Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(449,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.dc (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 16x^{14} + 174x^{12} + 1012x^{10} + 4243x^{8} + 9708x^{6} + 15858x^{4} + 12150x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 171) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.5 | ||
Root | \(0.484374 + 0.838961i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.449 |
Dual form | 2736.2.dc.c.1889.5 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.557544 | − | 0.321898i | 0.249341 | − | 0.143957i | −0.370121 | − | 0.928983i | \(-0.620684\pi\) |
0.619463 | + | 0.785026i | \(0.287351\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.15106 | −0.813024 | −0.406512 | − | 0.913645i | \(-0.633255\pi\) | ||||
−0.406512 | + | 0.913645i | \(0.633255\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.27164i | 0.684926i | 0.939531 | + | 0.342463i | \(0.111261\pi\) | ||||
−0.939531 | + | 0.342463i | \(0.888739\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.313530 | − | 0.181017i | −0.0869575 | − | 0.0502050i | 0.455891 | − | 0.890036i | \(-0.349321\pi\) |
−0.542848 | + | 0.839831i | \(0.682654\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.40976 | − | 0.813922i | 0.341916 | − | 0.197405i | −0.319203 | − | 0.947686i | \(-0.603415\pi\) |
0.661119 | + | 0.750281i | \(0.270082\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.64170 | + | 3.46719i | 0.606048 | + | 0.795428i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.64153 | − | 3.25714i | −1.17634 | − | 0.679161i | −0.221176 | − | 0.975234i | \(-0.570989\pi\) |
−0.955165 | + | 0.296073i | \(0.904323\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.29276 | + | 3.97118i | −0.458553 | + | 0.794236i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.968749 | + | 1.67792i | −0.179892 | + | 0.311582i | −0.941843 | − | 0.336052i | \(-0.890908\pi\) |
0.761951 | + | 0.647634i | \(0.224242\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.67274i | − | 1.19846i | −0.800577 | − | 0.599229i | \(-0.795474\pi\) | ||
0.800577 | − | 0.599229i | \(-0.204526\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.19931 | + | 0.692422i | −0.202721 | + | 0.117041i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.30902i | − | 0.544000i | −0.962297 | − | 0.272000i | \(-0.912315\pi\) | ||
0.962297 | − | 0.272000i | \(-0.0876851\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.49359 | + | 6.05108i | 0.545607 | + | 0.945020i | 0.998568 | + | 0.0534894i | \(0.0170343\pi\) |
−0.452961 | + | 0.891530i | \(0.649632\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.71723 | − | 4.70639i | −0.414374 | − | 0.717717i | 0.580988 | − | 0.813912i | \(-0.302666\pi\) |
−0.995363 | + | 0.0961948i | \(0.969333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.69557 | − | 4.44304i | −1.12251 | − | 0.648084i | −0.180473 | − | 0.983580i | \(-0.557763\pi\) |
−0.942042 | + | 0.335496i | \(0.891096\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.37294 | −0.338991 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.96730 | + | 3.40746i | −0.270229 | + | 0.468051i | −0.968920 | − | 0.247373i | \(-0.920433\pi\) |
0.698691 | + | 0.715423i | \(0.253766\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.731237 | + | 1.26654i | 0.0986000 | + | 0.170780i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.93605 | + | 5.08538i | 0.382241 | + | 0.662061i | 0.991382 | − | 0.131001i | \(-0.0418191\pi\) |
−0.609141 | + | 0.793062i | \(0.708486\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.91982 | + | 6.78933i | −0.501882 | + | 0.869285i | 0.498116 | + | 0.867111i | \(0.334025\pi\) |
−0.999998 | + | 0.00217438i | \(0.999308\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.233076 | −0.0289095 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4184 | − | 6.01507i | −1.27281 | − | 0.734858i | −0.297295 | − | 0.954786i | \(-0.596085\pi\) |
−0.975516 | + | 0.219928i | \(0.929418\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.60883 | + | 13.1789i | 0.903002 | + | 1.56405i | 0.823577 | + | 0.567205i | \(0.191975\pi\) |
0.0794258 | + | 0.996841i | \(0.474691\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.63029 | − | 13.2161i | −0.893058 | − | 1.54682i | −0.836189 | − | 0.548441i | \(-0.815222\pi\) |
−0.0568688 | − | 0.998382i | \(-0.518112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.88644i | − | 0.556861i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.77876 | + | 1.60432i | −0.312635 | + | 0.180500i | −0.648105 | − | 0.761551i | \(-0.724438\pi\) |
0.335470 | + | 0.942051i | \(0.391105\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.6883i | 1.39272i | 0.717691 | + | 0.696362i | \(0.245199\pi\) | ||||
−0.717691 | + | 0.696362i | \(0.754801\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.524000 | − | 0.907595i | 0.0568358 | − | 0.0984425i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.16638 | + | 14.1446i | −0.865634 | + | 1.49932i | 0.000781849 | 1.00000i | \(0.499751\pi\) | |
−0.866416 | + | 0.499323i | \(0.833582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.674422 | + | 0.389378i | 0.0706986 | + | 0.0408179i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.58895 | + | 1.08275i | 0.265620 | + | 0.111088i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.37105 | + | 4.25568i | −0.748416 | + | 0.432098i | −0.825121 | − | 0.564955i | \(-0.808893\pi\) |
0.0767050 | + | 0.997054i | \(0.475560\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.0399 | − | 7.52860i | −1.29752 | − | 0.749124i | −0.317545 | − | 0.948243i | \(-0.602859\pi\) |
−0.979975 | + | 0.199119i | \(0.936192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.56268i | 0.252509i | 0.991998 | + | 0.126254i | \(0.0402955\pi\) | ||||
