Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(47,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.be (of order \(18\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 47.5 | ||
Character | \(\chi\) | \(=\) | 432.47 |
Dual form | 432.2.be.a.239.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{7}{18}\right)\) |
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 | ||||||||
\(3\) | 0.991247 | − | 1.42036i | 0.572297 | − | 0.820047i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.85028 | + | 0.678908i | −1.72190 | + | 0.303617i | −0.945256 | − | 0.326328i | \(-0.894188\pi\) |
−0.776640 | + | 0.629945i | \(0.783077\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.90230 | + | 2.26708i | −0.719004 | + | 0.856875i | −0.994534 | − | 0.104417i | \(-0.966702\pi\) |
0.275530 | + | 0.961293i | \(0.411147\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.03486 | − | 2.81586i | −0.344953 | − | 0.938620i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.560068 | + | 3.17630i | −0.168867 | + | 0.957692i | 0.776120 | + | 0.630585i | \(0.217185\pi\) |
−0.944987 | + | 0.327107i | \(0.893926\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.43878 | + | 0.523674i | 0.399046 | + | 0.145241i | 0.533745 | − | 0.845646i | \(-0.320784\pi\) |
−0.134698 | + | 0.990887i | \(0.543007\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.85228 | + | 6.14175i | −0.736456 | + | 1.58579i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.60029 | + | 1.50128i | −0.630664 | + | 0.364114i | −0.781009 | − | 0.624520i | \(-0.785295\pi\) |
0.150345 | + | 0.988634i | \(0.451962\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.90409 | − | 2.83138i | −1.12508 | − | 0.649563i | −0.182384 | − | 0.983227i | \(-0.558381\pi\) |
−0.942692 | + | 0.333665i | \(0.891715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.33442 | + | 4.94920i | 0.291194 | + | 1.08000i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.11794 | + | 5.13356i | −1.27568 | + | 1.07042i | −0.281855 | + | 0.959457i | \(0.590950\pi\) |
−0.993824 | + | 0.110965i | \(0.964606\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.66525 | − | 3.51786i | 1.93305 | − | 0.703573i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.02534 | − | 1.32134i | −0.967127 | − | 0.254292i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.57709 | − | 4.33301i | −0.292858 | − | 0.804621i | −0.995645 | − | 0.0932208i | \(-0.970284\pi\) |
0.702788 | − | 0.711400i | \(-0.251938\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.11407 | + | 7.28646i | 1.09812 | + | 1.30869i | 0.947379 | + | 0.320114i | \(0.103721\pi\) |
0.150740 | + | 0.988573i | \(0.451834\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.95634 | + | 3.94400i | 0.688710 | + | 0.686563i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.78526 | − | 10.0204i | 0.977888 | − | 1.69375i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.24428 | − | 3.88720i | −0.368957 | − | 0.639052i | 0.620446 | − | 0.784249i | \(-0.286952\pi\) |
−0.989403 | + | 0.145197i | \(0.953618\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.17000 | − | 1.52450i | 0.347477 | − | 0.244116i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.210120 | − | 0.577300i | 0.0328152 | − | 0.0901591i | −0.922203 | − | 0.386706i | \(-0.873613\pi\) |
0.955018 | + | 0.296547i | \(0.0958351\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.35455 | + | 0.591498i | 0.511565 | + | 0.0902026i | 0.423471 | − | 0.905910i | \(-0.360811\pi\) |
0.0880934 | + | 0.996112i | \(0.471923\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.89620 | + | 10.1393i | 0.878953 | + | 1.51147i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.982922 | + | 0.824769i | 0.143374 | + | 0.120305i | 0.711654 | − | 0.702530i | \(-0.247946\pi\) |
−0.568280 | + | 0.822835i | \(0.692391\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.305345 | − | 1.73170i | −0.0436207 | − | 0.247385i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.445172 | + | 5.18150i | −0.0623366 | + | 0.725555i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.01133i | − | 0.688359i | −0.938904 | − | 0.344179i | \(-0.888157\pi\) | ||
0.938904 | − | 0.344179i | \(-0.111843\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 12.6099i | − | 1.70032i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.88275 | + | 4.15899i | −1.17655 | + | 0.550872i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.0386715 | + | 0.219317i | 0.00503460 | + | 0.0285526i | 0.987222 | − | 0.159354i | \(-0.0509410\pi\) |
−0.982187 | + | 0.187906i | \(0.939830\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.2571 | − | 8.60675i | −1.31329 | − | 1.10198i | −0.987682 | − | 0.156477i | \(-0.949986\pi\) |
−0.325609 | − | 0.945504i | \(-0.605569\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.35239 | + | 3.01052i | 1.05230 | + | 0.379290i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.89524 | − | 1.03949i | −0.731214 | − | 0.128933i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.16511 | + | 3.20112i | −0.142341 | + | 0.391079i | −0.990293 | − | 0.138994i | \(-0.955613\pi\) |
0.847952 | + | 0.530073i | \(0.177835\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.22713 | + | 13.7783i | 0.147729 | + | 1.65872i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.12205 | − | 7.13960i | −0.489197 | − | 0.847315i | 0.510725 | − | 0.859744i | \(-0.329377\pi\) |
−0.999923 | + | 0.0124293i | \(0.996044\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.87009 | − | 6.70320i | 0.452960 | − | 0.784550i | −0.545608 | − | 0.838040i | \(-0.683701\pi\) |
0.998568 | + | 0.0534906i | \(0.0170347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.58401 | − | 17.2152i | 0.529316 | − | 1.98784i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.13551 | − | 7.31202i | −0.699206 | − | 0.833282i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.28358 | + | 3.52662i | 0.144414 | + | 0.396775i | 0.990719 | − | 0.135923i | \(-0.0434001\pi\) |
−0.846305 | + | 0.532699i | \(0.821178\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.85814 | + | 5.82803i | −0.762015 | + | 0.647559i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.3755 | + | 4.14034i | −1.24862 | + | 0.454462i | −0.879936 | − | 0.475092i | \(-0.842415\pi\) |
−0.368687 | + | 0.929553i | \(0.620193\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.99262 | − | 7.54571i | 0.975387 | − | 0.818447i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.71773 | − | 2.05505i | −0.827428 | − | 0.220325i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.527753 | + | 0.304698i | 0.0559417 | + | 0.0322980i | 0.527710 | − | 0.849425i | \(-0.323051\pi\) |
−0.471768 | + | 0.881723i | \(0.656384\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.92421 | + | 2.26565i | −0.411369 | + | 0.237504i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.4100 | − | 1.46151i | 1.70163 | − | 0.151551i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.8044 | + | 7.57217i | 2.13448 | + | 0.776888i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.21509 | + | 18.2337i | −0.326443 | + | 1.85135i | 0.172893 | + | 0.984941i | \(0.444689\pi\) |
−0.499336 | + | 0.866409i | \(0.666422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.52362 | − | 1.70995i | 0.957160 | − | 0.171856i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.45656 | + | 6.50288i | −0.542948 | + | 0.647061i | −0.965846 | − | 0.259117i | \(-0.916569\pi\) |
0.422898 | + | 0.906177i | \(0.361013\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.08845 | + | 1.42621i | −0.796978 | + | 0.140529i | −0.557287 | − | 0.830320i | \(-0.688157\pi\) |
−0.239692 | + | 0.970849i | \(0.577046\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.49793 | − | 18.1498i | −0.829313 | − | 1.77124i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.6604 | 1.51395 | 0.756974 | − | 0.653445i | \(-0.226677\pi\) | ||||
0.756974 | + | 0.653445i | \(0.226677\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.01637 | 0.863611 | 0.431806 | − | 0.901967i | \(-0.357877\pi\) | ||||
