Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(369,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("920.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.e (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: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 6 x^{13} + 100 x^{12} - 196 x^{11} + 210 x^{10} + 702 x^{9} + 1572 x^{8} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.11 | ||
Root | \(0.303680 - 0.303680i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 920.369 |
Dual form | 920.2.e.c.369.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(281\) | \(461\) | \(737\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0.540724i | 0.312187i | 0.987742 | + | 0.156094i | \(0.0498901\pi\) | ||||
−0.987742 | + | 0.156094i | \(0.950110\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.21535 | − | 0.303680i | 0.990735 | − | 0.135810i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.15693i | 0.437279i | 0.975806 | + | 0.218639i | \(0.0701618\pi\) | ||||
−0.975806 | + | 0.218639i | \(0.929838\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.70762 | 0.902539 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.10688 | 0.635247 | 0.317624 | − | 0.948217i | \(-0.397115\pi\) | ||||
0.317624 | + | 0.948217i | \(0.397115\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.59296i | − | 1.55121i | −0.631220 | − | 0.775604i | \(-0.717446\pi\) | ||
0.631220 | − | 0.775604i | \(-0.282554\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.164207 | + | 1.19789i | 0.0423981 | + | 0.309295i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.244199i | 0.0592268i | 0.999561 | + | 0.0296134i | \(0.00942762\pi\) | ||||
−0.999561 | + | 0.0296134i | \(0.990572\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.45043 | −0.332752 | −0.166376 | − | 0.986062i | \(-0.553206\pi\) | ||||
−0.166376 | + | 0.986062i | \(0.553206\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.625580 | −0.136513 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.81556 | − | 1.34552i | 0.963111 | − | 0.269103i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.08625i | 0.593948i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.29653 | −0.797845 | −0.398922 | − | 0.916985i | \(-0.630616\pi\) | ||||
−0.398922 | + | 0.916985i | \(0.630616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.19717 | 0.574229 | 0.287114 | − | 0.957896i | \(-0.407304\pi\) | ||||
0.287114 | + | 0.957896i | \(0.407304\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.13924i | 0.198316i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.351337 | + | 2.56301i | 0.0593868 | + | 0.433227i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.807940i | − | 0.132824i | −0.997792 | − | 0.0664122i | \(-0.978845\pi\) | ||
0.997792 | − | 0.0664122i | \(-0.0211552\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.02425 | 0.484267 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.59546 | −0.249169 | −0.124585 | − | 0.992209i | \(-0.539760\pi\) | ||||
−0.124585 | + | 0.992209i | \(0.539760\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.98219i | 0.912275i | 0.889909 | + | 0.456138i | \(0.150768\pi\) | ||||
−0.889909 | + | 0.456138i | \(0.849232\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.99832 | − | 0.822250i | 0.894177 | − | 0.122574i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.624940i | − | 0.0911569i | −0.998961 | − | 0.0455784i | \(-0.985487\pi\) | ||
0.998961 | − | 0.0455784i | \(-0.0145131\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.66151 | 0.808787 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.132044 | −0.0184899 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.536087i | 0.0736372i | 0.999322 | + | 0.0368186i | \(0.0117224\pi\) | ||||
−0.999322 | + | 0.0368186i | \(0.988278\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.66747 | − | 0.639817i | 0.629362 | − | 0.0862729i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.784283i | − | 0.103881i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.03806 | 0.135144 | 0.0675721 | − | 0.997714i | \(-0.478475\pi\) | ||||
0.0675721 | + | 0.997714i | \(0.478475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.77846 | 0.483783 | 0.241891 | − | 0.970303i | \(-0.422232\pi\) | ||||
0.241891 | + | 0.970303i | \(0.422232\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.13253i | 0.394661i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.69847 | − | 12.3904i | −0.210669 | − | 1.53684i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.61571i | − | 0.563899i | −0.959429 | − | 0.281949i | \(-0.909019\pi\) | ||
0.959429 | − | 0.281949i | \(-0.0909811\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.540724 | −0.0650955 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.77489 | 0.804032 | 0.402016 | − | 0.915633i | \(-0.368310\pi\) | ||||
0.402016 | + | 0.915633i | \(0.368310\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.87290i | 1.03849i | 0.854624 | + | 0.519247i | \(0.173788\pi\) | ||||
−0.854624 | + | 0.519247i | \(0.826212\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.727553 | + | 2.60389i | 0.0840106 | + | 0.300671i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.43751i | 0.277780i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.8521 | −1.67099 | −0.835494 | − | 0.549500i | \(-0.814818\pi\) | ||||
−0.835494 | + | 0.549500i | \(0.814818\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.45405 | 0.717116 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 6.11896i | − | 0.671644i | −0.941926 | − | 0.335822i | \(-0.890986\pi\) | ||
0.941926 | − | 0.335822i | \(-0.109014\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0741583 | + | 0.540985i | 0.00804360 | + | 0.0586781i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.32323i | − | 0.249077i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.79942 | −0.614737 | −0.307369 | − | 0.951591i | \(-0.599448\pi\) | ||||
−0.307369 | + | 0.951591i | \(0.599448\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.47066 | 0.678310 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.72879i | 0.179267i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.21321 | + | 0.440467i | −0.329669 | + | 0.0451910i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.38582i | − | 0.242244i | −0.992638 | − | 0.121122i | \(-0.961351\pi\) | ||
0.992638 | − | 0.121122i | \(-0.0386492\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.70462 | 0.573336 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.33379 | 0.829243 | 0.414621 | − | 0.909994i | \(-0.363914\pi\) | ||||
0.414621 | + | 0.909994i | \(0.363914\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4250i | 1.22427i | 0.790754 | + | 0.612135i | \(0.209689\pi\) | ||||
−0.790754 | + | 0.612135i | \(0.790311\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.38588 | + | 0.189976i | −0.135248 | + | 0.0185398i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.5804i | 1.50621i | 0.657899 | + | 0.753106i | \(0.271445\pi\) | ||||
