Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(881,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.g (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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 8x^{12} + 80x^{10} + 1189x^{8} - 2028x^{6} + 1800x^{4} + 1080x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.3 | ||
Root | \(-0.221383 - 0.534465i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.881 |
Dual form | 1386.2.g.a.881.11 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.06893 | −0.478040 | −0.239020 | − | 0.971015i | \(-0.576826\pi\) | ||||
−0.239020 | + | 0.971015i | \(0.576826\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.884677 | − | 2.49346i | 0.334377 | − | 0.942440i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.06893i | 0.338026i | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −2.49346 | − | 0.884677i | −0.666405 | − | 0.236440i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.91799 | 0.950252 | 0.475126 | − | 0.879918i | \(-0.342402\pi\) | ||||
0.475126 | + | 0.879918i | \(0.342402\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.49534i | − | 1.71955i | −0.510674 | − | 0.859774i | \(-0.670604\pi\) | ||
0.510674 | − | 0.859774i | \(-0.329396\pi\) | |||||||
\(20\) | 1.06893 | 0.239020 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 5.33067i | 1.11152i | 0.831342 | + | 0.555761i | \(0.187573\pi\) | ||||
−0.831342 | + | 0.555761i | \(0.812427\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.85739 | −0.771477 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.884677 | + | 2.49346i | −0.167188 | + | 0.471220i | ||||
\(29\) | − | 8.01200i | − | 1.48779i | −0.668296 | − | 0.743895i | \(-0.732976\pi\) | ||
0.668296 | − | 0.743895i | \(-0.267024\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.65862i | − | 0.657108i | −0.944485 | − | 0.328554i | \(-0.893439\pi\) | ||
0.944485 | − | 0.328554i | \(-0.106561\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 3.91799i | − | 0.671930i | ||||||
\(35\) | −0.945659 | + | 2.66534i | −0.159846 | + | 0.450524i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.33067 | −1.20516 | −0.602578 | − | 0.798060i | \(-0.705860\pi\) | ||||
−0.602578 | + | 0.798060i | \(0.705860\pi\) | |||||||
\(38\) | −7.49534 | −1.21590 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 1.06893i | − | 0.169013i | ||||||
\(41\) | −2.50842 | −0.391749 | −0.195874 | − | 0.980629i | \(-0.562754\pi\) | ||||
−0.195874 | + | 0.980629i | \(0.562754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.230645 | 0.0351730 | 0.0175865 | − | 0.999845i | \(-0.494402\pi\) | ||||
0.0175865 | + | 0.999845i | \(0.494402\pi\) | |||||||
\(44\) | − | 1.00000i | − | 0.150756i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.33067 | 0.785965 | ||||||||
\(47\) | −0.370555 | −0.0540510 | −0.0270255 | − | 0.999635i | \(-0.508604\pi\) | ||||
−0.0270255 | + | 0.999635i | \(0.508604\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.43469 | − | 4.41182i | −0.776384 | − | 0.630260i | ||||
\(50\) | 3.85739i | 0.545517i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.56132i | 1.03863i | 0.854584 | + | 0.519313i | \(0.173812\pi\) | ||||
−0.854584 | + | 0.519313i | \(0.826188\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.06893i | − | 0.144135i | ||||||
\(56\) | 2.49346 | + | 0.884677i | 0.333203 | + | 0.118220i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.01200 | −1.05203 | ||||||||
\(59\) | −2.13786 | −0.278326 | −0.139163 | − | 0.990269i | \(-0.544441\pi\) | ||||
−0.139163 | + | 0.990269i | \(0.544441\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 14.2496i | − | 1.82447i | −0.409667 | − | 0.912235i | \(-0.634355\pi\) | ||
0.409667 | − | 0.912235i | \(-0.365645\pi\) | |||||||
\(62\) | −3.65862 | −0.464646 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.47329 | 0.302160 | 0.151080 | − | 0.988522i | \(-0.451725\pi\) | ||||
0.151080 | + | 0.988522i | \(0.451725\pi\) | |||||||
\(68\) | −3.91799 | −0.475126 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.66534 | + | 0.945659i | 0.318569 | + | 0.113028i | ||||
\(71\) | − | 3.15461i | − | 0.374383i | −0.982323 | − | 0.187192i | \(-0.940061\pi\) | ||
0.982323 | − | 0.187192i | \(-0.0599385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.370555i | − | 0.0433701i | −0.999765 | − | 0.0216851i | \(-0.993097\pi\) | ||
0.999765 | − | 0.0216851i | \(-0.00690311\pi\) | |||||||
\(74\) | 7.33067i | 0.852173i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.49534i | 0.859774i | ||||||||
\(77\) | 2.49346 | + | 0.884677i | 0.284156 | + | 0.100818i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.45068 | −0.500740 | −0.250370 | − | 0.968150i | \(-0.580552\pi\) | ||||
−0.250370 | + | 0.968150i | \(0.580552\pi\) | |||||||
\(80\) | −1.06893 | −0.119510 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.50842i | 0.277008i | ||||||||
\(83\) | −12.2229 | −1.34164 | −0.670818 | − | 0.741622i | \(-0.734057\pi\) | ||||
−0.670818 | + | 0.741622i | \(0.734057\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.18806 | −0.454259 | ||||||||
\(86\) | − | 0.230645i | − | 0.0248711i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −10.0038 | −1.06040 | −0.530198 | − | 0.847874i | \(-0.677882\pi\) | ||||
−0.530198 | + | 0.847874i | \(0.677882\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 5.33067i | − | 0.555761i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.370555i | 0.0382198i | ||||||||
\(95\) | 8.01200i | 0.822013i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.8528i | − | 1.30501i | −0.757786 | − | 0.652503i | \(-0.773719\pi\) | ||
0.757786 | − | 0.652503i | \(-0.226281\pi\) | |||||||
\(98\) | −4.41182 | + | 5.43469i | −0.445661 | + | 0.548987i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.85739 | 0.385739 | ||||||||
\(101\) | −14.0030 | −1.39335 | −0.696676 | − | 0.717386i | \(-0.745339\pi\) | ||||
−0.696676 | + | 0.717386i | \(0.745339\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2229i | 1.20436i | 0.798361 | + | 0.602179i | \(0.205701\pi\) | ||||
−0.798361 | + | 0.602179i | \(0.794299\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.56132 | 0.734420 | ||||||||
\(107\) | − | 20.4081i | − | 1.97292i | −0.163988 | − | 0.986462i | \(-0.552436\pi\) | ||
0.163988 | − | 0.986462i | \(-0.447564\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8814 | 1.23381 | 0.616906 | − | 0.787037i | \(-0.288386\pi\) | ||||
0.616906 | + | 0.787037i | \(0.288386\pi\) | |||||||
\(110\) | −1.06893 | −0.101919 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.884677 | − | 2.49346i | 0.0835942 | − | 0.235610i | ||||
\(113\) | − | 6.92396i | − | 0.651352i | −0.945481 | − | 0.325676i | \(-0.894408\pi\) | ||
0.945481 | − | 0.325676i | \(-0.105592\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.69812i | − | 0.531352i | ||||||
