Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,2,Mod(25,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.q (of order \(9\), degree \(6\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.72476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Character | \(\chi\) | \(=\) | 216.97 |
Dual form | 216.2.q.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.57237 | − | 0.726388i | −0.907811 | − | 0.419380i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.78916 | − | 0.651202i | −0.800137 | − | 0.291226i | −0.0905940 | − | 0.995888i | \(-0.528877\pi\) |
−0.709543 | + | 0.704662i | \(0.751099\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.623407 | + | 3.53552i | −0.235626 | + | 1.33630i | 0.605667 | + | 0.795718i | \(0.292907\pi\) |
−0.841292 | + | 0.540581i | \(0.818205\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.94472 | + | 2.28431i | 0.648240 | + | 0.761436i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.04987 | + | 1.47403i | −1.22108 | + | 0.444437i | −0.870534 | − | 0.492108i | \(-0.836227\pi\) |
−0.350547 | + | 0.936545i | \(0.614004\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0714443 | + | 0.0599489i | −0.0198151 | + | 0.0166268i | −0.652641 | − | 0.757667i | \(-0.726339\pi\) |
0.632826 | + | 0.774294i | \(0.281895\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.34021 | + | 2.32356i | 0.604239 | + | 0.599940i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.83982 | + | 3.18667i | 0.446223 | + | 0.772881i | 0.998137 | − | 0.0610206i | \(-0.0194355\pi\) |
−0.551914 | + | 0.833901i | \(0.686102\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.88233 | + | 6.72439i | −0.890667 | + | 1.54268i | −0.0515903 | + | 0.998668i | \(0.516429\pi\) |
−0.839077 | + | 0.544013i | \(0.816904\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.54838 | − | 5.10632i | 0.774321 | − | 1.11429i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.14509 | − | 6.49415i | −0.238769 | − | 1.35412i | −0.834530 | − | 0.550963i | \(-0.814261\pi\) |
0.595761 | − | 0.803162i | \(-0.296851\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.05319 | − | 0.883728i | −0.210637 | − | 0.176746i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.39854 | − | 5.00441i | −0.269149 | − | 0.963099i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.61880 | − | 3.03653i | −0.671993 | − | 0.563869i | 0.241661 | − | 0.970361i | \(-0.422308\pi\) |
−0.913655 | + | 0.406491i | \(0.866752\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0708700 | − | 0.401924i | −0.0127286 | − | 0.0721876i | 0.977782 | − | 0.209625i | \(-0.0672244\pi\) |
−0.990510 | + | 0.137438i | \(0.956113\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.43863 | + | 0.624046i | 1.29490 | + | 0.108632i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.41771 | − | 5.91964i | 0.577698 | − | 1.00060i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.11523 | + | 3.66369i | 0.347742 | + | 0.602307i | 0.985848 | − | 0.167641i | \(-0.0536151\pi\) |
−0.638106 | + | 0.769949i | \(0.720282\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.155883 | − | 0.0423658i | 0.0249613 | − | 0.00678396i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.23989 | + | 4.39679i | −0.818333 | + | 0.686663i | −0.952581 | − | 0.304285i | \(-0.901583\pi\) |
0.134248 | + | 0.990948i | \(0.457138\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2909 | − | 3.74557i | 1.56934 | − | 0.571195i | 0.596492 | − | 0.802619i | \(-0.296561\pi\) |
0.972853 | + | 0.231424i | \(0.0743386\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.99188 | − | 5.35340i | −0.296931 | − | 0.798038i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.472016 | + | 2.67694i | −0.0688506 | + | 0.390471i | 0.930836 | + | 0.365437i | \(0.119081\pi\) |
−0.999687 | + | 0.0250341i | \(0.992031\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.53338 | − | 2.01399i | −0.790483 | − | 0.287712i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.578134 | − | 6.34706i | −0.0809550 | − | 0.888766i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.12782 | 0.154918 | 0.0774590 | − | 0.996996i | \(-0.475319\pi\) | ||||
0.0774590 | + | 0.996996i | \(0.475319\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.20576 | 1.10646 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.9890 | − | 7.75318i | 1.45553 | − | 1.02693i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.48162 | + | 0.539264i | 0.192890 | + | 0.0702062i | 0.436659 | − | 0.899627i | \(-0.356162\pi\) |
−0.243769 | + | 0.969833i | \(0.578384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.39919 | − | 7.93519i | 0.179148 | − | 1.01600i | −0.754099 | − | 0.656761i | \(-0.771926\pi\) |
0.933247 | − | 0.359236i | \(-0.116963\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.28855 | + | 5.45154i | −1.17025 | + | 0.686829i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.166864 | − | 0.0607336i | 0.0206970 | − | 0.00753308i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.15926 | + | 6.00733i | −0.874642 | + | 0.733912i | −0.965070 | − | 0.261991i | \(-0.915621\pi\) |
0.0904279 | + | 0.995903i | \(0.471177\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.91676 | + | 11.0430i | −0.351136 | + | 1.32942i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.22008 | − | 3.84530i | −0.263475 | − | 0.456353i | 0.703688 | − | 0.710509i | \(-0.251535\pi\) |
−0.967163 | + | 0.254157i | \(0.918202\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.95978 | + | 8.59058i | −0.580498 | + | 1.00545i | 0.414922 | + | 0.909857i | \(0.363809\pi\) |
−0.995420 | + | 0.0955950i | \(0.969525\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.01407 | + | 2.15457i | 0.117095 | + | 0.248789i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.68675 | − | 15.2373i | −0.306183 | − | 1.73645i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.33935 | + | 3.64114i | 0.488215 | + | 0.409661i | 0.853386 | − | 0.521280i | \(-0.174545\pi\) |
−0.365171 | + | 0.930940i | \(0.618990\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.43612 | + | 8.88468i | −0.159569 | + | 0.987187i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.85999 | + | 4.91711i | 0.643217 | + | 0.539723i | 0.905004 | − | 0.425402i | \(-0.139867\pi\) |
−0.261787 | + | 0.965126i | \(0.584312\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.21658 | − | 6.89956i | −0.131957 | − | 0.748363i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.48440 | + | 7.40321i | 0.373567 | + | 0.793707i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.55242 | + | 9.61708i | −0.588556 | + | 1.01941i | 0.405866 | + | 0.913933i | \(0.366970\pi\) |
−0.994422 | + | 0.105476i | \(0.966363\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.167411 | − | 0.289965i | −0.0175495 | − | 0.0303966i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.180518 | + | 0.683453i | −0.0187189 | + | 0.0708708i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.3250 | − | 9.50284i | 1.16193 | − | 0.974971i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0206 | − | 4.73910i | 1.32204 | − | 0.481182i | 0.417927 | − | 0.908481i | \(-0.362757\pi\) |
0.904111 | + | 0.427298i | \(0.140535\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.2430 | − | 6.38456i | −1.12996 | − | 0.641673i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.08856 | + | 17.5161i | −0.307324 | + | 1.74292i | 0.305038 | + | 0.952340i | \(0.401331\pi\) |
−0.612361 | + | 0.790578i | \(0.709780\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.5354 | − | 5.29045i | −1.43222 | − | 0.521284i | −0.494650 | − | 0.869092i | \(-0.664704\pi\) |
−0.937566 | + | 0.347808i | \(0.886926\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.67387 | + | 6.82531i | −0.944074 | + | 0.666083i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.7763 | 1.52515 | 0.762576 | − | 0.646899i | \(-0.223935\pi\) | ||||
0.762576 | + | 0.646899i | \(0.223935\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1398 | −1.45013 | −0.725063 | − | 0.688683i | \(-0.758189\pi\) | ||||
