Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,2,Mod(17,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([0, 0, 38]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("688.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.bg (of order \(21\), degree \(12\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.49370765906\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{21})\) |
Twist minimal: | no (minimal twist has level 43) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{21}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Character | \(\chi\) | \(=\) | 688.17 |
Dual form | 688.2.bg.c.81.1 |
$q$-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 \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).
\(n\) | \(431\) | \(433\) | \(517\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{19}{21}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −1.28860 | + | 0.397480i | −0.743972 | + | 0.229485i | −0.643491 | − | 0.765454i | \(-0.722514\pi\) |
−0.100481 | + | 0.994939i | \(0.532038\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.48781 | + | 3.79089i | −0.665371 | + | 1.69534i | 0.0520012 | + | 0.998647i | \(0.483440\pi\) |
−0.717372 | + | 0.696690i | \(0.754655\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.38920 | + | 2.40617i | −0.525070 | + | 0.909448i | 0.474504 | + | 0.880253i | \(0.342627\pi\) |
−0.999574 | + | 0.0291942i | \(0.990706\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.976224 | + | 0.665578i | −0.325408 | + | 0.221859i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.678323 | + | 0.326663i | 0.204522 | + | 0.0984926i | 0.533341 | − | 0.845900i | \(-0.320936\pi\) |
−0.328819 | + | 0.944393i | \(0.606651\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.70167 | − | 0.256486i | 0.471959 | − | 0.0711364i | 0.0912435 | − | 0.995829i | \(-0.470916\pi\) |
0.380715 | + | 0.924692i | \(0.375678\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.410392 | − | 5.47630i | 0.105963 | − | 1.41398i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.18750 | − | 3.02571i | −0.288012 | − | 0.733842i | −0.999514 | − | 0.0311584i | \(-0.990080\pi\) |
0.711503 | − | 0.702683i | \(-0.248015\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0395049 | + | 0.0269340i | 0.00906304 | + | 0.00617908i | 0.567843 | − | 0.823137i | \(-0.307778\pi\) |
−0.558780 | + | 0.829316i | \(0.688730\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.833720 | − | 3.65277i | 0.181933 | − | 0.797099i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.152371 | − | 2.03326i | −0.0317717 | − | 0.423963i | −0.990298 | − | 0.138960i | \(-0.955624\pi\) |
0.958526 | − | 0.285004i | \(-0.0919948\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.49199 | − | 7.87942i | −1.69840 | − | 1.57588i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.51575 | − | 4.40861i | 0.676606 | − | 0.848437i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.714324 | + | 0.220340i | 0.132647 | + | 0.0409161i | 0.360368 | − | 0.932810i | \(-0.382651\pi\) |
−0.227721 | + | 0.973726i | \(0.573127\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.52247 | + | 2.34051i | −0.453050 | + | 0.420369i | −0.873408 | − | 0.486990i | \(-0.838095\pi\) |
0.420358 | + | 0.907358i | \(0.361904\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00393 | − | 0.151318i | −0.174761 | − | 0.0263410i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.05465 | − | 8.84626i | −1.19245 | − | 1.49529i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.91502 | + | 6.78101i | 0.643625 | + | 1.11479i | 0.984617 | + | 0.174725i | \(0.0559037\pi\) |
−0.340992 | + | 0.940066i | \(0.610763\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.09082 | + | 1.00689i | −0.334799 | + | 0.161231i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.86928 | − | 8.18985i | −0.291932 | − | 1.27904i | −0.881832 | − | 0.471563i | \(-0.843690\pi\) |
0.589900 | − | 0.807476i | \(-0.299167\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.39142 | + | 4.86985i | 0.669685 | + | 0.742645i | ||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.07069 | − | 4.69101i | −0.159610 | − | 0.699295i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.05780 | + | 3.39886i | −1.02949 | + | 0.495775i | −0.870843 | − | 0.491561i | \(-0.836426\pi\) |
−0.158644 | + | 0.987336i | \(0.550712\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.359777 | − | 0.623151i | −0.0513966 | − | 0.0890216i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.73287 | + | 3.42691i | 0.382678 | + | 0.479863i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.76849 | − | 0.266557i | −0.242920 | − | 0.0366144i | 0.0264535 | − | 0.999650i | \(-0.491579\pi\) |
−0.269374 | + | 0.963036i | \(0.586817\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.24756 | + | 2.08543i | −0.303061 | + | 0.281200i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0616116 | − | 0.0190047i | −0.00816065 | − | 0.00251723i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.60798 | + | 4.52427i | −0.469719 | + | 0.589009i | −0.959102 | − | 0.283060i | \(-0.908651\pi\) |
0.489383 | + | 0.872069i | \(0.337222\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.15836 | + | 2.00266i | 0.276349 | + | 0.256415i | 0.806155 | − | 0.591704i | \(-0.201545\pi\) |
−0.529806 | + | 0.848119i | \(0.677735\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.245321 | − | 3.27359i | −0.0309076 | − | 0.412433i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.55946 | + | 6.83245i | −0.193428 | + | 0.847462i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.62708 | − | 3.15469i | −0.565288 | − | 0.385407i | 0.246691 | − | 0.969094i | \(-0.420657\pi\) |
−0.811978 | + | 0.583688i | \(0.801609\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00452 | + | 2.55948i | 0.120930 | + | 0.308126i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.543672 | − | 7.25480i | 0.0645220 | − | 0.860987i | −0.867234 | − | 0.497901i | \(-0.834104\pi\) |
0.931756 | − | 0.363086i | \(-0.118277\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0746 | + | 1.51850i | −1.17914 | + | 0.177727i | −0.709224 | − | 0.704983i | \(-0.750955\pi\) |
−0.469918 | + | 0.882710i | \(0.655716\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.0747 | + | 6.77800i | 1.62520 | + | 0.782656i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.72834 | + | 1.17836i | −0.196962 | + | 0.134287i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.70519 | − | 11.6137i | 0.754393 | − | 1.30665i | −0.191283 | − | 0.981535i | \(-0.561265\pi\) |
0.945676 | − | 0.325112i | \(-0.105402\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.48307 | + | 3.77880i | −0.164785 | + | 0.419866i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.42706 | + | 1.67402i | −0.595697 | + | 0.183748i | −0.577919 | − | 0.816094i | \(-0.696135\pi\) |
−0.0177773 | + | 0.999842i | \(0.505659\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.2369 | 1.43574 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00806 | −0.108075 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7786 | + | 3.63323i | −1.24853 | + | 0.385121i | −0.847428 | − | 0.530911i | \(-0.821850\pi\) |
−0.401105 | + | 0.916032i | \(0.631374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.74682 | + | 4.45083i | −0.183117 | + | 0.466573i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.32015 | − | 4.01861i | 0.240588 | − | 0.416710i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.160880 | + | 0.109686i | −0.0165059 | + | 0.0112535i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.41101 | + | 4.53210i | 0.955543 | + | 0.460165i | 0.845626 | − | 0.533775i | \(-0.179227\pi\) |
0.109917 | + | 0.993941i | \(0.464941\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.879615 | + | 0.132581i | −0.0884046 | + | 0.0133249i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.171298 | − | 2.28582i | 0.0170448 | − | 0.227447i | −0.982175 | − | 0.187966i | \(-0.939810\pi\) |
0.999220 | − | 0.0394811i | \(-0.0125705\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.94001 | + | 4.94307i | 0.191155 | + | 0.487056i | 0.994032 | − | 0.109090i | \(-0.0347935\pi\) |
−0.802877 | + | 0.596145i | \(0.796698\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.6068 | + | 8.59518i | 1.23030 | + | 0.838804i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.800089 | + | 3.50542i | −0.0773475 | + | 0.338882i | −0.998765 | − | 0.0496936i | \(-0.984176\pi\) |
