Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(65,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.h (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: | \(39.6940658242\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.4 | ||
Root | \(1.58114 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.65 |
Dual form | 384.5.h.e.65.2 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −3.00000 | + | 8.48528i | −0.333333 | + | 0.942809i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 37.9473 | 1.51789 | 0.758947 | − | 0.651153i | \(-0.225714\pi\) | ||||
0.758947 | + | 0.651153i | \(0.225714\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 37.9473 | 0.774435 | 0.387218 | − | 0.921988i | \(-0.373436\pi\) | ||||
0.387218 | + | 0.921988i | \(0.373436\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −63.0000 | − | 50.9117i | −0.777778 | − | 0.628539i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 134.000 | 1.10744 | 0.553719 | − | 0.832704i | \(-0.313208\pi\) | ||||
0.553719 | + | 0.832704i | \(0.313208\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 321.994i | 1.90529i | 0.304087 | + | 0.952644i | \(0.401649\pi\) | ||||
−0.304087 | + | 0.952644i | \(0.598351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −113.842 | + | 321.994i | −0.505964 | + | 1.43108i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 237.588i | 0.822103i | 0.911612 | + | 0.411052i | \(0.134838\pi\) | ||||
−0.911612 | + | 0.411052i | \(0.865162\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 492.146i | − | 1.36329i | −0.731685 | − | 0.681643i | \(-0.761266\pi\) | ||
0.731685 | − | 0.681643i | \(-0.238734\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −113.842 | + | 321.994i | −0.258145 | + | 0.730145i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 643.988i | − | 1.21737i | −0.793413 | − | 0.608684i | \(-0.791698\pi\) | ||
0.793413 | − | 0.608684i | \(-0.208302\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 815.000 | 1.30400 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 621.000 | − | 381.838i | 0.851852 | − | 0.523783i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 796.894 | 0.947555 | 0.473778 | − | 0.880645i | \(-0.342890\pi\) | ||||
0.473778 | + | 0.880645i | \(0.342890\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1100.47 | 1.14513 | 0.572566 | − | 0.819858i | \(-0.305948\pi\) | ||||
0.572566 | + | 0.819858i | \(0.305948\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −402.000 | + | 1137.03i | −0.369146 | + | 1.04410i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1440.00 | 1.17551 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1609.97i | − | 1.17602i | −0.808854 | − | 0.588009i | \(-0.799912\pi\) | ||
0.808854 | − | 0.588009i | \(-0.200088\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2732.21 | − | 965.981i | −1.79632 | − | 0.635096i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1289.76i | 0.767259i | 0.923487 | + | 0.383630i | \(0.125326\pi\) | ||||
−0.923487 | + | 0.383630i | \(0.874674\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 424.264i | 0.229456i | 0.993397 | + | 0.114728i | \(0.0365996\pi\) | ||||
−0.993397 | + | 0.114728i | \(0.963400\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2390.68 | − | 1931.96i | −1.18058 | − | 0.954056i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2575.95i | 1.16612i | 0.812431 | + | 0.583058i | \(0.198144\pi\) | ||||
−0.812431 | + | 0.583058i | \(0.801856\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −961.000 | −0.400250 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2016.00 | − | 712.764i | −0.775087 | − | 0.274034i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1631.74 | −0.580895 | −0.290448 | − | 0.956891i | \(-0.593804\pi\) | ||||
−0.290448 | + | 0.956891i | \(0.593804\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5084.94 | 1.68097 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4176.00 | + | 1476.44i | 1.28532 | + | 0.454429i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1382.00 | −0.397012 | −0.198506 | − | 0.980100i | \(-0.563609\pi\) | ||||
−0.198506 | + | 0.980100i | \(0.563609\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 321.994i | 0.0865342i | 0.999064 | + | 0.0432671i | \(0.0137766\pi\) | ||||
−0.999064 | + | 0.0432671i | \(0.986223\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2390.68 | − | 1931.96i | −0.602339 | − | 0.486763i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12218.8i | 2.89202i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 186.676i | − | 0.0415853i | −0.999784 | − | 0.0207926i | \(-0.993381\pi\) | ||
0.999784 | − | 0.0207926i | \(-0.00661898\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5464.42 | + | 1931.96i | 1.14775 | + | 0.405789i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1931.96i | 0.383250i | 0.981468 | + | 0.191625i | \(0.0613757\pi\) | ||||
−0.981468 | + | 0.191625i | \(0.938624\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4894.00 | 0.918371 | 0.459186 | − | 0.888340i | \(-0.348141\pi\) | ||||
0.459186 | + | 0.888340i | \(0.348141\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2445.00 | + | 6915.50i | −0.434667 | + | 1.22942i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5084.94 | 0.857639 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1479.95 | −0.237133 | −0.118566 | − | 0.992946i | \(-0.537830\pi\) | ||||
−0.118566 | + | 0.992946i | \(0.537830\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1377.00 | + | 6414.87i | 0.209877 | + | 0.977728i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5914.00 | −0.858470 | −0.429235 | − | 0.903193i | \(-0.641217\pi\) | ||||
−0.429235 | + | 0.903193i | \(0.641217\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9015.83i | 1.24787i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2390.68 | + | 6761.87i | −0.315852 | + | 0.893364i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9062.28i | 1.14408i | 0.820225 | + | 0.572041i | \(0.193848\pi\) | ||||
−0.820225 | + | 0.572041i | \(0.806152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12218.8i | 1.47552i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3301.42 | + | 9337.82i | −0.381711 | + | 1.07964i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 18675.6i | − | 2.06932i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5858.00 | 0.622595 | 0.311298 | − | 0.950312i | \(-0.399236\pi\) | ||||
0.311298 | + | 0.950312i | \(0.399236\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8442.00 | − | 6822.17i | −0.861341 | − | 0.696068i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14837.4 | −1.45451 | −0.727253 | − | 0.686370i | \(-0.759203\pi\) | ||||
−0.727253 | + | 0.686370i | \(0.759203\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2846.05 | −0.268267 | −0.134134 | − | 0.990963i | \(-0.542825\pi\) | ||||
−0.134134 | + | 0.990963i | \(0.542825\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4320.00 | + | 12218.8i | −0.391837 | + | 1.10828i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 21274.0 | 1.85815 | 0.929077 | − | 0.369887i | \(-0.120604\pi\) | ||||
0.929077 | + | 0.369887i | \(0.120604\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7405.86i | − | 0.623336i | −0.950191 | − | 0.311668i | \(-0.899112\pi\) | ||
