Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(269,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.269");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.bb (of order \(6\), degree \(2\), 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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.8 | ||
Character | \(\chi\) | \(=\) | 945.269 |
Dual form | 945.2.bb.b.404.8 |
$q$-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 \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.187042 | − | 0.323967i | −0.132259 | − | 0.229079i | 0.792288 | − | 0.610147i | \(-0.208890\pi\) |
−0.924547 | + | 0.381068i | \(0.875556\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.930030 | − | 1.61086i | 0.465015 | − | 0.805430i | ||||
\(5\) | 2.23199 | − | 0.135023i | 0.998175 | − | 0.0603840i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46237 | − | 0.967860i | 0.930687 | − | 0.365817i | ||||
\(8\) | −1.44399 | −0.510527 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.461219 | − | 0.697834i | −0.145850 | − | 0.220675i | ||||
\(11\) | 0.947907 | + | 0.547275i | 0.285805 | + | 0.165009i | 0.636048 | − | 0.771649i | \(-0.280568\pi\) |
−0.350244 | + | 0.936659i | \(0.613901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.52806 | 1.53321 | 0.766604 | − | 0.642120i | \(-0.221945\pi\) | ||||
0.766604 | + | 0.642120i | \(0.221945\pi\) | |||||||
\(14\) | −0.774121 | − | 0.616694i | −0.206892 | − | 0.164818i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.58997 | − | 2.75392i | −0.397494 | − | 0.688479i | ||||
\(17\) | −0.343551 | − | 0.198349i | −0.0833234 | − | 0.0481068i | 0.457759 | − | 0.889076i | \(-0.348652\pi\) |
−0.541083 | + | 0.840969i | \(0.681985\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00979 | + | 2.31505i | −0.919909 | + | 0.531110i | −0.883606 | − | 0.468231i | \(-0.844892\pi\) |
−0.0363031 | + | 0.999341i | \(0.511558\pi\) | |||||||
\(20\) | 1.85831 | − | 3.72099i | 0.415532 | − | 0.832040i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.409454i | − | 0.0872958i | ||||||
\(23\) | 1.81197 | + | 3.13842i | 0.377822 | + | 0.654406i | 0.990745 | − | 0.135736i | \(-0.0433400\pi\) |
−0.612923 | + | 0.790142i | \(0.710007\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.96354 | − | 0.602738i | 0.992708 | − | 0.120548i | ||||
\(26\) | −1.03398 | − | 1.79091i | −0.202780 | − | 0.351226i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.730988 | − | 4.86667i | 0.138144 | − | 0.919714i | ||||
\(29\) | 7.19269i | 1.33565i | 0.744319 | + | 0.667825i | \(0.232774\pi\) | ||||
−0.744319 | + | 0.667825i | \(0.767226\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.46215 | − | 1.99887i | −0.621821 | − | 0.359008i | 0.155757 | − | 0.987795i | \(-0.450218\pi\) |
−0.777578 | + | 0.628787i | \(0.783552\pi\) | |||||||
\(32\) | −2.03877 | + | 3.53126i | −0.360407 | + | 0.624244i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.148399i | 0.0254502i | ||||||||
\(35\) | 5.36529 | − | 2.49273i | 0.906899 | − | 0.421348i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.338363 | − | 0.195354i | 0.0556265 | − | 0.0321160i | −0.471929 | − | 0.881637i | \(-0.656442\pi\) |
0.527555 | + | 0.849521i | \(0.323109\pi\) | |||||||
\(38\) | 1.50000 | + | 0.866025i | 0.243332 | + | 0.140488i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.22296 | + | 0.194971i | −0.509595 | + | 0.0308276i | ||||
\(41\) | −10.9717 | −1.71350 | −0.856748 | − | 0.515735i | \(-0.827519\pi\) | ||||
−0.856748 | + | 0.515735i | \(0.827519\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.44210i | − | 0.524916i | −0.964943 | − | 0.262458i | \(-0.915467\pi\) | ||
0.964943 | − | 0.262458i | \(-0.0845331\pi\) | |||||||
\(44\) | 1.76317 | − | 1.01796i | 0.265807 | − | 0.153464i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.677829 | − | 1.17403i | 0.0999404 | − | 0.173102i | ||||
\(47\) | −4.21599 | + | 2.43410i | −0.614965 | + | 0.355050i | −0.774906 | − | 0.632076i | \(-0.782203\pi\) |
0.159941 | + | 0.987127i | \(0.448870\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.12649 | − | 4.76645i | 0.732356 | − | 0.680922i | ||||
\(50\) | −1.12366 | − | 1.49528i | −0.158909 | − | 0.211465i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.14126 | − | 8.90493i | 0.712965 | − | 1.23489i | ||||
\(53\) | 2.58997 | − | 4.48597i | 0.355760 | − | 0.616195i | −0.631487 | − | 0.775386i | \(-0.717555\pi\) |
0.987248 | + | 0.159191i | \(0.0508886\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.18961 | + | 1.09352i | 0.295247 | + | 0.147450i | ||||
\(56\) | −3.55563 | + | 1.39758i | −0.475141 | + | 0.186759i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.33019 | − | 1.34534i | 0.305969 | − | 0.176651i | ||||
\(59\) | −4.11222 | + | 7.12257i | −0.535365 | + | 0.927280i | 0.463780 | + | 0.885950i | \(0.346493\pi\) |
−0.999146 | + | 0.0413294i | \(0.986841\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.91120 | + | 1.68078i | −0.372741 | + | 0.215202i | −0.674655 | − | 0.738133i | \(-0.735708\pi\) |
0.301914 | + | 0.953335i | \(0.402374\pi\) | |||||||
\(62\) | 1.49550i | 0.189928i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.83455 | −0.604319 | ||||||||
\(65\) | 12.3386 | − | 0.746413i | 1.53041 | − | 0.0925811i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.20617 | − | 2.42844i | −0.513866 | − | 0.296681i | 0.220555 | − | 0.975374i | \(-0.429213\pi\) |
−0.734421 | + | 0.678694i | \(0.762546\pi\) | |||||||
\(68\) | −0.639026 | + | 0.368942i | −0.0774933 | + | 0.0447408i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.81110 | − | 1.27193i | −0.216467 | − | 0.152025i | ||||
\(71\) | − | 2.84053i | − | 0.337109i | −0.985692 | − | 0.168555i | \(-0.946090\pi\) | ||
0.985692 | − | 0.168555i | \(-0.0539100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.357255 | + | 0.618785i | −0.0418136 | + | 0.0724233i | −0.886175 | − | 0.463351i | \(-0.846647\pi\) |
0.844361 | + | 0.535774i | \(0.179980\pi\) | |||||||
\(74\) | −0.126576 | − | 0.0730788i | −0.0147142 | − | 0.00849524i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.61228i | 0.987897i | ||||||||
\(77\) | 2.86378 | + | 0.430149i | 0.326358 | + | 0.0490200i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.40379 | − | 4.16348i | −0.270447 | − | 0.468428i | 0.698529 | − | 0.715582i | \(-0.253838\pi\) |
−0.968976 | + | 0.247153i | \(0.920505\pi\) | |||||||
\(80\) | −3.92064 | − | 5.93202i | −0.438341 | − | 0.663220i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.05218 | + | 3.55447i | 0.226625 | + | 0.392526i | ||||
\(83\) | − | 12.9498i | − | 1.42143i | −0.703481 | − | 0.710714i | \(-0.748372\pi\) | ||
0.703481 | − | 0.710714i | \(-0.251628\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.793583 | − | 0.396326i | −0.0860762 | − | 0.0429876i | ||||
\(86\) | −1.11513 | + | 0.643818i | −0.120247 | + | 0.0694247i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.36877 | − | 0.790258i | −0.145911 | − | 0.0842418i | ||||
\(89\) | 6.38611 | + | 11.0611i | 0.676926 | + | 1.17247i | 0.975902 | + | 0.218210i | \(0.0700218\pi\) |
−0.298975 | + | 0.954261i | \(0.596645\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.6121 | − | 5.35039i | 1.42694 | − | 0.560873i | ||||
\(92\) | 6.74074 | 0.702771 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.57713 | + | 0.910559i | 0.162669 | + | 0.0939170i | ||||
\(95\) | −8.63722 | + | 5.70858i | −0.886160 | + | 0.585688i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.84872 | 0.492313 | 0.246156 | − | 0.969230i | \(-0.420832\pi\) | ||||
0.246156 | + | 0.969230i | \(0.420832\pi\) | |||||||
\(98\) | −2.50304 | − | 0.769285i | −0.252845 | − | 0.0777095i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.64532 | − | 8.55613i | 0.364532 | − | 0.855613i | ||||
\(101\) | 9.38987 | − | 16.2637i | 0.934327 | − | 1.61830i | 0.158498 | − | 0.987359i | \(-0.449335\pi\) |
0.775829 | − | 0.630943i | \(-0.217332\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.20360 | + | 12.4770i | 0.709792 | + | 1.22940i | 0.964934 | + | 0.262492i | \(0.0845443\pi\) |
−0.255142 | + | 0.966904i | \(0.582122\pi\) | |||||||
\(104\) | −7.98245 | −0.782744 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.93774 | −0.188210 | ||||||||
\(107\) | −6.79378 | − | 11.7672i | −0.656779 | − | 1.13758i | −0.981445 | − | 0.191746i | \(-0.938585\pi\) |
0.324665 | − | 0.945829i | \(-0.394748\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.09325 | − | 5.35766i | 0.296279 | − | 0.513171i | −0.679002 | − | 0.734136i | \(-0.737587\pi\) |
0.975282 | + | 0.220965i | \(0.0709207\pi\) | |||||||