−0.725063 | + | 0.688683i | \(0.758189\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.664677 | − | 7.29718i | −0.0630884 | − | 0.692617i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.168455 | − | 0.0613127i | −0.0158469 | − | 0.00576782i | 0.334085 | − | 0.942543i | \(-0.391573\pi\) |
−0.349931 | + | 0.936775i | \(0.613795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.18024 | + | 12.3648i | −0.203309 | + | 1.15302i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.275881 | − | 0.0466169i | −0.0255052 | − | 0.00430973i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.4135 | + | 4.51813i | −1.13794 | + | 0.414177i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.80218 | − | 4.86861i | 0.527471 | − | 0.442601i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.4328 | − | 3.10721i | 1.03086 | − | 0.280167i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.06880 | + | 10.5115i | 0.542810 | + | 0.940175i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.32560 | − | 12.6883i | 0.650042 | − | 1.12591i | −0.333070 | − | 0.942902i | \(-0.608084\pi\) |
0.983112 | − | 0.183004i | \(-0.0585822\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.9019 | − | 1.58573i | −1.66422 | − | 0.139615i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.24848 | + | 12.7518i | 0.196451 | + | 1.11413i | 0.910338 | + | 0.413867i | \(0.135822\pi\) |
−0.713887 | + | 0.700261i | \(0.753067\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −21.3539 | − | 17.9181i | −1.85162 | − | 1.55369i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.756670 | + | 9.86442i | −0.0651238 | + | 0.848994i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.10358 | + | 2.60421i | 0.265157 | + | 0.222493i | 0.765666 | − | 0.643238i | \(-0.222410\pi\) |
−0.500509 | + | 0.865731i | \(0.666854\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.853818 | − | 4.84224i | −0.0724199 | − | 0.410714i | −0.999369 | − | 0.0355260i | \(-0.988689\pi\) |
0.926949 | − | 0.375188i | \(-0.122422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.68668 | − | 3.86628i | 0.226259 | − | 0.325599i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.200974 | − | 0.348096i | 0.0168063 | − | 0.0291093i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.49722 | + | 7.78941i | 0.373474 | + | 0.646875i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.23761 | + | 7.18612i | 0.596948 | + | 0.592701i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.61113 | + | 3.86920i | −0.377759 | + | 0.316977i | −0.811822 | − | 0.583905i | \(-0.801524\pi\) |
0.434063 | + | 0.900883i | \(0.357080\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3155 | − | 6.66631i | 1.49050 | − | 0.542497i | 0.536917 | − | 0.843635i | \(-0.319589\pi\) |
0.953581 | + | 0.301138i | \(0.0973665\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.70138 | + | 10.3999i | −0.299239 | + | 0.840783i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.134935 | + | 0.765257i | −0.0108383 | + | 0.0614669i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0274 | + | 5.46952i | 1.19932 | + | 0.436516i | 0.862986 | − | 0.505228i | \(-0.168592\pi\) |
0.336331 | + | 0.941744i | \(0.390814\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.77336 | − | 0.819235i | −0.140636 | − | 0.0649696i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.6740 | 1.86578 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.65600 | −0.364686 | −0.182343 | − | 0.983235i | \(-0.558368\pi\) | ||||
−0.182343 | + | 0.983235i | \(0.558368\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.9025 | − | 5.96057i | −1.00446 | − | 0.464029i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.66800 | − | 2.79092i | −0.593368 | − | 0.215968i | 0.0278422 | − | 0.999612i | \(-0.491136\pi\) |
−0.621210 | + | 0.783644i | \(0.713359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.25592 | + | 12.7939i | −0.173532 | + | 0.984149i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22.9106 | + | 4.20864i | −1.75202 | + | 0.321842i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.14124 | − | 2.96317i | 0.618967 | − | 0.225286i | −0.0134552 | − | 0.999909i | \(-0.504283\pi\) |
0.632422 | + | 0.774624i | \(0.282061\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.78100 | − | 3.17263i | 0.285817 | − | 0.239829i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.93794 | − | 1.92415i | −0.145665 | − | 0.144628i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.46176 | + | 5.99595i | 0.258744 | + | 0.448158i | 0.965906 | − | 0.258894i | \(-0.0833580\pi\) |
−0.707162 | + | 0.707052i | \(0.750025\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.68344 | − | 2.91581i | 0.125129 | − | 0.216730i | −0.796654 | − | 0.604435i | \(-0.793399\pi\) |
0.921783 | + | 0.387705i | \(0.126732\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.96407 | + | 11.4607i | −0.588721 | + | 0.847202i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.39869 | − | 7.93238i | −0.102834 | − | 0.583200i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.1483 | − | 10.1936i | −0.888371 | − | 0.745432i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 18.5650 | − | 1.82477i | 1.35041 | − | 0.132732i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.01432 | − | 6.72482i | −0.579896 | − | 0.486591i | 0.305017 | − | 0.952347i | \(-0.401338\pi\) |
−0.884913 | + | 0.465756i | \(0.845782\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.68702 | − | 9.56759i | −0.121435 | − | 0.688690i | −0.983362 | − | 0.181658i | \(-0.941854\pi\) |
0.861927 | − | 0.507032i | \(-0.169258\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.306489 | − | 0.0257122i | −0.0219482 | − | 0.00184129i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.11902 | − | 15.7946i | 0.649703 | − | 1.12532i | −0.333491 | − | 0.942753i | \(-0.608227\pi\) |
0.983194 | − | 0.182565i | \(-0.0584401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.84955 | − | 3.20351i | −0.131111 | − | 0.227091i | 0.792994 | − | 0.609229i | \(-0.208521\pi\) |
−0.924105 | + | 0.382138i | \(0.875188\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.6207 | − | 4.24537i | 1.10180 | − | 0.299446i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.9917 | − | 10.9013i | 0.911837 | − | 0.765122i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.2382 | − | 4.45434i | 0.854754 | − | 0.311105i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.6077 | − | 15.2451i | 0.876299 | − | 1.05961i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.81096 | − | 32.9556i | 0.401952 | − | 2.27958i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.4191 | − | 3.79222i | −0.717277 | − | 0.261068i | −0.0425077 | − | 0.999096i | \(-0.513535\pi\) |
−0.674769 | + | 0.738029i | \(0.735757\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.697625 | + | 7.65889i | 0.0478005 | + | 0.524778i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.8512 | −1.42204 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.46519 | 0.0994634 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.0387 | − | 9.90489i | 0.948649 | − | 0.669311i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.322482 | − | 0.117374i | −0.0216925 | − | 0.00789543i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.303478 | − | 1.72111i | 0.0203224 | − | 0.115254i | −0.972959 | − | 0.230978i | \(-0.925808\pi\) |
0.993281 | + | 0.115724i | \(0.0369187\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.0294473 | − | 4.12441i | −0.00196315 | − | 0.274960i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.20256 | + | 1.16564i | −0.212562 | + | 0.0773661i | −0.446106 | − | 0.894980i | \(-0.647190\pi\) |
0.233545 | + | 0.972346i | \(0.424967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.13172 | − | 5.98422i | 0.471277 | − | 0.395449i | −0.375983 | − | 0.926627i | \(-0.622695\pi\) |
0.847260 | + | 0.531178i | \(0.178250\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.84362 | + | 25.9103i | −0.450277 | + | 1.70478i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.129911 | + | 0.225012i | 0.00851074 | + | 0.0147410i | 0.870249 | − | 0.492611i | \(-0.163958\pi\) |
