Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(364,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1480160000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 27x^{4} + 31x^{2} + 11 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.7 | ||
Root | \(1.65458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.364 |
Dual form | 605.2.b.g.364.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.65458i | 1.16997i | 0.811046 | + | 0.584983i | \(0.198899\pi\) | ||||
−0.811046 | + | 0.584983i | \(0.801101\pi\) | |||||||
\(3\) | 1.97479i | 1.14014i | 0.821595 | + | 0.570072i | \(0.193085\pi\) | ||||
−0.821595 | + | 0.570072i | \(0.806915\pi\) | |||||||
\(4\) | −0.737640 | −0.368820 | ||||||||
\(5\) | 2.19353 | + | 0.434096i | 0.980975 | + | 0.194133i | ||||
\(6\) | −3.26745 | −1.33393 | ||||||||
\(7\) | − | 2.24307i | − | 0.847802i | −0.905708 | − | 0.423901i | \(-0.860660\pi\) | ||
0.905708 | − | 0.423901i | \(-0.139340\pi\) | |||||||
\(8\) | 2.08868i | 0.738459i | ||||||||
\(9\) | −0.899788 | −0.299929 | ||||||||
\(10\) | −0.718246 | + | 3.62937i | −0.227129 | + | 1.14771i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | − | 1.45668i | − | 0.420508i | ||||||
\(13\) | 3.69976i | 1.02613i | 0.858350 | + | 0.513064i | \(0.171490\pi\) | ||||
−0.858350 | + | 0.513064i | \(0.828510\pi\) | |||||||
\(14\) | 3.71135 | 0.991900 | ||||||||
\(15\) | −0.857247 | + | 4.33175i | −0.221340 | + | 1.11845i | ||||
\(16\) | −4.93117 | −1.23279 | ||||||||
\(17\) | − | 2.22461i | − | 0.539546i | −0.962924 | − | 0.269773i | \(-0.913051\pi\) | ||
0.962924 | − | 0.269773i | \(-0.0869487\pi\) | |||||||
\(18\) | − | 1.48877i | − | 0.350907i | ||||||
\(19\) | −5.28684 | −1.21288 | −0.606442 | − | 0.795127i | \(-0.707404\pi\) | ||||
−0.606442 | + | 0.795127i | \(0.707404\pi\) | |||||||
\(20\) | −1.61803 | − | 0.320206i | −0.361803 | − | 0.0716003i | ||||
\(21\) | 4.42960 | 0.966617 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.85415i | 0.803647i | 0.915717 | + | 0.401823i | \(0.131623\pi\) | ||||
−0.915717 | + | 0.401823i | \(0.868377\pi\) | |||||||
\(24\) | −4.12469 | −0.841950 | ||||||||
\(25\) | 4.62312 | + | 1.90440i | 0.924624 | + | 0.380880i | ||||
\(26\) | −6.12155 | −1.20053 | ||||||||
\(27\) | 4.14747i | 0.798182i | ||||||||
\(28\) | 1.65458i | 0.312687i | ||||||||
\(29\) | −0.188439 | −0.0349922 | −0.0174961 | − | 0.999847i | \(-0.505569\pi\) | ||||
−0.0174961 | + | 0.999847i | \(0.505569\pi\) | |||||||
\(30\) | −7.16724 | − | 1.41838i | −1.30855 | − | 0.258960i | ||||
\(31\) | 0.686867 | 0.123365 | 0.0616824 | − | 0.998096i | \(-0.480353\pi\) | ||||
0.0616824 | + | 0.998096i | \(0.480353\pi\) | |||||||
\(32\) | − | 3.98166i | − | 0.703866i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.68079 | 0.631251 | ||||||||
\(35\) | 0.973708 | − | 4.92024i | 0.164587 | − | 0.831673i | ||||
\(36\) | 0.663720 | 0.110620 | ||||||||
\(37\) | 2.59316i | 0.426313i | 0.977018 | + | 0.213156i | \(0.0683744\pi\) | ||||
−0.977018 | + | 0.213156i | \(0.931626\pi\) | |||||||
\(38\) | − | 8.74751i | − | 1.41903i | ||||||
\(39\) | −7.30624 | −1.16993 | ||||||||
\(40\) | −0.906685 | + | 4.58157i | −0.143360 | + | 0.724410i | ||||
\(41\) | 7.91604 | 1.23628 | 0.618139 | − | 0.786069i | \(-0.287887\pi\) | ||||
0.618139 | + | 0.786069i | \(0.287887\pi\) | |||||||
\(42\) | 7.32913i | 1.13091i | ||||||||
\(43\) | − | 8.41368i | − | 1.28307i | −0.767092 | − | 0.641537i | \(-0.778297\pi\) | ||
0.767092 | − | 0.641537i | \(-0.221703\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.97371 | − | 0.390594i | −0.294223 | − | 0.0582263i | ||||
\(46\) | −6.37701 | −0.940239 | ||||||||
\(47\) | − | 12.0132i | − | 1.75230i | −0.482037 | − | 0.876151i | \(-0.660103\pi\) | ||
0.482037 | − | 0.876151i | \(-0.339897\pi\) | |||||||
\(48\) | − | 9.73801i | − | 1.40556i | ||||||
\(49\) | 1.96862 | 0.281231 | ||||||||
\(50\) | −3.15099 | + | 7.64933i | −0.445617 | + | 1.08178i | ||||
\(51\) | 4.39313 | 0.615161 | ||||||||
\(52\) | − | 2.72909i | − | 0.378457i | ||||||
\(53\) | − | 12.6566i | − | 1.73851i | −0.494360 | − | 0.869257i | \(-0.664597\pi\) | ||
0.494360 | − | 0.869257i | \(-0.335403\pi\) | |||||||
\(54\) | −6.86233 | −0.933845 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.68506 | 0.626067 | ||||||||
\(57\) | − | 10.4404i | − | 1.38286i | ||||||
\(58\) | − | 0.311788i | − | 0.0409397i | ||||||
\(59\) | 0.343688 | 0.0447444 | 0.0223722 | − | 0.999750i | \(-0.492878\pi\) | ||||
0.0223722 | + | 0.999750i | \(0.492878\pi\) | |||||||
\(60\) | 0.632340 | − | 3.19527i | 0.0816347 | − | 0.412508i | ||||
\(61\) | 1.73338 | 0.221936 | 0.110968 | − | 0.993824i | \(-0.464605\pi\) | ||||
0.110968 | + | 0.993824i | \(0.464605\pi\) | |||||||
\(62\) | 1.13648i | 0.144333i | ||||||||
\(63\) | 2.01829i | 0.254281i | ||||||||
\(64\) | −3.27435 | −0.409293 | ||||||||
\(65\) | −1.60605 | + | 8.11552i | −0.199206 | + | 1.00661i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.650461i | 0.0794664i | 0.999210 | + | 0.0397332i | \(0.0126508\pi\) | ||||
−0.999210 | + | 0.0397332i | \(0.987349\pi\) | |||||||
\(68\) | 1.64096i | 0.198996i | ||||||||
\(69\) | −7.61114 | −0.916273 | ||||||||
\(70\) | 8.14094 | + | 1.61108i | 0.973029 | + | 0.192561i | ||||
\(71\) | 4.64760 | 0.551569 | 0.275785 | − | 0.961219i | \(-0.411062\pi\) | ||||
0.275785 | + | 0.961219i | \(0.411062\pi\) | |||||||
\(72\) | − | 1.87937i | − | 0.221485i | ||||||
\(73\) | 8.85841i | 1.03680i | 0.855139 | + | 0.518399i | \(0.173472\pi\) | ||||
−0.855139 | + | 0.518399i | \(0.826528\pi\) | |||||||
\(74\) | −4.29059 | −0.498772 | ||||||||
\(75\) | −3.76079 | + | 9.12969i | −0.434258 | + | 1.05421i | ||||
\(76\) | 3.89979 | 0.447336 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 12.0888i | − | 1.36878i | ||||||
\(79\) | 7.23426 | 0.813918 | 0.406959 | − | 0.913447i | \(-0.366589\pi\) | ||||
0.406959 | + | 0.913447i | \(0.366589\pi\) | |||||||
\(80\) | −10.8166 | − | 2.14060i | −1.20934 | − | 0.239326i | ||||
\(81\) | −10.8897 | −1.20997 | ||||||||
\(82\) | 13.0977i | 1.44640i | ||||||||
\(83\) | − | 3.18165i | − | 0.349232i | −0.984637 | − | 0.174616i | \(-0.944132\pi\) | ||
0.984637 | − | 0.174616i | \(-0.0558684\pi\) | |||||||
\(84\) | −3.26745 | −0.356508 | ||||||||
\(85\) | 0.965692 | − | 4.87974i | 0.104744 | − | 0.529282i | ||||
\(86\) | 13.9211 | 1.50115 | ||||||||
\(87\) | − | 0.372127i | − | 0.0398962i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.92195 | −1.05172 | −0.525862 | − | 0.850570i | \(-0.676257\pi\) | ||||
−0.525862 | + | 0.850570i | \(0.676257\pi\) | |||||||
\(90\) | 0.646269 | − | 3.26566i | 0.0681228 | − | 0.344231i | ||||
\(91\) | 8.29883 | 0.869954 | ||||||||
\(92\) | − | 2.84298i | − | 0.296401i | ||||||
\(93\) | 1.35642i | 0.140654i | ||||||||
\(94\) | 19.8768 | 2.05013 | ||||||||
\(95\) | −11.5968 | − | 2.29499i | −1.18981 | − | 0.235461i | ||||
\(96\) | 7.86294 | 0.802508 | ||||||||
\(97\) | 2.26811i | 0.230292i | 0.993349 | + | 0.115146i | \(0.0367335\pi\) | ||||
−0.993349 | + | 0.115146i | \(0.963266\pi\) | |||||||
\(98\) | 3.25724i | 0.329031i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.41020 | − | 1.40476i | −0.341020 | − | 0.140476i | ||||
\(101\) | 9.89686 | 0.984774 | 0.492387 | − | 0.870376i | \(-0.336124\pi\) | ||||
0.492387 | + | 0.870376i | \(0.336124\pi\) | |||||||
\(102\) | 7.26879i | 0.719717i | ||||||||
\(103\) | − | 10.2411i | − | 1.00909i | −0.863386 | − | 0.504544i | \(-0.831661\pi\) | ||
0.863386 | − | 0.504544i | \(-0.168339\pi\) | |||||||
\(104\) | −7.72760 | −0.757753 | ||||||||
\(105\) | 9.71644 | + | 1.92287i | 0.948227 | + | 0.187653i | ||||
\(106\) | 20.9413 | 2.03400 | ||||||||
\(107\) | 10.0468i | 0.971261i | 0.874164 | + | 0.485631i | \(0.161410\pi\) | ||||
−0.874164 | + | 0.485631i | \(0.838590\pi\) | |||||||
\(108\) | − | 3.05934i | − | 0.294386i | ||||||
