Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1122,2,Mod(1121,1122)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1122, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1122.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1122.h (of order \(2\), degree \(1\), 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: | \(8.95921510679\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.18 | ||
Character | \(\chi\) | \(=\) | 1122.1121 |
Dual form | 1122.2.h.g.1121.17 |
$q$-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 \(\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times\).
\(n\) | \(409\) | \(749\) | \(1057\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.524078 | + | 1.65086i | 0.302577 | + | 0.953125i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.81008 | −1.70392 | −0.851960 | − | 0.523607i | \(-0.824586\pi\) | ||||
−0.851960 | + | 0.523607i | \(0.824586\pi\) | |||||||
\(6\) | −0.524078 | − | 1.65086i | −0.213954 | − | 0.673961i | ||||
\(7\) | −0.269313 | −0.101791 | −0.0508953 | − | 0.998704i | \(-0.516207\pi\) | ||||
−0.0508953 | + | 0.998704i | \(0.516207\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.45068 | + | 1.73036i | −0.816895 | + | 0.576787i | ||||
\(10\) | 3.81008 | 1.20485 | ||||||||
\(11\) | −3.18733 | + | 0.917024i | −0.961016 | + | 0.276493i | ||||
\(12\) | 0.524078 | + | 1.65086i | 0.151288 | + | 0.476563i | ||||
\(13\) | 5.86421i | 1.62644i | 0.581957 | + | 0.813220i | \(0.302287\pi\) | ||||
−0.581957 | + | 0.813220i | \(0.697713\pi\) | |||||||
\(14\) | 0.269313 | 0.0719769 | ||||||||
\(15\) | −1.99678 | − | 6.28991i | −0.515567 | − | 1.62405i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.56790 | + | 2.06642i | 0.865343 | + | 0.501180i | ||||
\(18\) | 2.45068 | − | 1.73036i | 0.577632 | − | 0.407850i | ||||
\(19\) | − | 0.208190i | − | 0.0477620i | −0.999715 | − | 0.0238810i | \(-0.992398\pi\) | ||
0.999715 | − | 0.0238810i | \(-0.00760228\pi\) | |||||||
\(20\) | −3.81008 | −0.851960 | ||||||||
\(21\) | −0.141141 | − | 0.444598i | −0.0307995 | − | 0.0970192i | ||||
\(22\) | 3.18733 | − | 0.917024i | 0.679541 | − | 0.195510i | ||||
\(23\) | −1.63790 | −0.341526 | −0.170763 | − | 0.985312i | \(-0.554623\pi\) | ||||
−0.170763 | + | 0.985312i | \(0.554623\pi\) | |||||||
\(24\) | −0.524078 | − | 1.65086i | −0.106977 | − | 0.336981i | ||||
\(25\) | 9.51672 | 1.90334 | ||||||||
\(26\) | − | 5.86421i | − | 1.15007i | ||||||
\(27\) | −4.14094 | − | 3.13889i | −0.796923 | − | 0.604080i | ||||
\(28\) | −0.269313 | −0.0508953 | ||||||||
\(29\) | − | 3.84487i | − | 0.713975i | −0.934109 | − | 0.356987i | \(-0.883804\pi\) | ||
0.934109 | − | 0.356987i | \(-0.116196\pi\) | |||||||
\(30\) | 1.99678 | + | 6.28991i | 0.364561 | + | 1.14838i | ||||
\(31\) | − | 5.05736i | − | 0.908329i | −0.890918 | − | 0.454165i | \(-0.849938\pi\) | ||
0.890918 | − | 0.454165i | \(-0.150062\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.18429 | − | 4.78124i | −0.554314 | − | 0.832308i | ||||
\(34\) | −3.56790 | − | 2.06642i | −0.611890 | − | 0.354388i | ||||
\(35\) | 1.02610 | 0.173443 | ||||||||
\(36\) | −2.45068 | + | 1.73036i | −0.408447 | + | 0.288394i | ||||
\(37\) | − | 3.41040i | − | 0.560667i | −0.959903 | − | 0.280333i | \(-0.909555\pi\) | ||
0.959903 | − | 0.280333i | \(-0.0904450\pi\) | |||||||
\(38\) | 0.208190i | 0.0337728i | ||||||||
\(39\) | −9.68100 | + | 3.07331i | −1.55020 | + | 0.492123i | ||||
\(40\) | 3.81008 | 0.602427 | ||||||||
\(41\) | − | 5.05441i | − | 0.789366i | −0.918817 | − | 0.394683i | \(-0.870854\pi\) | ||
0.918817 | − | 0.394683i | \(-0.129146\pi\) | |||||||
\(42\) | 0.141141 | + | 0.444598i | 0.0217785 | + | 0.0686029i | ||||
\(43\) | − | 6.12589i | − | 0.934190i | −0.884207 | − | 0.467095i | \(-0.845301\pi\) | ||
0.884207 | − | 0.467095i | \(-0.154699\pi\) | |||||||
\(44\) | −3.18733 | + | 0.917024i | −0.480508 | + | 0.138247i | ||||
\(45\) | 9.33730 | − | 6.59282i | 1.39192 | − | 0.982799i | ||||
\(46\) | 1.63790 | 0.241495 | ||||||||
\(47\) | 2.90273i | 0.423406i | 0.977334 | + | 0.211703i | \(0.0679010\pi\) | ||||
−0.977334 | + | 0.211703i | \(0.932099\pi\) | |||||||
\(48\) | 0.524078 | + | 1.65086i | 0.0756442 | + | 0.238281i | ||||
\(49\) | −6.92747 | −0.989639 | ||||||||
\(50\) | −9.51672 | −1.34587 | ||||||||
\(51\) | −1.54151 | + | 6.97307i | −0.215854 | + | 0.976426i | ||||
\(52\) | 5.86421i | 0.813220i | ||||||||
\(53\) | − | 3.84226i | − | 0.527775i | −0.964554 | − | 0.263887i | \(-0.914995\pi\) | ||
0.964554 | − | 0.263887i | \(-0.0850047\pi\) | |||||||
\(54\) | 4.14094 | + | 3.13889i | 0.563510 | + | 0.427149i | ||||
\(55\) | 12.1440 | − | 3.49393i | 1.63749 | − | 0.471122i | ||||
\(56\) | 0.269313 | 0.0359884 | ||||||||
\(57\) | 0.343692 | − | 0.109108i | 0.0455232 | − | 0.0144517i | ||||
\(58\) | 3.84487i | 0.504856i | ||||||||
\(59\) | − | 9.06325i | − | 1.17993i | −0.807427 | − | 0.589967i | \(-0.799141\pi\) | ||
0.807427 | − | 0.589967i | \(-0.200859\pi\) | |||||||
\(60\) | −1.99678 | − | 6.28991i | −0.257783 | − | 0.812024i | ||||
\(61\) | −1.75411 | −0.224591 | −0.112295 | − | 0.993675i | \(-0.535820\pi\) | ||||
−0.112295 | + | 0.993675i | \(0.535820\pi\) | |||||||
\(62\) | 5.05736i | 0.642286i | ||||||||
\(63\) | 0.660000 | − | 0.466008i | 0.0831522 | − | 0.0587115i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | − | 22.3431i | − | 2.77132i | ||||||
\(66\) | 3.18429 | + | 4.78124i | 0.391959 | + | 0.588531i | ||||
\(67\) | −11.2937 | −1.37974 | −0.689872 | − | 0.723932i | \(-0.742333\pi\) | ||||
−0.689872 | + | 0.723932i | \(0.742333\pi\) | |||||||
\(68\) | 3.56790 | + | 2.06642i | 0.432672 | + | 0.250590i | ||||
\(69\) | −0.858388 | − | 2.70395i | −0.103338 | − | 0.325517i | ||||
\(70\) | −1.02610 | −0.122643 | ||||||||
\(71\) | −5.55374 | −0.659108 | −0.329554 | − | 0.944137i | \(-0.606898\pi\) | ||||
−0.329554 | + | 0.944137i | \(0.606898\pi\) | |||||||
\(72\) | 2.45068 | − | 1.73036i | 0.288816 | − | 0.203925i | ||||
\(73\) | −0.116536 | −0.0136395 | −0.00681973 | − | 0.999977i | \(-0.502171\pi\) | ||||
−0.00681973 | + | 0.999977i | \(0.502171\pi\) | |||||||
\(74\) | 3.41040i | 0.396451i | ||||||||
\(75\) | 4.98751 | + | 15.7108i | 0.575908 | + | 1.81412i | ||||
\(76\) | − | 0.208190i | − | 0.0238810i | ||||||
\(77\) | 0.858388 | − | 0.246966i | 0.0978224 | − | 0.0281444i | ||||
\(78\) | 9.68100 | − | 3.07331i | 1.09616 | − | 0.347983i | ||||
\(79\) | 12.9766 | 1.45998 | 0.729988 | − | 0.683460i | \(-0.239526\pi\) | ||||
0.729988 | + | 0.683460i | \(0.239526\pi\) | |||||||
\(80\) | −3.81008 | −0.425980 | ||||||||
\(81\) | 3.01170 | − | 8.48114i | 0.334633 | − | 0.942348i | ||||
\(82\) | 5.05441i | 0.558166i | ||||||||
\(83\) | 17.3693 | 1.90653 | 0.953264 | − | 0.302139i | \(-0.0977007\pi\) | ||||
0.953264 | + | 0.302139i | \(0.0977007\pi\) | |||||||
\(84\) | −0.141141 | − | 0.444598i | −0.0153997 | − | 0.0485096i | ||||
\(85\) | −13.5940 | − | 7.87322i | −1.47448 | − | 0.853971i | ||||
\(86\) | 6.12589i | 0.660572i | ||||||||
\(87\) | 6.34735 | − | 2.01501i | 0.680507 | − | 0.216032i | ||||
\(88\) | 3.18733 | − | 0.917024i | 0.339770 | − | 0.0977551i | ||||
\(89\) | 11.6319i | 1.23298i | 0.787362 | + | 0.616491i | \(0.211446\pi\) | ||||
−0.787362 | + | 0.616491i | \(0.788554\pi\) | |||||||
\(90\) | −9.33730 | + | 6.59282i | −0.984238 | + | 0.694944i | ||||
\(91\) | − | 1.57931i | − | 0.165556i | ||||||
\(92\) | −1.63790 | −0.170763 | ||||||||
\(93\) | 8.34900 | − | 2.65045i | 0.865751 | − | 0.274839i | ||||
\(94\) | − | 2.90273i | − | 0.299393i | ||||||
\(95\) | 0.793220i | 0.0813826i | ||||||||
\(96\) | −0.524078 | − | 1.65086i | −0.0534885 | − | 0.168490i | ||||
\(97\) | 12.7636i | 1.29595i | 0.761663 | + | 0.647974i | \(0.224383\pi\) | ||||
−0.761663 | + | 0.647974i | \(0.775617\pi\) | |||||||
\(98\) | 6.92747 | 0.699780 | ||||||||
\(99\) | 6.22435 | − | 7.76257i | 0.625571 | − | 0.780167i | ||||
\(100\) | 9.51672 | 0.951672 | ||||||||
\(101\) | −3.49705 | −0.347970 | −0.173985 | − | 0.984748i | \(-0.555664\pi\) | ||||
−0.173985 | + | 0.984748i | \(0.555664\pi\) | |||||||
\(102\) | 1.54151 | − | 6.97307i | 0.152632 | − | 0.690437i | ||||
\(103\) | 0.0298399 | 0.00294022 | 0.00147011 | − | 0.999999i | \(-0.499532\pi\) | ||||
0.00147011 | + | 0.999999i | \(0.499532\pi\) | |||||||
\(104\) | − | 5.86421i | − | 0.575033i | ||||||
\(105\) | 0.537759 | + | 1.69395i | 0.0524799 | + | 0.165313i | ||||
\(106\) | 3.84226i | 0.373193i | ||||||||
\(107\) | 14.6035i | 1.41177i | 0.708325 | + | 0.705886i | \(0.249451\pi\) | ||||
−0.708325 | + | 0.705886i | \(0.750549\pi\) | |||||||
\(108\) | −4.14094 | − | 3.13889i | −0.398462 | − | 0.302040i | ||||
\(109\) | −7.02399 | −0.672776 | −0.336388 | − | 0.941724i | \(-0.609205\pi\) | ||||
−0.336388 | + | 0.941724i | \(0.609205\pi\) | |||||||
\(110\) | −12.1440 | + | 3.49393i | −1.15788 | + | 0.333134i | ||||
\(111\) | 5.63010 | − | 1.78732i | 0.534385 | − | 0.169645i | ||||
