214721i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.2064 | + | 5.74797i | −0.650260 | + | 0.333531i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.32924 | − | 0.965752i | −0.0768722 | − | 0.0558509i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.35239 | − | 28.7837i | −0.539063 | − | 1.65906i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.38980 | + | 4.64246i | −0.367084 | + | 0.266702i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.45202 | − | 4.46885i | 0.0831422 | − | 0.255885i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.7552 | −0.613829 | −0.306915 | − | 0.951737i | \(-0.599297\pi\) | ||||
−0.306915 | + | 0.951737i | \(0.599297\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.50698 | −0.427057 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.06019 | + | 24.8067i | −0.457051 | + | 1.40666i | 0.411658 | + | 0.911338i | \(0.364950\pi\) |
−0.868710 | + | 0.495322i | \(0.835050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.43382 | − | 1.76827i | 0.137568 | − | 0.0999487i | −0.516873 | − | 0.856062i | \(-0.672904\pi\) |
0.654441 | + | 0.756113i | \(0.272904\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.79099 | − | 5.51210i | −0.100911 | − | 0.310572i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.2108 | − | 19.0433i | −1.47214 | − | 1.06958i | −0.979985 | − | 0.199071i | \(-0.936208\pi\) |
−0.492160 | − | 0.870505i | \(-0.663792\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.876127 | + | 5.43693i | 0.0490537 | + | 0.304410i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.16034 | + | 0.843034i | 0.0647637 | + | 0.0470536i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.03383 | − | 12.4149i | −0.224449 | − | 0.690782i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.2890 | + | 16.1939i | −1.23637 | + | 0.898277i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.825122 | + | 2.53946i | −0.0456294 | + | 0.140433i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −35.2197 | −1.94172 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.2715 | −1.05926 | −0.529629 | − | 0.848229i | \(-0.677669\pi\) | ||||
−0.529629 | + | 0.848229i | \(0.677669\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.84762 | − | 5.68640i | 0.101249 | − | 0.311613i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.71256 | + | 3.42388i | −0.257475 | + | 0.187066i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.07494 | − | 18.6967i | −0.330923 | − | 1.01848i | −0.968696 | − | 0.248252i | \(-0.920144\pi\) |
0.637772 | − | 0.770225i | \(-0.279856\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.56593 | − | 5.49697i | −0.410925 | − | 0.298555i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.86899 | − | 9.81602i | −0.534436 | − | 0.531568i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.5313 | + | 8.37801i | 0.622634 | + | 0.452370i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0421452 | − | 0.129710i | −0.00226902 | − | 0.00698333i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.04704 | − | 0.760720i | 0.0562081 | − | 0.0408376i | −0.559326 | − | 0.828947i | \(-0.688940\pi\) |
0.615535 | + | 0.788110i | \(0.288940\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.54495 | + | 10.9102i | −0.189757 | + | 0.584011i | −0.999998 | − | 0.00208547i | \(-0.999336\pi\) |
0.810241 | + | 0.586097i | \(0.199336\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.5792 | 1.25857 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.5104 | −0.825534 | −0.412767 | − | 0.910837i | \(-0.635438\pi\) | ||||
−0.412767 | + | 0.910837i | \(0.635438\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.40216 | + | 7.39310i | −0.127494 | + | 0.392385i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.23259 | − | 3.80170i | 0.276938 | − | 0.201207i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.31460 | + | 13.2790i | 0.227716 | + | 0.700837i | 0.998005 | + | 0.0631419i | \(0.0201121\pi\) |
−0.770289 | + | 0.637695i | \(0.779888\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.855919 | + | 0.621861i | 0.0450484 | + | 0.0327295i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.40842 | − | 6.13684i | 0.231382 | − | 0.322101i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.14052 | + | 3.73481i | 0.269067 | + | 0.195489i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.77524 | − | 14.6967i | −0.249266 | − | 0.767161i | −0.994906 | − | 0.100812i | \(-0.967856\pi\) |
0.745640 | − | 0.666349i | \(-0.232144\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.6143 | − | 8.43832i | 0.604619 | − | 0.439281i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.16114 | − | 12.8067i | 0.216035 | − | 0.664889i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.75664 | 0.349846 | 0.174923 | − | 0.984582i | \(-0.444032\pi\) | ||||
0.174923 | + | 0.984582i | \(0.444032\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.86404 | −0.251178 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.18604 | − | 9.80562i | 0.164089 | − | 0.505015i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7117 | − | 13.5948i | 0.961153 | − | 0.698319i | 0.00773497 | − | 0.999970i | \(-0.497538\pi\) |
0.953418 | + | 0.301651i | \(0.0975379\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.73514 | − | 5.34020i | −0.0888937 | − | 0.273587i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.3862 | + | 14.0849i | 0.990591 | + | 0.719706i | 0.960050 | − | 0.279827i | \(-0.0902772\pi\) |
