Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,2,Mod(369,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.6924739719\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.527896576.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 2x^{5} + 7x^{4} - 10x^{3} + 8x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 115) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.7 | ||
Root | \(1.47984 - 1.47984i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.369 |
Dual form | 1840.2.e.d.369.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1201\) | \(1381\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.95969i | 1.13143i | 0.824602 | + | 0.565713i | \(0.191399\pi\) | ||||
−0.824602 | + | 0.565713i | \(0.808601\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.479844 | + | 2.18398i | 0.214593 | + | 0.976704i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.28394i | 0.863249i | 0.902053 | + | 0.431624i | \(0.142059\pi\) | ||||
−0.902053 | + | 0.431624i | \(0.857941\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.840379 | −0.280126 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.12432 | −0.338996 | −0.169498 | − | 0.985531i | \(-0.554215\pi\) | ||||
−0.169498 | + | 0.985531i | \(0.554215\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.95969i | 1.65292i | 0.562995 | + | 0.826460i | \(0.309649\pi\) | ||||
−0.562995 | + | 0.826460i | \(0.690351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.27991 | + | 0.940345i | −1.10507 | + | 0.242796i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.80007i | − | 1.40672i | −0.710832 | − | 0.703362i | \(-0.751682\pi\) | ||
0.710832 | − | 0.703362i | \(-0.248318\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.08401 | −0.936936 | −0.468468 | − | 0.883480i | \(-0.655194\pi\) | ||||
−0.468468 | + | 0.883480i | \(0.655194\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.47581 | −0.976703 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.53950 | + | 2.09594i | −0.907900 | + | 0.419187i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.23218i | 0.814484i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.408263 | 0.0758125 | 0.0379062 | − | 0.999281i | \(-0.487931\pi\) | ||||
0.0379062 | + | 0.999281i | \(0.487931\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.19187 | 0.573277 | 0.286639 | − | 0.958039i | \(-0.407462\pi\) | ||||
0.286639 | + | 0.958039i | \(0.407462\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.20332i | − | 0.383549i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.98807 | + | 1.09594i | −0.843138 | + | 0.185247i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.80345i | 1.61168i | 0.592135 | + | 0.805839i | \(0.298285\pi\) | ||||
−0.592135 | + | 0.805839i | \(0.701715\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.6791 | −1.87016 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.27087 | 0.979345 | 0.489673 | − | 0.871906i | \(-0.337116\pi\) | ||||
0.489673 | + | 0.871906i | \(0.337116\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.75474i | − | 1.18259i | −0.806456 | − | 0.591294i | \(-0.798617\pi\) | ||
0.806456 | − | 0.591294i | \(-0.201383\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.403251 | − | 1.83537i | −0.0601131 | − | 0.273600i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.40020i | − | 0.933566i | −0.884372 | − | 0.466783i | \(-0.845413\pi\) | ||
0.884372 | − | 0.466783i | \(-0.154587\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.78361 | 0.254801 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.3663 | 1.59160 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 6.73590i | − | 0.925247i | −0.886555 | − | 0.462624i | \(-0.846908\pi\) | ||
0.886555 | − | 0.462624i | \(-0.153092\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.539499 | − | 2.45549i | −0.0727460 | − | 0.331098i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 8.00339i | − | 1.06007i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.75976 | −0.619667 | −0.309834 | − | 0.950791i | \(-0.600273\pi\) | ||||
−0.309834 | + | 0.950791i | \(0.600273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.33265 | −0.810813 | −0.405406 | − | 0.914137i | \(-0.632870\pi\) | ||||
−0.405406 | + | 0.914137i | \(0.632870\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.91938i | − | 0.241819i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.0158 | + | 2.85972i | −1.61441 | + | 0.354705i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.283942i | 0.0346890i | 0.999850 | + | 0.0173445i | \(0.00552120\pi\) | ||||
−0.999850 | + | 0.0173445i | \(0.994479\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.95969 | −0.235919 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9516 | 1.65575 | 0.827877 | − | 0.560910i | \(-0.189549\pi\) | ||||
0.827877 | + | 0.560910i | \(0.189549\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.61659i | 1.12554i | 0.826615 | + | 0.562769i | \(0.190264\pi\) | ||||
−0.826615 | + | 0.562769i | \(0.809736\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.10738 | − | 8.89600i | −0.474280 | − | 1.02722i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.56788i | − | 0.292637i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.48387 | 0.504475 | 0.252238 | − | 0.967665i | \(-0.418834\pi\) | ||||
0.252238 | + | 0.967665i | \(0.418834\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.8149 | −1.20166 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.8223i | 1.18790i | 0.804501 | + | 0.593951i | \(0.202433\pi\) | ||||
−0.804501 | + | 0.593951i | \(0.797567\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.6672 | − | 2.78313i | 1.37395 | − | 0.301873i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.800068i | 0.0857763i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.68414 | −0.602518 | −0.301259 | − | 0.953542i | \(-0.597407\pi\) | ||||
−0.301259 | + | 0.953542i | \(0.597407\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.6116 | −1.42688 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.25508i | 0.648621i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.95969 | − | 8.91938i | −0.201060 | − | 0.915109i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.0676i | − | 1.12374i | −0.827226 | − | 0.561870i | \(-0.810082\pi\) | ||
0.827226 | − | 0.561870i | \(-0.189918\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.944856 | 0.0949616 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.60014 | 0.159219 | 0.0796097 | − | 0.996826i | \(-0.474633\pi\) | ||||
0.0796097 | + | 0.996826i | \(0.474633\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.23218i | − | 0.121411i | −0.998156 | − | 0.0607054i | \(-0.980665\pi\) | ||
0.998156 | − | 0.0607054i | \(-0.0193350\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.14769 | − | 9.77507i | −0.209593 | − | 0.953949i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.235232i | − | 0.0227408i | −0.999935 | − | 0.0113704i | \(-0.996381\pi\) | ||