\(110\) | −0.0552855 | − | 0.913895i | −0.00527127 | − | 0.0871365i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.58050 | − | 5.24228i | −0.621799 | − | 0.495349i | ||||
\(113\) | −6.06737 | −0.570770 | −0.285385 | − | 0.958413i | \(-0.592121\pi\) | ||||
−0.285385 | + | 0.958413i | \(0.592121\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.46805 | + | 6.76026i | 0.416648 | + | 0.630398i | ||||
\(116\) | 11.5864 | + | 6.68942i | 1.07577 | + | 0.621097i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.07663 | 0.283227 | ||||||||
\(119\) | −1.03792 | − | 0.155899i | −0.0951462 | − | 0.0142913i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.90098 | − | 8.48875i | −0.445544 | − | 0.771704i | ||||
\(122\) | 1.08903 | + | 0.628754i | 0.0985965 | + | 0.0569247i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.43981 | + | 3.71803i | −0.578312 | + | 0.333889i | ||||
\(125\) | 10.9972 | − | 2.01549i | 0.983617 | − | 0.180271i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.41561i | 0.125615i | 0.998026 | + | 0.0628076i | \(0.0200055\pi\) | ||||
−0.998026 | + | 0.0628076i | \(0.979995\pi\) | |||||||
\(128\) | 4.98181 | + | 8.62875i | 0.440334 | + | 0.762681i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.54964 | − | 3.85767i | −0.223619 | − | 0.338340i | ||||
\(131\) | −6.05433 | − | 10.4864i | −0.528969 | − | 0.916201i | −0.999429 | − | 0.0337801i | \(-0.989245\pi\) |
0.470460 | − | 0.882421i | \(-0.344088\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.63293 | + | 9.58143i | −0.661859 | + | 0.830815i | ||||
\(134\) | 1.81688i | 0.156955i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.496084 | + | 0.286414i | 0.0425388 | + | 0.0245598i | ||||
\(137\) | 4.09062 | − | 7.08516i | 0.349485 | − | 0.605326i | −0.636673 | − | 0.771134i | \(-0.719690\pi\) |
0.986158 | + | 0.165808i | \(0.0530231\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.6624i | 0.904375i | 0.891923 | + | 0.452188i | \(0.149356\pi\) | ||||
−0.891923 | + | 0.452188i | \(0.850644\pi\) | |||||||
\(140\) | 0.974447 | − | 10.9610i | 0.0823558 | − | 0.926377i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.920237 | + | 0.531299i | −0.0772246 | + | 0.0445856i | ||||
\(143\) | 5.24009 | + | 3.02537i | 0.438198 | + | 0.252994i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.971176 | + | 16.0540i | 0.0806518 | + | 1.33321i | ||||
\(146\) | 0.267287 | 0.0221209 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 0.726740i | − | 0.0597377i | ||||||
\(149\) | −20.4554 | + | 11.8100i | −1.67578 | + | 0.967509i | −0.711470 | + | 0.702716i | \(0.751970\pi\) |
−0.964305 | + | 0.264793i | \(0.914696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.70250 | + | 11.6091i | −0.545441 | + | 0.944732i | 0.453138 | + | 0.891441i | \(0.350305\pi\) |
−0.998579 | + | 0.0532917i | \(0.983029\pi\) | |||||||
\(152\) | 5.79009 | − | 3.34291i | 0.469638 | − | 0.271146i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.396294 | − | 1.00822i | −0.0319343 | − | 0.0812451i | ||||
\(155\) | −7.99737 | − | 3.99399i | −0.642365 | − | 0.320805i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.11710 | + | 12.3272i | −0.568006 | + | 0.983816i | 0.428757 | + | 0.903420i | \(0.358952\pi\) |
−0.996763 | + | 0.0803959i | \(0.974382\pi\) | |||||||
\(158\) | −0.899219 | + | 1.55749i | −0.0715381 | + | 0.123908i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.07372 | + | 8.15700i | −0.322055 | + | 0.644868i | ||||
\(161\) | 7.49928 | + | 5.97421i | 0.591026 | + | 0.470834i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.8150 | + | 11.4402i | −1.55203 | + | 0.896064i | −0.554051 | + | 0.832483i | \(0.686919\pi\) |
−0.997977 | + | 0.0635808i | \(0.979748\pi\) | |||||||
\(164\) | −10.2040 | + | 17.6739i | −0.796802 | + | 1.38010i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.19531 | + | 2.42216i | −0.325619 | + | 0.187996i | ||||
\(167\) | 13.9243i | 1.07750i | 0.842466 | + | 0.538749i | \(0.181103\pi\) | ||||
−0.842466 | + | 0.538749i | \(0.818897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 17.5594 | 1.35073 | ||||||||
\(170\) | 0.0200372 | + | 0.331224i | 0.00153678 | + | 0.0254037i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.54474 | − | 3.20126i | −0.422783 | − | 0.244094i | ||||
\(173\) | −17.3793 | + | 10.0339i | −1.32132 | + | 0.762865i | −0.983939 | − | 0.178503i | \(-0.942875\pi\) |
−0.337382 | + | 0.941368i | \(0.609541\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.6387 | − | 6.28817i | 0.879802 | − | 0.475341i | ||||
\(176\) | − | 3.48061i | − | 0.262361i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.38894 | − | 4.13777i | 0.179059 | − | 0.310139i | ||||
\(179\) | −1.93844 | − | 1.11916i | −0.144886 | − | 0.0836501i | 0.425805 | − | 0.904815i | \(-0.359991\pi\) |
−0.570691 | + | 0.821165i | \(0.693324\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.19332i | 0.311687i | 0.987782 | + | 0.155843i | \(0.0498095\pi\) | ||||
−0.987782 | + | 0.155843i | \(0.950190\pi\) | |||||||
\(182\) | −4.27938 | − | 3.40912i | −0.317209 | − | 0.252701i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.61646 | − | 4.53184i | −0.192888 | − | 0.334092i | ||||
\(185\) | 0.728844 | − | 0.481714i | 0.0535857 | − | 0.0354163i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.217103 | − | 0.376034i | −0.0158761 | − | 0.0274983i | ||||
\(188\) | 9.05515i | 0.660415i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.46491 | + | 1.73042i | 0.251371 | + | 0.125538i | ||||
\(191\) | 5.82348 | − | 3.36219i | 0.421372 | − | 0.243279i | −0.274292 | − | 0.961646i | \(-0.588444\pi\) |
0.695664 | + | 0.718367i | \(0.255110\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.64343 | + | 1.52618i | 0.190278 | + | 0.109857i | 0.592113 | − | 0.805855i | \(-0.298294\pi\) |
−0.401835 | + | 0.915712i | \(0.631627\pi\) | |||||||
\(194\) | −0.906915 | − | 1.57082i | −0.0651127 | − | 0.112779i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.91029 | − | 12.6910i | −0.207878 | − | 0.906501i | ||||
\(197\) | 25.8426 | 1.84121 | 0.920606 | − | 0.390493i | \(-0.127696\pi\) | ||||
0.920606 | + | 0.390493i | \(0.127696\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.9566 | + | 8.63522i | 1.06025 | + | 0.612135i | 0.925501 | − | 0.378745i | \(-0.123644\pi\) |
0.134747 | + | 0.990880i | \(0.456978\pi\) | |||||||
\(200\) | −7.16729 | + | 0.870346i | −0.506804 | + | 0.0615428i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.02521 | −0.494292 | ||||||||
\(203\) | 6.96152 | + | 17.7110i | 0.488603 | + | 1.24307i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.4888 | + | 1.48143i | −1.71037 | + | 0.103468i | ||||
\(206\) | 2.69475 | − | 4.66745i | 0.187752 | − | 0.325197i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.78947 | − | 15.2238i | −0.609440 | − | 1.05558i | ||||
\(209\) | −5.06788 | −0.350553 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0537 | 1.58708 | 0.793540 | − | 0.608518i | \(-0.208236\pi\) | ||||
0.793540 | + | 0.608518i | \(0.208236\pi\) | |||||||
\(212\) | −4.81751 | − | 8.34417i | −0.330868 | − | 0.573080i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.54145 | + | 4.40191i | −0.173730 | + | 0.300909i | ||||
\(215\) | −0.464762 | − | 7.68273i | −0.0316965 | − | 0.523958i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.4597 | − | 1.57108i | −0.710052 | − | 0.106652i | ||||
\(218\) | −2.31427 | −0.156742 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.79791 | − | 2.51015i | 0.256055 | − | 0.169234i | ||||
\(221\) | −1.89917 | − | 1.09649i | −0.127752 | − | 0.0737577i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.2615 | −1.22288 | −0.611441 | − | 0.791290i | \(-0.709410\pi\) | ||||
−0.611441 | + | 0.791290i | \(0.709410\pi\) | |||||||
\(224\) | −1.60244 | + | 10.6685i | −0.107068 | + | 0.712819i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.13485 | + | 1.96562i | 0.0754893 | + | 0.130751i | ||||
\(227\) | −8.75085 | − | 5.05231i | −0.580814 | − | 0.335333i | 0.180643 | − | 0.983549i | \(-0.442182\pi\) |
−0.761457 | + | 0.648216i | \(0.775516\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.3730 | + | 11.1850i | −1.28021 | + | 0.739128i | −0.976886 | − | 0.213761i | \(-0.931429\pi\) |
−0.303320 | + | 0.952889i | \(0.598095\pi\) | |||||||
\(230\) | 1.35438 | − | 2.71195i | 0.0893055 | − | 0.178821i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 10.3862i | − | 0.681885i | ||||||
\(233\) | −11.3370 | − | 19.6362i | −0.742709 | − | 1.28641i | −0.951258 | − | 0.308398i | \(-0.900207\pi\) |
0.208549 | − | 0.978012i | \(-0.433126\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.08137 | + | 6.00214i | −0.592403 | + | 0.391536i | ||||