0.431806 | + | 0.901967i | \(0.357877\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.74587 | − | 0.665492i | −0.735205 | − | 0.0631657i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.84827 | − | 1.20753i | 0.644231 | − | 0.113595i | 0.158019 | − | 0.987436i | \(-0.449489\pi\) |
0.486212 | + | 0.873841i | \(0.338378\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.0706 | − | 23.9192i | 1.87159 | − | 2.23047i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.0143422 | − | 4.59334i | −0.00132593 | − | 0.424654i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.54303 | − | 8.75097i | 0.141449 | − | 0.802200i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.561386 | + | 0.204328i | 0.0510351 | + | 0.0185753i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.611694 | − | 0.870694i | −0.0551546 | − | 0.0785078i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −17.8962 | + | 10.3324i | −1.60069 | + | 0.924156i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.87022 | − | 5.12122i | −0.787105 | − | 0.454435i | 0.0518375 | − | 0.998656i | \(-0.483492\pi\) |
−0.838942 | + | 0.544220i | \(0.816826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.16533 | − | 4.17836i | 0.366737 | − | 0.367884i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.436664 | − | 0.366404i | 0.0381515 | − | 0.0320129i | −0.623513 | − | 0.781813i | \(-0.714295\pi\) |
0.661664 | + | 0.749800i | \(0.269851\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.7480 | − | 5.73182i | 1.36553 | − | 0.497011i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.2460 | + | 1.67579i | 1.74250 | + | 0.144229i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.42588 | + | 6.66504i | 0.207257 | + | 0.569433i | 0.999150 | − | 0.0412269i | \(-0.0131267\pi\) |
−0.791893 | + | 0.610659i | \(0.790904\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.82538 | − | 2.17540i | −0.154827 | − | 0.184515i | 0.683055 | − | 0.730367i | \(-0.260651\pi\) |
−0.837882 | + | 0.545851i | \(0.816206\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.14579 | − | 0.578555i | 0.180708 | − | 0.0487231i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.46916 | + | 4.27672i | −0.206482 | + | 0.357637i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.01394 | + | 15.6126i | 0.748567 | + | 1.29656i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.76231 | − | 1.28284i | −0.227831 | − | 0.105807i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.77050 | + | 7.61188i | −0.226968 | + | 0.623590i | −0.999941 | − | 0.0108491i | \(-0.996547\pi\) |
0.772973 | + | 0.634439i | \(0.218769\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.5383 | + | 3.26880i | 1.50862 | + | 0.266011i | 0.865950 | − | 0.500130i | \(-0.166715\pi\) |
0.642672 | + | 0.766141i | \(0.277826\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.91833 | + | 5.76845i | 0.559314 | + | 0.466352i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −28.4877 | − | 23.9040i | −2.28819 | − | 1.92002i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.04493 | − | 5.92610i | −0.0833945 | − | 0.472954i | −0.997691 | − | 0.0679094i | \(-0.978367\pi\) |
0.914297 | − | 0.405045i | \(-0.132744\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.11790 | − | 4.96746i | −0.564486 | − | 0.393945i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 23.6355i | − | 1.86273i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.4440i | 1.28800i | 0.765028 | + | 0.643998i | \(0.222725\pi\) | ||||
−0.765028 | + | 0.643998i | \(0.777275\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −17.9106 | − | 12.4995i | −1.39434 | − | 0.973086i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.56815 | + | 14.5647i | 0.198729 | + | 1.12705i | 0.907007 | + | 0.421115i | \(0.138361\pi\) |
−0.708278 | + | 0.705934i | \(0.750528\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.16272 | − | 6.84933i | −0.627901 | − | 0.526872i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.89773 | + | 16.7393i | −0.221595 | + | 1.28009i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00249 | + | 0.353093i | 0.152246 | + | 0.0268451i | 0.249252 | − | 0.968439i | \(-0.419815\pi\) |
−0.0970054 | + | 0.995284i | \(0.530926\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.4110 | + | 28.6039i | −0.786996 | + | 2.16225i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.349843 | + | 0.162470i | 0.0262958 | + | 0.0122120i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.253380 | + | 0.438867i | 0.0189385 | + | 0.0328024i | 0.875339 | − | 0.483509i | \(-0.160638\pi\) |
−0.856401 | + | 0.516312i | \(0.827305\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.56085 | + | 7.89962i | −0.339005 | + | 0.587174i | −0.984246 | − | 0.176805i | \(-0.943424\pi\) |
0.645241 | + | 0.763979i | \(0.276757\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.3921 | + | 6.03742i | −1.65527 | + | 0.446299i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.2801 | + | 13.4431i | 0.829332 | + | 0.988359i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.31218 | − | 9.10015i | −0.242211 | − | 0.665469i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.5553 | − | 8.87925i | 0.913265 | − | 0.645870i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.4556 | + | 4.53348i | −0.901259 | + | 0.328031i | −0.750757 | − | 0.660578i | \(-0.770311\pi\) |
−0.150502 | + | 0.988610i | \(0.548089\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.8300 | + | 13.2829i | −1.13947 | + | 0.956126i | −0.999421 | − | 0.0340192i | \(-0.989169\pi\) |
−0.140045 | + | 0.990145i | \(0.544725\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.32009 | + | 7.34298i | −0.524202 | + | 0.525842i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.7739 | + | 12.5711i | 1.55132 | + | 0.895657i | 0.998034 | + | 0.0626676i | \(0.0199608\pi\) |
0.553289 | + | 0.832989i | \(0.313373\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.870852 | + | 0.502786i | −0.0617330 | + | 0.0356416i | −0.530549 | − | 0.847654i | \(-0.678014\pi\) |
0.468816 | + | 0.883296i | \(0.344681\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.39184 | + | 4.82798i | 0.239242 | + | 0.340540i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.8234 | + | 4.66733i | 0.900025 | + | 0.327582i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.417087 | + | 2.36542i | −0.0291306 | + | 0.165208i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.7866 | + | 11.9148i | 1.44477 | + | 0.828133i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.7399 | − | 13.9911i | 0.812069 | − | 0.967786i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1122 | + | 1.95939i | −0.764998 | + | 0.134890i | −0.542514 | − | 0.840046i | \(-0.682528\pi\) |
−0.222484 | + | 0.974936i | \(0.571417\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.2268 | − | 1.22231i | −0.974803 | − | 0.0837510i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.3175 | −0.908248 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −28.1498 | −1.91093 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.68475 | − | 12.1415i | −0.384140 | − | 0.820444i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.52744 | + | 0.798310i | −0.304549 | + | 0.0537001i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.04837 | + | 2.44115i | −0.137169 | + | 0.163471i | −0.830256 | − | 0.557383i | \(-0.811806\pi\) |
0.693087 | + | 0.720854i | \(0.256250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.9080 | − | 23.5755i | −1.32720 | − | 1.57170i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.84631 | + | 16.1423i | −0.188917 | + | 1.07140i | 0.731903 | + | 0.681409i | \(0.238633\pi\) |
−0.920819 | + | 0.389990i | \(0.872479\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.62322 | − | 2.77463i | −0.503757 | − | 0.183352i | 0.0776261 | − | 0.996983i | \(-0.475266\pi\) |
−0.581383 | + | 0.813630i | \(0.697488\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16.4675 | + | 1.46663i | −1.08348 | + | 0.0964972i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.45161 | − | 3.14749i | 0.357147 | − | 0.206199i | −0.310682 | − | 0.950514i | \(-0.600557\pi\) |