−0.657899 | + | 0.753106i | \(0.728555\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.71396 | −0.930428 | −0.465214 | − | 0.885198i | \(-0.654023\pi\) | ||||
−0.465214 | + | 0.885198i | \(0.654023\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.436872 | 0.0414661 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.69724i | 0.253735i | 0.991920 | + | 0.126867i | \(0.0404922\pi\) | ||||
−0.991920 | + | 0.126867i | \(0.959508\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.303680 | + | 2.21535i | 0.0283183 | + | 0.206583i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 15.1436i | − | 1.40003i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.282521 | −0.0258986 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.56107 | −0.596461 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 0.862705i | − | 0.0777875i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.2595 | − | 4.44318i | 0.917641 | − | 0.397410i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.40424i | 0.390813i | 0.980722 | + | 0.195406i | \(0.0626026\pi\) | ||||
−0.980722 | + | 0.195406i | \(0.937397\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.23471 | −0.284801 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.65815 | 0.144873 | 0.0724367 | − | 0.997373i | \(-0.476922\pi\) | ||||
0.0724367 | + | 0.997373i | \(0.476922\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.67805i | − | 0.145505i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.937232 | + | 6.83712i | 0.0806641 | + | 0.588445i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.70894i | − | 0.231440i | −0.993282 | − | 0.115720i | \(-0.963082\pi\) | ||
0.993282 | − | 0.115720i | \(-0.0369176\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.99503 | −0.762949 | −0.381474 | − | 0.924379i | \(-0.624584\pi\) | ||||
−0.381474 | + | 0.924379i | \(0.624584\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.337920 | 0.0284580 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 11.7837i | − | 0.985400i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.51831 | + | 1.30477i | −0.790453 | + | 0.108355i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.06132i | 0.252493i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.54172 | −0.781688 | −0.390844 | − | 0.920457i | \(-0.627817\pi\) | ||||
−0.390844 | + | 0.920457i | \(0.627817\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.1471 | −0.988514 | −0.494257 | − | 0.869316i | \(-0.664560\pi\) | ||||
−0.494257 | + | 0.869316i | \(0.664560\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.661196i | 0.0534545i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.08285 | − | 0.970918i | 0.568909 | − | 0.0779860i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.1756i | − | 1.53038i | −0.643806 | − | 0.765189i | \(-0.722646\pi\) | ||
0.643806 | − | 0.765189i | \(-0.277354\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.289875 | −0.0229886 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.15693 | −0.0911789 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 17.3397i | − | 1.35815i | −0.734071 | − | 0.679073i | \(-0.762382\pi\) | ||
0.734071 | − | 0.679073i | \(-0.237618\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.345965 | + | 2.52381i | 0.0269333 | + | 0.196479i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 0.582642i | − | 0.0450862i | −0.999746 | − | 0.0225431i | \(-0.992824\pi\) | ||
0.999746 | − | 0.0225431i | \(-0.00717629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.2812 | −1.40624 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.92721 | −0.300321 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 12.0591i | − | 0.916840i | −0.888736 | − | 0.458420i | \(-0.848416\pi\) | ||
0.888736 | − | 0.458420i | \(-0.151584\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.55667 | + | 5.57126i | 0.117673 | + | 0.421148i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.561305i | 0.0421903i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.0142 | −1.34645 | −0.673223 | − | 0.739439i | \(-0.735091\pi\) | ||||
−0.673223 | + | 0.739439i | \(0.735091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.33577 | 0.247946 | 0.123973 | − | 0.992286i | \(-0.460436\pi\) | ||||
0.123973 | + | 0.992286i | \(0.460436\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.04311i | 0.151031i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.245355 | − | 1.78987i | −0.0180389 | − | 0.131594i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.514496i | 0.0376237i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.57057 | −0.259721 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.90013 | −0.209846 | −0.104923 | − | 0.994480i | \(-0.533460\pi\) | ||||
−0.104923 | + | 0.994480i | \(0.533460\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.6127i | 0.835898i | 0.908470 | + | 0.417949i | \(0.137251\pi\) | ||||
−0.908470 | + | 0.417949i | \(0.862749\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.69977 | − | 0.918404i | 0.479780 | − | 0.0657683i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.156603i | 0.0111575i | 0.999984 | + | 0.00557876i | \(0.00177579\pi\) | ||||
−0.999984 | + | 0.00557876i | \(0.998224\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.3474 | −1.65506 | −0.827528 | − | 0.561425i | \(-0.810253\pi\) | ||||
−0.827528 | + | 0.561425i | \(0.810253\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.49583 | 0.176042 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 4.97078i | − | 0.348880i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.53451 | + | 0.484511i | −0.246861 | + | 0.0338397i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.70762i | 0.188192i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.05588 | −0.211380 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.2620 | −1.46374 | −0.731870 | − | 0.681445i | \(-0.761352\pi\) | ||||
−0.731870 | + | 0.681445i | \(0.761352\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.66335i | 0.251008i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.81667 | + | 13.2526i | 0.123896 | + | 0.903823i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.69890i | 0.251098i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.79779 | −0.324205 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.36579 | 0.0918731 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 28.7628i | − | 1.92610i | −0.269328 | − | 0.963049i | \(-0.586801\pi\) | ||
0.269328 | − | 0.963049i | \(-0.413199\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.0387 | − | 3.64315i | 0.869246 | − | 0.242876i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.08990i | 0.404201i | 0.979365 | + | 0.202100i | \(0.0647768\pi\) | ||||
−0.979365 | + | 0.202100i | \(0.935223\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.9294 | −1.31697 | −0.658486 | − | 0.752593i | \(-0.728803\pi\) | ||||
