Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(2645,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.2645");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2645.11 | ||
Root | \(-0.130526 - 0.991445i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.2645 |
Dual form | 2646.2.d.e.2645.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.68412 | −0.753163 | −0.376581 | − | 0.926384i | \(-0.622900\pi\) | ||||
−0.376581 | + | 0.926384i | \(0.622900\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 1.68412i | − 0.532566i | ||||||||
\(11\) | 3.32565i | 1.00272i | 0.865238 | + | 0.501361i | \(0.167167\pi\) | ||||
−0.865238 | + | 0.501361i | \(0.832833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.34518i | − 1.20514i | −0.798068 | − | 0.602568i | \(-0.794144\pi\) | ||||
0.798068 | − | 0.602568i | \(-0.205856\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.81123 | 0.924358 | 0.462179 | − | 0.886787i | \(-0.347068\pi\) | ||||
0.462179 | + | 0.886787i | \(0.347068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.06583i | 0.932766i | 0.884583 | + | 0.466383i | \(0.154443\pi\) | ||||
−0.884583 | + | 0.466383i | \(0.845557\pi\) | |||||||
\(20\) | 1.68412 | 0.376581 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.32565 | −0.709032 | ||||||||
\(23\) | 4.69764i | 0.979526i | 0.871856 | + | 0.489763i | \(0.162917\pi\) | ||||
−0.871856 | + | 0.489763i | \(0.837083\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.16373 | −0.432746 | ||||||||
\(26\) | 4.34518 | 0.852159 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 2.50277i | − 0.464753i | −0.972626 | − | 0.232377i | \(-0.925350\pi\) | ||||
0.972626 | − | 0.232377i | \(-0.0746502\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 4.09593i | − 0.735651i | −0.929895 | − | 0.367826i | \(-0.880102\pi\) | ||||
0.929895 | − | 0.367826i | \(-0.119898\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.81123i | 0.653620i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.27558 | 1.03170 | 0.515850 | − | 0.856679i | \(-0.327476\pi\) | ||||
0.515850 | + | 0.856679i | \(0.327476\pi\) | |||||||
\(38\) | −4.06583 | −0.659565 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.68412i | 0.266283i | ||||||||
\(41\) | 5.46525 | 0.853529 | 0.426764 | − | 0.904363i | \(-0.359653\pi\) | ||||
0.426764 | + | 0.904363i | \(0.359653\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.7920 | −1.64576 | −0.822882 | − | 0.568212i | \(-0.807635\pi\) | ||||
−0.822882 | + | 0.568212i | \(0.807635\pi\) | |||||||
\(44\) | − 3.32565i | − 0.501361i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.69764 | −0.692629 | ||||||||
\(47\) | 0.412881 | 0.0602249 | 0.0301125 | − | 0.999547i | \(-0.490413\pi\) | ||||
0.0301125 | + | 0.999547i | \(0.490413\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 2.16373i | − 0.305998i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.34518i | 0.602568i | ||||||||
\(53\) | 9.09436i | 1.24921i | 0.780942 | + | 0.624603i | \(0.214739\pi\) | ||||
−0.780942 | + | 0.624603i | \(0.785261\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 5.60081i | − 0.755213i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.50277 | 0.328630 | ||||||||
\(59\) | −12.0887 | −1.57381 | −0.786907 | − | 0.617071i | \(-0.788319\pi\) | ||||
−0.786907 | + | 0.617071i | \(0.788319\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.9166i | 1.78184i | 0.454162 | + | 0.890919i | \(0.349939\pi\) | ||||
−0.454162 | + | 0.890919i | \(0.650061\pi\) | |||||||
\(62\) | 4.09593 | 0.520184 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 7.31781i | 0.907663i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.94993 | −0.726900 | −0.363450 | − | 0.931614i | \(-0.618401\pi\) | ||||
−0.363450 | + | 0.931614i | \(0.618401\pi\) | |||||||
\(68\) | −3.81123 | −0.462179 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.94028i | 0.586303i | 0.956066 | + | 0.293152i | \(0.0947041\pi\) | ||||
−0.956066 | + | 0.293152i | \(0.905296\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.78542i | − 0.677132i | −0.940943 | − | 0.338566i | \(-0.890058\pi\) | ||||
0.940943 | − | 0.338566i | \(-0.109942\pi\) | |||||||
\(74\) | 6.27558i | 0.729522i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 4.06583i | − 0.466383i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9228 | −1.45393 | −0.726964 | − | 0.686676i | \(-0.759069\pi\) | ||||
−0.726964 | + | 0.686676i | \(0.759069\pi\) | |||||||
\(80\) | −1.68412 | −0.188291 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.46525i | 0.603536i | ||||||||
\(83\) | −6.04915 | −0.663981 | −0.331990 | − | 0.943283i | \(-0.607720\pi\) | ||||
−0.331990 | + | 0.943283i | \(0.607720\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.41857 | −0.696192 | ||||||||
\(86\) | − 10.7920i | − 1.16373i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.32565 | 0.354516 | ||||||||
\(89\) | −6.31400 | −0.669283 | −0.334642 | − | 0.942345i | \(-0.608615\pi\) | ||||
−0.334642 | + | 0.942345i | \(0.608615\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 4.69764i | − 0.489763i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.412881i | 0.0425854i | ||||||||
\(95\) | − 6.84736i | − 0.702524i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 11.6415i | − 1.18201i | −0.806667 | − | 0.591006i | \(-0.798731\pi\) | ||||
0.806667 | − | 0.591006i | \(-0.201269\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.16373 | 0.216373 | ||||||||
\(101\) | 6.89588 | 0.686166 | 0.343083 | − | 0.939305i | \(-0.388529\pi\) | ||||
0.343083 | + | 0.939305i | \(0.388529\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 4.65462i | − 0.458633i | −0.973352 | − | 0.229317i | \(-0.926351\pi\) | ||||
0.973352 | − | 0.229317i | \(-0.0736491\pi\) | |||||||
\(104\) | −4.34518 | −0.426080 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.09436 | −0.883323 | ||||||||
\(107\) | 13.1098i | 1.26737i | 0.773590 | + | 0.633687i | \(0.218459\pi\) | ||||
−0.773590 | + | 0.633687i | \(0.781541\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.7553 | −1.70065 | −0.850326 | − | 0.526257i | \(-0.823595\pi\) | ||||
−0.850326 | + | 0.526257i | \(0.823595\pi\) | |||||||
\(110\) | 5.60081 | 0.534016 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.3234i | 1.72372i | 0.507149 | + | 0.861858i | \(0.330699\pi\) | ||||