0.999935 | − | 0.0113704i | \(-0.00361938\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.43550 | −0.712192 | −0.356096 | − | 0.934449i | \(-0.615892\pi\) | ||||
−0.356096 | + | 0.934449i | \(0.615892\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.2117 | −1.82350 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2.28394i | − | 0.214855i | −0.994213 | − | 0.107428i | \(-0.965739\pi\) | ||
0.994213 | − | 0.107428i | \(-0.0342614\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.18398 | + | 0.479844i | −0.203657 | + | 0.0447457i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.00840i | − | 0.463027i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.2470 | 1.21435 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.73590 | −0.885082 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.2890i | 1.10806i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.75573 | − | 8.90843i | −0.604251 | − | 0.796794i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.2151i | − | 0.906444i | −0.891398 | − | 0.453222i | \(-0.850275\pi\) | ||
0.891398 | − | 0.453222i | \(-0.149725\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.1969 | 1.33801 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.2232 | 1.41742 | 0.708712 | − | 0.705498i | \(-0.249276\pi\) | ||||
0.708712 | + | 0.705498i | \(0.249276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 9.32764i | − | 0.808809i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −9.24299 | + | 2.03079i | −0.795510 | + | 0.174783i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.89715i | 0.418392i | 0.977874 | + | 0.209196i | \(0.0670846\pi\) | ||||
−0.977874 | + | 0.209196i | \(0.932915\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.43889 | 0.376502 | 0.188251 | − | 0.982121i | \(-0.439718\pi\) | ||||
0.188251 | + | 0.982121i | \(0.439718\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.5424 | 1.05626 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.70060i | − | 0.560333i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.195903 | + | 0.891636i | 0.0162688 | + | 0.0740463i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.49532i | 0.288289i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.78361 | 0.228042 | 0.114021 | − | 0.993478i | \(-0.463627\pi\) | ||||
0.114021 | + | 0.993478i | \(0.463627\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.9278 | −0.970669 | −0.485334 | − | 0.874329i | \(-0.661302\pi\) | ||||
−0.485334 | + | 0.874329i | \(0.661302\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.87426i | 0.394060i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.53160 | + | 6.97097i | 0.123021 | + | 0.559922i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 22.9550i | − | 1.83201i | −0.401167 | − | 0.916005i | \(-0.631395\pi\) | ||
0.401167 | − | 0.916005i | \(-0.368605\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.2003 | 1.04685 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.28394 | −0.180000 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2083i | 0.799578i | 0.916607 | + | 0.399789i | \(0.130917\pi\) | ||||
−0.916607 | + | 0.399789i | \(0.869083\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.81199 | − | 1.05725i | 0.374613 | − | 0.0823068i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.84715i | 0.529849i | 0.964269 | + | 0.264924i | \(0.0853470\pi\) | ||||
−0.964269 | + | 0.264924i | \(0.914653\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −22.5179 | −1.73215 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.43212 | 0.262461 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.29539i | 0.326572i | 0.986579 | + | 0.163286i | \(0.0522094\pi\) | ||||
−0.986579 | + | 0.163286i | \(0.947791\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.78700 | − | 10.3680i | −0.361863 | − | 0.783743i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 9.32764i | − | 0.701108i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.8626 | −1.11088 | −0.555442 | − | 0.831555i | \(-0.687451\pi\) | ||||
−0.555442 | + | 0.831555i | \(0.687451\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1311 | 0.976027 | 0.488013 | − | 0.872836i | \(-0.337722\pi\) | ||||
0.488013 | + | 0.872836i | \(0.337722\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 12.4100i | − | 0.917375i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.4105 | + | 4.70413i | −1.57413 | + | 0.345855i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.52114i | 0.476873i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.66606 | −0.703103 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.9819 | −1.01170 | −0.505848 | − | 0.862623i | \(-0.668820\pi\) | ||||
−0.505848 | + | 0.862623i | \(0.668820\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.71267i | 0.627152i | 0.949563 | + | 0.313576i | \(0.101527\pi\) | ||||
−0.949563 | + | 0.313576i | \(0.898473\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.60417 | − | 25.5069i | −0.401323 | − | 1.82659i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.4876i | 1.60218i | 0.598547 | + | 0.801088i | \(0.295745\pi\) | ||||
−0.598547 | + | 0.801088i | \(0.704255\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.01078 | 0.638757 | 0.319379 | − | 0.947627i | \(-0.396526\pi\) | ||||
0.319379 | + | 0.947627i | \(0.396526\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.556437 | −0.0392481 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.932448i | 0.0654450i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00904 | + | 13.6954i | 0.210161 | + | 0.956530i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.840379i | − | 0.0584104i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.59174 | 0.317617 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.60014 | −0.385529 | −0.192765 | − | 0.981245i | \(-0.561745\pi\) | ||||
−0.192765 | + | 0.981245i | \(0.561745\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 27.3408i | 1.87336i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.9362 | − | 3.72107i | 1.15504 | − | 0.253775i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.29005i | 0.494881i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.8455 | −1.27346 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 34.5666 | 2.32520 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.06517i | 0.473119i | 0.971617 | + | 0.236559i | \(0.0760198\pi\) | ||||
−0.971617 | + | 0.236559i | \(0.923980\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.81490 | − | 1.76138i | 0.254327 | − | 0.117425i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.1072i | 1.66643i | 0.552952 | + | 0.833213i | \(0.313501\pi\) | ||||
−0.552952 | + | 0.833213i | \(0.686499\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.20366 | 0.211704 | 0.105852 | − | 0.994382i | \(-0.466243\pi\) | ||||
0.105852 | + | 0.994382i | \(0.466243\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.03225 | 0.331098 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.6388i | 1.22107i | 0.791989 | + | 0.610535i | \(0.209046\pi\) | ||||
