Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(49,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.i (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Character | \(\chi\) | \(=\) | 375.49 |
Dual form | 375.2.i.d.199.4 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0832830 | − | 0.114629i | 0.0588900 | − | 0.0810551i | −0.778556 | − | 0.627575i | \(-0.784048\pi\) |
0.837446 | + | 0.546520i | \(0.184048\pi\) | |||||||
\(3\) | 0.951057 | − | 0.309017i | 0.549093 | − | 0.178411i | ||||
\(4\) | 0.611830 | + | 1.88302i | 0.305915 | + | 0.941510i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0437845 | − | 0.134755i | 0.0178749 | − | 0.0550134i | ||||
\(7\) | 0.858311i | 0.324411i | 0.986757 | + | 0.162205i | \(0.0518607\pi\) | ||||
−0.986757 | + | 0.162205i | \(0.948139\pi\) | |||||||
\(8\) | 0.536314 | + | 0.174259i | 0.189615 | + | 0.0616098i | ||||
\(9\) | 0.809017 | − | 0.587785i | 0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.97713 | + | 2.16301i | 0.897637 | + | 0.652171i | 0.937858 | − | 0.347019i | \(-0.112806\pi\) |
−0.0402210 | + | 0.999191i | \(0.512806\pi\) | |||||||
\(12\) | 1.16377 | + | 1.60179i | 0.335952 | + | 0.462398i | ||||
\(13\) | −2.69285 | − | 3.70638i | −0.746861 | − | 1.02797i | −0.998194 | − | 0.0600653i | \(-0.980869\pi\) |
0.251334 | − | 0.967901i | \(-0.419131\pi\) | |||||||
\(14\) | 0.0983875 | + | 0.0714827i | 0.0262952 | + | 0.0191045i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.13894 | + | 2.28058i | −0.784736 | + | 0.570144i | ||||
\(17\) | 5.04728 | + | 1.63996i | 1.22414 | + | 0.397749i | 0.848590 | − | 0.529052i | \(-0.177452\pi\) |
0.375555 | + | 0.926800i | \(0.377452\pi\) | |||||||
\(18\) | − | 0.141689i | − | 0.0333965i | ||||||
\(19\) | −1.96804 | + | 6.05699i | −0.451499 | + | 1.38957i | 0.423699 | + | 0.905803i | \(0.360732\pi\) |
−0.875197 | + | 0.483766i | \(0.839268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.265233 | + | 0.816302i | 0.0578785 | + | 0.178132i | ||||
\(22\) | 0.495888 | − | 0.161124i | 0.105724 | − | 0.0343517i | ||||
\(23\) | 2.01245 | − | 2.76990i | 0.419625 | − | 0.577564i | −0.545908 | − | 0.837845i | \(-0.683815\pi\) |
0.965533 | + | 0.260281i | \(0.0838152\pi\) | |||||||
\(24\) | 0.563913 | 0.115108 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.649128 | −0.127304 | ||||||||
\(27\) | 0.587785 | − | 0.809017i | 0.113119 | − | 0.155695i | ||||
\(28\) | −1.61622 | + | 0.525140i | −0.305436 | + | 0.0992422i | ||||
\(29\) | −1.15388 | − | 3.55129i | −0.214271 | − | 0.659458i | −0.999205 | − | 0.0398784i | \(-0.987303\pi\) |
0.784934 | − | 0.619580i | \(-0.212697\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.387167 | − | 1.19158i | 0.0695373 | − | 0.214014i | −0.910249 | − | 0.414062i | \(-0.864110\pi\) |
0.979786 | + | 0.200048i | \(0.0641098\pi\) | |||||||
\(32\) | 1.67757i | 0.296556i | ||||||||
\(33\) | 3.49982 | + | 1.13716i | 0.609241 | + | 0.197954i | ||||
\(34\) | 0.608340 | − | 0.441985i | 0.104329 | − | 0.0757997i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.60179 | + | 1.16377i | 0.266965 | + | 0.193962i | ||||
\(37\) | −4.37939 | − | 6.02772i | −0.719968 | − | 0.990951i | −0.999525 | − | 0.0308218i | \(-0.990188\pi\) |
0.279557 | − | 0.960129i | \(-0.409812\pi\) | |||||||
\(38\) | 0.530404 | + | 0.730039i | 0.0860430 | + | 0.118428i | ||||
\(39\) | −3.70638 | − | 2.69285i | −0.593496 | − | 0.431200i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.04817 | − | 1.48808i | 0.319870 | − | 0.232399i | −0.416250 | − | 0.909250i | \(-0.636656\pi\) |
0.736120 | + | 0.676851i | \(0.236656\pi\) | |||||||
\(42\) | 0.115661 | + | 0.0375807i | 0.0178469 | + | 0.00579882i | ||||
\(43\) | − | 3.37972i | − | 0.515402i | −0.966225 | − | 0.257701i | \(-0.917035\pi\) | ||
0.966225 | − | 0.257701i | \(-0.0829650\pi\) | |||||||
\(44\) | −2.25149 | + | 6.92938i | −0.339425 | + | 1.04464i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.149909 | − | 0.461371i | −0.0221028 | − | 0.0680255i | ||||
\(47\) | −8.08338 | + | 2.62645i | −1.17908 | + | 0.383107i | −0.832026 | − | 0.554737i | \(-0.812819\pi\) |
−0.347057 | + | 0.937844i | \(0.612819\pi\) | |||||||
\(48\) | −2.28058 | + | 3.13894i | −0.329173 | + | 0.453067i | ||||
\(49\) | 6.26330 | 0.894758 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.30702 | 0.743132 | ||||||||
\(52\) | 5.33163 | − | 7.33836i | 0.739364 | − | 1.01765i | ||||
\(53\) | 2.23334 | − | 0.725656i | 0.306773 | − | 0.0996765i | −0.151585 | − | 0.988444i | \(-0.548438\pi\) |
0.458358 | + | 0.888768i | \(0.348438\pi\) | |||||||
\(54\) | −0.0437845 | − | 0.134755i | −0.00595831 | − | 0.0183378i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.149568 | + | 0.460324i | −0.0199869 | + | 0.0615133i | ||||
\(57\) | 6.36870i | 0.843555i | ||||||||
\(58\) | −0.503181 | − | 0.163493i | −0.0660709 | − | 0.0214677i | ||||
\(59\) | 10.6195 | − | 7.71550i | 1.38254 | − | 1.00447i | 0.385900 | − | 0.922541i | \(-0.373891\pi\) |
0.996638 | − | 0.0819317i | \(-0.0261089\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.37141 | − | 6.08218i | −1.07185 | − | 0.778744i | −0.0956052 | − | 0.995419i | \(-0.530479\pi\) |
−0.976244 | + | 0.216676i | \(0.930479\pi\) | |||||||
\(62\) | −0.104345 | − | 0.143619i | −0.0132519 | − | 0.0182396i | ||||
\(63\) | 0.504502 | + | 0.694388i | 0.0635613 | + | 0.0874846i | ||||
\(64\) | −6.08559 | − | 4.42144i | −0.760698 | − | 0.552680i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.421827 | − | 0.306475i | 0.0519234 | − | 0.0377245i | ||||
\(67\) | −3.18270 | − | 1.03412i | −0.388828 | − | 0.126338i | 0.108077 | − | 0.994142i | \(-0.465531\pi\) |
−0.496906 | + | 0.867805i | \(0.665531\pi\) | |||||||
\(68\) | 10.5075i | 1.27422i | ||||||||
\(69\) | 1.05801 | − | 3.25621i | 0.127369 | − | 0.392002i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.33585 | − | 4.11131i | −0.158536 | − | 0.487923i | 0.839966 | − | 0.542639i | \(-0.182575\pi\) |
−0.998502 | + | 0.0547158i | \(0.982575\pi\) | |||||||
\(72\) | 0.536314 | − | 0.174259i | 0.0632052 | − | 0.0205366i | ||||
\(73\) | −5.33713 | + | 7.34593i | −0.624664 | + | 0.859776i | −0.997682 | − | 0.0680477i | \(-0.978323\pi\) |
0.373018 | + | 0.927824i | \(0.378323\pi\) | |||||||
\(74\) | −1.05568 | −0.122721 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.6095 | −1.44641 | ||||||||
\(77\) | −1.85653 | + | 2.55530i | −0.211572 | + | 0.291203i | ||||
\(78\) | −0.617357 | + | 0.200592i | −0.0699020 | + | 0.0227125i | ||||
\(79\) | 1.00347 | + | 3.08837i | 0.112899 | + | 0.347469i | 0.991503 | − | 0.130083i | \(-0.0415244\pi\) |
−0.878604 | + | 0.477552i | \(0.841524\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | − | 0.358712i | − | 0.0396131i | ||||||
\(83\) | −7.03087 | − | 2.28447i | −0.771738 | − | 0.250753i | −0.103429 | − | 0.994637i | \(-0.532981\pi\) |
−0.668309 | + | 0.743884i | \(0.732981\pi\) | |||||||
\(84\) | −1.37484 | + | 0.998876i | −0.150007 | + | 0.108986i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.387414 | − | 0.281473i | −0.0417760 | − | 0.0303520i | ||||
\(87\) | −2.19482 | − | 3.02091i | −0.235309 | − | 0.323875i | ||||
\(88\) | 1.21975 | + | 1.67884i | 0.130026 | + | 0.178965i | ||||
\(89\) | −12.5378 | − | 9.10921i | −1.32900 | − | 0.965575i | −0.999773 | − | 0.0213236i | \(-0.993212\pi\) |
−0.329227 | − | 0.944251i | \(-0.606788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.18123 | − | 2.31130i | 0.333483 | − | 0.242290i | ||||
\(92\) | 6.44705 | + | 2.09478i | 0.672152 | + | 0.218395i | ||||
\(93\) | − | 1.25290i | − | 0.129920i | ||||||
\(94\) | −0.372140 | + | 1.14533i | −0.0383833 | + | 0.118132i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.518399 | + | 1.59547i | 0.0529089 | + | 0.162837i | ||||
\(97\) | −9.54725 | + | 3.10209i | −0.969377 | + | 0.314970i | −0.750564 | − | 0.660797i | \(-0.770218\pi\) |
−0.218812 | + | 0.975767i | \(0.570218\pi\) | |||||||
\(98\) | 0.521627 | − | 0.717957i | 0.0526922 | − | 0.0725247i | ||||
\(99\) | 3.67993 | 0.369847 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.714616 | −0.0711070 | −0.0355535 | − | 0.999368i | \(-0.511319\pi\) | ||||
−0.0355535 | + | 0.999368i | \(0.511319\pi\) | |||||||
\(102\) | 0.441985 | − | 0.608340i | 0.0437630 | − | 0.0602346i | ||||
\(103\) | −0.742551 | + | 0.241269i | −0.0731657 | + | 0.0237730i | −0.345371 | − | 0.938466i | \(-0.612247\pi\) |
0.272205 | + | 0.962239i | \(0.412247\pi\) | |||||||
\(104\) | −0.798339 | − | 2.45704i | −0.0782836 | − | 0.240932i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.102818 | − | 0.316441i | 0.00998655 | − | 0.0307354i | ||||
\(107\) | − | 11.9601i | − | 1.15623i | −0.815957 | − | 0.578113i | \(-0.803789\pi\) | ||
0.815957 | − | 0.578113i | \(-0.196211\pi\) | |||||||
\(108\) | 1.88302 | + | 0.611830i | 0.181194 | + | 0.0588734i | ||||
\(109\) | 1.96902 | − | 1.43057i | 0.188598 | − | 0.137024i | −0.489480 | − | 0.872015i | \(-0.662813\pi\) |
0.678078 | + | 0.734990i | \(0.262813\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.02772 | − | 4.37939i | −0.572126 | − | 0.415674i | ||||
\(112\) | −1.95744 | − | 2.69419i | −0.184961 | − | 0.254577i | ||||
\(113\) | 9.42535 | + | 12.9729i | 0.886662 | + | 1.22039i | 0.974531 | + | 0.224254i | \(0.0719945\pi\) |
−0.0878685 | + | 0.996132i | \(0.528006\pi\) | |||||||
