Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(218,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.r (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 342.26 | ||
Character | \(\chi\) | \(=\) | 403.342 |
Dual form | 403.2.r.a.218.26 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34884 | + | 0.778756i | 0.953777 | + | 0.550664i | 0.894252 | − | 0.447563i | \(-0.147708\pi\) |
0.0595251 | + | 0.998227i | \(0.481041\pi\) | |||||||
\(3\) | 1.55629 | − | 2.69558i | 0.898527 | − | 1.55629i | 0.0691483 | − | 0.997606i | \(-0.477972\pi\) |
0.829378 | − | 0.558687i | \(-0.188695\pi\) | |||||||
\(4\) | 0.212922 | + | 0.368791i | 0.106461 | + | 0.184396i | ||||
\(5\) | 3.93166i | 1.75829i | 0.476553 | + | 0.879146i | \(0.341886\pi\) | ||||
−0.476553 | + | 0.879146i | \(0.658114\pi\) | |||||||
\(6\) | 4.19840 | − | 2.42395i | 1.71399 | − | 0.989572i | ||||
\(7\) | 0.334531 | − | 0.193142i | 0.126441 | − | 0.0730006i | −0.435446 | − | 0.900215i | \(-0.643409\pi\) |
0.561886 | + | 0.827214i | \(0.310076\pi\) | |||||||
\(8\) | − | 2.45177i | − | 0.866831i | ||||||
\(9\) | −3.34410 | − | 5.79215i | −1.11470 | − | 1.93072i | ||||
\(10\) | −3.06180 | + | 5.30320i | −0.968227 | + | 1.67702i | ||||
\(11\) | 3.49001 | + | 2.01496i | 1.05228 | + | 0.607533i | 0.923286 | − | 0.384113i | \(-0.125493\pi\) |
0.128992 | + | 0.991646i | \(0.458826\pi\) | |||||||
\(12\) | 1.32548 | 0.382632 | ||||||||
\(13\) | 2.63743 | − | 2.45845i | 0.731490 | − | 0.681852i | ||||
\(14\) | 0.601640 | 0.160795 | ||||||||
\(15\) | 10.5981 | + | 6.11882i | 2.73642 | + | 1.57987i | ||||
\(16\) | 2.33517 | − | 4.04464i | 0.583793 | − | 1.01116i | ||||
\(17\) | −0.762516 | − | 1.32072i | −0.184937 | − | 0.320321i | 0.758618 | − | 0.651536i | \(-0.225875\pi\) |
−0.943555 | + | 0.331215i | \(0.892542\pi\) | |||||||
\(18\) | − | 10.4170i | − | 2.45530i | ||||||
\(19\) | −7.12111 | + | 4.11138i | −1.63370 | + | 0.943214i | −0.650755 | + | 0.759287i | \(0.725548\pi\) |
−0.982940 | + | 0.183927i | \(0.941119\pi\) | |||||||
\(20\) | −1.44996 | + | 0.837136i | −0.324221 | + | 0.187189i | ||||
\(21\) | − | 1.20234i | − | 0.262372i | ||||||
\(22\) | 3.13832 | + | 5.43573i | 0.669092 | + | 1.15890i | ||||
\(23\) | −1.71876 | + | 2.97698i | −0.358387 | + | 0.620744i | −0.987691 | − | 0.156415i | \(-0.950006\pi\) |
0.629305 | + | 0.777159i | \(0.283340\pi\) | |||||||
\(24\) | −6.60894 | − | 3.81567i | −1.34904 | − | 0.778870i | ||||
\(25\) | −10.4579 | −2.09159 | ||||||||
\(26\) | 5.47201 | − | 1.26216i | 1.07315 | − | 0.247530i | ||||
\(27\) | −11.4798 | −2.20930 | ||||||||
\(28\) | 0.142458 | + | 0.0822481i | 0.0269220 | + | 0.0155434i | ||||
\(29\) | −1.05886 | + | 1.83400i | −0.196625 | + | 0.340565i | −0.947432 | − | 0.319957i | \(-0.896331\pi\) |
0.750807 | + | 0.660522i | \(0.229665\pi\) | |||||||
\(30\) | 9.53013 | + | 16.5067i | 1.73996 | + | 3.01369i | ||||
\(31\) | − | 1.00000i | − | 0.179605i | ||||||
\(32\) | 2.05298 | − | 1.18529i | 0.362920 | − | 0.209532i | ||||
\(33\) | 10.8630 | − | 6.27173i | 1.89100 | − | 1.09177i | ||||
\(34\) | − | 2.37526i | − | 0.407353i | ||||||
\(35\) | 0.759366 | + | 1.31526i | 0.128356 | + | 0.222320i | ||||
\(36\) | 1.42406 | − | 2.46655i | 0.237344 | − | 0.411092i | ||||
\(37\) | −2.57744 | − | 1.48809i | −0.423729 | − | 0.244640i | 0.272942 | − | 0.962030i | \(-0.412003\pi\) |
−0.696672 | + | 0.717390i | \(0.745336\pi\) | |||||||
\(38\) | −12.8070 | −2.07758 | ||||||||
\(39\) | −2.52235 | − | 10.9355i | −0.403899 | − | 1.75108i | ||||
\(40\) | 9.63951 | 1.52414 | ||||||||
\(41\) | 0.913972 | + | 0.527682i | 0.142738 | + | 0.0824101i | 0.569668 | − | 0.821875i | \(-0.307072\pi\) |
−0.426930 | + | 0.904285i | \(0.640405\pi\) | |||||||
\(42\) | 0.936329 | − | 1.62177i | 0.144479 | − | 0.250245i | ||||
\(43\) | 5.54621 | + | 9.60631i | 0.845789 | + | 1.46495i | 0.884935 | + | 0.465715i | \(0.154203\pi\) |
−0.0391461 | + | 0.999233i | \(0.512464\pi\) | |||||||
\(44\) | 1.71611i | 0.258714i | ||||||||
\(45\) | 22.7728 | − | 13.1479i | 3.39476 | − | 1.95997i | ||||
\(46\) | −4.63669 | + | 2.67699i | −0.683642 | + | 0.394701i | ||||
\(47\) | − | 2.35312i | − | 0.343238i | −0.985163 | − | 0.171619i | \(-0.945100\pi\) | ||
0.985163 | − | 0.171619i | \(-0.0548998\pi\) | |||||||
\(48\) | −7.26843 | − | 12.5893i | −1.04911 | − | 1.81711i | ||||
\(49\) | −3.42539 | + | 5.93295i | −0.489342 | + | 0.847565i | ||||
\(50\) | −14.1061 | − | 8.14418i | −1.99491 | − | 1.15176i | ||||
\(51\) | −4.74680 | −0.664684 | ||||||||
\(52\) | 1.46822 | + | 0.449201i | 0.203606 | + | 0.0622930i | ||||
\(53\) | −1.26233 | −0.173394 | −0.0866971 | − | 0.996235i | \(-0.527631\pi\) | ||||
−0.0866971 | + | 0.996235i | \(0.527631\pi\) | |||||||
\(54\) | −15.4845 | − | 8.94000i | −2.10718 | − | 1.21658i | ||||
\(55\) | −7.92213 | + | 13.7215i | −1.06822 | + | 1.85021i | ||||
\(56\) | −0.473538 | − | 0.820192i | −0.0632792 | − | 0.109603i | ||||
\(57\) | 25.5940i | 3.39001i | ||||||||
\(58\) | −2.85647 | + | 1.64918i | −0.375073 | + | 0.216549i | ||||
\(59\) | 1.30053 | − | 0.750861i | 0.169315 | − | 0.0977538i | −0.412948 | − | 0.910755i | \(-0.635501\pi\) |
0.582263 | + | 0.813001i | \(0.302168\pi\) | |||||||
\(60\) | 5.21132i | 0.672778i | ||||||||
\(61\) | −4.96903 | − | 8.60662i | −0.636220 | − | 1.10196i | −0.986255 | − | 0.165228i | \(-0.947164\pi\) |
0.350036 | − | 0.936736i | \(-0.386169\pi\) | |||||||
\(62\) | 0.778756 | − | 1.34884i | 0.0989021 | − | 0.171303i | ||||
\(63\) | −2.23741 | − | 1.29177i | −0.281887 | − | 0.162748i | ||||
\(64\) | −5.64848 | −0.706060 | ||||||||
\(65\) | 9.66580 | + | 10.3695i | 1.19889 | + | 1.28617i | ||||
\(66\) | 19.5366 | 2.40479 | ||||||||
\(67\) | −4.58026 | − | 2.64442i | −0.559568 | − | 0.323067i | 0.193404 | − | 0.981119i | \(-0.438047\pi\) |
−0.752972 | + | 0.658052i | \(0.771381\pi\) | |||||||
\(68\) | 0.324712 | − | 0.562418i | 0.0393772 | − | 0.0682033i | ||||
\(69\) | 5.34980 | + | 9.26612i | 0.644040 | + | 1.11551i | ||||
\(70\) | 2.36544i | 0.282725i | ||||||||
\(71\) | 2.35566 | − | 1.36004i | 0.279565 | − | 0.161407i | −0.353661 | − | 0.935374i | \(-0.615063\pi\) |
0.633227 | + | 0.773966i | \(0.281730\pi\) | |||||||
\(72\) | −14.2010 | + | 8.19896i | −1.67361 | + | 0.966256i | ||||
\(73\) | 8.58823i | 1.00518i | 0.864526 | + | 0.502588i | \(0.167619\pi\) | ||||
−0.864526 | + | 0.502588i | \(0.832381\pi\) | |||||||
\(74\) | −2.31771 | − | 4.01440i | −0.269429 | − | 0.466664i | ||||
\(75\) | −16.2756 | + | 28.1902i | −1.87935 | + | 3.25512i | ||||
\(76\) | −3.03248 | − | 1.75080i | −0.347849 | − | 0.200831i | ||||
\(77\) | 1.55669 | 0.177401 | ||||||||
\(78\) | 5.11380 | − | 16.7145i | 0.579024 | − | 1.89255i | ||||
\(79\) | −4.04223 | −0.454786 | −0.227393 | − | 0.973803i | \(-0.573020\pi\) | ||||
−0.227393 | + | 0.973803i | \(0.573020\pi\) | |||||||
\(80\) | 15.9021 | + | 9.18110i | 1.77791 | + | 1.02648i | ||||
\(81\) | −7.83372 | + | 13.5684i | −0.870413 | + | 1.50760i | ||||
\(82\) | 0.821871 | + | 1.42352i | 0.0907604 | + | 0.157202i | ||||
\(83\) | − | 12.5086i | − | 1.37300i | −0.727131 | − | 0.686499i | \(-0.759147\pi\) | ||
0.727131 | − | 0.686499i | \(-0.240853\pi\) | |||||||
\(84\) | 0.443412 | − | 0.256004i | 0.0483803 | − | 0.0279324i | ||||
\(85\) | 5.19261 | − | 2.99795i | 0.563217 | − | 0.325174i | ||||
\(86\) | 17.2766i | 1.86298i | ||||||||
\(87\) | 3.29579 | + | 5.70847i | 0.353346 | + | 0.612013i | ||||
\(88\) | 4.94021 | − | 8.55669i | 0.526628 | − | 0.912147i | ||||
\(89\) | 12.4324 | + | 7.17786i | 1.31783 | + | 0.760851i | 0.983380 | − | 0.181561i | \(-0.0581151\pi\) |
0.334453 | + | 0.942412i | \(0.391448\pi\) | |||||||
\(90\) | 40.9559 | 4.31713 | ||||||||
\(91\) | 0.407471 | − | 1.33182i | 0.0427146 | − | 0.139613i | ||||
\(92\) | −1.46385 | −0.152617 | ||||||||
\(93\) | −2.69558 | − | 1.55629i | −0.279519 | − | 0.161380i | ||||
\(94\) | 1.83251 | − | 3.17399i | 0.189009 | − | 0.327373i | ||||
\(95\) | −16.1645 | − | 27.9978i | −1.65845 | − | 2.87251i | ||||
\(96\) | − | 7.37864i | − | 0.753080i | ||||||
\(97\) | 4.75884 | − | 2.74752i | 0.483187 | − | 0.278968i | −0.238557 | − | 0.971129i | \(-0.576674\pi\) |
0.721744 | + | 0.692161i | \(0.243341\pi\) | |||||||
\(98\) | −9.24065 | + | 5.33509i | −0.933446 | + | 0.538925i | ||||
\(99\) | − | 26.9529i | − | 2.70887i | ||||||
\(100\) | −2.22672 | − | 3.85680i | −0.222672 | − | 0.385680i | ||||
\(101\) | 8.40005 | − | 14.5493i | 0.835836 | − | 1.44771i | −0.0575114 | − | 0.998345i | \(-0.518317\pi\) |
0.893348 | − | 0.449366i | \(-0.148350\pi\) | |||||||
\(102\) | −6.40269 | − | 3.69660i | −0.633961 | − | 0.366017i | ||||
\(103\) | 5.85472 | 0.576882 | 0.288441 | − | 0.957498i | \(-0.406863\pi\) | ||||
0.288441 | + | 0.957498i | \(0.406863\pi\) | |||||||
\(104\) | −6.02755 | − | 6.46635i | −0.591050 | − | 0.634078i | ||||
\(105\) | 4.72719 | 0.461326 | ||||||||
\(106\) | −1.70269 | − | 0.983046i | −0.165379 | − | 0.0954819i | ||||
\(107\) | −2.18710 | + | 3.78817i | −0.211435 | + | 0.366216i | −0.952164 | − | 0.305588i | \(-0.901147\pi\) |
0.740729 | + | 0.671804i | \(0.234480\pi\) | |||||||
\(108\) | −2.44431 | − | 4.23367i | −0.235204 | − | 0.407385i | ||||
\(109\) | 9.80332i | 0.938988i | 0.882936 | + | 0.469494i | \(0.155564\pi\) | ||||
−0.882936 | + | 0.469494i | \(0.844436\pi\) | |||||||
\(110\) | −21.3714 | + | 12.3388i | −2.03769 | + | 1.17646i | ||||
\(111\) | −8.02252 | + | 4.63180i | −0.761464 | + | 0.439631i | ||||
\(112\) | − | 1.80407i | − | 0.170469i | ||||||
\(113\) | 5.35565 | + | 9.27626i | 0.503817 | + | 0.872637i | 0.999990 | + | 0.00441339i | \(0.00140483\pi\) |
