Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,2,Mod(35,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.14984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 35.3 | ||
Root | \(-1.40927 + 0.118126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.35 |
Dual form | 144.2.l.a.107.3 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.957325 | − | 1.04093i | −0.676931 | − | 0.736046i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.167056 | + | 1.99301i | −0.0835279 | + | 0.996505i | ||||
\(5\) | 0.236253 | + | 0.236253i | 0.105655 | + | 0.105655i | 0.757958 | − | 0.652303i | \(-0.226197\pi\) |
−0.652303 | + | 0.757958i | \(0.726197\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.27830 | 1.23908 | 0.619540 | − | 0.784965i | \(-0.287319\pi\) | ||||
0.619540 | + | 0.784965i | \(0.287319\pi\) | |||||||
\(8\) | 2.23450 | − | 1.73407i | 0.790017 | − | 0.613085i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.0197510 | − | 0.472092i | 0.00624580 | − | 0.149289i | ||||
\(11\) | 2.58229 | − | 2.58229i | 0.778590 | − | 0.778590i | −0.201001 | − | 0.979591i | \(-0.564420\pi\) |
0.979591 | + | 0.201001i | \(0.0644195\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.70773 | − | 1.70773i | −0.473638 | − | 0.473638i | 0.429452 | − | 0.903090i | \(-0.358707\pi\) |
−0.903090 | + | 0.429452i | \(0.858707\pi\) | |||||||
\(14\) | −3.13840 | − | 3.41247i | −0.838772 | − | 0.912020i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.94418 | − | 0.665888i | −0.986046 | − | 0.166472i | ||||
\(17\) | 7.05130i | 1.71019i | 0.518470 | + | 0.855096i | \(0.326502\pi\) | ||||
−0.518470 | + | 0.855096i | \(0.673498\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.04184 | − | 3.04184i | 0.697845 | − | 0.697845i | −0.266100 | − | 0.963945i | \(-0.585735\pi\) |
0.963945 | + | 0.266100i | \(0.0857352\pi\) | |||||||
\(20\) | −0.510322 | + | 0.431387i | −0.114111 | + | 0.0964610i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.16007 | − | 0.215882i | −1.10013 | − | 0.0460262i | ||||
\(23\) | − | 1.47338i | − | 0.307221i | −0.988131 | − | 0.153610i | \(-0.950910\pi\) | ||
0.988131 | − | 0.153610i | \(-0.0490901\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.88837i | − | 0.977674i | ||||||
\(26\) | −0.142768 | + | 3.41247i | −0.0279990 | + | 0.669240i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.547659 | + | 6.53368i | −0.103498 | + | 1.23475i | ||||
\(29\) | −2.98575 | + | 2.98575i | −0.554439 | + | 0.554439i | −0.927719 | − | 0.373280i | \(-0.878233\pi\) |
0.373280 | + | 0.927719i | \(0.378233\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.02552i | 1.44143i | 0.693233 | + | 0.720713i | \(0.256186\pi\) | ||||
−0.693233 | + | 0.720713i | \(0.743814\pi\) | |||||||
\(32\) | 3.08273 | + | 4.74308i | 0.544954 | + | 0.838466i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.33988 | − | 6.75039i | 1.25878 | − | 1.15768i | ||||
\(35\) | 0.774506 | + | 0.774506i | 0.130915 | + | 0.130915i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.93021 | + | 7.93021i | −1.30372 | + | 1.30372i | −0.377852 | + | 0.925866i | \(0.623337\pi\) |
−0.925866 | + | 0.377852i | \(0.876663\pi\) | |||||||
\(38\) | −6.07836 | − | 0.254301i | −0.986040 | − | 0.0412530i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.937586 | + | 0.118230i | 0.148245 | + | 0.0186938i | ||||
\(41\) | 2.22112 | 0.346881 | 0.173441 | − | 0.984844i | \(-0.444512\pi\) | ||||
0.173441 | + | 0.984844i | \(0.444512\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.61007 | − | 4.61007i | −0.703030 | − | 0.703030i | 0.262030 | − | 0.965060i | \(-0.415608\pi\) |
−0.965060 | + | 0.262030i | \(0.915608\pi\) | |||||||
\(44\) | 4.71515 | + | 5.57792i | 0.710835 | + | 0.840903i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.53368 | + | 1.41050i | −0.226129 | + | 0.207968i | ||||
\(47\) | −7.13023 | −1.04005 | −0.520026 | − | 0.854151i | \(-0.674078\pi\) | ||||
−0.520026 | + | 0.854151i | \(0.674078\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.74723 | 0.535318 | ||||||||
\(50\) | −5.08843 | + | 4.67976i | −0.719613 | + | 0.661818i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.68880 | − | 3.11823i | 0.511545 | − | 0.432421i | ||||
\(53\) | −5.81417 | − | 5.81417i | −0.798638 | − | 0.798638i | 0.184243 | − | 0.982881i | \(-0.441017\pi\) |
−0.982881 | + | 0.184243i | \(0.941017\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.22015 | 0.164524 | ||||||||
\(56\) | 7.32537 | − | 5.68479i | 0.978894 | − | 0.759662i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.96627 | + | 0.249611i | 0.783410 | + | 0.0327756i | ||||
\(59\) | 7.46464 | − | 7.46464i | 0.971813 | − | 0.971813i | −0.0278004 | − | 0.999613i | \(-0.508850\pi\) |
0.999613 | + | 0.0278004i | \(0.00885027\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.04184 | − | 4.04184i | −0.517504 | − | 0.517504i | 0.399311 | − | 0.916815i | \(-0.369249\pi\) |
−0.916815 | + | 0.399311i | \(0.869249\pi\) | |||||||
\(62\) | 8.35398 | − | 7.68304i | 1.06096 | − | 0.975747i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.98602 | − | 7.74956i | 0.248253 | − | 0.968695i | ||||
\(65\) | − | 0.806909i | − | 0.100085i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.90468 | + | 2.90468i | −0.354863 | + | 0.354863i | −0.861915 | − | 0.507052i | \(-0.830735\pi\) |
0.507052 | + | 0.861915i | \(0.330735\pi\) | |||||||
\(68\) | −14.0533 | − | 1.17796i | −1.70421 | − | 0.142849i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0647495 | − | 1.54766i | 0.00773904 | − | 0.184981i | ||||
\(71\) | − | 1.02064i | − | 0.121128i | −0.998164 | − | 0.0605640i | \(-0.980710\pi\) | ||
0.998164 | − | 0.0605640i | \(-0.0192899\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.08367i | 0.477958i | 0.971025 | + | 0.238979i | \(0.0768127\pi\) | ||||
−0.971025 | + | 0.238979i | \(0.923187\pi\) | |||||||
\(74\) | 15.8466 | + | 0.662973i | 1.84212 | + | 0.0770691i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.55426 | + | 6.57057i | 0.637117 | + | 0.753696i | ||||
\(77\) | 8.46551 | − | 8.46551i | 0.964735 | − | 0.964735i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.36197i | 0.603269i | 0.953424 | + | 0.301634i | \(0.0975322\pi\) | ||||
−0.953424 | + | 0.301634i | \(0.902468\pi\) | |||||||
\(80\) | −0.774506 | − | 1.08914i | −0.0865924 | − | 0.121770i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.12634 | − | 2.31203i | −0.234815 | − | 0.255321i | ||||
\(83\) | −3.93734 | − | 3.93734i | −0.432179 | − | 0.432179i | 0.457190 | − | 0.889369i | \(-0.348856\pi\) |
−0.889369 | + | 0.457190i | \(0.848856\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.66589 | + | 1.66589i | −0.180691 | + | 0.180691i | ||||
\(86\) | −0.385407 | + | 9.21209i | −0.0415595 | + | 0.993365i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.29227 | − | 10.2480i | 0.137757 | − | 1.09244i | ||||
\(89\) | −2.35922 | −0.250077 | −0.125039 | − | 0.992152i | \(-0.539905\pi\) | ||||
−0.125039 | + | 0.992152i | \(0.539905\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.59843 | − | 5.59843i | −0.586875 | − | 0.586875i | ||||
\(92\) | 2.93646 | + | 0.246137i | 0.306147 | + | 0.0256615i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.82596 | + | 7.42205i | 0.704044 | + | 0.765526i | ||||
\(95\) | 1.43728 | 0.147462 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.97204 | 1.01251 | 0.506254 | − | 0.862385i | \(-0.331030\pi\) | ||||
0.506254 | + | 0.862385i | \(0.331030\pi\) | |||||||
\(98\) | −3.58732 | − | 3.90059i | −0.362374 | − | 0.394019i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.74257 | + | 0.816631i | 0.974257 | + | 0.0816631i | ||||
\(101\) | −2.65134 | − | 2.65134i | −0.263818 | − | 0.263818i | 0.562785 | − | 0.826603i | \(-0.309730\pi\) |
−0.826603 | + | 0.562785i | \(0.809730\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.0255237 | −0.00251492 | −0.00125746 | − | 0.999999i | \(-0.500400\pi\) | ||||
−0.00125746 | + | 0.999999i | \(0.500400\pi\) | |||||||
\(104\) | −6.77723 | − | 0.854610i | −0.664562 | − | 0.0838014i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.486071 | + | 11.6182i | −0.0472113 | + | 1.12846i | ||||
\(107\) | −11.7664 | + | 11.7664i | −1.13751 | + | 1.13751i | −0.148609 | + | 0.988896i | \(0.547480\pi\) |
−0.988896 | + | 0.148609i | \(0.952520\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.26432 | + | 6.26432i | 0.600013 | + | 0.600013i | 0.940316 | − | 0.340303i | \(-0.110530\pi\) |
−0.340303 | + | 0.940316i | \(0.610530\pi\) | |||||||
\(110\) | −1.16808 | − | 1.27008i | −0.111372 | − | 0.121098i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.9302 | − | 2.18298i | −1.22179 | − | 0.206272i | ||||