0.667829 | + | 0.744315i | \(0.267224\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.34446 | − | 2.50828i | −0.283402 | − | 0.163622i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.28142 | + | 1.67260i | 0.408022 | + | 0.108647i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.17874 | − | 6.86278i | 0.529039 | − | 0.443916i | −0.338730 | − | 0.940883i | \(-0.609997\pi\) |
0.867769 | + | 0.496967i | \(0.165553\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.5678 | + | 6.39416i | −1.13164 | + | 0.411884i | −0.838888 | − | 0.544304i | \(-0.816794\pi\) |
−0.292754 | + | 0.956188i | \(0.594572\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.47980 | + | 15.5181i | 0.0949292 | + | 0.995484i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.35132 | + | 6.46021i | 0.150220 | + | 0.412727i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.57320 | − | 6.64188i | −0.354614 | − | 0.422613i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.39515 | + | 20.2614i | −0.341904 | + | 1.28402i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.86771 | − | 11.8952i | 0.433486 | − | 0.750820i | −0.563685 | − | 0.825990i | \(-0.690617\pi\) |
0.997171 | + | 0.0751704i | \(0.0239501\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.8793 | − | 22.3076i | −0.809714 | − | 1.40247i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.80372 | − | 20.2524i | −0.112954 | − | 1.26826i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.34803 | − | 25.6835i | 0.583114 | − | 1.60209i | −0.199713 | − | 0.979854i | \(-0.564001\pi\) |
0.782827 | − | 0.622239i | \(-0.213777\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.0819 | + | 2.30669i | 0.812869 | + | 0.143331i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.5691 | + | 8.92491i | −0.654211 | + | 0.552438i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.99737 | + | 5.87149i | 0.431476 | + | 0.362051i | 0.832508 | − | 0.554012i | \(-0.186904\pi\) |
−0.401032 | + | 0.916064i | \(0.631348\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.40223 | + | 19.2950i | 0.208997 | + | 1.18528i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.955916 | − | 0.447569i | 0.0585011 | − | 0.0273908i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.49499i | − | 0.0911509i | −0.998961 | − | 0.0455754i | \(-0.985488\pi\) | ||
0.998961 | − | 0.0455754i | \(-0.0145121\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 24.4160i | − | 1.48317i | −0.670861 | − | 0.741583i | \(-0.734075\pi\) | ||
0.670861 | − | 0.741583i | \(-0.265925\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.671828 | + | 7.81962i | −0.0406609 | + | 0.473265i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.76061 | + | 32.6700i | 0.347378 | + | 1.97008i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.49016 | + | 4.60679i | 0.329872 | + | 0.276795i | 0.792648 | − | 0.609680i | \(-0.208702\pi\) |
−0.462776 | + | 0.886475i | \(0.653147\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.1905 | − | 24.7568i | 0.849561 | − | 1.48215i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.8279 | + | 4.55416i | 1.54076 | + | 0.271678i | 0.878555 | − | 0.477641i | \(-0.158508\pi\) |
0.662209 | + | 0.749319i | \(0.269619\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.65241 | + | 12.7824i | −0.276557 | + | 0.759834i | 0.721190 | + | 0.692738i | \(0.243596\pi\) |
−0.997747 | + | 0.0670962i | \(0.978627\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 31.3775 | − | 22.0438i | 1.85864 | − | 1.30576i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.909072 | + | 1.57456i | 0.0536608 | + | 0.0929433i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.99231 | + | 6.91489i | −0.234842 | + | 0.406758i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.7115 | + | 22.6407i | 1.33137 | + | 1.32722i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.19618 | + | 6.19256i | 0.303564 | + | 0.361773i | 0.896164 | − | 0.443724i | \(-0.146343\pi\) |
−0.592600 | + | 0.805497i | \(0.701898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.297792 | − | 0.818177i | −0.0173381 | − | 0.0476361i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.01152 | − | 15.2220i | 0.406849 | − | 0.883268i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.4907 | + | 4.18227i | −0.664524 | + | 0.241867i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.72236 | + | 6.47983i | −0.445109 | + | 0.373491i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.82764 | + | 14.1963i | 0.219892 | + | 0.815554i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 45.3360 | + | 26.1747i | 2.59593 | + | 1.49876i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.6044 | + | 12.4733i | −1.23303 | + | 0.711890i | −0.967660 | − | 0.252257i | \(-0.918827\pi\) |
−0.265369 | + | 0.964147i | \(0.585494\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.99191 | + | 12.9023i | −0.340868 | + | 0.733983i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.1209 | − | 9.87120i | −1.53788 | − | 0.559744i | −0.572348 | − | 0.820011i | \(-0.693967\pi\) |
−0.965537 | + | 0.260267i | \(0.916189\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.406391 | − | 2.30476i | 0.0229706 | − | 0.130273i | −0.971166 | − | 0.238404i | \(-0.923376\pi\) |
0.994137 | + | 0.108132i | \(0.0344868\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −34.2029 | − | 5.92084i | −1.92711 | − | 0.333601i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.49865 | − | 6.55303i | 0.308835 | − | 0.368055i | −0.589194 | − | 0.807992i | \(-0.700555\pi\) |
0.898029 | + | 0.439937i | \(0.144999\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.6462 | − | 2.58253i | 0.820033 | − | 0.144594i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.5233 | − | 22.2434i | 0.866427 | − | 1.24151i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.0028 | 0.946060 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.7484 | 0.873564 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.93745 | − | 12.8065i | 0.494242 | − | 0.708202i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.73963 | + | 0.659398i | −0.206173 | + | 0.0363538i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.63073 | + | 7.90220i | −0.364458 | + | 0.434344i | −0.916845 | − | 0.399244i | \(-0.869273\pi\) |
0.552387 | + | 0.833588i | \(0.313717\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.62331 | + | 10.3423i | −0.472554 | + | 0.566753i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.31274 | − | 13.1162i | 0.126359 | − | 0.716615i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.42698 | + | 1.97526i | 0.295626 | + | 0.107599i | 0.485576 | − | 0.874195i | \(-0.338610\pi\) |
−0.189949 | + | 0.981794i | \(0.560832\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.07319 | − | 10.9240i | 0.275538 | − | 0.593309i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.5683 | + | 15.3392i | −1.43876 | + | 0.830666i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.4340 | − | 7.75614i | −0.725369 | − | 0.418792i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.0790 | − | 52.2173i | −0.757987 | − | 2.81128i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.31009 | + | 3.61659i | −0.231378 | + | 0.194149i | −0.751104 | − | 0.660184i | \(-0.770478\pi\) |
0.519726 | + | 0.854333i | \(0.326034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.8949 | + | 6.14924i | −0.904363 | + | 0.329161i | −0.752000 | − | 0.659163i | \(-0.770911\pi\) |
−0.152363 | + | 0.988325i | \(0.548688\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.53842 | − | 4.53276i | −0.348995 | − | 0.241941i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.25148 | − | 14.4283i | −0.279508 | − | 0.767942i | −0.997419 | − | 0.0718066i | \(-0.977124\pi\) |
0.717911 | − | 0.696135i | \(-0.245099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.7182 | + | 24.6909i | 1.09961 | + | 1.31046i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.9000 | − | 10.8660i | −0.576890 | − | 0.575092i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.4899 | − | 28.5614i | 0.870305 | − | 1.50741i | 0.00862297 | − | 0.999963i | \(-0.497255\pi\) |