0.0305402 | + | 0.999534i | \(0.490277\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.39084 | + | 5.36191i | 0.274743 | + | 0.273268i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −20.2603 | − | 14.7200i | −1.02989 | − | 0.748259i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.12049 | + | 12.6815i | 0.208917 | + | 0.642980i | 0.999530 | + | 0.0306637i | \(0.00976210\pi\) |
−0.790613 | + | 0.612316i | \(0.790238\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.659721 | + | 0.479315i | −0.0333635 | + | 0.0242400i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.25451 | − | 3.86098i | 0.0632816 | − | 0.194761i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.0458 | 0.555775 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.8585 | 1.19742 | 0.598712 | − | 0.800964i | \(-0.295679\pi\) | ||||
0.598712 | + | 0.800964i | \(0.295679\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.74712 | − | 8.45476i | 0.137528 | − | 0.423267i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.9262 | + | 7.93833i | −0.545627 | + | 0.396421i | −0.826171 | − | 0.563420i | \(-0.809485\pi\) |
0.280543 | + | 0.959841i | \(0.409485\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.05291 | + | 24.7843i | 0.401144 | + | 1.23459i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.02056 | − | 2.19457i | −0.150093 | − | 0.109049i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.24788 | + | 7.74389i | 0.0618551 | + | 0.383850i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.4632 | − | 22.1328i | −1.50631 | − | 1.09440i | −0.967782 | − | 0.251790i | \(-0.918981\pi\) |
−0.538528 | − | 0.842608i | \(-0.681019\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.76105 | − | 5.41997i | −0.0868664 | − | 0.267347i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.06690 | − | 1.50169i | 0.101706 | − | 0.0738934i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.54954 | + | 7.84668i | −0.125152 | + | 0.385178i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.4999 | 0.612124 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.2409 | −0.646862 | −0.323431 | − | 0.946252i | \(-0.604836\pi\) | ||||
−0.323431 | + | 0.946252i | \(0.604836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.716385 | + | 2.20481i | −0.0349145 | + | 0.107456i | −0.966995 | − | 0.254796i | \(-0.917992\pi\) |
0.932080 | + | 0.362251i | \(0.117992\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −23.5771 | + | 17.1298i | −1.14636 | + | 0.832879i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.22543 | + | 13.0045i | 0.204964 | + | 0.630813i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.4790 | − | 11.2461i | −0.749081 | − | 0.544239i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.5872 | + | 6.45624i | −0.607718 | + | 0.311710i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.16135 | + | 2.29685i | 0.152277 | + | 0.110636i | 0.661315 | − | 0.750108i | \(-0.269999\pi\) |
−0.509038 | + | 0.860744i | \(0.669999\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.06021 | + | 18.6514i | 0.291235 | + | 0.896329i | 0.984460 | + | 0.175608i | \(0.0561891\pi\) |
−0.693225 | + | 0.720721i | \(0.743811\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.692381 | − | 0.503044i | 0.0331971 | − | 0.0241191i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.346354 | + | 1.06597i | −0.0165684 | + | 0.0509922i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.69615 | 0.224135 | 0.112068 | − | 0.993701i | \(-0.464253\pi\) | ||||
0.112068 | + | 0.993701i | \(0.464253\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.90273 | −0.281082 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.9938 | − | 39.9908i | 0.617354 | − | 1.90002i | 0.264061 | − | 0.964506i | \(-0.414938\pi\) |
0.353292 | − | 0.935513i | \(-0.385062\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.68175 | − | 7.03420i | 0.458959 | − | 0.333453i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.33297 | + | 7.18015i | 0.110346 | + | 0.339610i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.9789 | + | 14.5156i | 0.942865 | + | 0.685031i | 0.949109 | − | 0.314949i | \(-0.101987\pi\) |
−0.00624385 | + | 0.999981i | \(0.501987\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.50507 | + | 16.8038i | −0.400488 | + | 0.791258i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.75564 | − | 7.08789i | −0.458360 | − | 0.333018i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.39882 | − | 13.5382i | −0.206220 | − | 0.634680i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.4508 | + | 10.4991i | −0.675978 | + | 0.491127i | −0.872021 | − | 0.489468i | \(-0.837191\pi\) |
0.196043 | + | 0.980595i | \(0.437191\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.61633 | − | 11.1299i | 0.168796 | − | 0.519500i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.9746 | 1.39606 | 0.698028 | − | 0.716071i | \(-0.254061\pi\) | ||||
0.698028 | + | 0.716071i | \(0.254061\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.0359 | −1.34941 | −0.674705 | − | 0.738087i | \(-0.735729\pi\) | ||||
−0.674705 | + | 0.738087i | \(0.735729\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.668454 | + | 2.05729i | −0.0309988 | + | 0.0954045i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.7821 | + | 16.5521i | −1.05423 | + | 0.765942i | −0.973012 | − | 0.230754i | \(-0.925881\pi\) |
−0.0812167 | + | 0.996696i | \(0.525881\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.32956 | + | 22.5581i | 0.338447 | + | 1.04163i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.35748 | + | 5.34552i | 0.339015 | + | 0.246309i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 32.4629 | + | 5.05212i | 1.49264 | + | 0.232297i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.2049 | + | 11.0470i | 0.697646 | + | 0.506870i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.44318 | − | 10.5970i | −0.157653 | − | 0.485205i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.9735 | − | 13.0585i | 0.821230 | − | 0.596659i | −0.0958345 | − | 0.995397i | \(-0.530552\pi\) |