−0.791989 | + | 0.610535i | \(0.790954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.9779 | − | 3.07110i | 0.911817 | − | 0.200337i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.78700i | 0.570777i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.18185 | 0.205817 | 0.102908 | − | 0.994691i | \(-0.467185\pi\) | ||||
0.102908 | + | 0.994691i | \(0.467185\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.79844 | 0.309095 | 0.154547 | − | 0.987985i | \(-0.450608\pi\) | ||||
0.154547 | + | 0.987985i | \(0.450608\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 8.49728i | − | 0.545101i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.855855 | + | 3.89536i | 0.0546786 | + | 0.248865i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 24.3394i | − | 1.54868i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.2083 | −1.34402 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.24668 | 0.141809 | 0.0709045 | − | 0.997483i | \(-0.477411\pi\) | ||||
0.0709045 | + | 0.997483i | \(0.477411\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.12432i | − | 0.0706855i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.45407 | + | 24.8238i | 0.341547 | + | 1.55453i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 11.0148i | − | 0.687086i | −0.939137 | − | 0.343543i | \(-0.888373\pi\) | ||
0.939137 | − | 0.343543i | \(-0.111627\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.3905 | −1.39128 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.343095 | −0.0212371 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0585i | 0.681898i | 0.940082 | + | 0.340949i | \(0.110748\pi\) | ||||
−0.940082 | + | 0.340949i | \(0.889252\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.7110 | − | 3.23218i | 0.903692 | − | 0.198551i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 11.1392i | − | 0.681705i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.90392 | 0.603853 | 0.301926 | − | 0.953331i | \(-0.402370\pi\) | ||||
0.301926 | + | 0.953331i | \(0.402370\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.82655 | −0.293192 | −0.146596 | − | 0.989196i | \(-0.546832\pi\) | ||||
−0.146596 | + | 0.989196i | \(0.546832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 26.6745i | − | 1.61441i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.10385 | − | 2.35651i | 0.307774 | − | 0.142103i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 7.54303i | − | 0.453217i | −0.973986 | − | 0.226608i | \(-0.927236\pi\) | ||
0.973986 | − | 0.226608i | \(-0.0727637\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.68238 | −0.160590 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.01145 | 0.358613 | 0.179306 | − | 0.983793i | \(-0.442615\pi\) | ||||
0.179306 | + | 0.983793i | \(0.442615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.6388i | 0.929631i | 0.885407 | + | 0.464816i | \(0.153879\pi\) | ||||
−0.885407 | + | 0.464816i | \(0.846121\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.4792 | − | 3.84038i | 1.03538 | − | 0.227484i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.3223i | 0.845419i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6408 | −0.978870 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.6890 | 1.27143 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 3.21639i | − | 0.187904i | −0.995577 | − | 0.0939518i | \(-0.970050\pi\) | ||
0.995577 | − | 0.0939518i | \(-0.0299499\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.28394 | − | 10.3952i | −0.132976 | − | 0.605231i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.75833i | − | 0.276106i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.95969 | −0.344658 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.7114 | 1.02087 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.13577i | 0.180145i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.03869 | − | 13.8304i | −0.173995 | − | 0.791924i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 34.4702i | − | 1.96732i | −0.180044 | − | 0.983659i | \(-0.557624\pi\) | ||
0.180044 | − | 0.983659i | \(-0.442376\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.41470 | 0.137367 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.7443 | 1.06289 | 0.531446 | − | 0.847092i | \(-0.321649\pi\) | ||||
0.531446 | + | 0.847092i | \(0.321649\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.91260i | 0.560294i | 0.959957 | + | 0.280147i | \(0.0903831\pi\) | ||||
−0.959957 | + | 0.280147i | \(0.909617\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.19187 | − | 0.921002i | 0.236185 | − | 0.0518926i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.24024i | 0.518984i | 0.965745 | + | 0.259492i | \(0.0835551\pi\) | ||||
−0.965745 | + | 0.259492i | \(0.916445\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.459018 | −0.0257001 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.460982 | 0.0257295 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.6875i | 1.31801i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.4911 | − | 27.0540i | −0.692883 | − | 1.50069i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 14.5713i | − | 0.805793i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.6177 | 0.805899 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.9684 | 1.31742 | 0.658712 | − | 0.752395i | \(-0.271102\pi\) | ||||
0.658712 | + | 0.752395i | \(0.271102\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 8.23862i | − | 0.451474i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.620122 | + | 0.136248i | −0.0338809 | + | 0.00744401i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.76477i | − | 0.531921i | −0.963984 | − | 0.265960i | \(-0.914311\pi\) | ||
0.963984 | − | 0.265960i | \(-0.0856890\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.47581 | 0.243093 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.58869 | −0.194338 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0613i | 1.08321i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.940345 | − | 4.27991i | −0.0506265 | − | 0.230423i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.38441i | 0.0743190i | 0.999309 | + | 0.0371595i | \(0.0118310\pi\) | ||||
−0.999309 | + | 0.0371595i | \(0.988169\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.3106 | 1.72954 | 0.864772 | − | 0.502164i | \(-0.167463\pi\) | ||||
0.864772 | + | 0.502164i | \(0.167463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.2225 | −1.34628 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.4386i | 0.608813i | 0.952542 | + | 0.304406i | \(0.0984581\pi\) | ||||
−0.952542 | + | 0.304406i | \(0.901542\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.69461 | + | 30.4700i | 0.355313 | + | 1.61718i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 25.9600i | 1.37395i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.95568 | 0.525441 | 0.262720 | − | 0.964872i | \(-0.415380\pi\) | ||||