\(113\) | − | 4.36097i | − | 0.410246i | −0.978736 | − | 0.205123i | \(-0.934241\pi\) | ||
0.978736 | − | 0.205123i | \(-0.0657594\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.348090 | − | 0.348090i | 0.0324596 | − | 0.0324596i | ||||
\(116\) | −5.45184 | − | 6.44941i | −0.506190 | − | 0.598813i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.9162 | − | 0.624051i | −1.37315 | − | 0.0574486i | ||||
\(119\) | 23.1162i | 2.11906i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.33645i | − | 0.212404i | ||||||
\(122\) | −0.337902 | + | 8.07661i | −0.0305922 | + | 0.731222i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −15.9950 | − | 1.34071i | −1.43639 | − | 0.120399i | ||||
\(125\) | 2.33615 | − | 2.33615i | 0.208952 | − | 0.208952i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.66579i | − | 0.768965i | −0.923132 | − | 0.384482i | \(-0.874380\pi\) | ||
0.923132 | − | 0.384482i | \(-0.125620\pi\) | |||||||
\(128\) | −9.96799 | + | 5.35155i | −0.881055 | + | 0.473015i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.839933 | + | 0.772475i | −0.0736670 | + | 0.0677505i | ||||
\(131\) | 14.9293 | + | 14.9293i | 1.30438 | + | 1.30438i | 0.925410 | + | 0.378967i | \(0.123720\pi\) |
0.378967 | + | 0.925410i | \(0.376280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.97204 | − | 9.97204i | 0.864686 | − | 0.864686i | ||||
\(134\) | 5.80429 | + | 0.242834i | 0.501414 | + | 0.0209777i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.2274 | + | 15.7562i | 1.04849 | + | 1.35108i | ||||
\(137\) | 10.9365 | 0.934365 | 0.467183 | − | 0.884161i | \(-0.345269\pi\) | ||||
0.467183 | + | 0.884161i | \(0.345269\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.09532 | − | 1.09532i | −0.0929036 | − | 0.0929036i | 0.659128 | − | 0.752031i | \(-0.270926\pi\) |
−0.752031 | + | 0.659128i | \(0.770926\pi\) | |||||||
\(140\) | −1.67299 | + | 1.41421i | −0.141393 | + | 0.119523i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.06241 | + | 0.977088i | −0.0891558 | + | 0.0819954i | ||||
\(143\) | −8.81969 | −0.737539 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.41078 | −0.117159 | ||||||||
\(146\) | 4.25080 | − | 3.90941i | 0.351799 | − | 0.323545i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −14.4802 | − | 17.1298i | −1.19027 | − | 1.40806i | ||||
\(149\) | 5.42060 | + | 5.42060i | 0.444073 | + | 0.444073i | 0.893378 | − | 0.449305i | \(-0.148328\pi\) |
−0.449305 | + | 0.893378i | \(0.648328\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5821 | −1.18668 | −0.593338 | − | 0.804953i | \(-0.702190\pi\) | ||||
−0.593338 | + | 0.804953i | \(0.702190\pi\) | |||||||
\(152\) | 1.52225 | − | 12.0717i | 0.123471 | − | 0.979148i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16.9162 | − | 0.707725i | −1.36315 | − | 0.0570301i | ||||
\(155\) | −1.89605 | + | 1.89605i | −0.152295 | + | 0.152295i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.04184 | + | 6.04184i | 0.482191 | + | 0.482191i | 0.905831 | − | 0.423640i | \(-0.139248\pi\) |
−0.423640 | + | 0.905831i | \(0.639248\pi\) | |||||||
\(158\) | 5.58142 | − | 5.13315i | 0.444034 | − | 0.408372i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.392262 | + | 1.84887i | −0.0310110 | + | 0.146166i | ||||
\(161\) | − | 4.83018i | − | 0.380671i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.16667 | − | 3.16667i | 0.248032 | − | 0.248032i | −0.572130 | − | 0.820163i | \(-0.693883\pi\) |
0.820163 | + | 0.572130i | \(0.193883\pi\) | |||||||
\(164\) | −0.371052 | + | 4.42672i | −0.0289743 | + | 0.345669i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.329165 | + | 7.86779i | −0.0255482 | + | 0.610659i | ||||
\(167\) | − | 15.5333i | − | 1.20200i | −0.799249 | − | 0.601001i | \(-0.794769\pi\) | ||
0.799249 | − | 0.601001i | \(-0.205231\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.16735i | − | 0.551334i | ||||||
\(170\) | 3.32886 | + | 0.139270i | 0.255312 | + | 0.0106815i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.95807 | − | 8.41779i | 0.759295 | − | 0.641850i | ||||
\(173\) | −11.0577 | + | 11.0577i | −0.840700 | + | 0.840700i | −0.988950 | − | 0.148250i | \(-0.952636\pi\) |
0.148250 | + | 0.988950i | \(0.452636\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 16.0255i | − | 1.21142i | ||||||
\(176\) | −11.9045 | + | 8.46551i | −0.897339 | + | 0.638112i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.25855 | + | 2.45578i | 0.169285 | + | 0.184068i | ||||
\(179\) | −3.84907 | − | 3.84907i | −0.287693 | − | 0.287693i | 0.548474 | − | 0.836167i | \(-0.315209\pi\) |
−0.836167 | + | 0.548474i | \(0.815209\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.29227 | − | 4.29227i | 0.319042 | − | 0.319042i | −0.529357 | − | 0.848399i | \(-0.677567\pi\) |
0.848399 | + | 0.529357i | \(0.177567\pi\) | |||||||
\(182\) | −0.468034 | + | 11.1871i | −0.0346930 | + | 0.829241i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.55494 | − | 3.29227i | −0.188353 | − | 0.242710i | ||||
\(185\) | −3.74706 | −0.275490 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.2085 | + | 18.2085i | 1.33154 | + | 1.33154i | ||||
\(188\) | 1.19115 | − | 14.2106i | 0.0868734 | − | 1.03642i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.37595 | − | 1.49611i | −0.0998218 | − | 0.108539i | ||||
\(191\) | 24.8057 | 1.79488 | 0.897439 | − | 0.441139i | \(-0.145425\pi\) | ||||
0.897439 | + | 0.441139i | \(0.145425\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.08367 | −0.581876 | −0.290938 | − | 0.956742i | \(-0.593967\pi\) | ||||
−0.290938 | + | 0.956742i | \(0.593967\pi\) | |||||||
\(194\) | −9.54649 | − | 10.3802i | −0.685398 | − | 0.745252i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.625996 | + | 7.46826i | −0.0447140 | + | 0.533447i | ||||
\(197\) | 7.34342 | + | 7.34342i | 0.523197 | + | 0.523197i | 0.918535 | − | 0.395339i | \(-0.129373\pi\) |
−0.395339 | + | 0.918535i | \(0.629373\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.5526 | 0.818942 | 0.409471 | − | 0.912323i | \(-0.365713\pi\) | ||||
0.409471 | + | 0.912323i | \(0.365713\pi\) | |||||||
\(200\) | −8.47676 | − | 10.9231i | −0.599398 | − | 0.772379i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.221655 | + | 5.29805i | −0.0155956 | + | 0.372769i | ||||
\(203\) | −9.78816 | + | 9.78816i | −0.686994 | + | 0.686994i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.524746 | + | 0.524746i | 0.0366499 | + | 0.0366499i | ||||
\(206\) | 0.0244345 | + | 0.0265683i | 0.00170243 | + | 0.00185110i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.59843 | + | 7.87274i | 0.388181 | + | 0.545876i | ||||
\(209\) | − | 15.7098i | − | 1.08667i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.821009 | − | 0.821009i | 0.0565206 | − | 0.0565206i | −0.678282 | − | 0.734802i | \(-0.737275\pi\) |
0.734802 | + | 0.678282i | \(0.237275\pi\) | |||||||
\(212\) | 12.5590 | − | 10.6164i | 0.862556 | − | 0.729138i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23.5123 | + | 0.983687i | 1.60727 | + | 0.0672434i | ||||
\(215\) | − | 2.17828i | − | 0.148558i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.3100i | 1.78604i | ||||||||
\(218\) | 0.523703 | − | 12.5177i | 0.0354697 | − | 0.847805i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.203833 | + | 2.43176i | −0.0137424 | + | 0.163950i | ||||
\(221\) | 12.0417 | − | 12.0417i | 0.810011 | − | 0.810011i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.83489i | 0.658593i | 0.944227 | + | 0.329296i | \(0.106812\pi\) | ||||
−0.944227 | + | 0.329296i | \(0.893188\pi\) | |||||||
\(224\) | 10.1061 | + | 15.5492i | 0.675242 | + | 1.03893i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.53945 | + | 4.17487i | −0.301960 | + | 0.277708i | ||||
\(227\) | −15.6642 | − | 15.6642i | −1.03967 | − | 1.03967i | −0.999180 | − | 0.0404927i | \(-0.987107\pi\) |
−0.0404927 | − | 0.999180i | \(-0.512893\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4845 | − | 11.4845i | 0.758915 | − | 0.758915i | −0.217210 | − | 0.976125i | \(-0.569696\pi\) |
0.976125 | + | 0.217210i | \(0.0696957\pi\) | |||||||
\(230\) | −0.695571 | − | 0.0291007i | −0.0458646 | − | 0.00191884i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.49418 | + | 11.8491i | −0.0980976 | + | 0.777934i | ||||
\(233\) | −22.8992 | −1.50018 | −0.750089 | − | 0.661337i | \(-0.769989\pi\) | ||||
−0.750089 | + | 0.661337i | \(0.769989\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.68454 | − | 1.68454i | −0.109887 | − | 0.109887i | ||||
\(236\) | 13.6301 | + | 16.1241i | 0.887244 | + | 1.04959i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 24.0623 | − | 22.1298i | 1.55973 | − | 1.43446i | ||||
