Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(197,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.c (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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 16x^{10} + 94x^{8} + 246x^{6} + 277x^{4} + 114x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.10 | ||
Root | \(0.319443i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.197 |
Dual form | 462.2.c.a.197.9 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.37401 | + | 1.05456i | 0.793283 | + | 0.608853i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | − | 3.92876i | − | 1.75700i | −0.477746 | − | 0.878498i | \(-0.658546\pi\) | ||
0.477746 | − | 0.878498i | \(-0.341454\pi\) | |||||||
\(6\) | −1.37401 | − | 1.05456i | −0.560936 | − | 0.430524i | ||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.775791 | + | 2.89796i | 0.258597 | + | 0.965985i | ||||
\(10\) | 3.92876i | 1.24238i | ||||||||
\(11\) | 1.42857 | − | 2.99319i | 0.430730 | − | 0.902481i | ||||
\(12\) | 1.37401 | + | 1.05456i | 0.396642 | + | 0.304426i | ||||
\(13\) | 0.109128i | 0.0302665i | 0.999885 | + | 0.0151333i | \(0.00481725\pi\) | ||||
−0.999885 | + | 0.0151333i | \(0.995183\pi\) | |||||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | 4.14313 | − | 5.39815i | 1.06975 | − | 1.39380i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.97666 | −1.69209 | −0.846045 | − | 0.533112i | \(-0.821022\pi\) | ||||
−0.846045 | + | 0.533112i | \(0.821022\pi\) | |||||||
\(18\) | −0.775791 | − | 2.89796i | −0.182856 | − | 0.683055i | ||||
\(19\) | − | 5.78023i | − | 1.32608i | −0.748586 | − | 0.663038i | \(-0.769267\pi\) | ||
0.748586 | − | 0.663038i | \(-0.230733\pi\) | |||||||
\(20\) | − | 3.92876i | − | 0.878498i | ||||||
\(21\) | 1.05456 | − | 1.37401i | 0.230125 | − | 0.299833i | ||||
\(22\) | −1.42857 | + | 2.99319i | −0.304572 | + | 0.638150i | ||||
\(23\) | − | 0.938770i | − | 0.195747i | −0.995199 | − | 0.0978736i | \(-0.968796\pi\) | ||
0.995199 | − | 0.0978736i | \(-0.0312041\pi\) | |||||||
\(24\) | −1.37401 | − | 1.05456i | −0.280468 | − | 0.215262i | ||||
\(25\) | −10.4352 | −2.08704 | ||||||||
\(26\) | − | 0.109128i | − | 0.0214017i | ||||||
\(27\) | −1.99014 | + | 4.79993i | −0.383002 | + | 0.923747i | ||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | 10.3479 | 1.92155 | 0.960776 | − | 0.277324i | \(-0.0894475\pi\) | ||||
0.960776 | + | 0.277324i | \(0.0894475\pi\) | |||||||
\(30\) | −4.14313 | + | 5.39815i | −0.756429 | + | 0.985563i | ||||
\(31\) | −2.61516 | −0.469697 | −0.234849 | − | 0.972032i | \(-0.575459\pi\) | ||||
−0.234849 | + | 0.972032i | \(0.575459\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 5.11938 | − | 2.60614i | 0.891169 | − | 0.453672i | ||||
\(34\) | 6.97666 | 1.19649 | ||||||||
\(35\) | −3.92876 | −0.664082 | ||||||||
\(36\) | 0.775791 | + | 2.89796i | 0.129298 | + | 0.482993i | ||||
\(37\) | 7.21864 | 1.18674 | 0.593369 | − | 0.804931i | \(-0.297798\pi\) | ||||
0.593369 | + | 0.804931i | \(0.297798\pi\) | |||||||
\(38\) | 5.78023i | 0.937677i | ||||||||
\(39\) | −0.115082 | + | 0.149942i | −0.0184279 | + | 0.0240099i | ||||
\(40\) | 3.92876i | 0.621192i | ||||||||
\(41\) | 8.95059 | 1.39785 | 0.698923 | − | 0.715197i | \(-0.253663\pi\) | ||||
0.698923 | + | 0.715197i | \(0.253663\pi\) | |||||||
\(42\) | −1.05456 | + | 1.37401i | −0.162723 | + | 0.212014i | ||||
\(43\) | − | 1.44880i | − | 0.220941i | −0.993879 | − | 0.110470i | \(-0.964764\pi\) | ||
0.993879 | − | 0.110470i | \(-0.0352357\pi\) | |||||||
\(44\) | 1.42857 | − | 2.99319i | 0.215365 | − | 0.451240i | ||||
\(45\) | 11.3854 | − | 3.04790i | 1.69723 | − | 0.454354i | ||||
\(46\) | 0.938770i | 0.138414i | ||||||||
\(47\) | 11.4115i | 1.66453i | 0.554376 | + | 0.832266i | \(0.312957\pi\) | ||||
−0.554376 | + | 0.832266i | \(0.687043\pi\) | |||||||
\(48\) | 1.37401 | + | 1.05456i | 0.198321 | + | 0.152213i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 10.4352 | 1.47576 | ||||||||
\(51\) | −9.58598 | − | 7.35733i | −1.34231 | − | 1.03023i | ||||
\(52\) | 0.109128i | 0.0151333i | ||||||||
\(53\) | − | 5.55158i | − | 0.762568i | −0.924458 | − | 0.381284i | \(-0.875482\pi\) | ||
0.924458 | − | 0.381284i | \(-0.124518\pi\) | |||||||
\(54\) | 1.99014 | − | 4.79993i | 0.270823 | − | 0.653188i | ||||
\(55\) | −11.7595 | − | 5.61252i | −1.58566 | − | 0.756792i | ||||
\(56\) | 1.00000i | 0.133631i | ||||||||
\(57\) | 6.09562 | − | 7.94207i | 0.807385 | − | 1.05195i | ||||
\(58\) | −10.3479 | −1.35874 | ||||||||
\(59\) | 7.60516i | 0.990107i | 0.868863 | + | 0.495053i | \(0.164852\pi\) | ||||
−0.868863 | + | 0.495053i | \(0.835148\pi\) | |||||||
\(60\) | 4.14313 | − | 5.39815i | 0.534876 | − | 0.696898i | ||||
\(61\) | 6.35346i | 0.813477i | 0.913545 | + | 0.406738i | \(0.133334\pi\) | ||||
−0.913545 | + | 0.406738i | \(0.866666\pi\) | |||||||
\(62\) | 2.61516 | 0.332126 | ||||||||
\(63\) | 2.89796 | − | 0.775791i | 0.365108 | − | 0.0977404i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.428736 | 0.0531782 | ||||||||
\(66\) | −5.11938 | + | 2.60614i | −0.630152 | + | 0.320794i | ||||
\(67\) | 5.60544 | 0.684814 | 0.342407 | − | 0.939552i | \(-0.388758\pi\) | ||||
0.342407 | + | 0.939552i | \(0.388758\pi\) | |||||||
\(68\) | −6.97666 | −0.846045 | ||||||||
\(69\) | 0.989993 | − | 1.28988i | 0.119181 | − | 0.155283i | ||||
\(70\) | 3.92876 | 0.469577 | ||||||||