\(236\) | 7.64897 | + | 13.2484i | 0.497906 | + | 0.862398i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.143629 | + | 0.365412i | 0.00931010 | + | 0.0236861i | ||||
\(239\) | 16.5614i | 1.07127i | 0.844451 | + | 0.535633i | \(0.179927\pi\) | ||||
−0.844451 | + | 0.535633i | \(0.820073\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.9504 | + | 12.6731i | 1.41395 | + | 0.816344i | 0.995758 | − | 0.0920147i | \(-0.0293307\pi\) |
0.418192 | + | 0.908359i | \(0.362664\pi\) | |||||||
\(242\) | −1.83338 | + | 3.17551i | −0.117854 | + | 0.204129i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.25271i | 0.400289i | ||||||||
\(245\) | 10.7987 | − | 11.3309i | 0.689903 | − | 0.723902i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.1664 | + | 12.7978i | −1.41041 | + | 0.814302i | ||||
\(248\) | 4.99931 | + | 2.88635i | 0.317456 | + | 0.183284i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.70989 | − | 3.18573i | −0.171388 | − | 0.201483i | ||||
\(251\) | 16.2074 | 1.02300 | 0.511501 | − | 0.859283i | \(-0.329090\pi\) | ||||
0.511501 | + | 0.859283i | \(0.329090\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.96658i | 0.249377i | ||||||||
\(254\) | 0.458611 | − | 0.264779i | 0.0287758 | − | 0.0166137i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.97093 | + | 5.14581i | −0.185683 | + | 0.321613i | ||||
\(257\) | 4.22870 | − | 2.44144i | 0.263779 | − | 0.152293i | −0.362278 | − | 0.932070i | \(-0.618001\pi\) |
0.626057 | + | 0.779777i | \(0.284668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.644098 | − | 0.808521i | 0.0400223 | − | 0.0502390i | ||||
\(260\) | 10.2729 | − | 20.5699i | 0.637096 | − | 1.27569i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.26483 | + | 3.92280i | −0.139922 | + | 0.242351i | ||||
\(263\) | 7.30925 | − | 12.6600i | 0.450707 | − | 0.780648i | −0.547723 | − | 0.836660i | \(-0.684505\pi\) |
0.998430 | + | 0.0560119i | \(0.0178385\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.17508 | − | 10.3623i | 0.317903 | − | 0.636553i | ||||
\(266\) | 4.53174 | + | 0.680682i | 0.277859 | + | 0.0417353i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.82374 | + | 4.51704i | −0.477911 | + | 0.275922i | ||||
\(269\) | −6.53241 | + | 11.3145i | −0.398288 | + | 0.689856i | −0.993515 | − | 0.113702i | \(-0.963729\pi\) |
0.595227 | + | 0.803558i | \(0.297062\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.4053 | + | 12.9357i | −1.36102 | + | 0.785787i | −0.989760 | − | 0.142740i | \(-0.954409\pi\) |
−0.371264 | + | 0.928528i | \(0.621075\pi\) | |||||||
\(272\) | 1.26148i | 0.0764885i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.06047 | −0.184890 | ||||||||
\(275\) | 5.03484 | + | 2.14508i | 0.303612 | + | 0.129353i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.3287 | + | 16.3556i | 1.70210 | + | 0.982710i | 0.943627 | + | 0.331011i | \(0.107390\pi\) |
0.758478 | + | 0.651699i | \(0.225943\pi\) | |||||||
\(278\) | 3.45427 | − | 1.99432i | 0.207173 | − | 0.119612i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.74741 | + | 3.59947i | −0.462996 | + | 0.215109i | ||||
\(281\) | − | 21.1295i | − | 1.26048i | −0.776400 | − | 0.630241i | \(-0.782956\pi\) | ||
0.776400 | − | 0.630241i | \(-0.217044\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.64369 | − | 4.57901i | 0.157151 | − | 0.272194i | −0.776689 | − | 0.629884i | \(-0.783102\pi\) |
0.933840 | + | 0.357690i | \(0.116436\pi\) | |||||||
\(284\) | −4.57570 | − | 2.64178i | −0.271518 | − | 0.156761i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 2.26348i | − | 0.133843i | ||||||
\(287\) | −27.0164 | + | 10.6191i | −1.59473 | + | 0.626826i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.42132 | − | 14.5861i | −0.495371 | − | 0.858009i | ||||
\(290\) | 5.01931 | − | 3.31740i | 0.294744 | − | 0.194805i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.664517 | + | 1.15098i | 0.0388879 | + | 0.0673558i | ||||
\(293\) | − | 19.2536i | − | 1.12481i | −0.826862 | − | 0.562405i | \(-0.809876\pi\) | ||
0.826862 | − | 0.562405i | \(-0.190124\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.21671 | + | 16.4527i | −0.478395 | + | 0.957915i | ||||
\(296\) | −0.488592 | + | 0.282089i | −0.0283988 | + | 0.0163961i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.65206 | + | 4.41792i | 0.443272 | + | 0.255923i | ||||
\(299\) | 10.0167 | + | 17.3494i | 0.579279 | + | 1.00334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.33147 | − | 8.47572i | −0.192023 | − | 0.488532i | ||||
\(302\) | 5.01460 | 0.288558 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.7509 | + | 7.36175i | 0.731316 | + | 0.422225i | ||||
\(305\) | −6.27082 | + | 4.14456i | −0.359066 | + | 0.237317i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.05816 | −0.402831 | −0.201415 | − | 0.979506i | \(-0.564554\pi\) | ||||
−0.201415 | + | 0.979506i | \(0.564554\pi\) | |||||||
\(308\) | 3.35631 | − | 4.21310i | 0.191244 | − | 0.240063i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.201926 | + | 3.33793i | 0.0114686 | + | 0.189582i | ||||
\(311\) | 0.923059 | − | 1.59878i | 0.0523418 | − | 0.0906587i | −0.838667 | − | 0.544644i | \(-0.816665\pi\) |
0.891009 | + | 0.453985i | \(0.149998\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.91811 | + | 15.4466i | 0.504081 | + | 0.873094i | 0.999989 | + | 0.00471916i | \(0.00150216\pi\) |
−0.495908 | + | 0.868375i | \(0.665165\pi\) | |||||||
\(314\) | 5.32479 | 0.300495 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.94238 | −0.503048 | ||||||||
\(317\) | 9.11366 | + | 15.7853i | 0.511874 | + | 0.886592i | 0.999905 | + | 0.0137658i | \(0.00438193\pi\) |
−0.488031 | + | 0.872826i | \(0.662285\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.93638 | + | 6.81801i | −0.220395 | + | 0.381735i | ||||
\(320\) | −10.7907 | + | 0.652774i | −0.603216 | + | 0.0364912i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.532762 | − | 3.54695i | 0.0296897 | − | 0.197664i | ||||
\(323\) | 1.83676 | 0.102200 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.4387 | − | 3.33197i | 1.52203 | − | 0.184824i | ||||
\(326\) | 7.41247 | + | 4.27959i | 0.410539 | + | 0.237025i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.8431 | 0.874786 | ||||||||
\(329\) | −8.02543 | + | 10.0741i | −0.442457 | + | 0.555405i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.47999 | − | 12.9557i | −0.411138 | − | 0.712111i | 0.583877 | − | 0.811842i | \(-0.301535\pi\) |
−0.995014 | + | 0.0997311i | \(0.968202\pi\) | |||||||
\(332\) | −20.8604 | − | 12.0437i | −1.14486 | − | 0.660986i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.51102 | − | 2.60444i | 0.246832 | − | 0.142509i | ||||
\(335\) | −9.71602 | − | 4.85231i | −0.530843 | − | 0.265110i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.43956i | 0.132891i | 0.997790 | + | 0.0664457i | \(0.0211659\pi\) | ||||
−0.997790 | + | 0.0664457i | \(0.978834\pi\) | |||||||
\(338\) | −3.28435 | − | 5.68867i | −0.178645 | − | 0.309423i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.37648 | + | 0.909757i | −0.0746502 | + | 0.0493385i | ||||
\(341\) | −2.18787 | − | 3.78950i | −0.118480 | − | 0.205213i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.01005 | − | 16.6985i | 0.432502 | − | 0.901633i | ||||
\(344\) | 4.97036i | 0.267984i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.50131 | + | 3.75353i | 0.349513 | + | 0.201791i | ||||
\(347\) | 1.22403 | − | 2.12008i | 0.0657093 | − | 0.113812i | −0.831299 | − | 0.555825i | \(-0.812402\pi\) |
0.897008 | + | 0.442013i | \(0.145736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.2047i | − | 0.813889i | −0.913453 | − | 0.406945i | \(-0.866594\pi\) | ||
0.913453 | − | 0.406945i | \(-0.133406\pi\) | |||||||
\(350\) | −4.21408 | − | 2.59439i | −0.225252 | − | 0.138676i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.86513 | + | 2.23154i | −0.206012 | + | 0.118941i | ||||
\(353\) | 22.4672 | + | 12.9714i | 1.19581 | + | 0.690400i | 0.959618 | − | 0.281307i | \(-0.0907678\pi\) |
0.236190 | + | 0.971707i | \(0.424101\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.383536 | − | 6.34003i | −0.0203560 | − | 0.336494i | ||||
\(356\) | 23.7571 | 1.25912 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.837322i | 0.0442538i | ||||||||
\(359\) | −27.7489 | + | 16.0208i | −1.46453 | + | 0.845546i | −0.999216 | − | 0.0396002i | \(-0.987392\pi\) |
−0.465313 | + | 0.885146i | \(0.654058\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.21895 | − | 2.11128i | 0.0641553 | − | 0.111120i | ||||
\(362\) | 1.35849 | − | 0.784327i | 0.0714009 | − | 0.0412233i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.04095 | − | 26.9032i | 0.211803 | − | 1.41011i | ||||