\(114\) | 0.730039 | + | 0.530404i | 0.0683744 | + | 0.0496769i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.98117 | − | 4.34558i | 0.555338 | − | 0.403477i | ||||
\(117\) | −4.35712 | − | 1.41571i | −0.402815 | − | 0.130883i | ||||
\(118\) | − | 1.85987i | − | 0.171215i | ||||||
\(119\) | −1.40759 | + | 4.33213i | −0.129034 | + | 0.397126i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.785483 | + | 2.41747i | 0.0714076 | + | 0.219770i | ||||
\(122\) | −1.39439 | + | 0.453065i | −0.126242 | + | 0.0410186i | ||||
\(123\) | 1.48808 | − | 2.04817i | 0.134176 | − | 0.184677i | ||||
\(124\) | 2.48065 | 0.222769 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.121614 | 0.0108342 | ||||||||
\(127\) | 2.25620 | − | 3.10539i | 0.200205 | − | 0.275559i | −0.697096 | − | 0.716978i | \(-0.745525\pi\) |
0.897301 | + | 0.441419i | \(0.145525\pi\) | |||||||
\(128\) | −4.20459 | + | 1.36615i | −0.371637 | + | 0.120752i | ||||
\(129\) | −1.04439 | − | 3.21430i | −0.0919534 | − | 0.283004i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.84709 | + | 11.8401i | −0.336122 | + | 1.03448i | 0.630044 | + | 0.776559i | \(0.283037\pi\) |
−0.966167 | + | 0.257919i | \(0.916963\pi\) | |||||||
\(132\) | 7.28598i | 0.634163i | ||||||||
\(133\) | −5.19878 | − | 1.68919i | −0.450791 | − | 0.146471i | ||||
\(134\) | −0.383605 | + | 0.278705i | −0.0331384 | + | 0.0240765i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.42115 | + | 1.75907i | 0.207611 | + | 0.150839i | ||||
\(137\) | −6.97049 | − | 9.59406i | −0.595529 | − | 0.819676i | 0.399761 | − | 0.916620i | \(-0.369093\pi\) |
−0.995290 | + | 0.0969439i | \(0.969093\pi\) | |||||||
\(138\) | −0.285143 | − | 0.392466i | −0.0242730 | − | 0.0334089i | ||||
\(139\) | −3.77074 | − | 2.73960i | −0.319830 | − | 0.232370i | 0.416273 | − | 0.909240i | \(-0.363336\pi\) |
−0.736103 | + | 0.676870i | \(0.763336\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.87614 | + | 4.99580i | −0.579075 | + | 0.420723i | ||||
\(142\) | −0.582530 | − | 0.189275i | −0.0488848 | − | 0.0158836i | ||||
\(143\) | − | 16.8590i | − | 1.40982i | ||||||
\(144\) | −1.19897 | + | 3.69005i | −0.0999141 | + | 0.307504i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.397566 | + | 1.22358i | 0.0329028 | + | 0.101264i | ||||
\(147\) | 5.95676 | − | 1.93547i | 0.491305 | − | 0.159635i | ||||
\(148\) | 8.67087 | − | 11.9344i | 0.712741 | − | 0.981004i | ||||
\(149\) | 11.5480 | 0.946053 | 0.473026 | − | 0.881048i | \(-0.343162\pi\) | ||||
0.473026 | + | 0.881048i | \(0.343162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.4694 | 1.99129 | 0.995646 | − | 0.0932103i | \(-0.0297129\pi\) | ||||
0.995646 | + | 0.0932103i | \(0.0297129\pi\) | |||||||
\(152\) | −2.11097 | + | 2.90550i | −0.171222 | + | 0.235667i | ||||
\(153\) | 5.04728 | − | 1.63996i | 0.408048 | − | 0.132583i | ||||
\(154\) | 0.138294 | + | 0.425626i | 0.0111441 | + | 0.0342979i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.80300 | − | 8.62676i | 0.224420 | − | 0.690693i | ||||
\(157\) | 22.3660i | 1.78500i | 0.451045 | + | 0.892501i | \(0.351052\pi\) | ||||
−0.451045 | + | 0.892501i | \(0.648948\pi\) | |||||||
\(158\) | 0.437589 | + | 0.142181i | 0.0348127 | + | 0.0113113i | ||||
\(159\) | 1.89979 | − | 1.38028i | 0.150663 | − | 0.109463i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.37743 | + | 1.72731i | 0.187368 | + | 0.136131i | ||||
\(162\) | −0.0832830 | − | 0.114629i | −0.00654333 | − | 0.00900612i | ||||
\(163\) | 0.478134 | + | 0.658095i | 0.0374503 | + | 0.0515460i | 0.827332 | − | 0.561714i | \(-0.189858\pi\) |
−0.789881 | + | 0.613260i | \(0.789858\pi\) | |||||||
\(164\) | 4.05522 | + | 2.94629i | 0.316659 | + | 0.230067i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.847418 | + | 0.615685i | −0.0657724 | + | 0.0477865i | ||||
\(167\) | 23.9343 | + | 7.77671i | 1.85209 | + | 0.601780i | 0.996448 | + | 0.0842082i | \(0.0268361\pi\) |
0.855640 | + | 0.517572i | \(0.173164\pi\) | |||||||
\(168\) | 0.484013i | 0.0373424i | ||||||||
\(169\) | −2.46864 | + | 7.59770i | −0.189896 | + | 0.584438i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.96804 | + | 6.05699i | 0.150500 | + | 0.463190i | ||||
\(172\) | 6.36408 | − | 2.06781i | 0.485256 | − | 0.157669i | ||||
\(173\) | 0.241548 | − | 0.332462i | 0.0183645 | − | 0.0252766i | −0.799736 | − | 0.600352i | \(-0.795027\pi\) |
0.818101 | + | 0.575075i | \(0.195027\pi\) | |||||||
\(174\) | −0.529076 | −0.0401091 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.2779 | −1.07624 | ||||||||
\(177\) | 7.71550 | − | 10.6195i | 0.579932 | − | 0.798208i | ||||
\(178\) | −2.08836 | + | 0.678550i | −0.156529 | + | 0.0508595i | ||||
\(179\) | 4.58896 | + | 14.1234i | 0.342995 | + | 1.05563i | 0.962648 | + | 0.270755i | \(0.0872733\pi\) |
−0.619653 | + | 0.784876i | \(0.712727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.228432 | − | 0.703043i | 0.0169792 | − | 0.0522568i | −0.942208 | − | 0.335029i | \(-0.891254\pi\) |
0.959187 | + | 0.282772i | \(0.0912540\pi\) | |||||||
\(182\) | − | 0.557153i | − | 0.0412990i | ||||||
\(183\) | −9.84118 | − | 3.19759i | −0.727481 | − | 0.236373i | ||||
\(184\) | 1.56198 | − | 1.13485i | 0.115151 | − | 0.0836621i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.143619 | − | 0.104345i | −0.0105307 | − | 0.00765097i | ||||
\(187\) | 11.4791 | + | 15.7997i | 0.839437 | + | 1.15539i | ||||
\(188\) | −9.89131 | − | 13.6142i | −0.721398 | − | 0.992920i | ||||
\(189\) | 0.694388 | + | 0.504502i | 0.0505093 | + | 0.0366971i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.20462 | − | 1.60175i | 0.159521 | − | 0.115899i | −0.505161 | − | 0.863025i | \(-0.668567\pi\) |
0.664682 | + | 0.747126i | \(0.268567\pi\) | |||||||
\(192\) | −7.15404 | − | 2.32449i | −0.516298 | − | 0.167755i | ||||
\(193\) | 14.2040i | 1.02243i | 0.859453 | + | 0.511215i | \(0.170804\pi\) | ||||
−0.859453 | + | 0.511215i | \(0.829196\pi\) | |||||||
\(194\) | −0.439534 | + | 1.35275i | −0.0315567 | + | 0.0971215i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.83208 | + | 11.7939i | 0.273720 | + | 0.842423i | ||||
\(197\) | −5.27447 | + | 1.71378i | −0.375791 | + | 0.122102i | −0.490821 | − | 0.871260i | \(-0.663303\pi\) |
0.115031 | + | 0.993362i | \(0.463303\pi\) | |||||||
\(198\) | 0.306475 | − | 0.421827i | 0.0217803 | − | 0.0299780i | ||||
\(199\) | −5.96371 | −0.422756 | −0.211378 | − | 0.977404i | \(-0.567795\pi\) | ||||
−0.211378 | + | 0.977404i | \(0.567795\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.34649 | −0.236043 | ||||||||
\(202\) | −0.0595154 | + | 0.0819159i | −0.00418749 | + | 0.00576358i | ||||
\(203\) | 3.04811 | − | 0.990391i | 0.213935 | − | 0.0695119i | ||||
\(204\) | 3.24700 | + | 9.99322i | 0.227335 | + | 0.699666i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.0341853 | + | 0.105212i | −0.00238181 | + | 0.00733044i | ||||
\(207\) | − | 3.42379i | − | 0.237970i | ||||||
\(208\) | 16.9054 | + | 5.49289i | 1.17218 | + | 0.380863i | ||||
\(209\) | −18.9604 | + | 13.7755i | −1.31152 | + | 0.952875i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0983 | + | 8.06342i | 0.764042 | + | 0.555109i | 0.900147 | − | 0.435586i | \(-0.143459\pi\) |
−0.136106 | + | 0.990694i | \(0.543459\pi\) | |||||||
\(212\) | 2.73285 | + | 3.76144i | 0.187693 | + | 0.258337i | ||||
\(213\) | −2.54093 | − | 3.49729i | −0.174102 | − | 0.239630i | ||||
\(214\) | −1.37098 | − | 0.996073i | −0.0937180 | − | 0.0680901i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.456216 | − | 0.331460i | 0.0310415 | − | 0.0225530i | ||||
\(217\) | 1.02274 | + | 0.332310i | 0.0694284 | + | 0.0225587i | ||||
\(218\) | − | 0.344849i | − | 0.0233561i | ||||||
\(219\) | −2.80590 | + | 8.63566i | −0.189605 | + | 0.583544i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.51322 | − | 23.1233i | −0.505394 | − | 1.55544i | ||||
\(222\) | −1.00401 | + | 0.326224i | −0.0673849 | + | 0.0218947i | ||||
\(223\) | 1.90543 | − | 2.62259i | 0.127597 | − | 0.175622i | −0.740439 | − | 0.672124i | \(-0.765382\pi\) |
0.868036 | + | 0.496502i | \(0.165382\pi\) | |||||||
\(224\) | −1.43988 | −0.0962060 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.27204 | 0.151134 | ||||||||
\(227\) | −7.74694 | + | 10.6627i | −0.514182 | + | 0.707711i | −0.984618 | − | 0.174723i | \(-0.944097\pi\) |
0.470435 | + | 0.882434i | \(0.344097\pi\) | |||||||
\(228\) | −11.9924 | + | 3.89656i | −0.794215 | + | 0.258056i | ||||
\(229\) | −1.80407 | − | 5.55236i | −0.119216 | − | 0.366911i | 0.873587 | − | 0.486669i | \(-0.161788\pi\) |
−0.992803 | + | 0.119758i | \(0.961788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.976037 | + | 3.00393i | −0.0642185 | + | 0.197644i | ||||
\(232\) | − | 2.10568i | − | 0.138245i | ||||||
\(233\) | 8.87767 | + | 2.88453i | 0.581595 | + | 0.188972i | 0.585015 | − | 0.811022i | \(-0.301089\pi\) |
−0.00341975 | + | 0.999994i | \(0.501089\pi\) | |||||||
\(234\) | −0.525156 | + | 0.381548i | −0.0343305 | + | 0.0249426i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 21.0258 | + | 15.2761i | 1.36866 | + | 0.994390i | ||||
\(237\) | 1.90872 | + | 2.62712i | 0.123984 | + | 0.170650i | ||||
\(238\) | 0.379360 | + | 0.522144i | 0.0245903 | + | 0.0338456i | ||||
\(239\) | 13.8748 | + | 10.0806i | 0.897485 | + | 0.652061i | 0.937819 | − | 0.347125i | \(-0.112842\pi\) |
−0.0403340 | + | 0.999186i | \(0.512842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.84169 | + | 4.24424i | −0.376296 | + | 0.273395i | −0.759817 | − | 0.650137i | \(-0.774711\pi\) |