\(71\) | − | 4.39287i | − | 0.521337i | −0.965428 | − | 0.260669i | \(-0.916057\pi\) | ||
0.965428 | − | 0.260669i | \(-0.0839430\pi\) | |||||||
\(72\) | −0.775791 | − | 2.89796i | −0.0914278 | − | 0.341527i | ||||
\(73\) | − | 3.31566i | − | 0.388069i | −0.980995 | − | 0.194035i | \(-0.937843\pi\) | ||
0.980995 | − | 0.194035i | \(-0.0621574\pi\) | |||||||
\(74\) | −7.21864 | −0.839150 | ||||||||
\(75\) | −14.3380 | − | 11.0046i | −1.65561 | − | 1.27070i | ||||
\(76\) | − | 5.78023i | − | 0.663038i | ||||||
\(77\) | −2.99319 | − | 1.42857i | −0.341106 | − | 0.162801i | ||||
\(78\) | 0.115082 | − | 0.149942i | 0.0130305 | − | 0.0169776i | ||||
\(79\) | 0.361499i | 0.0406719i | 0.999793 | + | 0.0203359i | \(0.00647357\pi\) | ||||
−0.999793 | + | 0.0203359i | \(0.993526\pi\) | |||||||
\(80\) | − | 3.92876i | − | 0.439249i | ||||||
\(81\) | −7.79630 | + | 4.49641i | −0.866255 | + | 0.499602i | ||||
\(82\) | −8.95059 | −0.988427 | ||||||||
\(83\) | −1.48034 | −0.162489 | −0.0812445 | − | 0.996694i | \(-0.525889\pi\) | ||||
−0.0812445 | + | 0.996694i | \(0.525889\pi\) | |||||||
\(84\) | 1.05456 | − | 1.37401i | 0.115062 | − | 0.149916i | ||||
\(85\) | 27.4097i | 2.97299i | ||||||||
\(86\) | 1.44880i | 0.156229i | ||||||||
\(87\) | 14.2181 | + | 10.9125i | 1.52434 | + | 1.16994i | ||||
\(88\) | −1.42857 | + | 2.99319i | −0.152286 | + | 0.319075i | ||||
\(89\) | − | 0.722227i | − | 0.0765559i | −0.999267 | − | 0.0382779i | \(-0.987813\pi\) | ||
0.999267 | − | 0.0382779i | \(-0.0121872\pi\) | |||||||
\(90\) | −11.3854 | + | 3.04790i | −1.20012 | + | 0.321277i | ||||
\(91\) | 0.109128 | 0.0114397 | ||||||||
\(92\) | − | 0.938770i | − | 0.0978736i | ||||||
\(93\) | −3.59325 | − | 2.75786i | −0.372603 | − | 0.285976i | ||||
\(94\) | − | 11.4115i | − | 1.17700i | ||||||
\(95\) | −22.7092 | −2.32991 | ||||||||
\(96\) | −1.37401 | − | 1.05456i | −0.140234 | − | 0.107631i | ||||
\(97\) | −3.48997 | −0.354352 | −0.177176 | − | 0.984179i | \(-0.556696\pi\) | ||||
−0.177176 | + | 0.984179i | \(0.556696\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 9.78240 | + | 1.81785i | 0.983169 | + | 0.182700i | ||||
\(100\) | −10.4352 | −1.04352 | ||||||||
\(101\) | 10.2648 | 1.02139 | 0.510694 | − | 0.859762i | \(-0.329388\pi\) | ||||
0.510694 | + | 0.859762i | \(0.329388\pi\) | |||||||
\(102\) | 9.58598 | + | 7.35733i | 0.949154 | + | 0.728485i | ||||
\(103\) | −3.64331 | −0.358986 | −0.179493 | − | 0.983759i | \(-0.557446\pi\) | ||||
−0.179493 | + | 0.983759i | \(0.557446\pi\) | |||||||
\(104\) | − | 0.109128i | − | 0.0107008i | ||||||
\(105\) | −5.39815 | − | 4.14313i | −0.526805 | − | 0.404328i | ||||
\(106\) | 5.55158i | 0.539217i | ||||||||
\(107\) | 10.3337 | 0.999000 | 0.499500 | − | 0.866314i | \(-0.333517\pi\) | ||||
0.499500 | + | 0.866314i | \(0.333517\pi\) | |||||||
\(108\) | −1.99014 | + | 4.79993i | −0.191501 | + | 0.461874i | ||||
\(109\) | 13.7090i | 1.31308i | 0.754290 | + | 0.656542i | \(0.227981\pi\) | ||||
−0.754290 | + | 0.656542i | \(0.772019\pi\) | |||||||
\(110\) | 11.7595 | + | 5.61252i | 1.12123 | + | 0.535133i | ||||
\(111\) | 9.91846 | + | 7.61252i | 0.941419 | + | 0.722548i | ||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | − | 0.803856i | − | 0.0756204i | −0.999285 | − | 0.0378102i | \(-0.987962\pi\) | ||
0.999285 | − | 0.0378102i | \(-0.0120382\pi\) | |||||||
\(114\) | −6.09562 | + | 7.94207i | −0.570907 | + | 0.743843i | ||||
\(115\) | −3.68821 | −0.343927 | ||||||||
\(116\) | 10.3479 | 0.960776 | ||||||||
\(117\) | −0.316247 | + | 0.0846601i | −0.0292370 | + | 0.00782683i | ||||
\(118\) | − | 7.60516i | − | 0.700111i | ||||||
\(119\) | 6.97666i | 0.639550i | ||||||||
\(120\) | −4.14313 | + | 5.39815i | −0.378214 | + | 0.492781i | ||||
\(121\) | −6.91837 | − | 8.55197i | −0.628943 | − | 0.777452i | ||||
\(122\) | − | 6.35346i | − | 0.575215i | ||||||
\(123\) | 12.2982 | + | 9.43896i | 1.10889 | + | 0.851083i | ||||
\(124\) | −2.61516 | −0.234849 | ||||||||
\(125\) | 21.3536i | 1.90992i | ||||||||
\(126\) | −2.89796 | + | 0.775791i | −0.258170 | + | 0.0691129i | ||||
\(127\) | 14.3201i | 1.27070i | 0.772223 | + | 0.635351i | \(0.219145\pi\) | ||||
−0.772223 | + | 0.635351i | \(0.780855\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.52786 | − | 1.99067i | 0.134520 | − | 0.175269i | ||||
\(130\) | −0.428736 | −0.0376026 | ||||||||
\(131\) | −17.8346 | −1.55822 | −0.779109 | − | 0.626889i | \(-0.784328\pi\) | ||||
−0.779109 | + | 0.626889i | \(0.784328\pi\) | |||||||
\(132\) | 5.11938 | − | 2.60614i | 0.445584 | − | 0.226836i | ||||
\(133\) | −5.78023 | −0.501209 | ||||||||
\(134\) | −5.60544 | −0.484237 | ||||||||
\(135\) | 18.8578 | + | 7.81878i | 1.62302 | + | 0.672933i | ||||
\(136\) | 6.97666 | 0.598244 | ||||||||
\(137\) | 6.72300i | 0.574385i | 0.957873 | + | 0.287192i | \(0.0927219\pi\) | ||||
−0.957873 | + | 0.287192i | \(0.907278\pi\) | |||||||
\(138\) | −0.989993 | + | 1.28988i | −0.0842738 | + | 0.109802i | ||||
\(139\) | 6.05064i | 0.513208i | 0.966517 | + | 0.256604i | \(0.0826036\pi\) | ||||
−0.966517 | + | 0.256604i | \(0.917396\pi\) | |||||||
\(140\) | −3.92876 | −0.332041 | ||||||||
\(141\) | −12.0341 | + | 15.6794i | −1.01346 | + | 1.32045i | ||||
\(142\) | 4.39287i | 0.368641i | ||||||||
\(143\) | 0.326639 | + | 0.155896i | 0.0273150 | + | 0.0130367i | ||||
\(144\) | 0.775791 | + | 2.89796i | 0.0646492 | + | 0.241496i | ||||
\(145\) | − | 40.6544i | − | 3.37616i | ||||||