−0.496173 | + | 0.868224i | \(0.665262\pi\) | |||||||
\(114\) | −19.9315 | + | 34.5224i | −1.86676 | + | 3.23332i | ||||
\(115\) | −11.7045 | − | 6.75759i | −1.09145 | − | 0.630148i | ||||
\(116\) | −0.901816 | −0.0837315 | ||||||||
\(117\) | −23.0595 | − | 7.05506i | −2.13186 | − | 0.652240i | ||||
\(118\) | 2.33895 | 0.215318 | ||||||||
\(119\) | −0.510170 | − | 0.294547i | −0.0467672 | − | 0.0270011i | ||||
\(120\) | 15.0019 | − | 25.9841i | 1.36948 | − | 2.37201i | ||||
\(121\) | 2.62011 | + | 4.53817i | 0.238192 | + | 0.412561i | ||||
\(122\) | − | 15.4787i | − | 1.40137i | ||||||
\(123\) | 2.84482 | − | 1.64246i | 0.256509 | − | 0.148095i | ||||
\(124\) | 0.368791 | − | 0.212922i | 0.0331184 | − | 0.0191209i | ||||
\(125\) | − | 21.4587i | − | 1.91933i | ||||||
\(126\) | −2.01195 | − | 3.48479i | −0.179238 | − | 0.310450i | ||||
\(127\) | 7.49734 | − | 12.9858i | 0.665282 | − | 1.15230i | −0.313927 | − | 0.949447i | \(-0.601645\pi\) |
0.979209 | − | 0.202855i | \(-0.0650219\pi\) | |||||||
\(128\) | −11.7249 | − | 6.76937i | −1.03634 | − | 0.598333i | ||||
\(129\) | 34.5261 | 3.03985 | ||||||||
\(130\) | 4.96238 | + | 21.5141i | 0.435230 | + | 1.88691i | ||||
\(131\) | −20.2449 | −1.76880 | −0.884402 | − | 0.466727i | \(-0.845433\pi\) | ||||
−0.884402 | + | 0.466727i | \(0.845433\pi\) | |||||||
\(132\) | 4.62592 | + | 2.67078i | 0.402635 | + | 0.232461i | ||||
\(133\) | −1.58815 | + | 2.75076i | −0.137710 | + | 0.238522i | ||||
\(134\) | −4.11871 | − | 7.13382i | −0.355802 | − | 0.616268i | ||||
\(135\) | − | 45.1348i | − | 3.88459i | ||||||
\(136\) | −3.23809 | + | 1.86951i | −0.277664 | + | 0.160309i | ||||
\(137\) | 0.175152 | − | 0.101124i | 0.0149642 | − | 0.00863959i | −0.492499 | − | 0.870313i | \(-0.663917\pi\) |
0.507463 | + | 0.861673i | \(0.330583\pi\) | |||||||
\(138\) | 16.6647i | 1.41860i | ||||||||
\(139\) | −3.03947 | − | 5.26452i | −0.257805 | − | 0.446531i | 0.707849 | − | 0.706364i | \(-0.249666\pi\) |
−0.965654 | + | 0.259833i | \(0.916333\pi\) | |||||||
\(140\) | −0.323371 | + | 0.560096i | −0.0273299 | + | 0.0473367i | ||||
\(141\) | −6.34302 | − | 3.66215i | −0.534179 | − | 0.308408i | ||||
\(142\) | 4.23656 | 0.355524 | ||||||||
\(143\) | 14.1583 | − | 3.26572i | 1.18398 | − | 0.273093i | ||||
\(144\) | −31.2362 | −2.60302 | ||||||||
\(145\) | −7.21065 | − | 4.16307i | −0.598812 | − | 0.345724i | ||||
\(146\) | −6.68814 | + | 11.5842i | −0.553514 | + | 0.958715i | ||||
\(147\) | 10.6618 | + | 18.4668i | 0.879373 | + | 1.52312i | ||||
\(148\) | − | 1.26738i | − | 0.104178i | ||||||
\(149\) | 17.4832 | − | 10.0939i | 1.43228 | − | 0.826927i | 0.434986 | − | 0.900437i | \(-0.356753\pi\) |
0.997294 | + | 0.0735101i | \(0.0234201\pi\) | |||||||
\(150\) | −43.9066 | + | 25.3495i | −3.58496 | + | 2.06978i | ||||
\(151\) | − | 10.2751i | − | 0.836177i | −0.908406 | − | 0.418088i | \(-0.862700\pi\) | ||
0.908406 | − | 0.418088i | \(-0.137300\pi\) | |||||||
\(152\) | 10.0801 | + | 17.4593i | 0.817607 | + | 1.41614i | ||||
\(153\) | −5.09986 | + | 8.83322i | −0.412299 | + | 0.714123i | ||||
\(154\) | 2.09973 | + | 1.21228i | 0.169201 | + | 0.0976883i | ||||
\(155\) | 3.93166 | 0.315798 | ||||||||
\(156\) | 3.49584 | − | 3.25862i | 0.279891 | − | 0.260898i | ||||
\(157\) | 7.72860 | 0.616809 | 0.308405 | − | 0.951255i | \(-0.400205\pi\) | ||||
0.308405 | + | 0.951255i | \(0.400205\pi\) | |||||||
\(158\) | −5.45234 | − | 3.14791i | −0.433765 | − | 0.250434i | ||||
\(159\) | −1.96455 | + | 3.40271i | −0.155799 | + | 0.269852i | ||||
\(160\) | 4.66016 | + | 8.07163i | 0.368418 | + | 0.638119i | ||||
\(161\) | 1.32786i | 0.104650i | ||||||||
\(162\) | −21.1329 | + | 12.2011i | −1.66036 | + | 0.958609i | ||||
\(163\) | −3.50186 | + | 2.02180i | −0.274287 | + | 0.158360i | −0.630834 | − | 0.775918i | \(-0.717287\pi\) |
0.356547 | + | 0.934277i | \(0.383954\pi\) | |||||||
\(164\) | 0.449420i | 0.0350938i | ||||||||
\(165\) | 24.6583 | + | 42.7095i | 1.91965 | + | 3.32493i | ||||
\(166\) | 9.74115 | − | 16.8722i | 0.756060 | − | 1.30953i | ||||
\(167\) | −7.12438 | − | 4.11326i | −0.551301 | − | 0.318294i | 0.198346 | − | 0.980132i | \(-0.436443\pi\) |
−0.749647 | + | 0.661838i | \(0.769777\pi\) | |||||||
\(168\) | −2.94786 | −0.227432 | ||||||||
\(169\) | 0.912023 | − | 12.9680i | 0.0701556 | − | 0.997536i | ||||
\(170\) | 9.33869 | 0.716245 | ||||||||
\(171\) | 47.6274 | + | 27.4977i | 3.64216 | + | 2.10280i | ||||
\(172\) | −2.36182 | + | 4.09079i | −0.180087 | + | 0.311919i | ||||
\(173\) | −3.16826 | − | 5.48758i | −0.240878 | − | 0.417213i | 0.720087 | − | 0.693884i | \(-0.244102\pi\) |
−0.960965 | + | 0.276671i | \(0.910769\pi\) | |||||||
\(174\) | 10.2665i | 0.778298i | ||||||||
\(175\) | −3.49850 | + | 2.01986i | −0.264462 | + | 0.152687i | ||||
\(176\) | 16.2995 | − | 9.41055i | 1.22862 | − | 0.709347i | ||||
\(177\) | − | 4.67424i | − | 0.351338i | ||||||
\(178\) | 11.1796 | + | 19.3636i | 0.837946 | + | 1.45137i | ||||
\(179\) | 4.75915 | − | 8.24309i | 0.355716 | − | 0.616117i | −0.631525 | − | 0.775356i | \(-0.717571\pi\) |
0.987240 | + | 0.159238i | \(0.0509039\pi\) | |||||||
\(180\) | 9.69763 | + | 5.59893i | 0.722819 | + | 0.417320i | ||||
\(181\) | −11.0298 | −0.819841 | −0.409920 | − | 0.912121i | \(-0.634443\pi\) | ||||
−0.409920 | + | 0.912121i | \(0.634443\pi\) | |||||||
\(182\) | 1.58678 | − | 1.47910i | 0.117620 | − | 0.109639i | ||||
\(183\) | −30.9331 | −2.28664 | ||||||||
\(184\) | 7.29887 | + | 4.21400i | 0.538080 | + | 0.310661i | ||||
\(185\) | 5.85065 | − | 10.1336i | 0.430148 | − | 0.745039i | ||||
\(186\) | −2.42395 | − | 4.19840i | −0.177732 | − | 0.307841i | ||||
\(187\) | − | 6.14575i | − | 0.449422i | ||||||
\(188\) | 0.867810 | − | 0.501031i | 0.0632916 | − | 0.0365414i | ||||
\(189\) | −3.84036 | + | 2.21724i | −0.279345 | + | 0.161280i | ||||
\(190\) | − | 50.3529i | − | 3.65298i | ||||||
\(191\) | 3.62865 | + | 6.28501i | 0.262560 | + | 0.454767i | 0.966921 | − | 0.255074i | \(-0.0820999\pi\) |
−0.704361 | + | 0.709841i | \(0.748767\pi\) | |||||||
\(192\) | −8.79069 | + | 15.2259i | −0.634414 | + | 1.09884i | ||||
\(193\) | 8.75000 | + | 5.05181i | 0.629839 | + | 0.363637i | 0.780690 | − | 0.624919i | \(-0.214868\pi\) |
−0.150851 | + | 0.988557i | \(0.548201\pi\) | |||||||
\(194\) | 8.55858 | 0.614470 | ||||||||
\(195\) | 42.9945 | − | 9.91701i | 3.07890 | − | 0.710172i | ||||
\(196\) | −2.91736 | −0.208383 | ||||||||
\(197\) | 7.72939 | + | 4.46257i | 0.550696 | + | 0.317945i | 0.749403 | − | 0.662114i | \(-0.230341\pi\) |
−0.198706 | + | 0.980059i | \(0.563674\pi\) | |||||||
\(198\) | 20.9897 | − | 36.3553i | 1.49167 | − | 2.58366i | ||||
\(199\) | −0.215237 | − | 0.372802i | −0.0152578 | − | 0.0264272i | 0.858296 | − | 0.513155i | \(-0.171524\pi\) |
−0.873553 | + | 0.486728i | \(0.838190\pi\) | |||||||
\(200\) | 25.6404i | 1.81305i | ||||||||
\(201\) | −14.2565 | + | 8.23098i | −1.00557 | + | 0.580568i | ||||
\(202\) | 22.6607 | − | 13.0832i | 1.59440 | − | 0.920529i | ||||
\(203\) | 0.818038i | 0.0574150i | ||||||||
\(204\) | −1.01070 | − | 1.75058i | −0.0707629 | − | 0.122565i | ||||
\(205\) | −2.07466 | + | 3.59342i | −0.144901 | + | 0.250976i | ||||
\(206\) | 7.89710 | + | 4.55939i | 0.550217 | + | 0.317668i | ||||
\(207\) | 22.9909 | 1.59797 | ||||||||
\(208\) | −3.78471 | − | 16.4083i | −0.262422 | − | 1.13771i | ||||
\(209\) | −33.1370 | −2.29213 | ||||||||
\(210\) | 6.37625 | + | 3.68133i | 0.440003 | + | 0.254036i | ||||
\(211\) | 2.13951 | − | 3.70573i | 0.147290 | − | 0.255113i | −0.782935 | − | 0.622103i | \(-0.786278\pi\) |
0.930225 | + | 0.366990i | \(0.119612\pi\) | |||||||
\(212\) | −0.268777 | − | 0.465536i | −0.0184597 | − | 0.0319731i | ||||
\(213\) | − | 8.46649i | − | 0.580115i | ||||||
\(214\) | −5.90011 | + | 3.40643i | −0.403324 | + | 0.232859i | ||||
\(215\) | −37.7687 | + | 21.8058i | −2.57581 | + | 1.48714i | ||||
\(216\) | 28.1459i | 1.91509i | ||||||||
\(217\) | −0.193142 | − | 0.334531i | −0.0131113 | − | 0.0227094i | ||||
\(218\) | −7.63440 | + | 13.2232i | −0.517067 | + | 0.895586i | ||||
\(219\) | 23.1503 | + | 13.3658i | 1.56435 | + | 0.903178i | ||||
\(220\) | −6.74717 | −0.454894 | ||||||||
\(221\) | −5.25800 | − | 1.60868i | −0.353691 | − | 0.108212i | ||||
\(222\) | −14.4282 | −0.968356 | ||||||||
\(223\) | 5.96804 | + | 3.44565i | 0.399650 | + | 0.230738i | 0.686333 | − | 0.727288i | \(-0.259219\pi\) |
−0.286683 | + | 0.958025i | \(0.592553\pi\) | |||||||
\(224\) | 0.457858 | − | 0.793033i | 0.0305919 | − | 0.0529867i | ||||
\(225\) | 34.9724 | + | 60.5740i | 2.33149 | + | 4.03826i | ||||
\(226\) | 16.6830i | 1.10974i | ||||||||
\(227\) | −6.22577 | + | 3.59445i | −0.413219 | + | 0.238572i | −0.692172 | − | 0.721733i | \(-0.743346\pi\) |
0.278953 | + | 0.960305i | \(0.410013\pi\) | |||||||
\(228\) | −9.43886 | + | 5.44953i | −0.625104 | + | 0.360904i | ||||
\(229\) | − | 19.9206i | − | 1.31639i | −0.752847 | − | 0.658196i | \(-0.771320\pi\) | ||
0.752847 | − | 0.658196i | \(-0.228680\pi\) | |||||||
\(230\) | −10.5250 | − | 18.2299i | −0.693999 | − | 1.20204i | ||||
\(231\) | 2.42266 | − | 4.19618i | 0.159400 | − | 0.276088i | ||||
\(232\) | 4.49653 | + | 2.59607i | 0.295212 | + | 0.170441i | ||||
\(233\) | 0.794951 | 0.0520790 | 0.0260395 | − | 0.999661i | \(-0.491710\pi\) | ||||
0.0260395 | + | 0.999661i | \(0.491710\pi\) | |||||||
\(234\) | −25.6096 | − | 27.4739i | −1.67415 | − | 1.79603i | ||||
\(235\) | 9.25167 | 0.603512 | ||||||||
\(236\) | 0.553822 | + | 0.319749i | 0.0360508 | + | 0.0208139i | ||||
\(237\) | −6.29090 | + | 10.8962i | −0.408638 | + | 0.707781i | ||||
\(238\) | −0.458760 | − | 0.794596i | −0.0297370 | − | 0.0515060i | ||||