\(109\) | 8.80173 | 0.843053 | 0.421527 | − | 0.906816i | \(-0.361494\pi\) | ||||
0.421527 | + | 0.906816i | \(0.361494\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.12094 | −0.486058 | ||||||||
\(112\) | 11.0610i | 1.04516i | ||||||||
\(113\) | − | 0.231352i | − | 0.0217638i | −0.999941 | − | 0.0108819i | \(-0.996536\pi\) | ||
0.999941 | − | 0.0108819i | \(-0.00346388\pi\) | |||||||
\(114\) | 17.2745 | 1.61790 | ||||||||
\(115\) | −1.67307 | + | 8.45419i | −0.156015 | + | 0.788357i | ||||
\(116\) | 0.139000 | 0.0129058 | ||||||||
\(117\) | − | 3.32900i | − | 0.307766i | ||||||
\(118\) | 0.568660i | 0.0523494i | ||||||||
\(119\) | −4.98996 | −0.457429 | ||||||||
\(120\) | −9.04763 | − | 1.79051i | −0.825932 | − | 0.163451i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2.86801i | 0.259658i | ||||||||
\(123\) | 15.6325i | 1.40953i | ||||||||
\(124\) | −0.506660 | −0.0454995 | ||||||||
\(125\) | 9.31425 | + | 6.18423i | 0.833092 | + | 0.553134i | ||||
\(126\) | −3.33943 | −0.297500 | ||||||||
\(127\) | − | 2.43034i | − | 0.215658i | −0.994169 | − | 0.107829i | \(-0.965610\pi\) | ||
0.994169 | − | 0.107829i | \(-0.0343899\pi\) | |||||||
\(128\) | − | 13.3810i | − | 1.18272i | ||||||
\(129\) | 16.6152 | 1.46289 | ||||||||
\(130\) | −13.4278 | − | 2.65734i | −1.17769 | − | 0.233064i | ||||
\(131\) | 1.58846 | 0.138785 | 0.0693924 | − | 0.997589i | \(-0.477894\pi\) | ||||
0.0693924 | + | 0.997589i | \(0.477894\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.8588i | 1.02829i | ||||||||
\(134\) | −1.07624 | −0.0929730 | ||||||||
\(135\) | −1.80040 | + | 9.09760i | −0.154954 | + | 0.782997i | ||||
\(136\) | 4.64649 | 0.398433 | ||||||||
\(137\) | − | 18.7019i | − | 1.59781i | −0.601457 | − | 0.798905i | \(-0.705413\pi\) | ||
0.601457 | − | 0.798905i | \(-0.294587\pi\) | |||||||
\(138\) | − | 12.5932i | − | 1.07201i | ||||||
\(139\) | −11.6274 | −0.986222 | −0.493111 | − | 0.869966i | \(-0.664140\pi\) | ||||
−0.493111 | + | 0.869966i | \(0.664140\pi\) | |||||||
\(140\) | −0.718246 | + | 3.62937i | −0.0607029 | + | 0.306738i | ||||
\(141\) | 23.7235 | 1.99788 | ||||||||
\(142\) | 7.68984i | 0.645317i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.43700 | 0.369750 | ||||||||
\(145\) | −0.413346 | − | 0.0818005i | −0.0343265 | − | 0.00679316i | ||||
\(146\) | −14.6570 | −1.21302 | ||||||||
\(147\) | 3.88761i | 0.320644i | ||||||||
\(148\) | − | 1.91282i | − | 0.157233i | ||||||
\(149\) | −5.91553 | −0.484619 | −0.242309 | − | 0.970199i | \(-0.577905\pi\) | ||||
−0.242309 | + | 0.970199i | \(0.577905\pi\) | |||||||
\(150\) | −15.1058 | − | 6.22253i | −1.23338 | − | 0.508067i | ||||
\(151\) | 12.7779 | 1.03985 | 0.519924 | − | 0.854213i | \(-0.325960\pi\) | ||||
0.519924 | + | 0.854213i | \(0.325960\pi\) | |||||||
\(152\) | − | 11.0425i | − | 0.895665i | ||||||
\(153\) | 2.00167i | 0.161826i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.50666 | + | 0.298166i | 0.121018 | + | 0.0239492i | ||||
\(156\) | 5.38937 | 0.431495 | ||||||||
\(157\) | 14.3487i | 1.14515i | 0.819853 | + | 0.572574i | \(0.194055\pi\) | ||||
−0.819853 | + | 0.572574i | \(0.805945\pi\) | |||||||
\(158\) | 11.9697i | 0.952256i | ||||||||
\(159\) | 24.9941 | 1.98216 | ||||||||
\(160\) | 1.72842 | − | 8.73389i | 0.136644 | − | 0.690475i | ||||
\(161\) | 8.64515 | 0.681333 | ||||||||
\(162\) | − | 18.0180i | − | 1.41563i | ||||||
\(163\) | 3.62716i | 0.284101i | 0.989859 | + | 0.142051i | \(0.0453696\pi\) | ||||
−0.989859 | + | 0.142051i | \(0.954630\pi\) | |||||||
\(164\) | −5.83919 | −0.455964 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.26430 | 0.408589 | ||||||||
\(167\) | − | 3.82070i | − | 0.295655i | −0.989013 | − | 0.147827i | \(-0.952772\pi\) | ||
0.989013 | − | 0.147827i | \(-0.0472280\pi\) | |||||||
\(168\) | 9.25199i | 0.713807i | ||||||||
\(169\) | −0.688202 | −0.0529386 | ||||||||
\(170\) | 8.07392 | + | 1.59782i | 0.619241 | + | 0.122547i | ||||
\(171\) | 4.75703 | 0.363779 | ||||||||
\(172\) | 6.20627i | 0.473224i | ||||||||
\(173\) | − | 2.10714i | − | 0.160203i | −0.996787 | − | 0.0801016i | \(-0.974476\pi\) | ||
0.996787 | − | 0.0801016i | \(-0.0255245\pi\) | |||||||
\(174\) | 0.615714 | 0.0466772 | ||||||||
\(175\) | 4.27171 | − | 10.3700i | 0.322911 | − | 0.783899i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.678711i | 0.0510151i | ||||||||
\(178\) | − | 16.4167i | − | 1.23048i | ||||||
\(179\) | −5.02397 | −0.375509 | −0.187755 | − | 0.982216i | \(-0.560121\pi\) | ||||
−0.187755 | + | 0.982216i | \(0.560121\pi\) | |||||||
\(180\) | 1.45589 | + | 0.288118i | 0.108515 | + | 0.0214750i | ||||
\(181\) | −15.6476 | −1.16308 | −0.581539 | − | 0.813519i | \(-0.697549\pi\) | ||||
−0.581539 | + | 0.813519i | \(0.697549\pi\) | |||||||
\(182\) | 13.7311i | 1.01782i | ||||||||
\(183\) | 3.42305i | 0.253039i | ||||||||
\(184\) | −8.05008 | −0.593460 | ||||||||
\(185\) | −1.12568 | + | 5.68817i | −0.0827616 | + | 0.418202i | ||||
\(186\) | −2.24430 | −0.164560 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.86140i | 0.646284i | ||||||||
\(189\) | 9.30309 | 0.676700 | ||||||||
\(190\) | 3.79726 | − | 19.1879i | 0.275482 | − | 1.39204i | ||||
\(191\) | 3.11585 | 0.225455 | 0.112728 | − | 0.993626i | \(-0.464041\pi\) | ||||
0.112728 | + | 0.993626i | \(0.464041\pi\) | |||||||
\(192\) | − | 6.46614i | − | 0.466653i | ||||||
\(193\) | 9.63638i | 0.693642i | 0.937931 | + | 0.346821i | \(0.112739\pi\) | ||||
−0.937931 | + | 0.346821i | \(0.887261\pi\) | |||||||
\(194\) | −3.75277 | −0.269433 | ||||||||
\(195\) | −16.0264 | − | 3.17160i | −1.14768 | − | 0.227123i | ||||
\(196\) | −1.45213 | −0.103724 | ||||||||
\(197\) | 14.3974i | 1.02577i | 0.858457 | + | 0.512885i | \(0.171423\pi\) | ||||
−0.858457 | + | 0.512885i | \(0.828577\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.7978 | −1.04899 | −0.524493 | − | 0.851415i | \(-0.675745\pi\) | ||||
−0.524493 | + | 0.851415i | \(0.675745\pi\) | |||||||
\(200\) | −3.97768 | + | 9.65621i | −0.281264 | + | 0.682797i | ||||
\(201\) | −1.28452 | −0.0906032 | ||||||||
\(202\) | 16.3752i | 1.15215i | ||||||||
\(203\) | 0.422682i | 0.0296665i | ||||||||
\(204\) | −3.24055 | −0.226884 | ||||||||
\(205\) | 17.3640 | + | 3.43632i | 1.21276 | + | 0.240003i | ||||
\(206\) | 16.9448 | 1.18060 | ||||||||
\(207\) | − | 3.46792i | − | 0.241037i | ||||||
\(208\) | − | 18.2441i | − | 1.26500i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.18154 | + | 16.0766i | −0.219547 | + | 1.10939i | ||||
\(211\) | −6.77147 | −0.466167 | −0.233084 | − | 0.972457i | \(-0.574882\pi\) | ||||
−0.233084 | + | 0.972457i | \(0.574882\pi\) | |||||||
\(212\) | 9.33600i | 0.641199i | ||||||||
\(213\) | 9.17803i | 0.628868i | ||||||||
\(214\) | −16.6233 | −1.13634 | ||||||||
\(215\) | 3.65234 | − | 18.4556i | 0.249088 | − | 1.25866i | ||||
\(216\) | −8.66273 | −0.589424 | ||||||||
\(217\) | − | 1.54069i | − | 0.104589i | ||||||
\(218\) | 14.5632i | 0.986344i | ||||||||
\(219\) | −17.4935 | −1.18210 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.23051 | 0.553644 | ||||||||
\(222\) | − | 8.47302i | − | 0.568672i | ||||||
\(223\) | − | 8.71727i | − | 0.583752i | −0.956456 | − | 0.291876i | \(-0.905721\pi\) | ||
0.956456 | − | 0.291876i | \(-0.0942794\pi\) | |||||||
\(224\) | −8.93117 | −0.596739 | ||||||||
\(225\) | −4.15983 | − | 1.71356i | −0.277322 | − | 0.114237i | ||||
\(226\) | 0.382791 | 0.0254629 | ||||||||
\(227\) | − | 3.80744i | − | 0.252708i | −0.991985 | − | 0.126354i | \(-0.959672\pi\) | ||
0.991985 | − | 0.126354i | \(-0.0403276\pi\) | |||||||
\(228\) | 7.70125i | 0.510028i | ||||||||
\(229\) | 2.71367 | 0.179324 | 0.0896621 | − | 0.995972i | \(-0.471421\pi\) | ||||
0.0896621 | + | 0.995972i | \(0.471421\pi\) | |||||||
\(230\) | −13.9881 | − | 2.76823i | −0.922351 | − | 0.182532i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 0.393588i | − | 0.0258403i | ||||||