−0.861739 | + | 0.507352i | \(0.830624\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.58774 | − | 4.48210i | 0.168805 | − | 0.292380i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.17819 | − | 8.87729i | −0.271403 | − | 0.576642i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.20753 | + | 23.8621i | 0.272163 | + | 1.54351i | 0.747833 | + | 0.663887i | \(0.231094\pi\) |
−0.475670 | + | 0.879624i | \(0.657794\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0881066 | + | 0.0739302i | 0.00567545 | + | 0.00476226i | 0.645621 | − | 0.763658i | \(-0.276599\pi\) |
−0.639945 | + | 0.768420i | \(0.721043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.71184 | − | 12.9269i | 0.558865 | − | 0.829259i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.58861 | + | 7.20670i | 0.548706 | + | 0.460419i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.125750 | − | 0.713161i | −0.00800125 | − | 0.0453773i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.64236 | − | 11.9882i | −0.357570 | − | 0.759719i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.67852 | + | 2.90728i | −0.105947 | + | 0.183506i | −0.914125 | − | 0.405433i | \(-0.867121\pi\) |
0.808178 | + | 0.588939i | \(0.200454\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.2101 | + | 24.6126i | 0.893379 | + | 1.54738i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.09884 | + | 11.7324i | −0.194057 | + | 0.734711i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.3304 | + | 9.50736i | −0.706773 | + | 0.593053i | −0.923692 | − | 0.383137i | \(-0.874844\pi\) |
0.216919 | + | 0.976190i | \(0.430399\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.2717 | + | 5.19447i | −0.886800 | + | 0.322769i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.101182 | − | 14.1716i | −0.00626302 | − | 0.877203i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.24341 | + | 24.0656i | −0.261660 | + | 1.48395i | 0.516720 | + | 0.856154i | \(0.327153\pi\) |
−0.778380 | + | 0.627793i | \(0.783958\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.01785 | − | 0.734439i | −0.123956 | − | 0.0451162i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.7162 | − | 11.0884i | 0.961817 | − | 0.678601i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.8785 | −1.63881 | −0.819405 | − | 0.573216i | \(-0.805696\pi\) | ||||
−0.819405 | + | 0.573216i | \(0.805696\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.72696 | 0.408634 | 0.204317 | − | 0.978905i | \(-0.434503\pi\) | ||||
0.204317 | + | 0.978905i | \(0.434503\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.0526063 | + | 0.577539i | 0.00318388 | + | 0.0349543i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.56791 | + | 2.02655i | 0.335758 | + | 0.122206i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.84460 | + | 21.8038i | −0.231000 | + | 1.31007i | 0.619877 | + | 0.784699i | \(0.287183\pi\) |
−0.850876 | + | 0.525366i | \(0.823928\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.780294 | − | 0.943518i | 0.0467150 | − | 0.0564870i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.1745 | − | 4.43114i | 0.726267 | − | 0.264340i | 0.0476833 | − | 0.998863i | \(-0.484816\pi\) |
0.678584 | + | 0.734523i | \(0.262594\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.1963 | + | 13.5903i | −0.962772 | + | 0.807862i | −0.981402 | − | 0.191965i | \(-0.938514\pi\) |
0.0186295 | + | 0.999826i | \(0.494070\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.7100 | + | 6.71565i | −1.46369 | + | 0.397801i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.2783 | − | 21.2667i | −0.724767 | − | 1.25533i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.73010 | − | 2.99661i | 0.101770 | − | 0.176271i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.9156 | − | 2.00634i | −1.40196 | − | 0.117614i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.165668 | + | 0.939551i | 0.00967844 | + | 0.0548891i | 0.989264 | − | 0.146136i | \(-0.0466838\pi\) |
−0.979586 | + | 0.201025i | \(0.935573\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.29968 | − | 1.92966i | −0.133893 | − | 0.112349i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.0405 | + | 18.2057i | 0.756689 | + | 1.05640i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.471128 | + | 0.395323i | 0.0272460 | + | 0.0228621i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.82713 | + | 38.7186i | 0.393509 | + | 2.23170i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.5799 | − | 25.2984i | 1.00994 | − | 1.45335i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.67078 | + | 13.2862i | −0.439228 | + | 0.760765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.13734 | − | 12.3622i | −0.407350 | − | 0.705550i | 0.587242 | − | 0.809411i | \(-0.300214\pi\) |
−0.994592 | + | 0.103861i | \(0.966880\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.0122 | + | 18.8769i | 1.08156 | + | 1.07387i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.7918 | + | 9.05541i | −0.611948 | + | 0.513485i | −0.895261 | − | 0.445542i | \(-0.853011\pi\) |
0.283313 | + | 0.959028i | \(0.408566\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.84547 | + | 0.671697i | −0.104312 | + | 0.0379666i | −0.393649 | − | 0.919261i | \(-0.628787\pi\) |
0.289337 | + | 0.957227i | \(0.406565\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 20.1688 | − | 3.70496i | 1.13638 | − | 0.208751i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.19130 | − | 18.0988i | 0.179241 | − | 1.01653i | −0.753892 | − | 0.656998i | \(-0.771826\pi\) |
0.933134 | − | 0.359530i | \(-0.117063\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.1316 | + | 6.96333i | 1.07116 | + | 0.389872i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.8062 | − | 11.4597i | −1.38455 | − | 0.639618i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.5712 | −1.58974 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.128223 | 0.00711252 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23.8054 | + | 10.9973i | 1.31644 | + | 0.608154i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.17009 | − | 3.33764i | −0.505564 | − | 0.184010i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.34429 | + | 18.9664i | −0.183819 | + | 1.04249i | 0.743645 | + | 0.668574i | \(0.233095\pi\) |
−0.927464 | + | 0.373913i | \(0.878016\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.25546 | + | 11.9567i | −0.233198 | + | 0.655223i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.7211 | − | 6.08597i | 0.913569 | − | 0.332512i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.2011 | + | 11.0771i | −0.719111 | + | 0.603406i | −0.927139 | − | 0.374717i | \(-0.877740\pi\) |
0.208028 | + | 0.978123i | \(0.433295\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.220338 | + | 0.218770i | 0.0119671 | + | 0.0118820i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.879462 | + | 1.52327i | 0.0476255 | + | 0.0824899i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.99517 | + | 3.45573i | −0.107729 | + | 0.186592i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.4098 | − | 17.8584i | 0.668120 | − | 0.961461i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.53577 | + | 14.3811i | 0.136127 | + | 0.772015i | 0.974068 | + | 0.226255i | \(0.0726481\pi\) |
−0.837941 | + | 0.545761i | \(0.816241\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.80655 | − | 7.38958i | −0.471404 | − | 0.395555i | 0.375902 | − | 0.926659i | \(-0.377333\pi\) |
−0.847306 | + | 0.531104i | \(0.821777\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.399926 | + | 0.273696i | 0.0213465 | + | 0.0146088i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.1652 | − | 17.7597i | −1.12651 | − | 0.945252i | −0.127593 | − | 0.991827i | \(-0.540725\pi\) |
−0.998915 | + | 0.0465747i | \(0.985169\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.46802 | + | 8.32558i | 0.0779147 | + | 0.441876i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.8005 | + | 1.91280i | 1.20673 | + | 0.101236i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.62882 | − | 8.01735i | 0.244300 | − | 0.423140i | −0.717635 | − | 0.696420i | \(-0.754775\pi\) |