−0.507149 | + | 0.861858i | \(0.669301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 7.91140i | − 0.737742i | ||||||||
\(116\) | 2.50277i | 0.232377i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 12.0887i | − 1.11285i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0599765 | −0.00545241 | ||||||||
\(122\) | −13.9166 | −1.25995 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.09593i | 0.367826i | ||||||||
\(125\) | 12.0646 | 1.07909 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.6723 | −1.65690 | −0.828450 | − | 0.560064i | \(-0.810777\pi\) | ||||
−0.828450 | + | 0.560064i | \(0.810777\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.31781 | −0.641815 | ||||||||
\(131\) | −15.5954 | −1.36257 | −0.681287 | − | 0.732017i | \(-0.738579\pi\) | ||||
−0.681287 | + | 0.732017i | \(0.738579\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 5.94993i | − 0.513996i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 3.81123i | − 0.326810i | ||||||||
\(137\) | − 12.7650i | − 1.09058i | −0.838246 | − | 0.545292i | \(-0.816419\pi\) | ||||
0.838246 | − | 0.545292i | \(-0.183581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 13.0451i | − 1.10647i | −0.833024 | − | 0.553237i | \(-0.813392\pi\) | ||||
0.833024 | − | 0.553237i | \(-0.186608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.94028 | −0.414579 | ||||||||
\(143\) | 14.4506 | 1.20842 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.21498i | 0.350035i | ||||||||
\(146\) | 5.78542 | 0.478804 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.27558 | −0.515850 | ||||||||
\(149\) | 5.81360i | 0.476268i | 0.971232 | + | 0.238134i | \(0.0765358\pi\) | ||||
−0.971232 | + | 0.238134i | \(0.923464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.17302 | 0.339595 | 0.169798 | − | 0.985479i | \(-0.445689\pi\) | ||||
0.169798 | + | 0.985479i | \(0.445689\pi\) | |||||||
\(152\) | 4.06583 | 0.329783 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.89805i | 0.554065i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2201i | 0.895461i | 0.894169 | + | 0.447730i | \(0.147768\pi\) | ||||
−0.894169 | + | 0.447730i | \(0.852232\pi\) | |||||||
\(158\) | − 12.9228i | − 1.02808i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 1.68412i | − 0.133142i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0941 | 0.947283 | 0.473642 | − | 0.880718i | \(-0.342939\pi\) | ||||
0.473642 | + | 0.880718i | \(0.342939\pi\) | |||||||
\(164\) | −5.46525 | −0.426764 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 6.04915i | − 0.469505i | ||||||||
\(167\) | −7.76449 | −0.600834 | −0.300417 | − | 0.953808i | \(-0.597126\pi\) | ||||
−0.300417 | + | 0.953808i | \(0.597126\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.88056 | −0.452351 | ||||||||
\(170\) | − 6.41857i | − 0.492282i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.7920 | 0.822882 | ||||||||
\(173\) | −7.28069 | −0.553541 | −0.276770 | − | 0.960936i | \(-0.589264\pi\) | ||||
−0.276770 | + | 0.960936i | \(0.589264\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.32565i | 0.250681i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 6.31400i | − 0.473255i | ||||||||
\(179\) | 14.8165i | 1.10744i | 0.832704 | + | 0.553718i | \(0.186791\pi\) | ||||
−0.832704 | + | 0.553718i | \(0.813209\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9676i | 0.889547i | 0.895643 | + | 0.444773i | \(0.146716\pi\) | ||||
−0.895643 | + | 0.444773i | \(0.853284\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.69764 | 0.346315 | ||||||||
\(185\) | −10.5689 | −0.777038 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.6748i | 0.926875i | ||||||||
\(188\) | −0.412881 | −0.0301125 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.84736 | 0.496760 | ||||||||
\(191\) | − 3.07927i | − 0.222808i | −0.993775 | − | 0.111404i | \(-0.964465\pi\) | ||||
0.993775 | − | 0.111404i | \(-0.0355348\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.6569 | −1.34295 | −0.671475 | − | 0.741027i | \(-0.734339\pi\) | ||||
−0.671475 | + | 0.741027i | \(0.734339\pi\) | |||||||
\(194\) | 11.6415 | 0.835809 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 23.6108i | − 1.68220i | −0.540881 | − | 0.841099i | \(-0.681909\pi\) | ||||
0.540881 | − | 0.841099i | \(-0.318091\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.4496i | 1.09519i | 0.836743 | + | 0.547595i | \(0.184457\pi\) | ||||
−0.836743 | + | 0.547595i | \(0.815543\pi\) | |||||||
\(200\) | 2.16373i | 0.152999i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.89588i | 0.485193i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.20415 | −0.642846 | ||||||||
\(206\) | 4.65462 | 0.324303 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 4.34518i | − 0.301284i | ||||||||
\(209\) | −13.5216 | −0.935305 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.7399 | −0.945892 | −0.472946 | − | 0.881092i | \(-0.656809\pi\) | ||||
−0.472946 | + | 0.881092i | \(0.656809\pi\) | |||||||
\(212\) | − 9.09436i | − 0.624603i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.1098 | −0.896168 | ||||||||
\(215\) | 18.1751 | 1.23953 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 17.7553i | − 1.20254i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.60081i | 0.377607i | ||||||||
\(221\) | − 16.5605i | − 1.11398i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.65684i | 0.311845i | 0.987769 | + | 0.155923i | \(0.0498350\pi\) | ||||
−0.987769 | + | 0.155923i | \(0.950165\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.3234 | −1.21885 | ||||||||
\(227\) | 27.6540 | 1.83546 | 0.917729 | − | 0.397207i | \(-0.130020\pi\) | ||||
0.917729 | + | 0.397207i | \(0.130020\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6394i | 0.835232i | 0.908624 | + | 0.417616i | \(0.137134\pi\) | ||||
−0.908624 | + | 0.417616i | \(0.862866\pi\) | |||||||
\(230\) | 7.91140 | 0.521662 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.50277 | −0.164315 | ||||||||
\(233\) | − 4.67061i | − 0.305982i | −0.988228 | − | 0.152991i | \(-0.951110\pi\) | ||||
0.988228 | − | 0.152991i | \(-0.0488905\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.695343 | −0.0453592 | ||||||||