0.950191 | − | 0.311668i | \(-0.100888\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13661.0 | + | 4829.91i | 1.10876 | + | 0.392006i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3461.99i | 0.271125i | 0.990769 | + | 0.135562i | \(0.0432842\pi\) | ||||
−0.990769 | + | 0.135562i | \(0.956716\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 24437.6i | − | 1.84783i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16393.2 | − | 20285.6i | 1.19755 | − | 1.48189i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9015.83i | 0.636666i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3315.00 | 0.226419 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10944.0 | − | 3869.29i | −0.723379 | − | 0.255753i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7209.99 | 0.461440 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21364.3 | −1.32459 | −0.662296 | − | 0.749242i | \(-0.730418\pi\) | ||||
−0.662296 | + | 0.749242i | \(0.730418\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3600.00 | − | 1272.79i | −0.216333 | − | 0.0764853i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17338.0 | 1.01031 | 0.505157 | − | 0.863027i | \(-0.331435\pi\) | ||||
0.505157 | + | 0.863027i | \(0.331435\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 18675.6i | − | 1.05578i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 23565.3 | − | 14489.7i | 1.29302 | − | 0.795046i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 27560.2i | 1.46839i | 0.678939 | + | 0.734195i | \(0.262440\pi\) | ||||
−0.678939 | + | 0.734195i | \(0.737560\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19668.9i | 1.01801i | 0.860765 | + | 0.509003i | \(0.169986\pi\) | ||||
−0.860765 | + | 0.509003i | \(0.830014\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21857.7 | − | 7727.85i | −1.09942 | − | 0.388705i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 43147.2i | 2.10999i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30240.0 | 1.43829 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2883.00 | − | 8154.36i | 0.133417 | − | 0.377359i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9372.99 | −0.422188 | −0.211094 | − | 0.977466i | \(-0.567703\pi\) | ||||
−0.211094 | + | 0.977466i | \(0.567703\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23489.4 | −1.03019 | −0.515096 | − | 0.857133i | \(-0.672244\pi\) | ||||
−0.515096 | + | 0.857133i | \(0.672244\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12096.0 | − | 14968.0i | 0.516724 | − | 0.639414i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 41760.0 | 1.73819 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4185.92i | 0.169821i | 0.996389 | + | 0.0849105i | \(0.0270604\pi\) | ||||
−0.996389 | + | 0.0849105i | \(0.972940\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4895.21 | − | 13845.7i | 0.193632 | − | 0.547673i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 24437.6i | − | 0.942773i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 44955.0i | − | 1.69201i | −0.533175 | − | 0.846005i | \(-0.679001\pi\) | ||
0.533175 | − | 0.846005i | \(-0.320999\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15254.8 | + | 43147.2i | −0.560324 | + | 1.58484i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 40571.2i | − | 1.45474i | −0.686246 | − | 0.727370i | \(-0.740743\pi\) | ||
0.686246 | − | 0.727370i | \(-0.259257\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −75119.0 | −2.63012 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −25056.0 | + | 31005.2i | −0.856879 | + | 1.06033i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23261.7 | 0.777230 | 0.388615 | − | 0.921400i | \(-0.372954\pi\) | ||||
0.388615 | + | 0.921400i | \(0.372954\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30927.1 | 1.00986 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4146.00 | − | 11726.7i | 0.132337 | − | 0.374307i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6586.00 | 0.205549 | 0.102775 | − | 0.994705i | \(-0.467228\pi\) | ||||
0.102775 | + | 0.994705i | \(0.467228\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 30589.4i | 0.933714i | 0.884333 | + | 0.466857i | \(0.154614\pi\) | ||||
−0.884333 | + | 0.466857i | \(0.845386\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2732.21 | − | 965.981i | −0.0815852 | − | 0.0288447i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 61094.0i | − | 1.78507i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31836.8i | 0.910429i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 23565.3 | − | 14489.7i | 0.659704 | − | 0.405636i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11591.8i | − | 0.317748i | −0.987299 | − | 0.158874i | \(-0.949214\pi\) | ||
0.987299 | − | 0.158874i | \(-0.0507864\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24386.0 | −0.654675 | −0.327338 | − | 0.944907i | \(-0.606151\pi\) | ||||
−0.327338 | + | 0.944907i | \(0.606151\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −103680. | − | 36656.4i | −2.72663 | − | 0.964008i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 64244.8 | 1.65541 | 0.827705 | − | 0.561163i | \(-0.189646\pi\) | ||||
0.827705 | + | 0.561163i | \(0.189646\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −34114.7 | −0.861459 | −0.430730 | − | 0.902481i | \(-0.641744\pi\) | ||||
−0.430730 | + | 0.902481i | \(0.641744\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1584.00 | + | 560.029i | 0.0392070 | + | 0.0138618i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 30240.0 | 0.733820 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 48943.1i | 1.16462i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −32786.5 | + | 40571.2i | −0.765164 | + | 0.946842i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 65947.6i | − | 1.50975i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17666.4i | 0.396810i | 0.980120 | + | 0.198405i | \(0.0635760\pi\) | ||||
−0.980120 | + | 0.198405i | \(0.936424\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16393.2 | − | 5795.89i | −0.361331 | − | 0.127750i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16099.7i | 0.348290i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 41760.0 | 0.886831 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14682.0 | + | 41527.0i | −0.306124 | + | 0.865849i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −76501.8 | −1.56634 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 43146.1 | 0.867625 | 0.433812 | − | 0.901003i | \(-0.357168\pi\) | ||||
0.433812 | + | 0.901003i | \(0.357168\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −51345.0 | − | 41493.0i | −1.01422 | − | 0.819615i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 32678.0 | 0.634167 | 0.317084 | − | 0.948398i | \(-0.397296\pi\) | ||||
0.317084 | + | 0.948398i | \(0.397296\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 55704.9i | − | 1.06224i | −0.847297 | − | 0.531120i | \(-0.821771\pi\) | ||
0.847297 | − | 0.531120i | \(-0.178229\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15254.8 | + | 43147.2i | −0.285880 | + | 0.808590i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 47687.3i | − | 0.878397i | −0.898390 | − | 0.439198i | \(-0.855263\pi\) | ||
