Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [420,2,Mod(71,420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(420, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("420.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 420.n (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: | \(3.35371688489\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.17 | ||
Character | \(\chi\) | \(=\) | 420.71 |
Dual form | 420.2.n.b.71.18 |
$q$-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 \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(241\) | \(281\) | \(337\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.09123 | − | 0.899566i | 0.771616 | − | 0.636089i | ||||
\(3\) | −0.826488 | − | 1.52214i | −0.477173 | − | 0.878809i | ||||
\(4\) | 0.381563 | − | 1.96327i | 0.190782 | − | 0.981633i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −2.27116 | − | 0.917526i | −0.927195 | − | 0.374578i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −1.34971 | − | 2.48561i | −0.477196 | − | 0.878797i | ||||
\(9\) | −1.63383 | + | 2.51607i | −0.544611 | + | 0.838689i | ||||
\(10\) | −0.899566 | − | 1.09123i | −0.284468 | − | 0.345077i | ||||
\(11\) | −2.07669 | −0.626146 | −0.313073 | − | 0.949729i | \(-0.601358\pi\) | ||||
−0.313073 | + | 0.949729i | \(0.601358\pi\) | |||||||
\(12\) | −3.30373 | + | 1.04182i | −0.953704 | + | 0.300748i | ||||
\(13\) | 3.88750 | 1.07820 | 0.539099 | − | 0.842243i | \(-0.318765\pi\) | ||||
0.539099 | + | 0.842243i | \(0.318765\pi\) | |||||||
\(14\) | −0.899566 | − | 1.09123i | −0.240419 | − | 0.291643i | ||||
\(15\) | −1.52214 | + | 0.826488i | −0.393015 | + | 0.213398i | ||||
\(16\) | −3.70882 | − | 1.49822i | −0.927205 | − | 0.374555i | ||||
\(17\) | 1.08277i | 0.262611i | 0.991342 | + | 0.131306i | \(0.0419169\pi\) | ||||
−0.991342 | + | 0.131306i | \(0.958083\pi\) | |||||||
\(18\) | 0.480479 | + | 4.21535i | 0.113250 | + | 0.993567i | ||||
\(19\) | − | 1.74609i | − | 0.400582i | −0.979737 | − | 0.200291i | \(-0.935811\pi\) | ||
0.979737 | − | 0.200291i | \(-0.0641887\pi\) | |||||||
\(20\) | −1.96327 | − | 0.381563i | −0.438999 | − | 0.0853201i | ||||
\(21\) | −1.52214 | + | 0.826488i | −0.332159 | + | 0.180355i | ||||
\(22\) | −2.26615 | + | 1.86812i | −0.483144 | + | 0.398284i | ||||
\(23\) | 0.0176032 | 0.00367053 | 0.00183526 | − | 0.999998i | \(-0.499416\pi\) | ||||
0.00183526 | + | 0.999998i | \(0.499416\pi\) | |||||||
\(24\) | −2.66794 | + | 4.10879i | −0.544590 | + | 0.838702i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 4.24215 | − | 3.49706i | 0.831954 | − | 0.685829i | ||||
\(27\) | 5.18015 | + | 0.407427i | 0.996921 | + | 0.0784095i | ||||
\(28\) | −1.96327 | − | 0.381563i | −0.371022 | − | 0.0721087i | ||||
\(29\) | 9.28540i | 1.72426i | 0.506691 | + | 0.862128i | \(0.330869\pi\) | ||||
−0.506691 | + | 0.862128i | \(0.669131\pi\) | |||||||
\(30\) | −0.917526 | + | 2.27116i | −0.167516 | + | 0.414654i | ||||
\(31\) | − | 10.8667i | − | 1.95171i | −0.218419 | − | 0.975855i | \(-0.570090\pi\) | ||
0.218419 | − | 0.975855i | \(-0.429910\pi\) | |||||||
\(32\) | −5.39492 | + | 1.70143i | −0.953696 | + | 0.300772i | ||||
\(33\) | 1.71636 | + | 3.16102i | 0.298780 | + | 0.550262i | ||||
\(34\) | 0.974026 | + | 1.18155i | 0.167044 | + | 0.202635i | ||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 4.31629 | + | 4.16769i | 0.719382 | + | 0.694614i | ||||
\(37\) | 6.46752 | 1.06325 | 0.531627 | − | 0.846978i | \(-0.321581\pi\) | ||||
0.531627 | + | 0.846978i | \(0.321581\pi\) | |||||||
\(38\) | −1.57073 | − | 1.90539i | −0.254805 | − | 0.309095i | ||||
\(39\) | −3.21297 | − | 5.91732i | −0.514487 | − | 0.947530i | ||||
\(40\) | −2.48561 | + | 1.34971i | −0.393010 | + | 0.213408i | ||||
\(41\) | − | 9.66961i | − | 1.51014i | −0.655645 | − | 0.755069i | \(-0.727603\pi\) | ||
0.655645 | − | 0.755069i | \(-0.272397\pi\) | |||||||
\(42\) | −0.917526 | + | 2.27116i | −0.141577 | + | 0.350447i | ||||
\(43\) | 3.43356i | 0.523613i | 0.965120 | + | 0.261807i | \(0.0843183\pi\) | ||||
−0.965120 | + | 0.261807i | \(0.915682\pi\) | |||||||
\(44\) | −0.792388 | + | 4.07709i | −0.119457 | + | 0.614645i | ||||
\(45\) | 2.51607 | + | 1.63383i | 0.375073 | + | 0.243558i | ||||
\(46\) | 0.0192092 | − | 0.0158353i | 0.00283224 | − | 0.00233478i | ||||
\(47\) | 0.213241 | 0.0311044 | 0.0155522 | − | 0.999879i | \(-0.495049\pi\) | ||||
0.0155522 | + | 0.999879i | \(0.495049\pi\) | |||||||
\(48\) | 0.784794 | + | 6.88361i | 0.113275 | + | 0.993564i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −1.09123 | + | 0.899566i | −0.154323 | + | 0.127218i | ||||
\(51\) | 1.64814 | − | 0.894900i | 0.230785 | − | 0.125311i | ||||
\(52\) | 1.48333 | − | 7.63218i | 0.205700 | − | 1.05839i | ||||
\(53\) | − | 7.93599i | − | 1.09009i | −0.838406 | − | 0.545046i | \(-0.816512\pi\) | ||
0.838406 | − | 0.545046i | \(-0.183488\pi\) | |||||||
\(54\) | 6.01924 | − | 4.21529i | 0.819115 | − | 0.573629i | ||||
\(55\) | 2.07669i | 0.280021i | ||||||||
\(56\) | −2.48561 | + | 1.34971i | −0.332154 | + | 0.180363i | ||||
\(57\) | −2.65780 | + | 1.44313i | −0.352035 | + | 0.191147i | ||||
\(58\) | 8.35283 | + | 10.1325i | 1.09678 | + | 1.33046i | ||||
\(59\) | 2.98100 | 0.388093 | 0.194046 | − | 0.980992i | \(-0.437839\pi\) | ||||
0.194046 | + | 0.980992i | \(0.437839\pi\) | |||||||
\(60\) | 1.04182 | + | 3.30373i | 0.134499 | + | 0.426509i | ||||
\(61\) | 8.36640 | 1.07121 | 0.535604 | − | 0.844469i | \(-0.320084\pi\) | ||||
0.535604 | + | 0.844469i | \(0.320084\pi\) | |||||||
\(62\) | −9.77528 | − | 11.8580i | −1.24146 | − | 1.50597i | ||||
\(63\) | 2.51607 | + | 1.63383i | 0.316995 | + | 0.205844i | ||||
\(64\) | −4.35655 | + | 6.70973i | −0.544569 | + | 0.838716i | ||||
\(65\) | − | 3.88750i | − | 0.482184i | ||||||
\(66\) | 4.71649 | + | 1.90542i | 0.580559 | + | 0.234541i | ||||
\(67\) | 7.12183i | 0.870070i | 0.900414 | + | 0.435035i | \(0.143264\pi\) | ||||
−0.900414 | + | 0.435035i | \(0.856736\pi\) | |||||||
\(68\) | 2.12577 | + | 0.413147i | 0.257788 | + | 0.0501014i | ||||
\(69\) | −0.0145489 | − | 0.0267946i | −0.00175148 | − | 0.00322569i | ||||
\(70\) | −1.09123 | + | 0.899566i | −0.130427 | + | 0.107519i | ||||
\(71\) | 4.44568 | 0.527605 | 0.263803 | − | 0.964577i | \(-0.415023\pi\) | ||||
0.263803 | + | 0.964577i | \(0.415023\pi\) | |||||||
\(72\) | 8.45917 | + | 0.665112i | 0.996923 | + | 0.0783842i | ||||
\(73\) | 5.62152 | 0.657950 | 0.328975 | − | 0.944339i | \(-0.393297\pi\) | ||||
0.328975 | + | 0.944339i | \(0.393297\pi\) | |||||||
\(74\) | 7.05755 | − | 5.81796i | 0.820424 | − | 0.676324i | ||||
\(75\) | 0.826488 | + | 1.52214i | 0.0954347 | + | 0.175762i | ||||
\(76\) | −3.42805 | − | 0.666245i | −0.393224 | − | 0.0764236i | ||||
\(77\) | 2.07669i | 0.236661i | ||||||||
\(78\) | −8.82911 | − | 3.56688i | −0.999699 | − | 0.403869i | ||||
\(79\) | − | 2.33735i | − | 0.262972i | −0.991318 | − | 0.131486i | \(-0.958025\pi\) | ||
0.991318 | − | 0.131486i | \(-0.0419748\pi\) | |||||||
\(80\) | −1.49822 | + | 3.70882i | −0.167506 | + | 0.414659i | ||||
\(81\) | −3.66118 | − | 8.22167i | −0.406797 | − | 0.913518i | ||||
\(82\) | −8.69845 | − | 10.5518i | −0.960583 | − | 1.16525i | ||||
\(83\) | 3.90649 | 0.428793 | 0.214397 | − | 0.976747i | \(-0.431222\pi\) | ||||
0.214397 | + | 0.976747i | \(0.431222\pi\) | |||||||
\(84\) | 1.04182 | + | 3.30373i | 0.113672 | + | 0.360466i | ||||
\(85\) | 1.08277 | 0.117443 | ||||||||
\(86\) | 3.08871 | + | 3.74680i | 0.333065 | + | 0.404028i | ||||
\(87\) | 14.1337 | − | 7.67428i | 1.51529 | − | 0.822769i | ||||
\(88\) | 2.80294 | + | 5.16185i | 0.298794 | + | 0.550255i | ||||
\(89\) | 1.16319i | 0.123297i | 0.998098 | + | 0.0616487i | \(0.0196358\pi\) | ||||
−0.998098 | + | 0.0616487i | \(0.980364\pi\) | |||||||
\(90\) | 4.21535 | − | 0.480479i | 0.444336 | − | 0.0506470i | ||||
\(91\) | − | 3.88750i | − | 0.407520i | ||||||
\(92\) | 0.00671675 | − | 0.0345598i | 0.000700269 | − | 0.00360311i | ||||
\(93\) | −16.5406 | + | 8.98117i | −1.71518 | + | 0.931304i | ||||
\(94\) | 0.232695 | − | 0.191824i | 0.0240006 | − | 0.0197852i | ||||
\(95\) | −1.74609 | −0.179146 | ||||||||
\(96\) | 7.04865 | + | 6.80563i | 0.719400 | + | 0.694596i | ||||
\(97\) | 11.4536 | 1.16294 | 0.581470 | − | 0.813568i | \(-0.302478\pi\) | ||||
0.581470 | + | 0.813568i | \(0.302478\pi\) | |||||||
\(98\) | −1.09123 | + | 0.899566i | −0.110231 | + | 0.0908699i | ||||
\(99\) | 3.39297 | − | 5.22509i | 0.341006 | − | 0.525141i | ||||
\(100\) | −0.381563 | + | 1.96327i | −0.0381563 | + | 0.196327i | ||||
\(101\) | 1.81896i | 0.180993i | 0.995897 | + | 0.0904966i | \(0.0288454\pi\) | ||||
−0.995897 | + | 0.0904966i | \(0.971155\pi\) | |||||||
\(102\) | 0.993473 | − | 2.45915i | 0.0983684 | − | 0.243492i | ||||
\(103\) | 19.5278i | 1.92413i | 0.272826 | + | 0.962063i | \(0.412042\pi\) | ||||
−0.272826 | + | 0.962063i | \(0.587958\pi\) | |||||||
\(104\) | −5.24700 | − | 9.66281i | −0.514511 | − | 0.947517i | ||||
\(105\) | 0.826488 | + | 1.52214i | 0.0806570 | + | 0.148546i | ||||
\(106\) | −7.13894 | − | 8.65998i | −0.693395 | − | 0.841132i | ||||
\(107\) | 17.1849 | 1.66133 | 0.830666 | − | 0.556771i | \(-0.187960\pi\) | ||||
0.830666 | + | 0.556771i | \(0.187960\pi\) | |||||||
\(108\) | 2.77644 | − | 10.0146i | 0.267163 | − | 0.963651i | ||||
\(109\) | −17.4510 | −1.67150 | −0.835750 | − | 0.549110i | \(-0.814967\pi\) | ||||
−0.835750 | + | 0.549110i | \(0.814967\pi\) | |||||||
\(110\) | 1.86812 | + | 2.26615i | 0.178118 | + | 0.216068i | ||||
\(111\) | −5.34533 | − | 9.84449i | −0.507357 | − | 0.934398i | ||||
\(112\) | −1.49822 | + | 3.70882i | −0.141568 | + | 0.350450i | ||||