\(112\) | −0.269313 | −0.0254477 | ||||||||
\(113\) | 3.62351 | 0.340871 | 0.170436 | − | 0.985369i | \(-0.445482\pi\) | ||||
0.170436 | + | 0.985369i | \(0.445482\pi\) | |||||||
\(114\) | −0.343692 | + | 0.109108i | −0.0321897 | + | 0.0102189i | ||||
\(115\) | 6.24053 | 0.581933 | ||||||||
\(116\) | − | 3.84487i | − | 0.356987i | ||||||
\(117\) | −10.1472 | − | 14.3713i | −0.938109 | − | 1.32863i | ||||
\(118\) | 9.06325i | 0.834340i | ||||||||
\(119\) | −0.960881 | − | 0.556513i | −0.0880838 | − | 0.0510154i | ||||
\(120\) | 1.99678 | + | 6.28991i | 0.182280 | + | 0.574188i | ||||
\(121\) | 9.31813 | − | 5.84571i | 0.847103 | − | 0.531428i | ||||
\(122\) | 1.75411 | 0.158809 | ||||||||
\(123\) | 8.34413 | − | 2.64891i | 0.752365 | − | 0.238844i | ||||
\(124\) | − | 5.05736i | − | 0.454165i | ||||||
\(125\) | −17.2091 | −1.53922 | ||||||||
\(126\) | −0.660000 | + | 0.466008i | −0.0587975 | + | 0.0415153i | ||||
\(127\) | − | 12.9055i | − | 1.14518i | −0.819842 | − | 0.572589i | \(-0.805939\pi\) | ||
0.819842 | − | 0.572589i | \(-0.194061\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.1130 | − | 3.21045i | 0.890400 | − | 0.282664i | ||||
\(130\) | 22.3431i | 1.95962i | ||||||||
\(131\) | 18.3231i | 1.60090i | 0.599401 | + | 0.800449i | \(0.295406\pi\) | ||||
−0.599401 | + | 0.800449i | \(0.704594\pi\) | |||||||
\(132\) | −3.18429 | − | 4.78124i | −0.277157 | − | 0.416154i | ||||
\(133\) | 0.0560682i | 0.00486173i | ||||||||
\(134\) | 11.2937 | 0.975626 | ||||||||
\(135\) | 15.7773 | + | 11.9594i | 1.35789 | + | 1.02930i | ||||
\(136\) | −3.56790 | − | 2.06642i | −0.305945 | − | 0.177194i | ||||
\(137\) | − | 18.3288i | − | 1.56593i | −0.622065 | − | 0.782965i | \(-0.713706\pi\) | ||
0.622065 | − | 0.782965i | \(-0.286294\pi\) | |||||||
\(138\) | 0.858388 | + | 2.70395i | 0.0730709 | + | 0.230175i | ||||
\(139\) | −14.6357 | −1.24138 | −0.620691 | − | 0.784055i | \(-0.713148\pi\) | ||||
−0.620691 | + | 0.784055i | \(0.713148\pi\) | |||||||
\(140\) | 1.02610 | 0.0867216 | ||||||||
\(141\) | −4.79200 | + | 1.52126i | −0.403559 | + | 0.128113i | ||||
\(142\) | 5.55374 | 0.466059 | ||||||||
\(143\) | −5.37762 | − | 18.6912i | −0.449699 | − | 1.56303i | ||||
\(144\) | −2.45068 | + | 1.73036i | −0.204224 | + | 0.144197i | ||||
\(145\) | 14.6493i | 1.21656i | ||||||||
\(146\) | 0.116536 | 0.00964455 | ||||||||
\(147\) | −3.63054 | − | 11.4363i | −0.299442 | − | 0.943249i | ||||
\(148\) | − | 3.41040i | − | 0.280333i | ||||||
\(149\) | −18.4154 | −1.50865 | −0.754323 | − | 0.656503i | \(-0.772035\pi\) | ||||
−0.754323 | + | 0.656503i | \(0.772035\pi\) | |||||||
\(150\) | −4.98751 | − | 15.7108i | −0.407228 | − | 1.28278i | ||||
\(151\) | − | 18.1694i | − | 1.47861i | −0.673373 | − | 0.739303i | \(-0.735155\pi\) | ||
0.673373 | − | 0.739303i | \(-0.264845\pi\) | |||||||
\(152\) | 0.208190i | 0.0168864i | ||||||||
\(153\) | −12.3194 | + | 1.10962i | −0.995968 | + | 0.0897074i | ||||
\(154\) | −0.858388 | + | 0.246966i | −0.0691709 | + | 0.0199011i | ||||
\(155\) | 19.2690i | 1.54772i | ||||||||
\(156\) | −9.68100 | + | 3.07331i | −0.775100 | + | 0.246061i | ||||
\(157\) | −10.0860 | −0.804947 | −0.402474 | − | 0.915432i | \(-0.631849\pi\) | ||||
−0.402474 | + | 0.915432i | \(0.631849\pi\) | |||||||
\(158\) | −12.9766 | −1.03236 | ||||||||
\(159\) | 6.34303 | − | 2.01364i | 0.503035 | − | 0.159692i | ||||
\(160\) | 3.81008 | 0.301213 | ||||||||
\(161\) | 0.441108 | 0.0347641 | ||||||||
\(162\) | −3.01170 | + | 8.48114i | −0.236622 | + | 0.666341i | ||||
\(163\) | 11.3349i | 0.887815i | 0.896073 | + | 0.443907i | \(0.146408\pi\) | ||||
−0.896073 | + | 0.443907i | \(0.853592\pi\) | |||||||
\(164\) | − | 5.05441i | − | 0.394683i | ||||||
\(165\) | 12.1324 | + | 18.2169i | 0.944506 | + | 1.41819i | ||||
\(166\) | −17.3693 | −1.34812 | ||||||||
\(167\) | − | 16.5010i | − | 1.27689i | −0.769668 | − | 0.638444i | \(-0.779578\pi\) | ||
0.769668 | − | 0.638444i | \(-0.220422\pi\) | |||||||
\(168\) | 0.141141 | + | 0.444598i | 0.0108893 | + | 0.0343015i | ||||
\(169\) | −21.3890 | −1.64530 | ||||||||
\(170\) | 13.5940 | + | 7.87322i | 1.04261 | + | 0.603848i | ||||
\(171\) | 0.360243 | + | 0.510207i | 0.0275485 | + | 0.0390165i | ||||
\(172\) | − | 6.12589i | − | 0.467095i | ||||||
\(173\) | 17.6882i | 1.34481i | 0.740183 | + | 0.672406i | \(0.234739\pi\) | ||||
−0.740183 | + | 0.672406i | \(0.765261\pi\) | |||||||
\(174\) | −6.34735 | + | 2.01501i | −0.481191 | + | 0.152758i | ||||
\(175\) | −2.56297 | −0.193743 | ||||||||
\(176\) | −3.18733 | + | 0.917024i | −0.240254 | + | 0.0691233i | ||||
\(177\) | 14.9622 | − | 4.74985i | 1.12463 | − | 0.357021i | ||||
\(178\) | − | 11.6319i | − | 0.871850i | ||||||
\(179\) | 13.1756i | 0.984787i | 0.870373 | + | 0.492394i | \(0.163878\pi\) | ||||
−0.870373 | + | 0.492394i | \(0.836122\pi\) | |||||||
\(180\) | 9.33730 | − | 6.59282i | 0.695961 | − | 0.491399i | ||||
\(181\) | − | 12.9449i | − | 0.962188i | −0.876669 | − | 0.481094i | \(-0.840239\pi\) | ||
0.876669 | − | 0.481094i | \(-0.159761\pi\) | |||||||
\(182\) | 1.57931i | 0.117066i | ||||||||
\(183\) | −0.919290 | − | 2.89579i | −0.0679559 | − | 0.214063i | ||||
\(184\) | 1.63790 | 0.120748 | ||||||||
\(185\) | 12.9939i | 0.955331i | ||||||||
\(186\) | −8.34900 | + | 2.65045i | −0.612178 | + | 0.194341i | ||||
\(187\) | −13.2670 | − | 3.31451i | −0.970181 | − | 0.242381i | ||||
\(188\) | 2.90273i | 0.211703i | ||||||||
\(189\) | 1.11521 | + | 0.845344i | 0.0811194 | + | 0.0614897i | ||||
\(190\) | − | 0.793220i | − | 0.0575462i | ||||||
\(191\) | 3.19904i | 0.231474i | 0.993280 | + | 0.115737i | \(0.0369230\pi\) | ||||
−0.993280 | + | 0.115737i | \(0.963077\pi\) | |||||||
\(192\) | 0.524078 | + | 1.65086i | 0.0378221 | + | 0.119141i | ||||
\(193\) | 19.3152 | 1.39034 | 0.695170 | − | 0.718845i | \(-0.255329\pi\) | ||||
0.695170 | + | 0.718845i | \(0.255329\pi\) | |||||||
\(194\) | − | 12.7636i | − | 0.916374i | ||||||
\(195\) | 36.8854 | − | 11.7095i | 2.64142 | − | 0.838538i | ||||
\(196\) | −6.92747 | −0.494819 | ||||||||
\(197\) | − | 19.6491i | − | 1.39994i | −0.714172 | − | 0.699971i | \(-0.753196\pi\) | ||
0.714172 | − | 0.699971i | \(-0.246804\pi\) | |||||||
\(198\) | −6.22435 | + | 7.76257i | −0.442346 | + | 0.551662i | ||||
\(199\) | − | 24.6476i | − | 1.74722i | −0.486624 | − | 0.873611i | \(-0.661772\pi\) | ||
0.486624 | − | 0.873611i | \(-0.338228\pi\) | |||||||
\(200\) | −9.51672 | −0.672933 | ||||||||
\(201\) | −5.91878 | − | 18.6443i | −0.417478 | − | 1.31507i | ||||
\(202\) | 3.49705 | 0.246052 | ||||||||
\(203\) | 1.03547i | 0.0726759i | ||||||||
\(204\) | −1.54151 | + | 6.97307i | −0.107927 | + | 0.488213i | ||||
\(205\) | 19.2577i | 1.34502i | ||||||||
\(206\) | −0.0298399 | −0.00207905 | ||||||||
\(207\) | 4.01398 | − | 2.83416i | 0.278991 | − | 0.196988i | ||||
\(208\) | 5.86421i | 0.406610i | ||||||||
\(209\) | 0.190915 | + | 0.663569i | 0.0132059 | + | 0.0459001i | ||||
\(210\) | −0.537759 | − | 1.69395i | −0.0371089 | − | 0.116894i | ||||
\(211\) | 9.47591 | 0.652348 | 0.326174 | − | 0.945310i | \(-0.394240\pi\) | ||||
0.326174 | + | 0.945310i | \(0.394240\pi\) | |||||||
\(212\) | − | 3.84226i | − | 0.263887i | ||||||
\(213\) | −2.91059 | − | 9.16845i | −0.199431 | − | 0.628212i | ||||
\(214\) | − | 14.6035i | − | 0.998274i | ||||||
\(215\) | 23.3401i | 1.59178i | ||||||||
\(216\) | 4.14094 | + | 3.13889i | 0.281755 | + | 0.213575i | ||||
\(217\) | 1.36201i | 0.0924594i | ||||||||
\(218\) | 7.02399 | 0.475724 | ||||||||
\(219\) | −0.0610738 | − | 0.192384i | −0.00412698 | − | 0.0130001i | ||||
\(220\) | 12.1440 | − | 3.49393i | 0.818747 | − | 0.235561i | ||||
\(221\) | −12.1179 | + | 20.9229i | −0.815139 | + | 1.40743i | ||||
\(222\) | −5.63010 | + | 1.78732i | −0.377868 | + | 0.119957i | ||||
\(223\) | −4.37502 | −0.292973 | −0.146486 | − | 0.989213i | \(-0.546796\pi\) | ||||
−0.146486 | + | 0.989213i | \(0.546796\pi\) | |||||||
\(224\) | 0.269313 | 0.0179942 | ||||||||
\(225\) | −23.3225 | + | 16.4674i | −1.55483 | + | 1.09782i | ||||
\(226\) | −3.62351 | −0.241032 | ||||||||
\(227\) | 2.57358i | 0.170815i | 0.996346 | + | 0.0854073i | \(0.0272192\pi\) | ||||
−0.996346 | + | 0.0854073i | \(0.972781\pi\) | |||||||
\(228\) | 0.343692 | − | 0.109108i | 0.0227616 | − | 0.00722584i | ||||
\(229\) | −15.5344 | −1.02655 | −0.513273 | − | 0.858226i | \(-0.671567\pi\) | ||||
−0.513273 | + | 0.858226i | \(0.671567\pi\) | |||||||
\(230\) | −6.24053 | −0.411489 | ||||||||
\(231\) | 0.857570 | + | 1.28765i | 0.0564239 | + | 0.0847212i | ||||
\(232\) | 3.84487i | 0.252428i | ||||||||
\(233\) | 17.0363i | 1.11608i | 0.829813 | + | 0.558042i | \(0.188447\pi\) | ||||
−0.829813 | + | 0.558042i | \(0.811553\pi\) | |||||||
\(234\) | 10.1472 | + | 14.3713i | 0.663343 | + | 0.939483i | ||||
\(235\) | − | 11.0596i | − | 0.721450i | ||||||
\(236\) | − | 9.06325i | − | 0.589967i | ||||||
\(237\) | 6.80073 | + | 21.4225i | 0.441755 | + | 1.39154i | ||||