0.262720 | + | 0.964872i | \(0.415380\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.32087 | −0.122151 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 19.0793i | − | 1.00141i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.0024 | + | 4.61447i | −1.09932 | + | 0.241532i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.6785i | 1.44481i | 0.691472 | + | 0.722403i | \(0.256963\pi\) | ||||
−0.691472 | + | 0.722403i | \(0.743037\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.26991 | −0.274341 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.3844 | 0.798719 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.7356i | 1.48787i | 0.668251 | + | 0.743936i | \(0.267043\pi\) | ||||
−0.668251 | + | 0.743936i | \(0.732957\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.4578 | − | 13.2391i | 0.901514 | − | 0.683665i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.43312i | 0.125312i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.2715 | −0.938546 | −0.469273 | − | 0.883053i | \(-0.655484\pi\) | ||||
−0.469273 | + | 0.883053i | \(0.655484\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.0184 | 1.02557 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.0356i | 1.48365i | 0.670593 | + | 0.741826i | \(0.266040\pi\) | ||||
−0.670593 | + | 0.741826i | \(0.733960\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.60819 | − | 1.23218i | 0.285820 | − | 0.0627979i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.51693i | 0.331274i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.86423 | −0.145222 | −0.0726112 | − | 0.997360i | \(-0.523133\pi\) | ||||
−0.0726112 | + | 0.997360i | \(0.523133\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.80007 | 0.293322 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.7923i | 1.60371i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.15156 | + | 9.79267i | 0.108257 | + | 0.492723i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.5592i | − | 0.831080i | −0.909575 | − | 0.415540i | \(-0.863593\pi\) | ||
0.909575 | − | 0.415540i | \(-0.136407\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18.2793 | 0.915108 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.09479 | −0.154547 | −0.0772733 | − | 0.997010i | \(-0.524621\pi\) | ||||
−0.0772733 | + | 0.997010i | \(0.524621\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.0226i | 0.947582i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.18947 | − | 23.6195i | −0.257867 | − | 1.17366i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 11.0222i | − | 0.546352i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.93617 | −0.441865 | −0.220933 | − | 0.975289i | \(-0.570910\pi\) | ||||
−0.220933 | + | 0.975289i | \(0.570910\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.59689 | −0.473379 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 10.8710i | − | 0.534927i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.6356 | + | 5.19302i | −1.16023 | + | 0.254915i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.69884i | 0.425984i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.1237 | 1.17852 | 0.589260 | − | 0.807944i | \(-0.299419\pi\) | ||||
0.589260 | + | 0.807944i | \(0.299419\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.8602 | 1.16288 | 0.581438 | − | 0.813591i | \(-0.302490\pi\) | ||||
0.581438 | + | 0.813591i | \(0.302490\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.37860i | 0.261516i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.1566 | + | 26.3294i | 0.589680 | + | 1.27716i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 14.4634i | − | 0.699933i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.1311 | 0.633975 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.45096 | −0.214395 | −0.107198 | − | 0.994238i | \(-0.534188\pi\) | ||||
−0.107198 | + | 0.994238i | \(0.534188\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.10929i | 0.389707i | 0.980832 | + | 0.194854i | \(0.0624232\pi\) | ||||
−0.980832 | + | 0.194854i | \(0.937577\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.74733 | + | 0.383908i | −0.0837780 | + | 0.0184070i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.08401i | − | 0.195365i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.47180 | 0.213428 | 0.106714 | − | 0.994290i | \(-0.465967\pi\) | ||||
0.106714 | + | 0.994290i | \(0.465967\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.49891 | −0.0713766 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 9.60047i | − | 0.456132i | −0.973646 | − | 0.228066i | \(-0.926760\pi\) | ||
0.973646 | − | 0.228066i | \(-0.0732402\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.72750 | − | 12.4140i | −0.129296 | − | 0.588482i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.45501i | 0.258013i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.79944 | 0.320886 | 0.160443 | − | 0.987045i | \(-0.448708\pi\) | ||||
0.160443 | + | 0.987045i | \(0.448708\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.05047 | −0.331994 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 23.3747i | − | 1.09824i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.53144 | − | 29.7274i | −0.306199 | − | 1.39364i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.5582i | 0.914894i | 0.889237 | + | 0.457447i | \(0.151236\pi\) | ||||
−0.889237 | + | 0.457447i | \(0.848764\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.5470 | 1.14575 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −42.7081 | −1.98912 | −0.994558 | − | 0.104184i | \(-0.966777\pi\) | ||||
−0.994558 | + | 0.104184i | \(0.966777\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.42209i | 0.344934i | 0.985015 | + | 0.172467i | \(0.0551738\pi\) | ||||
−0.985015 | + | 0.172467i | \(0.944826\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.6609 | + | 3.00146i | −0.633511 | + | 0.139189i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 22.5041i | − | 1.04136i | −0.853751 | − | 0.520682i | \(-0.825678\pi\) | ||
0.853751 | − | 0.520682i | \(-0.174322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.648506 | −0.0299452 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 44.9847 | 2.07278 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.71882i | 0.400892i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.5394 | − | 8.55982i | 0.850644 | − | 0.392752i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.66071i | 0.259186i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.1667 | −0.464530 | −0.232265 | − | 0.972653i | \(-0.574614\pi\) | ||||
−0.232265 | + | 0.972653i | \(0.574614\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −58.4255 | −2.66398 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4.47581i | − | 0.203657i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.1713 | − | 5.31070i | 1.09756 | − | 0.241147i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.9917i | 1.58562i | 0.609467 | + | 0.792812i | \(0.291384\pi\) | ||||
−0.609467 | + | 0.792812i | \(0.708616\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.0051 | −0.904664 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.27087 | 0.102483 | 0.0512415 | − | 0.998686i | \(-0.483682\pi\) | ||||