\(239\) | 10.5487i | 0.682337i | 0.940002 | + | 0.341168i | \(0.110823\pi\) | ||||
−0.940002 | + | 0.341168i | \(0.889177\pi\) | |||||||
\(240\) | 49.4968 | − | 28.5770i | 3.19500 | − | 1.84464i | ||||
\(241\) | −17.2232 | + | 9.94381i | −1.10944 | + | 0.640537i | −0.938685 | − | 0.344776i | \(-0.887955\pi\) |
−0.170758 | + | 0.985313i | \(0.554622\pi\) | |||||||
\(242\) | 8.16172i | 0.524655i | ||||||||
\(243\) | 7.16335 | + | 12.4073i | 0.459529 | + | 0.795928i | ||||
\(244\) | 2.11603 | − | 3.66507i | 0.135465 | − | 0.234632i | ||||
\(245\) | −23.3263 | − | 13.4675i | −1.49027 | − | 0.860405i | ||||
\(246\) | 5.11629 | 0.326203 | ||||||||
\(247\) | −8.67378 | + | 28.3504i | −0.551899 | + | 1.80389i | ||||
\(248\) | −2.45177 | −0.155687 | ||||||||
\(249\) | −33.7179 | − | 19.4671i | −2.13679 | − | 1.23367i | ||||
\(250\) | 16.7111 | − | 28.9445i | 1.05690 | − | 1.83061i | ||||
\(251\) | −1.61943 | − | 2.80494i | −0.102218 | − | 0.177046i | 0.810380 | − | 0.585904i | \(-0.199260\pi\) |
−0.912598 | + | 0.408858i | \(0.865927\pi\) | |||||||
\(252\) | − | 1.10018i | − | 0.0693050i | ||||||
\(253\) | −11.9970 | + | 6.92647i | −0.754245 | + | 0.435463i | ||||
\(254\) | 20.2255 | − | 11.6772i | 1.26906 | − | 0.732693i | ||||
\(255\) | − | 18.6628i | − | 1.16871i | ||||||
\(256\) | −4.89489 | − | 8.47821i | −0.305931 | − | 0.529888i | ||||
\(257\) | 2.32971 | − | 4.03518i | 0.145324 | − | 0.251708i | −0.784170 | − | 0.620546i | \(-0.786911\pi\) |
0.929494 | + | 0.368838i | \(0.120244\pi\) | |||||||
\(258\) | 46.5704 | + | 26.8874i | 2.89934 | + | 1.67394i | ||||
\(259\) | −1.14965 | −0.0714355 | ||||||||
\(260\) | −1.76611 | + | 5.77254i | −0.109529 | + | 0.357998i | ||||
\(261\) | 14.1637 | 0.876712 | ||||||||
\(262\) | −27.3072 | − | 15.7658i | −1.68704 | − | 0.974016i | ||||
\(263\) | −2.61128 | + | 4.52287i | −0.161018 | + | 0.278892i | −0.935234 | − | 0.354030i | \(-0.884811\pi\) |
0.774216 | + | 0.632922i | \(0.218144\pi\) | |||||||
\(264\) | −15.3768 | − | 26.6335i | −0.946379 | − | 1.63918i | ||||
\(265\) | − | 4.96305i | − | 0.304877i | ||||||
\(266\) | −4.28435 | + | 2.47357i | −0.262690 | + | 0.151664i | ||||
\(267\) | 38.6970 | − | 22.3417i | 2.36822 | − | 1.36729i | ||||
\(268\) | − | 2.25222i | − | 0.137576i | ||||||
\(269\) | −8.19404 | − | 14.1925i | −0.499599 | − | 0.865332i | 0.500400 | − | 0.865794i | \(-0.333186\pi\) |
−1.00000 | 0.000462433i | \(0.999853\pi\) | ||||||||
\(270\) | 35.1490 | − | 60.8799i | 2.13910 | − | 3.70503i | ||||
\(271\) | 22.7179 | + | 13.1162i | 1.38002 | + | 0.796753i | 0.992161 | − | 0.124968i | \(-0.0398827\pi\) |
0.387855 | + | 0.921720i | \(0.373216\pi\) | |||||||
\(272\) | −7.12242 | −0.431860 | ||||||||
\(273\) | −2.95590 | − | 3.17108i | −0.178899 | − | 0.191923i | ||||
\(274\) | 0.315003 | 0.0190300 | ||||||||
\(275\) | −36.4983 | − | 21.0723i | −2.20093 | − | 1.27071i | ||||
\(276\) | −2.27818 | + | 3.94592i | −0.137130 | + | 0.237516i | ||||
\(277\) | 12.6172 | + | 21.8536i | 0.758093 | + | 1.31305i | 0.943822 | + | 0.330454i | \(0.107202\pi\) |
−0.185730 | + | 0.982601i | \(0.559465\pi\) | |||||||
\(278\) | − | 9.46804i | − | 0.567855i | ||||||
\(279\) | −5.79215 | + | 3.34410i | −0.346767 | + | 0.200206i | ||||
\(280\) | 3.22471 | − | 1.86179i | 0.192714 | − | 0.111263i | ||||
\(281\) | 7.22657i | 0.431101i | 0.976493 | + | 0.215551i | \(0.0691546\pi\) | ||||
−0.976493 | + | 0.215551i | \(0.930845\pi\) | |||||||
\(282\) | −5.70384 | − | 9.87934i | −0.339659 | − | 0.588306i | ||||
\(283\) | 3.44518 | − | 5.96723i | 0.204795 | − | 0.354715i | −0.745272 | − | 0.666760i | \(-0.767681\pi\) |
0.950067 | + | 0.312045i | \(0.101014\pi\) | |||||||
\(284\) | 1.00314 | + | 0.579165i | 0.0595256 | + | 0.0343671i | ||||
\(285\) | −100.627 | −5.96063 | ||||||||
\(286\) | 21.6406 | + | 6.62092i | 1.27963 | + | 0.391503i | ||||
\(287\) | 0.407669 | 0.0240639 | ||||||||
\(288\) | −13.7308 | − | 7.92747i | −0.809094 | − | 0.467130i | ||||
\(289\) | 7.33714 | − | 12.7083i | 0.431596 | − | 0.747547i | ||||
\(290\) | −6.48403 | − | 11.2307i | −0.380755 | − | 0.659488i | ||||
\(291\) | − | 17.1038i | − | 1.00264i | ||||||
\(292\) | −3.16727 | + | 1.82862i | −0.185350 | + | 0.107012i | ||||
\(293\) | 24.1356 | − | 13.9347i | 1.41002 | − | 0.814075i | 0.414629 | − | 0.909990i | \(-0.363911\pi\) |
0.995389 | + | 0.0959156i | \(0.0305779\pi\) | |||||||
\(294\) | 33.2119i | 1.93696i | ||||||||
\(295\) | 2.95213 | + | 5.11324i | 0.171880 | + | 0.297704i | ||||
\(296\) | −3.64844 | + | 6.31929i | −0.212062 | + | 0.367301i | ||||
\(297\) | −40.0648 | − | 23.1314i | −2.32479 | − | 1.34222i | ||||
\(298\) | 31.4428 | 1.82144 | ||||||||
\(299\) | 2.78567 | + | 12.0771i | 0.161099 | + | 0.698435i | ||||
\(300\) | −13.8617 | −0.800308 | ||||||||
\(301\) | 3.71075 | + | 2.14241i | 0.213884 | + | 0.123486i | ||||
\(302\) | 8.00181 | − | 13.8595i | 0.460452 | − | 0.797527i | ||||
\(303\) | −26.1459 | − | 45.2860i | −1.50204 | − | 2.60161i | ||||
\(304\) | 38.4031i | 2.20257i | ||||||||
\(305\) | 33.8383 | − | 19.5365i | 1.93757 | − | 1.11866i | ||||
\(306\) | −13.7578 | + | 7.94309i | −0.786483 | + | 0.454076i | ||||
\(307\) | 20.5031i | 1.17018i | 0.810970 | + | 0.585088i | \(0.198940\pi\) | ||||
−0.810970 | + | 0.585088i | \(0.801060\pi\) | |||||||
\(308\) | 0.331453 | + | 0.574093i | 0.0188863 | + | 0.0327120i | ||||
\(309\) | 9.11166 | − | 15.7819i | 0.518344 | − | 0.897798i | ||||
\(310\) | 5.30320 | + | 3.06180i | 0.301201 | + | 0.173899i | ||||
\(311\) | −12.3549 | −0.700583 | −0.350291 | − | 0.936641i | \(-0.613917\pi\) | ||||
−0.350291 | + | 0.936641i | \(0.613917\pi\) | |||||||
\(312\) | −26.8112 | + | 6.18421i | −1.51789 | + | 0.350112i | ||||
\(313\) | 7.93108 | 0.448291 | 0.224146 | − | 0.974556i | \(-0.428041\pi\) | ||||
0.224146 | + | 0.974556i | \(0.428041\pi\) | |||||||
\(314\) | 10.4247 | + | 6.01869i | 0.588299 | + | 0.339654i | ||||
\(315\) | 5.07880 | − | 8.79673i | 0.286158 | − | 0.495640i | ||||
\(316\) | −0.860679 | − | 1.49074i | −0.0484170 | − | 0.0838606i | ||||
\(317\) | 19.1555i | 1.07588i | 0.842983 | + | 0.537940i | \(0.180797\pi\) | ||||
−0.842983 | + | 0.537940i | \(0.819203\pi\) | |||||||
\(318\) | −5.29976 | + | 3.05982i | −0.297196 | + | 0.171586i | ||||
\(319\) | −7.39085 | + | 4.26711i | −0.413808 | + | 0.238912i | ||||
\(320\) | − | 22.2079i | − | 1.24146i | ||||||
\(321\) | 6.80754 | + | 11.7910i | 0.379960 | + | 0.658109i | ||||
\(322\) | −1.03408 | + | 1.79107i | −0.0576268 | + | 0.0998126i | ||||
\(323\) | 10.8599 | + | 6.26998i | 0.604262 | + | 0.348871i | ||||
\(324\) | −6.67187 | −0.370660 | ||||||||
\(325\) | −27.5820 | + | 25.7103i | −1.52998 | + | 1.42615i | ||||
\(326\) | −6.29796 | −0.348812 | ||||||||
\(327\) | 26.4256 | + | 15.2568i | 1.46134 | + | 0.843706i | ||||
\(328\) | 1.29375 | − | 2.24085i | 0.0714356 | − | 0.123730i | ||||
\(329\) | −0.454485 | − | 0.787192i | −0.0250566 | − | 0.0433993i | ||||
\(330\) | 76.8112i | 4.22832i | ||||||||
\(331\) | −23.1894 | + | 13.3884i | −1.27460 | + | 0.735892i | −0.975851 | − | 0.218439i | \(-0.929904\pi\) |
−0.298752 | + | 0.954331i | \(0.596570\pi\) | |||||||
\(332\) | 4.61306 | − | 2.66335i | 0.253175 | − | 0.146171i | ||||
\(333\) | 19.9053i | 1.09080i | ||||||||
\(334\) | −6.40645 | − | 11.0963i | −0.350546 | − | 0.607163i | ||||
\(335\) | 10.3969 | − | 18.0080i | 0.568046 | − | 0.983884i | ||||
\(336\) | −4.86303 | − | 2.80767i | −0.265300 | − | 0.153171i | ||||
\(337\) | 18.3890 | 1.00171 | 0.500856 | − | 0.865531i | \(-0.333019\pi\) | ||||
0.500856 | + | 0.865531i | \(0.333019\pi\) | |||||||
\(338\) | 11.3291 | − | 16.7815i | 0.616220 | − | 0.912795i | ||||
\(339\) | 33.3399 | 1.81077 | ||||||||
\(340\) | 2.21124 | + | 1.27666i | 0.119921 | + | 0.0692365i | ||||
\(341\) | 2.01496 | − | 3.49001i | 0.109116 | − | 0.188995i | ||||
\(342\) | 42.8280 | + | 74.1803i | 2.31587 | + | 4.01121i | ||||
\(343\) | 5.35032i | 0.288890i | ||||||||
\(344\) | 23.5524 | − | 13.5980i | 1.26986 | − | 0.733155i | ||||
\(345\) | −36.4312 | + | 21.0336i | −1.96139 | + | 1.13241i | ||||
\(346\) | − | 9.86920i | − | 0.530571i | ||||||
\(347\) | 6.81729 | + | 11.8079i | 0.365971 | + | 0.633881i | 0.988932 | − | 0.148373i | \(-0.0474035\pi\) |
−0.622960 | + | 0.782254i | \(0.714070\pi\) | |||||||
\(348\) | −1.40349 | + | 2.43092i | −0.0752350 | + | 0.130311i | ||||
\(349\) | 10.3581 | + | 5.98024i | 0.554455 | + | 0.320115i | 0.750917 | − | 0.660397i | \(-0.229612\pi\) |
−0.196462 | + | 0.980511i | \(0.562945\pi\) | |||||||
\(350\) | −6.29192 | −0.336317 | ||||||||
\(351\) | −30.2772 | + | 28.2227i | −1.61608 | + | 1.50641i | ||||
\(352\) | 9.55325 | 0.509190 | ||||||||
\(353\) | 21.3229 | + | 12.3108i | 1.13490 | + | 0.655236i | 0.945163 | − | 0.326599i | \(-0.105903\pi\) |
0.189739 | + | 0.981835i | \(0.439236\pi\) | |||||||
\(354\) | 3.64009 | − | 6.30483i | 0.193469 | − | 0.335098i | ||||
\(355\) | 5.34722 | + | 9.26165i | 0.283801 | + | 0.491557i | ||||
\(356\) | 6.11329i | 0.324004i | ||||||||
\(357\) | −1.58795 | + | 0.916803i | −0.0840432 | + | 0.0485224i | ||||
\(358\) | 12.8387 | − | 7.41243i | 0.678547 | − | 0.391759i | ||||
\(359\) | − | 17.7747i | − | 0.938110i | −0.883169 | − | 0.469055i | \(-0.844595\pi\) | ||
0.883169 | − | 0.469055i | \(-0.155405\pi\) | |||||||
\(360\) | −32.2355 | − | 55.8335i | −1.69896 | − | 2.94269i | ||||
\(361\) | 24.3068 | − | 42.1007i | 1.27931 | − | 2.21582i | ||||
\(362\) | −14.8775 | − | 8.58954i | −0.781945 | − | 0.451456i | ||||
\(363\) | 16.3107 | 0.856088 | ||||||||
\(364\) | 0.577925 | − | 0.133303i | 0.0302915 | − | 0.00698696i | ||||