\(238\) | 0.960881 | + | 0.556513i | 0.0622847 | + | 0.0360734i | ||||
\(239\) | −20.4682 | −1.32398 | −0.661989 | − | 0.749514i | \(-0.730287\pi\) | ||||
−0.661989 | + | 0.749514i | \(0.730287\pi\) | |||||||
\(240\) | −1.99678 | − | 6.28991i | −0.128892 | − | 0.406012i | ||||
\(241\) | 5.03541 | 0.324360 | 0.162180 | − | 0.986761i | \(-0.448148\pi\) | ||||
0.162180 | + | 0.986761i | \(0.448148\pi\) | |||||||
\(242\) | −9.31813 | + | 5.84571i | −0.598992 | + | 0.375777i | ||||
\(243\) | 15.5795 | + | 0.527120i | 0.999428 | + | 0.0338148i | ||||
\(244\) | −1.75411 | −0.112295 | ||||||||
\(245\) | 26.3942 | 1.68627 | ||||||||
\(246\) | −8.34413 | + | 2.64891i | −0.532002 | + | 0.168888i | ||||
\(247\) | 1.22087 | 0.0776820 | ||||||||
\(248\) | 5.05736i | 0.321143i | ||||||||
\(249\) | 9.10287 | + | 28.6743i | 0.576871 | + | 1.81716i | ||||
\(250\) | 17.2091 | 1.08840 | ||||||||
\(251\) | − | 0.148694i | − | 0.00938550i | −0.999989 | − | 0.00469275i | \(-0.998506\pi\) | ||
0.999989 | − | 0.00469275i | \(-0.00149375\pi\) | |||||||
\(252\) | 0.660000 | − | 0.466008i | 0.0415761 | − | 0.0293558i | ||||
\(253\) | 5.22053 | − | 1.50199i | 0.328212 | − | 0.0944295i | ||||
\(254\) | 12.9055i | 0.809764i | ||||||||
\(255\) | 5.87328 | − | 26.5680i | 0.367799 | − | 1.66375i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.4139i | 0.649601i | 0.945783 | + | 0.324801i | \(0.105297\pi\) | ||||
−0.945783 | + | 0.324801i | \(0.894703\pi\) | |||||||
\(258\) | −10.1130 | + | 3.21045i | −0.629608 | + | 0.199874i | ||||
\(259\) | 0.918465i | 0.0570706i | ||||||||
\(260\) | − | 22.3431i | − | 1.38566i | ||||||
\(261\) | 6.65301 | + | 9.42256i | 0.411811 | + | 0.583242i | ||||
\(262\) | − | 18.3231i | − | 1.13201i | ||||||
\(263\) | −7.90242 | −0.487284 | −0.243642 | − | 0.969865i | \(-0.578342\pi\) | ||||
−0.243642 | + | 0.969865i | \(0.578342\pi\) | |||||||
\(264\) | 3.18429 | + | 4.78124i | 0.195979 | + | 0.294265i | ||||
\(265\) | 14.6393i | 0.899286i | ||||||||
\(266\) | − | 0.0560682i | − | 0.00343776i | ||||||
\(267\) | −19.2027 | + | 6.09604i | −1.17519 | + | 0.373072i | ||||
\(268\) | −11.2937 | −0.689872 | ||||||||
\(269\) | 17.6109 | 1.07375 | 0.536876 | − | 0.843661i | \(-0.319604\pi\) | ||||
0.536876 | + | 0.843661i | \(0.319604\pi\) | |||||||
\(270\) | −15.7773 | − | 11.9594i | −0.960176 | − | 0.727828i | ||||
\(271\) | 13.4427i | 0.816589i | 0.912850 | + | 0.408294i | \(0.133876\pi\) | ||||
−0.912850 | + | 0.408294i | \(0.866124\pi\) | |||||||
\(272\) | 3.56790 | + | 2.06642i | 0.216336 | + | 0.125295i | ||||
\(273\) | 2.60722 | − | 0.827680i | 0.157796 | − | 0.0500935i | ||||
\(274\) | 18.3288i | 1.10728i | ||||||||
\(275\) | −30.3329 | + | 8.72705i | −1.82914 | + | 0.526261i | ||||
\(276\) | −0.858388 | − | 2.70395i | −0.0516689 | − | 0.162758i | ||||
\(277\) | −25.8070 | −1.55059 | −0.775296 | − | 0.631597i | \(-0.782400\pi\) | ||||
−0.775296 | + | 0.631597i | \(0.782400\pi\) | |||||||
\(278\) | 14.6357 | 0.877790 | ||||||||
\(279\) | 8.75106 | + | 12.3940i | 0.523912 | + | 0.742009i | ||||
\(280\) | −1.02610 | −0.0613214 | ||||||||
\(281\) | 21.1784 | 1.26340 | 0.631700 | − | 0.775213i | \(-0.282357\pi\) | ||||
0.631700 | + | 0.775213i | \(0.282357\pi\) | |||||||
\(282\) | 4.79200 | − | 1.52126i | 0.285359 | − | 0.0905895i | ||||
\(283\) | −22.6034 | −1.34363 | −0.671817 | − | 0.740717i | \(-0.734486\pi\) | ||||
−0.671817 | + | 0.740717i | \(0.734486\pi\) | |||||||
\(284\) | −5.55374 | −0.329554 | ||||||||
\(285\) | −1.30950 | + | 0.415709i | −0.0775678 | + | 0.0246245i | ||||
\(286\) | 5.37762 | + | 18.6912i | 0.317985 | + | 1.10523i | ||||
\(287\) | 1.36122i | 0.0803501i | ||||||||
\(288\) | 2.45068 | − | 1.73036i | 0.144408 | − | 0.101963i | ||||
\(289\) | 8.45983 | + | 14.7456i | 0.497637 | + | 0.867385i | ||||
\(290\) | − | 14.6493i | − | 0.860235i | ||||||
\(291\) | −21.0709 | + | 6.68913i | −1.23520 | + | 0.392124i | ||||
\(292\) | −0.116536 | −0.00681973 | ||||||||
\(293\) | −10.2935 | −0.601352 | −0.300676 | − | 0.953726i | \(-0.597212\pi\) | ||||
−0.300676 | + | 0.953726i | \(0.597212\pi\) | |||||||
\(294\) | 3.63054 | + | 11.4363i | 0.211737 | + | 0.666978i | ||||
\(295\) | 34.5317i | 2.01051i | ||||||||
\(296\) | 3.41040i | 0.198226i | ||||||||
\(297\) | 16.0770 | + | 6.20735i | 0.932880 | + | 0.360187i | ||||
\(298\) | 18.4154 | 1.06677 | ||||||||
\(299\) | − | 9.60499i | − | 0.555471i | ||||||
\(300\) | 4.98751 | + | 15.7108i | 0.287954 | + | 0.907062i | ||||
\(301\) | 1.64978i | 0.0950918i | ||||||||
\(302\) | 18.1694i | 1.04553i | ||||||||
\(303\) | −1.83273 | − | 5.77314i | −0.105288 | − | 0.331658i | ||||
\(304\) | − | 0.208190i | − | 0.0119405i | ||||||
\(305\) | 6.68329 | 0.382684 | ||||||||
\(306\) | 12.3194 | − | 1.10962i | 0.704256 | − | 0.0634327i | ||||
\(307\) | − | 17.4371i | − | 0.995190i | −0.867409 | − | 0.497595i | \(-0.834217\pi\) | ||
0.867409 | − | 0.497595i | \(-0.165783\pi\) | |||||||
\(308\) | 0.858388 | − | 0.246966i | 0.0489112 | − | 0.0140722i | ||||
\(309\) | 0.0156385 | + | 0.0492616i | 0.000889641 | + | 0.00280239i | ||||
\(310\) | − | 19.2690i | − | 1.09440i | ||||||
\(311\) | 3.25884 | 0.184792 | 0.0923959 | − | 0.995722i | \(-0.470547\pi\) | ||||
0.0923959 | + | 0.995722i | \(0.470547\pi\) | |||||||
\(312\) | 9.68100 | − | 3.07331i | 0.548078 | − | 0.173992i | ||||
\(313\) | − | 12.0002i | − | 0.678292i | −0.940734 | − | 0.339146i | \(-0.889862\pi\) | ||
0.940734 | − | 0.339146i | \(-0.110138\pi\) | |||||||
\(314\) | 10.0860 | 0.569184 | ||||||||
\(315\) | −2.51465 | + | 1.77553i | −0.141685 | + | 0.100040i | ||||
\(316\) | 12.9766 | 0.729988 | ||||||||
\(317\) | −19.1540 | −1.07580 | −0.537898 | − | 0.843010i | \(-0.680781\pi\) | ||||
−0.537898 | + | 0.843010i | \(0.680781\pi\) | |||||||
\(318\) | −6.34303 | + | 2.01364i | −0.355700 | + | 0.112920i | ||||
\(319\) | 3.52584 | + | 12.2549i | 0.197409 | + | 0.686141i | ||||
\(320\) | −3.81008 | −0.212990 | ||||||||
\(321\) | −24.1083 | + | 7.65337i | −1.34560 | + | 0.427170i | ||||
\(322\) | −0.441108 | −0.0245820 | ||||||||
\(323\) | 0.430207 | − | 0.742800i | 0.0239374 | − | 0.0413305i | ||||
\(324\) | 3.01170 | − | 8.48114i | 0.167317 | − | 0.471174i | ||||
\(325\) | 55.8080i | 3.09567i | ||||||||
\(326\) | − | 11.3349i | − | 0.627780i | ||||||
\(327\) | −3.68112 | − | 11.5956i | −0.203566 | − | 0.641240i | ||||
\(328\) | 5.05441i | 0.279083i | ||||||||
\(329\) | − | 0.781741i | − | 0.0430988i | ||||||
\(330\) | −12.1324 | − | 18.2169i | −0.667867 | − | 1.00281i | ||||
\(331\) | −3.54602 | −0.194907 | −0.0974534 | − | 0.995240i | \(-0.531070\pi\) | ||||
−0.0974534 | + | 0.995240i | \(0.531070\pi\) | |||||||
\(332\) | 17.3693 | 0.953264 | ||||||||
\(333\) | 5.90123 | + | 8.35782i | 0.323385 | + | 0.458006i | ||||
\(334\) | 16.5010i | 0.902896i | ||||||||
\(335\) | 43.0299 | 2.35097 | ||||||||
\(336\) | −0.141141 | − | 0.444598i | −0.00769987 | − | 0.0242548i | ||||
\(337\) | −12.9518 | −0.705530 | −0.352765 | − | 0.935712i | \(-0.614758\pi\) | ||||
−0.352765 | + | 0.935712i | \(0.614758\pi\) | |||||||
\(338\) | 21.3890 | 1.16341 | ||||||||
\(339\) | 1.89900 | + | 5.98191i | 0.103140 | + | 0.324893i | ||||
\(340\) | −13.5940 | − | 7.87322i | −0.737238 | − | 0.426985i | ||||
\(341\) | 4.63772 | + | 16.1195i | 0.251147 | + | 0.872919i | ||||
\(342\) | −0.360243 | − | 0.510207i | −0.0194797 | − | 0.0275888i | ||||
\(343\) | 3.75085 | 0.202527 | ||||||||
\(344\) | 6.12589i | 0.330286i | ||||||||
\(345\) | 3.27053 | + | 10.3023i | 0.176079 | + | 0.554655i | ||||
\(346\) | − | 17.6882i | − | 0.950925i | ||||||
\(347\) | − | 14.1605i | − | 0.760177i | −0.924950 | − | 0.380088i | \(-0.875894\pi\) | ||
0.924950 | − | 0.380088i | \(-0.124106\pi\) | |||||||
\(348\) | 6.34735 | − | 2.01501i | 0.340254 | − | 0.108016i | ||||
\(349\) | 20.9198i | 1.11981i | 0.828556 | + | 0.559907i | \(0.189163\pi\) | ||||
−0.828556 | + | 0.559907i | \(0.810837\pi\) | |||||||
\(350\) | 2.56297 | 0.136997 | ||||||||
\(351\) | 18.4071 | − | 24.2833i | 0.982500 | − | 1.29615i | ||||
\(352\) | 3.18733 | − | 0.917024i | 0.169885 | − | 0.0488775i | ||||
\(353\) | − | 32.5359i | − | 1.73171i | −0.500296 | − | 0.865854i | \(-0.666775\pi\) | ||
0.500296 | − | 0.865854i | \(-0.333225\pi\) | |||||||
\(354\) | −14.9622 | + | 4.74985i | −0.795230 | + | 0.252452i | ||||
\(355\) | 21.1602 | 1.12307 | ||||||||
\(356\) | 11.6319i | 0.616491i | ||||||||
\(357\) | 0.415148 | − | 1.87794i | 0.0219720 | − | 0.0993910i | ||||
\(358\) | − | 13.1756i | − | 0.696350i | ||||||
\(359\) | −21.9753 | −1.15981 | −0.579907 | − | 0.814683i | \(-0.696911\pi\) | ||||
−0.579907 | + | 0.814683i | \(0.696911\pi\) | |||||||
\(360\) | −9.33730 | + | 6.59282i | −0.492119 | + | 0.347472i | ||||
\(361\) | 18.9567 | 0.997719 | ||||||||
\(362\) | 12.9449i | 0.680370i | ||||||||
\(363\) | 14.5339 | + | 12.3193i | 0.762832 | + | 0.646597i | ||||
\(364\) | − | 1.57931i | − | 0.0827781i | ||||||
\(365\) | 0.444010 | 0.0232405 | ||||||||