−0.658486 | + | 0.752593i | \(0.728803\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.31802 | −0.0867194 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.63207i | 0.631018i | 0.948923 | + | 0.315509i | \(0.102175\pi\) | ||||
−0.948923 | + | 0.315509i | \(0.897825\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.189782 | − | 1.38446i | −0.0123800 | − | 0.0903123i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 8.03087i | − | 0.521661i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.2583 | −0.857607 | −0.428803 | − | 0.903398i | \(-0.641065\pi\) | ||||
−0.428803 | + | 0.903398i | \(0.641065\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.4250 | −0.929195 | −0.464597 | − | 0.885522i | \(-0.653801\pi\) | ||||
−0.464597 | + | 0.885522i | \(0.653801\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.7486i | 0.817823i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.5422 | − | 1.71929i | 0.801294 | − | 0.109841i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.11220i | 0.516167i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.30867 | 0.209678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.6789 | 1.17900 | 0.589500 | − | 0.807768i | \(-0.299325\pi\) | ||||
0.589500 | + | 0.807768i | \(0.299325\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.10688i | 0.132458i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.292524 | + | 0.0400992i | −0.0183185 | + | 0.00251111i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.5035i | 1.59087i | 0.606042 | + | 0.795433i | \(0.292756\pi\) | ||||
−0.606042 | + | 0.795433i | \(0.707244\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.934730 | 0.0580813 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.6333 | −0.720086 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 18.4521i | − | 1.13780i | −0.822405 | − | 0.568902i | \(-0.807368\pi\) | ||
0.822405 | − | 0.568902i | \(-0.192632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.162799 | + | 1.18762i | 0.0100007 | + | 0.0729549i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 3.13589i | − | 0.191913i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.02723 | −0.123602 | −0.0618012 | − | 0.998088i | \(-0.519684\pi\) | ||||
−0.0618012 | + | 0.998088i | \(0.519684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.7402 | 1.62435 | 0.812175 | − | 0.583414i | \(-0.198284\pi\) | ||||
0.812175 | + | 0.583414i | \(0.198284\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.49884i | 0.211760i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.1458 | − | 2.83484i | 0.611814 | − | 0.170947i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 18.8601i | − | 1.13320i | −0.823995 | − | 0.566598i | \(-0.808259\pi\) | ||
0.823995 | − | 0.566598i | \(-0.191741\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.65672 | 0.518264 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.09240 | 0.363442 | 0.181721 | − | 0.983350i | \(-0.441833\pi\) | ||||
0.181721 | + | 0.983350i | \(0.441833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 15.6971i | − | 0.933095i | −0.884496 | − | 0.466548i | \(-0.845498\pi\) | ||
0.884496 | − | 0.466548i | \(-0.154502\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.238171 | − | 1.73746i | −0.0141080 | − | 0.102918i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.84584i | − | 0.108956i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9404 | 0.996492 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.29007 | 0.0756254 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.3629i | 1.18962i | 0.803868 | + | 0.594808i | \(0.202772\pi\) | ||||
−0.803868 | + | 0.594808i | \(0.797228\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.29967 | − | 0.315239i | 0.133892 | − | 0.0183539i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.50234i | 0.377304i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.59296 | 0.323449 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.92098 | −0.398918 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.50628i | 0.258879i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.37062 | − | 1.14744i | 0.479300 | − | 0.0657025i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.31386i | 0.360351i | 0.983634 | + | 0.180176i | \(0.0576666\pi\) | ||||
−0.983634 | + | 0.180176i | \(0.942333\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.71848 | −0.382201 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.26901 | −0.128664 | −0.0643318 | − | 0.997929i | \(-0.520492\pi\) | ||||
−0.0643318 | + | 0.997929i | \(0.520492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.8886i | 1.46331i | 0.681676 | + | 0.731654i | \(0.261251\pi\) | ||||
−0.681676 | + | 0.731654i | \(0.738749\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.951286 | + | 6.93964i | 0.0535989 | + | 0.391004i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.952783i | 0.0535136i | 0.999642 | + | 0.0267568i | \(0.00851798\pi\) | ||||
−0.999642 | + | 0.0267568i | \(0.991482\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.05225 | −0.506829 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.42468 | −0.470220 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.354193i | − | 0.0197078i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.52542 | − | 26.9332i | −0.417435 | − | 1.49399i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 5.25257i | − | 0.290468i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.723012 | 0.0398609 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.7188 | −0.809017 | −0.404509 | − | 0.914534i | \(-0.632557\pi\) | ||||
−0.404509 | + | 0.914534i | \(0.632557\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.18759i | − | 0.119879i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.40170 | − | 10.2254i | −0.0765831 | − | 0.558674i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.7550i | 1.29402i | 0.762482 | + | 0.647010i | \(0.223981\pi\) | ||||
−0.762482 | + | 0.647010i | \(0.776019\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.45846 | −0.0792127 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.73605 | 0.364777 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.6485i | 0.790944i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.19789 | + | 0.164207i | −0.0644924 | + | 0.00884062i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 20.8557i | − | 1.11959i | −0.828630 | − | 0.559797i | \(-0.810879\pi\) | ||
0.828630 | − | 0.559797i | \(-0.189121\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.8328 | 0.686922 | 0.343461 | − | 0.939167i | \(-0.388401\pi\) | ||||
0.343461 | + | 0.939167i | \(0.388401\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.2612 | 0.921337 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.4888i | 1.62275i | 0.584523 | + | 0.811377i | \(0.301282\pi\) | ||||
−0.584523 | + | 0.811377i | \(0.698718\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.0088 | − | 2.05740i | 0.796583 | − | 0.109196i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 0.152766i | − | 0.00808522i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.0247 | −0.581864 | −0.290932 | − | 0.956744i | \(-0.593965\pi\) | ||||
