Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(157,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.n (of order \(5\), degree \(4\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 157.6 | ||
Character | \(\chi\) | \(=\) | 429.157 |
Dual form | 429.2.n.c.235.6 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.18037 | − | 0.857589i | 0.834648 | − | 0.606407i | −0.0862228 | − | 0.996276i | \(-0.527480\pi\) |
0.920870 | + | 0.389869i | \(0.127480\pi\) | |||||||
\(3\) | −0.309017 | − | 0.951057i | −0.178411 | − | 0.549093i | ||||
\(4\) | 0.0397803 | − | 0.122431i | 0.0198902 | − | 0.0612156i | ||||
\(5\) | −0.326657 | − | 0.237330i | −0.146085 | − | 0.106137i | 0.512342 | − | 0.858782i | \(-0.328778\pi\) |
−0.658427 | + | 0.752644i | \(0.728778\pi\) | |||||||
\(6\) | −1.18037 | − | 0.857589i | −0.481884 | − | 0.350109i | ||||
\(7\) | 1.48593 | − | 4.57323i | 0.561629 | − | 1.72852i | −0.116130 | − | 0.993234i | \(-0.537049\pi\) |
0.677760 | − | 0.735283i | \(-0.262951\pi\) | |||||||
\(8\) | 0.843682 | + | 2.59659i | 0.298287 | + | 0.918032i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | −0.589108 | −0.186292 | ||||||||
\(11\) | 0.851691 | − | 3.20541i | 0.256794 | − | 0.966466i | ||||
\(12\) | −0.128732 | −0.0371617 | ||||||||
\(13\) | −0.809017 | + | 0.587785i | −0.224381 | + | 0.163022i | ||||
\(14\) | −2.16800 | − | 6.67242i | −0.579422 | − | 1.78328i | ||||
\(15\) | −0.124772 | + | 0.384008i | −0.0322160 | + | 0.0991505i | ||||
\(16\) | 3.43095 | + | 2.49273i | 0.857738 | + | 0.623183i | ||||
\(17\) | −2.90776 | − | 2.11261i | −0.705236 | − | 0.512384i | 0.176398 | − | 0.984319i | \(-0.443556\pi\) |
−0.881633 | + | 0.471935i | \(0.843556\pi\) | |||||||
\(18\) | −0.450861 | + | 1.38761i | −0.106269 | + | 0.327062i | ||||
\(19\) | 0.212342 | + | 0.653522i | 0.0487146 | + | 0.149928i | 0.972455 | − | 0.233091i | \(-0.0748842\pi\) |
−0.923740 | + | 0.383020i | \(0.874884\pi\) | |||||||
\(20\) | −0.0420512 | + | 0.0305520i | −0.00940293 | + | 0.00683163i | ||||
\(21\) | −4.80858 | −1.04932 | ||||||||
\(22\) | −1.74361 | − | 4.51396i | −0.371739 | − | 0.962380i | ||||
\(23\) | 3.65382 | 0.761874 | 0.380937 | − | 0.924601i | \(-0.375602\pi\) | ||||
0.380937 | + | 0.924601i | \(0.375602\pi\) | |||||||
\(24\) | 2.20879 | − | 1.60478i | 0.450867 | − | 0.327574i | ||||
\(25\) | −1.49471 | − | 4.60023i | −0.298941 | − | 0.920046i | ||||
\(26\) | −0.450861 | + | 1.38761i | −0.0884212 | + | 0.272132i | ||||
\(27\) | 0.809017 | + | 0.587785i | 0.155695 | + | 0.113119i | ||||
\(28\) | −0.500795 | − | 0.363849i | −0.0946414 | − | 0.0687610i | ||||
\(29\) | −0.367111 | + | 1.12985i | −0.0681708 | + | 0.209808i | −0.979339 | − | 0.202227i | \(-0.935182\pi\) |
0.911168 | + | 0.412035i | \(0.135182\pi\) | |||||||
\(30\) | 0.182044 | + | 0.560275i | 0.0332366 | + | 0.102292i | ||||
\(31\) | −1.30215 | + | 0.946071i | −0.233874 | + | 0.169919i | −0.698550 | − | 0.715562i | \(-0.746171\pi\) |
0.464676 | + | 0.885481i | \(0.346171\pi\) | |||||||
\(32\) | 0.727109 | 0.128536 | ||||||||
\(33\) | −3.31171 | + | 0.180518i | −0.576494 | + | 0.0314242i | ||||
\(34\) | −5.24399 | −0.899336 | ||||||||
\(35\) | −1.57076 | + | 1.14122i | −0.265506 | + | 0.192901i | ||||
\(36\) | 0.0397803 | + | 0.122431i | 0.00663006 | + | 0.0204052i | ||||
\(37\) | 1.26905 | − | 3.90574i | 0.208631 | − | 0.642100i | −0.790914 | − | 0.611928i | \(-0.790394\pi\) |
0.999545 | − | 0.0301724i | \(-0.00960563\pi\) | |||||||
\(38\) | 0.811095 | + | 0.589295i | 0.131577 | + | 0.0955963i | ||||
\(39\) | 0.809017 | + | 0.587785i | 0.129546 | + | 0.0941210i | ||||
\(40\) | 0.340654 | − | 1.04842i | 0.0538621 | − | 0.165770i | ||||
\(41\) | 3.78262 | + | 11.6417i | 0.590746 | + | 1.81813i | 0.574855 | + | 0.818255i | \(0.305058\pi\) |
0.0158904 | + | 0.999874i | \(0.494942\pi\) | |||||||
\(42\) | −5.67590 | + | 4.12378i | −0.875810 | + | 0.636313i | ||||
\(43\) | 10.6099 | 1.61799 | 0.808995 | − | 0.587816i | \(-0.200012\pi\) | ||||
0.808995 | + | 0.587816i | \(0.200012\pi\) | |||||||
\(44\) | −0.358561 | − | 0.231786i | −0.0540551 | − | 0.0349430i | ||||
\(45\) | 0.403770 | 0.0601905 | ||||||||
\(46\) | 4.31286 | − | 3.13347i | 0.635896 | − | 0.462005i | ||||
\(47\) | 4.06790 | + | 12.5197i | 0.593364 | + | 1.82619i | 0.562708 | + | 0.826655i | \(0.309759\pi\) |
0.0306553 | + | 0.999530i | \(0.490241\pi\) | |||||||
\(48\) | 1.31051 | − | 4.03333i | 0.189155 | − | 0.582161i | ||||
\(49\) | −13.0433 | − | 9.47651i | −1.86333 | − | 1.35379i | ||||
\(50\) | −5.70941 | − | 4.14813i | −0.807433 | − | 0.586634i | ||||
\(51\) | −1.11067 | + | 3.41828i | −0.155524 | + | 0.478655i | ||||
\(52\) | 0.0397803 | + | 0.122431i | 0.00551654 | + | 0.0169782i | ||||
\(53\) | −1.90226 | + | 1.38207i | −0.261296 | + | 0.189842i | −0.710718 | − | 0.703477i | \(-0.751630\pi\) |
0.449422 | + | 0.893319i | \(0.351630\pi\) | |||||||
\(54\) | 1.45902 | 0.198547 | ||||||||
\(55\) | −1.03895 | + | 0.844936i | −0.140092 | + | 0.113931i | ||||
\(56\) | 13.1284 | 1.75436 | ||||||||
\(57\) | 0.555919 | − | 0.403899i | 0.0736332 | − | 0.0534977i | ||||
\(58\) | 0.535621 | + | 1.64847i | 0.0703305 | + | 0.216455i | ||||
\(59\) | −2.83687 | + | 8.73098i | −0.369329 | + | 1.13668i | 0.577897 | + | 0.816110i | \(0.303874\pi\) |
−0.947226 | + | 0.320567i | \(0.896126\pi\) | |||||||
\(60\) | 0.0420512 | + | 0.0305520i | 0.00542878 | + | 0.00394424i | ||||
\(61\) | 9.32073 | + | 6.77191i | 1.19340 | + | 0.867054i | 0.993619 | − | 0.112787i | \(-0.0359779\pi\) |
0.199778 | + | 0.979841i | \(0.435978\pi\) | |||||||
\(62\) | −0.725684 | + | 2.23343i | −0.0921620 | + | 0.283645i | ||||
\(63\) | 1.48593 | + | 4.57323i | 0.187210 | + | 0.576172i | ||||
\(64\) | −6.00365 | + | 4.36191i | −0.750456 | + | 0.545238i | ||||
\(65\) | 0.403770 | 0.0500815 | ||||||||
\(66\) | −3.75423 | + | 3.05316i | −0.462114 | + | 0.375818i | ||||
\(67\) | −2.47381 | −0.302225 | −0.151112 | − | 0.988517i | \(-0.548286\pi\) | ||||
−0.151112 | + | 0.988517i | \(0.548286\pi\) | |||||||
\(68\) | −0.374321 | + | 0.271960i | −0.0453931 | + | 0.0329800i | ||||
\(69\) | −1.12909 | − | 3.47499i | −0.135927 | − | 0.418339i | ||||
\(70\) | −0.875374 | + | 2.69412i | −0.104627 | + | 0.322009i | ||||
\(71\) | −3.86231 | − | 2.80614i | −0.458372 | − | 0.333027i | 0.334520 | − | 0.942389i | \(-0.391426\pi\) |
−0.792892 | + | 0.609362i | \(0.791426\pi\) | |||||||
\(72\) | −2.20879 | − | 1.60478i | −0.260308 | − | 0.189125i | ||||
\(73\) | −2.21583 | + | 6.81964i | −0.259344 | + | 0.798178i | 0.733599 | + | 0.679583i | \(0.237839\pi\) |
−0.992943 | + | 0.118595i | \(0.962161\pi\) | |||||||
\(74\) | −1.85157 | − | 5.69855i | −0.215241 | − | 0.662442i | ||||
\(75\) | −3.91319 | + | 2.84310i | −0.451856 | + | 0.328293i | ||||
\(76\) | 0.0884585 | 0.0101469 | ||||||||
\(77\) | −13.3935 | − | 8.65799i | −1.52633 | − | 0.986669i | ||||
\(78\) | 1.45902 | 0.165201 | ||||||||
\(79\) | 5.00447 | − | 3.63596i | 0.563047 | − | 0.409077i | −0.269526 | − | 0.962993i | \(-0.586867\pi\) |
0.832573 | + | 0.553916i | \(0.186867\pi\) | |||||||
\(80\) | −0.529144 | − | 1.62854i | −0.0591601 | − | 0.182076i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 14.4487 | + | 10.4976i | 1.59559 | + | 1.15926i | ||||
\(83\) | −2.44208 | − | 1.77428i | −0.268054 | − | 0.194752i | 0.445636 | − | 0.895214i | \(-0.352977\pi\) |
−0.713690 | + | 0.700462i | \(0.752977\pi\) | |||||||
\(84\) | −0.191287 | + | 0.588720i | −0.0208711 | + | 0.0642346i | ||||
\(85\) | 0.448454 | + | 1.38020i | 0.0486417 | + | 0.149704i | ||||
\(86\) | 12.5236 | − | 9.09890i | 1.35045 | − | 0.981160i | ||||
\(87\) | 1.18800 | 0.127367 | ||||||||
\(88\) | 9.04167 | − | 0.492854i | 0.963845 | − | 0.0525384i | ||||
\(89\) | 3.70447 | 0.392673 | 0.196337 | − | 0.980537i | \(-0.437095\pi\) | ||||
0.196337 | + | 0.980537i | \(0.437095\pi\) | |||||||
\(90\) | 0.476598 | − | 0.346269i | 0.0502379 | − | 0.0365000i | ||||
\(91\) | 1.48593 | + | 4.57323i | 0.155768 | + | 0.479404i | ||||
\(92\) | 0.145350 | − | 0.447341i | 0.0151538 | − | 0.0466386i | ||||
\(93\) | 1.30215 | + | 0.946071i | 0.135027 | + | 0.0981030i | ||||
\(94\) | 15.5384 | + | 11.2893i | 1.60266 | + | 1.16440i | ||||
\(95\) | 0.0857374 | − | 0.263873i | 0.00879647 | − | 0.0270728i | ||||
\(96\) | −0.224689 | − | 0.691522i | −0.0229322 | − | 0.0705782i | ||||
\(97\) | 14.5850 | − | 10.5967i | 1.48089 | − | 1.07593i | 0.503617 | − | 0.863927i | \(-0.332002\pi\) |
0.977270 | − | 0.212000i | \(-0.0679978\pi\) | |||||||
\(98\) | −23.5229 | −2.37617 | ||||||||
\(99\) | 1.19506 | + | 3.09384i | 0.120108 | + | 0.310942i | ||||
\(100\) | −0.622672 | −0.0622672 | ||||||||
\(101\) | 7.89518 | − | 5.73618i | 0.785600 | − | 0.570772i | −0.121055 | − | 0.992646i | \(-0.538628\pi\) |
0.906654 | + | 0.421874i | \(0.138628\pi\) | |||||||
\(102\) | 1.62048 | + | 4.98733i | 0.160452 | + | 0.493819i | ||||
\(103\) | 3.03237 | − | 9.33267i | 0.298788 | − | 0.919575i | −0.683135 | − | 0.730292i | \(-0.739384\pi\) |
0.981923 | − | 0.189283i | \(-0.0606162\pi\) | |||||||
\(104\) | −2.20879 | − | 1.60478i | −0.216590 | − | 0.157362i | ||||
\(105\) | 1.57076 | + | 1.14122i | 0.153290 | + | 0.111372i | ||||
\(106\) | −1.06012 | + | 3.26272i | −0.102968 | + | 0.316903i | ||||
\(107\) | 3.49293 | + | 10.7501i | 0.337674 | + | 1.03925i | 0.965390 | + | 0.260811i | \(0.0839899\pi\) |
−0.627716 | + | 0.778442i | \(0.716010\pi\) | |||||||
\(108\) | 0.104146 | − | 0.0756667i | 0.0100215 | − | 0.00728103i | ||||
\(109\) | −15.6688 | −1.50080 | −0.750398 | − | 0.660986i | \(-0.770138\pi\) | ||||
−0.750398 | + | 0.660986i | \(0.770138\pi\) | |||||||
\(110\) | −0.501738 | + | 1.88833i | −0.0478388 | + | 0.180045i | ||||
\(111\) | −4.10674 | −0.389795 | ||||||||
\(112\) | 16.4980 | − | 11.9865i | 1.55891 | − | 1.13262i | ||||
\(113\) | 0.372451 | + | 1.14629i | 0.0350372 | + | 0.107833i | 0.967046 | − | 0.254603i | \(-0.0819449\pi\) |
−0.932008 | + | 0.362437i | \(0.881945\pi\) | |||||||
\(114\) | 0.309811 | − | 0.953499i | 0.0290164 | − | 0.0893034i | ||||
\(115\) | −1.19355 | − | 0.867161i | −0.111299 | − | 0.0808632i | ||||
