Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [880,3,Mod(769,880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("880.769");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 880 = 2^{4} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 880.i (of order \(2\), degree \(1\), not 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: | \(23.9782632637\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.130897030168576.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 169x^{4} - 112x^{2} + 1936 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 110) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.2 | ||
Root | \(-1.41421 - 3.43731i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 880.769 |
Dual form | 880.3.i.g.769.8 |
$q$-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 \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).
\(n\) | \(111\) | \(177\) | \(321\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.43731i | − | 1.14577i | −0.819636 | − | 0.572884i | \(-0.805824\pi\) | ||
0.819636 | − | 0.572884i | \(-0.194176\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.90754 | + | 3.11948i | −0.781507 | + | 0.623896i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.82843 | 0.404061 | 0.202031 | − | 0.979379i | \(-0.435246\pi\) | ||||
0.202031 | + | 0.979379i | \(0.435246\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.81507 | −0.312786 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.81507 | + | 7.74110i | 0.710461 | + | 0.703736i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.98111 | −0.306240 | −0.153120 | − | 0.988208i | \(-0.548932\pi\) | ||||
−0.153120 | + | 0.988208i | \(0.548932\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.7226 | + | 13.4314i | 0.714841 | + | 0.895427i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −23.2571 | −1.36806 | −0.684031 | − | 0.729453i | \(-0.739775\pi\) | ||||
−0.684031 | + | 0.729453i | \(0.739775\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 33.1286i | − | 1.74361i | −0.489850 | − | 0.871807i | \(-0.662949\pi\) | ||
0.489850 | − | 0.871807i | \(-0.337051\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 9.72217i | − | 0.462960i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.16600i | − | 0.0941741i | −0.998891 | − | 0.0470870i | \(-0.985006\pi\) | ||
0.998891 | − | 0.0470870i | \(-0.0149938\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.53768 | − | 24.3790i | 0.221507 | − | 0.975159i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 21.2595i | − | 0.787388i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 11.5201i | 0.397244i | 0.980076 | + | 0.198622i | \(0.0636465\pi\) | ||||
−0.980076 | + | 0.198622i | \(0.936353\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −36.7055 | −1.18405 | −0.592024 | − | 0.805920i | \(-0.701671\pi\) | ||||
−0.592024 | + | 0.805920i | \(0.701671\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 26.6085 | − | 26.8628i | 0.806319 | − | 0.814024i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.0522 | + | 8.82322i | −0.315777 | + | 0.252092i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 17.4456i | − | 0.471502i | −0.971813 | − | 0.235751i | \(-0.924245\pi\) | ||
0.971813 | − | 0.235751i | \(-0.0757550\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.6843i | 0.350880i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 45.0151i | 1.09793i | 0.835846 | + | 0.548964i | \(0.184978\pi\) | ||||
−0.835846 | + | 0.548964i | \(0.815022\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −63.4847 | −1.47639 | −0.738194 | − | 0.674589i | \(-0.764321\pi\) | ||||
−0.738194 | + | 0.674589i | \(0.764321\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.0000 | − | 8.78157i | 0.244444 | − | 0.195146i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 46.5919i | − | 0.991318i | −0.868517 | − | 0.495659i | \(-0.834927\pi\) | ||
0.868517 | − | 0.495659i | \(-0.165073\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −41.0000 | −0.836735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 79.9416i | 1.56748i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.2066i | 0.211446i | 0.994396 | + | 0.105723i | \(0.0337156\pi\) | ||||
−0.994396 | + | 0.105723i | \(0.966284\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −54.6859 | − | 5.86966i | −0.994289 | − | 0.106721i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −113.873 | −1.99778 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 44.7055 | 0.757721 | 0.378860 | − | 0.925454i | \(-0.376316\pi\) | ||||
0.378860 | + | 0.925454i | \(0.376316\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38.8887i | 0.637519i | 0.947836 | + | 0.318760i | \(0.103266\pi\) | ||||
−0.947836 | + | 0.318760i | \(0.896734\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.96223 | −0.126385 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.5563 | − | 12.4190i | 0.239328 | − | 0.191062i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 91.5360i | − | 1.36621i | −0.730321 | − | 0.683104i | \(-0.760629\pi\) | ||
0.730321 | − | 0.683104i | \(-0.239371\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.44522 | −0.107902 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −54.5548 | −0.768377 | −0.384189 | − | 0.923255i | \(-0.625519\pi\) | ||||
−0.384189 | + | 0.923255i | \(0.625519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −56.1521 | −0.769206 | −0.384603 | − | 0.923082i | \(-0.625662\pi\) | ||||
−0.384603 | + | 0.923082i | \(0.625662\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −83.7980 | − | 19.0347i | −1.11731 | − | 0.253796i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.1044 | + | 21.8951i | 0.287070 | + | 0.284352i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 101.917i | 1.29008i | 0.764148 | + | 0.645041i | \(0.223160\pi\) | ||||
−0.764148 | + | 0.645041i | \(0.776840\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −98.4110 | −1.21495 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.7113 | 0.189293 | 0.0946463 | − | 0.995511i | \(-0.469828\pi\) | ||||
0.0946463 | + | 0.995511i | \(0.469828\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 90.8778 | − | 72.5499i | 1.06915 | − | 0.853528i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 39.5980 | 0.455149 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −28.7055 | −0.322534 | −0.161267 | − | 0.986911i | \(-0.551558\pi\) | ||||
−0.161267 | + | 0.986911i | \(0.551558\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.2603 | −0.123739 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 126.168i | 1.35665i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 103.344 | + | 129.451i | 1.08783 | + | 1.36265i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 76.2564i | − | 0.786148i | −0.919507 | − | 0.393074i | \(-0.871412\pi\) | ||
0.919507 | − | 0.393074i | \(-0.128588\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.0000 | − | 21.7918i | −0.222222 | − | 0.220119i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 76.7122i | − | 0.759526i | −0.925084 | − | 0.379763i | \(-0.876005\pi\) | ||
0.925084 | − | 0.379763i | \(-0.123995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 113.314i | 1.10013i | 0.835121 | + | 0.550066i | \(0.185397\pi\) | ||||