0.961935 | + | 0.273280i | \(0.0881086\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −20.6450 | − | 35.7581i | −1.08658 | − | 1.88201i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.6597 | + | 3.44064i | −0.664462 | + | 0.180587i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.4680 | − | 12.1401i | 0.757292 | − | 0.635443i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.88697 | − | 3.23459i | 0.463896 | − | 0.168844i | −0.0994892 | − | 0.995039i | \(-0.531721\pi\) |
0.563385 | + | 0.826194i | \(0.309499\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.2337 | − | 3.41899i | −1.05333 | − | 0.177985i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.703091 | + | 3.98743i | −0.0365027 | + | 0.207017i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.6244 | + | 6.77871i | 0.964333 | + | 0.350989i | 0.775730 | − | 0.631065i | \(-0.217382\pi\) |
0.188603 | + | 0.982053i | \(0.439604\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.90702 | − | 20.9363i | −0.0984781 | − | 1.08114i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.440579 | 0.0226910 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.9928 | −0.564661 | −0.282331 | − | 0.959317i | \(-0.591107\pi\) | ||||
−0.282331 | + | 0.959317i | \(0.591107\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.7352 | + | 14.6296i | −1.06230 | + | 0.749495i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.8315 | − | 10.1298i | −1.42212 | − | 0.517610i | −0.487459 | − | 0.873146i | \(-0.662076\pi\) |
−0.934663 | + | 0.355536i | \(0.884298\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.11553 | + | 29.0116i | −0.260711 | + | 1.47857i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.5689 | + | 16.2234i | 1.45224 | + | 0.824683i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.6995 | + | 6.07813i | −0.846700 | + | 0.308174i | −0.728694 | − | 0.684839i | \(-0.759872\pi\) |
−0.118006 | + | 0.993013i | \(0.537650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.5879 | − | 15.5971i | 0.940033 | − | 0.788781i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.72728 | − | 21.6838i | 0.288903 | − | 1.09380i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.39267 | − | 9.34038i | −0.271335 | − | 0.469966i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0935 | + | 27.8748i | −0.807711 | + | 1.39900i | 0.106735 | + | 0.994287i | \(0.465960\pi\) |
−0.914446 | + | 0.404708i | \(0.867373\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.5609 | + | 43.6851i | 1.02933 | + | 2.18699i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.432589 | + | 2.45333i | 0.0216024 | + | 0.122514i | 0.993702 | − | 0.112055i | \(-0.0357433\pi\) |
−0.972100 | + | 0.234569i | \(0.924632\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0291581 | + | 0.0244666i | 0.00145247 | + | 0.00121877i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.35517 | − | 14.9609i | 0.415171 | − | 0.743415i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.9668 | − | 11.7196i | −0.692310 | − | 0.580917i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.905806 | + | 5.13708i | 0.0447892 | + | 0.254012i | 0.998978 | − | 0.0451919i | \(-0.0143899\pi\) |
−0.954189 | + | 0.299204i | \(0.903279\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.98832 | − | 6.34920i | −0.147403 | − | 0.313183i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.83023 | + | 4.90210i | −0.139266 | + | 0.241216i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.28244 | − | 12.6135i | −0.357481 | − | 0.619175i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.17483 | + | 8.23402i | −0.106502 | + | 0.403222i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.1987 | − | 16.9487i | 0.986770 | − | 0.827999i | 0.00167338 | − | 0.999999i | \(-0.499467\pi\) |
0.985097 | + | 0.172000i | \(0.0550229\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.90486 | + | 1.42125i | −0.190311 | + | 0.0692677i | −0.435418 | − | 0.900228i | \(-0.643399\pi\) |
0.245106 | + | 0.969496i | \(0.421177\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.03289 | + | 4.12767i | −0.341951 | + | 0.200694i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.878472 | − | 4.98206i | 0.0426121 | − | 0.241665i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.1827 | + | 9.89370i | 1.31546 | + | 0.478790i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.568859 | + | 0.401353i | −0.0274648 | + | 0.0193775i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.9050 | 0.717950 | 0.358975 | − | 0.933347i | \(-0.383126\pi\) | ||||
0.358975 | + | 0.933347i | \(0.383126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.2825 | 1.83974 | 0.919870 | − | 0.392223i | \(-0.128294\pi\) | ||||
0.919870 | + | 0.392223i | \(0.128294\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.41318 | − | 15.5146i | −0.0677566 | − | 0.743868i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 48.1149 | + | 17.5124i | 2.30165 | + | 0.837730i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.20756 | + | 23.8623i | −0.200816 | + | 1.13888i | 0.703073 | + | 0.711118i | \(0.251811\pi\) |
−0.903889 | + | 0.427767i | \(0.859300\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.16032 | − | 16.5566i | −0.293349 | − | 0.788409i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0820238 | − | 0.0298542i | 0.00389707 | − | 0.00141842i | −0.340071 | − | 0.940400i | \(-0.610451\pi\) |
0.343968 | + | 0.938981i | \(0.388229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.1968 | − | 13.5908i | 0.767804 | − | 0.644264i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.0610 | − | 2.73436i | 0.475868 | − | 0.129331i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.8525 | − | 20.5291i | −0.559352 | − | 0.968826i | −0.997551 | − | 0.0699482i | \(-0.977717\pi\) |
0.438198 | − | 0.898878i | \(-0.355617\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.7399 | − | 25.5302i | 0.694073 | − | 1.20217i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −33.6412 | − | 2.82225i | −1.58060 | − | 0.132601i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.110700 | + | 0.627813i | 0.00518971 | + | 0.0294323i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0590 | − | 11.7969i | −0.657651 | − | 0.551835i | 0.251731 | − | 0.967797i | \(-0.419000\pi\) |
−0.909382 | + | 0.415962i | \(0.863445\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.3743 | − | 13.6639i | 0.624260 | − | 0.637776i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.1996 | + | 22.8232i | 1.26681 | + | 1.06298i | 0.994922 | + | 0.100652i | \(0.0320928\pi\) |
0.271889 | + | 0.962329i | \(0.412352\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.05421 | + | 11.6500i | 0.0954674 | + | 0.541422i | 0.994603 | + | 0.103753i | \(0.0330850\pi\) |
−0.899136 | + | 0.437670i | \(0.855804\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.768042 | − | 1.10525i | 0.0356171 | − | 0.0512550i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.97741 | + | 15.5493i | −0.415425 | + | 0.719537i | −0.995473 | − | 0.0950451i | \(-0.969700\pi\) |
0.580048 | + | 0.814582i | \(0.303034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.7759 | − | 29.0567i | −0.774638 | − | 1.34171i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.6557 | − | 19.5159i | −0.905687 | − | 0.899243i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −36.1556 | + | 30.3382i | −1.66244 | + | 1.39495i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.0313 | − | 3.65111i | 0.460270 | − | 0.167525i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.19330 | + | 2.57629i | 0.100424 | + | 0.117960i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.00978 | − | 28.4119i | 0.228903 | − | 1.29817i | −0.626179 | − | 0.779679i | \(-0.715382\pi\) |
0.855082 | − | 0.518493i | \(-0.173507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.370756 | − | 0.134944i | −0.0169050 | − | 0.00615292i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −37.2244 | − | 17.1965i | −1.69377 | − | 0.782469i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.3820 | −1.19794 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.64498 | −0.437056 | −0.218528 | − | 0.975831i | \(-0.570125\pi\) | ||||
−0.218528 | + | 0.975831i | \(0.570125\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.32098 | + | 3.38207i | 0.331066 | + | 0.152942i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.847092 | + | 0.308316i | 0.0382287 | + | 0.0139141i | 0.361064 | − | 0.932541i | \(-0.382414\pi\) |