0.917065 | + | 0.398739i | \(0.130552\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.53792 | − | 13.9663i | 0.206911 | − | 0.636807i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.555343 | −0.0252690 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.661265 | −0.0300265 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.04875 | − | 12.4608i | 0.183466 | − | 0.564652i | −0.816452 | − | 0.577413i | \(-0.804062\pi\) |
0.999919 | + | 0.0127614i | \(0.00406220\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.5539 | − | 9.12094i | 0.567707 | − | 0.412463i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.19446 | − | 12.9092i | −0.189293 | − | 0.582585i | 0.810703 | − | 0.585458i | \(-0.199085\pi\) |
−0.999996 | + | 0.00287325i | \(0.999085\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.13982 | − | 3.00776i | −0.186448 | − | 0.135463i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.21667 | + | 0.967485i | 0.279419 | + | 0.0434852i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.6079 | + | 18.6052i | 1.14867 | + | 0.834558i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.16899 | + | 18.9862i | 0.276162 | + | 0.849940i | 0.988910 | + | 0.148519i | \(0.0474506\pi\) |
−0.712747 | + | 0.701421i | \(0.752549\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.94850 | + | 6.50147i | −0.399789 | + | 0.290464i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.50003 | + | 7.69431i | −0.111471 | + | 0.343072i | −0.991195 | − | 0.132413i | \(-0.957728\pi\) |
0.879724 | + | 0.475485i | \(0.157728\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.62740 | 0.383914 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.5548 | 0.779634 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.74481 | + | 29.9914i | −0.431931 | + | 1.32935i | 0.464268 | + | 0.885695i | \(0.346317\pi\) |
−0.896199 | + | 0.443652i | \(0.853683\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.9316 | − | 15.2077i | 0.925960 | − | 0.672750i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.97054 | − | 15.2977i | −0.219455 | − | 0.675412i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.63397 | + | 4.81986i | 0.292328 | + | 0.212388i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.2653 | − | 34.1117i | 0.759328 | − | 1.50023i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.79701 | − | 3.48523i | −0.210565 | − | 0.152985i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.4287 | + | 35.1740i | 0.500701 | + | 1.54100i | 0.807880 | + | 0.589347i | \(0.200615\pi\) |
−0.307179 | + | 0.951652i | \(0.599385\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.99740 | + | 4.35736i | −0.262248 | + | 0.190534i | −0.711137 | − | 0.703053i | \(-0.751820\pi\) |
0.448890 | + | 0.893587i | \(0.351820\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.87760 | + | 8.85634i | −0.125589 | + | 0.386522i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.9338 | 0.563405 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9300 | −0.996956 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.653270 | − | 2.01056i | 0.0283495 | − | 0.0872508i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.5258 | − | 20.7252i | 1.23559 | − | 0.897709i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.484127 | − | 1.48999i | −0.0209306 | − | 0.0644179i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.50104 | + | 5.44983i | 0.323694 | + | 0.235177i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.89019 | − | 3.53411i | 0.296782 | − | 0.152225i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.36829 | + | 6.80646i | 0.402774 | + | 0.292633i | 0.770670 | − | 0.637234i | \(-0.219922\pi\) |
−0.367896 | + | 0.929867i | \(0.619922\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.73933 | − | 5.35310i | −0.0746417 | − | 0.229723i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.35963 | − | 1.71437i | 0.101075 | − | 0.0734356i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.10133 | + | 9.54491i | −0.132603 | + | 0.408111i | −0.995210 | − | 0.0977649i | \(-0.968831\pi\) |
0.862606 | + | 0.505876i | \(0.168831\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.8319 | −0.675690 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.03331 | −0.299629 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.8987 | − | 42.7759i | 0.591035 | − | 1.81902i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.986167 | − | 0.716492i | 0.0418605 | − | 0.0304134i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.61618 | + | 29.5955i | 0.407450 | + | 1.25400i | 0.918832 | + | 0.394650i | \(0.129134\pi\) |
−0.511381 | + | 0.859354i | \(0.670866\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −49.7610 | − | 36.1535i | −2.10467 | − | 1.52913i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.11699 | + | 6.93164i | 0.0471593 | + | 0.292654i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.0268 | + | 13.0973i | 0.759741 | + | 0.551984i | 0.898831 | − | 0.438296i | \(-0.144418\pi\) |
−0.139090 | + | 0.990280i | \(0.544418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.15673 | + | 9.71542i | 0.132805 | + | 0.408731i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.2994 | + | 8.93603i | −0.516526 | + | 0.375278i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.66296 | + | 29.7395i | −0.405092 | + | 1.24675i | 0.515726 | + | 0.856754i | \(0.327522\pi\) |