\(233\) | − | 10.5108i | − | 0.688584i | −0.938863 | − | 0.344292i | \(-0.888119\pi\) | ||
0.938863 | − | 0.344292i | \(-0.111881\pi\) | |||||||
\(234\) | 5.50809 | 0.360075 | ||||||||
\(235\) | 5.21486 | − | 26.3512i | 0.340180 | − | 1.71896i | ||||
\(236\) | −0.253518 | −0.0165026 | ||||||||
\(237\) | 14.2861i | 0.927984i | ||||||||
\(238\) | − | 8.25629i | − | 0.535176i | ||||||
\(239\) | −20.0396 | −1.29625 | −0.648127 | − | 0.761532i | \(-0.724448\pi\) | ||||
−0.648127 | + | 0.761532i | \(0.724448\pi\) | |||||||
\(240\) | 4.22723 | − | 21.3606i | 0.272866 | − | 1.37882i | ||||
\(241\) | 28.4450 | 1.83230 | 0.916152 | − | 0.400832i | \(-0.131279\pi\) | ||||
0.916152 | + | 0.400832i | \(0.131279\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 9.06251i | − | 0.581361i | ||||||
\(244\) | −1.27861 | −0.0818545 | ||||||||
\(245\) | 4.31822 | + | 0.854569i | 0.275881 | + | 0.0545964i | ||||
\(246\) | −25.8652 | −1.64911 | ||||||||
\(247\) | − | 19.5600i | − | 1.24457i | ||||||
\(248\) | 1.43464i | 0.0910999i | ||||||||
\(249\) | 6.28309 | 0.398175 | ||||||||
\(250\) | −10.2323 | + | 15.4112i | −0.647148 | + | 0.974689i | ||||
\(251\) | −23.8370 | −1.50458 | −0.752289 | − | 0.658833i | \(-0.771050\pi\) | ||||
−0.752289 | + | 0.658833i | \(0.771050\pi\) | |||||||
\(252\) | − | 1.48877i | − | 0.0937838i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 4.02120 | 0.252313 | ||||||||
\(255\) | 9.63644 | + | 1.90704i | 0.603457 | + | 0.119423i | ||||
\(256\) | 15.5913 | 0.974454 | ||||||||
\(257\) | − | 24.6763i | − | 1.53927i | −0.638486 | − | 0.769633i | \(-0.720439\pi\) | ||
0.638486 | − | 0.769633i | \(-0.279561\pi\) | |||||||
\(258\) | 27.4913i | 1.71153i | ||||||||
\(259\) | 5.81665 | 0.361429 | ||||||||
\(260\) | 1.18469 | − | 5.98633i | 0.0734711 | − | 0.371257i | ||||
\(261\) | 0.169555 | 0.0104952 | ||||||||
\(262\) | 2.62824i | 0.162373i | ||||||||
\(263\) | 5.44098i | 0.335505i | 0.985829 | + | 0.167753i | \(0.0536510\pi\) | ||||
−0.985829 | + | 0.167753i | \(0.946349\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.49416 | − | 27.7625i | 0.337504 | − | 1.70544i | ||||
\(266\) | −19.6213 | −1.20306 | ||||||||
\(267\) | − | 19.5937i | − | 1.19912i | ||||||
\(268\) | − | 0.479806i | − | 0.0293088i | ||||||
\(269\) | 6.70557 | 0.408846 | 0.204423 | − | 0.978883i | \(-0.434468\pi\) | ||||
0.204423 | + | 0.978883i | \(0.434468\pi\) | |||||||
\(270\) | −15.0527 | − | 2.97891i | −0.916079 | − | 0.181291i | ||||
\(271\) | −5.05983 | −0.307363 | −0.153681 | − | 0.988120i | \(-0.549113\pi\) | ||||
−0.153681 | + | 0.988120i | \(0.549113\pi\) | |||||||
\(272\) | 10.9699i | 0.665148i | ||||||||
\(273\) | 16.3884i | 0.991873i | ||||||||
\(274\) | 30.9438 | 1.86938 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.61428 | 0.337940 | ||||||||
\(277\) | 10.6937i | 0.642522i | 0.946991 | + | 0.321261i | \(0.104107\pi\) | ||||
−0.946991 | + | 0.321261i | \(0.895893\pi\) | |||||||
\(278\) | − | 19.2385i | − | 1.15385i | ||||||
\(279\) | −0.618034 | −0.0370007 | ||||||||
\(280\) | 10.2768 | + | 2.03376i | 0.614156 | + | 0.121541i | ||||
\(281\) | −13.7197 | −0.818450 | −0.409225 | − | 0.912434i | \(-0.634201\pi\) | ||||
−0.409225 | + | 0.912434i | \(0.634201\pi\) | |||||||
\(282\) | 39.2524i | 2.33745i | ||||||||
\(283\) | − | 21.9693i | − | 1.30594i | −0.757385 | − | 0.652969i | \(-0.773523\pi\) | ||
0.757385 | − | 0.652969i | \(-0.226477\pi\) | |||||||
\(284\) | −3.42826 | −0.203430 | ||||||||
\(285\) | 4.53213 | − | 22.9013i | 0.268460 | − | 1.35655i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 17.7563i | − | 1.04812i | ||||||
\(288\) | 3.58265i | 0.211110i | ||||||||
\(289\) | 12.0511 | 0.708890 | ||||||||
\(290\) | 0.135346 | − | 0.683915i | 0.00794777 | − | 0.0401608i | ||||
\(291\) | −4.47903 | −0.262566 | ||||||||
\(292\) | − | 6.53432i | − | 0.382392i | ||||||
\(293\) | 14.0380i | 0.820110i | 0.912061 | + | 0.410055i | \(0.134491\pi\) | ||||
−0.912061 | + | 0.410055i | \(0.865509\pi\) | |||||||
\(294\) | −6.43236 | −0.375143 | ||||||||
\(295\) | 0.753889 | + | 0.149194i | 0.0438931 | + | 0.00868638i | ||||
\(296\) | −5.41627 | −0.314815 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 9.78772i | − | 0.566988i | ||||||
\(299\) | −14.2594 | −0.824644 | ||||||||
\(300\) | 2.77411 | − | 6.73442i | 0.160163 | − | 0.388812i | ||||
\(301\) | −18.8725 | −1.08779 | ||||||||
\(302\) | 21.1420i | 1.21659i | ||||||||
\(303\) | 19.5442i | 1.12278i | ||||||||
\(304\) | 26.0703 | 1.49523 | ||||||||
\(305\) | 3.80221 | + | 0.752451i | 0.217714 | + | 0.0430852i | ||||
\(306\) | −3.31193 | −0.189331 | ||||||||
\(307\) | 6.86951i | 0.392064i | 0.980598 | + | 0.196032i | \(0.0628056\pi\) | ||||
−0.980598 | + | 0.196032i | \(0.937194\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.2241 | 1.15051 | ||||||||
\(310\) | −0.493340 | + | 2.49289i | −0.0280198 | + | 0.141587i | ||||
\(311\) | −5.50157 | −0.311966 | −0.155983 | − | 0.987760i | \(-0.549854\pi\) | ||||
−0.155983 | + | 0.987760i | \(0.549854\pi\) | |||||||
\(312\) | − | 15.2604i | − | 0.863948i | ||||||
\(313\) | 14.2320i | 0.804440i | 0.915543 | + | 0.402220i | \(0.131761\pi\) | ||||
−0.915543 | + | 0.402220i | \(0.868239\pi\) | |||||||
\(314\) | −23.7411 | −1.33979 | ||||||||
\(315\) | −0.876131 | + | 4.42717i | −0.0493644 | + | 0.249443i | ||||
\(316\) | −5.33628 | −0.300189 | ||||||||
\(317\) | − | 18.6864i | − | 1.04953i | −0.851246 | − | 0.524767i | \(-0.824153\pi\) | ||
0.851246 | − | 0.524767i | \(-0.175847\pi\) | |||||||
\(318\) | 41.3547i | 2.31906i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −7.18237 | − | 1.42138i | −0.401506 | − | 0.0794575i | ||||
\(321\) | −19.8403 | −1.10738 | ||||||||
\(322\) | 14.3041i | 0.797137i | ||||||||
\(323\) | 11.7611i | 0.654408i | ||||||||
\(324\) | 8.03271 | 0.446262 | ||||||||
\(325\) | −7.04582 | + | 17.1044i | −0.390832 | + | 0.948783i | ||||
\(326\) | −6.00143 | −0.332389 | ||||||||
\(327\) | 17.3816i | 0.961202i | ||||||||
\(328\) | 16.5340i | 0.912940i | ||||||||
\(329\) | −26.9464 | −1.48560 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.468249 | 0.0257373 | 0.0128686 | − | 0.999917i | \(-0.495904\pi\) | ||||
0.0128686 | + | 0.999917i | \(0.495904\pi\) | |||||||
\(332\) | 2.34691i | 0.128804i | ||||||||
\(333\) | − | 2.33329i | − | 0.127864i | ||||||
\(334\) | 6.32166 | 0.345906 | ||||||||
\(335\) | −0.282362 | + | 1.42680i | −0.0154271 | + | 0.0779546i | ||||
\(336\) | −21.8431 | −1.19164 | ||||||||
\(337\) | − | 34.0872i | − | 1.85685i | −0.371522 | − | 0.928424i | \(-0.621164\pi\) | ||
0.371522 | − | 0.928424i | \(-0.378836\pi\) | |||||||
\(338\) | − | 1.13869i | − | 0.0619363i | ||||||
\(339\) | 0.456871 | 0.0248139 | ||||||||
\(340\) | −0.712333 | + | 3.59949i | −0.0386317 | + | 0.195210i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.87090i | 0.425610i | ||||||||
\(343\) | − | 20.1173i | − | 1.08623i | ||||||
\(344\) | 17.5735 | 0.947498 | ||||||||
\(345\) | −16.6952 | − | 3.30396i | −0.898841 | − | 0.177879i | ||||
\(346\) | 3.48644 | 0.187432 | ||||||||
\(347\) | − | 3.59292i | − | 0.192878i | −0.995339 | − | 0.0964391i | \(-0.969255\pi\) | ||
0.995339 | − | 0.0964391i | \(-0.0307453\pi\) | |||||||
\(348\) | 0.274496i | 0.0147145i | ||||||||
\(349\) | 6.37110 | 0.341037 | 0.170519 | − | 0.985354i | \(-0.445456\pi\) | ||||
0.170519 | + | 0.985354i | \(0.445456\pi\) | |||||||
\(350\) | 17.1580 | + | 7.06789i | 0.917135 | + | 0.377795i | ||||
\(351\) | −15.3446 | −0.819037 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 12.1971i | − | 0.649186i | −0.945854 | − | 0.324593i | \(-0.894773\pi\) | ||
0.945854 | − | 0.324593i | \(-0.105227\pi\) | |||||||
\(354\) | −1.12298 | −0.0596859 | ||||||||
\(355\) | 10.1946 | + | 2.01750i | 0.541076 | + | 0.107078i | ||||
\(356\) | 7.31883 | 0.387897 | ||||||||
\(357\) | − | 9.85411i | − | 0.521535i | ||||||
\(358\) | − | 8.31257i | − | 0.439333i | ||||||