\(366\) | 0.919290 | + | 2.89579i | 0.0480521 | + | 0.151365i | ||||
\(367\) | 15.0883i | 0.787604i | 0.919195 | + | 0.393802i | \(0.128840\pi\) | ||||
−0.919195 | + | 0.393802i | \(0.871160\pi\) | |||||||
\(368\) | −1.63790 | −0.0853815 | ||||||||
\(369\) | 8.74595 | + | 12.3868i | 0.455296 | + | 0.644829i | ||||
\(370\) | − | 12.9939i | − | 0.675521i | ||||||
\(371\) | 1.03477i | 0.0537225i | ||||||||
\(372\) | 8.34900 | − | 2.65045i | 0.432876 | − | 0.137420i | ||||
\(373\) | 5.93570i | 0.307339i | 0.988122 | + | 0.153670i | \(0.0491091\pi\) | ||||
−0.988122 | + | 0.153670i | \(0.950891\pi\) | |||||||
\(374\) | 13.2670 | + | 3.31451i | 0.686022 | + | 0.171389i | ||||
\(375\) | −9.01889 | − | 28.4098i | −0.465734 | − | 1.46707i | ||||
\(376\) | − | 2.90273i | − | 0.149697i | ||||||
\(377\) | 22.5471 | 1.16124 | ||||||||
\(378\) | −1.11521 | − | 0.845344i | −0.0573600 | − | 0.0434798i | ||||
\(379\) | − | 22.7715i | − | 1.16969i | −0.811143 | − | 0.584847i | \(-0.801154\pi\) | ||
0.811143 | − | 0.584847i | \(-0.198846\pi\) | |||||||
\(380\) | 0.793220i | 0.0406913i | ||||||||
\(381\) | 21.3052 | − | 6.76350i | 1.09150 | − | 0.346504i | ||||
\(382\) | − | 3.19904i | − | 0.163677i | ||||||
\(383\) | − | 17.8676i | − | 0.912991i | −0.889726 | − | 0.456496i | \(-0.849104\pi\) | ||
0.889726 | − | 0.456496i | \(-0.150896\pi\) | |||||||
\(384\) | −0.524078 | − | 1.65086i | −0.0267443 | − | 0.0842451i | ||||
\(385\) | −3.27053 | + | 0.940961i | −0.166682 | + | 0.0479558i | ||||
\(386\) | −19.3152 | −0.983119 | ||||||||
\(387\) | 10.6000 | + | 15.0126i | 0.538829 | + | 0.763135i | ||||
\(388\) | 12.7636i | 0.647974i | ||||||||
\(389\) | 19.2714i | 0.977101i | 0.872536 | + | 0.488550i | \(0.162474\pi\) | ||||
−0.872536 | + | 0.488550i | \(0.837526\pi\) | |||||||
\(390\) | −36.8854 | + | 11.7095i | −1.86776 | + | 0.592936i | ||||
\(391\) | −5.84387 | − | 3.38459i | −0.295537 | − | 0.171166i | ||||
\(392\) | 6.92747 | 0.349890 | ||||||||
\(393\) | −30.2489 | + | 9.60275i | −1.52586 | + | 0.484395i | ||||
\(394\) | 19.6491i | 0.989908i | ||||||||
\(395\) | −49.4417 | −2.48768 | ||||||||
\(396\) | 6.22435 | − | 7.76257i | 0.312786 | − | 0.390084i | ||||
\(397\) | − | 25.6830i | − | 1.28899i | −0.764606 | − | 0.644497i | \(-0.777067\pi\) | ||
0.764606 | − | 0.644497i | \(-0.222933\pi\) | |||||||
\(398\) | 24.6476i | 1.23547i | ||||||||
\(399\) | −0.0925607 | + | 0.0293841i | −0.00463383 | + | 0.00147105i | ||||
\(400\) | 9.51672 | 0.475836 | ||||||||
\(401\) | −18.8429 | −0.940971 | −0.470486 | − | 0.882408i | \(-0.655921\pi\) | ||||
−0.470486 | + | 0.882408i | \(0.655921\pi\) | |||||||
\(402\) | 5.91878 | + | 18.6443i | 0.295202 | + | 0.929893i | ||||
\(403\) | 29.6574 | 1.47734 | ||||||||
\(404\) | −3.49705 | −0.173985 | ||||||||
\(405\) | −11.4748 | + | 32.3138i | −0.570189 | + | 1.60569i | ||||
\(406\) | − | 1.03547i | − | 0.0513896i | ||||||
\(407\) | 3.12742 | + | 10.8701i | 0.155020 | + | 0.538810i | ||||
\(408\) | 1.54151 | − | 6.97307i | 0.0763161 | − | 0.345219i | ||||
\(409\) | 26.5587i | 1.31324i | 0.754221 | + | 0.656621i | \(0.228015\pi\) | ||||
−0.754221 | + | 0.656621i | \(0.771985\pi\) | |||||||
\(410\) | − | 19.2577i | − | 0.951071i | ||||||
\(411\) | 30.2582 | − | 9.60570i | 1.49253 | − | 0.473814i | ||||
\(412\) | 0.0298399 | 0.00147011 | ||||||||
\(413\) | 2.44085i | 0.120106i | ||||||||
\(414\) | −4.01398 | + | 2.83416i | −0.197276 | + | 0.139291i | ||||
\(415\) | −66.1784 | −3.24857 | ||||||||
\(416\) | − | 5.86421i | − | 0.287517i | ||||||
\(417\) | −7.67024 | − | 24.1615i | −0.375614 | − | 1.18319i | ||||
\(418\) | −0.190915 | − | 0.663569i | −0.00933796 | − | 0.0324562i | ||||
\(419\) | −12.8821 | −0.629333 | −0.314666 | − | 0.949202i | \(-0.601893\pi\) | ||||
−0.314666 | + | 0.949202i | \(0.601893\pi\) | |||||||
\(420\) | 0.537759 | + | 1.69395i | 0.0262399 | + | 0.0826565i | ||||
\(421\) | −27.6448 | −1.34733 | −0.673663 | − | 0.739039i | \(-0.735280\pi\) | ||||
−0.673663 | + | 0.739039i | \(0.735280\pi\) | |||||||
\(422\) | −9.47591 | −0.461280 | ||||||||
\(423\) | −5.02277 | − | 7.11367i | −0.244215 | − | 0.345878i | ||||
\(424\) | 3.84226i | 0.186597i | ||||||||
\(425\) | 33.9547 | + | 19.6655i | 1.64704 | + | 0.953918i | ||||
\(426\) | 2.91059 | + | 9.16845i | 0.141019 | + | 0.444213i | ||||
\(427\) | 0.472404 | 0.0228612 | ||||||||
\(428\) | 14.6035i | 0.705886i | ||||||||
\(429\) | 28.0382 | − | 18.6733i | 1.35370 | − | 0.901557i | ||||
\(430\) | − | 23.3401i | − | 1.12556i | ||||||
\(431\) | − | 19.3110i | − | 0.930179i | −0.885264 | − | 0.465089i | \(-0.846022\pi\) | ||
0.885264 | − | 0.465089i | \(-0.153978\pi\) | |||||||
\(432\) | −4.14094 | − | 3.13889i | −0.199231 | − | 0.151020i | ||||
\(433\) | 8.00193 | 0.384548 | 0.192274 | − | 0.981341i | \(-0.438414\pi\) | ||||
0.192274 | + | 0.981341i | \(0.438414\pi\) | |||||||
\(434\) | − | 1.36201i | − | 0.0653787i | ||||||
\(435\) | −24.1839 | + | 7.67737i | −1.15953 | + | 0.368101i | ||||
\(436\) | −7.02399 | −0.336388 | ||||||||
\(437\) | 0.340994i | 0.0163120i | ||||||||
\(438\) | 0.0610738 | + | 0.192384i | 0.00291822 | + | 0.00919247i | ||||
\(439\) | 22.5863 | 1.07799 | 0.538994 | − | 0.842310i | \(-0.318805\pi\) | ||||
0.538994 | + | 0.842310i | \(0.318805\pi\) | |||||||
\(440\) | −12.1440 | + | 3.49393i | −0.578942 | + | 0.166567i | ||||
\(441\) | 16.9770 | − | 11.9870i | 0.808430 | − | 0.570811i | ||||
\(442\) | 12.1179 | − | 20.9229i | 0.576390 | − | 0.995202i | ||||
\(443\) | − | 23.8935i | − | 1.13521i | −0.823300 | − | 0.567607i | \(-0.807869\pi\) | ||
0.823300 | − | 0.567607i | \(-0.192131\pi\) | |||||||
\(444\) | 5.63010 | − | 1.78732i | 0.267193 | − | 0.0848224i | ||||
\(445\) | − | 44.3186i | − | 2.10090i | ||||||
\(446\) | 4.37502 | 0.207163 | ||||||||
\(447\) | −9.65110 | − | 30.4012i | −0.456482 | − | 1.43793i | ||||
\(448\) | −0.269313 | −0.0127238 | ||||||||
\(449\) | −26.3217 | −1.24220 | −0.621099 | − | 0.783732i | \(-0.713314\pi\) | ||||
−0.621099 | + | 0.783732i | \(0.713314\pi\) | |||||||
\(450\) | 23.3225 | − | 16.4674i | 1.09943 | − | 0.776279i | ||||
\(451\) | 4.63501 | + | 16.1101i | 0.218254 | + | 0.758594i | ||||
\(452\) | 3.62351 | 0.170436 | ||||||||
\(453\) | 29.9952 | − | 9.52220i | 1.40930 | − | 0.447392i | ||||
\(454\) | − | 2.57358i | − | 0.120784i | ||||||
\(455\) | 6.01729i | 0.282095i | ||||||||
\(456\) | −0.343692 | + | 0.109108i | −0.0160949 | + | 0.00510944i | ||||
\(457\) | − | 4.89134i | − | 0.228807i | −0.993434 | − | 0.114404i | \(-0.963504\pi\) | ||
0.993434 | − | 0.114404i | \(-0.0364957\pi\) | |||||||
\(458\) | 15.5344 | 0.725877 | ||||||||
\(459\) | −8.28818 | − | 19.7562i | −0.386859 | − | 0.922139i | ||||
\(460\) | 6.24053 | 0.290966 | ||||||||
\(461\) | −12.4471 | −0.579718 | −0.289859 | − | 0.957069i | \(-0.593608\pi\) | ||||
−0.289859 | + | 0.957069i | \(0.593608\pi\) | |||||||
\(462\) | −0.857570 | − | 1.28765i | −0.0398977 | − | 0.0599069i | ||||
\(463\) | −13.4617 | −0.625618 | −0.312809 | − | 0.949816i | \(-0.601270\pi\) | ||||
−0.312809 | + | 0.949816i | \(0.601270\pi\) | |||||||
\(464\) | − | 3.84487i | − | 0.178494i | ||||||
\(465\) | −31.8104 | + | 10.0984i | −1.47517 | + | 0.468304i | ||||
\(466\) | − | 17.0363i | − | 0.789190i | ||||||
\(467\) | − | 38.7575i | − | 1.79348i | −0.442555 | − | 0.896741i | \(-0.645928\pi\) | ||
0.442555 | − | 0.896741i | \(-0.354072\pi\) | |||||||
\(468\) | −10.1472 | − | 14.3713i | −0.469055 | − | 0.664315i | ||||
\(469\) | 3.04153 | 0.140445 | ||||||||
\(470\) | 11.0596i | 0.510143i | ||||||||
\(471\) | −5.28583 | − | 16.6505i | −0.243558 | − | 0.767215i | ||||
\(472\) | 9.06325i | 0.417170i | ||||||||
\(473\) | 5.61759 | + | 19.5252i | 0.258297 | + | 0.897771i | ||||
\(474\) | −6.80073 | − | 21.4225i | −0.312368 | − | 0.983967i | ||||
\(475\) | − | 1.98128i | − | 0.0909075i | ||||||
\(476\) | −0.960881 | − | 0.556513i | −0.0440419 | − | 0.0255077i | ||||
\(477\) | 6.64849 | + | 9.41616i | 0.304414 | + | 0.431136i | ||||
\(478\) | 20.4682 | 0.936193 | ||||||||
\(479\) | − | 24.4680i | − | 1.11797i | −0.829177 | − | 0.558987i | \(-0.811190\pi\) | ||
0.829177 | − | 0.558987i | \(-0.188810\pi\) | |||||||
\(480\) | 1.99678 | + | 6.28991i | 0.0911402 | + | 0.287094i | ||||
\(481\) | 19.9993 | 0.911890 | ||||||||
\(482\) | −5.03541 | −0.229357 | ||||||||
\(483\) | 0.231175 | + | 0.728207i | 0.0105188 | + | 0.0331346i | ||||
\(484\) | 9.31813 | − | 5.84571i | 0.423552 | − | 0.265714i | ||||
\(485\) | − | 48.6304i | − | 2.20819i | ||||||
\(486\) | −15.5795 | − | 0.527120i | −0.706702 | − | 0.0239106i | ||||
\(487\) | − | 21.1813i | − | 0.959817i | −0.877319 | − | 0.479909i | \(-0.840670\pi\) | ||
0.877319 | − | 0.479909i | \(-0.159330\pi\) | |||||||
\(488\) | 1.75411 | 0.0794047 | ||||||||
\(489\) | −18.7123 | + | 5.94036i | −0.846199 | + | 0.268632i | ||||
\(490\) | −26.3942 | −1.19237 | ||||||||
\(491\) | 12.1109 | 0.546558 | 0.273279 | − | 0.961935i | \(-0.411892\pi\) | ||||