\(116\) | 0.123725 | + | 0.0898917i | 0.0114876 | + | 0.00834623i | ||||
\(117\) | 0.309017 | − | 0.951057i | 0.0285686 | − | 0.0879252i | ||||
\(118\) | 4.13904 | + | 12.7387i | 0.381029 | + | 1.17269i | ||||
\(119\) | −13.9822 | + | 10.1587i | −1.28175 | + | 0.931242i | ||||
\(120\) | −1.10238 | −0.100633 | ||||||||
\(121\) | −9.54925 | − | 5.46003i | −0.868113 | − | 0.496366i | ||||
\(122\) | 16.8094 | 1.52185 | ||||||||
\(123\) | 9.90302 | − | 7.19497i | 0.892926 | − | 0.648748i | ||||
\(124\) | 0.0640285 | + | 0.197059i | 0.00574993 | + | 0.0176965i | ||||
\(125\) | −1.22738 | + | 3.77748i | −0.109780 | + | 0.337868i | ||||
\(126\) | 5.67590 | + | 4.12378i | 0.505649 | + | 0.367376i | ||||
\(127\) | −7.78069 | − | 5.65300i | −0.690425 | − | 0.501623i | 0.186375 | − | 0.982479i | \(-0.440326\pi\) |
−0.876800 | + | 0.480856i | \(0.840326\pi\) | |||||||
\(128\) | −3.79518 | + | 11.6804i | −0.335450 | + | 1.03241i | ||||
\(129\) | −3.27863 | − | 10.0906i | −0.288667 | − | 0.888426i | ||||
\(130\) | 0.476598 | − | 0.346269i | 0.0418004 | − | 0.0303698i | ||||
\(131\) | −17.8134 | −1.55636 | −0.778182 | − | 0.628038i | \(-0.783858\pi\) | ||||
−0.778182 | + | 0.628038i | \(0.783858\pi\) | |||||||
\(132\) | −0.109640 | + | 0.412638i | −0.00954292 | + | 0.0359155i | ||||
\(133\) | 3.30423 | 0.286513 | ||||||||
\(134\) | −2.92002 | + | 2.12152i | −0.252251 | + | 0.183271i | ||||
\(135\) | −0.124772 | − | 0.384008i | −0.0107387 | − | 0.0330502i | ||||
\(136\) | 3.03235 | − | 9.33263i | 0.260022 | − | 0.800266i | ||||
\(137\) | −10.2735 | − | 7.46415i | −0.877727 | − | 0.637706i | 0.0549225 | − | 0.998491i | \(-0.482509\pi\) |
−0.932649 | + | 0.360785i | \(0.882509\pi\) | |||||||
\(138\) | −4.31286 | − | 3.13347i | −0.367135 | − | 0.266739i | ||||
\(139\) | −1.00836 | + | 3.10340i | −0.0855277 | + | 0.263227i | −0.984670 | − | 0.174430i | \(-0.944192\pi\) |
0.899142 | + | 0.437657i | \(0.144192\pi\) | |||||||
\(140\) | 0.0772359 | + | 0.237708i | 0.00652762 | + | 0.0200900i | ||||
\(141\) | 10.6499 | − | 7.73760i | 0.896883 | − | 0.651623i | ||||
\(142\) | −6.96547 | −0.584529 | ||||||||
\(143\) | 1.19506 | + | 3.09384i | 0.0999357 | + | 0.258720i | ||||
\(144\) | −4.24089 | −0.353408 | ||||||||
\(145\) | 0.388067 | − | 0.281947i | 0.0322272 | − | 0.0234144i | ||||
\(146\) | 3.23294 | + | 9.94997i | 0.267560 | + | 0.823465i | ||||
\(147\) | −4.98209 | + | 15.3333i | −0.410916 | + | 1.26467i | ||||
\(148\) | −0.427702 | − | 0.310743i | −0.0351569 | − | 0.0255430i | ||||
\(149\) | 3.02277 | + | 2.19617i | 0.247635 | + | 0.179917i | 0.704678 | − | 0.709527i | \(-0.251091\pi\) |
−0.457043 | + | 0.889445i | \(0.651091\pi\) | |||||||
\(150\) | −2.18080 | + | 6.71182i | −0.178062 | + | 0.548018i | ||||
\(151\) | −3.32997 | − | 10.2486i | −0.270989 | − | 0.834018i | −0.990253 | − | 0.139281i | \(-0.955521\pi\) |
0.719264 | − | 0.694737i | \(-0.244479\pi\) | |||||||
\(152\) | −1.51778 | + | 1.10273i | −0.123108 | + | 0.0894431i | ||||
\(153\) | 3.59419 | 0.290573 | ||||||||
\(154\) | −23.2343 | + | 1.26648i | −1.87227 | + | 0.102056i | ||||
\(155\) | 0.649889 | 0.0522004 | ||||||||
\(156\) | 0.104146 | − | 0.0756667i | 0.00833837 | − | 0.00605818i | ||||
\(157\) | 6.42953 | + | 19.7881i | 0.513133 | + | 1.57926i | 0.786654 | + | 0.617394i | \(0.211811\pi\) |
−0.273522 | + | 0.961866i | \(0.588189\pi\) | |||||||
\(158\) | 2.78897 | − | 8.58356i | 0.221878 | − | 0.682871i | ||||
\(159\) | 1.90226 | + | 1.38207i | 0.150859 | + | 0.109606i | ||||
\(160\) | −0.237515 | − | 0.172565i | −0.0187772 | − | 0.0136425i | ||||
\(161\) | 5.42932 | − | 16.7097i | 0.427891 | − | 1.31691i | ||||
\(162\) | −0.450861 | − | 1.38761i | −0.0354230 | − | 0.109021i | ||||
\(163\) | 11.0751 | − | 8.04652i | 0.867468 | − | 0.630252i | −0.0624385 | − | 0.998049i | \(-0.519888\pi\) |
0.929906 | + | 0.367797i | \(0.119888\pi\) | |||||||
\(164\) | 1.57578 | 0.123048 | ||||||||
\(165\) | 1.12464 | + | 0.727001i | 0.0875527 | + | 0.0565969i | ||||
\(166\) | −4.40416 | −0.341829 | ||||||||
\(167\) | −10.5448 | + | 7.66127i | −0.815983 | + | 0.592847i | −0.915559 | − | 0.402183i | \(-0.868251\pi\) |
0.0995757 | + | 0.995030i | \(0.468251\pi\) | |||||||
\(168\) | −4.05691 | − | 12.4859i | −0.312997 | − | 0.963307i | ||||
\(169\) | 0.309017 | − | 0.951057i | 0.0237705 | − | 0.0731582i | ||||
\(170\) | 1.71299 | + | 1.24456i | 0.131380 | + | 0.0954531i | ||||
\(171\) | −0.555919 | − | 0.403899i | −0.0425122 | − | 0.0308869i | ||||
\(172\) | 0.422064 | − | 1.29898i | 0.0321821 | − | 0.0990463i | ||||
\(173\) | 2.54604 | + | 7.83590i | 0.193572 | + | 0.595752i | 0.999990 | + | 0.00440714i | \(0.00140284\pi\) |
−0.806419 | + | 0.591345i | \(0.798597\pi\) | |||||||
\(174\) | 1.40227 | − | 1.01881i | 0.106306 | − | 0.0772359i | ||||
\(175\) | −23.2589 | −1.75821 | ||||||||
\(176\) | 10.9123 | − | 8.87456i | 0.822548 | − | 0.668945i | ||||
\(177\) | 9.18030 | 0.690033 | ||||||||
\(178\) | 4.37265 | − | 3.17691i | 0.327744 | − | 0.238120i | ||||
\(179\) | −3.21898 | − | 9.90700i | −0.240598 | − | 0.740484i | −0.996329 | − | 0.0856022i | \(-0.972719\pi\) |
0.755732 | − | 0.654881i | \(-0.227281\pi\) | |||||||
\(180\) | 0.0160621 | − | 0.0494341i | 0.00119720 | − | 0.00368460i | ||||
\(181\) | −10.6770 | − | 7.75729i | −0.793615 | − | 0.576595i | 0.115419 | − | 0.993317i | \(-0.463179\pi\) |
−0.909034 | + | 0.416722i | \(0.863179\pi\) | |||||||
\(182\) | 5.67590 | + | 4.12378i | 0.420726 | + | 0.305675i | ||||
\(183\) | 3.56020 | − | 10.9572i | 0.263178 | − | 0.809978i | ||||
\(184\) | 3.08266 | + | 9.48745i | 0.227257 | + | 0.699424i | ||||
\(185\) | −1.34150 | + | 0.974654i | −0.0986287 | + | 0.0716580i | ||||
\(186\) | 2.34836 | 0.172190 | ||||||||
\(187\) | −9.24829 | + | 7.52126i | −0.676302 | + | 0.550009i | ||||
\(188\) | 1.69462 | 0.123593 | ||||||||
\(189\) | 3.89022 | − | 2.82641i | 0.282972 | − | 0.205591i | ||||
\(190\) | −0.125092 | − | 0.384995i | −0.00907516 | − | 0.0279305i | ||||
\(191\) | −3.20612 | + | 9.86743i | −0.231987 | + | 0.713983i | 0.765520 | + | 0.643412i | \(0.222482\pi\) |
−0.997507 | + | 0.0705702i | \(0.977518\pi\) | |||||||
\(192\) | 6.00365 | + | 4.36191i | 0.433276 | + | 0.314793i | ||||
\(193\) | 6.16222 | + | 4.47711i | 0.443566 | + | 0.322270i | 0.787050 | − | 0.616889i | \(-0.211607\pi\) |
−0.343484 | + | 0.939158i | \(0.611607\pi\) | |||||||
\(194\) | 8.12817 | − | 25.0159i | 0.583569 | − | 1.79604i | ||||
\(195\) | −0.124772 | − | 0.384008i | −0.00893510 | − | 0.0274994i | ||||
\(196\) | −1.67909 | + | 1.21993i | −0.119935 | + | 0.0871377i | ||||
\(197\) | 2.63142 | 0.187481 | 0.0937404 | − | 0.995597i | \(-0.470118\pi\) | ||||
0.0937404 | + | 0.995597i | \(0.470118\pi\) | |||||||
\(198\) | 4.06385 | + | 2.62701i | 0.288805 | + | 0.186693i | ||||
\(199\) | −11.9393 | −0.846353 | −0.423177 | − | 0.906047i | \(-0.639085\pi\) | ||||
−0.423177 | + | 0.906047i | \(0.639085\pi\) | |||||||
\(200\) | 10.6838 | − | 7.76227i | 0.755462 | − | 0.548875i | ||||
\(201\) | 0.764451 | + | 2.35274i | 0.0539202 | + | 0.165949i | ||||
\(202\) | 4.39995 | − | 13.5416i | 0.309579 | − | 0.952786i | ||||
\(203\) | 4.62156 | + | 3.35776i | 0.324370 | + | 0.235669i | ||||
\(204\) | 0.374321 | + | 0.271960i | 0.0262077 | + | 0.0190410i | ||||
\(205\) | 1.52731 | − | 4.70057i | 0.106672 | − | 0.328302i | ||||
\(206\) | −4.42428 | − | 13.6165i | −0.308254 | − | 0.948708i | ||||
\(207\) | −2.95600 | + | 2.14766i | −0.205456 | + | 0.149273i | ||||
\(208\) | −4.24089 | −0.294053 | ||||||||
\(209\) | 2.27565 | − | 0.124044i | 0.157410 | − | 0.00858029i | ||||
\(210\) | 2.83277 | 0.195480 | ||||||||
\(211\) | 3.53112 | − | 2.56551i | 0.243092 | − | 0.176617i | −0.459568 | − | 0.888143i | \(-0.651996\pi\) |
0.702660 | + | 0.711526i | \(0.251996\pi\) | |||||||
\(212\) | 0.0935365 | + | 0.287876i | 0.00642411 | + | 0.0197714i | ||||
\(213\) | −1.47527 | + | 4.54042i | −0.101084 | + | 0.311105i | ||||
\(214\) | 13.3421 | + | 9.69362i | 0.912049 | + | 0.662643i | ||||
\(215\) | −3.46579 | − | 2.51804i | −0.236365 | − | 0.171729i | ||||
\(216\) | −0.843682 | + | 2.59659i | −0.0574053 | + | 0.176675i | ||||
\(217\) | 2.39168 | + | 7.36085i | 0.162358 | + | 0.499687i | ||||
\(218\) | −18.4949 | + | 13.4374i | −1.25264 | + | 0.910093i | ||||
\(219\) | 7.17059 | 0.484544 | ||||||||
\(220\) | 0.0621168 | + | 0.160812i | 0.00418792 | + | 0.0108419i | ||||
\(221\) | 3.59419 | 0.241771 | ||||||||
\(222\) | −4.84747 | + | 3.52189i | −0.325341 | + | 0.236374i | ||||
\(223\) | −0.383475 | − | 1.18022i | −0.0256794 | − | 0.0790330i | 0.937396 | − | 0.348267i | \(-0.113230\pi\) |
−0.963075 | + | 0.269234i | \(0.913230\pi\) | |||||||
\(224\) | 1.08043 | − | 3.32524i | 0.0721896 | − | 0.222177i | ||||
\(225\) | 3.91319 | + | 2.84310i | 0.260879 | + | 0.189540i | ||||
\(226\) | 1.42267 | + | 1.03363i | 0.0946347 | + | 0.0687561i | ||||
\(227\) | −4.46395 | + | 13.7386i | −0.296283 | + | 0.911864i | 0.686505 | + | 0.727125i | \(0.259144\pi\) |
−0.982788 | + | 0.184739i | \(0.940856\pi\) | |||||||
\(228\) | −0.0273352 | − | 0.0841291i | −0.00181032 | − | 0.00557158i | ||||
\(229\) | 3.53794 | − | 2.57047i | 0.233794 | − | 0.169861i | −0.464720 | − | 0.885458i | \(-0.653845\pi\) |
0.698514 | + | 0.715596i | \(0.253845\pi\) | |||||||
\(230\) | −2.15249 | −0.141931 | ||||||||
\(231\) | −4.09542 | + | 15.4134i | −0.269459 | + | 1.01413i | ||||
\(232\) | −3.24348 | −0.212945 | ||||||||
\(233\) | −1.78198 | + | 1.29468i | −0.116741 | + | 0.0848174i | −0.644624 | − | 0.764500i | \(-0.722986\pi\) |
0.527883 | + | 0.849317i | \(0.322986\pi\) | |||||||
\(234\) | −0.450861 | − | 1.38761i | −0.0294737 | − | 0.0907108i | ||||
\(235\) | 1.64250 | − | 5.05508i | 0.107145 | − | 0.329757i | ||||
\(236\) | 0.956094 | + | 0.694643i | 0.0622364 | + | 0.0452174i | ||||
\(237\) | −5.00447 | − | 3.63596i | −0.325075 | − | 0.236181i | ||||
\(238\) | −7.79220 | + | 23.9819i | −0.505094 | + | 1.55452i | ||||
\(239\) | −3.49304 | − | 10.7505i | −0.225946 | − | 0.695391i | −0.998194 | − | 0.0600696i | \(-0.980868\pi\) |