\(239\) | 1.50948 | 0.0976399 | 0.0488199 | − | 0.998808i | \(-0.484454\pi\) | ||||
0.0488199 | + | 0.998808i | \(0.484454\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.3922 | −1.24916 | −0.624580 | − | 0.780961i | \(-0.714730\pi\) | ||||
−0.624580 | + | 0.780961i | \(0.714730\pi\) | |||||||
\(242\) | −2.43207 | + | 2.23674i | −0.156339 | + | 0.143783i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.73064 | − | 7.38021i | 0.558922 | − | 0.472470i | ||||
\(245\) | 0.885292 | + | 0.885292i | 0.0565593 | + | 0.0565593i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.3892 | −0.661052 | ||||||||
\(248\) | 13.9168 | + | 17.9331i | 0.883718 | + | 1.13875i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.66822 | − | 0.195305i | −0.295244 | − | 0.0123522i | ||||
\(251\) | 12.3470 | − | 12.3470i | 0.779335 | − | 0.779335i | −0.200383 | − | 0.979718i | \(-0.564219\pi\) |
0.979718 | + | 0.200383i | \(0.0642186\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.80470 | − | 3.80470i | −0.239199 | − | 0.239199i | ||||
\(254\) | −9.02045 | + | 8.29598i | −0.565993 | + | 0.520536i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.1132 | + | 5.25277i | 0.944574 | + | 0.328298i | ||||
\(257\) | 10.5288i | 0.656766i | 0.944545 | + | 0.328383i | \(0.106504\pi\) | ||||
−0.944545 | + | 0.328383i | \(0.893496\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.9976 | + | 25.9976i | −1.61541 | + | 1.61541i | ||||
\(260\) | 1.60818 | + | 0.134799i | 0.0997350 | + | 0.00835987i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.24810 | − | 29.8325i | 0.0771080 | − | 1.84306i | ||||
\(263\) | − | 13.8725i | − | 0.855417i | −0.903917 | − | 0.427709i | \(-0.859321\pi\) | ||
0.903917 | − | 0.427709i | \(-0.140679\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.74723i | − | 0.168761i | ||||||
\(266\) | −19.9267 | − | 0.833673i | −1.22178 | − | 0.0511158i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.30382 | − | 6.27431i | −0.323982 | − | 0.383264i | ||||
\(269\) | −11.0971 | + | 11.0971i | −0.676601 | + | 0.676601i | −0.959230 | − | 0.282628i | \(-0.908794\pi\) |
0.282628 | + | 0.959230i | \(0.408794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 30.0022i | − | 1.82251i | −0.411847 | − | 0.911253i | \(-0.635116\pi\) | ||
0.411847 | − | 0.911253i | \(-0.364884\pi\) | |||||||
\(272\) | 4.69538 | − | 27.8116i | 0.284699 | − | 1.68633i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.4698 | − | 11.3841i | −0.632501 | − | 0.687736i | ||||
\(275\) | −12.6232 | − | 12.6232i | −0.761207 | − | 0.761207i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.62872 | + | 5.62872i | −0.338197 | + | 0.338197i | −0.855688 | − | 0.517491i | \(-0.826866\pi\) |
0.517491 | + | 0.855688i | \(0.326866\pi\) | |||||||
\(278\) | −0.0915696 | + | 2.18872i | −0.00549198 | + | 0.131271i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.07368 | + | 0.387592i | 0.183688 | + | 0.0231630i | ||||
\(281\) | 11.9012 | 0.709969 | 0.354984 | − | 0.934872i | \(-0.384486\pi\) | ||||
0.354984 | + | 0.934872i | \(0.384486\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3875 | + | 17.3875i | 1.03358 | + | 1.03358i | 0.999416 | + | 0.0341630i | \(0.0108765\pi\) |
0.0341630 | + | 0.999416i | \(0.489123\pi\) | |||||||
\(284\) | 2.03415 | + | 0.170504i | 0.120705 | + | 0.0101176i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.44331 | + | 9.18064i | 0.499263 | + | 0.542863i | ||||
\(287\) | 7.28150 | 0.429813 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −32.7208 | −1.92475 | ||||||||
\(290\) | 1.35058 | + | 1.46852i | 0.0793086 | + | 0.0862344i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.13881 | − | 0.682202i | −0.476288 | − | 0.0399228i | ||||
\(293\) | 5.14536 | + | 5.14536i | 0.300595 | + | 0.300595i | 0.841247 | − | 0.540651i | \(-0.181822\pi\) |
−0.540651 | + | 0.841247i | \(0.681822\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.52708 | 0.205355 | ||||||||
\(296\) | −3.96857 | + | 31.4716i | −0.230669 | + | 1.82925i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.453168 | − | 10.8317i | 0.0262513 | − | 0.627465i | ||||
\(299\) | −2.51613 | + | 2.51613i | −0.145511 | + | 0.145511i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.1132 | − | 15.1132i | −0.871110 | − | 0.871110i | ||||
\(302\) | 13.9598 | + | 15.1789i | 0.803298 | + | 0.873448i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14.0231 | + | 9.97204i | −0.804279 | + | 0.571936i | ||||
\(305\) | − | 1.90979i | − | 0.109354i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.9557 | − | 14.9557i | 0.853569 | − | 0.853569i | −0.137002 | − | 0.990571i | \(-0.543747\pi\) |
0.990571 | + | 0.137002i | \(0.0437467\pi\) | |||||||
\(308\) | 15.4576 | + | 18.2861i | 0.880781 | + | 1.04195i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.78879 | + | 0.158512i | 0.215189 | + | 0.00900286i | ||||
\(311\) | − | 16.8915i | − | 0.957829i | −0.877862 | − | 0.478914i | \(-0.841030\pi\) | ||
0.877862 | − | 0.478914i | \(-0.158970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.42012i | − | 0.0802700i | −0.999194 | − | 0.0401350i | \(-0.987221\pi\) | ||
0.999194 | − | 0.0401350i | \(-0.0127788\pi\) | |||||||
\(314\) | 0.505104 | − | 12.0731i | 0.0285046 | − | 0.681325i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.6865 | − | 0.895749i | −0.601161 | − | 0.0503898i | ||||
\(317\) | −23.3492 | + | 23.3492i | −1.31142 | + | 1.31142i | −0.391054 | + | 0.920368i | \(0.627889\pi\) |
−0.920368 | + | 0.391054i | \(0.872111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.4201i | 0.863361i | ||||||||
\(320\) | 2.30006 | − | 1.36165i | 0.128577 | − | 0.0761187i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.02786 | + | 4.62405i | −0.280192 | + | 0.257688i | ||||
\(323\) | 21.4489 | + | 21.4489i | 1.19345 | + | 1.19345i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.34799 | + | 8.34799i | −0.463063 | + | 0.463063i | ||||
\(326\) | −6.32780 | − | 0.264736i | −0.350464 | − | 0.0146624i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.96311 | − | 3.85158i | 0.274042 | − | 0.212668i | ||||
\(329\) | −23.3750 | −1.28871 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.95573 | + | 2.95573i | 0.162462 | + | 0.162462i | 0.783656 | − | 0.621195i | \(-0.213352\pi\) |
−0.621195 | + | 0.783656i | \(0.713352\pi\) | |||||||
\(332\) | 8.50491 | − | 7.18940i | 0.466768 | − | 0.394570i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.1690 | + | 14.8704i | −0.884728 | + | 0.813672i | ||||
\(335\) | −1.37248 | −0.0749865 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.41078 | −0.0768501 | −0.0384251 | − | 0.999261i | \(-0.512234\pi\) | ||||
−0.0384251 | + | 0.999261i | \(0.512234\pi\) | |||||||
\(338\) | −7.46068 | + | 6.86149i | −0.405808 | + | 0.373216i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.04184 | − | 3.59843i | −0.164967 | − | 0.195152i | ||||
\(341\) | 20.7242 | + | 20.7242i | 1.12228 | + | 1.12228i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.6636 | −0.575778 | ||||||||
\(344\) | −18.2954 | − | 2.30705i | −0.986422 | − | 0.124388i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.0960 | + | 0.924434i | 1.18789 | + | 0.0496979i | ||||
\(347\) | −3.11726 | + | 3.11726i | −0.167344 | + | 0.167344i | −0.785811 | − | 0.618467i | \(-0.787754\pi\) |
0.618467 | + | 0.785811i | \(0.287754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.8465 | + | 11.8465i | 0.634130 | + | 0.634130i | 0.949101 | − | 0.314971i | \(-0.101995\pi\) |
−0.314971 | + | 0.949101i | \(0.601995\pi\) | |||||||
\(350\) | −16.6814 | + | 15.3416i | −0.891658 | + | 0.820045i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.2085 | + | 4.28751i | 1.07712 | + | 0.228525i | ||||
\(353\) | 5.30598i | 0.282409i | 0.989980 | + | 0.141205i | \(0.0450975\pi\) | ||||
−0.989980 | + | 0.141205i | \(0.954902\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.241130 | − | 0.241130i | 0.0127978 | − | 0.0127978i | ||||
\(356\) | 0.394122 | − | 4.70196i | 0.0208884 | − | 0.249203i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.321786 | + | 7.69141i | −0.0170069 | + | 0.406504i | ||||
\(359\) | − | 17.8399i | − | 0.941556i | −0.882252 | − | 0.470778i | \(-0.843973\pi\) | ||
0.882252 | − | 0.470778i | \(-0.156027\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.494455i | 0.0260239i | ||||||||
\(362\) | −8.57705 | − | 0.358838i | −0.450800 | − | 0.0188601i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.0930 | − | 10.2225i | 0.633844 | − | 0.535804i | ||||
\(365\) | −0.964779 | + | 0.964779i | −0.0504988 | + | 0.0504988i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.05815i | − | 0.107435i | −0.998556 | − | 0.0537173i | \(-0.982893\pi\) | ||