\(146\) | 3.31566i | 0.274406i | ||||||||
\(147\) | −1.37401 | − | 1.05456i | −0.113326 | − | 0.0869790i | ||||
\(148\) | 7.21864 | 0.593369 | ||||||||
\(149\) | −6.65134 | −0.544899 | −0.272450 | − | 0.962170i | \(-0.587834\pi\) | ||||
−0.272450 | + | 0.962170i | \(0.587834\pi\) | |||||||
\(150\) | 14.3380 | + | 11.0046i | 1.17069 | + | 0.898519i | ||||
\(151\) | 0.977889i | 0.0795795i | 0.999208 | + | 0.0397897i | \(0.0126688\pi\) | ||||
−0.999208 | + | 0.0397897i | \(0.987331\pi\) | |||||||
\(152\) | 5.78023i | 0.468838i | ||||||||
\(153\) | −5.41243 | − | 20.2181i | −0.437569 | − | 1.63453i | ||||
\(154\) | 2.99319 | + | 1.42857i | 0.241198 | + | 0.115118i | ||||
\(155\) | 10.2744i | 0.825256i | ||||||||
\(156\) | −0.115082 | + | 0.149942i | −0.00921393 | + | 0.0120050i | ||||
\(157\) | −1.12491 | −0.0897774 | −0.0448887 | − | 0.998992i | \(-0.514293\pi\) | ||||
−0.0448887 | + | 0.998992i | \(0.514293\pi\) | |||||||
\(158\) | − | 0.361499i | − | 0.0287593i | ||||||
\(159\) | 5.85450 | − | 7.62791i | 0.464292 | − | 0.604933i | ||||
\(160\) | 3.92876i | 0.310596i | ||||||||
\(161\) | −0.938770 | −0.0739855 | ||||||||
\(162\) | 7.79630 | − | 4.49641i | 0.612535 | − | 0.353272i | ||||
\(163\) | −2.94048 | −0.230316 | −0.115158 | − | 0.993347i | \(-0.536737\pi\) | ||||
−0.115158 | + | 0.993347i | \(0.536737\pi\) | |||||||
\(164\) | 8.95059 | 0.698923 | ||||||||
\(165\) | −10.2389 | − | 20.1128i | −0.797099 | − | 1.56578i | ||||
\(166\) | 1.48034 | 0.114897 | ||||||||
\(167\) | −21.5860 | −1.67037 | −0.835186 | − | 0.549968i | \(-0.814640\pi\) | ||||
−0.835186 | + | 0.549968i | \(0.814640\pi\) | |||||||
\(168\) | −1.05456 | + | 1.37401i | −0.0813614 | + | 0.106007i | ||||
\(169\) | 12.9881 | 0.999084 | ||||||||
\(170\) | − | 27.4097i | − | 2.10222i | ||||||
\(171\) | 16.7508 | − | 4.48425i | 1.28097 | − | 0.342919i | ||||
\(172\) | − | 1.44880i | − | 0.110470i | ||||||
\(173\) | −5.10422 | −0.388067 | −0.194033 | − | 0.980995i | \(-0.562157\pi\) | ||||
−0.194033 | + | 0.980995i | \(0.562157\pi\) | |||||||
\(174\) | −14.2181 | − | 10.9125i | −1.07787 | − | 0.827274i | ||||
\(175\) | 10.4352i | 0.788826i | ||||||||
\(176\) | 1.42857 | − | 2.99319i | 0.107683 | − | 0.225620i | ||||
\(177\) | −8.02012 | + | 10.4495i | −0.602829 | + | 0.785435i | ||||
\(178\) | 0.722227i | 0.0541332i | ||||||||
\(179\) | − | 17.2258i | − | 1.28752i | −0.765229 | − | 0.643759i | \(-0.777374\pi\) | ||
0.765229 | − | 0.643759i | \(-0.222626\pi\) | |||||||
\(180\) | 11.3854 | − | 3.04790i | 0.848616 | − | 0.227177i | ||||
\(181\) | 11.9832 | 0.890701 | 0.445350 | − | 0.895356i | \(-0.353079\pi\) | ||||
0.445350 | + | 0.895356i | \(0.353079\pi\) | |||||||
\(182\) | −0.109128 | −0.00808907 | ||||||||
\(183\) | −6.70013 | + | 8.72970i | −0.495288 | + | 0.645318i | ||||
\(184\) | 0.938770i | 0.0692071i | ||||||||
\(185\) | − | 28.3603i | − | 2.08509i | ||||||
\(186\) | 3.59325 | + | 2.75786i | 0.263470 | + | 0.202216i | ||||
\(187\) | −9.96665 | + | 20.8825i | −0.728834 | + | 1.52708i | ||||
\(188\) | 11.4115i | 0.832266i | ||||||||
\(189\) | 4.79993 | + | 1.99014i | 0.349144 | + | 0.144761i | ||||
\(190\) | 22.7092 | 1.64750 | ||||||||
\(191\) | 13.1345i | 0.950381i | 0.879883 | + | 0.475191i | \(0.157621\pi\) | ||||
−0.879883 | + | 0.475191i | \(0.842379\pi\) | |||||||
\(192\) | 1.37401 | + | 1.05456i | 0.0991604 | + | 0.0761066i | ||||
\(193\) | 7.13624i | 0.513678i | 0.966454 | + | 0.256839i | \(0.0826810\pi\) | ||||
−0.966454 | + | 0.256839i | \(0.917319\pi\) | |||||||
\(194\) | 3.48997 | 0.250565 | ||||||||
\(195\) | 0.589087 | + | 0.452130i | 0.0421854 | + | 0.0323777i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −1.57331 | −0.112093 | −0.0560467 | − | 0.998428i | \(-0.517850\pi\) | ||||
−0.0560467 | + | 0.998428i | \(0.517850\pi\) | |||||||
\(198\) | −9.78240 | − | 1.81785i | −0.695205 | − | 0.129189i | ||||
\(199\) | −4.38353 | −0.310740 | −0.155370 | − | 0.987856i | \(-0.549657\pi\) | ||||
−0.155370 | + | 0.987856i | \(0.549657\pi\) | |||||||
\(200\) | 10.4352 | 0.737879 | ||||||||
\(201\) | 7.70192 | + | 5.91130i | 0.543252 | + | 0.416951i | ||||
\(202\) | −10.2648 | −0.722231 | ||||||||
\(203\) | − | 10.3479i | − | 0.726279i | ||||||
\(204\) | −9.58598 | − | 7.35733i | −0.671153 | − | 0.515116i | ||||
\(205\) | − | 35.1647i | − | 2.45601i | ||||||
\(206\) | 3.64331 | 0.253842 | ||||||||
\(207\) | 2.72052 | − | 0.728289i | 0.189089 | − | 0.0506196i | ||||
\(208\) | 0.109128i | 0.00756663i | ||||||||
\(209\) | −17.3013 | − | 8.25747i | −1.19676 | − | 0.571181i | ||||
\(210\) | 5.39815 | + | 4.14313i | 0.372508 | + | 0.285903i | ||||
\(211\) | − | 5.34526i | − | 0.367983i | −0.982928 | − | 0.183991i | \(-0.941098\pi\) | ||
0.982928 | − | 0.183991i | \(-0.0589018\pi\) | |||||||
\(212\) | − | 5.55158i | − | 0.381284i | ||||||
\(213\) | 4.63256 | − | 6.03583i | 0.317418 | − | 0.413568i | ||||
\(214\) | −10.3337 | −0.706399 | ||||||||
\(215\) | −5.69201 | −0.388192 | ||||||||
\(216\) | 1.99014 | − | 4.79993i | 0.135412 | − | 0.326594i | ||||
\(217\) | 2.61516i | 0.177529i | ||||||||
\(218\) | − | 13.7090i | − | 0.928490i | ||||||
\(219\) | 3.49658 | − | 4.55575i | 0.236277 | − | 0.307849i | ||||
\(220\) | −11.7595 | − | 5.61252i | −0.792828 | − | 0.378396i | ||||
\(221\) | − | 0.761346i | − | 0.0512137i | ||||||
\(222\) | −9.91846 | − | 7.61252i | −0.665684 | − | 0.510919i | ||||