\(116\) | 8.01200i | 0.743895i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.13786i | 0.196806i | ||||||||
\(119\) | 3.46616 | − | 9.76935i | 0.317742 | − | 0.895555i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −14.2496 | −1.29009 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.65862i | 0.328554i | ||||||||
\(125\) | 9.46793 | 0.846838 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.6267 | 0.942971 | 0.471485 | − | 0.881874i | \(-0.343718\pi\) | ||||
0.471485 | + | 0.881874i | \(0.343718\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.23670 | 0.282792 | 0.141396 | − | 0.989953i | \(-0.454841\pi\) | ||||
0.141396 | + | 0.989953i | \(0.454841\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.6893 | − | 6.63096i | −1.62057 | − | 0.574977i | ||||
\(134\) | − | 2.47329i | − | 0.213659i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.91799i | 0.335965i | ||||||||
\(137\) | 10.7159i | 0.915523i | 0.889075 | + | 0.457762i | \(0.151349\pi\) | ||||
−0.889075 | + | 0.457762i | \(0.848651\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 6.24832i | − | 0.529975i | −0.964252 | − | 0.264988i | \(-0.914632\pi\) | ||
0.964252 | − | 0.264988i | \(-0.0853679\pi\) | |||||||
\(140\) | 0.945659 | − | 2.66534i | 0.0799228 | − | 0.225262i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.15461 | −0.264729 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.56427i | 0.711224i | ||||||||
\(146\) | −0.370555 | −0.0306673 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.33067 | 0.602578 | ||||||||
\(149\) | 12.8694i | 1.05430i | 0.849772 | + | 0.527150i | \(0.176740\pi\) | ||||
−0.849772 | + | 0.527150i | \(0.823260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.61475 | −0.701058 | −0.350529 | − | 0.936552i | \(-0.613998\pi\) | ||||
−0.350529 | + | 0.936552i | \(0.613998\pi\) | |||||||
\(152\) | 7.49534 | 0.607952 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.884677 | − | 2.49346i | 0.0712893 | − | 0.200929i | ||||
\(155\) | 3.91082i | 0.314124i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.39973i | − | 0.351137i | −0.984467 | − | 0.175568i | \(-0.943824\pi\) | ||
0.984467 | − | 0.175568i | \(-0.0561763\pi\) | |||||||
\(158\) | 4.45068i | 0.354077i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.06893i | 0.0845064i | ||||||||
\(161\) | 13.2918 | + | 4.71593i | 1.04754 | + | 0.371667i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.6933 | 0.994217 | 0.497109 | − | 0.867688i | \(-0.334395\pi\) | ||||
0.497109 | + | 0.867688i | \(0.334395\pi\) | |||||||
\(164\) | 2.50842 | 0.195874 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.2229i | 0.948680i | ||||||||
\(167\) | −3.80680 | −0.294579 | −0.147290 | − | 0.989093i | \(-0.547055\pi\) | ||||
−0.147290 | + | 0.989093i | \(0.547055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 4.18806i | 0.321210i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.230645 | −0.0175865 | ||||||||
\(173\) | 20.9353 | 1.59168 | 0.795842 | − | 0.605504i | \(-0.207029\pi\) | ||||
0.795842 | + | 0.605504i | \(0.207029\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.41254 | + | 9.61824i | −0.257964 | + | 0.727071i | ||||
\(176\) | 1.00000i | 0.0753778i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.0038i | 0.749813i | ||||||||
\(179\) | 6.47329i | 0.483836i | 0.970297 | + | 0.241918i | \(0.0777765\pi\) | ||||
−0.970297 | + | 0.241918i | \(0.922223\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.1804i | 1.35134i | 0.737206 | + | 0.675668i | \(0.236145\pi\) | ||||
−0.737206 | + | 0.675668i | \(0.763855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.33067 | −0.392982 | ||||||||
\(185\) | 7.83598 | 0.576113 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.91799i | 0.286512i | ||||||||
\(188\) | 0.370555 | 0.0270255 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.01200 | 0.581251 | ||||||||
\(191\) | 18.2320i | 1.31922i | 0.751607 | + | 0.659612i | \(0.229279\pi\) | ||||
−0.751607 | + | 0.659612i | \(0.770721\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.05343 | −0.0758275 | −0.0379137 | − | 0.999281i | \(-0.512071\pi\) | ||||
−0.0379137 | + | 0.999281i | \(0.512071\pi\) | |||||||
\(194\) | −12.8528 | −0.922778 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.43469 | + | 4.41182i | 0.388192 | + | 0.315130i | ||||
\(197\) | − | 20.8494i | − | 1.48546i | −0.669592 | − | 0.742729i | \(-0.733531\pi\) | ||
0.669592 | − | 0.742729i | \(-0.266469\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.3736i | 1.01892i | 0.860496 | + | 0.509458i | \(0.170154\pi\) | ||||
−0.860496 | + | 0.509458i | \(0.829846\pi\) | |||||||
\(200\) | − | 3.85739i | − | 0.272758i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.0030i | 0.985249i | ||||||||
\(203\) | −19.9776 | − | 7.08803i | −1.40215 | − | 0.497482i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.68132 | 0.187272 | ||||||||
\(206\) | 12.2229 | 0.851609 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.49534 | 0.518463 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.94542 | 0.684671 | 0.342335 | − | 0.939578i | \(-0.388782\pi\) | ||||
0.342335 | + | 0.939578i | \(0.388782\pi\) | |||||||
\(212\) | − | 7.56132i | − | 0.519313i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −20.4081 | −1.39507 | ||||||||
\(215\) | −0.246544 | −0.0168141 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.12264 | − | 3.23670i | −0.619285 | − | 0.219722i | ||||
\(218\) | − | 12.8814i | − | 0.872437i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.06893i | 0.0720673i | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 20.5648i | − | 1.37712i | −0.725180 | − | 0.688560i | \(-0.758243\pi\) | ||
0.725180 | − | 0.688560i | \(-0.241757\pi\) | |||||||
\(224\) | −2.49346 | − | 0.884677i | −0.166601 | − | 0.0591100i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.92396 | −0.460575 | ||||||||
\(227\) | 22.9250 | 1.52159 | 0.760794 | − | 0.648994i | \(-0.224810\pi\) | ||||
0.760794 | + | 0.648994i | \(0.224810\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 27.2136i | − | 1.79832i | −0.437617 | − | 0.899162i | \(-0.644177\pi\) | ||
0.437617 | − | 0.899162i | \(-0.355823\pi\) | |||||||
\(230\) | −5.69812 | −0.375723 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.01200 | 0.526013 | ||||||||
\(233\) | − | 14.4853i | − | 0.948962i | −0.880266 | − | 0.474481i | \(-0.842636\pi\) | ||
0.880266 | − | 0.474481i | \(-0.157364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.396097 | 0.0258385 | ||||||||
\(236\) | 2.13786 | 0.139163 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.76935 | − | 3.46616i | −0.633253 | − | 0.224678i | ||||
\(239\) | − | 7.81595i | − | 0.505572i | −0.967522 | − | 0.252786i | \(-0.918653\pi\) | ||