−0.835121 | + | 0.550066i | \(0.814603\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 30.3281 | + | 37.9897i | 0.288839 | + | 0.361807i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −157.036 | −1.46763 | −0.733813 | − | 0.679352i | \(-0.762261\pi\) | ||||
−0.733813 | + | 0.679352i | \(0.762261\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 171.403i | 1.57251i | 0.617904 | + | 0.786254i | \(0.287982\pi\) | ||||
−0.617904 | + | 0.786254i | \(0.712018\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −59.9658 | −0.540232 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 83.6491i | − | 0.740258i | −0.928980 | − | 0.370129i | \(-0.879314\pi\) | ||
0.928980 | − | 0.370129i | \(-0.120686\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.75681 | + | 8.46374i | 0.0587548 | + | 0.0735977i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.2071 | 0.0957874 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −65.7809 | −0.552780 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.15073 | + | 120.995i | 0.00951016 | + | 0.999955i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 154.731 | 1.25797 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 54.4110 | + | 112.536i | 0.435288 | + | 0.900291i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −132.936 | −1.04674 | −0.523370 | − | 0.852105i | \(-0.675326\pi\) | ||||
−0.523370 | + | 0.852105i | \(0.675326\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 218.216i | 1.69160i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 49.3436i | − | 0.376668i | −0.982105 | − | 0.188334i | \(-0.939691\pi\) | ||
0.982105 | − | 0.188334i | \(-0.0603088\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 93.7020i | − | 0.704526i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 66.3186 | + | 83.0722i | 0.491249 | + | 0.615350i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.2957i | 0.162742i | 0.996684 | + | 0.0813711i | \(0.0259299\pi\) | ||||
−0.996684 | + | 0.0813711i | \(0.974070\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 261.766i | − | 1.88321i | −0.336723 | − | 0.941604i | \(-0.609318\pi\) | ||
0.336723 | − | 0.941604i | \(-0.390682\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −160.151 | −1.13582 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −31.1127 | − | 30.8182i | −0.217571 | − | 0.215512i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −35.9366 | − | 45.0151i | −0.247839 | − | 0.310449i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 140.930i | 0.958704i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 266.827i | − | 1.79079i | −0.445277 | − | 0.895393i | \(-0.646895\pi\) | ||
0.445277 | − | 0.895393i | \(-0.353105\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 123.858i | 0.820249i | 0.912030 | + | 0.410125i | \(0.134515\pi\) | ||||
−0.912030 | + | 0.410125i | \(0.865485\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 65.4703 | 0.427910 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 143.428 | − | 114.502i | 0.925343 | − | 0.738723i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 224.955i | − | 1.43284i | −0.697671 | − | 0.716418i | \(-0.745780\pi\) | ||
0.697671 | − | 0.716418i | \(-0.254220\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 38.5206 | 0.242268 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.12638i | − | 0.0380521i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 62.8838i | − | 0.385790i | −0.981219 | − | 0.192895i | \(-0.938212\pi\) | ||
0.981219 | − | 0.192895i | \(-0.0617877\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −20.1758 | + | 187.972i | −0.122278 | + | 1.13923i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 104.652 | 0.626658 | 0.313329 | − | 0.949645i | \(-0.398556\pi\) | ||||
0.313329 | + | 0.949645i | \(0.398556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −153.151 | −0.906217 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 93.2596i | 0.545378i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 109.059 | 0.630400 | 0.315200 | − | 0.949025i | \(-0.397928\pi\) | ||||
0.315200 | + | 0.949025i | \(0.397928\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.6629 | − | 68.9541i | 0.0895025 | − | 0.394024i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 153.667i | − | 0.868172i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 98.1165 | 0.548137 | 0.274069 | − | 0.961710i | \(-0.411630\pi\) | ||||
0.274069 | + | 0.961710i | \(0.411630\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 357.377 | 1.97446 | 0.987229 | − | 0.159309i | \(-0.0509266\pi\) | ||||
0.987229 | + | 0.159309i | \(0.0509266\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 133.672 | 0.730450 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 54.4212 | + | 68.1692i | 0.294168 | + | 0.368482i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −181.756 | − | 180.035i | −0.971955 | − | 0.962755i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 60.1309i | − | 0.318153i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −164.706 | −0.862333 | −0.431166 | − | 0.902272i | \(-0.641898\pi\) | ||||
−0.431166 | + | 0.902272i | \(0.641898\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −312.919 | −1.62134 | −0.810671 | − | 0.585501i | \(-0.800898\pi\) | ||||
−0.810671 | + | 0.585501i | \(0.800898\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −42.6879 | − | 53.4719i | −0.218912 | − | 0.274215i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −126.436 | −0.641809 | −0.320905 | − | 0.947112i | \(-0.603987\pi\) | ||||
−0.320905 | + | 0.947112i | \(0.603987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 197.411 | 0.992015 | 0.496008 | − | 0.868318i | \(-0.334799\pi\) | ||||
0.496008 | + | 0.868318i | \(0.334799\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −314.637 | −1.56536 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 32.5837i | 0.160511i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −140.424 | − | 175.898i | −0.684993 | − | 0.858039i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.09746i | 0.0294563i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 256.452 | − | 258.903i | 1.22704 | − | 1.23877i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 46.0802i | 0.218390i | 0.994020 | + | 0.109195i | \(0.0348273\pi\) | ||||
−0.994020 | + | 0.109195i | \(0.965173\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 187.521i | 0.880383i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 248.069 | − | 198.039i | 1.15381 | − | 0.921112i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −103.819 | −0.478428 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 193.012i | 0.881333i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 92.5890 | 0.418955 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 392.748i | − | 1.76120i | −0.473860 | − | 0.880600i | \(-0.657140\pi\) | ||
0.473860 | − | 0.880600i | \(-0.342860\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.5890 | + | 68.6286i | −0.0692844 | + | 0.305016i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −268.701 | −1.18370 | −0.591851 | − | 0.806047i | \(-0.701603\pi\) | ||||
−0.591851 | + | 0.806047i | \(0.701603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −205.528 | −0.897500 | −0.448750 | − | 0.893657i | \(-0.648131\pi\) | ||||
−0.448750 | + | 0.893657i | \(0.648131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 75.2603 | − | 75.9795i | 0.325802 | − | 0.328915i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 303.698 | 1.30342 | 0.651712 | − | 0.758467i | \(-0.274051\pi\) | ||||