−0.322835 | + | 0.946455i | \(0.604636\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.01847 | − | 17.1186i | 0.135945 | − | 0.770982i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.9579 | + | 18.7445i | 0.717255 | + | 0.842502i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.9791 | − | 5.45195i | 0.671905 | − | 0.244554i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.913635 | − | 0.766631i | 0.0408999 | − | 0.0343191i | −0.622109 | − | 0.782931i | \(-0.713724\pi\) |
0.663008 | + | 0.748612i | \(0.269279\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.0297 | + | 9.95832i | 0.448093 | + | 0.444905i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.7334 | + | 22.0550i | 0.567756 | + | 0.983383i | 0.996787 | + | 0.0800931i | \(0.0255218\pi\) |
−0.429031 | + | 0.903290i | \(0.641145\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.9325 | − | 29.3279i | 0.753485 | − | 1.30507i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.8405 | − | 18.4782i | 0.570267 | − | 0.820645i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.40094 | − | 13.6164i | −0.106420 | − | 0.603536i | −0.990644 | − | 0.136473i | \(-0.956423\pi\) |
0.884224 | − | 0.467063i | \(-0.154688\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.2802 | − | 22.8908i | −1.20680 | − | 1.01263i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 39.0812 | + | 10.0244i | 1.72548 | + | 0.442590i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.5610 | + | 18.9310i | 0.994158 | + | 0.834197i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.03429 | − | 11.5370i | −0.0894678 | − | 0.507397i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.9535 | − | 1.25449i | −0.656385 | − | 0.0550659i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.12013 | − | 1.94012i | 0.0490737 | − | 0.0849982i | −0.840445 | − | 0.541897i | \(-0.817706\pi\) |
0.889519 | + | 0.456898i | \(0.151040\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.58187 | + | 13.1322i | 0.331532 | + | 0.574230i | 0.982812 | − | 0.184607i | \(-0.0591012\pi\) |
−0.651280 | + | 0.758837i | \(0.725768\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.24971 | + | 2.24210i | −0.360047 | + | 0.0978531i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.15041 | − | 0.965308i | 0.0501126 | − | 0.0420495i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2499 | + | 7.00637i | −0.836950 | + | 0.304625i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.64949 | + | 4.43319i | 0.0715816 | + | 0.192384i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.110778 | − | 0.628252i | 0.00479831 | − | 0.0272126i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.2263 | − | 10.2735i | −1.22033 | − | 0.444164i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.08780 | − | 11.9425i | −0.0469421 | − | 0.515355i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.3782 | 1.09311 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.43395 | −0.0616501 | −0.0308251 | − | 0.999525i | \(-0.509813\pi\) | ||||
−0.0308251 | + | 0.999525i | \(0.509813\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.76501 | + | 3.36191i | −0.204486 | + | 0.144273i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.0875 | + | 9.85903i | 1.16030 | + | 0.422315i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.17185 | + | 17.9885i | −0.135619 | + | 0.769132i | 0.838808 | + | 0.544427i | \(0.183253\pi\) |
−0.974427 | + | 0.224705i | \(0.927858\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.8474 | − | 12.2356i | 0.889747 | − | 0.522201i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.4682 | − | 12.5454i | 1.46839 | − | 0.534451i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.5785 | + | 13.0719i | −0.662465 | + | 0.555874i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.56272 | + | 13.4887i | −0.151229 | + | 0.572562i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.3587 | − | 35.2623i | −0.862626 | − | 1.49411i | −0.869385 | − | 0.494135i | \(-0.835485\pi\) |
0.00675958 | − | 0.999977i | \(-0.497848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.510682 | + | 0.884527i | −0.0215995 | + | 0.0374115i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.6971 | + | 24.8526i | 0.493854 | + | 1.04928i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.81761 | + | 21.6507i | 0.160893 | + | 0.912469i | 0.953199 | + | 0.302345i | \(0.0977693\pi\) |
−0.792306 | + | 0.610124i | \(0.791120\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.261467 | + | 0.219397i | 0.0110000 | + | 0.00923009i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −30.5166 | − | 10.6162i | −1.28158 | − | 0.445838i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.66760 | + | 3.07748i | 0.153754 | + | 0.129015i | 0.716420 | − | 0.697670i | \(-0.245780\pi\) |
−0.562666 | + | 0.826685i | \(0.690224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.85551 | − | 33.2082i | −0.245045 | − | 1.38972i | −0.820387 | − | 0.571808i | \(-0.806242\pi\) |
0.575342 | − | 0.817913i | \(-0.304869\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.71669 | + | 16.3954i | 0.322369 | + | 0.684929i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.53307 | + | 7.85150i | −0.189042 | + | 0.327430i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.49507 | + | 2.58954i | 0.0622407 | + | 0.107804i | 0.895467 | − | 0.445129i | \(-0.146842\pi\) |
−0.833226 | + | 0.552933i | \(0.813509\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.29715 | + | 16.2693i | −0.178583 | + | 0.676128i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.0377 | + | 17.6527i | −0.872790 | + | 0.732358i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.56753 | + | 1.66244i | −0.189168 | + | 0.0688514i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.463239 | + | 0.263059i | 0.0191526 | + | 0.0108762i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.81406 | − | 27.3019i | 0.198698 | − | 1.12687i | −0.708356 | − | 0.705856i | \(-0.750563\pi\) |
0.907054 | − | 0.421015i | \(-0.138326\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.97783 | + | 1.08384i | 0.122699 | + | 0.0446589i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.8115 | + | 18.2111i | −1.06174 | + | 0.749104i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.5131 | 0.719175 | 0.359588 | − | 0.933111i | \(-0.382917\pi\) | ||||
0.359588 | + | 0.933111i | \(0.382917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 25.1519 | 1.03113 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.581190 | + | 6.38061i | 0.0237865 | + | 0.261141i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.5166 | + | 5.64757i | 0.633990 | + | 0.230754i | 0.638967 | − | 0.769234i | \(-0.279362\pi\) |
−0.00497679 | + | 0.999988i | \(0.501584\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.45317 | − | 25.2552i | 0.181649 | − | 1.03018i | −0.748538 | − | 0.663092i | \(-0.769244\pi\) |
0.930186 | − | 0.367088i | \(-0.119645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.6453 | − | 4.67136i | −1.12581 | − | 0.190232i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.5515 | + | 4.93234i | −0.550946 | + | 0.200528i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.3733 | − | 9.54334i | 0.461628 | − | 0.387352i | −0.382101 | − | 0.924120i | \(-0.624800\pi\) |
0.843730 | + | 0.536768i | \(0.180355\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −28.3464 | + | 7.70395i | −1.14865 | + | 0.312180i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.126757 | − | 0.219549i | −0.00512802 | − | 0.00888200i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.85101 | + | 11.8663i | −0.276709 | + | 0.479275i | −0.970565 | − | 0.240839i | \(-0.922577\pi\) |
0.693856 | + | 0.720114i | \(0.255911\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −22.4786 | − | 1.88579i | −0.906426 | − | 0.0760424i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.55504 | − | 14.4903i | −0.102862 | − | 0.583359i | −0.992053 | − | 0.125822i | \(-0.959843\pi\) |
0.889191 | − | 0.457536i | \(-0.151268\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.04409 | + | 5.91070i | 0.283126 | + | 0.237571i | 0.773280 | − | 0.634065i | \(-0.218615\pi\) |