−0.991998 | + | 0.126254i | \(0.959704\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.3982 | −1.19857 | −0.599287 | − | 0.800534i | \(-0.704549\pi\) | ||||
−0.599287 | + | 0.800534i | \(0.704549\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.5522 | − | 6.66965i | 1.10650 | − | 0.638836i | 0.168577 | − | 0.985688i | \(-0.446083\pi\) |
0.937920 | + | 0.346852i | \(0.112749\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.1581 | −1.42595 | −0.712975 | − | 0.701189i | \(-0.752653\pi\) | ||||
−0.712975 | + | 0.701189i | \(0.752653\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.19387 | −0.391081 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.03247 | + | 1.75080i | −0.277986 | + | 0.160495i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.83965 | 0.530877 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.17113i | 0.551962i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.36570 | + | 0.788486i | 0.121186 | + | 0.0699669i | 0.559368 | − | 0.828920i | \(-0.311044\pi\) |
−0.438182 | + | 0.898886i | \(0.644377\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.88308 | − | 1.08719i | 0.164525 | − | 0.0949886i | −0.415477 | − | 0.909604i | \(-0.636385\pi\) |
0.580002 | + | 0.814615i | \(0.303052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.68246 | − | 7.45813i | −0.492732 | − | 0.646702i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.8919 | + | 10.9072i | 1.61404 | + | 0.931869i | 0.988420 | + | 0.151744i | \(0.0484890\pi\) |
0.625624 | + | 0.780125i | \(0.284844\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.200474 | − | 0.347232i | 0.0170040 | − | 0.0294518i | −0.857398 | − | 0.514654i | \(-0.827921\pi\) |
0.874402 | + | 0.485202i | \(0.161254\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.411205 | − | 0.712227i | 0.0343867 | − | 0.0595595i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.24735i | 0.103587i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.5975 | + | 7.85050i | −1.11395 | + | 0.643138i | −0.939849 | − | 0.341590i | \(-0.889035\pi\) |
−0.174099 | + | 0.984728i | \(0.555701\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.82433i | 0.229840i | 0.993375 | + | 0.114920i | \(0.0366612\pi\) | ||||
−0.993375 | + | 0.114920i | \(0.963339\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.14794 | − | 3.72034i | −0.172527 | − | 0.298825i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.57082 | + | 4.45279i | 0.205174 | + | 0.355371i | 0.950188 | − | 0.311677i | \(-0.100891\pi\) |
−0.745014 | + | 0.667048i | \(0.767557\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.1353 | + | 7.00631i | 0.956394 | + | 0.552174i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.09504 | 0.477401 | 0.238700 | − | 0.971093i | \(-0.423279\pi\) | ||||
0.238700 | + | 0.971093i | \(0.423279\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.411205 | + | 0.712227i | −0.0318200 | + | 0.0551138i | −0.881497 | − | 0.472190i | \(-0.843464\pi\) |
0.849677 | + | 0.527304i | \(0.176797\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.43447 | − | 11.1448i | −0.494959 | − | 0.857294i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.822409 | + | 1.42445i | 0.0625266 | + | 0.108299i | 0.895594 | − | 0.444872i | \(-0.146751\pi\) |
−0.833068 | + | 0.553171i | \(0.813417\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.93187 | − | 8.54225i | 0.372814 | − | 0.645734i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.8099 | 1.03220 | 0.516100 | − | 0.856528i | \(-0.327383\pi\) | ||||
0.516100 | + | 0.856528i | \(0.327383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0783 | − | 8.70549i | −1.12076 | − | 0.647074i | −0.179169 | − | 0.983818i | \(-0.557341\pi\) |
−0.941596 | + | 0.336745i | \(0.890674\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.06517 | − | 1.84493i | −0.0783128 | − | 0.135642i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.84894 | + | 3.20246i | 0.135208 | + | 0.234187i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.85988i | 0.279291i | 0.990202 | + | 0.139645i | \(0.0445963\pi\) | ||||
−0.990202 | + | 0.139645i | \(0.955404\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.766710 | + | 0.442660i | −0.0551890 | + | 0.0318634i | −0.527341 | − | 0.849654i | \(-0.676811\pi\) |
0.472152 | + | 0.881517i | \(0.343477\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 16.1414i | − | 1.15003i | −0.818144 | − | 0.575014i | \(-0.804997\pi\) | ||
0.818144 | − | 0.575014i | \(-0.195003\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.978594 | − | 1.69498i | 0.0693707 | − | 0.120154i | −0.829254 | − | 0.558872i | \(-0.811234\pi\) |
0.898624 | + | 0.438719i | \(0.144568\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.08384 | − | 3.60931i | 0.146257 | − | 0.253324i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.89566 | + | 2.24916i | 0.272085 | + | 0.157088i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.87621 | + | 6.00100i | −0.544809 | + | 0.415098i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.9778 | + | 8.07010i | −0.962273 | + | 0.555568i | −0.896872 | − | 0.442291i | \(-0.854166\pi\) |
−0.0654010 | + | 0.997859i | \(0.520833\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.02995 | − | 1.74934i | −0.206641 | − | 0.119304i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.3535i | 0.974376i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.589334 | −0.0396429 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.1589 | + | 8.75202i | −1.01512 | + | 0.586079i | −0.912686 | − | 0.408662i | \(-0.865996\pi\) |
−0.102432 | + | 0.994740i | \(0.532662\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.35137 | −0.355183 | −0.177591 | − | 0.984104i | \(-0.556831\pi\) | ||||
−0.177591 | + | 0.984104i | \(0.556831\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.2233 | 1.07206 | 0.536032 | − | 0.844197i | \(-0.319922\pi\) | ||||