\(365\) | −0.713840 | + | 1.42936i | −0.0373641 | + | 0.0748160i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6515 | − | 25.3771i | 0.764800 | − | 1.32467i | −0.175552 | − | 0.984470i | \(-0.556171\pi\) |
0.940352 | − | 0.340203i | \(-0.110496\pi\) | |||||||
\(368\) | 5.76197 | − | 9.98002i | 0.300363 | − | 0.520244i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.292384 | − | 0.146020i | −0.0152003 | − | 0.00759124i | ||||
\(371\) | 2.03568 | − | 13.5528i | 0.105687 | − | 0.703628i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.6505 | − | 8.45847i | 0.758574 | − | 0.437963i | −0.0702095 | − | 0.997532i | \(-0.522367\pi\) |
0.828784 | + | 0.559569i | \(0.189033\pi\) | |||||||
\(374\) | −0.0812148 | + | 0.140668i | −0.00419952 | + | 0.00727378i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.08784 | − | 3.51481i | 0.313956 | − | 0.181263i | ||||
\(377\) | 39.7616i | 2.04783i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.5336 | 0.592443 | 0.296222 | − | 0.955119i | \(-0.404273\pi\) | ||||
0.296222 | + | 0.955119i | \(0.404273\pi\) | |||||||
\(380\) | 1.16285 | + | 19.2225i | 0.0596531 | + | 0.986094i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.17847 | − | 1.25774i | −0.111460 | − | 0.0643516i | ||||
\(383\) | 10.4841 | − | 6.05301i | 0.535714 | − | 0.309294i | −0.207626 | − | 0.978208i | \(-0.566574\pi\) |
0.743340 | + | 0.668914i | \(0.233240\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.45000 | + | 0.573411i | 0.328722 | + | 0.0292237i | ||||
\(386\) | − | 1.14184i | − | 0.0581182i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.50946 | − | 7.81061i | 0.228933 | − | 0.396524i | ||||
\(389\) | −5.80333 | − | 3.35055i | −0.294240 | − | 0.169880i | 0.345612 | − | 0.938377i | \(-0.387671\pi\) |
−0.639853 | + | 0.768498i | \(0.721005\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.43761i | − | 0.0727031i | ||||||
\(392\) | −7.40260 | + | 6.88270i | −0.373888 | + | 0.347629i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.83366 | − | 8.37215i | −0.243516 | − | 0.421783i | ||||
\(395\) | −5.92739 | − | 8.96828i | −0.298239 | − | 0.451243i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.4676 | + | 21.5945i | 0.625732 | + | 1.08380i | 0.988399 | + | 0.151880i | \(0.0485328\pi\) |
−0.362667 | + | 0.931919i | \(0.618134\pi\) | |||||||
\(398\) | − | 6.46060i | − | 0.323841i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.55179 | − | 12.7108i | −0.477589 | − | 0.635541i | ||||
\(401\) | 14.6397 | − | 8.45226i | 0.731074 | − | 0.422086i | −0.0877410 | − | 0.996143i | \(-0.527965\pi\) |
0.818815 | + | 0.574058i | \(0.194631\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.1390 | − | 11.0499i | −0.953381 | − | 0.550435i | ||||
\(404\) | −17.4657 | − | 30.2515i | −0.868953 | − | 1.50507i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.43569 | − | 5.56801i | 0.220139 | − | 0.276336i | ||||
\(407\) | 0.427649 | 0.0211978 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.4393 | + | 10.6459i | 0.911765 | + | 0.526408i | 0.880999 | − | 0.473119i | \(-0.156872\pi\) |
0.0307664 | + | 0.999527i | \(0.490205\pi\) | |||||||
\(410\) | 5.06037 | + | 7.65645i | 0.249914 | + | 0.378125i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 26.7983 | 1.32026 | ||||||||
\(413\) | −3.23213 | + | 21.5184i | −0.159043 | + | 1.05885i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.74852 | − | 28.9038i | −0.0858314 | − | 1.41883i | ||||
\(416\) | −11.2705 | + | 19.5210i | −0.552579 | + | 0.957096i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.947907 | + | 1.64182i | 0.0463637 | + | 0.0803042i | ||||
\(419\) | 4.84467 | 0.236678 | 0.118339 | − | 0.992973i | \(-0.462243\pi\) | ||||
0.118339 | + | 0.992973i | \(0.462243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.3110 | 0.502527 | 0.251264 | − | 0.967919i | \(-0.419154\pi\) | ||||
0.251264 | + | 0.967919i | \(0.419154\pi\) | |||||||
\(422\) | −4.31201 | − | 7.46862i | −0.209905 | − | 0.363567i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.73989 | + | 6.47768i | −0.181625 | + | 0.314584i | ||||
\(425\) | −1.82478 | − | 0.777443i | −0.0885149 | − | 0.0377115i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.54168 | + | 6.95633i | −0.268181 | + | 0.336641i | ||||
\(428\) | −25.2737 | −1.22165 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.40202 | + | 1.58756i | −0.115836 | + | 0.0765590i | ||||
\(431\) | −33.9307 | − | 19.5899i | −1.63439 | − | 0.943613i | −0.982718 | − | 0.185108i | \(-0.940736\pi\) |
−0.651667 | − | 0.758505i | \(-0.725930\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.1854 | 0.729763 | 0.364881 | − | 0.931054i | \(-0.381110\pi\) | ||||
0.364881 | + | 0.931054i | \(0.381110\pi\) | |||||||
\(434\) | 1.44743 | + | 3.68246i | 0.0694789 | + | 0.176764i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.75363 | − | 9.96558i | −0.275549 | − | 0.477265i | ||||
\(437\) | −14.5312 | − | 8.38961i | −0.695123 | − | 0.401329i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.5340 | + | 13.0100i | −1.07549 | + | 0.620935i | −0.929676 | − | 0.368377i | \(-0.879913\pi\) |
−0.145814 | + | 0.989312i | \(0.546580\pi\) | |||||||
\(440\) | −3.16177 | − | 1.57903i | −0.150732 | − | 0.0752774i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.820357i | 0.0390204i | ||||||||
\(443\) | −1.42237 | − | 2.46361i | −0.0675787 | − | 0.117050i | 0.830256 | − | 0.557382i | \(-0.188194\pi\) |
−0.897835 | + | 0.440332i | \(0.854861\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.7472 | + | 23.8259i | 0.746490 | + | 1.12946i | ||||
\(446\) | 3.41567 | + | 5.91612i | 0.161737 | + | 0.280137i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11.9044 | + | 4.67917i | −0.562432 | + | 0.221070i | ||||
\(449\) | − | 5.30598i | − | 0.250405i | −0.992131 | − | 0.125202i | \(-0.960042\pi\) | ||
0.992131 | − | 0.125202i | \(-0.0399580\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.4002 | − | 6.00455i | −0.489726 | − | 0.282743i | ||||
\(452\) | −5.64284 | + | 9.77368i | −0.265417 | + | 0.459715i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.77998i | 0.177403i | ||||||||
\(455\) | 29.6596 | − | 13.7799i | 1.39046 | − | 0.646014i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.1234 | − | 17.9691i | 1.45589 | − | 0.840560i | 0.457087 | − | 0.889422i | \(-0.348893\pi\) |
0.998806 | + | 0.0488621i | \(0.0155595\pi\) | |||||||
\(458\) | 7.24715 | + | 4.18414i | 0.338637 | + | 0.195512i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 15.0453 | − | 0.910153i | 0.701489 | − | 0.0424361i | ||||
\(461\) | −14.1168 | −0.657485 | −0.328743 | − | 0.944420i | \(-0.606625\pi\) | ||||
−0.328743 | + | 0.944420i | \(0.606625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.9693i | − | 0.835103i | −0.908653 | − | 0.417552i | \(-0.862888\pi\) | ||
0.908653 | − | 0.417552i | \(-0.137112\pi\) | |||||||
\(464\) | 19.8081 | − | 11.4362i | 0.919567 | − | 0.530912i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.24098 | + | 7.34559i | −0.196460 | + | 0.340278i | ||||
\(467\) | 13.3901 | − | 7.73079i | 0.619621 | − | 0.357738i | −0.157100 | − | 0.987583i | \(-0.550215\pi\) |
0.776721 | + | 0.629844i | \(0.216881\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7075 | − | 1.90871i | −0.586779 | − | 0.0881361i | ||||
\(470\) | 3.64309 | + | 1.81941i | 0.168043 | + | 0.0839230i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.93799 | − | 10.2849i | 0.273318 | − | 0.473401i | ||||
\(473\) | 1.88377 | − | 3.26279i | 0.0866161 | − | 0.150023i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.5074 | + | 13.9077i | −0.849177 | + | 0.638130i | ||||
\(476\) | −1.21643 | + | 1.52696i | −0.0557551 | + | 0.0699880i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.36533 | − | 3.09767i | 0.245404 | − | 0.141684i | ||||
\(479\) | 11.6425 | − | 20.1654i | 0.531959 | − | 0.921381i | −0.467344 | − | 0.884075i | \(-0.654789\pi\) |
0.999304 | − | 0.0373055i | \(-0.0118775\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.87049 | − | 1.07993i | 0.0852870 | − | 0.0492405i | ||||
\(482\) | − | 9.48159i | − | 0.431875i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18.2322 | −0.828739 | ||||||||
\(485\) | 10.8223 | − | 0.654687i | 0.491415 | − | 0.0297278i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.5395 | − | 6.08496i | −0.477588 | − | 0.275736i | 0.241823 | − | 0.970320i | \(-0.422255\pi\) |
−0.719411 | + | 0.694585i | \(0.755588\pi\) | |||||||
\(488\) | 4.20374 | − | 2.42703i | 0.190294 | − | 0.109866i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.69063 | − | 1.37907i | −0.257076 | − | 0.0622999i | ||||
\(491\) | 12.3672i | 0.558126i | 0.960273 | + | 0.279063i | \(0.0900238\pi\) | ||||