\(236\) | 12.0887 | 0.786907 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.7883i | 1.53873i | 0.638807 | + | 0.769367i | \(0.279428\pi\) | ||||
−0.638807 | + | 0.769367i | \(0.720572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 2.77410i | − 0.178695i | −0.996001 | − | 0.0893476i | \(-0.971522\pi\) | ||||
0.996001 | − | 0.0893476i | \(-0.0284782\pi\) | |||||||
\(242\) | − 0.0599765i | − 0.00385544i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 13.9166i | − 0.890919i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.6668 | 1.12411 | ||||||||
\(248\) | −4.09593 | −0.260092 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0646i | 0.763032i | ||||||||
\(251\) | −23.2943 | −1.47032 | −0.735162 | − | 0.677892i | \(-0.762894\pi\) | ||||
−0.735162 | + | 0.677892i | \(0.762894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.6227 | −0.982192 | ||||||||
\(254\) | − 18.6723i | − 1.17160i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −31.1100 | −1.94059 | −0.970296 | − | 0.241923i | \(-0.922222\pi\) | ||||
−0.970296 | + | 0.241923i | \(0.922222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 7.31781i | − 0.453831i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 15.5954i | − 0.963485i | ||||||||
\(263\) | 11.1363i | 0.686696i | 0.939208 | + | 0.343348i | \(0.111561\pi\) | ||||
−0.939208 | + | 0.343348i | \(0.888439\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 15.3160i | − 0.940856i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.94993 | 0.363450 | ||||||||
\(269\) | 30.5496 | 1.86264 | 0.931320 | − | 0.364201i | \(-0.118658\pi\) | ||||
0.931320 | + | 0.364201i | \(0.118658\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 15.8834i | − 0.964848i | −0.875938 | − | 0.482424i | \(-0.839756\pi\) | ||||
0.875938 | − | 0.482424i | \(-0.160244\pi\) | |||||||
\(272\) | 3.81123 | 0.231090 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.7650 | 0.771160 | ||||||||
\(275\) | − 7.19582i | − 0.433924i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.6470 | 1.66115 | 0.830573 | − | 0.556910i | \(-0.188013\pi\) | ||||
0.830573 | + | 0.556910i | \(0.188013\pi\) | |||||||
\(278\) | 13.0451 | 0.782395 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 13.2618i | − 0.791135i | −0.918437 | − | 0.395567i | \(-0.870548\pi\) | ||||
0.918437 | − | 0.395567i | \(-0.129452\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 25.4310i | − 1.51172i | −0.654735 | − | 0.755858i | \(-0.727220\pi\) | ||||
0.654735 | − | 0.755858i | \(-0.272780\pi\) | |||||||
\(284\) | − 4.94028i | − 0.293152i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.4506i | 0.854479i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.47455 | −0.145562 | ||||||||
\(290\) | −4.21498 | −0.247512 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.78542i | 0.338566i | ||||||||
\(293\) | −4.40649 | −0.257430 | −0.128715 | − | 0.991682i | \(-0.541085\pi\) | ||||
−0.128715 | + | 0.991682i | \(0.541085\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.3589 | 1.18534 | ||||||||
\(296\) | − 6.27558i | − 0.364761i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.81360 | −0.336773 | ||||||||
\(299\) | 20.4121 | 1.18046 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.17302i | 0.240130i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.06583i | 0.233191i | ||||||||
\(305\) | − 23.4373i | − 1.34201i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.72649i | 0.0985362i | 0.998786 | + | 0.0492681i | \(0.0156889\pi\) | ||||
−0.998786 | + | 0.0492681i | \(0.984311\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.89805 | −0.391783 | ||||||||
\(311\) | −13.0155 | −0.738040 | −0.369020 | − | 0.929421i | \(-0.620307\pi\) | ||||
−0.369020 | + | 0.929421i | \(0.620307\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.91566i | 0.164803i | 0.996599 | + | 0.0824014i | \(0.0262590\pi\) | ||||
−0.996599 | + | 0.0824014i | \(0.973741\pi\) | |||||||
\(314\) | −11.2201 | −0.633186 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12.9228 | 0.726964 | ||||||||
\(317\) | 28.3391i | 1.59168i | 0.605507 | + | 0.795840i | \(0.292971\pi\) | ||||
−0.605507 | + | 0.795840i | \(0.707029\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.32336 | 0.466019 | ||||||||
\(320\) | 1.68412 | 0.0941453 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.4958i | 0.862210i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.40179i | 0.521517i | ||||||||
\(326\) | 12.0941i | 0.669831i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 5.46525i | − 0.301768i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.60934 | 0.418247 | 0.209124 | − | 0.977889i | \(-0.432939\pi\) | ||||
0.209124 | + | 0.977889i | \(0.432939\pi\) | |||||||
\(332\) | 6.04915 | 0.331990 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 7.76449i | − 0.424854i | ||||||||
\(335\) | 10.0204 | 0.547474 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.4203 | 1.71157 | 0.855786 | − | 0.517331i | \(-0.173074\pi\) | ||||
0.855786 | + | 0.517331i | \(0.173074\pi\) | |||||||
\(338\) | − 5.88056i | − 0.319860i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.41857 | 0.348096 | ||||||||
\(341\) | 13.6217 | 0.737654 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.7920i | 0.581866i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 7.28069i | − 0.391412i | ||||||||
\(347\) | − 13.8398i | − 0.742958i | −0.928441 | − | 0.371479i | \(-0.878851\pi\) | ||||
0.928441 | − | 0.371479i | \(-0.121149\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.6085i | 1.10315i | 0.834126 | + | 0.551574i | \(0.185973\pi\) | ||||
−0.834126 | + | 0.551574i | \(0.814027\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.32565 | −0.177258 | ||||||||
\(353\) | 21.5019 | 1.14443 | 0.572214 | − | 0.820104i | \(-0.306085\pi\) | ||||
0.572214 | + | 0.820104i | \(0.306085\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 8.32004i | − 0.441582i | ||||||||
\(356\) | 6.31400 | 0.334642 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.8165 | −0.783075 | ||||||||
\(359\) | 25.9574i | 1.36998i | 0.728552 | + | 0.684990i | \(0.240194\pi\) | ||||
−0.728552 | + | 0.684990i | \(0.759806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.46901 | 0.129948 | ||||||||