0.772248 | − | 0.635321i | \(-0.219132\pi\) | |||||||
\(240\) | −1.38532 | + | 1.00649i | −0.0894218 | + | 0.0649688i | ||||
\(241\) | −7.16866 | −0.461774 | −0.230887 | − | 0.972981i | \(-0.574163\pi\) | ||||
−0.230887 | + | 0.972981i | \(0.574163\pi\) | |||||||
\(242\) | −15.9541 | + | 1.74447i | −1.02557 | + | 0.112139i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.19987 | − | 0.871760i | 0.0768141 | − | 0.0558087i | ||||
\(245\) | 2.01162 | + | 6.19114i | 0.128518 | + | 0.395537i | ||||
\(246\) | 5.51891 | − | 16.9854i | 0.351873 | − | 1.08295i | ||||
\(247\) | −0.555919 | − | 0.403899i | −0.0353723 | − | 0.0256995i | ||||
\(248\) | −3.55516 | − | 2.58297i | −0.225753 | − | 0.164019i | ||||
\(249\) | −0.932793 | + | 2.87084i | −0.0591134 | + | 0.181932i | ||||
\(250\) | 1.79076 | + | 5.51141i | 0.113258 | + | 0.348572i | ||||
\(251\) | 13.5672 | − | 9.85714i | 0.856353 | − | 0.622177i | −0.0705372 | − | 0.997509i | \(-0.522471\pi\) |
0.926890 | + | 0.375332i | \(0.122471\pi\) | |||||||
\(252\) | 0.619017 | 0.0389944 | ||||||||
\(253\) | 3.11192 | − | 11.7120i | 0.195645 | − | 0.736325i | ||||
\(254\) | −14.0320 | −0.880449 | ||||||||
\(255\) | 1.17407 | − | 0.853010i | 0.0735230 | − | 0.0534176i | ||||
\(256\) | 0.950857 | + | 2.92644i | 0.0594286 | + | 0.182902i | ||||
\(257\) | 8.16792 | − | 25.1383i | 0.509501 | − | 1.56808i | −0.283569 | − | 0.958952i | \(-0.591518\pi\) |
0.793070 | − | 0.609131i | \(-0.208482\pi\) | |||||||
\(258\) | −12.5236 | − | 9.09890i | −0.779683 | − | 0.566473i | ||||
\(259\) | −15.9761 | − | 11.6073i | −0.992708 | − | 0.721244i | ||||
\(260\) | 0.0160621 | − | 0.0494341i | 0.000996130 | − | 0.00306577i | ||||
\(261\) | −0.367111 | − | 1.12985i | −0.0227236 | − | 0.0699360i | ||||
\(262\) | −21.0264 | + | 15.2766i | −1.29902 | + | 0.943790i | ||||
\(263\) | 15.9258 | 0.982030 | 0.491015 | − | 0.871151i | \(-0.336626\pi\) | ||||
0.491015 | + | 0.871151i | \(0.336626\pi\) | |||||||
\(264\) | −3.26276 | − | 8.44684i | −0.200809 | − | 0.519867i | ||||
\(265\) | 0.949395 | 0.0583209 | ||||||||
\(266\) | 3.90021 | − | 2.83367i | 0.239137 | − | 0.173743i | ||||
\(267\) | −1.14474 | − | 3.52316i | −0.0700573 | − | 0.215614i | ||||
\(268\) | −0.0984092 | + | 0.302872i | −0.00601130 | + | 0.0185009i | ||||
\(269\) | 7.40966 | + | 5.38343i | 0.451775 | + | 0.328234i | 0.790296 | − | 0.612725i | \(-0.209927\pi\) |
−0.338521 | + | 0.940959i | \(0.609927\pi\) | |||||||
\(270\) | −0.476598 | − | 0.346269i | −0.0290049 | − | 0.0210733i | ||||
\(271\) | −5.93537 | + | 18.2672i | −0.360548 | + | 1.10965i | 0.592175 | + | 0.805810i | \(0.298270\pi\) |
−0.952722 | + | 0.303842i | \(0.901730\pi\) | |||||||
\(272\) | −4.71021 | − | 14.4965i | −0.285599 | − | 0.878982i | ||||
\(273\) | 3.89022 | − | 2.82641i | 0.235447 | − | 0.171062i | ||||
\(274\) | −18.5277 | −1.11930 | ||||||||
\(275\) | −16.0186 | + | 0.873162i | −0.965960 | + | 0.0526537i | ||||
\(276\) | −0.470363 | −0.0283125 | ||||||||
\(277\) | 2.75324 | − | 2.00035i | 0.165426 | − | 0.120189i | −0.501992 | − | 0.864872i | \(-0.667399\pi\) |
0.667418 | + | 0.744683i | \(0.267399\pi\) | |||||||
\(278\) | 1.47121 | + | 4.52792i | 0.0882374 | + | 0.271567i | ||||
\(279\) | 0.497379 | − | 1.53077i | 0.0297773 | − | 0.0916451i | ||||
\(280\) | −4.28850 | − | 3.11577i | −0.256287 | − | 0.186203i | ||||
\(281\) | −25.9782 | − | 18.8742i | −1.54973 | − | 1.12594i | −0.943845 | − | 0.330389i | \(-0.892820\pi\) |
−0.605882 | − | 0.795554i | \(-0.707180\pi\) | |||||||
\(282\) | 5.93513 | − | 18.2665i | 0.353432 | − | 1.08775i | ||||
\(283\) | 8.72796 | + | 26.8619i | 0.518823 | + | 1.59677i | 0.776216 | + | 0.630467i | \(0.217136\pi\) |
−0.257393 | + | 0.966307i | \(0.582864\pi\) | |||||||
\(284\) | −0.497203 | + | 0.361239i | −0.0295036 | + | 0.0214356i | ||||
\(285\) | −0.277452 | −0.0164348 | ||||||||
\(286\) | 4.06385 | + | 2.62701i | 0.240301 | + | 0.155338i | ||||
\(287\) | 58.8609 | 3.47445 | ||||||||
\(288\) | −0.588244 | + | 0.427384i | −0.0346626 | + | 0.0251839i | ||||
\(289\) | −1.26134 | − | 3.88202i | −0.0741967 | − | 0.228354i | ||||
\(290\) | 0.216268 | − | 0.665604i | 0.0126997 | − | 0.0390856i | ||||
\(291\) | −14.5850 | − | 10.5967i | −0.854990 | − | 0.621187i | ||||
\(292\) | 0.746790 | + | 0.542575i | 0.0437026 | + | 0.0317518i | ||||
\(293\) | 2.14703 | − | 6.60789i | 0.125431 | − | 0.386037i | −0.868548 | − | 0.495604i | \(-0.834947\pi\) |
0.993979 | + | 0.109567i | \(0.0349466\pi\) | |||||||
\(294\) | 7.26896 | + | 22.3716i | 0.423935 | + | 1.30474i | ||||
\(295\) | 2.99881 | − | 2.17876i | 0.174597 | − | 0.126852i | ||||
\(296\) | 11.2123 | 0.651700 | ||||||||
\(297\) | 2.57312 | − | 2.09262i | 0.149308 | − | 0.121426i | ||||
\(298\) | 5.45140 | 0.315791 | ||||||||
\(299\) | −2.95600 | + | 2.14766i | −0.170950 | + | 0.124202i | ||||
\(300\) | 0.192416 | + | 0.592196i | 0.0111092 | + | 0.0341905i | ||||
\(301\) | 15.7655 | − | 48.5213i | 0.908710 | − | 2.79672i | ||||
\(302\) | −12.7197 | − | 9.24138i | −0.731934 | − | 0.531781i | ||||
\(303\) | −7.89518 | − | 5.73618i | −0.453566 | − | 0.329535i | ||||
\(304\) | −0.900520 | + | 2.77151i | −0.0516483 | + | 0.158957i | ||||
\(305\) | −1.43750 | − | 4.42418i | −0.0823112 | − | 0.253328i | ||||
\(306\) | 4.24247 | − | 3.08234i | 0.242526 | − | 0.176206i | ||||
\(307\) | 10.7394 | 0.612930 | 0.306465 | − | 0.951882i | \(-0.400854\pi\) | ||||
0.306465 | + | 0.951882i | \(0.400854\pi\) | |||||||
\(308\) | −1.59281 | + | 1.29536i | −0.0907585 | + | 0.0738102i | ||||
\(309\) | −9.81295 | −0.558239 | ||||||||
\(310\) | 0.767110 | − | 0.557338i | 0.0435689 | − | 0.0316547i | ||||
\(311\) | −1.32439 | − | 4.07604i | −0.0750991 | − | 0.231131i | 0.906460 | − | 0.422293i | \(-0.138775\pi\) |
−0.981559 | + | 0.191162i | \(0.938775\pi\) | |||||||
\(312\) | −0.843682 | + | 2.59659i | −0.0477641 | + | 0.147003i | ||||
\(313\) | −19.0216 | − | 13.8200i | −1.07516 | − | 0.781152i | −0.0983298 | − | 0.995154i | \(-0.531350\pi\) |
−0.976833 | + | 0.214002i | \(0.931350\pi\) | |||||||
\(314\) | 24.5593 | + | 17.8433i | 1.38596 | + | 1.00696i | ||||
\(315\) | 0.599975 | − | 1.84653i | 0.0338048 | − | 0.104040i | ||||
\(316\) | −0.246076 | − | 0.757343i | −0.0138428 | − | 0.0426039i | ||||
\(317\) | 6.86086 | − | 4.98471i | 0.385345 | − | 0.279969i | −0.378201 | − | 0.925724i | \(-0.623457\pi\) |
0.763545 | + | 0.645754i | \(0.223457\pi\) | |||||||
\(318\) | 3.43062 | 0.192380 | ||||||||
\(319\) | 3.30897 | + | 2.13902i | 0.185266 | + | 0.119762i | ||||
\(320\) | 2.99635 | 0.167501 | ||||||||
\(321\) | 9.14460 | − | 6.64394i | 0.510402 | − | 0.370829i | ||||
\(322\) | −7.92148 | − | 24.3798i | −0.441447 | − | 1.35863i | ||||
\(323\) | 0.763198 | − | 2.34888i | 0.0424655 | − | 0.130695i | ||||
\(324\) | −0.104146 | − | 0.0756667i | −0.00578590 | − | 0.00420370i | ||||
\(325\) | 3.91319 | + | 2.84310i | 0.217065 | + | 0.157707i | ||||
\(326\) | 6.17209 | − | 18.9957i | 0.341841 | − | 1.05208i | ||||
\(327\) | 4.84192 | + | 14.9019i | 0.267759 | + | 0.824076i | ||||
\(328\) | −27.0374 | + | 19.6438i | −1.49289 | + | 1.08465i | ||||
\(329\) | 63.3000 | 3.48984 | ||||||||
\(330\) | 1.95095 | − | 0.106345i | 0.107396 | − | 0.00585409i | ||||
\(331\) | 32.5901 | 1.79132 | 0.895658 | − | 0.444743i | \(-0.146705\pi\) | ||||
0.895658 | + | 0.444743i | \(0.146705\pi\) | |||||||
\(332\) | −0.314374 | + | 0.228406i | −0.0172535 | + | 0.0125354i | ||||
\(333\) | 1.26905 | + | 3.90574i | 0.0695436 | + | 0.214033i | ||||
\(334\) | −5.87658 | + | 18.0863i | −0.321552 | + | 0.989636i | ||||
\(335\) | 0.808089 | + | 0.587111i | 0.0441506 | + | 0.0320773i | ||||
\(336\) | −16.4980 | − | 11.9865i | −0.900040 | − | 0.653917i | ||||
\(337\) | −9.61056 | + | 29.5783i | −0.523521 | + | 1.61123i | 0.243702 | + | 0.969850i | \(0.421638\pi\) |
−0.767223 | + | 0.641381i | \(0.778362\pi\) | |||||||
\(338\) | −0.450861 | − | 1.38761i | −0.0245236 | − | 0.0754759i | ||||
\(339\) | 0.975089 | − | 0.708443i | 0.0529595 | − | 0.0384774i | ||||
\(340\) | 0.186819 | 0.0101317 | ||||||||
\(341\) | 1.92351 | + | 4.97969i | 0.104164 | + | 0.269666i | ||||
\(342\) | −1.00257 | −0.0542127 | ||||||||
\(343\) | −35.4881 | + | 25.7836i | −1.91618 | + | 1.39219i | ||||
\(344\) | 8.95136 | + | 27.5494i | 0.482625 | + | 1.48537i | ||||
\(345\) | −0.455894 | + | 1.40310i | −0.0245445 | + | 0.0755402i | ||||
\(346\) | 9.72524 | + | 7.06580i | 0.522832 | + | 0.379860i | ||||
\(347\) | −4.07105 | − | 2.95779i | −0.218545 | − | 0.158783i | 0.473126 | − | 0.880995i | \(-0.343125\pi\) |
−0.691672 | + | 0.722212i | \(0.743125\pi\) | |||||||
\(348\) | 0.0472589 | − | 0.145448i | 0.00253334 | − | 0.00779682i | ||||
\(349\) | −9.29087 | − | 28.5944i | −0.497329 | − | 1.53062i | −0.813295 | − | 0.581851i | \(-0.802329\pi\) |
0.315966 | − | 0.948770i | \(-0.397671\pi\) | |||||||
\(350\) | −27.4541 | + | 19.9466i | −1.46749 | + | 1.06619i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0.619272 | − | 2.33068i | 0.0330073 | − | 0.124226i | ||||
\(353\) | −7.51069 | −0.399754 | −0.199877 | − | 0.979821i | \(-0.564054\pi\) | ||||
−0.199877 | + | 0.979821i | \(0.564054\pi\) | |||||||
\(354\) | 10.8361 | − | 7.87292i | 0.575935 | − | 0.418441i | ||||
\(355\) | 0.595671 | + | 1.83329i | 0.0316149 | + | 0.0973008i | ||||
\(356\) | 0.147365 | − | 0.453543i | 0.00781034 | − | 0.0240377i | ||||
\(357\) | 13.9822 | + | 10.1587i | 0.740016 | + | 0.537653i | ||||
\(358\) | −12.2957 | − | 8.93336i | −0.649849 | − | 0.472143i | ||||
\(359\) | −7.64921 | + | 23.5419i | −0.403710 | + | 1.24249i | 0.518258 | + | 0.855225i | \(0.326581\pi\) |
−0.921968 | + | 0.387267i | \(0.873419\pi\) | |||||||
\(360\) | 0.340654 | + | 1.04842i | 0.0179540 | + | 0.0552568i | ||||
\(361\) | 14.9893 | − | 10.8904i | 0.788912 | − | 0.573178i | ||||
\(362\) | −19.2554 | −1.01204 | ||||||||
\(363\) | −2.24192 | + | 10.7691i | −0.117670 | + | 0.565232i | ||||
\(364\) | 0.619017 | 0.0324453 | ||||||||
\(365\) | 2.34232 | − | 1.70180i | 0.122603 | − | 0.0890762i | ||||
\(366\) | −5.19440 | − | 15.9867i | −0.271515 | − | 0.835639i | ||||