0.383521 | + | 0.923532i | \(0.374711\pi\) | |||||||
\(242\) | 0.342530 | + | 0.111295i | 0.0220187 | + | 0.00715430i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 6.33099 | − | 19.4848i | 0.405300 | − | 1.24739i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.110848 | − | 0.341155i | −0.00706742 | − | 0.0217513i | ||||
\(247\) | 27.7492 | − | 9.01625i | 1.76564 | − | 0.573690i | ||||
\(248\) | 0.415286 | − | 0.571593i | 0.0263707 | − | 0.0362962i | ||||
\(249\) | −7.39269 | −0.468493 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.75708 | −0.363383 | −0.181692 | − | 0.983356i | \(-0.558157\pi\) | ||||
−0.181692 | + | 0.983356i | \(0.558157\pi\) | |||||||
\(252\) | −0.998876 | + | 1.37484i | −0.0629233 | + | 0.0866065i | ||||
\(253\) | 11.9826 | − | 3.89339i | 0.753342 | − | 0.244776i | ||||
\(254\) | −0.168066 | − | 0.517253i | −0.0105454 | − | 0.0324553i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.45541 | − | 13.7123i | 0.278463 | − | 0.857021i | ||||
\(257\) | − | 26.9602i | − | 1.68173i | −0.541242 | − | 0.840867i | \(-0.682046\pi\) | ||
0.541242 | − | 0.840867i | \(-0.317954\pi\) | |||||||
\(258\) | −0.455433 | − | 0.147979i | −0.0283540 | − | 0.00921278i | ||||
\(259\) | 5.17365 | − | 3.75888i | 0.321475 | − | 0.233565i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.02091 | − | 2.19482i | −0.186990 | − | 0.135856i | ||||
\(262\) | 1.03683 | + | 1.42707i | 0.0640555 | + | 0.0881648i | ||||
\(263\) | −12.1479 | − | 16.7202i | −0.749073 | − | 1.03101i | −0.998045 | − | 0.0625002i | \(-0.980093\pi\) |
0.248972 | − | 0.968511i | \(-0.419907\pi\) | |||||||
\(264\) | 1.67884 | + | 1.21975i | 0.103326 | + | 0.0750704i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.626600 | + | 0.455252i | −0.0384193 | + | 0.0279133i | ||||
\(267\) | −14.7390 | − | 4.78900i | −0.902013 | − | 0.293082i | ||||
\(268\) | − | 6.62579i | − | 0.404734i | ||||||
\(269\) | 4.24699 | − | 13.0709i | 0.258943 | − | 0.796946i | −0.734084 | − | 0.679059i | \(-0.762388\pi\) |
0.993027 | − | 0.117887i | \(-0.0376120\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.03333 | + | 3.18025i | 0.0627701 | + | 0.193187i | 0.977524 | − | 0.210826i | \(-0.0676153\pi\) |
−0.914754 | + | 0.404012i | \(0.867615\pi\) | |||||||
\(272\) | −19.5832 | + | 6.36296i | −1.18740 | + | 0.385811i | ||||
\(273\) | 2.31130 | − | 3.18123i | 0.139886 | − | 0.192537i | ||||
\(274\) | −1.68028 | −0.101510 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.77883 | 0.408038 | ||||||||
\(277\) | −5.23685 | + | 7.20791i | −0.314652 | + | 0.433081i | −0.936825 | − | 0.349799i | \(-0.886250\pi\) |
0.622173 | + | 0.782880i | \(0.286250\pi\) | |||||||
\(278\) | −0.628077 | + | 0.204075i | −0.0376696 | + | 0.0122396i | ||||
\(279\) | −0.387167 | − | 1.19158i | −0.0231791 | − | 0.0713380i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.95019 | + | 21.3905i | −0.414613 | + | 1.27605i | 0.497983 | + | 0.867187i | \(0.334074\pi\) |
−0.912596 | + | 0.408862i | \(0.865926\pi\) | |||||||
\(282\) | 1.20427i | 0.0717133i | ||||||||
\(283\) | 1.24297 | + | 0.403866i | 0.0738870 | + | 0.0240073i | 0.345727 | − | 0.938335i | \(-0.387632\pi\) |
−0.271840 | + | 0.962342i | \(0.587632\pi\) | |||||||
\(284\) | 6.92437 | − | 5.03085i | 0.410886 | − | 0.298526i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.93254 | − | 1.40407i | −0.114273 | − | 0.0830243i | ||||
\(287\) | 1.27724 | + | 1.75797i | 0.0753929 | + | 0.103769i | ||||
\(288\) | 0.986054 | + | 1.35719i | 0.0581038 | + | 0.0799730i | ||||
\(289\) | 9.03225 | + | 6.56231i | 0.531309 | + | 0.386018i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.12138 | + | 5.90053i | −0.476084 | + | 0.345895i | ||||
\(292\) | −17.0980 | − | 5.55546i | −1.00058 | − | 0.325109i | ||||
\(293\) | 1.97058i | 0.115123i | 0.998342 | + | 0.0575613i | \(0.0183325\pi\) | ||||
−0.998342 | + | 0.0575613i | \(0.981668\pi\) | |||||||
\(294\) | 0.274235 | − | 0.844010i | 0.0159937 | − | 0.0492236i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.29835 | − | 3.99590i | −0.0754648 | − | 0.232257i | ||||
\(297\) | 3.49982 | − | 1.13716i | 0.203080 | − | 0.0659847i | ||||
\(298\) | 0.961756 | − | 1.32374i | 0.0557130 | − | 0.0766824i | ||||
\(299\) | −15.6855 | −0.907118 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.90085 | 0.167202 | ||||||||
\(302\) | 2.03789 | − | 2.80491i | 0.117267 | − | 0.161404i | ||||
\(303\) | −0.679640 | + | 0.220829i | −0.0390443 | + | 0.0126863i | ||||
\(304\) | −7.63588 | − | 23.5008i | −0.437948 | − | 1.34786i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.232365 | − | 0.715146i | 0.0132834 | − | 0.0408822i | ||||
\(307\) | 15.2544i | 0.870617i | 0.900281 | + | 0.435308i | \(0.143361\pi\) | ||||
−0.900281 | + | 0.435308i | \(0.856639\pi\) | |||||||
\(308\) | −5.94756 | − | 1.93248i | −0.338894 | − | 0.110113i | ||||
\(309\) | −0.631652 | + | 0.458922i | −0.0359334 | + | 0.0261071i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −14.3562 | − | 10.4304i | −0.814065 | − | 0.591453i | 0.100941 | − | 0.994892i | \(-0.467815\pi\) |
−0.915006 | + | 0.403439i | \(0.867815\pi\) | |||||||
\(312\) | −1.51853 | − | 2.09008i | −0.0859699 | − | 0.118327i | ||||
\(313\) | 16.0976 | + | 22.1565i | 0.909890 | + | 1.25236i | 0.967204 | + | 0.254001i | \(0.0817465\pi\) |
−0.0573136 | + | 0.998356i | \(0.518253\pi\) | |||||||
\(314\) | 2.56380 | + | 1.86271i | 0.144684 | + | 0.105119i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.20150 | + | 3.77911i | −0.292607 | + | 0.212592i | ||||
\(317\) | −8.22248 | − | 2.67165i | −0.461821 | − | 0.150055i | 0.0688603 | − | 0.997626i | \(-0.478064\pi\) |
−0.530681 | + | 0.847572i | \(0.678064\pi\) | |||||||
\(318\) | − | 0.332725i | − | 0.0186583i | ||||||
\(319\) | 4.24621 | − | 13.0685i | 0.237742 | − | 0.731696i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.69587 | − | 11.3747i | −0.206283 | − | 0.634875i | ||||
\(322\) | 0.396000 | − | 0.128668i | 0.0220682 | − | 0.00717039i | ||||
\(323\) | −19.8664 | + | 27.3438i | −1.10540 | + | 1.52145i | ||||
\(324\) | 1.97992 | 0.109996 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.115257 | 0.00638351 | ||||||||
\(327\) | 1.43057 | − | 1.96902i | 0.0791109 | − | 0.108887i | ||||
\(328\) | 1.35777 | − | 0.441167i | 0.0749704 | − | 0.0243594i | ||||
\(329\) | −2.25431 | − | 6.93805i | −0.124284 | − | 0.382507i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.53353 | − | 4.71971i | 0.0842903 | − | 0.259419i | −0.900025 | − | 0.435839i | \(-0.856452\pi\) |
0.984315 | + | 0.176420i | \(0.0564517\pi\) | |||||||
\(332\) | − | 14.6370i | − | 0.803308i | ||||||
\(333\) | −7.08601 | − | 2.30238i | −0.388311 | − | 0.126170i | ||||
\(334\) | 2.88475 | − | 2.09590i | 0.157847 | − | 0.114682i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.69419 | − | 1.95744i | −0.146980 | − | 0.106787i | ||||
\(337\) | −4.29394 | − | 5.91011i | −0.233906 | − | 0.321944i | 0.675888 | − | 0.737005i | \(-0.263760\pi\) |
−0.909794 | + | 0.415061i | \(0.863760\pi\) | |||||||
\(338\) | 0.665322 | + | 0.915738i | 0.0361888 | + | 0.0498096i | ||||
\(339\) | 12.9729 | + | 9.42535i | 0.704590 | + | 0.511915i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.73004 | − | 2.71003i | 0.201993 | − | 0.146757i | ||||
\(342\) | 0.858212 | + | 0.278850i | 0.0464068 | + | 0.0150785i | ||||
\(343\) | 11.3840i | 0.614680i | ||||||||
\(344\) | 0.588946 | − | 1.81259i | 0.0317538 | − | 0.0977282i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0179930 | − | 0.0553768i | −0.000967311 | − | 0.00297708i | ||||
\(347\) | 15.1574 | − | 4.92493i | 0.813691 | − | 0.264384i | 0.127531 | − | 0.991835i | \(-0.459295\pi\) |
0.686160 | + | 0.727450i | \(0.259295\pi\) | |||||||
\(348\) | 4.34558 | − | 5.98117i | 0.232947 | − | 0.320624i | ||||
\(349\) | −16.5844 | −0.887743 | −0.443871 | − | 0.896091i | \(-0.646395\pi\) | ||||
−0.443871 | + | 0.896091i | \(0.646395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.58134 | −0.244534 | ||||||||
\(352\) | −3.62861 | + | 4.99435i | −0.193405 | + | 0.266200i | ||||
\(353\) | −12.3344 | + | 4.00768i | −0.656492 | + | 0.213307i | −0.618275 | − | 0.785962i | \(-0.712168\pi\) |
−0.0382177 | + | 0.999269i | \(0.512168\pi\) | |||||||
\(354\) | −0.574732 | − | 1.76884i | −0.0305467 | − | 0.0940129i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.48185 | − | 29.1821i | 0.502537 | − | 1.54665i | ||||
\(357\) | 4.55507i | 0.241080i | ||||||||
\(358\) | 2.00113 | + | 0.650208i | 0.105763 | + | 0.0343646i | ||||
\(359\) | −10.9153 | + | 7.93042i | −0.576087 | + | 0.418551i | −0.837311 | − | 0.546727i | \(-0.815874\pi\) |
0.261225 | + | 0.965278i | \(0.415874\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4427 | − | 12.6728i | −0.918036 | − | 0.666992i | ||||
\(362\) | −0.0615647 | − | 0.0847365i | −0.00323577 | − | 0.00445365i | ||||
\(363\) | 1.49408 | + | 2.05642i | 0.0784188 | + | 0.107934i | ||||
\(364\) | 6.29859 | + | 4.57619i | 0.330136 | + | 0.239858i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.18614 | + | 0.861781i | −0.0620006 | + | 0.0450460i | ||||
\(367\) | −4.35073 | − | 1.41364i | −0.227106 | − | 0.0737913i | 0.193253 | − | 0.981149i | \(-0.438096\pi\) |
−0.420360 | + | 0.907358i | \(0.638096\pi\) | |||||||
\(368\) | 13.2841i | 0.692482i | ||||||||