−0.920818 | + | 0.389992i | \(0.872478\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.93719 | −0.248464 | −0.124232 | − | 0.992253i | \(-0.539647\pi\) | ||||
−0.124232 | + | 0.992253i | \(0.539647\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.5254 | 0.565032 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.362805 | − | 1.11660i | 0.0151300 | − | 0.0465654i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.40311 | + | 3.92559i | −0.224934 | + | 0.163424i | −0.694545 | − | 0.719449i | \(-0.744394\pi\) |
0.469611 | + | 0.882874i | \(0.344394\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.06479 | − | 15.5878i | −0.210485 | − | 0.647808i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.1790 | + | 19.7467i | 1.12757 | + | 0.819230i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.3639 | + | 10.3083i | 0.429229 | + | 0.426926i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.52928 | − | 6.92343i | −0.393987 | − | 0.286249i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.6950 | + | 39.0713i | 0.523980 | + | 1.61264i | 0.766324 | + | 0.642454i | \(0.222084\pi\) |
−0.242345 | + | 0.970190i | \(0.577916\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.3820 | − | 10.4491i | 0.592600 | − | 0.430549i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.01189 | − | 12.3473i | 0.165027 | − | 0.507902i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.283994 | −0.0116622 | −0.00583111 | − | 0.999983i | \(-0.501856\pi\) | ||||
−0.00583111 | + | 0.999983i | \(0.501856\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.06496 | −0.289635 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.08412 | − | 6.41427i | 0.0852974 | − | 0.262519i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.6857 | + | 24.4741i | −1.37636 | + | 0.999985i | −0.379152 | + | 0.925334i | \(0.623784\pi\) |
−0.997210 | + | 0.0746511i | \(0.976216\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.90750 | + | 5.87068i | 0.0778085 | + | 0.239470i | 0.982394 | − | 0.186823i | \(-0.0598192\pi\) |
−0.904585 | + | 0.426293i | \(0.859819\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.8782 | + | 11.5362i | 0.646610 | + | 0.469790i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.83591 | + | 2.59274i | −0.318575 | + | 0.105410i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.9010 | + | 23.9040i | 1.33541 | + | 0.970232i | 0.999599 | + | 0.0283021i | \(0.00901005\pi\) |
0.335810 | + | 0.941930i | \(0.390990\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.07688 | − | 3.31428i | −0.0436372 | − | 0.134302i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −57.9075 | + | 42.0722i | −2.34269 | + | 1.70206i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.33390 | − | 16.4160i | 0.215434 | − | 0.663038i | −0.783688 | − | 0.621154i | \(-0.786664\pi\) |
0.999122 | − | 0.0418838i | \(-0.0133359\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.92684 | 0.118022 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.2729 | 0.534346 | 0.267173 | − | 0.963649i | \(-0.413911\pi\) | ||||
0.267173 | + | 0.963649i | \(0.413911\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.96107 | − | 12.1909i | 0.159209 | − | 0.489994i | −0.839354 | − | 0.543585i | \(-0.817067\pi\) |
0.998563 | + | 0.0535908i | \(0.0170667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.812916 | + | 0.590618i | −0.0326212 | + | 0.0237007i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.0582 | − | 46.3445i | −0.603296 | − | 1.85675i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.6496 | − | 9.91704i | −0.545985 | − | 0.396682i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.84209 | + | 6.80537i | 0.273247 | + | 0.271780i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.89640 | − | 4.28399i | −0.235105 | − | 0.170814i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.99094 | − | 6.12748i | −0.0792581 | − | 0.243931i | 0.903574 | − | 0.428431i | \(-0.140934\pi\) |
−0.982833 | + | 0.184500i | \(0.940934\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.23496 | + | 5.25650i | −0.287564 | + | 0.208927i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.89533 | + | 5.83321i | −0.0752137 | + | 0.231484i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.4976 | −0.574416 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 26.1917 | 1.03613 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.20170 | + | 19.0869i | −0.244953 | + | 0.753887i | 0.750692 | + | 0.660653i | \(0.229720\pi\) |
−0.995644 | + | 0.0932338i | \(0.970280\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.2589 | − | 19.0782i | 1.03555 | − | 0.752371i | 0.0661375 | − | 0.997811i | \(-0.478932\pi\) |
0.969412 | + | 0.245440i | \(0.0789324\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.57773 | − | 4.85576i | −0.0621231 | − | 0.191195i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.7925 | − | 9.29429i | −0.502925 | − | 0.365396i | 0.307208 | − | 0.951642i | \(-0.400605\pi\) |
−0.810133 | + | 0.586246i | \(0.800605\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.441217 | + | 2.73803i | 0.0173193 | + | 0.107477i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.12595 | + | 5.17730i | 0.279288 | + | 0.202915i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.927899 | − | 2.85578i | −0.0363115 | − | 0.111755i | 0.931258 | − | 0.364361i | \(-0.118713\pi\) |