−0.960273 | + | 0.279063i | \(0.909976\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.42667 | − | 2.47106i | 0.0642538 | − | 0.111291i | ||||
\(494\) | 8.29209 | + | 4.78744i | 0.373079 | + | 0.215397i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.7126i | 0.570814i | ||||||||
\(497\) | −2.74924 | − | 6.99443i | −0.123320 | − | 0.313743i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.18807 | − | 15.9142i | −0.411314 | − | 0.712418i | 0.583719 | − | 0.811956i | \(-0.301597\pi\) |
−0.995034 | + | 0.0995380i | \(0.968264\pi\) | |||||||
\(500\) | 6.98103 | − | 19.5894i | 0.312201 | − | 0.876063i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.03146 | − | 5.25065i | −0.135301 | − | 0.234348i | ||||
\(503\) | 29.8980i | 1.33308i | 0.745467 | + | 0.666542i | \(0.232226\pi\) | ||||
−0.745467 | + | 0.666542i | \(0.767774\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.7621 | − | 37.5683i | 0.834903 | − | 1.67177i | ||||
\(506\) | 1.28504 | − | 0.741917i | 0.0571269 | − | 0.0329822i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.28035 | + | 1.31656i | 0.101174 | + | 0.0584130i | ||||
\(509\) | 8.13717 | + | 14.0940i | 0.360674 | + | 0.624705i | 0.988072 | − | 0.153993i | \(-0.0492134\pi\) |
−0.627398 | + | 0.778699i | \(0.715880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.280797 | + | 1.86945i | −0.0124217 | + | 0.0826995i | ||||
\(512\) | 22.1500 | 0.978901 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.58189 | − | 0.913305i | −0.0697742 | − | 0.0402841i | ||||
\(515\) | 17.7630 | + | 26.8759i | 0.782732 | + | 1.18429i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.32849 | −0.234347 | ||||||||
\(518\) | −0.382407 | − | 0.0574387i | −0.0168020 | − | 0.00252371i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −17.8167 | + | 1.07781i | −0.781315 | + | 0.0472652i | ||||
\(521\) | −15.0293 | + | 26.0315i | −0.658446 | + | 1.14046i | 0.322572 | + | 0.946545i | \(0.395452\pi\) |
−0.981018 | + | 0.193917i | \(0.937881\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.0349180 | + | 0.0604797i | 0.00152686 | + | 0.00264459i | 0.866788 | − | 0.498677i | \(-0.166181\pi\) |
−0.865261 | + | 0.501322i | \(0.832847\pi\) | |||||||
\(524\) | −22.5228 | −0.983915 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.46855 | −0.238440 | ||||||||
\(527\) | 0.792951 | + | 1.37343i | 0.0345415 | + | 0.0598276i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.93354 | − | 8.54514i | 0.214502 | − | 0.371528i | ||||
\(530\) | −4.32501 | + | 0.261638i | −0.187866 | + | 0.0113648i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.33549 | + | 21.2066i | 0.361389 | + | 0.919422i | ||||
\(533\) | −60.6524 | −2.62715 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.7525 | − | 25.3469i | −0.724272 | − | 1.09584i | ||||
\(536\) | 6.07367 | + | 3.50663i | 0.262342 | + | 0.151463i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.88735 | 0.210708 | ||||||||
\(539\) | 7.46800 | − | 1.71255i | 0.321669 | − | 0.0737650i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.4662 | − | 28.5203i | −0.707938 | − | 1.22618i | −0.965621 | − | 0.259955i | \(-0.916292\pi\) |
0.257683 | − | 0.966229i | \(-0.417041\pi\) | |||||||
\(542\) | 8.38146 | + | 4.83904i | 0.360015 | + | 0.207855i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.40085 | − | 0.808778i | 0.0600607 | − | 0.0346761i | ||||
\(545\) | 6.18069 | − | 12.3759i | 0.264752 | − | 0.530125i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.8823i | − | 0.807349i | −0.914903 | − | 0.403674i | \(-0.867733\pi\) | ||
0.914903 | − | 0.403674i | \(-0.132267\pi\) | |||||||
\(548\) | −7.60880 | − | 13.1788i | −0.325032 | − | 0.562972i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.246793 | − | 2.03234i | −0.0105233 | − | 0.0866592i | ||||
\(551\) | −16.6515 | − | 28.8412i | −0.709377 | − | 1.22868i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.94868 | − | 7.92549i | −0.423061 | − | 0.337026i | ||||
\(554\) | − | 12.2367i | − | 0.519888i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.1757 | + | 9.91638i | 0.728411 | + | 0.420548i | ||||
\(557\) | 15.8907 | − | 27.5234i | 0.673309 | − | 1.16620i | −0.303652 | − | 0.952783i | \(-0.598206\pi\) |
0.976960 | − | 0.213421i | \(-0.0684607\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 19.0281i | − | 0.804805i | ||||||
\(560\) | −15.3954 | − | 10.8122i | −0.650576 | − | 0.456898i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.84526 | + | 3.95211i | −0.288750 | + | 0.166710i | ||||
\(563\) | 13.8669 | + | 8.00608i | 0.584421 | + | 0.337416i | 0.762889 | − | 0.646530i | \(-0.223780\pi\) |
−0.178467 | + | 0.983946i | \(0.557114\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.5423 | + | 0.819232i | −0.569728 | + | 0.0344653i | ||||
\(566\) | −1.97793 | −0.0831386 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.10170i | 0.172103i | ||||||||
\(569\) | 13.0585 | − | 7.53933i | 0.547441 | − | 0.316065i | −0.200648 | − | 0.979663i | \(-0.564305\pi\) |
0.748089 | + | 0.663598i | \(0.230971\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.49104 | + | 14.7069i | −0.355339 | + | 0.615465i | −0.987176 | − | 0.159636i | \(-0.948968\pi\) |
0.631837 | + | 0.775101i | \(0.282301\pi\) | |||||||
\(572\) | 9.74688 | − | 5.62736i | 0.407538 | − | 0.235292i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.49344 | + | 6.76620i | 0.354509 | + | 0.282416i | ||||
\(575\) | 10.8854 | + | 14.4855i | 0.453953 | + | 0.604088i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.39492 | − | 11.0763i | 0.266224 | − | 0.461114i | −0.701660 | − | 0.712512i | \(-0.747557\pi\) |
0.967884 | + | 0.251399i | \(0.0808906\pi\) | |||||||
\(578\) | −3.15028 | + | 5.45645i | −0.131034 | + | 0.226958i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 26.7640 | + | 13.3663i | 1.11131 | + | 0.555005i | ||||
\(581\) | −12.5336 | − | 31.8872i | −0.519982 | − | 1.32290i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.91011 | − | 2.83485i | 0.203356 | − | 0.117408i | ||||
\(584\) | 0.515873 | − | 0.893518i | 0.0213470 | − | 0.0369740i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.23753 | + | 3.60124i | −0.257670 | + | 0.148766i | ||||
\(587\) | − | 31.0957i | − | 1.28346i | −0.766932 | − | 0.641728i | \(-0.778218\pi\) | ||
0.766932 | − | 0.641728i | \(-0.221782\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.5100 | 0.762692 | ||||||||
\(590\) | 6.86700 | − | 0.415415i | 0.282710 | − | 0.0171024i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.07598 | − | 0.621215i | −0.0442224 | − | 0.0255318i | ||||
\(593\) | −14.2922 | + | 8.25163i | −0.586912 | + | 0.338854i | −0.763876 | − | 0.645363i | \(-0.776706\pi\) |
0.176963 | + | 0.984217i | \(0.443373\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.33768 | − | 0.207822i | −0.0958356 | − | 0.00851988i | ||||
\(596\) | 43.9345i | 1.79963i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.74708 | − | 6.49013i | 0.153229 | − | 0.265401i | ||||
\(599\) | 37.2474 | + | 21.5048i | 1.52189 | + | 0.878663i | 0.999666 | + | 0.0258548i | \(0.00823076\pi\) |
0.522224 | + | 0.852808i | \(0.325103\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.2911i | − | 0.909271i | −0.890678 | − | 0.454636i | \(-0.849770\pi\) | ||
0.890678 | − | 0.454636i | \(-0.150230\pi\) | |||||||
\(602\) | −2.12272 | + | 2.66460i | −0.0865157 | + | 0.108601i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.4671 | + | 21.5936i | 0.507277 | + | 0.878630i | ||||
\(605\) | −12.0851 | − | 18.2850i | −0.491329 | − | 0.743393i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.75293 | + | 4.76821i | 0.111738 | + | 0.193536i | 0.916471 | − | 0.400101i | \(-0.131025\pi\) |
−0.804733 | + | 0.593637i | \(0.797692\pi\) | |||||||
\(608\) | − | 18.8795i | − | 0.765664i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.51561 | + | 1.25633i | 0.101854 | + | 0.0508672i | ||||
\(611\) | −23.3062 | + | 13.4559i | −0.942869 | + | 0.544366i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.8640 | + | 17.8194i | 1.24659 | + | 0.719717i | 0.970427 | − | 0.241395i | \(-0.0776049\pi\) |
0.276159 | + | 0.961112i | \(0.410938\pi\) | |||||||
\(614\) | 1.32017 | + | 2.28661i | 0.0532779 | + | 0.0922800i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.13526 | − | 0.621130i | −0.166615 | − | 0.0250260i | ||||
\(617\) | 12.9253 | 0.520352 | 0.260176 | − | 0.965561i | \(-0.416219\pi\) | ||||
0.260176 | + | 0.965561i | \(0.416219\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.2224 | − | 15.7168i | −1.09416 | − | 0.631713i | −0.159478 | − | 0.987201i | \(-0.550981\pi\) |