−0.290932 | + | 0.956744i | \(0.593965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8963 | −0.889276 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.54773i | − | 0.186207i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.69453 | + | 19.6566i | 0.141038 | + | 1.02887i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18.5124i | − | 0.966340i | −0.875527 | − | 0.483170i | \(-0.839485\pi\) | ||
0.875527 | − | 0.483170i | \(-0.160515\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.31990 | −0.224885 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.620215 | −0.0322000 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.4707i | − | 1.37060i | −0.728260 | − | 0.685301i | \(-0.759670\pi\) | ||
0.728260 | − | 0.685301i | \(-0.240330\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.40254 | + | 5.54758i | 0.124066 | + | 0.286476i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.0303i | 1.23762i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.8785 | −0.558791 | −0.279395 | − | 0.960176i | \(-0.590134\pi\) | ||||
−0.279395 | + | 0.960176i | \(0.590134\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.38148 | −0.122007 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 21.6026i | − | 1.10384i | −0.833897 | − | 0.551920i | \(-0.813895\pi\) | ||
0.833897 | − | 0.551920i | \(-0.186105\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.740224 | + | 5.39994i | 0.0377253 | + | 0.275206i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.1975i | 0.823364i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.4117 | 1.49123 | 0.745617 | − | 0.666374i | \(-0.232155\pi\) | ||||
0.745617 | + | 0.666374i | \(0.232155\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.244199 | −0.0123497 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.896603i | 0.0452276i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −32.9025 | + | 4.51028i | −1.65551 | + | 0.226937i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 33.2753i | − | 1.67004i | −0.550219 | − | 0.835021i | \(-0.685456\pi\) | ||
0.550219 | − | 0.835021i | \(-0.314544\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.907360 | 0.0454248 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.7280 | 1.68429 | 0.842147 | − | 0.539248i | \(-0.181292\pi\) | ||||
0.842147 | + | 0.539248i | \(0.181292\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 17.8816i | − | 0.890748i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.2980 | − | 1.95997i | 0.710472 | − | 0.0973915i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.70223i | − | 0.0843764i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.6282 | −1.11889 | −0.559445 | − | 0.828867i | \(-0.688986\pi\) | ||||
−0.559445 | + | 0.828867i | \(0.688986\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.46479 | 0.0722527 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.20097i | 0.0590956i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.85821 | − | 13.5556i | −0.0912159 | − | 0.665421i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 4.86383i | − | 0.238183i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.6846 | 1.69446 | 0.847228 | − | 0.531230i | \(-0.178270\pi\) | ||||
0.847228 | + | 0.531230i | \(0.178270\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.348044 | −0.0169626 | −0.00848131 | − | 0.999964i | \(-0.502700\pi\) | ||||
−0.00848131 | + | 0.999964i | \(0.502700\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 1.69210i | − | 0.0822726i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.328573 | + | 1.17595i | 0.0159381 | + | 0.0570420i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.37142i | 0.211548i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.37172 | 0.307629 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.2559 | 1.02386 | 0.511930 | − | 0.859027i | \(-0.328931\pi\) | ||||
0.511930 | + | 0.859027i | \(0.328931\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.3363i | 1.40981i | 0.709301 | + | 0.704906i | \(0.249011\pi\) | ||||
−0.709301 | + | 0.704906i | \(0.750989\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.705521 | − | 5.14678i | −0.0338271 | − | 0.246769i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.45043i | − | 0.0693835i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.2210 | −0.965096 | −0.482548 | − | 0.875870i | \(-0.660289\pi\) | ||||
−0.482548 | + | 0.875870i | \(0.660289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.3292 | 0.729962 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 33.8124i | − | 1.60648i | −0.595657 | − | 0.803239i | \(-0.703108\pi\) | ||
0.595657 | − | 0.803239i | \(-0.296892\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.8478 | + | 1.76117i | −0.609042 | + | 0.0834875i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 5.15944i | − | 0.244033i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.7383 | −0.837120 | −0.418560 | − | 0.908189i | \(-0.637465\pi\) | ||||
−0.418560 | + | 0.908189i | \(0.637465\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.36144 | −0.158284 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 6.56821i | − | 0.308601i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14.3348 | − | 1.96501i | 0.672025 | − | 0.0921212i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.7861i | 1.48689i | 0.668797 | + | 0.743445i | \(0.266810\pi\) | ||||
−0.668797 | + | 0.743445i | \(0.733190\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.753657 | −0.0351777 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.2206 | 0.802044 | 0.401022 | − | 0.916068i | \(-0.368655\pi\) | ||||
0.401022 | + | 0.916068i | \(0.368655\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 40.0085i | − | 1.85935i | −0.368376 | − | 0.929677i | \(-0.620086\pi\) | ||
0.368376 | − | 0.929677i | \(-0.379914\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.524999 | + | 3.82987i | 0.0243462 | + | 0.177606i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 11.9947i | − | 0.555049i | −0.960719 | − | 0.277524i | \(-0.910486\pi\) | ||
0.960719 | − | 0.277524i | \(-0.0895140\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.34006 | 0.246581 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.3687 | 0.477764 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.6037i | 0.579520i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.98463 | + | 1.95158i | −0.320477 | + | 0.0895446i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.45152i | 0.0664604i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.8249 | 0.951514 | 0.475757 | − | 0.879577i | \(-0.342174\pi\) | ||||
0.475757 | + | 0.879577i | \(0.342174\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.51877 | −0.206038 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.625580i | − | 0.0284649i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.724528 | − | 5.28544i | −0.0328991 | − | 0.239999i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.5640i | 0.750584i | 0.926907 | + | 0.375292i | \(0.122458\pi\) | ||||
