Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [232,2,Mod(9,232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(232, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("232.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 232 = 2^{3} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 232.q (of order \(14\), degree \(6\), 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: | \(1.85252932689\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{14})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{14}]$ |
Embedding invariants
Embedding label | 9.6 | ||
Character | \(\chi\) | \(=\) | 232.9 |
Dual form | 232.2.q.a.129.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/232\mathbb{Z}\right)^\times\).
\(n\) | \(89\) | \(117\) | \(175\) |
\(\chi(n)\) | \(e\left(\frac{5}{14}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.884679 | − | 0.705508i | 0.510770 | − | 0.407325i | −0.333904 | − | 0.942607i | \(-0.608366\pi\) |
0.844674 | + | 0.535282i | \(0.179795\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.449269 | − | 0.216356i | 0.200919 | − | 0.0967575i | −0.330719 | − | 0.943729i | \(-0.607291\pi\) |
0.531638 | + | 0.846972i | \(0.321577\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.01029 | + | 2.52083i | 0.759820 | + | 0.952784i | 0.999838 | − | 0.0179842i | \(-0.00572486\pi\) |
−0.240018 | + | 0.970768i | \(0.577153\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.382647 | + | 1.67649i | −0.127549 | + | 0.558829i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.96468 | − | 0.676669i | 0.893885 | − | 0.204023i | 0.249182 | − | 0.968457i | \(-0.419838\pi\) |
0.644703 | + | 0.764433i | \(0.276981\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.36941 | − | 5.99976i | −0.379805 | − | 1.66403i | −0.698068 | − | 0.716032i | \(-0.745957\pi\) |
0.318263 | − | 0.948002i | \(-0.396900\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.244817 | − | 0.508369i | 0.0632116 | − | 0.131260i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.56896i | − | 0.623065i | −0.950235 | − | 0.311533i | \(-0.899158\pi\) | ||
0.950235 | − | 0.311533i | \(-0.100842\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.46765 | + | 1.17041i | 0.336702 | + | 0.268511i | 0.777215 | − | 0.629235i | \(-0.216632\pi\) |
−0.440512 | + | 0.897746i | \(0.645203\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.55693 | + | 0.811847i | 0.776186 | + | 0.177159i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.94699 | − | 1.90077i | −0.823005 | − | 0.396338i | −0.0255178 | − | 0.999674i | \(-0.508123\pi\) |
−0.797487 | + | 0.603336i | \(0.793838\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.96242 | + | 3.71475i | −0.592483 | + | 0.742951i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.31714 | + | 4.81158i | 0.445933 | + | 0.925989i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.30871 | − | 0.904210i | −0.985803 | − | 0.167908i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.42714 | + | 5.04001i | 0.435928 | + | 0.905213i | 0.996997 | + | 0.0774441i | \(0.0246759\pi\) |
−0.561069 | + | 0.827769i | \(0.689610\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.14540 | − | 2.69024i | 0.373466 | − | 0.468311i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.44856 | + | 0.697590i | 0.244851 | + | 0.117914i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.36573 | − | 0.539963i | −0.388924 | − | 0.0887694i | 0.0235874 | − | 0.999722i | \(-0.492491\pi\) |
−0.412511 | + | 0.910952i | \(0.635348\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.44437 | − | 4.34174i | −0.871796 | − | 0.695234i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.10666i | − | 0.953700i | −0.878985 | − | 0.476850i | \(-0.841779\pi\) | ||
0.878985 | − | 0.476850i | \(-0.158221\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.83073 | + | 5.87807i | −0.431682 | + | 0.896398i | 0.565736 | + | 0.824586i | \(0.308592\pi\) |
−0.997418 | + | 0.0718111i | \(0.977122\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.190807 | + | 0.835981i | 0.0284438 | + | 0.124621i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.57220 | + | 1.50006i | −0.958654 | + | 0.218806i | −0.673096 | − | 0.739555i | \(-0.735036\pi\) |
−0.285558 | + | 0.958362i | \(0.592179\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.755652 | + | 3.31073i | −0.107950 | + | 0.472961i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.81243 | − | 2.27271i | −0.253790 | − | 0.318243i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.169193 | + | 0.0814792i | −0.0232405 | + | 0.0111920i | −0.445468 | − | 0.895298i | \(-0.646963\pi\) |
0.422227 | + | 0.906490i | \(0.361248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.18554 | − | 0.945434i | 0.159858 | − | 0.127482i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.12414 | 0.281349 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.11377 | 0.795945 | 0.397973 | − | 0.917397i | \(-0.369714\pi\) | ||||
0.397973 | + | 0.917397i | \(0.369714\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.61388 | + | 6.86934i | −1.10289 | + | 0.879529i | −0.993428 | − | 0.114461i | \(-0.963486\pi\) |
−0.109467 | + | 0.993990i | \(0.534914\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.99537 | + | 2.40564i | −0.629358 | + | 0.303083i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.91332 | − | 2.39922i | −0.237318 | − | 0.297587i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.07788 | − | 9.10378i | 0.253853 | − | 1.11220i | −0.673845 | − | 0.738873i | \(-0.735358\pi\) |
0.927698 | − | 0.373331i | \(-0.121784\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.83283 | + | 1.10306i | −0.581805 | + | 0.132793i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.82023 | − | 7.97497i | −0.216022 | − | 0.946454i | −0.960384 | − | 0.278678i | \(-0.910104\pi\) |
0.744362 | − | 0.667776i | \(-0.232754\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.47425 | + | 5.13783i | −0.289589 | + | 0.601337i | −0.994114 | − | 0.108342i | \(-0.965446\pi\) |
0.704525 | + | 0.709679i | \(0.251160\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.37638i | 0.620810i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.66565 | + | 6.11315i | 0.873582 | + | 0.696659i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.1195 | − | 3.22268i | −1.58856 | − | 0.362579i | −0.665249 | − | 0.746622i | \(-0.731675\pi\) |
−0.923316 | + | 0.384042i | \(0.874532\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.796613 | + | 0.383629i | 0.0885126 | + | 0.0426254i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.09672 | − | 5.13713i | 0.449674 | − | 0.563873i | −0.504390 | − | 0.863476i | \(-0.668283\pi\) |
0.954064 | + | 0.299603i | \(0.0968542\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.555812 | − | 1.15416i | −0.0602863 | − | 0.125186i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.33443 | + | 2.94540i | −0.571911 | + | 0.315780i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.74003 | + | 5.68973i | 0.290442 | + | 0.603110i | 0.994226 | − | 0.107304i | \(-0.0342219\pi\) |
−0.703784 | + | 0.710414i | \(0.748508\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.3715 | − | 15.5133i | 1.29688 | − | 1.62624i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.70301 | + | 2.74643i | 0.591375 | + | 0.284791i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.912596 | + | 0.208294i | 0.0936304 | + | 0.0213705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.19837 | + | 4.94303i | 0.629349 | + | 0.501889i | 0.885434 | − | 0.464765i | \(-0.153861\pi\) |
−0.256085 | + | 0.966654i | \(0.582433\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.22917i | 0.525552i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.53540 | − | 13.5709i | 0.650297 | − | 1.35036i | −0.271408 | − | 0.962464i | \(-0.587489\pi\) |
0.921705 | − | 0.387891i | \(-0.126796\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.725283 | + | 3.17767i | 0.0714643 | + | 0.313105i | 0.998008 | − | 0.0630806i | \(-0.0200925\pi\) |