0.921417 | + | 0.388575i | \(0.127033\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.415847 | + | 5.54910i | 0.0398310 | + | 0.531507i | 0.981056 | + | 0.193726i | \(0.0620573\pi\) |
−0.941225 | + | 0.337781i | \(0.890324\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.74019 | − | 7.18185i | −0.734667 | − | 0.681671i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0874119 | − | 0.109611i | 0.00822302 | − | 0.0103113i | −0.777703 | − | 0.628632i | \(-0.783615\pi\) |
0.785926 | + | 0.618321i | \(0.212187\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.93455 | + | 2.44748i | 0.739901 | + | 0.228229i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.49050 | + | 1.38298i | −0.137797 | + | 0.127857i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.93005 | + | 1.34599i | 0.818617 | + | 0.123387i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.50497 | − | 8.15698i | −0.591361 | − | 0.741544i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.66405 | + | 9.81041i | 0.510710 | + | 0.884575i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 24.1590 | − | 11.6344i | 2.16084 | − | 1.04061i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.384858 | + | 1.68617i | 0.0341507 | + | 0.149624i | 0.989129 | − | 0.147053i | \(-0.0469788\pi\) |
−0.954978 | + | 0.296677i | \(0.904122\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.59444 | − | 4.52977i | −0.668653 | − | 0.398824i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.87229 | − | 21.3469i | −0.425694 | − | 1.86509i | −0.497180 | − | 0.867647i | \(-0.665631\pi\) |
0.0714858 | − | 0.997442i | \(-0.477226\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.119688 | + | 0.0576388i | −0.0103783 | + | 0.00499791i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.4818 | + | 19.8870i | 0.988193 | + | 1.71160i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.3197 | + | 16.7024i | 1.13798 | + | 1.42698i | 0.888665 | + | 0.458557i | \(0.151634\pi\) |
0.249314 | + | 0.968423i | \(0.419795\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0494 | + | 1.81616i | 1.02202 | + | 0.154044i | 0.638606 | − | 0.769534i | \(-0.279511\pi\) |
0.383411 | + | 0.923578i | \(0.374749\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.74369 | − | 7.18509i | 0.652136 | − | 0.605094i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.23807 | + | 0.381893i | 0.103532 | + | 0.0319355i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.89807 | + | 2.38010i | −0.157626 | + | 0.197656i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.711297 | + | 0.659987i | 0.0586668 | + | 0.0544348i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.617820 | − | 8.24424i | −0.0506138 | − | 0.675395i | −0.963590 | − | 0.267383i | \(-0.913841\pi\) |
0.912977 | − | 0.408012i | \(-0.133778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.01707 | + | 4.45608i | −0.0827681 | + | 0.362631i | −0.999303 | − | 0.0373233i | \(-0.988117\pi\) |
0.916535 | + | 0.399954i | \(0.130974\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.17311 | + | 2.16339i | 0.256531 | + | 0.174900i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.11966 | − | 13.0447i | −0.411221 | − | 1.04777i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.748623 | + | 9.98968i | −0.0597466 | + | 0.797263i | 0.884188 | + | 0.467131i | \(0.154712\pi\) |
−0.943935 | + | 0.330132i | \(0.892907\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.38482 | − | 0.359453i | 0.189128 | − | 0.0285065i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.10404 | + | 2.45798i | 0.402255 | + | 0.193716i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6610 | + | 12.0410i | −1.38331 | + | 0.943128i | −0.383506 | + | 0.923538i | \(0.625284\pi\) |
−0.999808 | + | 0.0195896i | \(0.993764\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.06728 | − | 3.58064i | 0.160938 | − | 0.278753i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.02372 | + | 20.4441i | −0.620894 | + | 1.58201i | 0.180302 | + | 0.983611i | \(0.442292\pi\) |
−0.801197 | + | 0.598401i | \(0.795803\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.59254 | + | 2.95891i | −0.737888 | + | 0.227608i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0564923 | −0.00432007 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.5770 | −1.18430 | −0.592151 | − | 0.805827i | \(-0.701721\pi\) | ||||
−0.592151 | + | 0.805827i | \(0.701721\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 30.7563 | − | 9.48708i | 2.32496 | − | 0.717155i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.85093 | − | 7.26405i | 0.214289 | − | 0.546000i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.49011 | + | 6.04505i | −0.260863 | + | 0.451828i | −0.966472 | − | 0.256774i | \(-0.917340\pi\) |
0.705608 | + | 0.708602i | \(0.250674\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.54803 | + | 3.10080i | −0.338053 | + | 0.230480i | −0.720433 | − | 0.693525i | \(-0.756057\pi\) |
0.382380 | + | 0.924005i | \(0.375104\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.57727 | − | 1.72272i | −0.264439 | − | 0.127347i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −31.5309 | + | 4.75252i | −2.31820 | + | 0.349412i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.182877 | − | 2.44032i | 0.0133733 | − | 0.178454i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.72378 | + | 14.5840i | 0.416344 | + | 1.06083i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.7034 | + | 10.7064i | 1.13626 | + | 0.774689i | 0.977146 | − | 0.212571i | \(-0.0681837\pi\) |
0.159115 | + | 0.987260i | \(0.449136\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.685255 | − | 3.00230i | 0.0493257 | − | 0.216110i | −0.944258 | − | 0.329205i | \(-0.893219\pi\) |
0.993584 | + | 0.113095i | \(0.0360764\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.706241 | − | 9.42413i | −0.0505750 | − | 0.674876i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.60862 | − | 7.98763i | −0.613339 | − | 0.569095i | 0.311123 | − | 0.950370i | \(-0.399295\pi\) |
−0.924462 | + | 0.381274i | \(0.875485\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.166901 | + | 0.209287i | −0.0118313 | + | 0.0148360i | −0.787712 | − | 0.616044i | \(-0.788734\pi\) |
0.775881 | + | 0.630880i | \(0.217306\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.21637 | + | 2.22595i | 0.509003 | + | 0.157007i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.52252 | + | 1.41269i | −0.106860 | + | 0.0991514i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 33.8280 | + | 5.09874i | 2.36265 | + | 0.356112i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.50204 | + | 1.88350i | 0.104399 | + | 0.130912i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0179987 | + | 0.0311747i | 0.00124500 | + | 0.00215640i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.7666 | − | 7.11124i | 1.01658 | − | 0.489558i | 0.150045 | − | 0.988679i | \(-0.452058\pi\) |
0.866532 | + | 0.499122i | \(0.166344\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.18306 | + | 9.56462i | 0.149581 | + | 0.655357i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −24.9947 | + | 9.40196i | −1.70462 | + | 0.641208i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.12745 | − | 9.32096i | −0.144421 | − | 0.632748i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.3785 | − | 5.96118i | 0.836463 | − | 0.402819i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.79679 | − | 4.84418i | −0.188132 | − | 0.325855i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.03608 | − | 3.80712i | −0.203311 | − | 0.254944i | 0.669714 | − | 0.742619i | \(-0.266417\pi\) |
−0.873025 | + | 0.487675i | \(0.837845\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13.5345 | + | 2.03999i | 0.902297 | + | 0.135999i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.1316 | + | 13.1122i | −0.937947 | + | 0.870288i | −0.991740 | − | 0.128265i | \(-0.959059\pi\) |
0.0537930 | + | 0.998552i | \(0.482869\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.90123 | − | 2.12875i | −0.456046 | − | 0.140672i | 0.0582171 | − | 0.998304i | \(-0.481458\pi\) |