\(369\) | 0.782331 | − | 2.40777i | 0.0407265 | − | 0.125343i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.622838 | + | 1.91690i | 0.0323361 | + | 0.0995204i | ||||
\(372\) | 2.35924 | − | 0.766562i | 0.122321 | − | 0.0397444i | ||||
\(373\) | −12.1944 | + | 16.7841i | −0.631401 | + | 0.869048i | −0.998120 | − | 0.0612830i | \(-0.980481\pi\) |
0.366720 | + | 0.930331i | \(0.380481\pi\) | |||||||
\(374\) | 2.76712 | 0.143084 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.79291 | −0.247175 | ||||||||
\(377\) | −10.0552 | + | 13.8398i | −0.517870 | + | 0.712787i | ||||
\(378\) | 0.115661 | − | 0.0375807i | 0.00594898 | − | 0.00193294i | ||||
\(379\) | 1.78662 | + | 5.49865i | 0.0917725 | + | 0.282447i | 0.986399 | − | 0.164368i | \(-0.0525584\pi\) |
−0.894627 | + | 0.446815i | \(0.852558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.18615 | − | 3.65061i | 0.0607686 | − | 0.187026i | ||||
\(382\) | − | 0.386113i | − | 0.0197553i | ||||||
\(383\) | 24.5491 | + | 7.97647i | 1.25440 | + | 0.407579i | 0.859495 | − | 0.511144i | \(-0.170778\pi\) |
0.394903 | + | 0.918723i | \(0.370778\pi\) | |||||||
\(384\) | −3.57664 | + | 2.59858i | −0.182519 | + | 0.132608i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.62820 | + | 1.18295i | 0.0828731 | + | 0.0602108i | ||||
\(387\) | −1.98655 | − | 2.73425i | −0.100982 | − | 0.138990i | ||||
\(388\) | −11.6826 | − | 16.0797i | −0.593094 | − | 0.816324i | ||||
\(389\) | −12.7053 | − | 9.23092i | −0.644183 | − | 0.468026i | 0.217102 | − | 0.976149i | \(-0.430340\pi\) |
−0.861285 | + | 0.508123i | \(0.830340\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6999 | − | 10.6801i | 0.743407 | − | 0.540117i | ||||
\(392\) | 3.35909 | + | 1.09144i | 0.169660 | + | 0.0551258i | ||||
\(393\) | 12.4495i | 0.627992i | ||||||||
\(394\) | −0.242825 | + | 0.747337i | −0.0122333 | + | 0.0376503i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.25149 | + | 6.92938i | 0.113142 | + | 0.348214i | ||||
\(397\) | −18.6445 | + | 6.05796i | −0.935740 | + | 0.304040i | −0.736908 | − | 0.675993i | \(-0.763715\pi\) |
−0.198832 | + | 0.980034i | \(0.563715\pi\) | |||||||
\(398\) | −0.496675 | + | 0.683615i | −0.0248961 | + | 0.0342665i | ||||
\(399\) | −5.46632 | −0.273658 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.4239 | −0.720297 | −0.360148 | − | 0.932895i | \(-0.617274\pi\) | ||||
−0.360148 | + | 0.932895i | \(0.617274\pi\) | |||||||
\(402\) | −0.278705 | + | 0.383605i | −0.0139006 | + | 0.0191325i | ||||
\(403\) | −5.45903 | + | 1.77375i | −0.271934 | + | 0.0883566i | ||||
\(404\) | −0.437224 | − | 1.34564i | −0.0217527 | − | 0.0669479i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.140328 | − | 0.431885i | 0.00696436 | − | 0.0214341i | ||||
\(407\) | − | 27.4179i | − | 1.35906i | ||||||
\(408\) | 2.84623 | + | 0.924795i | 0.140909 | + | 0.0457842i | ||||
\(409\) | −22.5507 | + | 16.3841i | −1.11506 | + | 0.810140i | −0.983453 | − | 0.181162i | \(-0.942014\pi\) |
−0.131609 | + | 0.991302i | \(0.542014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.59406 | − | 6.97049i | −0.473240 | − | 0.343829i | ||||
\(412\) | −0.908630 | − | 1.25062i | −0.0447650 | − | 0.0616137i | ||||
\(413\) | 6.62229 | + | 9.11481i | 0.325862 | + | 0.448510i | ||||
\(414\) | −0.392466 | − | 0.285143i | −0.0192886 | − | 0.0140140i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.21773 | − | 4.51745i | 0.304850 | − | 0.221486i | ||||
\(417\) | −4.43277 | − | 1.44030i | −0.217074 | − | 0.0705316i | ||||
\(418\) | 3.32069i | 0.162420i | ||||||||
\(419\) | 11.2137 | − | 34.5121i | 0.547823 | − | 1.68603i | −0.166359 | − | 0.986065i | \(-0.553201\pi\) |
0.714182 | − | 0.699960i | \(-0.246799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.04324 | − | 3.21077i | −0.0508445 | − | 0.156483i | 0.922410 | − | 0.386211i | \(-0.126216\pi\) |
−0.973255 | + | 0.229728i | \(0.926216\pi\) | |||||||
\(422\) | 1.84861 | − | 0.600649i | 0.0899888 | − | 0.0292391i | ||||
\(423\) | −4.99580 | + | 6.87614i | −0.242904 | + | 0.334329i | ||||
\(424\) | 1.32422 | 0.0643099 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.612508 | −0.0296761 | ||||||||
\(427\) | 5.22040 | − | 7.18527i | 0.252633 | − | 0.347719i | ||||
\(428\) | 22.5211 | − | 7.31755i | 1.08860 | − | 0.353707i | ||||
\(429\) | −5.20972 | − | 16.0339i | −0.251528 | − | 0.774123i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.93015 | + | 24.4065i | −0.381982 | + | 1.17562i | 0.556665 | + | 0.830737i | \(0.312081\pi\) |
−0.938646 | + | 0.344881i | \(0.887919\pi\) | |||||||
\(432\) | 3.87995i | 0.186674i | ||||||||
\(433\) | −37.8587 | − | 12.3010i | −1.81937 | − | 0.591150i | −0.999836 | − | 0.0181229i | \(-0.994231\pi\) |
−0.819536 | − | 0.573027i | \(-0.805769\pi\) | |||||||
\(434\) | 0.123270 | − | 0.0895606i | 0.00591713 | − | 0.00429905i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.89850 | + | 2.83243i | 0.186704 | + | 0.135649i | ||||
\(437\) | 12.8167 | + | 17.6407i | 0.613106 | + | 0.843867i | ||||
\(438\) | 0.756216 | + | 1.04084i | 0.0361334 | + | 0.0497333i | ||||
\(439\) | 27.4402 | + | 19.9365i | 1.30965 | + | 0.951516i | 1.00000 | 0.000665125i | \(0.000211716\pi\) | |
0.309649 | + | 0.950851i | \(0.399788\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.06712 | − | 3.68148i | 0.241291 | − | 0.175308i | ||||
\(442\) | −3.27633 | − | 1.06454i | −0.155839 | − | 0.0506352i | ||||
\(443\) | − | 28.9300i | − | 1.37451i | −0.726418 | − | 0.687253i | \(-0.758816\pi\) | ||
0.726418 | − | 0.687253i | \(-0.241184\pi\) | |||||||
\(444\) | 4.55855 | − | 14.0298i | 0.216339 | − | 0.665823i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.141936 | − | 0.436835i | −0.00672088 | − | 0.0206847i | ||||
\(447\) | 10.9828 | − | 3.56854i | 0.519471 | − | 0.168786i | ||||
\(448\) | 3.79497 | − | 5.22332i | 0.179295 | − | 0.246779i | ||||
\(449\) | 10.2089 | 0.481788 | 0.240894 | − | 0.970551i | \(-0.422559\pi\) | ||||
0.240894 | + | 0.970551i | \(0.422559\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.31639 | 0.438692 | ||||||||
\(452\) | −18.6615 | + | 25.6853i | −0.877762 | + | 1.20814i | ||||
\(453\) | 23.2718 | − | 7.56147i | 1.09340 | − | 0.355269i | ||||
\(454\) | 0.577074 | + | 1.77605i | 0.0270834 | + | 0.0833542i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.10980 | + | 3.41562i | −0.0519712 | + | 0.159951i | ||||
\(457\) | − | 32.4952i | − | 1.52006i | −0.649888 | − | 0.760030i | \(-0.725184\pi\) | ||
0.649888 | − | 0.760030i | \(-0.274816\pi\) | |||||||
\(458\) | −0.786712 | − | 0.255618i | −0.0367606 | − | 0.0119442i | ||||
\(459\) | 4.29347 | − | 3.11939i | 0.200402 | − | 0.145601i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.566772 | + | 0.411784i | 0.0263972 | + | 0.0191787i | 0.600906 | − | 0.799320i | \(-0.294807\pi\) |
−0.574508 | + | 0.818499i | \(0.694807\pi\) | |||||||
\(462\) | 0.263051 | + | 0.362059i | 0.0122382 | + | 0.0168445i | ||||
\(463\) | −1.27623 | − | 1.75659i | −0.0593117 | − | 0.0816355i | 0.778331 | − | 0.627854i | \(-0.216067\pi\) |
−0.837642 | + | 0.546219i | \(0.816067\pi\) | |||||||
\(464\) | 11.7210 | + | 8.51578i | 0.544132 | + | 0.395335i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.07001 | − | 0.777408i | 0.0495673 | − | 0.0360127i | ||||
\(467\) | 3.68734 | + | 1.19809i | 0.170630 | + | 0.0554410i | 0.393086 | − | 0.919502i | \(-0.371407\pi\) |
−0.222456 | + | 0.974943i | \(0.571407\pi\) | |||||||
\(468\) | − | 9.07071i | − | 0.419294i | ||||||
\(469\) | 0.887597 | − | 2.73174i | 0.0409854 | − | 0.126140i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.91148 | + | 21.2714i | 0.318464 | + | 0.980132i | ||||
\(472\) | 7.03986 | − | 2.28739i | 0.324036 | − | 0.105286i | ||||
\(473\) | 7.31036 | − | 10.0618i | 0.336131 | − | 0.462644i | ||||
\(474\) | 0.460109 | 0.0211335 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.01870 | −0.413371 | ||||||||
\(477\) | 1.38028 | − | 1.89979i | 0.0631986 | − | 0.0869855i | ||||
\(478\) | 2.31107 | − | 0.750911i | 0.105706 | − | 0.0343459i | ||||
\(479\) | 6.79817 | + | 20.9226i | 0.310617 | + | 0.955979i | 0.977521 | + | 0.210836i | \(0.0676187\pi\) |
−0.666905 | + | 0.745143i | \(0.732381\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.5480 | + | 32.4634i | −0.480948 | + | 1.48020i | ||||
\(482\) | 1.02310i | 0.0466010i | ||||||||
\(483\) | 2.79484 | + | 0.908099i | 0.127170 | + | 0.0413199i | ||||
\(484\) | −4.07156 | + | 2.95816i | −0.185071 | + | 0.134462i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.114629 | − | 0.0832830i | −0.00519969 | − | 0.00377779i | ||||
\(487\) | 16.6929 | + | 22.9759i | 0.756430 | + | 1.04114i | 0.997503 | + | 0.0706291i | \(0.0225007\pi\) |
−0.241073 | + | 0.970507i | \(0.577499\pi\) | |||||||
\(488\) | −3.42982 | − | 4.72075i | −0.155261 | − | 0.213698i | ||||
\(489\) | 0.658095 | + | 0.478134i | 0.0297601 | + | 0.0216220i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.3641 | − | 8.25653i | 0.512856 | − | 0.372612i | −0.301050 | − | 0.953608i | \(-0.597337\pi\) |
0.813906 | + | 0.580997i | \(0.197337\pi\) | |||||||
\(492\) | 4.76720 | + | 1.54896i | 0.214922 | + | 0.0698323i | ||||
\(493\) | − | 19.8167i | − | 0.892498i | ||||||
\(494\) | 1.27751 | − | 3.93176i | 0.0574778 | − | 0.176898i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.50219 | + | 4.62326i | 0.0674503 | + | 0.207591i | ||||
\(497\) | 3.52878 | − | 1.14657i | 0.158287 | − | 0.0514307i | ||||
