Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,2,Mod(35,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.l (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.58715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 143.12 | ||
Character | \(\chi\) | \(=\) | 324.143 |
Dual form | 324.2.l.a.179.12 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.818446 | − | 1.15332i | 0.578729 | − | 0.815520i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.660291 | − | 1.88786i | −0.330145 | − | 0.943930i | ||||
\(5\) | −0.532084 | + | 0.0938207i | −0.237955 | + | 0.0419579i | −0.291354 | − | 0.956615i | \(-0.594106\pi\) |
0.0533987 | + | 0.998573i | \(0.482995\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.18790 | − | 1.41568i | 0.448984 | − | 0.535078i | −0.493315 | − | 0.869851i | \(-0.664215\pi\) |
0.942299 | + | 0.334773i | \(0.108659\pi\) | |||||||
\(8\) | −2.71772 | − | 0.783586i | −0.960859 | − | 0.277039i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.327277 | + | 0.690450i | −0.103494 | + | 0.218339i | ||||
\(11\) | 0.867520 | − | 4.91995i | 0.261567 | − | 1.48342i | −0.517068 | − | 0.855944i | \(-0.672977\pi\) |
0.778635 | − | 0.627477i | \(-0.215912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.52553 | − | 0.555249i | −0.423107 | − | 0.153998i | 0.121687 | − | 0.992569i | \(-0.461170\pi\) |
−0.544793 | + | 0.838570i | \(0.683392\pi\) | |||||||
\(14\) | −0.660503 | − | 2.52869i | −0.176527 | − | 0.675821i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.12803 | + | 2.49307i | −0.782008 | + | 0.623268i | ||||
\(17\) | 0.683630 | − | 0.394694i | 0.165805 | − | 0.0957273i | −0.414802 | − | 0.909912i | \(-0.636149\pi\) |
0.580606 | + | 0.814185i | \(0.302816\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.86200 | + | 1.65238i | 0.656589 | + | 0.379082i | 0.790976 | − | 0.611847i | \(-0.209573\pi\) |
−0.134387 | + | 0.990929i | \(0.542907\pi\) | |||||||
\(20\) | 0.528451 | + | 0.942551i | 0.118165 | + | 0.210761i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.96425 | − | 5.02724i | −1.05838 | − | 1.07181i | ||||
\(23\) | 3.15234 | − | 2.64512i | 0.657307 | − | 0.551546i | −0.251971 | − | 0.967735i | \(-0.581079\pi\) |
0.909278 | + | 0.416188i | \(0.136634\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.42415 | + | 1.61026i | −0.884830 | + | 0.322052i | ||||
\(26\) | −1.88895 | + | 1.30499i | −0.370453 | + | 0.255929i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.45697 | − | 1.30783i | −0.653306 | − | 0.247156i | ||||
\(29\) | 3.24174 | + | 8.90660i | 0.601976 | + | 1.65391i | 0.747266 | + | 0.664525i | \(0.231366\pi\) |
−0.145290 | + | 0.989389i | \(0.546412\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.70462 | − | 4.41499i | −0.665369 | − | 0.792956i | 0.322777 | − | 0.946475i | \(-0.395384\pi\) |
−0.988146 | + | 0.153519i | \(0.950939\pi\) | |||||||
\(32\) | 0.315184 | + | 5.64807i | 0.0557172 | + | 0.998447i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.104306 | − | 1.11148i | 0.0178884 | − | 0.190617i | ||||
\(35\) | −0.499242 | + | 0.864712i | −0.0843873 | + | 0.146163i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.53013 | + | 9.57846i | 0.909147 | + | 1.57469i | 0.815251 | + | 0.579108i | \(0.196599\pi\) |
0.0938963 | + | 0.995582i | \(0.470068\pi\) | |||||||
\(38\) | 4.24812 | − | 1.94842i | 0.689136 | − | 0.316076i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.51957 | + | 0.161955i | 0.240265 | + | 0.0256074i | ||||
\(41\) | 2.62821 | − | 7.22095i | 0.410458 | − | 1.12772i | −0.546491 | − | 0.837465i | \(-0.684037\pi\) |
0.956948 | − | 0.290258i | \(-0.0937412\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.88044 | + | 1.38953i | 1.20176 | + | 0.211902i | 0.738458 | − | 0.674300i | \(-0.235555\pi\) |
0.463299 | + | 0.886202i | \(0.346666\pi\) | |||||||
\(44\) | −9.86099 | + | 1.61084i | −1.48660 | + | 0.242844i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.470654 | − | 5.80054i | −0.0693942 | − | 0.855243i | ||||
\(47\) | 2.39693 | + | 2.01126i | 0.349628 | + | 0.293372i | 0.800640 | − | 0.599145i | \(-0.204493\pi\) |
−0.451013 | + | 0.892517i | \(0.648937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.622483 | + | 3.53027i | 0.0889261 | + | 0.504325i | ||||
\(50\) | −1.76379 | + | 6.42037i | −0.249437 | + | 0.907978i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0409360 | + | 3.24662i | −0.00567681 | + | 0.450225i | ||||
\(53\) | − | 0.933485i | − | 0.128224i | −0.997943 | − | 0.0641120i | \(-0.979579\pi\) | ||
0.997943 | − | 0.0641120i | \(-0.0204215\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.69922i | 0.363962i | ||||||||
\(56\) | −4.33769 | + | 2.91661i | −0.579648 | + | 0.389748i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.9253 | + | 3.55082i | 1.69718 | + | 0.466245i | ||||
\(59\) | −0.461077 | − | 2.61490i | −0.0600271 | − | 0.340431i | 0.939973 | − | 0.341250i | \(-0.110850\pi\) |
−1.00000 | 0.000819421i | \(0.999739\pi\) | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.29949 | − | 3.60770i | −0.550493 | − | 0.461919i | 0.324615 | − | 0.945846i | \(-0.394765\pi\) |
−0.875108 | + | 0.483928i | \(0.839210\pi\) | |||||||
\(62\) | −8.12393 | + | 0.659173i | −1.03174 | + | 0.0837151i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.77199 | + | 4.25913i | 0.846498 | + | 0.532392i | ||||
\(65\) | 0.863806 | + | 0.152312i | 0.107142 | + | 0.0188920i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.15593 | + | 5.92336i | −0.263388 | + | 0.723653i | 0.735545 | + | 0.677476i | \(0.236926\pi\) |
−0.998933 | + | 0.0461775i | \(0.985296\pi\) | |||||||
\(68\) | −1.19652 | − | 1.02998i | −0.145100 | − | 0.124904i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.588687 | + | 1.28351i | 0.0703615 | + | 0.153408i | ||||
\(71\) | 4.53203 | + | 7.84970i | 0.537853 | + | 0.931588i | 0.999019 | + | 0.0442746i | \(0.0140977\pi\) |
−0.461167 | + | 0.887313i | \(0.652569\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.77108 | − | 9.99580i | 0.675454 | − | 1.16992i | −0.300882 | − | 0.953661i | \(-0.597281\pi\) |
0.976336 | − | 0.216259i | \(-0.0693855\pi\) | |||||||
\(74\) | 15.5731 | + | 1.46145i | 1.81034 | + | 0.169891i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.22970 | − | 6.49411i | 0.141057 | − | 0.744926i | ||||
\(77\) | −5.93457 | − | 7.07254i | −0.676307 | − | 0.805991i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.275423 | + | 0.756719i | 0.0309875 | + | 0.0851375i | 0.954222 | − | 0.299100i | \(-0.0966865\pi\) |
−0.923234 | + | 0.384238i | \(0.874464\pi\) | |||||||
\(80\) | 1.43047 | − | 1.62000i | 0.159932 | − | 0.181121i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.17702 | − | 8.94113i | −0.682137 | − | 0.987383i | ||||
\(83\) | −15.0247 | + | 5.46855i | −1.64918 | + | 0.600252i | −0.988608 | − | 0.150513i | \(-0.951907\pi\) |
−0.660570 | + | 0.750765i | \(0.729685\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.326718 | + | 0.274149i | −0.0354375 | + | 0.0297356i | ||||
\(86\) | 8.05230 | − | 7.95141i | 0.868302 | − | 0.857422i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.21288 | + | 12.6913i | −0.662295 | + | 1.35289i | ||||
\(89\) | 5.41508 | + | 3.12640i | 0.573997 | + | 0.331398i | 0.758744 | − | 0.651389i | \(-0.225813\pi\) |
−0.184747 | + | 0.982786i | \(0.559147\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.59824 | + | 1.50009i | −0.272369 | + | 0.157252i | ||||
\(92\) | −7.07508 | − | 4.20462i | −0.737628 | − | 0.438362i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.28138 | − | 1.11831i | 0.441591 | − | 0.115345i | ||||
\(95\) | −1.67785 | − | 0.610689i | −0.172144 | − | 0.0626553i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.63933 | − | 9.29708i | 0.166448 | − | 0.943975i | −0.781110 | − | 0.624393i | \(-0.785346\pi\) |
0.947559 | − | 0.319582i | \(-0.103543\pi\) | |||||||
\(98\) | 4.58100 | + | 2.17142i | 0.462751 | + | 0.219346i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.96117 | + | 7.28894i | 0.596117 | + | 0.728894i | ||||
\(101\) | −6.31653 | + | 7.52775i | −0.628518 | + | 0.749039i | −0.982510 | − | 0.186210i | \(-0.940380\pi\) |
0.353992 | + | 0.935249i | \(0.384824\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.85056 | − | 1.20794i | 0.675005 | − | 0.119022i | 0.174370 | − | 0.984680i | \(-0.444211\pi\) |
0.500635 | + | 0.865658i | \(0.333100\pi\) | |||||||
\(104\) | 3.71089 | + | 2.70440i | 0.363882 | + | 0.265188i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.07661 | − | 0.764008i | −0.104569 | − | 0.0742070i | ||||
\(107\) | 2.51779 | 0.243404 | 0.121702 | − | 0.992567i | \(-0.461165\pi\) | ||||
0.121702 | + | 0.992567i | \(0.461165\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.76924 | 0.552593 | 0.276296 | − | 0.961072i | \(-0.410893\pi\) | ||||
0.276296 | + | 0.961072i | \(0.410893\pi\) | |||||||
\(110\) | 3.11306 | + | 2.20916i | 0.296819 | + | 0.210636i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.186384 | + | 7.38983i | −0.0176116 | + | 0.698273i | ||||
\(113\) | −4.36693 | + | 0.770007i | −0.410806 | + | 0.0724362i | −0.375232 | − | 0.926931i | \(-0.622437\pi\) |