0.273279 | + | 0.961935i | \(0.411892\pi\) | |||||||
\(492\) | 8.34413 | − | 2.64891i | 0.376182 | − | 0.119422i | ||||
\(493\) | 7.94511 | − | 13.7181i | 0.357830 | − | 0.617833i | ||||
\(494\) | −1.22087 | −0.0549295 | ||||||||
\(495\) | −23.7153 | + | 29.5760i | −1.06592 | + | 1.32934i | ||||
\(496\) | − | 5.05736i | − | 0.227082i | ||||||
\(497\) | 1.49569 | 0.0670910 | ||||||||
\(498\) | −9.10287 | − | 28.6743i | −0.407909 | − | 1.28493i | ||||
\(499\) | 28.5486i | 1.27801i | 0.769202 | + | 0.639006i | \(0.220654\pi\) | ||||
−0.769202 | + | 0.639006i | \(0.779346\pi\) | |||||||
\(500\) | −17.2091 | −0.769612 | ||||||||
\(501\) | 27.2409 | − | 8.64784i | 1.21703 | − | 0.386357i | ||||
\(502\) | 0.148694i | 0.00663655i | ||||||||
\(503\) | − | 11.2713i | − | 0.502564i | −0.967914 | − | 0.251282i | \(-0.919148\pi\) | ||
0.967914 | − | 0.251282i | \(-0.0808521\pi\) | |||||||
\(504\) | −0.660000 | + | 0.466008i | −0.0293988 | + | 0.0207577i | ||||
\(505\) | 13.3240 | 0.592912 | ||||||||
\(506\) | −5.22053 | + | 1.50199i | −0.232081 | + | 0.0667718i | ||||
\(507\) | −11.2095 | − | 35.3102i | −0.497831 | − | 1.56818i | ||||
\(508\) | − | 12.9055i | − | 0.572589i | ||||||
\(509\) | − | 7.04140i | − | 0.312104i | −0.987749 | − | 0.156052i | \(-0.950123\pi\) | ||
0.987749 | − | 0.156052i | \(-0.0498768\pi\) | |||||||
\(510\) | −5.87328 | + | 26.5680i | −0.260073 | + | 1.17645i | ||||
\(511\) | 0.0313845 | 0.00138837 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.653485 | + | 0.862100i | −0.0288521 | + | 0.0380627i | ||||
\(514\) | − | 10.4139i | − | 0.459337i | ||||||
\(515\) | −0.113693 | −0.00500989 | ||||||||
\(516\) | 10.1130 | − | 3.21045i | 0.445200 | − | 0.141332i | ||||
\(517\) | −2.66187 | − | 9.25195i | −0.117069 | − | 0.406900i | ||||
\(518\) | − | 0.918465i | − | 0.0403550i | ||||||
\(519\) | −29.2008 | + | 9.27002i | −1.28177 | + | 0.406909i | ||||
\(520\) | 22.3431i | 0.979810i | ||||||||
\(521\) | 1.40526 | 0.0615655 | 0.0307828 | − | 0.999526i | \(-0.490200\pi\) | ||||
0.0307828 | + | 0.999526i | \(0.490200\pi\) | |||||||
\(522\) | −6.65301 | − | 9.42256i | −0.291195 | − | 0.412414i | ||||
\(523\) | 11.2578i | 0.492270i | 0.969236 | + | 0.246135i | \(0.0791607\pi\) | ||||
−0.969236 | + | 0.246135i | \(0.920839\pi\) | |||||||
\(524\) | 18.3231i | 0.800449i | ||||||||
\(525\) | −1.34320 | − | 4.23111i | −0.0586220 | − | 0.184661i | ||||
\(526\) | 7.90242 | 0.344562 | ||||||||
\(527\) | 10.4506 | − | 18.0442i | 0.455236 | − | 0.786016i | ||||
\(528\) | −3.18429 | − | 4.78124i | −0.138578 | − | 0.208077i | ||||
\(529\) | −20.3173 | −0.883360 | ||||||||
\(530\) | − | 14.6393i | − | 0.635891i | ||||||
\(531\) | 15.6827 | + | 22.2112i | 0.680571 | + | 0.963882i | ||||
\(532\) | 0.0560682i | 0.00243086i | ||||||||
\(533\) | 29.6401 | 1.28386 | ||||||||
\(534\) | 19.2027 | − | 6.09604i | 0.830982 | − | 0.263802i | ||||
\(535\) | − | 55.6405i | − | 2.40555i | ||||||
\(536\) | 11.2937 | 0.487813 | ||||||||
\(537\) | −21.7510 | + | 6.90502i | −0.938625 | + | 0.297974i | ||||
\(538\) | −17.6109 | −0.759258 | ||||||||
\(539\) | 22.0801 | − | 6.35266i | 0.951059 | − | 0.273628i | ||||
\(540\) | 15.7773 | + | 11.9594i | 0.678947 | + | 0.514652i | ||||
\(541\) | −39.0116 | −1.67724 | −0.838620 | − | 0.544716i | \(-0.816637\pi\) | ||||
−0.838620 | + | 0.544716i | \(0.816637\pi\) | |||||||
\(542\) | − | 13.4427i | − | 0.577416i | ||||||
\(543\) | 21.3703 | − | 6.78415i | 0.917086 | − | 0.291136i | ||||
\(544\) | −3.56790 | − | 2.06642i | −0.152972 | − | 0.0885970i | ||||
\(545\) | 26.7620 | 1.14636 | ||||||||
\(546\) | −2.60722 | + | 0.827680i | −0.111579 | + | 0.0354215i | ||||
\(547\) | 27.5470 | 1.17783 | 0.588913 | − | 0.808197i | \(-0.299556\pi\) | ||||
0.588913 | + | 0.808197i | \(0.299556\pi\) | |||||||
\(548\) | − | 18.3288i | − | 0.782965i | ||||||
\(549\) | 4.29876 | − | 3.03524i | 0.183467 | − | 0.129541i | ||||
\(550\) | 30.3329 | − | 8.72705i | 1.29340 | − | 0.372123i | ||||
\(551\) | −0.800463 | −0.0341009 | ||||||||
\(552\) | 0.858388 | + | 2.70395i | 0.0365354 | + | 0.115088i | ||||
\(553\) | −3.49475 | −0.148612 | ||||||||
\(554\) | 25.8070 | 1.09643 | ||||||||
\(555\) | −21.4511 | + | 6.80983i | −0.910550 | + | 0.289061i | ||||
\(556\) | −14.6357 | −0.620691 | ||||||||
\(557\) | 3.16908 | 0.134278 | 0.0671392 | − | 0.997744i | \(-0.478613\pi\) | ||||
0.0671392 | + | 0.997744i | \(0.478613\pi\) | |||||||
\(558\) | −8.75106 | − | 12.3940i | −0.370462 | − | 0.524680i | ||||
\(559\) | 35.9235 | 1.51940 | ||||||||
\(560\) | 1.02610 | 0.0433608 | ||||||||
\(561\) | −1.48118 | − | 23.6391i | −0.0625353 | − | 0.998043i | ||||
\(562\) | −21.1784 | −0.893359 | ||||||||
\(563\) | −9.09841 | −0.383452 | −0.191726 | − | 0.981448i | \(-0.561409\pi\) | ||||
−0.191726 | + | 0.981448i | \(0.561409\pi\) | |||||||
\(564\) | −4.79200 | + | 1.52126i | −0.201780 | + | 0.0640565i | ||||
\(565\) | −13.8059 | −0.580817 | ||||||||
\(566\) | 22.6034 | 0.950093 | ||||||||
\(567\) | −0.811089 | + | 2.28408i | −0.0340626 | + | 0.0959222i | ||||
\(568\) | 5.55374 | 0.233030 | ||||||||
\(569\) | −41.2110 | −1.72765 | −0.863827 | − | 0.503788i | \(-0.831939\pi\) | ||||
−0.863827 | + | 0.503788i | \(0.831939\pi\) | |||||||
\(570\) | 1.30950 | − | 0.415709i | 0.0548487 | − | 0.0174122i | ||||
\(571\) | 22.5012 | 0.941645 | 0.470823 | − | 0.882228i | \(-0.343957\pi\) | ||||
0.470823 | + | 0.882228i | \(0.343957\pi\) | |||||||
\(572\) | −5.37762 | − | 18.6912i | −0.224850 | − | 0.781517i | ||||
\(573\) | −5.28117 | + | 1.67655i | −0.220624 | + | 0.0700388i | ||||
\(574\) | − | 1.36122i | − | 0.0568161i | ||||||
\(575\) | −15.5874 | −0.650041 | ||||||||
\(576\) | −2.45068 | + | 1.73036i | −0.102112 | + | 0.0720984i | ||||
\(577\) | −26.3913 | −1.09869 | −0.549343 | − | 0.835597i | \(-0.685122\pi\) | ||||
−0.549343 | + | 0.835597i | \(0.685122\pi\) | |||||||
\(578\) | −8.45983 | − | 14.7456i | −0.351883 | − | 0.613334i | ||||
\(579\) | 10.1227 | + | 31.8867i | 0.420685 | + | 1.32517i | ||||
\(580\) | 14.6493i | 0.608278i | ||||||||
\(581\) | −4.67777 | −0.194067 | ||||||||
\(582\) | 21.0709 | − | 6.68913i | 0.873419 | − | 0.277273i | ||||
\(583\) | 3.52344 | + | 12.2465i | 0.145926 | + | 0.507200i | ||||
\(584\) | 0.116536 | 0.00482228 | ||||||||
\(585\) | 38.6617 | + | 54.7559i | 1.59846 | + | 2.26388i | ||||
\(586\) | 10.2935 | 0.425220 | ||||||||
\(587\) | 9.28281i | 0.383142i | 0.981479 | + | 0.191571i | \(0.0613583\pi\) | ||||
−0.981479 | + | 0.191571i | \(0.938642\pi\) | |||||||
\(588\) | −3.63054 | − | 11.4363i | −0.149721 | − | 0.471625i | ||||
\(589\) | −1.05289 | −0.0433836 | ||||||||
\(590\) | − | 34.5317i | − | 1.42165i | ||||||
\(591\) | 32.4380 | − | 10.2977i | 1.33432 | − | 0.423590i | ||||
\(592\) | − | 3.41040i | − | 0.140167i | ||||||
\(593\) | 16.9168 | 0.694689 | 0.347344 | − | 0.937738i | \(-0.387084\pi\) | ||||
0.347344 | + | 0.937738i | \(0.387084\pi\) | |||||||
\(594\) | −16.0770 | − | 6.20735i | −0.659646 | − | 0.254691i | ||||
\(595\) | 3.66103 | + | 2.12036i | 0.150088 | + | 0.0869262i | ||||
\(596\) | −18.4154 | −0.754323 | ||||||||
\(597\) | 40.6898 | − | 12.9173i | 1.66532 | − | 0.528669i | ||||
\(598\) | 9.60499i | 0.392777i | ||||||||
\(599\) | 27.9929i | 1.14376i | 0.820338 | + | 0.571879i | \(0.193785\pi\) | ||||
−0.820338 | + | 0.571879i | \(0.806215\pi\) | |||||||
\(600\) | −4.98751 | − | 15.7108i | −0.203614 | − | 0.641390i | ||||
\(601\) | −21.8984 | −0.893253 | −0.446626 | − | 0.894721i | \(-0.647375\pi\) | ||||
−0.446626 | + | 0.894721i | \(0.647375\pi\) | |||||||
\(602\) | − | 1.64978i | − | 0.0672400i | ||||||
\(603\) | 27.6773 | − | 19.5422i | 1.12710 | − | 0.795818i | ||||
\(604\) | − | 18.1694i | − | 0.739303i | ||||||
\(605\) | −35.5028 | + | 22.2726i | −1.44340 | + | 0.905512i | ||||
\(606\) | 1.83273 | + | 5.77314i | 0.0744495 | + | 0.234518i | ||||
\(607\) | −6.99844 | −0.284058 | −0.142029 | − | 0.989863i | \(-0.545363\pi\) | ||||
−0.142029 | + | 0.989863i | \(0.545363\pi\) | |||||||
\(608\) | 0.208190i | 0.00844321i | ||||||||
\(609\) | −1.70942 | + | 0.542669i | −0.0692692 | + | 0.0219901i | ||||
\(610\) | −6.68329 | −0.270599 | ||||||||
\(611\) | −17.0222 | −0.688645 | ||||||||
\(612\) | −12.3194 | + | 1.10962i | −0.497984 | + | 0.0448537i | ||||
\(613\) | 47.2562i | 1.90866i | 0.298754 | + | 0.954330i | \(0.403429\pi\) | ||||
−0.298754 | + | 0.954330i | \(0.596571\pi\) | |||||||
\(614\) | 17.4371i | 0.703706i | ||||||||
\(615\) | −31.7918 | + | 10.0926i | −1.28197 | + | 0.406971i | ||||
\(616\) | −0.858388 | + | 0.246966i | −0.0345855 | + | 0.00995055i | ||||
\(617\) | −9.53425 | −0.383835 | −0.191917 | − | 0.981411i | \(-0.561471\pi\) | ||||
−0.191917 | + | 0.981411i | \(0.561471\pi\) | |||||||
\(618\) | −0.0156385 | − | 0.0492616i | −0.000629071 | − | 0.00198159i | ||||
\(619\) | 9.14235i | 0.367462i | 0.982977 | + | 0.183731i | \(0.0588175\pi\) | ||||
−0.982977 | + | 0.183731i | \(0.941182\pi\) | |||||||