\(359\) | −24.1149 | −1.27273 | −0.636367 | − | 0.771386i | \(-0.719564\pi\) | ||||
−0.636367 | + | 0.771386i | \(0.719564\pi\) | |||||||
\(360\) | 0.815824 | − | 4.12244i | 0.0429977 | − | 0.217272i | ||||
\(361\) | 8.95069 | 0.471089 | ||||||||
\(362\) | − | 25.8902i | − | 1.36076i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.12155 | −0.320856 | ||||||||
\(365\) | −3.84539 | + | 19.4312i | −0.201277 | + | 1.01707i | ||||
\(366\) | −5.66372 | −0.296047 | ||||||||
\(367\) | 20.3899i | 1.06435i | 0.846636 | + | 0.532173i | \(0.178624\pi\) | ||||
−0.846636 | + | 0.532173i | \(0.821376\pi\) | |||||||
\(368\) | − | 19.0055i | − | 0.990729i | ||||||
\(369\) | −7.12275 | −0.370796 | ||||||||
\(370\) | −9.41154 | − | 1.86253i | −0.489282 | − | 0.0968282i | ||||
\(371\) | −28.3896 | −1.47392 | ||||||||
\(372\) | − | 1.00055i | − | 0.0518759i | ||||||
\(373\) | 7.51997i | 0.389369i | 0.980866 | + | 0.194685i | \(0.0623684\pi\) | ||||
−0.980866 | + | 0.194685i | \(0.937632\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.2125 | + | 18.3937i | −0.630653 | + | 0.949845i | ||||
\(376\) | 25.0916 | 1.29400 | ||||||||
\(377\) | − | 0.697178i | − | 0.0359065i | ||||||
\(378\) | 15.3927i | 0.791716i | ||||||||
\(379\) | −23.1912 | −1.19125 | −0.595627 | − | 0.803261i | \(-0.703096\pi\) | ||||
−0.595627 | + | 0.803261i | \(0.703096\pi\) | |||||||
\(380\) | 8.55429 | + | 1.69288i | 0.438826 | + | 0.0868429i | ||||
\(381\) | 4.79942 | 0.245881 | ||||||||
\(382\) | 5.15543i | 0.263775i | ||||||||
\(383\) | 2.44039i | 0.124698i | 0.998054 | + | 0.0623491i | \(0.0198592\pi\) | ||||
−0.998054 | + | 0.0623491i | \(0.980141\pi\) | |||||||
\(384\) | 26.4246 | 1.34848 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.9442 | −0.811537 | ||||||||
\(387\) | 7.57053i | 0.384832i | ||||||||
\(388\) | − | 1.67305i | − | 0.0849362i | ||||||
\(389\) | −33.9732 | −1.72251 | −0.861254 | − | 0.508175i | \(-0.830320\pi\) | ||||
−0.861254 | + | 0.508175i | \(0.830320\pi\) | |||||||
\(390\) | 5.24768 | − | 26.5170i | 0.265726 | − | 1.34274i | ||||
\(391\) | 8.57398 | 0.433605 | ||||||||
\(392\) | 4.11181i | 0.207678i | ||||||||
\(393\) | 3.13688i | 0.158235i | ||||||||
\(394\) | −23.8216 | −1.20012 | ||||||||
\(395\) | 15.8685 | + | 3.14036i | 0.798433 | + | 0.158009i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.4961i | 1.37999i | 0.723814 | + | 0.689995i | \(0.242387\pi\) | ||||
−0.723814 | + | 0.689995i | \(0.757613\pi\) | |||||||
\(398\) | − | 24.4841i | − | 1.22728i | ||||||
\(399\) | −23.4186 | −1.17239 | ||||||||
\(400\) | −22.7974 | − | 9.39092i | −1.13987 | − | 0.469546i | ||||
\(401\) | −1.88743 | −0.0942535 | −0.0471268 | − | 0.998889i | \(-0.515006\pi\) | ||||
−0.0471268 | + | 0.998889i | \(0.515006\pi\) | |||||||
\(402\) | − | 2.12535i | − | 0.106003i | ||||||
\(403\) | 2.54124i | 0.126588i | ||||||||
\(404\) | −7.30032 | −0.363205 | ||||||||
\(405\) | −23.8870 | − | 4.72719i | −1.18695 | − | 0.234896i | ||||
\(406\) | −0.699363 | −0.0347088 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 9.17582i | 0.454271i | ||||||||
\(409\) | −13.5575 | −0.670374 | −0.335187 | − | 0.942152i | \(-0.608799\pi\) | ||||
−0.335187 | + | 0.942152i | \(0.608799\pi\) | |||||||
\(410\) | −5.68567 | + | 28.7302i | −0.280795 | + | 1.41888i | ||||
\(411\) | 36.9323 | 1.82173 | ||||||||
\(412\) | 7.55427i | 0.372172i | ||||||||
\(413\) | − | 0.770918i | − | 0.0379344i | ||||||
\(414\) | 5.73796 | 0.282005 | ||||||||
\(415\) | 1.38114 | − | 6.97904i | 0.0677975 | − | 0.342588i | ||||
\(416\) | 14.7312 | 0.722256 | ||||||||
\(417\) | − | 22.9616i | − | 1.12444i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.1368 | 1.08145 | 0.540727 | − | 0.841198i | \(-0.318149\pi\) | ||||
0.540727 | + | 0.841198i | \(0.318149\pi\) | |||||||
\(420\) | −7.16724 | − | 1.41838i | −0.349725 | − | 0.0692101i | ||||
\(421\) | 17.9026 | 0.872517 | 0.436259 | − | 0.899821i | \(-0.356303\pi\) | ||||
0.436259 | + | 0.899821i | \(0.356303\pi\) | |||||||
\(422\) | − | 11.2040i | − | 0.545400i | ||||||
\(423\) | 10.8093i | 0.525566i | ||||||||
\(424\) | 26.4355 | 1.28382 | ||||||||
\(425\) | 4.23654 | − | 10.2846i | 0.205503 | − | 0.498878i | ||||
\(426\) | −15.1858 | −0.735755 | ||||||||
\(427\) | − | 3.88809i | − | 0.188158i | ||||||
\(428\) | − | 7.41093i | − | 0.358221i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 30.5364 | + | 6.04310i | 1.47259 | + | 0.291424i | ||||
\(431\) | 33.4457 | 1.61102 | 0.805510 | − | 0.592582i | \(-0.201891\pi\) | ||||
0.805510 | + | 0.592582i | \(0.201891\pi\) | |||||||
\(432\) | − | 20.4519i | − | 0.983992i | ||||||
\(433\) | 31.4914i | 1.51338i | 0.653774 | + | 0.756690i | \(0.273185\pi\) | ||||
−0.653774 | + | 0.756690i | \(0.726815\pi\) | |||||||
\(434\) | 2.54920 | 0.122366 | ||||||||
\(435\) | 0.161539 | − | 0.816270i | 0.00774518 | − | 0.0391372i | ||||
\(436\) | −6.49251 | −0.310935 | ||||||||
\(437\) | − | 20.3763i | − | 0.974731i | ||||||
\(438\) | − | 28.9444i | − | 1.38302i | ||||||
\(439\) | −35.6208 | −1.70009 | −0.850045 | − | 0.526710i | \(-0.823425\pi\) | ||||
−0.850045 | + | 0.526710i | \(0.823425\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.77134 | −0.0843495 | ||||||||
\(442\) | 13.6180i | 0.647744i | ||||||||
\(443\) | 23.4876i | 1.11593i | 0.829865 | + | 0.557964i | \(0.188417\pi\) | ||||
−0.829865 | + | 0.557964i | \(0.811583\pi\) | |||||||
\(444\) | 3.77741 | 0.179268 | ||||||||
\(445\) | −21.7641 | − | 4.30707i | −1.03172 | − | 0.204175i | ||||
\(446\) | 14.4234 | 0.682970 | ||||||||
\(447\) | − | 11.6819i | − | 0.552535i | ||||||
\(448\) | 7.34460i | 0.347000i | ||||||||
\(449\) | 31.3920 | 1.48148 | 0.740740 | − | 0.671792i | \(-0.234475\pi\) | ||||
0.740740 | + | 0.671792i | \(0.234475\pi\) | |||||||
\(450\) | 2.83522 | − | 6.88277i | 0.133653 | − | 0.324457i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.170655i | 0.00802692i | ||||||||
\(453\) | 25.2336i | 1.18558i | ||||||||
\(454\) | 6.29971 | 0.295660 | ||||||||
\(455\) | 18.2037 | + | 3.60248i | 0.853403 | + | 0.168887i | ||||
\(456\) | 21.8066 | 1.02119 | ||||||||
\(457\) | − | 39.1106i | − | 1.82952i | −0.404000 | − | 0.914759i | \(-0.632380\pi\) | ||
0.404000 | − | 0.914759i | \(-0.367620\pi\) | |||||||
\(458\) | 4.48999i | 0.209803i | ||||||||
\(459\) | 9.22650 | 0.430656 | ||||||||
\(460\) | 1.23412 | − | 6.23615i | 0.0575414 | − | 0.290762i | ||||
\(461\) | −8.88399 | −0.413769 | −0.206884 | − | 0.978365i | \(-0.566332\pi\) | ||||
−0.206884 | + | 0.978365i | \(0.566332\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.21081i | 0.195693i | 0.995202 | + | 0.0978464i | \(0.0311954\pi\) | ||||
−0.995202 | + | 0.0978464i | \(0.968805\pi\) | |||||||
\(464\) | 0.929224 | 0.0431381 | ||||||||
\(465\) | −0.588814 | + | 2.97534i | −0.0273056 | + | 0.137978i | ||||
\(466\) | 17.3909 | 0.805620 | ||||||||
\(467\) | 6.72844i | 0.311355i | 0.987808 | + | 0.155677i | \(0.0497560\pi\) | ||||
−0.987808 | + | 0.155677i | \(0.950244\pi\) | |||||||
\(468\) | 2.45560i | 0.113510i | ||||||||
\(469\) | 1.45903 | 0.0673718 | ||||||||
\(470\) | 43.6002 | + | 8.62842i | 2.01113 | + | 0.397999i | ||||
\(471\) | −28.3356 | −1.30564 | ||||||||
\(472\) | 0.717854i | 0.0330419i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −23.6376 | −1.08571 | ||||||||
\(475\) | −24.4417 | − | 10.0683i | −1.12146 | − | 0.461964i | ||||
\(476\) | 3.68079 | 0.168709 | ||||||||
\(477\) | 11.3882i | 0.521431i | ||||||||
\(478\) | − | 33.1572i | − | 1.51657i | ||||||
\(479\) | −20.8094 | −0.950806 | −0.475403 | − | 0.879768i | \(-0.657698\pi\) | ||||
−0.475403 | + | 0.879768i | \(0.657698\pi\) | |||||||
\(480\) | 17.2476 | + | 3.41327i | 0.787241 | + | 0.155794i | ||||
\(481\) | −9.59406 | −0.437452 | ||||||||
\(482\) | 47.0646i | 2.14373i | ||||||||
\(483\) | 17.0723i | 0.776818i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.984576 | + | 4.97516i | −0.0447073 | + | 0.225910i | ||||