\(365\) | −33.7660 | −1.76739 | ||||||||
\(366\) | −41.7240 | − | 24.0893i | −2.18095 | − | 1.25917i | ||||
\(367\) | −6.67953 | + | 11.5693i | −0.348668 | + | 0.603911i | −0.986013 | − | 0.166667i | \(-0.946699\pi\) |
0.637345 | + | 0.770579i | \(0.280033\pi\) | |||||||
\(368\) | 8.02721 | + | 13.9035i | 0.418447 | + | 0.724772i | ||||
\(369\) | − | 7.05848i | − | 0.367450i | ||||||
\(370\) | 15.7832 | − | 9.11246i | 0.820532 | − | 0.473734i | ||||
\(371\) | −0.422288 | + | 0.243808i | −0.0219241 | + | 0.0126579i | ||||
\(372\) | − | 1.32548i | − | 0.0687227i | ||||||
\(373\) | 7.17793 | + | 12.4325i | 0.371659 | + | 0.643732i | 0.989821 | − | 0.142318i | \(-0.0454557\pi\) |
−0.618162 | + | 0.786051i | \(0.712122\pi\) | |||||||
\(374\) | 4.78604 | − | 8.28967i | 0.247480 | − | 0.428648i | ||||
\(375\) | −57.8438 | − | 33.3961i | −2.98704 | − | 1.72457i | ||||
\(376\) | −5.76930 | −0.297529 | ||||||||
\(377\) | 1.71613 | + | 7.44018i | 0.0883854 | + | 0.383189i | ||||
\(378\) | −6.90674 | −0.355244 | ||||||||
\(379\) | 24.0127 | + | 13.8637i | 1.23345 | + | 0.712132i | 0.967747 | − | 0.251924i | \(-0.0810632\pi\) |
0.265701 | + | 0.964055i | \(0.414396\pi\) | |||||||
\(380\) | 6.88356 | − | 11.9227i | 0.353119 | − | 0.611620i | ||||
\(381\) | −23.3361 | − | 40.4194i | −1.19555 | − | 2.07075i | ||||
\(382\) | 11.3033i | 0.578329i | ||||||||
\(383\) | 2.79605 | − | 1.61430i | 0.142872 | − | 0.0824869i | −0.426860 | − | 0.904318i | \(-0.640380\pi\) |
0.569732 | + | 0.821831i | \(0.307047\pi\) | |||||||
\(384\) | −36.4947 | + | 21.0703i | −1.86236 | + | 1.07524i | ||||
\(385\) | 6.12037i | 0.311923i | ||||||||
\(386\) | 7.86826 | + | 13.6282i | 0.400484 | + | 0.693658i | ||||
\(387\) | 37.0941 | − | 64.2489i | 1.88560 | − | 3.26596i | ||||
\(388\) | 2.02652 | + | 1.17001i | 0.102881 | + | 0.0593984i | ||||
\(389\) | −25.3812 | −1.28688 | −0.643438 | − | 0.765498i | \(-0.722493\pi\) | ||||
−0.643438 | + | 0.765498i | \(0.722493\pi\) | |||||||
\(390\) | 65.7159 | + | 20.1057i | 3.32765 | + | 1.01809i | ||||
\(391\) | 5.24233 | 0.265116 | ||||||||
\(392\) | 14.5462 | + | 8.39827i | 0.734695 | + | 0.424177i | ||||
\(393\) | −31.5070 | + | 54.5717i | −1.58932 | + | 2.75278i | ||||
\(394\) | 6.95050 | + | 12.0386i | 0.350161 | + | 0.606497i | ||||
\(395\) | − | 15.8927i | − | 0.799647i | ||||||
\(396\) | 9.93999 | − | 5.73886i | 0.499503 | − | 0.288388i | ||||
\(397\) | −17.0403 | + | 9.83822i | −0.855228 | + | 0.493766i | −0.862411 | − | 0.506208i | \(-0.831047\pi\) |
0.00718321 | + | 0.999974i | \(0.497713\pi\) | |||||||
\(398\) | − | 0.670469i | − | 0.0336076i | ||||||
\(399\) | 4.94327 | + | 8.56200i | 0.247473 | + | 0.428636i | ||||
\(400\) | −24.4211 | + | 42.2986i | −1.22105 | + | 2.11493i | ||||
\(401\) | 4.98848 | + | 2.88010i | 0.249113 | + | 0.143825i | 0.619358 | − | 0.785109i | \(-0.287393\pi\) |
−0.370245 | + | 0.928934i | \(0.620726\pi\) | |||||||
\(402\) | −25.6397 | −1.27879 | ||||||||
\(403\) | −2.45845 | − | 2.63743i | −0.122464 | − | 0.131380i | ||||
\(404\) | 7.15421 | 0.355935 | ||||||||
\(405\) | −53.3463 | − | 30.7995i | −2.65080 | − | 1.53044i | ||||
\(406\) | −0.637052 | + | 1.10341i | −0.0316164 | + | 0.0547611i | ||||
\(407\) | −5.99687 | − | 10.3869i | −0.297254 | − | 0.514859i | ||||
\(408\) | 11.6380i | 0.576169i | ||||||||
\(409\) | −12.5781 | + | 7.26196i | −0.621946 | + | 0.359081i | −0.777626 | − | 0.628727i | \(-0.783576\pi\) |
0.155680 | + | 0.987808i | \(0.450243\pi\) | |||||||
\(410\) | −5.59680 | + | 3.23131i | −0.276406 | + | 0.159583i | ||||
\(411\) | − | 0.629513i | − | 0.0310516i | ||||||
\(412\) | 1.24660 | + | 2.15917i | 0.0614154 | + | 0.106375i | ||||
\(413\) | 0.290045 | − | 0.502373i | 0.0142722 | − | 0.0247201i | ||||
\(414\) | 31.0111 | + | 17.9043i | 1.52411 | + | 0.879947i | ||||
\(415\) | 49.1795 | 2.41413 | ||||||||
\(416\) | 2.50061 | − | 8.17328i | 0.122603 | − | 0.400728i | ||||
\(417\) | −18.9213 | −0.926578 | ||||||||
\(418\) | −44.6967 | − | 25.8056i | −2.18619 | − | 1.26220i | ||||
\(419\) | 3.77019 | − | 6.53017i | 0.184186 | − | 0.319020i | −0.759116 | − | 0.650955i | \(-0.774368\pi\) |
0.943302 | + | 0.331936i | \(0.107702\pi\) | |||||||
\(420\) | 1.00652 | + | 1.74335i | 0.0491132 | + | 0.0850666i | ||||
\(421\) | − | 10.0401i | − | 0.489324i | −0.969608 | − | 0.244662i | \(-0.921323\pi\) | ||
0.969608 | − | 0.244662i | \(-0.0786770\pi\) | |||||||
\(422\) | 5.77172 | − | 3.33231i | 0.280963 | − | 0.162214i | ||||
\(423\) | −13.6296 | + | 7.86907i | −0.662695 | + | 0.382607i | ||||
\(424\) | 3.09494i | 0.150303i | ||||||||
\(425\) | 7.97434 | + | 13.8120i | 0.386813 | + | 0.669979i | ||||
\(426\) | 6.59333 | − | 11.4200i | 0.319448 | − | 0.553300i | ||||
\(427\) | −3.32459 | − | 1.91945i | −0.160888 | − | 0.0928889i | ||||
\(428\) | −1.86272 | −0.0900382 | ||||||||
\(429\) | 13.2315 | − | 43.2473i | 0.638822 | − | 2.08800i | ||||
\(430\) | −67.9256 | −3.27566 | ||||||||
\(431\) | −23.8888 | − | 13.7922i | −1.15068 | − | 0.664348i | −0.201630 | − | 0.979462i | \(-0.564624\pi\) |
−0.949054 | + | 0.315114i | \(0.897957\pi\) | |||||||
\(432\) | −26.8074 | + | 46.4318i | −1.28977 | + | 2.23395i | ||||
\(433\) | −15.7733 | − | 27.3201i | −0.758015 | − | 1.31292i | −0.943862 | − | 0.330341i | \(-0.892836\pi\) |
0.185847 | − | 0.982579i | \(-0.440497\pi\) | |||||||
\(434\) | − | 0.601640i | − | 0.0288797i | ||||||
\(435\) | −22.4438 | + | 12.9579i | −1.07610 | + | 0.621285i | ||||
\(436\) | −3.61538 | + | 2.08734i | −0.173145 | + | 0.0999655i | ||||
\(437\) | − | 28.2659i | − | 1.35214i | ||||||
\(438\) | 20.8174 | + | 36.0568i | 0.994694 | + | 1.72286i | ||||
\(439\) | −10.4942 | + | 18.1764i | −0.500859 | + | 0.867514i | 0.499140 | + | 0.866521i | \(0.333649\pi\) |
−1.00000 | 0.000992689i | \(0.999684\pi\) | ||||||||
\(440\) | 33.6420 | + | 19.4232i | 1.60382 | + | 0.925966i | ||||
\(441\) | 45.8194 | 2.18188 | ||||||||
\(442\) | −5.83945 | − | 6.26456i | −0.277754 | − | 0.297975i | ||||
\(443\) | −20.0487 | −0.952541 | −0.476270 | − | 0.879299i | \(-0.658012\pi\) | ||||
−0.476270 | + | 0.879299i | \(0.658012\pi\) | |||||||
\(444\) | −3.41634 | − | 1.97242i | −0.162132 | − | 0.0936071i | ||||
\(445\) | −28.2209 | + | 48.8800i | −1.33780 | + | 2.31713i | ||||
\(446\) | 5.36664 | + | 9.29530i | 0.254118 | + | 0.440145i | ||||
\(447\) | − | 62.8365i | − | 2.97206i | ||||||
\(448\) | −1.88959 | + | 1.09096i | −0.0892748 | + | 0.0515428i | ||||
\(449\) | −26.9074 | + | 15.5350i | −1.26984 | + | 0.733142i | −0.974957 | − | 0.222392i | \(-0.928614\pi\) |
−0.294882 | + | 0.955534i | \(0.595280\pi\) | |||||||
\(450\) | 108.940i | 5.13547i | ||||||||
\(451\) | 2.12651 | + | 3.68323i | 0.100134 | + | 0.173437i | ||||
\(452\) | −2.28067 | + | 3.95023i | −0.107274 | + | 0.185803i | ||||
\(453\) | −27.6974 | − | 15.9911i | −1.30134 | − | 0.751327i | ||||
\(454\) | −11.1968 | −0.525492 | ||||||||
\(455\) | 5.23628 | + | 1.60204i | 0.245481 | + | 0.0751046i | ||||
\(456\) | 62.7506 | 2.93857 | ||||||||
\(457\) | −12.6727 | − | 7.31661i | −0.592806 | − | 0.342257i | 0.173400 | − | 0.984851i | \(-0.444525\pi\) |
−0.766206 | + | 0.642595i | \(0.777858\pi\) | |||||||
\(458\) | 15.5133 | − | 26.8698i | 0.724889 | − | 1.25554i | ||||
\(459\) | 8.75357 | + | 15.1616i | 0.408582 | + | 0.707684i | ||||
\(460\) | − | 5.75535i | − | 0.268344i | ||||||
\(461\) | 27.5347 | − | 15.8972i | 1.28242 | − | 0.740405i | 0.305129 | − | 0.952311i | \(-0.401300\pi\) |
0.977290 | + | 0.211906i | \(0.0679671\pi\) | |||||||
\(462\) | 6.53560 | − | 3.77333i | 0.304064 | − | 0.175551i | ||||
\(463\) | 18.3858i | 0.854459i | 0.904143 | + | 0.427230i | \(0.140510\pi\) | ||||
−0.904143 | + | 0.427230i | \(0.859490\pi\) | |||||||
\(464\) | 4.94523 | + | 8.56539i | 0.229577 | + | 0.397638i | ||||
\(465\) | 6.11882 | − | 10.5981i | 0.283753 | − | 0.491475i | ||||
\(466\) | 1.07227 | + | 0.619073i | 0.0496717 | + | 0.0286780i | ||||
\(467\) | −29.4316 | −1.36193 | −0.680965 | − | 0.732316i | \(-0.738440\pi\) | ||||
−0.680965 | + | 0.732316i | \(0.738440\pi\) | |||||||
\(468\) | −2.30804 | − | 10.0063i | −0.106689 | − | 0.462543i | ||||
\(469\) | −2.04299 | −0.0943363 | ||||||||
\(470\) | 12.4791 | + | 7.20479i | 0.575616 | + | 0.332332i | ||||
\(471\) | 12.0280 | − | 20.8331i | 0.554219 | − | 0.959936i | ||||
\(472\) | −1.84094 | − | 3.18860i | −0.0847360 | − | 0.146767i | ||||
\(473\) | 44.7015i | 2.05538i | ||||||||
\(474\) | −16.9709 | + | 9.79815i | −0.779499 | + | 0.450044i | ||||
\(475\) | 74.4722 | − | 42.9965i | 3.41702 | − | 1.97282i | ||||
\(476\) | − | 0.250862i | − | 0.0114982i | ||||||
\(477\) | 4.22135 | + | 7.31160i | 0.193283 | + | 0.334775i | ||||
\(478\) | −8.21484 | + | 14.2285i | −0.375738 | + | 0.650797i | ||||
\(479\) | −18.0631 | − | 10.4287i | −0.825325 | − | 0.476502i | 0.0269243 | − | 0.999637i | \(-0.491429\pi\) |
−0.852249 | + | 0.523136i | \(0.824762\pi\) | |||||||
\(480\) | 29.0103 | 1.32413 | ||||||||
\(481\) | −10.4562 | + | 2.41180i | −0.476762 | + | 0.109969i | ||||
\(482\) | −30.9752 | −1.41088 | ||||||||
\(483\) | 3.57935 | + | 2.06654i | 0.162866 | + | 0.0940306i | ||||
\(484\) | −1.11576 | + | 1.93255i | −0.0507163 | + | 0.0878432i | ||||
\(485\) | 10.8023 | + | 18.7101i | 0.490507 | + | 0.849583i | ||||
\(486\) | 22.3140i | 1.01218i | ||||||||
\(487\) | −3.82795 | + | 2.21007i | −0.173461 | + | 0.100148i | −0.584217 | − | 0.811598i | \(-0.698598\pi\) |
0.410756 | + | 0.911745i | \(0.365265\pi\) | |||||||
\(488\) | −21.1014 | + | 12.1829i | −0.955217 | + | 0.551495i | ||||
\(489\) | 12.5861i | 0.569162i | ||||||||
\(490\) | −20.9758 | − | 36.3311i | −0.947588 | − | 1.64127i | ||||