\(498\) | −0.615685 | + | 0.847418i | −0.0275895 | + | 0.0379737i | ||||
\(499\) | −13.0842 | −0.585731 | −0.292866 | − | 0.956154i | \(-0.594609\pi\) | ||||
−0.292866 | + | 0.956154i | \(0.594609\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.1660 | 1.12433 | ||||||||
\(502\) | −0.479467 | + | 0.659929i | −0.0213996 | + | 0.0294541i | ||||
\(503\) | −11.7022 | + | 3.80226i | −0.521773 | + | 0.169534i | −0.558050 | − | 0.829807i | \(-0.688450\pi\) |
0.0362767 | + | 0.999342i | \(0.488450\pi\) | |||||||
\(504\) | 0.149568 | + | 0.460324i | 0.00666230 | + | 0.0205044i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.551653 | − | 1.69781i | 0.0245240 | − | 0.0754770i | ||||
\(507\) | 7.98869i | 0.354790i | ||||||||
\(508\) | 7.22793 | + | 2.34850i | 0.320688 | + | 0.104198i | ||||
\(509\) | 0.0634186 | − | 0.0460763i | 0.00281098 | − | 0.00204230i | −0.586379 | − | 0.810037i | \(-0.699447\pi\) |
0.589190 | + | 0.807995i | \(0.299447\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.30509 | − | 4.58092i | −0.278921 | − | 0.202648i | ||||
\(512\) | −6.39793 | − | 8.80600i | −0.282751 | − | 0.389174i | ||||
\(513\) | 3.74343 | + | 5.15239i | 0.165276 | + | 0.227483i | ||||
\(514\) | −3.09043 | − | 2.24533i | −0.136313 | − | 0.0990372i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.41361 | − | 3.93321i | 0.238321 | − | 0.173150i | ||||
\(517\) | −29.7463 | − | 9.66515i | −1.30824 | − | 0.425073i | ||||
\(518\) | − | 0.906103i | − | 0.0398119i | ||||||
\(519\) | 0.126989 | − | 0.390832i | 0.00557420 | − | 0.0171556i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.59919 | + | 17.2325i | 0.245305 | + | 0.754971i | 0.995586 | + | 0.0938524i | \(0.0299182\pi\) |
−0.750281 | + | 0.661119i | \(0.770082\pi\) | |||||||
\(522\) | −0.503181 | + | 0.163493i | −0.0220236 | + | 0.00715591i | ||||
\(523\) | 6.83613 | − | 9.40913i | 0.298923 | − | 0.411432i | −0.632964 | − | 0.774181i | \(-0.718162\pi\) |
0.931887 | + | 0.362749i | \(0.118162\pi\) | |||||||
\(524\) | −24.6490 | −1.07680 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.92834 | −0.127682 | ||||||||
\(527\) | 3.90828 | − | 5.37929i | 0.170247 | − | 0.234326i | ||||
\(528\) | −13.5791 | + | 4.41212i | −0.590955 | + | 0.192013i | ||||
\(529\) | 3.48500 | + | 10.7257i | 0.151522 | + | 0.466336i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.05628 | − | 12.4839i | 0.176027 | − | 0.541757i | ||||
\(532\) | − | 10.8229i | − | 0.469232i | ||||||
\(533\) | −11.0308 | − | 3.58413i | −0.477797 | − | 0.155246i | ||||
\(534\) | −1.77647 | + | 1.29068i | −0.0768753 | + | 0.0558532i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.52672 | − | 1.10923i | −0.0659442 | − | 0.0479113i | ||||
\(537\) | 8.72873 | + | 12.0141i | 0.376672 | + | 0.518445i | ||||
\(538\) | −1.14460 | − | 1.57541i | −0.0493473 | − | 0.0679208i | ||||
\(539\) | 18.6466 | + | 13.5476i | 0.803167 | + | 0.583535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.6812 | + | 17.2054i | −1.01814 | + | 0.739719i | −0.965900 | − | 0.258916i | \(-0.916635\pi\) |
−0.0522359 | + | 0.998635i | \(0.516635\pi\) | |||||||
\(542\) | 0.450608 | + | 0.146412i | 0.0193553 | + | 0.00628891i | ||||
\(543\) | − | 0.739223i | − | 0.0317231i | ||||||
\(544\) | −2.75115 | + | 8.46718i | −0.117955 | + | 0.363027i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.172170 | − | 0.529884i | −0.00736819 | − | 0.0226770i | ||||
\(547\) | 11.4769 | − | 3.72908i | 0.490717 | − | 0.159444i | −0.0531977 | − | 0.998584i | \(-0.516941\pi\) |
0.543915 | + | 0.839140i | \(0.316941\pi\) | |||||||
\(548\) | 13.8010 | − | 18.9955i | 0.589551 | − | 0.811448i | ||||
\(549\) | −10.3476 | −0.441626 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.7810 | 1.01311 | ||||||||
\(552\) | 1.13485 | − | 1.56198i | 0.0483023 | − | 0.0664825i | ||||
\(553\) | −2.65078 | + | 0.861290i | −0.112723 | + | 0.0366258i | ||||
\(554\) | 0.390096 | + | 1.20059i | 0.0165736 | + | 0.0510083i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.85168 | − | 8.77655i | 0.120938 | − | 0.372209i | ||||
\(557\) | 41.4154i | 1.75483i | 0.479737 | + | 0.877413i | \(0.340732\pi\) | ||||
−0.479737 | + | 0.877413i | \(0.659268\pi\) | |||||||
\(558\) | −0.168834 | − | 0.0548576i | −0.00714732 | − | 0.00232231i | ||||
\(559\) | −12.5265 | + | 9.10106i | −0.529816 | + | 0.384934i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.7997 | + | 11.4791i | 0.667062 | + | 0.484649i | ||||
\(562\) | 1.87314 | + | 2.57816i | 0.0790137 | + | 0.108753i | ||||
\(563\) | 18.8954 | + | 26.0072i | 0.796345 | + | 1.09607i | 0.993289 | + | 0.115660i | \(0.0368982\pi\) |
−0.196944 | + | 0.980415i | \(0.563102\pi\) | |||||||
\(564\) | −13.6142 | − | 9.89131i | −0.573262 | − | 0.416499i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.149813 | − | 0.108846i | 0.00629712 | − | 0.00457513i | ||||
\(567\) | 0.816302 | + | 0.265233i | 0.0342815 | + | 0.0111387i | ||||
\(568\) | − | 2.43773i | − | 0.102285i | ||||||
\(569\) | −6.52273 | + | 20.0749i | −0.273447 | + | 0.841583i | 0.716179 | + | 0.697916i | \(0.245889\pi\) |
−0.989626 | + | 0.143667i | \(0.954111\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.64795 | − | 23.5380i | −0.320057 | − | 0.985034i | −0.973623 | − | 0.228164i | \(-0.926728\pi\) |
0.653566 | − | 0.756870i | \(-0.273272\pi\) | |||||||
\(572\) | 31.7459 | − | 10.3149i | 1.32736 | − | 0.431286i | ||||
\(573\) | 1.60175 | − | 2.20462i | 0.0669142 | − | 0.0920994i | ||||
\(574\) | 0.307886 | 0.0128509 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.52220 | −0.313425 | ||||||||
\(577\) | 11.0333 | − | 15.1861i | 0.459324 | − | 0.632205i | −0.515045 | − | 0.857163i | \(-0.672225\pi\) |
0.974368 | + | 0.224959i | \(0.0722247\pi\) | |||||||
\(578\) | 1.50446 | − | 0.488830i | 0.0625775 | − | 0.0203327i | ||||
\(579\) | 4.38929 | + | 13.5088i | 0.182413 | + | 0.561408i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.96078 | − | 6.03467i | 0.0813470 | − | 0.250360i | ||||
\(582\) | 1.42236i | 0.0589587i | ||||||||
\(583\) | 8.21853 | + | 2.67036i | 0.340377 | + | 0.110595i | ||||
\(584\) | −4.14247 | + | 3.00968i | −0.171417 | + | 0.124541i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.225886 | + | 0.164116i | 0.00933127 | + | 0.00677956i | ||||
\(587\) | 8.67406 | + | 11.9388i | 0.358017 | + | 0.492768i | 0.949595 | − | 0.313480i | \(-0.101495\pi\) |
−0.591578 | + | 0.806248i | \(0.701495\pi\) | |||||||
\(588\) | 7.28905 | + | 10.0325i | 0.300595 | + | 0.413734i | ||||
\(589\) | 6.45543 | + | 4.69014i | 0.265991 | + | 0.193254i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.48673 | + | 3.25980i | −0.184560 | + | 0.134090i | ||||
\(592\) | 27.4933 | + | 8.93313i | 1.12997 | + | 0.367149i | ||||
\(593\) | 8.01859i | 0.329284i | 0.986353 | + | 0.164642i | \(0.0526469\pi\) | ||||
−0.986353 | + | 0.164642i | \(0.947353\pi\) | |||||||
\(594\) | 0.161124 | − | 0.495888i | 0.00661099 | − | 0.0203465i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.06544 | + | 21.7452i | 0.289412 | + | 0.890718i | ||||
\(597\) | −5.67182 | + | 1.84289i | −0.232132 | + | 0.0754243i | ||||
\(598\) | −1.30634 | + | 1.79802i | −0.0534201 | + | 0.0735265i | ||||
\(599\) | 1.28951 | 0.0526878 | 0.0263439 | − | 0.999653i | \(-0.491614\pi\) | ||||
0.0263439 | + | 0.999653i | \(0.491614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.8813 | −0.688603 | −0.344302 | − | 0.938859i | \(-0.611884\pi\) | ||||
−0.344302 | + | 0.938859i | \(0.611884\pi\) | |||||||
\(602\) | 0.241591 | − | 0.332522i | 0.00984652 | − | 0.0135526i | ||||
\(603\) | −3.18270 | + | 1.03412i | −0.129609 | + | 0.0421127i | ||||
\(604\) | 14.9711 | + | 46.0764i | 0.609167 | + | 1.87482i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.0312891 | + | 0.0962979i | −0.00127103 | + | 0.00391184i | ||||
\(607\) | 0.499318i | 0.0202667i | 0.999949 | + | 0.0101334i | \(0.00322560\pi\) | ||||
−0.999949 | + | 0.0101334i | \(0.996774\pi\) | |||||||
\(608\) | −10.1611 | − | 3.30153i | −0.412085 | − | 0.133895i | ||||
\(609\) | 2.59288 | − | 1.88384i | 0.105069 | − | 0.0763369i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.5019 | + | 22.8875i | 1.27443 | + | 0.925929i | ||||
\(612\) | 6.17615 | + | 8.50074i | 0.249656 | + | 0.343622i | ||||
\(613\) | −16.1195 | − | 22.1866i | −0.651061 | − | 0.896108i | 0.348084 | − | 0.937463i | \(-0.386832\pi\) |
−0.999145 | + | 0.0413552i | \(0.986832\pi\) | |||||||
\(614\) | 1.74860 | + | 1.27043i | 0.0705679 | + | 0.0512706i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.44097 | + | 1.04692i | −0.0580582 | + | 0.0421818i | ||||
\(617\) | 26.9344 | + | 8.75151i | 1.08434 | + | 0.352323i | 0.796056 | − | 0.605223i | \(-0.206916\pi\) |
0.288282 | + | 0.957546i | \(0.406916\pi\) | |||||||
\(618\) | 0.110626i | 0.00445003i | ||||||||
\(619\) | 0.114894 | − | 0.353606i | 0.00461796 | − | 0.0142126i | −0.948721 | − | 0.316115i | \(-0.897622\pi\) |
0.953339 | + | 0.301902i | \(0.0976216\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.05801 | − | 3.25621i | −0.0424564 | − | 0.130667i | ||||
\(622\) | −2.39125 | + | 0.776966i | −0.0958806 | + | 0.0311535i | ||||
\(623\) | 7.81853 | − | 10.7613i | 0.313243 | − | 0.431142i | ||||
\(624\) | 17.7754 | 0.711584 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.88043 | 0.155093 | ||||||||
\(627\) | −13.7755 | + | 18.9604i | −0.550142 | + | 0.757206i | ||||