\(486\) | 14.9947 | 0.680172 | ||||||||
\(487\) | 15.7794i | 0.715032i | 0.933907 | + | 0.357516i | \(0.116376\pi\) | ||||
−0.933907 | + | 0.357516i | \(0.883624\pi\) | |||||||
\(488\) | 3.62047i | 0.163891i | ||||||||
\(489\) | −7.16287 | −0.323916 | ||||||||
\(490\) | −1.41395 | + | 7.14485i | −0.0638760 | + | 0.322771i | ||||
\(491\) | 19.3303 | 0.872366 | 0.436183 | − | 0.899858i | \(-0.356330\pi\) | ||||
0.436183 | + | 0.899858i | \(0.356330\pi\) | |||||||
\(492\) | − | 11.5312i | − | 0.519865i | ||||||
\(493\) | 0.419203i | 0.0188799i | ||||||||
\(494\) | 32.3637 | 1.45611 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.38705 | −0.152083 | ||||||||
\(497\) | − | 10.4249i | − | 0.467622i | ||||||
\(498\) | 10.3959i | 0.465851i | ||||||||
\(499\) | 41.4596 | 1.85599 | 0.927994 | − | 0.372594i | \(-0.121532\pi\) | ||||
0.927994 | + | 0.372594i | \(0.121532\pi\) | |||||||
\(500\) | −6.87057 | − | 4.56174i | −0.307261 | − | 0.204007i | ||||
\(501\) | 7.54507 | 0.337089 | ||||||||
\(502\) | − | 39.4403i | − | 1.76031i | ||||||
\(503\) | − | 32.6613i | − | 1.45630i | −0.685420 | − | 0.728148i | \(-0.740381\pi\) | ||
0.685420 | − | 0.728148i | \(-0.259619\pi\) | |||||||
\(504\) | −4.21556 | −0.187776 | ||||||||
\(505\) | 21.7090 | + | 4.29618i | 0.966039 | + | 0.191178i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.35905i | − | 0.0603576i | ||||||
\(508\) | 1.79272i | 0.0795391i | ||||||||
\(509\) | −16.6452 | −0.737785 | −0.368892 | − | 0.929472i | \(-0.620263\pi\) | ||||
−0.368892 | + | 0.929472i | \(0.620263\pi\) | |||||||
\(510\) | −3.15535 | + | 15.9443i | −0.139721 | + | 0.706025i | ||||
\(511\) | 19.8701 | 0.879000 | ||||||||
\(512\) | − | 0.964978i | − | 0.0426464i | ||||||
\(513\) | − | 21.9270i | − | 0.968102i | ||||||
\(514\) | 40.8290 | 1.80089 | ||||||||
\(515\) | 4.44563 | − | 22.4642i | 0.195898 | − | 0.989891i | ||||
\(516\) | −12.2561 | −0.539543 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 9.62412i | 0.422860i | ||||||||
\(519\) | 4.16116 | 0.182655 | ||||||||
\(520\) | −16.9507 | − | 3.35452i | −0.743337 | − | 0.147105i | ||||
\(521\) | 14.0563 | 0.615816 | 0.307908 | − | 0.951416i | \(-0.400371\pi\) | ||||
0.307908 | + | 0.951416i | \(0.400371\pi\) | |||||||
\(522\) | 0.280543i | 0.0122790i | ||||||||
\(523\) | − | 15.6677i | − | 0.685101i | −0.939499 | − | 0.342550i | \(-0.888709\pi\) | ||
0.939499 | − | 0.342550i | \(-0.111291\pi\) | |||||||
\(524\) | −1.17171 | −0.0511866 | ||||||||
\(525\) | 20.4786 | + | 8.43572i | 0.893758 | + | 0.368165i | ||||
\(526\) | −9.00255 | −0.392530 | ||||||||
\(527\) | − | 1.52801i | − | 0.0665611i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.14550 | 0.354152 | ||||||||
\(530\) | 45.9354 | + | 9.09054i | 1.99531 | + | 0.394868i | ||||
\(531\) | −0.309246 | −0.0134202 | ||||||||
\(532\) | − | 8.74751i | − | 0.379253i | ||||||
\(533\) | 29.2874i | 1.26858i | ||||||||
\(534\) | 32.4195 | 1.40293 | ||||||||
\(535\) | −4.36127 | + | 22.0379i | −0.188554 | + | 0.952783i | ||||
\(536\) | −1.35860 | −0.0586827 | ||||||||
\(537\) | − | 9.92128i | − | 0.428135i | ||||||
\(538\) | 11.0949i | 0.478336i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.32805 | − | 6.71075i | 0.0571501 | − | 0.288785i | ||||
\(541\) | −39.6384 | −1.70419 | −0.852094 | − | 0.523389i | \(-0.824667\pi\) | ||||
−0.852094 | + | 0.523389i | \(0.824667\pi\) | |||||||
\(542\) | − | 8.37190i | − | 0.359604i | ||||||
\(543\) | − | 30.9007i | − | 1.32608i | ||||||
\(544\) | −8.85764 | −0.379768 | ||||||||
\(545\) | 19.3068 | + | 3.82079i | 0.827014 | + | 0.163665i | ||||
\(546\) | −27.1160 | −1.16046 | ||||||||
\(547\) | 41.1664i | 1.76015i | 0.474835 | + | 0.880075i | \(0.342508\pi\) | ||||
−0.474835 | + | 0.880075i | \(0.657492\pi\) | |||||||
\(548\) | 13.7953i | 0.589305i | ||||||||
\(549\) | −1.55967 | −0.0665651 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.996247 | 0.0424415 | ||||||||
\(552\) | − | 15.8972i | − | 0.676630i | ||||||
\(553\) | − | 16.2270i | − | 0.690041i | ||||||
\(554\) | −17.6936 | −0.751728 | ||||||||
\(555\) | −11.2329 | − | 2.22298i | −0.476811 | − | 0.0943601i | ||||
\(556\) | 8.57683 | 0.363739 | ||||||||
\(557\) | 29.8760i | 1.26589i | 0.774199 | + | 0.632943i | \(0.218153\pi\) | ||||
−0.774199 | + | 0.632943i | \(0.781847\pi\) | |||||||
\(558\) | − | 1.02259i | − | 0.0432896i | ||||||
\(559\) | 31.1286 | 1.31660 | ||||||||
\(560\) | −4.80152 | + | 24.2625i | −0.202901 | + | 1.02528i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 22.7004i | − | 0.957558i | ||||||
\(563\) | − | 2.15779i | − | 0.0909401i | −0.998966 | − | 0.0454701i | \(-0.985521\pi\) | ||
0.998966 | − | 0.0454701i | \(-0.0144786\pi\) | |||||||
\(564\) | −17.4994 | −0.736857 | ||||||||
\(565\) | 0.100429 | − | 0.507477i | 0.00422508 | − | 0.0213497i | ||||
\(566\) | 36.3500 | 1.52790 | ||||||||
\(567\) | 24.4265i | 1.02582i | ||||||||
\(568\) | 9.70734i | 0.407311i | ||||||||
\(569\) | −0.717288 | −0.0300703 | −0.0150351 | − | 0.999887i | \(-0.504786\pi\) | ||||
−0.0150351 | + | 0.999887i | \(0.504786\pi\) | |||||||
\(570\) | 37.8920 | + | 7.49877i | 1.58712 | + | 0.314089i | ||||
\(571\) | −21.6311 | −0.905235 | −0.452617 | − | 0.891705i | \(-0.649510\pi\) | ||||
−0.452617 | + | 0.891705i | \(0.649510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.15315i | 0.257051i | ||||||||
\(574\) | 29.3792 | 1.22626 | ||||||||
\(575\) | −7.33985 | + | 17.8182i | −0.306093 | + | 0.743071i | ||||
\(576\) | 2.94622 | 0.122759 | ||||||||
\(577\) | 23.4276i | 0.975303i | 0.873038 | + | 0.487652i | \(0.162146\pi\) | ||||
−0.873038 | + | 0.487652i | \(0.837854\pi\) | |||||||
\(578\) | 19.9396i | 0.829377i | ||||||||
\(579\) | −19.0298 | −0.790852 | ||||||||
\(580\) | 0.304901 | + | 0.0603393i | 0.0126603 | + | 0.00250545i | ||||
\(581\) | −7.13668 | −0.296079 | ||||||||
\(582\) | − | 7.41093i | − | 0.307193i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −18.5023 | −0.765633 | ||||||||
\(585\) | 1.44510 | − | 7.30224i | 0.0597476 | − | 0.301911i | ||||
\(586\) | −23.2271 | −0.959501 | ||||||||
\(587\) | − | 2.24734i | − | 0.0927576i | −0.998924 | − | 0.0463788i | \(-0.985232\pi\) | ||
0.998924 | − | 0.0463788i | \(-0.0147681\pi\) | |||||||
\(588\) | − | 2.86766i | − | 0.118260i | ||||||
\(589\) | −3.63135 | −0.149627 | ||||||||
\(590\) | −0.246853 | + | 1.24737i | −0.0101628 | + | 0.0513535i | ||||
\(591\) | −28.4318 | −1.16953 | ||||||||
\(592\) | − | 12.7873i | − | 0.525555i | ||||||
\(593\) | − | 25.4034i | − | 1.04319i | −0.853193 | − | 0.521596i | \(-0.825337\pi\) | ||
0.853193 | − | 0.521596i | \(-0.174663\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.9456 | − | 2.16612i | −0.448726 | − | 0.0888022i | ||||
\(596\) | 4.36353 | 0.178737 | ||||||||
\(597\) | − | 29.2224i | − | 1.19600i | ||||||
\(598\) | − | 23.5934i | − | 0.964806i | ||||||
\(599\) | 18.2253 | 0.744667 | 0.372333 | − | 0.928099i | \(-0.378558\pi\) | ||||
0.372333 | + | 0.928099i | \(0.378558\pi\) | |||||||
\(600\) | −19.0690 | − | 7.85507i | −0.778487 | − | 0.320682i | ||||
\(601\) | −34.6398 | −1.41299 | −0.706494 | − | 0.707719i | \(-0.749724\pi\) | ||||
−0.706494 | + | 0.707719i | \(0.749724\pi\) | |||||||
\(602\) | − | 31.2261i | − | 1.27268i | ||||||
\(603\) | − | 0.585276i | − | 0.0238343i | ||||||
\(604\) | −9.42547 | −0.383517 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −32.3375 | −1.31362 | ||||||||
\(607\) | 25.4482i | 1.03291i | 0.856314 | + | 0.516456i | \(0.172749\pi\) | ||||
−0.856314 | + | 0.516456i | \(0.827251\pi\) | |||||||
\(608\) | 21.0504i | 0.853708i | ||||||||
\(609\) | −0.834708 | −0.0338241 | ||||||||
\(610\) | −1.24499 | + | 6.29107i | −0.0504083 | + | 0.254718i | ||||
\(611\) | 44.4458 | 1.79809 | ||||||||
\(612\) | − | 1.47652i | − | 0.0596846i | ||||||