−0.967569 | + | 0.252606i | \(0.918713\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.58756 | + | 2.60652i | −0.140178 | + | 0.101845i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.61570 | − | 20.3610i | 0.258103 | − | 0.794360i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.17515 | −0.123686 | −0.0618431 | − | 0.998086i | \(-0.519698\pi\) | ||||
−0.0618431 | + | 0.998086i | \(0.519698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.6169 | −1.19086 | −0.595430 | − | 0.803408i | \(-0.703018\pi\) | ||||
−0.595430 | + | 0.803408i | \(0.703018\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.06194 | − | 12.5014i | 0.157753 | − | 0.485513i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.85603 | + | 5.70774i | −0.304644 | + | 0.221337i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.135772 | + | 0.417862i | 0.00525710 | + | 0.0161797i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.94338 | + | 1.41195i | 0.0751354 | + | 0.0545891i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.4804 | − | 9.47897i | 0.713429 | − | 0.365932i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.1071 | + | 10.2494i | 0.543787 | + | 0.395084i | 0.825489 | − | 0.564417i | \(-0.190899\pi\) |
−0.281703 | + | 0.959502i | \(0.590899\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.20663 | + | 16.0244i | 0.200403 | + | 0.616778i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.2671 | + | 23.4434i | −1.24012 | + | 0.901003i | −0.997607 | − | 0.0691445i | \(-0.977973\pi\) |
−0.242517 | + | 0.970147i | \(0.577973\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.832059 | + | 2.56081i | −0.0319315 | + | 0.0982750i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.50705 | −0.287671 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.9702 | 1.45289 | 0.726445 | − | 0.687225i | \(-0.241171\pi\) | ||||
0.726445 | + | 0.687225i | \(0.241171\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.92364 | + | 5.92034i | −0.0734984 | + | 0.226205i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.49549 | + | 4.71925i | −0.247819 | + | 0.180051i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.45675 | − | 26.0272i | −0.322177 | − | 0.991558i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.5820 | − | 17.8599i | −0.935145 | − | 0.679423i | 0.0121022 | − | 0.999927i | \(-0.496148\pi\) |
−0.947247 | + | 0.320504i | \(0.896148\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.5690 | − | 22.8573i | 0.439470 | − | 0.868276i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.0463 | − | 8.02558i | −0.419009 | − | 0.304428i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.40777 | − | 16.6434i | −0.204834 | − | 0.630414i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.62229 | + | 1.90520i | −0.0991840 | + | 0.0720614i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.72041 | − | 14.5279i | 0.178287 | − | 0.548712i | −0.821481 | − | 0.570236i | \(-0.806852\pi\) |
0.999768 | + | 0.0215239i | \(0.00685180\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0176 | −0.377822 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.94149 | −0.223770 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.8557 | − | 33.4104i | 0.408271 | − | 1.25653i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.2924 | + | 20.5556i | −1.06254 | + | 0.771983i | −0.974557 | − | 0.224139i | \(-0.928043\pi\) |
−0.0879861 | + | 0.996122i | \(0.528043\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.5007 | − | 35.3955i | −0.431310 | − | 1.32743i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.898434 | − | 0.652750i | −0.0336466 | − | 0.0244457i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.2687 | + | 2.37623i | 0.571016 | + | 0.0888658i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.673152 | + | 0.489074i | 0.0251393 | + | 0.0182648i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.25274 | − | 10.0109i | −0.121307 | − | 0.373344i | 0.871903 | − | 0.489678i | \(-0.162886\pi\) |
−0.993210 | + | 0.116334i | \(0.962886\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.0128 | − | 19.6259i | 1.00601 | − | 0.730908i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.73916 | + | 11.5079i | −0.139061 | + | 0.427985i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.36738 | 0.273618 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.67301 | −0.321664 | −0.160832 | − | 0.986982i | \(-0.551418\pi\) | ||||
−0.160832 | + | 0.986982i | \(0.551418\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.46916 | + | 4.52160i | −0.0544132 | + | 0.167467i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.6970 | + | 17.9435i | −0.913453 | + | 0.663663i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.1926 | − | 40.6027i | −0.487280 | − | 1.49969i | −0.828651 | − | 0.559766i | \(-0.810891\pi\) |
0.341370 | − | 0.939929i | \(-0.389109\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.973582 | − | 0.707349i | −0.0359111 | − | 0.0260909i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.4415 | − | 3.95940i | −0.937149 | − | 0.145846i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.3721 | + | 24.2463i | 1.22761 | + | 0.891913i | 0.996709 | − | 0.0810632i | \(-0.0258316\pi\) |
0.230904 | + | 0.972976i | \(0.425832\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.58302 | − | 17.1828i | −0.205097 | − | 0.631225i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.1799 | + | 20.4739i | −1.03382 | + | 0.751115i | −0.969070 | − | 0.246786i | \(-0.920626\pi\) |
−0.0647518 | + | 0.997901i | \(0.520626\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.54836 | − | 7.84304i | 0.0933646 | − | 0.287347i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 27.7987 | 1.01710 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.37930 | −0.233094 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.0813 | − | 34.1047i | 0.404362 | − | 1.24450i | −0.517064 | − | 0.855947i | \(-0.672975\pi\) |
