Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [668,2,Mod(667,668)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(668, 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("668.667");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 668 = 2^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 668.b (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: | \(5.33400685502\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 667.4 | ||
Character | \(\chi\) | \(=\) | 668.667 |
Dual form | 668.2.b.a.667.3 |
$q$-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 \(\left(\mathbb{Z}/668\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(335\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.28464 | + | 0.591360i | −0.908376 | + | 0.418155i | ||||
\(3\) | 0.736748i | 0.425362i | 0.977122 | + | 0.212681i | \(0.0682195\pi\) | ||||
−0.977122 | + | 0.212681i | \(0.931781\pi\) | |||||||
\(4\) | 1.30059 | − | 1.51937i | 0.650294 | − | 0.759683i | ||||
\(5\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(6\) | −0.435683 | − | 0.946454i | −0.177867 | − | 0.386388i | ||||
\(7\) | 5.23983i | 1.98047i | 0.139411 | + | 0.990235i | \(0.455479\pi\) | ||||
−0.139411 | + | 0.990235i | \(0.544521\pi\) | |||||||
\(8\) | −0.772291 | + | 2.72095i | −0.273046 | + | 0.962001i | ||||
\(9\) | 2.45720 | 0.819067 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.06230i | 0.923317i | 0.887058 | + | 0.461659i | \(0.152746\pi\) | ||||
−0.887058 | + | 0.461659i | \(0.847254\pi\) | |||||||
\(12\) | 1.11939 | + | 0.958205i | 0.323140 | + | 0.276610i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −3.09862 | − | 6.73128i | −0.828142 | − | 1.79901i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.616947 | − | 3.95214i | −0.154237 | − | 0.988034i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | −3.15661 | + | 1.45309i | −0.744021 | + | 0.342497i | ||||
\(19\) | − | 8.39002i | − | 1.92480i | −0.271633 | − | 0.962401i | \(-0.587564\pi\) | ||
0.271633 | − | 0.962401i | \(-0.412436\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.86043 | −0.842416 | ||||||||
\(22\) | −1.81092 | − | 3.93394i | −0.386089 | − | 0.838719i | ||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | −2.00465 | − | 0.568984i | −0.409198 | − | 0.116143i | ||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.02058i | 0.773762i | ||||||||
\(28\) | 7.96122 | + | 6.81485i | 1.50453 | + | 1.28789i | ||||
\(29\) | −10.3057 | −1.91371 | −0.956857 | − | 0.290558i | \(-0.906159\pi\) | ||||
−0.956857 | + | 0.290558i | \(0.906159\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.9617i | 1.96878i | 0.175999 | + | 0.984390i | \(0.443684\pi\) | ||||
−0.175999 | + | 0.984390i | \(0.556316\pi\) | |||||||
\(32\) | 3.12969 | + | 4.71222i | 0.553256 | + | 0.833011i | ||||
\(33\) | −2.25614 | −0.392744 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.19581 | − | 3.73339i | 0.532634 | − | 0.622232i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 4.96152 | + | 10.7781i | 0.804865 | + | 1.74844i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 4.95926 | − | 2.28291i | 0.765230 | − | 0.352260i | ||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 4.65275 | + | 3.98278i | 0.701429 | + | 0.600427i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.40245i | 0.496299i | 0.968722 | + | 0.248150i | \(0.0798224\pi\) | ||||
−0.968722 | + | 0.248150i | \(0.920178\pi\) | |||||||
\(48\) | 2.91173 | − | 0.454534i | 0.420272 | − | 0.0656064i | ||||
\(49\) | −20.4558 | −2.92226 | ||||||||
\(50\) | −6.42319 | + | 2.95680i | −0.908376 | + | 0.418155i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −2.37761 | − | 5.16499i | −0.323552 | − | 0.702866i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −14.2573 | − | 4.04667i | −1.90521 | − | 0.540759i | ||||
\(57\) | 6.18133 | 0.818737 | ||||||||
\(58\) | 13.2390 | − | 6.09436i | 1.73837 | − | 0.800228i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.68676 | 0.984189 | 0.492094 | − | 0.870542i | \(-0.336231\pi\) | ||||
0.492094 | + | 0.870542i | \(0.336231\pi\) | |||||||
\(62\) | −6.48231 | − | 14.0818i | −0.823255 | − | 1.78839i | ||||
\(63\) | 12.8753i | 1.62214i | ||||||||
\(64\) | −6.80713 | − | 4.20273i | −0.850892 | − | 0.525341i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.89832 | − | 1.33419i | 0.356759 | − | 0.164228i | ||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −1.89767 | + | 6.68592i | −0.223643 | + | 0.787944i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.68374i | 0.425362i | ||||||||
\(76\) | −12.7475 | − | 10.9119i | −1.46224 | − | 1.25169i | ||||
\(77\) | −16.0459 | −1.82860 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.40945 | 0.489939 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −5.02083 | + | 5.86541i | −0.547818 | + | 0.639969i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 7.59268i | − | 0.814021i | ||||||
\(88\) | −8.33236 | − | 2.36498i | −0.888232 | − | 0.252108i | ||||