0.898390 | − | 0.439198i | \(-0.144737\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 97750.4i | 1.77004i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4439.84 | − | 12557.8i | 0.0790443 | − | 0.223571i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 74702.6i | − | 1.30780i | −0.756583 | − | 0.653898i | \(-0.773133\pi\) | ||
0.756583 | − | 0.653898i | \(-0.226867\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 766.000 | 0.0131885 | 0.00659424 | − | 0.999978i | \(-0.497901\pi\) | ||||
0.00659424 | + | 0.999978i | \(0.497901\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −58563.0 | − | 7560.39i | −0.991770 | − | 0.128036i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −36467.4 | −0.607537 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 158468. | 2.59745 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17742.0 | − | 50182.0i | 0.286157 | − | 0.809373i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2054.00 | 0.0326027 | 0.0163013 | − | 0.999867i | \(-0.494811\pi\) | ||||
0.0163013 | + | 0.999867i | \(0.494811\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 86294.3i | − | 1.34816i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −76501.8 | − | 27047.5i | −1.17650 | − | 0.415955i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18667.6i | 0.282633i | 0.989964 | + | 0.141316i | \(0.0451335\pi\) | ||||
−0.989964 | + | 0.141316i | \(0.954866\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 61094.0i | − | 0.910750i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −50204.3 | − | 40571.2i | −0.736987 | − | 0.595576i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 92090.2i | 1.33138i | 0.746228 | + | 0.665690i | \(0.231863\pi\) | ||||
−0.746228 | + | 0.665690i | \(0.768137\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −61920.0 | −0.881737 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −76896.0 | − | 27186.8i | −1.07865 | − | 0.381361i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7627.41 | 0.105408 | 0.0527039 | − | 0.998610i | \(-0.483216\pi\) | ||||
0.0527039 | + | 0.998610i | \(0.483216\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −53999.1 | −0.735271 | −0.367636 | − | 0.929970i | \(-0.619833\pi\) | ||||
−0.367636 | + | 0.929970i | \(0.619833\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −103680. | − | 36656.4i | −1.39114 | − | 0.491841i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 109210. | 1.44410 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 23505.5i | − | 0.306345i | −0.988199 | − | 0.153173i | \(-0.951051\pi\) | ||
0.988199 | − | 0.153173i | \(-0.0489490\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −69329.8 | − | 56026.9i | −0.890659 | − | 0.719761i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 118624.i | − | 1.50231i | −0.660123 | − | 0.751157i | \(-0.729496\pi\) | ||
0.660123 | − | 0.751157i | \(-0.270504\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 134763.i | − | 1.68267i | −0.540515 | − | 0.841334i | \(-0.681771\pi\) | ||
0.540515 | − | 0.841334i | \(-0.318229\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 158468. | + | 56026.9i | 1.95098 | + | 0.689774i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 48943.1i | 0.594193i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27073.0 | 0.324146 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17574.0 | + | 49706.8i | −0.207532 | + | 0.586989i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 34494.1 | 0.401800 | 0.200900 | − | 0.979612i | \(-0.435613\pi\) | ||||
0.200900 | + | 0.979612i | \(0.435613\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −52443.2 | −0.602622 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 83214.0 | − | 51166.2i | 0.943373 | − | 0.580057i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 207360. | 2.31944 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16099.7i | 0.177699i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 44512.2 | − | 125900.i | 0.484835 | − | 1.37132i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12218.8i | 0.131350i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23402.4i | − | 0.248304i | −0.992263 | − | 0.124152i | \(-0.960379\pi\) | ||
0.992263 | − | 0.124152i | \(-0.0396210\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8538.15 | − | 24149.5i | 0.0894225 | − | 0.252925i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 19963.6i | − | 0.206404i | −0.994660 | − | 0.103202i | \(-0.967091\pi\) | ||
0.994660 | − | 0.103202i | \(-0.0329088\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27458.0 | −0.280272 | −0.140136 | − | 0.990132i | \(-0.544754\pi\) | ||||
−0.140136 | + | 0.990132i | \(0.544754\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −90720.0 | − | 73312.8i | −0.914286 | − | 0.738854i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −168752. | −1.67931 | −0.839653 | − | 0.543123i | \(-0.817242\pi\) | ||||
−0.839653 | + | 0.543123i | \(0.817242\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 106784. | 1.04936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −63822.0 | + | 180516.i | −0.619385 | + | 1.75188i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 116928. | 1.12076 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 262425.i | 2.48450i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 62840.8 | + | 22217.6i | 0.587687 | + | 0.207779i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 97750.4i | 0.903081i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 79065.9i | 0.721661i | 0.932631 | + | 0.360830i | \(0.117507\pi\) | ||||
−0.932631 | + | 0.360830i | \(0.882493\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −81966.2 | + | 101428.i | −0.739174 | + | 0.914681i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 7083.86i | − | 0.0631220i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 63454.0 | 0.558726 | 0.279363 | − | 0.960186i | \(-0.409877\pi\) | ||||
0.279363 | + | 0.960186i | \(0.409877\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −29376.0 | − | 10386.0i | −0.255619 | − | 0.0903750i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 147463. | 1.26816 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −127579. | −1.08440 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 207360. | + | 73312.8i | 1.74216 | + | 0.615945i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28166.0 | 0.233919 | 0.116960 | − | 0.993137i | \(-0.462685\pi\) | ||||
0.116960 | + | 0.993137i | \(0.462685\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 67296.7i | 0.552514i | 0.961084 | + | 0.276257i | \(0.0890940\pi\) | ||||
−0.961084 | + | 0.276257i | \(0.910906\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 122949. | + | 199958.i | 0.997957 | + | 1.62302i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27831.7i | 0.223352i | 0.993745 | + | 0.111676i | \(0.0356220\pi\) | ||||
−0.993745 | + | 0.111676i | \(0.964378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 73312.8i | 0.581732i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −76501.8 | − | 27047.5i | −0.600254 | − | 0.212222i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 147473.i | − | 1.14426i | −0.820164 | − | 0.572129i | \(-0.806118\pi\) | ||