−0.0355738 | + | 0.999367i | \(0.511326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.42914 | + | 1.70318i | −0.133268 | + | 0.158823i | ||||
\(116\) | 14.6739 | − | 12.0009i | 1.36244 | − | 1.11426i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.39318 | − | 1.60838i | −0.312367 | − | 0.148064i | ||||
\(119\) | 0.253322 | − | 1.43666i | 0.0232220 | − | 0.131698i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.1167 | − | 4.77409i | −1.19243 | − | 0.434008i | ||||
\(122\) | −7.67973 | + | 2.00598i | −0.695290 | + | 0.181612i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.88876 | + | 9.90898i | −0.528826 | + | 0.889853i | ||||
\(125\) | 4.54248 | − | 2.62260i | 0.406292 | − | 0.234573i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.47118 | − | 2.00409i | −0.308018 | − | 0.177834i | 0.338021 | − | 0.941138i | \(-0.390242\pi\) |
−0.646039 | + | 0.763304i | \(0.723576\pi\) | |||||||
\(128\) | 10.4546 | − | 4.32439i | 0.924069 | − | 0.382226i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.882643 | − | 0.871584i | 0.0774129 | − | 0.0764430i | ||||
\(131\) | −1.84218 | + | 1.54577i | −0.160952 | + | 0.135055i | −0.719707 | − | 0.694278i | \(-0.755724\pi\) |
0.558755 | + | 0.829333i | \(0.311279\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.73902 | − | 2.08883i | 0.497636 | − | 0.181125i | ||||
\(134\) | 5.06701 | + | 7.33442i | 0.437723 | + | 0.633598i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.16719 | + | 0.536984i | −0.185835 | + | 0.0460460i | ||||
\(137\) | −1.46523 | − | 4.02570i | −0.125183 | − | 0.343939i | 0.861231 | − | 0.508213i | \(-0.169694\pi\) |
−0.986415 | + | 0.164275i | \(0.947472\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.4619 | − | 13.6598i | −0.972187 | − | 1.15861i | −0.987323 | − | 0.158722i | \(-0.949263\pi\) |
0.0151364 | − | 0.999885i | \(-0.495182\pi\) | |||||||
\(140\) | 1.96210 | + | 0.371537i | 0.165828 | + | 0.0314006i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.7624 | + | 1.19769i | 1.07100 | + | 0.100508i | ||||
\(143\) | −4.05523 | + | 7.02386i | −0.339115 | + | 0.587365i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.56050 | − | 4.43492i | −0.212638 | − | 0.368300i | ||||
\(146\) | −6.80503 | − | 14.8369i | −0.563188 | − | 1.22791i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.4313 | − | 16.7647i | 1.18625 | − | 1.37805i | ||||
\(149\) | −4.08657 | + | 11.2278i | −0.334785 | + | 0.919814i | 0.652063 | + | 0.758165i | \(0.273904\pi\) |
−0.986848 | + | 0.161650i | \(0.948319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.0852 | − | 3.18891i | −1.47175 | − | 0.259510i | −0.620475 | − | 0.784226i | \(-0.713060\pi\) |
−0.851277 | + | 0.524716i | \(0.824171\pi\) | |||||||
\(152\) | −6.48334 | − | 6.73333i | −0.525868 | − | 0.546145i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −13.0140 | + | 1.05595i | −1.04870 | + | 0.0850912i | ||||
\(155\) | 2.38539 | + | 2.00158i | 0.191599 | + | 0.160770i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.60079 | + | 20.4211i | 0.287374 | + | 1.62978i | 0.696680 | + | 0.717382i | \(0.254660\pi\) |
−0.409306 | + | 0.912397i | \(0.634229\pi\) | |||||||
\(158\) | 1.09816 | + | 0.301683i | 0.0873647 | + | 0.0240006i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.697610 | − | 2.97567i | −0.0551509 | − | 0.235248i | ||||
\(161\) | − | 7.60485i | − | 0.599346i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.03697i | − | 0.159548i | −0.996813 | − | 0.0797739i | \(-0.974580\pi\) | ||
0.996813 | − | 0.0797739i | \(-0.0254198\pi\) | |||||||
\(164\) | −15.3675 | − | 0.193767i | −1.20000 | − | 0.0151306i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.98994 | + | 21.8040i | −0.464910 | + | 1.69232i | ||||
\(167\) | −1.07213 | − | 6.08034i | −0.0829637 | − | 0.470511i | −0.997777 | − | 0.0666346i | \(-0.978774\pi\) |
0.914814 | − | 0.403876i | \(-0.132337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.93963 | − | 6.66214i | −0.610741 | − | 0.512472i | ||||
\(170\) | 0.0487801 | + | 0.601186i | 0.00374126 | + | 0.0461089i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.58014 | − | 15.7947i | −0.196734 | − | 1.20433i | ||||
\(173\) | −14.6443 | − | 2.58218i | −1.11338 | − | 0.196320i | −0.413450 | − | 0.910527i | \(-0.635676\pi\) |
−0.699934 | + | 0.714207i | \(0.746787\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.97583 | + | 8.17603i | −0.224952 | + | 0.618050i | ||||
\(176\) | 9.55217 | + | 17.5526i | 0.720022 | + | 1.32307i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.03769 | − | 3.68653i | 0.602450 | − | 0.276317i | ||||
\(179\) | −2.80761 | − | 4.86292i | −0.209850 | − | 0.363472i | 0.741817 | − | 0.670603i | \(-0.233964\pi\) |
−0.951667 | + | 0.307131i | \(0.900631\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.04279 | + | 5.27027i | −0.226169 | + | 0.391736i | −0.956670 | − | 0.291176i | \(-0.905954\pi\) |
0.730500 | + | 0.682912i | \(0.239287\pi\) | |||||||
\(182\) | −0.396432 | + | 4.22434i | −0.0293855 | + | 0.313129i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −10.6398 | + | 4.71857i | −0.784379 | + | 0.347858i | ||||
\(185\) | −3.84115 | − | 4.57770i | −0.282407 | − | 0.336560i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.34881 | − | 3.70583i | −0.0986349 | − | 0.270997i | ||||
\(188\) | 2.21431 | − | 5.85308i | 0.161495 | − | 0.426880i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.07755 | + | 1.43528i | −0.150721 | + | 0.104126i | ||||
\(191\) | −4.55974 | + | 1.65961i | −0.329931 | + | 0.120085i | −0.501674 | − | 0.865057i | \(-0.667282\pi\) |
0.171743 | + | 0.985142i | \(0.445060\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.04332 | − | 3.39275i | 0.291044 | − | 0.244215i | −0.485561 | − | 0.874203i | \(-0.661385\pi\) |
0.776605 | + | 0.629988i | \(0.216940\pi\) | |||||||
\(194\) | −9.38080 | − | 9.49982i | −0.673502 | − | 0.682048i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.25364 | − | 3.50617i | 0.446689 | − | 0.250441i | ||||
\(197\) | −2.31117 | − | 1.33435i | −0.164664 | − | 0.0950687i | 0.415403 | − | 0.909637i | \(-0.363640\pi\) |
−0.580067 | + | 0.814569i | \(0.696974\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.82614 | + | 5.67313i | −0.696557 | + | 0.402157i | −0.806064 | − | 0.591829i | \(-0.798406\pi\) |
0.109507 | + | 0.993986i | \(0.465073\pi\) | |||||||
\(200\) | 13.2854 | − | 0.909529i | 0.939418 | − | 0.0643134i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.51216 | + | 13.4460i | 0.247114 | + | 0.946060i | ||||
\(203\) | 16.4598 | + | 5.99087i | 1.15525 | + | 0.420477i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.720954 | + | 4.08873i | −0.0503536 | + | 0.285570i | ||||
\(206\) | 4.21368 | − | 8.88951i | 0.293581 | − | 0.619362i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.15619 | − | 2.06643i | 0.426855 | − | 0.143281i | ||||
\(209\) | 10.6125 | − | 12.6474i | 0.734080 | − | 0.874842i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.51015 | − | 0.795260i | 0.310491 | − | 0.0547480i | −0.0162314 | − | 0.999868i | \(-0.505167\pi\) |
0.326723 | + | 0.945120i | \(0.394056\pi\) | |||||||
\(212\) | −1.76229 | + | 0.616372i | −0.121035 | + | 0.0423326i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.06067 | − | 2.90381i | 0.140865 | − | 0.198501i | ||||
\(215\) | −4.32342 | −0.294855 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.6509 | −0.723033 | ||||||||
\(218\) | 4.72181 | − | 6.65378i | 0.319802 | − | 0.450651i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.09574 | − | 1.78227i | 0.343555 | − | 0.120161i | ||||
\(221\) | −1.26205 | + | 0.222534i | −0.0848949 | + | 0.0149693i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.8712 | − | 14.1475i | 0.794953 | − | 0.947388i | −0.204552 | − | 0.978856i | \(-0.565574\pi\) |
0.999505 | + | 0.0314676i | \(0.0100181\pi\) | |||||||
\(224\) | 8.37028 | + | 6.26314i | 0.559263 | + | 0.418473i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.68603 | + | 5.66667i | −0.178672 | + | 0.376941i | ||||
\(227\) | 2.30342 | − | 13.0633i | 0.152883 | − | 0.867043i | −0.807813 | − | 0.589439i | \(-0.799349\pi\) |
0.960696 | − | 0.277604i | \(-0.0895402\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.24361 | + | 1.18058i | 0.214344 | + | 0.0780147i | 0.446960 | − | 0.894554i | \(-0.352507\pi\) |
−0.232617 | + | 0.972569i | \(0.574729\pi\) | |||||||
\(230\) | 0.794639 | + | 3.04222i | 0.0523969 | + | 0.200598i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.83104 | − | 26.7458i | −0.120214 | − | 1.75595i | ||||
\(233\) | 14.1574 | − | 8.17379i | 0.927483 | − | 0.535483i | 0.0414686 | − | 0.999140i | \(-0.486796\pi\) |
0.886015 | + | 0.463657i | \(0.153463\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.46406 | − | 0.845277i | −0.0955050 | − | 0.0551398i | ||||
\(236\) | −4.63212 | + | 2.59704i | −0.301525 | + | 0.169053i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.44960 | − | 1.46799i | −0.0939634 | − | 0.0951557i | ||||
\(239\) | −0.797855 | + | 0.669480i | −0.0516089 | + | 0.0433050i | −0.668227 | − | 0.743957i | \(-0.732947\pi\) |
0.616618 | + | 0.787262i | \(0.288502\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.4743 | − | 5.63219i | 0.996788 | − | 0.362801i | 0.208443 | − | 0.978035i | \(-0.433160\pi\) |