−0.934681 | + | 0.355489i | \(0.884314\pi\) | |||||||
\(620\) | −13.8716 | + | 9.16811i | −0.557096 | + | 0.368200i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.690603 | −0.0276907 | ||||||||
\(623\) | 26.4305 | + | 21.0555i | 1.05892 | + | 0.843572i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.2734 | − | 5.98342i | 0.970937 | − | 0.239337i | ||||
\(626\) | 3.33612 | − | 5.77834i | 0.133338 | − | 0.230949i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.2382 | + | 22.9293i | 0.528263 | + | 0.914979i | ||||
\(629\) | −0.154993 | −0.00617998 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.43480 | −0.136737 | −0.0683687 | − | 0.997660i | \(-0.521779\pi\) | ||||
−0.0683687 | + | 0.997660i | \(0.521779\pi\) | |||||||
\(632\) | 3.47104 | + | 6.01202i | 0.138071 | + | 0.239145i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.40928 | − | 5.90504i | 0.135400 | − | 0.234519i | ||||
\(635\) | 0.191140 | + | 3.15963i | 0.00758515 | + | 0.125386i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.3396 | − | 26.3492i | 1.12285 | − | 1.04399i | ||||
\(638\) | 2.94507 | 0.116597 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.2844 | + | 18.5866i | 0.485584 | + | 0.734700i | ||||
\(641\) | −30.9544 | − | 17.8715i | −1.22262 | − | 0.705882i | −0.257147 | − | 0.966372i | \(-0.582782\pi\) |
−0.965476 | + | 0.260490i | \(0.916116\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.9624 | −1.29991 | −0.649955 | − | 0.759973i | \(-0.725212\pi\) | ||||
−0.649955 | + | 0.759973i | \(0.725212\pi\) | |||||||
\(644\) | 16.5982 | − | 6.52410i | 0.654060 | − | 0.257085i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.343551 | − | 0.595048i | −0.0135168 | − | 0.0234118i | ||||
\(647\) | −8.95584 | − | 5.17066i | −0.352090 | − | 0.203280i | 0.313515 | − | 0.949583i | \(-0.398493\pi\) |
−0.665606 | + | 0.746304i | \(0.731827\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.79600 | + | 4.50102i | −0.306020 | + | 0.176681i | ||||
\(650\) | −6.21164 | − | 8.26601i | −0.243641 | − | 0.324220i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 42.5588i | 1.66673i | ||||||||
\(653\) | 10.5884 | + | 18.3396i | 0.414356 | + | 0.717685i | 0.995361 | − | 0.0962151i | \(-0.0306737\pi\) |
−0.581005 | + | 0.813900i | \(0.697340\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.9291 | − | 22.5881i | −0.583328 | − | 0.882588i | ||||
\(656\) | 17.4448 | + | 30.2152i | 0.681104 | + | 1.17971i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.76478 | + | 0.715684i | 0.185750 | + | 0.0279003i | ||||
\(659\) | 2.65393i | 0.103382i | 0.998663 | + | 0.0516912i | \(0.0164612\pi\) | ||||
−0.998663 | + | 0.0516912i | \(0.983539\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.456098 | − | 0.263328i | −0.0177402 | − | 0.0102423i | 0.491104 | − | 0.871101i | \(-0.336594\pi\) |
−0.508844 | + | 0.860859i | \(0.669927\pi\) | |||||||
\(662\) | −2.79815 | + | 4.84653i | −0.108753 | + | 0.188366i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.6994i | 0.725677i | ||||||||
\(665\) | −15.7429 | + | 22.4162i | −0.610483 | + | 0.869265i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.5737 | + | 13.0329i | −0.874057 | + | 0.504637i | ||||
\(668\) | 22.4302 | + | 12.9501i | 0.867850 | + | 0.501053i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.245320 | + | 4.05525i | 0.00947753 | + | 0.156668i | ||||
\(671\) | −3.67940 | −0.142042 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 0.728879i | − | 0.0280962i | −0.999901 | − | 0.0140481i | \(-0.995528\pi\) | ||
0.999901 | − | 0.0140481i | \(-0.00447180\pi\) | |||||||
\(674\) | 0.790336 | − | 0.456301i | 0.0304426 | − | 0.0175761i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.3308 | − | 28.2858i | 0.628108 | − | 1.08791i | ||||
\(677\) | −9.62828 | + | 5.55889i | −0.370045 | + | 0.213646i | −0.673478 | − | 0.739207i | \(-0.735200\pi\) |
0.303433 | + | 0.952853i | \(0.401867\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.9393 | − | 4.69288i | 0.458189 | − | 0.180096i | ||||
\(680\) | 1.14593 | + | 0.572290i | 0.0439442 | + | 0.0219463i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.818446 | + | 1.41759i | −0.0313399 | + | 0.0542824i | ||||
\(683\) | 17.7885 | − | 30.8105i | 0.680656 | − | 1.17893i | −0.294124 | − | 0.955767i | \(-0.595028\pi\) |
0.974781 | − | 0.223164i | \(-0.0716387\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.17356 | − | 16.3663i | 0.312296 | − | 0.625325i | ||||
\(686\) | −6.90796 | + | 0.528332i | −0.263747 | + | 0.0201718i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.47926 | + | 5.47285i | −0.361393 | + | 0.208651i | ||||
\(689\) | 14.3175 | − | 24.7987i | 0.545454 | − | 0.944755i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.11870 | + | 4.68733i | −0.308850 | + | 0.178315i | −0.646412 | − | 0.762989i | \(-0.723731\pi\) |
0.337562 | + | 0.941303i | \(0.390398\pi\) | |||||||
\(692\) | 37.3274i | 1.41898i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.915780 | −0.0347625 | ||||||||
\(695\) | 1.43967 | + | 23.7984i | 0.0546098 | + | 0.902725i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.76935 | + | 2.17624i | 0.142774 | + | 0.0824308i | ||||
\(698\) | −4.92582 | + | 2.84392i | −0.186445 | + | 0.107644i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.694965 | − | 24.5965i | 0.0262672 | − | 0.929659i | ||||
\(701\) | − | 16.3197i | − | 0.616388i | −0.951324 | − | 0.308194i | \(-0.900275\pi\) | ||
0.951324 | − | 0.308194i | \(-0.0997246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.904510 | + | 1.56666i | −0.0341142 | + | 0.0590876i | ||||
\(704\) | −4.58271 | − | 2.64583i | −0.172717 | − | 0.0997183i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 9.70483i | − | 0.365246i | ||||||
\(707\) | 7.38028 | − | 49.1354i | 0.277564 | − | 1.84793i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.4461 | + | 31.9496i | 0.692758 | + | 1.19989i | 0.970931 | + | 0.239361i | \(0.0769379\pi\) |
−0.278173 | + | 0.960531i | \(0.589729\pi\) | |||||||
\(710\) | −1.98222 | + | 1.31011i | −0.0743914 | + | 0.0491674i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.22147 | − | 15.9721i | −0.345589 | − | 0.598578i | ||||
\(713\) | − | 14.4876i | − | 0.542565i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.1043 | + | 6.04505i | 0.452675 | + | 0.226072i | ||||
\(716\) | −3.60563 | + | 2.08171i | −0.134749 | + | 0.0777971i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.3804 | + | 5.99313i | 0.387394 | + | 0.223662i | ||||
\(719\) | 1.48159 | + | 2.56618i | 0.0552538 | + | 0.0957024i | 0.892329 | − | 0.451385i | \(-0.149070\pi\) |
−0.837076 | + | 0.547087i | \(0.815737\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29.8139 | + | 23.7509i | 1.11033 | + | 0.884529i | ||||
\(722\) | −0.911981 | −0.0339404 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.75484 | + | 3.89991i | 0.251042 | + | 0.144939i | ||||
\(725\) | 4.33531 | + | 35.7012i | 0.161009 | + | 1.32591i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.9409 | 1.18462 | 0.592312 | − | 0.805709i | \(-0.298215\pi\) | ||||
0.592312 | + | 0.805709i | \(0.298215\pi\) | |||||||
\(728\) | −19.6557 | + | 7.72590i | −0.728489 | + | 0.286341i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.596582 | − | 0.0360898i | 0.0220805 | − | 0.00133574i | ||||
\(731\) | −0.682739 | + | 1.18254i | −0.0252520 | + | 0.0437377i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.2819 | − | 26.4691i | −0.564450 | − | 0.977657i | −0.997101 | − | 0.0760949i | \(-0.975755\pi\) |
0.432650 | − | 0.901562i | \(-0.357579\pi\) | |||||||
\(734\) | −10.9618 | −0.404606 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.7768 | −0.544679 | ||||||||
\(737\) | −2.65804 | − | 4.60386i | −0.0979103 | − | 0.169586i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.58166 | + | 2.73951i | −0.0581822 | + | 0.100775i | −0.893649 | − | 0.448766i | \(-0.851864\pi\) |
0.835467 | + | 0.549540i | \(0.185197\pi\) | |||||||
\(740\) | −0.0981264 | − | 1.62208i | −0.00360720 | − | 0.0596287i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.77142 | + | 1.87546i | −0.175164 | + | 0.0688503i | ||||
\(743\) | −38.4235 | −1.40962 | −0.704811 | − | 0.709395i | \(-0.748968\pi\) | ||||
−0.704811 | + | 0.709395i | \(0.748968\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −44.0617 | + | 29.1216i | −1.61430 | + | 1.06693i | ||||
\(746\) | −5.48052 | − | 3.16418i | −0.200656 | − | 0.115849i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.807650 | −0.0295306 | ||||||||
\(749\) | −28.1177 | − | 22.3997i | −1.02740 | − | 0.818465i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.6749 | + | 21.9536i | 0.462513 | + | 0.801097i | 0.999085 | − | 0.0427578i | \(-0.0136144\pi\) |