0.0512415 | + | 0.998686i | \(0.483682\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.36795i | − | 0.106647i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.453384 | + | 2.06354i | 0.0203781 | + | 0.0927493i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.8647i | 1.42933i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.9929 | 0.939773 | 0.469887 | − | 0.882727i | \(-0.344295\pi\) | ||||
0.469887 | + | 0.882727i | \(0.344295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.4183 | −0.599485 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.5041i | 0.825055i | 0.910945 | + | 0.412528i | \(0.135354\pi\) | ||||
−0.910945 | + | 0.412528i | \(0.864646\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.767816 | + | 3.49466i | 0.0341674 | + | 0.155510i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 44.1280i | − | 1.95980i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.8472 | 1.85484 | 0.927421 | − | 0.374019i | \(-0.122020\pi\) | ||||
0.927421 | + | 0.374019i | \(0.122020\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.9637 | −0.971619 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 17.2843i | − | 0.763120i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.69106 | − | 0.591257i | 0.118582 | − | 0.0260539i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.19588i | 0.316475i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.41762 | −0.369493 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.1103 | 1.49440 | 0.747199 | − | 0.664600i | \(-0.231398\pi\) | ||||
0.747199 | + | 0.664600i | \(0.231398\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 36.4755i | − | 1.59496i | −0.603343 | − | 0.797482i | \(-0.706165\pi\) | ||
0.603343 | − | 0.797482i | \(-0.293835\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 20.3180 | − | 9.38102i | 0.886748 | − | 0.409421i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 18.5131i | − | 0.806442i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 37.3724i | 1.61878i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.513741 | − | 0.112875i | 0.0222110 | − | 0.00488000i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 29.1261i | − | 1.25688i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.00535 | −0.0863765 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.2171 | 1.21315 | 0.606573 | − | 0.795028i | \(-0.292544\pi\) | ||||
0.606573 | + | 0.795028i | \(0.292544\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.7329i | 1.10430i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.56788 | − | 16.2390i | −0.152831 | − | 0.695601i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.1638i | 0.648356i | 0.945996 | + | 0.324178i | \(0.105088\pi\) | ||||
−0.945996 | + | 0.324178i | \(0.894912\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.32183 | 0.227130 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.66735 | −0.0710314 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.2409i | 0.435488i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.21863 | − | 41.9579i | −0.391309 | − | 1.78101i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.52222i | 0.403469i | 0.979440 | + | 0.201735i | \(0.0646579\pi\) | ||||
−0.979440 | + | 0.201735i | \(0.935342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.2159 | 1.95472 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.7794 | −0.539547 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 32.7494i | − | 1.38022i | −0.723702 | − | 0.690112i | \(-0.757561\pi\) | ||
0.723702 | − | 0.690112i | \(-0.242439\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.98807 | − | 1.09594i | 0.209850 | − | 0.0461064i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 24.7006i | − | 1.03733i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.8926 | 1.12740 | 0.563698 | − | 0.825981i | \(-0.309378\pi\) | ||||
0.563698 | + | 0.825981i | \(0.309378\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.920000 | −0.0385008 | −0.0192504 | − | 0.999815i | \(-0.506128\pi\) | ||||
−0.0192504 | + | 0.999815i | \(0.506128\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 27.4002i | − | 1.14466i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.09594 | − | 4.53950i | −0.0874066 | − | 0.189310i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 42.5888i | − | 1.77300i | −0.462732 | − | 0.886498i | \(-0.653131\pi\) | ||
0.462732 | − | 0.886498i | \(-0.346869\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −17.0741 | −0.709576 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.7175 | −1.02545 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.57332i | 0.313655i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.9382 | − | 2.40325i | 0.452240 | − | 0.0993622i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.51212i | 0.392607i | 0.980543 | + | 0.196304i | \(0.0628938\pi\) | ||||
−0.980543 | + | 0.196304i | \(0.937106\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.0356 | −0.537124 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −44.0687 | −1.81274 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 31.0719i | − | 1.27597i | −0.770048 | − | 0.637986i | \(-0.779768\pi\) | ||
0.770048 | − | 0.637986i | \(-0.220232\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.35651 | + | 28.9312i | 0.260591 | + | 1.18606i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.6583i | 0.722707i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.04065 | 0.0833787 | 0.0416893 | − | 0.999131i | \(-0.486726\pi\) | ||||
0.0416893 | + | 0.999131i | \(0.486726\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25.2377 | −1.02947 | −0.514733 | − | 0.857351i | \(-0.672109\pi\) | ||||
−0.514733 | + | 0.857351i | \(0.672109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 0.238619i | − | 0.00971731i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.67172 | − | 21.2630i | −0.189932 | − | 0.864463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.4305i | 0.423361i | 0.977339 | + | 0.211680i | \(0.0678936\pi\) | ||||
−0.977339 | + | 0.211680i | \(0.932106\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.82731 | −0.0740463 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 38.1432 | 1.54311 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 4.97745i | − | 0.201037i | −0.994935 | − | 0.100519i | \(-0.967950\pi\) | ||
0.994935 | − | 0.100519i | \(-0.0320502\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −26.8388 | + | 5.89678i | −1.08224 | + | 0.237781i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 30.5881i | − | 1.23143i | −0.787969 | − | 0.615715i | \(-0.788867\pi\) | ||
0.787969 | − | 0.615715i | \(-0.211133\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −48.0404 | −1.93091 | −0.965453 | − | 0.260579i | \(-0.916087\pi\) | ||||