0.998556 | − | 0.0537173i | \(-0.0171070\pi\) | |||||||
\(368\) | −0.981107 | + | 5.81128i | −0.0511437 | + | 0.302934i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.58716 | + | 3.90042i | 0.186488 | + | 0.202773i | ||||
\(371\) | −19.0606 | − | 19.0606i | −0.989576 | − | 0.989576i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.7891 | − | 12.7891i | 0.662193 | − | 0.662193i | −0.293704 | − | 0.955896i | \(-0.594888\pi\) |
0.955896 | + | 0.293704i | \(0.0948879\pi\) | |||||||
\(374\) | 1.52225 | − | 36.3852i | 0.0787136 | − | 1.88143i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.9325 | + | 12.3643i | −0.821658 | + | 0.637640i | ||||
\(377\) | 10.1977 | 0.525206 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.76753 | + | 6.76753i | 0.347625 | + | 0.347625i | 0.859224 | − | 0.511599i | \(-0.170947\pi\) |
−0.511599 | + | 0.859224i | \(0.670947\pi\) | |||||||
\(380\) | −0.240107 | + | 2.86452i | −0.0123172 | + | 0.146947i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −23.7471 | − | 25.8209i | −1.21501 | − | 1.32111i | ||||
\(383\) | 7.48207 | 0.382316 | 0.191158 | − | 0.981559i | \(-0.438776\pi\) | ||||
0.191158 | + | 0.981559i | \(0.438776\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 7.73871 | + | 8.41451i | 0.393890 | + | 0.428287i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.66589 | + | 19.8744i | −0.0845727 | + | 1.00897i | ||||
\(389\) | −20.7180 | − | 20.7180i | −1.05045 | − | 1.05045i | −0.998658 | − | 0.0517883i | \(-0.983508\pi\) |
−0.0517883 | − | 0.998658i | \(-0.516492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.3892 | 0.525407 | ||||||||
\(392\) | 8.37320 | − | 6.49794i | 0.422910 | − | 0.328196i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.613917 | − | 14.6740i | 0.0309287 | − | 0.739265i | ||||
\(395\) | −1.26678 | + | 1.26678i | −0.0637386 | + | 0.0637386i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.5194 | + | 12.5194i | 0.628332 | + | 0.628332i | 0.947648 | − | 0.319316i | \(-0.103453\pi\) |
−0.319316 | + | 0.947648i | \(0.603453\pi\) | |||||||
\(398\) | −11.0596 | − | 12.0254i | −0.554368 | − | 0.602779i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.25511 | + | 19.2806i | −0.162755 | + | 0.964032i | ||||
\(401\) | 11.4935i | 0.573960i | 0.957937 | + | 0.286980i | \(0.0926514\pi\) | ||||
−0.957937 | + | 0.286980i | \(0.907349\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.7054 | − | 13.7054i | 0.682714 | − | 0.682714i | ||||
\(404\) | 5.72707 | − | 4.84123i | 0.284933 | − | 0.240860i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.5592 | + | 0.818300i | 0.970707 | + | 0.0406115i | ||||
\(407\) | 40.9562i | 2.03012i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 23.2432i | − | 1.14930i | −0.818398 | − | 0.574652i | \(-0.805137\pi\) | ||
0.818398 | − | 0.574652i | \(-0.194863\pi\) | |||||||
\(410\) | 0.0438693 | − | 1.04858i | 0.00216655 | − | 0.0517854i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.00426388 | − | 0.0508689i | 0.000210066 | − | 0.00250613i | ||||
\(413\) | 24.4713 | − | 24.4713i | 1.20415 | − | 1.20415i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.86041i | − | 0.0913241i | ||||||
\(416\) | 2.83542 | − | 13.3643i | 0.139018 | − | 0.655240i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16.3528 | + | 15.0394i | −0.799840 | + | 0.735601i | ||||
\(419\) | 21.1446 | + | 21.1446i | 1.03298 | + | 1.03298i | 0.999437 | + | 0.0335424i | \(0.0106789\pi\) |
0.0335424 | + | 0.999437i | \(0.489321\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.60077 | − | 9.60077i | 0.467913 | − | 0.467913i | −0.433325 | − | 0.901238i | \(-0.642660\pi\) |
0.901238 | + | 0.433325i | \(0.142660\pi\) | |||||||
\(422\) | −1.64058 | − | 0.0686371i | −0.0798623 | − | 0.00334120i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −23.0740 | − | 2.90963i | −1.12057 | − | 0.141304i | ||||
\(425\) | 34.4694 | 1.67201 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.2503 | − | 13.2503i | −0.641229 | − | 0.641229i | ||||
\(428\) | −21.4850 | − | 25.4163i | −1.03852 | − | 1.22854i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.26743 | + | 2.08533i | −0.109345 | + | 0.100563i | ||||
\(431\) | −18.2795 | −0.880491 | −0.440246 | − | 0.897877i | \(-0.645109\pi\) | ||||
−0.440246 | + | 0.897877i | \(0.645109\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.3844 | 1.65241 | 0.826204 | − | 0.563371i | \(-0.190496\pi\) | ||||
0.826204 | + | 0.563371i | \(0.190496\pi\) | |||||||
\(434\) | 27.3868 | − | 25.1873i | 1.31461 | − | 1.20903i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.5313 | + | 11.4384i | −0.648034 | + | 0.547798i | ||||
\(437\) | −4.48178 | − | 4.48178i | −0.214393 | − | 0.214393i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.1713 | 0.724088 | 0.362044 | − | 0.932161i | \(-0.382079\pi\) | ||||
0.362044 | + | 0.932161i | \(0.382079\pi\) | |||||||
\(440\) | 2.72642 | − | 2.11582i | 0.129977 | − | 0.100868i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.0623 | − | 1.00670i | −1.14453 | − | 0.0478837i | ||||
\(443\) | 18.1978 | − | 18.1978i | 0.864604 | − | 0.864604i | −0.127265 | − | 0.991869i | \(-0.540620\pi\) |
0.991869 | + | 0.127265i | \(0.0406198\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.557373 | − | 0.557373i | −0.0264220 | − | 0.0264220i | ||||
\(446\) | 10.2374 | − | 9.41519i | 0.484755 | − | 0.445822i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.51077 | − | 25.4054i | 0.307605 | − | 1.20029i | ||||
\(449\) | − | 8.89518i | − | 0.419789i | −0.977724 | − | 0.209895i | \(-0.932688\pi\) | ||
0.977724 | − | 0.209895i | \(-0.0673121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.73558 | − | 5.73558i | 0.270078 | − | 0.270078i | ||||
\(452\) | 8.69147 | + | 0.728526i | 0.408812 | + | 0.0342670i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.30955 | + | 31.3011i | −0.0614601 | + | 1.46903i | ||||
\(455\) | − | 2.64529i | − | 0.124013i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3085i | 0.528989i | 0.964387 | + | 0.264494i | \(0.0852051\pi\) | ||||
−0.964387 | + | 0.264494i | \(0.914795\pi\) | |||||||
\(458\) | −22.9489 | − | 0.960113i | −1.07233 | − | 0.0448631i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.635597 | + | 0.751898i | 0.0296348 | + | 0.0350574i | ||||
\(461\) | 10.8614 | − | 10.8614i | 0.505865 | − | 0.505865i | −0.407389 | − | 0.913255i | \(-0.633561\pi\) |
0.913255 | + | 0.407389i | \(0.133561\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.05504i | 0.141980i | 0.997477 | + | 0.0709898i | \(0.0226158\pi\) | ||||
−0.997477 | + | 0.0709898i | \(0.977384\pi\) | |||||||
\(464\) | 13.7645 | − | 9.78816i | 0.639001 | − | 0.454404i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.9220 | + | 23.8364i | 1.01552 | + | 1.10420i | ||||
\(467\) | −3.93734 | − | 3.93734i | −0.182198 | − | 0.182198i | 0.610115 | − | 0.792313i | \(-0.291123\pi\) |
−0.792313 | + | 0.610115i | \(0.791123\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.52241 | + | 9.52241i | −0.439704 | + | 0.439704i | ||||
\(470\) | −0.140829 | + | 3.36613i | −0.00649596 | + | 0.155268i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.73558 | − | 29.6240i | 0.171944 | − | 1.36355i | ||||
\(473\) | −23.8091 | −1.09474 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.8696 | − | 14.8696i | −0.682265 | − | 0.682265i | ||||
\(476\) | −46.0709 | − | 3.86170i | −2.11166 | − | 0.177001i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.44506 | − | 1.57125i | −0.0660955 | − | 0.0718675i | ||||
\(479\) | 27.6167 | 1.26184 | 0.630920 | − | 0.775848i | \(-0.282678\pi\) | ||||
0.630920 | + | 0.775848i | \(0.282678\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.0852 | 1.23498 | ||||||||
\(482\) | 18.5646 | + | 20.1858i | 0.845595 | + | 0.919439i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.65656 | + | 0.390317i | 0.211662 | + | 0.0177417i | ||||
\(485\) | 2.35592 | + | 2.35592i | 0.106977 | + | 0.106977i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0783 | 0.592635 | 0.296318 | − | 0.955089i | \(-0.404241\pi\) | ||||
0.296318 | + | 0.955089i | \(0.404241\pi\) | |||||||
\(488\) | −16.0403 | − | 2.02269i | −0.726111 | − | 0.0915627i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.0740113 | − | 1.76904i | 0.00334349 | − | 0.0799170i | ||||
\(491\) | −21.8368 | + | 21.8368i | −0.985483 | + | 0.985483i | −0.999896 | − | 0.0144135i | \(-0.995412\pi\) |
0.0144135 | + | 0.999896i | \(0.495412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.0534 | − | 21.0534i | −0.948197 | − | 0.948197i | ||||
\(494\) | 9.94589 | + | 10.8144i | 0.447487 | + | 0.486565i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.34410 | − | 31.6541i | 0.239957 | − | 1.42131i | ||||