0.651712 | + | 0.758467i | \(0.274051\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 145.343 | + | 182.060i | 0.618479 | + | 0.774722i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 350.318 | 1.47814 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 186.885i | − | 0.781948i | −0.920402 | − | 0.390974i | \(-0.872138\pi\) | ||
0.920402 | − | 0.390974i | \(-0.127862\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.1770i | − | 0.0837222i | −0.999123 | − | 0.0418611i | \(-0.986671\pi\) | ||
0.999123 | − | 0.0418611i | \(-0.0133287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 146.933i | 0.604664i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 160.209 | − | 127.899i | 0.653914 | − | 0.522036i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 131.889i | 0.533963i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 54.0045i | − | 0.216886i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −104.939 | −0.418082 | −0.209041 | − | 0.977907i | \(-0.567034\pi\) | ||||
−0.209041 | + | 0.977907i | \(0.567034\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.7673 | − | 16.9275i | 0.0662737 | − | 0.0669070i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −249.376 | − | 312.375i | −0.977946 | − | 1.22500i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 115.079i | 0.447778i | 0.974615 | + | 0.223889i | \(0.0718753\pi\) | ||||
−0.974615 | + | 0.223889i | \(0.928125\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 49.3436i | − | 0.190516i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 32.4298i | − | 0.124252i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −229.103 | −0.871113 | −0.435556 | − | 0.900162i | \(-0.643448\pi\) | ||||
−0.435556 | + | 0.900162i | \(0.643448\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −34.9588 | − | 43.7903i | −0.131920 | − | 0.165246i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 98.6696i | 0.369549i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 500.836 | 1.86184 | 0.930922 | − | 0.365218i | \(-0.119006\pi\) | ||||
0.930922 | + | 0.365218i | \(0.119006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 222.877i | 0.822425i | 0.911539 | + | 0.411213i | \(0.134895\pi\) | ||||
−0.911539 | + | 0.411213i | \(0.865105\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 38.7051i | 0.141777i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 231.997 | − | 147.656i | 0.843627 | − | 0.536930i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −162.470 | −0.586533 | −0.293267 | − | 0.956031i | \(-0.594742\pi\) | ||||
−0.293267 | + | 0.956031i | \(0.594742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 103.329 | 0.370354 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 352.861i | 1.25573i | 0.778321 | + | 0.627867i | \(0.216072\pi\) | ||||
−0.778321 | + | 0.627867i | \(0.783928\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 281.390 | 0.994311 | 0.497155 | − | 0.867661i | \(-0.334378\pi\) | ||||
0.497155 | + | 0.867661i | \(0.334378\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 444.964 | − | 355.226i | 1.56128 | − | 1.24641i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 127.322i | 0.443630i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 251.890 | 0.871593 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −262.117 | −0.900744 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 242.422 | 0.827378 | 0.413689 | − | 0.910418i | \(-0.364240\pi\) | ||||
0.413689 | + | 0.910418i | \(0.364240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −174.688 | + | 139.458i | −0.592164 | + | 0.472739i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 164.572 | − | 166.144i | 0.554114 | − | 0.559409i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.62311i | 0.0288398i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −179.562 | −0.596551 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −263.683 | −0.870242 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −121.312 | − | 151.959i | −0.397746 | − | 0.498226i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 487.226 | 1.58705 | 0.793527 | − | 0.608535i | \(-0.208242\pi\) | ||||
0.793527 | + | 0.608535i | \(0.208242\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 389.493 | 1.26050 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 421.411 | 1.35502 | 0.677510 | − | 0.735514i | \(-0.263059\pi\) | ||||
0.677510 | + | 0.735514i | \(0.263059\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 502.247i | 1.60462i | 0.596905 | + | 0.802312i | \(0.296397\pi\) | ||||
−0.596905 | + | 0.802312i | \(0.703603\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 31.1127 | − | 24.8380i | 0.0987705 | − | 0.0788508i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 616.290i | 1.94413i | 0.234706 | + | 0.972066i | \(0.424587\pi\) | ||||
−0.234706 | + | 0.972066i | \(0.575413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −89.1780 | + | 90.0301i | −0.279555 | + | 0.282226i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 539.781i | 1.68156i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 770.475i | 2.38537i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.0461 | + | 97.0555i | −0.0678343 | + | 0.298632i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 589.165 | 1.80173 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 131.782i | − | 0.400553i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −197.883 | −0.597835 | −0.298918 | − | 0.954279i | \(-0.596626\pi\) | ||||
−0.298918 | + | 0.954279i | \(0.596626\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 49.1106i | 0.147479i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 285.545 | + | 357.680i | 0.852372 | + | 1.06770i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 375.861 | 1.11531 | 0.557657 | − | 0.830071i | \(-0.311700\pi\) | ||||
0.557657 | + | 0.830071i | \(0.311700\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −287.528 | −0.848164 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −286.856 | − | 284.141i | −0.841221 | − | 0.833258i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −254.558 | −0.742153 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 29.0925 | − | 23.2252i | 0.0843260 | − | 0.0673195i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 310.624 | 0.895169 | 0.447584 | − | 0.894242i | \(-0.352284\pi\) | ||||
0.447584 | + | 0.894242i | \(0.352284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 474.256i | − | 1.35890i | −0.733722 | − | 0.679450i | \(-0.762219\pi\) | ||
0.733722 | − | 0.679450i | \(-0.237781\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 84.6364i | 0.241129i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 460.434i | − | 1.30434i | −0.758071 | − | 0.652172i | \(-0.773858\pi\) | ||
0.758071 | − | 0.652172i | \(-0.226142\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 213.175 | − | 170.183i | 0.600492 | − | 0.479388i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 226.109i | 0.633359i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 335.649i | − | 0.934955i | −0.884005 | − | 0.467477i | \(-0.845163\pi\) | ||