\(367\) | 4.38220 | − | 13.4870i | 0.228749 | − | 0.704016i | −0.769141 | − | 0.639080i | \(-0.779315\pi\) |
0.997889 | − | 0.0649368i | \(-0.0206846\pi\) | |||||||
\(368\) | 12.5361 | + | 9.10799i | 0.653488 | + | 0.474787i | ||||
\(369\) | −9.90302 | − | 7.19497i | −0.515531 | − | 0.374555i | ||||
\(370\) | −0.747609 | + | 2.30090i | −0.0388663 | + | 0.119618i | ||||
\(371\) | 3.49391 | + | 10.7531i | 0.181395 | + | 0.558275i | ||||
\(372\) | 0.167629 | − | 0.121789i | 0.00869115 | − | 0.00631449i | ||||
\(373\) | −14.5256 | −0.752105 | −0.376052 | − | 0.926598i | \(-0.622719\pi\) | ||||
−0.376052 | + | 0.926598i | \(0.622719\pi\) | |||||||
\(374\) | −4.46626 | + | 16.8091i | −0.230945 | + | 0.869178i | ||||
\(375\) | 3.97188 | 0.205107 | ||||||||
\(376\) | −29.0765 | + | 21.1253i | −1.49950 | + | 1.08945i | ||||
\(377\) | −0.367111 | − | 1.12985i | −0.0189072 | − | 0.0581903i | ||||
\(378\) | 2.16800 | − | 6.67242i | 0.111510 | − | 0.343192i | ||||
\(379\) | 14.2804 | + | 10.3753i | 0.733535 | + | 0.532944i | 0.890680 | − | 0.454631i | \(-0.150229\pi\) |
−0.157145 | + | 0.987576i | \(0.550229\pi\) | |||||||
\(380\) | −0.0288956 | − | 0.0209939i | −0.00148231 | − | 0.00107696i | ||||
\(381\) | −2.97196 | + | 9.14675i | −0.152258 | + | 0.468602i | ||||
\(382\) | 4.67779 | + | 14.3968i | 0.239337 | + | 0.736602i | ||||
\(383\) | −4.97199 | + | 3.61236i | −0.254057 | + | 0.184583i | −0.707523 | − | 0.706690i | \(-0.750187\pi\) |
0.453466 | + | 0.891274i | \(0.350187\pi\) | |||||||
\(384\) | 12.2815 | 0.626736 | ||||||||
\(385\) | 2.32028 | + | 6.00687i | 0.118252 | + | 0.306139i | ||||
\(386\) | 11.1132 | 0.565648 | ||||||||
\(387\) | −8.58356 | + | 6.23632i | −0.436327 | + | 0.317010i | ||||
\(388\) | −0.717164 | − | 2.20720i | −0.0364085 | − | 0.112054i | ||||
\(389\) | −0.853317 | + | 2.62624i | −0.0432649 | + | 0.133156i | −0.970356 | − | 0.241681i | \(-0.922301\pi\) |
0.927091 | + | 0.374837i | \(0.122301\pi\) | |||||||
\(390\) | −0.476598 | − | 0.346269i | −0.0241335 | − | 0.0175340i | ||||
\(391\) | −10.6244 | − | 7.71910i | −0.537300 | − | 0.390372i | ||||
\(392\) | 13.6022 | − | 41.8632i | 0.687014 | − | 2.11441i | ||||
\(393\) | 5.50465 | + | 16.9416i | 0.277673 | + | 0.854589i | ||||
\(394\) | 3.10605 | − | 2.25668i | 0.156480 | − | 0.113690i | ||||
\(395\) | −2.49767 | −0.125671 | ||||||||
\(396\) | 0.426322 | − | 0.0232385i | 0.0214235 | − | 0.00116778i | ||||
\(397\) | −30.0458 | −1.50796 | −0.753978 | − | 0.656899i | \(-0.771868\pi\) | ||||
−0.753978 | + | 0.656899i | \(0.771868\pi\) | |||||||
\(398\) | −14.0928 | + | 10.2390i | −0.706406 | + | 0.513234i | ||||
\(399\) | −1.02106 | − | 3.14251i | −0.0511171 | − | 0.157322i | ||||
\(400\) | 6.33889 | − | 19.5091i | 0.316944 | − | 0.975454i | ||||
\(401\) | 16.6224 | + | 12.0768i | 0.830081 | + | 0.603089i | 0.919582 | − | 0.392898i | \(-0.128527\pi\) |
−0.0895014 | + | 0.995987i | \(0.528527\pi\) | |||||||
\(402\) | 2.92002 | + | 2.12152i | 0.145637 | + | 0.105812i | ||||
\(403\) | 0.497379 | − | 1.53077i | 0.0247762 | − | 0.0762533i | ||||
\(404\) | −0.388215 | − | 1.19480i | −0.0193144 | − | 0.0594437i | ||||
\(405\) | −0.326657 | + | 0.237330i | −0.0162317 | + | 0.0117930i | ||||
\(406\) | 8.33473 | 0.413646 | ||||||||
\(407\) | −11.4386 | − | 7.39431i | −0.566993 | − | 0.366522i | ||||
\(408\) | −9.81290 | −0.485811 | ||||||||
\(409\) | −19.1984 | + | 13.9485i | −0.949301 | + | 0.689707i | −0.950641 | − | 0.310292i | \(-0.899573\pi\) |
0.00134071 | + | 0.999999i | \(0.499573\pi\) | |||||||
\(410\) | −2.22837 | − | 6.85822i | −0.110051 | − | 0.338703i | ||||
\(411\) | −3.92414 | + | 12.0773i | −0.193563 | + | 0.595727i | ||||
\(412\) | −1.02198 | − | 0.742513i | −0.0503494 | − | 0.0365810i | ||||
\(413\) | 35.7134 | + | 25.9473i | 1.75734 | + | 1.27678i | ||||
\(414\) | −1.64736 | + | 5.07007i | −0.0809635 | + | 0.249180i | ||||
\(415\) | 0.376634 | + | 1.15916i | 0.0184883 | + | 0.0569010i | ||||
\(416\) | −0.588244 | + | 0.427384i | −0.0288410 | + | 0.0209542i | ||||
\(417\) | 3.26311 | 0.159795 | ||||||||
\(418\) | 2.57973 | − | 2.09799i | 0.126179 | − | 0.102616i | ||||
\(419\) | 30.0526 | 1.46817 | 0.734083 | − | 0.679060i | \(-0.237612\pi\) | ||||
0.734083 | + | 0.679060i | \(0.237612\pi\) | |||||||
\(420\) | 0.202206 | − | 0.146911i | 0.00986665 | − | 0.00716854i | ||||
\(421\) | 3.48435 | + | 10.7237i | 0.169817 | + | 0.522642i | 0.999359 | − | 0.0358021i | \(-0.0113986\pi\) |
−0.829542 | + | 0.558444i | \(0.811399\pi\) | |||||||
\(422\) | 1.96787 | − | 6.05649i | 0.0957946 | − | 0.294825i | ||||
\(423\) | −10.6499 | − | 7.73760i | −0.517815 | − | 0.376215i | ||||
\(424\) | −5.19358 | − | 3.77336i | −0.252223 | − | 0.183250i | ||||
\(425\) | −5.37226 | + | 16.5341i | −0.260593 | + | 0.802022i | ||||
\(426\) | 2.15245 | + | 6.62456i | 0.104286 | + | 0.320961i | ||||
\(427\) | 44.8194 | − | 32.5632i | 2.16896 | − | 1.57585i | ||||
\(428\) | 1.45510 | 0.0703349 | ||||||||
\(429\) | 2.57312 | − | 2.09262i | 0.124232 | − | 0.101032i | ||||
\(430\) | −6.25036 | −0.301419 | ||||||||
\(431\) | −7.10862 | + | 5.16471i | −0.342410 | + | 0.248775i | −0.745678 | − | 0.666307i | \(-0.767874\pi\) |
0.403268 | + | 0.915082i | \(0.367874\pi\) | |||||||
\(432\) | 1.31051 | + | 4.03333i | 0.0630518 | + | 0.194054i | ||||
\(433\) | −3.70326 | + | 11.3975i | −0.177967 | + | 0.547727i | −0.999757 | − | 0.0220643i | \(-0.992976\pi\) |
0.821789 | + | 0.569792i | \(0.192976\pi\) | |||||||
\(434\) | 9.13565 | + | 6.63744i | 0.438525 | + | 0.318607i | ||||
\(435\) | −0.388067 | − | 0.281947i | −0.0186064 | − | 0.0135183i | ||||
\(436\) | −0.623309 | + | 1.91835i | −0.0298511 | + | 0.0918722i | ||||
\(437\) | 0.775859 | + | 2.38785i | 0.0371144 | + | 0.114226i | ||||
\(438\) | 8.46395 | − | 6.14942i | 0.404423 | − | 0.293831i | ||||
\(439\) | 13.2274 | 0.631312 | 0.315656 | − | 0.948874i | \(-0.397775\pi\) | ||||
0.315656 | + | 0.948874i | \(0.397775\pi\) | |||||||
\(440\) | −3.07049 | − | 1.98487i | −0.146380 | − | 0.0946248i | ||||
\(441\) | 16.1224 | 0.767733 | ||||||||
\(442\) | 4.24247 | − | 3.08234i | 0.201794 | − | 0.146612i | ||||
\(443\) | 6.42783 | + | 19.7828i | 0.305395 | + | 0.939910i | 0.979529 | + | 0.201301i | \(0.0645170\pi\) |
−0.674134 | + | 0.738609i | \(0.735483\pi\) | |||||||
\(444\) | −0.163367 | + | 0.502793i | −0.00775308 | + | 0.0238615i | ||||
\(445\) | −1.21009 | − | 0.879183i | −0.0573639 | − | 0.0416773i | ||||
\(446\) | −1.46478 | − | 1.06423i | −0.0693594 | − | 0.0503926i | ||||
\(447\) | 1.15459 | − | 3.55348i | 0.0546105 | − | 0.168074i | ||||
\(448\) | 11.0270 | + | 33.9375i | 0.520976 | + | 1.60340i | ||||
\(449\) | −14.0158 | + | 10.1831i | −0.661446 | + | 0.480569i | −0.867151 | − | 0.498045i | \(-0.834051\pi\) |
0.205705 | + | 0.978614i | \(0.434051\pi\) | |||||||
\(450\) | 7.05722 | 0.332681 | ||||||||
\(451\) | 40.5380 | − | 2.20969i | 1.90886 | − | 0.104050i | ||||
\(452\) | 0.155157 | 0.00729799 | ||||||||
\(453\) | −8.71796 | + | 6.33397i | −0.409606 | + | 0.297596i | ||||
\(454\) | 6.51298 | + | 20.0449i | 0.305669 | + | 0.940753i | ||||
\(455\) | 0.599975 | − | 1.84653i | 0.0281273 | − | 0.0865668i | ||||
\(456\) | 1.51778 | + | 1.10273i | 0.0710764 | + | 0.0516400i | ||||
\(457\) | 3.18200 | + | 2.31186i | 0.148848 | + | 0.108144i | 0.659717 | − | 0.751514i | \(-0.270676\pi\) |
−0.510869 | + | 0.859659i | \(0.670676\pi\) | |||||||
\(458\) | 1.97168 | − | 6.06820i | 0.0921305 | − | 0.283548i | ||||
\(459\) | −1.11067 | − | 3.41828i | −0.0518414 | − | 0.159552i | ||||
\(460\) | −0.153647 | + | 0.111631i | −0.00716384 | + | 0.00520484i | ||||
\(461\) | −9.60472 | −0.447336 | −0.223668 | − | 0.974665i | \(-0.571803\pi\) | ||||
−0.223668 | + | 0.974665i | \(0.571803\pi\) | |||||||
\(462\) | 8.38428 | + | 21.7057i | 0.390072 | + | 1.00984i | ||||
\(463\) | −26.5099 | −1.23202 | −0.616009 | − | 0.787739i | \(-0.711251\pi\) | ||||
−0.616009 | + | 0.787739i | \(0.711251\pi\) | |||||||
\(464\) | −4.07596 | + | 2.96136i | −0.189222 | + | 0.137478i | ||||
\(465\) | −0.200827 | − | 0.618081i | −0.00931312 | − | 0.0286628i | ||||
\(466\) | −0.993086 | + | 3.05640i | −0.0460038 | + | 0.141585i | ||||
\(467\) | 10.6180 | + | 7.71440i | 0.491340 | + | 0.356980i | 0.805700 | − | 0.592324i | \(-0.201790\pi\) |
−0.314359 | + | 0.949304i | \(0.601790\pi\) | |||||||
\(468\) | −0.104146 | − | 0.0756667i | −0.00481416 | − | 0.00349769i | ||||
\(469\) | −3.67592 | + | 11.3133i | −0.169738 | + | 0.522400i | ||||
\(470\) | −2.39643 | − | 7.37545i | −0.110539 | − | 0.340204i | ||||
\(471\) | 16.8327 | − | 12.2297i | 0.775612 | − | 0.563515i | ||||
\(472\) | −25.0642 | −1.15367 | ||||||||
\(473\) | 9.03633 | − | 34.0089i | 0.415491 | − | 1.56373i | ||||
\(474\) | −9.02528 | −0.414545 | ||||||||
\(475\) | 2.68896 | − | 1.95365i | 0.123378 | − | 0.0896394i | ||||
\(476\) | 0.687521 | + | 2.11597i | 0.0315125 | + | 0.0969854i | ||||
\(477\) | 0.726599 | − | 2.23624i | 0.0332687 | − | 0.102391i | ||||
\(478\) | −13.3426 | − | 9.69395i | −0.610275 | − | 0.443391i | ||||
\(479\) | −24.9416 | − | 18.1212i | −1.13961 | − | 0.827977i | −0.152547 | − | 0.988296i | \(-0.548748\pi\) |
−0.987065 | + | 0.160319i | \(0.948748\pi\) | |||||||
\(480\) | −0.0907228 | + | 0.279216i | −0.00414091 | + | 0.0127444i | ||||
\(481\) | 1.26905 | + | 3.90574i | 0.0578638 | + | 0.178087i | ||||
\(482\) | −8.46167 | + | 6.14776i | −0.385418 | + | 0.280023i | ||||
\(483\) | −17.5697 | −0.799447 | ||||||||
\(484\) | −1.04835 | + | 0.951924i | −0.0476523 | + | 0.0432693i | ||||
\(485\) | −7.27921 | −0.330532 | ||||||||
\(486\) | −1.18037 | + | 0.857589i | −0.0535427 | + | 0.0389010i | ||||
\(487\) | 7.80933 | + | 24.0346i | 0.353874 | + | 1.08911i | 0.956659 | + | 0.291210i | \(0.0940578\pi\) |
−0.602785 | + | 0.797904i | \(0.705942\pi\) | |||||||
\(488\) | −9.72011 | + | 29.9154i | −0.440009 | + | 1.35421i | ||||
\(489\) | −11.0751 | − | 8.04652i | −0.500833 | − | 0.363876i | ||||
\(490\) | 7.68391 | + | 5.58269i | 0.347124 | + | 0.252200i | ||||
\(491\) | −1.90662 | + | 5.86797i | −0.0860444 | + | 0.264818i | −0.984816 | − | 0.173599i | \(-0.944460\pi\) |