\(613\) | 37.0616i | 1.49690i | 0.663189 | + | 0.748452i | \(0.269203\pi\) | ||||
−0.663189 | + | 0.748452i | \(0.730797\pi\) | |||||||
\(614\) | −11.3662 | −0.458701 | ||||||||
\(615\) | −6.78600 | + | 34.2903i | −0.273638 | + | 1.38272i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 27.5937i | − | 1.11088i | −0.831557 | − | 0.555439i | \(-0.812550\pi\) | ||
0.831557 | − | 0.555439i | \(-0.187450\pi\) | |||||||
\(618\) | 33.4624i | 1.34605i | ||||||||
\(619\) | −20.4435 | −0.821694 | −0.410847 | − | 0.911704i | \(-0.634767\pi\) | ||||
−0.410847 | + | 0.911704i | \(0.634767\pi\) | |||||||
\(620\) | −1.11137 | − | 0.219939i | −0.0446338 | − | 0.00883296i | ||||
\(621\) | −15.9850 | −0.641456 | ||||||||
\(622\) | − | 9.10280i | − | 0.364989i | ||||||
\(623\) | 22.2557i | 0.891654i | ||||||||
\(624\) | 36.0283 | 1.44229 | ||||||||
\(625\) | 17.7465 | + | 17.6086i | 0.709861 | + | 0.704342i | ||||
\(626\) | −23.5480 | −0.941167 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 10.5842i | − | 0.422354i | ||||||
\(629\) | 5.76876 | 0.230016 | ||||||||
\(630\) | −7.32512 | − | 1.44963i | −0.291840 | − | 0.0577546i | ||||
\(631\) | 0.759137 | 0.0302208 | 0.0151104 | − | 0.999886i | \(-0.495190\pi\) | ||||
0.0151104 | + | 0.999886i | \(0.495190\pi\) | |||||||
\(632\) | 15.1100i | 0.601045i | ||||||||
\(633\) | − | 13.3722i | − | 0.531498i | ||||||
\(634\) | 30.9182 | 1.22792 | ||||||||
\(635\) | 1.05500 | − | 5.33103i | 0.0418665 | − | 0.211555i | ||||
\(636\) | −18.4366 | −0.731060 | ||||||||
\(637\) | 7.28342i | 0.288579i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.18186 | −0.165432 | ||||||||
\(640\) | 5.80863 | − | 29.3516i | 0.229606 | − | 1.16022i | ||||
\(641\) | −14.9050 | −0.588712 | −0.294356 | − | 0.955696i | \(-0.595105\pi\) | ||||
−0.294356 | + | 0.955696i | \(0.595105\pi\) | |||||||
\(642\) | − | 32.8274i | − | 1.29559i | ||||||
\(643\) | − | 27.6346i | − | 1.08980i | −0.838501 | − | 0.544900i | \(-0.816568\pi\) | ||
0.838501 | − | 0.544900i | \(-0.183432\pi\) | |||||||
\(644\) | −6.37701 | −0.251289 | ||||||||
\(645\) | 36.4460 | + | 7.21260i | 1.43506 | + | 0.283996i | ||||
\(646\) | −19.4598 | −0.765635 | ||||||||
\(647\) | 24.9785i | 0.982008i | 0.871157 | + | 0.491004i | \(0.163370\pi\) | ||||
−0.871157 | + | 0.491004i | \(0.836630\pi\) | |||||||
\(648\) | − | 22.7452i | − | 0.893514i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −28.3007 | − | 11.6579i | −1.11004 | − | 0.457260i | ||||
\(651\) | 3.04254 | 0.119247 | ||||||||
\(652\) | − | 2.67554i | − | 0.104782i | ||||||
\(653\) | − | 27.7630i | − | 1.08645i | −0.839587 | − | 0.543225i | \(-0.817203\pi\) | ||
0.839587 | − | 0.543225i | \(-0.182797\pi\) | |||||||
\(654\) | −28.7592 | −1.12457 | ||||||||
\(655\) | 3.48434 | + | 0.689545i | 0.136144 | + | 0.0269428i | ||||
\(656\) | −39.0353 | −1.52407 | ||||||||
\(657\) | − | 7.97068i | − | 0.310966i | ||||||
\(658\) | − | 44.5851i | − | 1.73811i | ||||||
\(659\) | 21.5863 | 0.840883 | 0.420442 | − | 0.907320i | \(-0.361875\pi\) | ||||
0.420442 | + | 0.907320i | \(0.361875\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0174 | −0.623003 | −0.311502 | − | 0.950246i | \(-0.600832\pi\) | ||||
−0.311502 | + | 0.950246i | \(0.600832\pi\) | |||||||
\(662\) | 0.774756i | 0.0301118i | ||||||||
\(663\) | 16.2535i | 0.631234i | ||||||||
\(664\) | 6.64544 | 0.257893 | ||||||||
\(665\) | −5.14784 | + | 26.0125i | −0.199625 | + | 1.00872i | ||||
\(666\) | 3.86062 | 0.149596 | ||||||||
\(667\) | − | 0.726273i | − | 0.0281214i | ||||||
\(668\) | 2.81830i | 0.109043i | ||||||||
\(669\) | 17.2148 | 0.665561 | ||||||||
\(670\) | −2.36076 | − | 0.467191i | −0.0912042 | − | 0.0180492i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 17.6372i | − | 0.680368i | ||||||
\(673\) | − | 31.3469i | − | 1.20834i | −0.796857 | − | 0.604168i | \(-0.793506\pi\) | ||
0.796857 | − | 0.604168i | \(-0.206494\pi\) | |||||||
\(674\) | 56.4001 | 2.17245 | ||||||||
\(675\) | −7.89845 | + | 19.1743i | −0.304012 | + | 0.738018i | ||||
\(676\) | 0.507645 | 0.0195248 | ||||||||
\(677\) | − | 30.6664i | − | 1.17860i | −0.807913 | − | 0.589302i | \(-0.799403\pi\) | ||
0.807913 | − | 0.589302i | \(-0.200597\pi\) | |||||||
\(678\) | 0.755931i | 0.0290314i | ||||||||
\(679\) | 5.08754 | 0.195242 | ||||||||
\(680\) | 10.1922 | + | 2.01702i | 0.390853 | + | 0.0773491i | ||||
\(681\) | 7.51888 | 0.288124 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.27236i | 0.125213i | 0.998038 | + | 0.0626066i | \(0.0199414\pi\) | ||||
−0.998038 | + | 0.0626066i | \(0.980059\pi\) | |||||||
\(684\) | −3.50898 | −0.134169 | ||||||||
\(685\) | 8.11841 | − | 41.0231i | 0.310188 | − | 1.56741i | ||||
\(686\) | 33.2857 | 1.27085 | ||||||||
\(687\) | 5.35892i | 0.204456i | ||||||||
\(688\) | 41.4893i | 1.58176i | ||||||||
\(689\) | 46.8263 | 1.78394 | ||||||||
\(690\) | 5.46667 | − | 27.6236i | 0.208113 | − | 1.05161i | ||||
\(691\) | −36.4946 | −1.38832 | −0.694160 | − | 0.719821i | \(-0.744224\pi\) | ||||
−0.694160 | + | 0.719821i | \(0.744224\pi\) | |||||||
\(692\) | 1.55431i | 0.0590862i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.94478 | 0.225661 | ||||||||
\(695\) | −25.5050 | − | 5.04740i | −0.967459 | − | 0.191459i | ||||
\(696\) | 0.777253 | 0.0294617 | ||||||||
\(697\) | − | 17.6101i | − | 0.667029i | ||||||
\(698\) | 10.5415i | 0.399002i | ||||||||
\(699\) | 20.7566 | 0.785085 | ||||||||
\(700\) | −3.15099 | + | 7.64933i | −0.119096 | + | 0.289118i | ||||
\(701\) | 46.5607 | 1.75857 | 0.879286 | − | 0.476293i | \(-0.158020\pi\) | ||||
0.879286 | + | 0.476293i | \(0.158020\pi\) | |||||||
\(702\) | − | 25.3890i | − | 0.958245i | ||||||
\(703\) | − | 13.7096i | − | 0.517068i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 52.0381 | + | 10.2983i | 1.95987 | + | 0.387855i | ||||
\(706\) | 20.1811 | 0.759525 | ||||||||
\(707\) | − | 22.1994i | − | 0.834894i | ||||||
\(708\) | − | 0.500645i | − | 0.0188154i | ||||||
\(709\) | 35.5966 | 1.33686 | 0.668429 | − | 0.743776i | \(-0.266967\pi\) | ||||
0.668429 | + | 0.743776i | \(0.266967\pi\) | |||||||
\(710\) | −3.33813 | + | 16.8679i | −0.125278 | + | 0.633040i | ||||
\(711\) | −6.50930 | −0.244118 | ||||||||
\(712\) | − | 20.7237i | − | 0.776655i | ||||||
\(713\) | 2.64729i | 0.0991418i | ||||||||
\(714\) | 16.3044 | 0.610178 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.70588 | 0.138495 | ||||||||
\(717\) | − | 39.5740i | − | 1.47792i | ||||||
\(718\) | − | 39.9000i | − | 1.48906i | ||||||
\(719\) | −22.0913 | −0.823866 | −0.411933 | − | 0.911214i | \(-0.635146\pi\) | ||||
−0.411933 | + | 0.911214i | \(0.635146\pi\) | |||||||
\(720\) | 9.73269 | + | 1.92608i | 0.362716 | + | 0.0717809i | ||||
\(721\) | −22.9716 | −0.855507 | ||||||||
\(722\) | 14.8097i | 0.551158i | ||||||||
\(723\) | 56.1728i | 2.08909i | ||||||||
\(724\) | 11.5423 | 0.428966 | ||||||||
\(725\) | −0.871176 | − | 0.358863i | −0.0323547 | − | 0.0133278i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.5415i | 1.68904i | 0.535522 | + | 0.844521i | \(0.320115\pi\) | ||||
−0.535522 | + | 0.844521i | \(0.679885\pi\) | |||||||
\(728\) | 17.3336i | 0.642425i | ||||||||
\(729\) | −14.7727 | −0.547137 | ||||||||
\(730\) | −32.1504 | − | 6.36252i | −1.18994 | − | 0.235487i | ||||
\(731\) | −18.7171 | −0.692278 | ||||||||
\(732\) | − | 2.52498i | − | 0.0933260i | ||||||
\(733\) | − | 11.3789i | − | 0.420289i | −0.977670 | − | 0.210145i | \(-0.932607\pi\) | ||
0.977670 | − | 0.210145i | \(-0.0673935\pi\) | |||||||
\(734\) | −33.7368 | −1.24525 | ||||||||
\(735\) | −1.68759 | + | 8.52757i | −0.0622478 | + | 0.314544i | ||||
\(736\) | 15.3459 | 0.565659 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 11.7852i | − | 0.433818i | ||||||
\(739\) | 4.33778 | 0.159568 | 0.0797838 | − | 0.996812i | \(-0.474577\pi\) | ||||
0.0797838 | + | 0.996812i | \(0.474577\pi\) | |||||||