0.884005 | − | 0.467477i | \(-0.154837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −736.507 | −2.04019 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 415.895 | − | 3.95541i | 1.14572 | − | 0.0108964i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 219.416 | − | 175.165i | 0.601140 | − | 0.479905i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 175.255i | − | 0.477533i | −0.971077 | − | 0.238767i | \(-0.923257\pi\) | ||
0.971077 | − | 0.238767i | \(-0.0767431\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 126.721i | − | 0.343416i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 31.6971i | 0.0854369i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −236.338 | −0.633615 | −0.316808 | − | 0.948490i | \(-0.602611\pi\) | ||||
−0.316808 | + | 0.948490i | \(0.602611\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 386.822 | − | 187.027i | 1.03153 | − | 0.498740i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 45.8627i | − | 0.121652i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 416.267 | 1.09833 | 0.549165 | − | 0.835714i | \(-0.314946\pi\) | ||||
0.549165 | + | 0.835714i | \(0.314946\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 456.942i | 1.19932i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 166.451i | − | 0.434599i | −0.976105 | − | 0.217299i | \(-0.930275\pi\) | ||
0.976105 | − | 0.217299i | \(-0.0697248\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −154.675 | − | 16.6019i | −0.401753 | − | 0.0431219i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 178.714 | 0.461793 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −232.939 | −0.598814 | −0.299407 | − | 0.954126i | \(-0.596789\pi\) | ||||
−0.299407 | + | 0.954126i | \(0.596789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 50.3749i | 0.128836i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −169.609 | −0.431575 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −317.927 | − | 398.243i | −0.804878 | − | 1.00821i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 705.825i | 1.77790i | 0.458006 | + | 0.888949i | \(0.348564\pi\) | ||||
−0.458006 | + | 0.888949i | \(0.651436\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −322.082 | −0.807224 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −92.2331 | −0.230008 | −0.115004 | − | 0.993365i | \(-0.536688\pi\) | ||||
−0.115004 | + | 0.993365i | \(0.536688\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 146.129 | 0.362603 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 384.545 | − | 306.991i | 0.949493 | − | 0.758003i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 135.048 | − | 136.338i | 0.331813 | − | 0.334984i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 111.673i | 0.273038i | 0.990637 | + | 0.136519i | \(0.0435915\pi\) | ||||
−0.990637 | + | 0.136519i | \(0.956409\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 76.6371 | 0.186465 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 126.446 | 0.306165 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −61.3925 | + | 49.0111i | −0.147934 | + | 0.118099i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −899.769 | −2.15772 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 70.1507 | 0.167424 | 0.0837121 | − | 0.996490i | \(-0.473322\pi\) | ||||
0.0837121 | + | 0.996490i | \(0.473322\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 299.644 | 0.711744 | 0.355872 | − | 0.934535i | \(-0.384184\pi\) | ||||
0.355872 | + | 0.934535i | \(0.384184\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 131.160i | 0.310070i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −128.790 | + | 566.983i | −0.303036 | + | 1.33408i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 109.994i | 0.257597i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −105.932 | + | 106.944i | −0.246927 | + | 0.249286i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 39.5875i | 0.0918504i | 0.998945 | + | 0.0459252i | \(0.0146236\pi\) | ||||
−0.998945 | + | 0.0459252i | \(0.985376\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 387.168i | − | 0.894153i | −0.894496 | − | 0.447076i | \(-0.852465\pi\) | ||
0.894496 | − | 0.447076i | \(-0.147535\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −154.731 | + | 123.525i | −0.355702 | + | 0.283966i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −71.7568 | −0.164203 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 84.9689i | − | 0.193551i | −0.995306 | − | 0.0967755i | \(-0.969147\pi\) | ||
0.995306 | − | 0.0967755i | \(-0.0308529\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 115.418 | 0.261719 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 113.196i | − | 0.255521i | −0.991805 | − | 0.127761i | \(-0.959221\pi\) | ||
0.991805 | − | 0.127761i | \(-0.0407790\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 112.168 | − | 89.5463i | 0.252063 | − | 0.201228i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −917.166 | −2.05183 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −112.390 | −0.250312 | −0.125156 | − | 0.992137i | \(-0.539943\pi\) | ||||
−0.125156 | + | 0.992137i | \(0.539943\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −348.466 | + | 351.796i | −0.772652 | + | 0.780035i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 425.737 | 0.939816 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 44.0000 | − | 35.1263i | 0.0967033 | − | 0.0772006i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 409.705 | 0.896511 | 0.448255 | − | 0.893906i | \(-0.352046\pi\) | ||||
0.448255 | + | 0.893906i | \(0.352046\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 494.433i | 1.07720i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 80.6404i | 0.174925i | 0.996168 | + | 0.0874625i | \(0.0278758\pi\) | ||||
−0.996168 | + | 0.0874625i | \(0.972124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 112.913i | − | 0.243873i | −0.992538 | − | 0.121936i | \(-0.961090\pi\) | ||
0.992538 | − | 0.121936i | \(-0.0389104\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −393.579 | − | 493.006i | −0.846406 | − | 1.06023i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 65.8748i | 0.141060i | 0.997510 | + | 0.0705298i | \(0.0224690\pi\) | ||||
−0.997510 | + | 0.0705298i | \(0.977531\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 258.903i | − | 0.552032i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −773.240 | −1.64170 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −496.137 | − | 491.441i | −1.04892 | − | 1.03899i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −807.642 | − | 183.456i | −1.70030 | − | 0.386223i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 31.5475i | − | 0.0661372i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 148.397i | 0.309806i | 0.987930 | + | 0.154903i | \(0.0495065\pi\) | ||||
−0.987930 | + | 0.154903i | \(0.950494\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 69.4529i | 0.144393i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −21.0583 | −0.0435989 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 237.880 | + | 297.975i | 0.490475 | + | 0.614381i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 104.062i | − | 0.213679i | −0.994276 | − | 0.106840i | \(-0.965927\pi\) | ||
0.994276 | − | 0.106840i | \(-0.0340731\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −216.151 | −0.442026 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 330.255i | − | 0.672617i | −0.941752 | − | 0.336309i | \(-0.890821\pi\) | ||