−0.926907 | + | 0.375292i | \(0.877542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.37597 | 0.423996 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.8494 | 1.30196 | 0.650978 | − | 0.759097i | \(-0.274359\pi\) | ||||
0.650978 | + | 0.759097i | \(0.274359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.04921i | − | 0.0472538i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.6377 | − | 1.73238i | 0.568024 | − | 0.0778647i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.83808i | 0.351586i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.0289 | 0.628021 | 0.314011 | − | 0.949419i | \(-0.398327\pi\) | ||||
0.314011 | + | 0.949419i | \(0.398327\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.315048 | 0.0140753 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.2157i | 1.03514i | 0.855642 | + | 0.517568i | \(0.173162\pi\) | ||||
−0.855642 | + | 0.517568i | \(0.826838\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.4623 | − | 2.53081i | 0.821560 | − | 0.112619i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 9.88507i | − | 0.439011i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.6290 | 0.781394 | 0.390697 | − | 0.920519i | \(-0.372234\pi\) | ||||
0.390697 | + | 0.920519i | \(0.372234\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.2653 | −0.454111 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 4.47638i | − | 0.197637i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.77322 | + | 27.5257i | 0.166268 | + | 1.21293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.31667i | − | 0.0579072i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.52067 | 0.286226 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.64734 | −0.0721711 | −0.0360855 | − | 0.999349i | \(-0.511489\pi\) | ||||
−0.0360855 | + | 0.999349i | \(0.511489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.1998i | 1.75781i | 0.476994 | + | 0.878907i | \(0.341726\pi\) | ||||
−0.476994 | + | 0.878907i | \(0.658274\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.01252 | + | 0.841729i | −0.131477 | + | 0.0367360i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.780744i | 0.0340098i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.81067 | 0.121973 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.92336i | 0.386513i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.73145 | + | 34.5160i | 0.204559 | + | 1.49226i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 9.74072i | − | 0.420343i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.9281 | 0.513780 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.8419 | 1.15403 | 0.577013 | − | 0.816735i | \(-0.304218\pi\) | ||||
0.577013 | + | 0.816735i | \(0.304218\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.80373i | 0.0774055i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.5198 | + | 2.94994i | −0.921808 | + | 0.126361i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.7472i | 0.887087i | 0.896253 | + | 0.443544i | \(0.146279\pi\) | ||||
−0.896253 | + | 0.443544i | \(0.853721\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.2306 | 0.436633 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.23181 | 0.265484 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 17.1828i | − | 0.730687i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.967826 | − | 0.132670i | 0.0410819 | − | 0.00563151i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.1711i | 0.769933i | 0.922931 | + | 0.384966i | \(0.125787\pi\) | ||||
−0.922931 | + | 0.384966i | \(0.874213\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.4581 | 1.41513 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.278201 | −0.0117456 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 22.9947i | − | 0.969110i | −0.874761 | − | 0.484555i | \(-0.838982\pi\) | ||
0.874761 | − | 0.484555i | \(-0.161018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.819098 | + | 5.97532i | 0.0344597 | + | 0.251384i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.46688i | 0.313580i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.0829 | −1.13537 | −0.567687 | − | 0.823245i | \(-0.692162\pi\) | ||||
−0.567687 | + | 0.823245i | \(0.692162\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.5631 | −0.442053 | −0.221027 | − | 0.975268i | \(-0.570941\pi\) | ||||
−0.221027 | + | 0.975268i | \(0.570941\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.56817i | − | 0.0655112i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.34552 | + | 4.81556i | 0.0561119 | + | 0.200823i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 2.51016i | − | 0.104499i | −0.998634 | − | 0.0522496i | \(-0.983361\pi\) | ||
0.998634 | − | 0.0522496i | \(-0.0166392\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.27925 | −0.260957 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.07922 | 0.293695 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.12947i | 0.0467778i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.59881 | − | 33.5484i | −0.190137 | − | 1.38705i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 43.0923i | − | 1.77861i | −0.457315 | − | 0.889305i | \(-0.651189\pi\) | ||
0.457315 | − | 0.889305i | \(-0.348811\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.63727 | −0.191076 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0846792 | −0.00348324 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 29.7306i | − | 1.22089i | −0.792059 | − | 0.610444i | \(-0.790991\pi\) | ||
0.792059 | − | 0.610444i | \(-0.209009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.625882 | + | 0.0857960i | −0.0256587 | + | 0.00351729i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 12.6245i | − | 0.516687i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.9491 | 0.937674 | 0.468837 | − | 0.883285i | \(-0.344673\pi\) | ||||
0.468837 | + | 0.883285i | \(0.344673\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.49920 | 0.142735 | 0.0713677 | − | 0.997450i | \(-0.477264\pi\) | ||||
0.0713677 | + | 0.997450i | \(0.477264\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12.4976i | − | 0.508941i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.5351 | + | 1.99247i | −0.590934 | + | 0.0810053i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.5670i | 1.72774i | 0.503714 | + | 0.863871i | \(0.331967\pi\) | ||||
−0.503714 | + | 0.863871i | \(0.668033\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.68782 | 0.108916 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.49526 | −0.141403 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.0072i | 1.13120i | 0.824679 | + | 0.565600i | \(0.191356\pi\) | ||||
−0.824679 | + | 0.565600i | \(0.808644\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.261987 | − | 1.91119i | −0.0105643 | − | 0.0770668i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.14856i | 0.126756i | 0.997990 | + | 0.0633781i | \(0.0201874\pi\) | ||||