\(620\) | 19.2690i | 0.773860i | ||||||||
\(621\) | 6.78244 | + | 5.14120i | 0.272170 | + | 0.206309i | ||||
\(622\) | −3.25884 | −0.130668 | ||||||||
\(623\) | − | 3.13263i | − | 0.125506i | ||||||
\(624\) | −9.68100 | + | 3.07331i | −0.387550 | + | 0.123031i | ||||
\(625\) | 17.9843 | 0.719372 | ||||||||
\(626\) | 12.0002i | 0.479625i | ||||||||
\(627\) | −0.995406 | + | 0.662936i | −0.0397527 | + | 0.0264751i | ||||
\(628\) | −10.0860 | −0.402474 | ||||||||
\(629\) | 7.04732 | − | 12.1680i | 0.280995 | − | 0.485169i | ||||
\(630\) | 2.51465 | − | 1.77553i | 0.100186 | − | 0.0707388i | ||||
\(631\) | −47.3286 | −1.88412 | −0.942061 | − | 0.335441i | \(-0.891115\pi\) | ||||
−0.942061 | + | 0.335441i | \(0.891115\pi\) | |||||||
\(632\) | −12.9766 | −0.516180 | ||||||||
\(633\) | 4.96612 | + | 15.6434i | 0.197386 | + | 0.621770i | ||||
\(634\) | 19.1540 | 0.760702 | ||||||||
\(635\) | 49.1710i | 1.95129i | ||||||||
\(636\) | 6.34303 | − | 2.01364i | 0.251518 | − | 0.0798462i | ||||
\(637\) | − | 40.6241i | − | 1.60959i | ||||||
\(638\) | −3.52584 | − | 12.2549i | −0.139589 | − | 0.485175i | ||||
\(639\) | 13.6105 | − | 9.60997i | 0.538421 | − | 0.380165i | ||||
\(640\) | 3.81008 | 0.150607 | ||||||||
\(641\) | −31.0101 | −1.22482 | −0.612412 | − | 0.790539i | \(-0.709801\pi\) | ||||
−0.612412 | + | 0.790539i | \(0.709801\pi\) | |||||||
\(642\) | 24.1083 | − | 7.65337i | 0.951480 | − | 0.302055i | ||||
\(643\) | − | 24.4740i | − | 0.965161i | −0.875852 | − | 0.482580i | \(-0.839700\pi\) | ||
0.875852 | − | 0.482580i | \(-0.160300\pi\) | |||||||
\(644\) | 0.441108 | 0.0173821 | ||||||||
\(645\) | −38.5313 | + | 12.2321i | −1.51717 | + | 0.481637i | ||||
\(646\) | −0.430207 | + | 0.742800i | −0.0169263 | + | 0.0292251i | ||||
\(647\) | − | 28.5158i | − | 1.12107i | −0.828130 | − | 0.560536i | \(-0.810595\pi\) | ||
0.828130 | − | 0.560536i | \(-0.189405\pi\) | |||||||
\(648\) | −3.01170 | + | 8.48114i | −0.118311 | + | 0.333170i | ||||
\(649\) | 8.31122 | + | 28.8876i | 0.326244 | + | 1.13394i | ||||
\(650\) | − | 55.8080i | − | 2.18897i | ||||||
\(651\) | −2.24849 | + | 0.713801i | −0.0881254 | + | 0.0279761i | ||||
\(652\) | 11.3349i | 0.443907i | ||||||||
\(653\) | 9.02355 | 0.353119 | 0.176559 | − | 0.984290i | \(-0.443503\pi\) | ||||
0.176559 | + | 0.984290i | \(0.443503\pi\) | |||||||
\(654\) | 3.68112 | + | 11.5956i | 0.143943 | + | 0.453425i | ||||
\(655\) | − | 69.8125i | − | 2.72780i | ||||||
\(656\) | − | 5.05441i | − | 0.197342i | ||||||
\(657\) | 0.285592 | − | 0.201649i | 0.0111420 | − | 0.00786706i | ||||
\(658\) | 0.781741i | 0.0304755i | ||||||||
\(659\) | 27.0968 | 1.05554 | 0.527770 | − | 0.849387i | \(-0.323028\pi\) | ||||
0.527770 | + | 0.849387i | \(0.323028\pi\) | |||||||
\(660\) | 12.1324 | + | 18.2169i | 0.472253 | + | 0.709093i | ||||
\(661\) | −39.2996 | −1.52858 | −0.764289 | − | 0.644874i | \(-0.776910\pi\) | ||||
−0.764289 | + | 0.644874i | \(0.776910\pi\) | |||||||
\(662\) | 3.54602 | 0.137820 | ||||||||
\(663\) | −40.8916 | − | 9.03974i | −1.58810 | − | 0.351074i | ||||
\(664\) | −17.3693 | −0.674059 | ||||||||
\(665\) | − | 0.213624i | − | 0.00828399i | ||||||
\(666\) | −5.90123 | − | 8.35782i | −0.228668 | − | 0.323859i | ||||
\(667\) | 6.29752i | 0.243841i | ||||||||
\(668\) | − | 16.5010i | − | 0.638444i | ||||||
\(669\) | −2.29285 | − | 7.22254i | −0.0886468 | − | 0.279240i | ||||
\(670\) | −43.0299 | −1.66239 | ||||||||
\(671\) | 5.59092 | − | 1.60856i | 0.215835 | − | 0.0620977i | ||||
\(672\) | 0.141141 | + | 0.444598i | 0.00544463 | + | 0.0171507i | ||||
\(673\) | −6.02707 | −0.232326 | −0.116163 | − | 0.993230i | \(-0.537060\pi\) | ||||
−0.116163 | + | 0.993230i | \(0.537060\pi\) | |||||||
\(674\) | 12.9518 | 0.498885 | ||||||||
\(675\) | −39.4081 | − | 29.8720i | −1.51682 | − | 1.14977i | ||||
\(676\) | −21.3890 | −0.822652 | ||||||||
\(677\) | 26.4702i | 1.01733i | 0.860964 | + | 0.508666i | \(0.169861\pi\) | ||||
−0.860964 | + | 0.508666i | \(0.830139\pi\) | |||||||
\(678\) | −1.89900 | − | 5.98191i | −0.0729308 | − | 0.229734i | ||||
\(679\) | − | 3.43740i | − | 0.131915i | ||||||
\(680\) | 13.5940 | + | 7.87322i | 0.521306 | + | 0.301924i | ||||
\(681\) | −4.24863 | + | 1.34876i | −0.162808 | + | 0.0516845i | ||||
\(682\) | −4.63772 | − | 16.1195i | −0.177588 | − | 0.617247i | ||||
\(683\) | 9.64828 | 0.369181 | 0.184591 | − | 0.982816i | \(-0.440904\pi\) | ||||
0.184591 | + | 0.982816i | \(0.440904\pi\) | |||||||
\(684\) | 0.360243 | + | 0.510207i | 0.0137743 | + | 0.0195083i | ||||
\(685\) | 69.8340i | 2.66822i | ||||||||
\(686\) | −3.75085 | −0.143208 | ||||||||
\(687\) | −8.14127 | − | 25.6452i | −0.310609 | − | 0.978426i | ||||
\(688\) | − | 6.12589i | − | 0.233547i | ||||||
\(689\) | 22.5318 | 0.858393 | ||||||||
\(690\) | −3.27053 | − | 10.3023i | −0.124507 | − | 0.392200i | ||||
\(691\) | 1.08690i | 0.0413474i | 0.999786 | + | 0.0206737i | \(0.00658112\pi\) | ||||
−0.999786 | + | 0.0206737i | \(0.993419\pi\) | |||||||
\(692\) | 17.6882i | 0.672406i | ||||||||
\(693\) | −1.67630 | + | 2.09056i | −0.0636773 | + | 0.0794137i | ||||
\(694\) | 14.1605i | 0.537526i | ||||||||
\(695\) | 55.7631 | 2.11522 | ||||||||
\(696\) | −6.34735 | + | 2.01501i | −0.240596 | + | 0.0763789i | ||||
\(697\) | 10.4445 | − | 18.0336i | 0.395615 | − | 0.683073i | ||||
\(698\) | − | 20.9198i | − | 0.791827i | ||||||
\(699\) | −28.1245 | + | 8.92834i | −1.06377 | + | 0.337701i | ||||
\(700\) | −2.56297 | −0.0968713 | ||||||||
\(701\) | −6.24159 | −0.235742 | −0.117871 | − | 0.993029i | \(-0.537607\pi\) | ||||
−0.117871 | + | 0.993029i | \(0.537607\pi\) | |||||||
\(702\) | −18.4071 | + | 24.2833i | −0.694732 | + | 0.916515i | ||||
\(703\) | −0.710011 | −0.0267786 | ||||||||
\(704\) | −3.18733 | + | 0.917024i | −0.120127 | + | 0.0345616i | ||||
\(705\) | 18.2579 | − | 5.79611i | 0.687632 | − | 0.218294i | ||||
\(706\) | 32.5359i | 1.22450i | ||||||||
\(707\) | 0.941800 | 0.0354200 | ||||||||
\(708\) | 14.9622 | − | 4.74985i | 0.562313 | − | 0.178510i | ||||
\(709\) | 31.1513i | 1.16991i | 0.811065 | + | 0.584956i | \(0.198888\pi\) | ||||
−0.811065 | + | 0.584956i | \(0.801112\pi\) | |||||||
\(710\) | −21.1602 | −0.794128 | ||||||||
\(711\) | −31.8014 | + | 22.4541i | −1.19265 | + | 0.842095i | ||||
\(712\) | − | 11.6319i | − | 0.435925i | ||||||
\(713\) | 8.28346i | 0.310218i | ||||||||
\(714\) | −0.415148 | + | 1.87794i | −0.0155365 | + | 0.0702800i | ||||
\(715\) | 20.4892 | + | 71.2149i | 0.766251 | + | 2.66328i | ||||
\(716\) | 13.1756i | 0.492394i | ||||||||
\(717\) | −10.7269 | − | 33.7901i | −0.400605 | − | 1.26192i | ||||
\(718\) | 21.9753 | 0.820112 | ||||||||
\(719\) | 23.2545 | 0.867245 | 0.433622 | − | 0.901095i | \(-0.357235\pi\) | ||||
0.433622 | + | 0.901095i | \(0.357235\pi\) | |||||||
\(720\) | 9.33730 | − | 6.59282i | 0.347981 | − | 0.245700i | ||||
\(721\) | −0.00803628 | −0.000299287 | ||||||||
\(722\) | −18.9567 | −0.705494 | ||||||||
\(723\) | 2.63895 | + | 8.31277i | 0.0981437 | + | 0.309155i | ||||
\(724\) | − | 12.9449i | − | 0.481094i | ||||||
\(725\) | − | 36.5905i | − | 1.35894i | ||||||
\(726\) | −14.5339 | − | 12.3193i | −0.539403 | − | 0.457213i | ||||
\(727\) | 37.6407 | 1.39602 | 0.698008 | − | 0.716090i | \(-0.254070\pi\) | ||||
0.698008 | + | 0.716090i | \(0.254070\pi\) | |||||||
\(728\) | 1.57931i | 0.0585330i | ||||||||
\(729\) | 7.29470 | + | 25.9959i | 0.270174 | + | 0.962811i | ||||
\(730\) | −0.444010 | −0.0164335 | ||||||||
\(731\) | 12.6587 | − | 21.8566i | 0.468197 | − | 0.808395i | ||||
\(732\) | −0.919290 | − | 2.89579i | −0.0339779 | − | 0.107031i | ||||
\(733\) | 17.8701i | 0.660048i | 0.943973 | + | 0.330024i | \(0.107057\pi\) | ||||
−0.943973 | + | 0.330024i | \(0.892943\pi\) | |||||||
\(734\) | − | 15.0883i | − | 0.556920i | ||||||
\(735\) | 13.8326 | + | 43.5732i | 0.510225 | + | 1.60722i | ||||
\(736\) | 1.63790 | 0.0603738 | ||||||||
\(737\) | 35.9967 | − | 10.3566i | 1.32596 | − | 0.381489i | ||||
\(738\) | −8.74595 | − | 12.3868i | −0.321943 | − | 0.455963i | ||||
\(739\) | 14.1890i | 0.521951i | 0.965345 | + | 0.260975i | \(0.0840441\pi\) | ||||
−0.965345 | + | 0.260975i | \(0.915956\pi\) | |||||||
\(740\) | 12.9939i | 0.477666i | ||||||||
\(741\) | 0.639831 | + | 2.01548i | 0.0235048 | + | 0.0740407i | ||||
\(742\) | − | 1.03477i | − | 0.0379876i | ||||||
\(743\) | − | 8.05189i | − | 0.295395i | −0.989033 | − | 0.147698i | \(-0.952814\pi\) | ||
0.989033 | − | 0.147698i | \(-0.0471862\pi\) | |||||||
\(744\) | −8.34900 | + | 2.65045i | −0.306089 | + | 0.0971704i | ||||
\(745\) | 70.1641 | 2.57061 | ||||||||
\(746\) | − | 5.93570i | − | 0.217322i | ||||||
\(747\) | −42.5666 | + | 30.0552i | −1.55743 | + | 1.09966i | ||||
\(748\) | −13.2670 | − | 3.31451i | −0.485091 | − | 0.121190i | ||||
\(749\) | − | 3.93291i | − | 0.143705i | ||||||
\(750\) | 9.01889 | + | 28.4098i | 0.329323 | + | 1.03738i | ||||
\(751\) | 51.0587i | 1.86316i | 0.363536 | + | 0.931580i | \(0.381569\pi\) | ||||