0.967522 | − | 0.252786i | \(-0.0813469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.1844i | 1.49344i | 0.665140 | + | 0.746719i | \(0.268372\pi\) | ||||
−0.665140 | + | 0.746719i | \(0.731628\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.2496i | 0.912235i | ||||||||
\(245\) | 5.80931 | + | 4.71593i | 0.371143 | + | 0.301289i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.65862 | 0.232323 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 9.46793i | − | 0.598805i | ||||||
\(251\) | 12.1117 | 0.764484 | 0.382242 | − | 0.924062i | \(-0.375152\pi\) | ||||
0.382242 | + | 0.924062i | \(0.375152\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.33067 | −0.335137 | ||||||||
\(254\) | − | 10.6267i | − | 0.666781i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.0038 | 0.624017 | 0.312008 | − | 0.950079i | \(-0.398998\pi\) | ||||
0.312008 | + | 0.950079i | \(0.398998\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.48528 | + | 18.2787i | −0.402976 | + | 1.13579i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 3.23670i | − | 0.199964i | ||||||
\(263\) | 7.37464i | 0.454740i | 0.973808 | + | 0.227370i | \(0.0730127\pi\) | ||||
−0.973808 | + | 0.227370i | \(0.926987\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.08252i | − | 0.496506i | ||||||
\(266\) | −6.63096 | + | 18.6893i | −0.406570 | + | 1.14592i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.47329 | −0.151080 | ||||||||
\(269\) | 9.41082 | 0.573788 | 0.286894 | − | 0.957962i | \(-0.407377\pi\) | ||||
0.286894 | + | 0.957962i | \(0.407377\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.0725i | 1.64454i | 0.569101 | + | 0.822268i | \(0.307291\pi\) | ||||
−0.569101 | + | 0.822268i | \(0.692709\pi\) | |||||||
\(272\) | 3.91799 | 0.237563 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.7159 | 0.647373 | ||||||||
\(275\) | − | 3.85739i | − | 0.232609i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.8279 | 1.07118 | 0.535589 | − | 0.844479i | \(-0.320090\pi\) | ||||
0.535589 | + | 0.844479i | \(0.320090\pi\) | |||||||
\(278\) | −6.24832 | −0.374749 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.66534 | − | 0.945659i | −0.159284 | − | 0.0565139i | ||||
\(281\) | − | 22.9706i | − | 1.37031i | −0.728398 | − | 0.685154i | \(-0.759735\pi\) | ||
0.728398 | − | 0.685154i | \(-0.240265\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10.3615i | − | 0.615926i | −0.951398 | − | 0.307963i | \(-0.900353\pi\) | ||
0.951398 | − | 0.307963i | \(-0.0996474\pi\) | |||||||
\(284\) | 3.15461i | 0.187192i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.21914 | + | 6.25464i | −0.130992 | + | 0.369200i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.64935 | −0.0970206 | ||||||||
\(290\) | 8.56427 | 0.502911 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.370555i | 0.0216851i | ||||||||
\(293\) | 10.9615 | 0.640377 | 0.320189 | − | 0.947354i | \(-0.396254\pi\) | ||||
0.320189 | + | 0.947354i | \(0.396254\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.28523 | 0.133051 | ||||||||
\(296\) | − | 7.33067i | − | 0.426087i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.8694 | 0.745503 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.204046 | − | 0.575104i | 0.0117610 | − | 0.0331485i | ||||
\(302\) | 8.61475i | 0.495723i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 7.49534i | − | 0.429887i | ||||||
\(305\) | 15.2318i | 0.872170i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.4845i | 1.73985i | 0.493188 | + | 0.869923i | \(0.335831\pi\) | ||||
−0.493188 | + | 0.869923i | \(0.664169\pi\) | |||||||
\(308\) | −2.49346 | − | 0.884677i | −0.142078 | − | 0.0504092i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.91082 | 0.222119 | ||||||||
\(311\) | −8.19371 | −0.464623 | −0.232311 | − | 0.972641i | \(-0.574629\pi\) | ||||
−0.232311 | + | 0.972641i | \(0.574629\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 33.2694i | − | 1.88050i | −0.340487 | − | 0.940249i | \(-0.610592\pi\) | ||
0.340487 | − | 0.940249i | \(-0.389408\pi\) | |||||||
\(314\) | −4.39973 | −0.248291 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.45068 | 0.250370 | ||||||||
\(317\) | − | 14.6627i | − | 0.823541i | −0.911288 | − | 0.411770i | \(-0.864911\pi\) | ||
0.911288 | − | 0.411770i | \(-0.135089\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.01200 | 0.448586 | ||||||||
\(320\) | 1.06893 | 0.0597550 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.71593 | − | 13.2918i | 0.262808 | − | 0.740724i | ||||
\(323\) | − | 29.3667i | − | 1.63400i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 12.6933i | − | 0.703018i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 2.50842i | − | 0.138504i | ||||||
\(329\) | −0.327821 | + | 0.923963i | −0.0180734 | + | 0.0509398i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.88936 | −0.378673 | −0.189337 | − | 0.981912i | \(-0.560634\pi\) | ||||
−0.189337 | + | 0.981912i | \(0.560634\pi\) | |||||||
\(332\) | 12.2229 | 0.670818 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.80680i | 0.208299i | ||||||||
\(335\) | −2.64377 | −0.144445 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.12264 | −0.279048 | −0.139524 | − | 0.990219i | \(-0.544557\pi\) | ||||
−0.139524 | + | 0.990219i | \(0.544557\pi\) | |||||||
\(338\) | − | 13.0000i | − | 0.707107i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.18806 | 0.227129 | ||||||||
\(341\) | 3.65862 | 0.198126 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.8086 | + | 9.64815i | −0.853586 | + | 0.520951i | ||||
\(344\) | 0.230645i | 0.0124355i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 20.9353i | − | 1.12549i | ||||||
\(347\) | 11.6399i | 0.624862i | 0.949940 | + | 0.312431i | \(0.101143\pi\) | ||||
−0.949940 | + | 0.312431i | \(0.898857\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 27.3248i | − | 1.46266i | −0.682023 | − | 0.731330i | \(-0.738900\pi\) | ||
0.682023 | − | 0.731330i | \(-0.261100\pi\) | |||||||
\(350\) | 9.61824 | + | 3.41254i | 0.514117 | + | 0.182408i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −1.45231 | −0.0772985 | −0.0386493 | − | 0.999253i | \(-0.512306\pi\) | ||||
−0.0386493 | + | 0.999253i | \(0.512306\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.37206i | 0.178970i | ||||||||
\(356\) | 10.0038 | 0.530198 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.47329 | 0.342124 | ||||||||
\(359\) | 0.196041i | 0.0103467i | 0.999987 | + | 0.00517333i | \(0.00164673\pi\) | ||||
−0.999987 | + | 0.00517333i | \(0.998353\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −37.1801 | −1.95685 | ||||||||
\(362\) | 18.1804 | 0.955539 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.396097i | 0.0207327i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.02667i | − | 0.105791i | −0.998600 | − | 0.0528957i | \(-0.983155\pi\) | ||
0.998600 | − | 0.0528957i | \(-0.0168451\pi\) | |||||||