0.536032 | + | 0.844197i | \(0.319922\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.728503 | + | 0.420601i | −0.0477258 | + | 0.0275545i | −0.523673 | − | 0.851919i | \(-0.675439\pi\) |
0.475947 | + | 0.879474i | \(0.342105\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.72083 | −0.373185 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.9723i | 1.42127i | 0.703561 | + | 0.710634i | \(0.251592\pi\) | ||||
−0.703561 | + | 0.710634i | \(0.748408\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.0648 | − | 9.85234i | −1.09924 | − | 0.634645i | −0.163217 | − | 0.986590i | \(-0.552187\pi\) |
−0.936021 | + | 0.351945i | \(0.885520\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.32302 | + | 0.763845i | −0.0845246 | + | 0.0488003i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.200634 | − | 1.56526i | −0.0127660 | − | 0.0995951i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.17073 | − | 2.98532i | −0.326373 | − | 0.188432i | 0.327856 | − | 0.944728i | \(-0.393674\pi\) |
−0.654230 | + | 0.756296i | \(0.727007\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.39906 | − | 12.8155i | 0.465175 | − | 0.805706i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.41242 | + | 7.64254i | −0.275239 | + | 0.476728i | −0.970195 | − | 0.242324i | \(-0.922090\pi\) |
0.694956 | + | 0.719052i | \(0.255424\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.11791i | 0.442285i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.1378 | − | 7.00776i | 0.748448 | − | 0.432117i | −0.0766847 | − | 0.997055i | \(-0.524433\pi\) |
0.825133 | + | 0.564939i | \(0.191100\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.53308i | 0.155606i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.3673 | − | 19.6887i | −0.693076 | − | 1.20044i | −0.970825 | − | 0.239789i | \(-0.922922\pi\) |
0.277749 | − | 0.960654i | \(-0.410412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.5147 | − | 18.2120i | −0.638723 | − | 1.10630i | −0.985713 | − | 0.168432i | \(-0.946130\pi\) |
0.346990 | − | 0.937869i | \(-0.387204\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.02110 | − | 5.20834i | −0.543993 | − | 0.314074i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4400 | 0.627277 | 0.313639 | − | 0.949542i | \(-0.398452\pi\) | ||||
0.313639 | + | 0.949542i | \(0.398452\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.90311 | − | 17.1527i | 0.590770 | − | 1.02324i | −0.403359 | − | 0.915042i | \(-0.632157\pi\) |
0.994129 | − | 0.108202i | \(-0.0345094\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.123052 | − | 0.213132i | −0.00731466 | − | 0.0126694i | 0.862345 | − | 0.506321i | \(-0.168995\pi\) |
−0.869660 | + | 0.493652i | \(0.835662\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.51493 | − | 13.0162i | −0.443592 | − | 0.768324i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.17506 | + | 12.4276i | −0.422062 | + | 0.731033i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.24330 | 0.0726342 | 0.0363171 | − | 0.999340i | \(-0.488437\pi\) | ||||
0.0363171 | + | 0.999340i | \(0.488437\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.27395 | + | 1.89022i | 0.190617 | + | 0.110053i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.17919 | + | 2.04242i | 0.0681945 | + | 0.118116i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.84493 | + | 10.1237i | 0.336896 | + | 0.583521i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.04714i | 0.288998i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.2943 | − | 15.1810i | 1.50069 | − | 0.866425i | 0.500693 | − | 0.865625i | \(-0.333078\pi\) |
1.00000 | 0.000800631i | \(-0.000254849\pi\) | ||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.5851i | 0.713634i | 0.934174 | + | 0.356817i | \(0.116138\pi\) | ||||
−0.934174 | + | 0.356817i | \(0.883862\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.9773 | + | 19.0133i | −0.620476 | + | 1.07470i | 0.368921 | + | 0.929461i | \(0.379727\pi\) |
−0.989397 | + | 0.145235i | \(0.953606\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.84229 | − | 10.1192i | 0.328136 | − | 0.568348i | −0.654006 | − | 0.756489i | \(-0.726913\pi\) |
0.982142 | + | 0.188141i | \(0.0602463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.81164 | − | 2.20065i | −0.213411 | − | 0.123213i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.54618 | + | 2.73775i | 0.364239 | + | 0.152332i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.43770 | − | 0.830056i | 0.0797492 | − | 0.0460432i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.5536 | + | 9.55724i | 0.912631 | + | 0.526908i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.64080i | 0.145151i | 0.997363 | + | 0.0725757i | \(0.0231219\pi\) | ||||
−0.997363 | + | 0.0725757i | \(0.976878\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.74496 | −0.423153 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.25123 | − | 5.34120i | 0.503947 | − | 0.290954i | −0.226395 | − | 0.974036i | \(-0.572694\pi\) |
0.730342 | + | 0.683082i | \(0.239361\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.1581 | 0.820855 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1618 | 1.08863 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.6462 | + | 11.9201i | −1.10835 | + | 0.639905i | −0.938401 | − | 0.345548i | \(-0.887693\pi\) |
−0.169947 | + | 0.985453i | \(0.554360\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.0252 | −1.44662 | −0.723312 | − | 0.690521i | \(-0.757381\pi\) | ||||
−0.723312 | + | 0.690521i | \(0.757381\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.2312i | 1.13002i | 0.825082 | + | 0.565012i | \(0.191129\pi\) | ||||
−0.825082 | + | 0.565012i | \(0.808871\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.48452 | + | 4.89854i | 0.450312 | + | 0.259987i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.6102 | − | 8.43520i | 0.771097 | − | 0.445193i | −0.0621688 | − | 0.998066i | \(-0.519802\pi\) |