\(223\) | 19.0577 | 1.27620 | 0.638100 | − | 0.769953i | \(-0.279721\pi\) | ||||
0.638100 | + | 0.769953i | \(0.279721\pi\) | |||||||
\(224\) | 1.00000i | 0.0668153i | ||||||||
\(225\) | −8.09552 | − | 30.2407i | −0.539701 | − | 2.01605i | ||||
\(226\) | 0.803856i | 0.0534717i | ||||||||
\(227\) | −17.2146 | −1.14258 | −0.571288 | − | 0.820750i | \(-0.693556\pi\) | ||||
−0.571288 | + | 0.820750i | \(0.693556\pi\) | |||||||
\(228\) | 6.09562 | − | 7.94207i | 0.403692 | − | 0.525977i | ||||
\(229\) | 20.4671 | 1.35250 | 0.676252 | − | 0.736670i | \(-0.263603\pi\) | ||||
0.676252 | + | 0.736670i | \(0.263603\pi\) | |||||||
\(230\) | 3.68821 | 0.243193 | ||||||||
\(231\) | −2.60614 | − | 5.11938i | −0.171472 | − | 0.336830i | ||||
\(232\) | −10.3479 | −0.679372 | ||||||||
\(233\) | 17.1712 | 1.12492 | 0.562460 | − | 0.826824i | \(-0.309855\pi\) | ||||
0.562460 | + | 0.826824i | \(0.309855\pi\) | |||||||
\(234\) | 0.316247 | − | 0.0846601i | 0.0206737 | − | 0.00553440i | ||||
\(235\) | 44.8329 | 2.92458 | ||||||||
\(236\) | 7.60516i | 0.495053i | ||||||||
\(237\) | −0.381224 | + | 0.496703i | −0.0247632 | + | 0.0322643i | ||||
\(238\) | − | 6.97666i | − | 0.452230i | ||||||
\(239\) | 9.38967 | 0.607367 | 0.303684 | − | 0.952773i | \(-0.401783\pi\) | ||||
0.303684 | + | 0.952773i | \(0.401783\pi\) | |||||||
\(240\) | 4.14313 | − | 5.39815i | 0.267438 | − | 0.348449i | ||||
\(241\) | − | 10.3774i | − | 0.668470i | −0.942490 | − | 0.334235i | \(-0.891522\pi\) | ||
0.942490 | − | 0.334235i | \(-0.108478\pi\) | |||||||
\(242\) | 6.91837 | + | 8.55197i | 0.444730 | + | 0.549741i | ||||
\(243\) | −15.4539 | − | 2.04359i | −0.991370 | − | 0.131096i | ||||
\(244\) | 6.35346i | 0.406738i | ||||||||
\(245\) | 3.92876i | 0.251000i | ||||||||
\(246\) | −12.2982 | − | 9.43896i | −0.784103 | − | 0.601806i | ||||
\(247\) | 0.630782 | 0.0401357 | ||||||||
\(248\) | 2.61516 | 0.166063 | ||||||||
\(249\) | −2.03400 | − | 1.56112i | −0.128900 | − | 0.0989318i | ||||
\(250\) | − | 21.3536i | − | 1.35052i | ||||||
\(251\) | − | 7.75369i | − | 0.489409i | −0.969598 | − | 0.244704i | \(-0.921309\pi\) | ||
0.969598 | − | 0.244704i | \(-0.0786909\pi\) | |||||||
\(252\) | 2.89796 | − | 0.775791i | 0.182554 | − | 0.0488702i | ||||
\(253\) | −2.80992 | − | 1.34110i | −0.176658 | − | 0.0843142i | ||||
\(254\) | − | 14.3201i | − | 0.898522i | ||||||
\(255\) | −28.9052 | + | 37.6611i | −1.81012 | + | 2.35843i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.2224i | 1.38619i | 0.720844 | + | 0.693097i | \(0.243754\pi\) | ||||
−0.720844 | + | 0.693097i | \(0.756246\pi\) | |||||||
\(258\) | −1.52786 | + | 1.99067i | −0.0951202 | + | 0.123934i | ||||
\(259\) | − | 7.21864i | − | 0.448545i | ||||||
\(260\) | 0.428736 | 0.0265891 | ||||||||
\(261\) | 8.02779 | + | 29.9877i | 0.496908 | + | 1.85619i | ||||
\(262\) | 17.8346 | 1.10183 | ||||||||
\(263\) | 18.9287 | 1.16720 | 0.583598 | − | 0.812043i | \(-0.301644\pi\) | ||||
0.583598 | + | 0.812043i | \(0.301644\pi\) | |||||||
\(264\) | −5.11938 | + | 2.60614i | −0.315076 | + | 0.160397i | ||||
\(265\) | −21.8109 | −1.33983 | ||||||||
\(266\) | 5.78023 | 0.354409 | ||||||||
\(267\) | 0.761634 | − | 0.992345i | 0.0466113 | − | 0.0607305i | ||||
\(268\) | 5.60544 | 0.342407 | ||||||||
\(269\) | − | 17.4450i | − | 1.06364i | −0.846857 | − | 0.531820i | \(-0.821508\pi\) | ||
0.846857 | − | 0.531820i | \(-0.178492\pi\) | |||||||
\(270\) | −18.8578 | − | 7.81878i | −1.14765 | − | 0.475836i | ||||
\(271\) | 8.89232i | 0.540170i | 0.962836 | + | 0.270085i | \(0.0870518\pi\) | ||||
−0.962836 | + | 0.270085i | \(0.912948\pi\) | |||||||
\(272\) | −6.97666 | −0.423022 | ||||||||
\(273\) | 0.149942 | + | 0.115082i | 0.00907490 | + | 0.00696507i | ||||
\(274\) | − | 6.72300i | − | 0.406151i | ||||||
\(275\) | −14.9074 | + | 31.2345i | −0.898950 | + | 1.88351i | ||||
\(276\) | 0.989993 | − | 1.28988i | 0.0595906 | − | 0.0776415i | ||||
\(277\) | 11.6381i | 0.699266i | 0.936887 | + | 0.349633i | \(0.113694\pi\) | ||||
−0.936887 | + | 0.349633i | \(0.886306\pi\) | |||||||
\(278\) | − | 6.05064i | − | 0.362893i | ||||||
\(279\) | −2.02882 | − | 7.57863i | −0.121462 | − | 0.453720i | ||||
\(280\) | 3.92876 | 0.234789 | ||||||||
\(281\) | 16.8968 | 1.00798 | 0.503989 | − | 0.863710i | \(-0.331865\pi\) | ||||
0.503989 | + | 0.863710i | \(0.331865\pi\) | |||||||
\(282\) | 12.0341 | − | 15.6794i | 0.716621 | − | 0.933696i | ||||
\(283\) | 6.18032i | 0.367382i | 0.982984 | + | 0.183691i | \(0.0588046\pi\) | ||||
−0.982984 | + | 0.183691i | \(0.941195\pi\) | |||||||
\(284\) | − | 4.39287i | − | 0.260669i | ||||||
\(285\) | −31.2025 | − | 23.9482i | −1.84828 | − | 1.41857i | ||||
\(286\) | −0.326639 | − | 0.155896i | −0.0193146 | − | 0.00921834i | ||||
\(287\) | − | 8.95059i | − | 0.528336i | ||||||
\(288\) | −0.775791 | − | 2.89796i | −0.0457139 | − | 0.170764i | ||||
\(289\) | 31.6738 | 1.86317 | ||||||||
\(290\) | 40.6544i | 2.38731i | ||||||||
\(291\) | −4.79524 | − | 3.68039i | −0.281102 | − | 0.215748i | ||||
\(292\) | − | 3.31566i | − | 0.194035i | ||||||
\(293\) | 13.0184 | 0.760544 | 0.380272 | − | 0.924875i | \(-0.375830\pi\) | ||||
0.380272 | + | 0.924875i | \(0.375830\pi\) | |||||||
\(294\) | 1.37401 | + | 1.05456i | 0.0801337 | + | 0.0615034i | ||||
\(295\) | 29.8789 | 1.73961 | ||||||||
\(296\) | −7.21864 | −0.419575 | ||||||||
\(297\) | 11.5241 | + | 12.8139i | 0.668694 | + | 0.743538i | ||||