\(89\) | −14.4565 | −1.53238 | −0.766191 | − | 0.642613i | \(-0.777850\pi\) | ||||
−0.766191 | + | 0.642613i | \(0.777850\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.07602 | −0.837444 | ||||||||
\(94\) | −2.01208 | − | 4.37092i | −0.207530 | − | 0.450826i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.47172 | + | 2.30579i | −0.354331 | + | 0.235334i | ||||
\(97\) | 12.4499 | 1.26409 | 0.632047 | − | 0.774930i | \(-0.282215\pi\) | ||||
0.632047 | + | 0.774930i | \(0.282215\pi\) | |||||||
\(98\) | 26.2783 | − | 12.0967i | 2.65451 | − | 1.22196i | ||||
\(99\) | 7.52468i | 0.756259i | ||||||||
\(100\) | 6.50294 | − | 7.59683i | 0.650294 | − | 0.759683i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.46067i | 0.914597i | 0.889313 | + | 0.457299i | \(0.151183\pi\) | ||||
−0.889313 | + | 0.457299i | \(0.848817\pi\) | |||||||
\(108\) | 6.10874 | + | 5.22912i | 0.587814 | + | 0.503172i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 20.7085 | − | 3.23270i | 1.95677 | − | 0.305461i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | −7.94077 | + | 3.65539i | −0.743721 | + | 0.342359i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −13.4034 | + | 15.6581i | −1.24448 | + | 1.45382i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.62233 | 0.147485 | ||||||||
\(122\) | −9.87470 | + | 4.54564i | −0.894013 | + | 0.411543i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 16.6548 | + | 14.2567i | 1.49565 | + | 1.28029i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.61395 | − | 16.5401i | −0.678304 | − | 1.47351i | ||||
\(127\) | − | 21.3418i | − | 1.89378i | −0.321557 | − | 0.946890i | \(-0.604206\pi\) | ||
0.321557 | − | 0.946890i | \(-0.395794\pi\) | |||||||
\(128\) | 11.2300 | + | 1.37352i | 0.992603 | + | 0.121403i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −2.93431 | + | 3.42791i | −0.255399 | + | 0.298361i | ||||
\(133\) | 43.9623 | 3.81201 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.72297 | 0.830689 | 0.415345 | − | 0.909664i | \(-0.363661\pi\) | ||||
0.415345 | + | 0.909664i | \(0.363661\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.50675 | −0.211107 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.51596 | − | 9.71120i | −0.126330 | − | 0.809266i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 15.0708i | − | 1.24302i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | −2.17842 | − | 4.73227i | −0.177867 | − | 0.386388i | ||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 22.8288 | + | 6.47953i | 1.85166 | + | 0.525560i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 20.6132 | − | 9.48891i | 1.66106 | − | 0.764638i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.3755 | 1.38672 | 0.693358 | − | 0.720594i | \(-0.256131\pi\) | ||||
0.693358 | + | 0.720594i | \(0.256131\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.66454 | + | 2.60757i | −0.445049 | + | 0.204870i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.9228i | 1.00000i | ||||||||
\(168\) | 2.98138 | − | 10.5040i | 0.230018 | − | 0.810405i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 20.6160i | − | 1.57654i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.4911 | −1.63394 | −0.816970 | − | 0.576681i | \(-0.804348\pi\) | ||||
−0.816970 | + | 0.576681i | \(0.804348\pi\) | |||||||
\(174\) | 4.49001 | + | 9.75384i | 0.340387 | + | 0.739437i | ||||
\(175\) | 26.1991i | 1.98047i | ||||||||
\(176\) | 12.1026 | − | 1.88927i | 0.912269 | − | 0.142409i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 18.5713 | − | 8.54897i | 1.39198 | − | 0.640772i | ||||
\(179\) | − | 18.3651i | − | 1.37268i | −0.727283 | − | 0.686338i | \(-0.759217\pi\) | ||
0.727283 | − | 0.686338i | \(-0.240783\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6355 | 0.864862 | 0.432431 | − | 0.901667i | \(-0.357656\pi\) | ||||
0.432431 | + | 0.901667i | \(0.357656\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.66321i | 0.418636i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.3748 | − | 4.77583i | 0.760714 | − | 0.350181i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.16957 | + | 4.42519i | 0.377030 | + | 0.322740i | ||||
\(189\) | −21.0672 | −1.53241 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 23.4234i | − | 1.69486i | −0.530911 | − | 0.847428i | \(-0.678150\pi\) | ||
0.530911 | − | 0.847428i | \(-0.321850\pi\) | |||||||
\(192\) | 3.09635 | − | 5.01514i | 0.223460 | − | 0.361937i | ||||
\(193\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(194\) | −15.9936 | + | 7.36236i | −1.14827 | + | 0.528586i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −26.6046 | + | 31.0799i | −1.90033 | + | 2.21999i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | −4.44980 | − | 9.66649i | −0.316233 | − | 0.686968i | ||||
\(199\) | 2.96804i | 0.210398i | 0.994451 | + | 0.105199i | \(0.0335480\pi\) | ||||
−0.994451 | + | 0.105199i | \(0.966452\pi\) | |||||||