0.820164 | − | 0.572129i | \(-0.193882\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −111887. | −0.858549 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9945.00 | + | 28128.7i | −0.0754730 | + | 0.213470i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 185714. | 1.39399 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −216565. | −1.60789 | −0.803946 | − | 0.594702i | \(-0.797270\pi\) | ||||
−0.803946 | + | 0.594702i | \(0.797270\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 65664.0 | − | 81255.1i | 0.482253 | − | 0.596757i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −61920.0 | −0.449866 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 163895.i | − | 1.17801i | −0.808131 | − | 0.589003i | \(-0.799521\pi\) | ||
0.808131 | − | 0.589003i | \(-0.200479\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −21630.0 | + | 61178.8i | −0.153813 | + | 0.435049i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 256595.i | 1.80537i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 259836.i | − | 1.80893i | −0.426550 | − | 0.904464i | \(-0.640271\pi\) | ||
0.426550 | − | 0.904464i | \(-0.359729\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 64093.0 | − | 181283.i | 0.441531 | − | 1.24884i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 222820.i | 1.51899i | 0.650511 | + | 0.759497i | \(0.274555\pi\) | ||||
−0.650511 | + | 0.759497i | \(0.725445\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 192960. | 1.30180 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21600.0 | − | 26728.6i | 0.144222 | − | 0.178466i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −59008.1 | −0.389953 | −0.194977 | − | 0.980808i | \(-0.562463\pi\) | ||||
−0.194977 | + | 0.980808i | \(0.562463\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 153004. | 1.00080 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −52014.0 | + | 147118.i | −0.336771 | + | 0.952533i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −56160.0 | −0.359942 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 236665.i | − | 1.50160i | −0.660530 | − | 0.750799i | \(-0.729669\pi\) | ||
0.660530 | − | 0.750799i | \(-0.270331\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 158468. | + | 56026.9i | 0.995396 | + | 0.351926i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 193906.i | 1.20587i | 0.797789 | + | 0.602937i | \(0.206003\pi\) | ||||
−0.797789 | + | 0.602937i | \(0.793997\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 354345.i | 2.18181i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 52253.5 | + | 243427.i | 0.318570 | + | 1.48409i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 215736.i | − | 1.30237i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −125086. | −0.747760 | −0.373880 | − | 0.927477i | \(-0.621973\pi\) | ||||
−0.373880 | + | 0.927477i | \(0.621973\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −233856. | − | 82680.6i | −1.38441 | − | 0.489463i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −52443.2 | −0.307460 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −224421. | −1.30307 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −166896. | − | 59006.6i | −0.959785 | − | 0.339335i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −72346.0 | −0.412085 | −0.206042 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206042 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 254053.i | − | 1.43338i | −0.697394 | − | 0.716688i | \(-0.745657\pi\) | ||
0.697394 | − | 0.716688i | \(-0.254343\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 131146. | − | 162285.i | 0.732950 | − | 0.906979i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 193634.i | 1.07202i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12218.8i | 0.0670151i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −366116. | − | 129442.i | −1.98932 | − | 0.703330i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 280779.i | − | 1.51150i | −0.654858 | − | 0.755752i | \(-0.727271\pi\) | ||
0.654858 | − | 0.755752i | \(-0.272729\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 303266. | 1.61751 | 0.808757 | − | 0.588143i | \(-0.200141\pi\) | ||||
0.808757 | + | 0.588143i | \(0.200141\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −90720.0 | + | 256595.i | −0.479429 | + | 1.35603i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −316936. | −1.65962 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −235387. | −1.22139 | −0.610694 | − | 0.791866i | \(-0.709110\pi\) | ||||
−0.610694 | + | 0.791866i | \(0.709110\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 60543.0 | + | 48926.1i | 0.311305 | + | 0.251573i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −151354. | −0.771235 | −0.385617 | − | 0.922659i | \(-0.626011\pi\) | ||||
−0.385617 | + | 0.922659i | \(0.626011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 343889.i | 1.73660i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28119.0 | − | 79532.5i | 0.140729 | − | 0.398042i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 86312.3i | 0.428134i | 0.976819 | + | 0.214067i | \(0.0686711\pi\) | ||||
−0.976819 | + | 0.214067i | \(0.931329\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 172828.i | 0.849692i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 70468.2 | − | 199314.i | 0.343397 | − | 0.971274i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 463671.i | 2.23969i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30626.0 | 0.146642 | 0.0733209 | − | 0.997308i | \(-0.476640\pi\) | ||||
0.0733209 | + | 0.997308i | \(0.476640\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 90720.0 | + | 147542.i | 0.430604 | + | 0.700310i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 326233. | 1.53506 | 0.767532 | − | 0.641011i | \(-0.221485\pi\) | ||||
0.767532 | + | 0.641011i | \(0.221485\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 305286. | 1.42412 | 0.712058 | − | 0.702121i | \(-0.247763\pi\) | ||||
0.712058 | + | 0.702121i | \(0.247763\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −125280. | + | 354345.i | −0.579396 | + | 1.63878i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 299558. | 1.37356 | 0.686779 | − | 0.726866i | \(-0.259024\pi\) | ||||
0.686779 | + | 0.726866i | \(0.259024\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 7083.86i | − | 0.0322051i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35518.7 | − | 12557.8i | −0.160109 | − | 0.0566070i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 56851.4i | 0.254108i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 401099.i | − | 1.77773i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 102799. | + | 83074.4i | 0.451808 | + | 0.365116i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 43791.2i | − | 0.190860i | −0.995436 | − | 0.0954301i | \(-0.969577\pi\) | ||
0.995436 | − | 0.0954301i | \(-0.0304226\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 518400. | 2.24065 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 207360. | + | 73312.8i | 0.888855 | + | 0.314258i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 222295. | 0.945033 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −152662. | −0.643685 | −0.321842 | − | 0.946793i | \(-0.604302\pi\) | ||||
−0.321842 | + | 0.946793i | \(0.604302\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 381456. | + | 134865.i | 1.59524 | + | 0.564003i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −367142. | −1.52290 | −0.761449 | − | 0.648224i | \(-0.775512\pi\) | ||||