\(497\) | − | 3.34597i | − | 0.150087i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.4170 | + | 16.4170i | −0.734926 | + | 0.734926i | −0.971591 | − | 0.236665i | \(-0.923946\pi\) |
0.236665 | + | 0.971591i | \(0.423946\pi\) | |||||||
\(500\) | 4.26571 | + | 5.04625i | 0.190768 | + | 0.225675i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.6724 | − | 1.03222i | −1.10118 | − | 0.0460703i | ||||
\(503\) | 22.1243i | 0.986475i | 0.869895 | + | 0.493237i | \(0.164187\pi\) | ||||
−0.869895 | + | 0.493237i | \(0.835813\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.25277i | − | 0.0557477i | ||||||
\(506\) | −0.318076 | + | 7.60274i | −0.0141402 | + | 0.337983i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.2710 | + | 1.44767i | 0.766277 | + | 0.0642300i | ||||
\(509\) | −13.7152 | + | 13.7152i | −0.607916 | + | 0.607916i | −0.942401 | − | 0.334485i | \(-0.891438\pi\) |
0.334485 | + | 0.942401i | \(0.391438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.3875i | 0.592228i | ||||||||
\(512\) | −9.00049 | − | 20.7603i | −0.397769 | − | 0.917486i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.9597 | − | 10.0795i | 0.483410 | − | 0.444586i | ||||
\(515\) | −0.00603003 | − | 0.00603003i | −0.000265715 | − | 0.000265715i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.4123 | + | 18.4123i | −0.809774 | + | 0.809774i | ||||
\(518\) | 51.9497 | + | 2.17342i | 2.28254 | + | 0.0954947i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.39923 | − | 1.80304i | −0.0613605 | − | 0.0790686i | ||||
\(521\) | 0.888181 | 0.0389119 | 0.0194560 | − | 0.999811i | \(-0.493807\pi\) | ||||
0.0194560 | + | 0.999811i | \(0.493807\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.8186 | − | 14.8186i | −0.647971 | − | 0.647971i | 0.304531 | − | 0.952502i | \(-0.401500\pi\) |
−0.952502 | + | 0.304531i | \(0.901500\pi\) | |||||||
\(524\) | −32.2482 | + | 27.2602i | −1.40877 | + | 1.19087i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.4403 | + | 13.2805i | −0.629627 | + | 0.579059i | ||||
\(527\) | −56.5904 | −2.46512 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8292 | 0.905615 | ||||||||
\(530\) | −2.85966 | + | 2.62999i | −0.124216 | + | 0.114239i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 18.2085 | + | 21.5403i | 0.789439 | + | 0.933890i | ||||
\(533\) | −3.79307 | − | 3.79307i | −0.164296 | − | 0.164296i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.55971 | −0.240367 | ||||||||
\(536\) | −1.45361 | + | 11.5274i | −0.0627865 | + | 0.497910i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.1748 | + | 0.927727i | 0.956022 | + | 0.0399972i | ||||
\(539\) | 9.67643 | − | 9.67643i | 0.416793 | − | 0.416793i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.26432 | − | 4.26432i | −0.183337 | − | 0.183337i | 0.609471 | − | 0.792808i | \(-0.291382\pi\) |
−0.792808 | + | 0.609471i | \(0.791382\pi\) | |||||||
\(542\) | −31.2301 | + | 28.7219i | −1.34145 | + | 1.23371i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −33.4449 | + | 21.7372i | −1.43394 | + | 0.931976i | ||||
\(545\) | 2.95992i | 0.126789i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.559026 | + | 0.559026i | −0.0239022 | + | 0.0239022i | −0.718957 | − | 0.695055i | \(-0.755380\pi\) |
0.695055 | + | 0.718957i | \(0.255380\pi\) | |||||||
\(548\) | −1.82700 | + | 21.7965i | −0.0780456 | + | 0.931100i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.05531 | + | 25.2243i | −0.0449986 | + | 1.07557i | ||||
\(551\) | 18.1643i | 0.773825i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.5781i | 0.747498i | ||||||||
\(554\) | 11.2476 | + | 0.470567i | 0.477865 | + | 0.0199925i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.36596 | − | 2.00000i | 0.100339 | − | 0.0848189i | ||||
\(557\) | 20.4287 | − | 20.4287i | 0.865591 | − | 0.865591i | −0.126390 | − | 0.991981i | \(-0.540339\pi\) |
0.991981 | + | 0.126390i | \(0.0403390\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.7455i | 0.665963i | ||||||||
\(560\) | −2.53906 | − | 3.57053i | −0.107295 | − | 0.150882i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.3934 | − | 12.3883i | −0.480600 | − | 0.522570i | ||||
\(563\) | 13.9682 | + | 13.9682i | 0.588689 | + | 0.588689i | 0.937276 | − | 0.348587i | \(-0.113339\pi\) |
−0.348587 | + | 0.937276i | \(0.613339\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.03029 | − | 1.03029i | 0.0433447 | − | 0.0433447i | ||||
\(566\) | 1.45361 | − | 34.7446i | 0.0610999 | − | 1.46042i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.76986 | − | 2.28063i | −0.0742618 | − | 0.0956932i | ||||
\(569\) | 21.3052 | 0.893159 | 0.446579 | − | 0.894744i | \(-0.352642\pi\) | ||||
0.446579 | + | 0.894744i | \(0.352642\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.3333 | − | 18.3333i | −0.767226 | − | 0.767226i | 0.210391 | − | 0.977617i | \(-0.432526\pi\) |
−0.977617 | + | 0.210391i | \(0.932526\pi\) | |||||||
\(572\) | 1.47338 | − | 17.5777i | 0.0616051 | − | 0.734962i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.97076 | − | 7.57951i | −0.290954 | − | 0.316362i | ||||
\(575\) | −7.20243 | −0.300362 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.57813 | 0.315482 | 0.157741 | − | 0.987481i | \(-0.449579\pi\) | ||||
0.157741 | + | 0.987481i | \(0.449579\pi\) | |||||||
\(578\) | 31.3245 | + | 34.0600i | 1.30293 | + | 1.41671i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.235679 | − | 2.81170i | 0.00978604 | − | 0.116750i | ||||
\(581\) | −12.9078 | − | 12.9078i | −0.535504 | − | 0.535504i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.0278 | −1.24362 | ||||||||
\(584\) | 7.08137 | + | 9.12499i | 0.293029 | + | 0.377595i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.430158 | − | 10.2817i | 0.0177696 | − | 0.424735i | ||||
\(587\) | −2.75279 | + | 2.75279i | −0.113620 | + | 0.113620i | −0.761631 | − | 0.648011i | \(-0.775601\pi\) |
0.648011 | + | 0.761631i | \(0.275601\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.4123 | + | 24.4123i | 1.00589 | + | 1.00589i | ||||
\(590\) | −3.37656 | − | 3.67143i | −0.139011 | − | 0.151150i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 36.5588 | − | 25.9976i | 1.50256 | − | 1.06849i | ||||
\(593\) | 11.3554i | 0.466312i | 0.972439 | + | 0.233156i | \(0.0749053\pi\) | ||||
−0.972439 | + | 0.233156i | \(0.925095\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.46128 | + | 5.46128i | −0.223890 | + | 0.223890i | ||||
\(596\) | −11.7089 | + | 9.89777i | −0.479614 | + | 0.405429i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.02786 | + | 0.210351i | 0.205604 | + | 0.00860189i | ||||
\(599\) | 25.8985i | 1.05819i | 0.848564 | + | 0.529093i | \(0.177468\pi\) | ||||
−0.848564 | + | 0.529093i | \(0.822532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15.9753i | − | 0.651648i | −0.945430 | − | 0.325824i | \(-0.894358\pi\) | ||
0.945430 | − | 0.325824i | \(-0.105642\pi\) | |||||||
\(602\) | −1.26348 | + | 30.2000i | −0.0514955 | + | 1.23086i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.43603 | − | 29.0623i | 0.0991206 | − | 1.18253i | ||||
\(605\) | 0.551992 | − | 0.551992i | 0.0224417 | − | 0.0224417i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.9745i | 0.648384i | 0.945991 | + | 0.324192i | \(0.105092\pi\) | ||||
−0.945991 | + | 0.324192i | \(0.894908\pi\) | |||||||
\(608\) | 23.8048 | + | 5.05052i | 0.965413 | + | 0.204825i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.98795 | + | 1.82829i | −0.0804898 | + | 0.0740253i | ||||
\(611\) | 12.1765 | + | 12.1765i | 0.492608 | + | 0.492608i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.2125 | + | 20.2125i | −0.816375 | + | 0.816375i | −0.985581 | − | 0.169206i | \(-0.945880\pi\) |
0.169206 | + | 0.985581i | \(0.445880\pi\) | |||||||
\(614\) | −29.8853 | − | 1.25031i | −1.20607 | − | 0.0504586i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.23646 | − | 33.5960i | 0.170692 | − | 1.35362i | ||||
\(617\) | 4.04523 | 0.162855 | 0.0814275 | − | 0.996679i | \(-0.474052\pi\) | ||||
0.0814275 | + | 0.996679i | \(0.474052\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.7472 | − | 20.7472i | −0.833901 | − | 0.833901i | 0.154147 | − | 0.988048i | \(-0.450737\pi\) |
−0.988048 | + | 0.154147i | \(0.950737\pi\) | |||||||
\(620\) | −3.46210 | − | 4.09560i | −0.139041 | − | 0.164483i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −17.5828 | + | 16.1707i | −0.705006 | + | 0.648384i | ||||
\(623\) | −7.73424 | −0.309866 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.3380 | −0.933520 | ||||||||
\(626\) | −1.47824 | + | 1.35952i | −0.0590824 | + | 0.0543373i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.0508 | + | 11.0321i | −0.520782 | + | 0.440230i | ||||