\(200\) | −3.86145 | + | 13.6047i | −0.273046 | + | 0.962001i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 53.9999i | − | 3.79005i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.6927 | 1.77720 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.23093i | − | 0.222426i | −0.993797 | − | 0.111213i | \(-0.964526\pi\) | ||
0.993797 | − | 0.111213i | \(-0.0354736\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.59466 | − | 12.1535i | −0.382443 | − | 0.830798i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.9398 | − | 3.10506i | −0.744359 | − | 0.211273i | ||||
\(217\) | −57.4375 | −3.89911 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 29.4068i | 1.96923i | 0.174744 | + | 0.984614i | \(0.444090\pi\) | ||||
−0.174744 | + | 0.984614i | \(0.555910\pi\) | |||||||
\(224\) | −24.6912 | + | 16.3990i | −1.64975 | + | 1.09571i | ||||
\(225\) | 12.2860 | 0.819067 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 8.03936 | − | 9.39170i | 0.532419 | − | 0.621981i | ||||
\(229\) | 27.9662 | 1.84806 | 0.924030 | − | 0.382319i | \(-0.124875\pi\) | ||||
0.924030 | + | 0.382319i | \(0.124875\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 11.8218i | − | 0.777817i | ||||||
\(232\) | 7.95897 | − | 28.0412i | 0.522532 | − | 1.84100i | ||||
\(233\) | −0.740976 | −0.0485430 | −0.0242715 | − | 0.999705i | \(-0.507727\pi\) | ||||
−0.0242715 | + | 0.999705i | \(0.507727\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 30.8803i | − | 1.99748i | −0.0501540 | − | 0.998741i | \(-0.515971\pi\) | ||
0.0501540 | − | 0.998741i | \(-0.484029\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −2.08411 | + | 0.959383i | −0.133972 | + | 0.0616715i | ||||
\(243\) | 15.3104i | 0.982163i | ||||||||
\(244\) | 9.99730 | − | 11.6790i | 0.640012 | − | 0.747672i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −29.8263 | − | 8.46563i | −1.89397 | − | 0.537568i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.9783i | 1.38726i | 0.720332 | + | 0.693629i | \(0.243989\pi\) | ||||
−0.720332 | + | 0.693629i | \(0.756011\pi\) | |||||||
\(252\) | 19.5623 | + | 16.7455i | 1.23231 | + | 1.05487i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 12.6207 | + | 27.4165i | 0.791893 | + | 1.72026i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.2388 | + | 4.87651i | −0.952422 | + | 0.304782i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −25.3231 | −1.56746 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.4598i | 1.63158i | 0.578345 | + | 0.815792i | \(0.303699\pi\) | ||||
−0.578345 | + | 0.815792i | \(0.696301\pi\) | |||||||
\(264\) | 1.74240 | − | 6.13885i | 0.107237 | − | 0.377820i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −56.4756 | + | 25.9975i | −3.46274 | + | 1.59401i | ||||
\(267\) | − | 10.6508i | − | 0.651816i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.4905 | + | 5.74977i | −0.754578 | + | 0.347357i | ||||
\(275\) | 15.3115i | 0.923317i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 26.9351i | 1.61256i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.1617 | 1.56068 | 0.780339 | − | 0.625357i | \(-0.215047\pi\) | ||||
0.780339 | + | 0.625357i | \(0.215047\pi\) | |||||||
\(282\) | 3.22027 | − | 1.48239i | 0.191764 | − | 0.0882752i | ||||
\(283\) | − | 33.4968i | − | 1.99118i | −0.0938371 | − | 0.995588i | \(-0.529913\pi\) | ||
0.0938371 | − | 0.995588i | \(-0.470087\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.69027 | + | 11.5789i | 0.453154 | + | 0.682292i | ||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.17242i | 0.537697i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.0903 | 1.75790 | 0.878948 | − | 0.476918i | \(-0.158246\pi\) | ||||
0.878948 | + | 0.476918i | \(0.158246\pi\) | |||||||
\(294\) | 8.91225 | + | 19.3605i | 0.519773 | + | 1.12913i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.3122 | −0.714428 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.59695 | + | 4.79103i | 0.323140 | + | 0.276610i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −33.1585 | + | 5.17619i | −1.90177 | + | 0.296875i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | −20.8691 | + | 24.3796i | −1.18913 | + | 1.38916i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.8457i | 1.46557i | 0.680458 | + | 0.732787i | \(0.261781\pi\) | ||||
−0.680458 | + | 0.732787i | \(0.738219\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | −22.3212 | + | 10.2752i | −1.25966 | + | 0.579861i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 34.7656 | 1.95263 | 0.976314 | − | 0.216359i | \(-0.0694181\pi\) | ||||
0.976314 | + | 0.216359i | \(0.0694181\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 31.5590i | − | 1.76697i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.97013 | −0.389035 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 5.73487 | − | 6.69957i | 0.318604 | − | 0.372198i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.8283 | −0.982905 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.64205 | − | 16.6012i | −0.418155 | − | 0.908376i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.38168 | + | 15.2570i | 0.129931 | + | 0.832335i | ||||