\(491\) | −1.65327 | + | 2.86354i | −0.0746109 | + | 0.129230i | −0.900917 | − | 0.433991i | \(-0.857105\pi\) |
0.826306 | + | 0.563221i | \(0.190438\pi\) | |||||||
\(492\) | 1.21145 | + | 0.699429i | 0.0546162 | + | 0.0315327i | ||||
\(493\) | 3.22958 | 0.145453 | ||||||||
\(494\) | −33.7776 | + | 31.4855i | −1.51973 | + | 1.41660i | ||||
\(495\) | 105.970 | 4.76298 | ||||||||
\(496\) | −4.04464 | − | 2.33517i | −0.181610 | − | 0.104852i | ||||
\(497\) | 0.525361 | − | 0.909951i | 0.0235656 | − | 0.0408169i | ||||
\(498\) | −30.3202 | − | 52.5161i | −1.35868 | − | 2.35330i | ||||
\(499\) | 22.4108i | 1.00325i | 0.865086 | + | 0.501624i | \(0.167264\pi\) | ||||
−0.865086 | + | 0.501624i | \(0.832736\pi\) | |||||||
\(500\) | 7.91380 | − | 4.56903i | 0.353916 | − | 0.204333i | ||||
\(501\) | −22.1753 | + | 12.8029i | −0.990717 | + | 0.571991i | ||||
\(502\) | − | 5.04457i | − | 0.225150i | ||||||
\(503\) | −20.0569 | − | 34.7395i | −0.894291 | − | 1.54896i | −0.834679 | − | 0.550737i | \(-0.814347\pi\) |
−0.0596122 | − | 0.998222i | \(-0.518986\pi\) | |||||||
\(504\) | −3.16712 | + | 5.48561i | −0.141075 | + | 0.244348i | ||||
\(505\) | 57.2029 | + | 33.0261i | 2.54550 | + | 1.46964i | ||||
\(506\) | −21.5761 | −0.959175 | ||||||||
\(507\) | −33.5368 | − | 22.6404i | −1.48942 | − | 1.00550i | ||||
\(508\) | 6.38539 | 0.283306 | ||||||||
\(509\) | 29.2473 | + | 16.8859i | 1.29636 | + | 0.748455i | 0.979774 | − | 0.200108i | \(-0.0641294\pi\) |
0.316588 | + | 0.948563i | \(0.397463\pi\) | |||||||
\(510\) | 14.5337 | − | 25.1732i | 0.643565 | − | 1.11469i | ||||
\(511\) | 1.65874 | + | 2.87303i | 0.0733785 | + | 0.127095i | ||||
\(512\) | 11.8298i | 0.522807i | ||||||||
\(513\) | 81.7493 | − | 47.1980i | 3.60932 | − | 2.08384i | ||||
\(514\) | 6.28485 | − | 3.62856i | 0.277213 | − | 0.160049i | ||||
\(515\) | 23.0187i | 1.01433i | ||||||||
\(516\) | 7.35136 | + | 12.7329i | 0.323626 | + | 0.560536i | ||||
\(517\) | 4.74144 | − | 8.21241i | 0.208528 | − | 0.361182i | ||||
\(518\) | −1.55069 | − | 0.895294i | −0.0681336 | − | 0.0393369i | ||||
\(519\) | −19.7230 | −0.865742 | ||||||||
\(520\) | 25.4235 | − | 23.6983i | 1.11489 | − | 1.03924i | ||||
\(521\) | −10.5292 | −0.461293 | −0.230647 | − | 0.973038i | \(-0.574084\pi\) | ||||
−0.230647 | + | 0.973038i | \(0.574084\pi\) | |||||||
\(522\) | 19.1047 | + | 11.0301i | 0.836188 | + | 0.482773i | ||||
\(523\) | 6.94737 | − | 12.0332i | 0.303787 | − | 0.526175i | −0.673203 | − | 0.739457i | \(-0.735082\pi\) |
0.976991 | + | 0.213282i | \(0.0684154\pi\) | |||||||
\(524\) | −4.31058 | − | 7.46614i | −0.188308 | − | 0.326160i | ||||
\(525\) | 12.5740i | 0.548774i | ||||||||
\(526\) | −7.04442 | + | 4.06710i | −0.307151 | + | 0.177334i | ||||
\(527\) | −1.32072 | + | 0.762516i | −0.0575313 | + | 0.0332157i | ||||
\(528\) | − | 58.5823i | − | 2.54947i | ||||||
\(529\) | 5.59171 | + | 9.68513i | 0.243118 | + | 0.421093i | ||||
\(530\) | 3.86500 | − | 6.69438i | 0.167885 | − | 0.290785i | ||||
\(531\) | −8.69820 | − | 5.02191i | −0.377470 | − | 0.217932i | ||||
\(532\) | −1.35261 | −0.0586431 | ||||||||
\(533\) | 3.70781 | − | 0.855235i | 0.160603 | − | 0.0370443i | ||||
\(534\) | 69.5949 | 3.01167 | ||||||||
\(535\) | −14.8938 | − | 8.59893i | −0.643914 | − | 0.371764i | ||||
\(536\) | −6.48349 | + | 11.2297i | −0.280044 | + | 0.485051i | ||||
\(537\) | −14.8133 | − | 25.6573i | −0.639240 | − | 1.10720i | ||||
\(538\) | − | 25.5246i | − | 1.10045i | ||||||
\(539\) | −23.9093 | + | 13.8040i | −1.02985 | + | 0.594582i | ||||
\(540\) | 16.6453 | − | 9.61019i | 0.716301 | − | 0.413557i | ||||
\(541\) | − | 27.7598i | − | 1.19349i | −0.802431 | − | 0.596744i | \(-0.796461\pi\) | ||
0.802431 | − | 0.596744i | \(-0.203539\pi\) | |||||||
\(542\) | 20.4286 | + | 35.3834i | 0.877485 | + | 1.51985i | ||||
\(543\) | −17.1657 | + | 29.7318i | −0.736649 | + | 1.27591i | ||||
\(544\) | −3.13087 | − | 1.80761i | −0.134235 | − | 0.0775005i | ||||
\(545\) | −38.5433 | −1.65101 | ||||||||
\(546\) | −1.51755 | − | 6.57922i | −0.0649450 | − | 0.281565i | ||||
\(547\) | −36.7202 | −1.57004 | −0.785021 | − | 0.619469i | \(-0.787348\pi\) | ||||
−0.785021 | + | 0.619469i | \(0.787348\pi\) | |||||||
\(548\) | 0.0745872 | + | 0.0430629i | 0.00318621 | + | 0.00183956i | ||||
\(549\) | −33.2339 | + | 57.5628i | −1.41839 | + | 2.45672i | ||||
\(550\) | −32.8204 | − | 56.8466i | −1.39947 | − | 2.42395i | ||||
\(551\) | − | 17.4135i | − | 0.741838i | ||||||
\(552\) | 22.7184 | − | 13.1165i | 0.966958 | − | 0.558274i | ||||
\(553\) | −1.35225 | + | 0.780722i | −0.0575035 | + | 0.0331997i | ||||
\(554\) | 39.3028i | 1.66982i | ||||||||
\(555\) | −18.2107 | − | 31.5418i | −0.773000 | − | 1.33887i | ||||
\(556\) | 1.29434 | − | 2.24186i | 0.0548923 | − | 0.0950762i | ||||
\(557\) | 19.7951 | + | 11.4287i | 0.838746 | + | 0.484250i | 0.856838 | − | 0.515586i | \(-0.172426\pi\) |
−0.0180919 | + | 0.999836i | \(0.505759\pi\) | |||||||
\(558\) | −10.4170 | −0.440985 | ||||||||
\(559\) | 38.2444 | + | 11.7008i | 1.61756 | + | 0.494893i | ||||
\(560\) | 7.09301 | 0.299734 | ||||||||
\(561\) | −16.5664 | − | 9.56459i | −0.699432 | − | 0.403817i | ||||
\(562\) | −5.62774 | + | 9.74753i | −0.237392 | + | 0.411175i | ||||
\(563\) | 6.59564 | + | 11.4240i | 0.277973 | + | 0.481463i | 0.970881 | − | 0.239563i | \(-0.0770041\pi\) |
−0.692908 | + | 0.721026i | \(0.743671\pi\) | |||||||
\(564\) | − | 3.11900i | − | 0.131334i | ||||||
\(565\) | −36.4711 | + | 21.0566i | −1.53435 | + | 0.885857i | ||||
\(566\) | 9.29403 | − | 5.36591i | 0.390657 | − | 0.225546i | ||||
\(567\) | 6.05206i | 0.254163i | ||||||||
\(568\) | −3.33450 | − | 5.77553i | −0.139913 | − | 0.242336i | ||||
\(569\) | −0.808452 | + | 1.40028i | −0.0338921 | + | 0.0587028i | −0.882474 | − | 0.470361i | \(-0.844124\pi\) |
0.848582 | + | 0.529064i | \(0.177457\pi\) | |||||||
\(570\) | −135.730 | − | 78.3639i | −5.68511 | − | 3.28230i | ||||
\(571\) | −25.0746 | −1.04934 | −0.524670 | − | 0.851306i | \(-0.675811\pi\) | ||||
−0.524670 | + | 0.851306i | \(0.675811\pi\) | |||||||
\(572\) | 4.21898 | + | 4.52612i | 0.176405 | + | 0.189247i | ||||
\(573\) | 22.5890 | 0.943669 | ||||||||
\(574\) | 0.549882 | + | 0.317475i | 0.0229516 | + | 0.0132511i | ||||
\(575\) | 17.9747 | − | 31.1331i | 0.749597 | − | 1.29834i | ||||
\(576\) | 18.8891 | + | 32.7168i | 0.787045 | + | 1.36320i | ||||
\(577\) | − | 26.8857i | − | 1.11927i | −0.828740 | − | 0.559633i | \(-0.810942\pi\) | ||
0.828740 | − | 0.559633i | \(-0.189058\pi\) | |||||||
\(578\) | 19.7933 | − | 11.4277i | 0.823294 | − | 0.475329i | ||||
\(579\) | 27.2351 | − | 15.7242i | 1.13185 | − | 0.653476i | ||||
\(580\) | − | 3.54563i | − | 0.147224i | ||||||
\(581\) | −2.41593 | − | 4.18451i | −0.100230 | − | 0.173603i | ||||
\(582\) | 13.3197 | − | 23.0703i | 0.552118 | − | 0.956296i | ||||
\(583\) | −4.40554 | − | 2.54354i | −0.182459 | − | 0.105343i | ||||
\(584\) | 21.0563 | 0.871318 | ||||||||
\(585\) | 27.7381 | − | 90.6623i | 1.14683 | − | 3.74842i | ||||
\(586\) | 43.4070 | 1.79313 | ||||||||
\(587\) | −26.8577 | − | 15.5063i | −1.10854 | − | 0.640015i | −0.170088 | − | 0.985429i | \(-0.554405\pi\) |
−0.938450 | + | 0.345414i | \(0.887738\pi\) | |||||||
\(588\) | −4.54027 | + | 7.86398i | −0.187238 | + | 0.324305i | ||||
\(589\) | 4.11138 | + | 7.12111i | 0.169406 | + | 0.293420i | ||||
\(590\) | 9.19595i | 0.378591i | ||||||||
\(591\) | 24.0584 | − | 13.8901i | 0.989631 | − | 0.571364i | ||||
\(592\) | −12.0375 | + | 6.94988i | −0.494740 | + | 0.285638i | ||||
\(593\) | 16.1249i | 0.662169i | 0.943601 | + | 0.331085i | \(0.107415\pi\) | ||||
−0.943601 | + | 0.331085i | \(0.892585\pi\) | |||||||
\(594\) | −36.0275 | − | 62.4014i | −1.47822 | − | 2.56036i | ||||
\(595\) | 1.15806 | − | 2.00582i | 0.0474757 | − | 0.0822304i | ||||
\(596\) | 7.44511 | + | 4.29844i | 0.304964 | + | 0.176071i | ||||
\(597\) | −1.33989 | −0.0548381 | ||||||||
\(598\) | −5.64766 | + | 18.4594i | −0.230950 | + | 0.754863i | ||||
\(599\) | 47.4928 | 1.94050 | 0.970252 | − | 0.242097i | \(-0.0778354\pi\) | ||||
0.970252 | + | 0.242097i | \(0.0778354\pi\) | |||||||
\(600\) | 69.1158 | + | 39.9040i | 2.82164 | + | 1.62908i | ||||
\(601\) | −0.568035 | + | 0.983865i | −0.0231706 | + | 0.0401327i | −0.877378 | − | 0.479799i | \(-0.840709\pi\) |
0.854208 | + | 0.519932i | \(0.174043\pi\) | |||||||
\(602\) | 3.33682 | + | 5.77955i | 0.135999 | + | 0.235557i | ||||
\(603\) | 35.3728i | 1.44049i | ||||||||
\(604\) | 3.78937 | − | 2.18780i | 0.154187 | − | 0.0890201i | ||||
\(605\) | −17.8425 | + | 10.3014i | −0.725402 | + | 0.418811i | ||||
\(606\) | − | 81.4451i | − | 3.30848i | ||||||
\(607\) | −5.54869 | − | 9.61061i | −0.225214 | − | 0.390083i | 0.731169 | − | 0.682196i | \(-0.238975\pi\) |
−0.956384 | + | 0.292113i | \(0.905642\pi\) | |||||||
\(608\) | −9.74636 | + | 16.8812i | −0.395267 | + | 0.684622i | ||||
\(609\) | 2.20509 | + | 1.27311i | 0.0893546 | + | 0.0515889i | ||||
\(610\) | 60.8568 | 2.46402 | ||||||||
\(611\) | −5.78504 | − | 6.20618i | −0.234037 | − | 0.251075i | ||||
\(612\) | −4.34348 | −0.175575 | ||||||||
\(613\) | −15.7879 | − | 9.11514i | −0.637667 | − | 0.368157i | 0.146048 | − | 0.989277i | \(-0.453345\pi\) |
−0.783715 | + | 0.621120i | \(0.786678\pi\) | |||||||
\(614\) | −15.9669 | + | 27.6556i | −0.644374 | + | 1.11609i | ||||
\(615\) | 6.45758 | + | 11.1848i | 0.260395 | + | 0.451017i | ||||
\(616\) | − | 3.81664i | − | 0.153777i | ||||||
\(617\) | 27.3674 | − | 15.8006i | 1.10177 | − | 0.636106i | 0.165084 | − | 0.986280i | \(-0.447211\pi\) |
0.936685 | + | 0.350173i | \(0.113877\pi\) | |||||||