\(113\) | − | 3.38532i | − | 0.318464i | −0.987241 | − | 0.159232i | \(-0.949098\pi\) | ||
0.987241 | − | 0.159232i | \(-0.0509018\pi\) | |||||||
\(114\) | −1.60209 | + | 3.96565i | −0.150049 | + | 0.371417i | ||||
\(115\) | − | 0.0176032i | − | 0.00164151i | ||||||
\(116\) | 18.2297 | + | 3.54297i | 1.69259 | + | 0.328956i | ||||
\(117\) | −6.35152 | + | 9.78120i | −0.587198 | + | 0.904272i | ||||
\(118\) | 3.25295 | − | 2.68160i | 0.299458 | − | 0.246862i | ||||
\(119\) | 1.08277 | 0.0992577 | ||||||||
\(120\) | 4.10879 | + | 2.66794i | 0.375079 | + | 0.243548i | ||||
\(121\) | −6.68736 | −0.607942 | ||||||||
\(122\) | 9.12966 | − | 7.52613i | 0.826561 | − | 0.681384i | ||||
\(123\) | −14.7185 | + | 7.99182i | −1.32712 | + | 0.720598i | ||||
\(124\) | −21.3341 | − | 4.14632i | −1.91586 | − | 0.372350i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 4.21535 | − | 0.480479i | 0.375533 | − | 0.0428045i | ||||
\(127\) | 15.8920i | 1.41019i | 0.709113 | + | 0.705095i | \(0.249096\pi\) | ||||
−0.709113 | + | 0.705095i | \(0.750904\pi\) | |||||||
\(128\) | 1.28185 | + | 11.2409i | 0.113300 | + | 0.993561i | ||||
\(129\) | 5.22637 | − | 2.83780i | 0.460156 | − | 0.249854i | ||||
\(130\) | −3.49706 | − | 4.24215i | −0.306712 | − | 0.372061i | ||||
\(131\) | −13.2810 | −1.16036 | −0.580182 | − | 0.814487i | \(-0.697019\pi\) | ||||
−0.580182 | + | 0.814487i | \(0.697019\pi\) | |||||||
\(132\) | 6.86081 | − | 2.16354i | 0.597157 | − | 0.188312i | ||||
\(133\) | −1.74609 | −0.151406 | ||||||||
\(134\) | 6.40655 | + | 7.77155i | 0.553442 | + | 0.671360i | ||||
\(135\) | 0.407427 | − | 5.18015i | 0.0350658 | − | 0.445837i | ||||
\(136\) | 2.69136 | − | 1.46143i | 0.230782 | − | 0.125317i | ||||
\(137\) | − | 15.2183i | − | 1.30019i | −0.759853 | − | 0.650095i | \(-0.774729\pi\) | ||
0.759853 | − | 0.650095i | \(-0.225271\pi\) | |||||||
\(138\) | −0.0399797 | − | 0.0161514i | −0.00340330 | − | 0.00137490i | ||||
\(139\) | 13.5504i | 1.14933i | 0.818390 | + | 0.574664i | \(0.194867\pi\) | ||||
−0.818390 | + | 0.574664i | \(0.805133\pi\) | |||||||
\(140\) | −0.381563 | + | 1.96327i | −0.0322480 | + | 0.165926i | ||||
\(141\) | −0.176241 | − | 0.324583i | −0.0148422 | − | 0.0273348i | ||||
\(142\) | 4.85126 | − | 3.99918i | 0.407108 | − | 0.335604i | ||||
\(143\) | −8.07312 | −0.675108 | ||||||||
\(144\) | 9.82921 | − | 6.88379i | 0.819101 | − | 0.573649i | ||||
\(145\) | 9.28540 | 0.771111 | ||||||||
\(146\) | 6.13437 | − | 5.05693i | 0.507684 | − | 0.418514i | ||||
\(147\) | 0.826488 | + | 1.52214i | 0.0681676 | + | 0.125544i | ||||
\(148\) | 2.46777 | − | 12.6975i | 0.202849 | − | 1.04373i | ||||
\(149\) | − | 4.07558i | − | 0.333885i | −0.985967 | − | 0.166942i | \(-0.946611\pi\) | ||
0.985967 | − | 0.166942i | \(-0.0533894\pi\) | |||||||
\(150\) | 2.27116 | + | 0.917526i | 0.185439 | + | 0.0749157i | ||||
\(151\) | − | 6.96098i | − | 0.566477i | −0.959050 | − | 0.283238i | \(-0.908591\pi\) | ||
0.959050 | − | 0.283238i | \(-0.0914087\pi\) | |||||||
\(152\) | −4.34012 | + | 2.35673i | −0.352030 | + | 0.191156i | ||||
\(153\) | −2.72433 | − | 1.76907i | −0.220249 | − | 0.143021i | ||||
\(154\) | 1.86812 | + | 2.26615i | 0.150537 | + | 0.182611i | ||||
\(155\) | −10.8667 | −0.872831 | ||||||||
\(156\) | −12.8432 | + | 4.05008i | −1.02828 | + | 0.324266i | ||||
\(157\) | −18.2695 | −1.45806 | −0.729031 | − | 0.684481i | \(-0.760029\pi\) | ||||
−0.729031 | + | 0.684481i | \(0.760029\pi\) | |||||||
\(158\) | −2.10260 | − | 2.55058i | −0.167274 | − | 0.202913i | ||||
\(159\) | −12.0797 | + | 6.55900i | −0.957983 | + | 0.520163i | ||||
\(160\) | 1.70143 | + | 5.39492i | 0.134510 | + | 0.426506i | ||||
\(161\) | − | 0.0176032i | − | 0.00138733i | ||||||
\(162\) | −11.3911 | − | 5.67826i | −0.894970 | − | 0.446126i | ||||
\(163\) | 4.26875i | 0.334354i | 0.985927 | + | 0.167177i | \(0.0534652\pi\) | ||||
−0.985927 | + | 0.167177i | \(0.946535\pi\) | |||||||
\(164\) | −18.9840 | − | 3.68957i | −1.48240 | − | 0.288107i | ||||
\(165\) | 3.16102 | − | 1.71636i | 0.246085 | − | 0.133618i | ||||
\(166\) | 4.26288 | − | 3.51415i | 0.330864 | − | 0.272751i | ||||
\(167\) | −19.7862 | −1.53110 | −0.765550 | − | 0.643376i | \(-0.777533\pi\) | ||||
−0.765550 | + | 0.643376i | \(0.777533\pi\) | |||||||
\(168\) | 4.10879 | + | 2.66794i | 0.317000 | + | 0.205836i | ||||
\(169\) | 2.11262 | 0.162509 | ||||||||
\(170\) | 1.18155 | − | 0.974026i | 0.0906211 | − | 0.0747044i | ||||
\(171\) | 4.39329 | + | 2.85283i | 0.335963 | + | 0.218161i | ||||
\(172\) | 6.74099 | + | 1.31012i | 0.513996 | + | 0.0998958i | ||||
\(173\) | 15.7824i | 1.19991i | 0.800032 | + | 0.599957i | \(0.204816\pi\) | ||||
−0.800032 | + | 0.599957i | \(0.795184\pi\) | |||||||
\(174\) | 8.51959 | − | 21.0886i | 0.645869 | − | 1.59872i | ||||
\(175\) | 1.00000i | 0.0755929i | ||||||||
\(176\) | 7.70207 | + | 3.11134i | 0.580565 | + | 0.234526i | ||||
\(177\) | −2.46376 | − | 4.53750i | −0.185188 | − | 0.341059i | ||||
\(178\) | 1.04636 | + | 1.26930i | 0.0784281 | + | 0.0951382i | ||||
\(179\) | 21.5974 | 1.61427 | 0.807134 | − | 0.590369i | \(-0.201018\pi\) | ||||
0.807134 | + | 0.590369i | \(0.201018\pi\) | |||||||
\(180\) | 4.16769 | − | 4.31629i | 0.310641 | − | 0.321718i | ||||
\(181\) | 21.1987 | 1.57569 | 0.787845 | − | 0.615874i | \(-0.211197\pi\) | ||||
0.787845 | + | 0.615874i | \(0.211197\pi\) | |||||||
\(182\) | −3.49706 | − | 4.24215i | −0.259219 | − | 0.314449i | ||||
\(183\) | −6.91473 | − | 12.7349i | −0.511152 | − | 0.941387i | ||||
\(184\) | −0.0237593 | − | 0.0437549i | −0.00175156 | − | 0.00322565i | ||||
\(185\) | − | 6.46752i | − | 0.475502i | ||||||
\(186\) | −9.97044 | + | 24.6799i | −0.731068 | + | 1.80962i | ||||
\(187\) | − | 2.24859i | − | 0.164433i | ||||||
\(188\) | 0.0813649 | − | 0.418648i | 0.00593414 | − | 0.0305331i | ||||
\(189\) | 0.407427 | − | 5.18015i | 0.0296360 | − | 0.376801i | ||||
\(190\) | −1.90539 | + | 1.57073i | −0.138231 | + | 0.113952i | ||||
\(191\) | −19.1594 | −1.38633 | −0.693164 | − | 0.720780i | \(-0.743784\pi\) | ||||
−0.693164 | + | 0.720780i | \(0.743784\pi\) | |||||||
\(192\) | 13.8138 | + | 1.08577i | 0.996925 | + | 0.0783590i | ||||
\(193\) | 11.6629 | 0.839516 | 0.419758 | − | 0.907636i | \(-0.362115\pi\) | ||||
0.419758 | + | 0.907636i | \(0.362115\pi\) | |||||||
\(194\) | 12.4985 | − | 10.3033i | 0.897343 | − | 0.739734i | ||||
\(195\) | −5.91732 | + | 3.21297i | −0.423748 | + | 0.230086i | ||||
\(196\) | −0.381563 | + | 1.96327i | −0.0272545 | + | 0.140233i | ||||
\(197\) | 24.8253i | 1.76873i | 0.466796 | + | 0.884365i | \(0.345408\pi\) | ||||
−0.466796 | + | 0.884365i | \(0.654592\pi\) | |||||||
\(198\) | −0.997807 | − | 8.75397i | −0.0709110 | − | 0.622117i | ||||
\(199\) | 23.6092i | 1.67361i | 0.547502 | + | 0.836804i | \(0.315579\pi\) | ||||
−0.547502 | + | 0.836804i | \(0.684421\pi\) | |||||||
\(200\) | 1.34971 | + | 2.48561i | 0.0954391 | + | 0.175759i | ||||
\(201\) | 10.8404 | − | 5.88611i | 0.764626 | − | 0.415174i | ||||
\(202\) | 1.63627 | + | 1.98490i | 0.115128 | + | 0.139657i | ||||
\(203\) | 9.28540 | 0.651707 | ||||||||
\(204\) | −1.12806 | − | 3.57719i | −0.0789799 | − | 0.250453i | ||||
\(205\) | −9.66961 | −0.675355 | ||||||||
\(206\) | 17.5665 | + | 21.3093i | 1.22392 | + | 1.48469i | ||||
\(207\) | −0.0287608 | + | 0.0442909i | −0.00199901 | + | 0.00307843i | ||||
\(208\) | −14.4180 | − | 5.82432i | −0.999710 | − | 0.403844i | ||||
\(209\) | 3.62610i | 0.250822i | ||||||||
\(210\) | 2.27116 | + | 0.917526i | 0.156725 | + | 0.0633153i | ||||
\(211\) | 13.6589i | 0.940318i | 0.882582 | + | 0.470159i | \(0.155803\pi\) | ||||
−0.882582 | + | 0.470159i | \(0.844197\pi\) | |||||||
\(212\) | −15.5804 | − | 3.02808i | −1.07007 | − | 0.207969i | ||||
\(213\) | −3.67430 | − | 6.76696i | −0.251759 | − | 0.463664i | ||||
\(214\) | 18.7527 | − | 15.4590i | 1.28191 | − | 1.05675i | ||||
\(215\) | 3.43356 | 0.234167 | ||||||||
\(216\) | −5.97901 | − | 13.4258i | −0.406820 | − | 0.913508i | ||||
\(217\) | −10.8667 | −0.737677 | ||||||||
\(218\) | −19.0430 | + | 15.6983i | −1.28976 | + | 1.06322i | ||||
\(219\) | −4.64612 | − | 8.55676i | −0.313956 | − | 0.578212i | ||||
\(220\) | 4.07709 | + | 0.792388i | 0.274878 | + | 0.0534228i | ||||
\(221\) | 4.20928i | 0.283147i | ||||||||
\(222\) | −14.6888 | − | 5.93412i | −0.985845 | − | 0.398272i | ||||
\(223\) | − | 20.4231i | − | 1.36763i | −0.729655 | − | 0.683816i | \(-0.760319\pi\) | ||
0.729655 | − | 0.683816i | \(-0.239681\pi\) | |||||||
\(224\) | 1.70143 | + | 5.39492i | 0.113681 | + | 0.360463i | ||||
\(225\) | 1.63383 | − | 2.51607i | 0.108922 | − | 0.167738i | ||||
\(226\) | −3.04532 | − | 3.69416i | −0.202572 | − | 0.245732i | ||||
\(227\) | −0.876538 | −0.0581778 | −0.0290889 | − | 0.999577i | \(-0.509261\pi\) | ||||
−0.0290889 | + | 0.999577i | \(0.509261\pi\) | |||||||
\(228\) | 1.81912 | + | 5.76862i | 0.120474 | + | 0.382036i | ||||
\(229\) | −6.67620 | −0.441176 | −0.220588 | − | 0.975367i | \(-0.570798\pi\) | ||||
−0.220588 | + | 0.975367i | \(0.570798\pi\) | |||||||
\(230\) | −0.0158353 | − | 0.0192092i | −0.00104415 | − | 0.00126662i | ||||
\(231\) | 3.16102 | − | 1.71636i | 0.207980 | − | 0.112928i | ||||
\(232\) | 23.0799 | − | 12.5326i | 1.51527 | − | 0.822807i | ||||
\(233\) | 6.09775i | 0.399477i | 0.979849 | + | 0.199739i | \(0.0640093\pi\) | ||||
−0.979849 | + | 0.199739i | \(0.935991\pi\) | |||||||
\(234\) | 1.86786 | + | 16.3871i | 0.122106 | + | 1.07126i | ||||
\(235\) | − | 0.213241i | − | 0.0139103i | ||||||
\(236\) | 1.13744 | − | 5.85249i | 0.0740409 | − | 0.380964i | ||||
\(237\) | −3.55777 | + | 1.93179i | −0.231102 | + | 0.125483i | ||||