−0.926544 | + | 0.376186i | \(0.877235\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.77367 | − | 0.404828i | 0.173092 | − | 0.0395071i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.776551 | − | 3.40229i | 0.0750720 | − | 0.328912i | −0.923421 | − | 0.383788i | \(-0.874619\pi\) |
0.998493 | + | 0.0548762i | \(0.0174764\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.12398 | + | 10.1871i | 0.778136 | + | 0.975751i | 1.00000 | 0.000673747i | \(0.000214461\pi\) | |
−0.221864 | + | 0.975078i | \(0.571214\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.47386 | + | 1.19135i | −0.234809 | + | 0.113078i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.4963 | − | 9.16801i | 1.08148 | − | 0.862453i | 0.0904269 | − | 0.995903i | \(-0.471177\pi\) |
0.991056 | + | 0.133450i | \(0.0426054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.18450 | −0.203706 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.5825 | 0.978354 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.47592 | − | 5.16438i | 0.593647 | − | 0.473418i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.57920 | + | 0.760503i | −0.143564 | + | 0.0691366i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.30830 | − | 5.40243i | −0.388466 | − | 0.487121i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.08201 | + | 4.74060i | −0.0967780 | + | 0.424012i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.83891 | − | 1.56094i | 0.606855 | − | 0.138511i | 0.0919582 | − | 0.995763i | \(-0.470687\pi\) |
0.514897 | + | 0.857252i | \(0.327830\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.64274 | + | 7.19731i | 0.144635 | + | 0.633688i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.60098 | + | 11.6306i | −0.489360 | + | 1.01617i | 0.499361 | + | 0.866394i | \(0.333568\pi\) |
−0.988721 | + | 0.149772i | \(0.952146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.05258i | 0.524825i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.08203 | + | 1.66037i | 0.179193 | + | 0.142901i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.8440 | − | 3.84453i | −1.43908 | − | 0.328461i | −0.569394 | − | 0.822065i | \(-0.692822\pi\) |
−0.869687 | + | 0.493604i | \(0.835679\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.2905 | + | 8.32666i | 1.46656 | + | 0.706258i | 0.985381 | − | 0.170364i | \(-0.0544943\pi\) |
0.481179 | + | 0.876622i | \(0.340209\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.75598 | + | 5.96381i | −0.400526 | + | 0.502244i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.11971 | − | 16.8607i | −0.679004 | − | 1.40997i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.58067 | + | 0.742340i | −0.214313 | + | 0.0616480i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.66724 | + | 3.46205i | 0.137511 | + | 0.285545i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.42867 | − | 10.5692i | 0.690503 | − | 0.865864i | −0.305771 | − | 0.952105i | \(-0.598914\pi\) |
0.996274 | + | 0.0862414i | \(0.0274856\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.0846 | + | 7.74595i | 1.30895 | + | 0.630356i | 0.952665 | − | 0.304022i | \(-0.0983295\pi\) |
0.356283 | + | 0.934378i | \(0.384044\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.30683 | + | 0.983007i | 0.348187 | + | 0.0794714i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.18088 | + | 1.73919i | 0.175172 | + | 0.139695i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.3561i | − | 1.54479i | −0.635145 | − | 0.772393i | \(-0.719059\pi\) | ||
0.635145 | − | 0.772393i | \(-0.280941\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0921976 | + | 0.191450i | −0.00731174 | + | 0.0151830i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.14310 | − | 13.7708i | −0.247711 | − | 1.08529i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.1995 | − | 2.32796i | 0.798883 | − | 0.182340i | 0.196455 | − | 0.980513i | \(-0.437057\pi\) |
0.602428 | + | 0.798173i | \(0.294200\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.381808 | − | 1.67281i | 0.0297237 | − | 0.130228i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.5074 | − | 13.1758i | −0.813085 | − | 1.01958i | −0.999313 | − | 0.0370695i | \(-0.988198\pi\) |
0.186228 | − | 0.982507i | \(-0.440374\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −22.4093 | + | 10.7917i | −1.72379 | + | 0.830133i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.52377 | + | 2.01264i | −0.192998 | + | 0.153911i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.74382 | 0.740809 | 0.370404 | − | 0.928871i | \(-0.379219\pi\) | ||||
0.370404 | + | 0.928871i | \(0.379219\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.3196 | −1.15805 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.40873 | − | 4.31332i | 0.406545 | − | 0.324209i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.4501 | + | 9.36669i | −1.45377 | + | 0.700099i | −0.983245 | − | 0.182287i | \(-0.941650\pi\) |
−0.470526 | + | 0.882386i | \(0.655936\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.00986916 | − | 0.0123755i | −0.000733569 | − | 0.000919866i | 0.781465 | − | 0.623950i | \(-0.214473\pi\) |
−0.782198 | + | 0.623030i | \(0.785902\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.77415 | + | 12.1543i | −0.205071 | + | 0.898474i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.17967 | + | 0.269253i | −0.0867313 | + | 0.0197959i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.73834 | − | 7.61616i | −0.127120 | − | 0.556949i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.47105 | + | 15.5138i | −0.543439 | + | 1.12846i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8382i | 1.00129i | 0.865651 | + | 0.500647i | \(0.166905\pi\) | ||||
−0.865651 | + | 0.500647i | \(0.833095\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.45404 | − | 1.95703i | −0.176646 | − | 0.140870i | 0.531176 | − | 0.847262i | \(-0.321750\pi\) |
−0.707821 | + | 0.706391i | \(0.750322\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.38534 | − | 0.772683i | −0.242430 | − | 0.0553330i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.549977 | + | 0.264855i | 0.0391842 | + | 0.0188701i | 0.453373 | − | 0.891321i | \(-0.350220\pi\) |
−0.414189 | + | 0.910191i | \(0.635935\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.78476 | + | 9.76178i | −0.551847 | + | 0.691994i | −0.977027 | − | 0.213115i | \(-0.931639\pi\) |
0.425180 | + | 0.905109i | \(0.360211\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.58454 | − | 9.51989i | −0.323368 | − | 0.671481i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.39271 | − | 15.2001i | −0.589053 | − | 1.06684i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.32121 | − | 2.74353i | −0.0922776 | − | 0.191616i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.69692 | − | 5.88975i | 0.326459 | − | 0.409366i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.14310 | + | 2.47679i | 0.355756 | + | 0.171323i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.7015 | + | 3.12728i | 0.943250 | + | 0.215291i | 0.666376 | − | 0.745616i | \(-0.267845\pi\) |
0.276874 | + | 0.960906i | \(0.410702\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.23673 | − | 5.77110i | −0.495852 | − | 0.395429i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.25328i | 0.221872i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.82574 | + | 16.2503i | −0.531246 | + | 1.10314i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.43586 | + | 6.29093i | 0.0970267 | + | 0.425102i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.4132 | + | 3.51796i | −1.03680 | + | 0.236643i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.433198 | − | 1.89796i | 0.0290091 | − | 0.127097i | −0.958350 | − | 0.285596i | \(-0.907808\pi\) |
0.987359 | + | 0.158499i | \(0.0506655\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.09417 | − | 6.38789i | −0.339612 | − | 0.425859i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.13778 | − | 2.47422i | 0.341007 | − | 0.164220i | −0.255540 | − | 0.966798i | \(-0.582253\pi\) |
0.596547 | + | 0.802578i | \(0.296539\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5753 | + | 10.0285i | −0.830999 | + | 0.662700i | −0.943654 | − | 0.330934i | \(-0.892636\pi\) |