−0.514263 | + | 0.857632i | \(0.671935\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.75875 | − | 2.20541i | 0.115718 | − | 0.145105i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.45459 | − | 5.98898i | −0.422854 | − | 0.392351i | 0.439841 | − | 0.898076i | \(-0.355035\pi\) |
−0.862695 | + | 0.505724i | \(0.831225\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.38400 | − | 31.8122i | −0.155515 | − | 2.07520i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.02407 | + | 17.6306i | −0.261391 | + | 1.14523i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.97430 | − | 3.39142i | −0.321761 | − | 0.219373i | 0.391658 | − | 0.920111i | \(-0.371902\pi\) |
−0.713418 | + | 0.700738i | \(0.752854\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.42983 | − | 16.3830i | −0.414182 | − | 1.05532i | −0.973969 | − | 0.226682i | \(-0.927212\pi\) |
0.559787 | − | 0.828637i | \(-0.310883\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.855086 | + | 11.4103i | −0.0548538 | + | 0.731973i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.89758 | − | 0.436740i | 0.185119 | − | 0.0279023i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0741325 | + | 0.0357003i | 0.00471694 | + | 0.00227156i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.32790 | − | 4.31429i | 0.401014 | − | 0.273407i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.69184 | + | 15.0547i | −0.548624 | + | 0.950245i | 0.449745 | + | 0.893157i | \(0.351515\pi\) |
−0.998369 | + | 0.0570882i | \(0.981818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.560833 | − | 1.42898i | 0.0352592 | − | 0.0898391i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.0570 | + | 5.26140i | −1.06815 | + | 0.329481i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.3517 | −1.51902 | −0.759508 | − | 0.650498i | \(-0.774560\pi\) | ||||
−0.759508 | + | 0.650498i | \(0.774560\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.7550 | −1.35179 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.843994 | + | 0.260338i | −0.0522419 | + | 0.0161145i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.49599 | − | 19.0995i | 0.462223 | − | 1.17772i | −0.489838 | − | 0.871814i | \(-0.662944\pi\) |
0.952060 | − | 0.305910i | \(-0.0989608\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.64167 | − | 6.30755i | 0.223706 | − | 0.387470i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.7338 | − | 9.36353i | 0.840493 | − | 0.573039i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.3360 | + | 7.38545i | 0.935055 | + | 0.450299i | 0.838422 | − | 0.545021i | \(-0.183478\pi\) |
0.0966331 | + | 0.995320i | \(0.469193\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.41724 | − | 0.515067i | 0.207583 | − | 0.0312881i | −0.0444275 | − | 0.999013i | \(-0.514146\pi\) |
0.252010 | + | 0.967725i | \(0.418908\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.481835 | − | 6.42965i | 0.0291620 | − | 0.389140i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.18640 | − | 8.11881i | −0.192147 | − | 0.489582i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.9087 | + | 13.5735i | 1.19619 | + | 0.815552i | 0.986747 | − | 0.162268i | \(-0.0518809\pi\) |
0.209448 | + | 0.977820i | \(0.432833\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.904705 | − | 3.96377i | 0.0541632 | − | 0.237305i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.429939 | + | 5.73714i | 0.0256480 | + | 0.342249i | 0.995235 | + | 0.0975031i | \(0.0310856\pi\) |
−0.969587 | + | 0.244746i | \(0.921295\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.6970 | − | 10.8533i | −0.695317 | − | 0.645160i | 0.251154 | − | 0.967947i | \(-0.419190\pi\) |
−0.946472 | + | 0.322787i | \(0.895380\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.163711 | − | 0.205287i | 0.00969741 | − | 0.0121602i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.3030 | + | 6.87956i | 1.31650 | + | 0.406088i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.71715 | − | 4.37687i | 0.277479 | − | 0.257463i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.9284 | − | 2.09937i | −0.816498 | − | 0.123067i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.77347 | − | 4.73178i | −0.220449 | − | 0.276434i | 0.659293 | − | 0.751886i | \(-0.270856\pi\) |
−0.879741 | + | 0.475453i | \(0.842284\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.7830 | − | 20.4087i | −0.686032 | − | 1.18824i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.82494 | − | 1.84199i | 0.221946 | − | 0.106883i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.780788 | − | 3.42085i | −0.0451541 | − | 0.197833i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.8183 | + | 3.80130i | −1.02703 | + | 0.219103i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.687831 | + | 3.01359i | 0.0395149 | + | 0.173126i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.8031 | + | 5.20250i | −0.618584 | + | 0.297894i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.7476 | + | 20.3475i | 0.670472 | + | 1.16129i | 0.977770 | + | 0.209679i | \(0.0672418\pi\) |
−0.307298 | + | 0.951613i | \(0.599425\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.46467 | − | 5.59852i | −0.253986 | − | 0.318488i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.16489 | − | 0.175579i | −0.0660550 | − | 0.00995619i | 0.115932 | − | 0.993257i | \(-0.463015\pi\) |
−0.181987 | + | 0.983301i | \(0.558253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.8138 | − | 20.2403i | 1.23299 | − | 1.14405i | 0.248496 | − | 0.968633i | \(-0.420064\pi\) |
0.984495 | − | 0.175415i | \(-0.0561268\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.7748 | + | 3.94050i | 0.719778 | + | 0.222022i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.7284 | + | 20.9767i | −0.939560 | + | 1.17817i | 0.0442619 | + | 0.999020i | \(0.485906\pi\) |
−0.983822 | + | 0.179151i | \(0.942665\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.412565 | + | 0.382805i | 0.0230992 | + | 0.0214330i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.362340 | − | 4.83509i | −0.0202239 | − | 0.269869i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0345821 | − | 0.151514i | 0.00192420 | − | 0.00843048i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.4715 | − | 11.2301i | −0.913677 | − | 0.622934i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.74151 | − | 6.98526i | −0.151606 | − | 0.386286i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.62649 | − | 21.7040i | 0.0896713 | − | 1.19658i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.75598 | + | 0.415397i | −0.151482 | + | 0.0228323i | −0.224346 | − | 0.974510i | \(-0.572024\pi\) |
0.0728632 | + | 0.997342i | \(0.476786\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.33523 | − | 4.01403i | −0.456768 | − | 0.219968i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 18.8433 | − | 12.8472i | 1.02952 | − | 0.701915i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.52447 | + | 7.83661i | −0.246463 | + | 0.426887i | −0.962542 | − | 0.271132i | \(-0.912602\pi\) |
0.716079 | + | 0.698020i | \(0.245935\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.0690706 | + | 0.175989i | −0.00375140 | + | 0.00955841i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.47561 | + | 0.763625i | −0.134062 | + | 0.0413526i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4496 | −0.942192 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.1973 | −0.602840 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.0705 | + | 3.10634i | −0.540613 | + | 0.166757i | −0.553023 | − | 0.833166i | \(-0.686526\pi\) |
0.0124100 | + | 0.999923i | \(0.496050\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.48874 | + | 11.4371i | −0.240277 | + | 0.612215i | −0.999242 | − | 0.0389157i | \(-0.987610\pi\) |
0.758966 | + | 0.651130i | \(0.225705\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.85190 | − | 8.40374i | 0.258975 | − | 0.448559i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.53890 | − | 2.41278i | 0.188356 | − | 0.128419i | −0.465470 | − | 0.885063i | \(-0.654115\pi\) |
0.653827 | + | 0.756644i | \(0.273162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 26.6933 | + | 12.8548i | 1.41673 | + | 0.682262i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.0422 | + | 1.81508i | −0.637343 | + | 0.0960640i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.55838 | − | 34.1392i | 0.135026 | − | 1.80180i | −0.360036 | − | 0.932938i | \(-0.617236\pi\) |