−0.536572 | + | 0.843854i | \(0.680281\pi\) | |||||||
\(752\) | 13.4066 | + | 7.74032i | 0.488889 | + | 0.282260i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.8814 | − | 7.43710i | 0.469114 | − | 0.270843i | ||||
\(755\) | −13.3924 | + | 26.8163i | −0.487399 | + | 0.975944i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.58908i | − | 0.0577562i | −0.999583 | − | 0.0288781i | \(-0.990807\pi\) | ||
0.999583 | − | 0.0288781i | \(-0.00919346\pi\) | |||||||
\(758\) | −2.15728 | − | 3.73651i | −0.0783558 | − | 0.135716i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.4720 | − | 8.24313i | 0.452409 | − | 0.299010i | ||||
\(761\) | 15.7201 | + | 27.2279i | 0.569852 | + | 0.987012i | 0.996580 | + | 0.0826325i | \(0.0263328\pi\) |
−0.426728 | + | 0.904380i | \(0.640334\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.43124 | − | 16.1864i | 0.0880169 | − | 0.585986i | ||||
\(764\) | − | 12.5077i | − | 0.452514i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.92195 | − | 2.26434i | −0.141706 | − | 0.0818138i | ||||
\(767\) | −22.7326 | + | 39.3740i | −0.820826 | + | 1.42171i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.88576i | − | 0.140124i | −0.997543 | − | 0.0700620i | \(-0.977680\pi\) | ||
0.997543 | − | 0.0700620i | \(-0.0223197\pi\) | |||||||
\(770\) | −1.02066 | − | 2.19684i | −0.0367819 | − | 0.0791685i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.91693 | − | 2.83879i | 0.176964 | − | 0.102170i | ||||
\(773\) | 34.2935 | + | 19.7994i | 1.23345 | + | 0.712133i | 0.967748 | − | 0.251922i | \(-0.0810625\pi\) |
0.265703 | + | 0.964055i | \(0.414396\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.3893 | − | 7.83472i | −0.660564 | − | 0.281431i | ||||
\(776\) | −7.00150 | −0.251339 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.50678i | 0.0898724i | ||||||||
\(779\) | 43.9944 | − | 25.4002i | 1.57626 | − | 0.910055i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.55455 | − | 2.69256i | 0.0556262 | − | 0.0963474i | ||||
\(782\) | −0.465738 | + | 0.268894i | −0.0166547 | + | 0.00961562i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −21.2774 | − | 6.53940i | −0.759907 | − | 0.233550i | ||||
\(785\) | −14.2208 | + | 28.4751i | −0.507563 | + | 1.01632i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.7573 | + | 39.4167i | −0.811209 | + | 1.40505i | 0.100810 | + | 0.994906i | \(0.467857\pi\) |
−0.912019 | + | 0.410149i | \(0.865477\pi\) | |||||||
\(788\) | 24.0344 | − | 41.6289i | 0.856191 | − | 1.48297i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.79675 | + | 3.59772i | −0.0639255 | + | 0.128001i | ||||
\(791\) | −14.9401 | + | 5.87236i | −0.531208 | + | 0.208797i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.0933 | + | 9.29146i | −0.571489 | + | 0.329949i | ||||
\(794\) | 4.66394 | − | 8.07818i | 0.165517 | − | 0.286684i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.8203 | − | 16.0620i | 0.986063 | − | 0.569304i | ||||
\(797\) | 8.62946i | 0.305671i | 0.988252 | + | 0.152836i | \(0.0488405\pi\) | ||||
−0.988252 | + | 0.152836i | \(0.951160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.93121 | 0.0683213 | ||||||||
\(800\) | −7.99110 | + | 18.7564i | −0.282528 | + | 0.663138i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.47650 | − | 3.16186i | −0.193382 | − | 0.111649i | ||||
\(803\) | −0.677290 | + | 0.391034i | −0.0239010 | + | 0.0137993i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.5450 | + | 12.3218i | 0.618379 | + | 0.434286i | ||||
\(806\) | 8.26719i | 0.291199i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.5589 | + | 23.4846i | −0.476999 | + | 0.826187i | ||||
\(809\) | −15.8019 | − | 9.12322i | −0.555564 | − | 0.320755i | 0.195799 | − | 0.980644i | \(-0.437270\pi\) |
−0.751363 | + | 0.659889i | \(0.770603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.3072i | 1.73141i | 0.500555 | + | 0.865704i | \(0.333129\pi\) | ||||
−0.500555 | + | 0.865704i | \(0.666871\pi\) | |||||||
\(812\) | 35.0044 | + | 5.25777i | 1.22841 | + | 0.184512i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.0799883 | − | 0.138544i | −0.00280359 | − | 0.00485596i | ||||
\(815\) | −42.6821 | + | 28.2098i | −1.49509 | + | 0.988146i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.96865 | + | 13.8021i | 0.278788 | + | 0.482875i | ||||
\(818\) | − | 7.96496i | − | 0.278488i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.3889 | + | 40.8258i | −0.712012 | + | 1.42570i | ||||
\(821\) | 20.0547 | − | 11.5786i | 0.699915 | − | 0.404096i | −0.107401 | − | 0.994216i | \(-0.534253\pi\) |
0.807316 | + | 0.590120i | \(0.200919\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.5779 | − | 7.26186i | −0.438438 | − | 0.253132i | 0.264497 | − | 0.964387i | \(-0.414794\pi\) |
−0.702935 | + | 0.711254i | \(0.748128\pi\) | |||||||
\(824\) | −10.4019 | − | 18.0166i | −0.362368 | − | 0.627640i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.57579 | − | 2.97775i | 0.263596 | − | 0.103609i | ||||
\(827\) | 21.6632 | 0.753302 | 0.376651 | − | 0.926355i | \(-0.377076\pi\) | ||||
0.376651 | + | 0.926355i | \(0.377076\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.8166 | − | 9.13174i | −0.549334 | − | 0.317158i | 0.199519 | − | 0.979894i | \(-0.436062\pi\) |
−0.748853 | + | 0.662736i | \(0.769395\pi\) | |||||||
\(830\) | −9.03683 | + | 5.97270i | −0.313673 | + | 0.207315i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −26.7257 | −0.926546 | ||||||||
\(833\) | −2.70663 | + | 0.620683i | −0.0937793 | + | 0.0215054i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.88010 | + | 31.0790i | 0.0650636 | + | 1.07553i | ||||
\(836\) | −4.71328 | + | 8.16365i | −0.163012 | + | 0.282346i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.906158 | − | 1.56951i | −0.0313027 | − | 0.0542179i | ||||
\(839\) | 38.8296 | 1.34055 | 0.670273 | − | 0.742114i | \(-0.266177\pi\) | ||||
0.670273 | + | 0.742114i | \(0.266177\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.7348 | −0.783959 | ||||||||
\(842\) | −1.92859 | − | 3.34042i | −0.0664636 | − | 0.115118i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 21.4406 | − | 37.1362i | 0.738016 | − | 1.27828i | ||||
\(845\) | 39.1924 | − | 2.37092i | 1.34826 | − | 0.0815621i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.2839 | − | 16.1589i | −0.696964 | − | 0.555228i | ||||
\(848\) | −16.4720 | −0.565650 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.0894455 | + | 0.736583i | 0.00306796 | + | 0.0252646i | ||||
\(851\) | 1.22621 | + | 0.707950i | 0.0420338 | + | 0.0242682i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.803330 | 0.0275055 | 0.0137527 | − | 0.999905i | \(-0.495622\pi\) | ||||
0.0137527 | + | 0.999905i | \(0.495622\pi\) | |||||||
\(854\) | 3.29015 | + | 0.494190i | 0.112586 | + | 0.0169108i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.81014 | + | 16.9917i | 0.335304 | + | 0.580763i | ||||
\(857\) | −9.24262 | − | 5.33623i | −0.315722 | − | 0.182282i | 0.333762 | − | 0.942657i | \(-0.391682\pi\) |
−0.649484 | + | 0.760375i | \(0.725015\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.8831 | + | 25.3359i | −1.49727 | + | 0.864450i | −0.999995 | − | 0.00314281i | \(-0.999000\pi\) |
−0.497276 | + | 0.867593i | \(0.665666\pi\) | |||||||
\(860\) | −12.8080 | − | 6.39651i | −0.436751 | − | 0.218119i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.6566i | 0.499204i | ||||||||
\(863\) | −18.2131 | − | 31.5460i | −0.619981 | − | 1.07384i | −0.989489 | − | 0.144610i | \(-0.953807\pi\) |
0.369508 | − | 0.929228i | \(-0.379526\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.4355 | + | 24.7422i | −1.27285 | + | 0.841260i | ||||
\(866\) | −2.84031 | − | 4.91955i | −0.0965175 | − | 0.167173i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.2586 | + | 15.3880i | −0.416086 | + | 0.522302i | ||||
\(869\) | − | 5.26213i | − | 0.178505i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.2520 | − | 13.4245i | −0.787863 | − | 0.454873i | ||||
\(872\) | −4.46661 | + | 7.73640i | −0.151259 | + | 0.261988i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.27684i | 0.212317i | ||||||||
\(875\) | 25.1283 | − | 15.6066i | 0.849493 | − | 0.527600i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.6537 | + | 11.9244i | −0.697425 | + | 0.402659i | −0.806388 | − | 0.591387i | \(-0.798580\pi\) |
0.108963 | + | 0.994046i | \(0.465247\pi\) | |||||||
\(878\) | 8.42962 | + | 4.86685i | 0.284486 | + | 0.164248i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.469961 | − | 7.76868i | −0.0158424 | − | 0.261882i | ||||
\(881\) | −1.65600 | −0.0557920 | −0.0278960 | − | 0.999611i | \(-0.508881\pi\) | ||||