\(628\) | −42.1157 | + | 13.6842i | −1.68060 | + | 0.546059i | ||||
\(629\) | −12.2188 | − | 37.6056i | −0.487195 | − | 1.49943i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.08354 | − | 15.6455i | 0.202373 | − | 0.622839i | −0.797438 | − | 0.603400i | \(-0.793812\pi\) |
0.999811 | − | 0.0194386i | \(-0.00618787\pi\) | |||||||
\(632\) | 1.83120i | 0.0728411i | ||||||||
\(633\) | 13.0469 | + | 4.23919i | 0.518567 | + | 0.168493i | ||||
\(634\) | −0.991042 | + | 0.720034i | −0.0393593 | + | 0.0285962i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.76144 | + | 2.73285i | 0.149151 | + | 0.108364i | ||||
\(637\) | −16.8661 | − | 23.2142i | −0.668259 | − | 0.919780i | ||||
\(638\) | −1.14439 | − | 1.57512i | −0.0453070 | − | 0.0623598i | ||||
\(639\) | −3.49729 | − | 2.54093i | −0.138351 | − | 0.100518i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.63910 | − | 1.19088i | 0.0647407 | − | 0.0470368i | −0.554944 | − | 0.831888i | \(-0.687260\pi\) |
0.619685 | + | 0.784851i | \(0.287260\pi\) | |||||||
\(642\) | −1.61168 | − | 0.523666i | −0.0636079 | − | 0.0206675i | ||||
\(643\) | − | 33.2034i | − | 1.30941i | −0.755883 | − | 0.654706i | \(-0.772792\pi\) | ||
0.755883 | − | 0.654706i | \(-0.227208\pi\) | |||||||
\(644\) | −1.79797 | + | 5.53357i | −0.0708498 | + | 0.218053i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.47986 | + | 4.55455i | 0.0582244 | + | 0.179196i | ||||
\(647\) | −38.5936 | + | 12.5398i | −1.51727 | + | 0.492992i | −0.944999 | − | 0.327072i | \(-0.893938\pi\) |
−0.572273 | + | 0.820064i | \(0.693938\pi\) | |||||||
\(648\) | 0.331460 | − | 0.456216i | 0.0130210 | − | 0.0179218i | ||||
\(649\) | 48.3042 | 1.89611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.07538 | 0.0421474 | ||||||||
\(652\) | −0.946669 | + | 1.30298i | −0.0370744 | + | 0.0510286i | ||||
\(653\) | 8.84208 | − | 2.87297i | 0.346017 | − | 0.112428i | −0.130852 | − | 0.991402i | \(-0.541771\pi\) |
0.476870 | + | 0.878974i | \(0.341771\pi\) | |||||||
\(654\) | −0.106564 | − | 0.327971i | −0.00416699 | − | 0.0128247i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.03540 | + | 9.34201i | −0.118513 | + | 0.364744i | ||||
\(657\) | 9.08007i | 0.354247i | ||||||||
\(658\) | −0.983049 | − | 0.319412i | −0.0383232 | − | 0.0124520i | ||||
\(659\) | −2.81185 | + | 2.04293i | −0.109534 | + | 0.0795811i | −0.641204 | − | 0.767371i | \(-0.721565\pi\) |
0.531670 | + | 0.846952i | \(0.321565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.29515 | − | 2.39407i | −0.128166 | − | 0.0931184i | 0.521855 | − | 0.853034i | \(-0.325240\pi\) |
−0.650022 | + | 0.759916i | \(0.725240\pi\) | |||||||
\(662\) | −0.413300 | − | 0.568859i | −0.0160634 | − | 0.0221093i | ||||
\(663\) | −14.2910 | − | 19.6699i | −0.555016 | − | 0.763914i | ||||
\(664\) | −3.37266 | − | 2.45038i | −0.130885 | − | 0.0950932i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.854064 | + | 0.620514i | −0.0330943 | + | 0.0240444i | ||||
\(667\) | −12.1589 | − | 3.95065i | −0.470793 | − | 0.152970i | ||||
\(668\) | 49.8267i | 1.92785i | ||||||||
\(669\) | 1.00174 | − | 3.08304i | 0.0387296 | − | 0.119197i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.7669 | − | 36.2148i | −0.454257 | − | 1.39806i | ||||
\(672\) | −1.36941 | + | 0.444947i | −0.0528260 | + | 0.0171642i | ||||
\(673\) | 12.5694 | − | 17.3003i | 0.484514 | − | 0.666877i | −0.494850 | − | 0.868978i | \(-0.664777\pi\) |
0.979365 | + | 0.202102i | \(0.0647771\pi\) | |||||||
\(674\) | −1.03508 | −0.0398699 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.8170 | −0.608346 | ||||||||
\(677\) | 11.9472 | − | 16.4438i | 0.459166 | − | 0.631988i | −0.515169 | − | 0.857088i | \(-0.672271\pi\) |
0.974336 | + | 0.225100i | \(0.0722709\pi\) | |||||||
\(678\) | 2.16084 | − | 0.702100i | 0.0829866 | − | 0.0269640i | ||||
\(679\) | −2.66256 | − | 8.19451i | −0.102180 | − | 0.314476i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.07281 | + | 12.5348i | −0.156070 | + | 0.480335i | ||||
\(682\) | − | 0.653271i | − | 0.0250150i | ||||||
\(683\) | −18.0312 | − | 5.85868i | −0.689943 | − | 0.224176i | −0.0569998 | − | 0.998374i | \(-0.518153\pi\) |
−0.632943 | + | 0.774198i | \(0.718153\pi\) | |||||||
\(684\) | −10.2013 | + | 7.41170i | −0.390058 | + | 0.283394i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.30494 | + | 0.948096i | 0.0498229 | + | 0.0361985i | ||||
\(687\) | −3.43155 | − | 4.72312i | −0.130922 | − | 0.180198i | ||||
\(688\) | 7.70770 | + | 10.6087i | 0.293853 | + | 0.404455i | ||||
\(689\) | −8.70359 | − | 6.32353i | −0.331580 | − | 0.240907i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.9893 | + | 8.71071i | −0.456093 | + | 0.331371i | −0.791997 | − | 0.610525i | \(-0.790958\pi\) |
0.335904 | + | 0.941896i | \(0.390958\pi\) | |||||||
\(692\) | 0.773818 | + | 0.251429i | 0.0294162 | + | 0.00955789i | ||||
\(693\) | 3.15852i | 0.119982i | ||||||||
\(694\) | 0.697811 | − | 2.14764i | 0.0264885 | − | 0.0815234i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.650691 | − | 2.00262i | −0.0246644 | − | 0.0759092i | ||||
\(697\) | 12.7781 | − | 4.15185i | 0.484004 | − | 0.157262i | ||||
\(698\) | −1.38120 | + | 1.90106i | −0.0522791 | + | 0.0719560i | ||||
\(699\) | 9.33453 | 0.353064 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.3996 | 1.18595 | 0.592973 | − | 0.805222i | \(-0.297954\pi\) | ||||
0.592973 | + | 0.805222i | \(0.297954\pi\) | |||||||
\(702\) | −0.381548 | + | 0.525156i | −0.0144006 | + | 0.0198207i | ||||
\(703\) | 45.1287 | − | 14.6632i | 1.70206 | − | 0.553033i | ||||
\(704\) | −8.55395 | − | 26.3264i | −0.322389 | − | 0.992212i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.567846 | + | 1.74765i | −0.0213712 | + | 0.0657737i | ||||
\(707\) | − | 0.613363i | − | 0.0230679i | ||||||
\(708\) | 24.7173 | + | 8.03112i | 0.928931 | + | 0.301828i | ||||
\(709\) | 20.4944 | − | 14.8900i | 0.769682 | − | 0.559207i | −0.132183 | − | 0.991225i | \(-0.542199\pi\) |
0.901865 | + | 0.432019i | \(0.142199\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.62712 | + | 1.90872i | 0.0985248 | + | 0.0715825i | ||||
\(712\) | −5.13681 | − | 7.07021i | −0.192510 | − | 0.264967i | ||||
\(713\) | −2.52140 | − | 3.47041i | −0.0944272 | − | 0.129968i | ||||
\(714\) | 0.522144 | + | 0.379360i | 0.0195408 | + | 0.0141972i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.7869 | + | 17.2822i | −0.888959 | + | 0.645867i | ||||
\(717\) | 16.3108 | + | 5.29969i | 0.609137 | + | 0.197921i | ||||
\(718\) | 1.91168i | 0.0713432i | ||||||||
\(719\) | 1.27535 | − | 3.92511i | 0.0475624 | − | 0.146382i | −0.924455 | − | 0.381292i | \(-0.875479\pi\) |
0.972017 | + | 0.234910i | \(0.0754794\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.207084 | − | 0.637339i | −0.00771221 | − | 0.0237358i | ||||
\(722\) | −2.90536 | + | 0.944008i | −0.108126 | + | 0.0351323i | ||||
\(723\) | −4.24424 | + | 5.84169i | −0.157845 | + | 0.217255i | ||||
\(724\) | 1.46361 | 0.0543945 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.360157 | 0.0133667 | ||||||||
\(727\) | −13.5214 | + | 18.6106i | −0.501479 | + | 0.690227i | −0.982454 | − | 0.186508i | \(-0.940283\pi\) |
0.480974 | + | 0.876735i | \(0.340283\pi\) | |||||||
\(728\) | 2.10890 | − | 0.685223i | 0.0781610 | − | 0.0253961i | ||||
\(729\) | −0.309017 | − | 0.951057i | −0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.54260 | − | 17.0584i | 0.205000 | − | 0.630927i | ||||
\(732\) | − | 20.4875i | − | 0.757240i | ||||||
\(733\) | −8.89896 | − | 2.89145i | −0.328690 | − | 0.106798i | 0.140023 | − | 0.990148i | \(-0.455282\pi\) |
−0.468714 | + | 0.883350i | \(0.655282\pi\) | |||||||
\(734\) | −0.524386 | + | 0.380989i | −0.0193554 | + | 0.0140625i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.64671 | + | 3.37604i | 0.171280 | + | 0.124442i | ||||
\(737\) | −7.23847 | − | 9.96291i | −0.266633 | − | 0.366988i | ||||
\(738\) | −0.210846 | − | 0.290204i | −0.00776133 | − | 0.0106826i | ||||
\(739\) | −38.1657 | − | 27.7290i | −1.40395 | − | 1.02003i | −0.994168 | − | 0.107844i | \(-0.965605\pi\) |
−0.409781 | − | 0.912184i | \(-0.634395\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 23.6048 | − | 17.1499i | 0.867146 | − | 0.630018i | ||||
\(742\) | 0.271604 | + | 0.0882496i | 0.00997091 | + | 0.00323974i | ||||
\(743\) | 2.39450i | 0.0878455i | 0.999035 | + | 0.0439228i | \(0.0139855\pi\) | ||||
−0.999035 | + | 0.0439228i | \(0.986014\pi\) | |||||||
\(744\) | 0.218329 | − | 0.671947i | 0.00800433 | − | 0.0246348i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.908366 | + | 2.79566i | 0.0332576 | + | 0.102356i | ||||
\(747\) | −7.03087 | + | 2.28447i | −0.257246 | + | 0.0835843i | ||||
\(748\) | −22.7278 | + | 31.2821i | −0.831011 | + | 1.14379i | ||||
\(749\) | 10.2655 | 0.375092 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.21632 | −0.263327 | −0.131664 | − | 0.991294i | \(-0.542032\pi\) | ||||
−0.131664 | + | 0.991294i | \(0.542032\pi\) | |||||||
\(752\) | 19.3835 | − | 26.6790i | 0.706842 | − | 0.972885i | ||||
\(753\) | −5.47530 | + | 1.77903i | −0.199531 | + | 0.0648316i | ||||
\(754\) | 0.749019 | + | 2.30524i | 0.0272777 | + | 0.0839520i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.525140 | + | 1.61622i | −0.0190992 | + | 0.0587812i | ||||
\(757\) | − | 13.3742i | − | 0.486094i | −0.970015 | − | 0.243047i | \(-0.921853\pi\) | ||
0.970015 | − | 0.243047i | \(-0.0781469\pi\) | |||||||