\(238\) | 1.18155 | − | 0.974026i | 0.0765888 | − | 0.0631367i | ||||
\(239\) | 1.02568 | 0.0663460 | 0.0331730 | − | 0.999450i | \(-0.489439\pi\) | ||||
0.0331730 | + | 0.999450i | \(0.489439\pi\) | |||||||
\(240\) | 6.88361 | − | 0.784794i | 0.444335 | − | 0.0506582i | ||||
\(241\) | −3.40650 | −0.219432 | −0.109716 | − | 0.993963i | \(-0.534994\pi\) | ||||
−0.109716 | + | 0.993963i | \(0.534994\pi\) | |||||||
\(242\) | −7.29744 | + | 6.01572i | −0.469097 | + | 0.386705i | ||||
\(243\) | −9.48863 | + | 12.3679i | −0.608696 | + | 0.793404i | ||||
\(244\) | 3.19231 | − | 16.4255i | 0.204367 | − | 1.05153i | ||||
\(245\) | 1.00000i | 0.0638877i | ||||||||
\(246\) | −8.87211 | + | 21.9612i | −0.565665 | + | 1.40019i | ||||
\(247\) | − | 6.78793i | − | 0.431906i | ||||||
\(248\) | −27.0103 | + | 14.6669i | −1.71516 | + | 0.931347i | ||||
\(249\) | −3.22867 | − | 5.94624i | −0.204609 | − | 0.376827i | ||||
\(250\) | 0.899566 | + | 1.09123i | 0.0568935 | + | 0.0690154i | ||||
\(251\) | −15.1214 | −0.954451 | −0.477226 | − | 0.878781i | \(-0.658358\pi\) | ||||
−0.477226 | + | 0.878781i | \(0.658358\pi\) | |||||||
\(252\) | 4.16769 | − | 4.31629i | 0.262540 | − | 0.271901i | ||||
\(253\) | −0.0365565 | −0.00229829 | ||||||||
\(254\) | 14.2959 | + | 17.3418i | 0.897006 | + | 1.08812i | ||||
\(255\) | −0.894900 | − | 1.64814i | −0.0560408 | − | 0.103210i | ||||
\(256\) | 11.5107 | + | 11.1132i | 0.719417 | + | 0.694578i | ||||
\(257\) | − | 7.85725i | − | 0.490122i | −0.969508 | − | 0.245061i | \(-0.921192\pi\) | ||
0.969508 | − | 0.245061i | \(-0.0788079\pi\) | |||||||
\(258\) | 3.15038 | − | 7.79815i | 0.196134 | − | 0.485492i | ||||
\(259\) | − | 6.46752i | − | 0.401872i | ||||||
\(260\) | −7.63218 | − | 1.48333i | −0.473328 | − | 0.0919919i | ||||
\(261\) | −23.3627 | − | 15.1708i | −1.44611 | − | 0.939049i | ||||
\(262\) | −14.4926 | + | 11.9471i | −0.895355 | + | 0.738095i | ||||
\(263\) | 12.1722 | 0.750573 | 0.375286 | − | 0.926909i | \(-0.377544\pi\) | ||||
0.375286 | + | 0.926909i | \(0.377544\pi\) | |||||||
\(264\) | 5.54047 | − | 8.53267i | 0.340993 | − | 0.525150i | ||||
\(265\) | −7.93599 | −0.487504 | ||||||||
\(266\) | −1.90539 | + | 1.57073i | −0.116827 | + | 0.0963074i | ||||
\(267\) | 1.77053 | − | 0.961359i | 0.108355 | − | 0.0588342i | ||||
\(268\) | 13.9820 | + | 2.71743i | 0.854089 | + | 0.165993i | ||||
\(269\) | − | 8.80637i | − | 0.536934i | −0.963289 | − | 0.268467i | \(-0.913483\pi\) | ||
0.963289 | − | 0.268467i | \(-0.0865170\pi\) | |||||||
\(270\) | −4.21529 | − | 6.01924i | −0.256535 | − | 0.366320i | ||||
\(271\) | − | 1.27004i | − | 0.0771494i | −0.999256 | − | 0.0385747i | \(-0.987718\pi\) | ||
0.999256 | − | 0.0385747i | \(-0.0122818\pi\) | |||||||
\(272\) | 1.62223 | − | 4.01581i | 0.0983623 | − | 0.243494i | ||||
\(273\) | −5.91732 | + | 3.21297i | −0.358133 | + | 0.194458i | ||||
\(274\) | −13.6899 | − | 16.6067i | −0.827037 | − | 1.00325i | ||||
\(275\) | 2.07669 | 0.125229 | ||||||||
\(276\) | −0.0581563 | + | 0.0183395i | −0.00350060 | + | 0.00110391i | ||||
\(277\) | −19.7185 | −1.18477 | −0.592384 | − | 0.805656i | \(-0.701813\pi\) | ||||
−0.592384 | + | 0.805656i | \(0.701813\pi\) | |||||||
\(278\) | 12.1894 | + | 14.7866i | 0.731074 | + | 0.886839i | ||||
\(279\) | 27.3412 | + | 17.7543i | 1.63688 | + | 1.06292i | ||||
\(280\) | 1.34971 | + | 2.48561i | 0.0806608 | + | 0.148544i | ||||
\(281\) | 7.41059i | 0.442079i | 0.975265 | + | 0.221039i | \(0.0709449\pi\) | ||||
−0.975265 | + | 0.221039i | \(0.929055\pi\) | |||||||
\(282\) | −0.484303 | − | 0.195654i | −0.0288398 | − | 0.0116510i | ||||
\(283\) | − | 5.40388i | − | 0.321227i | −0.987017 | − | 0.160614i | \(-0.948653\pi\) | ||
0.987017 | − | 0.160614i | \(-0.0513473\pi\) | |||||||
\(284\) | 1.69631 | − | 8.72805i | 0.100657 | − | 0.517914i | ||||
\(285\) | 1.44313 | + | 2.65780i | 0.0854835 | + | 0.157435i | ||||
\(286\) | −8.80963 | + | 7.26230i | −0.520924 | + | 0.429429i | ||||
\(287\) | −9.66961 | −0.570779 | ||||||||
\(288\) | 4.53350 | − | 16.3538i | 0.267139 | − | 0.963658i | ||||
\(289\) | 15.8276 | 0.931035 | ||||||||
\(290\) | 10.1325 | − | 8.35283i | 0.595001 | − | 0.490495i | ||||
\(291\) | −9.46630 | − | 17.4341i | −0.554924 | − | 1.02200i | ||||
\(292\) | 2.14497 | − | 11.0365i | 0.125525 | − | 0.645865i | ||||
\(293\) | − | 20.9154i | − | 1.22189i | −0.791672 | − | 0.610946i | \(-0.790789\pi\) | ||
0.791672 | − | 0.610946i | \(-0.209211\pi\) | |||||||
\(294\) | 2.27116 | + | 0.917526i | 0.132456 | + | 0.0535112i | ||||
\(295\) | − | 2.98100i | − | 0.173560i | ||||||
\(296\) | −8.72930 | − | 16.0758i | −0.507380 | − | 0.934385i | ||||
\(297\) | −10.7576 | − | 0.846101i | −0.624218 | − | 0.0490957i | ||||
\(298\) | −3.66626 | − | 4.44740i | −0.212381 | − | 0.257631i | ||||
\(299\) | 0.0684325 | 0.00395755 | ||||||||
\(300\) | 3.30373 | − | 1.04182i | 0.190741 | − | 0.0601497i | ||||
\(301\) | 3.43356 | 0.197907 | ||||||||
\(302\) | −6.26186 | − | 7.59603i | −0.360330 | − | 0.437102i | ||||
\(303\) | 2.76872 | − | 1.50335i | 0.159059 | − | 0.0863652i | ||||
\(304\) | −2.61603 | + | 6.47595i | −0.150040 | + | 0.371421i | ||||
\(305\) | − | 8.36640i | − | 0.479059i | ||||||
\(306\) | −4.56427 | + | 0.520250i | −0.260922 | + | 0.0297407i | ||||
\(307\) | − | 11.4504i | − | 0.653508i | −0.945109 | − | 0.326754i | \(-0.894045\pi\) | ||
0.945109 | − | 0.326754i | \(-0.105955\pi\) | |||||||
\(308\) | 4.07709 | + | 0.792388i | 0.232314 | + | 0.0451505i | ||||
\(309\) | 29.7240 | − | 16.1395i | 1.69094 | − | 0.918142i | ||||
\(310\) | −11.8580 | + | 9.77528i | −0.673490 | + | 0.555198i | ||||
\(311\) | −11.4635 | −0.650037 | −0.325018 | − | 0.945708i | \(-0.605370\pi\) | ||||
−0.325018 | + | 0.945708i | \(0.605370\pi\) | |||||||
\(312\) | −10.3716 | + | 15.9729i | −0.587175 | + | 0.904287i | ||||
\(313\) | 10.7557 | 0.607949 | 0.303975 | − | 0.952680i | \(-0.401686\pi\) | ||||
0.303975 | + | 0.952680i | \(0.401686\pi\) | |||||||
\(314\) | −19.9362 | + | 16.4346i | −1.12506 | + | 0.927457i | ||||
\(315\) | 1.63383 | − | 2.51607i | 0.0920561 | − | 0.141764i | ||||
\(316\) | −4.58883 | − | 0.891845i | −0.258142 | − | 0.0501702i | ||||
\(317\) | 29.2336i | 1.64192i | 0.570985 | + | 0.820960i | \(0.306561\pi\) | ||||
−0.570985 | + | 0.820960i | \(0.693439\pi\) | |||||||
\(318\) | −7.28147 | + | 18.0239i | −0.408325 | + | 1.01073i | ||||
\(319\) | − | 19.2829i | − | 1.07964i | ||||||
\(320\) | 6.70973 | + | 4.35655i | 0.375085 | + | 0.243539i | ||||
\(321\) | −14.2032 | − | 26.1579i | −0.792743 | − | 1.45999i | ||||
\(322\) | −0.0158353 | − | 0.0192092i | −0.000882465 | − | 0.00107049i | ||||
\(323\) | 1.89062 | 0.105197 | ||||||||
\(324\) | −17.5383 | + | 4.05077i | −0.974349 | + | 0.225043i | ||||
\(325\) | −3.88750 | −0.215639 | ||||||||
\(326\) | 3.84002 | + | 4.65818i | 0.212679 | + | 0.257993i | ||||
\(327\) | 14.4230 | + | 26.5629i | 0.797596 | + | 1.46893i | ||||
\(328\) | −24.0349 | + | 13.0512i | −1.32711 | + | 0.720632i | ||||
\(329\) | − | 0.213241i | − | 0.0117563i | ||||||
\(330\) | 1.90542 | − | 4.71649i | 0.104890 | − | 0.259634i | ||||
\(331\) | − | 3.93597i | − | 0.216340i | −0.994132 | − | 0.108170i | \(-0.965501\pi\) | ||
0.994132 | − | 0.108170i | \(-0.0344991\pi\) | |||||||
\(332\) | 1.49057 | − | 7.66948i | 0.0818058 | − | 0.420917i | ||||
\(333\) | −10.5669 | + | 16.2727i | −0.579060 | + | 0.891739i | ||||
\(334\) | −21.5913 | + | 17.7990i | −1.18142 | + | 0.973916i | ||||
\(335\) | 7.12183 | 0.389107 | ||||||||
\(336\) | 6.88361 | − | 0.784794i | 0.375532 | − | 0.0428140i | ||||
\(337\) | −2.52822 | −0.137721 | −0.0688605 | − | 0.997626i | \(-0.521936\pi\) | ||||
−0.0688605 | + | 0.997626i | \(0.521936\pi\) | |||||||
\(338\) | 2.30536 | − | 1.90044i | 0.125395 | − | 0.103370i | ||||
\(339\) | −5.15294 | + | 2.79793i | −0.279869 | + | 0.151963i | ||||
\(340\) | 0.413147 | − | 2.12577i | 0.0224060 | − | 0.115286i | ||||
\(341\) | 22.5667i | 1.22205i | ||||||||
\(342\) | 7.36039 | − | 0.838962i | 0.398004 | − | 0.0453659i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 8.53451 | − | 4.63432i | 0.460150 | − | 0.249866i | ||||
\(345\) | −0.0267946 | + | 0.0145489i | −0.00144257 | + | 0.000783285i | ||||
\(346\) | 14.1973 | + | 17.2222i | 0.763252 | + | 0.925872i | ||||
\(347\) | 32.6521 | 1.75286 | 0.876428 | − | 0.481533i | \(-0.159920\pi\) | ||||
0.876428 | + | 0.481533i | \(0.159920\pi\) | |||||||
\(348\) | −9.67374 | − | 30.6764i | −0.518567 | − | 1.64443i | ||||
\(349\) | −0.574408 | −0.0307474 | −0.0153737 | − | 0.999882i | \(-0.504894\pi\) | ||||
−0.0153737 | + | 0.999882i | \(0.504894\pi\) | |||||||
\(350\) | 0.899566 | + | 1.09123i | 0.0480838 | + | 0.0583287i | ||||
\(351\) | 20.1378 | + | 1.58387i | 1.07488 | + | 0.0845409i | ||||
\(352\) | 11.2036 | − | 3.53333i | 0.597153 | − | 0.188327i | ||||
\(353\) | − | 15.2498i | − | 0.811664i | −0.913948 | − | 0.405832i | \(-0.866982\pi\) | ||
0.913948 | − | 0.405832i | \(-0.133018\pi\) | |||||||
\(354\) | −6.77031 | − | 2.73514i | −0.359838 | − | 0.145371i | ||||
\(355\) | − | 4.44568i | − | 0.235952i | ||||||
\(356\) | 2.28364 | + | 0.443829i | 0.121033 | + | 0.0235229i | ||||
\(357\) | −0.894900 | − | 1.64814i | −0.0473631 | − | 0.0872286i | ||||
\(358\) | 23.5677 | − | 19.4283i | 1.24559 | − | 1.02682i | ||||
\(359\) | −6.80601 | −0.359207 | −0.179604 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179604 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(360\) | 0.665112 | − | 8.45917i | 0.0350545 | − | 0.445838i | ||||
\(361\) | 15.9512 | 0.839534 | ||||||||
\(362\) | 23.1327 | − | 19.0697i | 1.21583 | − | 1.00228i | ||||