0.833266 | + | 0.552873i | \(0.186468\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.04281 | + | 18.3186i | −0.265411 | + | 0.964135i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.50845 | − | 4.91236i | −0.445353 | − | 0.257124i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.413060 | + | 0.715441i | −0.0215616 | + | 0.0373457i | −0.876605 | − | 0.481211i | \(-0.840197\pi\) |
0.855043 | + | 0.518557i | \(0.173530\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.23178 | − | 7.32966i | 0.219703 | − | 0.380537i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.0097i | − | 0.673616i | −0.941573 | − | 0.336808i | \(-0.890653\pi\) | ||
0.941573 | − | 0.336808i | \(-0.109347\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.607463 | − | 0.350719i | 0.0312860 | − | 0.0180630i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 21.3820i | − | 1.09832i | −0.835717 | − | 0.549161i | \(-0.814947\pi\) | ||
0.835717 | − | 0.549161i | \(-0.185053\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.1554 | − | 21.0538i | −0.621112 | − | 1.07580i | −0.989279 | − | 0.146038i | \(-0.953348\pi\) |
0.368167 | − | 0.929760i | \(-0.379985\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.57294 | − | 2.72440i | −0.0801642 | − | 0.138848i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.74124 | + | 1.00530i | 0.0882843 | + | 0.0509710i | 0.543492 | − | 0.839414i | \(-0.317102\pi\) |
−0.455208 | + | 0.890385i | \(0.650435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.6042 | −0.536279 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.03285 | + | 1.78895i | −0.0519685 | + | 0.0900121i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.37506 | + | 12.7740i | 0.370143 | + | 0.641107i | 0.989587 | − | 0.143934i | \(-0.0459752\pi\) |
−0.619444 | + | 0.785041i | \(0.712642\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.2748 | + | 31.6528i | 0.912598 | + | 1.58067i | 0.810381 | + | 0.585903i | \(0.199260\pi\) |
0.102217 | + | 0.994762i | \(0.467407\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.20788 | + | 2.09210i | −0.0601686 | + | 0.104215i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.51691 | 0.372600 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.08559 | + | 4.09087i | 0.350360 | + | 0.202280i | 0.664844 | − | 0.746982i | \(-0.268498\pi\) |
−0.314484 | + | 0.949263i | \(0.601831\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.31562 | − | 10.9390i | −0.310771 | − | 0.538271i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.08434 | + | 7.07429i | 0.200493 | + | 0.347263i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 30.7373i | − | 1.50161i | −0.660522 | − | 0.750807i | \(-0.729665\pi\) | ||
0.660522 | − | 0.750807i | \(-0.270335\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.2702 | − | 18.0538i | 1.52401 | − | 0.879890i | 0.524419 | − | 0.851460i | \(-0.324283\pi\) |
0.999596 | − | 0.0284299i | \(-0.00905073\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.46453i | 0.362083i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.43177 | − | 14.6043i | 0.408042 | − | 0.706750i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.5648 | + | 26.9590i | −0.749728 | + | 1.29857i | 0.198224 | + | 0.980157i | \(0.436483\pi\) |
−0.947953 | + | 0.318411i | \(0.896851\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.962315 | + | 0.555593i | 0.0462459 | + | 0.0267001i | 0.522945 | − | 0.852367i | \(-0.324833\pi\) |
−0.476699 | + | 0.879067i | \(0.658167\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.61013 | − | 28.1647i | −0.172696 | − | 1.34730i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.24345 | + | 3.60465i | −0.297983 | + | 0.172041i | −0.641537 | − | 0.767092i | \(-0.721703\pi\) |
0.343553 | + | 0.939133i | \(0.388369\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.55411 | − | 0.897264i | −0.0738378 | − | 0.0426303i | 0.462627 | − | 0.886553i | \(-0.346907\pi\) |
−0.536464 | + | 0.843923i | \(0.680240\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.5150i | 0.498457i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.922248 | 0.0435236 | 0.0217618 | − | 0.999763i | \(-0.493072\pi\) | ||||
0.0217618 | + | 0.999763i | \(0.493072\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.7459 | + | 7.93619i | −0.647268 | + | 0.373700i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.501360 | 0.0235041 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3504 | −0.671285 | −0.335643 | − | 0.941989i | \(-0.608953\pi\) | ||||
−0.335643 | + | 0.941989i | \(0.608953\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.90876 | − | 1.67937i | 0.135474 | − | 0.0782162i | −0.430731 | − | 0.902480i | \(-0.641744\pi\) |
0.566205 | + | 0.824264i | \(0.308411\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.1766 | 0.658841 | 0.329420 | − | 0.944183i | \(-0.393147\pi\) | ||||
0.329420 | + | 0.944183i | \(0.393147\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 9.04097i | − | 0.418366i | −0.977876 | − | 0.209183i | \(-0.932920\pi\) | ||
0.977876 | − | 0.209183i | \(-0.0670805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.4106 | + | 12.9388i | 1.03483 | + | 0.597457i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.6912 | − | 6.17258i | 0.491583 | − | 0.283815i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.8256 | + | 2.54124i | −0.909663 | + | 0.116600i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.8635 | + | 10.3135i | 0.816206 | + | 0.471237i | 0.849107 | − | 0.528222i | \(-0.177141\pi\) |
−0.0329001 | + | 0.999459i | \(0.510474\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.598988 | + | 1.03748i | −0.0273115 | + | 0.0473049i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.73979 | + | 4.74545i | −0.124407 | + | 0.215480i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.1950i | 1.05107i | 0.850773 | + | 0.525533i | \(0.176134\pi\) | ||||