0.788345 | + | 0.615233i | \(0.210938\pi\) | |||||||
\(242\) | −16.2414 | + | 11.2204i | −1.04403 | + | 0.721275i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.97192 | + | 10.4990i | −0.254276 | + | 0.672128i | ||||
\(245\) | −0.662426 | − | 1.82000i | −0.0423208 | − | 0.116276i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.44860 | − | 4.10988i | −0.219429 | − | 0.261506i | ||||
\(248\) | 6.60858 | + | 14.9016i | 0.419645 | + | 0.946252i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.693078 | − | 7.38539i | 0.0438341 | − | 0.467093i | ||||
\(251\) | 6.70961 | − | 11.6214i | 0.423507 | − | 0.733535i | −0.572773 | − | 0.819714i | \(-0.694132\pi\) |
0.996280 | + | 0.0861790i | \(0.0274657\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.2792 | − | 17.8040i | −0.646245 | − | 1.11933i | ||||
\(254\) | −5.15233 | + | 2.36314i | −0.323286 | + | 0.148277i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.56916 | − | 15.5968i | 0.223073 | − | 0.974802i | ||||
\(257\) | −0.987706 | + | 2.71370i | −0.0616114 | + | 0.169276i | −0.966679 | − | 0.255992i | \(-0.917598\pi\) |
0.905068 | + | 0.425268i | \(0.139820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.1293 | + | 3.54934i | 1.25077 | + | 0.220545i | ||||
\(260\) | −0.282819 | − | 1.73131i | −0.0175397 | − | 0.107372i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.275044 | + | 3.38975i | 0.0169922 | + | 0.209420i | ||||
\(263\) | 10.7439 | + | 9.01519i | 0.662496 | + | 0.555900i | 0.910834 | − | 0.412773i | \(-0.135440\pi\) |
−0.248338 | + | 0.968674i | \(0.579884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0875803 | + | 0.496692i | 0.00538001 | + | 0.0305116i | ||||
\(266\) | 2.28799 | − | 8.32852i | 0.140286 | − | 0.510654i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.6060 | + | 0.158947i | 0.770035 | + | 0.00970923i | ||||
\(269\) | 20.1185i | 1.22665i | 0.789831 | + | 0.613325i | \(0.210168\pi\) | ||||
−0.789831 | + | 0.613325i | \(0.789832\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.1968i | 1.16612i | 0.812428 | + | 0.583062i | \(0.198145\pi\) | ||||
−0.812428 | + | 0.583062i | \(0.801855\pi\) | |||||||
\(272\) | −1.15441 | + | 2.93895i | −0.0699967 | + | 0.178200i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.84213 | − | 1.60493i | −0.352936 | − | 0.0969577i | ||||
\(275\) | 4.08436 | + | 23.1635i | 0.246296 | + | 1.39681i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.3674 | + | 17.0903i | 1.22376 | + | 1.02686i | 0.998619 | + | 0.0525311i | \(0.0167289\pi\) |
0.225141 | + | 0.974326i | \(0.427716\pi\) | |||||||
\(278\) | −25.1350 | + | 2.03945i | −1.50750 | + | 0.122318i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.03437 | − | 1.95885i | 0.121577 | − | 0.117063i | ||||
\(281\) | −2.17919 | − | 0.384249i | −0.129999 | − | 0.0229224i | 0.108270 | − | 0.994122i | \(-0.465469\pi\) |
−0.238269 | + | 0.971199i | \(0.576580\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.19432 | + | 22.5137i | −0.487102 | + | 1.33830i | 0.416192 | + | 0.909277i | \(0.363365\pi\) |
−0.903293 | + | 0.429024i | \(0.858858\pi\) | |||||||
\(284\) | 11.8267 | − | 13.7389i | 0.701784 | − | 0.815255i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.78177 | + | 10.4256i | 0.282752 | + | 0.616480i | ||||
\(287\) | −7.10053 | − | 12.2985i | −0.419131 | − | 0.725957i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.18843 | + | 14.1828i | −0.481673 | + | 0.834281i | ||||
\(290\) | −7.21051 | − | 0.676667i | −0.423416 | − | 0.0397353i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −22.6813 | − | 4.29485i | −1.32732 | − | 0.251337i | ||||
\(293\) | 17.5281 | + | 20.8891i | 1.02400 | + | 1.22036i | 0.975149 | + | 0.221550i | \(0.0711116\pi\) |
0.0488514 | + | 0.998806i | \(0.484444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.490663 | + | 1.34809i | 0.0285675 | + | 0.0784886i | ||||
\(296\) | −7.52378 | − | 30.3649i | −0.437311 | − | 1.76492i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.60456 | + | 13.9024i | 0.556377 | + | 0.805347i | ||||
\(299\) | −6.27769 | + | 2.28489i | −0.363048 | + | 0.132139i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.3283 | − | 9.50559i | 0.652953 | − | 0.547893i | ||||
\(302\) | −18.4796 | + | 18.2481i | −1.06338 | + | 1.05006i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.0719 | + | 1.96649i | −0.749727 | + | 0.112786i | ||||
\(305\) | 2.62617 | + | 1.51622i | 0.150374 | + | 0.0868184i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.0055 | − | 12.1276i | 1.19885 | − | 0.692156i | 0.238551 | − | 0.971130i | \(-0.423328\pi\) |
0.960299 | + | 0.278974i | \(0.0899944\pi\) | |||||||
\(308\) | −9.43343 | + | 15.8736i | −0.537519 | + | 0.904480i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.26077 | − | 1.11293i | 0.241995 | − | 0.0632101i | ||||
\(311\) | −18.0900 | − | 6.58424i | −1.02579 | − | 0.373358i | −0.226315 | − | 0.974054i | \(-0.572668\pi\) |
−0.799477 | + | 0.600696i | \(0.794890\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.18433 | + | 6.71666i | −0.0669422 | + | 0.379648i | 0.932869 | + | 0.360216i | \(0.117297\pi\) |
−0.999811 | + | 0.0194321i | \(0.993814\pi\) | |||||||
\(314\) | 26.4991 | + | 12.5607i | 1.49543 | + | 0.708841i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.24672 | − | 1.01961i | 0.0701335 | − | 0.0573578i | ||||
\(317\) | 7.41728 | − | 8.83957i | 0.416596 | − | 0.496480i | −0.516409 | − | 0.856342i | \(-0.672732\pi\) |
0.933006 | + | 0.359862i | \(0.117176\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 46.6323 | − | 8.22253i | 2.61091 | − | 0.460373i | ||||
\(320\) | −4.00286 | − | 1.63086i | −0.223767 | − | 0.0911680i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.77082 | − | 6.22416i | −0.488779 | − | 0.346859i | ||||
\(323\) | 2.60873 | 0.145154 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.64329 | 0.423973 | ||||||||
\(326\) | −2.34928 | − | 1.66715i | −0.130114 | − | 0.0923349i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −12.8010 | + | 17.5651i | −0.706816 | + | 0.969870i | ||||
\(329\) | 5.69461 | − | 1.00411i | 0.313954 | − | 0.0553586i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.2173 | + | 15.7517i | −0.726487 | + | 0.865793i | −0.995244 | − | 0.0974147i | \(-0.968943\pi\) |
0.268757 | + | 0.963208i | \(0.413387\pi\) | |||||||
\(332\) | 20.2446 | + | 24.7537i | 1.11106 | + | 1.35854i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.89005 | − | 3.73993i | −0.431724 | − | 0.204640i | ||||
\(335\) | 0.591400 | − | 3.35399i | 0.0323116 | − | 0.183248i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0326 | − | 3.65156i | −0.546509 | − | 0.198913i | 0.0539858 | − | 0.998542i | \(-0.482807\pi\) |
−0.600495 | + | 0.799629i | \(0.705030\pi\) | |||||||
\(338\) | −14.1817 | + | 3.70432i | −0.771384 | + | 0.201489i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.733284 | + | 0.435780i | 0.0397679 | + | 0.0236335i | ||||
\(341\) | −24.9354 | + | 14.3964i | −1.35033 | + | 0.779611i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.9404 | + | 9.78053i | 0.914694 | + | 0.528099i | ||||
\(344\) | −20.3280 | − | 9.95137i | −1.09601 | − | 0.536542i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.9636 | + | 14.7762i | −0.804451 | + | 0.794371i | ||||
\(347\) | 0.957389 | − | 0.803344i | 0.0513953 | − | 0.0431258i | −0.616728 | − | 0.787176i | \(-0.711542\pi\) |
0.668123 | + | 0.744050i | \(0.267098\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0738 | + | 6.57834i | −0.967470 | + | 0.352130i | −0.776957 | − | 0.629554i | \(-0.783238\pi\) |
−0.190514 | + | 0.981685i | \(0.561015\pi\) | |||||||
\(350\) | 6.99401 | + | 10.1237i | 0.373846 | + | 0.541136i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 28.0616 | + | 3.34912i | 1.49569 | + | 0.178509i | ||||
\(353\) | 2.12947 | + | 5.85067i | 0.113340 | + | 0.311400i | 0.983374 | − | 0.181593i | \(-0.0581253\pi\) |
−0.870034 | + | 0.492992i | \(0.835903\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.14788 | − | 3.75150i | −0.167072 | − | 0.199109i | ||||
\(356\) | 2.32667 | − | 12.2872i | 0.123313 | − | 0.651223i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.90637 | − | 0.741970i | −0.417865 | − | 0.0392143i | ||||
\(359\) | −4.51666 | + | 7.82308i | −0.238380 | + | 0.412886i | −0.960250 | − | 0.279143i | \(-0.909950\pi\) |
0.721870 | + | 0.692029i | \(0.243283\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.03929 | − | 6.99626i | −0.212594 | − | 0.368224i | ||||
\(362\) | 3.58794 | + | 7.82275i | 0.188578 | + | 0.411155i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.54756 | + | 3.91461i | 0.238357 | + | 0.205181i | ||||
\(365\) | −2.13288 | + | 5.86005i | −0.111640 | + | 0.306729i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.28951 | − | 1.28534i | −0.380509 | − | 0.0670941i | −0.0198778 | − | 0.999802i | \(-0.506328\pi\) |
−0.360632 | + | 0.932708i | \(0.617439\pi\) | |||||||
\(368\) | −3.26612 | + | 16.1330i | −0.170258 | + | 0.840993i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.42333 | + | 0.683467i | −0.437908 | + | 0.0355318i | ||||
\(371\) | −1.32152 | − | 1.10889i | −0.0686099 | − | 0.0575705i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.532880 | + | 3.02211i | 0.0275915 | + | 0.156479i | 0.995491 | − | 0.0948598i | \(-0.0302403\pi\) |