−0.761449 | + | 0.648224i | \(0.775512\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 189332.i | 0.778988i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −320351. | − | 258883.i | −1.30742 | − | 1.05656i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 73312.8i | 0.296802i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 60160.6i | 0.241608i | 0.992676 | + | 0.120804i | \(0.0385473\pi\) | ||||
−0.992676 | + | 0.120804i | \(0.961453\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 344258. | + | 121714.i | 1.37154 | + | 0.484913i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 263391.i | 1.04103i | 0.853851 | + | 0.520517i | \(0.174261\pi\) | ||||
−0.853851 | + | 0.520517i | \(0.825739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −563040. | −2.20778 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 225357. | − | 637406.i | 0.876708 | − | 2.47971i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15975.8 | 0.0616634 | 0.0308317 | − | 0.999525i | \(-0.490184\pi\) | ||||
0.0308317 | + | 0.999525i | \(0.490184\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 185714. | 0.711219 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −187920. | − | 305623.i | −0.714066 | − | 1.16132i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −108000. | −0.407201 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 345177.i | 1.29140i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −69785.1 | + | 197382.i | −0.259077 | + | 0.732779i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 210707.i | − | 0.776252i | −0.921606 | − | 0.388126i | \(-0.873123\pi\) | ||
0.921606 | − | 0.388126i | \(-0.126877\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 92812.0i | 0.339313i | 0.985503 | + | 0.169657i | \(0.0542659\pi\) | ||||
−0.985503 | + | 0.169657i | \(0.945734\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −92781.2 | + | 262425.i | −0.336621 | + | 0.952109i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 261459.i | 0.941418i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −134879. | −0.481984 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 87066.0 | + | 70360.0i | 0.308787 | + | 0.249538i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −415296. | −1.46185 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 807292. | 2.82048 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19758.0 | + | 55884.1i | −0.0685164 | + | 0.193794i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −128774. | −0.443252 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 249545.i | − | 0.852618i | −0.904578 | − | 0.426309i | \(-0.859814\pi\) | ||
0.904578 | − | 0.426309i | \(-0.140186\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −259560. | − | 91768.2i | −0.880314 | − | 0.311238i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 281033.i | − | 0.946158i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 258309.i | − | 0.863306i | −0.902040 | − | 0.431653i | \(-0.857930\pi\) | ||
0.902040 | − | 0.431653i | \(-0.142070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16393.2 | − | 20285.6i | 0.0543902 | − | 0.0673044i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 392188.i | − | 1.29179i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −56160.0 | −0.183644 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 518400. | + | 183282.i | 1.68298 | + | 0.595023i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −151448. | −0.488149 | −0.244075 | − | 0.969756i | \(-0.578484\pi\) | ||||
−0.244075 | + | 0.969756i | \(0.578484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −136610. | −0.437180 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −270144. | − | 95510.3i | −0.858360 | − | 0.303476i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 238118. | 0.751234 | 0.375617 | − | 0.926775i | \(-0.377431\pi\) | ||||
0.375617 | + | 0.926775i | \(0.377431\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 131373.i | 0.411539i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 52253.5 | + | 243427.i | 0.162536 | + | 0.757187i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 163868.i | 0.506138i | 0.967448 | + | 0.253069i | \(0.0814400\pi\) | ||||
−0.967448 | + | 0.253069i | \(0.918560\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 207126.i | − | 0.635275i | −0.948212 | − | 0.317638i | \(-0.897110\pi\) | ||
0.948212 | − | 0.317638i | \(-0.102890\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 98359.5 | + | 34775.3i | 0.299576 | + | 0.105916i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 524850.i | − | 1.58745i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −306146. | −0.919553 | −0.459777 | − | 0.888035i | \(-0.652071\pi\) | ||||
−0.459777 | + | 0.888035i | \(0.652071\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 73158.0 | − | 206922.i | 0.218225 | − | 0.617234i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −224421. | −0.664830 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −218653. | −0.643306 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 622080. | − | 769785.i | 1.81775 | − | 2.24935i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 460954. | 1.33777 | 0.668885 | − | 0.743366i | \(-0.266772\pi\) | ||||
0.668885 | + | 0.743366i | \(0.266772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 541594.i | − | 1.56114i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −192734. | + | 545135.i | −0.551804 | + | 1.56074i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 254966.i | − | 0.725057i | −0.931973 | − | 0.362529i | \(-0.881913\pi\) | ||
0.931973 | − | 0.362529i | \(-0.118087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 342127.i | 0.966391i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 102344. | − | 289472.i | 0.287153 | − | 0.812192i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 245359.i | − | 0.683831i | −0.939731 | − | 0.341916i | \(-0.888924\pi\) | ||
0.939731 | − | 0.341916i | \(-0.111076\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 74206.0 | 0.205442 | 0.102721 | − | 0.994710i | \(-0.467245\pi\) | ||||
0.102721 | + | 0.994710i | \(0.467245\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9504.00 | + | 11760.6i | −0.0261380 | + | 0.0323441i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 125795. | 0.343680 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 299518. | 0.812917 | 0.406458 | − | 0.913669i | \(-0.366764\pi\) | ||||
0.406458 | + | 0.913669i | \(0.366764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −90720.0 | + | 256595.i | −0.244607 | + | 0.691852i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −829440. | −2.22179 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 206398.i | − | 0.549268i | −0.961549 | − | 0.274634i | \(-0.911443\pi\) | ||
0.961549 | − | 0.274634i | \(-0.0885567\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −415296. | − | 146829.i | −1.09801 | − | 0.388206i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 716667.i | − | 1.88255i | −0.337638 | − | 0.941276i | \(-0.609628\pi\) | ||
0.337638 | − | 0.941276i | \(-0.390372\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 153329.i | 0.400169i | 0.979779 | + | 0.200084i | \(0.0641216\pi\) | ||||