0.921427 | − | 0.388553i | \(-0.127025\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.442570 | − | 0.321546i | 0.0161281 | − | 0.0117178i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.07034 | + | 12.5272i | 0.148135 | + | 0.455913i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.92416 | − | 6.48378i | −0.324354 | − | 0.235657i | 0.413677 | − | 0.910424i | \(-0.364244\pi\) |
−0.738031 | + | 0.674767i | \(0.764244\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.272239 | − | 0.537873i | 0.00988167 | − | 0.0195235i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.07652 | − | 5.14139i | −0.256524 | − | 0.186375i | 0.452089 | − | 0.891973i | \(-0.350679\pi\) |
−0.708613 | + | 0.705597i | \(0.750679\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.66999 | − | 11.2951i | −0.132862 | − | 0.408909i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.72950 | + | 3.43619i | −0.170996 | + | 0.124236i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.60449 | − | 4.93810i | 0.0579347 | − | 0.178305i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.61551 | 0.346744 | 0.173372 | − | 0.984856i | \(-0.444534\pi\) | ||||
0.173372 | + | 0.984856i | \(0.444534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.5899 | −0.381384 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.03122 | + | 6.25146i | −0.0730580 | + | 0.224849i | −0.980917 | − | 0.194426i | \(-0.937716\pi\) |
0.907859 | + | 0.419275i | \(0.137716\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.0651 | + | 10.9454i | −0.541155 | + | 0.393172i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.53381 | − | 4.72058i | −0.0550251 | − | 0.169350i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.4594 | − | 14.1381i | −0.697205 | − | 0.506549i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.5734 | + | 15.6817i | −1.09400 | + | 0.561134i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.10114 | − | 3.70620i | −0.182300 | − | 0.132449i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.06976 | − | 9.44775i | −0.109564 | − | 0.337205i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.30052 | − | 0.944881i | 0.0463584 | − | 0.0336814i | −0.564365 | − | 0.825526i | \(-0.690879\pi\) |
0.610723 | + | 0.791844i | \(0.290879\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.90962 | + | 15.1102i | −0.174787 | + | 0.537939i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41.5960 | 1.47898 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.8845 | −1.38083 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.701976 | − | 2.16046i | 0.0248965 | − | 0.0766236i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.9525 | + | 11.5902i | −0.565068 | + | 0.410546i | −0.833310 | − | 0.552805i | \(-0.813557\pi\) |
0.268242 | + | 0.963352i | \(0.413557\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.9778 | + | 33.7862i | 0.388366 | + | 1.19527i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.6211 | − | 23.7006i | −1.15261 | − | 0.837419i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.46823 | + | 27.7282i | 0.157680 | + | 0.978508i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.490761 | + | 0.356558i | 0.0172970 | + | 0.0125670i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.12115 | + | 15.7613i | 0.180273 | + | 0.554823i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.70085 | − | 2.68882i | 0.130115 | − | 0.0945340i | −0.520824 | − | 0.853664i | \(-0.674375\pi\) |
0.650939 | + | 0.759130i | \(0.274375\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.08998 | − | 3.35461i | 0.0382743 | − | 0.117796i | −0.930094 | − | 0.367322i | \(-0.880275\pi\) |
0.968368 | + | 0.249526i | \(0.0802747\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.47973 | −0.122040 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.9501 | −0.593735 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.9660 | + | 39.9052i | −0.453622 | + | 1.39611i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −38.8022 | + | 28.1914i | −1.35586 | + | 0.985088i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.762466 | − | 2.34663i | −0.0266102 | − | 0.0818979i | 0.936869 | − | 0.349679i | \(-0.113709\pi\) |
−0.963480 | + | 0.267781i | \(0.913709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.02028 | − | 4.37399i | −0.209854 | − | 0.152468i | 0.477894 | − | 0.878418i | \(-0.341400\pi\) |
−0.687748 | + | 0.725950i | \(0.741400\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.16707 | − | 7.12861i | −0.249525 | − | 0.248186i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.74279 | − | 6.35201i | −0.304016 | − | 0.220881i | 0.425308 | − | 0.905049i | \(-0.360166\pi\) |
−0.729325 | + | 0.684168i | \(0.760166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.89204 | − | 21.2115i | −0.239371 | − | 0.736707i | −0.996512 | − | 0.0834553i | \(-0.973404\pi\) |
0.757141 | − | 0.653252i | \(-0.226596\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.26053 | − | 2.36891i | 0.113106 | − | 0.0821767i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.22348 | + | 6.84318i | −0.0770391 | + | 0.237102i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0821 | 0.418119 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.9372 | 0.550869 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.86396 | − | 30.3581i | 0.340542 | − | 1.04808i | −0.623386 | − | 0.781914i | \(-0.714243\pi\) |