−0.997990 | + | 0.0633781i | \(0.979813\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.1433 | −0.528275 | −0.264137 | − | 0.964485i | \(-0.585087\pi\) | ||||
−0.264137 | + | 0.964485i | \(0.585087\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.08625 | −0.123847 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 6.70953i | − | 0.268812i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.3792 | − | 12.9588i | 0.855167 | − | 0.518353i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1.65239i | − | 0.0659900i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.197298 | 0.00786677 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.4545 | −1.41142 | −0.705711 | − | 0.708500i | \(-0.749372\pi\) | ||||
−0.705711 | + | 0.708500i | \(0.749372\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 11.4969i | − | 0.456961i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.33748 | + | 9.75693i | 0.0530763 | + | 0.387192i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 31.6646i | − | 1.25460i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.3438 | 0.725670 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.79611 | 0.386923 | 0.193462 | − | 0.981108i | \(-0.438029\pi\) | ||||
0.193462 | + | 0.981108i | \(0.438029\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.6613i | 0.617621i | 0.951124 | + | 0.308810i | \(0.0999308\pi\) | ||||
−0.951124 | + | 0.308810i | \(0.900069\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.16602 | + | 0.982319i | −0.282162 | + | 0.0386788i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 38.6953i | − | 1.52127i | −0.649180 | − | 0.760634i | \(-0.724888\pi\) | ||
0.649180 | − | 0.760634i | \(-0.275112\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.18707 | 0.0858500 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.00009 | −0.0783896 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.8261i | 1.48025i | 0.672469 | + | 0.740125i | \(0.265234\pi\) | ||||
−0.672469 | + | 0.740125i | \(0.734766\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.67339 | − | 0.503548i | 0.143531 | − | 0.0196753i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.0244i | 0.937282i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.00852 | −0.350922 | −0.175461 | − | 0.984486i | \(-0.556142\pi\) | ||||
−0.175461 | + | 0.984486i | \(0.556142\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.0490 | −1.01319 | −0.506594 | − | 0.862185i | \(-0.669096\pi\) | ||||
−0.506594 | + | 0.862185i | \(0.669096\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.738517i | 0.0286816i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.509590 | − | 3.71746i | −0.0197611 | − | 0.144157i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 4.29653i | − | 0.166362i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.5527 | 0.601303 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.96076 | 0.307322 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 4.68835i | − | 0.180722i | −0.995909 | − | 0.0903612i | \(-0.971198\pi\) | ||
0.995909 | − | 0.0903612i | \(-0.0288022\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.15260 | + | 14.8620i | 0.159834 | + | 0.572038i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 31.1370i | − | 1.19669i | −0.801238 | − | 0.598346i | \(-0.795825\pi\) | ||
0.801238 | − | 0.598346i | \(-0.204175\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.76023 | 0.105928 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.29296 | −0.126186 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.2671i | 0.584180i | 0.956391 | + | 0.292090i | \(0.0943507\pi\) | ||||
−0.956391 | + | 0.292090i | \(0.905649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.822652 | − | 6.00125i | −0.0314319 | − | 0.229296i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 10.7763i | − | 0.411142i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.99831 | 0.114227 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.3229 | −1.15354 | −0.576768 | − | 0.816908i | \(-0.695686\pi\) | ||||
−0.576768 | + | 0.816908i | \(0.695686\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.59985i | 0.250707i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.9271 | + | 2.73161i | −0.755880 | + | 0.103616i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.389610i | − | 0.0147575i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.20829 | −0.196996 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.7545 | −0.746118 | −0.373059 | − | 0.927808i | \(-0.621691\pi\) | ||||
−0.373059 | + | 0.927808i | \(0.621691\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.17186i | 0.0441975i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.748611 | − | 0.102620i | 0.0281943 | − | 0.00386488i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.64161i | 0.362610i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.45728 | −0.280064 | −0.140032 | − | 0.990147i | \(-0.544721\pi\) | ||||
−0.140032 | + | 0.990147i | \(0.544721\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.2137 | −1.50813 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.19717i | 0.119735i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.57847 | − | 26.1050i | −0.133827 | − | 0.976271i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 7.16907i | − | 0.267734i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −48.4683 | −1.80756 | −0.903781 | − | 0.427995i | \(-0.859220\pi\) | ||||
−0.903781 | + | 0.427995i | \(0.859220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.3748 | −0.535347 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 7.79993i | − | 0.290083i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.6902 | + | 5.78105i | −0.768413 | + | 0.214703i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 49.7498i | 1.84512i | 0.385856 | + | 0.922559i | \(0.373906\pi\) | ||||
−0.385856 | + | 0.922559i | \(0.626094\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.4687 | 0.461802 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.46084 | −0.0540312 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.1579i | 0.449063i | 0.974467 | + | 0.224531i | \(0.0720851\pi\) | ||||
−0.974467 | + | 0.224531i | \(0.927915\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.929661 | + | 6.78189i | 0.0342911 | + | 0.250154i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 9.72474i | − | 0.358215i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.5807 | 0.757075 | 0.378537 | − | 0.925586i | \(-0.376427\pi\) | ||||
0.378537 | + | 0.925586i | \(0.376427\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.38646 | −0.161141 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.7862i | 0.835944i | 0.908460 | + | 0.417972i | \(0.137259\pi\) | ||||
−0.908460 | + | 0.417972i | \(0.862741\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.1383 | + | 2.89763i | −0.774446 | + | 0.106161i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 16.5678i | − | 0.606185i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.0254 | −0.658634 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.69147 | 0.0617226 | 0.0308613 | − | 0.999524i | \(-0.490175\pi\) | ||||
