Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(17,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(44))
chi = DirichletCharacter(H, H._module([0, 0, 11, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("920.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.bv (of order \(44\), degree \(20\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(720\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{44})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{44}]$ |
Embedding invariants
Embedding label | 17.12 | ||
Character | \(\chi\) | \(=\) | 920.17 |
Dual form | 920.2.bv.a.433.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(281\) | \(461\) | \(737\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{7}{22}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.21475 | + | 0.663302i | −0.701334 | + | 0.382957i | −0.790002 | − | 0.613104i | \(-0.789921\pi\) |
0.0886682 | + | 0.996061i | \(0.471739\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.933470 | − | 2.03190i | 0.417460 | − | 0.908695i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.205002 | − | 0.273851i | −0.0774835 | − | 0.103506i | 0.760125 | − | 0.649777i | \(-0.225138\pi\) |
−0.837608 | + | 0.546271i | \(0.816047\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.586283 | + | 0.912274i | −0.195428 | + | 0.304091i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.437876 | − | 0.199971i | 0.132024 | − | 0.0602935i | −0.348307 | − | 0.937380i | \(-0.613243\pi\) |
0.480332 | + | 0.877087i | \(0.340516\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.45611 | − | 1.09003i | −0.403852 | − | 0.302320i | 0.377974 | − | 0.925816i | \(-0.376621\pi\) |
−0.781826 | + | 0.623496i | \(0.785712\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.213837 | + | 3.08742i | 0.0552124 | + | 0.797169i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.429113 | − | 5.99978i | −0.104075 | − | 1.45516i | −0.734341 | − | 0.678781i | \(-0.762509\pi\) |
0.630266 | − | 0.776379i | \(-0.282946\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.24436 | + | 2.59013i | 0.514892 | + | 0.594217i | 0.952345 | − | 0.305024i | \(-0.0986646\pi\) |
−0.437452 | + | 0.899242i | \(0.644119\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.430671 | + | 0.196681i | 0.0939802 | + | 0.0429193i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.77197 | + | 0.477794i | 0.995025 | + | 0.0996270i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.25727 | − | 3.79344i | −0.651454 | − | 0.758688i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.403282 | − | 5.63862i | 0.0776116 | − | 1.08515i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.06351 | − | 6.12056i | −1.31166 | − | 1.13656i | −0.981253 | − | 0.192722i | \(-0.938268\pi\) |
−0.330407 | − | 0.943838i | \(-0.607186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.81071 | + | 2.58706i | −1.58245 | + | 0.464649i | −0.950594 | − | 0.310436i | \(-0.899525\pi\) |
−0.631856 | + | 0.775086i | \(0.717707\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.399267 | + | 0.533358i | −0.0695034 | + | 0.0928457i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.747802 | + | 0.160913i | −0.126402 | + | 0.0271993i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.51781 | − | 0.982790i | 0.742724 | − | 0.161570i | 0.174746 | − | 0.984614i | \(-0.444090\pi\) |
0.567978 | + | 0.823044i | \(0.307726\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.49182 | + | 0.358270i | 0.399011 | + | 0.0573691i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.19934 | + | 3.34142i | −0.812001 | + | 0.521841i | −0.879512 | − | 0.475877i | \(-0.842131\pi\) |
0.0675106 | + | 0.997719i | \(0.478494\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.67559 | + | 4.89997i | 0.408023 | + | 0.747239i | 0.998196 | − | 0.0600382i | \(-0.0191223\pi\) |
−0.590173 | + | 0.807277i | \(0.700940\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.30638 | + | 2.04285i | 0.194743 | + | 0.304530i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.66836 | − | 6.66836i | −0.972680 | − | 0.972680i | 0.0269569 | − | 0.999637i | \(-0.491418\pi\) |
−0.999637 | + | 0.0269569i | \(0.991418\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.93916 | − | 6.60417i | 0.277023 | − | 0.943453i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.50093 | + | 7.00358i | 0.630256 | + | 0.980697i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.8030 | − | 8.08702i | 1.48390 | − | 1.11084i | 0.516911 | − | 0.856039i | \(-0.327082\pi\) |
0.966994 | − | 0.254798i | \(-0.0820089\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.00242150 | − | 1.07639i | 0.000326515 | − | 0.145140i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.44437 | − | 1.65766i | −0.588671 | − | 0.219563i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.21327 | + | 0.749555i | −0.678710 | + | 0.0975838i | −0.473045 | − | 0.881039i | \(-0.656845\pi\) |
−0.205666 | + | 0.978622i | \(0.565936\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.23334 | − | 14.4174i | −0.542024 | − | 1.84596i | −0.533177 | − | 0.846004i | \(-0.679002\pi\) |
−0.00884702 | − | 0.999961i | \(-0.502816\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.370016 | − | 0.0264641i | 0.0466177 | − | 0.00333416i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.57407 | + | 1.94117i | −0.443309 | + | 0.240772i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.35479 | − | 6.31343i | −0.287683 | − | 0.771308i | −0.997742 | − | 0.0671659i | \(-0.978604\pi\) |
0.710059 | − | 0.704143i | \(-0.248668\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.11366 | + | 2.58486i | −0.735998 | + | 0.311180i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.71261 | − | 12.5089i | 0.677962 | − | 1.48453i | −0.186827 | − | 0.982393i | \(-0.559820\pi\) |
0.864789 | − | 0.502136i | \(-0.167452\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.25371 | + | 0.232710i | 0.380818 | + | 0.0272367i | 0.260436 | − | 0.965491i | \(-0.416134\pi\) |
0.120382 | + | 0.992728i | \(0.461588\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.47295 | + | 2.44752i | 0.747432 | + | 0.282615i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.144528 | − | 0.0789181i | −0.0164705 | − | 0.00899355i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00791 | − | 7.01019i | −0.113399 | − | 0.788708i | −0.964571 | − | 0.263822i | \(-0.915017\pi\) |
0.851172 | − | 0.524886i | \(-0.175892\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.89876 | + | 4.15771i | 0.210974 | + | 0.461968i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.64364 | + | 7.55568i | 0.180413 | + | 0.829344i | 0.975002 | + | 0.222196i | \(0.0713226\pi\) |
−0.794589 | + | 0.607147i | \(0.792314\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.5915 | − | 4.72870i | −1.36574 | − | 0.512899i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.6402 | + | 2.74970i | 1.35517 | + | 0.294798i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.505952 | + | 0.148561i | 0.0536308 | + | 0.0157474i | 0.308438 | − | 0.951244i | \(-0.400194\pi\) |
−0.254807 | + | 0.966992i | \(0.582012\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.622215i | 0.0652259i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.98678 | − | 8.98678i | 0.931885 | − | 0.931885i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.35795 | − | 2.14252i | 0.754909 | − | 0.219818i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.554245 | + | 2.54782i | −0.0562750 | + | 0.258692i | −0.996686 | − | 0.0813487i | \(-0.974077\pi\) |
0.940411 | + | 0.340041i | \(0.110441\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.0742905 | + | 0.516702i | −0.00746648 | + | 0.0519305i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8433 | + | 8.89658i | 1.37746 | + | 0.885243i | 0.999182 | − | 0.0404471i | \(-0.0128782\pi\) |
0.378283 | + | 0.925690i | \(0.376515\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.44225 | + | 11.9101i | −0.437708 | + | 1.17354i | 0.511609 | + | 0.859218i | \(0.329050\pi\) |
−0.949317 | + | 0.314321i | \(0.898223\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.801656 | − | 0.691487i | 0.0782336 | − | 0.0674822i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.07858 | − | 11.1321i | 0.587638 | − | 1.07618i | −0.399564 | − | 0.916705i | \(-0.630838\pi\) |