−0.0278960 | + | 0.999611i | \(0.508881\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.62010i | 0.290089i | 0.989425 | + | 0.145045i | \(0.0463326\pi\) | ||||
−0.989425 | + | 0.145045i | \(0.953667\pi\) | |||||||
\(884\) | −3.53257 | + | 2.03953i | −0.118813 | + | 0.0685969i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.532085 | + | 0.921598i | −0.0178757 | + | 0.0309617i | ||||
\(887\) | −16.2378 | + | 9.37492i | −0.545213 | + | 0.314779i | −0.747189 | − | 0.664612i | \(-0.768597\pi\) |
0.201976 | + | 0.979390i | \(0.435264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.37011 | + | 3.48576i | 0.0459522 | + | 0.116909i | ||||
\(890\) | 4.77340 | − | 9.55802i | 0.160005 | − | 0.320386i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.9838 | + | 29.4168i | −0.568659 | + | 0.984946i | ||||
\(893\) | 11.2702 | − | 19.5205i | 0.377141 | − | 0.653228i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.47770 | − | 2.23622i | −0.149673 | − | 0.0747486i | ||||
\(896\) | 20.6185 | + | 16.4254i | 0.688814 | + | 0.548736i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.71896 | + | 0.992443i | −0.0573625 | + | 0.0331182i | ||||
\(899\) | 14.3773 | − | 24.9022i | 0.479509 | − | 0.830535i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.77958 | + | 1.02744i | −0.0592863 | + | 0.0342290i | ||||
\(902\) | 4.49242i | 0.149581i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.76121 | 0.291393 | ||||||||
\(905\) | 0.566193 | + | 9.35943i | 0.0188209 | + | 0.311118i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.7308 | − | 18.8971i | −1.08681 | − | 0.627469i | −0.154084 | − | 0.988058i | \(-0.549243\pi\) |
−0.932725 | + | 0.360588i | \(0.882576\pi\) | |||||||
\(908\) | −16.2771 | + | 9.39760i | −0.540175 | + | 0.311870i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.0118 | − | 7.03130i | −0.331889 | − | 0.233085i | ||||
\(911\) | 27.9845i | 0.927167i | 0.886053 | + | 0.463584i | \(0.153437\pi\) | ||||
−0.886053 | + | 0.463584i | \(0.846563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.08711 | − | 12.2752i | 0.234549 | − | 0.406251i | ||||
\(914\) | −11.6428 | − | 6.72197i | −0.385109 | − | 0.222343i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 41.6097i | 1.37482i | ||||||||
\(917\) | −25.0573 | − | 19.9616i | −0.827466 | − | 0.659191i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.7199 | + | 39.3521i | 0.749461 | + | 1.29810i | 0.948081 | + | 0.318028i | \(0.103021\pi\) |
−0.198620 | + | 0.980077i | \(0.563646\pi\) | |||||||
\(920\) | −6.45181 | − | 9.76174i | −0.212710 | − | 0.321835i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.64044 | + | 4.57337i | 0.0869582 | + | 0.150616i | ||||
\(923\) | − | 15.7026i | − | 0.516858i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.56173 | − | 1.17359i | 0.0513493 | − | 0.0385874i | ||||
\(926\) | −5.82145 | + | 3.36101i | −0.191305 | + | 0.110450i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −25.3993 | − | 14.6643i | −0.833771 | − | 0.481378i | ||||
\(929\) | −23.6347 | − | 40.9366i | −0.775430 | − | 1.34308i | −0.934552 | − | 0.355826i | \(-0.884200\pi\) |
0.159122 | − | 0.987259i | \(-0.449134\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.52158 | + | 30.9806i | −0.312057 | + | 1.01535i | ||||
\(932\) | −42.1749 | −1.38148 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.00904 | − | 2.89197i | −0.163901 | − | 0.0946281i | ||||
\(935\) | −0.535344 | − | 0.809988i | −0.0175076 | − | 0.0264895i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.3420 | −1.28525 | −0.642624 | − | 0.766182i | \(-0.722154\pi\) | ||||
−0.642624 | + | 0.766182i | \(0.722154\pi\) | |||||||
\(938\) | 1.75849 | + | 4.47382i | 0.0574166 | + | 0.146076i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.22265 | + | 20.2110i | 0.0398785 | + | 0.659210i | ||||
\(941\) | −6.13749 | + | 10.6304i | −0.200076 | + | 0.346542i | −0.948553 | − | 0.316619i | \(-0.897452\pi\) |
0.748476 | + | 0.663161i | \(0.230786\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.8804 | − | 34.4339i | −0.647396 | − | 1.12132i | ||||
\(944\) | 26.1533 | 0.851217 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.40938 | −0.0458229 | ||||||||
\(947\) | −10.1694 | − | 17.6139i | −0.330460 | − | 0.572374i | 0.652142 | − | 0.758097i | \(-0.273871\pi\) |
−0.982602 | + | 0.185723i | \(0.940537\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.97493 | + | 3.42068i | −0.0641089 | + | 0.111040i | ||||
\(950\) | 7.96729 | + | 3.39444i | 0.258493 | + | 0.110130i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.49875 | + | 0.225117i | 0.0485747 | + | 0.00729607i | ||||
\(953\) | 30.6485 | 0.992804 | 0.496402 | − | 0.868093i | \(-0.334654\pi\) | ||||
0.496402 | + | 0.868093i | \(0.334654\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.5440 | − | 8.29066i | 0.405913 | − | 0.268279i | ||||
\(956\) | 26.6780 | + | 15.4026i | 0.862830 | + | 0.498155i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.71055 | −0.281425 | ||||||||
\(959\) | 3.21516 | − | 21.4054i | 0.103823 | − | 0.691217i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.50900 | − | 13.0060i | −0.242226 | − | 0.419547i | ||||
\(962\) | −0.699721 | − | 0.403984i | −0.0225599 | − | 0.0130250i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 40.8291 | − | 23.5727i | 1.31502 | − | 0.759225i | ||||
\(965\) | 6.10616 | + | 3.04950i | 0.196564 | + | 0.0981668i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52.7201i | − | 1.69536i | −0.530504 | − | 0.847682i | \(-0.677997\pi\) | ||
0.530504 | − | 0.847682i | \(-0.322003\pi\) | |||||||
\(968\) | 7.07696 | + | 12.2577i | 0.227462 | + | 0.393976i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.23632 | − | 3.38360i | −0.0718039 | − | 0.108641i | ||||
\(971\) | −23.3979 | − | 40.5264i | −0.750876 | − | 1.30055i | −0.947399 | − | 0.320056i | \(-0.896298\pi\) |
0.196523 | − | 0.980499i | \(-0.437035\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.3197 | + | 26.2548i | 0.330836 | + | 0.841690i | ||||
\(974\) | 4.55257i | 0.145874i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.25746 | + | 5.34480i | 0.296324 | + | 0.171083i | ||||
\(977\) | −7.77187 | + | 13.4613i | −0.248644 | + | 0.430664i | −0.963150 | − | 0.268965i | \(-0.913318\pi\) |
0.714506 | + | 0.699630i | \(0.246652\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.9798i | 0.446797i | ||||||||
\(980\) | −8.20931 | − | 27.9332i | −0.262237 | − | 0.892294i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.00657 | − | 2.31319i | 0.127855 | − | 0.0738170i | ||||
\(983\) | 27.3467 | + | 15.7886i | 0.872225 | + | 0.503579i | 0.868087 | − | 0.496412i | \(-0.165349\pi\) |
0.00413812 | + | 0.999991i | \(0.498683\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 57.6804 | − | 3.48934i | 1.83785 | − | 0.111180i | ||||
\(986\) | −1.06739 | −0.0339925 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 47.6092i | 1.51465i | ||||||||
\(989\) | 10.8028 | − | 6.23698i | 0.343508 | − | 0.198324i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.5907 | − | 44.3244i | 0.812916 | − | 1.40801i | −0.0978991 | − | 0.995196i | \(-0.531212\pi\) |
0.910815 | − | 0.412815i | \(-0.135454\pi\) | |||||||
\(992\) | 14.1171 | − | 8.15050i | 0.448218 | − | 0.258779i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.75174 | + | 2.19891i | −0.0555618 | + | 0.0697453i | ||||
\(995\) | 34.5490 | + | 17.2542i | 1.09528 | + | 0.546996i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.255934 | − | 0.443291i | 0.00810551 | − | 0.0140392i | −0.861944 | − | 0.507003i | \(-0.830753\pi\) |
0.870050 | + | 0.492964i | \(0.164087\pi\) | |||||||
\(998\) | −3.43711 | + | 5.95325i | −0.108800 | + | 0.188447i | ||||
\(999\) | 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 | 945.2.bb.b.269.8 | yes | 32 | |
3.2 | odd | 2 | 945.2.bb.a.269.9 | ✓ | 32 | ||
5.4 | even | 2 | 945.2.bb.a.269.10 | yes | 32 | ||
7.5 | odd | 6 | inner | 945.2.bb.b.404.7 | yes | 32 | |
15.14 | odd | 2 | inner | 945.2.bb.b.269.7 | yes | 32 | |
21.5 | even | 6 | 945.2.bb.a.404.10 | yes | 32 | ||
35.19 | odd | 6 | 945.2.bb.a.404.9 | yes | 32 | ||
105.89 | even | 6 | inner | 945.2.bb.b.404.8 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.bb.a.269.9 | ✓ | 32 | 3.2 | odd | 2 | ||
945.2.bb.a.269.10 | yes | 32 | 5.4 | even | 2 | ||
945.2.bb.a.404.9 | yes | 32 | 35.19 | odd | 6 | ||
945.2.bb.a.404.10 | yes | 32 | 21.5 | even | 6 | ||
945.2.bb.b.269.7 | yes | 32 | 15.14 | odd | 2 | inner | |
945.2.bb.b.269.8 | yes | 32 | 1.1 | even | 1 | trivial | |
945.2.bb.b.404.7 | yes | 32 | 7.5 | odd | 6 | inner | |
945.2.bb.b.404.8 | yes | 32 | 105.89 | even | 6 | inner |