−0.967899 | + | 0.251339i | \(0.919129\pi\) | |||||||
\(374\) | −5.37793 | − | 1.47741i | −0.278086 | − | 0.0763952i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.93817 | − | 7.34423i | −0.254667 | − | 0.378750i | ||||
\(377\) | − | 15.3873i | − | 0.792486i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 30.1832i | − | 1.55041i | −0.631712 | − | 0.775203i | \(-0.717647\pi\) | ||
0.631712 | − | 0.775203i | \(-0.282353\pi\) | |||||||
\(380\) | −0.0450234 | + | 3.57078i | −0.00230965 | + | 0.183177i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.81784 | + | 6.61714i | −0.0930090 | + | 0.338562i | ||||
\(383\) | −3.37652 | − | 19.1492i | −0.172532 | − | 0.978479i | −0.940954 | − | 0.338535i | \(-0.890069\pi\) |
0.768422 | − | 0.639944i | \(-0.221042\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.82124 | + | 3.20640i | 0.194748 | + | 0.163413i | ||||
\(386\) | −0.603681 | − | 7.44002i | −0.0307266 | − | 0.378687i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.6340 | + | 3.04396i | −0.945999 | + | 0.154534i | ||||
\(389\) | 20.0904 | + | 3.54247i | 1.01862 | + | 0.179610i | 0.657933 | − | 0.753076i | \(-0.271431\pi\) |
0.360688 | + | 0.932687i | \(0.382542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.11102 | − | 3.05249i | 0.0561865 | − | 0.154371i | ||||
\(392\) | 1.07454 | − | 10.0821i | 0.0542725 | − | 0.509221i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.43050 | + | 1.57342i | −0.172826 | + | 0.0792676i | ||||
\(395\) | −0.217544 | − | 0.376797i | −0.0109458 | − | 0.0189587i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.78858 | + | 15.2223i | −0.441086 | + | 0.763984i | −0.997770 | − | 0.0667406i | \(-0.978740\pi\) |
0.556684 | + | 0.830724i | \(0.312073\pi\) | |||||||
\(398\) | −1.49924 | + | 15.9758i | −0.0751504 | + | 0.800796i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.82439 | − | 16.0667i | 0.491220 | − | 0.803334i | ||||
\(401\) | 15.5813 | + | 18.5691i | 0.778094 | + | 0.927297i | 0.998846 | − | 0.0480334i | \(-0.0152954\pi\) |
−0.220751 | + | 0.975330i | \(0.570851\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.20010 | + | 8.79220i | 0.159408 | + | 0.437971i | ||||
\(404\) | 18.3821 | + | 6.95422i | 0.914543 | + | 0.345986i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.3808 | − | 14.0802i | 1.01148 | − | 0.698788i | ||||
\(407\) | 51.9231 | − | 18.8984i | 2.57373 | − | 0.936761i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.8369 | − | 13.2887i | 0.783085 | − | 0.657086i | −0.160939 | − | 0.986964i | \(-0.551452\pi\) |
0.944024 | + | 0.329878i | \(0.107008\pi\) | |||||||
\(410\) | 4.12555 | + | 4.17790i | 0.203747 | + | 0.206332i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.80378 | − | 12.1353i | −0.335198 | − | 0.597863i | ||||
\(413\) | −4.24958 | − | 2.45350i | −0.209108 | − | 0.120729i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.48135 | − | 4.31936i | 0.367245 | − | 0.212029i | ||||
\(416\) | 2.65526 | − | 8.79132i | 0.130185 | − | 0.431030i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.90081 | − | 22.5908i | −0.288618 | − | 1.10495i | ||||
\(419\) | −8.00463 | − | 2.91345i | −0.391052 | − | 0.142331i | 0.139009 | − | 0.990291i | \(-0.455608\pi\) |
−0.530060 | + | 0.847960i | \(0.677831\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.47727 | + | 14.0493i | −0.120735 | + | 0.684721i | 0.863015 | + | 0.505178i | \(0.168573\pi\) |
−0.983750 | + | 0.179543i | \(0.942538\pi\) | |||||||
\(422\) | 2.77412 | − | 5.85252i | 0.135042 | − | 0.284896i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.731466 | + | 2.53695i | −0.0355231 | + | 0.123205i | ||||
\(425\) | −2.38892 | + | 2.84701i | −0.115880 | + | 0.138100i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2147 | + | 1.80113i | −0.494325 | + | 0.0871629i | ||||
\(428\) | −1.66247 | − | 4.75323i | −0.0803586 | − | 0.229756i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.53849 | + | 4.98629i | −0.170641 | + | 0.240460i | ||||
\(431\) | −1.49028 | −0.0717841 | −0.0358920 | − | 0.999356i | \(-0.511427\pi\) | ||||
−0.0358920 | + | 0.999356i | \(0.511427\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.83288 | 0.136139 | 0.0680697 | − | 0.997681i | \(-0.478316\pi\) | ||||
0.0680697 | + | 0.997681i | \(0.478316\pi\) | |||||||
\(434\) | −8.71723 | + | 12.2839i | −0.418440 | + | 0.589648i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.80938 | − | 10.8915i | −0.182436 | − | 0.521609i | ||||
\(437\) | 13.3927 | − | 2.36150i | 0.640662 | − | 0.112966i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.2666 | + | 20.5775i | −0.824089 | + | 0.982112i | −0.999997 | − | 0.00229504i | \(-0.999269\pi\) |
0.175908 | + | 0.984407i | \(0.443714\pi\) | |||||||
\(440\) | 2.11507 | − | 7.33571i | 0.100832 | − | 0.349716i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.776270 | + | 1.63768i | −0.0369234 | + | 0.0778966i | ||||
\(443\) | −4.52430 | + | 25.6586i | −0.214956 | + | 1.21908i | 0.666027 | + | 0.745928i | \(0.267994\pi\) |
−0.880983 | + | 0.473148i | \(0.843118\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.17460 | − | 1.15546i | −0.150490 | − | 0.0547740i | ||||
\(446\) | −6.60069 | − | 25.2703i | −0.312552 | − | 1.19658i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14.0740 | − | 4.52757i | 0.664935 | − | 0.213908i | ||||
\(449\) | −19.5356 | + | 11.2789i | −0.921940 | + | 0.532282i | −0.884254 | − | 0.467007i | \(-0.845332\pi\) |
−0.0376867 | + | 0.999290i | \(0.511999\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.2467 | − | 19.1950i | −1.56553 | − | 0.903857i | ||||
\(452\) | 4.33711 | + | 7.73572i | 0.204000 | + | 0.363858i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.1810 | − | 13.3482i | −0.618613 | − | 0.626462i | ||||
\(455\) | 1.24174 | − | 1.04194i | 0.0582137 | − | 0.0488471i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.9247 | + | 5.06817i | −0.651370 | + | 0.237079i | −0.646506 | − | 0.762909i | \(-0.723770\pi\) |
−0.00486385 | + | 0.999988i | \(0.501548\pi\) | |||||||
\(458\) | 4.01630 | − | 2.77468i | 0.187669 | − | 0.129652i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.15902 | + | 1.57342i | 0.193915 | + | 0.0733611i | ||||
\(461\) | −10.5924 | − | 29.1025i | −0.493339 | − | 1.35544i | −0.897606 | − | 0.440798i | \(-0.854696\pi\) |
0.404267 | − | 0.914641i | \(-0.367527\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.7162 | + | 17.5380i | 0.683918 | + | 0.815062i | 0.990606 | − | 0.136748i | \(-0.0436651\pi\) |
−0.306687 | + | 0.951810i | \(0.599221\pi\) | |||||||
\(464\) | −32.3451 | − | 19.7782i | −1.50158 | − | 0.918182i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.16010 | − | 23.0178i | 0.100065 | − | 1.06628i | ||||
\(467\) | 17.9763 | − | 31.1359i | 0.831844 | − | 1.44080i | −0.0647308 | − | 0.997903i | \(-0.520619\pi\) |
0.896575 | − | 0.442893i | \(-0.146048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.82458 | + | 10.0885i | 0.268954 | + | 0.465842i | ||||
\(470\) | −2.17313 | + | 0.996718i | −0.100239 | + | 0.0459752i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.795920 | + | 7.46785i | −0.0366352 | + | 0.343736i | ||||
\(473\) | 13.6729 | − | 37.5659i | 0.628680 | − | 1.72728i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.3227 | − | 2.70181i | −0.703054 | − | 0.123967i | ||||
\(476\) | −2.87948 | + | 0.470377i | −0.131981 | + | 0.0215597i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.119122 | + | 1.46811i | 0.00544853 | + | 0.0671500i | ||||
\(479\) | −15.6682 | − | 13.1472i | −0.715899 | − | 0.600711i | 0.210348 | − | 0.977627i | \(-0.432540\pi\) |
−0.926248 | + | 0.376916i | \(0.876985\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.11797 | − | 17.6829i | −0.142167 | − | 0.806269i | ||||
\(482\) | 6.16918 | − | 22.4565i | 0.280998 | − | 1.02286i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.351972 | + | 27.9148i | −0.0159987 | + | 1.26885i | ||||
\(485\) | 5.10063i | 0.231608i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.0248i | − | 0.771469i | −0.922610 | − | 0.385734i | \(-0.873948\pi\) | ||
0.922610 | − | 0.385734i | \(-0.126052\pi\) | |||||||
\(488\) | 8.85786 | + | 13.1737i | 0.400976 | + | 0.596347i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.64120 | − | 0.725584i | −0.119317 | − | 0.0327785i | ||||
\(491\) | 2.46802 | + | 13.9968i | 0.111380 | + | 0.631668i | 0.988479 | + | 0.151358i | \(0.0483647\pi\) |
−0.877099 | + | 0.480310i | \(0.840524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.73153 | + | 4.80932i | 0.258135 | + | 0.216601i | ||||
\(494\) | −7.56250 | + | 0.613620i | −0.340253 | + | 0.0276080i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 22.5951 | + | 4.57435i | 1.01455 | + | 0.205394i | ||||
\(497\) | 16.4963 | + | 2.90874i | 0.739960 | + | 0.130475i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.45044 | + | 6.73253i | −0.109697 | + | 0.301390i | −0.982379 | − | 0.186899i | \(-0.940156\pi\) |
0.872682 | + | 0.488288i | \(0.162379\pi\) | |||||||
\(500\) | −7.95046 | − | 6.84388i | −0.355555 | − | 0.306068i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7.91171 | − | 17.2498i | −0.353117 | − | 0.769896i | ||||