0.987202 | − | 0.159474i | \(-0.0509798\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.75520 | + | 5.48779i | −0.455465 | + | 0.525635i | −0.936312 | − | 0.351170i | \(-0.885784\pi\) |
0.480847 | + | 0.876805i | \(0.340329\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.83611 | + | 4.19051i | −0.459023 | + | 0.397746i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.5184 | + | 3.92314i | −0.989483 | + | 0.369058i | −0.791515 | − | 0.611150i | \(-0.790707\pi\) |
−0.197969 | + | 0.980208i | \(0.563434\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.42532 | − | 9.25018i | 0.505914 | − | 0.862584i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.84810 | − | 0.689305i | 0.170857 | − | 0.0637262i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.55508 | + | 1.34748i | −0.142554 | + | 0.123523i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.05172 | + | 8.13812i | −0.641066 | + | 0.739829i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.09952 | − | 7.50771i | 0.369641 | − | 0.676947i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.7485 | + | 3.07740i | −0.961373 | + | 0.275251i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.79731 | − | 10.1810i | 0.336957 | − | 0.903417i | −0.652396 | − | 0.757879i | \(-0.726236\pi\) |
0.989353 | − | 0.145538i | \(-0.0464914\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.50032 | − | 4.17750i | −0.572321 | − | 0.367808i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.730718 | + | 5.08226i | −0.0638432 | + | 0.444039i | 0.932679 | + | 0.360708i | \(0.117465\pi\) |
−0.996522 | + | 0.0833309i | \(0.973444\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.249211 | − | 1.14560i | 0.0216093 | − | 0.0993364i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.0807 | − | 6.08291i | −0.953673 | − | 0.523533i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.18289 | − | 5.18289i | 0.442804 | − | 0.442804i | −0.450149 | − | 0.892953i | \(-0.648629\pi\) |
0.892953 | + | 0.450149i | \(0.148629\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.3063i | 1.72236i | 0.508302 | + | 0.861179i | \(0.330273\pi\) | ||||
−0.508302 | + | 0.861179i | \(0.669727\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.5235 | + | 3.67723i | 1.05467 | + | 0.309679i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.855569 | − | 0.186118i | −0.0715463 | − | 0.0155639i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.0300 | + | 8.63901i | −1.58035 | + | 0.717431i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.02497 | + | 9.30864i | 0.167017 | + | 0.767764i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.20474 | + | 15.7762i | 0.590235 | + | 1.29243i | 0.935300 | + | 0.353856i | \(0.115130\pi\) |
−0.345065 | + | 0.938579i | \(0.612143\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.43401 | + | 9.97378i | 0.116698 | + | 0.811655i | 0.961151 | + | 0.276024i | \(0.0890170\pi\) |
−0.844452 | + | 0.535631i | \(0.820074\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.72502 | + | 3.12610i | 0.462841 | + | 0.252730i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.96788 | + | 20.3175i | −0.238386 | + | 1.63194i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.7521 | + | 0.983567i | 1.09753 | + | 0.0784972i | 0.608339 | − | 0.793677i | \(-0.291836\pi\) |
0.489195 | + | 0.872174i | \(0.337291\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.75876 | + | 16.9893i | −0.615310 | + | 1.34734i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.847420 | − | 1.40476i | −0.0667861 | − | 0.110710i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.606290 | − | 1.62553i | −0.0474883 | − | 0.127321i | 0.911040 | − | 0.412317i | \(-0.135280\pi\) |
−0.958529 | + | 0.284996i | \(0.908008\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.711029 | + | 1.30914i | 0.0553535 | + | 0.101917i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.50157 | + | 0.679565i | −0.735253 | + | 0.0525863i | −0.433944 | − | 0.900940i | \(-0.642878\pi\) |
−0.301310 | + | 0.953526i | \(0.597424\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.73043 | − | 9.29900i | −0.210033 | − | 0.715308i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.67874 | + | 0.528923i | −0.281320 | + | 0.0404478i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.0778291 | + | 0.0290287i | 0.00591723 | + | 0.00220701i | 0.352421 | − | 0.935842i | \(-0.385359\pi\) |
−0.346504 | + | 0.938049i | \(0.612631\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.371090 | + | 1.66967i | −0.0280518 | + | 0.126215i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.83562 | − | 4.36849i | 0.438632 | − | 0.328356i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.07713 | + | 6.34413i | 0.304739 | + | 0.474183i | 0.959522 | − | 0.281634i | \(-0.0908764\pi\) |
−0.654783 | + | 0.755817i | \(0.727240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.155884 | − | 0.530891i | 0.0115867 | − | 0.0394608i | −0.953497 | − | 0.301403i | \(-0.902545\pi\) |
0.965083 | + | 0.261943i | \(0.0843631\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.7056 | + | 14.7056i | 1.08707 | + | 1.08707i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.22031 | − | 10.0972i | 0.163240 | − | 0.742359i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.38768 | − | 2.54135i | −0.101477 | − | 0.185842i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.62681 | + | 1.04549i | −0.118333 | + | 0.0760482i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.89106 | − | 0.990785i | −0.498619 | − | 0.0716907i | −0.111583 | − | 0.993755i | \(-0.535592\pi\) |
−0.387036 | + | 0.922064i | \(0.626501\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.6814 | + | 2.97621i | −0.984808 | + | 0.214232i | −0.676007 | − | 0.736895i | \(-0.736291\pi\) |
−0.308801 | + | 0.951127i | \(0.599928\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.05401 | − | 4.72871i | 0.218702 | − | 0.338630i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.28101 | + | 7.05460i | −0.376256 | + | 0.502619i | −0.948200 | − | 0.317673i | \(-0.897099\pi\) |
0.571944 | + | 0.820293i | \(0.306189\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.6566 | + | 4.89080i | −1.18075 | + | 0.346700i | −0.812464 | − | 0.583012i | \(-0.801874\pi\) |
−0.368288 | + | 0.929712i | \(0.620056\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.04818 | + | 6.10728i | 0.497140 | + | 0.430775i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.228087 | + | 3.18908i | −0.0160086 | + | 0.223829i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.93601 | + | 13.6837i | 0.135217 | + | 0.955710i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.23360 | + | 4.07322i | −0.224751 | + | 0.283109i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.50070 | + | 0.685348i | 0.103806 | + | 0.0474065i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.14939 | − | 4.78865i | −0.285656 | − | 0.329664i | 0.594727 | − | 0.803927i | \(-0.297260\pi\) |
−0.880383 | + | 0.474263i | \(0.842715\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.35778 | + | 18.9843i | 0.0930337 | + | 1.30078i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.4539 | − | 0.862561i | 0.849346 | − | 0.0588262i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.51468 | + | 1.88247i | 0.170708 | + | 0.127790i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.10679 | + | 1.87551i | −0.277511 | + | 0.126735i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.91510 | + | 9.20408i | −0.397893 | + | 0.619134i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.42173 | − | 11.2501i | −0.563961 | − | 0.753364i | 0.424403 | − | 0.905474i | \(-0.360484\pi\) |
−0.988364 | + | 0.152110i | \(0.951393\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.37034 | − | 0.747492i | 0.358023 | − | 0.0498328i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.23215 | − | 3.94905i | 0.480015 | − | 0.262108i | −0.220975 | − | 0.975280i | \(-0.570924\pi\) |
0.700989 | + | 0.713172i | \(0.252742\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.9303 | 0.854461 | 0.427230 | − | 0.904143i | \(-0.359489\pi\) | ||||
0.427230 | + | 0.904143i | \(0.359489\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.227911 | 0.0149954 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.05078 | − | 0.573767i | 0.0688386 | − | 0.0375887i | −0.444461 | − | 0.895798i | \(-0.646605\pi\) |