\(629\) | −55.9183 | − | 55.9183i | −2.22961 | − | 2.22961i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.0533 | −1.51488 | −0.757439 | − | 0.652906i | \(-0.773550\pi\) | ||||
−0.757439 | + | 0.652906i | \(0.773550\pi\) | |||||||
\(632\) | 9.29802 | + | 11.9813i | 0.369855 | + | 0.476592i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 46.6576 | + | 1.95202i | 1.85301 | + | 0.0775245i | ||||
\(635\) | 2.04732 | − | 2.04732i | 0.0812453 | − | 0.0812453i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.39923 | − | 6.39923i | −0.253547 | − | 0.253547i | ||||
\(638\) | 16.0512 | − | 14.7621i | 0.635474 | − | 0.584436i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.61928 | − | 1.09065i | −0.143065 | − | 0.0431116i | ||||
\(641\) | − | 27.3678i | − | 1.08096i | −0.841355 | − | 0.540482i | \(-0.818242\pi\) | ||
0.841355 | − | 0.540482i | \(-0.181758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.88438 | − | 8.88438i | 0.350366 | − | 0.350366i | −0.509880 | − | 0.860246i | \(-0.670310\pi\) |
0.860246 | + | 0.509880i | \(0.170310\pi\) | |||||||
\(644\) | 9.62659 | + | 0.806909i | 0.379341 | + | 0.0317967i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.79315 | − | 42.8603i | 0.0705505 | − | 1.68632i | ||||
\(647\) | − | 40.9923i | − | 1.61157i | −0.592206 | − | 0.805787i | \(-0.701743\pi\) | ||
0.592206 | − | 0.805787i | \(-0.298257\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 38.5517i | − | 1.51329i | ||||||
\(650\) | 16.6814 | + | 0.697900i | 0.654298 | + | 0.0273739i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.78219 | + | 6.84021i | 0.226448 | + | 0.267883i | ||||
\(653\) | 22.0952 | − | 22.0952i | 0.864652 | − | 0.864652i | −0.127222 | − | 0.991874i | \(-0.540606\pi\) |
0.991874 | + | 0.127222i | \(0.0406062\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.05416i | 0.275629i | ||||||||
\(656\) | −8.76052 | − | 1.47902i | −0.342041 | − | 0.0577460i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22.3775 | + | 24.3317i | 0.872366 | + | 0.948548i | ||||
\(659\) | −14.3943 | − | 14.3943i | −0.560722 | − | 0.560722i | 0.368790 | − | 0.929513i | \(-0.379772\pi\) |
−0.929513 | + | 0.368790i | \(0.879772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.1550 | + | 27.1550i | −1.05621 | + | 1.05621i | −0.0578847 | + | 0.998323i | \(0.518436\pi\) |
−0.998323 | + | 0.0578847i | \(0.981564\pi\) | |||||||
\(662\) | 0.247102 | − | 5.90629i | 0.00960389 | − | 0.229555i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.6256 | − | 1.97039i | −0.606391 | − | 0.0764660i | ||||
\(665\) | 4.71184 | 0.182717 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.39914 | + | 4.39914i | 0.170335 | + | 0.170335i | ||||
\(668\) | 30.9580 | + | 2.59493i | 1.19780 | + | 0.100401i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.31391 | + | 1.42865i | 0.0507607 | + | 0.0551935i | ||||
\(671\) | −20.8744 | −0.805847 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.8899 | 0.805247 | 0.402624 | − | 0.915366i | \(-0.368098\pi\) | ||||
0.402624 | + | 0.915366i | \(0.368098\pi\) | |||||||
\(674\) | 1.35058 | + | 1.46852i | 0.0520222 | + | 0.0565652i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.2846 | + | 1.19735i | 0.549408 | + | 0.0460518i | ||||
\(677\) | 19.2536 | + | 19.2536i | 0.739976 | + | 0.739976i | 0.972573 | − | 0.232597i | \(-0.0747223\pi\) |
−0.232597 | + | 0.972573i | \(0.574722\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.6913 | 1.25458 | ||||||||
\(680\) | −0.833673 | + | 6.61120i | −0.0319699 | + | 0.253528i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.73257 | − | 41.4122i | 0.0663434 | − | 1.58576i | ||||
\(683\) | 4.11387 | − | 4.11387i | 0.157413 | − | 0.157413i | −0.624006 | − | 0.781419i | \(-0.714496\pi\) |
0.781419 | + | 0.624006i | \(0.214496\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.58377 | + | 2.58377i | 0.0987207 | + | 0.0987207i | ||||
\(686\) | 10.2085 | + | 11.1000i | 0.389762 | + | 0.423799i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.1132 | + | 21.2528i | 0.576185 | + | 0.810254i | ||||
\(689\) | 19.8580i | 0.756530i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.2503 | − | 25.2503i | 0.960568 | − | 0.960568i | −0.0386833 | − | 0.999252i | \(-0.512316\pi\) |
0.999252 | + | 0.0386833i | \(0.0123164\pi\) | |||||||
\(692\) | −20.1908 | − | 23.8853i | −0.767541 | − | 0.907985i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.22908 | + | 0.260606i | 0.236453 | + | 0.00989248i | ||||
\(695\) | − | 0.517543i | − | 0.0196315i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.6618i | 0.593233i | ||||||||
\(698\) | 0.990382 | − | 23.6724i | 0.0374865 | − | 0.896012i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 31.9390 | + | 2.67716i | 1.20718 | + | 0.101187i | ||||
\(701\) | −5.51930 | + | 5.51930i | −0.208461 | + | 0.208461i | −0.803613 | − | 0.595152i | \(-0.797092\pi\) |
0.595152 | + | 0.803613i | \(0.297092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 48.2448i | 1.81959i | ||||||||
\(704\) | −14.8831 | − | 25.1401i | −0.560929 | − | 0.947503i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.52314 | − | 5.07955i | 0.207866 | − | 0.191172i | ||||
\(707\) | −8.69188 | − | 8.69188i | −0.326892 | − | 0.326892i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.23948 | + | 5.23948i | −0.196773 | + | 0.196773i | −0.798615 | − | 0.601842i | \(-0.794434\pi\) |
0.601842 | + | 0.798615i | \(0.294434\pi\) | |||||||
\(710\) | −0.481838 | − | 0.0201587i | −0.0180830 | − | 0.000756542i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.27170 | + | 4.09105i | −0.197565 | + | 0.153319i | ||||
\(713\) | 11.8246 | 0.442837 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.08367 | − | 2.08367i | −0.0779250 | − | 0.0779250i | ||||
\(716\) | 8.31425 | − | 7.02823i | 0.310718 | − | 0.262657i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.5701 | + | 17.0786i | −0.693029 | + | 0.637369i | ||||
\(719\) | 36.4570 | 1.35962 | 0.679808 | − | 0.733390i | \(-0.262063\pi\) | ||||
0.679808 | + | 0.733390i | \(0.262063\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0836741 | −0.00311619 | ||||||||
\(722\) | 0.514691 | − | 0.473354i | 0.0191548 | − | 0.0176164i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.83750 | + | 9.27160i | 0.291278 | + | 0.344576i | ||||
\(725\) | 14.5954 | + | 14.5954i | 0.542060 | + | 0.542060i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.5790 | 1.17120 | 0.585600 | − | 0.810600i | \(-0.300859\pi\) | ||||
0.585600 | + | 0.810600i | \(0.300859\pi\) | |||||||
\(728\) | −22.2178 | − | 2.80166i | −0.823445 | − | 0.103837i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.92787 | + | 0.0806565i | 0.0713537 | + | 0.00298523i | ||||
\(731\) | 32.5070 | − | 32.5070i | 1.20232 | − | 1.20232i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.8720 | − | 10.8720i | −0.401565 | − | 0.401565i | 0.477219 | − | 0.878784i | \(-0.341645\pi\) |
−0.878784 | + | 0.477219i | \(0.841645\pi\) | |||||||
\(734\) | −2.14238 | + | 1.97032i | −0.0790768 | + | 0.0727258i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.98836 | − | 4.54203i | 0.257594 | − | 0.167421i | ||||
\(737\) | 15.0015i | 0.552586i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.2774 | + | 34.2774i | −1.26092 | + | 1.26092i | −0.310265 | + | 0.950650i | \(0.600418\pi\) |
−0.950650 | + | 0.310265i | \(0.899582\pi\) | |||||||
\(740\) | 0.625969 | − | 7.46794i | 0.0230111 | − | 0.274527i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.59348 | + | 38.0878i | −0.0584986 | + | 1.39825i | ||||
\(743\) | − | 16.5900i | − | 0.608629i | −0.952572 | − | 0.304314i | \(-0.901573\pi\) | ||
0.952572 | − | 0.304314i | \(-0.0984273\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.56126i | 0.0938374i | ||||||||
\(746\) | −25.5558 | − | 1.06918i | −0.935663 | − | 0.0391454i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −39.3316 | + | 33.2479i | −1.43811 | + | 1.21566i | ||||
\(749\) | −38.5739 | + | 38.5739i | −1.40946 | + | 1.40946i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 14.8054i | − | 0.540256i | −0.962824 | − | 0.270128i | \(-0.912934\pi\) | ||
0.962824 | − | 0.270128i | \(-0.0870660\pi\) | |||||||
\(752\) | 28.1230 | + | 4.74794i | 1.02554 | + | 0.173140i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.76248 | − | 10.6150i | −0.355529 | − | 0.386576i | ||||
\(755\) | −3.44506 | − | 3.44506i | −0.125379 | − | 0.125379i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.8209 | − | 32.8209i | 1.19290 | − | 1.19290i | 0.216646 | − | 0.976250i | \(-0.430488\pi\) |
0.976250 | − | 0.216646i | \(-0.0695118\pi\) | |||||||