\(362\) | −11.9676 | −0.629005 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.74335i | 0.509990i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 7.42133i | − 0.387390i | −0.981062 | − | 0.193695i | \(-0.937953\pi\) | ||||
0.981062 | − | 0.193695i | \(-0.0620473\pi\) | |||||||
\(368\) | 4.69764i | 0.244881i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 10.5689i | − 0.549449i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.97671 | −0.361240 | −0.180620 | − | 0.983553i | \(-0.557810\pi\) | ||||
−0.180620 | + | 0.983553i | \(0.557810\pi\) | |||||||
\(374\) | −12.6748 | −0.655399 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 0.412881i | − 0.0212927i | ||||||||
\(377\) | −10.8750 | −0.560090 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.68980 | 0.394998 | 0.197499 | − | 0.980303i | \(-0.436718\pi\) | ||||
0.197499 | + | 0.980303i | \(0.436718\pi\) | |||||||
\(380\) | 6.84736i | 0.351262i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.07927 | 0.157549 | ||||||||
\(383\) | −7.15314 | −0.365509 | −0.182754 | − | 0.983159i | \(-0.558501\pi\) | ||||
−0.182754 | + | 0.983159i | \(0.558501\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 18.6569i | − 0.949609i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.6415i | 0.591006i | ||||||||
\(389\) | 6.21550i | 0.315138i | 0.987508 | + | 0.157569i | \(0.0503657\pi\) | ||||
−0.987508 | + | 0.157569i | \(0.949634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.9038i | 0.905432i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 23.6108 | 1.18949 | ||||||||
\(395\) | 21.7636 | 1.09504 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 15.8118i | − 0.793574i | −0.917911 | − | 0.396787i | \(-0.870125\pi\) | ||||
0.917911 | − | 0.396787i | \(-0.129875\pi\) | |||||||
\(398\) | −15.4496 | −0.774416 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.16373 | −0.108187 | ||||||||
\(401\) | − 13.7471i | − 0.686498i | −0.939244 | − | 0.343249i | \(-0.888473\pi\) | ||||
0.939244 | − | 0.343249i | \(-0.111527\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.7975 | −0.886559 | ||||||||
\(404\) | −6.89588 | −0.343083 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.8704i | 1.03451i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.3972i | 0.761342i | 0.924711 | + | 0.380671i | \(0.124307\pi\) | ||||
−0.924711 | + | 0.380671i | \(0.875693\pi\) | |||||||
\(410\) | − 9.20415i | − 0.454561i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.65462i | 0.229317i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.1875 | 0.500085 | ||||||||
\(416\) | 4.34518 | 0.213040 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 13.5216i | − 0.661361i | ||||||||
\(419\) | 3.80384 | 0.185830 | 0.0929149 | − | 0.995674i | \(-0.470382\pi\) | ||||
0.0929149 | + | 0.995674i | \(0.470382\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.2583 | 0.987332 | 0.493666 | − | 0.869652i | \(-0.335657\pi\) | ||||
0.493666 | + | 0.869652i | \(0.335657\pi\) | |||||||
\(422\) | − 13.7399i | − 0.668846i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.09436 | 0.441661 | ||||||||
\(425\) | −8.24647 | −0.400012 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 13.1098i | − 0.633687i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 18.1751i | 0.876479i | ||||||||
\(431\) | 11.3141i | 0.544980i | 0.962159 | + | 0.272490i | \(0.0878471\pi\) | ||||
−0.962159 | + | 0.272490i | \(0.912153\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.3925i | 0.883885i | 0.897043 | + | 0.441943i | \(0.145710\pi\) | ||||
−0.897043 | + | 0.441943i | \(0.854290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.7553 | 0.850326 | ||||||||
\(437\) | −19.0998 | −0.913668 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 3.97200i | − 0.189573i | −0.995498 | − | 0.0947866i | \(-0.969783\pi\) | ||||
0.995498 | − | 0.0947866i | \(-0.0302169\pi\) | |||||||
\(440\) | −5.60081 | −0.267008 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.5605 | 0.787700 | ||||||||
\(443\) | − 24.5779i | − 1.16773i | −0.811850 | − | 0.583867i | \(-0.801539\pi\) | ||||
0.811850 | − | 0.583867i | \(-0.198461\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.6336 | 0.504079 | ||||||||
\(446\) | −4.65684 | −0.220508 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 19.7867i | − 0.933793i | −0.884312 | − | 0.466896i | \(-0.845372\pi\) | ||||
0.884312 | − | 0.466896i | \(-0.154628\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.1755i | 0.855852i | ||||||||
\(452\) | − 18.3234i | − 0.861858i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.6540i | 1.29786i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.24264 | 0.151684 | 0.0758422 | − | 0.997120i | \(-0.475835\pi\) | ||||
0.0758422 | + | 0.997120i | \(0.475835\pi\) | |||||||
\(458\) | −12.6394 | −0.590599 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.91140i | 0.368871i | ||||||||
\(461\) | 12.9170 | 0.601603 | 0.300801 | − | 0.953687i | \(-0.402746\pi\) | ||||
0.300801 | + | 0.953687i | \(0.402746\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.9016 | 1.20375 | 0.601874 | − | 0.798591i | \(-0.294421\pi\) | ||||
0.601874 | + | 0.798591i | \(0.294421\pi\) | |||||||
\(464\) | − 2.50277i | − 0.116188i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.67061 | 0.216362 | ||||||||
\(467\) | −7.30432 | −0.338004 | −0.169002 | − | 0.985616i | \(-0.554054\pi\) | ||||
−0.169002 | + | 0.985616i | \(0.554054\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 0.695343i | − 0.0320738i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.0887i | 0.556427i | ||||||||
\(473\) | − 35.8905i | − 1.65025i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 8.79736i | − 0.403651i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −23.7883 | −1.08805 | ||||||||
\(479\) | −15.0285 | −0.686668 | −0.343334 | − | 0.939213i | \(-0.611556\pi\) | ||||
−0.343334 | + | 0.939213i | \(0.611556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 27.2685i | − 1.24334i | ||||||||
\(482\) | 2.77410 | 0.126357 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0599765 | 0.00272620 | ||||||||
\(485\) | 19.6057i | 0.890248i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.14335 | 0.369011 | 0.184505 | − | 0.982832i | \(-0.440932\pi\) | ||||
0.184505 | + | 0.982832i | \(0.440932\pi\) | |||||||