0.513300 | + | 0.858209i | \(0.328423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.7742 | + | 7.32475i | −1.28992 | + | 0.477814i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.87423 | + | 7.84706i | 0.381572 | + | 0.509721i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.67177 | − | 10.3815i | 0.431561 | − | 0.671522i | −0.555564 | − | 0.831474i | \(-0.687497\pi\) |
0.987125 | + | 0.159952i | \(0.0511338\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5578 | − | 5.27826i | 0.744502 | − | 0.340003i | −0.00678624 | − | 0.999977i | \(-0.502160\pi\) |
0.751288 | + | 0.659974i | \(0.229433\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.51209 | + | 6.37207i | 0.546051 | + | 0.408769i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.6089 | − | 10.1050i | −0.741665 | − | 0.645583i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.444716 | − | 6.21794i | −0.0282966 | − | 0.395638i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.00830 | − | 8.08801i | −0.444133 | − | 0.512557i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.1458 | + | 10.1136i | 1.39783 | + | 0.638366i | 0.964793 | − | 0.263011i | \(-0.0847155\pi\) |
0.433035 | + | 0.901377i | \(0.357443\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.18507 | − | 0.745042i | 0.137374 | − | 0.0468404i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.4321 | − | 2.60782i | 1.15426 | − | 0.163308i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.0525736 | + | 0.735075i | −0.00327945 | + | 0.0458527i | −0.998828 | − | 0.0483940i | \(-0.984590\pi\) |
0.995549 | + | 0.0942467i | \(0.0300442\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.19530 | − | 1.03573i | −0.0742723 | − | 0.0643573i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.72484 | − | 2.85547i | 0.601953 | − | 0.176749i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.9762 | − | 14.6624i | 0.676820 | − | 0.904125i | −0.322276 | − | 0.946646i | \(-0.604448\pi\) |
0.999096 | + | 0.0425205i | \(0.0135388\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.34778 | − | 29.4996i | −0.389941 | − | 1.81215i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.713144 | + | 0.155135i | −0.0436437 | + | 0.00949410i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.0708 | + | 2.31063i | 0.979855 | + | 0.140882i | 0.613586 | − | 0.789628i | \(-0.289726\pi\) |
0.366268 | + | 0.930509i | \(0.380635\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.55320 | − | 1.64084i | 0.155096 | − | 0.0996740i | −0.460791 | − | 0.887509i | \(-0.652434\pi\) |
0.615887 | + | 0.787835i | \(0.288798\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.412717 | − | 0.755834i | −0.0249787 | − | 0.0457451i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.18486 | − | 1.00970i | −0.131752 | − | 0.0608870i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0723 | + | 11.0723i | 0.665268 | + | 0.665268i | 0.956617 | − | 0.291349i | \(-0.0941041\pi\) |
−0.291349 | + | 0.956617i | \(0.594104\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.80546 | − | 9.55453i | 0.167959 | − | 0.572015i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.41198 | + | 3.75311i | 0.143887 | + | 0.223892i | 0.905715 | − | 0.423887i | \(-0.139335\pi\) |
−0.761829 | + | 0.647779i | \(0.775698\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.71562 | − | 1.28430i | 0.101983 | − | 0.0763435i | −0.547069 | − | 0.837087i | \(-0.684257\pi\) |
0.649052 | + | 0.760744i | \(0.275166\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.51690 | + | 7.48316i | −0.445263 | + | 0.443264i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.98093 | + | 0.738847i | 0.116930 | + | 0.0436128i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.9863 | + | 2.72981i | −1.11684 | + | 0.160577i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.01671 | − | 3.46259i | −0.0596005 | − | 0.202981i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.5945 | − | 0.972299i | 0.794200 | − | 0.0568023i | 0.331658 | − | 0.943400i | \(-0.392392\pi\) |
0.462542 | + | 0.886597i | \(0.346937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.34341 | + | 11.2926i | −0.194661 | + | 0.657478i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.950973 | − | 2.54966i | −0.0551811 | − | 0.147946i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.42770 | − | 5.89731i | −0.371724 | − | 0.341050i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.793360 | − | 1.73722i | 0.0457285 | − | 0.100131i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −22.7173 | − | 1.62477i | −1.30507 | − | 0.0933407i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −33.2466 | − | 4.85650i | −1.90369 | − | 0.278082i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.6713 | − | 15.6557i | −1.63636 | − | 0.893519i | −0.991631 | − | 0.129108i | \(-0.958789\pi\) |
−0.644728 | − | 0.764412i | \(-0.723029\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.50380 | − | 17.4143i | −0.142436 | − | 0.990667i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.3216 | + | 31.3600i | 0.812105 | + | 1.77826i | 0.598085 | + | 0.801433i | \(0.295929\pi\) |
0.214020 | + | 0.976829i | \(0.431344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.401614 | − | 1.84619i | −0.0227005 | − | 0.104353i | 0.964403 | − | 0.264438i | \(-0.0851866\pi\) |
−0.987103 | + | 0.160086i | \(0.948823\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.291626 | − | 0.776541i | 0.0164313 | − | 0.0437531i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.6509 | + | 6.45016i | 1.66536 | + | 0.362277i | 0.943913 | − | 0.330193i | \(-0.107114\pi\) |
0.721446 | + | 0.692470i | \(0.243478\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.31687 | − | 1.26755i | −0.241699 | − | 0.0709691i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.5546i | 0.979802i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.5771 | − | 14.5771i | 0.811094 | − | 0.811094i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.607975 | + | 9.07419i | 0.0337244 | + | 0.503345i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.13630 | − | 9.82040i | 0.118138 | − | 0.543069i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.459107 | + | 3.19316i | −0.0253114 | + | 0.176045i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.0838 | − | 7.12312i | −0.609220 | − | 0.391522i | 0.199344 | − | 0.979930i | \(-0.436119\pi\) |
−0.808565 | + | 0.588407i | \(0.799755\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.75214 | + | 4.69768i | −0.0960168 | + | 0.257431i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.0264 | − | 1.10869i | −0.820981 | − | 0.0605744i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.9104 | − | 25.4751i | 0.757750 | − | 1.38772i | −0.158602 | − | 0.987343i | \(-0.550699\pi\) |
0.916352 | − | 0.400373i | \(-0.131119\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.1749 | − | 11.7425i | 0.552625 | − | 0.637763i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.34066 | + | 2.89470i | −0.180907 | + | 0.156757i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.44969 | + | 1.65965i | −0.240260 | + | 0.0896125i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.454729 | + | 14.8353i | −0.0244818 | + | 0.798703i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.6424 | − | 7.69921i | 1.10814 | − | 0.413315i | 0.272258 | − | 0.962224i | \(-0.412229\pi\) |
0.835882 | + | 0.548909i | \(0.184957\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.46026 | − | 8.19736i | 0.506396 | − | 0.438795i | −0.363817 | − | 0.931470i | \(-0.618527\pi\) |
0.870213 | + | 0.492676i | \(0.163981\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.73348 | + | 7.77085i | −0.359407 | + | 0.414778i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.6828 | + | 26.8895i | −0.781485 | + | 1.43118i | 0.117439 | + | 0.993080i | \(0.462532\pi\) |
−0.898924 | + | 0.438104i | \(0.855650\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.0843 | − | 23.2841i | −1.06596 | − | 1.23579i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.995236 | − | 2.66833i | 0.0526735 | − | 0.141223i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.5733 | + | 17.7203i | 1.45526 | + | 0.935240i | 0.998968 | + | 0.0454098i | \(0.0144593\pi\) |