\(758\) | 0.565772 | − | 13.5232i | 0.0205498 | − | 0.491186i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.21162 | − | 2.49235i | 0.116498 | − | 0.0904069i | ||||
\(761\) | −42.5206 | −1.54137 | −0.770685 | − | 0.637217i | \(-0.780086\pi\) | ||||
−0.770685 | + | 0.637217i | \(0.780086\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.5363 | + | 20.5363i | 0.743464 | + | 0.743464i | ||||
\(764\) | −4.14394 | + | 49.4380i | −0.149922 | + | 1.78861i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.16278 | − | 7.78828i | −0.258802 | − | 0.281402i | ||||
\(767\) | −25.4951 | −0.920575 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.9146 | 0.826321 | 0.413160 | − | 0.910658i | \(-0.364425\pi\) | ||||
0.413160 | + | 0.910658i | \(0.364425\pi\) | |||||||
\(770\) | −3.82930 | − | 4.16371i | −0.137998 | − | 0.150050i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.35043 | − | 16.1109i | 0.0486029 | − | 0.579842i | ||||
\(773\) | 15.8155 | + | 15.8155i | 0.568845 | + | 0.568845i | 0.931805 | − | 0.362960i | \(-0.118234\pi\) |
−0.362960 | + | 0.931805i | \(0.618234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.2317 | 1.40925 | ||||||||
\(776\) | 22.2826 | − | 17.2922i | 0.799898 | − | 0.620754i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.73205 | + | 41.3999i | −0.0620970 | + | 1.48426i | ||||
\(779\) | 6.75629 | − | 6.75629i | 0.242069 | − | 0.242069i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.63560 | − | 2.63560i | −0.0943091 | − | 0.0943091i | ||||
\(782\) | −9.94589 | − | 10.8144i | −0.355664 | − | 0.386724i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14.7798 | − | 2.49523i | −0.527848 | − | 0.0891155i | ||||
\(785\) | 2.85480i | 0.101892i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.8790 | − | 18.8790i | 0.672962 | − | 0.672962i | −0.285436 | − | 0.958398i | \(-0.592138\pi\) |
0.958398 | + | 0.285436i | \(0.0921382\pi\) | |||||||
\(788\) | −15.8623 | + | 13.4087i | −0.565070 | + | 0.477667i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.53135 | + | 0.105904i | 0.0900612 | + | 0.00376790i | ||||
\(791\) | − | 14.2966i | − | 0.508327i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.8047i | 0.490219i | ||||||||
\(794\) | 1.04664 | − | 25.0170i | 0.0371437 | − | 0.887819i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.92993 | + | 23.0245i | −0.0684046 | + | 0.816081i | ||||
\(797\) | 15.5930 | − | 15.5930i | 0.552332 | − | 0.552332i | −0.374781 | − | 0.927113i | \(-0.622282\pi\) |
0.927113 | + | 0.374781i | \(0.122282\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 50.2774i | − | 1.77869i | ||||||
\(800\) | 23.1859 | − | 15.0695i | 0.819746 | − | 0.532788i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.9639 | − | 11.0031i | 0.422461 | − | 0.388532i | ||||
\(803\) | 10.5452 | + | 10.5452i | 0.372133 | + | 0.372133i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.14114 | − | 1.14114i | 0.0402200 | − | 0.0402200i | ||||
\(806\) | −27.3868 | − | 1.14578i | −0.964660 | − | 0.0403585i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.5220 | − | 1.32683i | −0.370164 | − | 0.0466777i | ||||
\(809\) | 14.7494 | 0.518563 | 0.259281 | − | 0.965802i | \(-0.416514\pi\) | ||||
0.259281 | + | 0.965802i | \(0.416514\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.71473 | + | 9.71473i | 0.341130 | + | 0.341130i | 0.856792 | − | 0.515662i | \(-0.172454\pi\) |
−0.515662 | + | 0.856792i | \(0.672454\pi\) | |||||||
\(812\) | −17.8727 | − | 21.1431i | −0.627210 | − | 0.741976i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 42.6324 | − | 39.2084i | 1.49426 | − | 1.37425i | ||||
\(815\) | 1.49627 | 0.0524119 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.0462 | −0.981212 | ||||||||
\(818\) | −24.1945 | + | 22.2513i | −0.845941 | + | 0.778000i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.13349 | + | 0.958163i | −0.0395831 | + | 0.0334605i | ||||
\(821\) | −10.2311 | − | 10.2311i | −0.357070 | − | 0.357070i | 0.505662 | − | 0.862732i | \(-0.331248\pi\) |
−0.862732 | + | 0.505662i | \(0.831248\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.8564 | −0.796725 | −0.398362 | − | 0.917228i | \(-0.630421\pi\) | ||||
−0.398362 | + | 0.917228i | \(0.630421\pi\) | |||||||
\(824\) | −0.0570327 | + | 0.0442597i | −0.00198683 | + | 0.00154186i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −48.8998 | − | 2.04582i | −1.70144 | − | 0.0711834i | ||||
\(827\) | −19.1488 | + | 19.1488i | −0.665871 | + | 0.665871i | −0.956757 | − | 0.290887i | \(-0.906050\pi\) |
0.290887 | + | 0.956757i | \(0.406050\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.8813 | − | 32.8813i | −1.14201 | − | 1.14201i | −0.988081 | − | 0.153934i | \(-0.950806\pi\) |
−0.153934 | − | 0.988081i | \(-0.549194\pi\) | |||||||
\(830\) | −1.93655 | + | 1.78102i | −0.0672187 | + | 0.0618201i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16.6257 | + | 9.84254i | −0.576393 | + | 0.341229i | ||||
\(833\) | 26.4228i | 0.915497i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.66978 | − | 3.66978i | 0.126998 | − | 0.126998i | ||||
\(836\) | 31.3098 | + | 2.62442i | 1.08287 | + | 0.0907673i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.76771 | − | 42.2522i | 0.0610644 | − | 1.45958i | ||||
\(839\) | 41.2084i | 1.42267i | 0.702853 | + | 0.711335i | \(0.251909\pi\) | ||||
−0.702853 | + | 0.711335i | \(0.748091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.1707i | 0.385195i | ||||||||
\(842\) | −19.1847 | − | 0.802634i | −0.661150 | − | 0.0276606i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.49912 | + | 1.77343i | 0.0516020 | + | 0.0610441i | ||||
\(845\) | 1.69331 | − | 1.69331i | 0.0582515 | − | 0.0582515i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.65957i | − | 0.263186i | ||||||
\(848\) | 19.0606 | + | 26.8038i | 0.654543 | + | 0.920445i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −32.9984 | − | 35.8801i | −1.13184 | − | 1.23068i | ||||
\(851\) | 11.6842 | + | 11.6842i | 0.400530 | + | 0.400530i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.3985 | + | 16.3985i | −0.561472 | + | 0.561472i | −0.929726 | − | 0.368253i | \(-0.879956\pi\) |
0.368253 | + | 0.929726i | \(0.379956\pi\) | |||||||
\(854\) | −1.10774 | + | 26.4775i | −0.0379061 | + | 0.906042i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.88837 | + | 46.6960i | −0.201260 | + | 1.59604i | ||||
\(857\) | −3.15292 | −0.107702 | −0.0538509 | − | 0.998549i | \(-0.517150\pi\) | ||||
−0.0538509 | + | 0.998549i | \(0.517150\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.6691 | + | 14.6691i | 0.500503 | + | 0.500503i | 0.911594 | − | 0.411091i | \(-0.134852\pi\) |
−0.411091 | + | 0.911594i | \(0.634852\pi\) | |||||||
\(860\) | 4.34134 | + | 0.363895i | 0.148039 | + | 0.0124087i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.4994 | + | 19.0276i | 0.596032 | + | 0.648082i | ||||
\(863\) | 42.0851 | 1.43259 | 0.716297 | − | 0.697795i | \(-0.245836\pi\) | ||||
0.716297 | + | 0.697795i | \(0.245836\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.22482 | −0.177649 | ||||||||
\(866\) | −32.9170 | − | 35.7916i | −1.11857 | − | 1.21625i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −52.4362 | − | 4.39525i | −1.77980 | − | 0.149184i | ||||
\(869\) | 13.8462 | + | 13.8462i | 0.469699 | + | 0.469699i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.92080 | 0.336154 | ||||||||
\(872\) | 24.8604 | + | 3.13490i | 0.841879 | + | 0.106161i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.374681 | + | 8.95573i | −0.0126738 | + | 0.302932i | ||||
\(875\) | 7.65860 | − | 7.65860i | 0.258908 | − | 0.258908i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.42641 | − | 2.42641i | −0.0819341 | − | 0.0819341i | 0.664952 | − | 0.746886i | \(-0.268452\pi\) |
−0.746886 | + | 0.664952i | \(0.768452\pi\) | |||||||
\(878\) | −14.5239 | − | 15.7922i | −0.490158 | − | 0.532962i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.81248 | − | 0.812481i | −0.162229 | − | 0.0273887i | ||||
\(881\) | 32.2178i | 1.08544i | 0.839912 | + | 0.542722i | \(0.182606\pi\) | ||||
−0.839912 | + | 0.542722i | \(0.817394\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.924984 | − | 0.924984i | 0.0311282 | − | 0.0311282i | −0.691371 | − | 0.722500i | \(-0.742993\pi\) |
0.722500 | + | 0.691371i | \(0.242993\pi\) | |||||||
\(884\) | 21.9876 | + | 26.0108i | 0.739522 | + | 0.874839i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −36.3638 | − | 1.52135i | −1.22167 | − | 0.0511109i | ||||
\(887\) | − | 17.9482i | − | 0.602643i | −0.953523 | − | 0.301321i | \(-0.902572\pi\) | ||
0.953523 | − | 0.301321i | \(-0.0974277\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 28.4090i | − | 0.952808i | ||||||