\(488\) | 13.9166 | 0.629975 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.6719i | 1.20369i | 0.798614 | + | 0.601844i | \(0.205567\pi\) | ||||
−0.798614 | + | 0.601844i | \(0.794433\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 9.53863i | − 0.429598i | ||||||||
\(494\) | 17.6668i | 0.794865i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 4.09593i | − 0.183913i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.5456 | −1.41218 | −0.706088 | − | 0.708124i | \(-0.749542\pi\) | ||||
−0.706088 | + | 0.708124i | \(0.749542\pi\) | |||||||
\(500\) | −12.0646 | −0.539545 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 23.2943i | − 1.03968i | ||||||||
\(503\) | −9.08274 | −0.404979 | −0.202490 | − | 0.979284i | \(-0.564903\pi\) | ||||
−0.202490 | + | 0.979284i | \(0.564903\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.6135 | −0.516795 | ||||||||
\(506\) | − 15.6227i | − 0.694515i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 18.6723 | 0.828450 | ||||||||
\(509\) | −41.2308 | −1.82752 | −0.913762 | − | 0.406249i | \(-0.866836\pi\) | ||||
−0.913762 | + | 0.406249i | \(0.866836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 31.1100i | − 1.37221i | ||||||||
\(515\) | 7.83895i | 0.345426i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.37310i | 0.0603889i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.31781 | 0.320907 | ||||||||
\(521\) | −24.4010 | −1.06903 | −0.534513 | − | 0.845160i | \(-0.679505\pi\) | ||||
−0.534513 | + | 0.845160i | \(0.679505\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.4857i | 0.677141i | 0.940941 | + | 0.338570i | \(0.109943\pi\) | ||||
−0.940941 | + | 0.338570i | \(0.890057\pi\) | |||||||
\(524\) | 15.5954 | 0.681287 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.1363 | −0.485567 | ||||||||
\(527\) | − 15.6105i | − 0.680005i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.932181 | 0.0405296 | ||||||||
\(530\) | 15.3160 | 0.665286 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 23.7475i | − 1.02862i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 22.0785i | − 0.954538i | ||||||||
\(536\) | 5.94993i | 0.256998i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30.5496i | 1.31709i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.12150 | −0.349171 | −0.174585 | − | 0.984642i | \(-0.555858\pi\) | ||||
−0.174585 | + | 0.984642i | \(0.555858\pi\) | |||||||
\(542\) | 15.8834 | 0.682251 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.81123i | 0.163405i | ||||||||
\(545\) | 29.9021 | 1.28087 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.1593 | 1.24676 | 0.623381 | − | 0.781919i | \(-0.285759\pi\) | ||||
0.623381 | + | 0.781919i | \(0.285759\pi\) | |||||||
\(548\) | 12.7650i | 0.545292i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.19582 | 0.306831 | ||||||||
\(551\) | 10.1759 | 0.433506 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 27.6470i | 1.17461i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.0451i | 0.553237i | ||||||||
\(557\) | 33.5006i | 1.41947i | 0.704470 | + | 0.709734i | \(0.251185\pi\) | ||||
−0.704470 | + | 0.709734i | \(0.748815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.8932i | 1.98337i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.2618 | 0.559417 | ||||||||
\(563\) | −36.7289 | −1.54794 | −0.773970 | − | 0.633222i | \(-0.781732\pi\) | ||||
−0.773970 | + | 0.633222i | \(0.781732\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 30.8588i | − 1.29824i | ||||||||
\(566\) | 25.4310 | 1.06894 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.94028 | 0.207290 | ||||||||
\(569\) | 5.10811i | 0.214143i | 0.994251 | + | 0.107072i | \(0.0341474\pi\) | ||||
−0.994251 | + | 0.107072i | \(0.965853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0982 | 1.67806 | 0.839029 | − | 0.544086i | \(-0.183124\pi\) | ||||
0.839029 | + | 0.544086i | \(0.183124\pi\) | |||||||
\(572\) | −14.4506 | −0.604208 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 10.1644i | − 0.423886i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.0600i | 0.960001i | 0.877268 | + | 0.480001i | \(0.159364\pi\) | ||||
−0.877268 | + | 0.480001i | \(0.840636\pi\) | |||||||
\(578\) | − 2.47455i | − 0.102928i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 4.21498i | − 0.175017i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.2447 | −1.25261 | ||||||||
\(584\) | −5.78542 | −0.239402 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 4.40649i | − 0.182031i | ||||||||
\(587\) | −5.62333 | −0.232100 | −0.116050 | − | 0.993243i | \(-0.537023\pi\) | ||||
−0.116050 | + | 0.993243i | \(0.537023\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.6534 | 0.686190 | ||||||||
\(590\) | 20.3589i | 0.838161i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.27558 | 0.257925 | ||||||||
\(593\) | 11.9230 | 0.489621 | 0.244810 | − | 0.969571i | \(-0.421274\pi\) | ||||
0.244810 | + | 0.969571i | \(0.421274\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 5.81360i | − 0.238134i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 20.4121i | 0.834712i | ||||||||
\(599\) | 5.73868i | 0.234476i | 0.993104 | + | 0.117238i | \(0.0374041\pi\) | ||||
−0.993104 | + | 0.117238i | \(0.962596\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 42.3941i | − 1.72929i | −0.502382 | − | 0.864646i | \(-0.667543\pi\) | ||||
0.502382 | − | 0.864646i | \(-0.332457\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.17302 | −0.169798 | ||||||||
\(605\) | 0.101008 | 0.00410655 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 7.60327i | − 0.308607i | −0.988023 | − | 0.154304i | \(-0.950687\pi\) | ||||
0.988023 | − | 0.154304i | \(-0.0493134\pi\) | |||||||
\(608\) | −4.06583 | −0.164891 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 23.4373 | 0.948947 | ||||||||
\(611\) | − 1.79404i | − 0.0725792i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.9823 | 1.21097 | 0.605486 | − | 0.795856i | \(-0.292979\pi\) | ||||
0.605486 | + | 0.795856i | \(0.292979\pi\) | |||||||
\(614\) | −1.72649 | −0.0696756 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 12.6950i | − 0.511081i | −0.966798 | − | 0.255540i | \(-0.917747\pi\) | ||||