\(740\) | 0.830346 | − | 4.19582i | 0.0305241 | − | 0.154241i | ||||
\(741\) | 38.6269 | 1.41900 | ||||||||
\(742\) | − | 46.9730i | − | 1.72443i | ||||||
\(743\) | − | 17.2945i | − | 0.634473i | −0.948346 | − | 0.317237i | \(-0.897245\pi\) | ||
0.948346 | − | 0.317237i | \(-0.102755\pi\) | |||||||
\(744\) | −2.83311 | −0.103867 | ||||||||
\(745\) | −12.9759 | − | 2.56790i | −0.475399 | − | 0.0940807i | ||||
\(746\) | −12.4424 | −0.455549 | ||||||||
\(747\) | 2.86281i | 0.104745i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.5357 | 0.823437 | ||||||||
\(750\) | −30.4338 | − | 20.2067i | −1.11129 | − | 0.737843i | ||||
\(751\) | −31.5130 | −1.14993 | −0.574963 | − | 0.818179i | \(-0.694984\pi\) | ||||
−0.574963 | + | 0.818179i | \(0.694984\pi\) | |||||||
\(752\) | 59.2390i | 2.16022i | ||||||||
\(753\) | − | 47.0730i | − | 1.71544i | ||||||
\(754\) | 1.15354 | 0.0420094 | ||||||||
\(755\) | 28.0286 | + | 5.54681i | 1.02006 | + | 0.201869i | ||||
\(756\) | −6.86233 | −0.249581 | ||||||||
\(757\) | 9.27739i | 0.337192i | 0.985685 | + | 0.168596i | \(0.0539234\pi\) | ||||
−0.985685 | + | 0.168596i | \(0.946077\pi\) | |||||||
\(758\) | − | 38.3718i | − | 1.39373i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.79350 | − | 24.2220i | 0.173879 | − | 0.878626i | ||||
\(761\) | −4.15810 | −0.150731 | −0.0753655 | − | 0.997156i | \(-0.524012\pi\) | ||||
−0.0753655 | + | 0.997156i | \(0.524012\pi\) | |||||||
\(762\) | 7.94102i | 0.287673i | ||||||||
\(763\) | − | 19.7429i | − | 0.714742i | ||||||
\(764\) | −2.29838 | −0.0831524 | ||||||||
\(765\) | −0.868918 | + | 4.39073i | −0.0314158 | + | 0.158747i | ||||
\(766\) | −4.03783 | −0.145893 | ||||||||
\(767\) | 1.27156i | 0.0459135i | ||||||||
\(768\) | 30.7894i | 1.11102i | ||||||||
\(769\) | −16.8800 | −0.608709 | −0.304355 | − | 0.952559i | \(-0.598441\pi\) | ||||
−0.304355 | + | 0.952559i | \(0.598441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 48.7305 | 1.75499 | ||||||||
\(772\) | − | 7.10818i | − | 0.255829i | ||||||
\(773\) | 8.47760i | 0.304918i | 0.988310 | + | 0.152459i | \(0.0487192\pi\) | ||||
−0.988310 | + | 0.152459i | \(0.951281\pi\) | |||||||
\(774\) | −12.5261 | −0.450240 | ||||||||
\(775\) | 3.17547 | + | 1.30807i | 0.114066 | + | 0.0469872i | ||||
\(776\) | −4.73735 | −0.170061 | ||||||||
\(777\) | 11.4866i | 0.412081i | ||||||||
\(778\) | − | 56.2114i | − | 2.01527i | ||||||
\(779\) | −41.8508 | −1.49946 | ||||||||
\(780\) | 11.8217 | + | 2.33950i | 0.423286 | + | 0.0837676i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 14.1863i | 0.507303i | ||||||||
\(783\) | − | 0.781546i | − | 0.0279302i | ||||||
\(784\) | −9.70760 | −0.346700 | ||||||||
\(785\) | −6.22870 | + | 31.4742i | −0.222312 | + | 1.12336i | ||||
\(786\) | −5.19022 | −0.185129 | ||||||||
\(787\) | 53.6166i | 1.91122i | 0.294628 | + | 0.955612i | \(0.404804\pi\) | ||||
−0.294628 | + | 0.955612i | \(0.595196\pi\) | |||||||
\(788\) | − | 10.6201i | − | 0.378325i | ||||||
\(789\) | −10.7448 | −0.382525 | ||||||||
\(790\) | −5.19598 | + | 26.2558i | −0.184865 | + | 0.934139i | ||||
\(791\) | −0.518940 | −0.0184514 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.41307i | 0.227735i | ||||||||
\(794\) | −45.4946 | −1.61454 | ||||||||
\(795\) | 54.8251 | + | 10.8498i | 1.94445 | + | 0.384803i | ||||
\(796\) | 10.9154 | 0.386887 | ||||||||
\(797\) | 28.5448i | 1.01111i | 0.862795 | + | 0.505554i | \(0.168712\pi\) | ||||
−0.862795 | + | 0.505554i | \(0.831288\pi\) | |||||||
\(798\) | − | 38.7479i | − | 1.37166i | ||||||
\(799\) | −26.7246 | −0.945448 | ||||||||
\(800\) | 7.58268 | − | 18.4077i | 0.268088 | − | 0.650811i | ||||
\(801\) | 8.92765 | 0.315443 | ||||||||
\(802\) | − | 3.12290i | − | 0.110273i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.947515 | 0.0334163 | ||||||||
\(805\) | 18.9634 | + | 3.75282i | 0.668371 | + | 0.132270i | ||||
\(806\) | −4.20469 | −0.148104 | ||||||||
\(807\) | 13.2421i | 0.466143i | ||||||||
\(808\) | 20.6713i | 0.727215i | ||||||||
\(809\) | −36.9460 | −1.29895 | −0.649477 | − | 0.760382i | \(-0.725012\pi\) | ||||
−0.649477 | + | 0.760382i | \(0.725012\pi\) | |||||||
\(810\) | 7.82152 | − | 39.5229i | 0.274820 | − | 1.38869i | ||||
\(811\) | −38.3768 | −1.34759 | −0.673795 | − | 0.738918i | \(-0.735337\pi\) | ||||
−0.673795 | + | 0.738918i | \(0.735337\pi\) | |||||||
\(812\) | − | 0.311788i | − | 0.0109416i | ||||||
\(813\) | − | 9.99209i | − | 0.350438i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.57453 | + | 7.95628i | −0.0551535 | + | 0.278696i | ||||
\(816\) | −21.6632 | −0.758365 | ||||||||
\(817\) | 44.4818i | 1.55622i | ||||||||
\(818\) | − | 22.4319i | − | 0.784314i | ||||||
\(819\) | −7.46718 | −0.260924 | ||||||||
\(820\) | −12.8084 | − | 2.53477i | −0.447289 | − | 0.0885178i | ||||
\(821\) | −10.2496 | −0.357715 | −0.178858 | − | 0.983875i | \(-0.557240\pi\) | ||||
−0.178858 | + | 0.983875i | \(0.557240\pi\) | |||||||
\(822\) | 61.1074i | 2.13137i | ||||||||
\(823\) | − | 25.2296i | − | 0.879448i | −0.898133 | − | 0.439724i | \(-0.855076\pi\) | ||
0.898133 | − | 0.439724i | \(-0.144924\pi\) | |||||||
\(824\) | 21.3904 | 0.745170 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.27555 | 0.0443820 | ||||||||
\(827\) | − | 18.3485i | − | 0.638041i | −0.947748 | − | 0.319020i | \(-0.896646\pi\) | ||
0.947748 | − | 0.319020i | \(-0.103354\pi\) | |||||||
\(828\) | 2.55808i | 0.0888993i | ||||||||
\(829\) | −24.3826 | −0.846842 | −0.423421 | − | 0.905933i | \(-0.639171\pi\) | ||||
−0.423421 | + | 0.905933i | \(0.639171\pi\) | |||||||
\(830\) | 11.5474 | + | 2.28521i | 0.400816 | + | 0.0793208i | ||||
\(831\) | −21.1178 | −0.732567 | ||||||||
\(832\) | − | 12.1143i | − | 0.419987i | ||||||
\(833\) | − | 4.37941i | − | 0.151737i | ||||||
\(834\) | 37.9919 | 1.31555 | ||||||||
\(835\) | 1.65855 | − | 8.38081i | 0.0573964 | − | 0.290030i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.84876i | 0.0984676i | ||||||||
\(838\) | 36.6272i | 1.26526i | ||||||||
\(839\) | 42.2808 | 1.45970 | 0.729848 | − | 0.683609i | \(-0.239591\pi\) | ||||
0.729848 | + | 0.683609i | \(0.239591\pi\) | |||||||
\(840\) | −4.01625 | + | 20.2945i | −0.138574 | + | 0.700227i | ||||
\(841\) | −28.9645 | −0.998776 | ||||||||
\(842\) | 29.6212i | 1.02082i | ||||||||
\(843\) | − | 27.0935i | − | 0.933151i | ||||||
\(844\) | 4.99491 | 0.171932 | ||||||||
\(845\) | −1.50959 | − | 0.298745i | −0.0519314 | − | 0.0102771i | ||||
\(846\) | −17.8849 | −0.614895 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 62.4117i | 2.14323i | ||||||||
\(849\) | 43.3847 | 1.48896 | ||||||||
\(850\) | 17.0168 | + | 7.00971i | 0.583670 | + | 0.240431i | ||||
\(851\) | −9.99444 | −0.342605 | ||||||||
\(852\) | − | 6.77009i | − | 0.231939i | ||||||
\(853\) | − | 15.3885i | − | 0.526891i | −0.964674 | − | 0.263445i | \(-0.915141\pi\) | ||
0.964674 | − | 0.263445i | \(-0.0848589\pi\) | |||||||
\(854\) | 6.43317 | 0.220138 | ||||||||
\(855\) | 10.4347 | + | 2.06501i | 0.356859 | + | 0.0706218i | ||||
\(856\) | −20.9845 | −0.717236 | ||||||||
\(857\) | 36.1038i | 1.23328i | 0.787245 | + | 0.616641i | \(0.211507\pi\) | ||||
−0.787245 | + | 0.616641i | \(0.788493\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.3509 | −1.64971 | −0.824855 | − | 0.565344i | \(-0.808743\pi\) | ||||
−0.824855 | + | 0.565344i | \(0.808743\pi\) | |||||||
\(860\) | −2.69411 | + | 13.6136i | −0.0918685 | + | 0.464221i | ||||
\(861\) | 35.0648 | 1.19501 | ||||||||
\(862\) | 55.3386i | 1.88484i | ||||||||
\(863\) | − | 37.1887i | − | 1.26592i | −0.774186 | − | 0.632959i | \(-0.781840\pi\) | ||
0.774186 | − | 0.632959i | \(-0.218160\pi\) | |||||||
\(864\) | 16.5139 | 0.561813 | ||||||||
\(865\) | 0.914702 | − | 4.62208i | 0.0311008 | − | 0.157155i | ||||
\(866\) | −52.1051 | −1.77060 | ||||||||
\(867\) | 23.7984i | 0.808237i | ||||||||