−0.850773 | + | 0.525533i | \(0.823866\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.6050 | − | 8.43221i | 0.659115 | − | 0.380540i | −0.132824 | − | 0.991140i | \(-0.542405\pi\) |
0.791940 | + | 0.610599i | \(0.209071\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.15395i | 0.142047i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.3671 | − | 28.3486i | −0.734163 | − | 1.27161i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.912997 | − | 1.58136i | −0.0408714 | − | 0.0707913i | 0.844866 | − | 0.534978i | \(-0.179680\pi\) |
−0.885737 | + | 0.464187i | \(0.846347\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.54206 | + | 2.62236i | 0.202521 | + | 0.116925i | 0.597831 | − | 0.801622i | \(-0.296030\pi\) |
−0.395310 | + | 0.918548i | \(0.629363\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.69377 | −0.431367 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.9161 | − | 36.2278i | 0.927091 | − | 1.60577i | 0.138929 | − | 0.990302i | \(-0.455634\pi\) |
0.788163 | − | 0.615467i | \(-0.211033\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.4132 | + | 28.4285i | 0.726078 | + | 1.25760i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.824923 | + | 1.42881i | 0.0363505 | + | 0.0629608i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.0930 | − | 17.4816i | 0.443889 | − | 0.768839i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.461124 | −0.0202022 | −0.0101011 | − | 0.999949i | \(-0.503215\pi\) | ||||
−0.0101011 | + | 0.999949i | \(0.503215\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.5957 | + | 19.3965i | 1.46904 | + | 0.848150i | 0.999398 | − | 0.0347068i | \(-0.0110497\pi\) |
0.469642 | + | 0.882857i | \(0.344383\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.43109 | − | 9.40692i | −0.236582 | − | 0.409772i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.71793 | + | 16.8320i | 0.422519 | + | 0.731824i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.52959i | − | 0.109569i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.91252 | + | 3.99094i | −0.298854 | + | 0.172544i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 5.39047i | − | 0.232184i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.4679 | − | 26.7912i | 0.665016 | − | 1.15184i | −0.314264 | − | 0.949335i | \(-0.601758\pi\) |
0.979281 | − | 0.202507i | \(-0.0649088\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.29390 | − | 7.43724i | 0.183930 | − | 0.318577i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.9526 | − | 8.63291i | −0.639329 | − | 0.369117i | 0.145027 | − | 0.989428i | \(-0.453673\pi\) |
−0.784356 | + | 0.620311i | \(0.787006\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.37682 | + | 1.07374i | −0.356865 | + | 0.0457427i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.97728 | − | 3.45098i | 0.254180 | − | 0.146751i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.3157 | − | 10.5746i | −0.776060 | − | 0.448058i | 0.0589723 | − | 0.998260i | \(-0.481218\pi\) |
−0.835032 | + | 0.550201i | \(0.814551\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.96746i | 0.0832146i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.9292 | 1.85140 | 0.925698 | − | 0.378264i | \(-0.123479\pi\) | ||||
0.925698 | + | 0.378264i | \(0.123479\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.45129 | + | 4.87935i | −0.355548 | + | 0.205276i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.6631 | 1.03393 | 0.516965 | − | 0.856007i | \(-0.327062\pi\) | ||||
0.516965 | + | 0.856007i | \(0.327062\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.9160 | 1.41934 | 0.709670 | − | 0.704535i | \(-0.248844\pi\) | ||||
0.709670 | + | 0.704535i | \(0.248844\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25.8694 | − | 14.9357i | 1.07883 | − | 0.622862i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.08575 | 0.294984 | 0.147492 | − | 0.989063i | \(-0.452880\pi\) | ||||
0.147492 | + | 0.989063i | \(0.452880\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 27.2933i | − | 1.13232i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.74053 | − | 4.46900i | −0.320580 | − | 0.185087i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.8990 | − | 6.29254i | 0.449850 | − | 0.259721i | −0.257917 | − | 0.966167i | \(-0.583036\pi\) |
0.707767 | + | 0.706446i | \(0.249703\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.1356 | − | 17.6274i | 0.953288 | − | 0.726324i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.8796 | + | 15.5190i | 1.10381 | + | 0.637287i | 0.937220 | − | 0.348738i | \(-0.113390\pi\) |
0.166594 | + | 0.986026i | \(0.446723\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.12716 | + | 1.95229i | −0.0462089 | + | 0.0800362i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.5973 | − | 18.3551i | 0.432994 | − | 0.749968i | −0.564135 | − | 0.825683i | \(-0.690790\pi\) |
0.997130 | + | 0.0757140i | \(0.0241236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.03577i | 0.246204i | 0.992394 | + | 0.123102i | \(0.0392843\pi\) | ||||
−0.992394 | + | 0.123102i | \(0.960716\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.25586 | − | 1.87977i | 0.132370 | − | 0.0764236i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 46.3226i | − | 1.88018i | −0.340930 | − | 0.940089i | \(-0.610742\pi\) | ||
0.340930 | − | 0.940089i | \(-0.389258\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.60853 | + | 2.78605i | 0.0650741 | + | 0.112712i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.55012 | − | 7.88103i | −0.183777 | − | 0.318312i | 0.759386 | − | 0.650640i | \(-0.225499\pi\) |
−0.943164 | + | 0.332328i | \(0.892166\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.99382 | − | 3.46053i | −0.241302 | − | 0.139316i | 0.374473 | − | 0.927238i | \(-0.377824\pi\) |