0.0308613 | + | 0.999524i | \(0.490175\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.1001i | 0.368069i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −26.9100 | + | 3.68883i | −0.979355 | + | 0.134250i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25.7514i | − | 0.935952i | −0.883741 | − | 0.467976i | \(-0.844983\pi\) | ||
0.883741 | − | 0.467976i | \(-0.155017\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.13924 | −0.0413518 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.5286 | 1.50541 | 0.752706 | − | 0.658357i | \(-0.228748\pi\) | ||||
0.752706 | + | 0.658357i | \(0.228748\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 11.2384i | − | 0.406856i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.200792 | + | 1.46478i | 0.00725966 | + | 0.0529593i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 5.80584i | − | 0.209637i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.962676 | −0.0347150 | −0.0173575 | − | 0.999849i | \(-0.505525\pi\) | ||||
−0.0173575 | + | 0.999849i | \(0.505525\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.7904 | −0.496648 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.5570i | 1.53067i | 0.643633 | + | 0.765334i | \(0.277426\pi\) | ||||
−0.643633 | + | 0.765334i | \(0.722574\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.3962 | − | 4.30185i | 0.553046 | − | 0.154527i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.505431i | 0.0181322i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.31411 | 0.0829115 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.2739 | 0.510759 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 13.2601i | − | 0.473879i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.82325 | − | 42.4806i | −0.207841 | − | 1.51620i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.0542i | 1.14261i | 0.820738 | + | 0.571304i | \(0.193562\pi\) | ||||
−0.820738 | + | 0.571304i | \(0.806438\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.97749 | 0.355208 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.12051 | −0.110953 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 21.1328i | − | 0.750447i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.642175 | + | 0.0880293i | −0.0227756 | + | 0.00312208i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.6339i | 1.51017i | 0.655628 | + | 0.755084i | \(0.272404\pi\) | ||||
−0.655628 | + | 0.755084i | \(0.727596\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.152609 | 0.00539893 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.7026 | −0.554825 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.6941i | 0.659701i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.56301 | + | 0.351337i | −0.0903341 | + | 0.0123830i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1.09617i | − | 0.0385871i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.90921 | 0.207757 | 0.103878 | − | 0.994590i | \(-0.466875\pi\) | ||||
0.103878 | + | 0.994590i | \(0.466875\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.1150 | −1.33840 | −0.669199 | − | 0.743084i | \(-0.733362\pi\) | ||||
−0.669199 | + | 0.743084i | \(0.733362\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.4591i | 0.507101i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.26571 | − | 38.4134i | −0.184450 | − | 1.34556i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.67675i | − | 0.303561i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17.5201 | 0.612201 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.4861 | −1.09887 | −0.549437 | − | 0.835535i | \(-0.685158\pi\) | ||||
−0.549437 | + | 0.835535i | \(0.685158\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.04415i | − | 0.0712546i | −0.999365 | − | 0.0356273i | \(-0.988657\pi\) | ||
0.999365 | − | 0.0356273i | \(-0.0113429\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.53287 | + | 5.48607i | 0.0533675 | + | 0.191000i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 34.9513i | − | 1.21538i | −0.794175 | − | 0.607689i | \(-0.792097\pi\) | ||
0.794175 | − | 0.607689i | \(-0.207903\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.48455 | 0.0862919 | 0.0431460 | − | 0.999069i | \(-0.486262\pi\) | ||||
0.0431460 | + | 0.999069i | \(0.486262\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.1981 | 0.353769 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.38253i | 0.0479019i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.176937 | − | 1.29076i | −0.00612315 | − | 0.0446684i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.86726i | 0.341062i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.5747 | 1.60794 | 0.803969 | − | 0.594672i | \(-0.202718\pi\) | ||||
0.803969 | + | 0.594672i | \(0.202718\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5399 | −0.363444 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.29431i | 0.113462i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.4992 | + | 5.55163i | −1.39322 | + | 0.190982i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.59070i | − | 0.260820i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.48780 | 0.291300 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.807940 | 0.0276958 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.74956i | 0.0599036i | 0.999551 | + | 0.0299518i | \(0.00953538\pi\) | ||||
−0.999551 | + | 0.0299518i | \(0.990465\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.70015 | + | 1.19262i | −0.297539 | + | 0.0407866i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 5.88603i | − | 0.201063i | −0.994934 | − | 0.100532i | \(-0.967946\pi\) | ||
0.994934 | − | 0.100532i | \(-0.0320543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.4929 | 1.31336 | 0.656680 | − | 0.754169i | \(-0.271960\pi\) | ||||
0.656680 | + | 0.754169i | \(0.271960\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.998090 | 0.0340148 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 36.8687i | − | 1.25503i | −0.778606 | − | 0.627513i | \(-0.784073\pi\) | ||
0.778606 | − | 0.627513i | \(-0.215927\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.66213 | − | 26.7152i | −0.124516 | − | 0.908345i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.16006i | 0.311092i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.2915 | −1.06149 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.8155 | −0.874724 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 6.45990i | − | 0.218634i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.14045 | + | 11.8696i | 0.173779 | + | 0.401265i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 46.7182i | − | 1.57756i | −0.614676 | − | 0.788780i | \(-0.710713\pi\) | ||
0.614676 | − | 0.788780i | \(-0.289287\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −11.0107 | −0.371383 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.8791 | −0.467600 | −0.233800 | − | 0.972285i | \(-0.575116\pi\) | ||||