0.963927 | − | 0.266165i | \(-0.0857566\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.2310 | − | 15.4252i | 0.732102 | − | 0.531904i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.94000 | − | 18.2814i | −0.204584 | − | 0.629646i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.5133 | − | 11.2710i | −0.533672 | − | 0.387736i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.180846 | + | 33.6077i | 0.00621394 | + | 1.15478i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.22478 | + | 3.06948i | 0.144994 | + | 0.105344i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.193381 | + | 0.595166i | 0.00662903 | + | 0.0204020i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.5827 | − | 9.86844i | 0.465064 | − | 0.337889i | −0.330450 | − | 0.943823i | \(-0.607201\pi\) |
0.795515 | + | 0.605934i | \(0.207201\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.48300 | + | 7.64188i | −0.0849167 | + | 0.261347i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.2278 | −0.383534 | −0.191767 | − | 0.981440i | \(-0.561422\pi\) | ||||
−0.191767 | + | 0.981440i | \(0.561422\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.2349 | −1.71399 | −0.856996 | − | 0.515324i | \(-0.827672\pi\) | ||||
−0.856996 | + | 0.515324i | \(0.827672\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.68279 | − | 11.3345i | 0.125509 | − | 0.386278i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.32058 | − | 3.86562i | 0.181115 | − | 0.131587i | −0.493534 | − | 0.869726i | \(-0.664295\pi\) |
0.674649 | + | 0.738139i | \(0.264295\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00146 | + | 6.15985i | 0.0680515 | + | 0.209441i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.16948 | + | 3.02930i | 0.141603 | + | 0.102881i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.6168 | + | 34.4310i | 1.17429 | + | 1.16799i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.9982 | + | 28.3339i | 1.32140 | + | 0.960056i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.688498 | + | 2.11898i | 0.0233021 | + | 0.0717166i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.5025 | − | 12.7163i | 0.591694 | − | 0.429891i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.6684 | − | 42.0671i | 0.461550 | − | 1.42050i | −0.401720 | − | 0.915762i | \(-0.631588\pi\) |
0.863270 | − | 0.504742i | \(-0.168412\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.70736 | 0.0913170 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.0273 | 1.24748 | 0.623741 | − | 0.781631i | \(-0.285612\pi\) | ||||
0.623741 | + | 0.781631i | \(0.285612\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.59827 | − | 26.4627i | 0.289355 | − | 0.890542i | −0.695705 | − | 0.718328i | \(-0.744908\pi\) |
0.985059 | − | 0.172214i | \(-0.0550922\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.348683 | − | 0.253333i | 0.0117208 | − | 0.00851569i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.66741 | − | 11.2871i | −0.123140 | − | 0.378985i | 0.870418 | − | 0.492314i | \(-0.163849\pi\) |
−0.993558 | + | 0.113329i | \(0.963849\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.2048 | + | 14.6797i | 0.677648 | + | 0.492340i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.62552 | − | 16.2931i | −0.0879583 | − | 0.545838i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.5026 | + | 28.7003i | 1.32190 | + | 0.960420i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.12966 | − | 9.63210i | −0.104613 | − | 0.321965i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.913085 | + | 0.663395i | −0.0304870 | + | 0.0221501i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.15344 | − | 6.62760i | 0.0718212 | − | 0.221043i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.5824 | −0.452496 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.7896 | −0.691835 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.89990 | + | 5.84730i | −0.0631549 | + | 0.194371i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.23782 | + | 5.98513i | −0.273532 | + | 0.198733i | −0.716092 | − | 0.698006i | \(-0.754071\pi\) |
0.442559 | + | 0.896739i | \(0.354071\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.98269 | − | 27.6459i | −0.297937 | − | 0.916956i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.0498 | + | 9.48123i | 0.432359 | + | 0.314127i | 0.782591 | − | 0.622536i | \(-0.213897\pi\) |
−0.350233 | + | 0.936663i | \(0.613897\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.4491 | + | 16.6438i | −1.07391 | + | 0.550828i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.61128 | − | 1.89721i | −0.0863262 | − | 0.0627197i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.57982 | + | 17.1729i | 0.184262 | + | 0.567099i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.2546 | + | 11.0831i | −0.503203 | + | 0.365598i | −0.810239 | − | 0.586100i | \(-0.800663\pi\) |
0.307036 | + | 0.951698i | \(0.400663\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.28300 | + | 7.02635i | −0.0752273 | + | 0.231526i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 64.3291 | 2.11742 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.4935 | 0.345023 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.53773 | − | 26.2764i | 0.280416 | − | 0.863031i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.2972 | + | 7.48135i | −0.337840 | + | 0.245455i | −0.743750 | − | 0.668458i | \(-0.766955\pi\) |
0.405910 | + | 0.913913i | \(0.366955\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.05612 | + | 9.40576i | 0.100160 | + | 0.308261i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.4953 | + | 10.5314i | 0.474555 | + | 0.344784i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.46337 | − | 6.84270i | 0.113264 | − | 0.223780i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.21762 | − | 5.24391i | −0.235789 | − | 0.171311i | 0.463616 | − | 0.886036i | \(-0.346552\pi\) |