−0.615775 | + | 0.787922i | \(0.711157\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.717872 | 0.0288537 | 0.0144269 | − | 0.999896i | \(-0.495408\pi\) | ||||
0.0144269 | + | 0.999896i | \(0.495408\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 17.5664 | − | 30.4258i | 0.703782 | − | 1.21899i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.47734 | − | 16.4152i | −0.379094 | − | 0.656609i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.69329 | − | 4.66491i | −0.107388 | − | 0.186002i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.4205 | + | 24.9770i | −0.574070 | + | 0.994318i | 0.422073 | + | 0.906562i | \(0.361303\pi\) |
−0.996142 | + | 0.0877555i | \(0.972031\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.01525 | 0.0402889 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.743988 | + | 0.429541i | 0.0294779 | + | 0.0170191i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.88506 | − | 3.26503i | −0.0744556 | − | 0.128961i | 0.826394 | − | 0.563093i | \(-0.190389\pi\) |
−0.900849 | + | 0.434132i | \(0.857055\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.8957 | + | 37.9244i | 0.863482 | + | 1.49559i | 0.868547 | + | 0.495607i | \(0.165054\pi\) |
−0.00506540 | + | 0.999987i | \(0.501612\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 40.9746i | − | 1.61088i | −0.592680 | − | 0.805438i | \(-0.701930\pi\) | ||
0.592680 | − | 0.805438i | \(-0.298070\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.5522 | + | 6.66965i | −0.453462 | + | 0.261807i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.5028i | 1.35020i | 0.737727 | + | 0.675099i | \(0.235899\pi\) | ||||
−0.737727 | + | 0.675099i | \(0.764101\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.699932 | − | 1.21232i | 0.0273486 | − | 0.0473692i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.53041 | + | 6.11485i | −0.137525 | + | 0.238201i | −0.926559 | − | 0.376149i | \(-0.877248\pi\) |
0.789034 | + | 0.614349i | \(0.210581\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.3836 | + | 18.6967i | 1.25958 | + | 0.727217i | 0.972992 | − | 0.230837i | \(-0.0741465\pi\) |
0.286585 | + | 0.958055i | \(0.407480\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.56898 | − | 2.32906i | −0.215956 | − | 0.0903172i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.9305 | − | 6.31070i | 0.423229 | − | 0.244351i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.4229 | − | 8.90443i | −0.595396 | − | 0.343752i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.5910i | 0.523895i | 0.965082 | + | 0.261948i | \(0.0843648\pi\) | ||||
−0.965082 | + | 0.261948i | \(0.915635\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.5478 | −1.51995 | −0.759973 | − | 0.649954i | \(-0.774788\pi\) | ||||
−0.759973 | + | 0.649954i | \(0.774788\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.8556 | − | 9.15422i | 0.608481 | − | 0.351307i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.0705 | −1.64805 | −0.824024 | − | 0.566555i | \(-0.808276\pi\) | ||||
−0.824024 | + | 0.566555i | \(0.808276\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.0441 | 0.536597 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.23361 | − | 0.712227i | 0.0469970 | − | 0.0271337i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.41460 | 0.282065 | 0.141032 | − | 0.990005i | \(-0.454958\pi\) | ||||
0.141032 | + | 0.990005i | \(0.454958\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.258129i | − | 0.00979141i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.85022 | + | 5.68703i | 0.373104 | + | 0.215411i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.85633 | − | 1.64910i | 0.107882 | − | 0.0622857i | −0.445088 | − | 0.895487i | \(-0.646828\pi\) |
0.552970 | + | 0.833201i | \(0.313494\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.4730 | − | 8.74146i | 0.432713 | − | 0.329690i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.0497 | + | 16.1945i | 1.05492 | + | 0.609056i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.1244 | + | 43.5167i | −0.943566 | + | 1.63430i | −0.184970 | + | 0.982744i | \(0.559219\pi\) |
−0.758597 | + | 0.651561i | \(0.774115\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.7340 | + | 37.6445i | −0.813946 | + | 1.40980i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 0.529464i | − | 0.0198008i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.54366 | + | 3.77799i | −0.244037 | + | 0.140895i | −0.617031 | − | 0.786939i | \(-0.711665\pi\) |
0.372994 | + | 0.927834i | \(0.378331\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 5.51249i | − | 0.205296i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.44222 | − | 7.69416i | −0.164980 | − | 0.285754i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.3363 | + | 26.5632i | 0.568791 | + | 0.985175i | 0.996686 | + | 0.0813464i | \(0.0259220\pi\) |
−0.427895 | + | 0.903829i | \(0.640745\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.66127 | − | 4.42323i | −0.283362 | − | 0.163599i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.24989 | −0.304717 | −0.152358 | − | 0.988325i | \(-0.548687\pi\) | ||||
−0.152358 | + | 0.988325i | \(0.548687\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.6641 | − | 23.6669i | 0.503323 | − | 0.871781i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.605814 | − | 1.04930i | −0.0222852 | − | 0.0385991i | 0.854668 | − | 0.519175i | \(-0.173761\pi\) |
−0.876953 | + | 0.480576i | \(0.840428\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.1052 | + | 29.6272i | 0.627531 | + | 1.08691i | 0.988046 | + | 0.154161i | \(0.0492676\pi\) |
−0.360515 | + | 0.932753i | \(0.617399\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.05412 | + | 8.75400i | −0.185169 | + | 0.320722i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.6692 | 0.974471 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.95075 | − | 2.85831i | −0.180655 | − | 0.104301i | 0.406945 | − | 0.913453i | \(-0.366594\pi\) |