\(758\) | 0.779101 | + | 0.253145i | 0.0282982 | + | 0.00919465i | ||||
\(759\) | 10.1930 | − | 7.40567i | 0.369984 | − | 0.268809i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.5994 | − | 12.7867i | −0.637978 | − | 0.463518i | 0.221177 | − | 0.975234i | \(-0.429010\pi\) |
−0.859155 | + | 0.511716i | \(0.829010\pi\) | |||||||
\(762\) | −0.319680 | − | 0.440002i | −0.0115808 | − | 0.0159396i | ||||
\(763\) | 1.22788 | + | 1.69003i | 0.0444521 | + | 0.0611831i | ||||
\(764\) | 4.36499 | + | 3.17135i | 0.157920 | + | 0.114735i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.95886 | − | 2.14973i | 0.106908 | − | 0.0776730i | ||||
\(767\) | −57.1932 | − | 18.5832i | −2.06513 | − | 0.671000i | ||||
\(768\) | − | 14.4180i | − | 0.520265i | ||||||
\(769\) | −4.38814 | + | 13.5053i | −0.158240 | + | 0.487014i | −0.998475 | − | 0.0552094i | \(-0.982417\pi\) |
0.840234 | + | 0.542223i | \(0.182417\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.33117 | − | 25.6407i | −0.300040 | − | 0.923427i | ||||
\(772\) | −26.7465 | + | 8.69046i | −0.962627 | + | 0.312777i | ||||
\(773\) | 13.4230 | − | 18.4752i | 0.482791 | − | 0.664505i | −0.496247 | − | 0.868181i | \(-0.665289\pi\) |
0.979038 | + | 0.203676i | \(0.0652890\pi\) | |||||||
\(774\) | −0.478870 | −0.0172126 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.66089 | −0.203214 | ||||||||
\(777\) | 3.75888 | − | 5.17365i | 0.134849 | − | 0.185604i | ||||
\(778\) | −2.11627 | + | 0.687616i | −0.0758718 | + | 0.0246522i | ||||
\(779\) | 4.98243 | + | 15.3343i | 0.178514 | + | 0.549410i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.91582 | − | 15.1293i | 0.175902 | − | 0.541370i | ||||
\(782\) | − | 2.57451i | − | 0.0920644i | ||||||
\(783\) | −3.55129 | − | 1.15388i | −0.126913 | − | 0.0412365i | ||||
\(784\) | −19.6602 | + | 14.2839i | −0.702148 | + | 0.510141i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.42707 | + | 1.03683i | 0.0509020 | + | 0.0369824i | ||||
\(787\) | −22.6157 | − | 31.1279i | −0.806163 | − | 1.10959i | −0.991904 | − | 0.126990i | \(-0.959469\pi\) |
0.185741 | − | 0.982599i | \(-0.440531\pi\) | |||||||
\(788\) | −6.45416 | − | 8.88339i | −0.229920 | − | 0.316458i | ||||
\(789\) | −16.7202 | − | 12.1479i | −0.595254 | − | 0.432478i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.1348 | + | 8.08988i | −0.395906 | + | 0.287643i | ||||
\(792\) | 1.97360 | + | 0.641260i | 0.0701287 | + | 0.0227862i | ||||
\(793\) | 47.4060i | 1.68344i | ||||||||
\(794\) | −0.858349 | + | 2.64173i | −0.0304617 | + | 0.0937514i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.64878 | − | 11.2298i | −0.129327 | − | 0.398029i | ||||
\(797\) | −1.77599 | + | 0.577055i | −0.0629089 | + | 0.0204404i | −0.340302 | − | 0.940316i | \(-0.610529\pi\) |
0.277393 | + | 0.960756i | \(0.410529\pi\) | |||||||
\(798\) | −0.455252 | + | 0.626600i | −0.0161157 | + | 0.0221814i | ||||
\(799\) | −45.1063 | −1.59575 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.4975 | −0.547578 | ||||||||
\(802\) | −1.20127 | + | 1.65340i | −0.0424182 | + | 0.0583837i | ||||
\(803\) | −31.7786 | + | 10.3255i | −1.12144 | + | 0.364379i | ||||
\(804\) | −2.04748 | − | 6.30150i | −0.0722091 | − | 0.222237i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.251321 | + | 0.773487i | −0.00885241 | + | 0.0272449i | ||||
\(807\) | − | 13.7435i | − | 0.483796i | ||||||
\(808\) | −0.383258 | − | 0.124528i | −0.0134830 | − | 0.00438089i | ||||
\(809\) | 28.4381 | − | 20.6615i | 0.999831 | − | 0.726420i | 0.0377789 | − | 0.999286i | \(-0.487972\pi\) |
0.962052 | + | 0.272866i | \(0.0879717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.33270 | + | 3.87443i | 0.187256 | + | 0.136050i | 0.677464 | − | 0.735556i | \(-0.263079\pi\) |
−0.490208 | + | 0.871606i | \(0.663079\pi\) | |||||||
\(812\) | 3.72985 | + | 5.13370i | 0.130892 | + | 0.180158i | ||||
\(813\) | 1.96550 | + | 2.70528i | 0.0689332 | + | 0.0948785i | ||||
\(814\) | −3.14290 | − | 2.28345i | −0.110158 | − | 0.0800348i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −16.6584 | + | 12.1031i | −0.583162 | + | 0.423692i | ||||
\(817\) | 20.4709 | + | 6.65141i | 0.716187 | + | 0.232703i | ||||
\(818\) | 3.94949i | 0.138091i | ||||||||
\(819\) | 1.21512 | − | 3.73976i | 0.0424598 | − | 0.130678i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.62463 | + | 5.00011i | 0.0567001 | + | 0.174505i | 0.975396 | − | 0.220461i | \(-0.0707563\pi\) |
−0.918696 | + | 0.394966i | \(0.870756\pi\) | |||||||
\(822\) | −1.59804 | + | 0.519236i | −0.0557382 | + | 0.0181104i | ||||
\(823\) | −13.0440 | + | 17.9536i | −0.454687 | + | 0.625823i | −0.973396 | − | 0.229128i | \(-0.926413\pi\) |
0.518709 | + | 0.854951i | \(0.326413\pi\) | |||||||
\(824\) | −0.440283 | −0.0153380 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.59635 | 0.0555440 | ||||||||
\(827\) | 3.85738 | − | 5.30922i | 0.134134 | − | 0.184620i | −0.736666 | − | 0.676256i | \(-0.763601\pi\) |
0.870800 | + | 0.491637i | \(0.163601\pi\) | |||||||
\(828\) | 6.44705 | − | 2.09478i | 0.224051 | − | 0.0727985i | ||||
\(829\) | −7.74316 | − | 23.8310i | −0.268931 | − | 0.827685i | −0.990762 | − | 0.135615i | \(-0.956699\pi\) |
0.721831 | − | 0.692070i | \(-0.243301\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.75318 | + | 8.47340i | −0.0955066 | + | 0.293939i | ||||
\(832\) | 34.4618i | 1.19475i | ||||||||
\(833\) | 31.6126 | + | 10.2716i | 1.09531 | + | 0.355889i | ||||
\(834\) | −0.534274 | + | 0.388173i | −0.0185004 | + | 0.0134413i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −37.5402 | − | 27.2745i | −1.29835 | − | 0.943310i | ||||
\(837\) | −0.736436 | − | 1.01362i | −0.0254550 | − | 0.0350357i | ||||
\(838\) | −3.02219 | − | 4.15968i | −0.104400 | − | 0.143694i | ||||
\(839\) | −34.0989 | − | 24.7743i | −1.17722 | − | 0.855303i | −0.185368 | − | 0.982669i | \(-0.559348\pi\) |
−0.991856 | + | 0.127366i | \(0.959348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1813 | − | 8.85021i | 0.420044 | − | 0.305180i | ||||
\(842\) | −0.454932 | − | 0.147816i | −0.0156780 | − | 0.00509409i | ||||
\(843\) | 22.4913i | 0.774641i | ||||||||
\(844\) | −8.39327 | + | 25.8318i | −0.288908 | + | 0.889169i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.372140 | + | 1.14533i | 0.0127944 | + | 0.0393773i | ||||
\(847\) | −2.07494 | + | 0.674189i | −0.0712957 | + | 0.0231654i | ||||
\(848\) | −5.35541 | + | 7.37109i | −0.183906 | + | 0.253124i | ||||
\(849\) | 1.30694 | 0.0448540 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.5095 | −0.874454 | ||||||||
\(852\) | 5.03085 | − | 6.92437i | 0.172354 | − | 0.237225i | ||||
\(853\) | −41.1306 | + | 13.3641i | −1.40829 | + | 0.457580i | −0.911861 | − | 0.410500i | \(-0.865354\pi\) |
−0.496425 | + | 0.868080i | \(0.665354\pi\) | |||||||
\(854\) | −0.388871 | − | 1.19682i | −0.0133069 | − | 0.0409544i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.08415 | − | 6.41436i | 0.0712349 | − | 0.219238i | ||||
\(857\) | 39.2430i | 1.34052i | 0.742128 | + | 0.670258i | \(0.233817\pi\) | ||||
−0.742128 | + | 0.670258i | \(0.766183\pi\) | |||||||
\(858\) | −2.27183 | − | 0.738163i | −0.0775590 | − | 0.0252005i | ||||
\(859\) | 42.5617 | − | 30.9229i | 1.45219 | − | 1.05508i | 0.466872 | − | 0.884325i | \(-0.345381\pi\) |
0.985314 | − | 0.170750i | \(-0.0546192\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.75797 | + | 1.27724i | 0.0599113 | + | 0.0435281i | ||||
\(862\) | 2.13725 | + | 2.94167i | 0.0727950 | + | 0.100194i | ||||
\(863\) | 25.2009 | + | 34.6861i | 0.857850 | + | 1.18073i | 0.982078 | + | 0.188476i | \(0.0603546\pi\) |
−0.124228 | + | 0.992254i | \(0.539645\pi\) | |||||||
\(864\) | 1.35719 | + | 0.986054i | 0.0461724 | + | 0.0335462i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.56304 | + | 3.31524i | −0.155058 | + | 0.112657i | ||||
\(867\) | 10.6180 | + | 3.45001i | 0.360608 | + | 0.117169i | ||||
\(868\) | 2.12917i | 0.0722686i | ||||||||
\(869\) | −3.69270 | + | 11.3650i | −0.125266 | + | 0.385530i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.73766 | + | 14.5810i | 0.160530 | + | 0.494059i | ||||
\(872\) | 1.30530 | − | 0.424118i | 0.0442031 | − | 0.0143624i | ||||
\(873\) | −5.90053 | + | 8.12138i | −0.199703 | + | 0.274867i | ||||
\(874\) | 3.08955 | 0.104506 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.9779 | −0.607415 | ||||||||
\(877\) | 0.229421 | − | 0.315771i | 0.00774700 | − | 0.0106628i | −0.805126 | − | 0.593104i | \(-0.797902\pi\) |
0.812873 | + | 0.582441i | \(0.197902\pi\) | |||||||
\(878\) | 4.57060 | − | 1.48508i | 0.154250 | − | 0.0501190i | ||||
\(879\) | 0.608943 | + | 1.87413i | 0.0205391 | + | 0.0632129i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.8131 | − | 42.5124i | 0.465376 | − | 1.43228i | −0.393133 | − | 0.919481i | \(-0.628609\pi\) |
0.858509 | − | 0.512798i | \(-0.171391\pi\) | |||||||
\(882\) | − | 0.887444i | − | 0.0298818i | ||||||
\(883\) | 31.1534 | + | 10.1224i | 1.04840 | + | 0.340645i | 0.782039 | − | 0.623230i | \(-0.214180\pi\) |
0.266358 | + | 0.963874i | \(0.414180\pi\) | |||||||
\(884\) | 38.9448 | − | 28.2951i | 1.30986 | − | 0.951666i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.31622 | − | 2.40938i | −0.111411 | − | 0.0809446i | ||||
\(887\) | −9.23588 | − | 12.7121i | −0.310110 | − | 0.426830i | 0.625305 | − | 0.780380i | \(-0.284974\pi\) |
−0.935416 | + | 0.353550i | \(0.884974\pi\) | |||||||