0.898772 | + | 0.438416i | \(0.144460\pi\) | |||||||
\(492\) | −0.486944 | − | 1.49866i | −0.0219531 | − | 0.0675647i | ||||
\(493\) | 3.45441 | − | 2.50977i | 0.155579 | − | 0.113035i | ||||
\(494\) | −1.00257 | −0.0451077 | ||||||||
\(495\) | 0.343888 | − | 1.29425i | 0.0154566 | − | 0.0581721i | ||||
\(496\) | −6.82593 | −0.306494 | ||||||||
\(497\) | −18.5722 | + | 13.4935i | −0.833078 | + | 0.605267i | ||||
\(498\) | 1.36096 | + | 4.18861i | 0.0609862 | + | 0.187696i | ||||
\(499\) | −3.46316 | + | 10.6585i | −0.155032 | + | 0.477141i | −0.998164 | − | 0.0605663i | \(-0.980709\pi\) |
0.843132 | + | 0.537707i | \(0.180709\pi\) | |||||||
\(500\) | 0.413656 | + | 0.300539i | 0.0184993 | + | 0.0134405i | ||||
\(501\) | 10.5448 | + | 7.66127i | 0.471108 | + | 0.342280i | ||||
\(502\) | 7.56093 | − | 23.2701i | 0.337461 | − | 1.03860i | ||||
\(503\) | −8.01988 | − | 24.6826i | −0.357589 | − | 1.10054i | −0.954493 | − | 0.298233i | \(-0.903603\pi\) |
0.596905 | − | 0.802312i | \(-0.296397\pi\) | |||||||
\(504\) | −10.6211 | + | 7.71670i | −0.473103 | + | 0.343729i | ||||
\(505\) | −3.94039 | −0.175345 | ||||||||
\(506\) | −6.37083 | − | 16.4932i | −0.283218 | − | 0.733212i | ||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | −1.00162 | + | 0.727722i | −0.0444398 | + | 0.0322874i | ||||
\(509\) | 5.56979 | + | 17.1420i | 0.246876 | + | 0.759807i | 0.995322 | + | 0.0966114i | \(0.0308004\pi\) |
−0.748446 | + | 0.663196i | \(0.769200\pi\) | |||||||
\(510\) | 0.654302 | − | 2.01373i | 0.0289730 | − | 0.0891697i | ||||
\(511\) | 27.8952 | + | 20.2670i | 1.23401 | + | 0.896560i | ||||
\(512\) | −16.2398 | − | 11.7989i | −0.717704 | − | 0.521442i | ||||
\(513\) | −0.212342 | + | 0.653522i | −0.00937513 | + | 0.0288537i | ||||
\(514\) | −11.9171 | − | 36.6772i | −0.525643 | − | 1.61776i | ||||
\(515\) | −3.20547 | + | 2.32891i | −0.141250 | + | 0.102624i | ||||
\(516\) | −1.36583 | −0.0601272 | ||||||||
\(517\) | 43.5953 | − | 2.37634i | 1.91732 | − | 0.104511i | ||||
\(518\) | −28.8120 | −1.26593 | ||||||||
\(519\) | 6.66561 | − | 4.84285i | 0.292588 | − | 0.212578i | ||||
\(520\) | 0.340654 | + | 1.04842i | 0.0149387 | + | 0.0459765i | ||||
\(521\) | 11.0329 | − | 33.9556i | 0.483358 | − | 1.48762i | −0.350986 | − | 0.936381i | \(-0.614154\pi\) |
0.834345 | − | 0.551243i | \(-0.185846\pi\) | |||||||
\(522\) | −1.40227 | − | 1.01881i | −0.0613759 | − | 0.0445922i | ||||
\(523\) | 18.1423 | + | 13.1812i | 0.793309 | + | 0.576373i | 0.908944 | − | 0.416919i | \(-0.136890\pi\) |
−0.115634 | + | 0.993292i | \(0.536890\pi\) | |||||||
\(524\) | −0.708623 | + | 2.18092i | −0.0309564 | + | 0.0952739i | ||||
\(525\) | 7.18741 | + | 22.1206i | 0.313684 | + | 0.965420i | ||||
\(526\) | 18.7984 | − | 13.6578i | 0.819649 | − | 0.595510i | ||||
\(527\) | 5.78503 | 0.252000 | ||||||||
\(528\) | −11.8123 | − | 7.63586i | −0.514064 | − | 0.332308i | ||||
\(529\) | −9.64962 | −0.419549 | ||||||||
\(530\) | 1.12064 | − | 0.814191i | 0.0486774 | − | 0.0353662i | ||||
\(531\) | −2.83687 | − | 8.73098i | −0.123110 | − | 0.378892i | ||||
\(532\) | 0.131443 | − | 0.404541i | 0.00569879 | − | 0.0175391i | ||||
\(533\) | −9.90302 | − | 7.19497i | −0.428948 | − | 0.311649i | ||||
\(534\) | −4.37265 | − | 3.17691i | −0.189223 | − | 0.137479i | ||||
\(535\) | 1.41034 | − | 4.34058i | 0.0609743 | − | 0.187660i | ||||
\(536\) | −2.08711 | − | 6.42347i | −0.0901496 | − | 0.277452i | ||||
\(537\) | −8.42739 | + | 6.12286i | −0.363669 | + | 0.264221i | ||||
\(538\) | 13.3629 | 0.576116 | ||||||||
\(539\) | −41.4849 | + | 33.7380i | −1.78688 | + | 1.45320i | ||||
\(540\) | −0.0519781 | −0.00223678 | ||||||||
\(541\) | −8.58965 | + | 6.24074i | −0.369298 | + | 0.268311i | −0.756920 | − | 0.653508i | \(-0.773297\pi\) |
0.387622 | + | 0.921818i | \(0.373297\pi\) | |||||||
\(542\) | 8.65980 | + | 26.6521i | 0.371970 | + | 1.14481i | ||||
\(543\) | −4.07825 | + | 12.5516i | −0.175014 | + | 0.538639i | ||||
\(544\) | −2.11426 | − | 1.53610i | −0.0906482 | − | 0.0658597i | ||||
\(545\) | 5.11831 | + | 3.71867i | 0.219244 | + | 0.159290i | ||||
\(546\) | 2.16800 | − | 6.67242i | 0.0927818 | − | 0.285553i | ||||
\(547\) | 12.8380 | + | 39.5112i | 0.548912 | + | 1.68938i | 0.711501 | + | 0.702685i | \(0.248016\pi\) |
−0.162589 | + | 0.986694i | \(0.551984\pi\) | |||||||
\(548\) | −1.32253 | + | 0.960874i | −0.0564957 | + | 0.0410465i | ||||
\(549\) | −11.5211 | −0.491707 | ||||||||
\(550\) | −18.1591 | + | 14.7681i | −0.774307 | + | 0.629712i | ||||
\(551\) | −0.816335 | −0.0347770 | ||||||||
\(552\) | 8.07051 | − | 5.86357i | 0.343504 | − | 0.249570i | ||||
\(553\) | −9.19177 | − | 28.2894i | −0.390874 | − | 1.20299i | ||||
\(554\) | 1.53437 | − | 4.72230i | 0.0651890 | − | 0.200631i | ||||
\(555\) | 1.34150 | + | 0.974654i | 0.0569433 | + | 0.0413717i | ||||
\(556\) | 0.339841 | + | 0.246909i | 0.0144125 | + | 0.0104713i | ||||
\(557\) | 12.4931 | − | 38.4497i | 0.529348 | − | 1.62917i | −0.226205 | − | 0.974080i | \(-0.572632\pi\) |
0.755553 | − | 0.655087i | \(-0.227368\pi\) | |||||||
\(558\) | −0.725684 | − | 2.23343i | −0.0307207 | − | 0.0945485i | ||||
\(559\) | −8.58356 | + | 6.23632i | −0.363046 | + | 0.263768i | ||||
\(560\) | −8.23395 | −0.347948 | ||||||||
\(561\) | 10.0110 | + | 6.47145i | 0.422666 | + | 0.273225i | ||||
\(562\) | −46.8502 | −1.97626 | ||||||||
\(563\) | −14.6039 | + | 10.6104i | −0.615481 | + | 0.447173i | −0.851340 | − | 0.524614i | \(-0.824210\pi\) |
0.235859 | + | 0.971787i | \(0.424210\pi\) | |||||||
\(564\) | −0.523668 | − | 1.61168i | −0.0220504 | − | 0.0678641i | ||||
\(565\) | 0.150385 | − | 0.462836i | 0.00632673 | − | 0.0194717i | ||||
\(566\) | 33.3387 | + | 24.2220i | 1.40133 | + | 1.01813i | ||||
\(567\) | −3.89022 | − | 2.82641i | −0.163374 | − | 0.118698i | ||||
\(568\) | 4.02781 | − | 12.3963i | 0.169003 | − | 0.520138i | ||||
\(569\) | −4.37526 | − | 13.4657i | −0.183420 | − | 0.564510i | 0.816497 | − | 0.577349i | \(-0.195913\pi\) |
−0.999918 | + | 0.0128395i | \(0.995913\pi\) | |||||||
\(570\) | −0.327496 | + | 0.237940i | −0.0137173 | + | 0.00996620i | ||||
\(571\) | 26.7585 | 1.11981 | 0.559903 | − | 0.828558i | \(-0.310838\pi\) | ||||
0.559903 | + | 0.828558i | \(0.310838\pi\) | |||||||
\(572\) | 0.426322 | − | 0.0232385i | 0.0178254 | − | 0.000971650i | ||||
\(573\) | 10.3752 | 0.433432 | ||||||||
\(574\) | 69.4776 | − | 50.4784i | 2.89994 | − | 2.10693i | ||||
\(575\) | −5.46138 | − | 16.8084i | −0.227755 | − | 0.700959i | ||||
\(576\) | 2.29319 | − | 7.05771i | 0.0955496 | − | 0.294071i | ||||
\(577\) | 10.1084 | + | 7.34415i | 0.420816 | + | 0.305741i | 0.777966 | − | 0.628306i | \(-0.216251\pi\) |
−0.357150 | + | 0.934047i | \(0.616251\pi\) | |||||||
\(578\) | −4.81803 | − | 3.50050i | −0.200404 | − | 0.145602i | ||||
\(579\) | 2.35376 | − | 7.24412i | 0.0978189 | − | 0.301056i | ||||
\(580\) | −0.0190817 | − | 0.0587275i | −0.000792326 | − | 0.00243853i | ||||
\(581\) | −11.7429 | + | 8.53175i | −0.487180 | + | 0.353957i | ||||
\(582\) | −26.3033 | −1.09031 | ||||||||
\(583\) | 2.80997 | + | 7.27462i | 0.116377 | + | 0.301284i | ||||
\(584\) | −19.5772 | −0.810112 | ||||||||
\(585\) | −0.326657 | + | 0.237330i | −0.0135056 | + | 0.00981240i | ||||
\(586\) | −3.13256 | − | 9.64103i | −0.129405 | − | 0.398267i | ||||
\(587\) | −1.87270 | + | 5.76359i | −0.0772947 | + | 0.237889i | −0.982237 | − | 0.187646i | \(-0.939914\pi\) |
0.904942 | + | 0.425535i | \(0.139914\pi\) | |||||||
\(588\) | 1.67909 | + | 1.21993i | 0.0692444 | + | 0.0503090i | ||||
\(589\) | −0.894780 | − | 0.650096i | −0.0368688 | − | 0.0267867i | ||||
\(590\) | 1.67122 | − | 5.14349i | 0.0688031 | − | 0.211754i | ||||
\(591\) | −0.813153 | − | 2.50263i | −0.0334487 | − | 0.102944i | ||||
\(592\) | 14.0900 | − | 10.2370i | 0.579097 | − | 0.420738i | ||||
\(593\) | −40.4407 | −1.66070 | −0.830350 | − | 0.557242i | \(-0.811859\pi\) | ||||
−0.830350 | + | 0.557242i | \(0.811859\pi\) | |||||||
\(594\) | 1.24263 | − | 4.67674i | 0.0509858 | − | 0.191889i | ||||
\(595\) | 6.97834 | 0.286084 | ||||||||
\(596\) | 0.389127 | − | 0.282717i | 0.0159392 | − | 0.0115805i | ||||
\(597\) | 3.68944 | + | 11.3549i | 0.150999 | + | 0.464726i | ||||
\(598\) | −1.64736 | + | 5.07007i | −0.0673657 | + | 0.207330i | ||||
\(599\) | −14.0963 | − | 10.2416i | −0.575959 | − | 0.418459i | 0.261306 | − | 0.965256i | \(-0.415847\pi\) |
−0.837265 | + | 0.546797i | \(0.815847\pi\) | |||||||
\(600\) | −10.6838 | − | 7.76227i | −0.436166 | − | 0.316893i | ||||
\(601\) | 1.75035 | − | 5.38702i | 0.0713982 | − | 0.219741i | −0.908990 | − | 0.416819i | \(-0.863145\pi\) |
0.980388 | + | 0.197077i | \(0.0631451\pi\) | |||||||
\(602\) | −23.0022 | − | 70.7935i | −0.937499 | − | 2.88533i | ||||
\(603\) | 2.00136 | − | 1.45407i | 0.0815016 | − | 0.0592144i | ||||
\(604\) | −1.38721 | −0.0564449 | ||||||||
\(605\) | 1.82350 | + | 4.04988i | 0.0741357 | + | 0.164651i | ||||
\(606\) | −14.2385 | −0.578400 | ||||||||
\(607\) | −14.2692 | + | 10.3672i | −0.579167 | + | 0.420790i | −0.838424 | − | 0.545019i | \(-0.816523\pi\) |
0.259256 | + | 0.965809i | \(0.416523\pi\) | |||||||
\(608\) | 0.154396 | + | 0.475182i | 0.00626158 | + | 0.0192712i | ||||
\(609\) | 1.76528 | − | 5.43297i | 0.0715328 | − | 0.220155i | ||||
\(610\) | −5.49092 | − | 3.98938i | −0.222321 | − | 0.161525i | ||||
\(611\) | −10.6499 | − | 7.73760i | −0.430848 | − | 0.313030i | ||||
\(612\) | 0.142978 | − | 0.440041i | 0.00577955 | − | 0.0177876i | ||||
\(613\) | −13.2037 | − | 40.6370i | −0.533294 | − | 1.64131i | −0.747306 | − | 0.664480i | \(-0.768653\pi\) |
0.214011 | − | 0.976831i | \(-0.431347\pi\) | |||||||
\(614\) | 12.6765 | − | 9.20999i | 0.511580 | − | 0.371685i | ||||
\(615\) | −4.94248 | −0.199300 | ||||||||
\(616\) | 11.1814 | − | 42.0820i | 0.450510 | − | 1.69553i | ||||
\(617\) | 27.5212 | 1.10796 | 0.553982 | − | 0.832529i | \(-0.313108\pi\) | ||||
0.553982 | + | 0.832529i | \(0.313108\pi\) | |||||||
\(618\) | −11.5829 | + | 8.41547i | −0.465933 | + | 0.338520i | ||||