0.966798 | − | 0.255540i | \(-0.0822534\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.36054i | 0.0948783i | 0.998874 | + | 0.0474391i | \(0.0151060\pi\) | ||||
−0.998874 | + | 0.0474391i | \(0.984894\pi\) | |||||||
\(620\) | − 6.89805i | − 0.277032i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 13.0155i | − 0.521873i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.49962 | −0.379985 | ||||||||
\(626\) | −2.91566 | −0.116533 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 11.2201i | − 0.447730i | ||||||||
\(629\) | 23.9177 | 0.953660 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.1986 | 1.67990 | 0.839950 | − | 0.542663i | \(-0.182584\pi\) | ||||
0.839950 | + | 0.542663i | \(0.182584\pi\) | |||||||
\(632\) | 12.9228i | 0.514041i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −28.3391 | −1.12549 | ||||||||
\(635\) | 31.4465 | 1.24791 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.32336i | 0.329525i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.68412i | 0.0665708i | ||||||||
\(641\) | 4.40611i | 0.174031i | 0.996207 | + | 0.0870155i | \(0.0277330\pi\) | ||||
−0.996207 | + | 0.0870155i | \(0.972267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.9171i | 0.430529i | 0.976556 | + | 0.215264i | \(0.0690613\pi\) | ||||
−0.976556 | + | 0.215264i | \(0.930939\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.4958 | −0.609674 | ||||||||
\(647\) | 4.73821 | 0.186278 | 0.0931390 | − | 0.995653i | \(-0.470310\pi\) | ||||
0.0931390 | + | 0.995653i | \(0.470310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 40.2028i | − 1.57810i | ||||||||
\(650\) | −9.40179 | −0.368769 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.0941 | −0.473642 | ||||||||
\(653\) | 14.2119i | 0.556153i | 0.960559 | + | 0.278077i | \(0.0896969\pi\) | ||||
−0.960559 | + | 0.278077i | \(0.910303\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.2645 | 1.02624 | ||||||||
\(656\) | 5.46525 | 0.213382 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.5374i | 0.527343i | 0.964613 | + | 0.263671i | \(0.0849335\pi\) | ||||
−0.964613 | + | 0.263671i | \(0.915067\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 0.345298i | − 0.0134305i | −0.999977 | − | 0.00671526i | \(-0.997862\pi\) | ||||
0.999977 | − | 0.00671526i | \(-0.00213755\pi\) | |||||||
\(662\) | 7.60934i | 0.295745i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.04915i | 0.234753i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.7571 | 0.455238 | ||||||||
\(668\) | 7.76449 | 0.300417 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.0204i | 0.387122i | ||||||||
\(671\) | −46.2818 | −1.78669 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.4060 | 0.632405 | 0.316203 | − | 0.948692i | \(-0.397592\pi\) | ||||
0.316203 | + | 0.948692i | \(0.397592\pi\) | |||||||
\(674\) | 31.4203i | 1.21026i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.88056 | 0.226175 | ||||||||
\(677\) | −25.0364 | −0.962228 | −0.481114 | − | 0.876658i | \(-0.659768\pi\) | ||||
−0.481114 | + | 0.876658i | \(0.659768\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.41857i | 0.246141i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.6217i | 0.521600i | ||||||||
\(683\) | 29.5011i | 1.12883i | 0.825492 | + | 0.564414i | \(0.190898\pi\) | ||||
−0.825492 | + | 0.564414i | \(0.809102\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.4978i | 0.821388i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −10.7920 | −0.411441 | ||||||||
\(689\) | 39.5166 | 1.50546 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 22.7916i | − 0.867032i | −0.901146 | − | 0.433516i | \(-0.857273\pi\) | ||||
0.901146 | − | 0.433516i | \(-0.142727\pi\) | |||||||
\(692\) | 7.28069 | 0.276770 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.8398 | 0.525351 | ||||||||
\(695\) | 21.9696i | 0.833355i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.8293 | 0.788966 | ||||||||
\(698\) | −20.6085 | −0.780043 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 31.6849i | − 1.19672i | −0.801227 | − | 0.598361i | \(-0.795819\pi\) | ||||
0.801227 | − | 0.598361i | \(-0.204181\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.5155i | 0.962334i | ||||||||
\(704\) | − 3.32565i | − 0.125340i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.5019i | 0.809233i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.9692 | −0.487070 | −0.243535 | − | 0.969892i | \(-0.578307\pi\) | ||||
−0.243535 | + | 0.969892i | \(0.578307\pi\) | |||||||
\(710\) | 8.32004 | 0.312246 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.31400i | 0.236627i | ||||||||
\(713\) | 19.2412 | 0.720589 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.3365 | −0.910134 | ||||||||
\(716\) | − 14.8165i | − 0.553718i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −25.9574 | −0.968723 | ||||||||
\(719\) | −18.5782 | −0.692849 | −0.346424 | − | 0.938078i | \(-0.612604\pi\) | ||||
−0.346424 | + | 0.938078i | \(0.612604\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.46901i | 0.0918870i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 11.9676i | − 0.444773i | ||||||||
\(725\) | 5.41532i | 0.201120i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 35.5818i | − 1.31966i | −0.751416 | − | 0.659828i | \(-0.770629\pi\) | ||||
0.751416 | − | 0.659828i | \(-0.229371\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.74335 | −0.360618 | ||||||||
\(731\) | −41.1308 | −1.52128 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 42.4329i | 1.56729i | 0.621206 | + | 0.783647i | \(0.286643\pi\) | ||||
−0.621206 | + | 0.783647i | \(0.713357\pi\) | |||||||
\(734\) | 7.42133 | 0.273926 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.69764 | −0.173157 | ||||||||
\(737\) | − 19.7874i | − 0.728879i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.3081 | −0.930972 | −0.465486 | − | 0.885055i | \(-0.654120\pi\) | ||||
−0.465486 | + | 0.885055i | \(0.654120\pi\) | |||||||
\(740\) | 10.5689 | 0.388519 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.1867i | 1.21750i | 0.793362 | + | 0.608751i | \(0.208329\pi\) | ||||
−0.793362 | + | 0.608751i | \(0.791671\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 9.79081i | − 0.358708i | ||||||||