0.112654 | + | 0.993634i | \(0.464065\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 11.0945 | 0.729966 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 30.3854 | 1.99061 | 0.995305 | − | 0.0967850i | \(-0.0308559\pi\) | ||||
0.995305 | + | 0.0967850i | \(0.0308559\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.62813 | + | 2.09587i | −0.171441 | + | 0.136719i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.7648 | + | 7.11037i | −0.959079 | + | 0.461868i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.6603 | + | 19.6374i | 1.01298 | + | 1.27024i | 0.962433 | + | 0.271519i | \(0.0875261\pi\) |
0.0505504 | + | 0.998722i | \(0.483902\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.10459 | − | 26.7460i | 0.393231 | − | 1.72286i | −0.259919 | − | 0.965631i | \(-0.583696\pi\) |
0.653150 | − | 0.757229i | \(-0.273447\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.6443 | + | 3.34246i | −0.939430 | + | 0.214419i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.376806 | + | 1.65090i | 0.0240733 | + | 0.105472i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.01239 | − | 10.4083i | 0.318931 | − | 0.662266i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 7.43498i | − | 0.471173i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.52803 | − | 2.01603i | −0.159568 | − | 0.127251i | 0.540451 | − | 0.841375i | \(-0.318254\pi\) |
−0.700019 | + | 0.714124i | \(0.746825\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.9878 | − | 2.96437i | −0.816534 | − | 0.186369i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.30598 | − | 0.628927i | −0.0817837 | − | 0.0393850i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.7866 | + | 23.5576i | −1.17187 | + | 1.46948i | −0.318703 | + | 0.947855i | \(0.603247\pi\) |
−0.853172 | + | 0.521630i | \(0.825324\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.39466 | − | 7.04909i | −0.210934 | − | 0.438009i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.54726 | − | 8.55399i | 0.219570 | − | 0.529478i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.01350 | + | 10.4106i | 0.309146 | + | 0.641947i | 0.996428 | − | 0.0844426i | \(-0.0269110\pi\) |
−0.687283 | + | 0.726390i | \(0.741197\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.0583847 | + | 0.0732121i | −0.00358654 | + | 0.00449738i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.43820 | + | 3.10047i | 0.394011 | + | 0.189746i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.61113 | − | 0.824216i | −0.220174 | − | 0.0502533i | 0.111011 | − | 0.993819i | \(-0.464591\pi\) |
−0.331185 | + | 0.943566i | \(0.607448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.96690 | + | 5.55592i | 0.423209 | + | 0.337498i | 0.811824 | − | 0.583902i | \(-0.198475\pi\) |
−0.388615 | + | 0.921400i | \(0.627046\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 22.4525i | − | 1.35889i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.26896 | + | 13.0176i | −0.378033 | + | 0.784993i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.47276 | − | 23.9777i | −0.328826 | − | 1.44068i | −0.821371 | − | 0.570394i | \(-0.806790\pi\) |
0.492545 | − | 0.870287i | \(-0.336067\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.37825 | + | 2.14053i | −0.561461 | + | 0.128150i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.92059 | + | 12.7960i | −0.174228 | + | 0.763342i | 0.809999 | + | 0.586431i | \(0.199468\pi\) |
−0.984227 | + | 0.176911i | \(0.943390\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8043 | − | 16.0561i | −0.761138 | − | 0.954437i | 0.238723 | − | 0.971088i | \(-0.423271\pi\) |
−0.999861 | + | 0.0166504i | \(0.994700\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.954308 | − | 0.459571i | 0.0565283 | − | 0.0272226i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.3938 | − | 12.2762i | 0.908670 | − | 0.724640i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.4004 | 0.611789 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.97092 | 0.525885 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.6075 | − | 12.4466i | 0.911799 | − | 0.727136i | −0.0506158 | − | 0.998718i | \(-0.516118\pi\) |
0.962415 | + | 0.271583i | \(0.0875470\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.74672 | − | 1.32275i | 0.159921 | − | 0.0770137i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.1254 | + | 12.6969i | 0.587536 | + | 0.736747i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.99914 | + | 26.2839i | −0.346939 | + | 1.52004i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.5082 | + | 4.68087i | −1.18207 | + | 0.269801i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.79265 | − | 16.6167i | −0.217882 | − | 0.954604i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.38372 | + | 4.94985i | −0.136491 | + | 0.283427i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.2931i | 1.32941i | 0.747107 | + | 0.664704i | \(0.231442\pi\) | ||||
−0.747107 | + | 0.664704i | \(0.768558\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.88352 | + | 2.29953i | 0.164038 | + | 0.130816i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.9338 | + | 3.18030i | 0.790113 | + | 0.180338i | 0.598490 | − | 0.801131i | \(-0.295768\pi\) |
0.191623 | + | 0.981469i | \(0.438625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.70690 | + | 4.67460i | 0.548666 | + | 0.264224i | 0.687615 | − | 0.726076i | \(-0.258658\pi\) |
−0.138948 | + | 0.990300i | \(0.544372\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.72379 | + | 2.16156i | −0.0971244 | + | 0.121790i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.09045 | − | 6.41738i | −0.173577 | − | 0.360436i | 0.795972 | − | 0.605333i | \(-0.206960\pi\) |
−0.969549 | + | 0.244897i | \(0.921246\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.3505 | + | 0.911545i | −0.915452 | + | 0.0510367i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.71335 | − | 3.55780i | −0.0956297 | − | 0.198577i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.00675 | − | 3.77035i | 0.167300 | − | 0.209788i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.3444 | + | 12.6868i | 1.46132 | + | 0.703736i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.3742 | + | 3.28082i | 0.794897 | + | 0.181430i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.9935 | − | 13.5518i | −0.936879 | − | 0.747136i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 15.7331i | − | 0.864769i | −0.901689 | − | 0.432385i | \(-0.857672\pi\) | ||
0.901689 | − | 0.432385i | \(-0.142328\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.81048 | − | 3.75950i | 0.0992138 | − | 0.206019i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.03614 | − | 4.53960i | −0.0566101 | − | 0.248025i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.6927 | − | 3.35351i | 0.800362 | − | 0.182677i | 0.197270 | − | 0.980349i | \(-0.436792\pi\) |
0.603092 | + | 0.797672i | \(0.293935\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.70245 | − | 16.2215i | 0.201089 | − | 0.881031i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.6061 | + | 13.2997i | 0.574354 | + | 0.720217i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.4699 | − | 5.04202i | 0.565319 | − | 0.272243i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.93259 | + | 1.54119i | −0.104047 | + | 0.0829746i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.1733 | −0.814548 | −0.407274 | − | 0.913306i | \(-0.633521\pi\) | ||||
−0.407274 | + | 0.913306i | \(0.633521\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.5059 | 0.883540 | 0.441770 | − | 0.897128i | \(-0.354351\pi\) | ||||
0.441770 | + | 0.897128i | \(0.354351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25.6952 | − | 20.4913i | 1.37151 | − | 1.09374i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.5048 | − | 10.3562i | 1.14459 | − | 0.551204i | 0.237184 | − | 0.971465i | \(-0.423776\pi\) |
0.907404 | + | 0.420260i | \(0.138061\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.54321 | − | 3.18908i | −0.134979 | − | 0.169259i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.08561 | − | 9.13764i | 0.110382 | − | 0.483615i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −24.4200 | + | 5.57371i | −1.28884 | + | 0.294169i | −0.811398 | − | 0.584494i | \(-0.801293\pi\) |