−0.587601 | + | 0.809151i | \(0.699927\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.909146 | + | 1.57469i | 0.0330872 | + | 0.0573087i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.2419 | − | 22.9357i | −0.481286 | − | 0.833612i | 0.518483 | − | 0.855088i | \(-0.326497\pi\) |
−0.999769 | + | 0.0214755i | \(0.993164\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15.0147i | − | 0.544282i | −0.962257 | − | 0.272141i | \(-0.912268\pi\) | ||
0.962257 | − | 0.272141i | \(-0.0877317\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.8494 | + | 14.3468i | −0.899609 | + | 0.519390i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.12589i | − | 0.0767616i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.42918 | + | 11.1357i | −0.231842 | + | 0.401562i | −0.958350 | − | 0.285596i | \(-0.907809\pi\) |
0.726508 | + | 0.687158i | \(0.241142\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.7780 | − | 37.7207i | 0.783301 | − | 1.35672i | −0.146707 | − | 0.989180i | \(-0.546868\pi\) |
0.930009 | − | 0.367538i | \(-0.119799\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.4986 | + | 15.2990i | 0.951860 | + | 0.549556i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.7512 | + | 28.0981i | −0.421031 | + | 1.00672i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.9377 | + | 17.2845i | −1.07126 | + | 0.618489i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.86669 | + | 1.65508i | 0.102317 | + | 0.0590725i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.5389i | 0.803426i | 0.915766 | + | 0.401713i | \(0.131585\pi\) | ||||
−0.915766 | + | 0.401713i | \(0.868415\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.6059 | 1.15933 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.45796 | − | 1.41911i | 0.0872848 | − | 0.0503939i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.1329 | −0.677722 | −0.338861 | − | 0.940836i | \(-0.610042\pi\) | ||||
−0.338861 | + | 0.940836i | \(0.610042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.4652 | −0.511740 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.0221 | − | 17.3333i | 1.05946 | − | 0.611679i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.02127 | 0.317958 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.1712i | 0.463076i | 0.972826 | + | 0.231538i | \(0.0743757\pi\) | ||||
−0.972826 | + | 0.231538i | \(0.925624\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.4914 | − | 27.9965i | −1.70276 | − | 0.983092i | −0.942940 | − | 0.332964i | \(-0.891951\pi\) |
−0.759825 | − | 0.650128i | \(-0.774715\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.39826 | − | 1.96198i | 0.119036 | − | 0.0687253i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.13981 | − | 21.8540i | 0.319761 | − | 0.764576i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.2744 | − | 9.97336i | −0.602880 | − | 0.348073i | 0.167294 | − | 0.985907i | \(-0.446497\pi\) |
−0.770174 | + | 0.637834i | \(0.779830\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.2253 | − | 29.8352i | 0.600437 | − | 1.03999i | −0.392317 | − | 0.919830i | \(-0.628326\pi\) |
0.992755 | − | 0.120158i | \(-0.0383402\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.21205 | − | 3.83138i | 0.0769204 | − | 0.133230i | −0.824999 | − | 0.565134i | \(-0.808825\pi\) |
0.901920 | + | 0.431904i | \(0.142158\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 46.9000i | − | 1.62890i | −0.580230 | − | 0.814452i | \(-0.697038\pi\) | ||
0.580230 | − | 0.814452i | \(-0.302962\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.34526 | + | 1.93139i | −0.115907 | + | 0.0669187i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.529464i | 0.0183229i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.97765 | + | 17.2818i | 0.344467 | + | 0.596634i | 0.985257 | − | 0.171082i | \(-0.0547264\pi\) |
−0.640790 | + | 0.767716i | \(0.721393\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.6231 | + | 21.8638i | 0.435278 | + | 0.753923i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.17500 | − | 4.14249i | −0.246827 | − | 0.142506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.5614 | −0.431616 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.7780 | + | 18.6680i | −0.369464 | + | 0.639930i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.4564 | + | 19.8431i | 0.392260 | + | 0.679415i | 0.992747 | − | 0.120220i | \(-0.0383600\pi\) |
−0.600487 | + | 0.799634i | \(0.705027\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.32820 | + | 7.49666i | 0.147848 | + | 0.256081i | 0.930432 | − | 0.366465i | \(-0.119432\pi\) |
−0.782584 | + | 0.622546i | \(0.786099\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.64029 | − | 13.2334i | 0.260683 | − | 0.451517i | −0.705740 | − | 0.708471i | \(-0.749385\pi\) |
0.966424 | + | 0.256954i | \(0.0827188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.4317 | −1.24015 | −0.620074 | − | 0.784543i | \(-0.712897\pi\) | ||||
−0.620074 | + | 0.784543i | \(0.712897\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.917059 | + | 0.529464i | 0.0311809 | + | 0.0180023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.64443 | − | 6.31234i | −0.123629 | − | 0.214132i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.17766 | + | 3.77181i | 0.0737870 | + | 0.127803i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 13.2745i | − | 0.448759i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.5420 | − | 21.0976i | 1.23394 | − | 0.712414i | 0.266089 | − | 0.963949i | \(-0.414269\pi\) |
0.967848 | + | 0.251535i | \(0.0809353\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.3580i | 0.753258i | 0.926364 | + | 0.376629i | \(0.122917\pi\) | ||||
−0.926364 | + | 0.376629i | \(0.877083\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.7843 | + | 35.9994i | −0.699446 | + | 1.21148i | 0.269212 | + | 0.963081i | \(0.413237\pi\) |