0.861682 | − | 0.507449i | \(-0.169411\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.53341 | + | 11.3162i | 0.343864 | + | 0.595589i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.846692 | − | 0.594832i | 0.0444398 | − | 0.0312206i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.3501 | + | 28.4366i | −0.541748 | + | 1.48844i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.19429 | + | 0.210586i | 0.0623416 | + | 0.0109925i | 0.204732 | − | 0.978818i | \(-0.434368\pi\) |
−0.142390 | + | 0.989811i | \(0.545479\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.84304 | + | 0.00575468i | −0.0959449 | + | 0.000299577i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.3611 | + | 9.53307i | 0.589837 | + | 0.494932i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.14523 | + | 6.49494i | 0.0592979 | + | 0.336295i | 0.999996 | − | 0.00295067i | \(-0.000939230\pi\) |
−0.940698 | + | 0.339246i | \(0.889828\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.06384 | + | 35.6610i | −0.158216 | + | 1.84153i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.06014i | − | 0.363616i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.0138i | − | 1.18214i | −0.806620 | − | 0.591070i | \(-0.798706\pi\) | ||
0.806620 | − | 0.591070i | \(-0.201294\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0666 | + | 7.52253i | −0.823116 | + | 0.385391i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.25873 | − | 18.4812i | −0.166513 | − | 0.944344i | −0.947490 | − | 0.319784i | \(-0.896390\pi\) |
0.780977 | − | 0.624560i | \(-0.214722\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28.5876 | + | 23.9878i | 1.45696 | + | 1.22253i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.80591 | − | 10.0581i | −0.0917995 | − | 0.511280i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.3690 | − | 4.64957i | −1.33696 | − | 0.235743i | −0.540967 | − | 0.841044i | \(-0.681942\pi\) |
−0.795996 | + | 0.605301i | \(0.793053\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.20153 | − | 22.5335i | 0.414769 | − | 1.13957i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.0875852 | − | 0.983418i | −0.00441809 | − | 0.0496069i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.33640 | − | 12.7070i | −0.369134 | − | 0.639359i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.33339 | + | 16.1659i | −0.468429 | + | 0.811343i | −0.999349 | − | 0.0360788i | \(-0.988513\pi\) |
0.530920 | + | 0.847422i | \(0.321847\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.46894 | − | 28.0496i | 0.373915 | − | 1.40423i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.2927 | − | 12.2664i | −0.513994 | − | 0.612554i | 0.445156 | − | 0.895453i | \(-0.353148\pi\) |
−0.959150 | + | 0.282899i | \(0.908704\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.98108 | + | 13.6854i | 0.248125 | + | 0.681719i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.4490 | − | 27.0956i | 1.11550 | − | 1.34639i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.6039 | − | 4.95141i | 0.674319 | − | 0.245432i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0693 | − | 10.1274i | 0.596791 | − | 0.500767i | −0.293622 | − | 0.955922i | \(-0.594861\pi\) |
0.890412 | + | 0.455155i | \(0.150416\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8714 | + | 3.16108i | 0.585573 | + | 0.155925i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.570774 | − | 0.329537i | −0.0280860 | − | 0.0162154i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 40.9879 | − | 23.6644i | 2.01202 | − | 1.16164i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.89926 | + | 0.436338i | −0.239918 | + | 0.0213676i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.8780 | − | 5.77912i | −0.775691 | − | 0.282329i | −0.0763166 | − | 0.997084i | \(-0.524316\pi\) |
−0.699375 | + | 0.714755i | \(0.746538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.75431 | − | 26.9630i | 0.231711 | − | 1.31410i | −0.617720 | − | 0.786398i | \(-0.711944\pi\) |
0.849431 | − | 0.527700i | \(-0.176945\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.30525 | − | 3.62129i | 0.0634635 | − | 0.176073i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.8512 | + | 23.6577i | −0.962925 | + | 1.14757i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.0244 | − | 6.88105i | 1.88852 | − | 0.332997i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.62694 | + | 7.74639i | 0.175110 | + | 0.373999i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.64210 | −0.319939 | −0.159969 | − | 0.987122i | \(-0.551140\pi\) | ||||
−0.159969 | + | 0.987122i | \(0.551140\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.60807 | −0.365621 | −0.182810 | − | 0.983148i | \(-0.558519\pi\) | ||||
−0.182810 | + | 0.983148i | \(0.558519\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 31.1106 | + | 2.67289i | 1.49164 | + | 0.128155i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 44.5380 | − | 7.85325i | 2.13054 | − | 0.375672i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.70790 | − | 2.03539i | 0.0815135 | − | 0.0971440i | −0.723746 | − | 0.690066i | \(-0.757581\pi\) |
0.805260 | + | 0.592922i | \(0.202026\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.56022 | + | 2.65187i | −0.217154 | + | 0.126279i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.28130 | + | 7.26659i | −0.0608762 | + | 0.345246i | 0.939122 | + | 0.343583i | \(0.111641\pi\) |
−0.999999 | + | 0.00166347i | \(0.999471\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.23886 | − | 0.814878i | −0.106132 | − | 0.0386289i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.06538 | + | 11.4804i | 0.381479 | + | 0.543003i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.2078 | + | 16.2858i | −1.33121 | + | 0.768573i | −0.985485 | − | 0.169764i | \(-0.945700\pi\) |
−0.345723 | + | 0.938337i | \(0.612366\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.71600 | + | 0.990733i | 0.0808032 | + | 0.0466518i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.0189 | − | 23.0909i | 1.08152 | − | 1.08490i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.5711 | − | 11.3875i | 0.636225 | − | 0.533856i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.9862 | + | 9.09423i | −1.16880 | + | 0.425410i | −0.852235 | − | 0.523159i | \(-0.824753\pi\) |
−0.316570 | + | 0.948569i | \(0.602531\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.0511 | − | 4.10857i | 0.702524 | − | 0.191772i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.89899 | + | 18.9548i | 0.321318 | + | 0.882814i | 0.990226 | + | 0.139469i | \(0.0445395\pi\) |
−0.668909 | + | 0.743345i | \(0.733238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.25098 | − | 6.25787i | −0.244034 | − | 0.290828i | 0.630099 | − | 0.776514i | \(-0.283014\pi\) |
−0.874133 | + | 0.485686i | \(0.838570\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −62.1907 | + | 16.7681i | −2.88403 | + | 0.777600i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.73312 | − | 11.6621i | 0.311571 | − | 0.539658i | −0.667131 | − | 0.744940i | \(-0.732478\pi\) |
0.978703 | + | 0.205283i | \(0.0658113\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.04079 | − | 8.73091i | −0.232762 | − | 0.403156i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.45299 | − | 4.39005i | −0.435571 | − | 0.202283i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.75756 | + | 10.3238i | −0.172773 | + | 0.474689i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −57.3597 | − | 10.1141i | −2.63184 | − | 0.464065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.1112 | + | 5.18601i | −0.646107 | + | 0.237451i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.8908 | + | 21.7250i | 1.18298 | + | 0.992641i | 0.999955 | + | 0.00953287i | \(0.00303445\pi\) |
0.183028 | + | 0.983108i | \(0.441410\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.19340 | − | 6.76810i | −0.0544143 | − | 0.308599i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −33.5709 | − | 23.4286i | −1.52753 | − | 1.06604i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 72.3874i | − | 3.28694i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.6103i | 0.707368i | 0.935365 | + | 0.353684i | \(0.115071\pi\) | ||||