\(363\) | 5.52703 | + | 10.1791i | 0.290094 | + | 0.534265i | ||||
\(364\) | −7.63218 | − | 1.48333i | −0.400035 | − | 0.0777474i | ||||
\(365\) | − | 5.62152i | − | 0.294244i | ||||||
\(366\) | −19.0014 | − | 7.67639i | −0.993219 | − | 0.401251i | ||||
\(367\) | − | 3.82872i | − | 0.199857i | −0.994995 | − | 0.0999287i | \(-0.968139\pi\) | ||
0.994995 | − | 0.0999287i | \(-0.0318615\pi\) | |||||||
\(368\) | −0.0652872 | − | 0.0263735i | −0.00340333 | − | 0.00137481i | ||||
\(369\) | 24.3294 | + | 15.7985i | 1.26654 | + | 0.822439i | ||||
\(370\) | −5.81796 | − | 7.05755i | −0.302462 | − | 0.366905i | ||||
\(371\) | −7.93599 | −0.412016 | ||||||||
\(372\) | 11.3211 | + | 35.9005i | 0.586973 | + | 1.86135i | ||||
\(373\) | −1.52917 | −0.0791777 | −0.0395888 | − | 0.999216i | \(-0.512605\pi\) | ||||
−0.0395888 | + | 0.999216i | \(0.512605\pi\) | |||||||
\(374\) | −2.02275 | − | 2.45372i | −0.104594 | − | 0.126879i | ||||
\(375\) | 1.52214 | − | 0.826488i | 0.0786031 | − | 0.0426797i | ||||
\(376\) | −0.287814 | − | 0.530034i | −0.0148429 | − | 0.0273344i | ||||
\(377\) | 36.0970i | 1.85909i | ||||||||
\(378\) | −4.21529 | − | 6.01924i | −0.216811 | − | 0.309597i | ||||
\(379\) | 14.1473i | 0.726697i | 0.931653 | + | 0.363348i | \(0.118366\pi\) | ||||
−0.931653 | + | 0.363348i | \(0.881634\pi\) | |||||||
\(380\) | −0.666245 | + | 3.42805i | −0.0341777 | + | 0.175855i | ||||
\(381\) | 24.1899 | − | 13.1346i | 1.23929 | − | 0.672905i | ||||
\(382\) | −20.9073 | + | 17.2352i | −1.06971 | + | 0.881827i | ||||
\(383\) | 27.7958 | 1.42030 | 0.710149 | − | 0.704051i | \(-0.248628\pi\) | ||||
0.710149 | + | 0.704051i | \(0.248628\pi\) | |||||||
\(384\) | 16.0508 | − | 11.2416i | 0.819086 | − | 0.573670i | ||||
\(385\) | 2.07669 | 0.105838 | ||||||||
\(386\) | 12.7269 | − | 10.4916i | 0.647784 | − | 0.534007i | ||||
\(387\) | −8.63907 | − | 5.60987i | −0.439149 | − | 0.285166i | ||||
\(388\) | 4.37029 | − | 22.4865i | 0.221868 | − | 1.14158i | ||||
\(389\) | 34.8498i | 1.76696i | 0.468472 | + | 0.883478i | \(0.344805\pi\) | ||||
−0.468472 | + | 0.883478i | \(0.655195\pi\) | |||||||
\(390\) | −3.56688 | + | 8.82911i | −0.180616 | + | 0.447079i | ||||
\(391\) | 0.0190603i | 0.000963922i | ||||||||
\(392\) | 1.34971 | + | 2.48561i | 0.0681708 | + | 0.125542i | ||||
\(393\) | 10.9766 | + | 20.2155i | 0.553695 | + | 1.01974i | ||||
\(394\) | 22.3320 | + | 27.0901i | 1.12507 | + | 1.36478i | ||||
\(395\) | −2.33735 | −0.117605 | ||||||||
\(396\) | −8.96360 | − | 8.65499i | −0.450438 | − | 0.434930i | ||||
\(397\) | 31.4624 | 1.57905 | 0.789525 | − | 0.613718i | \(-0.210327\pi\) | ||||
0.789525 | + | 0.613718i | \(0.210327\pi\) | |||||||
\(398\) | 21.2380 | + | 25.7630i | 1.06456 | + | 1.29138i | ||||
\(399\) | 1.44313 | + | 2.65780i | 0.0722467 | + | 0.133057i | ||||
\(400\) | 3.70882 | + | 1.49822i | 0.185441 | + | 0.0749110i | ||||
\(401\) | − | 29.4959i | − | 1.47295i | −0.676463 | − | 0.736477i | \(-0.736488\pi\) | ||
0.676463 | − | 0.736477i | \(-0.263512\pi\) | |||||||
\(402\) | 6.53446 | − | 16.1748i | 0.325909 | − | 0.806725i | ||||
\(403\) | − | 42.2441i | − | 2.10433i | ||||||
\(404\) | 3.57110 | + | 0.694048i | 0.177669 | + | 0.0345302i | ||||
\(405\) | −8.22167 | + | 3.66118i | −0.408538 | + | 0.181925i | ||||
\(406\) | 10.1325 | − | 8.35283i | 0.502868 | − | 0.414544i | ||||
\(407\) | −13.4310 | −0.665752 | ||||||||
\(408\) | −4.44889 | − | 2.88877i | −0.220253 | − | 0.143015i | ||||
\(409\) | −31.3821 | −1.55174 | −0.775872 | − | 0.630890i | \(-0.782690\pi\) | ||||
−0.775872 | + | 0.630890i | \(0.782690\pi\) | |||||||
\(410\) | −10.5518 | + | 8.69845i | −0.521114 | + | 0.429586i | ||||
\(411\) | −23.1645 | + | 12.5778i | −1.14262 | + | 0.620416i | ||||
\(412\) | 38.3382 | + | 7.45107i | 1.88879 | + | 0.367088i | ||||
\(413\) | − | 2.98100i | − | 0.146685i | ||||||
\(414\) | 0.00845799 | + | 0.0742037i | 0.000415688 | + | 0.00364691i | ||||
\(415\) | − | 3.90649i | − | 0.191762i | ||||||
\(416\) | −20.9727 | + | 6.61428i | −1.02827 | + | 0.324292i | ||||
\(417\) | 20.6256 | − | 11.1992i | 1.01004 | − | 0.548428i | ||||
\(418\) | 3.26191 | + | 3.95690i | 0.159545 | + | 0.193538i | ||||
\(419\) | 4.89374 | 0.239075 | 0.119537 | − | 0.992830i | \(-0.461859\pi\) | ||||
0.119537 | + | 0.992830i | \(0.461859\pi\) | |||||||
\(420\) | 3.30373 | − | 1.04182i | 0.161205 | − | 0.0508357i | ||||
\(421\) | −14.1782 | −0.691004 | −0.345502 | − | 0.938418i | \(-0.612291\pi\) | ||||
−0.345502 | + | 0.938418i | \(0.612291\pi\) | |||||||
\(422\) | 12.2871 | + | 14.9050i | 0.598126 | + | 0.725564i | ||||
\(423\) | −0.348400 | + | 0.536528i | −0.0169398 | + | 0.0260869i | ||||
\(424\) | −19.7258 | + | 10.7113i | −0.957969 | + | 0.520187i | ||||
\(425\) | − | 1.08277i | − | 0.0525222i | ||||||
\(426\) | −10.0968 | − | 4.07903i | −0.489193 | − | 0.197629i | ||||
\(427\) | − | 8.36640i | − | 0.404879i | ||||||
\(428\) | 6.55714 | − | 33.7386i | 0.316951 | − | 1.63082i | ||||
\(429\) | 6.67234 | + | 12.2884i | 0.322144 | + | 0.593292i | ||||
\(430\) | 3.74680 | − | 3.08871i | 0.180687 | − | 0.148951i | ||||
\(431\) | 15.9143 | 0.766564 | 0.383282 | − | 0.923631i | \(-0.374794\pi\) | ||||
0.383282 | + | 0.923631i | \(0.374794\pi\) | |||||||
\(432\) | −18.6018 | − | 9.27208i | −0.894982 | − | 0.446103i | ||||
\(433\) | 23.8485 | 1.14609 | 0.573043 | − | 0.819525i | \(-0.305763\pi\) | ||||
0.573043 | + | 0.819525i | \(0.305763\pi\) | |||||||
\(434\) | −11.8580 | + | 9.77528i | −0.569203 | + | 0.469228i | ||||
\(435\) | −7.67428 | − | 14.1337i | −0.367953 | − | 0.677659i | ||||
\(436\) | −6.65865 | + | 34.2609i | −0.318892 | + | 1.64080i | ||||
\(437\) | − | 0.0307369i | − | 0.00147035i | ||||||
\(438\) | −12.7674 | − | 5.15789i | −0.610048 | − | 0.246454i | ||||
\(439\) | − | 3.11342i | − | 0.148596i | −0.997236 | − | 0.0742978i | \(-0.976328\pi\) | ||
0.997236 | − | 0.0742978i | \(-0.0236715\pi\) | |||||||
\(440\) | 5.16185 | − | 2.80294i | 0.246081 | − | 0.133625i | ||||
\(441\) | 1.63383 | − | 2.51607i | 0.0778016 | − | 0.119813i | ||||
\(442\) | 3.78652 | + | 4.59329i | 0.180106 | + | 0.218480i | ||||
\(443\) | 35.4423 | 1.68391 | 0.841957 | − | 0.539545i | \(-0.181404\pi\) | ||||
0.841957 | + | 0.539545i | \(0.181404\pi\) | |||||||
\(444\) | −21.3669 | + | 6.73801i | −1.01403 | + | 0.319772i | ||||
\(445\) | 1.16319 | 0.0551403 | ||||||||
\(446\) | −18.3719 | − | 22.2863i | −0.869935 | − | 1.05529i | ||||
\(447\) | −6.20362 | + | 3.36842i | −0.293421 | + | 0.159321i | ||||
\(448\) | 6.70973 | + | 4.35655i | 0.317005 | + | 0.205828i | ||||
\(449\) | − | 25.4194i | − | 1.19961i | −0.800145 | − | 0.599807i | \(-0.795244\pi\) | ||
0.800145 | − | 0.599807i | \(-0.204756\pi\) | |||||||
\(450\) | −0.480479 | − | 4.21535i | −0.0226500 | − | 0.198713i | ||||
\(451\) | 20.0808i | 0.945567i | ||||||||
\(452\) | −6.64628 | − | 1.29171i | −0.312615 | − | 0.0607571i | ||||
\(453\) | −10.5956 | + | 5.75317i | −0.497825 | + | 0.270308i | ||||
\(454\) | −0.956504 | + | 0.788503i | −0.0448909 | + | 0.0370063i | ||||
\(455\) | −3.88750 | −0.182249 | ||||||||
\(456\) | 7.17433 | + | 4.65847i | 0.335969 | + | 0.218153i | ||||
\(457\) | 11.5206 | 0.538912 | 0.269456 | − | 0.963013i | \(-0.413156\pi\) | ||||
0.269456 | + | 0.963013i | \(0.413156\pi\) | |||||||
\(458\) | −7.28526 | + | 6.00568i | −0.340418 | + | 0.280627i | ||||
\(459\) | −0.441152 | + | 5.60894i | −0.0205912 | + | 0.261803i | ||||
\(460\) | −0.0345598 | − | 0.00671675i | −0.00161136 | − | 0.000313170i | ||||
\(461\) | 11.5780i | 0.539240i | 0.962967 | + | 0.269620i | \(0.0868982\pi\) | ||||
−0.962967 | + | 0.269620i | \(0.913102\pi\) | |||||||
\(462\) | 1.90542 | − | 4.71649i | 0.0886480 | − | 0.219431i | ||||
\(463\) | 16.8353i | 0.782404i | 0.920305 | + | 0.391202i | \(0.127941\pi\) | ||||
−0.920305 | + | 0.391202i | \(0.872059\pi\) | |||||||
\(464\) | 13.9116 | − | 34.4379i | 0.645828 | − | 1.59874i | ||||
\(465\) | 8.98117 | + | 16.5406i | 0.416492 | + | 0.767052i | ||||
\(466\) | 5.48533 | + | 6.65405i | 0.254103 | + | 0.308243i | ||||
\(467\) | −8.52455 | −0.394469 | −0.197235 | − | 0.980356i | \(-0.563196\pi\) | ||||
−0.197235 | + | 0.980356i | \(0.563196\pi\) | |||||||
\(468\) | 16.7796 | + | 16.2019i | 0.775636 | + | 0.748931i | ||||
\(469\) | 7.12183 | 0.328856 | ||||||||
\(470\) | −0.191824 | − | 0.232695i | −0.00884819 | − | 0.0107334i | ||||
\(471\) | 15.0995 | + | 27.8087i | 0.695748 | + | 1.28136i | ||||
\(472\) | −4.02349 | − | 7.40961i | −0.185196 | − | 0.341055i | ||||
\(473\) | − | 7.13044i | − | 0.327858i | ||||||
\(474\) | −2.14457 | + | 5.30847i | −0.0985036 | + | 0.243826i | ||||
\(475\) | 1.74609i | 0.0801163i | ||||||||
\(476\) | 0.413147 | − | 2.12577i | 0.0189365 | − | 0.0974346i | ||||
\(477\) | 19.9675 | + | 12.9661i | 0.914247 | + | 0.593676i | ||||
\(478\) | 1.11926 | − | 0.922670i | 0.0511936 | − | 0.0422019i | ||||
\(479\) | −8.18702 | −0.374074 | −0.187037 | − | 0.982353i | \(-0.559889\pi\) | ||||
−0.187037 | + | 0.982353i | \(0.559889\pi\) | |||||||
\(480\) | 6.80563 | − | 7.04865i | 0.310633 | − | 0.321725i | ||||
\(481\) | 25.1425 | 1.14640 | ||||||||
\(482\) | −3.71727 | + | 3.06437i | −0.169317 | + | 0.139578i | ||||
\(483\) | −0.0267946 | + | 0.0145489i | −0.00121920 | + | 0.000661997i | ||||
\(484\) | −2.55165 | + | 13.1291i | −0.115984 | + | 0.596775i | ||||
\(485\) | − | 11.4536i | − | 0.520083i | ||||||
\(486\) | 0.771510 | + | 22.0319i | 0.0349964 | + | 0.999387i | ||||
\(487\) | 9.64886i | 0.437231i | 0.975811 | + | 0.218616i | \(0.0701541\pi\) | ||||
−0.975811 | + | 0.218616i | \(0.929846\pi\) | |||||||
\(488\) | −11.2922 | − | 20.7956i | −0.511176 | − | 0.941374i | ||||