\(503\) | 2.15953 | + | 3.74041i | 0.0962886 | + | 0.166777i | 0.910146 | − | 0.414288i | \(-0.135969\pi\) |
−0.813857 | + | 0.581065i | \(0.802636\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.65467 | − | 4.59802i | 0.118131 | − | 0.204609i | ||||
\(506\) | −28.9467 | − | 2.71649i | −1.28684 | − | 0.120763i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.49145 | + | 7.87639i | −0.0661723 | + | 0.349458i | ||||
\(509\) | −25.4341 | − | 30.3112i | −1.12735 | − | 1.34352i | −0.931861 | − | 0.362816i | \(-0.881815\pi\) |
−0.195488 | − | 0.980706i | \(-0.562629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.29543 | − | 20.0440i | −0.322731 | − | 0.886696i | ||||
\(512\) | −15.0670 | − | 16.8816i | −0.665872 | − | 0.746066i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.32138 | + | 3.36016i | 0.102392 | + | 0.148210i | ||||
\(515\) | −3.53174 | + | 1.28545i | −0.155627 | + | 0.0566436i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.9747 | − | 10.0479i | 0.526646 | − | 0.441908i | ||||
\(518\) | 20.5683 | − | 20.3106i | 0.903719 | − | 0.892396i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.22823 | − | 1.09081i | −0.0977144 | − | 0.0478351i | ||||
\(521\) | −39.1169 | − | 22.5841i | −1.71374 | − | 0.989429i | −0.929380 | − | 0.369123i | \(-0.879658\pi\) |
−0.784360 | − | 0.620305i | \(-0.787009\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.99933 | − | 1.73166i | 0.131152 | − | 0.0757204i | −0.432989 | − | 0.901399i | \(-0.642541\pi\) |
0.564140 | + | 0.825679i | \(0.309208\pi\) | |||||||
\(524\) | 4.13457 | + | 2.45712i | 0.180620 | + | 0.107340i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.1907 | − | 5.01268i | 0.836754 | − | 0.218563i | ||||
\(527\) | −4.27516 | − | 1.55603i | −0.186229 | − | 0.0677817i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.05337 | + | 5.97395i | −0.0457986 | + | 0.259737i | ||||
\(530\) | 0.644525 | + | 0.305508i | 0.0279964 | + | 0.0132704i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.73284 | − | 9.45523i | −0.335261 | − | 0.409936i | ||||
\(533\) | −8.01885 | + | 9.55650i | −0.347335 | + | 0.413938i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.33967 | + | 0.236221i | −0.0579192 | + | 0.0102127i | ||||
\(536\) | 10.5007 | − | 14.4087i | 0.453559 | − | 0.622360i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 23.2031 | + | 16.4660i | 1.00036 | + | 0.709898i | ||||
\(539\) | 17.9088 | 0.771386 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.6206 | −0.628588 | −0.314294 | − | 0.949326i | \(-0.601768\pi\) | ||||
−0.314294 | + | 0.949326i | \(0.601768\pi\) | |||||||
\(542\) | 22.1401 | + | 15.7116i | 0.950997 | + | 0.674869i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.44473 | + | 3.73679i | 0.104817 | + | 0.160213i | ||||
\(545\) | −3.06972 | + | 0.541274i | −0.131492 | + | 0.0231856i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.74169 | − | 10.4179i | 0.373768 | − | 0.445439i | −0.546069 | − | 0.837740i | \(-0.683876\pi\) |
0.919837 | + | 0.392301i | \(0.128321\pi\) | |||||||
\(548\) | −6.63247 | + | 5.42429i | −0.283325 | + | 0.231714i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 30.0578 | + | 14.2475i | 1.28167 | + | 0.607517i | ||||
\(551\) | −5.43921 | + | 30.8473i | −0.231718 | + | 1.31414i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.39845 | + | 0.508994i | 0.0594681 | + | 0.0216446i | ||||
\(554\) | 36.3802 | − | 9.50266i | 1.54565 | − | 0.403729i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.2196 | + | 30.6579i | −0.772681 | + | 1.30019i | ||||
\(557\) | −5.66207 | + | 3.26900i | −0.239909 | + | 0.138512i | −0.615135 | − | 0.788422i | \(-0.710899\pi\) |
0.375226 | + | 0.926933i | \(0.377565\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.2503 | − | 6.49539i | −0.475839 | − | 0.274726i | ||||
\(560\) | −0.594147 | − | 3.94949i | −0.0251073 | − | 0.166897i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.22671 | + | 2.19881i | −0.0939280 | + | 0.0927512i | ||||
\(563\) | −18.1068 | + | 15.1934i | −0.763110 | + | 0.640325i | −0.938934 | − | 0.344096i | \(-0.888185\pi\) |
0.175824 | + | 0.984422i | \(0.443741\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.25133 | − | 0.819417i | 0.0947141 | − | 0.0344731i | ||||
\(566\) | 19.2589 | + | 27.8769i | 0.809511 | + | 1.17175i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.16586 | − | 24.8845i | −0.258714 | − | 1.04413i | ||||
\(569\) | −3.88872 | − | 10.6842i | −0.163024 | − | 0.447904i | 0.831104 | − | 0.556117i | \(-0.187709\pi\) |
−0.994128 | + | 0.108213i | \(0.965487\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.2613 | − | 16.9960i | −0.596818 | − | 0.711260i | 0.380083 | − | 0.924952i | \(-0.375895\pi\) |
−0.976901 | + | 0.213692i | \(0.931451\pi\) | |||||||
\(572\) | 15.9377 | + | 3.01791i | 0.666388 | + | 0.126185i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.9955 | − | 1.87647i | −0.834596 | − | 0.0783223i | ||||
\(575\) | −9.68708 | + | 16.7785i | −0.403979 | + | 0.699712i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.30268 | + | 9.18452i | 0.220754 | + | 0.382357i | 0.955037 | − | 0.296487i | \(-0.0958150\pi\) |
−0.734283 | + | 0.678843i | \(0.762482\pi\) | |||||||
\(578\) | 9.65548 | + | 21.0517i | 0.401615 | + | 0.875636i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.68183 | + | 7.76220i | −0.277448 | + | 0.322308i | ||||
\(581\) | −10.1061 | + | 27.7664i | −0.419273 | + | 1.15194i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.59270 | − | 0.809817i | −0.190210 | − | 0.0335392i | ||||
\(584\) | −23.5167 | + | 22.6436i | −0.973129 | + | 0.937000i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 38.4376 | − | 3.11882i | 1.58784 | − | 0.128837i | ||||
\(587\) | −8.09141 | − | 6.78950i | −0.333968 | − | 0.280233i | 0.460346 | − | 0.887740i | \(-0.347725\pi\) |
−0.794314 | + | 0.607507i | \(0.792170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.30739 | − | 18.7572i | −0.136279 | − | 0.772875i | ||||
\(590\) | 1.95636 | + | 0.537445i | 0.0805419 | + | 0.0221263i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −41.1782 | − | 16.1747i | −1.69241 | − | 0.664777i | ||||
\(593\) | 27.5676i | 1.13207i | 0.824383 | + | 0.566033i | \(0.191522\pi\) | ||||
−0.824383 | + | 0.566033i | \(0.808478\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.788191i | 0.0323127i | ||||||||
\(596\) | 23.8948 | + | 0.301285i | 0.978768 | + | 0.0123411i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.50274 | + | 9.11025i | −0.102345 | + | 0.372546i | ||||
\(599\) | −2.13432 | − | 12.1044i | −0.0872061 | − | 0.494571i | −0.996859 | − | 0.0792006i | \(-0.974763\pi\) |
0.909653 | − | 0.415370i | \(-0.136348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.68745 | − | 8.12873i | −0.395159 | − | 0.331578i | 0.423460 | − | 0.905915i | \(-0.360815\pi\) |
−0.818619 | + | 0.574337i | \(0.805260\pi\) | |||||||
\(602\) | −1.69136 | − | 20.8450i | −0.0689346 | − | 0.849578i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.92128 | + | 36.2479i | 0.240933 | + | 1.47491i | ||||
\(605\) | 7.42709 | + | 1.30960i | 0.301954 | + | 0.0532427i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.12432 | + | 5.83652i | −0.0862235 | + | 0.236897i | −0.975309 | − | 0.220844i | \(-0.929119\pi\) |
0.889086 | + | 0.457741i | \(0.151341\pi\) | |||||||
\(608\) | −8.43069 | + | 16.6856i | −0.341909 | + | 0.676690i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.89806 | − | 1.78787i | 0.157828 | − | 0.0723886i | ||||
\(611\) | −2.53984 | − | 4.39913i | −0.102751 | − | 0.177970i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.5009 | − | 21.6522i | 0.504907 | − | 0.874524i | −0.495077 | − | 0.868849i | \(-0.664860\pi\) |
0.999984 | − | 0.00567529i | \(-0.00180651\pi\) | |||||||
\(614\) | 3.20497 | − | 34.1518i | 0.129342 | − | 1.37826i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.5865 | + | 23.8714i | 0.426544 | + | 0.961807i | ||||
\(617\) | 20.9893 | + | 25.0141i | 0.844997 | + | 1.00703i | 0.999818 | + | 0.0190859i | \(0.00607561\pi\) |
−0.154821 | + | 0.987943i | \(0.549480\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.2843 | + | 36.4984i | 0.533942 | + | 1.46699i | 0.854342 | + | 0.519711i | \(0.173960\pi\) |
−0.320401 | + | 0.947282i | \(0.603818\pi\) | |||||||
\(620\) | 2.20365 | − | 5.82490i | 0.0885006 | − | 0.233933i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.3995 | + | 15.4748i | −0.898136 | + | 0.620481i | ||||
\(623\) | 10.8586 | − | 3.95219i | 0.435039 | − | 0.158341i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.8621 | − | 13.3099i | 0.634483 | − | 0.532395i | ||||
\(626\) | 6.77714 | + | 6.86313i | 0.270869 | + | 0.274306i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 36.1746 | − | 20.2816i | 1.44352 | − | 0.809325i | ||||
\(629\) | 7.56112 | + | 4.36541i | 0.301482 | + | 0.174060i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.2601 | + | 15.7386i | −1.08521 | + | 0.626544i | −0.932296 | − | 0.361696i | \(-0.882198\pi\) |
−0.152911 | + | 0.988240i | \(0.548865\pi\) | |||||||