−0.363536 | + | 0.931580i | \(0.618431\pi\) | |||||||
\(752\) | 2.90273i | 0.105852i | ||||||||
\(753\) | 0.245474 | − | 0.0779275i | 0.00894556 | − | 0.00283984i | ||||
\(754\) | −22.5471 | −0.821118 | ||||||||
\(755\) | 69.2270i | 2.51943i | ||||||||
\(756\) | 1.11521 | + | 0.845344i | 0.0405597 | + | 0.0307449i | ||||
\(757\) | 6.55550 | 0.238264 | 0.119132 | − | 0.992878i | \(-0.461989\pi\) | ||||
0.119132 | + | 0.992878i | \(0.461989\pi\) | |||||||
\(758\) | 22.7715i | 0.827099i | ||||||||
\(759\) | 5.21555 | + | 7.83120i | 0.189312 | + | 0.284255i | ||||
\(760\) | − | 0.793220i | − | 0.0287731i | ||||||
\(761\) | 10.6078 | 0.384534 | 0.192267 | − | 0.981343i | \(-0.438416\pi\) | ||||
0.192267 | + | 0.981343i | \(0.438416\pi\) | |||||||
\(762\) | −21.3052 | + | 6.76350i | −0.771806 | + | 0.245016i | ||||
\(763\) | 1.89165 | 0.0684823 | ||||||||
\(764\) | 3.19904i | 0.115737i | ||||||||
\(765\) | 46.9381 | − | 4.22774i | 1.69705 | − | 0.152854i | ||||
\(766\) | 17.8676i | 0.645582i | ||||||||
\(767\) | 53.1488 | 1.91909 | ||||||||
\(768\) | 0.524078 | + | 1.65086i | 0.0189110 | + | 0.0595703i | ||||
\(769\) | − | 0.919165i | − | 0.0331459i | −0.999863 | − | 0.0165730i | \(-0.994724\pi\) | ||
0.999863 | − | 0.0165730i | \(-0.00527558\pi\) | |||||||
\(770\) | 3.27053 | − | 0.940961i | 0.117862 | − | 0.0339099i | ||||
\(771\) | −17.1919 | + | 5.45770i | −0.619151 | + | 0.196554i | ||||
\(772\) | 19.3152 | 0.695170 | ||||||||
\(773\) | − | 43.8952i | − | 1.57880i | −0.613879 | − | 0.789400i | \(-0.710392\pi\) | ||
0.613879 | − | 0.789400i | \(-0.289608\pi\) | |||||||
\(774\) | −10.6000 | − | 15.0126i | −0.381009 | − | 0.539618i | ||||
\(775\) | − | 48.1295i | − | 1.72886i | ||||||
\(776\) | − | 12.7636i | − | 0.458187i | ||||||
\(777\) | −1.51626 | + | 0.481348i | −0.0543954 | + | 0.0172682i | ||||
\(778\) | − | 19.2714i | − | 0.690915i | ||||||
\(779\) | −1.05228 | −0.0377017 | ||||||||
\(780\) | 36.8854 | − | 11.7095i | 1.32071 | − | 0.419269i | ||||
\(781\) | 17.7016 | − | 5.09291i | 0.633413 | − | 0.182239i | ||||
\(782\) | 5.84387 | + | 3.38459i | 0.208976 | + | 0.121033i | ||||
\(783\) | −12.0686 | + | 15.9214i | −0.431298 | + | 0.568983i | ||||
\(784\) | −6.92747 | −0.247410 | ||||||||
\(785\) | 38.4283 | 1.37157 | ||||||||
\(786\) | 30.2489 | − | 9.60275i | 1.07894 | − | 0.342519i | ||||
\(787\) | 4.88175 | 0.174016 | 0.0870078 | − | 0.996208i | \(-0.472269\pi\) | ||||
0.0870078 | + | 0.996208i | \(0.472269\pi\) | |||||||
\(788\) | − | 19.6491i | − | 0.699971i | ||||||
\(789\) | −4.14149 | − | 13.0458i | −0.147441 | − | 0.464443i | ||||
\(790\) | 49.4417 | 1.75906 | ||||||||
\(791\) | −0.975858 | −0.0346975 | ||||||||
\(792\) | −6.22435 | + | 7.76257i | −0.221173 | + | 0.275831i | ||||
\(793\) | − | 10.2865i | − | 0.365283i | ||||||
\(794\) | 25.6830i | 0.911457i | ||||||||
\(795\) | −24.1675 | + | 7.67215i | −0.857132 | + | 0.272103i | ||||
\(796\) | − | 24.6476i | − | 0.873611i | ||||||
\(797\) | − | 17.4545i | − | 0.618269i | −0.951018 | − | 0.309135i | \(-0.899961\pi\) | ||
0.951018 | − | 0.309135i | \(-0.100039\pi\) | |||||||
\(798\) | 0.0925607 | − | 0.0293841i | 0.00327661 | − | 0.00104019i | ||||
\(799\) | −5.99825 | + | 10.3566i | −0.212203 | + | 0.366392i | ||||
\(800\) | −9.51672 | −0.336467 | ||||||||
\(801\) | −20.1274 | − | 28.5062i | −0.711168 | − | 1.00722i | ||||
\(802\) | 18.8429 | 0.665367 | ||||||||
\(803\) | 0.371437 | − | 0.106866i | 0.0131077 | − | 0.00377122i | ||||
\(804\) | −5.91878 | − | 18.6443i | −0.208739 | − | 0.657534i | ||||
\(805\) | −1.68066 | −0.0592353 | ||||||||
\(806\) | −29.6574 | −1.04464 | ||||||||
\(807\) | 9.22947 | + | 29.0731i | 0.324893 | + | 1.02342i | ||||
\(808\) | 3.49705 | 0.123026 | ||||||||
\(809\) | 38.3336i | 1.34774i | 0.738851 | + | 0.673869i | \(0.235369\pi\) | ||||
−0.738851 | + | 0.673869i | \(0.764631\pi\) | |||||||
\(810\) | 11.4748 | − | 32.3138i | 0.403184 | − | 1.13539i | ||||
\(811\) | −3.03947 | −0.106730 | −0.0533651 | − | 0.998575i | \(-0.516995\pi\) | ||||
−0.0533651 | + | 0.998575i | \(0.516995\pi\) | |||||||
\(812\) | 1.03547i | 0.0363380i | ||||||||
\(813\) | −22.1921 | + | 7.04505i | −0.778311 | + | 0.247081i | ||||
\(814\) | −3.12742 | − | 10.8701i | −0.109616 | − | 0.380996i | ||||
\(815\) | − | 43.1867i | − | 1.51277i | ||||||
\(816\) | −1.54151 | + | 6.97307i | −0.0539636 | + | 0.244106i | ||||
\(817\) | −1.27535 | −0.0446188 | ||||||||
\(818\) | − | 26.5587i | − | 0.928602i | ||||||
\(819\) | 2.73277 | + | 3.87038i | 0.0954907 | + | 0.135242i | ||||
\(820\) | 19.2577i | 0.672508i | ||||||||
\(821\) | − | 27.0637i | − | 0.944531i | −0.881456 | − | 0.472265i | \(-0.843436\pi\) | ||
0.881456 | − | 0.472265i | \(-0.156564\pi\) | |||||||
\(822\) | −30.2582 | + | 9.60570i | −1.05538 | + | 0.335037i | ||||
\(823\) | 21.9205i | 0.764102i | 0.924141 | + | 0.382051i | \(0.124782\pi\) | ||||
−0.924141 | + | 0.382051i | \(0.875218\pi\) | |||||||
\(824\) | −0.0298399 | −0.00103952 | ||||||||
\(825\) | −30.3040 | − | 45.5018i | −1.05505 | − | 1.58417i | ||||
\(826\) | − | 2.44085i | − | 0.0849280i | ||||||
\(827\) | − | 8.71197i | − | 0.302945i | −0.988461 | − | 0.151473i | \(-0.951598\pi\) | ||
0.988461 | − | 0.151473i | \(-0.0484015\pi\) | |||||||
\(828\) | 4.01398 | − | 2.83416i | 0.139495 | − | 0.0984939i | ||||
\(829\) | 15.2626 | 0.530091 | 0.265045 | − | 0.964236i | \(-0.414613\pi\) | ||||
0.265045 | + | 0.964236i | \(0.414613\pi\) | |||||||
\(830\) | 66.1784 | 2.29709 | ||||||||
\(831\) | −13.5249 | − | 42.6038i | −0.469173 | − | 1.47791i | ||||
\(832\) | 5.86421i | 0.203305i | ||||||||
\(833\) | −24.7165 | − | 14.3151i | −0.856377 | − | 0.495987i | ||||
\(834\) | 7.67024 | + | 24.1615i | 0.265599 | + | 0.836644i | ||||
\(835\) | 62.8703i | 2.17572i | ||||||||
\(836\) | 0.190915 | + | 0.663569i | 0.00660293 | + | 0.0229500i | ||||
\(837\) | −15.8745 | + | 20.9422i | −0.548704 | + | 0.723869i | ||||
\(838\) | 12.8821 | 0.445006 | ||||||||
\(839\) | −7.91778 | −0.273352 | −0.136676 | − | 0.990616i | \(-0.543642\pi\) | ||||
−0.136676 | + | 0.990616i | \(0.543642\pi\) | |||||||
\(840\) | −0.537759 | − | 1.69395i | −0.0185544 | − | 0.0584470i | ||||
\(841\) | 14.2170 | 0.490240 | ||||||||
\(842\) | 27.6448 | 0.952703 | ||||||||
\(843\) | 11.0992 | + | 34.9627i | 0.382275 | + | 1.20418i | ||||
\(844\) | 9.47591 | 0.326174 | ||||||||
\(845\) | 81.4937 | 2.80347 | ||||||||
\(846\) | 5.02277 | + | 7.11367i | 0.172686 | + | 0.244573i | ||||
\(847\) | −2.50949 | + | 1.57433i | −0.0862272 | + | 0.0540944i | ||||
\(848\) | − | 3.84226i | − | 0.131944i | ||||||
\(849\) | −11.8460 | − | 37.3151i | −0.406553 | − | 1.28065i | ||||
\(850\) | −33.9547 | − | 19.6655i | −1.16464 | − | 0.674522i | ||||
\(851\) | 5.58590i | 0.191482i | ||||||||
\(852\) | −2.91059 | − | 9.16845i | −0.0997153 | − | 0.314106i | ||||
\(853\) | 49.7498 | 1.70340 | 0.851701 | − | 0.524029i | \(-0.175572\pi\) | ||||
0.851701 | + | 0.524029i | \(0.175572\pi\) | |||||||
\(854\) | −0.472404 | −0.0161653 | ||||||||
\(855\) | −1.37256 | − | 1.94393i | −0.0469405 | − | 0.0664810i | ||||
\(856\) | − | 14.6035i | − | 0.499137i | ||||||
\(857\) | − | 7.50176i | − | 0.256255i | −0.991758 | − | 0.128128i | \(-0.959103\pi\) | ||
0.991758 | − | 0.128128i | \(-0.0408967\pi\) | |||||||
\(858\) | −28.0382 | + | 18.6733i | −0.957209 | + | 0.637497i | ||||
\(859\) | −28.9765 | −0.988665 | −0.494333 | − | 0.869273i | \(-0.664587\pi\) | ||||
−0.494333 | + | 0.869273i | \(0.664587\pi\) | |||||||
\(860\) | 23.3401i | 0.795892i | ||||||||
\(861\) | −2.24718 | + | 0.713384i | −0.0765837 | + | 0.0243121i | ||||
\(862\) | 19.3110i | 0.657736i | ||||||||
\(863\) | 2.03665i | 0.0693283i | 0.999399 | + | 0.0346641i | \(0.0110362\pi\) | ||||
−0.999399 | + | 0.0346641i | \(0.988964\pi\) | |||||||
\(864\) | 4.14094 | + | 3.13889i | 0.140877 | + | 0.106787i | ||||
\(865\) | − | 67.3936i | − | 2.29145i | ||||||
\(866\) | −8.00193 | −0.271917 | ||||||||
\(867\) | −19.9092 | + | 21.6938i | −0.676153 | + | 0.736761i | ||||
\(868\) | 1.36201i | 0.0462297i | ||||||||
\(869\) | −41.3606 | + | 11.8998i | −1.40306 | + | 0.403673i | ||||
\(870\) | 24.1839 | − | 7.67737i | 0.819911 | − | 0.260287i | ||||
\(871\) | − | 66.2285i | − | 2.24407i | ||||||
\(872\) | 7.02399 | 0.237862 | ||||||||
\(873\) | −22.0856 | − | 31.2796i | −0.747486 | − | 1.05865i | ||||
\(874\) | − | 0.340994i | − | 0.0115343i | ||||||
\(875\) | 4.63462 | 0.156679 | ||||||||
\(876\) | −0.0610738 | − | 0.192384i | −0.00206349 | − | 0.00650005i | ||||
\(877\) | 8.67875 | 0.293061 | 0.146530 | − | 0.989206i | \(-0.453189\pi\) | ||||
0.146530 | + | 0.989206i | \(0.453189\pi\) | |||||||
\(878\) | −22.5863 | −0.762252 | ||||||||
\(879\) | −5.39459 | − | 16.9931i | −0.181955 | − | 0.573163i | ||||
\(880\) | 12.1440 | − | 3.49393i | 0.409374 | − | 0.117781i | ||||
\(881\) | 25.2532 | 0.850801 | 0.425400 | − | 0.905005i | \(-0.360133\pi\) | ||||