−0.979779 | + | 0.200084i | \(0.935878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −245899. | − | 399916.i | −0.637636 | − | 1.03702i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 343889.i | 0.886018i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −235775. | −0.603584 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 559584. | + | 197843.i | 1.42341 | + | 0.503252i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 382509. | 0.966809 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −448955. | −1.12757 | −0.563786 | − | 0.825921i | \(-0.690656\pi\) | ||||
−0.563786 | + | 0.825921i | \(0.690656\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −149904. | − | 52999.1i | −0.374116 | − | 0.132270i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −810720. | −2.01059 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 309436.i | − | 0.762592i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 98359.5 | − | 121714.i | 0.240888 | − | 0.298083i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 73482.5i | 0.178841i | 0.995994 | + | 0.0894207i | \(0.0285016\pi\) | ||||
−0.995994 | + | 0.0894207i | \(0.971498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 260753.i | − | 0.630677i | −0.948979 | − | 0.315338i | \(-0.897882\pi\) | ||
0.948979 | − | 0.315338i | \(-0.102118\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −136610. | − | 48299.1i | −0.328371 | − | 0.116097i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 226040.i | − | 0.539978i | −0.962863 | − | 0.269989i | \(-0.912980\pi\) | ||
0.962863 | − | 0.269989i | \(-0.0870201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −185188. | −0.439667 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −125280. | + | 354345.i | −0.295610 | + | 0.836113i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 144390. | 0.338618 | 0.169309 | − | 0.985563i | \(-0.445846\pi\) | ||||
0.169309 | + | 0.985563i | \(0.445846\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 657931. | 1.53355 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −308322. | − | 249162.i | −0.714289 | − | 0.577232i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −383174. | −0.882318 | −0.441159 | − | 0.897429i | \(-0.645433\pi\) | ||||
−0.441159 | + | 0.897429i | \(0.645433\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 57636.9i | 0.131916i | 0.997822 | + | 0.0659580i | \(0.0210103\pi\) | ||||
−0.997822 | + | 0.0659580i | \(0.978990\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 229505. | − | 649139.i | 0.522115 | − | 1.47676i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 708691.i | − | 1.60256i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 513190.i | − | 1.15352i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −129438. | + | 366107.i | −0.289208 | + | 0.818005i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43147.2i | 0.0958313i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 679778. | 1.50085 | 0.750424 | − | 0.660956i | \(-0.229849\pi\) | ||||
0.750424 | + | 0.660956i | \(0.229849\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 506115. | − | 311198.i | 1.11081 | − | 0.683013i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6716.68 | 0.0146547 | 0.00732735 | − | 0.999973i | \(-0.497668\pi\) | ||||
0.00732735 | + | 0.999973i | \(0.497668\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 222295. | 0.482160 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −98034.0 | + | 277282.i | −0.211389 | + | 0.597899i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −552634. | −1.18467 | −0.592333 | − | 0.805693i | \(-0.701793\pi\) | ||||
−0.592333 | + | 0.805693i | \(0.701793\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.04584e6i | 2.22886i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 472672. | + | 167115.i | 1.00149 | + | 0.354080i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 525409.i | − | 1.10677i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 327719.i | 0.686349i | 0.939272 | + | 0.343174i | \(0.111502\pi\) | ||||
−0.939272 | + | 0.343174i | \(0.888498\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −320351. | − | 258883.i | −0.667053 | − | 0.539060i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 746382.i | 1.54522i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −306432. | −0.630766 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 404640. | + | 143062.i | 0.828160 | + | 0.292799i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −838750. | −1.70685 | −0.853427 | − | 0.521212i | \(-0.825480\pi\) | ||||
−0.853427 | + | 0.521212i | \(0.825480\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −792340. | −1.60325 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −829440. | − | 293251.i | −1.66881 | − | 0.590013i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −563040. | −1.12642 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3541.93i | 0.00704608i | 0.999994 | + | 0.00352304i | \(0.00112142\pi\) | ||||
−0.999994 | + | 0.00352304i | \(0.998879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 93236.6 | + | 75346.5i | 0.184437 | + | 0.149047i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 708691.i | − | 1.39405i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.63732e6i | 3.20274i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 633872. | + | 224108.i | 1.23300 | + | 0.435932i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.02909e6i | 1.99066i | 0.0965451 | + | 0.995329i | \(0.469221\pi\) | ||||
−0.0965451 | + | 0.995329i | \(0.530779\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −108000. | −0.207756 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2298.00 | + | 6499.73i | −0.00439616 | + | 0.0124342i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 649469. | 1.23561 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −821901. | −1.55507 | −0.777537 | − | 0.628838i | \(-0.783531\pi\) | ||||
−0.777537 | + | 0.628838i | \(0.783531\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 239841. | − | 474242.i | 0.451303 | − | 0.892371i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −100800. | −0.188637 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 118816.i | 0.221139i | 0.993868 | + | 0.110570i | \(0.0352675\pi\) | ||||
−0.993868 | + | 0.110570i | \(0.964732\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 109402. | − | 309436.i | 0.202512 | − | 0.572791i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 25014.6i | − | 0.0460531i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 349169.i | − | 0.639363i | −0.947525 | − | 0.319681i | \(-0.896424\pi\) | ||
0.947525 | − | 0.319681i | \(-0.103576\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −475404. | + | 1.34465e6i | −0.865818 | + | 2.44890i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 532578.i | − | 0.964729i | −0.875971 | − | 0.482365i | \(-0.839778\pi\) | ||
0.875971 | − | 0.482365i | \(-0.160222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −355680. | −0.640836 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 372582. | + | 301092.i | 0.667699 | + | 0.539582i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 807292. | 1.43902 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −753444. | −1.33589 | −0.667946 | − | 0.744210i | \(-0.732826\pi\) | ||||