\(368\) | 5.33067i | 0.277881i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 7.83598i | − | 0.407373i | ||||||
\(371\) | 18.8538 | + | 6.68933i | 0.978843 | + | 0.347293i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.2001 | 1.35659 | 0.678294 | − | 0.734791i | \(-0.262720\pi\) | ||||
0.678294 | + | 0.734791i | \(0.262720\pi\) | |||||||
\(374\) | 3.91799 | 0.202594 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 0.370555i | − | 0.0191099i | ||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.69332 | 0.446546 | 0.223273 | − | 0.974756i | \(-0.428326\pi\) | ||||
0.223273 | + | 0.974756i | \(0.428326\pi\) | |||||||
\(380\) | − | 8.01200i | − | 0.411007i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.2320 | 0.932832 | ||||||||
\(383\) | −5.89330 | −0.301133 | −0.150567 | − | 0.988600i | \(-0.548110\pi\) | ||||
−0.150567 | + | 0.988600i | \(0.548110\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.66534 | − | 0.945659i | −0.135838 | − | 0.0481952i | ||||
\(386\) | 1.05343i | 0.0536181i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.8528i | 0.652503i | ||||||||
\(389\) | 11.5853i | 0.587398i | 0.955898 | + | 0.293699i | \(0.0948864\pi\) | ||||
−0.955898 | + | 0.293699i | \(0.905114\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.8855i | 1.05623i | ||||||||
\(392\) | 4.41182 | − | 5.43469i | 0.222830 | − | 0.274493i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.8494 | −1.05038 | ||||||||
\(395\) | 4.75747 | 0.239374 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.1414i | 1.41238i | 0.708024 | + | 0.706188i | \(0.249587\pi\) | ||||
−0.708024 | + | 0.706188i | \(0.750413\pi\) | |||||||
\(398\) | 14.3736 | 0.720482 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.85739 | −0.192869 | ||||||||
\(401\) | − | 24.4547i | − | 1.22121i | −0.791936 | − | 0.610605i | \(-0.790927\pi\) | ||
0.791936 | − | 0.610605i | \(-0.209073\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.0030 | 0.696676 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.08803 | + | 19.9776i | −0.351773 | + | 0.991471i | ||||
\(407\) | − | 7.33067i | − | 0.363368i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.8503i | − | 0.536513i | −0.963348 | − | 0.268257i | \(-0.913553\pi\) | ||
0.963348 | − | 0.268257i | \(-0.0864475\pi\) | |||||||
\(410\) | − | 2.68132i | − | 0.132421i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 12.2229i | − | 0.602179i | ||||||
\(413\) | −1.89132 | + | 5.33067i | −0.0930657 | + | 0.262305i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.0654 | 0.641356 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 7.49534i | − | 0.366609i | ||||||
\(419\) | −8.57709 | −0.419018 | −0.209509 | − | 0.977807i | \(-0.567187\pi\) | ||||
−0.209509 | + | 0.977807i | \(0.567187\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.36011 | 0.115025 | 0.0575124 | − | 0.998345i | \(-0.481683\pi\) | ||||
0.0575124 | + | 0.998345i | \(0.481683\pi\) | |||||||
\(422\) | − | 9.94542i | − | 0.484135i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.56132 | −0.367210 | ||||||||
\(425\) | −15.1132 | −0.733098 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −35.5307 | − | 12.6063i | −1.71945 | − | 0.610060i | ||||
\(428\) | 20.4081i | 0.986462i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.246544i | 0.0118894i | ||||||||
\(431\) | 39.7508i | 1.91473i | 0.288886 | + | 0.957363i | \(0.406715\pi\) | ||||
−0.288886 | + | 0.957363i | \(0.593285\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.765276i | 0.0367768i | 0.999831 | + | 0.0183884i | \(0.00585354\pi\) | ||||
−0.999831 | + | 0.0183884i | \(0.994146\pi\) | |||||||
\(434\) | −3.23670 | + | 9.12264i | −0.155367 | + | 0.437901i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.8814 | −0.616906 | ||||||||
\(437\) | 39.9552 | 1.91132 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.9149i | 1.47549i | 0.675080 | + | 0.737744i | \(0.264109\pi\) | ||||
−0.675080 | + | 0.737744i | \(0.735891\pi\) | |||||||
\(440\) | 1.06893 | 0.0509593 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.3641i | 0.872506i | 0.899824 | + | 0.436253i | \(0.143695\pi\) | ||||
−0.899824 | + | 0.436253i | \(0.856305\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.6933 | 0.506912 | ||||||||
\(446\) | −20.5648 | −0.973771 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.884677 | + | 2.49346i | −0.0417971 | + | 0.117805i | ||||
\(449\) | − | 3.80133i | − | 0.179396i | −0.995969 | − | 0.0896979i | \(-0.971410\pi\) | ||
0.995969 | − | 0.0896979i | \(-0.0285901\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.50842i | − | 0.118117i | ||||||
\(452\) | 6.92396i | 0.325676i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 22.9250i | − | 1.07592i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.48528 | 0.303369 | 0.151684 | − | 0.988429i | \(-0.451530\pi\) | ||||
0.151684 | + | 0.988429i | \(0.451530\pi\) | |||||||
\(458\) | −27.2136 | −1.27161 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.69812i | 0.265676i | ||||||||
\(461\) | 11.1839 | 0.520885 | 0.260442 | − | 0.965489i | \(-0.416132\pi\) | ||||
0.260442 | + | 0.965489i | \(0.416132\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.7840 | 1.57007 | 0.785037 | − | 0.619448i | \(-0.212644\pi\) | ||||
0.785037 | + | 0.619448i | \(0.212644\pi\) | |||||||
\(464\) | − | 8.01200i | − | 0.371948i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.4853 | −0.671018 | ||||||||
\(467\) | 31.8968 | 1.47601 | 0.738005 | − | 0.674796i | \(-0.235768\pi\) | ||||
0.738005 | + | 0.674796i | \(0.235768\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.18806 | − | 6.16704i | 0.101035 | − | 0.284767i | ||||
\(470\) | − | 0.396097i | − | 0.0182706i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 2.13786i | − | 0.0984030i | ||||||
\(473\) | 0.230645i | 0.0106051i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.9124i | 1.32659i | ||||||||
\(476\) | −3.46616 | + | 9.76935i | −0.158871 | + | 0.447778i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.81595 | −0.357493 | ||||||||
\(479\) | −40.1419 | −1.83413 | −0.917065 | − | 0.398737i | \(-0.869449\pi\) | ||||
−0.917065 | + | 0.398737i | \(0.869449\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 23.1844 | 1.05602 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 13.7388i | 0.623845i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.82394 | −0.263908 | −0.131954 | − | 0.991256i | \(-0.542125\pi\) | ||||
−0.131954 | + | 0.991256i | \(0.542125\pi\) | |||||||
\(488\) | 14.2496 | 0.645047 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.71593 | − | 5.80931i | 0.213044 | − | 0.262438i | ||||
\(491\) | − | 15.9920i | − | 0.721710i | −0.932622 | − | 0.360855i | \(-0.882485\pi\) | ||