−0.699405 | + | 0.714725i | \(0.746552\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.638586 | − | 1.96537i | −0.0208395 | − | 0.0641373i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.1981 | − | 8.13587i | 0.365047 | − | 0.265222i | −0.390107 | − | 0.920769i | \(-0.627562\pi\) |
0.755154 | + | 0.655548i | \(0.227562\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.464324 | + | 1.42904i | −0.0151205 | + | 0.0465360i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.70553 | −0.283191 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.5104 | −1.12144 | −0.560719 | − | 0.828006i | \(-0.689475\pi\) | ||||
−0.560719 | + | 0.828006i | \(0.689475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.2487 | − | 50.0084i | 0.527456 | − | 1.62334i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0047 | + | 13.0812i | −0.583843 | + | 0.424187i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.13241 | + | 25.0290i | 0.263435 | + | 0.810769i | 0.992050 | + | 0.125845i | \(0.0401643\pi\) |
−0.728615 | + | 0.684923i | \(0.759836\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.9525 | − | 8.68399i | −0.386773 | − | 0.281007i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.73792 | + | 0.581724i | 0.120830 | + | 0.0188045i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.5066 | + | 14.8989i | 0.662193 | + | 0.481112i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.13658 | − | 12.7311i | −0.133438 | − | 0.410680i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.27050 | + | 3.10270i | −0.137615 | + | 0.0999831i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.53238 | + | 17.0269i | −0.178094 | + | 0.548116i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.18054 | −0.134437 | −0.0672185 | − | 0.997738i | \(-0.521412\pi\) | ||||
−0.0672185 | + | 0.997738i | \(0.521412\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.96690 | −0.288058 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.41506 | − | 16.6658i | 0.173777 | − | 0.534832i | −0.825798 | − | 0.563966i | \(-0.809275\pi\) |
0.999576 | + | 0.0291339i | \(0.00927491\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.9792 | + | 32.6793i | −1.44197 | + | 1.04765i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.84820 | + | 17.9989i | 0.187292 | + | 0.576426i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.7304 | + | 12.8819i | 0.567246 | + | 0.412128i | 0.834104 | − | 0.551608i | \(-0.185985\pi\) |
−0.266858 | + | 0.963736i | \(0.585985\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 52.2684 | + | 8.13440i | 1.67050 | + | 0.259977i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.95039 | − | 5.77629i | −0.253836 | − | 0.184423i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.3243 | + | 31.7749i | 0.329293 | + | 1.01346i | 0.969465 | + | 0.245229i | \(0.0788632\pi\) |
−0.640172 | + | 0.768232i | \(0.721137\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.4730 | + | 8.33559i | −0.365559 | + | 0.265594i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.47608 | + | 23.0090i | −0.237966 | + | 0.732385i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.62114 | 0.0833473 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.4811 | −0.555307 | −0.277653 | − | 0.960681i | \(-0.589557\pi\) | ||||
−0.277653 | + | 0.960681i | \(0.589557\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.09077 | + | 12.5901i | −0.129817 | + | 0.399534i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.96004 | + | 4.33022i | −0.188946 | + | 0.137277i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.7737 | + | 48.5464i | 0.499558 | + | 1.53748i | 0.809732 | + | 0.586800i | \(0.199613\pi\) |
−0.310174 | + | 0.950680i | \(0.600387\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.26562 | − | 5.27878i | −0.229874 | − | 0.167013i |
(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 | 352.2.m.f.257.3 | yes | 12 | |
4.3 | odd | 2 | 352.2.m.e.257.1 | ✓ | 12 | ||
8.3 | odd | 2 | 704.2.m.m.257.3 | 12 | |||
8.5 | even | 2 | 704.2.m.n.257.1 | 12 | |||
11.3 | even | 5 | inner | 352.2.m.f.289.3 | yes | 12 | |
11.5 | even | 5 | 3872.2.a.bn.1.5 | 6 | |||
11.6 | odd | 10 | 3872.2.a.bo.1.5 | 6 | |||
44.3 | odd | 10 | 352.2.m.e.289.1 | yes | 12 | ||
44.27 | odd | 10 | 3872.2.a.bq.1.2 | 6 | |||
44.39 | even | 10 | 3872.2.a.bp.1.2 | 6 | |||
88.3 | odd | 10 | 704.2.m.m.641.3 | 12 | |||
88.5 | even | 10 | 7744.2.a.dv.1.2 | 6 | |||
88.27 | odd | 10 | 7744.2.a.du.1.5 | 6 | |||
88.61 | odd | 10 | 7744.2.a.dw.1.2 | 6 | |||
88.69 | even | 10 | 704.2.m.n.641.1 | 12 | |||
88.83 | even | 10 | 7744.2.a.dt.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
352.2.m.e.257.1 | ✓ | 12 | 4.3 | odd | 2 | ||
352.2.m.e.289.1 | yes | 12 | 44.3 | odd | 10 | ||
352.2.m.f.257.3 | yes | 12 | 1.1 | even | 1 | trivial | |
352.2.m.f.289.3 | yes | 12 | 11.3 | even | 5 | inner | |
704.2.m.m.257.3 | 12 | 8.3 | odd | 2 | |||
704.2.m.m.641.3 | 12 | 88.3 | odd | 10 | |||
704.2.m.n.257.1 | 12 | 8.5 | even | 2 | |||
704.2.m.n.641.1 | 12 | 88.69 | even | 10 | |||
3872.2.a.bn.1.5 | 6 | 11.5 | even | 5 | |||
3872.2.a.bo.1.5 | 6 | 11.6 | odd | 10 | |||
3872.2.a.bp.1.2 | 6 | 44.39 | even | 10 | |||
3872.2.a.bq.1.2 | 6 | 44.27 | odd | 10 | |||
7744.2.a.dt.1.5 | 6 | 88.83 | even | 10 | |||
7744.2.a.du.1.5 | 6 | 88.27 | odd | 10 | |||
7744.2.a.dv.1.2 | 6 | 88.5 | even | 10 | |||
7744.2.a.dw.1.2 | 6 | 88.61 | odd | 10 |