\(337\) | −25.8438 | −1.40780 | −0.703900 | − | 0.710299i | \(-0.748560\pi\) | ||||
−0.703900 | + | 0.710299i | \(0.748560\pi\) | |||||||
\(338\) | −16.7003 | + | 7.68768i | −0.908376 | + | 0.418155i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.5680 | −1.81781 | ||||||||
\(342\) | 12.1915 | + | 26.4840i | 0.659238 | + | 1.43209i | ||||
\(343\) | − | 70.5061i | − | 3.80697i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 27.6083 | − | 12.7090i | 1.48423 | − | 0.683239i | ||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | −11.5361 | − | 9.87494i | −0.618398 | − | 0.529353i | ||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | −15.4931 | − | 33.6564i | −0.828142 | − | 1.79901i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14.4302 | + | 9.58403i | −0.769134 | + | 0.510831i | ||||
\(353\) | 14.7318 | 0.784096 | 0.392048 | − | 0.919945i | \(-0.371767\pi\) | ||||
0.392048 | + | 0.919945i | \(0.371767\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −18.8019 | + | 21.9647i | −0.996498 | + | 1.16412i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.8604 | + | 23.5926i | 0.573990 | + | 1.24691i | ||||
\(359\) | − | 13.9616i | − | 0.736865i | −0.929654 | − | 0.368433i | \(-0.879895\pi\) | ||
0.929654 | − | 0.368433i | \(-0.120105\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −51.3924 | −2.70486 | ||||||||
\(362\) | −14.9474 | + | 6.88078i | −0.785620 | + | 0.361646i | ||||
\(363\) | 1.19525i | 0.0627344i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.34899 | − | 7.27517i | −0.175055 | − | 0.380279i | ||||
\(367\) | 23.3527i | 1.21900i | 0.792786 | + | 0.609501i | \(0.208630\pi\) | ||||
−0.792786 | + | 0.609501i | \(0.791370\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10.5036 | + | 12.2704i | −0.544584 | + | 0.636192i | ||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.25791 | − | 2.62768i | −0.477440 | − | 0.135512i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 27.0637 | − | 12.4583i | 1.39201 | − | 0.640785i | ||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.7235 | 0.805542 | ||||||||
\(382\) | 13.8516 | + | 30.0905i | 0.708711 | + | 1.53957i | ||||
\(383\) | − | 3.20185i | − | 0.163607i | −0.996648 | − | 0.0818034i | \(-0.973932\pi\) | ||
0.996648 | − | 0.0818034i | \(-0.0260679\pi\) | |||||||
\(384\) | −1.01194 | + | 8.27370i | −0.0516402 | + | 0.422215i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.1921 | − | 18.9159i | 0.822032 | − | 0.960310i | ||||
\(389\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 15.7978 | − | 55.6592i | 0.797911 | − | 2.81122i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 11.4328 | + | 9.78651i | 0.574517 | + | 0.491790i | ||||
\(397\) | −32.9314 | −1.65278 | −0.826390 | − | 0.563097i | \(-0.809610\pi\) | ||||
−0.826390 | + | 0.563097i | \(0.809610\pi\) | |||||||
\(398\) | −1.75518 | − | 3.81285i | −0.0879791 | − | 0.191121i | ||||
\(399\) | 32.3891i | 1.62148i | ||||||||
\(400\) | −3.08473 | − | 19.7607i | −0.154237 | − | 0.988034i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 31.9334 | + | 69.3703i | 1.58483 | + | 3.44279i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.35952 | −0.413352 | −0.206676 | − | 0.978409i | \(-0.566265\pi\) | ||||
−0.206676 | + | 0.978409i | \(0.566265\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.16338i | 0.353343i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −33.0058 | + | 15.1936i | −1.61437 | + | 0.743146i | ||||
\(419\) | − | 37.6160i | − | 1.83766i | −0.394651 | − | 0.918831i | \(-0.629135\pi\) | ||
0.394651 | − | 0.918831i | \(-0.370865\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.0155 | 1.21918 | 0.609589 | − | 0.792717i | \(-0.291334\pi\) | ||||
0.609589 | + | 0.792717i | \(0.291334\pi\) | |||||||
\(422\) | 1.91064 | + | 4.15057i | 0.0930086 | + | 0.202047i | ||||
\(423\) | 8.36052i | 0.406502i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 40.2773i | 1.94916i | ||||||||
\(428\) | 14.3742 | + | 12.3044i | 0.694804 | + | 0.594757i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.3008i | 1.70038i | 0.526475 | + | 0.850190i | \(0.323513\pi\) | ||||
−0.526475 | + | 0.850190i | \(0.676487\pi\) | |||||||
\(432\) | 15.8899 | − | 2.48049i | 0.764503 | − | 0.119342i | ||||
\(433\) | −6.89945 | −0.331566 | −0.165783 | − | 0.986162i | \(-0.553015\pi\) | ||||
−0.165783 | + | 0.986162i | \(0.553015\pi\) | |||||||
\(434\) | 73.7863 | − | 33.9662i | 3.54186 | − | 1.63043i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −50.2641 | −2.39353 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −17.3900 | − | 37.7771i | −0.823442 | − | 1.78880i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 22.0216 | − | 35.6682i | 1.04042 | − | 1.68516i | ||||