0.941752 | − | 0.336309i | \(-0.109179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 267.923i | − | 0.543454i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 153.945 | + | 16.5235i | 0.311000 | + | 0.0333809i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −154.304 | −0.310471 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 214.589 | 0.430038 | 0.215019 | − | 0.976610i | \(-0.431019\pi\) | ||||
0.215019 | + | 0.976610i | \(0.431019\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 359.720i | − | 0.718005i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −848.122 | −1.68613 | −0.843063 | − | 0.537815i | \(-0.819250\pi\) | ||||
−0.843063 | + | 0.537815i | \(0.819250\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 239.302 | + | 299.756i | 0.473866 | + | 0.593575i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 526.426i | 1.03832i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 130.472 | 0.256331 | 0.128165 | − | 0.991753i | \(-0.459091\pi\) | ||||
0.128165 | + | 0.991753i | \(0.459091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −158.822 | −0.310806 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −704.298 | −1.37290 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −353.479 | − | 442.777i | −0.686368 | − | 0.859761i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 360.673 | − | 364.119i | 0.697626 | − | 0.704293i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 374.870i | − | 0.722293i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 168.939 | 0.324258 | 0.162129 | − | 0.986770i | \(-0.448164\pi\) | ||||
0.162129 | + | 0.986770i | \(0.448164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.1331 | −0.0346713 | −0.0173357 | − | 0.999850i | \(-0.505518\pi\) | ||||
−0.0173357 | + | 0.999850i | \(0.505518\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −237.016 | − | 53.8383i | −0.451460 | − | 0.102549i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 853.662 | 1.61985 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 524.308 | 0.991131 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −125.849 | −0.237004 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 179.210i | − | 0.336229i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 613.624 | − | 489.871i | 1.14696 | − | 0.915646i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 337.257i | − | 0.628038i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −320.418 | − | 317.385i | −0.594468 | − | 0.588841i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 98.2869i | − | 0.181676i | −0.995866 | − | 0.0908382i | \(-0.971045\pi\) | ||
0.995866 | − | 0.0908382i | \(-0.0289546\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1228.41i | − | 2.26227i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −534.689 | − | 669.765i | −0.981081 | − | 1.22893i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −207.231 | −0.378850 | −0.189425 | − | 0.981895i | \(-0.560662\pi\) | ||||
−0.189425 | + | 0.981895i | \(0.560662\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 109.474i | − | 0.199407i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 381.644 | 0.692639 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 288.264i | 0.521272i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 234.319 | − | 187.062i | 0.422196 | − | 0.337049i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 959.370 | 1.72239 | 0.861194 | − | 0.508277i | \(-0.169717\pi\) | ||||
0.861194 | + | 0.508277i | \(0.169717\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 252.740 | 0.452128 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −618.836 | + | 624.749i | −1.10309 | + | 1.11364i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 51.7446 | 0.0919088 | 0.0459544 | − | 0.998944i | \(-0.485367\pi\) | ||||
0.0459544 | + | 0.998944i | \(0.485367\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 260.942 | + | 326.862i | 0.461844 | + | 0.578517i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −278.348 | −0.490914 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 362.183i | − | 0.636526i | −0.948003 | − | 0.318263i | \(-0.896901\pi\) | ||
0.948003 | − | 0.318263i | \(-0.103099\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 698.164i | 1.22270i | 0.791358 | + | 0.611352i | \(0.209374\pi\) | ||||
−0.791358 | + | 0.611352i | \(0.790626\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 566.143i | 0.988034i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −52.8049 | − | 11.9946i | −0.0918347 | − | 0.0208602i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.2829i | 0.0334192i | 0.999860 | + | 0.0167096i | \(0.00531908\pi\) | ||||
−0.999860 | + | 0.0167096i | \(0.994681\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1075.60i | 1.85768i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.4383 | 0.0764858 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −86.7516 | + | 87.5806i | −0.148802 | + | 0.150224i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −43.7923 | + | 34.9604i | −0.0748586 | + | 0.0597614i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 137.281i | − | 0.233869i | −0.993140 | − | 0.116934i | \(-0.962693\pi\) | ||
0.993140 | − | 0.116934i | \(-0.0373068\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1216.00i | 2.06452i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 434.601i | 0.735365i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 307.049 | 0.517789 | 0.258895 | − | 0.965906i | \(-0.416642\pi\) | ||||
0.258895 | + | 0.965906i | \(0.416642\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 257.041 | − | 205.202i | 0.432002 | − | 0.344878i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 678.562i | − | 1.13662i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 810.343 | 1.35283 | 0.676413 | − | 0.736522i | \(-0.263533\pi\) | ||||
0.676413 | + | 0.736522i | \(0.263533\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 382.095i | − | 0.635766i | −0.948130 | − | 0.317883i | \(-0.897028\pi\) | ||
0.948130 | − | 0.317883i | \(-0.102972\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 257.680i | 0.427331i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −381.937 | − | 469.201i | −0.631300 | − | 0.775539i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 302.312 | 0.498043 | 0.249022 | − | 0.968498i | \(-0.419891\pi\) | ||||
0.249022 | + | 0.968498i | \(0.419891\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 112.000 | 0.183908 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 185.488i | 0.303581i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −520.344 | −0.848848 | −0.424424 | − | 0.905464i | \(-0.639523\pi\) | ||||
−0.424424 | + | 0.905464i | \(0.639523\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −604.615 | + | 482.679i | −0.983114 | + | 0.784844i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1040.89i | 1.68702i | 0.537113 | + | 0.843511i | \(0.319515\pi\) | ||||
−0.537113 | + | 0.843511i | \(0.680485\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1076.13 | −1.73850 | −0.869249 | − | 0.494374i | \(-0.835397\pi\) | ||||