0.456293 | + | 0.889830i | \(0.349177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.03236 | − | 7.18021i | 0.0543347 | − | 0.377906i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.16802 | − | 14.5632i | 0.166278 | − | 0.764368i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.51009 | − | 6.39400i | 0.183726 | − | 0.334677i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.9996 | + | 16.9996i | −0.887373 | + | 0.887373i | −0.994270 | − | 0.106897i | \(-0.965909\pi\) |
0.106897 | + | 0.994270i | \(0.465909\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6.70224i | − | 0.348905i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.42927 | − | 1.30055i | −0.229956 | − | 0.0675213i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.74434 | + | 0.814532i | 0.193875 | + | 0.0421749i | 0.308454 | − | 0.951239i | \(-0.400188\pi\) |
−0.114579 | + | 0.993414i | \(0.536552\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.0154 | − | 10.8677i | 0.568834 | − | 0.561207i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.61364 | + | 16.6116i | 0.186112 | + | 0.855543i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.26503 | + | 7.14942i | 0.167713 | + | 0.367241i | 0.974763 | − | 0.223243i | \(-0.0716643\pi\) |
−0.807050 | + | 0.590484i | \(0.798937\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.14030 | + | 14.8861i | 0.109651 | + | 0.762637i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.1566 | − | 11.0063i | −1.02995 | − | 0.562398i | −0.126896 | − | 0.991916i | \(-0.540501\pi\) |
−0.903058 | + | 0.429519i | \(0.858683\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.295266 | + | 0.219999i | −0.0150482 | + | 0.0112122i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.03877 | − | 0.431901i | −0.306968 | − | 0.0219548i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.91792 | − | 21.7172i | 0.502859 | − | 1.10111i | −0.472671 | − | 0.881239i | \(-0.656710\pi\) |
0.975530 | − | 0.219868i | \(-0.0705626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.818945 | − | 28.8358i | 0.0414159 | − | 1.45829i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.48343 | − | 6.65834i | −0.125273 | − | 0.335869i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.1849 | − | 4.49582i | −0.764035 | − | 0.226209i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.9011 | + | 2.13857i | −1.50069 | + | 0.107332i | −0.797348 | − | 0.603519i | \(-0.793765\pi\) |
−0.703343 | + | 0.710851i | \(0.748310\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.457153 | + | 1.55692i | 0.0228863 | + | 0.0779435i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.2622 | + | 2.62571i | −0.911971 | + | 0.131122i | −0.582300 | − | 0.812974i | \(-0.697847\pi\) |
−0.329671 | + | 0.944096i | \(0.606938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.6493 | + | 5.83690i | 0.779549 | + | 0.290757i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.2205 | + | 0.0229926i | 0.507861 | + | 0.00114251i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.78171 | − | 1.33377i | 0.0883161 | − | 0.0661126i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.32710 | + | 5.17708i | 0.164515 | + | 0.255990i | 0.913717 | − | 0.406352i | \(-0.133199\pi\) |
−0.749202 | + | 0.662341i | \(0.769563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.85807 | + | 9.73371i | −0.140978 | + | 0.480128i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.27400 | + | 1.27400i | 0.0626894 | + | 0.0626894i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.8867 | + | 3.71328i | 0.828936 | + | 0.182278i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.4692 | − | 24.6670i | −0.659590 | − | 1.20795i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.3546 | + | 10.5104i | −0.798973 | + | 0.513469i | −0.875281 | − | 0.483615i | \(-0.839323\pi\) |
0.0763072 | + | 0.997084i | \(0.475687\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.8972 | + | 3.29212i | 1.11594 | + | 0.160448i | 0.675520 | − | 0.737342i | \(-0.263919\pi\) |
0.440423 | + | 0.897790i | \(0.354829\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.99291 | − | 2.17382i | 0.485872 | − | 0.105695i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.3621 | + | 21.1707i | −1.03621 | + | 1.02693i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.08038 | + | 4.11491i | −0.149070 | + | 0.199135i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.16275 | − | 0.341415i | 0.0561382 | − | 0.0164837i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.28791 | − | 4.58200i | −0.254710 | − | 0.220707i | 0.518141 | − | 0.855295i | \(-0.326624\pi\) |
−0.772851 | + | 0.634588i | \(0.781170\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.355679 | + | 4.97304i | −0.0170928 | + | 0.238989i | 0.981722 | + | 0.190320i | \(0.0609525\pi\) |
−0.998815 | + | 0.0486692i | \(0.984502\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 17.3863 | − | 23.1168i | 0.833610 | − | 1.10837i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.47249 | + | 13.4324i | 0.453130 | + | 0.642558i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.42656 | − | 1.10817i | −0.115813 | − | 0.0528901i | 0.356666 | − | 0.934232i | \(-0.383913\pi\) |
−0.472479 | + | 0.881342i | \(0.656641\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.88792 | + | 5.64096i | 0.232758 | + | 0.268617i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.09727 | + | 15.3419i | 0.0521331 | + | 0.728916i | 0.954550 | + | 0.298052i | \(0.0963368\pi\) |
−0.902417 | + | 0.430864i | \(0.858209\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.774152 | − | 0.889368i | 0.0366983 | − | 0.0421601i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.2163 | − | 14.3851i | −0.908900 | − | 0.680394i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.7182 | − | 5.35152i | 0.553016 | − | 0.252554i | −0.119249 | − | 0.992864i | \(-0.538049\pi\) |
0.672265 | + | 0.740311i | \(0.265322\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.60848 | + | 2.50284i | −0.0757403 | + | 0.117854i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.35759 | − | 11.1644i | −0.392674 | − | 0.524551i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.26428 | + | 0.580819i | 0.0592705 | + | 0.0272292i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.54577 | + | 3.57426i | −0.306198 | + | 0.167197i | −0.625000 | − | 0.780624i | \(-0.714901\pi\) |
0.318802 | + | 0.947821i | \(0.396719\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −34.0035 | −1.58715 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.78272 | 0.0830295 | 0.0415147 | − | 0.999138i | \(-0.486782\pi\) | ||||
0.0415147 | + | 0.999138i | \(0.486782\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.4286 | − | 8.42465i | 0.717028 | − | 0.391527i | −0.0789291 | − | 0.996880i | \(-0.525150\pi\) |
0.795957 | + | 0.605354i | \(0.206968\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.87139 | − | 26.6492i | −0.457775 | − | 1.23583i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.4916 | − | 31.3812i | −1.08706 | − | 1.45215i | −0.880702 | − | 0.473671i | \(-0.842929\pi\) |
−0.206362 | − | 0.978476i | \(-0.566162\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.24620 | + | 1.93913i | −0.0575443 | + | 0.0895406i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.3577 | + | 7.92699i | −0.799800 | + | 0.365256i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.15143 | + | 1.61054i | 0.0989227 | + | 0.0740526i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.51502 | − | 16.9506i | 0.115397 | − | 0.777748i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.04397 | + | 14.5966i | 0.0478000 | + | 0.668331i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.50775 | + | 2.89410i | 0.114582 | + | 0.132235i | 0.810143 | − | 0.586232i | \(-0.199389\pi\) |
−0.695561 | + | 0.718467i | \(0.744844\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.64970 | − | 3.49350i | −0.348796 | − | 0.159290i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.96118 | + | 1.14433i | 0.0892367 | + | 0.0520688i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.65956 | + | 3.50449i | 0.211580 | + | 0.159131i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.72669 | − | 38.1241i | 0.123558 | − | 1.72757i | −0.437006 | − | 0.899458i | \(-0.643961\pi\) |