−0.490154 | + | 0.871636i | \(0.663059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −30.8979 | + | 14.8128i | −1.23989 | + | 0.594418i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.5399 | − | 25.6260i | −1.22356 | − | 1.02669i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.81929 | − | 15.9890i | −0.112772 | − | 0.639559i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −33.0755 | + | 47.5975i | −1.32091 | + | 1.90086i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.78332 | + | 13.4811i | −0.310341 | + | 0.537527i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.0133 | + | 19.0757i | 0.438434 | + | 0.759390i | 0.997569 | − | 0.0696865i | \(-0.0221999\pi\) |
−0.559135 | + | 0.829077i | \(0.688867\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.6280 | + | 13.5311i | 0.541665 | + | 0.537812i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21.3693 | + | 17.9310i | −0.848017 | + | 0.711570i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.516065 | − | 0.187832i | 0.0204472 | − | 0.00744219i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.46640 | − | 12.5494i | 0.176688 | − | 0.496446i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.36992 | + | 24.7830i | −0.172601 | + | 0.978871i | 0.768275 | + | 0.640120i | \(0.221115\pi\) |
−0.940876 | + | 0.338751i | \(0.889996\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.95532 | + | 1.43962i | 0.155982 | + | 0.0567730i | 0.418831 | − | 0.908064i | \(-0.362440\pi\) |
−0.262849 | + | 0.964837i | \(0.584662\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 32.7858 | + | 15.1460i | 1.29094 | + | 0.596375i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.11266 | 0.161685 | 0.0808427 | − | 0.996727i | \(-0.474239\pi\) | ||||
0.0808427 | + | 0.996727i | \(0.474239\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.79524 | −0.266737 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.30382 | − | 1.06429i | −0.0902940 | − | 0.0417130i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 41.8307 | + | 15.2251i | 1.63696 | + | 0.595806i | 0.986504 | − | 0.163736i | \(-0.0523544\pi\) |
0.650459 | + | 0.759541i | \(0.274577\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.28108 | − | 24.2792i | 0.167276 | − | 0.948667i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −29.2689 | + | 5.37664i | −1.14189 | + | 0.209763i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.48613 | − | 2.36076i | 0.252664 | − | 0.0919621i | −0.212583 | − | 0.977143i | \(-0.568188\pi\) |
0.465247 | + | 0.885181i | \(0.345965\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.46406 | − | 7.10219i | 0.329214 | − | 0.276243i | −0.463166 | − | 0.886272i | \(-0.653287\pi\) |
0.792379 | + | 0.610029i | \(0.208842\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.421804 | + | 0.418803i | 0.0163815 | + | 0.0162650i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.5373 | + | 45.9640i | 1.02907 | + | 1.78241i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.5758 | + | 26.9781i | −0.603098 | + | 1.04460i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.72737 | + | 2.48578i | −0.0667841 | + | 0.0961059i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.03019 | + | 34.1989i | 0.232793 | + | 1.32023i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.9308 | + | 25.1149i | 1.15375 | + | 0.968108i | 0.999801 | − | 0.0199715i | \(-0.00635755\pi\) |
0.153945 | + | 0.988079i | \(0.450802\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.94962 | + | 6.50650i | −0.113531 | + | 0.250435i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.70666 | − | 2.27115i | −0.104025 | − | 0.0872875i | 0.589292 | − | 0.807920i | \(-0.299407\pi\) |
−0.693317 | + | 0.720633i | \(0.743851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.63804 | + | 48.9888i | 0.331498 | + | 1.88002i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.88234 | + | 0.493485i | 0.225412 | + | 0.0189104i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.32049 | − | 12.6795i | 0.280111 | − | 0.485166i | −0.691301 | − | 0.722567i | \(-0.742962\pi\) |
0.971412 | + | 0.237401i | \(0.0762955\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.85694 | − | 6.68041i | −0.147366 | − | 0.255245i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.5606 | + | 4.22904i | −0.593674 | + | 0.161348i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0805764 | + | 0.0676116i | −0.00306972 | + | 0.00257580i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.6717 | + | 7.52387i | −0.786387 | + | 0.286221i | −0.703833 | − | 0.710365i | \(-0.748530\pi\) |
−0.0825536 | + | 0.996587i | \(0.526308\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 29.5817 | − | 35.7696i | 1.12372 | − | 1.35878i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.62566 | + | 9.21956i | −0.0616647 | + | 0.349718i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.6516 | − | 8.60848i | −0.895868 | − | 0.326069i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.0408223 | − | 0.448169i | −0.00154404 | − | 0.0169513i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.32994 | −0.125770 | −0.0628850 | − | 0.998021i | \(-0.520030\pi\) | ||||
−0.0628850 | + | 0.998021i | \(0.520030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.8481 | −1.23889 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.32463 | + | 5.16783i | −0.275862 | + | 0.194632i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −60.0031 | − | 21.8393i | −2.25665 | − | 0.821352i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.92601 | − | 39.2793i | 0.260112 | − | 1.47517i | −0.522491 | − | 0.852645i | \(-0.674997\pi\) |
0.782603 | − | 0.622522i | \(-0.213892\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.121329 | + | 16.9934i | 0.00455019 | + | 0.637303i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.52900 | + | 0.920481i | −0.0947118 | + | 0.0344723i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.586255 | + | 0.491927i | −0.0219247 | + | 0.0183970i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.7173 | − | 40.5764i | 0.400246 | − | 1.51536i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.91776 | + | 6.78576i | 0.146108 | + | 0.253066i | 0.929786 | − | 0.368101i | \(-0.119992\pi\) |
−0.783678 | + | 0.621167i | \(0.786659\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.7659 | − | 48.0920i | 1.03406 | − | 1.79104i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.0848346 | − | 0.180246i | −0.00315503 | − | 0.00670340i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.12780 | + | 6.39606i | 0.0418854 | + | 0.237544i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.7514 | − | 12.3779i | −0.547100 | − | 0.459072i | 0.326857 | − | 0.945074i | \(-0.394010\pi\) |
−0.873958 | + | 0.486002i | \(0.838455\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0882 | + | 13.9977i | −0.855118 | + | 0.518433i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.8693 | + | 25.9024i | 1.14174 | + | 0.958036i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.67878 | − | 26.5347i | −0.172815 | − | 0.980081i | −0.940636 | − | 0.339417i | \(-0.889770\pi\) |
0.767821 | − | 0.640664i | \(-0.221341\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.26965 | − | 17.5703i | −0.305030 | − | 0.648090i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.1391 | − | 34.8819i | 0.741832 | − | 1.28489i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.49490 | + | 14.7136i | 0.312490 | + | 0.541249i | 0.978901 | − | 0.204336i | \(-0.0655036\pi\) |
−0.666411 | + | 0.745585i | \(0.732170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.320306 | + | 1.21270i | −0.0117667 | + | 0.0445496i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.7413 | − | 30.8296i | 1.34791 | − | 1.13103i | 0.368389 | − | 0.929672i | \(-0.379910\pi\) |
0.979518 | − | 0.201356i | \(-0.0645348\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.7697 | − | 3.91985i | 0.394571 | − | 0.143612i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.163846 | + | 22.9484i | 0.00599482 | + | 0.839639i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.83504 | + | 55.7773i | −0.359365 | + | 2.03806i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.6185 | + | 15.8758i | 1.59166 | + | 0.579317i | 0.977698 | − | 0.210018i | \(-0.0673522\pi\) |