−0.477442 | + | 0.878663i | \(0.658436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.44376 | − | 15.0881i | −0.181251 | − | 0.794111i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.860545 | + | 1.78694i | −0.0451669 | + | 0.0937900i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.84358i | 0.148840i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.1136 | + | 14.4451i | 0.945523 | + | 0.754030i | 0.969349 | − | 0.245686i | \(-0.0790133\pi\) |
−0.0238259 | + | 0.999716i | \(0.507585\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.2377 | + | 2.33669i | 0.532955 | + | 0.121643i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.545524 | − | 0.262710i | −0.0283222 | − | 0.0136392i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.49553 | − | 11.9070i | 0.491660 | − | 0.616522i | −0.472666 | − | 0.881242i | \(-0.656708\pi\) |
0.964325 | + | 0.264720i | \(0.0852796\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.38730 | + | 4.95728i | 0.123280 | + | 0.255993i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.84473 | + | 33.0892i | 0.0950087 | + | 1.70418i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.10982 | + | 6.45761i | 0.159741 | + | 0.331705i | 0.965442 | − | 0.260616i | \(-0.0839258\pi\) |
−0.805702 | + | 0.592322i | \(0.798212\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.94899 | − | 6.20583i | 0.253544 | − | 0.317935i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.9725 | + | 11.0630i | 1.17384 | + | 0.565292i | 0.916111 | − | 0.400924i | \(-0.131311\pi\) |
0.257731 | + | 0.966217i | \(0.417025\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.76656 | + | 1.08794i | 0.242926 | + | 0.0554463i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.77134 | − | 6.99491i | −0.445872 | − | 0.355571i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 8.78365i | − | 0.445349i | −0.974893 | − | 0.222674i | \(-0.928521\pi\) | ||
0.974893 | − | 0.222674i | \(-0.0714787\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.88301 | + | 10.1397i | −0.246945 | + | 0.512786i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.25038 | + | 14.2409i | 0.163960 | + | 0.718356i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.04068 | + | 1.60699i | −0.354255 | + | 0.0808564i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.47770 | + | 6.47421i | −0.0741635 | + | 0.324931i | −0.998377 | − | 0.0569437i | \(-0.981864\pi\) |
0.924214 | + | 0.381875i | \(0.124722\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.27014 | + | 5.35459i | 0.213774 | + | 0.268065i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.4070 | + | 15.1248i | −1.56839 | + | 0.755298i | −0.997823 | − | 0.0659520i | \(-0.978992\pi\) |
−0.570569 | + | 0.821250i | \(0.693277\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.9151 | − | 21.4641i | 1.34074 | − | 1.06920i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.440894 | 0.0219082 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.37902 | −0.365764 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.1095 | + | 20.8216i | −1.29103 | + | 1.02956i | −0.293749 | + | 0.955883i | \(0.594903\pi\) |
−0.997282 | + | 0.0736798i | \(0.976526\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.6139 | + | 8.48240i | −0.868829 | + | 0.418406i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.2905 | + | 15.4118i | 0.604775 | + | 0.758364i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.729078 | − | 3.19430i | 0.0357890 | − | 0.156802i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.1711 | − | 4.83216i | 1.03675 | − | 0.236632i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.92977 | − | 21.5987i | −0.240835 | − | 1.05517i | −0.940259 | − | 0.340460i | \(-0.889417\pi\) |
0.699424 | − | 0.714707i | \(-0.253440\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.7328 | + | 22.2868i | −0.523083 | + | 1.08619i | 0.457340 | + | 0.889292i | \(0.348802\pi\) |
−0.980423 | + | 0.196902i | \(0.936912\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 11.5922i | − | 0.563632i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.54307 | + | 7.61034i | 0.462907 | + | 0.369156i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.6329 | − | 7.90473i | −1.67600 | − | 0.382537i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.0787 | − | 9.18783i | −0.921130 | − | 0.443593i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0340 | − | 18.8521i | 0.724164 | − | 0.908073i | −0.274402 | − | 0.961615i | \(-0.588480\pi\) |
0.998566 | + | 0.0535422i | \(0.0170512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.71721 | + | 3.56582i | 0.0825238 | + | 0.171362i | 0.938147 | − | 0.346236i | \(-0.112540\pi\) |
−0.855624 | + | 0.517598i | \(0.826826\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.75934 | + | 2.47742i | −0.0843538 | + | 0.118783i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.56812 | − | 7.40928i | −0.170686 | − | 0.354434i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.06081 | − | 1.33021i | 0.0506297 | − | 0.0634877i | −0.755872 | − | 0.654720i | \(-0.772787\pi\) |
0.806502 | + | 0.591232i | \(0.201358\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.26124 | − | 2.53368i | −0.250535 | − | 0.120651i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0108 | + | 2.28491i | 0.475629 | + | 0.108559i | 0.453614 | − | 0.891198i | \(-0.350135\pi\) |
0.0220155 | + | 0.999758i | \(0.492992\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.46202 | + | 1.96339i | 0.116711 | + | 0.0930738i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 15.2969i | − | 0.723517i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.781405 | + | 1.62260i | −0.0368768 | + | 0.0765755i | −0.918593 | − | 0.395204i | \(-0.870674\pi\) |
0.881717 | + | 0.471780i | \(0.156388\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.13219 | − | 18.1043i | −0.194577 | − | 0.852498i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.6946 | − | 4.49516i | 0.925332 | − | 0.211201i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.20170 | − | 9.64629i | 0.103217 | − | 0.452225i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.9146 | − | 24.9722i | −0.931567 | − | 1.16815i | −0.985512 | − | 0.169604i | \(-0.945751\pi\) |
0.0539450 | − | 0.998544i | \(-0.482820\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.3608 | − | 5.95264i | 0.576952 | − | 0.277845i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0616 | + | 14.4037i | −0.841214 | + | 0.670846i | −0.946184 | − | 0.323630i | \(-0.895097\pi\) |
0.104970 | + | 0.994475i | \(0.466525\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.1958 | −1.49626 | −0.748132 | − | 0.663550i | \(-0.769049\pi\) | ||||
−0.748132 | + | 0.663550i | \(0.769049\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.15639 | 0.146374 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.6432 | + | 23.6396i | −1.37172 | + | 1.09391i | −0.386563 | + | 0.922263i | \(0.626338\pi\) |
−0.985158 | + | 0.171649i | \(0.945091\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.1262 | − | 13.0633i | 1.25257 | − | 0.603207i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.6559 | − | 17.1240i | −0.629231 | − | 0.789031i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.41470 | + | 19.3421i | −0.202988 | + | 0.889350i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.69559 | + | 1.98471i | −0.398981 | + | 0.0910648i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0718574 | − | 0.314828i | −0.00329013 | − | 0.0144150i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.8601 | + | 30.8572i | −0.678974 | + | 1.40990i | 0.221573 | + | 0.975144i | \(0.428881\pi\) |
−0.900547 | + | 0.434759i | \(0.856833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.9333i | 0.680898i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.4961 | − | 9.96527i | −0.568590 | − | 0.453435i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.85419 | + | 0.879693i | 0.175010 | + | 0.0399448i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.3197 | + | 12.1933i | 1.14735 | + | 0.552533i | 0.908236 | − | 0.418459i | \(-0.137430\pi\) |