0.560564 | − | 0.828111i | \(-0.310584\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.81470 | + | 1.57245i | 0.0820638 | + | 0.0711087i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.5271 | + | 4.26553i | −0.655598 | + | 0.192501i | −0.592580 | − | 0.805512i | \(-0.701891\pi\) |
−0.0630177 | + | 0.998012i | \(0.520072\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.6910 | + | 45.0059i | −1.51737 | + | 2.02696i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.980541 | + | 0.633277i | 0.0440720 | + | 0.0284637i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.59666 | + | 0.999942i | −0.206188 | + | 0.0448535i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.1033 | − | 3.03420i | −0.944714 | − | 0.135829i | −0.347293 | − | 0.937757i | \(-0.612899\pi\) |
−0.597422 | + | 0.801927i | \(0.703808\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.0912 | − | 7.12790i | 0.495520 | − | 0.318451i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.730270 | + | 1.33739i | 0.0325611 | + | 0.0596312i | 0.893453 | − | 0.449157i | \(-0.148276\pi\) |
−0.860892 | + | 0.508788i | \(0.830094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.9993 | − | 19.8237i | 1.37945 | − | 0.882142i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.48483 | + | 9.48483i | 0.421236 | + | 0.421236i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.13431 | − | 10.6745i | 0.138926 | − | 0.473138i | −0.860409 | − | 0.509604i | \(-0.829792\pi\) |
0.999335 | + | 0.0364663i | \(0.0116102\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.603290 | − | 0.938738i | −0.0266880 | − | 0.0415273i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15.5099 | − | 11.6105i | 0.684778 | − | 0.512618i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.0535 | + | 20.1440i | 0.883664 | + | 0.887649i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.25339 | − | 1.58643i | −0.187064 | − | 0.0697712i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.113797 | + | 0.0163616i | −0.00499515 | + | 0.000718194i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.21793 | + | 4.14789i | 0.0533586 | + | 0.181723i | 0.981860 | − | 0.189605i | \(-0.0607208\pi\) |
−0.928502 | + | 0.371328i | \(0.878903\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.0370 | + | 1.00394i | −0.613793 | + | 0.0438994i | −0.374775 | − | 0.927116i | \(-0.622280\pi\) |
−0.239018 | + | 0.971015i | \(0.576826\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.656715 | − | 2.27437i | −0.0286614 | − | 0.0992616i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.3026 | + | 51.7522i | 0.840833 | + | 2.25436i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.5434 | + | 4.56004i | 0.980149 | + | 0.198263i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.37265 | − | 5.19538i | 0.102964 | − | 0.225460i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.2131 | + | 0.801974i | 0.485691 | + | 0.0347373i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.9452 | − | 22.7426i | −0.732603 | − | 0.983246i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.16075 | − | 5.00215i | −0.395315 | − | 0.215859i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.471533 | − | 3.27958i | −0.0203103 | − | 0.141262i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.8761 | − | 34.7639i | −0.682568 | − | 1.49462i | −0.859899 | − | 0.510465i | \(-0.829473\pi\) |
0.177330 | − | 0.984151i | \(-0.443254\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.162782 | + | 0.748296i | 0.00698564 | + | 0.0321125i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.71183 | + | 14.7848i | 0.287503 | + | 0.633311i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.9966 | + | 2.60970i | 0.512937 | + | 0.111583i | 0.461581 | − | 0.887098i | \(-0.347282\pi\) |
0.0513554 | + | 0.998680i | \(0.483646\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.6346 | + | 4.59073i | 0.667268 | + | 0.195928i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 32.0322i | − | 1.36462i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.71312 | + | 1.71312i | −0.0728494 | + | 0.0728494i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.00036 | + | 13.7382i | 0.169806 | + | 0.583155i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.43979 | − | 15.8125i | 0.145749 | − | 0.669995i | −0.845054 | − | 0.534681i | \(-0.820432\pi\) |
0.990803 | − | 0.135315i | \(-0.0432045\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.44517 | − | 10.0514i | 0.0611241 | − | 0.425127i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.37136 | + | 2.16664i | 0.142339 | + | 0.0914757i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.8213 | − | 42.4186i | 0.666789 | − | 1.78773i | 0.0525413 | − | 0.998619i | \(-0.483268\pi\) |
0.614248 | − | 0.789113i | \(-0.289459\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.84711 | + | 25.0344i | −0.0777086 | + | 1.05321i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.749342 | − | 1.37232i | 0.0314694 | − | 0.0576320i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.6434 | − | 16.8994i | 0.613883 | − | 0.708459i | −0.360650 | − | 0.932701i | \(-0.617445\pi\) |
0.974533 | + | 0.224242i | \(0.0719906\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.23046 | + | 2.79921i | −0.135190 | + | 0.117143i | −0.719831 | − | 0.694149i | \(-0.755781\pi\) |
0.584641 | + | 0.811292i | \(0.301235\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.02808 | − | 3.36730i | 0.377153 | − | 0.140671i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.7311 | − | 19.6585i | −0.572627 | − | 0.819816i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.97385 | − | 2.60111i | 0.290325 | − | 0.108286i | −0.200082 | − | 0.979779i | \(-0.564121\pi\) |
0.490407 | + | 0.871493i | \(0.336848\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.6453 | − | 12.6902i | 0.608638 | − | 0.527388i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.73218 | − | 1.99904i | 0.0718629 | − | 0.0829343i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.11320 | − | 5.70139i | 0.128935 | − | 0.236128i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.324542 | − | 4.39860i | 0.0134182 | − | 0.181860i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.72897 | − | 7.31666i | 0.112637 | − | 0.301991i | −0.868384 | − | 0.495892i | \(-0.834841\pi\) |
0.981021 | + | 0.193901i | \(0.0621140\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.4753 | − | 17.0146i | −1.09089 | − | 0.701075i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.73576 | − | 12.0725i | 0.0713995 | − | 0.496594i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.731036 | − | 3.36052i | 0.0300201 | − | 0.138000i | −0.959698 | − | 0.281035i | \(-0.909322\pi\) |
0.989718 | + | 0.143035i | \(0.0456860\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.28634 | + | 4.41760i | 0.0527346 | + | 0.181104i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.9894 | − | 16.9894i | 0.695330 | − | 0.695330i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.17302i | 0.374799i | 0.982284 | + | 0.187400i | \(0.0600060\pi\) | ||||
−0.982284 | + | 0.187400i | \(0.939994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.24243 | − | 0.364811i | −0.0506799 | − | 0.0148810i | 0.256294 | − | 0.966599i | \(-0.417498\pi\) |
−0.306974 | + | 0.951718i | \(0.599317\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.14015 | + | 1.55324i | 0.290769 | + | 0.0632530i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.95331 | + | 21.9251i | 0.404660 | + | 0.891382i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.38250 | + | 20.1460i | 0.177880 | + | 0.817702i | 0.976440 | + | 0.215787i | \(0.0692318\pi\) |
−0.798560 | + | 0.601915i | \(0.794405\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.83825 | − | 4.02521i | −0.0744897 | − | 0.163110i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.44115 | + | 16.9786i | 0.0987583 | + | 0.686879i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.7353 | + | 8.59214i | 0.635544 | + | 0.347033i | 0.764506 | − | 0.644616i | \(-0.222983\pi\) |
−0.128962 | + | 0.991649i | \(0.541165\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.4282 | − | 15.3380i | −0.460828 | − | 0.618490i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.7290 | − | 1.91170i | −1.07607 | − | 0.0769620i | −0.477964 | − | 0.878379i | \(-0.658625\pi\) |