\(489\) | 6.49764 | − | 3.52807i | 0.293834 | − | 0.159545i | ||||
\(490\) | 0.899566 | + | 1.09123i | 0.0406382 | + | 0.0492967i | ||||
\(491\) | −10.3699 | −0.467987 | −0.233993 | − | 0.972238i | \(-0.575179\pi\) | ||||
−0.233993 | + | 0.972238i | \(0.575179\pi\) | |||||||
\(492\) | 10.0740 | + | 31.9457i | 0.454172 | + | 1.44022i | ||||
\(493\) | −10.0540 | −0.452809 | ||||||||
\(494\) | −6.10619 | − | 7.40719i | −0.274731 | − | 0.333265i | ||||
\(495\) | −5.22509 | − | 3.39297i | −0.234850 | − | 0.152502i | ||||
\(496\) | −16.2806 | + | 40.3025i | −0.731022 | + | 1.80963i | ||||
\(497\) | − | 4.44568i | − | 0.199416i | ||||||
\(498\) | −8.87225 | − | 3.58431i | −0.397575 | − | 0.160617i | ||||
\(499\) | − | 28.8552i | − | 1.29174i | −0.763449 | − | 0.645868i | \(-0.776496\pi\) | ||
0.763449 | − | 0.645868i | \(-0.223504\pi\) | |||||||
\(500\) | 1.96327 | + | 0.381563i | 0.0877999 | + | 0.0170640i | ||||
\(501\) | 16.3531 | + | 30.1174i | 0.730601 | + | 1.34555i | ||||
\(502\) | −16.5009 | + | 13.6027i | −0.736470 | + | 0.607116i | ||||
\(503\) | −4.78556 | −0.213378 | −0.106689 | − | 0.994292i | \(-0.534025\pi\) | ||||
−0.106689 | + | 0.994292i | \(0.534025\pi\) | |||||||
\(504\) | 0.665112 | − | 8.45917i | 0.0296265 | − | 0.376802i | ||||
\(505\) | 1.81896 | 0.0809427 | ||||||||
\(506\) | −0.0398915 | + | 0.0328849i | −0.00177339 | + | 0.00146191i | ||||
\(507\) | −1.74606 | − | 3.21571i | −0.0775451 | − | 0.142815i | ||||
\(508\) | 31.2003 | + | 6.06381i | 1.38429 | + | 0.269038i | ||||
\(509\) | 11.5277i | 0.510958i | 0.966815 | + | 0.255479i | \(0.0822331\pi\) | ||||
−0.966815 | + | 0.255479i | \(0.917767\pi\) | |||||||
\(510\) | −2.45915 | − | 0.993473i | −0.108893 | − | 0.0439917i | ||||
\(511\) | − | 5.62152i | − | 0.248682i | ||||||
\(512\) | 22.5579 | + | 1.77249i | 0.996927 | + | 0.0783338i | ||||
\(513\) | 0.711407 | − | 9.04504i | 0.0314094 | − | 0.399348i | ||||
\(514\) | −7.06811 | − | 8.57406i | −0.311761 | − | 0.378186i | ||||
\(515\) | 19.5278 | 0.860496 | ||||||||
\(516\) | −3.57716 | − | 11.3435i | −0.157476 | − | 0.499372i | ||||
\(517\) | −0.442835 | −0.0194759 | ||||||||
\(518\) | −5.81796 | − | 7.05755i | −0.255627 | − | 0.310091i | ||||
\(519\) | 24.0231 | − | 13.0440i | 1.05449 | − | 0.572567i | ||||
\(520\) | −9.66281 | + | 5.24700i | −0.423742 | + | 0.230096i | ||||
\(521\) | 28.5564i | 1.25108i | 0.780193 | + | 0.625539i | \(0.215121\pi\) | ||||
−0.780193 | + | 0.625539i | \(0.784879\pi\) | |||||||
\(522\) | −39.1412 | + | 4.46144i | −1.71316 | + | 0.195272i | ||||
\(523\) | − | 23.0389i | − | 1.00742i | −0.863873 | − | 0.503710i | \(-0.831968\pi\) | ||
0.863873 | − | 0.503710i | \(-0.168032\pi\) | |||||||
\(524\) | −5.06753 | + | 26.0741i | −0.221376 | + | 1.13905i | ||||
\(525\) | 1.52214 | − | 0.826488i | 0.0664317 | − | 0.0360709i | ||||
\(526\) | 13.2827 | − | 10.9497i | 0.579154 | − | 0.477431i | ||||
\(527\) | 11.7661 | 0.512541 | ||||||||
\(528\) | −1.62977 | − | 14.2951i | −0.0709268 | − | 0.622115i | ||||
\(529\) | −22.9997 | −0.999987 | ||||||||
\(530\) | −8.65998 | + | 7.13894i | −0.376166 | + | 0.310096i | ||||
\(531\) | −4.87045 | + | 7.50038i | −0.211360 | + | 0.325489i | ||||
\(532\) | −0.666245 | + | 3.42805i | −0.0288854 | + | 0.148625i | ||||
\(533\) | − | 37.5906i | − | 1.62823i | ||||||
\(534\) | 1.06725 | − | 2.64177i | 0.0461845 | − | 0.114321i | ||||
\(535\) | − | 17.1849i | − | 0.742970i | ||||||
\(536\) | 17.7021 | − | 9.61243i | 0.764615 | − | 0.415194i | ||||
\(537\) | −17.8500 | − | 32.8743i | −0.770285 | − | 1.41863i | ||||
\(538\) | −7.92191 | − | 9.60977i | −0.341538 | − | 0.414306i | ||||
\(539\) | 2.07669 | 0.0894494 | ||||||||
\(540\) | −10.0146 | − | 2.77644i | −0.430958 | − | 0.119479i | ||||
\(541\) | −30.0318 | −1.29117 | −0.645584 | − | 0.763689i | \(-0.723386\pi\) | ||||
−0.645584 | + | 0.763689i | \(0.723386\pi\) | |||||||
\(542\) | −1.14248 | − | 1.38590i | −0.0490739 | − | 0.0595297i | ||||
\(543\) | −17.5205 | − | 32.2675i | −0.751877 | − | 1.38473i | ||||
\(544\) | −1.84226 | − | 5.84148i | −0.0789862 | − | 0.250451i | ||||
\(545\) | 17.4510i | 0.747518i | ||||||||
\(546\) | −3.56688 | + | 8.82911i | −0.152648 | + | 0.377851i | ||||
\(547\) | − | 16.6927i | − | 0.713730i | −0.934156 | − | 0.356865i | \(-0.883846\pi\) | ||
0.934156 | − | 0.356865i | \(-0.116154\pi\) | |||||||
\(548\) | −29.8776 | − | 5.80676i | −1.27631 | − | 0.248052i | ||||
\(549\) | −13.6693 | + | 21.0504i | −0.583392 | + | 0.898410i | ||||
\(550\) | 2.26615 | − | 1.86812i | 0.0966288 | − | 0.0796569i | ||||
\(551\) | 16.2132 | 0.690705 | ||||||||
\(552\) | −0.0469643 | + | 0.0723279i | −0.00199893 | + | 0.00307848i | ||||
\(553\) | −2.33735 | −0.0993940 | ||||||||
\(554\) | −21.5174 | + | 17.7381i | −0.914186 | + | 0.753618i | ||||
\(555\) | −9.84449 | + | 5.34533i | −0.417875 | + | 0.226897i | ||||
\(556\) | 26.6030 | + | 5.17032i | 1.12822 | + | 0.219270i | ||||
\(557\) | − | 7.22921i | − | 0.306311i | −0.988202 | − | 0.153156i | \(-0.951056\pi\) | ||
0.988202 | − | 0.153156i | \(-0.0489436\pi\) | |||||||
\(558\) | 45.8067 | − | 5.22121i | 1.93915 | − | 0.221031i | ||||
\(559\) | 13.3480i | 0.564558i | ||||||||
\(560\) | 3.70882 | + | 1.49822i | 0.156726 | + | 0.0633113i | ||||
\(561\) | −3.42267 | + | 1.85843i | −0.144505 | + | 0.0784630i | ||||
\(562\) | 6.66631 | + | 8.08665i | 0.281201 | + | 0.341115i | ||||
\(563\) | −0.606001 | −0.0255399 | −0.0127699 | − | 0.999918i | \(-0.504065\pi\) | ||||
−0.0127699 | + | 0.999918i | \(0.504065\pi\) | |||||||
\(564\) | −0.704489 | + | 0.222159i | −0.0296644 | + | 0.00935459i | ||||
\(565\) | −3.38532 | −0.142421 | ||||||||
\(566\) | −4.86114 | − | 5.89687i | −0.204329 | − | 0.247864i | ||||
\(567\) | −8.22167 | + | 3.66118i | −0.345278 | + | 0.153755i | ||||
\(568\) | −6.00039 | − | 11.0502i | −0.251771 | − | 0.463658i | ||||
\(569\) | − | 4.54488i | − | 0.190531i | −0.995452 | − | 0.0952657i | \(-0.969630\pi\) | ||
0.995452 | − | 0.0952657i | \(-0.0303701\pi\) | |||||||
\(570\) | 3.96565 | + | 1.60209i | 0.166103 | + | 0.0671040i | ||||
\(571\) | 26.1093i | 1.09264i | 0.837577 | + | 0.546320i | \(0.183972\pi\) | ||||
−0.837577 | + | 0.546320i | \(0.816028\pi\) | |||||||
\(572\) | −3.08041 | + | 15.8497i | −0.128798 | + | 0.662708i | ||||
\(573\) | 15.8350 | + | 29.1634i | 0.661518 | + | 1.21832i | ||||
\(574\) | −10.5518 | + | 8.69845i | −0.440422 | + | 0.363066i | ||||
\(575\) | −0.0176032 | −0.000734106 | ||||||||
\(576\) | −9.76424 | − | 21.9239i | −0.406844 | − | 0.913498i | ||||
\(577\) | −27.2597 | −1.13484 | −0.567419 | − | 0.823429i | \(-0.692058\pi\) | ||||
−0.567419 | + | 0.823429i | \(0.692058\pi\) | |||||||
\(578\) | 17.2715 | − | 14.2380i | 0.718402 | − | 0.592221i | ||||
\(579\) | −9.63927 | − | 17.7526i | −0.400595 | − | 0.737774i | ||||
\(580\) | 3.54297 | − | 18.2297i | 0.147114 | − | 0.756947i | ||||
\(581\) | − | 3.90649i | − | 0.162069i | ||||||
\(582\) | −26.0130 | − | 10.5090i | −1.07827 | − | 0.435612i | ||||
\(583\) | 16.4806i | 0.682556i | ||||||||
\(584\) | −7.58744 | − | 13.9729i | −0.313971 | − | 0.578204i | ||||
\(585\) | 9.78120 | + | 6.35152i | 0.404403 | + | 0.262603i | ||||
\(586\) | −18.8148 | − | 22.8235i | −0.777232 | − | 0.942831i | ||||
\(587\) | −13.8384 | −0.571170 | −0.285585 | − | 0.958353i | \(-0.592188\pi\) | ||||
−0.285585 | + | 0.958353i | \(0.592188\pi\) | |||||||
\(588\) | 3.30373 | − | 1.04182i | 0.136243 | − | 0.0429640i | ||||
\(589\) | −18.9742 | −0.781819 | ||||||||
\(590\) | −2.68160 | − | 3.25295i | −0.110400 | − | 0.133922i | ||||
\(591\) | 37.7877 | − | 20.5178i | 1.55438 | − | 0.843991i | ||||
\(592\) | −23.9869 | − | 9.68977i | −0.985855 | − | 0.398247i | ||||
\(593\) | − | 9.50707i | − | 0.390409i | −0.980763 | − | 0.195204i | \(-0.937463\pi\) | ||
0.980763 | − | 0.195204i | \(-0.0625370\pi\) | |||||||
\(594\) | −12.5001 | + | 8.75386i | −0.512886 | + | 0.359175i | ||||
\(595\) | − | 1.08277i | − | 0.0443894i | ||||||
\(596\) | −8.00145 | − | 1.55509i | −0.327752 | − | 0.0636991i | ||||
\(597\) | 35.9365 | − | 19.5127i | 1.47078 | − | 0.798601i | ||||
\(598\) | 0.0746756 | − | 0.0615595i | 0.00305371 | − | 0.00251736i | ||||
\(599\) | −41.0068 | −1.67549 | −0.837747 | − | 0.546059i | \(-0.816128\pi\) | ||||
−0.837747 | + | 0.546059i | \(0.816128\pi\) | |||||||
\(600\) | 2.66794 | − | 4.10879i | 0.108918 | − | 0.167740i | ||||
\(601\) | −37.2130 | −1.51795 | −0.758974 | − | 0.651121i | \(-0.774299\pi\) | ||||
−0.758974 | + | 0.651121i | \(0.774299\pi\) | |||||||
\(602\) | 3.74680 | − | 3.08871i | 0.152708 | − | 0.125887i | ||||
\(603\) | −17.9190 | − | 11.6359i | −0.729718 | − | 0.473850i | ||||
\(604\) | −13.6663 | − | 2.65605i | −0.556072 | − | 0.108073i | ||||
\(605\) | 6.68736i | 0.271880i | ||||||||
\(606\) | 1.66894 | − | 4.13114i | 0.0677961 | − | 0.167816i | ||||
\(607\) | 4.07839i | 0.165537i | 0.996569 | + | 0.0827685i | \(0.0263762\pi\) | ||||
−0.996569 | + | 0.0827685i | \(0.973624\pi\) | |||||||
\(608\) | 2.97085 | + | 9.42004i | 0.120484 | + | 0.382033i | ||||
\(609\) | −7.67428 | − | 14.1337i | −0.310977 | − | 0.572726i | ||||
\(610\) | −7.52613 | − | 9.12966i | −0.304724 | − | 0.369649i | ||||
\(611\) | 0.828973 | 0.0335367 | ||||||||
\(612\) | −4.51266 | + | 4.67357i | −0.182414 | + | 0.188918i | ||||
\(613\) | −42.0474 | −1.69828 | −0.849139 | − | 0.528169i | \(-0.822879\pi\) | ||||
−0.849139 | + | 0.528169i | \(0.822879\pi\) | |||||||
\(614\) | −10.3004 | − | 12.4950i | −0.415689 | − | 0.504257i | ||||
\(615\) | 7.99182 | + | 14.7185i | 0.322261 | + | 0.593508i | ||||
\(616\) | 5.16185 | − | 2.80294i | 0.207977 | − | 0.112933i | ||||