0.239111 | + | 0.970992i | \(0.423144\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.38085 | − | 9.25529i | 0.333774 | − | 0.418539i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.93180 | − | 6.08795i | −0.132310 | − | 0.274745i | 0.824279 | − | 0.566183i | \(-0.191581\pi\) |
−0.956590 | + | 0.291438i | \(0.905866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.32288 | + | 13.6379i | −0.104617 | + | 0.614220i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.13136 | + | 2.34930i | 0.0508511 | + | 0.105593i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.4443 | − | 20.6205i | 0.737629 | − | 0.924957i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.7715 | − | 9.52144i | −0.885092 | − | 0.426238i | −0.0646105 | − | 0.997911i | \(-0.520580\pi\) |
−0.820482 | + | 0.571673i | \(0.806295\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.5913 | − | 4.24335i | −0.830599 | − | 0.189579i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.9422 | − | 12.7134i | −0.710826 | − | 0.566865i | 0.199930 | − | 0.979810i | \(-0.435929\pi\) |
−0.910756 | + | 0.412946i | \(0.864500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 7.51096i | − | 0.334233i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.2114 | + | 25.3571i | −0.542325 | + | 1.12615i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.82202 | + | 16.7453i | 0.169408 | + | 0.742225i | 0.986236 | + | 0.165343i | \(0.0528733\pi\) |
−0.816828 | + | 0.576881i | \(0.804270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.9256 | + | 4.09139i | −0.792980 | + | 0.180993i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.23079 | + | 9.77373i | −0.0984918 | + | 0.431521i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.01336 | + | 1.27071i | 0.0446538 | + | 0.0559941i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.4694 | + | 8.89441i | −0.812285 | + | 0.391176i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.62015 | − | 6.87434i | 0.378383 | − | 0.301750i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.50737 | 0.372715 | 0.186357 | − | 0.982482i | \(-0.440332\pi\) | ||||
0.186357 | + | 0.982482i | \(0.440332\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.75899 | −0.426731 | −0.213365 | − | 0.976972i | \(-0.568442\pi\) | ||||
−0.213365 | + | 0.976972i | \(0.568442\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −13.5529 | + | 10.8081i | −0.591498 | + | 0.471704i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.9476 | − | 6.23524i | 0.564007 | − | 0.271611i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.37445 | − | 2.97746i | −0.103237 | − | 0.129455i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.33942 | + | 10.2497i | −0.101522 | + | 0.444797i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.6385 | + | 8.36249i | −1.58699 | + | 0.362220i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.387228 | − | 1.69656i | −0.0167413 | − | 0.0733485i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.5989 | + | 22.0088i | −0.457374 | + | 0.949748i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.3266i | 0.444797i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.9775 | + | 15.9315i | 0.858901 | + | 0.684950i | 0.950459 | − | 0.310849i | \(-0.100613\pi\) |
−0.0915587 | + | 0.995800i | \(0.529185\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.0174621 | − | 0.00398561i | −0.000749369 | − | 0.000171039i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.85390 | + | 2.81909i | 0.250754 | + | 0.120757i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.96032 | − | 12.4898i | 0.425873 | − | 0.534027i | −0.521886 | − | 0.853015i | \(-0.674771\pi\) |
0.947759 | + | 0.318988i | \(0.103343\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.22028 | − | 17.0696i | −0.350833 | − | 0.728512i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.73304 | − | 7.54045i | −0.286837 | − | 0.321234i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.2605 | − | 42.0713i | −0.861563 | − | 1.78905i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.853673 | + | 1.07047i | −0.0362364 | + | 0.0454390i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.5258 | − | 6.51370i | −0.573108 | − | 0.275994i | 0.124800 | − | 0.992182i | \(-0.460171\pi\) |
−0.697908 | + | 0.716188i | \(0.745885\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 39.1434 | + | 8.93423i | 1.65559 | + | 0.377878i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.91114 | − | 5.51145i | −0.291789 | − | 0.232694i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.8811i | 0.964324i | 0.876082 | + | 0.482162i | \(0.160148\pi\) | ||||
−0.876082 | + | 0.482162i | \(0.839852\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.18138 | − | 6.60620i | 0.133842 | − | 0.277925i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.634365 | + | 2.77933i | 0.0266408 | + | 0.116721i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.17874 | − | 1.41026i | 0.259026 | − | 0.0591211i | −0.0910355 | − | 0.995848i | \(-0.529018\pi\) |
0.350062 | + | 0.936727i | \(0.386161\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.34309 | − | 27.7909i | 0.265450 | − | 1.16301i | −0.649793 | − | 0.760111i | \(-0.725144\pi\) |
0.915243 | − | 0.402902i | \(-0.131998\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.76295 | + | 12.2423i | 0.407853 | + | 0.511431i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.7535 | − | 9.03123i | 0.782076 | − | 0.376628i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.3981 | − | 13.8745i | 0.724291 | − | 0.577602i | −0.190425 | − | 0.981702i | \(-0.560986\pi\) |
0.914715 | + | 0.404099i | \(0.132415\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.55175 | −0.147606 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21.1854 | 0.878920 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.446470 | + | 0.356048i | −0.0184909 | + | 0.0147460i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.75439 | − | 2.28959i | 0.196570 | − | 0.0946631i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.20045 | + | 10.2830i | 0.338469 | + | 0.424426i | 0.921714 | − | 0.387870i | \(-0.126789\pi\) |
−0.583246 | + | 0.812296i | \(0.698217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.33670 | + | 10.2377i | −0.0962820 | + | 0.421839i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.673411 | − | 0.153702i | 0.0277004 | − | 0.00632244i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.90152 | + | 12.7124i | 0.119151 | + | 0.522036i | 0.998913 | + | 0.0466202i | \(0.0148451\pi\) |
−0.879761 | + | 0.475415i | \(0.842298\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.79208 | − | 3.72130i | 0.0734682 | − | 0.152558i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.1283i | 0.578231i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.36327 | + | 1.08718i | 0.0557019 | + | 0.0444208i | 0.650945 | − | 0.759125i | \(-0.274373\pi\) |
−0.595243 | + | 0.803546i | \(0.702944\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.6144 | − | 2.42266i | −0.432970 | − | 0.0988225i | 0.000480812 | − | 1.00000i | \(-0.499847\pi\) |
−0.433450 | + | 0.901177i | \(0.642704\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.4673 | + | 6.96707i | 0.589153 | + | 0.283721i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.544945 | + | 0.683340i | −0.0221552 | + | 0.0277817i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0667 | + | 25.0567i | 0.489771 | + | 1.01702i | 0.988634 | + | 0.150339i | \(0.0480365\pi\) |
−0.498864 | + | 0.866680i | \(0.666249\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.1486 | − | 7.52607i | −0.735420 | − | 0.304972i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0000 | + | 37.3774i | 0.728203 | + | 1.51213i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.4057 | − | 24.3340i | 0.783790 | − | 0.982842i | −0.216189 | − | 0.976352i | \(-0.569363\pi\) |
0.999979 | − | 0.00649029i | \(-0.00206594\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.10443 | − | 1.49502i | −0.125183 | − | 0.0602849i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.9695 | − | 6.84034i | −1.20653 | − | 0.275382i | −0.428458 | − | 0.903561i | \(-0.640943\pi\) |