\(868\) | 1.13648i | 0.0385745i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.35059 | + | 0.267279i | 0.0457892 | + | 0.00906160i | ||||
\(871\) | −2.40655 | −0.0815427 | ||||||||
\(872\) | 18.3840i | 0.622560i | ||||||||
\(873\) | − | 2.04082i | − | 0.0690712i | ||||||
\(874\) | 33.7143 | 1.14040 | ||||||||
\(875\) | 13.8717 | − | 20.8926i | 0.468949 | − | 0.706297i | ||||
\(876\) | 12.9039 | 0.435982 | ||||||||
\(877\) | − | 25.7932i | − | 0.870976i | −0.900195 | − | 0.435488i | \(-0.856576\pi\) | ||
0.900195 | − | 0.435488i | \(-0.143424\pi\) | |||||||
\(878\) | − | 58.9376i | − | 1.98905i | ||||||
\(879\) | −27.7221 | −0.935044 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.6820 | −1.53906 | −0.769532 | − | 0.638608i | \(-0.779511\pi\) | ||||
−0.769532 | + | 0.638608i | \(0.779511\pi\) | |||||||
\(882\) | − | 2.93083i | − | 0.0986861i | ||||||
\(883\) | 4.96631i | 0.167130i | 0.996502 | + | 0.0835648i | \(0.0266306\pi\) | ||||
−0.996502 | + | 0.0835648i | \(0.973369\pi\) | |||||||
\(884\) | −6.07115 | −0.204195 | ||||||||
\(885\) | −0.294626 | + | 1.48877i | −0.00990373 | + | 0.0500445i | ||||
\(886\) | −38.8621 | −1.30560 | ||||||||
\(887\) | 28.9232i | 0.971147i | 0.874196 | + | 0.485573i | \(0.161389\pi\) | ||||
−0.874196 | + | 0.485573i | \(0.838611\pi\) | |||||||
\(888\) | − | 10.6960i | − | 0.358934i | ||||||
\(889\) | −5.45144 | −0.182836 | ||||||||
\(890\) | 7.12641 | − | 36.0104i | 0.238878 | − | 1.20707i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.43021i | 0.215299i | ||||||||
\(893\) | 63.5117i | 2.12534i | ||||||||
\(894\) | 19.3287 | 0.646448 | ||||||||
\(895\) | −11.0202 | − | 2.18088i | −0.368365 | − | 0.0728989i | ||||
\(896\) | −30.0146 | −1.00272 | ||||||||
\(897\) | − | 28.1594i | − | 0.940213i | ||||||
\(898\) | 51.9406i | 1.73328i | ||||||||
\(899\) | −0.129432 | −0.00431681 | ||||||||
\(900\) | 3.06846 | + | 1.26399i | 0.102282 | + | 0.0421329i | ||||
\(901\) | −28.1559 | −0.938010 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 37.2692i | − | 1.24024i | ||||||
\(904\) | 0.483220 | 0.0160717 | ||||||||
\(905\) | −34.3234 | − | 6.79255i | −1.14095 | − | 0.225792i | ||||
\(906\) | −41.7510 | −1.38708 | ||||||||
\(907\) | − | 13.2527i | − | 0.440049i | −0.975494 | − | 0.220024i | \(-0.929386\pi\) | ||
0.975494 | − | 0.220024i | \(-0.0706137\pi\) | |||||||
\(908\) | 2.80852i | 0.0932040i | ||||||||
\(909\) | −8.90507 | −0.295363 | ||||||||
\(910\) | −5.96060 | + | 30.1195i | −0.197592 | + | 0.998452i | ||||
\(911\) | 13.7326 | 0.454982 | 0.227491 | − | 0.973780i | \(-0.426948\pi\) | ||||
0.227491 | + | 0.973780i | \(0.426948\pi\) | |||||||
\(912\) | 51.4833i | 1.70478i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 64.7117 | 2.14047 | ||||||||
\(915\) | −1.48593 | + | 7.50856i | −0.0491234 | + | 0.248225i | ||||
\(916\) | −2.00171 | −0.0661384 | ||||||||
\(917\) | − | 3.56304i | − | 0.117662i | ||||||
\(918\) | 15.2660i | 0.503853i | ||||||||
\(919\) | −59.3800 | −1.95876 | −0.979382 | − | 0.202016i | \(-0.935251\pi\) | ||||
−0.979382 | + | 0.202016i | \(0.935251\pi\) | |||||||
\(920\) | −17.6581 | − | 3.49450i | −0.582169 | − | 0.115210i | ||||
\(921\) | −13.5658 | −0.447009 | ||||||||
\(922\) | − | 14.6993i | − | 0.484095i | ||||||
\(923\) | 17.1950i | 0.565981i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.93842 | + | 11.9885i | −0.162374 | + | 0.394179i | ||||
\(926\) | −6.96713 | −0.228954 | ||||||||
\(927\) | 9.21484i | 0.302655i | ||||||||
\(928\) | 0.750301i | 0.0246298i | ||||||||
\(929\) | −19.5881 | −0.642664 | −0.321332 | − | 0.946967i | \(-0.604131\pi\) | ||||
−0.321332 | + | 0.946967i | \(0.604131\pi\) | |||||||
\(930\) | −4.92293 | − | 0.974241i | −0.161429 | − | 0.0319466i | ||||
\(931\) | −10.4078 | −0.341101 | ||||||||
\(932\) | 7.75317i | 0.253964i | ||||||||
\(933\) | − | 10.8644i | − | 0.355686i | ||||||
\(934\) | −11.1327 | −0.364275 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.95320 | 0.227272 | ||||||||
\(937\) | 40.5452i | 1.32455i | 0.749259 | + | 0.662277i | \(0.230410\pi\) | ||||
−0.749259 | + | 0.662277i | \(0.769590\pi\) | |||||||
\(938\) | 2.41409i | 0.0788227i | ||||||||
\(939\) | −28.1052 | −0.917178 | ||||||||
\(940\) | −3.84669 | + | 19.4377i | −0.125465 | + | 0.633989i | ||||
\(941\) | −0.409691 | −0.0133556 | −0.00667778 | − | 0.999978i | \(-0.502126\pi\) | ||||
−0.00667778 | + | 0.999978i | \(0.502126\pi\) | |||||||
\(942\) | − | 46.8835i | − | 1.52755i | ||||||
\(943\) | 30.5096i | 0.993530i | ||||||||
\(944\) | −1.69478 | −0.0551605 | ||||||||
\(945\) | 20.4066 | + | 4.03843i | 0.663826 | + | 0.131370i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.45729i | 0.0798511i | 0.999203 | + | 0.0399256i | \(0.0127121\pi\) | ||||
−0.999203 | + | 0.0399256i | \(0.987288\pi\) | |||||||
\(948\) | − | 10.5380i | − | 0.342259i | ||||||
\(949\) | −32.7739 | −1.06389 | ||||||||
\(950\) | 16.6588 | − | 40.4408i | 0.540482 | − | 1.31207i | ||||
\(951\) | 36.9017 | 1.19662 | ||||||||
\(952\) | − | 10.4224i | − | 0.337792i | ||||||
\(953\) | − | 61.0264i | − | 1.97684i | −0.151744 | − | 0.988420i | \(-0.548489\pi\) | ||
0.151744 | − | 0.988420i | \(-0.451511\pi\) | |||||||
\(954\) | −18.8428 | −0.610057 | ||||||||
\(955\) | 6.83471 | + | 1.35258i | 0.221166 | + | 0.0437684i | ||||
\(956\) | 14.7820 | 0.478085 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 34.4309i | − | 1.11241i | ||||||
\(959\) | −41.9497 | −1.35463 | ||||||||
\(960\) | 2.80692 | − | 14.1837i | 0.0905930 | − | 0.457775i | ||||
\(961\) | −30.5282 | −0.984781 | ||||||||
\(962\) | − | 15.8742i | − | 0.511803i | ||||||
\(963\) | − | 9.03999i | − | 0.291310i | ||||||
\(964\) | −20.9822 | −0.675790 | ||||||||
\(965\) | −4.18311 | + | 21.1377i | −0.134659 | + | 0.680445i | ||||
\(966\) | −28.2476 | −0.908851 | ||||||||
\(967\) | 17.1997i | 0.553106i | 0.960999 | + | 0.276553i | \(0.0891921\pi\) | ||||
−0.960999 | + | 0.276553i | \(0.910808\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −23.2258 | −0.746119 | ||||||||
\(970\) | −8.23180 | − | 1.62906i | −0.264307 | − | 0.0523060i | ||||
\(971\) | 27.2090 | 0.873177 | 0.436589 | − | 0.899661i | \(-0.356187\pi\) | ||||
0.436589 | + | 0.899661i | \(0.356187\pi\) | |||||||
\(972\) | 6.68488i | 0.214417i | ||||||||
\(973\) | 26.0811i | 0.836121i | ||||||||
\(974\) | −26.1083 | −0.836563 | ||||||||
\(975\) | −33.7776 | − | 13.9140i | −1.08175 | − | 0.445605i | ||||
\(976\) | −8.54757 | −0.273601 | ||||||||
\(977\) | − | 19.1722i | − | 0.613374i | −0.951810 | − | 0.306687i | \(-0.900780\pi\) | ||
0.951810 | − | 0.306687i | \(-0.0992204\pi\) | |||||||
\(978\) | − | 11.8516i | − | 0.378971i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.18529 | − | 0.630365i | −0.101750 | − | 0.0201363i | ||||
\(981\) | −7.91969 | −0.252856 | ||||||||
\(982\) | 31.9836i | 1.02064i | ||||||||
\(983\) | 24.1305i | 0.769642i | 0.922991 | + | 0.384821i | \(0.125737\pi\) | ||||
−0.922991 | + | 0.384821i | \(0.874263\pi\) | |||||||
\(984\) | −32.6512 | −1.04088 | ||||||||
\(985\) | −6.24984 | + | 31.5810i | −0.199136 | + | 1.00626i | ||||
\(986\) | −0.693605 | −0.0220889 | ||||||||
\(987\) | − | 53.2135i | − | 1.69380i | ||||||
\(988\) | 14.4283i | 0.459024i | ||||||||
\(989\) | 32.4276 | 1.03114 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.7081 | 0.880177 | 0.440089 | − | 0.897954i | \(-0.354947\pi\) | ||||
0.440089 | + | 0.897954i | \(0.354947\pi\) | |||||||
\(992\) | − | 2.73487i | − | 0.0868323i | ||||||
\(993\) | 0.924692i | 0.0293442i | ||||||||
\(994\) | 17.2489 | 0.547101 | ||||||||
\(995\) | −32.4593 | − | 6.42364i | −1.02903 | − | 0.203643i | ||||
\(996\) | −4.63466 | −0.146855 | ||||||||
\(997\) | 33.4912i | 1.06068i | 0.847786 | + | 0.530339i | \(0.177935\pi\) | ||||
−0.847786 | + | 0.530339i | \(0.822065\pi\) | |||||||
\(998\) | 68.5984i | 2.17144i | ||||||||
\(999\) | −10.7551 | −0.340275 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))