0.613963 | + | 0.789335i | \(0.289574\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.75107 | − | 3.35207i | 0.173139 | − | 0.122156i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.1106 | −1.35059 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.3033 | −0.919663 | −0.459831 | − | 0.888006i | \(-0.652090\pi\) | ||||
−0.459831 | + | 0.888006i | \(0.652090\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.46528 | − | 49.0222i | −0.162079 | − | 1.77939i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.2576 | − | 4.09745i | −0.408089 | − | 0.148532i | 0.129815 | − | 0.991538i | \(-0.458562\pi\) |
−0.537904 | + | 0.843006i | \(0.680784\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.43823 | − | 53.5268i | 0.341687 | − | 1.93780i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.3948 | − | 16.1968i | 0.484290 | − | 0.585595i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.138181 | + | 0.0502939i | −0.00498944 | + | 0.00181601i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.38352 | + | 2.00001i | −0.0859521 | + | 0.0721224i | −0.684751 | − | 0.728777i | \(-0.740089\pi\) |
0.598799 | + | 0.800899i | \(0.295645\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.7217 | − | 6.71884i | 0.890331 | − | 0.241973i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.22463 | + | 3.85318i | 0.0800144 | + | 0.138589i | 0.903256 | − | 0.429102i | \(-0.141170\pi\) |
−0.823241 | + | 0.567691i | \(0.807837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.280552 | + | 0.485930i | −0.0100777 | + | 0.0174551i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 26.2136 | + | 2.19913i | 0.940409 | + | 0.0788934i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.22276 | − | 52.3049i | −0.330440 | − | 1.87402i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.6591 | + | 12.3005i | 0.524545 | + | 0.440146i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.1350 | + | 22.3566i | −0.362196 | + | 0.798961i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.3247 | − | 19.5717i | −0.832493 | − | 0.698545i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.0870600 | + | 0.493742i | 0.00310335 | + | 0.0176000i | 0.986320 | − | 0.164841i | \(-0.0527112\pi\) |
−0.983217 | + | 0.182441i | \(0.941600\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.1532 | − | 34.7577i | 0.859876 | − | 1.23741i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.321788 | − | 0.557354i | 0.0114415 | − | 0.0198172i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.375742 | + | 0.650804i | 0.0133430 | + | 0.0231107i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.63933 | + | 2.62056i | 0.0936075 | + | 0.0929416i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.8816 | − | 12.4871i | 0.527132 | − | 0.442316i | −0.339978 | − | 0.940434i | \(-0.610419\pi\) |
0.867110 | + | 0.498117i | \(0.165975\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.39894 | + | 3.42093i | −0.332510 | + | 0.121024i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.7663 | + | 6.01910i | −1.15774 | + | 0.212674i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.42365 | − | 42.1016i | 0.261975 | − | 1.48573i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −42.3567 | − | 15.4166i | −1.49288 | − | 0.543363i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 42.2630 | + | 19.5242i | 1.48773 | + | 0.687284i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.1598 | 1.02520 | 0.512602 | − | 0.858626i | \(-0.328682\pi\) | ||||
0.512602 | + | 0.858626i | \(0.328682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.5541 | −0.405718 | −0.202859 | − | 0.979208i | \(-0.565023\pi\) | ||||
−0.202859 | + | 0.979208i | \(0.565023\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.5773 | − | 4.88639i | −0.370962 | − | 0.171373i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.33035 | + | 3.03200i | 0.291799 | + | 0.106206i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.7659 | + | 83.7415i | −0.516593 | + | 2.92974i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.336801 | − | 0.946320i | 0.0117688 | − | 0.0330671i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.3219 | + | 5.94070i | −0.569640 | + | 0.207332i | −0.610751 | − | 0.791823i | \(-0.709132\pi\) |
0.0411112 | + | 0.999155i | \(0.486910\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.4607 | + | 13.8122i | −0.573785 | + | 0.481463i | −0.882899 | − | 0.469562i | \(-0.844412\pi\) |
0.309114 | + | 0.951025i | \(0.399967\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.28277 | − | 7.23096i | −0.253554 | − | 0.251750i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.01618 | + | 15.6165i | 0.313523 | + | 0.543039i | 0.979123 | − | 0.203271i | \(-0.0651572\pi\) |
−0.665599 | + | 0.746309i | \(0.731824\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.72545 | − | 8.18473i | 0.164122 | − | 0.284267i | −0.772221 | − | 0.635354i | \(-0.780854\pi\) |
0.936343 | + | 0.351086i | \(0.114188\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.8832 | − | 31.4911i | 0.759120 | − | 1.09241i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.76254 | − | 21.3384i | −0.130364 | − | 0.739333i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.9018 | + | 9.98683i | 0.411880 | + | 0.345609i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.91228 | + | 0.916767i | −0.0660979 | + | 0.0316881i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.4071 | + | 13.7672i | 0.566437 | + | 0.475297i | 0.880462 | − | 0.474118i | \(-0.157233\pi\) |
−0.314024 | + | 0.949415i | \(0.601677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.16063 | − | 6.58227i | −0.0400218 | − | 0.226975i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.3615 | − | 1.87597i | −0.770172 | − | 0.0646118i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.3676 | − | 21.4214i | 0.425459 | − | 0.736917i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.5959 | + | 23.5488i | 0.467161 | + | 0.809147i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.3386 | − | 9.60428i | 1.21282 | − | 0.329618i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.3704 | − | 17.9319i | 0.732569 | − | 0.614698i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.5008 | − | 4.91390i | 0.462260 | − | 0.168249i | −0.100383 | − | 0.994949i | \(-0.532007\pi\) |
0.562643 | + | 0.826700i | \(0.309785\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 43.7315 | + | 7.38950i | 1.49558 | + | 0.252716i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.16456 | + | 17.9471i | −0.108099 | + | 0.613062i | 0.881838 | + | 0.471553i | \(0.156307\pi\) |
−0.989937 | + | 0.141509i | \(0.954805\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.36124 | + | 0.859419i | 0.0805643 | + | 0.0293230i | 0.381988 | − | 0.924167i | \(-0.375240\pi\) |
−0.301424 | + | 0.953490i | \(0.597462\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.85827 | + | 42.3580i | 0.131489 | + | 1.44356i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.8427 | 0.709494 | 0.354747 | − | 0.934962i | \(-0.384567\pi\) | ||||
0.354747 | + | 0.934962i | \(0.384567\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.4956 | −0.560868 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.89706 | + | 3.45508i | −0.166313 | + | 0.117341i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.9409 | − | 8.34982i | −0.778218 | − | 0.283248i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.151355 | − | 0.858379i | 0.00512848 | − | 0.0290851i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.1469 | + | 20.5267i | 1.22339 | + | 0.694725i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −40.9468 | + | 14.9034i | −1.38425 | + | 0.503827i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.3397 | + | 16.2279i | −0.653055 | + | 0.547978i | −0.907996 | − | 0.418978i | \(-0.862388\pi\) |
0.254941 | + | 0.966957i | \(0.417944\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.421986 | − | 1.59766i | 0.0142332 | − | 0.0538879i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.53902 | + | 2.66567i | 0.0518510 | + | 0.0898087i | 0.890786 | − | 0.454423i | \(-0.150155\pi\) |