−0.778068 | + | 0.628180i | \(0.783800\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.9819 | − | 22.3148i | −1.12469 | − | 0.896908i | −0.129182 | − | 0.991621i | \(-0.541235\pi\) |
−0.995505 | + | 0.0947131i | \(0.969807\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 23.3956i | − | 0.938834i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.83457 | + | 18.3452i | −0.353950 | + | 0.734984i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.74683 | − | 20.7972i | −0.189873 | − | 0.831888i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.29739 | − | 1.43734i | 0.251494 | − | 0.0574018i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.38715 | + | 6.07748i | −0.0553091 | + | 0.242325i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.807873 | − | 1.01304i | −0.0321609 | − | 0.0403285i | 0.765491 | − | 0.643447i | \(-0.222496\pi\) |
−0.797652 | + | 0.603118i | \(0.793925\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.3277 | − | 6.89988i | 0.569477 | − | 0.274246i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.73479 | − | 2.18092i | 0.108527 | − | 0.0865472i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.8984 | 0.828023 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.0664 | 0.556459 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.79784 | − | 6.21857i | 0.307996 | − | 0.245619i | −0.457277 | − | 0.889324i | \(-0.651175\pi\) |
0.765273 | + | 0.643705i | \(0.222604\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.80963 | − | 2.31619i | 0.189673 | − | 0.0913418i | −0.336637 | − | 0.941635i | \(-0.609289\pi\) |
0.526310 | + | 0.850293i | \(0.323575\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.29522 | + | 2.87811i | 0.0903740 | + | 0.113325i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.69886 | − | 24.9683i | 0.224045 | − | 0.981607i | −0.730353 | − | 0.683070i | \(-0.760644\pi\) |
0.954398 | − | 0.298537i | \(-0.0964985\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.1254 | − | 4.13700i | 0.711484 | − | 0.162392i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.54146 | + | 19.8975i | 0.177994 | + | 0.779843i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.0437 | − | 29.1620i | 0.549571 | − | 1.14120i | −0.422468 | − | 0.906378i | \(-0.638836\pi\) |
0.972039 | − | 0.234819i | \(-0.0754496\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.43705i | 0.251516i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.66673 | − | 6.11402i | −0.299108 | − | 0.238531i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.94198 | + | 1.81271i | 0.309376 | + | 0.0706130i | 0.374390 | − | 0.927271i | \(-0.377852\pi\) |
−0.0650143 | + | 0.997884i | \(0.520709\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.79092 | + | 1.82561i | 0.147450 | + | 0.0710080i | 0.506153 | − | 0.862443i | \(-0.331067\pi\) |
−0.358704 | + | 0.933451i | \(0.616781\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.1538 | + | 13.9864i | −0.433177 | + | 0.543186i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.30951 | + | 2.71923i | 0.0507807 | + | 0.105447i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.2347 | + | 13.6596i | 0.744772 | + | 0.528900i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.955788 | − | 1.98471i | −0.0369529 | − | 0.0767335i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.8892 | + | 26.1942i | −0.806417 | + | 1.01121i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.2946 | + | 6.40233i | 0.512468 | + | 0.246792i | 0.672201 | − | 0.740369i | \(-0.265349\pi\) |
−0.159733 | + | 0.987160i | \(0.551063\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −24.7382 | − | 5.64632i | −0.952172 | − | 0.217327i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.88854 | − | 5.49343i | −0.264748 | − | 0.211130i | 0.482114 | − | 0.876108i | \(-0.339869\pi\) |
−0.746862 | + | 0.664979i | \(0.768441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.5620i | 0.980979i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.79970 | − | 5.81364i | 0.107285 | − | 0.222779i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.165355 | − | 0.724467i | −0.00632713 | − | 0.0277210i | 0.971666 | − | 0.236359i | \(-0.0759541\pi\) |
−0.977993 | + | 0.208638i | \(0.933097\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.39927 | + | 1.91708i | −0.320920 | + | 0.0732478i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.04994 | + | 17.7440i | −0.154515 | + | 0.676974i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.720550 | + | 0.903541i | 0.0274508 | + | 0.0344222i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.9866 | − | 9.14344i | 0.722283 | − | 0.347833i | −0.0363611 | − | 0.999339i | \(-0.511577\pi\) |
0.758644 | + | 0.651506i | \(0.225862\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.1819 | + | 10.5122i | −0.500737 | + | 0.399325i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.56960 | 0.362996 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.6878 | −0.594217 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.8813 | − | 21.4371i | 1.01674 | − | 0.810826i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.5359 | + | 7.00011i | −0.549013 | + | 0.264391i | −0.687761 | − | 0.725937i | \(-0.741406\pi\) |
0.138748 | + | 0.990328i | \(0.455692\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.84009 | − | 3.56136i | −0.107116 | − | 0.134319i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.846405 | + | 3.70834i | −0.0318774 | + | 0.139664i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 47.3480 | − | 10.8069i | 1.78071 | − | 0.406435i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.21880 | + | 14.1025i | 0.120884 | + | 0.529629i | 0.998716 | + | 0.0506598i | \(0.0161324\pi\) |
−0.877832 | + | 0.478970i | \(0.841010\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.8055 | − | 22.4380i | 0.405240 | − | 0.841489i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 24.5063i | − | 0.917770i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.29586 | − | 5.81825i | −0.272850 | − | 0.217590i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.7088 | + | 6.32435i | 1.03480 | + | 0.236187i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.597255 | + | 0.287623i | 0.0222738 | + | 0.0107265i | 0.444988 | − | 0.895537i | \(-0.353208\pi\) |
−0.422714 | + | 0.906263i | \(0.638922\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.55234 | + | 8.21637i | −0.244022 | + | 0.305994i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.4689 | − | 27.9684i | −0.500914 | − | 1.04016i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19.0855 | − | 17.0419i | 0.708819 | − | 0.632920i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.74191 | + | 3.61711i | 0.0646038 | + | 0.134151i | 0.930770 | − | 0.365604i | \(-0.119138\pi\) |
−0.866167 | + | 0.499755i | \(0.833423\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.2512 | + | 15.3625i | −0.453747 | + | 0.568981i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.1006 | + | 7.27205i | 0.558514 | + | 0.268966i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.8873 | − | 4.76739i | −0.771491 | − | 0.176088i | −0.181383 | − | 0.983412i | \(-0.558057\pi\) |
−0.590107 | + | 0.807325i | \(0.700915\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.49807 | + | 1.19467i | 0.0552573 | + | 0.0440662i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 28.3959i | − | 1.04597i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.0121 | − | 43.6320i | 0.772942 | − | 1.60503i | −0.0230587 | − | 0.999734i | \(-0.507340\pi\) |
0.796000 | − | 0.605296i | \(-0.206945\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.90881 | − | 12.7443i | −0.106858 | − | 0.468174i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.44747 | − | 1.47159i | 0.236535 | − | 0.0539875i | −0.102610 | − | 0.994722i | \(-0.532719\pi\) |