−0.869249 | + | 0.494374i | \(0.835397\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −46.0481 | −0.0741516 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −81.1914 | −0.130323 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −563.668 | − | 270.006i | −0.901869 | − | 0.432010i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −889.928 | − | 881.505i | −1.41934 | − | 1.40591i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 405.733i | 0.645044i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −705.843 | −1.11861 | −0.559305 | − | 0.828962i | \(-0.688932\pi\) | ||||
−0.559305 | + | 0.828962i | \(0.688932\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 158.392 | 0.250224 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 519.453 | − | 414.691i | 0.818036 | − | 0.653057i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 163.226 | 0.256241 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 153.576 | 0.240338 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −530.802 | −0.828084 | −0.414042 | − | 0.910258i | \(-0.635883\pi\) | ||||
−0.414042 | + | 0.910258i | \(0.635883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 415.065i | − | 0.645513i | −0.946482 | − | 0.322757i | \(-0.895390\pi\) | ||
0.946482 | − | 0.322757i | \(-0.104610\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −680.721 | − | 852.688i | −1.05538 | − | 1.32200i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 890.968i | 1.37708i | 0.725201 | + | 0.688538i | \(0.241747\pi\) | ||||
−0.725201 | + | 0.688538i | \(0.758253\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 349.377 | + | 346.070i | 0.538331 | + | 0.533236i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 356.857i | 0.548168i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 368.900i | 0.564931i | 0.959277 | + | 0.282465i | \(0.0911522\pi\) | ||||
−0.959277 | + | 0.282465i | \(0.908848\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 153.926 | + | 192.812i | 0.235002 | + | 0.294369i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 158.072 | 0.240597 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 272.221i | − | 0.413082i | −0.978438 | − | 0.206541i | \(-0.933779\pi\) | ||
0.978438 | − | 0.206541i | \(-0.0662206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −784.336 | −1.18659 | −0.593295 | − | 0.804985i | \(-0.702173\pi\) | ||||
−0.593295 | + | 0.804985i | \(0.702173\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 318.257i | − | 0.480025i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 292.301 | + | 366.144i | 0.439551 | + | 0.550592i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.9525 | 0.0374100 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1349.99 | −2.01793 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −301.041 | + | 303.918i | −0.448646 | + | 0.452933i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 165.395 | 0.245758 | 0.122879 | − | 0.992422i | \(-0.460787\pi\) | ||||
0.122879 | + | 0.992422i | \(0.460787\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −518.284 | − | 117.728i | −0.767829 | − | 0.174412i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −469.955 | −0.694173 | −0.347086 | − | 0.937833i | \(-0.612829\pi\) | ||||
−0.347086 | + | 0.937833i | \(0.612829\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 215.686i | − | 0.317652i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 923.606i | 1.35625i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 592.512i | 0.867514i | 0.901030 | + | 0.433757i | \(0.142812\pi\) | ||||
−0.901030 | + | 0.433757i | \(0.857188\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −69.5510 | − | 87.1212i | −0.101534 | − | 0.127184i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 706.461i | 1.02833i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 44.6148i | − | 0.0647530i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −586.418 | −0.848651 | −0.424326 | − | 0.905510i | \(-0.639489\pi\) | ||||
−0.424326 | + | 0.905510i | \(0.639489\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −62.2254 | − | 61.6364i | −0.0897913 | − | 0.0889414i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 816.574 | + | 1022.86i | 1.17493 | + | 1.47174i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1046.92i | − | 1.50203i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1043.90i | − | 1.49342i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1185.11i | 1.69060i | 0.534296 | + | 0.845298i | \(0.320577\pi\) | ||||
−0.534296 | + | 0.845298i | \(0.679423\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −577.949 | −0.822117 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 625.795 | − | 499.587i | 0.887652 | − | 0.708634i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 216.975i | − | 0.306895i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 230.583 | 0.325222 | 0.162611 | − | 0.986690i | \(-0.448008\pi\) | ||||
0.162611 | + | 0.986690i | \(0.448008\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 286.902i | − | 0.403520i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 79.5043i | 0.111507i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 217.711 | + | 23.3678i | 0.304491 | + | 0.0326822i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −642.383 | −0.895931 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −647.117 | −0.900024 | −0.450012 | − | 0.893023i | \(-0.648580\pi\) | ||||
−0.450012 | + | 0.893023i | \(0.648580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 320.499i | 0.444520i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −69.3547 | −0.0959263 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 280.847 | + | 63.7944i | 0.387375 | + | 0.0879923i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1381.75i | 1.90062i | 0.311304 | + | 0.950310i | \(0.399234\pi\) | ||||
−0.311304 | + | 0.950310i | \(0.600766\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −380.644 | −0.522146 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1476.47 | 2.01979 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −354.823 | −0.484069 | −0.242034 | − | 0.970268i | \(-0.577815\pi\) | ||||
−0.242034 | + | 0.970268i | \(0.577815\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −439.627 | − | 550.687i | −0.598132 | − | 0.749234i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 708.589 | − | 715.360i | 0.961451 | − | 0.970638i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 198.704i | − | 0.268882i | −0.990922 | − | 0.134441i | \(-0.957076\pi\) | ||
0.990922 | − | 0.134441i | \(-0.0429239\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 453.343 | 0.611798 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1120.12 | 1.50756 | 0.753779 | − | 0.657127i | \(-0.228229\pi\) | ||||
0.753779 | + | 0.657127i | \(0.228229\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 832.362 | + | 1042.64i | 1.11726 | + | 1.39951i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −44.2284 | −0.0592081 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −444.165 | −0.593010 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −869.405 | −1.15766 | −0.578831 | − | 0.815447i | \(-0.696491\pi\) | ||||
−0.578831 | + | 0.815447i | \(0.696491\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 360.706i | 0.479025i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −386.371 | − | 483.978i | −0.511750 | − | 0.641031i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 874.961i | − | 1.15583i | −0.816098 | − | 0.577913i | \(-0.803867\pi\) | ||