0.495062 | − | 0.868858i | \(-0.335145\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.94064 | − | 17.6845i | −0.365297 | − | 0.930762i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.6245 | + | 7.92547i | 0.610129 | + | 0.415979i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.23266 | − | 40.4509i | 0.483259 | − | 2.11730i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.31138 | + | 30.8433i | 0.120653 | + | 1.61000i | 0.648873 | + | 0.760897i | \(0.275241\pi\) |
−0.528219 | + | 0.849108i | \(0.677140\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.27582 | + | 6.75098i | 0.378764 | + | 0.351442i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.09817 | − | 3.88498i | 0.160849 | − | 0.201698i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.58815 | + | 2.34063i | 0.392900 | + | 0.121193i | 0.484909 | − | 0.874565i | \(-0.338853\pi\) |
−0.0920093 | + | 0.995758i | \(0.529329\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −26.5068 | + | 24.5947i | −1.36880 | + | 1.27006i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.27206 | + | 0.191732i | 0.0655144 | + | 0.00987471i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.9219 | − | 17.4576i | −0.715122 | − | 0.896735i | 0.282929 | − | 0.959141i | \(-0.408694\pi\) |
−0.998051 | + | 0.0624060i | \(0.980123\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.16615 | − | 2.01983i | −0.0597435 | − | 0.103479i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.6340 | + | 10.8999i | −1.15654 | + | 0.556961i | −0.910992 | − | 0.412423i | \(-0.864682\pi\) |
−0.245549 | + | 0.969384i | \(0.578968\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.89559 | − | 8.30511i | −0.0966081 | − | 0.423268i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.52828 | − | 1.83123i | −0.382684 | − | 0.0930867i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.91826 | + | 17.1670i | 0.198664 | + | 0.870403i | 0.971733 | + | 0.236081i | \(0.0758632\pi\) |
−0.773070 | + | 0.634321i | \(0.781280\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.97109 | + | 2.87553i | −0.301971 | + | 0.145422i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.7634 | + | 25.5709i | 0.744714 | + | 1.28988i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 34.0503 | + | 42.6977i | 1.71326 | + | 2.14836i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.43147 | − | 0.215759i | −0.0718434 | − | 0.0108287i | 0.113022 | − | 0.993592i | \(-0.463947\pi\) |
−0.184866 | + | 0.982764i | \(0.559185\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.131320 | − | 0.121847i | 0.00657420 | − | 0.00609996i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.37812 | + | 2.27585i | 0.368446 | + | 0.113650i | 0.473448 | − | 0.880822i | \(-0.343009\pi\) |
−0.105003 | + | 0.994472i | \(0.533485\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.69211 | + | 4.62976i | −0.183917 | + | 0.230625i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.1185 | − | 11.2443i | −0.602172 | − | 0.558734i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.440541 | + | 5.87861i | 0.0218368 | + | 0.291392i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.12781 | + | 31.2290i | −0.352448 | + | 1.54417i | 0.419063 | + | 0.907957i | \(0.362359\pi\) |
−0.771511 | + | 0.636216i | \(0.780499\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.8026 | − | 16.2283i | −1.17409 | − | 0.800484i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.87394 | − | 14.9666i | −0.289038 | − | 0.736456i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.72841 | − | 23.0640i | 0.0848442 | − | 1.13217i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.2487 | + | 2.44910i | −0.795703 | + | 0.119933i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.9028 | − | 9.58467i | −0.972314 | − | 0.468242i | −0.120859 | − | 0.992670i | \(-0.538565\pi\) |
−0.851455 | + | 0.524428i | \(0.824279\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.5748 | + | 8.57335i | −0.612858 | + | 0.417840i | −0.829575 | − | 0.558395i | \(-0.811417\pi\) |
0.216717 | + | 0.976234i | \(0.430465\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.62779 | − | 8.01557i | 0.225011 | − | 0.389730i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.7565 | + | 35.0511i | −0.667290 | + | 1.70023i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.81715 | + | 2.41127i | −0.378298 | + | 0.116690i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.74716 | −0.0843539 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.5109 | −0.795301 | −0.397651 | − | 0.917537i | \(-0.630174\pi\) | ||||
−0.397651 | + | 0.917537i | \(0.630174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.1153 | − | 7.43859i | 1.15891 | − | 0.357476i | 0.345075 | − | 0.938575i | \(-0.387853\pi\) |
0.813833 | + | 0.581099i | \(0.197377\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.49980 | − | 3.82143i | 0.0719100 | − | 0.183224i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0487442 | − | 0.0844275i | 0.00233175 | − | 0.00403872i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.6707 | + | 10.6841i | −0.747922 | + | 0.509924i | −0.876279 | − | 0.481804i | \(-0.839982\pi\) |
0.128358 | + | 0.991728i | \(0.459029\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.765978 | + | 0.368876i | 0.0364752 | + | 0.0175655i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 37.0756 | − | 5.58825i | 1.76152 | − | 0.265506i | 0.813007 | − | 0.582254i | \(-0.197829\pi\) |
0.948510 | + | 0.316748i | \(0.102591\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.75126 | − | 50.0571i | 0.177827 | − | 2.37293i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.07304 | + | 10.3779i | 0.192648 | + | 0.490859i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.9462 | − | 10.1902i | −0.705357 | − | 0.480904i | 0.156745 | − | 0.987639i | \(-0.449900\pi\) |
−0.862102 | + | 0.506735i | \(0.830852\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.40735 | − | 6.16599i | 0.0662693 | − | 0.290345i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.460606 | − | 6.14636i | −0.0216412 | − | 0.288781i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.2736 | − | 13.2440i | −0.669159 | − | 0.620889i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.42658 | − | 5.55075i | 0.207067 | − | 0.259653i | −0.667444 | − | 0.744660i | \(-0.732612\pi\) |
0.874510 | + | 0.485007i | \(0.161183\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −17.5141 | − | 5.40239i | −0.817489 | − | 0.252162i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.48177 | − | 1.37488i | 0.0690130 | − | 0.0640347i | −0.644912 | − | 0.764257i | \(-0.723106\pi\) |
0.713925 | + | 0.700222i | \(0.246916\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.5610 | + | 3.55125i | 1.09497 | + | 0.165041i | 0.671600 | − | 0.740914i | \(-0.265608\pi\) |
0.423374 | + | 0.905955i | \(0.360846\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 11.7822 | + | 14.7744i | 0.546385 | + | 0.685145i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.68583 | + | 15.0443i | 0.401932 | + | 0.696167i | 0.993959 | − | 0.109751i | \(-0.0350054\pi\) |
−0.592027 | + | 0.805918i | \(0.701672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.0187 | − | 6.75104i | 0.647323 | − | 0.311734i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00602 | − | 13.1702i | −0.138510 | − | 0.606852i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.38800 | + | 4.73784i | 0.0638203 | + | 0.217846i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.123251 | − | 0.539998i | −0.00565515 | − | 0.0247768i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.90385 | − | 0.916848i | 0.0871715 | − | 0.0419796i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.86370 | + | 6.69213i | 0.176537 | + | 0.305771i | 0.940692 | − | 0.339261i | \(-0.110177\pi\) |
−0.764155 | + | 0.645033i | \(0.776844\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.40131 | + | 10.5349i | 0.383067 | + | 0.480350i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −7.55405 | − | 1.13859i | −0.343721 | − | 0.0518076i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −31.1825 | + | 28.9332i | −1.41593 | + | 1.31379i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.7051 | − | 5.15285i | −0.756982 | − | 0.233498i | −0.107843 | − | 0.994168i | \(-0.534394\pi\) |