\(746\) | − 6.97671i | − 0.255435i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 12.6748i | − 0.463437i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.1858 | 0.444666 | 0.222333 | − | 0.974971i | \(-0.428633\pi\) | ||||
0.222333 | + | 0.974971i | \(0.428633\pi\) | |||||||
\(752\) | 0.412881 | 0.0150562 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 10.8750i | − 0.396044i | ||||||||
\(755\) | −7.02787 | −0.255770 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.64439 | −0.350531 | −0.175266 | − | 0.984521i | \(-0.556078\pi\) | ||||
−0.175266 | + | 0.984521i | \(0.556078\pi\) | |||||||
\(758\) | 7.68980i | 0.279306i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.84736 | −0.248380 | ||||||||
\(761\) | 15.8333 | 0.573955 | 0.286978 | − | 0.957937i | \(-0.407349\pi\) | ||||
0.286978 | + | 0.957937i | \(0.407349\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.07927i | 0.111404i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 7.15314i | − 0.258454i | ||||||||
\(767\) | 52.5275i | 1.89666i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.1428i | 1.15910i | 0.814938 | + | 0.579549i | \(0.196771\pi\) | ||||
−0.814938 | + | 0.579549i | \(0.803229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.6569 | 0.671475 | ||||||||
\(773\) | 11.4606 | 0.412211 | 0.206105 | − | 0.978530i | \(-0.433921\pi\) | ||||
0.206105 | + | 0.978530i | \(0.433921\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.86249i | 0.318350i | ||||||||
\(776\) | −11.6415 | −0.417905 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.21550 | −0.222836 | ||||||||
\(779\) | 22.2208i | 0.796142i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.4297 | −0.587900 | ||||||||
\(782\) | −17.9038 | −0.640237 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 18.8960i | − 0.674428i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 54.3428i | 1.93711i | 0.248794 | + | 0.968557i | \(0.419966\pi\) | ||||
−0.248794 | + | 0.968557i | \(0.580034\pi\) | |||||||
\(788\) | 23.6108i | 0.841099i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.7636i | 0.774313i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 60.4701 | 2.14736 | ||||||||
\(794\) | 15.8118 | 0.561141 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 15.4496i | − 0.547595i | ||||||||
\(797\) | 38.3049 | 1.35683 | 0.678415 | − | 0.734679i | \(-0.262667\pi\) | ||||
0.678415 | + | 0.734679i | \(0.262667\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.57358 | 0.0556694 | ||||||||
\(800\) | − 2.16373i | − 0.0764994i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.7471 | 0.485427 | ||||||||
\(803\) | 19.2403 | 0.678975 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 17.7975i | − 0.626892i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 6.89588i | − 0.242596i | ||||||||
\(809\) | − 31.0615i | − 1.09207i | −0.837764 | − | 0.546033i | \(-0.816137\pi\) | ||||
0.837764 | − | 0.546033i | \(-0.183863\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40.8494i | 1.43442i | 0.696860 | + | 0.717208i | \(0.254580\pi\) | ||||
−0.696860 | + | 0.717208i | \(0.745420\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.8704 | −0.731508 | ||||||||
\(815\) | −20.3680 | −0.713458 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 43.8785i | − 1.53511i | ||||||||
\(818\) | −15.3972 | −0.538350 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.20415 | 0.321423 | ||||||||
\(821\) | − 20.2714i | − 0.707476i | −0.935345 | − | 0.353738i | \(-0.884910\pi\) | ||||
0.935345 | − | 0.353738i | \(-0.115090\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.80986 | −0.0979454 | −0.0489727 | − | 0.998800i | \(-0.515595\pi\) | ||||
−0.0489727 | + | 0.998800i | \(0.515595\pi\) | |||||||
\(824\) | −4.65462 | −0.162151 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.7733i | 0.861453i | 0.902483 | + | 0.430726i | \(0.141743\pi\) | ||||
−0.902483 | + | 0.430726i | \(0.858257\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 52.8045i | − 1.83398i | −0.398914 | − | 0.916988i | \(-0.630613\pi\) | ||||
0.398914 | − | 0.916988i | \(-0.369387\pi\) | |||||||
\(830\) | 10.1875i | 0.353614i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.34518i | 0.150642i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.0764 | 0.452526 | ||||||||
\(836\) | 13.5216 | 0.467653 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.80384i | 0.131402i | ||||||||
\(839\) | −1.13410 | −0.0391536 | −0.0195768 | − | 0.999808i | \(-0.506232\pi\) | ||||
−0.0195768 | + | 0.999808i | \(0.506232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.7361 | 0.784004 | ||||||||
\(842\) | 20.2583i | 0.698149i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.7399 | 0.472946 | ||||||||
\(845\) | 9.90359 | 0.340694 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.09436i | 0.312302i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 8.24647i | − 0.282851i | ||||||||
\(851\) | 29.4804i | 1.01058i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 4.16705i | − 0.142677i | −0.997452 | − | 0.0713385i | \(-0.977273\pi\) | ||||
0.997452 | − | 0.0713385i | \(-0.0227271\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.1098 | 0.448084 | ||||||||
\(857\) | 19.5114 | 0.666498 | 0.333249 | − | 0.942839i | \(-0.391855\pi\) | ||||
0.333249 | + | 0.942839i | \(0.391855\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 31.6734i | − 1.08068i | −0.841445 | − | 0.540342i | \(-0.818295\pi\) | ||||
0.841445 | − | 0.540342i | \(-0.181705\pi\) | |||||||
\(860\) | −18.1751 | −0.619764 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.3141 | −0.385359 | ||||||||
\(863\) | − 26.6082i | − 0.905755i | −0.891573 | − | 0.452877i | \(-0.850398\pi\) | ||||
0.891573 | − | 0.452877i | \(-0.149602\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.2616 | 0.416906 | ||||||||
\(866\) | −18.3925 | −0.625001 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 42.9767i | − 1.45789i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.8535i | 0.876012i | ||||||||
\(872\) | 17.7553i | 0.601271i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 19.0998i | − 0.646061i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.5348 | −0.558339 | −0.279169 | − | 0.960242i | \(-0.590059\pi\) | ||||
−0.279169 | + | 0.960242i | \(0.590059\pi\) | |||||||
\(878\) | 3.97200 | 0.134049 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 5.60081i | − 0.188803i | ||||||||