0.339145 | + | 0.940734i | \(0.389862\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.50002 | − | 6.57201i | 0.0549564 | − | 0.240780i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7.04472 | + | 8.83380i | 0.257753 | + | 0.323212i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.1377 | − | 4.88206i | 0.370423 | − | 0.178387i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.07046 | + | 6.43598i | −0.294495 | + | 0.234852i | −0.759580 | − | 0.650414i | \(-0.774595\pi\) |
0.465084 | + | 0.885266i | \(0.346024\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.65882 | −0.133335 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.90220 | 0.323984 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.0238 | − | 8.79118i | 0.400667 | − | 0.319521i | −0.402341 | − | 0.915490i | \(-0.631803\pi\) |
0.803007 | + | 0.595969i | \(0.203232\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.5814 | + | 6.54046i | −0.492974 | + | 0.237404i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.6023 | + | 20.8186i | 0.601833 | + | 0.754675i | 0.985662 | − | 0.168729i | \(-0.0539664\pi\) |
−0.383829 | + | 0.923404i | \(0.625395\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.34847 | + | 40.9583i | −0.338437 | + | 1.48279i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.14761 | − | 0.490177i | 0.0776468 | − | 0.0177224i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.37224 | − | 36.6812i | −0.302304 | − | 1.32448i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.54732 | + | 17.7487i | −0.308224 | + | 0.640034i | −0.996332 | − | 0.0855747i | \(-0.972727\pi\) |
0.688108 | + | 0.725609i | \(0.258442\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 34.0950i | 1.22790i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.66892 | − | 3.72334i | −0.167929 | − | 0.133919i | 0.535919 | − | 0.844269i | \(-0.319965\pi\) |
−0.703849 | + | 0.710350i | \(0.748537\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −25.9126 | − | 5.91439i | −0.930809 | − | 0.212451i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.97638 | − | 3.84122i | −0.286151 | − | 0.137803i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.14731 | − | 8.96245i | 0.256079 | − | 0.321113i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.7928 | − | 22.4115i | −0.386198 | − | 0.801948i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.95032 | − | 27.6385i | −0.284121 | − | 0.987718i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.18782 | − | 8.69610i | −0.149470 | − | 0.310377i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.5200 | + | 24.4773i | −0.695812 | + | 0.872520i | −0.996703 | − | 0.0811382i | \(-0.974144\pi\) |
0.300891 | + | 0.953658i | \(0.402716\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.7801 | + | 5.67301i | 0.419384 | + | 0.201965i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 46.2220 | + | 10.5499i | 1.64346 | + | 0.375110i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53.0103 | + | 42.2743i | 1.88245 | + | 1.50120i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.105960i | 0.00375802i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.0149 | + | 20.7962i | −0.354747 | + | 0.736640i | −0.999618 | − | 0.0276518i | \(-0.991197\pi\) |
0.644870 | + | 0.764292i | \(0.276911\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.85360 | + | 16.8837i | 0.136331 | + | 0.597304i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.5872 | + | 2.41646i | −0.374081 | + | 0.0853815i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.85875 | + | 16.9063i | −0.136172 | + | 0.596609i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.39150 | − | 5.50676i | −0.154780 | − | 0.194088i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.77618 | + | 1.81851i | −0.132928 | + | 0.0640147i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.0373 | + | 28.7388i | −1.26700 | + | 1.01040i | −0.268111 | + | 0.963388i | \(0.586399\pi\) |
−0.998894 | + | 0.0470146i | \(0.985029\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.2865 | 0.501668 | 0.250834 | − | 0.968030i | \(-0.419295\pi\) | ||||
0.250834 | + | 0.968030i | \(0.419295\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.0832 | 0.353634 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.07862 | − | 3.25259i | 0.142868 | − | 0.113933i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.0343 | + | 5.31384i | −0.386041 | + | 0.185908i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.2740 | + | 26.6767i | 0.743373 | + | 0.932160i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.49751 | − | 6.56103i | 0.0522635 | − | 0.228981i | −0.942050 | − | 0.335472i | \(-0.891104\pi\) |
0.994314 | + | 0.106490i | \(0.0339614\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.6239 | + | 6.53321i | −0.997766 | + | 0.227734i | −0.690063 | − | 0.723749i | \(-0.742417\pi\) |
−0.307703 | + | 0.951483i | \(0.599560\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.63803 | + | 15.9392i | 0.126660 | + | 0.554933i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.2870 | − | 23.4377i | 0.392488 | − | 0.815010i | −0.607301 | − | 0.794472i | \(-0.707748\pi\) |
0.999789 | − | 0.0205381i | \(-0.00653793\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 40.0544i | − | 1.39115i | −0.718456 | − | 0.695573i | \(-0.755151\pi\) | ||
0.718456 | − | 0.695573i | \(-0.244849\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.7581 | − | 17.3515i | −0.754781 | − | 0.601917i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.50514 | + | 1.94124i | 0.294686 | + | 0.0672601i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.57130 | − | 3.64615i | −0.262016 | − | 0.126180i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.6264 | + | 23.3568i | −0.643823 | + | 0.807329i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.0150 | + | 20.7964i | 0.345757 | + | 0.717972i | 0.999240 | − | 0.0389691i | \(-0.0124074\pi\) |
−0.653483 | + | 0.756941i | \(0.726693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.3648 | + | 9.60038i | 0.943614 | + | 0.331048i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.44386 | + | 13.3808i | 0.221938 | + | 0.460860i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.73291 | + | 9.69677i | −0.266020 | + | 0.333579i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.09176 | − | 2.45206i | −0.174955 | − | 0.0842538i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.6555 | − | 5.17096i | −0.777533 | − | 0.177467i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.31118 | + | 6.62795i | 0.284904 | + | 0.227203i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.5499i | 0.737853i | 0.929459 | + | 0.368926i | \(0.120275\pi\) | ||||
−0.929459 | + | 0.368926i | \(0.879725\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.698404 | + | 1.45025i | −0.0238849 | + | 0.0495976i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.07097 | − | 39.7425i | −0.309859 | − | 1.35758i | −0.854736 | − | 0.519063i | \(-0.826281\pi\) |
0.544877 | − | 0.838516i | \(-0.316576\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.06981 | − | 1.15715i | 0.172980 | − | 0.0394815i | −0.135154 | − | 0.990825i | \(-0.543153\pi\) |
0.308133 | + | 0.951343i | \(0.400296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.95767 | − | 21.7210i | 0.168957 | − | 0.740249i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.8937 | − | 42.5013i | −1.15375 | − | 1.44676i | −0.873493 | − | 0.486837i | \(-0.838151\pi\) |
−0.280261 | − | 0.959924i | \(-0.590421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.37759 | − | 2.10814i | 0.148843 | − | 0.0716788i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.20104 | − | 7.33758i | 0.312484 | − | 0.249197i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −44.0404 | −1.49397 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.4660 | −1.94716 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.6587 | + | 8.50004i | −0.360743 | + | 0.287683i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.1254 | + | 6.80244i | −0.477526 | + | 0.229964i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.0111 | − | 33.8709i | −0.912101 | − | 1.14374i | −0.989179 | − | 0.146713i | \(-0.953130\pi\) |