−0.649139 | + | 0.760670i | \(0.724871\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.9718 | − | 22.5359i | 0.812713 | − | 1.01911i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.9175 | − | 14.7693i | −0.718346 | − | 0.666528i | 0.233760 | − | 0.972294i | \(-0.424897\pi\) |
−0.952107 | + | 0.305766i | \(0.901087\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.181578 | − | 2.42299i | −0.00817786 | − | 0.109126i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.806105 | − | 3.53178i | 0.0362317 | − | 0.158742i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.7010 | + | 11.3866i | 0.749144 | + | 0.510758i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.1125 | + | 33.4100i | 0.586995 | + | 1.49564i | 0.847837 | + | 0.530257i | \(0.177905\pi\) |
−0.260842 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.21323 | − | 29.5335i | 0.0988797 | − | 1.31946i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.0899578 | + | 0.0135590i | −0.00401102 | + | 0.000604564i | −0.151047 | − | 0.988527i | \(-0.548265\pi\) |
0.147036 | + | 0.989131i | \(0.453027\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.41042 | + | 4.05025i | 0.374259 | + | 0.180234i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.1848 | − | 7.62568i | 0.496735 | − | 0.338668i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.3425 | + | 19.6459i | −0.502749 | + | 0.870787i | 0.497246 | + | 0.867610i | \(0.334345\pi\) |
−0.999995 | + | 0.00317746i | \(0.998989\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.3419 | − | 26.3507i | 0.457498 | − | 1.16569i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.257630 | − | 0.0794685i | 0.0113747 | − | 0.00350862i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −21.6250 | −0.952913 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.89775 | −0.259383 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.0725 | − | 6.19156i | 0.881087 | − | 0.271779i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.72346 | − | 4.39129i | 0.0755060 | − | 0.192386i | −0.888137 | − | 0.459578i | \(-0.848001\pi\) |
0.963643 | + | 0.267192i | \(0.0860958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.853098 | − | 1.47761i | 0.0373034 | − | 0.0646113i | −0.846771 | − | 0.531958i | \(-0.821457\pi\) |
0.884074 | + | 0.467346i | \(0.154790\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −35.8616 | + | 24.4500i | −1.56513 | + | 1.06709i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.0771 | + | 4.85290i | 0.438968 | + | 0.211396i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.6322 | − | 2.80835i | 0.810095 | − | 0.122102i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.510945 | − | 6.81809i | 0.0221731 | − | 0.295880i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.28148 | − | 13.4570i | −0.228766 | − | 0.582887i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0983 | − | 8.24846i | −0.523054 | − | 0.356612i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.09456 | − | 9.17688i | 0.0903870 | − | 0.396011i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.0404841 | − | 0.540223i | −0.00174378 | − | 0.0232691i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.33253 | − | 7.73145i | −0.358243 | − | 0.332401i | 0.480433 | − | 0.877031i | \(-0.340480\pi\) |
−0.838676 | + | 0.544630i | \(0.816670\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.62808 | − | 5.80343i | 0.198610 | − | 0.249049i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.6547 | − | 6.67960i | −0.927586 | − | 0.286123i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.1076 | − | 15.8735i | 0.731467 | − | 0.678703i | −0.223737 | − | 0.974650i | \(-0.571826\pi\) |
0.955204 | + | 0.295947i | \(0.0956352\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.43997 | − | 0.518492i | −0.146814 | − | 0.0221287i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0222847 | + | 0.0279441i | 0.000949358 | + | 0.00119046i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.6298 | + | 32.2677i | 0.792218 | + | 1.37216i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 38.7416 | − | 18.6570i | 1.64449 | − | 0.791944i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.28534 | − | 5.63146i | −0.0544618 | − | 0.238613i | 0.940369 | − | 0.340155i | \(-0.110479\pi\) |
−0.994831 | + | 0.101542i | \(0.967622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.72180 | + | 7.16055i | 0.368893 | + | 0.302859i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.734322 | + | 3.21728i | 0.0310031 | + | 0.135834i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.42474 | − | 1.64927i | 0.144336 | − | 0.0695084i | −0.360322 | − | 0.932828i | \(-0.617333\pi\) |
0.504657 | + | 0.863320i | \(0.331619\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.285471 | + | 0.494450i | 0.0120098 | + | 0.0208017i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.03215 | − | 8.81804i | −0.295323 | − | 0.370323i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.8718 | + | 5.40680i | 1.50382 | + | 0.226665i | 0.848707 | − | 0.528863i | \(-0.177381\pi\) |
0.655116 | + | 0.755528i | \(0.272620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.4633 | − | 18.0593i | 0.814514 | − | 0.755758i | −0.158289 | − | 0.987393i | \(-0.550598\pi\) |
0.972803 | + | 0.231635i | \(0.0744073\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −24.4910 | − | 7.55446i | −1.02312 | − | 0.315592i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −14.7269 | + | 18.4670i | −0.614156 | + | 0.770127i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.54816 | + | 8.85940i | 0.397495 | + | 0.368821i | 0.853444 | − | 0.521184i | \(-0.174510\pi\) |
−0.455949 | + | 0.890006i | \(0.650700\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.310335 | + | 4.14113i | 0.0128971 | + | 0.172099i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.51130 | − | 15.3840i | 0.145673 | − | 0.638236i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.11253 | − | 0.758511i | −0.0460763 | − | 0.0314143i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.02515 | − | 7.70795i | −0.125074 | − | 0.318685i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.430770 | − | 5.74822i | 0.0177798 | − | 0.237255i | −0.981233 | − | 0.192827i | \(-0.938234\pi\) |
0.999013 | − | 0.0444278i | \(-0.0141465\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.162689 | + | 0.0245215i | −0.00670350 | + | 0.00101039i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.2680 | + | 6.87109i | 0.586905 | + | 0.282639i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.69370 | − | 4.56369i | 0.274877 | − | 0.187408i | −0.418033 | − | 0.908432i | \(-0.637280\pi\) |
0.692911 | + | 0.721024i | \(0.256328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.3888 | + | 31.8503i | −0.753866 | + | 1.30573i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.131881 | − | 0.336026i | 0.00539752 | − | 0.0137526i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.12129 | − | 2.50509i | 0.331827 | − | 0.102355i | −0.124365 | − | 0.992237i | \(-0.539689\pi\) |
0.456192 | + | 0.889882i | \(0.349213\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.6791 | 1.45538 | 0.727691 | − | 0.685905i | \(-0.240594\pi\) | ||||
0.727691 | + | 0.685905i | \(0.240594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.61676 | 0.269455 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 40.6004 | − | 12.5236i | 1.65064 | − | 0.509155i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.0041 | + | 30.5861i | −0.487233 | + | 1.24145i | 0.450088 | + | 0.892984i | \(0.351393\pi\) |
−0.937321 | + | 0.348466i | \(0.886703\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.40040 | − | 2.42556i | 0.0567469 | − | 0.0982886i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11.1383 | + | 7.59397i | −0.450608 | + | 0.307219i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.01111 | + | 0.968499i | 0.0812280 | + | 0.0391173i | 0.474057 | − | 0.880494i | \(-0.342789\pi\) |
−0.392829 | + | 0.919612i | \(0.628503\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −45.6172 | + | 6.87569i | −1.83946 | + | 0.277255i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.983300 | + | 13.1212i | −0.0395862 | + | 0.528241i | 0.941797 | + | 0.336182i | \(0.109136\pi\) |