\(618\) | 24.5804 | − | 14.1915i | 0.988770 | − | 0.570866i | ||||
\(619\) | − | 20.5534i | − | 0.826111i | −0.910706 | − | 0.413055i | \(-0.864462\pi\) | ||
0.910706 | − | 0.413055i | \(-0.135538\pi\) | |||||||
\(620\) | 0.837136 | + | 1.44996i | 0.0336202 | + | 0.0582319i | ||||
\(621\) | 19.7311 | − | 34.1753i | 0.791783 | − | 1.37141i | ||||
\(622\) | −16.6649 | − | 9.62146i | −0.668200 | − | 0.385785i | ||||
\(623\) | 5.54537 | 0.222170 | ||||||||
\(624\) | −50.1201 | − | 15.3342i | −2.00641 | − | 0.613860i | ||||
\(625\) | 32.0788 | 1.28315 | ||||||||
\(626\) | 10.6978 | + | 6.17638i | 0.427570 | + | 0.246858i | ||||
\(627\) | −51.5709 | + | 89.3235i | −2.05954 | + | 3.56724i | ||||
\(628\) | 1.64559 | + | 2.85024i | 0.0656661 | + | 0.113737i | ||||
\(629\) | 4.53876i | 0.180972i | ||||||||
\(630\) | 13.7010 | − | 7.91028i | 0.545862 | − | 0.315153i | ||||
\(631\) | 18.1113 | − | 10.4566i | 0.721000 | − | 0.416269i | −0.0941208 | − | 0.995561i | \(-0.530004\pi\) |
0.815121 | + | 0.579291i | \(0.196671\pi\) | |||||||
\(632\) | 9.91061i | 0.394223i | ||||||||
\(633\) | −6.65940 | − | 11.5344i | −0.264687 | − | 0.458452i | ||||
\(634\) | −14.9175 | + | 25.8378i | −0.592448 | + | 1.02615i | ||||
\(635\) | 51.0557 | + | 29.4770i | 2.02608 | + | 1.16976i | ||||
\(636\) | −1.67319 | −0.0663461 | ||||||||
\(637\) | 5.55167 | + | 24.0689i | 0.219965 | + | 0.953644i | ||||
\(638\) | −13.2922 | −0.526241 | ||||||||
\(639\) | −15.7551 | − | 9.09623i | −0.623263 | − | 0.359841i | ||||
\(640\) | 26.6148 | − | 46.0983i | 1.05204 | − | 1.82219i | ||||
\(641\) | 15.1333 | + | 26.2116i | 0.597729 | + | 1.03530i | 0.993155 | + | 0.116800i | \(0.0372635\pi\) |
−0.395426 | + | 0.918498i | \(0.629403\pi\) | |||||||
\(642\) | 21.2056i | 0.836920i | ||||||||
\(643\) | −20.3995 | + | 11.7777i | −0.804478 | + | 0.464465i | −0.845034 | − | 0.534712i | \(-0.820420\pi\) |
0.0405568 | + | 0.999177i | \(0.487087\pi\) | |||||||
\(644\) | −0.489702 | + | 0.282730i | −0.0192970 | + | 0.0111411i | ||||
\(645\) | 135.745i | 5.34495i | ||||||||
\(646\) | 9.76557 | + | 16.9145i | 0.384221 | + | 0.665491i | ||||
\(647\) | 6.68235 | − | 11.5742i | 0.262710 | − | 0.455028i | −0.704251 | − | 0.709951i | \(-0.748717\pi\) |
0.966961 | + | 0.254924i | \(0.0820503\pi\) | |||||||
\(648\) | 33.2665 | + | 19.2064i | 1.30683 | + | 0.754501i | ||||
\(649\) | 6.05182 | 0.237555 | ||||||||
\(650\) | −57.2260 | + | 13.1996i | −2.24459 | + | 0.517731i | ||||
\(651\) | −1.20234 | −0.0471234 | ||||||||
\(652\) | −1.49125 | − | 0.860971i | −0.0584017 | − | 0.0337182i | ||||
\(653\) | −3.99327 | + | 6.91654i | −0.156269 | + | 0.270665i | −0.933520 | − | 0.358525i | \(-0.883280\pi\) |
0.777252 | + | 0.629190i | \(0.216613\pi\) | |||||||
\(654\) | 23.7627 | + | 41.1582i | 0.929196 | + | 1.60941i | ||||
\(655\) | − | 79.5960i | − | 3.11007i | ||||||
\(656\) | 4.26856 | − | 2.46446i | 0.166659 | − | 0.0962208i | ||||
\(657\) | 49.7443 | − | 28.7199i | 1.94071 | − | 1.12047i | ||||
\(658\) | − | 1.41573i | − | 0.0551910i | ||||||
\(659\) | 9.53212 | + | 16.5101i | 0.371319 | + | 0.643143i | 0.989769 | − | 0.142681i | \(-0.0455724\pi\) |
−0.618450 | + | 0.785824i | \(0.712239\pi\) | |||||||
\(660\) | −10.5006 | + | 18.1875i | −0.408735 | + | 0.707949i | ||||
\(661\) | 15.7355 | + | 9.08488i | 0.612039 | + | 0.353361i | 0.773763 | − | 0.633475i | \(-0.218372\pi\) |
−0.161724 | + | 0.986836i | \(0.551705\pi\) | |||||||
\(662\) | −41.7051 | −1.62092 | ||||||||
\(663\) | −12.5193 | + | 11.6698i | −0.486210 | + | 0.453216i | ||||
\(664\) | −30.6682 | −1.19016 | ||||||||
\(665\) | −10.8151 | − | 6.24408i | −0.419390 | − | 0.242135i | ||||
\(666\) | −15.5013 | + | 26.8491i | −0.600665 | + | 1.04038i | ||||
\(667\) | −3.63985 | − | 6.30441i | −0.140936 | − | 0.244108i | ||||
\(668\) | − | 3.50321i | − | 0.135543i | ||||||
\(669\) | 18.5761 | − | 10.7249i | 0.718192 | − | 0.414648i | ||||
\(670\) | 28.0477 | − | 16.1934i | 1.08358 | − | 0.625604i | ||||
\(671\) | − | 40.0496i | − | 1.54610i | ||||||
\(672\) | −1.42512 | − | 2.46838i | −0.0549753 | − | 0.0952200i | ||||
\(673\) | 6.23632 | − | 10.8016i | 0.240392 | − | 0.416372i | −0.720434 | − | 0.693524i | \(-0.756057\pi\) |
0.960826 | + | 0.277152i | \(0.0893905\pi\) | |||||||
\(674\) | 24.8039 | + | 14.3205i | 0.955410 | + | 0.551606i | ||||
\(675\) | 120.056 | 4.62094 | ||||||||
\(676\) | 4.97666 | − | 2.42482i | 0.191410 | − | 0.0932622i | ||||
\(677\) | −6.96465 | −0.267673 | −0.133837 | − | 0.991003i | \(-0.542730\pi\) | ||||
−0.133837 | + | 0.991003i | \(0.542730\pi\) | |||||||
\(678\) | 44.9703 | + | 25.9636i | 1.72707 | + | 0.997127i | ||||
\(679\) | 1.06132 | − | 1.83826i | 0.0407297 | − | 0.0705459i | ||||
\(680\) | −7.35028 | − | 12.7311i | −0.281870 | − | 0.488214i | ||||
\(681\) | 22.3761i | 0.857453i | ||||||||
\(682\) | 5.43573 | − | 3.13832i | 0.208145 | − | 0.120173i | ||||
\(683\) | 4.28697 | − | 2.47508i | 0.164036 | − | 0.0947064i | −0.415734 | − | 0.909486i | \(-0.636475\pi\) |
0.579771 | + | 0.814780i | \(0.303142\pi\) | |||||||
\(684\) | 23.4194i | 0.895465i | ||||||||
\(685\) | 0.397584 | + | 0.688636i | 0.0151909 | + | 0.0263114i | ||||
\(686\) | −4.16660 | + | 7.21676i | −0.159081 | + | 0.275537i | ||||
\(687\) | −53.6976 | − | 31.0023i | −2.04869 | − | 1.18281i | ||||
\(688\) | 51.8054 | 1.97506 | ||||||||
\(689\) | −3.32930 | + | 3.10338i | −0.126836 | + | 0.118229i | ||||
\(690\) | −65.5201 | −2.49431 | ||||||||
\(691\) | −28.3429 | − | 16.3638i | −1.07821 | − | 0.622507i | −0.147799 | − | 0.989017i | \(-0.547219\pi\) |
−0.930414 | + | 0.366511i | \(0.880552\pi\) | |||||||
\(692\) | 1.34918 | − | 2.33685i | 0.0512882 | − | 0.0888338i | ||||
\(693\) | −5.20572 | − | 9.01658i | −0.197749 | − | 0.342511i | ||||
\(694\) | 21.2360i | 0.806108i | ||||||||
\(695\) | 20.6983 | − | 11.9502i | 0.785132 | − | 0.453296i | ||||
\(696\) | 13.9959 | − | 8.08051i | 0.530511 | − | 0.306291i | ||||
\(697\) | − | 1.60946i | − | 0.0609628i | ||||||
\(698\) | 9.31429 | + | 16.1328i | 0.352551 | + | 0.610636i | ||||
\(699\) | 1.23718 | − | 2.14285i | 0.0467943 | − | 0.0810502i | ||||
\(700\) | −1.48982 | − | 0.860145i | −0.0563097 | − | 0.0325104i | ||||
\(701\) | 39.5337 | 1.49317 | 0.746583 | − | 0.665292i | \(-0.231693\pi\) | ||||
0.746583 | + | 0.665292i | \(0.231693\pi\) | |||||||
\(702\) | −62.8179 | + | 14.4894i | −2.37091 | + | 0.546868i | ||||
\(703\) | 24.4724 | 0.922992 | ||||||||
\(704\) | −19.7132 | − | 11.3814i | −0.742971 | − | 0.428955i | ||||
\(705\) | 14.3983 | − | 24.9386i | 0.542272 | − | 0.939242i | ||||
\(706\) | 19.1742 | + | 33.2106i | 0.721629 | + | 1.24990i | ||||
\(707\) | − | 6.48959i | − | 0.244066i | ||||||
\(708\) | 1.72382 | − | 0.995248i | 0.0647851 | − | 0.0374037i | ||||
\(709\) | −33.8354 | + | 19.5349i | −1.27071 | + | 0.733648i | −0.975123 | − | 0.221667i | \(-0.928850\pi\) |
−0.295592 | + | 0.955314i | \(0.595517\pi\) | |||||||
\(710\) | 16.6567i | 0.625115i | ||||||||
\(711\) | 13.5176 | + | 23.4132i | 0.506950 | + | 0.878064i | ||||
\(712\) | 17.5984 | − | 30.4814i | 0.659529 | − | 1.14234i | ||||
\(713\) | 2.97698 | + | 1.71876i | 0.111489 | + | 0.0643681i | ||||
\(714\) | −2.85586 | −0.106878 | ||||||||
\(715\) | 12.8397 | + | 55.6657i | 0.480178 | + | 2.08178i | ||||
\(716\) | 4.05331 | 0.151479 | ||||||||
\(717\) | 28.4348 | + | 16.4168i | 1.06192 | + | 0.613098i | ||||
\(718\) | 13.8421 | − | 23.9753i | 0.516583 | − | 0.894748i | ||||
\(719\) | 12.5080 | + | 21.6645i | 0.466469 | + | 0.807949i | 0.999267 | − | 0.0382942i | \(-0.0121924\pi\) |
−0.532797 | + | 0.846243i | \(0.678859\pi\) | |||||||
\(720\) | − | 122.810i | − | 4.57686i | ||||||
\(721\) | 1.95858 | − | 1.13079i | 0.0729414 | − | 0.0421128i | ||||
\(722\) | 65.5723 | − | 37.8582i | 2.44035 | − | 1.40894i | ||||
\(723\) | 61.9019i | 2.30216i | ||||||||
\(724\) | −2.34849 | − | 4.06770i | −0.0872810 | − | 0.151175i | ||||
\(725\) | 11.0735 | − | 19.1798i | 0.411258 | − | 0.712321i | ||||
\(726\) | 22.0006 | + | 12.7020i | 0.816518 | + | 0.471417i | ||||
\(727\) | −42.7085 | −1.58397 | −0.791986 | − | 0.610540i | \(-0.790953\pi\) | ||||
−0.791986 | + | 0.610540i | \(0.790953\pi\) | |||||||
\(728\) | −3.26532 | − | 0.999024i | −0.121021 | − | 0.0370263i | ||||
\(729\) | −2.40917 | −0.0892286 | ||||||||
\(730\) | −45.5451 | − | 26.2955i | −1.68570 | − | 0.973239i | ||||
\(731\) | 8.45814 | − | 14.6499i | 0.312836 | − | 0.541847i | ||||
\(732\) | −6.58633 | − | 11.4079i | −0.243438 | − | 0.421647i | ||||
\(733\) | − | 16.7037i | − | 0.616965i | −0.951230 | − | 0.308482i | \(-0.900179\pi\) | ||
0.951230 | − | 0.308482i | \(-0.0998211\pi\) | |||||||
\(734\) | −18.0193 | + | 10.4034i | −0.665104 | + | 0.383998i | ||||
\(735\) | −72.6053 | + | 41.9187i | −2.67809 | + | 1.54619i | ||||
\(736\) | 8.14893i | 0.300374i | ||||||||
\(737\) | −10.6568 | − | 18.4581i | −0.392547 | − | 0.679912i | ||||
\(738\) | 5.49684 | − | 9.52080i | 0.202341 | − | 0.350466i | ||||
\(739\) | 27.0391 | + | 15.6110i | 0.994649 | + | 0.574261i | 0.906661 | − | 0.421860i | \(-0.138623\pi\) |
0.0879886 | + | 0.996121i | \(0.471956\pi\) | |||||||
\(740\) | 4.98292 | 0.183176 | ||||||||
\(741\) | 62.9217 | + | 67.5024i | 2.31149 | + | 2.47976i | ||||
\(742\) | −0.759468 | −0.0278809 | ||||||||
\(743\) | −40.5132 | − | 23.3903i | −1.48628 | − | 0.858107i | −0.486407 | − | 0.873733i | \(-0.661693\pi\) |
−0.999878 | + | 0.0156259i | \(0.995026\pi\) | |||||||
\(744\) | −3.81567 | + | 6.60894i | −0.139889 | + | 0.242295i | ||||
\(745\) | 39.6859 | + | 68.7380i | 1.45398 | + | 2.51837i | ||||
\(746\) | 22.3594i | 0.818637i | ||||||||