−0.965453 | + | 0.260579i | \(0.916087\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.23218 | −0.169832 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 12.9823i | − | 0.520123i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.2141 | − | 19.0290i | 0.648564 | − | 0.761160i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.99837i | 0.359360i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 56.8607 | 2.26718 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.6157 | −0.422605 | −0.211303 | − | 0.977421i | \(-0.567771\pi\) | ||||
−0.211303 | + | 0.977421i | \(0.567771\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 10.9745i | − | 0.436198i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.3095 | − | 4.90166i | 0.885327 | − | 0.194516i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.6298i | 0.421166i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.7247 | −0.463820 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.47844 | 0.137390 | 0.0686951 | − | 0.997638i | \(-0.478116\pi\) | ||||
0.0686951 | + | 0.997638i | \(0.478116\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.05348i | − | 0.0809813i | −0.999180 | − | 0.0404906i | \(-0.987108\pi\) | ||
0.999180 | − | 0.0404906i | \(-0.0128921\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.29214 | + | 33.1896i | 0.287128 | + | 1.30684i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 19.3408i | − | 0.760367i | −0.924911 | − | 0.380184i | \(-0.875861\pi\) | ||
0.924911 | − | 0.380184i | \(-0.124139\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.35149 | 0.210064 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.2862 | −0.559922 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.9288i | 0.858139i | 0.903271 | + | 0.429070i | \(0.141159\pi\) | ||||
−0.903271 | + | 0.429070i | \(0.858841\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.78459 | + | 35.4310i | 0.304169 | + | 1.38440i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 8.08158i | − | 0.315293i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.1351 | 1.48553 | 0.742767 | − | 0.669550i | \(-0.233513\pi\) | ||||
0.742767 | + | 0.669550i | \(0.233513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.9007 | −1.12411 | −0.562053 | − | 0.827101i | \(-0.689988\pi\) | ||||
−0.562053 | + | 0.827101i | \(0.689988\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 67.7398i | 2.63079i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.3713 | − | 4.47581i | 0.789967 | − | 0.173565i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.408263i | 0.0158080i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.8455 | −0.535299 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.11993 | 0.274862 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.5051i | 1.90828i | 0.299361 | + | 0.954140i | \(0.403226\pi\) | ||||
−0.299361 | + | 0.954140i | \(0.596774\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.87039 | − | 19.2120i | −0.341421 | − | 0.739470i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 6.87426i | − | 0.264199i | −0.991236 | − | 0.132100i | \(-0.957828\pi\) | ||
0.991236 | − | 0.132100i | \(-0.0421719\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.2776 | 0.970067 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −49.2024 | −1.88544 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.9887i | 1.41533i | 0.706547 | + | 0.707666i | \(0.250252\pi\) | ||||
−0.706547 | + | 0.707666i | \(0.749748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.6953 | + | 2.34987i | −0.408645 | + | 0.0897839i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.27817i | 0.239527i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.1439 | 1.52936 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.5485 | −1.46645 | −0.733227 | − | 0.679984i | \(-0.761987\pi\) | ||||
−0.733227 | + | 0.679984i | \(0.761987\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.15800i | 0.0819755i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.12998 | + | 9.69443i | 0.0807946 | + | 0.367731i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 36.3715i | − | 1.37767i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −36.5263 | −1.38155 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.3146 | −1.37158 | −0.685791 | − | 0.727798i | \(-0.740544\pi\) | ||||
−0.685791 | + | 0.727798i | \(0.740544\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 40.0374i | − | 1.51004i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.01840 | + | 27.3923i | 0.226666 | + | 1.03165i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.65462i | 0.137446i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.24463 | 0.121855 | 0.0609274 | − | 0.998142i | \(-0.480594\pi\) | ||||
0.0609274 | + | 0.998142i | \(0.480594\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.76815 | −0.141317 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.19187i | 0.119537i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.6340 | − | 3.21525i | 0.547279 | − | 0.120243i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.23543i | 0.232867i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.4214 | 0.388654 | 0.194327 | − | 0.980937i | \(-0.437748\pi\) | ||||
0.194327 | + | 0.980937i | \(0.437748\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.81424 | 0.104808 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.40345i | 0.349718i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.85331 | + | 0.855693i | −0.0688301 | + | 0.0317796i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.67651i | − | 0.358882i | −0.983769 | − | 0.179441i | \(-0.942571\pi\) | ||
0.983769 | − | 0.179441i | \(-0.0574289\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.7927 | −0.584914 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.9780 | −1.66357 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.5782i | 0.575396i | 0.957721 | + | 0.287698i | \(0.0928899\pi\) | ||||
−0.957721 | + | 0.287698i | \(0.907110\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.63369 | + | 1.67721i | −0.281573 | + | 0.0618648i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.319242i | − | 0.0117594i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.4328 | 0.530919 | 0.265459 | − | 0.964122i | \(-0.414476\pi\) | ||||
0.265459 | + | 0.964122i | \(0.414476\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 47.6977 | 1.75222 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.50305i | 0.165201i | 0.996583 | + | 0.0826005i | \(0.0263226\pi\) | ||||
−0.996583 | + | 0.0826005i | \(0.973677\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.33570 | + | 6.07934i | 0.0489362 | + | 0.222730i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 9.09483i | − | 0.332763i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.537257 | 0.0196309 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.5451 | −0.676721 | −0.338361 | − | 0.941017i | \(-0.609872\pi\) | ||||
−0.338361 | + | 0.941017i | \(0.609872\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.40279i | 0.160447i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.72347 | − | 26.0500i | −0.208299 | − | 0.948055i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.0366i | 0.982663i | 0.870973 | + | 0.491332i | \(0.163490\pi\) | ||||