0.0770781 | − | 0.997025i | \(-0.475441\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.02648 | − | 22.0224i | 0.169539 | − | 0.742798i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.94111 | + | 0.899532i | −0.132779 | + | 0.0303060i | −0.288394 | − | 0.957512i | \(-0.593121\pi\) |
0.155615 | + | 0.987818i | \(0.450264\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.70910 | + | 16.2506i | 0.124821 | + | 0.546877i | 0.998207 | + | 0.0598490i | \(0.0190619\pi\) |
−0.873386 | + | 0.487028i | \(0.838081\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.49676 | − | 3.10805i | 0.0503130 | − | 0.104476i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 47.3352i | − | 1.58936i | −0.607029 | − | 0.794680i | \(-0.707639\pi\) | ||
0.607029 | − | 0.794680i | \(-0.292361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.6831 | + | 14.1018i | 0.593071 | + | 0.472959i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.62129 | + | 0.598293i | 0.0878167 | + | 0.0200436i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.4014 | − | 5.49062i | −0.381533 | − | 0.183737i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.71179 | + | 8.41632i | −0.224350 | + | 0.281327i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.2362 | + | 27.4853i | 0.441945 | + | 0.917707i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.32776 | − | 28.9506i | −0.277746 | − | 0.965557i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.209317 | + | 0.434652i | 0.00697337 | + | 0.0144803i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.8408 | + | 18.6098i | −0.493871 | + | 0.619295i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.00711143 | − | 0.00342468i | −0.000236392 | − | 0.000113840i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.49972 | + | 1.25527i | 0.182615 | + | 0.0416807i | 0.312850 | − | 0.949802i | \(-0.398716\pi\) |
−0.130235 | + | 0.991483i | \(0.541573\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20.2507 | + | 16.1494i | 0.671673 | + | 0.535641i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 0.641362i | − | 0.0212493i | −0.999944 | − | 0.0106246i | \(-0.996618\pi\) | ||
0.999944 | − | 0.0106246i | \(-0.00338199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.66934 | − | 18.0021i | 0.286913 | − | 0.595782i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.38333 | + | 6.06076i | 0.0457315 | + | 0.200363i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40.5783 | + | 9.26173i | −1.34001 | + | 0.305849i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.24537 | + | 27.3627i | −0.206016 | + | 0.902613i | 0.761172 | + | 0.648550i | \(0.224624\pi\) |
−0.967188 | + | 0.254063i | \(0.918233\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.4335 | + | 20.6069i | 0.541502 | + | 0.679022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45.3552 | + | 21.8419i | −1.49289 | + | 0.718936i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.01411 | − | 7.18852i | 0.296382 | − | 0.236357i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.60485 | −0.184087 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.5246 | −0.345302 | −0.172651 | − | 0.984983i | \(-0.555233\pi\) | ||||
−0.172651 | + | 0.984983i | \(0.555233\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.98395 | + | 3.97457i | −0.163342 | + | 0.130261i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.5707 | − | 7.01686i | 0.477022 | − | 0.229722i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.42879 | − | 3.04560i | −0.0794298 | − | 0.0996018i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.93731 | − | 43.5382i | 0.324638 | − | 1.42233i | −0.504560 | − | 0.863376i | \(-0.668345\pi\) |
0.829198 | − | 0.558955i | \(-0.188797\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.8855 | − | 2.71278i | 0.387867 | − | 0.0885282i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.22072 | + | 22.8735i | 0.170191 | + | 0.745654i | 0.985920 | + | 0.167220i | \(0.0534790\pi\) |
−0.815729 | + | 0.578434i | \(0.803664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.6074 | + | 24.1029i | −0.377988 | + | 0.784899i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.58627i | 0.279311i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −47.2705 | − | 37.6970i | −1.53609 | − | 1.22499i | −0.884622 | − | 0.466308i | \(-0.845584\pi\) |
−0.651464 | − | 0.758680i | \(-0.725845\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.2140 | + | 7.80912i | 1.11063 | + | 0.253495i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.26157 | − | 3.49699i | −0.235473 | − | 0.113398i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.3109 | + | 35.5007i | −0.917079 | + | 1.14998i | 0.0712208 | + | 0.997461i | \(0.477310\pi\) |
−0.988300 | + | 0.152521i | \(0.951261\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.99398 | + | 6.21706i | 0.0968828 | + | 0.201179i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.8218 | + | 12.3418i | −0.446797 | + | 0.398955i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.1700 | − | 50.1895i | −0.780490 | − | 1.62070i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.182532 | + | 0.228887i | −0.00588811 | + | 0.00738346i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.40675 | + | 2.60376i | 0.174230 | + | 0.0839048i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.52594 | − | 0.348286i | −0.0491218 | − | 0.0112117i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.268035 | + | 0.213751i | 0.00861942 | + | 0.00687375i | 0.627790 | − | 0.778383i | \(-0.283960\pi\) |
−0.619171 | + | 0.785256i | \(0.712531\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 5.45683i | − | 0.175299i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.6584 | − | 53.2803i | 0.823418 | − | 1.70984i | 0.127363 | − | 0.991856i | \(-0.459349\pi\) |
0.696055 | − | 0.717988i | \(-0.254937\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.7689 | + | 60.3254i | 0.441410 | + | 1.93394i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 32.2570 | − | 7.36244i | 1.03305 | − | 0.235787i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.95732 | − | 17.3382i | 0.126606 | − | 0.554697i | −0.871343 | − | 0.490675i | \(-0.836750\pi\) |
0.997949 | − | 0.0640217i | \(-0.0203927\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.9734 | + | 15.0141i | 0.382671 | + | 0.479854i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.1872 | + | 9.72165i | −0.644528 | + | 0.310389i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −46.9498 | + | 37.4412i | −1.49747 | + | 1.19419i | −0.569243 | + | 0.822169i | \(0.692764\pi\) |
−0.928224 | + | 0.372021i | \(0.878665\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.304390 | 0.00969868 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −24.5947 | −0.782857 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.3457 | − | 17.8201i | 0.710553 | − | 0.566647i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.5554 | + | 22.9015i | −1.51065 | + | 0.727490i | −0.991851 | − | 0.127407i | \(-0.959335\pi\) |
−0.518798 | + | 0.854897i | \(0.673620\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.0998 | − | 13.9187i | −0.352242 | − | 0.441698i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.38542 | + | 6.06994i | −0.0439209 | + | 0.192430i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.20871 | − | 0.960611i | 0.133291 | − | 0.0304228i | −0.155355 | − | 0.987859i | \(-0.549652\pi\) |
0.288646 | + | 0.957436i | \(0.406795\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.88365 | − | 12.6341i | −0.0912345 | − | 0.399725i |
(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 | 232.2.q.a.9.6 | ✓ | 48 | |
4.3 | odd | 2 | 464.2.y.e.241.3 | 48 | |||
29.10 | odd | 28 | 6728.2.a.be.1.16 | 24 | |||
29.13 | even | 14 | inner | 232.2.q.a.129.6 | yes | 48 | |
29.19 | odd | 28 | 6728.2.a.bf.1.9 | 24 | |||
116.71 | odd | 14 | 464.2.y.e.129.3 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.2.q.a.9.6 | ✓ | 48 | 1.1 | even | 1 | trivial | |
232.2.q.a.129.6 | yes | 48 | 29.13 | even | 14 | inner | |
464.2.y.e.129.3 | 48 | 116.71 | odd | 14 | |||
464.2.y.e.241.3 | 48 | 4.3 | odd | 2 | |||
6728.2.a.be.1.16 | 24 | 29.10 | odd | 28 | |||
6728.2.a.bf.1.9 | 24 | 29.19 | odd | 28 |