0.425400 | + | 0.905005i | \(0.360133\pi\) | |||||||
\(882\) | −16.9770 | + | 11.9870i | −0.571647 | + | 0.403624i | ||||
\(883\) | −33.0923 | −1.11364 | −0.556822 | − | 0.830632i | \(-0.687979\pi\) | ||||
−0.556822 | + | 0.830632i | \(0.687979\pi\) | |||||||
\(884\) | −12.1179 | + | 20.9229i | −0.407569 | + | 0.703714i | ||||
\(885\) | −57.0071 | + | 18.0973i | −1.91627 | + | 0.608335i | ||||
\(886\) | 23.8935i | 0.802718i | ||||||||
\(887\) | − | 8.09508i | − | 0.271806i | −0.990722 | − | 0.135903i | \(-0.956606\pi\) | ||
0.990722 | − | 0.135903i | \(-0.0433936\pi\) | |||||||
\(888\) | −5.63010 | + | 1.78732i | −0.188934 | + | 0.0599785i | ||||
\(889\) | 3.47562i | 0.116568i | ||||||||
\(890\) | 44.3186i | 1.48556i | ||||||||
\(891\) | −1.82188 | + | 29.7940i | −0.0610353 | + | 0.998136i | ||||
\(892\) | −4.37502 | −0.146486 | ||||||||
\(893\) | 0.604318 | 0.0202227 | ||||||||
\(894\) | 9.65110 | + | 30.4012i | 0.322781 | + | 1.01677i | ||||
\(895\) | − | 50.1999i | − | 1.67800i | ||||||
\(896\) | 0.269313 | 0.00899711 | ||||||||
\(897\) | 15.8565 | − | 5.03377i | 0.529433 | − | 0.168073i | ||||
\(898\) | 26.3217 | 0.878367 | ||||||||
\(899\) | −19.4449 | −0.648524 | ||||||||
\(900\) | −23.3225 | + | 16.4674i | −0.777415 | + | 0.548912i | ||||
\(901\) | 7.93971 | − | 13.7088i | 0.264510 | − | 0.456706i | ||||
\(902\) | −4.63501 | − | 16.1101i | −0.154329 | − | 0.536407i | ||||
\(903\) | −2.72356 | + | 0.864614i | −0.0906344 | + | 0.0287726i | ||||
\(904\) | −3.62351 | −0.120516 | ||||||||
\(905\) | 49.3212i | 1.63949i | ||||||||
\(906\) | −29.9952 | + | 9.52220i | −0.996523 | + | 0.316354i | ||||
\(907\) | − | 5.27434i | − | 0.175132i | −0.996159 | − | 0.0875658i | \(-0.972091\pi\) | ||
0.996159 | − | 0.0875658i | \(-0.0279088\pi\) | |||||||
\(908\) | 2.57358i | 0.0854073i | ||||||||
\(909\) | 8.57017 | − | 6.05116i | 0.284254 | − | 0.200704i | ||||
\(910\) | − | 6.01729i | − | 0.199471i | ||||||
\(911\) | 8.17760 | 0.270936 | 0.135468 | − | 0.990782i | \(-0.456746\pi\) | ||||
0.135468 | + | 0.990782i | \(0.456746\pi\) | |||||||
\(912\) | 0.343692 | − | 0.109108i | 0.0113808 | − | 0.00361292i | ||||
\(913\) | −55.3617 | + | 15.9281i | −1.83220 | + | 0.527142i | ||||
\(914\) | 4.89134i | 0.161791i | ||||||||
\(915\) | 3.50257 | + | 11.0332i | 0.115791 | + | 0.364746i | ||||
\(916\) | −15.5344 | −0.513273 | ||||||||
\(917\) | − | 4.93465i | − | 0.162956i | ||||||
\(918\) | 8.28818 | + | 19.7562i | 0.273551 | + | 0.652051i | ||||
\(919\) | − | 57.1993i | − | 1.88683i | −0.331613 | − | 0.943416i | \(-0.607593\pi\) | ||
0.331613 | − | 0.943416i | \(-0.392407\pi\) | |||||||
\(920\) | −6.24053 | −0.205744 | ||||||||
\(921\) | 28.7863 | − | 9.13843i | 0.948540 | − | 0.301121i | ||||
\(922\) | 12.4471 | 0.409922 | ||||||||
\(923\) | − | 32.5683i | − | 1.07200i | ||||||
\(924\) | 0.857570 | + | 1.28765i | 0.0282120 | + | 0.0423606i | ||||
\(925\) | − | 32.4558i | − | 1.06714i | ||||||
\(926\) | 13.4617 | 0.442379 | ||||||||
\(927\) | −0.0731283 | + | 0.0516339i | −0.00240185 | + | 0.00169588i | ||||
\(928\) | 3.84487i | 0.126214i | ||||||||
\(929\) | 26.5037 | 0.869558 | 0.434779 | − | 0.900537i | \(-0.356826\pi\) | ||||
0.434779 | + | 0.900537i | \(0.356826\pi\) | |||||||
\(930\) | 31.8104 | − | 10.0984i | 1.04310 | − | 0.331141i | ||||
\(931\) | 1.44223i | 0.0472671i | ||||||||
\(932\) | 17.0363i | 0.558042i | ||||||||
\(933\) | 1.70789 | + | 5.37989i | 0.0559137 | + | 0.176130i | ||||
\(934\) | 38.7575i | 1.26818i | ||||||||
\(935\) | 50.5485 | + | 12.6285i | 1.65311 | + | 0.412997i | ||||
\(936\) | 10.1472 | + | 14.3713i | 0.331672 | + | 0.469741i | ||||
\(937\) | 1.25415i | 0.0409713i | 0.999790 | + | 0.0204856i | \(0.00652123\pi\) | ||||
−0.999790 | + | 0.0204856i | \(0.993479\pi\) | |||||||
\(938\) | −3.04153 | −0.0993096 | ||||||||
\(939\) | 19.8107 | − | 6.28905i | 0.646497 | − | 0.205236i | ||||
\(940\) | − | 11.0596i | − | 0.360725i | ||||||
\(941\) | 17.3204i | 0.564629i | 0.959322 | + | 0.282314i | \(0.0911021\pi\) | ||||
−0.959322 | + | 0.282314i | \(0.908898\pi\) | |||||||
\(942\) | 5.28583 | + | 16.6505i | 0.172222 | + | 0.542503i | ||||
\(943\) | 8.27862i | 0.269589i | ||||||||
\(944\) | − | 9.06325i | − | 0.294984i | ||||||
\(945\) | −4.24903 | − | 3.22083i | −0.138221 | − | 0.104774i | ||||
\(946\) | −5.61759 | − | 19.5252i | −0.182644 | − | 0.634820i | ||||
\(947\) | 24.8033 | 0.806000 | 0.403000 | − | 0.915200i | \(-0.367967\pi\) | ||||
0.403000 | + | 0.915200i | \(0.367967\pi\) | |||||||
\(948\) | 6.80073 | + | 21.4225i | 0.220878 | + | 0.695770i | ||||
\(949\) | − | 0.683389i | − | 0.0221838i | ||||||
\(950\) | 1.98128i | 0.0642813i | ||||||||
\(951\) | −10.0382 | − | 31.6206i | −0.325511 | − | 1.02537i | ||||
\(952\) | 0.960881 | + | 0.556513i | 0.0311423 | + | 0.0180367i | ||||
\(953\) | 5.01668 | 0.162506 | 0.0812531 | − | 0.996693i | \(-0.474108\pi\) | ||||
0.0812531 | + | 0.996693i | \(0.474108\pi\) | |||||||
\(954\) | −6.64849 | − | 9.41616i | −0.215253 | − | 0.304859i | ||||
\(955\) | − | 12.1886i | − | 0.394414i | ||||||
\(956\) | −20.4682 | −0.661989 | ||||||||
\(957\) | −18.3833 | + | 12.2432i | −0.594247 | + | 0.395766i | ||||
\(958\) | 24.4680i | 0.790526i | ||||||||
\(959\) | 4.93617i | 0.159397i | ||||||||
\(960\) | −1.99678 | − | 6.28991i | −0.0644458 | − | 0.203006i | ||||
\(961\) | 5.42309 | 0.174938 | ||||||||
\(962\) | −19.9993 | −0.644804 | ||||||||
\(963\) | −25.2693 | − | 35.7885i | −0.814292 | − | 1.15327i | ||||
\(964\) | 5.03541 | 0.162180 | ||||||||
\(965\) | −73.5925 | −2.36903 | ||||||||
\(966\) | −0.231175 | − | 0.728207i | −0.00743793 | − | 0.0234297i | ||||
\(967\) | 0.403403i | 0.0129726i | 0.999979 | + | 0.00648628i | \(0.00206466\pi\) | ||||
−0.999979 | + | 0.00648628i | \(0.997935\pi\) | |||||||
\(968\) | −9.31813 | + | 5.84571i | −0.299496 | + | 0.187888i | ||||
\(969\) | 1.45172 | + | 0.320926i | 0.0466360 | + | 0.0103096i | ||||
\(970\) | 48.6304i | 1.56143i | ||||||||
\(971\) | − | 16.5716i | − | 0.531809i | −0.963999 | − | 0.265905i | \(-0.914329\pi\) | ||
0.963999 | − | 0.265905i | \(-0.0856707\pi\) | |||||||
\(972\) | 15.5795 | + | 0.527120i | 0.499714 | + | 0.0169074i | ||||
\(973\) | 3.94158 | 0.126361 | ||||||||
\(974\) | 21.1813i | 0.678693i | ||||||||
\(975\) | −92.1313 | + | 29.2478i | −2.95056 | + | 0.936679i | ||||
\(976\) | −1.75411 | −0.0561476 | ||||||||
\(977\) | 24.7025i | 0.790304i | 0.918616 | + | 0.395152i | \(0.129308\pi\) | ||||
−0.918616 | + | 0.395152i | \(0.870692\pi\) | |||||||
\(978\) | 18.7123 | − | 5.94036i | 0.598353 | − | 0.189952i | ||||
\(979\) | −10.6668 | − | 37.0748i | −0.340911 | − | 1.18492i | ||||
\(980\) | 26.3942 | 0.843133 | ||||||||
\(981\) | 17.2136 | − | 12.1540i | 0.549587 | − | 0.388048i | ||||
\(982\) | −12.1109 | −0.386475 | ||||||||
\(983\) | −2.97699 | −0.0949512 | −0.0474756 | − | 0.998872i | \(-0.515118\pi\) | ||||
−0.0474756 | + | 0.998872i | \(0.515118\pi\) | |||||||
\(984\) | −8.34413 | + | 2.64891i | −0.266001 | + | 0.0844441i | ||||
\(985\) | 74.8647i | 2.38539i | ||||||||
\(986\) | −7.94511 | + | 13.7181i | −0.253024 | + | 0.436874i | ||||
\(987\) | 1.29055 | − | 0.409694i | 0.0410785 | − | 0.0130407i | ||||
\(988\) | 1.22087 | 0.0388410 | ||||||||
\(989\) | 10.0336i | 0.319050i | ||||||||
\(990\) | 23.7153 | − | 29.5760i | 0.753721 | − | 0.939987i | ||||
\(991\) | 3.69608i | 0.117410i | 0.998275 | + | 0.0587049i | \(0.0186971\pi\) | ||||
−0.998275 | + | 0.0587049i | \(0.981303\pi\) | |||||||
\(992\) | 5.05736i | 0.160571i | ||||||||
\(993\) | −1.85839 | − | 5.85398i | −0.0589742 | − | 0.185770i | ||||
\(994\) | −1.49569 | −0.0474405 | ||||||||
\(995\) | 93.9094i | 2.97713i | ||||||||
\(996\) | 9.10287 | + | 28.6743i | 0.288436 | + | 0.908580i | ||||
\(997\) | 21.7776 | 0.689704 | 0.344852 | − | 0.938657i | \(-0.387929\pi\) | ||||
0.344852 | + | 0.938657i | \(0.387929\pi\) | |||||||
\(998\) | − | 28.5486i | − | 0.903691i | ||||||
\(999\) | −10.7049 | + | 14.1223i | −0.338688 | + | 0.446808i |
(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 | 1122.2.h.g.1121.18 | yes | 28 | |
3.2 | odd | 2 | 1122.2.h.h.1121.12 | yes | 28 | ||
11.10 | odd | 2 | 1122.2.h.h.1121.18 | yes | 28 | ||
17.16 | even | 2 | inner | 1122.2.h.g.1121.11 | ✓ | 28 | |
33.32 | even | 2 | inner | 1122.2.h.g.1121.12 | yes | 28 | |
51.50 | odd | 2 | 1122.2.h.h.1121.17 | yes | 28 | ||
187.186 | odd | 2 | 1122.2.h.h.1121.11 | yes | 28 | ||
561.560 | even | 2 | inner | 1122.2.h.g.1121.17 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1122.2.h.g.1121.11 | ✓ | 28 | 17.16 | even | 2 | inner | |
1122.2.h.g.1121.12 | yes | 28 | 33.32 | even | 2 | inner | |
1122.2.h.g.1121.17 | yes | 28 | 561.560 | even | 2 | inner | |
1122.2.h.g.1121.18 | yes | 28 | 1.1 | even | 1 | trivial | |
1122.2.h.h.1121.11 | yes | 28 | 187.186 | odd | 2 | ||
1122.2.h.h.1121.12 | yes | 28 | 3.2 | odd | 2 | ||
1122.2.h.h.1121.17 | yes | 28 | 51.50 | odd | 2 | ||
1122.2.h.h.1121.18 | yes | 28 | 11.10 | odd | 2 |