\(888\) | −2.46960 | − | 3.39911i | −0.0828743 | − | 0.114067i | ||||
\(889\) | 2.66539 | + | 1.93652i | 0.0893944 | + | 0.0649488i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.97713 | − | 2.16301i | 0.0997374 | − | 0.0724635i | ||||
\(892\) | 6.10419 | + | 1.98337i | 0.204383 | + | 0.0664082i | ||||
\(893\) | − | 54.1299i | − | 1.81139i | ||||||
\(894\) | 0.505625 | − | 1.55615i | 0.0169106 | − | 0.0520456i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.17258 | − | 3.60884i | −0.0391733 | − | 0.120563i | ||||
\(897\) | −14.9178 | + | 4.84710i | −0.498092 | + | 0.161840i | ||||
\(898\) | 0.850228 | − | 1.17024i | 0.0283725 | − | 0.0390514i | ||||
\(899\) | −4.67839 | −0.156033 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.4623 | 0.415180 | ||||||||
\(902\) | 0.775897 | − | 1.06793i | 0.0258345 | − | 0.0355582i | ||||
\(903\) | 2.75887 | − | 0.896411i | 0.0918094 | − | 0.0298307i | ||||
\(904\) | 2.79430 | + | 8.59998i | 0.0929372 | + | 0.286031i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.07138 | − | 3.29737i | 0.0355942 | − | 0.109548i | ||||
\(907\) | 1.50466i | 0.0499613i | 0.999688 | + | 0.0249806i | \(0.00795241\pi\) | ||||
−0.999688 | + | 0.0249806i | \(0.992048\pi\) | |||||||
\(908\) | −24.8180 | − | 8.06385i | −0.823613 | − | 0.267608i | ||||
\(909\) | −0.578137 | + | 0.420041i | −0.0191756 | + | 0.0139319i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.26400 | − | 6.73069i | −0.306930 | − | 0.222998i | 0.423648 | − | 0.905827i | \(-0.360749\pi\) |
−0.730578 | + | 0.682829i | \(0.760749\pi\) | |||||||
\(912\) | −14.5243 | − | 19.9910i | −0.480948 | − | 0.661968i | ||||
\(913\) | −15.9904 | − | 22.0090i | −0.529207 | − | 0.728390i | ||||
\(914\) | −3.72489 | − | 2.70629i | −0.123209 | − | 0.0895162i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.35142 | − | 6.79421i | 0.308980 | − | 0.224487i | ||||
\(917\) | −10.1625 | − | 3.30200i | −0.335596 | − | 0.109042i | ||||
\(918\) | − | 0.751949i | − | 0.0248180i | ||||||
\(919\) | 6.73660 | − | 20.7331i | 0.222220 | − | 0.683923i | −0.776342 | − | 0.630312i | \(-0.782927\pi\) |
0.998562 | − | 0.0536108i | \(-0.0170730\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.71388 | + | 14.5078i | 0.155328 | + | 0.478049i | ||||
\(922\) | 0.0944049 | − | 0.0306740i | 0.00310906 | − | 0.00101019i | ||||
\(923\) | −11.6409 | + | 16.0223i | −0.383164 | + | 0.527380i | ||||
\(924\) | −6.25363 | −0.205729 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.307645 | −0.0101098 | ||||||||
\(927\) | −0.458922 | + | 0.631652i | −0.0150730 | + | 0.0207462i | ||||
\(928\) | 5.95756 | − | 1.93573i | 0.195566 | − | 0.0635434i | ||||
\(929\) | 9.50249 | + | 29.2457i | 0.311767 | + | 0.959519i | 0.977065 | + | 0.212941i | \(0.0683043\pi\) |
−0.665298 | + | 0.746578i | \(0.731696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.3264 | + | 37.9368i | −0.403982 | + | 1.24333i | ||||
\(932\) | 18.4817i | 0.605387i | ||||||||
\(933\) | −16.8767 | − | 5.48358i | −0.552519 | − | 0.179524i | ||||
\(934\) | 0.444429 | − | 0.322896i | 0.0145421 | − | 0.0105655i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.09008 | − | 1.51853i | −0.0683164 | − | 0.0496348i | ||||
\(937\) | −2.23982 | − | 3.08284i | −0.0731716 | − | 0.100712i | 0.770862 | − | 0.637002i | \(-0.219826\pi\) |
−0.844034 | + | 0.536289i | \(0.819826\pi\) | |||||||
\(938\) | −0.239216 | − | 0.329252i | −0.00781067 | − | 0.0107505i | ||||
\(939\) | 22.1565 | + | 16.0976i | 0.723049 | + | 0.525326i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.7501 | − | 12.1697i | 0.546037 | − | 0.396719i | −0.280285 | − | 0.959917i | \(-0.590429\pi\) |
0.826322 | + | 0.563197i | \(0.190429\pi\) | |||||||
\(942\) | 3.01393 | + | 0.979284i | 0.0981990 | + | 0.0319068i | ||||
\(943\) | − | 8.66792i | − | 0.282266i | ||||||
\(944\) | −15.7381 | + | 48.4370i | −0.512233 | + | 1.57649i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.544553 | − | 1.67596i | −0.0177049 | − | 0.0544902i | ||||
\(947\) | 14.9157 | − | 4.84640i | 0.484695 | − | 0.157487i | −0.0564684 | − | 0.998404i | \(-0.517984\pi\) |
0.541163 | + | 0.840917i | \(0.317984\pi\) | |||||||
\(948\) | −3.77911 | + | 5.20150i | −0.122740 | + | 0.168937i | ||||
\(949\) | 41.5989 | 1.35036 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.64563 | −0.280354 | ||||||||
\(952\) | −1.50982 | + | 2.07809i | −0.0489337 | + | 0.0673514i | ||||
\(953\) | 7.37266 | − | 2.39552i | 0.238824 | − | 0.0775985i | −0.187160 | − | 0.982330i | \(-0.559928\pi\) |
0.425983 | + | 0.904731i | \(0.359928\pi\) | |||||||
\(954\) | −0.102818 | − | 0.316441i | −0.00332885 | − | 0.0102451i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.4930 | + | 32.2941i | −0.339368 | + | 1.04447i | ||||
\(957\) | − | 13.7410i | − | 0.444185i | ||||||
\(958\) | 2.96452 | + | 0.963230i | 0.0957792 | + | 0.0311205i | ||||
\(959\) | 8.23468 | − | 5.98285i | 0.265912 | − | 0.193196i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.8096 | + | 17.2987i | 0.768050 | + | 0.558021i | ||||
\(962\) | 2.84279 | + | 3.91276i | 0.0916551 | + | 0.126152i | ||||
\(963\) | −7.02997 | − | 9.67592i | −0.226538 | − | 0.311802i | ||||
\(964\) | −11.5661 | − | 8.40326i | −0.372519 | − | 0.270651i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.336857 | − | 0.244741i | 0.0108382 | − | 0.00787442i | ||||
\(967\) | 46.0571 | + | 14.9649i | 1.48110 | + | 0.481238i | 0.934441 | − | 0.356119i | \(-0.115900\pi\) |
0.546657 | + | 0.837357i | \(0.315900\pi\) | |||||||
\(968\) | 1.43340i | 0.0460712i | ||||||||
\(969\) | −10.4444 | + | 32.1446i | −0.335523 | + | 1.03263i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.82895 | + | 24.0950i | 0.251243 | + | 0.773246i | 0.994547 | + | 0.104292i | \(0.0332577\pi\) |
−0.743304 | + | 0.668954i | \(0.766742\pi\) | |||||||
\(972\) | 1.88302 | − | 0.611830i | 0.0603979 | − | 0.0196245i | ||||
\(973\) | 2.35143 | − | 3.23647i | 0.0753834 | − | 0.103756i | ||||
\(974\) | 4.02394 | 0.128936 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 40.1483 | 1.28511 | ||||||||
\(977\) | 0.687033 | − | 0.945620i | 0.0219801 | − | 0.0302531i | −0.797885 | − | 0.602809i | \(-0.794048\pi\) |
0.819866 | + | 0.572556i | \(0.194048\pi\) | |||||||
\(978\) | 0.109616 | − | 0.0356165i | 0.00350514 | − | 0.00113889i | ||||
\(979\) | −17.6232 | − | 54.2385i | −0.563239 | − | 1.73347i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.752097 | − | 2.31472i | 0.0240126 | − | 0.0739033i | ||||
\(982\) | − | 1.99029i | − | 0.0635127i | ||||||
\(983\) | −22.8199 | − | 7.41464i | −0.727842 | − | 0.236490i | −0.0784223 | − | 0.996920i | \(-0.524988\pi\) |
−0.649420 | + | 0.760430i | \(0.724988\pi\) | |||||||
\(984\) | 1.15499 | − | 0.839150i | 0.0368197 | − | 0.0267511i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.27157 | − | 1.65039i | −0.0723415 | − | 0.0525592i | ||||
\(987\) | −4.28795 | − | 5.90186i | −0.136487 | − | 0.187858i | ||||
\(988\) | 33.9555 | + | 46.7358i | 1.08027 | + | 1.48686i | ||||
\(989\) | −9.36148 | − | 6.80151i | −0.297678 | − | 0.216276i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.6688 | − | 21.5556i | 0.942459 | − | 0.684737i | −0.00655196 | − | 0.999979i | \(-0.502086\pi\) |
0.949011 | + | 0.315242i | \(0.102086\pi\) | |||||||
\(992\) | 1.99896 | + | 0.649502i | 0.0634671 | + | 0.0206217i | ||||
\(993\) | − | 4.96260i | − | 0.157483i | ||||||
\(994\) | 0.162457 | − | 0.499991i | 0.00515282 | − | 0.0158588i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.52307 | − | 13.9206i | −0.143319 | − | 0.441091i | ||||
\(997\) | −54.2295 | + | 17.6202i | −1.71747 | + | 0.558038i | −0.991548 | − | 0.129743i | \(-0.958585\pi\) |
−0.725918 | + | 0.687782i | \(0.758585\pi\) | |||||||
\(998\) | −1.08970 | + | 1.49984i | −0.0344937 | + | 0.0474765i | ||||
\(999\) | −7.45067 | −0.235729 |
(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 | 375.2.i.d.49.4 | 24 | ||
5.2 | odd | 4 | 75.2.g.c.16.2 | ✓ | 12 | ||
5.3 | odd | 4 | 375.2.g.c.76.2 | 12 | |||
5.4 | even | 2 | inner | 375.2.i.d.49.3 | 24 | ||
15.2 | even | 4 | 225.2.h.d.91.2 | 12 | |||
25.2 | odd | 20 | 75.2.g.c.61.2 | yes | 12 | ||
25.6 | even | 5 | 1875.2.b.f.1249.7 | 12 | |||
25.8 | odd | 20 | 1875.2.a.k.1.4 | 6 | |||
25.11 | even | 5 | inner | 375.2.i.d.199.3 | 24 | ||
25.14 | even | 10 | inner | 375.2.i.d.199.4 | 24 | ||
25.17 | odd | 20 | 1875.2.a.j.1.3 | 6 | |||
25.19 | even | 10 | 1875.2.b.f.1249.6 | 12 | |||
25.23 | odd | 20 | 375.2.g.c.301.2 | 12 | |||
75.2 | even | 20 | 225.2.h.d.136.2 | 12 | |||
75.8 | even | 20 | 5625.2.a.q.1.3 | 6 | |||
75.17 | even | 20 | 5625.2.a.p.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.2 | ✓ | 12 | 5.2 | odd | 4 | ||
75.2.g.c.61.2 | yes | 12 | 25.2 | odd | 20 | ||
225.2.h.d.91.2 | 12 | 15.2 | even | 4 | |||
225.2.h.d.136.2 | 12 | 75.2 | even | 20 | |||
375.2.g.c.76.2 | 12 | 5.3 | odd | 4 | |||
375.2.g.c.301.2 | 12 | 25.23 | odd | 20 | |||
375.2.i.d.49.3 | 24 | 5.4 | even | 2 | inner | ||
375.2.i.d.49.4 | 24 | 1.1 | even | 1 | trivial | ||
375.2.i.d.199.3 | 24 | 25.11 | even | 5 | inner | ||
375.2.i.d.199.4 | 24 | 25.14 | even | 10 | inner | ||
1875.2.a.j.1.3 | 6 | 25.17 | odd | 20 | |||
1875.2.a.k.1.4 | 6 | 25.8 | odd | 20 | |||
1875.2.b.f.1249.6 | 12 | 25.19 | even | 10 | |||
1875.2.b.f.1249.7 | 12 | 25.6 | even | 5 | |||
5625.2.a.p.1.4 | 6 | 75.17 | even | 20 | |||
5625.2.a.q.1.3 | 6 | 75.8 | even | 20 |