0.932622 | − | 0.360855i | \(-0.117515\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 31.3909i | − | 1.41378i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.65862i | − | 0.164277i | ||||||
\(497\) | −7.86589 | − | 2.79081i | −0.352833 | − | 0.125185i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.6199 | 0.788776 | 0.394388 | − | 0.918944i | \(-0.370957\pi\) | ||||
0.394388 | + | 0.918944i | \(0.370957\pi\) | |||||||
\(500\) | −9.46793 | −0.423419 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 12.1117i | − | 0.540572i | ||||||
\(503\) | −0.468921 | −0.0209081 | −0.0104541 | − | 0.999945i | \(-0.503328\pi\) | ||||
−0.0104541 | + | 0.999945i | \(0.503328\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.9683 | 0.666079 | ||||||||
\(506\) | 5.33067i | 0.236977i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.6267 | −0.471485 | ||||||||
\(509\) | 13.6865 | 0.606645 | 0.303323 | − | 0.952888i | \(-0.401904\pi\) | ||||
0.303323 | + | 0.952888i | \(0.401904\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.923963 | − | 0.327821i | −0.0408737 | − | 0.0145020i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 10.0038i | − | 0.441247i | ||||||
\(515\) | − | 13.0654i | − | 0.575731i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.370555i | − | 0.0162970i | ||||||
\(518\) | 18.2787 | + | 6.48528i | 0.803122 | + | 0.284947i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.70239 | 0.249826 | 0.124913 | − | 0.992168i | \(-0.460135\pi\) | ||||
0.124913 | + | 0.992168i | \(0.460135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.94790i | 0.172630i | 0.996268 | + | 0.0863148i | \(0.0275091\pi\) | ||||
−0.996268 | + | 0.0863148i | \(0.972491\pi\) | |||||||
\(524\) | −3.23670 | −0.141396 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.37464 | 0.321550 | ||||||||
\(527\) | − | 14.3345i | − | 0.624419i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.41607 | −0.235481 | ||||||||
\(530\) | −8.08252 | −0.351082 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.6893 | + | 6.63096i | 0.810285 | + | 0.287488i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.8148i | 0.943138i | ||||||||
\(536\) | 2.47329i | 0.106830i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 9.41082i | − | 0.405729i | ||||||
\(539\) | 4.41182 | − | 5.43469i | 0.190030 | − | 0.234089i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.6613 | 1.31823 | 0.659117 | − | 0.752040i | \(-0.270930\pi\) | ||||
0.659117 | + | 0.752040i | \(0.270930\pi\) | |||||||
\(542\) | 27.0725 | 1.16286 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 3.91799i | − | 0.167982i | ||||||
\(545\) | −13.7693 | −0.589812 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.05458 | 0.0878475 | 0.0439238 | − | 0.999035i | \(-0.486014\pi\) | ||||
0.0439238 | + | 0.999035i | \(0.486014\pi\) | |||||||
\(548\) | − | 10.7159i | − | 0.457762i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.85739 | −0.164480 | ||||||||
\(551\) | −60.0526 | −2.55833 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.93741 | + | 11.0976i | −0.167436 | + | 0.471918i | ||||
\(554\) | − | 17.8279i | − | 0.757437i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.24832i | 0.264988i | ||||||||
\(557\) | − | 20.8494i | − | 0.883418i | −0.897158 | − | 0.441709i | \(-0.854372\pi\) | ||
0.897158 | − | 0.441709i | \(-0.145628\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.945659 | + | 2.66534i | −0.0399614 | + | 0.112631i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22.9706 | −0.968955 | ||||||||
\(563\) | −41.7225 | −1.75839 | −0.879197 | − | 0.476459i | \(-0.841920\pi\) | ||||
−0.879197 | + | 0.476459i | \(0.841920\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.40124i | 0.311372i | ||||||||
\(566\) | −10.3615 | −0.435526 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.15461 | 0.132364 | ||||||||
\(569\) | − | 2.48528i | − | 0.104188i | −0.998642 | − | 0.0520942i | \(-0.983410\pi\) | ||
0.998642 | − | 0.0520942i | \(-0.0165896\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.4412 | −0.813590 | −0.406795 | − | 0.913520i | \(-0.633354\pi\) | ||||
−0.406795 | + | 0.913520i | \(0.633354\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.25464 | + | 2.21914i | 0.261063 | + | 0.0926251i | ||||
\(575\) | − | 20.5625i | − | 0.857514i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 4.49810i | − | 0.187258i | −0.995607 | − | 0.0936292i | \(-0.970153\pi\) | ||
0.995607 | − | 0.0936292i | \(-0.0298468\pi\) | |||||||
\(578\) | 1.64935i | 0.0686039i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 8.56427i | − | 0.355612i | ||||||
\(581\) | −10.8133 | + | 30.4773i | −0.448612 | + | 1.26441i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.56132 | −0.313158 | ||||||||
\(584\) | 0.370555 | 0.0153337 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 10.9615i | − | 0.452815i | ||||||
\(587\) | −37.2388 | −1.53701 | −0.768504 | − | 0.639845i | \(-0.778999\pi\) | ||||
−0.768504 | + | 0.639845i | \(0.778999\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.4226 | −1.12993 | ||||||||
\(590\) | − | 2.28523i | − | 0.0940812i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.33067 | −0.301289 | ||||||||
\(593\) | −25.1127 | −1.03125 | −0.515627 | − | 0.856813i | \(-0.672441\pi\) | ||||
−0.515627 | + | 0.856813i | \(0.672441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.70508 | + | 10.4428i | −0.151894 | + | 0.428112i | ||||
\(596\) | − | 12.8694i | − | 0.527150i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.99202i | 0.163109i | 0.996669 | + | 0.0815547i | \(0.0259885\pi\) | ||||
−0.996669 | + | 0.0815547i | \(0.974011\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0624i | 0.981526i | 0.871293 | + | 0.490763i | \(0.163282\pi\) | ||||
−0.871293 | + | 0.490763i | \(0.836718\pi\) | |||||||
\(602\) | −0.575104 | − | 0.204046i | −0.0234395 | − | 0.00831631i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.61475 | 0.350529 | ||||||||
\(605\) | 1.06893 | 0.0434582 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.9243i | 0.646345i | 0.946340 | + | 0.323173i | \(0.104749\pi\) | ||||
−0.946340 | + | 0.323173i | \(0.895251\pi\) | |||||||
\(608\) | −7.49534 | −0.303976 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.2318 | 0.616717 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.6105 | 0.751669 | 0.375835 | − | 0.926687i | \(-0.377356\pi\) | ||||
0.375835 | + | 0.926687i | \(0.377356\pi\) | |||||||
\(614\) | 30.4845 | 1.23026 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.884677 | + | 2.49346i | −0.0356447 | + | 0.100464i | ||||
\(617\) | − | 15.8053i | − | 0.636299i | −0.948041 | − | 0.318150i | \(-0.896939\pi\) | ||
0.948041 | − | 0.318150i | \(-0.103061\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.09487i | − | 0.285167i | −0.989783 | − | 0.142583i | \(-0.954459\pi\) | ||
0.989783 | − | 0.142583i | \(-0.0455409\pi\) | |||||||