−0.870973 | + | 0.491332i | \(0.836510\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.20332 | 0.0799754 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.4066 | 0.558490 | 0.279245 | − | 0.960220i | \(-0.409916\pi\) | ||||
0.279245 | + | 0.960220i | \(0.409916\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 16.9823i | − | 0.614799i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.6453 | + | 2.33888i | −0.384880 | + | 0.0845625i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 28.3667i | − | 1.02426i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.1216 | −0.545299 | −0.272650 | − | 0.962113i | \(-0.587900\pi\) | ||||
−0.272650 | + | 0.962113i | \(0.587900\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.5856 | 0.777388 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 28.7131i | − | 1.03274i | −0.856366 | − | 0.516370i | \(-0.827283\pi\) | ||
0.856366 | − | 0.516370i | \(-0.172717\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.4895 | + | 6.68996i | −0.520478 | + | 0.240311i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 43.8784i | − | 1.57413i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.6103 | −0.917584 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.6861 | −0.561293 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.72784i | 0.0617481i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 50.1332 | − | 11.0148i | 1.78933 | − | 0.393136i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 16.3131i | − | 0.581501i | −0.956799 | − | 0.290750i | \(-0.906095\pi\) | ||
0.956799 | − | 0.290750i | \(-0.0939049\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.6713 | −0.771518 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.21639 | 0.185473 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 37.7406i | − | 1.34021i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.33407 | + | 28.8291i | 0.224646 | + | 1.02246i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.88374i | − | 0.102147i | −0.998695 | − | 0.0510736i | \(-0.983736\pi\) | ||
0.998695 | − | 0.0510736i | \(-0.0162643\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.1216 | −1.31327 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.77684 | 0.168781 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 10.8121i | − | 0.381552i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.09594 | − | 4.98807i | −0.0386267 | − | 0.175806i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19.4086i | 0.683215i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.7878 | −1.39886 | −0.699432 | − | 0.714699i | \(-0.746564\pi\) | ||||
−0.699432 | + | 0.714699i | \(0.746564\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.5454 | −1.35351 | −0.676756 | − | 0.736208i | \(-0.736615\pi\) | ||||
−0.676756 | + | 0.736208i | \(0.736615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 9.45853i | − | 0.331725i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.2947 | + | 4.89841i | −0.780951 | + | 0.171584i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.6705i | 1.10801i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.4389 | 0.399707 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.3428 | −0.570368 | −0.285184 | − | 0.958473i | \(-0.592055\pi\) | ||||
−0.285184 | + | 0.958473i | \(0.592055\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 38.6446i | − | 1.34707i | −0.739157 | − | 0.673534i | \(-0.764776\pi\) | ||
0.739157 | − | 0.673534i | \(-0.235224\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.61802 | + | 10.0020i | 0.160779 | + | 0.348224i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.6969i | 0.754474i | 0.926117 | + | 0.377237i | \(0.123126\pi\) | ||||
−0.926117 | + | 0.377237i | \(0.876874\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.9429 | −0.484259 | −0.242129 | − | 0.970244i | \(-0.577846\pi\) | ||||
−0.242129 | + | 0.970244i | \(0.577846\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.7820 | 0.512781 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 10.3451i | − | 0.358435i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.9540 | + | 3.28557i | −0.517505 | + | 0.113702i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.5086i | 0.466925i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.4484 | 1.81072 | 0.905360 | − | 0.424644i | \(-0.139601\pi\) | ||||
0.905360 | + | 0.424644i | \(0.139601\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8333 | −0.994252 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.7806i | 0.405744i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.8051 | − | 49.1785i | −0.371706 | − | 1.69179i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 22.2362i | − | 0.764046i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.6472 | −1.05181 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.80345 | −0.336058 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.4634i | 1.04305i | 0.853237 | + | 0.521524i | \(0.174636\pi\) | ||||
−0.853237 | + | 0.521524i | \(0.825364\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.64688 | + | 7.49566i | 0.0563222 | + | 0.256346i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.4911i | 1.45147i | 0.687975 | + | 0.725735i | \(0.258500\pi\) | ||||
−0.687975 | + | 0.725735i | \(0.741500\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.5856 | −0.531775 | −0.265888 | − | 0.964004i | \(-0.585665\pi\) | ||||
−0.265888 | + | 0.964004i | \(0.585665\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.0673 | −0.956529 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 50.8852i | − | 1.73215i | −0.499913 | − | 0.866076i | \(-0.666635\pi\) | ||
0.499913 | − | 0.866076i | \(-0.333365\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.38102 | + | 2.06112i | −0.318964 | + | 0.0700801i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 32.6108i | − | 1.10752i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.04131 | −0.171015 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.69220 | −0.0573382 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.30094i | 0.314789i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.3463 | − | 15.4297i | 0.687832 | − | 0.521619i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.1080i | 1.01667i | 0.861158 | + | 0.508337i | \(0.169740\pi\) | ||||
−0.861158 | + | 0.508337i | \(0.830260\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.30312 | 0.212599 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.2245 | 0.681379 | 0.340690 | − | 0.940176i | \(-0.389339\pi\) | ||||
0.340690 | + | 0.940176i | \(0.389339\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.6482i | 1.03139i | 0.856771 | + | 0.515697i | \(0.172467\pi\) | ||||
−0.856771 | + | 0.515697i | \(0.827533\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.3713 | − | 4.47581i | 0.684775 | − | 0.150453i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.0064i | 0.470290i | 0.971960 | + | 0.235145i | \(0.0755565\pi\) | ||||