\(617\) | − | 16.9882i | − | 0.683917i | −0.939715 | − | 0.341959i | \(-0.888910\pi\) | ||
0.939715 | − | 0.341959i | \(-0.111090\pi\) | |||||||
\(618\) | 17.9172 | − | 44.3506i | 0.720736 | − | 1.78404i | ||||
\(619\) | − | 18.8674i | − | 0.758344i | −0.925326 | − | 0.379172i | \(-0.876209\pi\) | ||
0.925326 | − | 0.379172i | \(-0.123791\pi\) | |||||||
\(620\) | −4.14632 | + | 21.3341i | −0.166520 | + | 0.856800i | ||||
\(621\) | 0.0911875 | + | 0.00717204i | 0.00365923 | + | 0.000287804i | ||||
\(622\) | −12.5093 | + | 10.3122i | −0.501578 | + | 0.413481i | ||||
\(623\) | 1.16319 | 0.0466020 | ||||||||
\(624\) | 3.05088 | + | 26.7600i | 0.122133 | + | 1.07126i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.7370 | − | 9.67548i | 0.469103 | − | 0.386710i | ||||
\(627\) | 5.51943 | − | 2.99693i | 0.220425 | − | 0.119686i | ||||
\(628\) | −6.97095 | + | 35.8678i | −0.278171 | + | 1.43128i | ||||
\(629\) | 7.00287i | 0.279223i | ||||||||
\(630\) | −0.480479 | − | 4.21535i | −0.0191428 | − | 0.167943i | ||||
\(631\) | 19.6701i | 0.783055i | 0.920166 | + | 0.391528i | \(0.128053\pi\) | ||||
−0.920166 | + | 0.391528i | \(0.871947\pi\) | |||||||
\(632\) | −5.80974 | + | 3.15475i | −0.231099 | + | 0.125489i | ||||
\(633\) | 20.7908 | − | 11.2889i | 0.826360 | − | 0.448695i | ||||
\(634\) | 26.2975 | + | 31.9005i | 1.04441 | + | 1.26693i | ||||
\(635\) | 15.8920 | 0.630656 | ||||||||
\(636\) | 8.26789 | + | 26.2183i | 0.327843 | + | 1.03962i | ||||
\(637\) | −3.88750 | −0.154028 | ||||||||
\(638\) | −17.3462 | − | 21.0421i | −0.686744 | − | 0.833063i | ||||
\(639\) | −7.26350 | + | 11.1856i | −0.287340 | + | 0.442496i | ||||
\(640\) | 11.2409 | − | 1.28185i | 0.444334 | − | 0.0506695i | ||||
\(641\) | − | 9.20814i | − | 0.363700i | −0.983326 | − | 0.181850i | \(-0.941792\pi\) | ||
0.983326 | − | 0.181850i | \(-0.0582085\pi\) | |||||||
\(642\) | −39.0297 | − | 15.7676i | −1.54038 | − | 0.622299i | ||||
\(643\) | − | 25.9331i | − | 1.02270i | −0.859372 | − | 0.511351i | \(-0.829145\pi\) | ||
0.859372 | − | 0.511351i | \(-0.170855\pi\) | |||||||
\(644\) | −0.0345598 | − | 0.00671675i | −0.00136185 | − | 0.000264677i | ||||
\(645\) | −2.83780 | − | 5.22637i | −0.111738 | − | 0.205788i | ||||
\(646\) | 2.06311 | − | 1.70074i | 0.0811718 | − | 0.0669148i | ||||
\(647\) | −27.5894 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(648\) | −15.4943 | + | 20.1972i | −0.608676 | + | 0.793419i | ||||
\(649\) | −6.19061 | −0.243003 | ||||||||
\(650\) | −4.24215 | + | 3.49706i | −0.166391 | + | 0.137166i | ||||
\(651\) | 8.98117 | + | 16.5406i | 0.352000 | + | 0.648277i | ||||
\(652\) | 8.38069 | + | 1.62880i | 0.328213 | + | 0.0637886i | ||||
\(653\) | − | 14.0786i | − | 0.550939i | −0.961310 | − | 0.275470i | \(-0.911167\pi\) | ||
0.961310 | − | 0.275470i | \(-0.0888333\pi\) | |||||||
\(654\) | 39.6339 | + | 16.0117i | 1.54981 | + | 0.626108i | ||||
\(655\) | 13.2810i | 0.518930i | ||||||||
\(656\) | −14.4872 | + | 35.8628i | −0.565630 | + | 1.40021i | ||||
\(657\) | −9.18463 | + | 14.1441i | −0.358327 | + | 0.551815i | ||||
\(658\) | −0.191824 | − | 0.232695i | −0.00747808 | − | 0.00907138i | ||||
\(659\) | −34.5048 | −1.34412 | −0.672058 | − | 0.740499i | \(-0.734589\pi\) | ||||
−0.672058 | + | 0.740499i | \(0.734589\pi\) | |||||||
\(660\) | −2.16354 | − | 6.86081i | −0.0842158 | − | 0.267057i | ||||
\(661\) | 40.0292 | 1.55695 | 0.778477 | − | 0.627673i | \(-0.215993\pi\) | ||||
0.778477 | + | 0.627673i | \(0.215993\pi\) | |||||||
\(662\) | −3.54066 | − | 4.29504i | −0.137612 | − | 0.166932i | ||||
\(663\) | 6.40712 | − | 3.47892i | 0.248832 | − | 0.135110i | ||||
\(664\) | −5.27264 | − | 9.71003i | −0.204618 | − | 0.376822i | ||||
\(665\) | 1.74609i | 0.0677106i | ||||||||
\(666\) | 3.10751 | + | 27.2629i | 0.120414 | + | 1.05641i | ||||
\(667\) | 0.163453i | 0.00632893i | ||||||||
\(668\) | −7.54968 | + | 38.8455i | −0.292106 | + | 1.50298i | ||||
\(669\) | −31.0868 | + | 16.8794i | −1.20189 | + | 0.652597i | ||||
\(670\) | 7.77155 | − | 6.40655i | 0.300241 | − | 0.247507i | ||||
\(671\) | −17.3744 | −0.670732 | ||||||||
\(672\) | 6.80563 | − | 7.04865i | 0.262533 | − | 0.271908i | ||||
\(673\) | −4.17387 | −0.160891 | −0.0804454 | − | 0.996759i | \(-0.525634\pi\) | ||||
−0.0804454 | + | 0.996759i | \(0.525634\pi\) | |||||||
\(674\) | −2.75887 | + | 2.27430i | −0.106268 | + | 0.0876028i | ||||
\(675\) | −5.18015 | − | 0.407427i | −0.199384 | − | 0.0156819i | ||||
\(676\) | 0.806099 | − | 4.14764i | 0.0310038 | − | 0.159525i | ||||
\(677\) | − | 49.7553i | − | 1.91225i | −0.292956 | − | 0.956126i | \(-0.594639\pi\) | ||
0.292956 | − | 0.956126i | \(-0.405361\pi\) | |||||||
\(678\) | −3.10612 | + | 7.68859i | −0.119290 | + | 0.295278i | ||||
\(679\) | − | 11.4536i | − | 0.439550i | ||||||
\(680\) | −1.46143 | − | 2.69136i | −0.0560434 | − | 0.103209i | ||||
\(681\) | 0.724448 | + | 1.33421i | 0.0277609 | + | 0.0511272i | ||||
\(682\) | 20.3002 | + | 24.6254i | 0.777335 | + | 0.942957i | ||||
\(683\) | 0.268279 | 0.0102654 | 0.00513270 | − | 0.999987i | \(-0.498366\pi\) | ||||
0.00513270 | + | 0.999987i | \(0.498366\pi\) | |||||||
\(684\) | 7.27717 | − | 7.53666i | 0.278250 | − | 0.288171i | ||||
\(685\) | −15.2183 | −0.581463 | ||||||||
\(686\) | 0.899566 | + | 1.09123i | 0.0343456 | + | 0.0416633i | ||||
\(687\) | 5.51780 | + | 10.1621i | 0.210517 | + | 0.387709i | ||||
\(688\) | 5.14423 | − | 12.7345i | 0.196122 | − | 0.485497i | ||||
\(689\) | − | 30.8511i | − | 1.17533i | ||||||
\(690\) | −0.0161514 | + | 0.0399797i | −0.000614874 | + | 0.00152200i | ||||
\(691\) | − | 40.1141i | − | 1.52601i | −0.646392 | − | 0.763006i | \(-0.723723\pi\) | ||
0.646392 | − | 0.763006i | \(-0.276277\pi\) | |||||||
\(692\) | 30.9850 | + | 6.02198i | 1.17787 | + | 0.228921i | ||||
\(693\) | −5.22509 | − | 3.39297i | −0.198485 | − | 0.128888i | ||||
\(694\) | 35.6309 | − | 29.3727i | 1.35253 | − | 1.11497i | ||||
\(695\) | 13.5504 | 0.513995 | ||||||||
\(696\) | −38.1517 | − | 24.7728i | −1.44614 | − | 0.939012i | ||||
\(697\) | 10.4700 | 0.396579 | ||||||||
\(698\) | −0.626811 | + | 0.516718i | −0.0237252 | + | 0.0195581i | ||||
\(699\) | 9.28165 | − | 5.03972i | 0.351064 | − | 0.190620i | ||||
\(700\) | 1.96327 | + | 0.381563i | 0.0742044 | + | 0.0144217i | ||||
\(701\) | 12.1460i | 0.458748i | 0.973338 | + | 0.229374i | \(0.0736678\pi\) | ||||
−0.973338 | + | 0.229374i | \(0.926332\pi\) | |||||||
\(702\) | 23.3998 | − | 16.3869i | 0.883168 | − | 0.618485i | ||||
\(703\) | − | 11.2929i | − | 0.425920i | ||||||
\(704\) | 9.04720 | − | 13.9340i | 0.340979 | − | 0.525158i | ||||
\(705\) | −0.324583 | + | 0.176241i | −0.0122245 | + | 0.00663762i | ||||
\(706\) | −13.7182 | − | 16.6410i | −0.516291 | − | 0.626293i | ||||
\(707\) | 1.81896 | 0.0684090 | ||||||||
\(708\) | −9.84840 | + | 3.10567i | −0.370125 | + | 0.116718i | ||||
\(709\) | 19.4332 | 0.729829 | 0.364915 | − | 0.931041i | \(-0.381098\pi\) | ||||
0.364915 | + | 0.931041i | \(0.381098\pi\) | |||||||
\(710\) | −3.99918 | − | 4.85126i | −0.150087 | − | 0.182064i | ||||
\(711\) | 5.88091 | + | 3.81883i | 0.220552 | + | 0.143217i | ||||
\(712\) | 2.89123 | − | 1.56997i | 0.108353 | − | 0.0588370i | ||||
\(713\) | − | 0.191288i | − | 0.00716381i | ||||||
\(714\) | −2.45915 | − | 0.993473i | −0.0920313 | − | 0.0371798i | ||||
\(715\) | 8.07312i | 0.301918i | ||||||||
\(716\) | 8.24078 | − | 42.4015i | 0.307972 | − | 1.58462i | ||||
\(717\) | −0.847716 | − | 1.56124i | −0.0316585 | − | 0.0583054i | ||||
\(718\) | −7.42691 | + | 6.12245i | −0.277170 | + | 0.228488i | ||||
\(719\) | −40.9225 | −1.52615 | −0.763076 | − | 0.646309i | \(-0.776312\pi\) | ||||
−0.763076 | + | 0.646309i | \(0.776312\pi\) | |||||||
\(720\) | −6.88379 | − | 9.82921i | −0.256544 | − | 0.366313i | ||||
\(721\) | 19.5278 | 0.727252 | ||||||||
\(722\) | 17.4064 | − | 14.3491i | 0.647798 | − | 0.534019i | ||||
\(723\) | 2.81543 | + | 5.18518i | 0.104707 | + | 0.192839i | ||||
\(724\) | 8.08866 | − | 41.6187i | 0.300613 | − | 1.54675i | ||||
\(725\) | − | 9.28540i | − | 0.344851i | ||||||
\(726\) | 15.1880 | + | 6.13582i | 0.563681 | + | 0.227722i | ||||
\(727\) | 8.73982i | 0.324142i | 0.986779 | + | 0.162071i | \(0.0518173\pi\) | ||||
−0.986779 | + | 0.162071i | \(0.948183\pi\) | |||||||
\(728\) | −9.66281 | + | 5.24700i | −0.358128 | + | 0.194467i | ||||
\(729\) | 26.6680 | + | 4.22107i | 0.987704 | + | 0.156336i | ||||
\(730\) | −5.05693 | − | 6.13437i | −0.187165 | − | 0.227043i | ||||
\(731\) | −3.71777 | −0.137507 | ||||||||
\(732\) | −27.6403 | + | 8.71631i | −1.02161 | + | 0.322164i | ||||
\(733\) | −28.1014 | −1.03795 | −0.518974 | − | 0.854790i | \(-0.673686\pi\) | ||||
−0.518974 | + | 0.854790i | \(0.673686\pi\) | |||||||
\(734\) | −3.44418 | − | 4.17801i | −0.127127 | − | 0.154213i | ||||
\(735\) | 1.52214 | − | 0.826488i | 0.0561451 | − | 0.0304855i | ||||
\(736\) | −0.0949681 | + | 0.0299506i | −0.00350057 | + | 0.00110399i | ||||
\(737\) | − | 14.7898i | − | 0.544791i | ||||||
\(738\) | 40.7607 | − | 4.64605i | 1.50042 | − | 0.171023i | ||||
\(739\) | 40.7137i | 1.49768i | 0.662751 | + | 0.748840i | \(0.269389\pi\) | ||||
−0.662751 | + | 0.748840i | \(0.730611\pi\) | |||||||
\(740\) | −12.6975 | − | 2.46777i | −0.466768 | − | 0.0907170i | ||||
\(741\) | −10.3322 | + | 5.61015i | −0.379563 | + | 0.206094i | ||||
\(742\) | −8.65998 | + | 7.13894i | −0.317918 | + | 0.262079i | ||||
\(743\) | −13.9305 | −0.511062 | −0.255531 | − | 0.966801i | \(-0.582250\pi\) | ||||
−0.255531 | + | 0.966801i | \(0.582250\pi\) | |||||||
\(744\) | 44.6488 | + | 28.9915i | 1.63690 | + | 1.06288i | ||||
\(745\) | −4.07558 | −0.149318 | ||||||||