−0.935365 | + | 0.353684i | \(0.884929\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.3565 | + | 16.3001i | 1.05622 | + | 0.737116i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.17929 | + | 18.0307i | 0.143479 | + | 0.813712i | 0.968575 | + | 0.248720i | \(0.0800098\pi\) |
−0.825096 | + | 0.564992i | \(0.808879\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.6060 | + | 8.89946i | 0.477669 | + | 0.400812i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −35.5077 | + | 13.0494i | −1.59595 | + | 0.586529i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.0274 | + | 4.23668i | 1.07778 | + | 0.190041i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.65791 | − | 26.5349i | 0.432348 | − | 1.18787i | −0.512020 | − | 0.858973i | \(-0.671103\pi\) |
0.944368 | − | 0.328892i | \(-0.106675\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.2328 | + | 10.7895i | 1.03796 | + | 0.482039i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.320624 | + | 0.555338i | 0.0142959 | + | 0.0247613i | 0.873085 | − | 0.487568i | \(-0.162116\pi\) |
−0.858789 | + | 0.512330i | \(0.828783\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.5944 | − | 28.7424i | 0.738442 | − | 1.27902i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.8198 | + | 4.80463i | −0.791405 | + | 0.213381i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.99662 | − | 10.7218i | −0.398768 | − | 0.475233i | 0.528876 | − | 0.848699i | \(-0.322614\pi\) |
−0.927644 | + | 0.373466i | \(0.878169\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.83458 | + | 21.5253i | 0.346581 | + | 0.952224i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.9035 | + | 20.7086i | 0.922913 | + | 0.914308i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 30.1745 | − | 10.9826i | 1.32965 | − | 0.483952i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.17022 | + | 2.66013i | −0.139426 | + | 0.116992i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.48648 | − | 2.49426i | 0.109144 | − | 0.109486i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.55944 | + | 2.63240i | 0.199753 | + | 0.115327i | 0.596540 | − | 0.802583i | \(-0.296542\pi\) |
−0.396787 | + | 0.917911i | \(0.629875\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.39941 | + | 4.84940i | −0.367280 | + | 0.212049i | −0.672270 | − | 0.740306i | \(-0.734680\pi\) |
0.304989 | + | 0.952356i | \(0.401347\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 30.3081 | + | 43.1409i | 1.32275 | + | 1.88283i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −26.8374 | − | 9.76802i | −1.16906 | − | 0.425502i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.08184 | − | 40.1631i | 0.307906 | − | 1.74622i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.577547 | − | 0.335856i | 0.0250634 | − | 0.0145749i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.604634 | − | 0.720575i | 0.0261896 | − | 0.0312116i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −60.2969 | + | 10.6320i | −2.60686 | + | 0.459660i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.874512 | + | 0.0751343i | 0.0377380 | + | 0.00324229i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.67141 | 0.244285 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0789 | 0.992241 | 0.496121 | − | 0.868254i | \(-0.334757\pi\) | ||||
0.496121 | + | 0.868254i | \(0.334757\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.69940 | + | 14.3085i | 0.287499 | + | 0.614038i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −34.7155 | + | 6.12128i | −1.48705 | + | 0.262207i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.3472 | + | 12.3313i | −0.442414 | + | 0.527249i | −0.940461 | − | 0.339901i | \(-0.889606\pi\) |
0.498047 | + | 0.867150i | \(0.334051\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.6207 | + | 37.7894i | −0.581319 | + | 1.61281i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.53422 | + | 25.7148i | −0.193164 | + | 1.09549i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.4369 | − | 3.79871i | −0.443821 | − | 0.161538i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 30.2755 | − | 2.69640i | 1.28512 | − | 0.114456i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.287981 | − | 0.166266i | 0.0122022 | − | 0.00704492i | −0.493887 | − | 0.869526i | \(-0.664424\pi\) |
0.506089 | + | 0.862481i | \(0.331091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.51672 | + | 2.60773i | 0.191037 | + | 0.110295i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.2087 | − | 4.31600i | −0.684332 | − | 0.182222i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.2634 | + | 19.5203i | −0.980435 | + | 0.822682i | −0.984155 | − | 0.177311i | \(-0.943260\pi\) |
0.00372038 | + | 0.999993i | \(0.498816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.5479 | + | 9.29868i | −1.07481 | + | 0.391199i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.166329 | − | 26.6346i | −0.00698515 | − | 1.11855i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.31656 | − | 9.11217i | −0.139037 | − | 0.382002i | 0.850558 | − | 0.525881i | \(-0.176264\pi\) |
−0.989595 | + | 0.143880i | \(0.954042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.1651 | + | 15.6896i | 0.550944 | + | 0.656590i | 0.967604 | − | 0.252473i | \(-0.0812438\pi\) |
−0.416660 | + | 0.909063i | \(0.636799\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.90744 | + | 22.1853i | −0.246787 | + | 0.926806i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −41.0723 | + | 71.1393i | −1.71283 | + | 2.96671i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.3818 | + | 33.5702i | 0.806873 | + | 1.39755i | 0.915019 | + | 0.403410i | \(0.132175\pi\) |
−0.108146 | + | 0.994135i | \(0.534491\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.17515 | + | 35.6510i | 0.131955 | + | 1.48160i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.2532 | − | 33.6654i | 0.508348 | − | 1.39667i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.9175 | + | 2.80668i | 0.659235 | + | 0.116241i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.17367 | + | 17.6759i | 0.131215 | + | 0.730808i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.0219 | − | 26.8696i | −1.32169 | − | 1.10903i | −0.985945 | − | 0.167073i | \(-0.946568\pi\) |
−0.335742 | − | 0.941954i | \(-0.608987\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.35322 | − | 53.0447i | −0.385393 | − | 2.18567i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 39.4389 | − | 18.4657i | 1.62230 | − | 0.759576i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 16.1880i | − | 0.664760i | −0.943146 | − | 0.332380i | \(-0.892148\pi\) | ||
0.943146 | − | 0.332380i | \(-0.107852\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 34.7412i | 1.42425i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.149090 | + | 1.73531i | −0.00610187 | + | 0.0710215i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.02017 | − | 34.1421i | −0.245977 | − | 1.39501i | −0.818212 | − | 0.574917i | \(-0.805034\pi\) |
0.572234 | − | 0.820090i | \(-0.306077\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.59895 | − | 2.18078i | −0.106013 | − | 0.0889558i | 0.588240 | − | 0.808686i | \(-0.299821\pi\) |
−0.694254 | + | 0.719730i | \(0.744265\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.2196 | − | 0.0319096i | 0.416176 | − | 0.00129946i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.30021 | − | 0.405589i | −0.0935169 | − | 0.0164896i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.0868318 | − | 0.238568i | 0.00352439 | − | 0.00968319i | −0.937918 | − | 0.346857i | \(-0.887249\pi\) |
0.941442 | + | 0.337174i | \(0.109471\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.3404 | − | 13.5874i | 0.783715 | − | 0.550588i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.982300 | + | 1.70139i | 0.0397396 | + | 0.0688310i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.676216 | + | 1.17124i | −0.0273121 | + | 0.0473059i | −0.879358 | − | 0.476161i | \(-0.842028\pi\) |
0.852046 | + | 0.523466i | \(0.175361\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.94631 | + | 2.93713i | 0.118807 | + | 0.118436i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.9230 | + | 28.5104i | 0.963105 | + | 1.14778i | 0.988970 | + | 0.148118i | \(0.0473216\pi\) |