−0.233800 | + | 0.972285i | \(0.575116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.8941i | 0.804100i | 0.915618 | + | 0.402050i | \(0.131702\pi\) | ||||
−0.915618 | + | 0.402050i | \(0.868298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.170457 | + | 1.24349i | 0.00572986 | + | 0.0417994i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.36292i | 0.0793391i | 0.999213 | + | 0.0396695i | \(0.0126305\pi\) | ||||
−0.999213 | + | 0.0396695i | \(0.987369\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.09540 | −0.170894 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.5979 | 0.455546 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.906432i | 0.0303326i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.9078 | + | 5.47057i | −1.33397 | + | 0.182861i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.02425i | 0.100977i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.7367 | −0.458145 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.130912 | −0.00436130 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 3.74234i | − | 0.124537i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.38990 | − | 1.01301i | 0.245649 | − | 0.0336735i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 23.1649i | − | 0.769179i | −0.923088 | − | 0.384590i | \(-0.874343\pi\) | ||
0.923088 | − | 0.384590i | \(-0.125657\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.5647 | 0.748424 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.6423 | −1.44593 | −0.722967 | − | 0.690882i | \(-0.757222\pi\) | ||||
−0.722967 | + | 0.690882i | \(0.757222\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.8919i | − | 0.426660i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.620451 | + | 4.52619i | 0.0205115 | + | 0.149631i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.91837i | 0.0633500i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.3644 | 0.341890 | 0.170945 | − | 0.985281i | \(-0.445318\pi\) | ||||
0.170945 | + | 0.985281i | \(0.445318\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.41406 | −0.112497 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 37.8917i | − | 1.24722i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.08710 | − | 3.89068i | −0.0357435 | − | 0.127925i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 33.6421i | 1.10495i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.1805 | 1.25266 | 0.626331 | − | 0.779557i | \(-0.284556\pi\) | ||||
0.626331 | + | 0.779557i | \(0.284556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.21163 | −0.269125 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 1.22691i | − | 0.0401671i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.156242 | + | 1.13979i | 0.00510967 | + | 0.0372751i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.1405i | 0.396613i | 0.980140 | + | 0.198306i | \(0.0635441\pi\) | ||||
−0.980140 | + | 0.198306i | \(0.936456\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.9986 | −0.456826 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.2871 | −0.596141 | −0.298071 | − | 0.954544i | \(-0.596343\pi\) | ||||
−0.298071 | + | 0.954544i | \(0.596343\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.59546i | − | 0.0519554i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.91007 | + | 1.08431i | −0.257315 | + | 0.0352727i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.7376i | 1.68125i | 0.541621 | + | 0.840623i | \(0.317811\pi\) | ||||
−0.541621 | + | 0.840623i | \(0.682189\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.6257 | 1.61092 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.515193 | −0.0167063 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 58.1675i | − | 1.88423i | −0.335292 | − | 0.942114i | \(-0.608835\pi\) | ||
0.335292 | − | 0.942114i | \(-0.391165\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.42480 | + | 0.880712i | −0.207902 | + | 0.0284992i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 4.89477i | − | 0.158225i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.13406 | 0.101204 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.7781 | −0.670261 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.1857i | 1.35942i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.52654 | + | 25.7261i | 0.113523 | + | 0.828153i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.1138i | 0.389555i | 0.980847 | + | 0.194777i | \(0.0623984\pi\) | ||||
−0.980847 | + | 0.194777i | \(0.937602\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.191521 | 0.00615253 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.5922 | 1.17430 | 0.587149 | − | 0.809479i | \(-0.300250\pi\) | ||||
0.587149 | + | 0.809479i | \(0.300250\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 10.4066i | − | 0.333621i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.5634 | − | 4.06917i | 0.466403 | − | 0.130318i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 22.3327i | − | 0.714487i | −0.934011 | − | 0.357243i | \(-0.883717\pi\) | ||
0.934011 | − | 0.357243i | \(-0.116283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.2187 | −0.390510 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.3017 | −0.839748 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 49.8139i | 1.58882i | 0.607384 | + | 0.794408i | \(0.292219\pi\) | ||||
−0.607384 | + | 0.794408i | \(0.707781\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0475574 | + | 0.346931i | 0.00151530 | + | 0.0110542i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.390950i | 0.0124441i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.98219 | −0.190223 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.3340 | −0.455334 | −0.227667 | − | 0.973739i | \(-0.573110\pi\) | ||||
−0.227667 | + | 0.973739i | \(0.573110\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 7.95880i | − | 0.252565i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.7227 | + | 7.09016i | −1.63972 | + | 0.224773i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 51.7021i | − | 1.63742i | −0.574205 | − | 0.818711i | \(-0.694689\pi\) | ||
0.574205 | − | 0.818711i | \(-0.305311\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.49350 | 0.0788909 |
(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 | 920.2.e.c.369.11 | yes | 16 | |
4.3 | odd | 2 | 1840.2.e.h.369.6 | 16 | |||
5.2 | odd | 4 | 4600.2.a.bj.1.6 | 8 | |||
5.3 | odd | 4 | 4600.2.a.bk.1.3 | 8 | |||
5.4 | even | 2 | inner | 920.2.e.c.369.6 | ✓ | 16 | |
20.3 | even | 4 | 9200.2.a.dd.1.6 | 8 | |||
20.7 | even | 4 | 9200.2.a.de.1.3 | 8 | |||
20.19 | odd | 2 | 1840.2.e.h.369.11 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.c.369.6 | ✓ | 16 | 5.4 | even | 2 | inner | |
920.2.e.c.369.11 | yes | 16 | 1.1 | even | 1 | trivial | |
1840.2.e.h.369.6 | 16 | 4.3 | odd | 2 | |||
1840.2.e.h.369.11 | 16 | 20.19 | odd | 2 | |||
4600.2.a.bj.1.6 | 8 | 5.2 | odd | 4 | |||
4600.2.a.bk.1.3 | 8 | 5.3 | odd | 4 | |||
9200.2.a.dd.1.6 | 8 | 20.3 | even | 4 | |||
9200.2.a.de.1.3 | 8 | 20.7 | even | 4 |