\(747\) | −72.4517 | + | 41.8300i | −2.65087 | + | 1.53048i | ||||
\(748\) | 2.26650 | − | 1.30856i | 0.0828714 | − | 0.0478458i | ||||
\(749\) | 1.68968i | 0.0617395i | ||||||||
\(750\) | −52.0149 | − | 90.0924i | −1.89931 | − | 3.28971i | ||||
\(751\) | −4.60438 | + | 7.97502i | −0.168016 | + | 0.291013i | −0.937722 | − | 0.347386i | \(-0.887069\pi\) |
0.769706 | + | 0.638398i | \(0.220403\pi\) | |||||||
\(752\) | −9.51752 | − | 5.49494i | −0.347068 | − | 0.200380i | ||||
\(753\) | −10.0812 | −0.367381 | ||||||||
\(754\) | −3.47929 | + | 11.3721i | −0.126708 | + | 0.414147i | ||||
\(755\) | 40.3982 | 1.47024 | ||||||||
\(756\) | −1.63539 | − | 0.944195i | −0.0594787 | − | 0.0343401i | ||||
\(757\) | 0.861232 | − | 1.49170i | 0.0313020 | − | 0.0542167i | −0.849950 | − | 0.526863i | \(-0.823368\pi\) |
0.881252 | + | 0.472647i | \(0.156701\pi\) | |||||||
\(758\) | 21.5929 | + | 37.4000i | 0.784290 | + | 1.35843i | ||||
\(759\) | 43.1185i | 1.56510i | ||||||||
\(760\) | −68.6441 | + | 39.6317i | −2.48998 | + | 1.43759i | ||||
\(761\) | −6.13109 | + | 3.53979i | −0.222252 | + | 0.128317i | −0.606993 | − | 0.794708i | \(-0.707624\pi\) |
0.384741 | + | 0.923025i | \(0.374291\pi\) | |||||||
\(762\) | − | 72.6926i | − | 2.63338i | ||||||
\(763\) | 1.89343 | + | 3.27951i | 0.0685467 | + | 0.118726i | ||||
\(764\) | −1.54524 | + | 2.67643i | −0.0559047 | + | 0.0968299i | ||||
\(765\) | −34.7292 | − | 20.0509i | −1.25564 | − | 0.724942i | ||||
\(766\) | 5.02859 | 0.181690 | ||||||||
\(767\) | 1.58409 | − | 5.17763i | 0.0571983 | − | 0.186953i | ||||
\(768\) | −30.4716 | −1.09955 | ||||||||
\(769\) | 10.8757 | + | 6.27909i | 0.392188 | + | 0.226430i | 0.683108 | − | 0.730318i | \(-0.260628\pi\) |
−0.290920 | + | 0.956747i | \(0.593961\pi\) | |||||||
\(770\) | −4.76627 | + | 8.25543i | −0.171765 | + | 0.297505i | ||||
\(771\) | −7.25144 | − | 12.5599i | −0.261154 | − | 0.452332i | ||||
\(772\) | 4.30256i | 0.154853i | ||||||||
\(773\) | −41.5793 | + | 24.0058i | −1.49550 | + | 0.863430i | −0.999987 | − | 0.00516857i | \(-0.998355\pi\) |
−0.495517 | + | 0.868598i | \(0.665021\pi\) | |||||||
\(774\) | 100.068 | − | 57.7746i | 3.59689 | − | 2.07666i | ||||
\(775\) | 10.4579i | 0.375660i | ||||||||
\(776\) | −6.73627 | − | 11.6676i | −0.241818 | − | 0.418841i | ||||
\(777\) | −1.78919 | + | 3.09896i | −0.0641867 | + | 0.111175i | ||||
\(778\) | −34.2352 | − | 19.7657i | −1.22739 | − | 0.708636i | ||||
\(779\) | −8.67799 | −0.310921 | ||||||||
\(780\) | 12.8118 | + | 13.7445i | 0.458735 | + | 0.492130i | ||||
\(781\) | 10.9617 | 0.392241 | ||||||||
\(782\) | 7.07109 | + | 4.08250i | 0.252862 | + | 0.145990i | ||||
\(783\) | 12.1555 | − | 21.0540i | 0.434403 | − | 0.752409i | ||||
\(784\) | 15.9978 | + | 27.7089i | 0.571349 | + | 0.989605i | ||||
\(785\) | 30.3862i | 1.08453i | ||||||||
\(786\) | −84.9961 | + | 49.0725i | −3.03171 | + | 1.75036i | ||||
\(787\) | −45.3009 | + | 26.1545i | −1.61480 | + | 0.932307i | −0.626568 | + | 0.779367i | \(0.715541\pi\) |
−0.988235 | + | 0.152941i | \(0.951126\pi\) | |||||||
\(788\) | 3.80071i | 0.135395i | ||||||||
\(789\) | 8.12783 | + | 14.0778i | 0.289358 | + | 0.501184i | ||||
\(790\) | 12.3765 | − | 21.4367i | 0.440336 | − | 0.762685i | ||||
\(791\) | 3.58326 | + | 2.06880i | 0.127406 | + | 0.0735580i | ||||
\(792\) | −66.0822 | −2.34813 | ||||||||
\(793\) | −34.2644 | − | 10.4832i | −1.21677 | − | 0.372269i | ||||
\(794\) | −30.6463 | −1.08760 | ||||||||
\(795\) | −13.3783 | − | 7.72396i | −0.474479 | − | 0.273941i | ||||
\(796\) | 0.0916574 | − | 0.158755i | 0.00324871 | − | 0.00562693i | ||||
\(797\) | −1.57178 | − | 2.72241i | −0.0556754 | − | 0.0964326i | 0.836844 | − | 0.547441i | \(-0.184398\pi\) |
−0.892520 | + | 0.451008i | \(0.851065\pi\) | |||||||
\(798\) | 15.3984i | 0.545098i | ||||||||
\(799\) | −3.10780 | + | 1.79429i | −0.109946 | + | 0.0634775i | ||||
\(800\) | −21.4700 | + | 12.3957i | −0.759079 | + | 0.438254i | ||||
\(801\) | − | 96.0139i | − | 3.39248i | ||||||
\(802\) | 4.48579 | + | 7.76962i | 0.158399 | + | 0.274355i | ||||
\(803\) | −17.3049 | + | 29.9730i | −0.610678 | + | 1.05772i | ||||
\(804\) | −6.07103 | − | 3.50511i | −0.214109 | − | 0.123616i | ||||
\(805\) | −5.22068 | −0.184005 | ||||||||
\(806\) | −1.26216 | − | 5.47201i | −0.0444577 | − | 0.192743i | ||||
\(807\) | −51.0093 | −1.79561 | ||||||||
\(808\) | −35.6715 | − | 20.5950i | −1.25492 | − | 0.724529i | ||||
\(809\) | 27.3312 | − | 47.3391i | 0.960915 | − | 1.66435i | 0.240704 | − | 0.970599i | \(-0.422622\pi\) |
0.720211 | − | 0.693755i | \(-0.244045\pi\) | |||||||
\(810\) | −47.9706 | − | 83.0875i | −1.68551 | − | 2.91940i | ||||
\(811\) | − | 33.0229i | − | 1.15959i | −0.814762 | − | 0.579796i | \(-0.803132\pi\) | ||
0.814762 | − | 0.579796i | \(-0.196868\pi\) | |||||||
\(812\) | −0.301685 | + | 0.174178i | −0.0105871 | + | 0.00611245i | ||||
\(813\) | 70.7115 | − | 40.8253i | 2.47996 | − | 1.43181i | ||||
\(814\) | − | 18.6804i | − | 0.654747i | ||||||
\(815\) | −7.94903 | − | 13.7681i | −0.278442 | − | 0.482277i | ||||
\(816\) | −11.0846 | + | 19.1991i | −0.388038 | + | 0.672102i | ||||
\(817\) | −78.9903 | − | 45.6051i | −2.76352 | − | 1.59552i | ||||
\(818\) | −22.6212 | −0.790931 | ||||||||
\(819\) | −9.07675 | + | 2.09362i | −0.317167 | + | 0.0731571i | ||||
\(820\) | −1.76697 | −0.0617051 | ||||||||
\(821\) | 33.6432 | + | 19.4239i | 1.17415 | + | 0.677899i | 0.954655 | − | 0.297714i | \(-0.0962242\pi\) |
0.219500 | + | 0.975613i | \(0.429558\pi\) | |||||||
\(822\) | 0.490237 | − | 0.849116i | 0.0170990 | − | 0.0296163i | ||||
\(823\) | 11.9488 | + | 20.6959i | 0.416508 | + | 0.721413i | 0.995585 | − | 0.0938597i | \(-0.0299205\pi\) |
−0.579078 | + | 0.815272i | \(0.696587\pi\) | |||||||
\(824\) | − | 14.3544i | − | 0.500059i | ||||||
\(825\) | −113.604 | + | 65.5894i | −3.95519 | + | 2.28353i | ||||
\(826\) | 0.782451 | − | 0.451748i | 0.0272250 | − | 0.0157183i | ||||
\(827\) | 22.3088i | 0.775752i | 0.921712 | + | 0.387876i | \(0.126791\pi\) | ||||
−0.921712 | + | 0.387876i | \(0.873209\pi\) | |||||||
\(828\) | 4.89525 | + | 8.47883i | 0.170122 | + | 0.294660i | ||||
\(829\) | −3.19511 | + | 5.53410i | −0.110971 | + | 0.192207i | −0.916162 | − | 0.400808i | \(-0.868729\pi\) |
0.805191 | + | 0.593015i | \(0.202063\pi\) | |||||||
\(830\) | 66.3356 | + | 38.2989i | 2.30254 | + | 1.32937i | ||||
\(831\) | 78.5441 | 2.72467 | ||||||||
\(832\) | −14.8974 | + | 13.8865i | −0.516476 | + | 0.481428i | ||||
\(833\) | 10.4477 | 0.361990 | ||||||||
\(834\) | −25.5218 | − | 14.7350i | −0.883749 | − | 0.510233i | ||||
\(835\) | 16.1719 | − | 28.0106i | 0.559653 | − | 0.969348i | ||||
\(836\) | −7.05559 | − | 12.2206i | −0.244023 | − | 0.422660i | ||||
\(837\) | 11.4798i | 0.396802i | ||||||||
\(838\) | 10.1708 | − | 5.87212i | 0.351345 | − | 0.202849i | ||||
\(839\) | 6.48916 | − | 3.74652i | 0.224031 | − | 0.129344i | −0.383785 | − | 0.923423i | \(-0.625379\pi\) |
0.607815 | + | 0.794078i | \(0.292046\pi\) | |||||||
\(840\) | − | 11.5900i | − | 0.399892i | ||||||
\(841\) | 12.2576 | + | 21.2309i | 0.422677 | + | 0.732098i | ||||
\(842\) | 7.81878 | − | 13.5425i | 0.269453 | − | 0.466706i | ||||
\(843\) | 19.4798 | + | 11.2467i | 0.670920 | + | 0.387356i | ||||
\(844\) | 1.82219 | 0.0627223 | ||||||||
\(845\) | 50.9856 | + | 3.58576i | 1.75396 | + | 0.123354i | ||||
\(846\) | −24.5123 | −0.842752 | ||||||||
\(847\) | 1.75302 | + | 1.01211i | 0.0602344 | + | 0.0347764i | ||||
\(848\) | −2.94775 | + | 5.10566i | −0.101226 | + | 0.175329i | ||||
\(849\) | −10.7234 | − | 18.5735i | −0.368027 | − | 0.637442i | ||||
\(850\) | 24.8403i | 0.852014i | ||||||||
\(851\) | 8.86002 | − | 5.11534i | 0.303718 | − | 0.175351i | ||||
\(852\) | 3.12237 | − | 1.80270i | 0.106971 | − | 0.0617595i | ||||
\(853\) | 7.20149i | 0.246574i | 0.992371 | + | 0.123287i | \(0.0393436\pi\) | ||||
−0.992371 | + | 0.123287i | \(0.960656\pi\) | |||||||
\(854\) | −2.98957 | − | 5.17809i | −0.102301 | − | 0.177191i | ||||
\(855\) | −108.112 | + | 187.255i | −3.69734 | + | 6.40398i | ||||
\(856\) | 9.28770 | + | 5.36226i | 0.317447 | + | 0.183278i | ||||
\(857\) | 19.6227 | 0.670300 | 0.335150 | − | 0.942165i | \(-0.391213\pi\) | ||||
0.335150 | + | 0.942165i | \(0.391213\pi\) | |||||||
\(858\) | 51.5263 | − | 48.0298i | 1.75908 | − | 1.63971i | ||||
\(859\) | −29.6441 | −1.01145 | −0.505723 | − | 0.862696i | \(-0.668774\pi\) | ||||
−0.505723 | + | 0.862696i | \(0.668774\pi\) | |||||||
\(860\) | −16.0836 | − | 9.28585i | −0.548445 | − | 0.316645i | ||||
\(861\) | 0.634453 | − | 1.09890i | 0.0216221 | − | 0.0374506i | ||||
\(862\) | −21.4815 | − | 37.2071i | −0.731664 | − | 1.26728i | ||||
\(863\) | 4.20129i | 0.143014i | 0.997440 | + | 0.0715068i | \(0.0227808\pi\) | ||||
−0.997440 | + | 0.0715068i | \(0.977219\pi\) | |||||||
\(864\) | −23.5680 | + | 13.6070i | −0.801798 | + | 0.462918i | ||||
\(865\) | 21.5753 | − | 12.4565i | 0.733582 | − | 0.423534i | ||||
\(866\) | − | 49.1341i | − | 1.66964i | ||||||
\(867\) | −22.8375 | − | 39.5557i | −0.775602 | − | 1.34338i | ||||
\(868\) | 0.0822481 | − | 0.142458i | 0.00279168 | − | 0.00483533i | ||||
\(869\) | −14.1074 | − | 8.14492i | −0.478561 | − | 0.276298i | ||||
\(870\) | −40.3642 | −1.36848 | ||||||||
\(871\) | −18.5813 | + | 4.28591i | −0.629602 | + | 0.145223i | ||||
\(872\) | 24.0355 | 0.813944 | ||||||||
\(873\) | −31.8281 | − | 18.3759i | −1.07722 | − | 0.621931i | ||||
\(874\) | 22.0122 | − | 38.1263i | 0.744575 | − | 1.28964i | ||||
\(875\) | −4.14458 | − | 7.17861i | −0.140112 | − | 0.242681i | ||||
\(876\) | 11.3835i | 0.384612i | ||||||||