−0.0258648 | + | 0.999665i | \(0.508234\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.9951 | − | 41.1988i | −0.602705 | − | 1.65592i | −0.745768 | − | 0.666206i | \(-0.767917\pi\) |
0.143063 | − | 0.989714i | \(-0.454305\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 37.5279 | − | 17.7140i | 1.50594 | − | 0.710839i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.69472 | + | 0.616829i | −0.0678976 | + | 0.0247127i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.4947 | − | 18.8753i | 0.899788 | − | 0.755012i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.23527 | − | 30.5436i | −0.328885 | − | 1.21980i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.6716 | + | 6.73858i | 0.465376 | + | 0.268685i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.7443 | + | 9.08996i | −0.626770 | + | 0.361866i | −0.779500 | − | 0.626402i | \(-0.784527\pi\) |
0.152730 | + | 0.988268i | \(0.451193\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.23194 | + | 17.7256i | −0.327190 | + | 0.704531i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.6296 | + | 13.6961i | 1.49329 | + | 0.543512i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.467519 | − | 2.65143i | 0.0185238 | − | 0.105054i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.8384 | + | 18.9956i | −0.626557 | + | 0.751454i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.1322 | − | 18.0338i | 0.597685 | − | 0.712293i | −0.379379 | − | 0.925241i | \(-0.623862\pi\) |
0.977063 | + | 0.212949i | \(0.0683067\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.8082 | − | 3.31639i | 0.741722 | − | 0.130786i | 0.209996 | − | 0.977702i | \(-0.432655\pi\) |
0.531726 | + | 0.846917i | \(0.321544\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.2010 | + | 18.9157i | −0.519788 | + | 0.744806i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.40584 | 0.173211 | 0.0866057 | − | 0.996243i | \(-0.472398\pi\) | ||||
0.0866057 | + | 0.996243i | \(0.472398\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.718276 | −0.0281948 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −27.9034 | + | 39.9829i | −1.09362 | + | 1.56705i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.9597 | + | 3.16677i | −0.702816 | + | 0.123925i | −0.513625 | − | 0.858015i | \(-0.671698\pi\) |
−0.189191 | + | 0.981940i | \(0.560587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.43252 | + | 1.70721i | −0.0559733 | + | 0.0667063i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.8803 | − | 3.96078i | −0.892644 | − | 0.154525i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.46263 | − | 36.6514i | 0.251748 | − | 1.42773i | −0.552536 | − | 0.833489i | \(-0.686340\pi\) |
0.804284 | − | 0.594246i | \(-0.202549\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.82083 | + | 3.21052i | 0.343090 | + | 0.124875i | 0.507818 | − | 0.861464i | \(-0.330452\pi\) |
−0.164727 | + | 0.986339i | \(0.552674\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.35392 | + | 7.22193i | −0.130256 | + | 0.280476i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −56.7429 | + | 32.7605i | −2.20040 | + | 1.27040i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.8923 | + | 18.4130i | 1.23488 | + | 0.712956i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.43688 | + | 5.32920i | 0.0555528 | + | 0.206039i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33.0824 | − | 27.7594i | 1.27713 | − | 1.07164i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.1849 | − | 6.98275i | 0.739525 | − | 0.269165i | 0.0553340 | − | 0.998468i | \(-0.482378\pi\) |
0.684191 | + | 0.729303i | \(0.260155\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −53.2195 | + | 4.90737i | −2.04842 | + | 0.188885i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.4047 | − | 31.3341i | −0.438317 | − | 1.20427i | −0.940586 | − | 0.339555i | \(-0.889724\pi\) |
0.502269 | − | 0.864711i | \(-0.332499\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.2211 | − | 41.9749i | −1.35166 | − | 1.61085i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.1064 | + | 20.0438i | 0.770481 | + | 0.768079i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.7613 | + | 39.4237i | −0.870937 | + | 1.50851i | −0.00990835 | + | 0.999951i | \(0.503154\pi\) |
−0.861029 | + | 0.508556i | \(0.830179\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.8652 | − | 24.0153i | −0.529763 | − | 0.917577i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.4975 | + | 8.07740i | −0.438656 | + | 0.308172i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.62430 | − | 7.21021i | 0.0999779 | − | 0.274687i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.27547 | + | 0.930207i | 0.200688 | + | 0.0353867i | 0.273089 | − | 0.961989i | \(-0.411955\pi\) |
−0.0724003 | + | 0.997376i | \(0.523066\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.2402 | + | 24.8436i | −0.540942 | + | 0.943732i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.50512 | + | 7.13664i | 0.322618 | + | 0.270708i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.320315 | + | 1.81660i | 0.0121328 | + | 0.0688086i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.933320 | − | 10.8632i | 0.0353014 | − | 0.410884i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.2531i | 0.802717i | 0.915921 | + | 0.401358i | \(0.131462\pi\) | ||||
−0.915921 | + | 0.401358i | \(0.868538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.4176i | 0.958642i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.86910 | + | 3.68439i | −0.296367 | + | 0.138762i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.36249 | − | 24.7409i | −0.164068 | − | 0.930478i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.3373 | + | 30.4906i | 1.36468 | + | 1.14510i | 0.974507 | + | 0.224358i | \(0.0720284\pi\) |
0.390170 | + | 0.920743i | \(0.372416\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.60213 | − | 7.26394i | 0.322605 | − | 0.272419i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −74.8110 | − | 13.1912i | −2.80170 | − | 0.494014i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.60347 | − | 18.1429i | 0.246956 | − | 0.678505i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.64048 | − | 18.4195i | −0.0612647 | − | 0.687889i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.7915 | + | 32.5479i | 0.700806 | + | 1.21383i | 0.968184 | + | 0.250240i | \(0.0805095\pi\) |
−0.267378 | + | 0.963592i | \(0.586157\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.1534 | − | 21.0502i | 0.452615 | − | 0.783952i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.33202 | + | 31.2908i | −0.309871 | + | 1.16372i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −30.4859 | − | 36.3317i | −1.13222 | − | 1.34933i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.85023 | + | 21.5683i | 0.291149 | + | 0.799925i | 0.995899 | + | 0.0904698i | \(0.0288369\pi\) |
−0.704750 | + | 0.709456i | \(0.748941\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.5081 | + | 13.2804i | 0.870671 | + | 0.491866i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.61083 | + | 3.49806i | −0.355469 | + | 0.129380i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.21278 | + | 3.53494i | −0.155603 | + | 0.130566i | −0.717265 | − | 0.696800i | \(-0.754606\pi\) |
0.561663 | + | 0.827366i | \(0.310162\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.5066 | + | 3.06393i | 0.424426 | + | 0.113015i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.51519 | − | 5.49360i | −0.350497 | − | 0.202359i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.63042 | − | 1.51867i | 0.0967614 | − | 0.0558652i | −0.450838 | − | 0.892606i | \(-0.648875\pi\) |
0.547600 | + | 0.836740i | \(0.315542\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.9583 | + | 1.33222i | −0.549507 | + | 0.0489402i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.90477 | − | 2.87710i | −0.289998 | − | 0.105551i | 0.192925 | − | 0.981214i | \(-0.438203\pi\) |