−0.598106 | + | 0.801417i | \(0.704080\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.48869 | + | 16.3979i | −0.300996 | + | 0.659089i | −0.998337 | − | 0.0576506i | \(-0.981639\pi\) |
0.697341 | + | 0.716740i | \(0.254366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.61855 | − | 26.7146i | 0.185336 | − | 1.07202i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.0630377 | − | 0.169011i | −0.00252555 | − | 0.00677127i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.78040 | + | 24.7125i | −0.151216 | + | 0.988501i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.27757 | + | 0.162895i | −0.0909573 | + | 0.00650539i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.83518 | − | 26.6842i | −0.312409 | − | 1.06397i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.3844 | + | 2.78705i | −0.771680 | + | 0.110951i | −0.516897 | − | 0.856048i | \(-0.672913\pi\) |
−0.254783 | + | 0.966998i | \(0.582004\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.21678 | + | 3.06470i | 0.326588 | + | 0.121811i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.1421 | − | 17.2194i | −0.680264 | − | 0.683332i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.0224 | + | 7.50265i | −0.397101 | + | 0.297266i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.06230 | + | 12.5452i | 0.318940 | + | 0.496280i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.91160 | + | 23.5387i | −0.272992 | + | 0.929724i | 0.702867 | + | 0.711321i | \(0.251903\pi\) |
−0.975859 | + | 0.218403i | \(0.929915\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.6055 | − | 22.6055i | −0.891474 | − | 0.891474i | 0.103188 | − | 0.994662i | \(-0.467096\pi\) |
−0.994662 | + | 0.103188i | \(0.967096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.5561 | + | 9.30845i | −0.573147 | + | 0.366520i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.2300 | + | 31.5544i | 0.677381 | + | 1.24053i | 0.959651 | + | 0.281195i | \(0.0907309\pi\) |
−0.282270 | + | 0.959335i | \(0.591087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.13288 | + | 1.37072i | −0.0837227 | + | 0.0538053i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.30335 | − | 0.618728i | −0.168661 | − | 0.0242499i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.38617 | − | 1.38923i | 0.249910 | − | 0.0543646i | −0.0858650 | − | 0.996307i | \(-0.527365\pi\) |
0.335775 | + | 0.941942i | \(0.391002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.64456 | + | 6.22888i | 0.376844 | + | 0.243383i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.11989 | + | 2.83184i | −0.0827048 | + | 0.110481i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 42.0499 | − | 12.3470i | 1.63803 | − | 0.480970i | 0.672250 | − | 0.740324i | \(-0.265328\pi\) |
0.965782 | + | 0.259355i | \(0.0835099\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.70631 | + | 3.21154i | 0.144159 | + | 0.124914i | 0.723955 | − | 0.689847i | \(-0.242322\pi\) |
−0.579796 | + | 0.814762i | \(0.696868\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.08027 | − | 15.1041i | 0.0419541 | − | 0.586596i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.09513 | − | 1.57576i | −0.0812455 | − | 0.0611053i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.7825 | − | 32.5821i | −1.19190 | − | 1.26158i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.6925 | + | 8.07989i | 0.684031 | + | 0.312387i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.73675 | − | 5.46650i | −0.182860 | − | 0.211032i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.74162 | − | 24.3510i | −0.0671344 | − | 0.938661i | −0.913703 | − | 0.406382i | \(-0.866790\pi\) |
0.846569 | − | 0.532279i | \(-0.178664\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −22.7034 | + | 16.8367i | −0.873853 | + | 0.648044i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.3048 | − | 12.2056i | −0.626646 | − | 0.469101i | 0.238148 | − | 0.971229i | \(-0.423460\pi\) |
−0.864793 | + | 0.502128i | \(0.832551\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.811345 | − | 0.370529i | 0.0311366 | − | 0.0142196i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.16581 | + | 9.59419i | −0.236275 | + | 0.367650i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.17237 | + | 4.23779i | 0.121387 | + | 0.162155i | 0.857119 | − | 0.515119i | \(-0.172252\pi\) |
−0.735731 | + | 0.677274i | \(0.763161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.69306 | − | 15.3692i | −0.217521 | − | 0.587227i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.7071 | + | 8.57672i | −0.599263 | + | 0.327222i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −24.5454 | −0.935106 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.3261 | −0.735198 | −0.367599 | − | 0.929984i | \(-0.619820\pi\) | ||||
−0.367599 | + | 0.929984i | \(0.619820\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.156729 | − | 0.0855805i | 0.00595364 | − | 0.00325094i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 41.2605 | + | 18.9553i | 1.56510 | + | 0.719016i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.2789 | + | 29.7611i | 0.843872 | + | 1.12728i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.895845 | + | 1.39396i | −0.0338840 | + | 0.0527245i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.11833 | + | 4.16420i | −0.344395 | + | 0.157280i | −0.580101 | − | 0.814545i | \(-0.696987\pi\) |
0.235706 | + | 0.971824i | \(0.424260\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.6852 | + | 9.49600i | 0.478430 | + | 0.358148i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.1621 | − | 22.0140i | 0.721686 | − | 0.829094i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.401581 | − | 5.61483i | −0.0151030 | − | 0.211167i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.38474 | − | 10.8306i | −0.352451 | − | 0.406750i | 0.551645 | − | 0.834079i | \(-0.314000\pi\) |
−0.904096 | + | 0.427328i | \(0.859455\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.98614 | + | 3.19046i | 0.262001 | + | 0.119652i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.2805 | + | 8.13566i | −1.62087 | + | 0.304683i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.17682 | + | 1.56470i | −0.0440106 | + | 0.0585164i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.21846 | + | 17.0363i | −0.0455041 | + | 0.636231i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.3929 | + | 14.2045i | 0.611352 | + | 0.529739i | 0.904580 | − | 0.426303i | \(-0.140184\pi\) |
−0.293229 | + | 0.956042i | \(0.594730\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.17227 | − | 1.22509i | 0.155383 | − | 0.0456247i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.5387 | + | 14.0780i | −0.391938 | + | 0.523568i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.210259 | + | 46.7313i | −0.00780884 | + | 1.73556i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.1405 | − | 2.64100i | 0.450266 | − | 0.0979494i | 0.0182865 | − | 0.999833i | \(-0.494179\pi\) |
0.431980 | + | 0.901883i | \(0.357815\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.1394 | − | 4.04583i | −1.04220 | − | 0.149846i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.2506 | − | 18.1556i | 1.04489 | − | 0.671508i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.90727 | + | 12.6497i | 0.255126 | + | 0.467228i | 0.973580 | − | 0.228346i | \(-0.0733318\pi\) |
−0.718454 | + | 0.695574i | \(0.755150\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20.8045 | + | 4.57479i | 0.767386 | + | 0.168744i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.29361 | − | 2.29361i | −0.0844861 | − | 0.0844861i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.19622 | + | 31.3194i | −0.338288 | + | 1.15210i | 0.598183 | + | 0.801360i | \(0.295890\pi\) |
−0.936471 | + | 0.350745i | \(0.885929\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.66459 | + | 7.25824i | 0.171358 | + | 0.266638i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.8905 | − | 19.3814i | 0.949832 | − | 0.711035i | −0.00751631 | − | 0.999972i | \(-0.502393\pi\) |