−0.981383 | + | 0.192059i | \(0.938483\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.06713 | + | 12.9108i | 0.203665 | + | 0.518930i | 0.995815 | − | 0.0913968i | \(-0.0291332\pi\) |
−0.792149 | + | 0.610327i | \(0.791038\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.49953 | − | 6.47667i | −0.381203 | − | 0.259900i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.62076 | − | 33.3887i | 0.305319 | − | 1.33769i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.83193 | + | 51.1336i | 0.153277 | + | 2.04534i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0355844 | − | 0.0330175i | −0.00142110 | − | 0.00131859i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.8683 | − | 19.8982i | 0.632709 | − | 0.793392i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.11794 | + | 1.57867i | 0.203742 | + | 0.0628461i | 0.394946 | − | 0.918704i | \(-0.370763\pi\) |
−0.191204 | + | 0.981550i | \(0.561239\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.2017 | + | 15.0330i | −0.643959 | + | 0.597506i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.96470 | − | 1.04976i | −0.276386 | − | 0.0416584i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.772051 | − | 0.968121i | −0.0305898 | − | 0.0383584i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.29789 | + | 7.44417i | 0.170022 | + | 0.294487i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.56273 | + | 2.19729i | −0.180217 | + | 0.0867879i | −0.521817 | − | 0.853058i | \(-0.674746\pi\) |
0.341600 | + | 0.939845i | \(0.389031\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.59652 | + | 20.1387i | 0.181269 | + | 0.794191i | 0.981027 | + | 0.193869i | \(0.0621037\pi\) |
−0.799758 | + | 0.600322i | \(0.795039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.4710 | − | 22.0502i | 1.12104 | − | 0.868226i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.78518 | + | 29.7278i | 0.266753 | + | 1.16872i | 0.913766 | + | 0.406242i | \(0.133161\pi\) |
−0.647013 | + | 0.762479i | \(0.723982\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.92529 | + | 1.89032i | −0.154081 | + | 0.0742015i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.44631 | + | 11.1653i | 0.252651 | + | 0.437604i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.9574 | + | 32.5496i | 1.01579 | + | 1.27376i | 0.961374 | + | 0.275244i | \(0.0887587\pi\) |
0.0544173 | + | 0.998518i | \(0.482670\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 88.1729 | + | 13.2899i | 3.44520 | + | 0.519280i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.82438 | − | 8.18783i | 0.344272 | − | 0.319438i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.9158 | + | 6.45166i | 0.814762 | + | 0.251321i | 0.674008 | − | 0.738724i | \(-0.264571\pi\) |
0.140754 | + | 0.990045i | \(0.455047\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.40742 | + | 4.27277i | −0.132533 | + | 0.166191i | −0.843670 | − | 0.536863i | \(-0.819609\pi\) |
0.711136 | + | 0.703054i | \(0.248181\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.52940 | + | 5.13053i | 0.214744 | + | 0.199253i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0404284 | − | 0.539480i | −0.00156775 | − | 0.0209201i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.339165 | − | 1.48598i | 0.0131325 | − | 0.0575373i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.42554 | + | 3.69907i | 0.209763 | + | 0.143014i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.809867 | + | 2.06351i | 0.0312646 | + | 0.0796608i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.265593 | − | 3.54410i | 0.0102379 | − | 0.136615i | −0.989743 | − | 0.142862i | \(-0.954369\pi\) |
0.999980 | + | 0.00624712i | \(0.00198853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −64.5930 | + | 9.73582i | −2.48618 | + | 0.374732i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.78571 | − | 4.23097i | −0.337662 | − | 0.162610i | 0.257367 | − | 0.966314i | \(-0.417145\pi\) |
−0.595029 | + | 0.803704i | \(0.702859\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.9788 | + | 16.3485i | −0.920223 | + | 0.627398i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.9981 | − | 22.5134i | 0.498088 | − | 0.862714i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.66440 | − | 19.5286i | 0.293270 | − | 0.747240i | −0.705969 | − | 0.708242i | \(-0.749488\pi\) |
0.999239 | − | 0.0389974i | \(-0.0124164\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −83.1341 | + | 25.6435i | −3.17639 | + | 0.979787i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.73904 | 0.371568 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.07775 | −0.117253 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.48595 | + | 2.61757i | −0.322821 | + | 0.0995770i | −0.451930 | − | 0.892053i | \(-0.649264\pi\) |
0.129109 | + | 0.991630i | \(0.458788\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.902953 | − | 2.30069i | 0.0343003 | − | 0.0873958i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −24.8121 | + | 42.9758i | −0.941177 | + | 1.63017i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.5603 | + | 15.3814i | −0.854532 | + | 0.582610i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.6979 | + | 5.15182i | 0.404630 | + | 0.194860i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.8182 | − | 3.74074i | 0.937370 | − | 0.141286i | 0.337448 | − | 0.941344i | \(-0.390436\pi\) |
0.599922 | + | 0.800058i | \(0.295198\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0279772 | + | 0.373330i | −0.00105518 | + | 0.0140804i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.7167 | + | 40.0456i | 0.591926 | + | 1.50820i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.26210 | + | 3.58764i | 0.197902 | + | 0.134927i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.1254 | + | 48.7436i | −0.417824 | + | 1.83060i | 0.126806 | + | 0.991928i | \(0.459528\pi\) |
−0.544629 | + | 0.838677i | \(0.683330\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.18408 | + | 15.8004i | 0.0444064 | + | 0.592563i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.14322 | + | 4.77221i | 0.192615 | + | 0.178721i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.28973 | + | 4.12519i | −0.123029 | + | 0.154273i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.75789 | + | 2.39299i | 0.289724 | + | 0.0893679i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.04392 | − | 7.46367i | 0.299988 | − | 0.278348i | −0.515788 | − | 0.856716i | \(-0.672501\pi\) |
0.815776 | + | 0.578368i | \(0.196310\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.5890 | − | 2.19893i | −0.543321 | − | 0.0818925i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.7974 | + | 18.5553i | 0.550319 | + | 0.690079i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.32989 | − | 7.49958i | −0.160808 | − | 0.278527i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.2553 | − | 10.2360i | 0.788316 | − | 0.379633i | 0.00399815 | − | 0.999992i | \(-0.498727\pi\) |
0.784318 | + | 0.620359i | \(0.213013\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.14342 | − | 26.9161i | −0.227534 | − | 0.996892i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.51991 | − | 19.0701i | 0.352107 | − | 0.705333i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.85287 | + | 34.4057i | 0.290052 | + | 1.27080i | 0.884451 | + | 0.466633i | \(0.154533\pi\) |
−0.594399 | + | 0.804170i | \(0.702610\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.56022 | + | 1.71451i | −0.131321 | + | 0.0632406i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.10813 | − | 3.65139i | −0.0776541 | − | 0.134501i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.7042 | + | 17.1846i | 0.504119 | + | 0.632145i | 0.967153 | − | 0.254196i | \(-0.0818107\pi\) |
−0.463034 | + | 0.886340i | \(0.653239\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.109717 | − | 0.0165372i | −0.00403056 | − | 0.000607509i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.34948 | − | 1.25213i | 0.0495075 | − | 0.0459362i | −0.655031 | − | 0.755602i | \(-0.727344\pi\) |
0.704539 | + | 0.709666i | \(0.251154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.1722 | + | 9.92381i | 1.17870 | + | 0.363580i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.18383 | − | 5.24635i | 0.153078 | − | 0.191954i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.32316 | − | 6.79490i | −0.267582 | − | 0.248280i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.39276 | + | 31.9291i | 0.0873129 | + | 1.16511i | 0.853005 | + | 0.521903i | \(0.174778\pi\) |