\(619\) | −11.4646 | − | 35.2844i | −0.460800 | − | 1.41820i | −0.864188 | − | 0.503169i | \(-0.832167\pi\) |
0.403388 | − | 0.915029i | \(-0.367833\pi\) | |||||||
\(620\) | 0.0258528 | − | 0.0795668i | 0.00103827 | − | 0.00319548i | ||||
\(621\) | 2.95600 | + | 2.14766i | 0.118620 | + | 0.0861826i | ||||
\(622\) | −5.05884 | − | 3.67546i | −0.202841 | − | 0.147372i | ||||
\(623\) | 5.50459 | − | 16.9414i | 0.220537 | − | 0.678743i | ||||
\(624\) | 1.31051 | + | 4.03333i | 0.0524623 | + | 0.161462i | ||||
\(625\) | −18.2685 | + | 13.2729i | −0.730740 | + | 0.530914i | ||||
\(626\) | −34.3044 | −1.37108 | ||||||||
\(627\) | −0.821188 | − | 2.12594i | −0.0327951 | − | 0.0849019i | ||||
\(628\) | 2.67845 | 0.106882 | ||||||||
\(629\) | −11.9414 | + | 8.67595i | −0.476136 | + | 0.345933i | ||||
\(630\) | −0.875374 | − | 2.69412i | −0.0348757 | − | 0.107336i | ||||
\(631\) | 0.0232317 | − | 0.0714998i | 0.000924839 | − | 0.00284636i | −0.950593 | − | 0.310440i | \(-0.899524\pi\) |
0.951518 | + | 0.307593i | \(0.0995237\pi\) | |||||||
\(632\) | 13.6633 | + | 9.92694i | 0.543496 | + | 0.394873i | ||||
\(633\) | −3.53112 | − | 2.56551i | −0.140349 | − | 0.101970i | ||||
\(634\) | 3.82353 | − | 11.7676i | 0.151852 | − | 0.467351i | ||||
\(635\) | 1.19999 | + | 3.69319i | 0.0476201 | + | 0.146560i | ||||
\(636\) | 0.244882 | − | 0.177917i | 0.00971019 | − | 0.00705487i | ||||
\(637\) | 16.1224 | 0.638793 | ||||||||
\(638\) | 5.74021 | − | 0.312894i | 0.227257 | − | 0.0123876i | ||||
\(639\) | 4.77408 | 0.188860 | ||||||||
\(640\) | 4.01183 | − | 2.91476i | 0.158581 | − | 0.115216i | ||||
\(641\) | 11.2671 | + | 34.6765i | 0.445023 | + | 1.36964i | 0.882459 | + | 0.470390i | \(0.155887\pi\) |
−0.437436 | + | 0.899250i | \(0.644113\pi\) | |||||||
\(642\) | 5.09624 | − | 15.6846i | 0.201133 | − | 0.619022i | ||||
\(643\) | −8.91202 | − | 6.47496i | −0.351456 | − | 0.255348i | 0.398024 | − | 0.917375i | \(-0.369696\pi\) |
−0.749479 | + | 0.662028i | \(0.769696\pi\) | |||||||
\(644\) | −1.82981 | − | 1.32944i | −0.0721048 | − | 0.0523872i | ||||
\(645\) | −1.32381 | + | 4.07428i | −0.0521251 | + | 0.160425i | ||||
\(646\) | −1.11352 | − | 3.42706i | −0.0438108 | − | 0.134836i | ||||
\(647\) | −3.55787 | + | 2.58494i | −0.139874 | + | 0.101625i | −0.655522 | − | 0.755176i | \(-0.727551\pi\) |
0.515648 | + | 0.856801i | \(0.327551\pi\) | |||||||
\(648\) | 2.73021 | 0.107253 | ||||||||
\(649\) | 25.5702 | + | 16.5294i | 1.00372 | + | 0.648836i | ||||
\(650\) | 7.05722 | 0.276807 | ||||||||
\(651\) | 6.26151 | − | 4.54925i | 0.245408 | − | 0.178299i | ||||
\(652\) | −0.544575 | − | 1.67603i | −0.0213272 | − | 0.0656384i | ||||
\(653\) | 12.8100 | − | 39.4250i | 0.501293 | − | 1.54282i | −0.305622 | − | 0.952153i | \(-0.598864\pi\) |
0.806915 | − | 0.590668i | \(-0.201136\pi\) | |||||||
\(654\) | 18.4949 | + | 13.4374i | 0.723209 | + | 0.525442i | ||||
\(655\) | 5.81888 | + | 4.22766i | 0.227362 | + | 0.165188i | ||||
\(656\) | −16.0417 | + | 49.3712i | −0.626322 | + | 1.92762i | ||||
\(657\) | −2.21583 | − | 6.81964i | −0.0864479 | − | 0.266059i | ||||
\(658\) | 74.7175 | − | 54.2854i | 2.91279 | − | 2.11627i | ||||
\(659\) | −0.460087 | −0.0179224 | −0.00896121 | − | 0.999960i | \(-0.502852\pi\) | ||||
−0.00896121 | + | 0.999960i | \(0.502852\pi\) | |||||||
\(660\) | 0.133746 | − | 0.108770i | 0.00520606 | − | 0.00423387i | ||||
\(661\) | 18.5250 | 0.720537 | 0.360269 | − | 0.932849i | \(-0.382685\pi\) | ||||
0.360269 | + | 0.932849i | \(0.382685\pi\) | |||||||
\(662\) | 38.4684 | − | 27.9489i | 1.49512 | − | 1.08627i | ||||
\(663\) | −1.11067 | − | 3.41828i | −0.0431347 | − | 0.132755i | ||||
\(664\) | 2.54672 | − | 7.83801i | 0.0988321 | − | 0.304174i | ||||
\(665\) | −1.07935 | − | 0.784193i | −0.0418554 | − | 0.0304097i | ||||
\(666\) | 4.84747 | + | 3.52189i | 0.187836 | + | 0.136471i | ||||
\(667\) | −1.34136 | + | 4.12827i | −0.0519375 | + | 0.159847i | ||||
\(668\) | 0.518502 | + | 1.59578i | 0.0200614 | + | 0.0617428i | ||||
\(669\) | −1.00395 | + | 0.729413i | −0.0388150 | + | 0.0282007i | ||||
\(670\) | 1.45734 | 0.0563021 | ||||||||
\(671\) | 29.6451 | − | 24.1091i | 1.14444 | − | 0.930723i | ||||
\(672\) | −3.49636 | −0.134875 | ||||||||
\(673\) | 0.623408 | − | 0.452932i | 0.0240306 | − | 0.0174593i | −0.575705 | − | 0.817657i | \(-0.695272\pi\) |
0.599736 | + | 0.800198i | \(0.295272\pi\) | |||||||
\(674\) | 14.0220 | + | 43.1552i | 0.540106 | + | 1.66228i | ||||
\(675\) | 1.49471 | − | 4.60023i | 0.0575313 | − | 0.177063i | ||||
\(676\) | −0.104146 | − | 0.0756667i | −0.00400563 | − | 0.00291026i | ||||
\(677\) | 9.64587 | + | 7.00813i | 0.370721 | + | 0.269344i | 0.757510 | − | 0.652824i | \(-0.226416\pi\) |
−0.386789 | + | 0.922168i | \(0.626416\pi\) | |||||||
\(678\) | 0.543412 | − | 1.67245i | 0.0208696 | − | 0.0642301i | ||||
\(679\) | −26.7885 | − | 82.4466i | −1.02805 | − | 3.16401i | ||||
\(680\) | −3.20545 | + | 2.32890i | −0.122924 | + | 0.0893092i | ||||
\(681\) | 14.4456 | 0.553558 | ||||||||
\(682\) | 6.54098 | + | 4.22830i | 0.250467 | + | 0.161910i | ||||
\(683\) | −1.22385 | −0.0468294 | −0.0234147 | − | 0.999726i | \(-0.507454\pi\) | ||||
−0.0234147 | + | 0.999726i | \(0.507454\pi\) | |||||||
\(684\) | −0.0715644 | + | 0.0519946i | −0.00273634 | + | 0.00198806i | ||||
\(685\) | 1.58445 | + | 4.87644i | 0.0605387 | + | 0.186319i | ||||
\(686\) | −19.7774 | + | 60.8684i | −0.755103 | + | 2.32397i | ||||
\(687\) | −3.53794 | − | 2.57047i | −0.134981 | − | 0.0980694i | ||||
\(688\) | 36.4020 | + | 26.4476i | 1.38781 | + | 1.00830i | ||||
\(689\) | 0.726599 | − | 2.23624i | 0.0276812 | − | 0.0851941i | ||||
\(690\) | 0.665157 | + | 2.04714i | 0.0253221 | + | 0.0779334i | ||||
\(691\) | −24.6558 | + | 17.9135i | −0.937950 | + | 0.681461i | −0.947926 | − | 0.318490i | \(-0.896824\pi\) |
0.00997618 | + | 0.999950i | \(0.496824\pi\) | |||||||
\(692\) | 1.06064 | 0.0403195 | ||||||||
\(693\) | 15.9246 | − | 0.868037i | 0.604926 | − | 0.0329740i | ||||
\(694\) | −7.34191 | −0.278695 | ||||||||
\(695\) | 1.06592 | − | 0.774435i | 0.0404326 | − | 0.0293760i | ||||
\(696\) | 1.00229 | + | 3.08473i | 0.0379917 | + | 0.116927i | ||||
\(697\) | 13.5955 | − | 41.8425i | 0.514964 | − | 1.58490i | ||||
\(698\) | −35.4889 | − | 25.7842i | −1.34327 | − | 0.975946i | ||||
\(699\) | 1.78198 | + | 1.29468i | 0.0674005 | + | 0.0489693i | ||||
\(700\) | −0.925248 | + | 2.84762i | −0.0349711 | + | 0.107630i | ||||
\(701\) | −6.31001 | − | 19.4202i | −0.238326 | − | 0.733492i | −0.996663 | − | 0.0816289i | \(-0.973988\pi\) |
0.758337 | − | 0.651863i | \(-0.226012\pi\) | |||||||
\(702\) | −1.18037 | + | 0.857589i | −0.0445502 | + | 0.0323676i | ||||
\(703\) | 2.82196 | 0.106432 | ||||||||
\(704\) | 8.86842 | + | 22.9591i | 0.334241 | + | 0.865305i | ||||
\(705\) | −5.31523 | −0.200183 | ||||||||
\(706\) | −8.86539 | + | 6.44108i | −0.333653 | + | 0.242413i | ||||
\(707\) | −14.5012 | − | 44.6300i | −0.545373 | − | 1.67848i | ||||
\(708\) | 0.365195 | − | 1.12396i | 0.0137249 | − | 0.0422408i | ||||
\(709\) | −37.2775 | − | 27.0837i | −1.39999 | − | 1.01715i | −0.994685 | − | 0.102967i | \(-0.967166\pi\) |
−0.405302 | − | 0.914183i | \(-0.632834\pi\) | |||||||
\(710\) | 2.27532 | + | 1.65312i | 0.0853912 | + | 0.0620404i | ||||
\(711\) | −1.91154 | + | 5.88311i | −0.0716883 | + | 0.220634i | ||||
\(712\) | 3.12540 | + | 9.61898i | 0.117129 | + | 0.360487i | ||||
\(713\) | −4.75784 | + | 3.45677i | −0.178182 | + | 0.129457i | ||||
\(714\) | 25.2161 | 0.943689 | ||||||||
\(715\) | 0.343888 | − | 1.29425i | 0.0128607 | − | 0.0484021i | ||||
\(716\) | −1.34098 | −0.0501147 | ||||||||
\(717\) | −9.14491 | + | 6.64416i | −0.341523 | + | 0.248131i | ||||
\(718\) | 11.1603 | + | 34.3480i | 0.416500 | + | 1.28186i | ||||
\(719\) | 1.50587 | − | 4.63458i | 0.0561594 | − | 0.172841i | −0.919042 | − | 0.394159i | \(-0.871036\pi\) |
0.975202 | + | 0.221318i | \(0.0710359\pi\) | |||||||
\(720\) | 1.38532 | + | 1.00649i | 0.0516277 | + | 0.0375097i | ||||
\(721\) | −38.1745 | − | 27.7354i | −1.42169 | − | 1.03292i | ||||
\(722\) | 8.35347 | − | 25.7094i | 0.310884 | − | 0.956803i | ||||
\(723\) | 2.21524 | + | 6.81780i | 0.0823856 | + | 0.253557i | ||||
\(724\) | −1.37447 | + | 0.998610i | −0.0510817 | + | 0.0371131i | ||||
\(725\) | 5.74630 | 0.213412 | ||||||||
\(726\) | 6.58918 | + | 14.6342i | 0.244547 | + | 0.543125i | ||||
\(727\) | −28.8112 | −1.06855 | −0.534274 | − | 0.845311i | \(-0.679415\pi\) | ||||
−0.534274 | + | 0.845311i | \(0.679415\pi\) | |||||||
\(728\) | −10.6211 | + | 7.71670i | −0.393645 | + | 0.286000i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 1.30537 | − | 4.01750i | 0.0483137 | − | 0.148694i | ||||
\(731\) | −30.8510 | − | 22.4145i | −1.14106 | − | 0.829031i | ||||
\(732\) | −1.19987 | − | 0.871760i | −0.0443487 | − | 0.0322212i | ||||
\(733\) | −6.21975 | + | 19.1424i | −0.229732 | + | 0.707042i | 0.768045 | + | 0.640396i | \(0.221230\pi\) |
−0.997777 | + | 0.0666457i | \(0.978770\pi\) | |||||||
\(734\) | −6.39370 | − | 19.6778i | −0.235996 | − | 0.726320i | ||||
\(735\) | 5.26649 | − | 3.82633i | 0.194258 | − | 0.141136i | ||||
\(736\) | 2.65672 | 0.0979282 | ||||||||
\(737\) | −2.10693 | + | 7.92958i | −0.0776096 | + | 0.292090i | ||||
\(738\) | −17.8596 | −0.657419 | ||||||||
\(739\) | 4.66310 | − | 3.38794i | 0.171535 | − | 0.124628i | −0.498705 | − | 0.866772i | \(-0.666191\pi\) |
0.670240 | + | 0.742144i | \(0.266191\pi\) | |||||||
\(740\) | 0.0659629 | + | 0.203013i | 0.00242485 | + | 0.00746291i | ||||
\(741\) | −0.212342 | + | 0.653522i | −0.00780058 | + | 0.0240077i | ||||
\(742\) | 13.3459 | + | 9.69635i | 0.489943 | + | 0.355964i | ||||
\(743\) | −30.2933 | − | 22.0094i | −1.11135 | − | 0.807446i | −0.128478 | − | 0.991712i | \(-0.541009\pi\) |
−0.982876 | + | 0.184266i | \(0.941009\pi\) | |||||||
\(744\) | −1.35795 | + | 4.17934i | −0.0497849 | + | 0.153222i | ||||
\(745\) | −0.466191 | − | 1.43479i | −0.0170799 | − | 0.0525666i | ||||
\(746\) | −17.1455 | + | 12.4570i | −0.627742 | + | 0.456082i | ||||
\(747\) | 3.01858 | 0.110444 | ||||||||