−0.482923 | + | 0.875663i | \(0.660425\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.49942 | − | 31.1888i | 0.201483 | − | 1.14267i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.4307 | + | 27.7472i | 0.857283 | + | 1.01522i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.7908 | + | 35.5033i | −1.08853 | + | 1.29726i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.4856 | + | 6.43340i | −1.33138 | + | 0.234758i | −0.793658 | − | 0.608364i | \(-0.791826\pi\) |
−0.537722 | + | 0.843122i | \(0.680715\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.0879 | − | 21.5457i | −0.367624 | − | 0.785170i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −73.5967 | −2.67846 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.63964 | −0.168630 | −0.0843152 | − | 0.996439i | \(-0.526870\pi\) | ||||
−0.0843152 | + | 0.996439i | \(0.526870\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −44.4514 | − | 3.81908i | −1.61348 | − | 0.138624i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.9212 | + | 5.09959i | −1.04839 | + | 0.184860i | −0.671201 | − | 0.741276i | \(-0.734221\pi\) |
−0.377191 | + | 0.926135i | \(0.623110\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.1519 | + | 20.4408i | −0.620940 | + | 0.740007i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −30.5537 | − | 17.5132i | −1.10467 | − | 0.633192i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0592107 | + | 0.335801i | −0.00213798 | + | 0.0121251i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.0305 | + | 15.6618i | 1.55172 | + | 0.564780i | 0.968821 | − | 0.247764i | \(-0.0796956\pi\) |
0.582900 | + | 0.812544i | \(0.301918\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.2137 | − | 38.7363i | −0.980077 | − | 1.39505i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.09568 | + | 4.09670i | −0.255214 | + | 0.147348i | −0.622149 | − | 0.782899i | \(-0.713740\pi\) |
0.366935 | + | 0.930246i | \(0.380407\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 84.7268 | + | 48.9170i | 3.04348 | + | 1.75715i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.2437 | − | 16.2945i | 0.582740 | − | 0.584563i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.66500 | + | 2.23620i | −0.0954836 | + | 0.0801203i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.9862 | − | 9.09422i | 0.894075 | − | 0.325417i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.20002 | + | 23.8588i | 0.0786222 | + | 0.852642i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.04654 | + | 22.1077i | 0.287193 | + | 0.789058i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.8770 | − | 30.8390i | −0.922415 | − | 1.09929i | −0.994793 | − | 0.101915i | \(-0.967503\pi\) |
0.0723778 | − | 0.997377i | \(-0.476941\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.2758 | − | 4.11870i | 0.543832 | − | 0.146630i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.2899 | + | 17.8227i | −0.365867 | + | 0.633701i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.2506 | − | 17.7546i | −0.364011 | − | 0.630486i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 30.7783 | + | 14.2937i | 1.09159 | + | 0.506946i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.3722 | + | 33.9923i | −0.438245 | + | 1.20407i | 0.502387 | + | 0.864643i | \(0.332455\pi\) |
−0.940632 | + | 0.339427i | \(0.889767\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.79410 | − | 0.669002i | −0.134226 | − | 0.0236676i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.311839 | − | 1.80140i | 0.0110183 | − | 0.0636493i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.1239 | + | 16.0468i | 0.674867 | + | 0.566280i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0463 | + | 91.0030i | 0.565558 | + | 3.20744i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.12342 | − | 1.48190i | −0.0747479 | − | 0.0521654i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 32.9789i | − | 1.15948i | −0.814803 | − | 0.579738i | \(-0.803155\pi\) | ||
0.814803 | − | 0.579738i | \(-0.196845\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.6015i | 0.372268i | 0.982524 | + | 0.186134i | \(0.0595959\pi\) | ||||
−0.982524 | + | 0.186134i | \(0.940404\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34.6795 | − | 24.2023i | −1.21626 | − | 0.848811i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.1640 | − | 63.3140i | −0.391057 | − | 2.21779i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.7763 | − | 12.3988i | −0.516957 | − | 0.433778i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.4407 | + | 8.70541i | 0.364829 | + | 0.304192i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.9146 | + | 5.45109i | 1.07893 | + | 0.190244i | 0.684742 | − | 0.728786i | \(-0.259915\pi\) |
0.394187 | + | 0.919030i | \(0.371026\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.8809 | − | 32.6426i | 0.414143 | − | 1.13785i | −0.540824 | − | 0.841136i | \(-0.681888\pi\) |
0.954967 | − | 0.296712i | \(-0.0958903\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 52.1135 | + | 24.2019i | 1.81436 | + | 0.842603i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.6425 | + | 18.4334i | 0.370077 | + | 0.640992i | 0.989577 | − | 0.144004i | \(-0.0459979\pi\) |
−0.619500 | + | 0.784997i | \(0.712665\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.7208 | − | 27.2293i | 0.546007 | − | 0.945712i | −0.452536 | − | 0.891746i | \(-0.649480\pi\) |
0.998543 | − | 0.0539659i | \(-0.0171862\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.9854 | − | 3.23155i | 0.415770 | − | 0.112101i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.39375 | + | 4.04451i | 0.117586 | + | 0.140134i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.7761 | − | 54.3345i | −0.684382 | − | 1.88032i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.0974 | − | 44.6957i | −0.729232 | − | 1.54491i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.2629 | − | 10.6508i | 1.01027 | − | 0.367708i | 0.216733 | − | 0.976231i | \(-0.430460\pi\) |
0.793536 | + | 0.608523i | \(0.208238\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.92748 | − | 4.97375i | 0.204396 | − | 0.171509i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.0704 | − | 32.1707i | 1.10456 | − | 1.10802i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.0788 | + | 20.8301i | 1.24115 | + | 0.716577i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.53115 | + | 0.884013i | −0.0526111 | + | 0.0303750i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.5439 | + | 19.2786i | 0.464827 | + | 0.661640i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.6855 | + | 12.2605i | 1.15473 | + | 0.420286i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.05089 | + | 17.3024i | −0.104460 | + | 0.592424i | 0.886974 | + | 0.461819i | \(0.152803\pi\) |
−0.991434 | + | 0.130605i | \(0.958308\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.207383 | − | 66.4183i | −0.00709236 | − | 2.27146i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.18052 | − | 8.55740i | 0.245282 | − | 0.292315i | −0.629331 | − | 0.777137i | \(-0.716671\pi\) |
0.874613 | + | 0.484822i | \(0.161116\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.7491 | − | 6.47986i | 1.25386 | − | 0.221090i | 0.493016 | − | 0.870021i | \(-0.335895\pi\) |
0.760848 | + | 0.648931i | \(0.224783\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.13756 | + | 0.269566i | 0.106928 | + | 0.00918678i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.20635 | −0.109145 | −0.0545727 | − | 0.998510i | \(-0.517380\pi\) | ||||
−0.0545727 | + | 0.998510i | \(0.517380\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.94985 | −0.270303 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.86428 | + | 12.5249i | 0.199161 | + | 0.425368i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.9205 | + | 2.10191i | −0.404375 | + | 0.0713023i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.35269 | + | 3.99558i | −0.113601 | + | 0.135385i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 54.6706 | − | 9.81602i | 1.85032 | − | 0.332222i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.6197 | − | 60.2274i | 0.359012 | − | 2.03606i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.62013 | + | 2.77350i | 0.257314 | + | 0.0936545i | 0.467456 | − | 0.884016i | \(-0.345171\pi\) |