\(449\) | 36.7582 | 1.73473 | 0.867363 | − | 0.497677i | \(-0.165813\pi\) | ||||
0.867363 | + | 0.497677i | \(0.165813\pi\) | |||||||
\(450\) | −15.7831 | + | 7.26545i | −0.744021 | + | 0.342497i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.77378 | + | 16.8191i | −0.223553 | + | 0.787626i | ||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | −35.9265 | + | 16.5381i | −1.67873 | + | 0.772775i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 42.9365 | 1.99975 | 0.999876 | − | 0.0157523i | \(-0.00501433\pi\) | ||||
0.999876 | + | 0.0157523i | \(0.00501433\pi\) | |||||||
\(462\) | 6.99094 | + | 15.1867i | 0.325248 | + | 0.706550i | ||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 6.35805 | + | 40.7294i | 0.295165 | + | 1.89081i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.951886 | − | 0.438183i | 0.0440953 | − | 0.0202985i | ||||
\(467\) | − | 40.8996i | − | 1.89261i | −0.323276 | − | 0.946305i | \(-0.604784\pi\) | ||
0.323276 | − | 0.946305i | \(-0.395216\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.8014i | 0.589856i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 41.9501i | − | 1.92480i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.2614 | + | 39.6700i | 0.835257 | + | 1.81447i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.10999 | − | 2.46492i | 0.0959084 | − | 0.112042i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.05396 | − | 19.6683i | −0.410696 | − | 0.892173i | ||||
\(487\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | −5.93641 | + | 20.9153i | −0.268729 | + | 0.946791i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 25.8457i | − | 1.16640i | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||
0.812329 | − | 0.583200i | \(-0.198200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 43.3222 | − | 6.76279i | 1.94522 | − | 0.303658i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.52088 | −0.425362 | ||||||||
\(502\) | −12.9971 | − | 28.2342i | −0.580088 | − | 1.26015i | ||||
\(503\) | − | 22.0394i | − | 0.982686i | −0.870966 | − | 0.491343i | \(-0.836506\pi\) | ||
0.870966 | − | 0.491343i | \(-0.163494\pi\) | |||||||
\(504\) | −35.0331 | − | 9.94349i | −1.56050 | − | 0.442918i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.57773i | 0.425362i | ||||||||
\(508\) | −32.4260 | − | 27.7569i | −1.43867 | − | 1.23151i | ||||
\(509\) | −45.0274 | −1.99581 | −0.997903 | − | 0.0647334i | \(-0.979380\pi\) | ||||
−0.997903 | + | 0.0647334i | \(0.979380\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.6925 | − | 15.2761i | 0.737711 | − | 0.675116i | ||||
\(513\) | 33.7328 | 1.48934 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.4193 | −0.458242 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 15.8335i | − | 0.695015i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 32.5310 | − | 14.9751i | 1.42384 | − | 0.655441i | ||||
\(523\) | 40.6159i | 1.77601i | 0.459835 | + | 0.888005i | \(0.347909\pi\) | ||||
−0.459835 | + | 0.888005i | \(0.652091\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19.3022 | −0.842416 | ||||||||
\(526\) | −15.6473 | − | 33.9913i | −0.682254 | − | 1.48209i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.39192 | + | 8.91658i | 0.0605755 | + | 0.388044i | ||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 57.1767 | − | 66.7948i | 2.47893 | − | 2.89592i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.29844 | + | 13.6824i | 0.272560 | + | 0.592094i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.5305 | 0.583884 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 62.6418i | − | 2.69817i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.57245i | 0.367879i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | 12.6456 | − | 14.7728i | 0.540192 | − | 0.631061i | ||||
\(549\) | 18.8879 | 0.806117 | ||||||||
\(550\) | −9.05460 | − | 19.6697i | −0.386089 | − | 0.838719i | ||||
\(551\) | 86.4647i | 3.68352i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.5815 | 1.08392 | 0.541961 | − | 0.840404i | \(-0.317682\pi\) | ||||
0.541961 | + | 0.840404i | \(0.317682\pi\) | |||||||
\(558\) | −15.9284 | − | 34.6019i | −0.674301 | − | 1.46481i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −33.6083 | + | 15.4710i | −1.41768 | + | 0.652605i | ||||
\(563\) | 11.5602i | 0.487206i | 0.969875 | + | 0.243603i | \(0.0783293\pi\) | ||||
−0.969875 | + | 0.243603i | \(0.921671\pi\) | |||||||
\(564\) | −3.26025 | + | 3.80867i | −0.137281 | + | 0.160374i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 19.8086 | + | 43.0312i | 0.832619 | + | 1.80874i | ||||
\(567\) | 23.1048i | 0.970309i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.2571 | 0.720927 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −16.7265 | − | 10.3270i | −0.696938 | − | 0.430290i | ||||
\(577\) | −5.61644 | −0.233815 | −0.116908 | − | 0.993143i | \(-0.537298\pi\) | ||||
−0.116908 | + | 0.993143i | \(0.537298\pi\) | |||||||