−0.667946 | + | 0.744210i | \(0.732826\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6162.00 | + | 17428.8i | −0.0108676 | + | 0.0307381i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −891360. | −1.56372 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 87904.3i | − | 0.153398i | −0.997054 | − | 0.0766988i | \(-0.975562\pi\) | ||
0.997054 | − | 0.0766988i | \(-0.0244380\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 732232. | + | 258883.i | 1.27106 | + | 0.449386i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.06243e6i | 1.83455i | 0.398257 | + | 0.917274i | \(0.369615\pi\) | ||||
−0.398257 | + | 0.917274i | \(0.630385\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 281033.i | − | 0.482734i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 459011. | − | 567997.i | 0.784332 | − | 0.970562i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 444995.i | − | 0.756423i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 259006. | 0.437983 | 0.218991 | − | 0.975727i | \(-0.429723\pi\) | ||||
0.218991 | + | 0.975727i | \(0.429723\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −158400. | − | 56002.9i | −0.266469 | − | 0.0942110i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 597784. | 1.00043 | 0.500214 | − | 0.865902i | \(-0.333255\pi\) | ||||
0.500214 | + | 0.865902i | \(0.333255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 896885. | 1.49325 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 518400. | + | 183282.i | 0.858663 | + | 0.303583i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 634752. | 1.04599 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 258883.i | 0.424426i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 494871. | − | 304284.i | 0.807177 | − | 0.496313i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 158844.i | 0.257770i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 916156.i | − | 1.47918i | −0.673060 | − | 0.739588i | \(-0.735020\pi\) | ||
0.673060 | − | 0.739588i | \(-0.264980\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −781411. | − | 276271.i | −1.25524 | − | 0.443793i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 131373.i | 0.209969i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −103680. | −0.164873 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 185760. | − | 525409.i | 0.293912 | − | 0.831310i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33735.2 | 0.0531088 | 0.0265544 | − | 0.999647i | \(-0.491546\pi\) | ||||
0.0265544 | + | 0.999647i | \(0.491546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −612015. | −0.958668 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 461376. | − | 570924.i | 0.719101 | − | 0.889842i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 655796. | 1.01704 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 927342.i | − | 1.43103i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22882.2 | + | 64720.8i | −0.0351359 | + | 0.0993794i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 914035.i | 1.39658i | 0.715815 | + | 0.698290i | \(0.246055\pi\) | ||||
−0.715815 | + | 0.698290i | \(0.753945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.20567e6i | 1.83311i | 0.399911 | + | 0.916554i | \(0.369041\pi\) | ||||
−0.399911 | + | 0.916554i | \(0.630959\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 161997. | − | 458197.i | 0.245090 | − | 0.693220i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1.70592e6i | − | 2.56829i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 208800. | 0.312814 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 622080. | − | 769785.i | 0.927424 | − | 1.14763i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −447741. | −0.664263 | −0.332132 | − | 0.943233i | \(-0.607768\pi\) | ||||
−0.332132 | + | 0.943233i | \(0.607768\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −327220. | −0.483103 | −0.241552 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241552 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −327630. | + | 926678.i | −0.481366 | + | 1.36151i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44966.0 | −0.0657466 | −0.0328733 | − | 0.999460i | \(-0.510466\pi\) | ||||
−0.0328733 | + | 0.999460i | \(0.510466\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6761.87i | 0.00983915i | 0.999988 | + | 0.00491958i | \(0.00156596\pi\) | ||||
−0.999988 | + | 0.00491958i | \(0.998434\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 199451. | + | 70516.6i | 0.288825 | + | 0.102115i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 228322.i | − | 0.329047i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.53957e6i | − | 2.20814i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 683394. | − | 420202.i | 0.975484 | − | 0.599801i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 455299.i | 0.646804i | 0.946262 | + | 0.323402i | \(0.104827\pi\) | ||||
−0.946262 | + | 0.323402i | \(0.895173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −72241.0 | −0.102139 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.00656e6 | + | 355873.i | 1.41640 | + | 0.500771i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.85057e6 | −3.99225 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 125795. | 0.175347 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.14350e6 | + | 404290.i | 1.58644 | + | 0.560890i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.03680e6 | −1.43165 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 629498.i | 0.865160i | 0.901596 | + | 0.432580i | \(0.142397\pi\) | ||||
−0.901596 | + | 0.432580i | \(0.857603\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −950808. | + | 1.17657e6i | −1.30065 | + | 1.60947i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 118522.i | − | 0.161376i | −0.996739 | − | 0.0806880i | \(-0.974288\pi\) | ||
0.996739 | − | 0.0806880i | \(-0.0257117\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 667944.i | − | 0.905220i | −0.891709 | − | 0.452610i | \(-0.850493\pi\) | ||
0.891709 | − | 0.452610i | \(-0.149507\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −415296. | − | 146829.i | −0.560210 | − | 0.198064i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 233124.i | 0.313015i | 0.987677 | + | 0.156507i | \(0.0500235\pi\) | ||||
−0.987677 | + | 0.156507i | \(0.949977\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 882720. | 1.17975 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −81219.0 | + | 229722.i | −0.108049 | + | 0.305608i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −198313. | −0.262610 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60108.6 | 0.0792319 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −369054. | − | 298241.i | −0.484241 | − | 0.391326i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 273600. | 0.357355 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 930884.i | − | 1.21031i | −0.796108 | − | 0.605155i | \(-0.793111\pi\) | ||
0.796108 | − | 0.605155i | \(-0.206889\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −103482. | + | 292692.i | −0.133933 | + | 0.378821i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 862444.i | 1.11117i | 0.831461 | + | 0.555583i | \(0.187505\pi\) | ||||