\(298\) | 6.65134 | 0.385302 | ||||||||
\(299\) | 0.102446 | 0.00592459 | ||||||||
\(300\) | −14.3380 | − | 11.0046i | −0.827806 | − | 0.635349i | ||||
\(301\) | −1.44880 | −0.0835077 | ||||||||
\(302\) | − | 0.977889i | − | 0.0562712i | ||||||
\(303\) | 14.1039 | + | 10.8249i | 0.810250 | + | 0.621875i | ||||
\(304\) | − | 5.78023i | − | 0.331519i | ||||||
\(305\) | 24.9612 | 1.42928 | ||||||||
\(306\) | 5.41243 | + | 20.2181i | 0.309408 | + | 1.15579i | ||||
\(307\) | − | 14.2481i | − | 0.813182i | −0.913610 | − | 0.406591i | \(-0.866717\pi\) | ||
0.913610 | − | 0.406591i | \(-0.133283\pi\) | |||||||
\(308\) | −2.99319 | − | 1.42857i | −0.170553 | − | 0.0814004i | ||||
\(309\) | −5.00594 | − | 3.84211i | −0.284778 | − | 0.218570i | ||||
\(310\) | − | 10.2744i | − | 0.583544i | ||||||
\(311\) | 19.9015i | 1.12851i | 0.825601 | + | 0.564255i | \(0.190836\pi\) | ||||
−0.825601 | + | 0.564255i | \(0.809164\pi\) | |||||||
\(312\) | 0.115082 | − | 0.149942i | 0.00651523 | − | 0.00848879i | ||||
\(313\) | −30.6797 | −1.73412 | −0.867059 | − | 0.498206i | \(-0.833992\pi\) | ||||
−0.867059 | + | 0.498206i | \(0.833992\pi\) | |||||||
\(314\) | 1.12491 | 0.0634822 | ||||||||
\(315\) | −3.04790 | − | 11.3854i | −0.171730 | − | 0.641494i | ||||
\(316\) | 0.361499i | 0.0203359i | ||||||||
\(317\) | − | 15.9925i | − | 0.898226i | −0.893475 | − | 0.449113i | \(-0.851740\pi\) | ||
0.893475 | − | 0.449113i | \(-0.148260\pi\) | |||||||
\(318\) | −5.85450 | + | 7.62791i | −0.328304 | + | 0.427752i | ||||
\(319\) | 14.7827 | − | 30.9732i | 0.827671 | − | 1.73416i | ||||
\(320\) | − | 3.92876i | − | 0.219625i | ||||||
\(321\) | 14.1986 | + | 10.8976i | 0.792490 | + | 0.608244i | ||||
\(322\) | 0.938770 | 0.0523156 | ||||||||
\(323\) | 40.3267i | 2.24384i | ||||||||
\(324\) | −7.79630 | + | 4.49641i | −0.433128 | + | 0.249801i | ||||
\(325\) | − | 1.13877i | − | 0.0631673i | ||||||
\(326\) | 2.94048 | 0.162858 | ||||||||
\(327\) | −14.4570 | + | 18.8363i | −0.799474 | + | 1.04165i | ||||
\(328\) | −8.95059 | −0.494213 | ||||||||
\(329\) | 11.4115 | 0.629134 | ||||||||
\(330\) | 10.2389 | + | 20.1128i | 0.563634 | + | 1.10717i | ||||
\(331\) | −0.500933 | −0.0275338 | −0.0137669 | − | 0.999905i | \(-0.504382\pi\) | ||||
−0.0137669 | + | 0.999905i | \(0.504382\pi\) | |||||||
\(332\) | −1.48034 | −0.0812445 | ||||||||
\(333\) | 5.60015 | + | 20.9193i | 0.306887 | + | 1.14637i | ||||
\(334\) | 21.5860 | 1.18113 | ||||||||
\(335\) | − | 22.0225i | − | 1.20322i | ||||||
\(336\) | 1.05456 | − | 1.37401i | 0.0575312 | − | 0.0749582i | ||||
\(337\) | 11.7562i | 0.640402i | 0.947350 | + | 0.320201i | \(0.103750\pi\) | ||||
−0.947350 | + | 0.320201i | \(0.896250\pi\) | |||||||
\(338\) | −12.9881 | −0.706459 | ||||||||
\(339\) | 0.847717 | − | 1.10450i | 0.0460417 | − | 0.0599884i | ||||
\(340\) | 27.4097i | 1.48650i | ||||||||
\(341\) | −3.73594 | + | 7.82768i | −0.202313 | + | 0.423892i | ||||
\(342\) | −16.7508 | + | 4.48425i | −0.905782 | + | 0.242480i | ||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 1.44880i | 0.0781143i | ||||||||
\(345\) | −5.06762 | − | 3.88945i | −0.272832 | − | 0.209401i | ||||
\(346\) | 5.10422 | 0.274405 | ||||||||
\(347\) | −31.2589 | −1.67806 | −0.839032 | − | 0.544083i | \(-0.816878\pi\) | ||||
−0.839032 | + | 0.544083i | \(0.816878\pi\) | |||||||
\(348\) | 14.2181 | + | 10.9125i | 0.762168 | + | 0.584971i | ||||
\(349\) | − | 26.8168i | − | 1.43547i | −0.696316 | − | 0.717736i | \(-0.745179\pi\) | ||
0.696316 | − | 0.717736i | \(-0.254821\pi\) | |||||||
\(350\) | − | 10.4352i | − | 0.557784i | ||||||
\(351\) | −0.523805 | − | 0.217179i | −0.0279586 | − | 0.0115921i | ||||
\(352\) | −1.42857 | + | 2.99319i | −0.0761431 | + | 0.159538i | ||||
\(353\) | − | 30.7700i | − | 1.63772i | −0.573992 | − | 0.818861i | \(-0.694606\pi\) | ||
0.573992 | − | 0.818861i | \(-0.305394\pi\) | |||||||
\(354\) | 8.02012 | − | 10.4495i | 0.426265 | − | 0.555387i | ||||
\(355\) | −17.2585 | −0.915988 | ||||||||
\(356\) | − | 0.722227i | − | 0.0382779i | ||||||
\(357\) | −7.35733 | + | 9.58598i | −0.389391 | + | 0.507344i | ||||
\(358\) | 17.2258i | 0.910412i | ||||||||
\(359\) | −14.7885 | −0.780510 | −0.390255 | − | 0.920707i | \(-0.627613\pi\) | ||||
−0.390255 | + | 0.920707i | \(0.627613\pi\) | |||||||
\(360\) | −11.3854 | + | 3.04790i | −0.600062 | + | 0.160638i | ||||
\(361\) | −14.4110 | −0.758476 | ||||||||
\(362\) | −11.9832 | −0.629820 | ||||||||
\(363\) | −0.487296 | − | 19.0463i | −0.0255764 | − | 0.999673i | ||||
\(364\) | 0.109128 | 0.00571984 | ||||||||
\(365\) | −13.0265 | −0.681836 | ||||||||
\(366\) | 6.70013 | − | 8.72970i | 0.350221 | − | 0.456309i | ||||
\(367\) | −16.5826 | −0.865606 | −0.432803 | − | 0.901488i | \(-0.642475\pi\) | ||||
−0.432803 | + | 0.901488i | \(0.642475\pi\) | |||||||
\(368\) | − | 0.938770i | − | 0.0489368i | ||||||
\(369\) | 6.94378 | + | 25.9384i | 0.361479 | + | 1.35030i | ||||
\(370\) | 28.3603i | 1.47438i | ||||||||
\(371\) | −5.55158 | −0.288224 | ||||||||
\(372\) | −3.59325 | − | 2.75786i | −0.186301 | − | 0.142988i | ||||
\(373\) | 18.1538i | 0.939970i | 0.882674 | + | 0.469985i | \(0.155741\pi\) | ||||
−0.882674 | + | 0.469985i | \(0.844259\pi\) | |||||||
\(374\) | 9.96665 | − | 20.8825i | 0.515363 | − | 1.07981i | ||||
\(375\) | −22.5187 | + | 29.3399i | −1.16286 | + | 1.51511i | ||||
\(376\) | − | 11.4115i | − | 0.588501i | ||||||
\(377\) | 1.12924i | 0.0581587i | ||||||||