−0.210143 | + | 0.977671i | \(0.567393\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.9464 | − | 1.24209i | 0.470400 | − | 0.0418948i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.0617 | − | 8.69590i | 0.507443 | − | 0.292972i | −0.224339 | − | 0.974511i | \(-0.572022\pi\) |
0.731782 | + | 0.681539i | \(0.238689\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.9181 | − | 13.8091i | −0.804909 | − | 0.464714i | 0.0402760 | − | 0.999189i | \(-0.487176\pi\) |
−0.845185 | + | 0.534474i | \(0.820510\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.45729 | − | 0.388043i | −0.0489864 | − | 0.0130439i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −28.8677 | + | 24.2229i | −0.969282 | + | 0.813324i | −0.982438 | − | 0.186590i | \(-0.940257\pi\) |
0.0131564 | + | 0.999913i | \(0.495812\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.4841 | − | 10.3674i | 0.955325 | − | 0.347710i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.6706 | − | 25.0476i | −0.491483 | − | 0.839127i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.48510 | − | 6.82777i | −0.0831609 | − | 0.228483i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.27353 | − | 1.51774i | −0.0425695 | − | 0.0507323i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.44978 | + | 20.4666i | −0.181963 | + | 0.683361i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.9299 | − | 37.9837i | 0.731404 | − | 1.26683i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.52341 | + | 13.0309i | 0.250641 | + | 0.434123i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.54894 | + | 17.3917i | 0.0515454 | + | 0.578758i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.1974 | − | 33.5121i | 0.405456 | − | 1.11398i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.9368 | − | 3.16274i | −0.595582 | − | 0.105017i | −0.132272 | − | 0.991213i | \(-0.542227\pi\) |
−0.463310 | + | 0.886196i | \(0.653338\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 23.9580 | + | 8.63537i | 0.794636 | + | 0.286417i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.3643 | + | 19.6049i | 0.774092 | + | 0.649540i | 0.941753 | − | 0.336304i | \(-0.109177\pi\) |
−0.167661 | + | 0.985845i | \(0.553621\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.77994 | − | 38.4509i | −0.224383 | − | 1.27254i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 82.1168 | − | 38.4479i | 2.71470 | − | 1.27105i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.68696i | 0.0557085i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.8471i | 0.819631i | 0.912168 | + | 0.409816i | \(0.134407\pi\) | ||||
−0.912168 | + | 0.409816i | \(0.865593\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.69869 | + | 43.0502i | −0.121876 | + | 1.41855i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.19191 | − | 12.4309i | −0.0721476 | − | 0.409169i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.3661 | − | 29.6757i | −1.16283 | − | 0.975732i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.3864 | + | 21.3000i | 0.406823 | + | 0.699584i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.94694 | − | 1.22493i | −0.227922 | − | 0.0401887i | 0.0585208 | − | 0.998286i | \(-0.481362\pi\) |
−0.286442 | + | 0.958097i | \(0.592473\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.40565 | + | 9.35694i | −0.111616 | + | 0.306661i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −40.9042 | + | 28.7367i | −1.33914 | + | 0.940797i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.9310 | + | 32.7894i | 0.619109 | + | 1.07233i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.2685 | + | 33.3739i | −0.629473 | + | 1.09028i | 0.358184 | + | 0.933651i | \(0.383396\pi\) |
−0.987658 | + | 0.156629i | \(0.949937\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.87076 | − | 2.86181i | −0.0936836 | − | 0.0933915i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.15039 | + | 3.75448i | 0.102700 | + | 0.122393i | 0.814946 | − | 0.579537i | \(-0.196767\pi\) |
−0.712246 | + | 0.701930i | \(0.752322\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.67810 | + | 4.61055i | 0.0546466 | + | 0.150140i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −42.3133 | + | 42.7115i | −1.37645 | + | 1.38940i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.5745 | − | 9.67234i | 0.863556 | − | 0.314309i | 0.128001 | − | 0.991774i | \(-0.459144\pi\) |
0.735555 | + | 0.677465i | \(0.236922\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.07851 | − | 7.61777i | 0.294701 | − | 0.247283i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.85716 | − | 14.3057i | −0.125077 | − | 0.463896i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 40.9267 | + | 23.6291i | 1.32575 | + | 0.765420i | 0.984639 | − | 0.174604i | \(-0.0558644\pi\) |
0.341108 | + | 0.940024i | \(0.389198\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 44.8799 | − | 25.9114i | 1.45228 | − | 0.838473i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.8499 | − | 23.3629i | 0.350728 | − | 0.755215i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.7249 | − | 7.17928i | −0.636951 | − | 0.231831i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.3276 | + | 58.5708i | −0.333149 | + | 1.88938i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.2063 | − | 44.0975i | −0.522240 | − | 1.42102i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 51.9319 | − | 61.8900i | 1.67175 | − | 1.99231i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.9336 | − | 7.92300i | 1.44497 | − | 0.254786i | 0.604480 | − | 0.796620i | \(-0.293381\pi\) |
0.840486 | + | 0.541834i | \(0.182270\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.8540 | − | 24.1501i | 0.541427 | − | 0.775813i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.8881 | 0.766605 | 0.383302 | − | 0.923623i | \(-0.374787\pi\) | ||||
0.383302 | + | 0.923623i | \(0.374787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.40424 | 0.269428 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.6106 | − | 22.3684i | 0.499938 | − | 0.716363i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.8784 | − | 4.56305i | 0.827922 | − | 0.145985i | 0.256399 | − | 0.966571i | \(-0.417464\pi\) |
0.571523 | + | 0.820586i | \(0.306353\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.26339 | + | 1.50565i | −0.0403782 | + | 0.0481209i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.33066 | − | 25.3888i | −0.297905 | − | 0.810603i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.70819 | + | 26.7015i | −0.150168 | + | 0.851645i | 0.812903 | + | 0.582398i | \(0.197886\pi\) |
−0.963071 | + | 0.269246i | \(0.913225\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −92.3700 | − | 33.6199i | −2.94315 | − | 1.07122i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.77032 | + | 5.96526i | −0.0881802 | + | 0.189876i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.5595 | + | 13.6021i | −0.749147 | + | 0.432520i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.0489 | − | 20.2355i | −1.11337 | − | 0.642802i | −0.173667 | − | 0.984804i | \(-0.555562\pi\) |
−0.939699 | + | 0.342002i | \(0.888895\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.65129 | + | 17.2511i | 0.147604 | + | 0.547446i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.01167 | − | 2.52709i | 0.0954765 | − | 0.0801143i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.05161 | + | 1.11069i | −0.0966454 | + | 0.0351760i | −0.389890 | − | 0.920861i | \(-0.627487\pi\) |
0.293245 | + | 0.956037i | \(0.405265\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.14194 | + | 22.5000i | 0.194322 | + | 0.711867i |
(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 | 432.2.be.a.47.5 | yes | 36 | |
4.3 | odd | 2 | inner | 432.2.be.a.47.2 | ✓ | 36 | |
27.23 | odd | 18 | inner | 432.2.be.a.239.2 | yes | 36 | |
108.23 | even | 18 | inner | 432.2.be.a.239.5 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.be.a.47.2 | ✓ | 36 | 4.3 | odd | 2 | inner | |
432.2.be.a.47.5 | yes | 36 | 1.1 | even | 1 | trivial | |
432.2.be.a.239.2 | yes | 36 | 27.23 | odd | 18 | inner | |
432.2.be.a.239.5 | yes | 36 | 108.23 | even | 18 | inner |