\(881\) | 37.3162 | 1.25721 | 0.628607 | − | 0.777723i | \(-0.283625\pi\) | ||||
0.628607 | + | 0.777723i | \(0.283625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.2822 | −0.514287 | −0.257144 | − | 0.966373i | \(-0.582781\pi\) | ||||
−0.257144 | + | 0.966373i | \(0.582781\pi\) | |||||||
\(884\) | 16.5605i | 0.556988i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.5779 | 0.825712 | ||||||||
\(887\) | 52.7708 | 1.77187 | 0.885936 | − | 0.463808i | \(-0.153517\pi\) | ||||
0.885936 | + | 0.463808i | \(0.153517\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 10.6336i | 0.356438i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 4.65684i | − 0.155923i | ||||||||
\(893\) | 1.67871i | 0.0561757i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 24.9528i | − 0.834079i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.7867 | 0.660291 | ||||||||
\(899\) | −10.2512 | −0.341896 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.6607i | 1.15471i | ||||||||
\(902\) | −18.1755 | −0.605179 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.3234 | 0.609426 | ||||||||
\(905\) | − 20.1550i | − 0.669973i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.12346 | 0.170122 | 0.0850608 | − | 0.996376i | \(-0.472892\pi\) | ||||
0.0850608 | + | 0.996376i | \(0.472892\pi\) | |||||||
\(908\) | −27.6540 | −0.917729 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 56.0918i | − 1.85841i | −0.369571 | − | 0.929203i | \(-0.620495\pi\) | ||||
0.369571 | − | 0.929203i | \(-0.379505\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 20.1174i | − 0.665788i | ||||||||
\(914\) | 3.24264i | 0.107257i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 12.6394i | − 0.417616i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.3448 | −0.605141 | −0.302570 | − | 0.953127i | \(-0.597845\pi\) | ||||
−0.302570 | + | 0.953127i | \(0.597845\pi\) | |||||||
\(920\) | −7.91140 | −0.260831 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.9170i | 0.425397i | ||||||||
\(923\) | 21.4664 | 0.706575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.5787 | −0.446464 | ||||||||
\(926\) | 25.9016i | 0.851178i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.50277 | 0.0821575 | ||||||||
\(929\) | −7.51183 | −0.246455 | −0.123228 | − | 0.992378i | \(-0.539324\pi\) | ||||
−0.123228 | + | 0.992378i | \(0.539324\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.67061i | 0.152991i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 7.30432i | − 0.239005i | ||||||||
\(935\) | − 21.3460i | − 0.698087i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.8522i | 0.583207i | 0.956539 | + | 0.291603i | \(0.0941887\pi\) | ||||
−0.956539 | + | 0.291603i | \(0.905811\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.695343 | 0.0226796 | ||||||||
\(941\) | −47.7965 | −1.55812 | −0.779061 | − | 0.626949i | \(-0.784304\pi\) | ||||
−0.779061 | + | 0.626949i | \(0.784304\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.6738i | 0.836053i | ||||||||
\(944\) | −12.0887 | −0.393454 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35.8905 | 1.16690 | ||||||||
\(947\) | 29.3751i | 0.954563i | 0.878750 | + | 0.477282i | \(0.158378\pi\) | ||||
−0.878750 | + | 0.477282i | \(0.841622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.1387 | −0.816035 | ||||||||
\(950\) | 8.79736 | 0.285424 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 7.66147i | − 0.248179i | −0.992271 | − | 0.124090i | \(-0.960399\pi\) | ||||
0.992271 | − | 0.124090i | \(-0.0396011\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.18588i | 0.167811i | ||||||||
\(956\) | − 23.7883i | − 0.769367i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 15.0285i | − 0.485547i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.2233 | 0.458818 | ||||||||
\(962\) | 27.2685 | 0.879172 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.77410i | 0.0893476i | ||||||||
\(965\) | 31.4204 | 1.01146 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.64987 | −0.310319 | −0.155159 | − | 0.987889i | \(-0.549589\pi\) | ||||
−0.155159 | + | 0.987889i | \(0.549589\pi\) | |||||||
\(968\) | 0.0599765i | 0.00192772i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.6057 | −0.629500 | ||||||||
\(971\) | 53.0563 | 1.70266 | 0.851328 | − | 0.524633i | \(-0.175798\pi\) | ||||
0.851328 | + | 0.524633i | \(0.175798\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.14335i | 0.260930i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.9166i | 0.445460i | ||||||||
\(977\) | − 38.1550i | − 1.22069i | −0.792138 | − | 0.610343i | \(-0.791032\pi\) | ||||
0.792138 | − | 0.610343i | \(-0.208968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 20.9982i | − 0.671105i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −26.6719 | −0.851136 | ||||||||
\(983\) | −6.95322 | −0.221773 | −0.110887 | − | 0.993833i | \(-0.535369\pi\) | ||||
−0.110887 | + | 0.993833i | \(0.535369\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 39.7635i | 1.26697i | ||||||||
\(986\) | 9.53863 | 0.303772 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.6668 | −0.562055 | ||||||||
\(989\) | − 50.6969i | − 1.61207i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.9327 | −1.23674 | −0.618369 | − | 0.785888i | \(-0.712206\pi\) | ||||
−0.618369 | + | 0.785888i | \(0.712206\pi\) | |||||||
\(992\) | 4.09593 | 0.130046 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 26.0190i | − 0.824856i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 8.66626i | − 0.274463i | −0.990539 | − | 0.137232i | \(-0.956180\pi\) | ||||
0.990539 | − | 0.137232i | \(-0.0438204\pi\) | |||||||
\(998\) | − 31.5456i | − 0.998559i | ||||||||
\(999\) | 0 | 0 |
(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 | 2646.2.d.e.2645.11 | yes | 16 | |
3.2 | odd | 2 | inner | 2646.2.d.e.2645.6 | yes | 16 | |
7.6 | odd | 2 | inner | 2646.2.d.e.2645.14 | yes | 16 | |
21.20 | even | 2 | inner | 2646.2.d.e.2645.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2646.2.d.e.2645.3 | ✓ | 16 | 21.20 | even | 2 | inner | |
2646.2.d.e.2645.6 | yes | 16 | 3.2 | odd | 2 | inner | |
2646.2.d.e.2645.11 | yes | 16 | 1.1 | even | 1 | trivial | |
2646.2.d.e.2645.14 | yes | 16 | 7.6 | odd | 2 | inner |