−0.968659 | + | 0.248396i | \(0.920097\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.77689 | − | 16.9341i | 0.328276 | − | 0.568591i | −0.653894 | − | 0.756586i | \(-0.726866\pi\) |
0.982170 | + | 0.187996i | \(0.0601991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.93770 | − | 1.69608i | −0.0985273 | − | 0.0568848i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.92455 | − | 38.4192i | −0.164794 | − | 1.28565i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.69963 | − | 4.44538i | 0.257370 | − | 0.148593i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.1963 | + | 6.46420i | 0.373419 | + | 0.215593i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.40492i | 0.213379i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.2091 | −0.372604 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.7459 | − | 7.93619i | 0.456424 | − | 0.263517i | −0.254115 | − | 0.967174i | \(-0.581784\pi\) |
0.710540 | + | 0.703657i | \(0.248451\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.4664 | −1.73829 | −0.869145 | − | 0.494558i | \(-0.835330\pi\) | ||||
−0.869145 | + | 0.494558i | \(0.835330\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.8233 | −0.953912 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.05061 | + | 2.33862i | −0.133763 | + | 0.0772281i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.6867 | −1.40810 | −0.704052 | − | 0.710148i | \(-0.748628\pi\) | ||||
−0.704052 | + | 0.710148i | \(0.748628\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 5.50930i | − | 0.181341i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.1407 | + | 7.58681i | 0.432065 | + | 0.249453i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.6161 | − | 13.0574i | 0.742009 | − | 0.428399i | −0.0807905 | − | 0.996731i | \(-0.525744\pi\) |
0.822799 | + | 0.568332i | \(0.192411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.26860 | − | 8.22743i | −0.205445 | − | 0.269643i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.06173 | + | 1.19034i | 0.0674258 | + | 0.0389283i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.3858 | − | 33.5771i | 0.633305 | − | 1.09692i | −0.353567 | − | 0.935409i | \(-0.615031\pi\) |
0.986872 | − | 0.161507i | \(-0.0516354\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.50473 | + | 4.33831i | −0.0816517 | + | 0.141425i | −0.903960 | − | 0.427618i | \(-0.859353\pi\) |
0.822308 | + | 0.569043i | \(0.192686\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 45.5165i | − | 1.48222i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.5887 | − | 6.11340i | 0.344087 | − | 0.198659i | −0.317991 | − | 0.948094i | \(-0.603008\pi\) |
0.662078 | + | 0.749435i | \(0.269675\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.52484i | 0.179344i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.4783 | + | 18.1489i | 0.339424 | + | 0.587900i | 0.984325 | − | 0.176367i | \(-0.0564345\pi\) |
−0.644900 | + | 0.764267i | \(0.723101\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.24249 | + | 2.15205i | 0.0402059 | + | 0.0696387i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.6376 | − | 23.4621i | −1.31226 | − | 0.757632i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5254 | −0.436303 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.284983 | + | 0.493605i | −0.00917393 | + | 0.0158897i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.4393 | + | 23.2776i | 0.432180 | + | 0.748558i | 0.997061 | − | 0.0766149i | \(-0.0244112\pi\) |
−0.564881 | + | 0.825172i | \(0.691078\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.60883 | + | 13.1789i | 0.244179 | + | 0.422931i | 0.961900 | − | 0.273400i | \(-0.0881482\pi\) |
−0.717721 | + | 0.696330i | \(0.754815\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.431232 | + | 0.746917i | −0.0138247 | + | 0.0239450i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.1283 | 0.963890 | 0.481945 | − | 0.876201i | \(-0.339930\pi\) | ||||
0.481945 | + | 0.876201i | \(0.339930\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.1314 | − | 18.5511i | −1.02692 | − | 0.592895i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.52751 | + | 9.57393i | 0.176300 | + | 0.305361i | 0.940610 | − | 0.339488i | \(-0.110254\pi\) |
−0.764310 | + | 0.644849i | \(0.776920\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.19589 | − | 8.99955i | −0.165555 | − | 0.286749i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 35.4016i | 1.12571i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.9706 | − | 23.0770i | 1.26971 | − | 0.733066i | 0.294775 | − | 0.955567i | \(-0.404755\pi\) |
0.974932 | + | 0.222501i | \(0.0714220\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.26003i | − | 0.0399457i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.17506 | + | 8.96347i | −0.163896 | + | 0.283876i | −0.936263 | − | 0.351301i | \(-0.885739\pi\) |
0.772367 | + | 0.635177i | \(0.219073\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2736.2.dc.c.449.5 | 16 | ||
3.2 | odd | 2 | inner | 2736.2.dc.c.449.4 | 16 | ||
4.3 | odd | 2 | 171.2.m.a.107.4 | yes | 16 | ||
12.11 | even | 2 | 171.2.m.a.107.5 | yes | 16 | ||
19.8 | odd | 6 | inner | 2736.2.dc.c.1889.4 | 16 | ||
57.8 | even | 6 | inner | 2736.2.dc.c.1889.5 | 16 | ||
76.27 | even | 6 | 171.2.m.a.8.5 | yes | 16 | ||
228.179 | odd | 6 | 171.2.m.a.8.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.m.a.8.4 | ✓ | 16 | 228.179 | odd | 6 | ||
171.2.m.a.8.5 | yes | 16 | 76.27 | even | 6 | ||
171.2.m.a.107.4 | yes | 16 | 4.3 | odd | 2 | ||
171.2.m.a.107.5 | yes | 16 | 12.11 | even | 2 | ||
2736.2.dc.c.449.4 | 16 | 3.2 | odd | 2 | inner | ||
2736.2.dc.c.449.5 | 16 | 1.1 | even | 1 | trivial | ||
2736.2.dc.c.1889.4 | 16 | 19.8 | odd | 6 | inner | ||
2736.2.dc.c.1889.5 | 16 | 57.8 | even | 6 | inner |