\(748\) | 0.552937 | + | 1.43148i | 0.0202174 | + | 0.0523400i | ||||
\(749\) | 54.3530 | 1.98602 | ||||||||
\(750\) | 4.68828 | − | 3.40624i | 0.171192 | − | 0.124378i | ||||
\(751\) | 1.16180 | + | 3.57564i | 0.0423945 | + | 0.130477i | 0.970014 | − | 0.243051i | \(-0.0781481\pi\) |
−0.927619 | + | 0.373528i | \(0.878148\pi\) | |||||||
\(752\) | −17.2515 | + | 53.0947i | −0.629098 | + | 1.93616i | ||||
\(753\) | −13.5672 | − | 9.85714i | −0.494416 | − | 0.359214i | ||||
\(754\) | −1.40227 | − | 1.01881i | −0.0510678 | − | 0.0371029i | ||||
\(755\) | −1.34454 | + | 4.13807i | −0.0489329 | + | 0.150600i | ||||
\(756\) | −0.191287 | − | 0.588720i | −0.00695703 | − | 0.0214115i | ||||
\(757\) | 0.984033 | − | 0.714942i | 0.0357653 | − | 0.0259850i | −0.569759 | − | 0.821812i | \(-0.692963\pi\) |
0.605524 | + | 0.795827i | \(0.292963\pi\) | |||||||
\(758\) | 25.7539 | 0.935424 | ||||||||
\(759\) | −12.1004 | + | 0.659582i | −0.439216 | + | 0.0239413i | ||||
\(760\) | 0.757503 | 0.0274775 | ||||||||
\(761\) | −27.7301 | + | 20.1471i | −1.00522 | + | 0.730333i | −0.963200 | − | 0.268784i | \(-0.913378\pi\) |
−0.0420162 | + | 0.999117i | \(0.513378\pi\) | |||||||
\(762\) | 4.33614 | + | 13.3453i | 0.157082 | + | 0.483448i | ||||
\(763\) | −23.2827 | + | 71.6568i | −0.842891 | + | 2.59415i | ||||
\(764\) | 1.08054 | + | 0.785060i | 0.0390926 | + | 0.0284025i | ||||
\(765\) | −1.17407 | − | 0.853010i | −0.0424485 | − | 0.0308406i | ||||
\(766\) | −2.77087 | + | 8.52785i | −0.100115 | + | 0.308124i | ||||
\(767\) | −2.83687 | − | 8.73098i | −0.102433 | − | 0.315257i | ||||
\(768\) | 2.48938 | − | 1.80864i | 0.0898277 | − | 0.0652636i | ||||
\(769\) | −22.7421 | −0.820101 | −0.410050 | − | 0.912063i | \(-0.634489\pi\) | ||||
−0.410050 | + | 0.912063i | \(0.634489\pi\) | |||||||
\(770\) | 7.89021 | + | 5.10049i | 0.284344 | + | 0.183809i | ||||
\(771\) | −26.4320 | −0.951923 | ||||||||
\(772\) | 0.793274 | − | 0.576347i | 0.0285506 | − | 0.0207432i | ||||
\(773\) | −4.00653 | − | 12.3308i | −0.144105 | − | 0.443509i | 0.852790 | − | 0.522254i | \(-0.174909\pi\) |
−0.996895 | + | 0.0787448i | \(0.974909\pi\) | |||||||
\(774\) | −4.78358 | + | 14.7223i | −0.171942 | + | 0.529183i | ||||
\(775\) | 6.29848 | + | 4.57612i | 0.226248 | + | 0.164379i | ||||
\(776\) | 39.8203 | + | 28.9311i | 1.42946 | + | 1.03857i | ||||
\(777\) | −6.10233 | + | 18.7811i | −0.218920 | + | 0.673767i | ||||
\(778\) | 1.24500 | + | 3.83173i | 0.0446355 | + | 0.137374i | ||||
\(779\) | −6.80490 | + | 4.94405i | −0.243811 | + | 0.177139i | ||||
\(780\) | −0.0519781 | −0.00186111 | ||||||||
\(781\) | −12.2843 | + | 9.99032i | −0.439567 | + | 0.357482i | ||||
\(782\) | −19.1606 | −0.685180 | ||||||||
\(783\) | −0.961109 | + | 0.698286i | −0.0343472 | + | 0.0249547i | ||||
\(784\) | −21.1285 | − | 65.0269i | −0.754590 | − | 2.32239i | ||||
\(785\) | 2.59605 | − | 7.98983i | 0.0926572 | − | 0.285169i | ||||
\(786\) | 21.0264 | + | 15.2766i | 0.749987 | + | 0.544898i | ||||
\(787\) | 34.1558 | + | 24.8156i | 1.21752 | + | 0.884582i | 0.995892 | − | 0.0905492i | \(-0.0288622\pi\) |
0.221630 | + | 0.975131i | \(0.428862\pi\) | |||||||
\(788\) | 0.104679 | − | 0.322168i | 0.00372903 | − | 0.0114768i | ||||
\(789\) | −4.92136 | − | 15.1464i | −0.175205 | − | 0.539225i | ||||
\(790\) | −2.94817 | + | 2.14197i | −0.104891 | + | 0.0762080i | ||||
\(791\) | 5.79566 | 0.206070 | ||||||||
\(792\) | −7.02517 | + | 5.71329i | −0.249629 | + | 0.203013i | ||||
\(793\) | −11.5211 | −0.409125 | ||||||||
\(794\) | −35.4652 | + | 25.7670i | −1.25861 | + | 0.914436i | ||||
\(795\) | −0.293379 | − | 0.902929i | −0.0104051 | − | 0.0320236i | ||||
\(796\) | −0.474948 | + | 1.46174i | −0.0168341 | + | 0.0518100i | ||||
\(797\) | −36.5842 | − | 26.5800i | −1.29588 | − | 0.941511i | −0.295972 | − | 0.955197i | \(-0.595644\pi\) |
−0.999906 | + | 0.0136857i | \(0.995644\pi\) | |||||||
\(798\) | −3.90021 | − | 2.83367i | −0.138066 | − | 0.100311i | ||||
\(799\) | 14.6208 | − | 44.9982i | 0.517246 | − | 1.59192i | ||||
\(800\) | −1.08681 | − | 3.34487i | −0.0384247 | − | 0.118259i | ||||
\(801\) | −2.99698 | + | 2.17743i | −0.105893 | + | 0.0769359i | ||||
\(802\) | 29.9775 | 1.05854 | ||||||||
\(803\) | 19.9725 | + | 12.9109i | 0.704814 | + | 0.455615i | ||||
\(804\) | 0.318459 | 0.0112312 | ||||||||
\(805\) | −5.73925 | + | 4.16981i | −0.202282 | + | 0.146967i | ||||
\(806\) | −0.725684 | − | 2.23343i | −0.0255611 | − | 0.0786691i | ||||
\(807\) | 2.83024 | − | 8.71058i | 0.0996291 | − | 0.306627i | ||||
\(808\) | 21.5555 | + | 15.6610i | 0.758321 | + | 0.550952i | ||||
\(809\) | 27.2757 | + | 19.8170i | 0.958963 | + | 0.696728i | 0.952910 | − | 0.303254i | \(-0.0980731\pi\) |
0.00605350 | + | 0.999982i | \(0.498073\pi\) | |||||||
\(810\) | −0.182044 | + | 0.560275i | −0.00639639 | + | 0.0196861i | ||||
\(811\) | 7.60022 | + | 23.3911i | 0.266880 | + | 0.821372i | 0.991254 | + | 0.131965i | \(0.0421287\pi\) |
−0.724374 | + | 0.689407i | \(0.757871\pi\) | |||||||
\(812\) | 0.594942 | − | 0.432251i | 0.0208784 | − | 0.0151690i | ||||
\(813\) | 19.2072 | 0.673628 | ||||||||
\(814\) | −19.8431 | + | 1.08163i | −0.695501 | + | 0.0379112i | ||||
\(815\) | −5.52744 | −0.193618 | ||||||||
\(816\) | −12.3315 | + | 8.95936i | −0.431689 | + | 0.313640i | ||||
\(817\) | 2.25292 | + | 6.93378i | 0.0788197 | + | 0.242582i | ||||
\(818\) | −10.6992 | + | 32.9287i | −0.374088 | + | 1.15133i | ||||
\(819\) | −3.89022 | − | 2.82641i | −0.135935 | − | 0.0987627i | ||||
\(820\) | −0.514740 | − | 0.373981i | −0.0179755 | − | 0.0130600i | ||||
\(821\) | 6.36699 | − | 19.5956i | 0.222210 | − | 0.683891i | −0.776353 | − | 0.630298i | \(-0.782933\pi\) |
0.998563 | − | 0.0535929i | \(-0.0170673\pi\) | |||||||
\(822\) | 5.72539 | + | 17.6209i | 0.199696 | + | 0.614600i | ||||
\(823\) | 19.5953 | − | 14.2369i | 0.683051 | − | 0.496265i | −0.191318 | − | 0.981528i | \(-0.561276\pi\) |
0.874368 | + | 0.485263i | \(0.161276\pi\) | |||||||
\(824\) | 26.7914 | 0.933324 | ||||||||
\(825\) | 5.78046 | + | 14.9648i | 0.201250 | + | 0.521008i | ||||
\(826\) | 64.4071 | 2.24101 | ||||||||
\(827\) | 0.910993 | − | 0.661875i | 0.0316783 | − | 0.0230157i | −0.571833 | − | 0.820370i | \(-0.693768\pi\) |
0.603512 | + | 0.797354i | \(0.293768\pi\) | |||||||
\(828\) | 0.145350 | + | 0.447341i | 0.00505126 | + | 0.0155462i | ||||
\(829\) | 3.20601 | − | 9.86708i | 0.111349 | − | 0.342698i | −0.879819 | − | 0.475309i | \(-0.842336\pi\) |
0.991168 | + | 0.132611i | \(0.0423362\pi\) | |||||||
\(830\) | 1.43865 | + | 1.04524i | 0.0499363 | + | 0.0362809i | ||||
\(831\) | −2.75324 | − | 2.00035i | −0.0955088 | − | 0.0693912i | ||||
\(832\) | 2.29319 | − | 7.05771i | 0.0795021 | − | 0.244682i | ||||
\(833\) | 17.9066 | + | 55.1108i | 0.620427 | + | 1.90948i | ||||
\(834\) | 3.85168 | − | 2.79841i | 0.133373 | − | 0.0969010i | ||||
\(835\) | 5.26279 | 0.182126 | ||||||||
\(836\) | 0.0753393 | − | 0.283545i | 0.00260566 | − | 0.00980662i | ||||
\(837\) | −1.60955 | −0.0556342 | ||||||||
\(838\) | 35.4732 | − | 25.7728i | 1.22540 | − | 0.890306i | ||||
\(839\) | −4.95645 | − | 15.2544i | −0.171116 | − | 0.526640i | 0.828319 | − | 0.560257i | \(-0.189297\pi\) |
−0.999435 | + | 0.0336167i | \(0.989297\pi\) | |||||||
\(840\) | −1.63806 | + | 5.04143i | −0.0565184 | + | 0.173946i | ||||
\(841\) | 22.3197 | + | 16.2162i | 0.769645 | + | 0.559180i | ||||
\(842\) | 13.3094 | + | 9.66981i | 0.458671 | + | 0.333244i | ||||
\(843\) | −9.92278 | + | 30.5392i | −0.341759 | + | 1.05182i | ||||
\(844\) | −0.173629 | − | 0.534376i | −0.00597656 | − | 0.0183940i | ||||
\(845\) | −0.326657 | + | 0.237330i | −0.0112373 | + | 0.00816441i | ||||
\(846\) | −19.2065 | −0.660333 | ||||||||
\(847\) | −39.1595 | + | 35.5576i | −1.34554 | + | 1.22177i | ||||
\(848\) | −9.97172 | −0.342430 | ||||||||
\(849\) | 22.8501 | − | 16.6016i | 0.784213 | − | 0.569764i | ||||
\(850\) | 7.83822 | + | 24.1235i | 0.268849 | + | 0.827431i | ||||
\(851\) | 4.63689 | − | 14.2709i | 0.158950 | − | 0.489199i | ||||
\(852\) | 0.497203 | + | 0.361239i | 0.0170339 | + | 0.0123758i | ||||
\(853\) | −25.8294 | − | 18.7662i | −0.884382 | − | 0.642541i | 0.0500251 | − | 0.998748i | \(-0.484070\pi\) |
−0.934407 | + | 0.356207i | \(0.884070\pi\) | |||||||
\(854\) | 24.9777 | − | 76.8733i | 0.854718 | − | 2.63055i | ||||
\(855\) | 0.0857374 | + | 0.263873i | 0.00293216 | + | 0.00902425i | ||||
\(856\) | −24.9667 | + | 18.1394i | −0.853344 | + | 0.619991i | ||||
\(857\) | −35.3804 | −1.20857 | −0.604285 | − | 0.796768i | \(-0.706541\pi\) | ||||
−0.604285 | + | 0.796768i | \(0.706541\pi\) | |||||||
\(858\) | 1.24263 | − | 4.67674i | 0.0424228 | − | 0.159661i | ||||
\(859\) | −8.95220 | −0.305445 | −0.152723 | − | 0.988269i | \(-0.548804\pi\) | ||||
−0.152723 | + | 0.988269i | \(0.548804\pi\) | |||||||
\(860\) | −0.446157 | + | 0.324152i | −0.0152138 | + | 0.0110535i | ||||
\(861\) | −18.1890 | − | 55.9800i | −0.619880 | − | 1.90779i | ||||
\(862\) | −3.96160 | + | 12.1925i | −0.134933 | + | 0.415280i | ||||
\(863\) | 23.6101 | + | 17.1537i | 0.803697 | + | 0.583920i | 0.911996 | − | 0.410198i | \(-0.134540\pi\) |
−0.108299 | + | 0.994118i | \(0.534540\pi\) | |||||||
\(864\) | 0.588244 | + | 0.427384i | 0.0200125 | + | 0.0145399i | ||||
\(865\) | 1.02801 | − | 3.16390i | 0.0349535 | − | 0.107576i | ||||
\(866\) | 5.40312 | + | 16.6291i | 0.183606 | + | 0.565080i | ||||
\(867\) | −3.30224 | + | 2.39922i | −0.112150 | + | 0.0814818i | ||||
\(868\) | 0.996340 | 0.0338180 | ||||||||
\(869\) | −7.39246 | − | 19.1381i | −0.250772 | − | 0.649214i | ||||
\(870\) | −0.699858 | −0.0237274 | ||||||||
\(871\) | 2.00136 | − | 1.45407i | 0.0678134 | − | 0.0492693i | ||||
\(872\) | −13.2195 | − | 40.6853i | −0.447667 | − | 1.37778i | ||||
\(873\) | −5.57099 | + | 17.1457i | −0.188549 | + | 0.580296i | ||||
\(874\) | 2.96359 | + | 2.15318i | 0.100245 | + | 0.0728323i | ||||
\(875\) | 15.4515 | + | 11.2261i | 0.522355 | + | 0.379513i | ||||
\(876\) | 0.285248 | − | 0.877904i | 0.00963765 | − | 0.0296616i | ||||