\(620\) | − | 3.91082i | − | 0.157062i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.19371i | 0.328538i | ||||||||
\(623\) | −8.85010 | + | 24.9440i | −0.354572 | + | 0.999359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.16637 | 0.366655 | ||||||||
\(626\) | −33.2694 | −1.32971 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.39973i | 0.175568i | ||||||||
\(629\) | −28.7215 | −1.14520 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.3521 | 0.491730 | 0.245865 | − | 0.969304i | \(-0.420928\pi\) | ||||
0.245865 | + | 0.969304i | \(0.420928\pi\) | |||||||
\(632\) | − | 4.45068i | − | 0.177038i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.6627 | −0.582331 | ||||||||
\(635\) | −11.3593 | −0.450778 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 8.01200i | − | 0.317198i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 1.06893i | − | 0.0422532i | ||||||
\(641\) | 7.32006i | 0.289125i | 0.989496 | + | 0.144563i | \(0.0461775\pi\) | ||||
−0.989496 | + | 0.144563i | \(0.953823\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 37.8173i | − | 1.49137i | −0.666299 | − | 0.745685i | \(-0.732122\pi\) | ||
0.666299 | − | 0.745685i | \(-0.267878\pi\) | |||||||
\(644\) | −13.2918 | − | 4.71593i | −0.523771 | − | 0.185834i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −29.3667 | −1.15542 | ||||||||
\(647\) | 1.94268 | 0.0763748 | 0.0381874 | − | 0.999271i | \(-0.487842\pi\) | ||||
0.0381874 | + | 0.999271i | \(0.487842\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 2.13786i | − | 0.0839184i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.6933 | −0.497109 | ||||||||
\(653\) | 23.6305i | 0.924734i | 0.886689 | + | 0.462367i | \(0.153000\pi\) | ||||
−0.886689 | + | 0.462367i | \(0.847000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.45981 | −0.135186 | ||||||||
\(656\) | −2.50842 | −0.0979372 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.923963 | + | 0.327821i | 0.0360198 | + | 0.0127798i | ||||
\(659\) | 35.4535i | 1.38107i | 0.723297 | + | 0.690537i | \(0.242626\pi\) | ||||
−0.723297 | + | 0.690537i | \(0.757374\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 4.84582i | − | 0.188481i | −0.995549 | − | 0.0942403i | \(-0.969958\pi\) | ||
0.995549 | − | 0.0942403i | \(-0.0300422\pi\) | |||||||
\(662\) | 6.88936i | 0.267763i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 12.2229i | − | 0.474340i | ||||||
\(665\) | 19.9776 | + | 7.08803i | 0.774698 | + | 0.274862i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 42.7093 | 1.65371 | ||||||||
\(668\) | 3.80680 | 0.147290 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.64377i | 0.102138i | ||||||||
\(671\) | 14.2496 | 0.550098 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −51.0185 | −1.96662 | −0.983310 | − | 0.181937i | \(-0.941763\pi\) | ||||
−0.983310 | + | 0.181937i | \(0.941763\pi\) | |||||||
\(674\) | 5.12264i | 0.197317i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | −24.3330 | −0.935195 | −0.467597 | − | 0.883942i | \(-0.654880\pi\) | ||||
−0.467597 | + | 0.883942i | \(0.654880\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.0480 | − | 11.3706i | −1.22989 | − | 0.436363i | ||||
\(680\) | − | 4.18806i | − | 0.160605i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 3.65862i | − | 0.140096i | ||||||
\(683\) | 25.9028i | 0.991144i | 0.868567 | + | 0.495572i | \(0.165042\pi\) | ||||
−0.868567 | + | 0.495572i | \(0.834958\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 11.4546i | − | 0.437657i | ||||||
\(686\) | 9.64815 | + | 15.8086i | 0.368368 | + | 0.603577i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.230645 | 0.00879326 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 37.7917i | − | 1.43766i | −0.695184 | − | 0.718832i | \(-0.744677\pi\) | ||
0.695184 | − | 0.718832i | \(-0.255323\pi\) | |||||||
\(692\) | −20.9353 | −0.795842 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.6399 | 0.441844 | ||||||||
\(695\) | 6.67902i | 0.253350i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.82795 | −0.372260 | ||||||||
\(698\) | −27.3248 | −1.03426 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.41254 | − | 9.61824i | 0.128982 | − | 0.363535i | ||||
\(701\) | − | 31.8479i | − | 1.20288i | −0.798918 | − | 0.601440i | \(-0.794594\pi\) | ||
0.798918 | − | 0.601440i | \(-0.205406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.9459i | 2.07232i | ||||||||
\(704\) | − | 1.00000i | − | 0.0376889i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.45231i | 0.0546583i | ||||||||
\(707\) | −12.3882 | + | 34.9160i | −0.465905 | + | 1.31315i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.7682 | −0.404408 | −0.202204 | − | 0.979343i | \(-0.564810\pi\) | ||||
−0.202204 | + | 0.979343i | \(0.564810\pi\) | |||||||
\(710\) | 3.37206 | 0.126551 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 10.0038i | − | 0.374906i | ||||||
\(713\) | 19.5029 | 0.730390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 6.47329i | − | 0.241918i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.196041 | 0.00731620 | ||||||||
\(719\) | −22.1726 | −0.826897 | −0.413449 | − | 0.910527i | \(-0.635676\pi\) | ||||
−0.413449 | + | 0.910527i | \(0.635676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.4773 | + | 10.8133i | 1.13503 | + | 0.402709i | ||||
\(722\) | 37.1801i | 1.38370i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 18.1804i | − | 0.675668i | ||||||
\(725\) | 30.9054i | 1.14780i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.6830i | 1.06379i | 0.846810 | + | 0.531896i | \(0.178520\pi\) | ||||
−0.846810 | + | 0.531896i | \(0.821480\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.396097 | 0.0146602 | ||||||||
\(731\) | 0.903665 | 0.0334233 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 24.2234i | − | 0.894712i | −0.894356 | − | 0.447356i | \(-0.852366\pi\) | ||
0.894356 | − | 0.447356i | \(-0.147634\pi\) | |||||||
\(734\) | −2.02667 | −0.0748059 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.33067 | 0.196491 | ||||||||
\(737\) | 2.47329i | 0.0911046i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.17722 | 0.190447 | 0.0952235 | − | 0.995456i | \(-0.469643\pi\) | ||||
0.0952235 | + | 0.995456i | \(0.469643\pi\) | |||||||
\(740\) | −7.83598 | −0.288056 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.68933 | − | 18.8538i | 0.245573 | − | 0.692147i | ||||
\(743\) | − | 26.7625i | − | 0.981822i | −0.871210 | − | 0.490911i | \(-0.836664\pi\) | ||
0.871210 | − | 0.490911i | \(-0.163336\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 13.7565i | − | 0.503998i | ||||||
\(746\) | − | 26.2001i | − | 0.959252i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3.91799i | − | 0.143256i | ||||||
\(749\) | −50.8868 | − | 18.0546i | −1.85936 | − | 0.659700i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 54.2933 | 1.98119 | 0.990594 | − | 0.136830i | \(-0.0436915\pi\) | ||||