\(632\) | −0.155568 | − | 2.27237i | −0.00618817 | − | 0.0903899i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.12420 | − | 15.7892i | −0.163793 | − | 0.627070i | ||||
\(635\) | 2.03499 | + | 0.740675i | 0.0807560 | + | 0.0293928i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.01056 | − | 5.73118i | 0.0400399 | − | 0.227078i | ||||
\(638\) | 28.6828 | − | 60.5116i | 1.13556 | − | 2.39568i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5.15703 | + | 3.28180i | −0.203850 | + | 0.129725i | ||||
\(641\) | −6.98262 | + | 8.32156i | −0.275797 | + | 0.328682i | −0.886107 | − | 0.463481i | \(-0.846600\pi\) |
0.610310 | + | 0.792163i | \(0.291045\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.8032 | + | 1.90489i | −0.426036 | + | 0.0751217i | −0.382555 | − | 0.923933i | \(-0.624956\pi\) |
−0.0434808 | + | 0.999054i | \(0.513845\pi\) | |||||||
\(644\) | −14.3569 | + | 5.02141i | −0.565741 | + | 0.197871i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.13511 | − | 3.00870i | 0.0840047 | − | 0.118376i | ||||
\(647\) | −47.2138 | −1.85616 | −0.928082 | − | 0.372375i | \(-0.878544\pi\) | ||||
−0.928082 | + | 0.372375i | \(0.878544\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.2652 | −0.520703 | ||||||||
\(650\) | 6.25562 | − | 8.81515i | 0.245366 | − | 0.345759i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.84551 | + | 1.34499i | −0.150602 | + | 0.0526740i | ||||
\(653\) | 28.9484 | − | 5.10438i | 1.13284 | − | 0.199750i | 0.424367 | − | 0.905490i | \(-0.360497\pi\) |
0.708471 | + | 0.705740i | \(0.249385\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.835168 | − | 0.995314i | 0.0326327 | − | 0.0388902i | ||||
\(656\) | 9.78124 | + | 29.1397i | 0.381893 | + | 1.13771i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.50267 | − | 7.38952i | 0.136548 | − | 0.288074i | ||||
\(659\) | −0.0149056 | + | 0.0845336i | −0.000580638 | + | 0.00329296i | −0.985097 | − | 0.172001i | \(-0.944977\pi\) |
0.984516 | + | 0.175294i | \(0.0560877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6865 | − | 4.61752i | −0.493449 | − | 0.179601i | 0.0832963 | − | 0.996525i | \(-0.473455\pi\) |
−0.576745 | + | 0.816924i | \(0.695677\pi\) | |||||||
\(662\) | 7.34915 | + | 28.1357i | 0.285633 | + | 1.09352i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 45.1181 | − | 3.08882i | 1.75092 | − | 0.119870i | ||||
\(665\) | −2.85766 | + | 1.64987i | −0.110815 | + | 0.0639793i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 33.7781 | + | 19.5018i | 1.30789 | + | 0.755113i | ||||
\(668\) | −10.7709 | + | 6.03882i | −0.416739 | + | 0.233649i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.38420 | − | 3.42714i | −0.130743 | − | 0.132402i | ||||
\(671\) | −21.4796 | + | 18.0235i | −0.829211 | + | 0.695790i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.01426 | + | 1.82504i | −0.193285 | + | 0.0703501i | −0.436849 | − | 0.899535i | \(-0.643906\pi\) |
0.243564 | + | 0.969885i | \(0.421683\pi\) | |||||||
\(674\) | −12.4225 | + | 8.58215i | −0.478498 | + | 0.330572i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.33472 | + | 19.3879i | −0.282105 | + | 0.745687i | ||||
\(677\) | 8.95953 | + | 24.6161i | 0.344343 | + | 0.946074i | 0.984119 | + | 0.177512i | \(0.0568050\pi\) |
−0.639776 | + | 0.768562i | \(0.720973\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.2144 | − | 13.3648i | −0.430368 | − | 0.512892i | ||||
\(680\) | 1.10275 | − | 0.489048i | 0.0422884 | − | 0.0187541i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.80457 | + | 40.5412i | −0.145684 | + | 1.55240i | ||||
\(683\) | −16.4032 | + | 28.4113i | −0.627653 | + | 1.08713i | 0.360369 | + | 0.932810i | \(0.382651\pi\) |
−0.988021 | + | 0.154317i | \(0.950682\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.15732 | + | 2.00454i | 0.0442190 | + | 0.0765895i | ||||
\(686\) | 25.1449 | − | 11.5328i | 0.960035 | − | 0.440325i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28.1145 | + | 15.3000i | −1.07185 | + | 0.583308i | ||||
\(689\) | −0.518316 | + | 1.42406i | −0.0197463 | + | 0.0542525i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.03144 | + | 0.887178i | 0.191405 | + | 0.0337498i | 0.268529 | − | 0.963272i | \(-0.413463\pi\) |
−0.0771239 | + | 0.997022i | \(0.524574\pi\) | |||||||
\(692\) | 4.79469 | + | 29.3514i | 0.182267 | + | 1.11577i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.142941 | − | 1.76167i | −0.00542598 | − | 0.0668721i | ||||
\(695\) | 7.38027 | + | 6.19278i | 0.279950 | + | 0.234906i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.05334 | − | 5.97380i | −0.0398982 | − | 0.226274i | ||||
\(698\) | −7.20554 | + | 26.2289i | −0.272734 | + | 0.992779i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17.4001 | + | 0.219395i | 0.657662 | + | 0.00829235i | ||||
\(701\) | − | 40.9095i | − | 1.54513i | −0.634936 | − | 0.772565i | \(-0.718974\pi\) | ||
0.634936 | − | 0.772565i | \(-0.281026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.5515i | 1.37856i | ||||||||
\(704\) | 26.8295 | − | 29.6230i | 1.01118 | − | 1.11646i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.49054 | + | 2.33250i | 0.319546 | + | 0.0877848i | ||||
\(707\) | 3.15351 | + | 17.8844i | 0.118600 | + | 0.672613i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.2104 | − | 10.2458i | −0.458572 | − | 0.384787i | 0.384033 | − | 0.923319i | \(-0.374535\pi\) |
−0.842605 | + | 0.538532i | \(0.818979\pi\) | |||||||
\(710\) | −6.90305 | + | 0.560112i | −0.259067 | + | 0.0210206i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.2669 | − | 12.7399i | −0.459720 | − | 0.477446i | ||||
\(713\) | −23.3564 | − | 4.11836i | −0.874704 | − | 0.154234i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.49874 | − | 4.11775i | 0.0560496 | − | 0.153995i | ||||
\(716\) | −7.32667 | + | 8.51131i | −0.273811 | + | 0.318083i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.32587 | + | 11.6119i | 0.198760 | + | 0.433353i | ||||
\(719\) | 15.8103 | + | 27.3843i | 0.589626 | + | 1.02126i | 0.994281 | + | 0.106793i | \(0.0340582\pi\) |
−0.404655 | + | 0.914469i | \(0.632608\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.42772 | − | 11.1331i | 0.239381 | − | 0.414619i | ||||
\(722\) | −11.3749 | − | 1.06747i | −0.423328 | − | 0.0397271i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.9587 | + | 2.26446i | 0.444440 | + | 0.0841578i | ||||
\(725\) | −28.6839 | − | 34.1841i | −1.06529 | − | 1.26957i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.85979 | − | 27.0896i | −0.365680 | − | 1.00470i | −0.976986 | − | 0.213302i | \(-0.931578\pi\) |
0.611307 | − | 0.791394i | \(-0.290644\pi\) | |||||||
\(728\) | 8.23673 | − | 2.04089i | 0.305273 | − | 0.0756403i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.01286 | + | 7.25603i | 0.185534 | + | 0.268558i | ||||
\(731\) | 5.93575 | − | 2.16044i | 0.219542 | − | 0.0799066i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.8057 | + | 21.6536i | −0.953157 | + | 0.799793i | −0.979826 | − | 0.199851i | \(-0.935954\pi\) |
0.0266696 | + | 0.999644i | \(0.491510\pi\) | |||||||
\(734\) | −7.44848 | + | 7.35515i | −0.274928 | + | 0.271484i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.9334 | + | 16.9709i | 0.587313 | + | 0.625556i | ||||
\(737\) | 27.2723 | + | 15.7457i | 1.00459 | + | 0.580000i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.3214 | − | 5.95905i | 0.379678 | − | 0.219207i | −0.298000 | − | 0.954566i | \(-0.596320\pi\) |
0.677678 | + | 0.735359i | \(0.262986\pi\) | |||||||
\(740\) | −6.10579 | + | 10.2742i | −0.224453 | + | 0.377686i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.36049 | + | 0.616570i | −0.0866564 | + | 0.0226350i | ||||
\(743\) | 9.08444 | + | 3.30647i | 0.333276 | + | 0.121302i | 0.503237 | − | 0.864148i | \(-0.332142\pi\) |
−0.169962 | + | 0.985451i | \(0.554364\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.12100 | − | 6.35752i | 0.0410703 | − | 0.232921i | ||||
\(746\) | 3.92160 | + | 1.85886i | 0.143580 | + | 0.0680576i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.10548 | + | 4.99329i | −0.223238 | + | 0.182573i | ||||
\(749\) | 2.99088 | − | 3.56439i | 0.109284 | − | 0.130240i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.0213 | + | 3.88295i | −0.803570 | + | 0.141691i | −0.560324 | − | 0.828274i | \(-0.689323\pi\) |
−0.243246 | + | 0.969965i | \(0.578212\pi\) | |||||||
\(752\) | −12.5119 | − | 0.315570i | −0.456261 | − | 0.0115077i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.7465 | − | 12.5937i | −0.646288 | − | 0.458634i | ||||
\(755\) | 9.92203 | 0.361100 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.40365 | 0.123708 | 0.0618540 | − | 0.998085i | \(-0.480299\pi\) | ||||
0.0618540 | + | 0.998085i | \(0.480299\pi\) | |||||||
\(758\) | −34.8109 | − | 24.7033i | −1.26439 | − | 0.897265i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.08141 | + | 2.97442i | 0.148048 | + | 0.107894i | ||||
\(761\) | −43.2514 | + | 7.62639i | −1.56786 | + | 0.276457i | −0.889034 | − | 0.457840i | \(-0.848623\pi\) |
−0.678829 | + | 0.734297i | \(0.737512\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.85328 | − | 8.16742i | 0.248105 | − | 0.295680i | ||||
\(764\) | 6.14387 | + | 7.51233i | 0.222277 | + | 0.271787i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −24.8486 | − | 11.7784i | −0.897818 | − | 0.425571i | ||||