0.957348 | + | 0.288936i | \(0.0933016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 38.7811 | + | 0.0872439i | 1.42083 | + | 0.00319637i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.85649 | − | 2.93032i | −0.287454 | − | 0.107215i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.29465 | + | 0.617478i | −0.156923 | + | 0.0225622i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.87817 | − | 26.8306i | −0.287479 | − | 0.979062i | −0.968958 | − | 0.247225i | \(-0.920481\pi\) |
0.681480 | − | 0.731837i | \(-0.261337\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −33.6099 | + | 2.40382i | −1.22481 | + | 0.0876002i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.6044 | + | 6.39645i | 0.786264 | + | 0.232790i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.74260 | + | 23.4398i | 0.317755 | + | 0.851935i | 0.993399 | + | 0.114707i | \(0.0365929\pi\) |
−0.675644 | + | 0.737228i | \(0.736134\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.16012 | + | 2.35440i | −0.0784075 | + | 0.0854593i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.0409 | − | 30.7452i | 0.508981 | − | 1.11451i | −0.464464 | − | 0.885592i | \(-0.653753\pi\) |
0.973445 | − | 0.228921i | \(-0.0735198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.47766 | + | 0.177206i | 0.0896974 | + | 0.00641528i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.6961 | − | 8.71458i | 0.422872 | − | 0.315076i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.40813 | + | 4.59119i | 0.303600 | + | 0.165778i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.25665 | + | 22.6505i | 0.117438 | + | 0.816798i | 0.960360 | + | 0.278762i | \(0.0899242\pi\) |
−0.842922 | + | 0.538035i | \(0.819167\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.423713 | − | 0.927802i | −0.0152597 | − | 0.0334140i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.13807 | − | 14.4255i | −0.112868 | − | 0.518848i | −0.998514 | − | 0.0544868i | \(-0.982648\pi\) |
0.885646 | − | 0.464361i | \(-0.153716\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.5127 | + | 24.9962i | 1.38342 | + | 0.897889i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.13899 | + | 0.465309i | 0.0767358 | + | 0.0166929i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.3239 | − | 5.96764i | −0.728180 | − | 0.213813i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.61968i | − | 0.236871i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −37.3601 | + | 37.3601i | −1.33514 | + | 1.33514i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.8357 | − | 27.0248i | 0.529507 | − | 0.964555i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.460569 | − | 2.11720i | 0.0164175 | − | 0.0754702i | −0.968209 | − | 0.250142i | \(-0.919523\pi\) |
0.984627 | + | 0.174672i | \(0.0558864\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.60764 | + | 25.0917i | −0.128435 | + | 0.893287i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.23064 | + | 2.07621i | 0.114868 | + | 0.0738214i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.55123 | + | 25.6078i | −0.339174 | + | 0.909361i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.2781 | + | 31.6241i | 0.967454 | + | 1.12159i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.0460 | − | 31.2174i | 0.603800 | − | 1.10578i | −0.379741 | − | 0.925093i | \(-0.623987\pi\) |
0.983541 | − | 0.180684i | \(-0.0578311\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.1472 | + | 42.8701i | −1.31417 | + | 1.51664i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.432159 | + | 0.374468i | −0.0152696 | + | 0.0132312i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.47126 | − | 0.548750i | 0.0519195 | − | 0.0193650i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.64537 | + | 0.410578i | −0.128483 | + | 0.0144710i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.0546 | + | 7.85296i | −0.741157 | + | 0.276437i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.63341 | − | 7.48089i | 0.303535 | − | 0.263014i | −0.489753 | − | 0.871861i | \(-0.662913\pi\) |
0.793288 | + | 0.608847i | \(0.208368\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.12440 | − | 5.91387i | 0.179942 | − | 0.207664i | −0.658612 | − | 0.752483i | \(-0.728856\pi\) |
0.838554 | + | 0.544819i | \(0.183402\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.01312 | + | 3.68675i | −0.0706031 | + | 0.129300i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.86887 | − | 0.285457i | −0.135521 | − | 0.00999911i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.68659 | + | 17.9274i | −0.233934 | + | 0.627202i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.567631 | − | 0.364794i | −0.0198346 | − | 0.0127469i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.49638 | − | 38.2282i | 0.191825 | − | 1.33417i | −0.635349 | − | 0.772225i | \(-0.719144\pi\) |
0.827174 | − | 0.561946i | \(-0.189947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.81542 | + | 17.5392i | −0.132997 | + | 0.611377i | 0.861602 | + | 0.507585i | \(0.169462\pi\) |
−0.994599 | + | 0.103793i | \(0.966902\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.32378 | − | 0.222695i | 0.115719 | − | 0.00775325i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21.8354 | + | 21.8354i | −0.759291 | + | 0.759291i | −0.976193 | − | 0.216902i | \(-0.930405\pi\) |
0.216902 | + | 0.976193i | \(0.430405\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.2747i | − | 1.29460i | −0.762234 | − | 0.647302i | \(-0.775897\pi\) | ||
0.762234 | − | 0.647302i | \(-0.224103\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.7942 | − | 6.10574i | −0.721344 | − | 0.211806i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −40.4557 | − | 8.80060i | −1.40171 | − | 0.304923i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.48861 | + | 19.9406i | −0.259154 | + | 0.690074i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 11.0342 | + | 50.7235i | 0.381399 | + | 1.75326i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.22273 | + | 7.05680i | 0.111261 | + | 0.243628i | 0.957069 | − | 0.289859i | \(-0.0936085\pi\) |
−0.845808 | + | 0.533487i | \(0.820881\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.30471 | + | 57.7605i | 0.286369 | + | 1.99174i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.41939 | − | 2.95921i | −0.186654 | − | 0.101921i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.4435 | − | 3.13236i | −0.737677 | − | 0.107756i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.67425 | + | 0.262788i | 0.126249 | + | 0.00902949i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.23217 | + | 2.69807i | −0.0422878 | + | 0.0925974i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.0284 | − | 2.53126i | 0.755126 | − | 0.0867706i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.59897 | − | 9.64922i | −0.123226 | − | 0.330383i | 0.860659 | − | 0.509181i | \(-0.170052\pi\) |
−0.983886 | + | 0.178798i | \(0.942779\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.35927 | + | 7.96858i | −0.0806854 | + | 0.272520i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −34.4775 | + | 2.46588i | −1.17773 | + | 0.0842329i | −0.646445 | − | 0.762961i | \(-0.723745\pi\) |
−0.531284 | + | 0.847193i | \(0.678290\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.50305 | + | 18.7417i | 0.187762 | + | 0.639458i | 0.998536 | + | 0.0540983i | \(0.0172284\pi\) |
−0.810774 | + | 0.585360i | \(0.800953\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.89640 | + | 0.416440i | −0.0987091 | + | 0.0141922i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.968710 | − | 0.361310i | −0.0329753 | − | 0.0122991i | 0.332922 | − | 0.942954i | \(-0.391965\pi\) |
−0.365898 | + | 0.930655i | \(0.619238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.131635 | − | 0.131044i | 0.00447571 | − | 0.00445562i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.2528 | − | 15.9096i | 0.721783 | − | 0.540320i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.84318 | − | 2.86804i | −0.0625255 | − | 0.0972916i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.45300 | + | 11.7598i | −0.117000 | + | 0.398467i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.99937 | − | 1.99937i | −0.0676683 | − | 0.0676683i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.04621 | + | 2.31261i | 0.102981 | + | 0.0781803i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.6553 | + | 28.6705i | 0.528641 | + | 0.968134i | 0.996440 | + | 0.0842994i | \(0.0268652\pi\) |