0.990594 | + | 0.136830i | \(0.0436915\pi\) | |||||||
\(752\) | −0.370555 | −0.0135127 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.20857 | 0.335134 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.6294 | −0.459022 | −0.229511 | − | 0.973306i | \(-0.573713\pi\) | ||||
−0.229511 | + | 0.973306i | \(0.573713\pi\) | |||||||
\(758\) | − | 8.69332i | − | 0.315756i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.01200 | −0.290626 | ||||||||
\(761\) | −11.0599 | −0.400920 | −0.200460 | − | 0.979702i | \(-0.564244\pi\) | ||||
−0.200460 | + | 0.979702i | \(0.564244\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.3959 | − | 32.1192i | 0.412558 | − | 1.16279i | ||||
\(764\) | − | 18.2320i | − | 0.659612i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.89330i | 0.212933i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.96499i | 0.142981i | 0.997441 | + | 0.0714906i | \(0.0227756\pi\) | ||||
−0.997441 | + | 0.0714906i | \(0.977224\pi\) | |||||||
\(770\) | −0.945659 | + | 2.66534i | −0.0340792 | + | 0.0960521i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.05343 | 0.0379137 | ||||||||
\(773\) | −10.5369 | −0.378985 | −0.189492 | − | 0.981882i | \(-0.560684\pi\) | ||||
−0.189492 | + | 0.981882i | \(0.560684\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.1127i | 0.506944i | ||||||||
\(776\) | 12.8528 | 0.461389 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.5853 | 0.415353 | ||||||||
\(779\) | 18.8014i | 0.673631i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.15461 | 0.112881 | ||||||||
\(782\) | 20.8855 | 0.746865 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.43469 | − | 4.41182i | −0.194096 | − | 0.157565i | ||||
\(785\) | 4.70301i | 0.167858i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.4277i | 0.514290i | 0.966373 | + | 0.257145i | \(0.0827818\pi\) | ||||
−0.966373 | + | 0.257145i | \(0.917218\pi\) | |||||||
\(788\) | 20.8494i | 0.742729i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 4.75747i | − | 0.169263i | ||||||
\(791\) | −17.2646 | − | 6.12547i | −0.613860 | − | 0.217797i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 28.1414 | 0.998701 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 14.3736i | − | 0.509458i | ||||||
\(797\) | 23.3640 | 0.827596 | 0.413798 | − | 0.910369i | \(-0.364202\pi\) | ||||
0.413798 | + | 0.910369i | \(0.364202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.45183 | −0.0513620 | ||||||||
\(800\) | 3.85739i | 0.136379i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.4547 | −0.863525 | ||||||||
\(803\) | 0.370555 | 0.0130766 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.2080 | − | 5.04100i | −0.500768 | − | 0.177672i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 14.0030i | − | 0.492625i | ||||||
\(809\) | 43.3467i | 1.52399i | 0.647584 | + | 0.761994i | \(0.275780\pi\) | ||||
−0.647584 | + | 0.761994i | \(0.724220\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.72552i | 0.130821i | 0.997858 | + | 0.0654104i | \(0.0208357\pi\) | ||||
−0.997858 | + | 0.0654104i | \(0.979164\pi\) | |||||||
\(812\) | 19.9776 | + | 7.08803i | 0.701076 | + | 0.248741i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.33067 | −0.256940 | ||||||||
\(815\) | −13.5683 | −0.475276 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.72876i | − | 0.0604817i | ||||||
\(818\) | −10.8503 | −0.379372 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.68132 | −0.0936359 | ||||||||
\(821\) | − | 0.200056i | − | 0.00698200i | −0.999994 | − | 0.00349100i | \(-0.998889\pi\) | ||
0.999994 | − | 0.00349100i | \(-0.00111122\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.02944 | 0.105600 | 0.0527998 | − | 0.998605i | \(-0.483185\pi\) | ||||
0.0527998 | + | 0.998605i | \(0.483185\pi\) | |||||||
\(824\) | −12.2229 | −0.425805 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.33067 | + | 1.89132i | 0.185478 | + | 0.0658074i | ||||
\(827\) | 10.3012i | 0.358209i | 0.983830 | + | 0.179105i | \(0.0573200\pi\) | ||||
−0.983830 | + | 0.179105i | \(0.942680\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16.4858i | 0.572575i | 0.958144 | + | 0.286288i | \(0.0924213\pi\) | ||||
−0.958144 | + | 0.286288i | \(0.907579\pi\) | |||||||
\(830\) | − | 13.0654i | − | 0.453507i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.2931 | − | 17.2855i | −0.737761 | − | 0.598906i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.06921 | 0.140821 | ||||||||
\(836\) | −7.49534 | −0.259232 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.57709i | 0.296291i | ||||||||
\(839\) | −45.7887 | −1.58080 | −0.790400 | − | 0.612591i | \(-0.790127\pi\) | ||||
−0.790400 | + | 0.612591i | \(0.790127\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.1921 | −1.21352 | ||||||||
\(842\) | − | 2.36011i | − | 0.0813348i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.94542 | −0.342335 | ||||||||
\(845\) | −13.8961 | −0.478040 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.884677 | + | 2.49346i | −0.0303979 | + | 0.0856763i | ||||
\(848\) | 7.56132i | 0.259657i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15.1132i | 0.518379i | ||||||||
\(851\) | − | 39.0774i | − | 1.33956i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.0777i | 0.995601i | 0.867292 | + | 0.497800i | \(0.165859\pi\) | ||||
−0.867292 | + | 0.497800i | \(0.834141\pi\) | |||||||
\(854\) | −12.6063 | + | 35.5307i | −0.431378 | + | 1.21584i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.4081 | 0.697534 | ||||||||
\(857\) | 11.0983 | 0.379112 | 0.189556 | − | 0.981870i | \(-0.439295\pi\) | ||||
0.189556 | + | 0.981870i | \(0.439295\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 48.6350i | − | 1.65941i | −0.558206 | − | 0.829703i | \(-0.688510\pi\) | ||
0.558206 | − | 0.829703i | \(-0.311490\pi\) | |||||||
\(860\) | 0.246544 | 0.00840706 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 39.7508 | 1.35392 | ||||||||
\(863\) | 46.3012i | 1.57611i | 0.615603 | + | 0.788056i | \(0.288912\pi\) | ||||
−0.615603 | + | 0.788056i | \(0.711088\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.3784 | −0.760889 | ||||||||
\(866\) | 0.765276 | 0.0260051 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.12264 | + | 3.23670i | 0.309642 | + | 0.109861i | ||||
\(869\) | − | 4.45068i | − | 0.150979i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 12.8814i | 0.436219i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 39.9552i | − | 1.35150i | ||||||
\(875\) | 8.37607 | − | 23.6079i | 0.283163 | − | 0.798093i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −49.3267 | −1.66564 | −0.832822 | − | 0.553540i | \(-0.813276\pi\) | ||||
−0.832822 | + | 0.553540i | \(0.813276\pi\) | |||||||