−0.765692 | + | 0.643207i | \(0.777603\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.21634 | − | 22.8543i | 0.190094 | − | 0.832857i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.3793 | − | 10.4854i | −0.559710 | − | 0.381604i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.22743 | + | 15.8672i | 0.226340 | + | 0.576704i | 0.998257 | − | 0.0590188i | \(-0.0187972\pi\) |
−0.771917 | + | 0.635723i | \(0.780702\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.154698 | + | 2.06430i | −0.00561517 | + | 0.0749292i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.81970 | + | 0.425001i | −0.102214 | + | 0.0154063i | −0.199950 | − | 0.979806i | \(-0.564078\pi\) |
0.0977361 | + | 0.995212i | \(0.468840\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.9298 | − | 6.70823i | −0.504292 | − | 0.242854i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −12.9222 | + | 8.81019i | −0.467202 | + | 0.318533i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.97919 | + | 8.62421i | −0.179788 | + | 0.311402i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.5058 | − | 44.6040i | 0.631275 | − | 1.60846i | −0.153126 | − | 0.988207i | \(-0.548934\pi\) |
0.784400 | − | 0.620255i | \(-0.212971\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.3795 | − | 9.67930i | 1.13011 | − | 0.348591i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.7995 | 0.460366 | 0.230183 | − | 0.973147i | \(-0.426067\pi\) | ||||
0.230183 | + | 0.973147i | \(0.426067\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.8627 | 1.43191 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 28.0335 | − | 8.64718i | 1.00570 | − | 0.310216i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.146739 | − | 0.373886i | 0.00525749 | − | 0.0133959i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.73866 | − | 4.74350i | 0.0979970 | − | 0.169736i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.48278 | − | 2.37452i | 0.124464 | − | 0.0848583i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.7559 | − | 17.7007i | −1.31188 | − | 0.631766i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.0915 | − | 1.97322i | 0.466660 | − | 0.0703377i | 0.0884966 | − | 0.996076i | \(-0.471794\pi\) |
0.378164 | + | 0.925739i | \(0.376556\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.06766 | + | 27.5910i | −0.0736107 | + | 0.982267i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.142310 | + | 0.362600i | 0.00505997 | + | 0.0128926i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.18647 | + | 2.85429i | 0.148666 | + | 0.101359i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.18552 | + | 9.57538i | −0.0775123 | + | 0.339604i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.866491 | + | 11.5625i | 0.0306927 | + | 0.409566i | 0.991297 | + | 0.131645i | \(0.0420260\pi\) |
−0.960604 | + | 0.277920i | \(0.910355\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.6651 | + | 17.3187i | 0.660324 | + | 0.612691i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.08039 | − | 11.3864i | 0.320840 | − | 0.402320i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.32986 | − | 2.26096i | −0.258665 | − | 0.0797876i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.9118 | + | 15.6918i | −0.596062 | + | 0.553065i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.6976 | − | 3.42111i | −0.798992 | − | 0.120429i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0173 | − | 18.8311i | −0.527980 | − | 0.662066i | 0.444302 | − | 0.895877i | \(-0.353452\pi\) |
−0.972282 | + | 0.233811i | \(0.924880\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.67307 | − | 16.7542i | −0.339667 | − | 0.588321i | 0.644703 | − | 0.764433i | \(-0.276981\pi\) |
−0.984370 | + | 0.176112i | \(0.943648\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.19872 | + | 2.02200i | −0.147256 | + | 0.0709146i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.3700 | − | 84.8657i | −0.678503 | − | 2.97271i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0423181 | + | 0.310661i | 0.00148052 | + | 0.0108687i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.25709 | − | 5.50765i | −0.0439261 | − | 0.192453i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.68010 | − | 2.25382i | 0.163336 | − | 0.0786587i | −0.350429 | − | 0.936589i | \(-0.613964\pi\) |
0.513766 | + | 0.857930i | \(0.328250\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.1185 | − | 46.9706i | −0.945290 | − | 1.63729i | −0.755169 | − | 0.655530i | \(-0.772445\pi\) |
−0.190122 | − | 0.981761i | \(-0.560888\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.33304 | + | 9.19534i | 0.255304 | + | 0.320141i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.32662 | + | 0.501407i | 0.115678 | + | 0.0174356i | 0.206626 | − | 0.978420i | \(-0.433752\pi\) |
−0.0909482 | + | 0.995856i | \(0.528990\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.6523 | + | 27.5133i | −1.02987 | + | 0.955578i | −0.999034 | − | 0.0439467i | \(-0.986007\pi\) |
−0.0308341 | + | 0.999525i | \(0.509816\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.0494 | − | 9.57747i | −1.07709 | − | 0.332239i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.45824 | + | 1.82857i | −0.0505249 | + | 0.0633562i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −65.5635 | − | 60.8341i | −2.26892 | − | 2.10525i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.45003 | + | 19.3493i | 0.0501202 | + | 0.668808i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.0182394 | + | 0.0799120i | −0.000629694 | + | 0.00275887i | −0.975242 | − | 0.221141i | \(-0.929022\pi\) |
0.974612 | + | 0.223900i | \(0.0718790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4992 | − | 16.0215i | −0.810318 | − | 0.552465i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.83442 | − | 7.22197i | −0.0976225 | − | 0.248738i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.05503 | − | 40.7666i | 0.105096 | − | 1.40241i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.6638 | − | 4.32038i | 0.984901 | − | 0.148450i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.3867 | + | 9.33616i | 0.665351 | + | 0.320416i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.1910 | − | 8.99347i | 0.452181 | − | 0.308292i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.0750 | − | 20.9145i | 0.413441 | − | 0.716101i | −0.581823 | − | 0.813316i | \(-0.697660\pi\) |
0.995263 | + | 0.0972152i | \(0.0309935\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0840500 | − | 0.214156i | 0.00287445 | − | 0.00732398i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.2162 | − | 12.4051i | 1.37376 | − | 0.423749i | 0.481966 | − | 0.876190i | \(-0.339923\pi\) |
0.891794 | + | 0.452441i | \(0.149447\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.35350 | 0.0803004 | 0.0401502 | − | 0.999194i | \(-0.487216\pi\) | ||||
0.0401502 | + | 0.999194i | \(0.487216\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −31.4741 | −1.07263 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.2992 | − | 9.03761i | 0.997356 | − | 0.307644i | 0.247243 | − | 0.968953i | \(-0.420475\pi\) |
0.750113 | + | 0.661310i | \(0.229999\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.1758 | − | 59.0509i | 0.787999 | − | 2.00779i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.33878 | + | 7.51499i | −0.147353 | + | 0.255222i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.34206 | − | 5.68752i | 0.282985 | − | 0.192936i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.68290 | − | 4.18147i | −0.294209 | − | 0.141684i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.2037 | + | 1.83942i | −0.413033 | + | 0.0622548i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.56750 | + | 74.2932i | −0.188216 | + | 2.51157i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.8677 | − | 42.9782i | −0.569582 | − | 1.45127i | −0.867868 | − | 0.496794i | \(-0.834510\pi\) |
0.298287 | − | 0.954476i | \(-0.403585\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.74327 | + | 4.59748i | 0.227445 | + | 0.155069i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.29329 | + | 10.0475i | −0.0772627 | + | 0.338510i | −0.998755 | − | 0.0498868i | \(-0.984114\pi\) |