\(767\) | −0.748530 | + | 4.24513i | −0.0270279 | + | 0.153283i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.4127 | + | 15.8009i | 1.56550 | + | 0.569797i | 0.971989 | − | 0.235027i | \(-0.0755178\pi\) |
0.593514 | + | 0.804823i | \(0.297740\pi\) | |||||||
\(770\) | 6.82548 | − | 1.78284i | 0.245973 | − | 0.0642492i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.07480 | − | 5.39302i | −0.326609 | − | 0.194099i | ||||
\(773\) | 35.3857 | − | 20.4299i | 1.27273 | − | 0.734813i | 0.297232 | − | 0.954805i | \(-0.403936\pi\) |
0.975502 | + | 0.219992i | \(0.0706031\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.4991 | + | 13.5672i | 0.844112 | + | 0.487348i | ||||
\(776\) | −11.7403 | + | 23.9823i | −0.421452 | + | 0.860914i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.5285 | − | 20.2713i | 0.735982 | − | 0.726760i | ||||
\(779\) | 19.4537 | − | 16.3236i | 0.697001 | − | 0.584853i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42.5518 | − | 15.4876i | 1.52262 | − | 0.554189i | ||||
\(782\) | −2.61119 | − | 3.77966i | −0.0933760 | − | 0.135160i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.7484 | − | 9.49091i | −0.383871 | − | 0.338961i | ||||
\(785\) | −3.83184 | − | 10.5279i | −0.136764 | − | 0.375757i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.6313 | + | 31.7379i | 0.949302 | + | 1.13133i | 0.991221 | + | 0.132214i | \(0.0422085\pi\) |
−0.0419189 | + | 0.999121i | \(0.513347\pi\) | |||||||
\(788\) | −0.993029 | + | 5.24422i | −0.0353752 | + | 0.186818i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.612616 | − | 0.0574907i | −0.0217959 | − | 0.00204543i | ||||
\(791\) | −4.09738 | + | 7.09688i | −0.145686 | + | 0.252336i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.55584 | + | 7.89095i | 0.161783 | + | 0.280216i | ||||
\(794\) | 10.3632 | + | 22.5946i | 0.367774 | + | 0.801854i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.1982 | + | 14.8045i | 0.609573 | + | 0.524730i | ||||
\(797\) | −4.25196 | + | 11.6822i | −0.150612 | + | 0.413803i | −0.991938 | − | 0.126725i | \(-0.959553\pi\) |
0.841326 | + | 0.540528i | \(0.181776\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.43244 | + | 0.428905i | 0.0860536 | + | 0.0151736i | ||||
\(800\) | −10.4893 | − | 24.4804i | −0.370852 | − | 0.865512i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 34.1686 | − | 2.77243i | 1.20653 | − | 0.0978979i | ||||
\(803\) | −44.1723 | − | 37.0650i | −1.55881 | − | 1.30799i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.713493 | + | 4.04642i | 0.0251473 | + | 0.142618i | ||||
\(806\) | 12.7593 | + | 3.50521i | 0.449428 | + | 0.123466i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 23.0652 | − | 15.5088i | 0.811431 | − | 0.545596i | ||||
\(809\) | − | 4.57993i | − | 0.161022i | −0.996754 | − | 0.0805109i | \(-0.974345\pi\) | ||
0.996754 | − | 0.0805109i | \(-0.0256552\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 23.9708i | − | 0.841727i | −0.907124 | − | 0.420864i | \(-0.861727\pi\) | ||
0.907124 | − | 0.420864i | \(-0.138273\pi\) | |||||||
\(812\) | 0.441681 | − | 35.0295i | 0.0155000 | − | 1.22929i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.7003 | − | 75.3512i | 0.725545 | − | 2.64106i | ||||
\(815\) | 0.191110 | + | 1.08384i | 0.00669429 | + | 0.0379652i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.2578 | + | 16.9983i | 0.708731 | + | 0.594696i | ||||
\(818\) | −2.36451 | − | 29.1411i | −0.0826730 | − | 1.01890i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.19500 | − | 1.33869i | 0.286182 | − | 0.0467492i | ||||
\(821\) | −7.46457 | − | 1.31620i | −0.260515 | − | 0.0459359i | 0.0418649 | − | 0.999123i | \(-0.486670\pi\) |
−0.302380 | + | 0.953187i | \(0.597781\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.9886 | − | 43.9282i | 0.557326 | − | 1.53124i | −0.266174 | − | 0.963925i | \(-0.585760\pi\) |
0.823500 | − | 0.567316i | \(-0.192018\pi\) | |||||||
\(824\) | −19.5644 | − | 2.08516i | −0.681558 | − | 0.0726402i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.30772 | + | 2.89307i | −0.219474 | + | 0.100663i | ||||
\(827\) | −15.4331 | − | 26.7308i | −0.536660 | − | 0.929522i | −0.999081 | − | 0.0428620i | \(-0.986352\pi\) |
0.462421 | − | 0.886661i | \(-0.346981\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.56407 | − | 9.63724i | 0.193248 | − | 0.334715i | −0.753077 | − | 0.657933i | \(-0.771431\pi\) |
0.946325 | + | 0.323217i | \(0.104764\pi\) | |||||||
\(830\) | 1.14148 | − | 12.1636i | 0.0396215 | − | 0.422203i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.96601 | − | 10.2576i | −0.276172 | − | 0.355618i | ||||
\(833\) | 1.81892 | + | 2.16771i | 0.0630220 | + | 0.0751067i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.14092 | + | 3.13466i | 0.0394833 | + | 0.108479i | ||||
\(836\) | −30.8839 | − | 11.6839i | −1.06814 | − | 0.404095i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.91149 | + | 6.84739i | −0.342387 | + | 0.236539i | ||||
\(839\) | 8.74658 | − | 3.18349i | 0.301965 | − | 0.109906i | −0.186594 | − | 0.982437i | \(-0.559745\pi\) |
0.488559 | + | 0.872531i | \(0.337523\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −46.6034 | + | 39.1049i | −1.60701 | + | 1.34844i | ||||
\(842\) | 14.1758 | + | 14.3557i | 0.488531 | + | 0.494730i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.47935 | − | 7.98942i | −0.154186 | − | 0.275007i | ||||
\(845\) | 4.84959 | + | 2.79991i | 0.166831 | + | 0.0963200i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.3399 | + | 12.8980i | −0.767609 | + | 0.443179i | ||||
\(848\) | 2.32725 | + | 2.91997i | 0.0799180 | + | 0.100272i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.32830 | + | 5.08531i | 0.0455604 | + | 0.174425i | ||||
\(851\) | 42.7690 | + | 15.5667i | 1.46610 | + | 0.533618i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.28870 | − | 12.9798i | 0.0783634 | − | 0.444421i | −0.920229 | − | 0.391381i | \(-0.871998\pi\) |
0.998592 | − | 0.0530406i | \(-0.0168913\pi\) | |||||||
\(854\) | −6.28293 | + | 13.2550i | −0.214997 | + | 0.453576i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.84264 | − | 1.97290i | −0.233877 | − | 0.0674324i | ||||
\(857\) | 9.69516 | − | 11.5542i | 0.331180 | − | 0.394685i | −0.574599 | − | 0.818435i | \(-0.694842\pi\) |
0.905779 | + | 0.423750i | \(0.139286\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.5457 | + | 4.32808i | −0.837490 | + | 0.147672i | −0.575914 | − | 0.817511i | \(-0.695354\pi\) |
−0.261577 | + | 0.965183i | \(0.584242\pi\) | |||||||
\(860\) | 2.85472 | + | 8.16202i | 0.0973451 | + | 0.278323i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.21971 | + | 1.71876i | −0.0415435 | + | 0.0585413i | ||||
\(863\) | 22.0216 | 0.749626 | 0.374813 | − | 0.927101i | \(-0.377707\pi\) | ||||
0.374813 | + | 0.927101i | \(0.377707\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.03425 | 0.273173 | ||||||||
\(866\) | 2.31856 | − | 3.26721i | 0.0787879 | − | 0.111024i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.03272 | + | 20.1075i | 0.238706 | + | 0.682493i | ||||
\(869\) | 3.96195 | − | 0.698599i | 0.134400 | − | 0.0236984i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.57787 | − | 7.83921i | 0.222883 | − | 0.265621i | ||||
\(872\) | −15.6792 | − | 4.52070i | −0.530964 | − | 0.153090i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.23767 | − | 17.3789i | 0.278643 | − | 0.587849i | ||||
\(875\) | 1.68323 | − | 9.54610i | 0.0569037 | − | 0.322717i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.5090 | − | 7.46466i | −0.692539 | − | 0.252064i | −0.0283170 | − | 0.999599i | \(-0.509015\pi\) |
−0.664222 | + | 0.747535i | \(0.731237\pi\) | |||||||
\(878\) | 9.60067 | + | 36.7555i | 0.324007 | + | 1.24044i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.72935 | − | 8.44324i | −0.226846 | − | 0.284621i | ||||
\(881\) | 7.29454 | − | 4.21150i | 0.245759 | − | 0.141889i | −0.372062 | − | 0.928208i | \(-0.621349\pi\) |
0.617821 | + | 0.786319i | \(0.288016\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.6426 | − | 12.4953i | −0.728330 | − | 0.420502i | 0.0894807 | − | 0.995989i | \(-0.471479\pi\) |
−0.817811 | + | 0.575487i | \(0.804813\pi\) | |||||||
\(884\) | 1.25344 | + | 2.23564i | 0.0421576 | + | 0.0751928i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.8896 | + | 26.2181i | 0.869779 | + | 0.880815i | ||||
\(887\) | 34.3044 | − | 28.7848i | 1.15183 | − | 0.966499i | 0.152068 | − | 0.988370i | \(-0.451407\pi\) |
0.999761 | + | 0.0218707i | \(0.00696222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.96058 | + | 2.53344i | −0.233450 | + | 0.0849689i | ||||
\(890\) | −3.93085 | + | 2.71564i | −0.131762 | + | 0.0910286i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −34.5470 | − | 13.0696i | −1.15672 | − | 0.437604i | ||||
\(893\) | 3.53665 | + | 9.71686i | 0.118349 | + | 0.325162i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.95013 | + | 2.32407i | 0.0651855 | + | 0.0776850i | ||||
\(896\) | 6.29710 | − | 19.9374i | 0.210371 | − | 0.666062i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.98068 | + | 31.7619i | −0.0994666 | + | 1.05991i | ||||