−0.838935 | + | 0.544232i | \(0.816821\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.97051 | + | 5.14507i | −0.0999655 | + | 0.173145i | −0.911670 | − | 0.410923i | \(-0.865207\pi\) |
0.811705 | + | 0.584068i | \(0.198540\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.21428 | + | 4.70461i | 0.0744321 | + | 0.158144i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.28140 | − | 46.9662i | −0.278062 | − | 1.57697i | −0.729064 | − | 0.684446i | \(-0.760044\pi\) |
0.451001 | − | 0.892523i | \(-0.351067\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40.2929 | + | 33.8098i | 1.35138 | + | 1.13394i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.28021 | − | 38.0987i | −0.243896 | − | 1.27635i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.1682 | − | 13.5668i | −0.541050 | − | 0.453995i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.28908 | − | 12.9820i | −0.0765155 | − | 0.433941i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.453631 | − | 0.963818i | −0.0151463 | − | 0.0321809i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.963989 | + | 1.66968i | −0.0321508 | + | 0.0556869i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.07499 | + | 3.59399i | 0.0691280 | + | 0.119733i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 17.3899 | − | 65.8392i | 0.578700 | − | 2.19099i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.91073 | + | 4.12059i | −0.163238 | + | 0.136973i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.3493 | − | 6.67861i | 0.609280 | − | 0.221760i | −0.0189083 | − | 0.999821i | \(-0.506019\pi\) |
0.628188 | + | 0.778062i | \(0.283797\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −46.0186 | + | 27.0087i | −1.52634 | + | 0.895823i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.17655 | + | 40.7002i | −0.237770 | + | 1.34846i | 0.598932 | + | 0.800800i | \(0.295592\pi\) |
−0.836702 | + | 0.547659i | \(0.815519\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.9802 | − | 11.2759i | −1.02529 | − | 0.373177i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.7123 | − | 15.3189i | 0.717785 | − | 0.506427i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −46.4858 | −1.53510 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.8664 | 0.358451 | 0.179225 | − | 0.983808i | \(-0.442641\pi\) | ||||
0.179225 | + | 0.983808i | \(0.442641\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.24279 | + | 24.6225i | 0.0739025 | + | 0.811341i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.389134 | + | 0.141633i | 0.0128085 | + | 0.00466191i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.00997 | − | 5.72784i | 0.0332077 | − | 0.188330i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.1823 | − | 43.4918i | −0.531496 | − | 1.42846i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −38.8774 | + | 14.1502i | −1.27552 | + | 0.464253i | −0.888950 | − | 0.458005i | \(-0.848564\pi\) |
−0.386575 | + | 0.922258i | \(0.626342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.0252 | − | 29.3897i | 1.14791 | − | 0.963208i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23.5465 | − | 6.39945i | 0.770878 | − | 0.209509i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.0972 | + | 26.1490i | 0.493730 | + | 0.855165i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.37182 | − | 2.37606i | 0.0448154 | − | 0.0776226i | −0.842748 | − | 0.538309i | \(-0.819063\pi\) |
0.887563 | + | 0.460686i | \(0.152397\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.38969 | + | 0.284370i | 0.110618 | + | 0.00928005i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.52803 | − | 37.0223i | −0.212808 | − | 1.20689i | −0.884671 | − | 0.466216i | \(-0.845617\pi\) |
0.671863 | − | 0.740675i | \(-0.265494\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.5536 | + | 28.9939i | 1.12522 | + | 0.944172i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −34.4041 | − | 8.82476i | −1.11917 | − | 0.287070i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.2257 | − | 10.2586i | −0.397283 | − | 0.333360i | 0.422159 | − | 0.906522i | \(-0.361272\pi\) |
−0.819442 | + | 0.573161i | \(0.805717\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.160648 | − | 0.911082i | −0.00521486 | − | 0.0295750i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.1646 | + | 26.1399i | −0.589029 | + | 0.847644i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.2253 | + | 28.1031i | −0.525589 | + | 0.910347i | 0.473966 | + | 0.880543i | \(0.342822\pi\) |
−0.999556 | + | 0.0298045i | \(0.990512\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.95971 | + | 17.2507i | 0.322289 | + | 0.558220i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −25.0239 | − | 24.8459i | −0.808909 | − | 0.803154i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.1420 | + | 9.34927i | −0.359795 | + | 0.301904i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.9740 | − | 10.5457i | 0.934644 | − | 0.340182i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.6805 | + | 36.0379i | 0.988665 | + | 1.16130i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.21207 | + | 18.2166i | −0.103400 | + | 0.586412i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.1492 | − | 6.24181i | −0.551482 | − | 0.200723i | 0.0512227 | − | 0.998687i | \(-0.483688\pi\) |
−0.602705 | + | 0.797964i | \(0.705910\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 44.9246 | + | 20.7538i | 1.44319 | + | 0.666707i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.9067 | 1.08812 | 0.544058 | − | 0.839047i | \(-0.316887\pi\) | ||||
0.544058 | + | 0.839047i | \(0.316887\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.6521 | 0.565900 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.201614 | − | 0.0931394i | −0.00645682 | − | 0.00298285i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.5514 | − | 10.3919i | −0.913441 | − | 0.332465i | −0.157815 | − | 0.987469i | \(-0.550445\pi\) |
−0.755626 | + | 0.655003i | \(0.772667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.31071 | − | 47.1324i | 0.265611 | − | 1.50636i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −29.4426 | − | 34.5839i | −0.940030 | − | 1.10418i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.45754 | − | 0.894473i | 0.0783835 | − | 0.0285292i | −0.302531 | − | 0.953140i | \(-0.597832\pi\) |
0.380914 | + | 0.924610i | \(0.375609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.6009 | + | 22.3208i | −0.847574 | + | 0.711199i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.9944 | + | 11.9091i | 0.381786 | + | 0.379070i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.1084 | − | 62.5415i | −1.14818 | − | 1.98870i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.0413 | + | 46.8370i | −0.858996 | + | 1.48783i | 0.0138913 | + | 0.999904i | \(0.495578\pi\) |
−0.872888 | + | 0.487922i | \(0.837755\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.0354 | − | 27.3930i | 0.604071 | − | 0.869291i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.22301 | + | 6.93603i | 0.0387720 | + | 0.219887i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.1904 | − | 11.0680i | −0.417743 | − | 0.350528i | 0.409561 | − | 0.912283i | \(-0.365682\pi\) |
−0.827304 | + | 0.561755i | \(0.810126\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15.3764 | − | 15.7093i | 0.486487 | − | 0.497020i |
(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 | 216.2.q.a.97.1 | yes | 24 | |
3.2 | odd | 2 | 648.2.q.a.289.4 | 24 | |||
4.3 | odd | 2 | 432.2.u.e.97.4 | 24 | |||
27.5 | odd | 18 | 648.2.q.a.361.4 | 24 | |||
27.7 | even | 9 | 5832.2.a.h.1.10 | 12 | |||
27.20 | odd | 18 | 5832.2.a.i.1.3 | 12 | |||
27.22 | even | 9 | inner | 216.2.q.a.49.1 | ✓ | 24 | |
108.103 | odd | 18 | 432.2.u.e.49.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.q.a.49.1 | ✓ | 24 | 27.22 | even | 9 | inner | |
216.2.q.a.97.1 | yes | 24 | 1.1 | even | 1 | trivial | |
432.2.u.e.49.4 | 24 | 108.103 | odd | 18 | |||
432.2.u.e.97.4 | 24 | 4.3 | odd | 2 | |||
648.2.q.a.289.4 | 24 | 3.2 | odd | 2 | |||
648.2.q.a.361.4 | 24 | 27.5 | odd | 18 | |||
5832.2.a.h.1.10 | 12 | 27.7 | even | 9 | |||
5832.2.a.i.1.3 | 12 | 27.20 | odd | 18 |