\(878\) | 30.9149 | 1.04333 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 1.06893i | − | 0.0360336i | ||||||
\(881\) | −33.8710 | −1.14114 | −0.570571 | − | 0.821248i | \(-0.693278\pi\) | ||||
−0.570571 | + | 0.821248i | \(0.693278\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.7548 | −1.60708 | −0.803538 | − | 0.595253i | \(-0.797052\pi\) | ||||
−0.803538 | + | 0.595253i | \(0.797052\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.3641 | 0.616955 | ||||||||
\(887\) | 53.6860 | 1.80260 | 0.901300 | − | 0.433195i | \(-0.142614\pi\) | ||||
0.901300 | + | 0.433195i | \(0.142614\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.40124 | − | 26.4974i | 0.315307 | − | 0.888693i | ||||
\(890\) | − | 10.6933i | − | 0.358441i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.5648i | 0.688560i | ||||||||
\(893\) | 2.77743i | 0.0929432i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 6.91949i | − | 0.231293i | ||||||
\(896\) | 2.49346 | + | 0.884677i | 0.0833007 | + | 0.0295550i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.80133 | −0.126852 | ||||||||
\(899\) | −29.3129 | −0.977639 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.6252i | 0.986958i | ||||||||
\(902\) | −2.50842 | −0.0835211 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.92396 | 0.230288 | ||||||||
\(905\) | − | 19.4336i | − | 0.645994i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5425 | −0.615693 | −0.307847 | − | 0.951436i | \(-0.599608\pi\) | ||||
−0.307847 | + | 0.951436i | \(0.599608\pi\) | |||||||
\(908\) | −22.9250 | −0.760794 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.8694i | 0.823959i | 0.911193 | + | 0.411980i | \(0.135163\pi\) | ||||
−0.911193 | + | 0.411980i | \(0.864837\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.2229i | − | 0.404519i | ||||||
\(914\) | − | 6.48528i | − | 0.214514i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.2136i | 0.899162i | ||||||||
\(917\) | 2.86344 | − | 8.07059i | 0.0945591 | − | 0.266514i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.9080 | 1.01956 | 0.509780 | − | 0.860305i | \(-0.329727\pi\) | ||||
0.509780 | + | 0.860305i | \(0.329727\pi\) | |||||||
\(920\) | 5.69812 | 0.187861 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 11.1839i | − | 0.368321i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.2772 | 0.929750 | ||||||||
\(926\) | − | 33.7840i | − | 1.11021i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.01200 | −0.263007 | ||||||||
\(929\) | 25.6501 | 0.841552 | 0.420776 | − | 0.907165i | \(-0.361758\pi\) | ||||
0.420776 | + | 0.907165i | \(0.361758\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.0681 | + | 40.7348i | −1.08376 | + | 1.33503i | ||||
\(932\) | 14.4853i | 0.474481i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 31.8968i | − | 1.04370i | ||||||
\(935\) | − | 4.18806i | − | 0.136964i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 35.3089i | − | 1.15349i | −0.816924 | − | 0.576746i | \(-0.804322\pi\) | ||
0.816924 | − | 0.576746i | \(-0.195678\pi\) | |||||||
\(938\) | −6.16704 | − | 2.18806i | −0.201361 | − | 0.0714427i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.396097 | −0.0129193 | ||||||||
\(941\) | −27.5713 | −0.898799 | −0.449399 | − | 0.893331i | \(-0.648362\pi\) | ||||
−0.449399 | + | 0.893331i | \(0.648362\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 13.3715i | − | 0.435437i | ||||||
\(944\) | −2.13786 | −0.0695815 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.230645 | 0.00749892 | ||||||||
\(947\) | 0.341189i | 0.0110872i | 0.999985 | + | 0.00554358i | \(0.00176459\pi\) | ||||
−0.999985 | + | 0.00554358i | \(0.998235\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 28.9124 | 0.938043 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.76935 | + | 3.46616i | 0.316627 | + | 0.112339i | ||||
\(953\) | − | 14.9226i | − | 0.483390i | −0.970352 | − | 0.241695i | \(-0.922297\pi\) | ||
0.970352 | − | 0.241695i | \(-0.0777033\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 19.4888i | − | 0.630642i | ||||||
\(956\) | 7.81595i | 0.252786i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.1419i | 1.29693i | ||||||||
\(959\) | 26.7197 | + | 9.48014i | 0.862825 | + | 0.306130i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.6145 | 0.568209 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 23.1844i | − | 0.746719i | ||||||
\(965\) | 1.12604 | 0.0362486 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.6013 | 1.27349 | 0.636746 | − | 0.771073i | \(-0.280280\pi\) | ||||
0.636746 | + | 0.771073i | \(0.280280\pi\) | |||||||
\(968\) | − | 1.00000i | − | 0.0321412i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.7388 | 0.441125 | ||||||||
\(971\) | 36.6913 | 1.17748 | 0.588740 | − | 0.808323i | \(-0.299624\pi\) | ||||
0.588740 | + | 0.808323i | \(0.299624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.5799 | − | 5.52775i | −0.499470 | − | 0.177211i | ||||
\(974\) | 5.82394i | 0.186611i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 14.2496i | − | 0.456117i | ||||||
\(977\) | − | 51.8053i | − | 1.65740i | −0.559693 | − | 0.828700i | \(-0.689081\pi\) | ||
0.559693 | − | 0.828700i | \(-0.310919\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 10.0038i | − | 0.319721i | ||||||
\(980\) | −5.80931 | − | 4.71593i | −0.185572 | − | 0.150645i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.9920 | −0.510326 | ||||||||
\(983\) | −17.6616 | −0.563319 | −0.281660 | − | 0.959514i | \(-0.590885\pi\) | ||||
−0.281660 | + | 0.959514i | \(0.590885\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.2866i | 0.710109i | ||||||||
\(986\) | −31.3909 | −0.999691 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.22949i | 0.0390956i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.4535 | 0.872090 | 0.436045 | − | 0.899925i | \(-0.356379\pi\) | ||||
0.436045 | + | 0.899925i | \(0.356379\pi\) | |||||||
\(992\) | −3.65862 | −0.116161 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.79081 | + | 7.86589i | −0.0885192 | + | 0.249491i | ||||
\(995\) | − | 15.3644i | − | 0.487083i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 23.0234i | − | 0.729158i | −0.931172 | − | 0.364579i | \(-0.881213\pi\) | ||
0.931172 | − | 0.364579i | \(-0.118787\pi\) | |||||||
\(998\) | − | 17.6199i | − | 0.557749i | ||||||
\(999\) | 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 | 1386.2.g.a.881.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 1386.2.g.a.881.14 | yes | 16 | |
7.6 | odd | 2 | inner | 1386.2.g.a.881.6 | yes | 16 | |
21.20 | even | 2 | inner | 1386.2.g.a.881.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.g.a.881.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1386.2.g.a.881.6 | yes | 16 | 7.6 | odd | 2 | inner | |
1386.2.g.a.881.11 | yes | 16 | 21.20 | even | 2 | inner | |
1386.2.g.a.881.14 | yes | 16 | 3.2 | odd | 2 | inner |