\(746\) | −1.66868 | + | 1.37559i | −0.0610947 | + | 0.0503640i | ||||
\(747\) | −6.38256 | + | 9.82899i | −0.233526 | + | 0.359624i | ||||
\(748\) | −4.41457 | − | 0.857977i | −0.161413 | − | 0.0313708i | ||||
\(749\) | − | 17.1849i | − | 0.627924i | ||||||
\(750\) | 0.917526 | − | 2.27116i | 0.0335033 | − | 0.0829309i | ||||
\(751\) | − | 35.7046i | − | 1.30288i | −0.758700 | − | 0.651440i | \(-0.774165\pi\) | ||
0.758700 | − | 0.651440i | \(-0.225835\pi\) | |||||||
\(752\) | −0.790872 | − | 0.319482i | −0.0288401 | − | 0.0116503i | ||||
\(753\) | 12.4976 | + | 23.0169i | 0.455439 | + | 0.838781i | ||||
\(754\) | 32.4716 | + | 39.3901i | 1.18255 | + | 1.43450i | ||||
\(755\) | −6.96098 | −0.253336 | ||||||||
\(756\) | −10.0146 | − | 2.77644i | −0.364226 | − | 0.100978i | ||||
\(757\) | 1.44168 | 0.0523987 | 0.0261994 | − | 0.999657i | \(-0.491660\pi\) | ||||
0.0261994 | + | 0.999657i | \(0.491660\pi\) | |||||||
\(758\) | 12.7264 | + | 15.4379i | 0.462244 | + | 0.560730i | ||||
\(759\) | 0.0302135 | + | 0.0556441i | 0.00109668 | + | 0.00201975i | ||||
\(760\) | 2.35673 | + | 4.34012i | 0.0854874 | + | 0.157433i | ||||
\(761\) | 29.6645i | 1.07534i | 0.843156 | + | 0.537670i | \(0.180695\pi\) | ||||
−0.843156 | + | 0.537670i | \(0.819305\pi\) | |||||||
\(762\) | 14.5813 | − | 36.0933i | 0.528226 | − | 1.30752i | ||||
\(763\) | 17.4510i | 0.631768i | ||||||||
\(764\) | −7.31053 | + | 37.6150i | −0.264486 | + | 1.36086i | ||||
\(765\) | −1.76907 | + | 2.72433i | −0.0639609 | + | 0.0984984i | ||||
\(766\) | 30.3316 | − | 25.0041i | 1.09592 | − | 0.903436i | ||||
\(767\) | 11.5886 | 0.418441 | ||||||||
\(768\) | 7.40250 | − | 26.7059i | 0.267115 | − | 0.963665i | ||||
\(769\) | −30.7667 | −1.10948 | −0.554739 | − | 0.832025i | \(-0.687182\pi\) | ||||
−0.554739 | + | 0.832025i | \(0.687182\pi\) | |||||||
\(770\) | 2.26615 | − | 1.86812i | 0.0816662 | − | 0.0673223i | ||||
\(771\) | −11.9598 | + | 6.49392i | −0.430723 | + | 0.233873i | ||||
\(772\) | 4.45014 | − | 22.8974i | 0.160164 | − | 0.824096i | ||||
\(773\) | 9.78554i | 0.351962i | 0.984394 | + | 0.175981i | \(0.0563097\pi\) | ||||
−0.984394 | + | 0.175981i | \(0.943690\pi\) | |||||||
\(774\) | −14.4737 | + | 1.64976i | −0.520245 | + | 0.0592992i | ||||
\(775\) | 10.8667i | 0.390342i | ||||||||
\(776\) | −15.4591 | − | 28.4693i | −0.554950 | − | 1.02199i | ||||
\(777\) | −9.84449 | + | 5.34533i | −0.353169 | + | 0.191763i | ||||
\(778\) | 31.3497 | + | 38.0292i | 1.12394 | + | 1.36341i | ||||
\(779\) | −16.8840 | −0.604934 | ||||||||
\(780\) | 4.05008 | + | 12.8432i | 0.145016 | + | 0.459861i | ||||
\(781\) | −9.23230 | −0.330358 | ||||||||
\(782\) | 0.0171460 | + | 0.0207992i | 0.000613140 | + | 0.000743777i | ||||
\(783\) | −3.78313 | + | 48.0998i | −0.135198 | + | 1.71895i | ||||
\(784\) | 3.70882 | + | 1.49822i | 0.132458 | + | 0.0535078i | ||||
\(785\) | 18.2695i | 0.652065i | ||||||||
\(786\) | 30.1631 | + | 12.1856i | 1.07588 | + | 0.434647i | ||||
\(787\) | 29.5634i | 1.05382i | 0.849920 | + | 0.526911i | \(0.176650\pi\) | ||||
−0.849920 | + | 0.526911i | \(0.823350\pi\) | |||||||
\(788\) | 48.7387 | + | 9.47242i | 1.73624 | + | 0.337441i | ||||
\(789\) | −10.0602 | − | 18.5279i | −0.358153 | − | 0.659610i | ||||
\(790\) | −2.55058 | + | 2.10260i | −0.0907456 | + | 0.0748070i | ||||
\(791\) | −3.38532 | −0.120368 | ||||||||
\(792\) | −17.5671 | − | 1.38123i | −0.624219 | − | 0.0490799i | ||||
\(793\) | 32.5243 | 1.15497 | ||||||||
\(794\) | 34.3327 | − | 28.3025i | 1.21842 | − | 1.00442i | ||||
\(795\) | 6.55900 | + | 12.0797i | 0.232624 | + | 0.428423i | ||||
\(796\) | 46.3510 | + | 9.00838i | 1.64287 | + | 0.319294i | ||||
\(797\) | − | 11.0944i | − | 0.392985i | −0.980505 | − | 0.196492i | \(-0.937045\pi\) | ||
0.980505 | − | 0.196492i | \(-0.0629551\pi\) | |||||||
\(798\) | 3.96565 | + | 1.60209i | 0.140383 | + | 0.0567132i | ||||
\(799\) | 0.230892i | 0.00816836i | ||||||||
\(800\) | 5.39492 | − | 1.70143i | 0.190739 | − | 0.0601545i | ||||
\(801\) | −2.92665 | − | 1.90045i | −0.103408 | − | 0.0671491i | ||||
\(802\) | −26.5335 | − | 32.1868i | −0.936930 | − | 1.13655i | ||||
\(803\) | −11.6742 | −0.411972 | ||||||||
\(804\) | −7.41968 | − | 23.5286i | −0.261672 | − | 0.829789i | ||||
\(805\) | −0.0176032 | −0.000620433 | ||||||||
\(806\) | −38.0013 | − | 46.0980i | −1.33854 | − | 1.62373i | ||||
\(807\) | −13.4045 | + | 7.27836i | −0.471862 | + | 0.256210i | ||||
\(808\) | 4.52123 | − | 2.45507i | 0.159056 | − | 0.0863692i | ||||
\(809\) | 36.6219i | 1.28756i | 0.765211 | + | 0.643779i | \(0.222634\pi\) | ||||
−0.765211 | + | 0.643779i | \(0.777366\pi\) | |||||||
\(810\) | −5.67826 | + | 11.3911i | −0.199514 | + | 0.400243i | ||||
\(811\) | 3.51939i | 0.123583i | 0.998089 | + | 0.0617913i | \(0.0196813\pi\) | ||||
−0.998089 | + | 0.0617913i | \(0.980319\pi\) | |||||||
\(812\) | 3.54297 | − | 18.2297i | 0.124334 | − | 0.639737i | ||||
\(813\) | −1.93318 | + | 1.04967i | −0.0677996 | + | 0.0368136i | ||||
\(814\) | −14.6563 | + | 12.0821i | −0.513705 | + | 0.423478i | ||||
\(815\) | 4.26875 | 0.149528 | ||||||||
\(816\) | −7.45339 | + | 0.849754i | −0.260921 | + | 0.0297473i | ||||
\(817\) | 5.99532 | 0.209750 | ||||||||
\(818\) | −34.2450 | + | 28.2302i | −1.19735 | + | 0.987047i | ||||
\(819\) | 9.78120 | + | 6.35152i | 0.341783 | + | 0.221940i | ||||
\(820\) | −3.68957 | + | 18.9840i | −0.128845 | + | 0.662950i | ||||
\(821\) | 11.5056i | 0.401549i | 0.979637 | + | 0.200775i | \(0.0643459\pi\) | ||||
−0.979637 | + | 0.200775i | \(0.935654\pi\) | |||||||
\(822\) | −13.9632 | + | 34.5632i | −0.487023 | + | 1.20553i | ||||
\(823\) | 11.6775i | 0.407051i | 0.979070 | + | 0.203525i | \(0.0652399\pi\) | ||||
−0.979070 | + | 0.203525i | \(0.934760\pi\) | |||||||
\(824\) | 48.5385 | − | 26.3569i | 1.69092 | − | 0.918185i | ||||
\(825\) | −1.71636 | − | 3.16102i | −0.0597560 | − | 0.110052i | ||||
\(826\) | −2.68160 | − | 3.25295i | −0.0933049 | − | 0.113185i | ||||
\(827\) | 0.702333 | 0.0244225 | 0.0122113 | − | 0.999925i | \(-0.496113\pi\) | ||||
0.0122113 | + | 0.999925i | \(0.496113\pi\) | |||||||
\(828\) | 0.0759808 | + | 0.0733648i | 0.00264051 | + | 0.00254960i | ||||
\(829\) | 36.4866 | 1.26723 | 0.633615 | − | 0.773648i | \(-0.281570\pi\) | ||||
0.633615 | + | 0.773648i | \(0.281570\pi\) | |||||||
\(830\) | −3.51415 | − | 4.26288i | −0.121978 | − | 0.147967i | ||||
\(831\) | 16.2971 | + | 30.0143i | 0.565340 | + | 1.04119i | ||||
\(832\) | −16.9361 | + | 26.0840i | −0.587153 | + | 0.904302i | ||||
\(833\) | − | 1.08277i | − | 0.0375159i | ||||||
\(834\) | 12.4328 | − | 30.7750i | 0.430513 | − | 1.06565i | ||||
\(835\) | 19.7862i | 0.684729i | ||||||||
\(836\) | 7.11899 | + | 1.38358i | 0.246215 | + | 0.0478523i | ||||
\(837\) | 4.42738 | − | 56.2910i | 0.153033 | − | 1.94570i | ||||
\(838\) | 5.34020 | − | 4.40224i | 0.184474 | − | 0.152073i | ||||
\(839\) | 31.6506 | 1.09270 | 0.546349 | − | 0.837557i | \(-0.316017\pi\) | ||||
0.546349 | + | 0.837557i | \(0.316017\pi\) | |||||||
\(840\) | 2.66794 | − | 4.10879i | 0.0920525 | − | 0.141767i | ||||
\(841\) | −57.2187 | −1.97306 | ||||||||
\(842\) | −15.4717 | + | 12.7542i | −0.533189 | + | 0.439540i | ||||
\(843\) | 11.2800 | − | 6.12477i | 0.388503 | − | 0.210948i | ||||
\(844\) | 26.8161 | + | 5.21174i | 0.923047 | + | 0.179395i | ||||
\(845\) | − | 2.11262i | − | 0.0726764i | ||||||
\(846\) | 0.102458 | + | 0.898884i | 0.00352257 | + | 0.0309043i | ||||
\(847\) | 6.68736i | 0.229780i | ||||||||
\(848\) | −11.8898 | + | 29.4331i | −0.408299 | + | 1.01074i | ||||
\(849\) | −8.22547 | + | 4.46624i | −0.282297 | + | 0.153281i | ||||
\(850\) | −0.974026 | − | 1.18155i | −0.0334088 | − | 0.0405270i | ||||
\(851\) | 0.113849 | 0.00390271 | ||||||||
\(852\) | −14.6873 | + | 4.63161i | −0.503179 | + | 0.158676i | ||||
\(853\) | −5.58114 | −0.191094 | −0.0955472 | − | 0.995425i | \(-0.530460\pi\) | ||||
−0.0955472 | + | 0.995425i | \(0.530460\pi\) | |||||||
\(854\) | −7.52613 | − | 9.12966i | −0.257539 | − | 0.312411i | ||||
\(855\) | 2.85283 | − | 4.39329i | 0.0975646 | − | 0.150247i | ||||
\(856\) | −23.1947 | − | 42.7151i | −0.792780 | − | 1.45997i | ||||
\(857\) | 40.4096i | 1.38036i | 0.723636 | + | 0.690182i | \(0.242470\pi\) | ||||
−0.723636 | + | 0.690182i | \(0.757530\pi\) | |||||||
\(858\) | 18.3353 | + | 7.40730i | 0.625957 | + | 0.252881i | ||||
\(859\) | − | 3.55494i | − | 0.121293i | −0.998159 | − | 0.0606465i | \(-0.980684\pi\) | ||
0.998159 | − | 0.0606465i | \(-0.0193162\pi\) | |||||||
\(860\) | 1.31012 | − | 6.74099i | 0.0446747 | − | 0.229866i | ||||
\(861\) | 7.99182 | + | 14.7185i | 0.272360 | + | 0.501606i | ||||
\(862\) | 17.3661 | − | 14.3159i | 0.591493 | − | 0.487603i | ||||
\(863\) | −39.1611 | −1.33306 | −0.666530 | − | 0.745479i | \(-0.732221\pi\) | ||||
−0.666530 | + | 0.745479i | \(0.732221\pi\) | |||||||
\(864\) | −28.6397 | + | 6.61561i | −0.974343 | + | 0.225068i | ||||
\(865\) | 15.7824 | 0.536618 | ||||||||
\(866\) | 26.0242 | − | 21.4533i | 0.884338 | − | 0.729013i | ||||
\(867\) | −13.0813 | − | 24.0919i | −0.444265 | − | 0.818202i | ||||
\(868\) | −4.14632 | + | 21.3341i | −0.140735 | + | 0.724128i | ||||
\(869\) | 4.85394i | 0.164659i | ||||||||
\(870\) | −21.0886 | − | 8.51959i | −0.714970 | − | 0.288841i | ||||
\(871\) | 27.6861i | 0.938107i | ||||||||
\(872\) | 23.5538 | + | 43.3764i | 0.797633 | + | 1.46891i | ||||
\(873\) | −18.7133 | + | 28.8181i | −0.633350 | + | 0.975345i | ||||
\(874\) | −0.0276499 | − | 0.0335410i | −0.000935271 | − | 0.00113454i | ||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −18.5720 | + | 5.85663i | −0.627489 | + | 0.197877i | ||||