0.921492 | + | 0.388397i | \(0.126971\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.882701 | − | 11.7788i | −0.0297053 | − | 0.396389i | −0.992162 | − | 0.124955i | \(-0.960121\pi\) |
0.962457 | − | 0.271434i | \(-0.0874978\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.2956 | + | 21.6151i | 0.783072 | + | 0.726585i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.8680 | − | 17.3899i | 0.465640 | − | 0.583895i | −0.492457 | − | 0.870337i | \(-0.663901\pi\) |
0.958098 | + | 0.286442i | \(0.0924726\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.59187 | − | 1.41641i | −0.154006 | − | 0.0475047i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.24039 | + | 2.07878i | −0.0750560 | + | 0.0696418i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.370362 | − | 0.0558232i | −0.0123937 | − | 0.00186805i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.7235 | − | 22.2245i | −0.592430 | − | 0.742884i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.36584 | + | 4.09776i | 0.0789931 | + | 0.136820i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.31757 | + | 1.11608i | −0.0772954 | + | 0.0372235i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.29356 | + | 5.66746i | 0.0430947 | + | 0.188810i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 21.4496 | − | 11.9807i | 0.713799 | − | 0.398694i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.98815 | − | 21.8545i | −0.165812 | − | 0.726468i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.5843 | − | 15.2102i | 1.04874 | − | 0.505046i | 0.171541 | − | 0.985177i | \(-0.445125\pi\) |
0.877197 | + | 0.480131i | \(0.159411\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.35416 | + | 2.34548i | 0.0449148 | + | 0.0777947i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.7823 | − | 43.6156i | −1.15239 | − | 1.44505i | −0.874890 | − | 0.484322i | \(-0.839066\pi\) |
−0.277498 | − | 0.960726i | \(-0.589505\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.22814 | − | 0.637289i | −0.139931 | − | 0.0210912i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11.8530 | − | 10.9979i | 0.391847 | − | 0.363581i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 58.1330 | + | 17.9316i | 1.91972 | + | 0.592155i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.4108 | + | 34.3720i | −0.904198 | + | 1.13383i | 0.0862951 | + | 0.996270i | \(0.472497\pi\) |
−0.990494 | + | 0.137559i | \(0.956074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.2257 | − | 21.5503i | −0.765312 | − | 0.710105i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.935602 | − | 12.4847i | −0.0307957 | − | 0.410940i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.1841 | − | 88.4323i | 0.663649 | − | 2.90764i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.18389 | − | 3.53432i | −0.170261 | − | 0.116082i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.10522 | − | 5.36400i | −0.0690699 | − | 0.175987i | 0.892171 | − | 0.451699i | \(-0.149182\pi\) |
−0.961240 | + | 0.275711i | \(0.911087\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.00257101 | − | 0.0343077i | 8.42614e−5 | − | 0.00112439i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.57087 | − | 0.236770i | 0.0514278 | − | 0.00775150i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.97889 | + | 4.32401i | 0.293641 | + | 0.141410i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.1263 | + | 12.3583i | −0.592161 | + | 0.403729i | −0.821990 | − | 0.569503i | \(-0.807136\pi\) |
0.229828 | + | 0.973231i | \(0.426184\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.0641 | + | 34.7521i | −0.654769 | + | 1.13409i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.91668 | + | 17.6234i | −0.225477 | + | 0.574507i | −0.998183 | − | 0.0602578i | \(-0.980808\pi\) |
0.772706 | + | 0.634765i | \(0.218903\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.3672 | + | 5.04862i | −0.532991 | + | 0.164406i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −63.8021 | −2.07548 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.2434 | −1.30774 | −0.653868 | − | 0.756609i | \(-0.726855\pi\) | ||||
−0.653868 | + | 0.756609i | \(0.726855\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.7542 | + | 5.16798i | −0.543864 | + | 0.167760i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.2183 | − | 33.6797i | 0.428634 | − | 1.09214i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.3255 | + | 31.7407i | −0.593621 | + | 1.02818i | 0.400119 | + | 0.916463i | \(0.368969\pi\) |
−0.993740 | + | 0.111718i | \(0.964365\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63.9506 | + | 43.6008i | −2.06939 | + | 1.41089i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.683788 | − | 0.329295i | −0.0221037 | − | 0.0106446i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −58.6926 | + | 8.84648i | −1.89528 | + | 0.285668i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.43176 | + | 19.1056i | −0.0461859 | + | 0.616308i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.55207 | − | 3.95460i | −0.0500146 | − | 0.127435i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.3619 | + | 7.06459i | 0.333560 | + | 0.227417i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.90500 | + | 8.34635i | −0.0612607 | + | 0.268400i | −0.996278 | − | 0.0862025i | \(-0.972527\pi\) |
0.935017 | + | 0.354603i | \(0.115384\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0156614 | + | 0.208987i | 0.000503116 | + | 0.00671362i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.2742 | − | 33.6575i | −1.16409 | − | 1.08012i | −0.995531 | − | 0.0944301i | \(-0.969897\pi\) |
−0.168562 | − | 0.985691i | \(-0.553912\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.1091 | + | 26.4699i | −0.676725 | + | 0.848587i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25.6889 | + | 7.92398i | 0.822704 | + | 0.253770i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.4546 | + | 12.4840i | −0.430450 | + | 0.399399i | −0.865421 | − | 0.501045i | \(-0.832949\pi\) |
0.434971 | + | 0.900444i | \(0.356759\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.17655 | − | 1.38314i | −0.293284 | − | 0.0442054i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.09932 | − | 5.14038i | −0.130881 | − | 0.164120i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.35817 | − | 4.08447i | −0.0752140 | − | 0.130274i | 0.825965 | − | 0.563721i | \(-0.190631\pi\) |
−0.901179 | + | 0.433446i | \(0.857297\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43.0882 | − | 20.7502i | 1.37291 | − | 0.661157i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.53101 | + | 28.6142i | 0.207884 | + | 0.910800i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.23252 | − | 9.67091i | 0.293577 | − | 0.307517i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0778 | + | 44.1536i | 0.320131 | + | 1.40259i | 0.837319 | + | 0.546714i | \(0.184122\pi\) |
−0.517188 | + | 0.855872i | \(0.673021\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.38623 | − | 1.63072i | 0.107459 | − | 0.0517495i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.545067 | − | 0.944083i | −0.0172798 | − | 0.0299295i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.2570 | − | 22.8935i | −0.578204 | − | 0.725045i | 0.403601 | − | 0.914935i | \(-0.367758\pi\) |
−0.981805 | + | 0.189890i | \(0.939187\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 43.6590 | + | 6.58054i | 1.38131 | + | 0.208199i |
(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 | 688.2.bg.c.17.1 | 36 | ||
4.3 | odd | 2 | 43.2.g.a.17.1 | ✓ | 36 | ||
12.11 | even | 2 | 387.2.y.c.361.3 | 36 | |||
43.38 | even | 21 | inner | 688.2.bg.c.81.1 | 36 | ||
172.95 | odd | 42 | 1849.2.a.n.1.18 | 18 | |||
172.163 | even | 42 | 1849.2.a.o.1.1 | 18 | |||
172.167 | odd | 42 | 43.2.g.a.38.1 | yes | 36 | ||
516.167 | even | 42 | 387.2.y.c.253.3 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.2.g.a.17.1 | ✓ | 36 | 4.3 | odd | 2 | ||
43.2.g.a.38.1 | yes | 36 | 172.167 | odd | 42 | ||
387.2.y.c.253.3 | 36 | 516.167 | even | 42 | |||
387.2.y.c.361.3 | 36 | 12.11 | even | 2 | |||
688.2.bg.c.17.1 | 36 | 1.1 | even | 1 | trivial | ||
688.2.bg.c.81.1 | 36 | 43.38 | even | 21 | inner | ||
1849.2.a.n.1.18 | 18 | 172.95 | odd | 42 | |||
1849.2.a.o.1.1 | 18 | 172.163 | even | 42 |