\(578\) | −21.8388 | + | 10.0531i | −0.908376 | + | 0.418155i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5.42420 | − | 11.7832i | −0.224840 | − | 0.488431i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.6552 | + | 17.7942i | −1.59683 | + | 0.735072i | ||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −22.8980 | − | 19.6009i | −0.944299 | − | 0.808326i | ||||
\(589\) | 91.9689 | 3.78951 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 15.8167 | − | 7.28095i | 0.648969 | − | 0.298741i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.18670 | −0.0894955 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.6408i | 1.41539i | 0.706520 | + | 0.707693i | \(0.250264\pi\) | ||||
−0.706520 | + | 0.707693i | \(0.749736\pi\) | |||||||
\(600\) | −10.0233 | − | 2.84492i | −0.409198 | − | 0.116143i | ||||
\(601\) | −23.5401 | −0.960219 | −0.480110 | − | 0.877208i | \(-0.659403\pi\) | ||||
−0.480110 | + | 0.877208i | \(0.659403\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 39.5356 | − | 26.2581i | 1.60338 | − | 1.06491i | ||||
\(609\) | 39.7844 | 1.61214 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.4477 | −1.47211 | −0.736055 | − | 0.676922i | \(-0.763314\pi\) | ||||
−0.736055 | + | 0.676922i | \(0.763314\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.3921 | − | 43.6601i | 0.499292 | − | 1.75912i | ||||
\(617\) | 47.1022 | 1.89626 | 0.948131 | − | 0.317879i | \(-0.102971\pi\) | ||||
0.948131 | + | 0.317879i | \(0.102971\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.2841 | − | 33.2024i | −0.612837 | − | 1.33129i | ||||
\(623\) | − | 75.7494i | − | 3.03483i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.9291i | 0.755954i | ||||||||
\(628\) | 22.5983 | − | 26.3997i | 0.901772 | − | 1.05346i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.5659i | 0.818714i | 0.912374 | + | 0.409357i | \(0.134247\pi\) | ||||
−0.912374 | + | 0.409357i | \(0.865753\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.38038 | 0.0946117 | ||||||||
\(634\) | −44.6611 | + | 20.5590i | −1.77372 | + | 0.816500i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.6627 | + | 40.5419i | 0.738865 | + | 1.60507i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 8.95409 | − | 4.12185i | 0.353390 | − | 0.162677i | ||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | −3.40538 | + | 11.9979i | −0.133776 | + | 0.471322i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 42.3170i | − | 1.65853i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 50.6445 | 1.98187 | 0.990937 | − | 0.134330i | \(-0.0428881\pi\) | ||||
0.990937 | + | 0.134330i | \(0.0428881\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22.9029 | − | 10.5429i | 0.892847 | − | 0.411006i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 19.6345 | + | 16.8073i | 0.759683 | + | 0.650294i | ||||
\(669\) | −21.6654 | −0.837634 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.5391i | 0.908719i | ||||||||
\(672\) | −12.0820 | − | 18.1912i | −0.466071 | − | 0.701742i | ||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 33.1999 | − | 15.2830i | 1.27881 | − | 0.588678i | ||||
\(675\) | 20.1029i | 0.773762i | ||||||||
\(676\) | 16.9076 | − | 19.7518i | 0.650294 | − | 0.759683i | ||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 65.2352i | 2.50350i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 43.1227 | − | 19.8508i | 1.65125 | − | 0.760125i | ||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | −31.3232 | − | 26.8129i | −1.19767 | − | 1.02522i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 41.6945 | + | 90.5748i | 1.59190 | + | 3.45816i | ||||
\(687\) | 20.6041i | 0.786094i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | −27.9511 | + | 32.6529i | −1.06254 | + | 1.24128i | ||||
\(693\) | −39.4281 | −1.49775 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 20.6593 | + | 5.86376i | 0.783089 | + | 0.222265i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 0.545913i | − | 0.0206483i | ||||||
\(700\) | 39.8061 | + | 34.0743i | 1.50453 | + | 1.28789i | ||||
\(701\) | −46.4708 | −1.75518 | −0.877589 | − | 0.479413i | \(-0.840850\pi\) | ||||
−0.877589 | + | 0.479413i | \(0.840850\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 12.8700 | − | 20.8455i | 0.485057 | − | 0.785643i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.9251 | + | 8.71181i | −0.712254 | + | 0.327873i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.1646 | − | 39.3353i | 0.418411 | − | 1.47415i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −27.9034 | − | 23.8855i | −1.04280 | − | 0.892642i | ||||
\(717\) | 22.7510 | 0.849653 | ||||||||
\(718\) | 8.25633 | + | 17.9356i | 0.308124 | + | 0.669351i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 66.0206 | − | 30.3914i | 2.45703 | − | 1.13105i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.1330 | − | 17.6786i | 0.562414 | − | 0.657021i | ||||
\(725\) | −51.5283 | −1.91371 | ||||||||