−0.971960 | + | 0.235145i | \(0.924443\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.3307 | 0.782487 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.1594 | 0.407356 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.1385i | 0.874691i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.13174 | − | 32.4596i | −0.238388 | − | 1.08500i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 11.6791i | − | 0.389955i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.30312 | 0.0434616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.0687 | −1.30157 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 34.7088i | 1.15504i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.30088 | + | 28.6780i | 0.209448 | + | 0.953289i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 36.4739i | − | 1.21109i | −0.795809 | − | 0.605547i | \(-0.792954\pi\) | ||
0.795809 | − | 0.605547i | \(-0.207046\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.34472 | −0.0446016 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.2327 | 0.471549 | 0.235775 | − | 0.971808i | \(-0.424237\pi\) | ||||
0.235775 | + | 0.971808i | \(0.424237\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.1677i | − | 0.402693i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 27.1032 | − | 5.95488i | 0.896004 | − | 0.196862i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37.0528i | 1.22359i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.3246 | 1.13226 | 0.566132 | − | 0.824315i | \(-0.308439\pi\) | ||||
0.566132 | + | 0.824315i | \(0.308439\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 67.5508 | 2.22588 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 83.1474i | 2.73683i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.5474 | − | 44.5028i | −0.675595 | − | 1.46324i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.03550i | 0.0340103i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.14579 | −0.201637 | −0.100818 | − | 0.994905i | \(-0.532146\pi\) | ||||
−0.100818 | + | 0.994905i | \(0.532146\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.28428 | −0.238733 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 36.7330i | 1.20258i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.2420 | + | 3.12913i | −0.465763 | + | 0.102334i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 18.4581i | − | 0.602998i | −0.953466 | − | 0.301499i | \(-0.902513\pi\) | ||
0.953466 | − | 0.301499i | \(-0.0974871\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.4256 | −0.633931 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.7623 | 1.00282 | 0.501411 | − | 0.865209i | \(-0.332815\pi\) | ||||
0.501411 | + | 0.865209i | \(0.332815\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.27087i | 0.204208i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.63820 | − | 21.1104i | −0.150881 | − | 0.686723i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.4692i | 0.372698i | 0.982484 | + | 0.186349i | \(0.0596655\pi\) | ||||
−0.982484 | + | 0.186349i | \(0.940334\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −57.3119 | −1.86042 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.1080 | −0.587192 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.40664i | 0.0779586i | 0.999240 | + | 0.0389793i | \(0.0124106\pi\) | ||||
−0.999240 | + | 0.0389793i | \(0.987589\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.70914 | − | 30.5362i | −0.217103 | − | 0.988127i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.899533i | − | 0.0290778i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.1848 | −0.361176 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.8119 | −0.671353 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.197684i | 0.00637029i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.0283 | + | 4.18073i | −0.612541 | + | 0.134582i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.4766i | 1.84832i | 0.382001 | + | 0.924162i | \(0.375235\pi\) | ||||
−0.382001 | + | 0.924162i | \(0.624765\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −46.4202 | −1.49123 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.1909 | −1.70698 | −0.853489 | − | 0.521111i | \(-0.825518\pi\) | ||||
−0.853489 | + | 0.521111i | \(0.825518\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.1382i | 0.325015i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 53.0174 | − | 24.4787i | 1.69792 | − | 0.783946i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 54.4716i | − | 1.74270i | −0.490661 | − | 0.871350i | \(-0.663245\pi\) | ||
0.490661 | − | 0.871350i | \(-0.336755\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.39080 | 0.204251 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.24864 | 0.199504 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 37.5908i | − | 1.19896i | −0.800390 | − | 0.599480i | \(-0.795374\pi\) | ||
0.800390 | − | 0.599480i | \(-0.204626\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49.1124 | + | 10.7905i | −1.56485 | + | 0.343815i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.6461i | 0.911816i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.75474 | 0.246587 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.0545 | −0.446455 | −0.223228 | − | 0.974766i | \(-0.571659\pi\) | ||||
−0.223228 | + | 0.974766i | \(0.571659\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 46.9706i | 1.49057i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.32377 | + | 19.6793i | 0.137073 | + | 0.623877i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 10.9378i | − | 0.346404i | −0.984886 | − | 0.173202i | \(-0.944589\pi\) | ||
0.984886 | − | 0.173202i | \(-0.0554113\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −41.4900 | −1.31269 |
(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 | 1840.2.e.d.369.7 | 8 | ||
4.3 | odd | 2 | 115.2.b.b.24.1 | ✓ | 8 | ||
5.2 | odd | 4 | 9200.2.a.ck.1.4 | 4 | |||
5.3 | odd | 4 | 9200.2.a.cq.1.1 | 4 | |||
5.4 | even | 2 | inner | 1840.2.e.d.369.2 | 8 | ||
12.11 | even | 2 | 1035.2.b.e.829.8 | 8 | |||
20.3 | even | 4 | 575.2.a.i.1.1 | 4 | |||
20.7 | even | 4 | 575.2.a.j.1.4 | 4 | |||
20.19 | odd | 2 | 115.2.b.b.24.8 | yes | 8 | ||
60.23 | odd | 4 | 5175.2.a.bv.1.4 | 4 | |||
60.47 | odd | 4 | 5175.2.a.bw.1.1 | 4 | |||
60.59 | even | 2 | 1035.2.b.e.829.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.b.b.24.1 | ✓ | 8 | 4.3 | odd | 2 | ||
115.2.b.b.24.8 | yes | 8 | 20.19 | odd | 2 | ||
575.2.a.i.1.1 | 4 | 20.3 | even | 4 | |||
575.2.a.j.1.4 | 4 | 20.7 | even | 4 | |||
1035.2.b.e.829.1 | 8 | 60.59 | even | 2 | |||
1035.2.b.e.829.8 | 8 | 12.11 | even | 2 | |||
1840.2.e.d.369.2 | 8 | 5.4 | even | 2 | inner | ||
1840.2.e.d.369.7 | 8 | 1.1 | even | 1 | trivial | ||
5175.2.a.bv.1.4 | 4 | 60.23 | odd | 4 | |||
5175.2.a.bw.1.1 | 4 | 60.47 | odd | 4 | |||
9200.2.a.ck.1.4 | 4 | 5.2 | odd | 4 | |||
9200.2.a.cq.1.1 | 4 | 5.3 | odd | 4 |