\(877\) | 11.1460 | − | 6.43515i | 0.376374 | − | 0.217300i | −0.299866 | − | 0.953981i | \(-0.596942\pi\) |
0.676239 | + | 0.736682i | \(0.263608\pi\) | |||||||
\(878\) | −28.3100 | + | 16.3448i | −0.955417 | + | 0.551610i | ||||
\(879\) | − | 86.7460i | − | 2.92587i | ||||||
\(880\) | 36.9991 | + | 64.0843i | 1.24724 | + | 2.16028i | ||||
\(881\) | 9.72849 | − | 16.8502i | 0.327761 | − | 0.567699i | −0.654306 | − | 0.756230i | \(-0.727039\pi\) |
0.982067 | + | 0.188531i | \(0.0603725\pi\) | |||||||
\(882\) | 61.8033 | + | 35.6822i | 2.08103 | + | 1.20148i | ||||
\(883\) | −31.3682 | −1.05562 | −0.527812 | − | 0.849361i | \(-0.676988\pi\) | ||||
−0.527812 | + | 0.849361i | \(0.676988\pi\) | |||||||
\(884\) | −0.526274 | − | 2.28163i | −0.0177005 | − | 0.0767394i | ||||
\(885\) | 18.3775 | 0.617754 | ||||||||
\(886\) | −27.0425 | − | 15.6130i | −0.908512 | − | 0.524530i | ||||
\(887\) | 17.5355 | − | 30.3723i | 0.588783 | − | 1.01980i | −0.405609 | − | 0.914047i | \(-0.632941\pi\) |
0.994392 | − | 0.105756i | \(-0.0337261\pi\) | |||||||
\(888\) | 11.3561 | + | 19.6693i | 0.381086 | + | 0.660060i | ||||
\(889\) | − | 5.79219i | − | 0.194264i | ||||||
\(890\) | −76.1312 | + | 43.9544i | −2.55192 | + | 1.47335i | ||||
\(891\) | −54.6795 | + | 31.5692i | −1.83183 | + | 1.05761i | ||||
\(892\) | 2.93462i | 0.0982582i | ||||||||
\(893\) | 9.67456 | + | 16.7568i | 0.323747 | + | 0.560746i | ||||
\(894\) | 48.9343 | − | 84.7567i | 1.63661 | − | 2.83469i | ||||
\(895\) | 32.4090 | + | 18.7113i | 1.08331 | + | 0.625451i | ||||
\(896\) | −5.22978 | −0.174715 | ||||||||
\(897\) | 36.8900 | + | 11.2865i | 1.23172 | + | 0.376844i | ||||
\(898\) | −48.3919 | −1.61486 | ||||||||
\(899\) | 1.83400 | + | 1.05886i | 0.0611672 | + | 0.0353149i | ||||
\(900\) | −14.8928 | + | 25.7950i | −0.496426 | + | 0.859834i | ||||
\(901\) | 0.962546 | + | 1.66718i | 0.0320670 | + | 0.0555418i | ||||
\(902\) | 6.62414i | 0.220560i | ||||||||
\(903\) | 11.5500 | − | 6.66842i | 0.384362 | − | 0.221911i | ||||
\(904\) | 22.7432 | − | 13.1308i | 0.756429 | − | 0.436724i | ||||
\(905\) | − | 43.3655i | − | 1.44152i | ||||||
\(906\) | −24.9063 | − | 43.1390i | −0.827457 | − | 1.43320i | ||||
\(907\) | −22.1205 | + | 38.3139i | −0.734500 | + | 1.27219i | 0.220443 | + | 0.975400i | \(0.429250\pi\) |
−0.954943 | + | 0.296791i | \(0.904084\pi\) | |||||||
\(908\) | −2.65120 | − | 1.53067i | −0.0879833 | − | 0.0507972i | ||||
\(909\) | −112.362 | −3.72683 | ||||||||
\(910\) | 5.81533 | + | 6.23868i | 0.192776 | + | 0.206810i | ||||
\(911\) | 55.3587 | 1.83411 | 0.917057 | − | 0.398756i | \(-0.130558\pi\) | ||||
0.917057 | + | 0.398756i | \(0.130558\pi\) | |||||||
\(912\) | 103.519 | + | 59.7665i | 3.42784 | + | 1.97907i | ||||
\(913\) | 25.2043 | − | 43.6551i | 0.834141 | − | 1.44477i | ||||
\(914\) | −11.3957 | − | 19.7379i | −0.376937 | − | 0.652873i | ||||
\(915\) | − | 121.618i | − | 4.02058i | ||||||
\(916\) | 7.34655 | − | 4.24153i | 0.242737 | − | 0.140144i | ||||
\(917\) | −6.77254 | + | 3.91013i | −0.223649 | + | 0.129124i | ||||
\(918\) | 27.2676i | 0.899964i | ||||||||
\(919\) | −5.39811 | − | 9.34979i | −0.178067 | − | 0.308421i | 0.763151 | − | 0.646220i | \(-0.223651\pi\) |
−0.941218 | + | 0.337799i | \(0.890318\pi\) | |||||||
\(920\) | −16.5680 | + | 28.6967i | −0.546232 | + | 0.946101i | ||||
\(921\) | 55.2679 | + | 31.9089i | 1.82114 | + | 1.05143i | ||||
\(922\) | 49.5201 | 1.63086 | ||||||||
\(923\) | 2.86928 | − | 9.37828i | 0.0944435 | − | 0.308690i | ||||
\(924\) | 2.06335 | 0.0678793 | ||||||||
\(925\) | 26.9547 | + | 15.5623i | 0.886266 | + | 0.511686i | ||||
\(926\) | −14.3180 | + | 24.7996i | −0.470520 | + | 0.814964i | ||||
\(927\) | −19.5788 | − | 33.9114i | −0.643051 | − | 1.11380i | ||||
\(928\) | 5.02022i | 0.164797i | ||||||||
\(929\) | −12.0761 | + | 6.97215i | −0.396205 | + | 0.228749i | −0.684845 | − | 0.728689i | \(-0.740130\pi\) |
0.288640 | + | 0.957438i | \(0.406797\pi\) | |||||||
\(930\) | 16.5067 | − | 9.53013i | 0.541275 | − | 0.312505i | ||||
\(931\) | − | 56.3323i | − | 1.84622i | ||||||
\(932\) | 0.169262 | + | 0.293171i | 0.00554437 | + | 0.00960314i | ||||
\(933\) | −19.2279 | + | 33.3037i | −0.629492 | + | 1.09031i | ||||
\(934\) | −39.6986 | − | 22.9200i | −1.29898 | − | 0.749966i | ||||
\(935\) | 24.1630 | 0.790214 | ||||||||
\(936\) | −17.2974 | + | 56.5366i | −0.565382 | + | 1.84796i | ||||
\(937\) | −33.0062 | −1.07827 | −0.539133 | − | 0.842221i | \(-0.681248\pi\) | ||||
−0.539133 | + | 0.842221i | \(0.681248\pi\) | |||||||
\(938\) | −2.75567 | − | 1.59099i | −0.0899759 | − | 0.0519476i | ||||
\(939\) | 12.3431 | − | 21.3789i | 0.402802 | − | 0.697673i | ||||
\(940\) | 1.96988 | + | 3.41193i | 0.0642504 | + | 0.111285i | ||||
\(941\) | 22.1716i | 0.722772i | 0.932416 | + | 0.361386i | \(0.117696\pi\) | ||||
−0.932416 | + | 0.361386i | \(0.882304\pi\) | |||||||
\(942\) | 32.4477 | − | 18.7337i | 1.05720 | − | 0.610377i | ||||
\(943\) | −3.14180 | + | 1.81392i | −0.102311 | + | 0.0590693i | ||||
\(944\) | − | 7.01356i | − | 0.228272i | ||||||
\(945\) | −8.71741 | − | 15.0990i | −0.283577 | − | 0.491171i | ||||
\(946\) | −34.8116 | + | 60.2954i | −1.13182 | + | 1.96037i | ||||
\(947\) | 29.2080 | + | 16.8632i | 0.949132 | + | 0.547982i | 0.892811 | − | 0.450431i | \(-0.148730\pi\) |
0.0563208 | + | 0.998413i | \(0.482063\pi\) | |||||||
\(948\) | −5.35787 | −0.174016 | ||||||||
\(949\) | 21.1138 | + | 22.6508i | 0.685382 | + | 0.735277i | ||||
\(950\) | 133.935 | 4.34543 | ||||||||
\(951\) | 51.6352 | + | 29.8116i | 1.67439 | + | 0.966707i | ||||
\(952\) | −0.722161 | + | 1.25082i | −0.0234054 | + | 0.0405393i | ||||
\(953\) | −4.28453 | − | 7.42102i | −0.138790 | − | 0.240390i | 0.788249 | − | 0.615356i | \(-0.210988\pi\) |
−0.927039 | + | 0.374966i | \(0.877654\pi\) | |||||||
\(954\) | 13.1496i | 0.425735i | ||||||||
\(955\) | −24.7105 | + | 14.2666i | −0.799613 | + | 0.461657i | ||||
\(956\) | −3.89026 | + | 2.24604i | −0.125820 | + | 0.0726422i | ||||
\(957\) | 26.5635i | 0.858676i | ||||||||
\(958\) | −16.2429 | − | 28.1335i | −0.524784 | − | 0.908953i | ||||
\(959\) | 0.0390624 | − | 0.0676581i | 0.00126139 | − | 0.00218479i | ||||
\(960\) | −59.8631 | − | 34.5620i | −1.93207 | − | 1.11548i | ||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | −15.9820 | − | 4.88969i | −0.515281 | − | 0.157650i | ||||
\(963\) | 29.2555 | 0.942746 | ||||||||
\(964\) | −7.33438 | − | 4.23451i | −0.236224 | − | 0.136384i | ||||
\(965\) | −19.8620 | + | 34.4020i | −0.639381 | + | 1.10744i | ||||
\(966\) | 3.21865 | + | 5.57487i | 0.103559 | + | 0.179369i | ||||
\(967\) | − | 38.8918i | − | 1.25068i | −0.780353 | − | 0.625339i | \(-0.784961\pi\) | ||
0.780353 | − | 0.625339i | \(-0.215039\pi\) | |||||||
\(968\) | 11.1265 | − | 6.42391i | 0.357621 | − | 0.206472i | ||||
\(969\) | 33.8025 | − | 19.5159i | 1.08589 | − | 0.626940i | ||||
\(970\) | 33.6494i | 1.08042i | ||||||||
\(971\) | 13.4253 | + | 23.2534i | 0.430840 | + | 0.746236i | 0.996946 | − | 0.0780960i | \(-0.0248841\pi\) |
−0.566106 | + | 0.824332i | \(0.691551\pi\) | |||||||
\(972\) | −3.05047 | + | 5.28356i | −0.0978438 | + | 0.169470i | ||||
\(973\) | −2.03360 | − | 1.17410i | −0.0651941 | − | 0.0376398i | ||||
\(974\) | −6.88442 | −0.220591 | ||||||||
\(975\) | 26.3785 | + | 114.362i | 0.844790 | + | 3.66253i | ||||
\(976\) | −46.4142 | −1.48568 | ||||||||
\(977\) | 28.7656 | + | 16.6078i | 0.920292 | + | 0.531331i | 0.883728 | − | 0.468000i | \(-0.155025\pi\) |
0.0365639 | + | 0.999331i | \(0.488359\pi\) | |||||||
\(978\) | −9.80148 | + | 16.9767i | −0.313417 | + | 0.542854i | ||||
\(979\) | 28.9262 | + | 50.1016i | 0.924484 | + | 1.60125i | ||||
\(980\) | − | 11.4701i | − | 0.366398i | ||||||
\(981\) | 56.7823 | − | 32.7833i | 1.81292 | − | 1.04669i | ||||
\(982\) | −4.46000 | + | 2.57498i | −0.142324 | + | 0.0821710i | ||||
\(983\) | 10.7635i | 0.343301i | 0.985158 | + | 0.171651i | \(0.0549100\pi\) | ||||
−0.985158 | + | 0.171651i | \(0.945090\pi\) | |||||||
\(984\) | −4.02692 | − | 6.97483i | −0.128374 | − | 0.222349i | ||||
\(985\) | −17.5453 | + | 30.3893i | −0.559039 | + | 0.968285i | ||||
\(986\) | 4.35621 | + | 2.51506i | 0.138730 | + | 0.0800958i | ||||
\(987\) | −2.82925 | −0.0900560 | ||||||||
\(988\) | −12.3022 | + | 2.83760i | −0.391385 | + | 0.0902759i | ||||
\(989\) | −38.1304 | −1.21248 | ||||||||
\(990\) | 142.937 | + | 82.5244i | 4.54282 | + | 2.62280i | ||||
\(991\) | −27.4734 | + | 47.5852i | −0.872720 | + | 1.51160i | −0.0135477 | + | 0.999908i | \(0.504313\pi\) |
−0.859172 | + | 0.511687i | \(0.829021\pi\) | |||||||
\(992\) | −1.18529 | − | 2.05298i | −0.0376330 | − | 0.0651823i | ||||
\(993\) | 83.3450i | 2.64487i | ||||||||
\(994\) | 1.41726 | − | 0.818256i | 0.0449528 | − | 0.0259535i | ||||
\(995\) | 1.46573 | − | 0.846240i | 0.0464668 | − | 0.0268276i | ||||
\(996\) | − | 16.5798i | − | 0.525352i | ||||||
\(997\) | −7.56205 | − | 13.0979i | −0.239493 | − | 0.414813i | 0.721076 | − | 0.692856i | \(-0.243648\pi\) |
−0.960569 | + | 0.278042i | \(0.910314\pi\) | |||||||
\(998\) | −17.4526 | + | 30.2288i | −0.552452 | + | 0.956875i | ||||
\(999\) | 29.5887 | + | 17.0830i | 0.936144 | + | 0.540483i |
(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 | 403.2.r.a.342.26 | yes | 68 | |
13.6 | odd | 12 | 5239.2.a.r.1.7 | 34 | |||
13.7 | odd | 12 | 5239.2.a.q.1.28 | 34 | |||
13.10 | even | 6 | inner | 403.2.r.a.218.26 | ✓ | 68 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.r.a.218.26 | ✓ | 68 | 13.10 | even | 6 | inner | |
403.2.r.a.342.26 | yes | 68 | 1.1 | even | 1 | trivial | |
5239.2.a.q.1.28 | 34 | 13.7 | odd | 12 | |||
5239.2.a.r.1.7 | 34 | 13.6 | odd | 12 |