\(877\) | 13.8717 | + | 42.6928i | 0.468416 | + | 1.44163i | 0.854636 | + | 0.519228i | \(0.173781\pi\) |
−0.386220 | + | 0.922407i | \(0.626219\pi\) | |||||||
\(878\) | 15.6133 | − | 11.3437i | 0.526923 | − | 0.382832i | ||||
\(879\) | −6.94795 | −0.234348 | ||||||||
\(880\) | −5.67079 | + | 0.309110i | −0.191162 | + | 0.0104201i | ||||
\(881\) | −15.2732 | −0.514568 | −0.257284 | − | 0.966336i | \(-0.582828\pi\) | ||||
−0.257284 | + | 0.966336i | \(0.582828\pi\) | |||||||
\(882\) | 19.0304 | − | 13.8264i | 0.640787 | − | 0.465559i | ||||
\(883\) | 1.05049 | + | 3.23309i | 0.0353520 | + | 0.108802i | 0.967175 | − | 0.254110i | \(-0.0817825\pi\) |
−0.931823 | + | 0.362912i | \(0.881783\pi\) | |||||||
\(884\) | 0.142978 | − | 0.440041i | 0.00480887 | − | 0.0148002i | ||||
\(885\) | −2.99881 | − | 2.17876i | −0.100804 | − | 0.0732383i | ||||
\(886\) | 24.5527 | + | 17.8386i | 0.824865 | + | 0.599300i | ||||
\(887\) | −6.49395 | + | 19.9863i | −0.218045 | + | 0.671075i | 0.780878 | + | 0.624684i | \(0.214772\pi\) |
−0.998923 | + | 0.0463912i | \(0.985228\pi\) | |||||||
\(888\) | −3.46478 | − | 10.6635i | −0.116271 | − | 0.357844i | ||||
\(889\) | −37.4140 | + | 27.1829i | −1.25483 | + | 0.911685i | ||||
\(890\) | −2.18233 | −0.0731520 | ||||||||
\(891\) | −2.78533 | − | 1.80053i | −0.0933122 | − | 0.0603201i | ||||
\(892\) | −0.159750 | −0.00534883 | ||||||||
\(893\) | −7.31811 | + | 5.31692i | −0.244891 | + | 0.177924i | ||||
\(894\) | −1.68457 | − | 5.18459i | −0.0563406 | − | 0.173399i | ||||
\(895\) | −1.29973 | + | 4.00015i | −0.0434451 | + | 0.133710i | ||||
\(896\) | 47.7776 | + | 34.7125i | 1.59614 | + | 1.15966i | ||||
\(897\) | 2.95600 | + | 2.14766i | 0.0986980 | + | 0.0717083i | ||||
\(898\) | −7.81093 | + | 24.0396i | −0.260654 | + | 0.802211i | ||||
\(899\) | −0.590884 | − | 1.81855i | −0.0197071 | − | 0.0606522i | ||||
\(900\) | 0.503752 | − | 0.365997i | 0.0167917 | − | 0.0121999i | ||||
\(901\) | 8.45111 | 0.281547 | ||||||||
\(902\) | 45.9548 | − | 37.3732i | 1.53013 | − | 1.24439i | ||||
\(903\) | −51.0183 | −1.69778 | ||||||||
\(904\) | −2.66220 | + | 1.93420i | −0.0885434 | + | 0.0643306i | ||||
\(905\) | 1.64668 | + | 5.06795i | 0.0547373 | + | 0.168464i | ||||
\(906\) | −4.85848 | + | 14.9529i | −0.161412 | + | 0.496775i | ||||
\(907\) | 9.69570 | + | 7.04434i | 0.321940 | + | 0.233903i | 0.737003 | − | 0.675889i | \(-0.236240\pi\) |
−0.415063 | + | 0.909793i | \(0.636240\pi\) | |||||||
\(908\) | 1.50446 | + | 1.09305i | 0.0499272 | + | 0.0362743i | ||||
\(909\) | −3.01569 | + | 9.28134i | −0.100024 | + | 0.307843i | ||||
\(910\) | −0.875374 | − | 2.69412i | −0.0290184 | − | 0.0893094i | ||||
\(911\) | 9.13361 | − | 6.63596i | 0.302610 | − | 0.219859i | −0.426109 | − | 0.904672i | \(-0.640116\pi\) |
0.728719 | + | 0.684813i | \(0.240116\pi\) | |||||||
\(912\) | 2.91414 | 0.0964969 | ||||||||
\(913\) | −7.76718 | + | 6.31673i | −0.257056 | + | 0.209053i | ||||
\(914\) | 5.73856 | 0.189815 | ||||||||
\(915\) | −3.76343 | + | 2.73430i | −0.124415 | + | 0.0903930i | ||||
\(916\) | −0.173965 | − | 0.535409i | −0.00574796 | − | 0.0176904i | ||||
\(917\) | −26.4695 | + | 81.4648i | −0.874100 | + | 2.69020i | ||||
\(918\) | −4.24247 | − | 3.08234i | −0.140023 | − | 0.101732i | ||||
\(919\) | −32.8982 | − | 23.9019i | −1.08521 | − | 0.788452i | −0.106627 | − | 0.994299i | \(-0.534005\pi\) |
−0.978584 | + | 0.205847i | \(0.934005\pi\) | |||||||
\(920\) | 1.24469 | − | 3.83075i | 0.0410361 | − | 0.126296i | ||||
\(921\) | −3.31866 | − | 10.2138i | −0.109353 | − | 0.336555i | ||||
\(922\) | −11.3371 | + | 8.23690i | −0.373368 | + | 0.271268i | ||||
\(923\) | 4.77408 | 0.157141 | ||||||||
\(924\) | 1.72417 | + | 1.11456i | 0.0567210 | + | 0.0366663i | ||||
\(925\) | −19.8642 | −0.653130 | ||||||||
\(926\) | −31.2914 | + | 22.7346i | −1.02830 | + | 0.747104i | ||||
\(927\) | 3.03237 | + | 9.33267i | 0.0995960 | + | 0.306525i | ||||
\(928\) | −0.266930 | + | 0.821525i | −0.00876240 | + | 0.0269679i | ||||
\(929\) | −5.93082 | − | 4.30899i | −0.194584 | − | 0.141373i | 0.486227 | − | 0.873832i | \(-0.338373\pi\) |
−0.680811 | + | 0.732459i | \(0.738373\pi\) | |||||||
\(930\) | −0.767110 | − | 0.557338i | −0.0251545 | − | 0.0182758i | ||||
\(931\) | 3.42346 | − | 10.5363i | 0.112199 | − | 0.345314i | ||||
\(932\) | 0.0876218 | + | 0.269672i | 0.00287015 | + | 0.00883341i | ||||
\(933\) | −3.46729 | + | 2.51913i | −0.113514 | + | 0.0824727i | ||||
\(934\) | 19.1489 | 0.626571 | ||||||||
\(935\) | 4.80604 | − | 0.261973i | 0.157174 | − | 0.00856745i | ||||
\(936\) | 2.73021 | 0.0892398 | ||||||||
\(937\) | 5.11320 | − | 3.71496i | 0.167041 | − | 0.121362i | −0.501124 | − | 0.865375i | \(-0.667080\pi\) |
0.668165 | + | 0.744013i | \(0.267080\pi\) | |||||||
\(938\) | 5.36323 | + | 16.5063i | 0.175116 | + | 0.538951i | ||||
\(939\) | −7.26559 | + | 22.3612i | −0.237104 | + | 0.729730i | ||||
\(940\) | −0.553561 | − | 0.402186i | −0.0180552 | − | 0.0131179i | ||||
\(941\) | 21.9859 | + | 15.9737i | 0.716720 | + | 0.520728i | 0.885335 | − | 0.464954i | \(-0.153929\pi\) |
−0.168615 | + | 0.985682i | \(0.553929\pi\) | |||||||
\(942\) | 9.38080 | − | 28.8711i | 0.305643 | − | 0.940672i | ||||
\(943\) | 13.8210 | + | 42.5367i | 0.450074 | + | 1.38518i | ||||
\(944\) | −31.4972 | + | 22.8840i | −1.02515 | + | 0.744812i | ||||
\(945\) | −1.94156 | −0.0631590 | ||||||||
\(946\) | −18.4995 | − | 47.8926i | −0.601470 | − | 1.55712i | ||||
\(947\) | 10.0638 | 0.327029 | 0.163515 | − | 0.986541i | \(-0.447717\pi\) | ||||
0.163515 | + | 0.986541i | \(0.447717\pi\) | |||||||
\(948\) | −0.644235 | + | 0.468064i | −0.0209238 | + | 0.0152020i | ||||
\(949\) | −2.21583 | − | 6.81964i | −0.0719290 | − | 0.221375i | ||||
\(950\) | 1.49855 | − | 4.61205i | 0.0486192 | − | 0.149635i | ||||
\(951\) | −6.86086 | − | 4.98471i | −0.222479 | − | 0.161640i | ||||
\(952\) | −38.1743 | − | 27.7353i | −1.23724 | − | 0.898906i | ||||
\(953\) | −6.71291 | + | 20.6602i | −0.217452 | + | 0.669250i | 0.781518 | + | 0.623883i | \(0.214446\pi\) |
−0.998970 | + | 0.0453670i | \(0.985554\pi\) | |||||||
\(954\) | −1.06012 | − | 3.26272i | −0.0343227 | − | 0.105634i | ||||
\(955\) | 3.38914 | − | 2.46236i | 0.109670 | − | 0.0796800i | ||||
\(956\) | −1.45515 | −0.0470629 | ||||||||
\(957\) | 1.01181 | − | 3.80801i | 0.0327070 | − | 0.123095i | ||||
\(958\) | −44.9809 | −1.45327 | ||||||||
\(959\) | −49.4010 | + | 35.8919i | −1.59524 | + | 1.15901i | ||||
\(960\) | −0.925922 | − | 2.84969i | −0.0298840 | − | 0.0919735i | ||||
\(961\) | −8.77897 | + | 27.0189i | −0.283193 | + | 0.871577i | ||||
\(962\) | 4.84747 | + | 3.52189i | 0.156289 | + | 0.113550i | ||||
\(963\) | −9.14460 | − | 6.64394i | −0.294681 | − | 0.214098i | ||||
\(964\) | −0.285172 | + | 0.877668i | −0.00918476 | + | 0.0282678i | ||||
\(965\) | −0.950378 | − | 2.92496i | −0.0305937 | − | 0.0941579i | ||||
\(966\) | −20.7387 | + | 15.0675i | −0.667257 | + | 0.484790i | ||||
\(967\) | 34.3030 | 1.10311 | 0.551555 | − | 0.834139i | \(-0.314035\pi\) | ||||
0.551555 | + | 0.834139i | \(0.314035\pi\) | |||||||
\(968\) | 6.12091 | − | 29.4020i | 0.196734 | − | 0.945015i | ||||
\(969\) | −2.46976 | −0.0793401 | ||||||||
\(970\) | −8.59217 | + | 6.24257i | −0.275878 | + | 0.200437i | ||||
\(971\) | −3.46576 | − | 10.6665i | −0.111221 | − | 0.342304i | 0.879919 | − | 0.475124i | \(-0.157597\pi\) |
−0.991140 | + | 0.132820i | \(0.957597\pi\) | |||||||
\(972\) | −0.0397803 | + | 0.122431i | −0.00127595 | + | 0.00392698i | ||||
\(973\) | 12.6942 | + | 9.22289i | 0.406958 | + | 0.295672i | ||||
\(974\) | 29.8297 | + | 21.6726i | 0.955806 | + | 0.694434i | ||||
\(975\) | 1.49471 | − | 4.60023i | 0.0478689 | − | 0.147325i | ||||
\(976\) | 15.0984 | + | 46.4682i | 0.483289 | + | 1.48741i | ||||
\(977\) | 3.59858 | − | 2.61452i | 0.115129 | − | 0.0836460i | −0.528731 | − | 0.848789i | \(-0.677332\pi\) |
0.643860 | + | 0.765143i | \(0.277332\pi\) | |||||||
\(978\) | −19.9733 | −0.638676 | ||||||||
\(979\) | 3.15507 | − | 11.8743i | 0.100836 | − | 0.379505i | ||||
\(980\) | 0.838012 | 0.0267693 | ||||||||
\(981\) | 12.6763 | − | 9.20987i | 0.404723 | − | 0.294049i | ||||
\(982\) | 2.78179 | + | 8.56146i | 0.0887704 | + | 0.273207i | ||||
\(983\) | −6.95946 | + | 21.4190i | −0.221972 | + | 0.683161i | 0.776612 | + | 0.629979i | \(0.216936\pi\) |
−0.998585 | + | 0.0531820i | \(0.983064\pi\) | |||||||
\(984\) | 27.0374 | + | 19.6438i | 0.861920 | + | 0.626221i | ||||
\(985\) | −0.859572 | − | 0.624515i | −0.0273882 | − | 0.0198987i | ||||
\(986\) | 1.92512 | − | 5.92492i | 0.0613084 | − | 0.188688i | ||||
\(987\) | −19.5608 | − | 60.2019i | −0.622627 | − | 1.91625i | ||||
\(988\) | −0.0715644 | + | 0.0519946i | −0.00227677 | + | 0.00165417i | ||||
\(989\) | 38.7665 | 1.23270 | ||||||||
\(990\) | −0.704018 | − | 1.82260i | −0.0223752 | − | 0.0579262i | ||||
\(991\) | 34.9481 | 1.11016 | 0.555081 | − | 0.831796i | \(-0.312687\pi\) | ||||
0.555081 | + | 0.831796i | \(0.312687\pi\) | |||||||
\(992\) | −0.946809 | + | 0.687897i | −0.0300612 | + | 0.0218407i | ||||
\(993\) | −10.0709 | − | 30.9951i | −0.319591 | − | 0.983599i | ||||
\(994\) | −10.3502 | + | 31.8547i | −0.328289 | + | 1.01037i | ||||
\(995\) | 3.90005 | + | 2.83355i | 0.123640 | + | 0.0898296i | ||||
\(996\) | 0.314374 | + | 0.228406i | 0.00996132 | + | 0.00723733i | ||||
\(997\) | −3.97682 | + | 12.2394i | −0.125947 | + | 0.387625i | −0.994072 | − | 0.108720i | \(-0.965325\pi\) |
0.868125 | + | 0.496345i | \(0.165325\pi\) | |||||||
\(998\) | 5.05281 | + | 15.5510i | 0.159944 | + | 0.492257i | ||||
\(999\) | 3.32242 | − | 2.41388i | 0.105117 | − | 0.0763718i |
(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 | 429.2.n.c.157.6 | ✓ | 28 | |
11.2 | odd | 10 | 4719.2.a.bo.1.11 | 14 | |||
11.4 | even | 5 | inner | 429.2.n.c.235.6 | yes | 28 | |
11.9 | even | 5 | 4719.2.a.bp.1.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.n.c.157.6 | ✓ | 28 | 1.1 | even | 1 | trivial | |
429.2.n.c.235.6 | yes | 28 | 11.4 | even | 5 | inner | |
4719.2.a.bo.1.11 | 14 | 11.2 | odd | 10 | |||
4719.2.a.bp.1.4 | 14 | 11.9 | even | 5 |