\(378\) | −4.79993 | − | 1.99014i | −0.246882 | − | 0.102362i | ||||
\(379\) | −12.5603 | −0.645180 | −0.322590 | − | 0.946539i | \(-0.604554\pi\) | ||||
−0.322590 | + | 0.946539i | \(0.604554\pi\) | |||||||
\(380\) | −22.7092 | −1.16495 | ||||||||
\(381\) | −15.1014 | + | 19.6759i | −0.773671 | + | 1.00803i | ||||
\(382\) | − | 13.1345i | − | 0.672021i | ||||||
\(383\) | − | 3.12388i | − | 0.159623i | −0.996810 | − | 0.0798114i | \(-0.974568\pi\) | ||
0.996810 | − | 0.0798114i | \(-0.0254318\pi\) | |||||||
\(384\) | −1.37401 | − | 1.05456i | −0.0701170 | − | 0.0538155i | ||||
\(385\) | −5.61252 | + | 11.7595i | −0.286040 | + | 0.599321i | ||||
\(386\) | − | 7.13624i | − | 0.363225i | ||||||
\(387\) | 4.19857 | − | 1.12397i | 0.213425 | − | 0.0571346i | ||||
\(388\) | −3.48997 | −0.177176 | ||||||||
\(389\) | − | 25.8114i | − | 1.30869i | −0.756196 | − | 0.654345i | \(-0.772944\pi\) | ||
0.756196 | − | 0.654345i | \(-0.227056\pi\) | |||||||
\(390\) | −0.589087 | − | 0.452130i | −0.0298296 | − | 0.0228945i | ||||
\(391\) | 6.54948i | 0.331222i | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −24.5049 | − | 18.8077i | −1.23611 | − | 0.948725i | ||||
\(394\) | 1.57331 | 0.0792620 | ||||||||
\(395\) | 1.42025 | 0.0714603 | ||||||||
\(396\) | 9.78240 | + | 1.81785i | 0.491584 | + | 0.0913502i | ||||
\(397\) | 26.4518 | 1.32758 | 0.663789 | − | 0.747920i | \(-0.268947\pi\) | ||||
0.663789 | + | 0.747920i | \(0.268947\pi\) | |||||||
\(398\) | 4.38353 | 0.219727 | ||||||||
\(399\) | −7.94207 | − | 6.09562i | −0.397601 | − | 0.305163i | ||||
\(400\) | −10.4352 | −0.521759 | ||||||||
\(401\) | 28.0552i | 1.40101i | 0.713649 | + | 0.700504i | \(0.247041\pi\) | ||||
−0.713649 | + | 0.700504i | \(0.752959\pi\) | |||||||
\(402\) | −7.70192 | − | 5.91130i | −0.384137 | − | 0.294829i | ||||
\(403\) | − | 0.285386i | − | 0.0142161i | ||||||
\(404\) | 10.2648 | 0.510694 | ||||||||
\(405\) | 17.6653 | + | 30.6298i | 0.877798 | + | 1.52201i | ||||
\(406\) | 10.3479i | 0.513557i | ||||||||
\(407\) | 10.3123 | − | 21.6068i | 0.511164 | − | 1.07101i | ||||
\(408\) | 9.58598 | + | 7.35733i | 0.474577 | + | 0.364242i | ||||
\(409\) | − | 1.22795i | − | 0.0607183i | −0.999539 | − | 0.0303591i | \(-0.990335\pi\) | ||
0.999539 | − | 0.0303591i | \(-0.00966510\pi\) | |||||||
\(410\) | 35.1647i | 1.73666i | ||||||||
\(411\) | −7.08983 | + | 9.23745i | −0.349716 | + | 0.455650i | ||||
\(412\) | −3.64331 | −0.179493 | ||||||||
\(413\) | 7.60516 | 0.374225 | ||||||||
\(414\) | −2.72052 | + | 0.728289i | −0.133706 | + | 0.0357935i | ||||
\(415\) | 5.81593i | 0.285493i | ||||||||
\(416\) | − | 0.109128i | − | 0.00535042i | ||||||
\(417\) | −6.38078 | + | 8.31362i | −0.312468 | + | 0.407120i | ||||
\(418\) | 17.3013 | + | 8.25747i | 0.846235 | + | 0.403886i | ||||
\(419\) | − | 10.5048i | − | 0.513192i | −0.966519 | − | 0.256596i | \(-0.917399\pi\) | ||
0.966519 | − | 0.256596i | \(-0.0826010\pi\) | |||||||
\(420\) | −5.39815 | − | 4.14313i | −0.263403 | − | 0.202164i | ||||
\(421\) | −14.6003 | −0.711575 | −0.355787 | − | 0.934567i | \(-0.615787\pi\) | ||||
−0.355787 | + | 0.934567i | \(0.615787\pi\) | |||||||
\(422\) | 5.34526i | 0.260203i | ||||||||
\(423\) | −33.0699 | + | 8.85290i | −1.60791 | + | 0.430443i | ||||
\(424\) | 5.55158i | 0.269609i | ||||||||
\(425\) | 72.8028 | 3.53145 | ||||||||
\(426\) | −4.63256 | + | 6.03583i | −0.224448 | + | 0.292437i | ||||
\(427\) | 6.35346 | 0.307465 | ||||||||
\(428\) | 10.3337 | 0.499500 | ||||||||
\(429\) | 0.284402 | + | 0.558665i | 0.0137311 | + | 0.0269726i | ||||
\(430\) | 5.69201 | 0.274493 | ||||||||
\(431\) | 15.1801 | 0.731198 | 0.365599 | − | 0.930772i | \(-0.380864\pi\) | ||||
0.365599 | + | 0.930772i | \(0.380864\pi\) | |||||||
\(432\) | −1.99014 | + | 4.79993i | −0.0957505 | + | 0.230937i | ||||
\(433\) | 17.1583 | 0.824577 | 0.412289 | − | 0.911053i | \(-0.364730\pi\) | ||||
0.412289 | + | 0.911053i | \(0.364730\pi\) | |||||||
\(434\) | − | 2.61516i | − | 0.125532i | ||||||
\(435\) | 42.8726 | − | 55.8594i | 2.05559 | − | 2.67825i | ||||
\(436\) | 13.7090i | 0.656542i | ||||||||
\(437\) | −5.42631 | −0.259576 | ||||||||
\(438\) | −3.49658 | + | 4.55575i | −0.167073 | + | 0.217682i | ||||
\(439\) | − | 17.7286i | − | 0.846141i | −0.906097 | − | 0.423070i | \(-0.860952\pi\) | ||
0.906097 | − | 0.423070i | \(-0.139048\pi\) | |||||||
\(440\) | 11.7595 | + | 5.61252i | 0.560614 | + | 0.267566i | ||||
\(441\) | −0.775791 | − | 2.89796i | −0.0369424 | − | 0.137998i | ||||
\(442\) | 0.761346i | 0.0362135i | ||||||||
\(443\) | − | 6.70808i | − | 0.318711i | −0.987221 | − | 0.159355i | \(-0.949058\pi\) | ||
0.987221 | − | 0.159355i | \(-0.0509415\pi\) | |||||||
\(444\) | 9.91846 | + | 7.61252i | 0.470709 | + | 0.361274i | ||||
\(445\) | −2.83746 | −0.134508 | ||||||||
\(446\) | −19.0577 | −0.902410 | ||||||||
\(447\) | −9.13899 | − | 7.01426i | −0.432259 | − | 0.331763i | ||||
\(448\) | − | 1.00000i | − | 0.0472456i | ||||||
\(449\) | 2.86960i | 0.135425i | 0.997705 | + | 0.0677123i | \(0.0215700\pi\) | ||||
−0.997705 | + | 0.0677123i | \(0.978430\pi\) | |||||||
\(450\) | 8.09552 | + | 30.2407i | 0.381626 | + | 1.42556i | ||||
\(451\) | 12.7865 | − | 26.7908i | 0.602095 | − | 1.26153i | ||||
\(452\) | − | 0.803856i | − | 0.0378102i | ||||||
\(453\) | −1.03125 | + | 1.34363i | −0.0484522 | + | 0.0631291i | ||||
\(454\) | 17.2146 | 0.807923 | ||||||||