−0.831461 | + | 0.555583i | \(0.812495\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 402219.i | − | 0.515871i | −0.966162 | − | 0.257936i | \(-0.916958\pi\) | ||
0.966162 | − | 0.257936i | \(-0.0830423\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 157330. | − | 444995.i | 0.200874 | − | 0.568158i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 465603.i | − | 0.591791i | −0.955220 | − | 0.295896i | \(-0.904382\pi\) | ||
0.955220 | − | 0.295896i | \(-0.0956181\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −810720. | −1.02581 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 184518. | + | 859593.i | 0.232425 | + | 1.08277i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.26774e6 | 1.58975 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 249921. | 0.312002 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −622080. | + | 1.75951e6i | −0.773146 | + | 2.18679i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 876960. | 1.08508 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 387681.i | − | 0.477556i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −136610. | − | 48299.1i | −0.167536 | − | 0.0592329i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.16079e6i | 1.41728i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.04785e6i | 1.27375i | 0.770968 | + | 0.636874i | \(0.219773\pi\) | ||||
−0.770968 | + | 0.636874i | \(0.780227\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 934757. | + | 755397.i | 1.13128 | + | 0.914214i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56670.9i | 0.0682847i | 0.999417 | + | 0.0341424i | \(0.0108700\pi\) | ||||
−0.999417 | + | 0.0341424i | \(0.989130\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −792476. | −0.950702 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −103680. | − | 36656.4i | −0.123838 | − | 0.0437832i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 657931. | 0.782423 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 887702. | 1.05108 | 0.525540 | − | 0.850769i | \(-0.323863\pi\) | ||||
0.525540 | + | 0.850769i | \(0.323863\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 198576. | + | 70207.2i | 0.234103 | + | 0.0827680i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −622080. | −0.730202 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.31212e6i | − | 1.53353i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 179301. | + | 144897.i | 0.208652 | + | 0.168617i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 255068.i | − | 0.295545i | −0.989021 | − | 0.147773i | \(-0.952790\pi\) | ||
0.989021 | − | 0.147773i | \(-0.0472104\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 472953.i | 0.545655i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 169397. | + | 59890.8i | 0.194600 | + | 0.0688014i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.20812e6i | 1.38193i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 952706. | 1.08512 | 0.542562 | − | 0.840015i | \(-0.317454\pi\) | ||||
0.542562 | + | 0.840015i | \(0.317454\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 82374.0 | − | 232989.i | 0.0934241 | − | 0.264243i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 691438. | 0.780862 | 0.390431 | − | 0.920632i | \(-0.372326\pi\) | ||||
0.390431 | + | 0.920632i | \(0.372326\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 830591. | 0.934037 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 894240. | − | 549846.i | 1.00136 | − | 0.615712i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.24172e6 | 1.38460 | 0.692300 | − | 0.721610i | \(-0.256597\pi\) | ||||
0.692300 | + | 0.721610i | \(0.256597\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.57584e6i | 1.74976i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 506255. | − | 1.43191e6i | 0.559769 | − | 1.58326i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 101552.i | 0.111816i | 0.998436 | + | 0.0559078i | \(0.0178053\pi\) | ||||
−0.998436 | + | 0.0559078i | \(0.982195\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 439877.i | − | 0.482308i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −320351. | + | 906091.i | −0.349786 | + | 0.989345i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.04584e6i | 1.13717i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 287519. | 0.311329 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.34026e6 | − | 1.08310e6i | −1.44523 | − | 1.16792i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −925384. | −0.993727 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −675121. | −0.721986 | −0.360993 | − | 0.932569i | \(-0.617562\pi\) | ||||
−0.360993 | + | 0.932569i | \(0.617562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −350784. | + | 992167.i | −0.373587 | + | 1.05666i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 125894. | 0.133526 | 0.0667631 | − | 0.997769i | \(-0.478733\pi\) | ||||
0.0667631 | + | 0.997769i | \(0.478733\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 746382.i | 0.788379i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.22675e6 | − | 787275.i | −2.34241 | − | 0.828165i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.77319e6i | 1.85766i | 0.370512 | + | 0.928828i | \(0.379182\pi\) | ||||
−0.370512 | + | 0.928828i | \(0.620818\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.21435e6i | 1.26700i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −377045. | + | 466569.i | −0.391791 | + | 0.484817i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 839116.i | − | 0.868390i | −0.900819 | − | 0.434195i | \(-0.857033\pi\) | ||
0.900819 | − | 0.434195i | \(-0.142967\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.43792e6 | 2.51274 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −829440. | − | 293251.i | −0.851433 | − | 0.301027i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 273221. | 0.279332 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.48909e6 | 1.51626 | 0.758131 | − | 0.652103i | \(-0.226113\pi\) | ||||
0.758131 | + | 0.652103i | \(0.226113\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −670896. | − | 237198.i | −0.680388 | − | 0.240554i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.29456e6 | −1.30760 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.59290e6i | 1.60250i | 0.598327 | + | 0.801252i | \(0.295832\pi\) | ||||
−0.598327 | + | 0.801252i | \(0.704168\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −614747. | − | 999791.i | −0.615978 | − | 1.00179i |
(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 | 384.5.h.e.65.4 | yes | 4 | |
3.2 | odd | 2 | 384.5.h.f.65.3 | yes | 4 | ||
4.3 | odd | 2 | 384.5.h.f.65.2 | yes | 4 | ||
8.3 | odd | 2 | inner | 384.5.h.e.65.3 | yes | 4 | |
8.5 | even | 2 | 384.5.h.f.65.1 | yes | 4 | ||
12.11 | even | 2 | inner | 384.5.h.e.65.1 | ✓ | 4 | |
24.5 | odd | 2 | inner | 384.5.h.e.65.2 | yes | 4 | |
24.11 | even | 2 | 384.5.h.f.65.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.h.e.65.1 | ✓ | 4 | 12.11 | even | 2 | inner | |
384.5.h.e.65.2 | yes | 4 | 24.5 | odd | 2 | inner | |
384.5.h.e.65.3 | yes | 4 | 8.3 | odd | 2 | inner | |
384.5.h.e.65.4 | yes | 4 | 1.1 | even | 1 | trivial | |
384.5.h.f.65.1 | yes | 4 | 8.5 | even | 2 | ||
384.5.h.f.65.2 | yes | 4 | 4.3 | odd | 2 | ||
384.5.h.f.65.3 | yes | 4 | 3.2 | odd | 2 | ||
384.5.h.f.65.4 | yes | 4 | 24.11 | even | 2 |