\(877\) | 30.8860 | 1.04295 | 0.521473 | − | 0.853268i | \(-0.325383\pi\) | ||||
0.521473 | + | 0.853268i | \(0.325383\pi\) | |||||||
\(878\) | −2.80073 | − | 3.39746i | −0.0945200 | − | 0.114659i | ||||
\(879\) | −31.8362 | + | 17.2863i | −1.07381 | + | 0.583054i | ||||
\(880\) | 3.11134 | − | 7.70207i | 0.104883 | − | 0.259637i | ||||
\(881\) | 12.3355i | 0.415594i | 0.978172 | + | 0.207797i | \(0.0666293\pi\) | ||||
−0.978172 | + | 0.207797i | \(0.933371\pi\) | |||||||
\(882\) | −0.480479 | − | 4.21535i | −0.0161786 | − | 0.141938i | ||||
\(883\) | 51.1513i | 1.72138i | 0.509130 | + | 0.860690i | \(0.329967\pi\) | ||||
−0.509130 | + | 0.860690i | \(0.670033\pi\) | |||||||
\(884\) | 8.26393 | + | 1.60611i | 0.277946 | + | 0.0540192i | ||||
\(885\) | −4.53750 | + | 2.46376i | −0.152526 | + | 0.0828184i | ||||
\(886\) | 38.6757 | − | 31.8827i | 1.29933 | − | 1.07112i | ||||
\(887\) | 4.10786 | 0.137928 | 0.0689642 | − | 0.997619i | \(-0.478031\pi\) | ||||
0.0689642 | + | 0.997619i | \(0.478031\pi\) | |||||||
\(888\) | −17.2549 | + | 26.5737i | −0.579038 | + | 0.891754i | ||||
\(889\) | 15.8920 | 0.533002 | ||||||||
\(890\) | 1.26930 | − | 1.04636i | 0.0425471 | − | 0.0350741i | ||||
\(891\) | 7.60313 | + | 17.0739i | 0.254714 | + | 0.571996i | ||||
\(892\) | −40.0959 | − | 7.79270i | −1.34251 | − | 0.260919i | ||||
\(893\) | − | 0.372339i | − | 0.0124598i | ||||||
\(894\) | −3.73945 | + | 9.25629i | −0.125066 | + | 0.309577i | ||||
\(895\) | − | 21.5974i | − | 0.721922i | ||||||
\(896\) | 11.2409 | − | 1.28185i | 0.375531 | − | 0.0428235i | ||||
\(897\) | −0.0565587 | − | 0.104164i | −0.00188844 | − | 0.00347794i | ||||
\(898\) | −22.8664 | − | 27.7384i | −0.763061 | − | 0.925641i | ||||
\(899\) | 100.901 | 3.36525 | ||||||||
\(900\) | −4.31629 | − | 4.16769i | −0.143876 | − | 0.138923i | ||||
\(901\) | 8.59288 | 0.286270 | ||||||||
\(902\) | 18.0640 | + | 21.9127i | 0.601465 | + | 0.729614i | ||||
\(903\) | −2.83780 | − | 5.22637i | −0.0944360 | − | 0.173923i | ||||
\(904\) | −8.41460 | + | 4.56921i | −0.279865 | + | 0.151970i | ||||
\(905\) | − | 21.1987i | − | 0.704670i | ||||||
\(906\) | −6.38688 | + | 15.8095i | −0.212190 | + | 0.525234i | ||||
\(907\) | 28.5278i | 0.947252i | 0.880726 | + | 0.473626i | \(0.157055\pi\) | ||||
−0.880726 | + | 0.473626i | \(0.842945\pi\) | |||||||
\(908\) | −0.334454 | + | 1.72088i | −0.0110993 | + | 0.0571093i | ||||
\(909\) | −4.57662 | − | 2.97188i | −0.151797 | − | 0.0985710i | ||||
\(910\) | −4.24215 | + | 3.49706i | −0.140626 | + | 0.115926i | ||||
\(911\) | 31.7510 | 1.05196 | 0.525979 | − | 0.850497i | \(-0.323699\pi\) | ||||
0.525979 | + | 0.850497i | \(0.323699\pi\) | |||||||
\(912\) | 12.0194 | − | 1.37032i | 0.398003 | − | 0.0453760i | ||||
\(913\) | −8.11257 | −0.268487 | ||||||||
\(914\) | 12.5716 | − | 10.3636i | 0.415833 | − | 0.342796i | ||||
\(915\) | −12.7349 | + | 6.91473i | −0.421001 | + | 0.228594i | ||||
\(916\) | −2.54739 | + | 13.1071i | −0.0841682 | + | 0.433072i | ||||
\(917\) | 13.2810i | 0.438576i | ||||||||
\(918\) | 4.56421 | + | 6.51748i | 0.150641 | + | 0.215109i | ||||
\(919\) | − | 48.0995i | − | 1.58665i | −0.608795 | − | 0.793327i | \(-0.708347\pi\) | ||
0.608795 | − | 0.793327i | \(-0.291653\pi\) | |||||||
\(920\) | −0.0437549 | + | 0.0237593i | −0.00144255 | + | 0.000783322i | ||||
\(921\) | −17.4291 | + | 9.46361i | −0.574309 | + | 0.311837i | ||||
\(922\) | 10.4152 | + | 12.6342i | 0.343005 | + | 0.416086i | ||||
\(923\) | 17.2826 | 0.568862 | ||||||||
\(924\) | −2.16354 | − | 6.86081i | −0.0711753 | − | 0.225704i | ||||
\(925\) | −6.46752 | −0.212651 | ||||||||
\(926\) | 15.1445 | + | 18.3712i | 0.497679 | + | 0.603716i | ||||
\(927\) | −49.1331 | − | 31.9051i | −1.61374 | − | 1.04790i | ||||
\(928\) | −15.7984 | − | 50.0940i | −0.518609 | − | 1.64442i | ||||
\(929\) | − | 41.1804i | − | 1.35108i | −0.737321 | − | 0.675542i | \(-0.763910\pi\) | ||
0.737321 | − | 0.675542i | \(-0.236090\pi\) | |||||||
\(930\) | 24.6799 | + | 9.97044i | 0.809285 | + | 0.326944i | ||||
\(931\) | 1.74609i | 0.0572259i | ||||||||
\(932\) | 11.9715 | + | 2.32668i | 0.392140 | + | 0.0762129i | ||||
\(933\) | 9.47447 | + | 17.4491i | 0.310180 | + | 0.571258i | ||||
\(934\) | −9.30224 | + | 7.66840i | −0.304379 | + | 0.250918i | ||||
\(935\) | −2.24859 | −0.0735366 | ||||||||
\(936\) | 32.8850 | + | 2.58562i | 1.07488 | + | 0.0845137i | ||||
\(937\) | 11.5893 | 0.378606 | 0.189303 | − | 0.981919i | \(-0.439377\pi\) | ||||
0.189303 | + | 0.981919i | \(0.439377\pi\) | |||||||
\(938\) | 7.77155 | − | 6.40655i | 0.253750 | − | 0.209181i | ||||
\(939\) | −8.88948 | − | 16.3717i | −0.290097 | − | 0.534271i | ||||
\(940\) | −0.418648 | − | 0.0813649i | −0.0136548 | − | 0.00265383i | ||||
\(941\) | 31.7808i | 1.03602i | 0.855373 | + | 0.518012i | \(0.173328\pi\) | ||||
−0.855373 | + | 0.518012i | \(0.826672\pi\) | |||||||
\(942\) | 41.4928 | + | 16.7627i | 1.35191 | + | 0.546158i | ||||
\(943\) | − | 0.170216i | − | 0.00554301i | ||||||
\(944\) | −11.0560 | − | 4.46619i | −0.359841 | − | 0.145362i | ||||
\(945\) | −5.18015 | − | 0.407427i | −0.168510 | − | 0.0132536i | ||||
\(946\) | −6.41430 | − | 7.78095i | −0.208547 | − | 0.252980i | ||||
\(947\) | −0.973758 | −0.0316429 | −0.0158214 | − | 0.999875i | \(-0.505036\pi\) | ||||
−0.0158214 | + | 0.999875i | \(0.505036\pi\) | |||||||
\(948\) | 2.43510 | + | 7.72195i | 0.0790883 | + | 0.250797i | ||||
\(949\) | 21.8536 | 0.709399 | ||||||||
\(950\) | 1.57073 | + | 1.90539i | 0.0509611 | + | 0.0618190i | ||||
\(951\) | 44.4976 | − | 24.1612i | 1.44293 | − | 0.783481i | ||||
\(952\) | −1.46143 | − | 2.69136i | −0.0473653 | − | 0.0872274i | ||||
\(953\) | − | 19.4218i | − | 0.629133i | −0.949235 | − | 0.314566i | \(-0.898141\pi\) | ||
0.949235 | − | 0.314566i | \(-0.101859\pi\) | |||||||
\(954\) | 33.4529 | − | 3.81308i | 1.08308 | − | 0.123453i | ||||
\(955\) | 19.1594i | 0.619984i | ||||||||
\(956\) | 0.391363 | − | 2.01369i | 0.0126576 | − | 0.0651274i | ||||
\(957\) | −29.3513 | + | 15.9371i | −0.948793 | + | 0.515173i | ||||
\(958\) | −8.93392 | + | 7.36476i | −0.288642 | + | 0.237945i | ||||
\(959\) | −15.2183 | −0.491426 | ||||||||
\(960\) | 1.08577 | − | 13.8138i | 0.0350432 | − | 0.445839i | ||||
\(961\) | −87.0843 | −2.80917 | ||||||||
\(962\) | 27.4362 | − | 22.6173i | 0.884579 | − | 0.729211i | ||||
\(963\) | −28.0773 | + | 43.2385i | −0.904780 | + | 1.39334i | ||||
\(964\) | −1.29979 | + | 6.68786i | −0.0418636 | + | 0.215402i | ||||
\(965\) | − | 11.6629i | − | 0.375443i | ||||||
\(966\) | −0.0161514 | + | 0.0399797i | −0.000519664 | + | 0.00128633i | ||||
\(967\) | − | 27.4809i | − | 0.883728i | −0.897082 | − | 0.441864i | \(-0.854317\pi\) | ||
0.897082 | − | 0.441864i | \(-0.145683\pi\) | |||||||
\(968\) | 9.02601 | + | 16.6222i | 0.290107 | + | 0.534257i | ||||
\(969\) | −1.56258 | − | 2.87780i | −0.0501973 | − | 0.0924483i | ||||
\(970\) | −10.3033 | − | 12.4985i | −0.330819 | − | 0.401304i | ||||
\(971\) | 38.6485 | 1.24029 | 0.620144 | − | 0.784488i | \(-0.287074\pi\) | ||||
0.620144 | + | 0.784488i | \(0.287074\pi\) | |||||||
\(972\) | 20.6610 | + | 23.3478i | 0.662703 | + | 0.748882i | ||||
\(973\) | 13.5504 | 0.434405 | ||||||||
\(974\) | 8.67978 | + | 10.5291i | 0.278118 | + | 0.337375i | ||||
\(975\) | 3.21297 | + | 5.91732i | 0.102897 | + | 0.189506i | ||||
\(976\) | −31.0295 | − | 12.5347i | −0.993229 | − | 0.401226i | ||||
\(977\) | − | 51.1792i | − | 1.63737i | −0.574243 | − | 0.818685i | \(-0.694704\pi\) | ||
0.574243 | − | 0.818685i | \(-0.305296\pi\) | |||||||
\(978\) | 3.91669 | − | 9.69499i | 0.125242 | − | 0.310012i | ||||
\(979\) | − | 2.41558i | − | 0.0772021i | ||||||
\(980\) | 1.96327 | + | 0.381563i | 0.0627142 | + | 0.0121886i | ||||
\(981\) | 28.5120 | − | 43.9078i | 0.910318 | − | 1.40187i | ||||
\(982\) | −11.3159 | + | 9.32840i | −0.361106 | + | 0.297681i | ||||
\(983\) | 6.19182 | 0.197489 | 0.0987443 | − | 0.995113i | \(-0.468517\pi\) | ||||
0.0987443 | + | 0.995113i | \(0.468517\pi\) | |||||||
\(984\) | 39.7303 | + | 25.7979i | 1.26656 | + | 0.822407i | ||||
\(985\) | 24.8253 | 0.791000 | ||||||||
\(986\) | −10.9712 | + | 9.04422i | −0.349394 | + | 0.288027i | ||||
\(987\) | −0.324583 | + | 0.176241i | −0.0103316 | + | 0.00560982i | ||||
\(988\) | −13.3265 | − | 2.59003i | −0.423973 | − | 0.0823997i | ||||
\(989\) | 0.0604418i | 0.00192194i | ||||||||
\(990\) | −8.75397 | + | 0.997807i | −0.278219 | + | 0.0317124i | ||||
\(991\) | − | 5.68339i | − | 0.180539i | −0.995917 | − | 0.0902695i | \(-0.971227\pi\) | ||
0.995917 | − | 0.0902695i | \(-0.0287728\pi\) | |||||||
\(992\) | 18.4888 | + | 58.6248i | 0.587021 | + | 1.86134i | ||||
\(993\) | −5.99110 | + | 3.25303i | −0.190122 | + | 0.103232i | ||||
\(994\) | −3.99918 | − | 4.85126i | −0.126846 | − | 0.153873i | ||||
\(995\) | 23.6092 | 0.748460 | ||||||||
\(996\) | −12.9060 | + | 4.06987i | −0.408942 | + | 0.128959i | ||||
\(997\) | 15.0648 | 0.477106 | 0.238553 | − | 0.971129i | \(-0.423327\pi\) | ||||
0.238553 | + | 0.971129i | \(0.423327\pi\) | |||||||
\(998\) | −25.9572 | − | 31.4876i | −0.821659 | − | 0.996724i | ||||
\(999\) | 33.5028 | + | 2.63505i | 1.05998 | + | 0.0833692i |
(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 | 420.2.n.b.71.17 | yes | 24 | |
3.2 | odd | 2 | 420.2.n.a.71.8 | yes | 24 | ||
4.3 | odd | 2 | 420.2.n.a.71.7 | ✓ | 24 | ||
12.11 | even | 2 | inner | 420.2.n.b.71.18 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.n.a.71.7 | ✓ | 24 | 4.3 | odd | 2 | ||
420.2.n.a.71.8 | yes | 24 | 3.2 | odd | 2 | ||
420.2.n.b.71.17 | yes | 24 | 1.1 | even | 1 | trivial | |
420.2.n.b.71.18 | yes | 24 | 12.11 | even | 2 | inner |