\(726\) | −0.706824 | − | 1.53546i | −0.0262327 | − | 0.0569864i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.94843 | 0.0721642 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 8.60448 | + | 7.36549i | 0.318031 | + | 0.272236i | ||||
\(733\) | −53.8509 | −1.98903 | −0.994514 | − | 0.104602i | \(-0.966643\pi\) | ||||
−0.994514 | + | 0.104602i | \(0.966643\pi\) | |||||||
\(734\) | −13.8099 | − | 29.9998i | −0.509731 | − | 1.10731i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.8457i | 0.948187i | 0.880475 | + | 0.474093i | \(0.157224\pi\) | ||||
−0.880475 | + | 0.474093i | \(0.842776\pi\) | |||||||
\(744\) | 6.23703 | − | 21.9744i | 0.228661 | − | 0.805622i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −49.5723 | −1.81133 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | 13.4470 | − | 2.09913i | 0.490360 | − | 0.0765475i | ||||
\(753\) | −16.1925 | −0.590087 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −27.3997 | + | 32.0087i | −0.996517 | + | 1.16415i | ||||
\(757\) | −18.7642 | −0.681997 | −0.340998 | − | 0.940064i | \(-0.610765\pi\) | ||||
−0.340998 | + | 0.940064i | \(0.610765\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −55.0746 | −1.99645 | −0.998227 | − | 0.0595193i | \(-0.981043\pi\) | ||||
−0.998227 | + | 0.0595193i | \(0.981043\pi\) | |||||||
\(762\) | −20.1991 | + | 9.29827i | −0.731735 | + | 0.336841i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −35.5887 | − | 30.4641i | −1.28755 | − | 1.10215i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.89344 | + | 4.11321i | 0.0684129 | + | 0.148616i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −3.59276 | − | 11.2271i | −0.129643 | − | 0.405124i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 54.8085i | 1.96878i | ||||||||
\(776\) | −9.61492 | + | 33.8755i | −0.345156 | + | 1.21606i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 41.4348i | − | 1.48076i | ||||||
\(784\) | 12.6201 | + | 80.8441i | 0.450719 | + | 2.88729i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.4942 | −0.694013 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −20.4743 | − | 5.81124i | −0.727522 | − | 0.206494i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 42.3049 | − | 19.4743i | 1.50135 | − | 0.691118i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.50953 | + | 3.86019i | 0.159836 | + | 0.136821i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | −19.1536 | − | 41.6083i | −0.678031 | − | 1.47292i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 15.6484 | + | 23.5611i | 0.553256 | + | 0.833011i | ||||
\(801\) | −35.5224 | −1.25512 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 56.7956 | 1.99683 | 0.998413 | − | 0.0563179i | \(-0.0179360\pi\) | ||||
0.998413 | + | 0.0563179i | \(0.0179360\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | −82.0457 | − | 70.2316i | −2.87924 | − | 2.46465i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 10.7389 | − | 4.94348i | 0.375479 | − | 0.172845i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | −4.23614 | − | 9.20235i | −0.147752 | − | 0.320969i | ||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.2807 | −0.392744 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 33.4156 | − | 39.0367i | 1.15570 | − | 1.35011i | ||||
\(837\) | −44.0725 | −1.52337 | ||||||||
\(838\) | 22.2446 | + | 48.3229i | 0.768427 | + | 1.66929i | ||||
\(839\) | − | 39.7213i | − | 1.37133i | −0.727916 | − | 0.685666i | \(-0.759511\pi\) | ||
0.727916 | − | 0.685666i | \(-0.240489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 77.2068 | 2.66230 | ||||||||
\(842\) | −32.1358 | + | 14.7931i | −1.10747 | + | 0.509805i | ||||
\(843\) | 19.2746i | 0.663853i | ||||||||
\(844\) | −4.90896 | − | 4.20211i | −0.168974 | − | 0.144642i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.94408 | − | 10.7402i | −0.169981 | − | 0.369257i | ||||
\(847\) | 8.50075i | 0.292089i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.6787 | 0.846970 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.7543 | −1.63508 | −0.817538 | − | 0.575874i | \(-0.804662\pi\) | ||||
−0.817538 | + | 0.575874i | \(0.804662\pi\) | |||||||
\(854\) | −23.8184 | − | 51.7417i | −0.815048 | − | 1.77057i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.7420 | − | 7.30639i | −0.879843 | − | 0.249727i | ||||
\(857\) | −28.7283 | −0.981339 | −0.490669 | − | 0.871346i | \(-0.663248\pi\) | ||||
−0.490669 | + | 0.871346i | \(0.663248\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 7.42268i | − | 0.253259i | −0.991950 | − | 0.126629i | \(-0.959584\pi\) | ||
0.991950 | − | 0.126629i | \(-0.0404159\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.8755 | − | 45.3488i | −0.711022 | − | 1.54459i | ||||
\(863\) | − | 57.9009i | − | 1.97097i | −0.169767 | − | 0.985484i | \(-0.554301\pi\) | ||
0.169767 | − | 0.985484i | \(-0.445699\pi\) | |||||||