\(455\) | − | 0.428736i | − | 0.0200995i | ||||||
\(456\) | −6.09562 | + | 7.94207i | −0.285454 | + | 0.371922i | ||||
\(457\) | − | 10.7141i | − | 0.501183i | −0.968093 | − | 0.250591i | \(-0.919375\pi\) | ||
0.968093 | − | 0.250591i | \(-0.0806250\pi\) | |||||||
\(458\) | −20.4671 | −0.956365 | ||||||||
\(459\) | 13.8845 | − | 33.4875i | 0.648074 | − | 1.56306i | ||||
\(460\) | −3.68821 | −0.171964 | ||||||||
\(461\) | 5.60949 | 0.261260 | 0.130630 | − | 0.991431i | \(-0.458300\pi\) | ||||
0.130630 | + | 0.991431i | \(0.458300\pi\) | |||||||
\(462\) | 2.60614 | + | 5.11938i | 0.121249 | + | 0.238175i | ||||
\(463\) | −3.97144 | −0.184569 | −0.0922843 | − | 0.995733i | \(-0.529417\pi\) | ||||
−0.0922843 | + | 0.995733i | \(0.529417\pi\) | |||||||
\(464\) | 10.3479 | 0.480388 | ||||||||
\(465\) | −10.8350 | + | 14.1170i | −0.502459 | + | 0.654662i | ||||
\(466\) | −17.1712 | −0.795439 | ||||||||
\(467\) | 6.98066i | 0.323026i | 0.986871 | + | 0.161513i | \(0.0516374\pi\) | ||||
−0.986871 | + | 0.161513i | \(0.948363\pi\) | |||||||
\(468\) | −0.316247 | + | 0.0846601i | −0.0146185 | + | 0.00391341i | ||||
\(469\) | − | 5.60544i | − | 0.258835i | ||||||
\(470\) | −44.8329 | −2.06799 | ||||||||
\(471\) | −1.54563 | − | 1.18629i | −0.0712189 | − | 0.0546612i | ||||
\(472\) | − | 7.60516i | − | 0.350056i | ||||||
\(473\) | −4.33655 | − | 2.06972i | −0.199395 | − | 0.0951658i | ||||
\(474\) | 0.381224 | − | 0.496703i | 0.0175102 | − | 0.0228143i | ||||
\(475\) | 60.3178i | 2.76757i | ||||||||
\(476\) | 6.97666i | 0.319775i | ||||||||
\(477\) | 16.0882 | − | 4.30686i | 0.736630 | − | 0.197198i | ||||
\(478\) | −9.38967 | −0.429474 | ||||||||
\(479\) | 22.5631 | 1.03093 | 0.515467 | − | 0.856909i | \(-0.327618\pi\) | ||||
0.515467 | + | 0.856909i | \(0.327618\pi\) | |||||||
\(480\) | −4.14313 | + | 5.39815i | −0.189107 | + | 0.246391i | ||||
\(481\) | 0.787752i | 0.0359184i | ||||||||
\(482\) | 10.3774i | 0.472679i | ||||||||
\(483\) | −1.28988 | − | 0.989993i | −0.0586914 | − | 0.0450463i | ||||
\(484\) | −6.91837 | − | 8.55197i | −0.314471 | − | 0.388726i | ||||
\(485\) | 13.7113i | 0.622596i | ||||||||
\(486\) | 15.4539 | + | 2.04359i | 0.701004 | + | 0.0926991i | ||||
\(487\) | −9.83009 | −0.445444 | −0.222722 | − | 0.974882i | \(-0.571494\pi\) | ||||
−0.222722 | + | 0.974882i | \(0.571494\pi\) | |||||||
\(488\) | − | 6.35346i | − | 0.287608i | ||||||
\(489\) | −4.04024 | − | 3.10093i | −0.182706 | − | 0.140229i | ||||
\(490\) | − | 3.92876i | − | 0.177483i | ||||||
\(491\) | −7.60395 | −0.343161 | −0.171581 | − | 0.985170i | \(-0.554887\pi\) | ||||
−0.171581 | + | 0.985170i | \(0.554887\pi\) | |||||||
\(492\) | 12.2982 | + | 9.43896i | 0.554444 | + | 0.425541i | ||||
\(493\) | −72.1937 | −3.25144 | ||||||||
\(494\) | −0.630782 | −0.0283802 | ||||||||
\(495\) | 7.14189 | − | 38.4328i | 0.321004 | − | 1.72742i | ||||
\(496\) | −2.61516 | −0.117424 | ||||||||
\(497\) | −4.39287 | −0.197047 | ||||||||
\(498\) | 2.03400 | + | 1.56112i | 0.0911459 | + | 0.0699554i | ||||
\(499\) | −40.0276 | −1.79188 | −0.895941 | − | 0.444173i | \(-0.853498\pi\) | ||||
−0.895941 | + | 0.444173i | \(0.853498\pi\) | |||||||
\(500\) | 21.3536i | 0.954960i | ||||||||
\(501\) | −29.6593 | − | 22.7638i | −1.32508 | − | 1.01701i | ||||
\(502\) | 7.75369i | 0.346064i | ||||||||
\(503\) | −15.7056 | −0.700279 | −0.350139 | − | 0.936698i | \(-0.613866\pi\) | ||||
−0.350139 | + | 0.936698i | \(0.613866\pi\) | |||||||
\(504\) | −2.89796 | + | 0.775791i | −0.129085 | + | 0.0345565i | ||||
\(505\) | − | 40.3281i | − | 1.79458i | ||||||
\(506\) | 2.80992 | + | 1.34110i | 0.124916 | + | 0.0596192i | ||||
\(507\) | 17.8457 | + | 13.6968i | 0.792557 | + | 0.608295i | ||||
\(508\) | 14.3201i | 0.635351i | ||||||||
\(509\) | 3.26942i | 0.144915i | 0.997372 | + | 0.0724573i | \(0.0230841\pi\) | ||||
−0.997372 | + | 0.0724573i | \(0.976916\pi\) | |||||||
\(510\) | 28.9052 | − | 37.6611i | 1.27995 | − | 1.66766i | ||||
\(511\) | −3.31566 | −0.146676 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 27.7447 | + | 11.5035i | 1.22496 | + | 0.507890i | ||||
\(514\) | − | 22.2224i | − | 0.980187i | ||||||
\(515\) | 14.3137i | 0.630738i | ||||||||
\(516\) | 1.52786 | − | 1.99067i | 0.0672602 | − | 0.0876343i | ||||
\(517\) | 34.1567 | + | 16.3021i | 1.50221 | + | 0.716965i | ||||
\(518\) | 7.21864i | 0.317169i | ||||||||
\(519\) | −7.01324 | − | 5.38273i | −0.307847 | − | 0.236276i | ||||
\(520\) | −0.428736 | −0.0188013 | ||||||||
\(521\) | − | 31.6143i | − | 1.38505i | −0.721395 | − | 0.692524i | \(-0.756499\pi\) | ||
0.721395 | − | 0.692524i | \(-0.243501\pi\) | |||||||
\(522\) | −8.02779 | − | 29.9877i | −0.351367 | − | 1.31253i | ||||
\(523\) | 13.1081i | 0.573177i | 0.958054 | + | 0.286589i | \(0.0925213\pi\) | ||||
−0.958054 | + | 0.286589i | \(0.907479\pi\) | |||||||
\(524\) | −17.8346 | −0.779109 | ||||||||
\(525\) | −11.0046 | + | 14.3380i | −0.480279 | + | 0.625762i | ||||
\(526\) | −18.9287 | −0.825332 | ||||||||
\(527\) | 18.2451 | 0.794769 | ||||||||
\(528\) | 5.11938 | − | 2.60614i | 0.222792 | − | 0.113418i | ||||
\(529\) | 22.1187 | 0.961683 | ||||||||
\(530\) | 21.8109 | 0.947403 | ||||||||
\(531\) | −22.0394 | + | 5.90001i | −0.956429 | + | 0.256039i | ||||
\(532\) | −5.78023 | −0.250605 | ||||||||
\(533\) | 0.976755i | 0.0423080i | ||||||||
\(534\) | −0.761634 | + | 0.992345i | −0.0329591 | + | 0.0429430i | ||||