−0.467799 | + | 0.883835i | \(0.654953\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.8690 | + | 10.1984i | −0.535247 | + | 0.343982i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.4824 | + | 2.36981i | 0.555306 | + | 0.0798410i | 0.414254 | − | 0.910161i | \(-0.364042\pi\) |
0.141052 | + | 0.990002i | \(0.454952\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.8688 | − | 5.62741i | 0.870554 | − | 0.189377i | 0.244967 | − | 0.969532i | \(-0.421223\pi\) |
0.625587 | + | 0.780154i | \(0.284859\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.42898 | − | 15.9353i | −0.115264 | − | 0.535659i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.42395 | − | 1.90218i | 0.0478116 | − | 0.0638688i | −0.775998 | − | 0.630735i | \(-0.782753\pi\) |
0.823810 | + | 0.566866i | \(0.191844\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.56653 | + | 1.04723i | −0.119618 | + | 0.0351229i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.66284 | + | 1.44086i | 0.0557074 | + | 0.0482707i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.30572 | − | 32.2381i | 0.0771579 | − | 1.07881i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.6965 | − | 2.36227i | 0.558104 | − | 0.0789621i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.7197 | + | 2.90023i | 0.391310 | + | 0.0968359i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 78.0688 | + | 35.6528i | 2.60374 | + | 1.18909i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.1560 | − | 61.3453i | −1.77088 | − | 2.04371i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.188567 | + | 2.63651i | 0.00627513 | + | 0.0877377i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.933207 | − | 0.812312i | −0.0310209 | − | 0.0270022i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.1744 | + | 8.36505i | 0.371040 | + | 0.277757i | 0.768483 | − | 0.639870i | \(-0.221012\pi\) |
−0.397444 | + | 0.917627i | \(0.630103\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.2322 | + | 7.41301i | −0.538389 | + | 0.245874i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.12898 | + | 6.42481i | −0.136799 | + | 0.212864i | −0.902893 | − | 0.429865i | \(-0.858561\pi\) |
0.766094 | + | 0.642728i | \(0.222198\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.23063 | + | 2.97977i | 0.0738230 | + | 0.0986159i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 43.6075 | − | 16.1531i | 1.44162 | − | 0.534005i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.54158 | − | 0.841766i | 0.0509074 | − | 0.0277976i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.5874 | 0.646130 | 0.323065 | − | 0.946377i | \(-0.395287\pi\) | ||||
0.323065 | + | 0.946377i | \(0.395287\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45.2129 | 1.48981 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.9532 | + | 11.9874i | −0.722599 | + | 0.394569i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.4439 | − | 13.9368i | −0.606431 | − | 0.458241i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.26088 | − | 11.0352i | −0.271323 | − | 0.362445i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.0422 | + | 26.5181i | −0.559135 | + | 0.870031i | −0.999615 | − | 0.0277309i | \(-0.991172\pi\) |
0.440480 | + | 0.897762i | \(0.354808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.4579 | − | 9.79947i | 0.703253 | − | 0.321165i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −38.1983 | − | 28.5949i | −1.25056 | − | 0.936154i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.45913 | + | 0.447363i | −0.211236 | + | 0.0146303i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.28410 | − | 17.9541i | −0.0419498 | − | 0.586535i | −0.974340 | − | 0.225081i | \(-0.927735\pi\) |
0.932390 | − | 0.361453i | \(-0.117719\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.71244 | + | 1.97626i | 0.0558833 | + | 0.0644928i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45.7808 | + | 20.9074i | 1.49241 | + | 0.681562i | 0.983773 | − | 0.179418i | \(-0.0574214\pi\) |
0.508639 | + | 0.860980i | \(0.330149\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −26.4076 | + | 13.4609i | −0.859951 | + | 0.438348i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.605754 | + | 4.28146i | 0.0197052 | + | 0.139276i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.01599 | + | 42.1691i | −0.0980065 | + | 1.37031i | 0.675892 | + | 0.737001i | \(0.263759\pi\) |
−0.773898 | + | 0.633310i | \(0.781696\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.48410 | − | 3.88549i | −0.145560 | − | 0.126128i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.2967 | + | 11.8322i | −1.30671 | + | 0.383685i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.45650 | + | 7.28903i | −0.176753 | + | 0.236115i | −0.880165 | − | 0.474668i | \(-0.842568\pi\) |
0.703412 | + | 0.710783i | \(0.251659\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.44577 | + | 13.0771i | −0.273299 | + | 0.423165i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.08467 | − | 1.32364i | 0.196690 | − | 0.0427872i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.48184 | − | 0.356835i | −0.0801428 | − | 0.0115228i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.8569 | − | 28.8278i | 1.44700 | − | 0.929928i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.59174 | + | 12.0719i | 0.212416 | + | 0.389011i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.72380 | + | 30.5775i | −0.216447 | + | 0.984324i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38.9774 | + | 38.9774i | 1.25343 | + | 1.25343i | 0.954174 | + | 0.299254i | \(0.0967376\pi\) |
0.299254 | + | 0.954174i | \(0.403262\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.03849 | + | 27.3766i | −0.258233 | + | 0.879462i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.1330 | − | 40.6638i | −0.838649 | − | 1.30496i | −0.950338 | − | 0.311219i | \(-0.899263\pi\) |
0.111689 | − | 0.993743i | \(-0.464374\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.56090 | − | 4.16284i | 0.178274 | − | 0.133454i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.75746 | − | 10.6196i | −0.216412 | − | 0.340098i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.30510 | − | 3.09764i | −0.265704 | − | 0.0991023i | 0.213082 | − | 0.977034i | \(-0.431650\pi\) |
−0.478785 | + | 0.877932i | \(0.658923\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.251252 | − | 0.0361245i | 0.00803004 | − | 0.00115455i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.21848 | − | 7.55544i | −0.0708305 | − | 0.241227i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.1545 | − | 2.80039i | 1.24883 | − | 0.0893184i | 0.568786 | − | 0.822486i | \(-0.307413\pi\) |
0.680049 | + | 0.733167i | \(0.261959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.40461 | + | 17.3158i | 0.299656 | + | 0.551726i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.56033 | − | 4.18341i | −0.0496659 | − | 0.133159i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.4266 | + | 24.6609i | 0.331548 | + | 0.784171i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.1771 | − | 35.4229i | 0.513883 | − | 1.12525i | −0.457821 | − | 0.889044i | \(-0.651370\pi\) |
0.971704 | − | 0.236202i | \(-0.0759028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.1888 | + | 1.30089i | 0.577203 | + | 0.0412824i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.61074 | + | 38.4099i | −0.177872 | + | 1.21768i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.1410 | + | 15.9122i | 0.922905 | + | 0.503944i | 0.869116 | − | 0.494608i | \(-0.164688\pi\) |
0.0537891 | + | 0.998552i | \(0.482870\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.71963 | − | 25.8706i | −0.117684 | − | 0.818508i |
(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 | 920.2.bv.a.17.12 | ✓ | 720 | |
5.3 | odd | 4 | inner | 920.2.bv.a.753.12 | yes | 720 | |
23.19 | odd | 22 | inner | 920.2.bv.a.617.12 | yes | 720 | |
115.88 | even | 44 | inner | 920.2.bv.a.433.12 | yes | 720 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.bv.a.17.12 | ✓ | 720 | 1.1 | even | 1 | trivial | |
920.2.bv.a.433.12 | yes | 720 | 115.88 | even | 44 | inner | |
920.2.bv.a.617.12 | yes | 720 | 23.19 | odd | 22 | inner | |
920.2.bv.a.753.12 | yes | 720 | 5.3 | odd | 4 | inner |