\(864\) | −18.9459 | + | 12.5832i | −0.644552 | + | 0.428088i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.86329 | − | 4.08006i | 0.301187 | − | 0.138646i | ||||
\(867\) | 12.5247i | 0.425362i | ||||||||
\(868\) | −74.7024 | + | 87.2685i | −2.53557 | + | 2.96209i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.5919 | 1.03538 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.3787 | −1.49856 | −0.749282 | − | 0.662251i | \(-0.769601\pi\) | ||||
−0.749282 | + | 0.662251i | \(0.769601\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.1690i | 0.747742i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 64.5711 | − | 29.7241i | 2.17422 | − | 1.00086i | ||||
\(883\) | 17.9023i | 0.602462i | 0.953551 | + | 0.301231i | \(0.0973975\pi\) | ||||
−0.953551 | + | 0.301231i | \(0.902603\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 111.827 | 3.75057 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.5030i | 0.452369i | ||||||||
\(892\) | 44.6798 | + | 38.2462i | 1.49599 | + | 1.28058i | ||||
\(893\) | 28.5467 | 0.955277 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.19700 | + | 58.8434i | −0.240435 | + | 1.96582i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −47.2209 | + | 21.7373i | −1.57578 | + | 0.725383i | ||||
\(899\) | − | 112.968i | − | 3.76768i | ||||||
\(900\) | 15.9790 | − | 18.6669i | 0.532634 | − | 0.622232i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 56.6034i | − | 1.87949i | −0.341881 | − | 0.939743i | \(-0.611064\pi\) | ||
0.341881 | − | 0.939743i | \(-0.388936\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 53.7426i | − | 1.78057i | −0.455403 | − | 0.890285i | \(-0.650505\pi\) | ||
0.455403 | − | 0.890285i | \(-0.349495\pi\) | |||||||
\(912\) | −3.81355 | − | 24.4295i | −0.126279 | − | 0.808940i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.3725 | − | 42.4909i | 1.20178 | − | 1.40394i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.9128i | 1.87738i | 0.344763 | + | 0.938690i | \(0.387959\pi\) | ||||
−0.344763 | + | 0.938690i | \(0.612041\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −55.1578 | + | 25.3909i | −1.81653 | + | 0.836205i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −17.9616 | − | 15.3753i | −0.590895 | − | 0.505810i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −32.2535 | − | 48.5626i | −1.05877 | − | 1.59415i | ||||
\(929\) | 60.9216 | 1.99877 | 0.999387 | − | 0.0350138i | \(-0.0111475\pi\) | ||||
0.999387 | + | 0.0350138i | \(0.0111475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 171.625i | 5.62477i | ||||||||
\(932\) | −0.963704 | + | 1.12581i | −0.0315672 | + | 0.0368773i | ||||
\(933\) | −19.0418 | −0.623400 | ||||||||
\(934\) | 24.1864 | + | 52.5412i | 0.791403 | + | 1.71920i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | −7.57021 | − | 16.4451i | −0.246651 | − | 0.535811i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 55.1299i | 1.79148i | 0.444576 | + | 0.895741i | \(0.353354\pi\) | ||||
−0.444576 | + | 0.895741i | \(0.646646\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 24.8076 | + | 53.8907i | 0.804865 | + | 1.74844i | ||||
\(951\) | 25.6135i | 0.830573i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −46.9185 | − | 40.1626i | −1.51745 | − | 1.29895i | ||||
\(957\) | 23.2511 | 0.751600 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 50.9467i | 1.64515i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −89.1590 | −2.87610 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 23.2468i | 0.749117i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.4236i | − | 0.560304i | −0.959956 | − | 0.280152i | \(-0.909615\pi\) | ||
0.959956 | − | 0.280152i | \(-0.0903849\pi\) | |||||||
\(968\) | −1.25291 | + | 4.41429i | −0.0402702 | + | 0.141881i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 23.2621 | + | 19.9125i | 0.746132 | + | 0.638694i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.74232 | − | 30.3791i | −0.151798 | − | 0.972412i | ||||
\(977\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 44.2700i | − | 1.41487i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.2841 | + | 33.2024i | 0.487735 | + | 1.05953i | ||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 13.1350i | − | 0.418090i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | −51.6540 | + | 34.3067i | −1.64002 | + | 1.08924i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.8186 | 1.16606 | 0.583028 | − | 0.812452i | \(-0.301868\pi\) | ||||
0.583028 | + | 0.812452i | \(0.301868\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 668.2.b.a.667.4 | yes | 22 | |
4.3 | odd | 2 | inner | 668.2.b.a.667.3 | ✓ | 22 | |
167.166 | odd | 2 | CM | 668.2.b.a.667.4 | yes | 22 | |
668.667 | even | 2 | inner | 668.2.b.a.667.3 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
668.2.b.a.667.3 | ✓ | 22 | 4.3 | odd | 2 | inner | |
668.2.b.a.667.3 | ✓ | 22 | 668.667 | even | 2 | inner | |
668.2.b.a.667.4 | yes | 22 | 1.1 | even | 1 | trivial | |
668.2.b.a.667.4 | yes | 22 | 167.166 | odd | 2 | CM |