\(890\) | −0.0465969 | + | 1.11377i | −0.00156193 | + | 0.0373337i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.6010 | − | 1.64298i | −0.656291 | − | 0.0550109i | ||||
\(893\) | −21.6890 | + | 21.6890i | −0.725795 | + | 0.725795i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.81871i | − | 0.0607926i | ||||||
\(896\) | −32.6780 | + | 17.5440i | −1.09170 | + | 0.586103i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.25923 | + | 8.51558i | −0.308984 | + | 0.284169i | ||||
\(899\) | −23.9622 | − | 23.9622i | −0.799183 | − | 0.799183i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.9975 | − | 40.9975i | 1.36582 | − | 1.36582i | ||||
\(902\) | −11.4611 | − | 0.479501i | −0.381614 | − | 0.0159656i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.56222 | − | 9.74462i | −0.251516 | − | 0.324101i | ||||
\(905\) | 2.02812 | 0.0674171 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.2503 | − | 17.2503i | −0.572788 | − | 0.572788i | 0.360118 | − | 0.932907i | \(-0.382736\pi\) |
−0.932907 | + | 0.360118i | \(0.882736\pi\) | |||||||
\(908\) | 33.8358 | − | 28.6022i | 1.12288 | − | 0.949198i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.75355 | + | 2.53240i | −0.0912793 | + | 0.0839483i | ||||
\(911\) | 19.5368 | 0.647282 | 0.323641 | − | 0.946180i | \(-0.395093\pi\) | ||||
0.323641 | + | 0.946180i | \(0.395093\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.3347 | −0.672980 | ||||||||
\(914\) | 11.7713 | − | 10.8259i | 0.389360 | − | 0.358089i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.9701 | + | 24.8072i | 0.692872 | + | 0.819653i | ||||
\(917\) | 48.9426 | + | 48.9426i | 1.61623 | + | 1.61623i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.9943 | 0.527602 | 0.263801 | − | 0.964577i | \(-0.415024\pi\) | ||||
0.263801 | + | 0.964577i | \(0.415024\pi\) | |||||||
\(920\) | 0.174197 | − | 1.38142i | 0.00574311 | − | 0.0455441i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21.7038 | − | 0.908023i | −0.714776 | − | 0.0299041i | ||||
\(923\) | −1.74298 | + | 1.74298i | −0.0573708 | + | 0.0573708i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.7658 | + | 38.7658i | 1.27461 | + | 1.27461i | ||||
\(926\) | 3.18007 | − | 2.92466i | 0.104503 | − | 0.0961104i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −23.3659 | − | 4.95738i | −0.767022 | − | 0.162734i | ||||
\(929\) | − | 1.11164i | − | 0.0364717i | −0.999834 | − | 0.0182358i | \(-0.994195\pi\) | ||
0.999834 | − | 0.0182358i | \(-0.00580497\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.3985 | − | 11.3985i | 0.373569 | − | 0.373569i | ||||
\(932\) | 3.82545 | − | 45.6384i | 0.125307 | − | 1.49493i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.329165 | + | 7.86779i | −0.0107706 | + | 0.257442i | ||||
\(935\) | 8.60361i | 0.281368i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 17.7208i | − | 0.578914i | −0.957191 | − | 0.289457i | \(-0.906525\pi\) | ||
0.957191 | − | 0.289457i | \(-0.0934747\pi\) | |||||||
\(938\) | 19.0282 | + | 0.796083i | 0.621292 | + | 0.0259930i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.63871 | − | 3.07589i | 0.118682 | − | 0.100324i | ||||
\(941\) | −30.8171 | + | 30.8171i | −1.00461 | + | 1.00461i | −0.00462076 | + | 0.999989i | \(0.501471\pi\) |
−0.999989 | + | 0.00462076i | \(0.998529\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 3.27256i | − | 0.106569i | ||||||
\(944\) | −34.4125 | + | 24.4713i | −1.12003 | + | 0.796473i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.7931 | + | 24.7835i | 0.741066 | + | 0.805782i | ||||
\(947\) | −16.6327 | − | 16.6327i | −0.540491 | − | 0.540491i | 0.383182 | − | 0.923673i | \(-0.374828\pi\) |
−0.923673 | + | 0.383182i | \(0.874828\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.97379 | − | 6.97379i | 0.226379 | − | 0.226379i | ||||
\(950\) | −1.24312 | + | 29.7133i | −0.0403320 | + | 0.964025i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 40.0851 | + | 51.6534i | 1.29917 | + | 1.67410i | ||||
\(953\) | −14.5520 | −0.471387 | −0.235693 | − | 0.971827i | \(-0.575736\pi\) | ||||
−0.235693 | + | 0.971827i | \(0.575736\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.86041 | + | 5.86041i | 0.189639 | + | 0.189639i | ||||
\(956\) | −0.252167 | + | 3.00840i | −0.00815566 | + | 0.0972987i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.4382 | − | 28.7470i | −0.854178 | − | 0.928772i | ||||
\(959\) | 35.8530 | 1.15775 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −33.4090 | −1.07771 | ||||||||
\(962\) | −25.9294 | − | 28.1937i | −0.835997 | − | 0.909002i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.23957 | − | 38.6488i | 0.104340 | − | 1.24479i | ||||
\(965\) | −1.90979 | − | 1.90979i | −0.0614783 | − | 0.0614783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.3884 | −0.559172 | −0.279586 | − | 0.960121i | \(-0.590197\pi\) | ||||
−0.279586 | + | 0.960121i | \(0.590197\pi\) | |||||||
\(968\) | −4.05156 | − | 5.22080i | −0.130222 | − | 0.167803i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.196957 | − | 4.70773i | 0.00632392 | − | 0.151156i | ||||
\(971\) | −20.2644 | + | 20.2644i | −0.650314 | + | 0.650314i | −0.953069 | − | 0.302754i | \(-0.902094\pi\) |
0.302754 | + | 0.953069i | \(0.402094\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.59077 | − | 3.59077i | −0.115115 | − | 0.115115i | ||||
\(974\) | −12.5202 | − | 13.6136i | −0.401173 | − | 0.436207i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.2503 | + | 18.6332i | 0.424133 | + | 0.596433i | ||||
\(977\) | − | 35.3026i | − | 1.12943i | −0.825285 | − | 0.564716i | \(-0.808986\pi\) | ||
0.825285 | − | 0.564716i | \(-0.191014\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.09220 | + | 6.09220i | −0.194708 | + | 0.194708i | ||||
\(980\) | −1.91229 | + | 1.61650i | −0.0610859 | + | 0.0516373i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 43.6355 | + | 1.82558i | 1.39246 | + | 0.0582566i | ||||
\(983\) | − | 51.7381i | − | 1.65019i | −0.564995 | − | 0.825094i | \(-0.691122\pi\) | ||
0.564995 | − | 0.825094i | \(-0.308878\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.46980i | 0.110557i | ||||||||
\(986\) | −1.76008 | + | 42.0700i | −0.0560525 | + | 1.33978i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.73558 | − | 20.7059i | 0.0552163 | − | 0.658742i | ||||
\(989\) | −6.79239 | + | 6.79239i | −0.215985 | + | 0.215985i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.0317i | 0.795160i | 0.917568 | + | 0.397580i | \(0.130150\pi\) | ||||
−0.917568 | + | 0.397580i | \(0.869850\pi\) | |||||||
\(992\) | −38.0657 | + | 24.7405i | −1.20859 | + | 0.785512i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.48291 | + | 3.20318i | −0.110471 | + | 0.101599i | ||||
\(995\) | 2.72933 | + | 2.72933i | 0.0865257 | + | 0.0865257i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.3224 | + | 17.3224i | −0.548605 | + | 0.548605i | −0.926037 | − | 0.377432i | \(-0.876807\pi\) |
0.377432 | + | 0.926037i | \(0.376807\pi\) | |||||||
\(998\) | 32.8053 | + | 1.37248i | 1.03843 | + | 0.0434450i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 144.2.l.a.35.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 144.2.l.a.35.6 | yes | 16 | |
4.3 | odd | 2 | 576.2.l.a.431.5 | 16 | |||
8.3 | odd | 2 | 1152.2.l.b.863.4 | 16 | |||
8.5 | even | 2 | 1152.2.l.a.863.4 | 16 | |||
12.11 | even | 2 | 576.2.l.a.431.4 | 16 | |||
16.3 | odd | 4 | 1152.2.l.a.287.5 | 16 | |||
16.5 | even | 4 | 576.2.l.a.143.4 | 16 | |||
16.11 | odd | 4 | inner | 144.2.l.a.107.6 | yes | 16 | |
16.13 | even | 4 | 1152.2.l.b.287.5 | 16 | |||
24.5 | odd | 2 | 1152.2.l.a.863.5 | 16 | |||
24.11 | even | 2 | 1152.2.l.b.863.5 | 16 | |||
48.5 | odd | 4 | 576.2.l.a.143.5 | 16 | |||
48.11 | even | 4 | inner | 144.2.l.a.107.3 | yes | 16 | |
48.29 | odd | 4 | 1152.2.l.b.287.4 | 16 | |||
48.35 | even | 4 | 1152.2.l.a.287.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.l.a.35.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
144.2.l.a.35.6 | yes | 16 | 3.2 | odd | 2 | inner | |
144.2.l.a.107.3 | yes | 16 | 48.11 | even | 4 | inner | |
144.2.l.a.107.6 | yes | 16 | 16.11 | odd | 4 | inner | |
576.2.l.a.143.4 | 16 | 16.5 | even | 4 | |||
576.2.l.a.143.5 | 16 | 48.5 | odd | 4 | |||
576.2.l.a.431.4 | 16 | 12.11 | even | 2 | |||
576.2.l.a.431.5 | 16 | 4.3 | odd | 2 | |||
1152.2.l.a.287.4 | 16 | 48.35 | even | 4 | |||
1152.2.l.a.287.5 | 16 | 16.3 | odd | 4 | |||
1152.2.l.a.863.4 | 16 | 8.5 | even | 2 | |||
1152.2.l.a.863.5 | 16 | 24.5 | odd | 2 | |||
1152.2.l.b.287.4 | 16 | 48.29 | odd | 4 | |||
1152.2.l.b.287.5 | 16 | 16.13 | even | 4 | |||
1152.2.l.b.863.4 | 16 | 8.3 | odd | 2 | |||
1152.2.l.b.863.5 | 16 | 24.11 | even | 2 |