\(899\) | 27.3132 | − | 47.3078i | 0.910945 | − | 1.57780i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.368441 | − | 0.638158i | −0.0122745 | − | 0.0212601i | ||||
\(902\) | −49.3486 | + | 22.6340i | −1.64313 | + | 0.753630i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.4714 | + | 1.32920i | 0.414794 | + | 0.0442085i | ||||
\(905\) | 1.12456 | − | 3.08970i | 0.0373817 | − | 0.102705i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.5142 | + | 5.55680i | 1.04641 | + | 0.184511i | 0.670320 | − | 0.742072i | \(-0.266157\pi\) |
0.376091 | + | 0.926583i | \(0.377268\pi\) | |||||||
\(908\) | −26.1826 | + | 4.27707i | −0.868902 | + | 0.141939i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.185396 | − | 2.28490i | −0.00614582 | − | 0.0757436i | ||||
\(911\) | 21.9054 | + | 18.3808i | 0.725757 | + | 0.608983i | 0.928971 | − | 0.370152i | \(-0.120694\pi\) |
−0.203214 | + | 0.979134i | \(0.565139\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.8708 | + | 78.6650i | 0.459055 | + | 2.60343i | ||||
\(914\) | −5.55139 | + | 20.2076i | −0.183624 | + | 0.668410i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.0870387 | − | 6.90300i | 0.00287584 | − | 0.228082i | ||||
\(917\) | 4.44416i | 0.146759i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.7726i | 0.916132i | 0.888918 | + | 0.458066i | \(0.151458\pi\) | ||||
−0.888918 | + | 0.458066i | \(0.848542\pi\) | |||||||
\(920\) | 5.21859 | − | 3.50892i | 0.172052 | − | 0.115686i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −42.2338 | − | 11.6024i | −1.39090 | − | 0.382104i | ||||
\(923\) | −2.55522 | − | 14.4914i | −0.0841062 | − | 0.476990i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −39.8899 | − | 33.4716i | −1.31157 | − | 1.10054i | ||||
\(926\) | 32.2714 | − | 2.61849i | 1.06050 | − | 0.0860489i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −49.2833 | + | 21.1168i | −1.61780 | + | 0.693192i | ||||
\(929\) | 9.40060 | + | 1.65758i | 0.308424 | + | 0.0543834i | 0.325718 | − | 0.945467i | \(-0.394394\pi\) |
−0.0172941 | + | 0.999850i | \(0.505505\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.05180 | + | 11.1322i | −0.132792 | + | 0.364844i | ||||
\(932\) | −24.7790 | − | 21.3301i | −0.811663 | − | 0.698692i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.1970 | − | 46.2154i | −0.693585 | − | 1.51222i | ||||
\(935\) | 1.06536 | + | 1.84527i | 0.0348411 | + | 0.0603466i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.13866 | + | 1.97222i | −0.0371986 | + | 0.0644298i | −0.884025 | − | 0.467439i | \(-0.845177\pi\) |
0.846827 | + | 0.531869i | \(0.178510\pi\) | |||||||
\(938\) | 16.4023 | + | 1.53927i | 0.535555 | + | 0.0502589i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.629058 | + | 3.32208i | −0.0205176 | + | 0.108354i | ||||
\(941\) | 4.48164 | + | 5.34101i | 0.146097 | + | 0.174112i | 0.834130 | − | 0.551567i | \(-0.185970\pi\) |
−0.688033 | + | 0.725679i | \(0.741526\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.8153 | − | 29.7148i | −0.352195 | − | 0.967647i | ||||
\(944\) | 7.96140 | + | 7.02998i | 0.259121 | + | 0.228806i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.1350 | − | 46.5149i | −1.04480 | − | 1.51233i | ||||
\(947\) | −42.9198 | + | 15.6215i | −1.39471 | + | 0.507631i | −0.926603 | − | 0.376042i | \(-0.877285\pi\) |
−0.468103 | + | 0.883674i | \(0.655063\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.3541 | + | 12.0445i | −0.465955 | + | 0.390982i | ||||
\(950\) | −15.6569 | + | 15.4607i | −0.507975 | + | 0.501611i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.81420 | + | 3.70594i | −0.0587987 | + | 0.120110i | ||||
\(953\) | 26.2534 | + | 15.1574i | 0.850431 | + | 0.490997i | 0.860796 | − | 0.508950i | \(-0.169966\pi\) |
−0.0103652 | + | 0.999946i | \(0.503299\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.27046 | − | 1.31085i | 0.0734704 | − | 0.0424181i | ||||
\(956\) | 1.79070 | + | 1.06419i | 0.0579154 | + | 0.0344183i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −27.9865 | + | 7.31019i | −0.904204 | + | 0.236181i | ||||
\(959\) | −7.43966 | − | 2.70782i | −0.240239 | − | 0.0874400i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.384864 | + | 2.18267i | −0.0124150 | + | 0.0704089i | ||||
\(962\) | −22.9459 | − | 10.8765i | −0.739805 | − | 0.350671i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.8503 | − | 25.4944i | −0.671544 | − | 0.821121i | ||||
\(965\) | −1.83307 | + | 2.18457i | −0.0590088 | + | 0.0703239i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.8569 | − | 5.44090i | 0.992290 | − | 0.174967i | 0.346144 | − | 0.938181i | \(-0.387491\pi\) |
0.646146 | + | 0.763214i | \(0.276380\pi\) | |||||||
\(968\) | 31.9066 | + | 23.2527i | 1.02552 | + | 0.747370i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.88265 | + | 4.17459i | 0.188881 | + | 0.134038i | ||||
\(971\) | −1.61116 | −0.0517047 | −0.0258523 | − | 0.999666i | \(-0.508230\pi\) | ||||
−0.0258523 | + | 0.999666i | \(0.508230\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.9535 | −1.05644 | ||||||||
\(974\) | −19.6351 | − | 13.9339i | −0.629148 | − | 0.446471i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.4432 | + | 0.566055i | 0.718389 | + | 0.0181190i | ||||
\(977\) | −26.4012 | + | 4.65524i | −0.844648 | + | 0.148934i | −0.579194 | − | 0.815190i | \(-0.696633\pi\) |
−0.265453 | + | 0.964124i | \(0.585522\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0794 | − | 23.9297i | 0.641741 | − | 0.764797i | ||||
\(980\) | −2.99851 | + | 2.45230i | −0.0957839 | + | 0.0783358i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.1628 | + | 8.60924i | 0.579597 | + | 0.274732i | ||||
\(983\) | 4.56612 | − | 25.8958i | 0.145637 | − | 0.825947i | −0.821217 | − | 0.570616i | \(-0.806704\pi\) |
0.966854 | − | 0.255331i | \(-0.0821844\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.35492 | + | 0.493152i | 0.0431715 | + | 0.0157131i | ||||
\(986\) | 10.2376 | − | 2.67411i | 0.326033 | − | 0.0851610i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.48180 | + | 9.22419i | −0.174399 | + | 0.293461i | ||||
\(989\) | 28.5173 | − | 16.4645i | 0.906797 | − | 0.523540i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.2827 | − | 11.7102i | −0.644302 | − | 0.371988i | 0.141968 | − | 0.989871i | \(-0.454657\pi\) |
−0.786270 | + | 0.617883i | \(0.787990\pi\) | |||||||
\(992\) | 23.7685 | − | 22.3155i | 0.754652 | − | 0.708517i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.8560 | − | 16.6448i | 0.534641 | − | 0.527942i | ||||
\(995\) | 4.69607 | − | 3.94047i | 0.148876 | − | 0.124921i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.48788 | − | 1.99742i | 0.173803 | − | 0.0632590i | −0.253653 | − | 0.967295i | \(-0.581632\pi\) |
0.427456 | + | 0.904036i | \(0.359410\pi\) | |||||||
\(998\) | 5.75921 | + | 8.33636i | 0.182304 | + | 0.263883i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.2.l.a.143.12 | 96 | ||
3.2 | odd | 2 | 108.2.l.a.47.5 | yes | 96 | ||
4.3 | odd | 2 | inner | 324.2.l.a.143.1 | 96 | ||
9.2 | odd | 6 | 972.2.l.d.107.16 | 96 | |||
9.4 | even | 3 | 972.2.l.b.755.11 | 96 | |||
9.5 | odd | 6 | 972.2.l.c.755.6 | 96 | |||
9.7 | even | 3 | 972.2.l.a.107.1 | 96 | |||
12.11 | even | 2 | 108.2.l.a.47.16 | yes | 96 | ||
27.4 | even | 9 | 108.2.l.a.23.16 | yes | 96 | ||
27.5 | odd | 18 | 972.2.l.b.215.12 | 96 | |||
27.13 | even | 9 | 972.2.l.d.863.7 | 96 | |||
27.14 | odd | 18 | 972.2.l.a.863.10 | 96 | |||
27.22 | even | 9 | 972.2.l.c.215.5 | 96 | |||
27.23 | odd | 18 | inner | 324.2.l.a.179.1 | 96 | ||
36.7 | odd | 6 | 972.2.l.a.107.10 | 96 | |||
36.11 | even | 6 | 972.2.l.d.107.7 | 96 | |||
36.23 | even | 6 | 972.2.l.c.755.5 | 96 | |||
36.31 | odd | 6 | 972.2.l.b.755.12 | 96 | |||
108.23 | even | 18 | inner | 324.2.l.a.179.12 | 96 | ||
108.31 | odd | 18 | 108.2.l.a.23.5 | ✓ | 96 | ||
108.59 | even | 18 | 972.2.l.b.215.11 | 96 | |||
108.67 | odd | 18 | 972.2.l.d.863.16 | 96 | |||
108.95 | even | 18 | 972.2.l.a.863.1 | 96 | |||
108.103 | odd | 18 | 972.2.l.c.215.6 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.l.a.23.5 | ✓ | 96 | 108.31 | odd | 18 | ||
108.2.l.a.23.16 | yes | 96 | 27.4 | even | 9 | ||
108.2.l.a.47.5 | yes | 96 | 3.2 | odd | 2 | ||
108.2.l.a.47.16 | yes | 96 | 12.11 | even | 2 | ||
324.2.l.a.143.1 | 96 | 4.3 | odd | 2 | inner | ||
324.2.l.a.143.12 | 96 | 1.1 | even | 1 | trivial | ||
324.2.l.a.179.1 | 96 | 27.23 | odd | 18 | inner | ||
324.2.l.a.179.12 | 96 | 108.23 | even | 18 | inner | ||
972.2.l.a.107.1 | 96 | 9.7 | even | 3 | |||
972.2.l.a.107.10 | 96 | 36.7 | odd | 6 | |||
972.2.l.a.863.1 | 96 | 108.95 | even | 18 | |||
972.2.l.a.863.10 | 96 | 27.14 | odd | 18 | |||
972.2.l.b.215.11 | 96 | 108.59 | even | 18 | |||
972.2.l.b.215.12 | 96 | 27.5 | odd | 18 | |||
972.2.l.b.755.11 | 96 | 9.4 | even | 3 | |||
972.2.l.b.755.12 | 96 | 36.31 | odd | 6 | |||
972.2.l.c.215.5 | 96 | 27.22 | even | 9 | |||
972.2.l.c.215.6 | 96 | 108.103 | odd | 18 | |||
972.2.l.c.755.5 | 96 | 36.23 | even | 6 | |||
972.2.l.c.755.6 | 96 | 9.5 | odd | 6 | |||
972.2.l.d.107.7 | 96 | 36.11 | even | 6 | |||
972.2.l.d.107.16 | 96 | 9.2 | odd | 6 | |||
972.2.l.d.863.7 | 96 | 27.13 | even | 9 | |||
972.2.l.d.863.16 | 96 | 108.67 | odd | 18 |