0.816098 | − | 0.577913i | \(-0.196133\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −58.1849 | − | 57.6342i | −0.0766600 | − | 0.0759344i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 645.727i | − | 0.848524i | −0.905539 | − | 0.424262i | \(-0.860534\pi\) | ||
0.905539 | − | 0.424262i | \(-0.139466\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 484.802i | 0.635389i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −255.828 | + | 204.233i | −0.334415 | + | 0.266972i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −177.978 | −0.232044 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 670.097i | − | 0.871388i | −0.900095 | − | 0.435694i | \(-0.856503\pi\) | ||
0.900095 | − | 0.435694i | \(-0.143497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 395.562 | 0.513050 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 612.123i | − | 0.791880i | −0.918276 | − | 0.395940i | \(-0.870419\pi\) | ||
0.918276 | − | 0.395940i | \(-0.129581\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −203.263 | + | 894.842i | −0.262275 | + | 1.15464i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −169.609 | −0.218287 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1491.29 | 1.91436 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −426.350 | − | 422.314i | −0.545902 | − | 0.540735i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 244.911 | 0.312785 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 701.744 | + | 879.021i | 0.893941 | + | 1.11977i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1391.41 | −1.76800 | −0.883998 | − | 0.467491i | \(-0.845158\pi\) | ||||
−0.883998 | + | 0.467491i | \(0.845158\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 787.496i | 0.998093i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 236.595i | − | 0.299109i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 154.820i | − | 0.195234i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −150.521 | + | 120.164i | −0.189334 | + | 0.151150i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 621.140i | − | 0.779348i | −0.920953 | − | 0.389674i | \(-0.872588\pi\) | ||
0.920953 | − | 0.389674i | \(-0.127412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1083.59i | 1.35618i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 80.8081 | 0.100884 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −438.833 | − | 434.679i | −0.546491 | − | 0.541319i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.1111 | + | 23.9391i | 0.0237405 | + | 0.0297380i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1721.53i | − | 2.13324i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 492.303i | − | 0.608532i | −0.952587 | − | 0.304266i | \(-0.901589\pi\) | ||
0.952587 | − | 0.304266i | \(-0.0984112\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 581.566i | − | 0.717098i | −0.933511 | − | 0.358549i | \(-0.883272\pi\) | ||
0.933511 | − | 0.358549i | \(-0.116728\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 766.097 | 0.942309 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 196.165 | + | 245.721i | 0.240693 | + | 0.301498i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2103.16i | 2.57425i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 31.6985 | 0.0387040 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 623.019i | 0.758854i | 0.925222 | + | 0.379427i | \(0.123879\pi\) | ||||
−0.925222 | + | 0.379427i | \(0.876121\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1073.90i | − | 1.30486i | −0.757849 | − | 0.652430i | \(-0.773750\pi\) | ||
0.757849 | − | 0.652430i | \(-0.226250\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −507.538 | − | 797.446i | −0.615197 | − | 0.966601i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1446.64 | 1.74927 | 0.874634 | − | 0.484784i | \(-0.161102\pi\) | ||||
0.874634 | + | 0.484784i | \(0.161102\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −784.117 | −0.945858 | −0.472929 | − | 0.881100i | \(-0.656803\pi\) | ||||
−0.472929 | + | 0.881100i | \(0.656803\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 558.458i | 0.672032i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 953.539 | 1.14470 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −408.931 | + | 326.459i | −0.489737 | + | 0.390969i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 780.340i | 0.932306i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −306.117 | −0.364859 | −0.182429 | − | 0.983219i | \(-0.558396\pi\) | ||||
−0.182429 | + | 0.983219i | \(0.558396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 708.288 | 0.842198 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1212.89 | 1.43878 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 598.442 | − | 477.751i | 0.708215 | − | 0.565385i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.25475 | + | 342.224i | 0.00384268 | + | 0.404043i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 967.224i | − | 1.13925i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.7872 | −0.0444033 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 113.883 | 0.133509 | 0.0667545 | − | 0.997769i | \(-0.478736\pi\) | ||||
0.0667545 | + | 0.997769i | \(0.478736\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −290.921 | − | 364.415i | −0.340259 | − | 0.426217i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −581.910 | −0.679008 | −0.339504 | − | 0.940605i | \(-0.610259\pi\) | ||||
−0.339504 | + | 0.940605i | \(0.610259\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 118.281 | 0.137696 | 0.0688482 | − | 0.997627i | \(-0.478068\pi\) | ||||
0.0688482 | + | 0.997627i | \(0.478068\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 437.644 | 0.508297 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1030.51i | 1.19410i | 0.802203 | + | 0.597051i | \(0.203661\pi\) | ||||
−0.802203 | + | 0.597051i | \(0.796339\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −426.153 | + | 340.208i | −0.492662 | + | 0.393304i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 865.825i | − | 0.998644i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −788.946 | + | 796.485i | −0.907878 | + | 0.916554i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 364.415i | 0.418387i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 214.667i | 0.245896i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 153.898 | + | 318.301i | 0.175883 | + | 0.363773i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −378.593 | −0.431691 | −0.215845 | − | 0.976428i | \(-0.569251\pi\) | ||||
−0.215845 | + | 0.976428i | \(0.569251\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 833.277i | − | 0.947983i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 810.076 | 0.919496 | 0.459748 | − | 0.888049i | \(-0.347940\pi\) | ||||
0.459748 | + | 0.888049i | \(0.347940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 188.555i | 0.213540i | 0.994284 | + | 0.106770i | \(0.0340508\pi\) | ||||
−0.994284 | + | 0.106770i | \(0.965949\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 479.360 | + | 600.458i | 0.541649 | + | 0.678483i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −234.430 | −0.264295 | −0.132148 | − | 0.991230i | \(-0.542187\pi\) | ||||
−0.132148 | + | 0.991230i | \(0.542187\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −376.000 | −0.422947 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −769.089 | − | 761.810i | −0.863175 | − | 0.855005i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1543.53 | −1.72847 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −383.394 | + | 306.073i | −0.428373 | + | 0.341981i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.6403 | 0.0330438 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 422.850i | − | 0.470356i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 260.633i | − | 0.289271i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 617.209i | 0.683509i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1396.46 | + | 1114.83i | −1.54305 | + | 1.23186i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 855.676i | − | 0.943413i | −0.881756 | − | 0.471707i | \(-0.843638\pi\) | ||
0.881756 | − | 0.471707i | \(-0.156362\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 215.950i | 0.237569i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.2609 | 0.0178495 | 0.00892477 | − | 0.999960i | \(-0.497159\pi\) | ||||
0.00892477 | + | 0.999960i | \(0.497159\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 122.785 | + | 121.623i | 0.134485 | + | 0.133212i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −522.329 | + | 416.988i | −0.570852 | + | 0.455725i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 139.565i | − | 0.152197i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 166.342i | 0.181003i | 0.995896 | + | 0.0905017i | \(0.0288470\pi\) | ||||
−0.995896 | + | 0.0905017i | \(0.971153\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 1674.74i | − | 1.81840i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 217.189 | 0.235307 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −425.305 | − | 96.6081i | −0.459789 | − | 0.104441i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 318.986i | − | 0.344106i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 965.712 | 1.03952 | 0.519759 | − | 0.854313i | \(-0.326022\pi\) | ||||
0.519759 | + | 0.854313i | \(0.326022\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1358.27i | 1.45894i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1448.52i | − | 1.55254i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1271.83 | + | 136.511i | 1.36025 | + | 0.146001i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −842.861 | −0.899532 | −0.449766 | − | 0.893146i | \(-0.648493\pi\) | ||||
−0.449766 | + | 0.893146i | \(0.648493\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1726.38 | 1.83853 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1467.05i | − | 1.55903i | −0.626382 | − | 0.779517i | \(-0.715465\pi\) | ||
0.626382 | − | 0.779517i | \(-0.284535\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 97.5028 | 0.103396 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 187.577 | + | 234.964i | 0.198494 | + | 0.248639i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 463.518i | 0.489460i | 0.969591 | + | 0.244730i | \(0.0786993\pi\) | ||||
−0.969591 | + | 0.244730i | \(0.921301\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 223.548 | 0.235561 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2118.38 | 2.22753 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1260.06 | 1.32220 | 0.661099 | − | 0.750298i | \(-0.270090\pi\) | ||||
0.661099 | + | 0.750298i | \(0.270090\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 643.593 | − | 513.796i | 0.673919 | − | 0.538006i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 309.461 | + | 306.532i | 0.323366 | + | 0.320305i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 63.0617i | 0.0657578i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 386.294 | 0.401971 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 442.068 | 0.459053 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1222.74 | − | 976.145i | 1.26709 | − | 1.01155i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 857.576 | 0.886842 | 0.443421 | − | 0.896314i | \(-0.353765\pi\) | ||||
0.443421 | + | 0.896314i | \(0.353765\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2648.36 | 2.73308 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −110.816 | −0.114125 | −0.0570627 | − | 0.998371i | \(-0.518173\pi\) | ||||
−0.0570627 | + | 0.998371i | \(0.518173\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 740.386i | − | 0.760931i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 333.609 | + | 75.7794i | 0.342163 | + | 0.0777224i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 687.248i | 0.703427i | 0.936108 | + | 0.351713i | \(0.114401\pi\) | ||||
−0.936108 | + | 0.351713i | \(0.885599\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −224.336 | − | 222.212i | −0.229148 | − | 0.226979i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 482.513i | − | 0.491858i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 120.258i | 0.122338i | 0.998127 | + | 0.0611688i | \(0.0194828\pi\) | ||||
−0.998127 | + | 0.0611688i | \(0.980517\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 494.055 | − | 394.416i | 0.501579 | − | 0.400422i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −452.975 | −0.458941 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 137.508i | 0.139037i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −220.836 | −0.222842 | −0.111421 | − | 0.993773i | \(-0.535540\pi\) | ||||
−0.111421 | + | 0.993773i | \(0.535540\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 680.186i | 0.684981i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −771.391 | + | 615.820i | −0.775267 | + | 0.618914i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −968.398 | −0.971312 | −0.485656 | − | 0.874150i | \(-0.661419\pi\) | ||||
−0.485656 | + | 0.874150i | \(0.661419\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −370.884 | −0.371255 |
(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 | 880.3.i.g.769.2 | 8 | ||
4.3 | odd | 2 | 110.3.c.b.109.4 | yes | 8 | ||
5.4 | even | 2 | inner | 880.3.i.g.769.7 | 8 | ||
11.10 | odd | 2 | inner | 880.3.i.g.769.1 | 8 | ||
12.11 | even | 2 | 990.3.h.b.109.7 | 8 | |||
20.3 | even | 4 | 550.3.d.d.351.5 | 8 | |||
20.7 | even | 4 | 550.3.d.d.351.4 | 8 | |||
20.19 | odd | 2 | 110.3.c.b.109.5 | yes | 8 | ||
44.43 | even | 2 | 110.3.c.b.109.8 | yes | 8 | ||
55.54 | odd | 2 | inner | 880.3.i.g.769.8 | 8 | ||
60.59 | even | 2 | 990.3.h.b.109.4 | 8 | |||
132.131 | odd | 2 | 990.3.h.b.109.3 | 8 | |||
220.43 | odd | 4 | 550.3.d.d.351.1 | 8 | |||
220.87 | odd | 4 | 550.3.d.d.351.8 | 8 | |||
220.219 | even | 2 | 110.3.c.b.109.1 | ✓ | 8 | ||
660.659 | odd | 2 | 990.3.h.b.109.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
110.3.c.b.109.1 | ✓ | 8 | 220.219 | even | 2 | ||
110.3.c.b.109.4 | yes | 8 | 4.3 | odd | 2 | ||
110.3.c.b.109.5 | yes | 8 | 20.19 | odd | 2 | ||
110.3.c.b.109.8 | yes | 8 | 44.43 | even | 2 | ||
550.3.d.d.351.1 | 8 | 220.43 | odd | 4 | |||
550.3.d.d.351.4 | 8 | 20.7 | even | 4 | |||
550.3.d.d.351.5 | 8 | 20.3 | even | 4 | |||
550.3.d.d.351.8 | 8 | 220.87 | odd | 4 | |||
880.3.i.g.769.1 | 8 | 11.10 | odd | 2 | inner | ||
880.3.i.g.769.2 | 8 | 1.1 | even | 1 | trivial | ||
880.3.i.g.769.7 | 8 | 5.4 | even | 2 | inner | ||
880.3.i.g.769.8 | 8 | 55.54 | odd | 2 | inner | ||
990.3.h.b.109.3 | 8 | 132.131 | odd | 2 | |||
990.3.h.b.109.4 | 8 | 60.59 | even | 2 | |||
990.3.h.b.109.7 | 8 | 12.11 | even | 2 | |||
990.3.h.b.109.8 | 8 | 660.659 | odd | 2 |