\(535\) | − | 40.5988i | − | 1.75524i | ||||||
\(536\) | −5.60544 | −0.242118 | ||||||||
\(537\) | 18.1657 | − | 23.6684i | 0.783908 | − | 1.02137i | ||||
\(538\) | 17.4450i | 0.752107i | ||||||||
\(539\) | −1.42857 | + | 2.99319i | −0.0615329 | + | 0.128926i | ||||
\(540\) | 18.8578 | + | 7.81878i | 0.811511 | + | 0.336467i | ||||
\(541\) | − | 22.4743i | − | 0.966244i | −0.875553 | − | 0.483122i | \(-0.839503\pi\) | ||
0.875553 | − | 0.483122i | \(-0.160497\pi\) | |||||||
\(542\) | − | 8.89232i | − | 0.381958i | ||||||
\(543\) | 16.4649 | + | 12.6370i | 0.706578 | + | 0.542305i | ||||
\(544\) | 6.97666 | 0.299122 | ||||||||
\(545\) | 53.8594 | 2.30708 | ||||||||
\(546\) | −0.149942 | − | 0.115082i | −0.00641692 | − | 0.00492505i | ||||
\(547\) | 42.0607i | 1.79839i | 0.437553 | + | 0.899193i | \(0.355845\pi\) | ||||
−0.437553 | + | 0.899193i | \(0.644155\pi\) | |||||||
\(548\) | 6.72300i | 0.287192i | ||||||||
\(549\) | −18.4120 | + | 4.92895i | −0.785807 | + | 0.210363i | ||||
\(550\) | 14.9074 | − | 31.2345i | 0.635654 | − | 1.33184i | ||||
\(551\) | − | 59.8131i | − | 2.54812i | ||||||
\(552\) | −0.989993 | + | 1.28988i | −0.0421369 | + | 0.0549008i | ||||
\(553\) | 0.361499 | 0.0153725 | ||||||||
\(554\) | − | 11.6381i | − | 0.494456i | ||||||
\(555\) | 29.9078 | − | 38.9673i | 1.26951 | − | 1.65407i | ||||
\(556\) | 6.05064i | 0.256604i | ||||||||
\(557\) | 19.4913 | 0.825873 | 0.412937 | − | 0.910760i | \(-0.364503\pi\) | ||||
0.412937 | + | 0.910760i | \(0.364503\pi\) | |||||||
\(558\) | 2.02882 | + | 7.57863i | 0.0858867 | + | 0.320829i | ||||
\(559\) | 0.158104 | 0.00668711 | ||||||||
\(560\) | −3.92876 | −0.166021 | ||||||||
\(561\) | −35.7162 | + | 18.1822i | −1.50794 | + | 0.767653i | ||||
\(562\) | −16.8968 | −0.712749 | ||||||||
\(563\) | 15.9611 | 0.672679 | 0.336340 | − | 0.941741i | \(-0.390811\pi\) | ||||
0.336340 | + | 0.941741i | \(0.390811\pi\) | |||||||
\(564\) | −12.0341 | + | 15.6794i | −0.506728 | + | 0.660223i | ||||
\(565\) | −3.15816 | −0.132865 | ||||||||
\(566\) | − | 6.18032i | − | 0.259778i | ||||||
\(567\) | 4.49641 | + | 7.79630i | 0.188832 | + | 0.327414i | ||||
\(568\) | 4.39287i | 0.184321i | ||||||||
\(569\) | −13.4452 | −0.563653 | −0.281827 | − | 0.959465i | \(-0.590940\pi\) | ||||
−0.281827 | + | 0.959465i | \(0.590940\pi\) | |||||||
\(570\) | 31.2025 | + | 23.9482i | 1.30693 | + | 1.00308i | ||||
\(571\) | 7.63852i | 0.319662i | 0.987144 | + | 0.159831i | \(0.0510950\pi\) | ||||
−0.987144 | + | 0.159831i | \(0.948905\pi\) | |||||||
\(572\) | 0.326639 | + | 0.155896i | 0.0136575 | + | 0.00651835i | ||||
\(573\) | −13.8512 | + | 18.0469i | −0.578642 | + | 0.753922i | ||||
\(574\) | 8.95059i | 0.373590i | ||||||||
\(575\) | 9.79624i | 0.408532i | ||||||||
\(576\) | 0.775791 | + | 2.89796i | 0.0323246 | + | 0.120748i | ||||
\(577\) | −34.2239 | −1.42476 | −0.712380 | − | 0.701794i | \(-0.752383\pi\) | ||||
−0.712380 | + | 0.701794i | \(0.752383\pi\) | |||||||
\(578\) | −31.6738 | −1.31746 | ||||||||
\(579\) | −7.52562 | + | 9.80524i | −0.312754 | + | 0.407492i | ||||
\(580\) | − | 40.6544i | − | 1.68808i | ||||||
\(581\) | 1.48034i | 0.0614151i | ||||||||
\(582\) | 4.79524 | + | 3.68039i | 0.198769 | + | 0.152557i | ||||
\(583\) | −16.6169 | − | 7.93083i | −0.688203 | − | 0.328461i | ||||
\(584\) | 3.31566i | 0.137203i | ||||||||
\(585\) | 0.332609 | + | 1.24246i | 0.0137517 | + | 0.0513693i | ||||
\(586\) | −13.0184 | −0.537786 | ||||||||
\(587\) | 6.57288i | 0.271292i | 0.990757 | + | 0.135646i | \(0.0433109\pi\) | ||||
−0.990757 | + | 0.135646i | \(0.956689\pi\) | |||||||
\(588\) | −1.37401 | − | 1.05456i | −0.0566631 | − | 0.0434895i | ||||
\(589\) | 15.1162i | 0.622854i | ||||||||
\(590\) | −29.8789 | −1.23009 | ||||||||
\(591\) | −2.16173 | − | 1.65915i | −0.0889218 | − | 0.0682484i | ||||
\(592\) | 7.21864 | 0.296684 | ||||||||
\(593\) | 9.78733 | 0.401917 | 0.200959 | − | 0.979600i | \(-0.435594\pi\) | ||||
0.200959 | + | 0.979600i | \(0.435594\pi\) | |||||||
\(594\) | −11.5241 | − | 12.8139i | −0.472838 | − | 0.525761i | ||||
\(595\) | 27.4097 | 1.12369 | ||||||||
\(596\) | −6.65134 | −0.272450 | ||||||||
\(597\) | −6.02301 | − | 4.62272i | −0.246505 | − | 0.189195i | ||||
\(598\) | −0.102446 | −0.00418932 | ||||||||
\(599\) | 34.2466i | 1.39928i | 0.714497 | + | 0.699639i | \(0.246656\pi\) | ||||
−0.714497 | + | 0.699639i | \(0.753344\pi\) | |||||||
\(600\) | 14.3380 | + | 11.0046i | 0.585347 | + | 0.449260i | ||||
\(601\) | 41.4594i | 1.69117i | 0.533845 | + | 0.845583i | \(0.320747\pi\) | ||||
−0.533845 | + | 0.845583i | \(0.679253\pi\) | |||||||
\(602\) | 1.44880 | 0.0590489 | ||||||||
\(603\) | 4.34865 | + | 16.2443i | 0.177091 | + | 0.661520i | ||||
\(604\) | 0.977889i | 0.0397897i | ||||||||
\(605\) | −33.5987 | + | 27.1806i | −1.36598 | + | 1.10505i | ||||
\(606\) | −14.1039 | − | 10.8249i | −0.572934 | − | 0.439732i | ||||
\(607\) | − | 2.09167i | − | 0.0848983i | −0.999099 | − | 0.0424491i | \(-0.986484\pi\) | ||
0.999099 | − | 0.0424491i | \(-0.0135160\pi\) | |||||||
\(608\) | 5.78023i | 0.234419i | ||||||||
\(609\) | 10.9125 | − | 14.2181i | 0.442197 | − | 0.576145i | ||||
\(610\) | −24.9612 | −1.01065 | ||||||||
\(611\) | −1.24530 | −0.0503796 | ||||||||
\(612\) | −5.41243 | − | 20.2181i | −0.218784 | − | 0.817267i | ||||
\(613\) | 9.03532i | 0.364933i | 0.983212 | + | 0.182467i | \(0.0584081\pi\) | ||||
−0.983212 | + | 0.182467i | \(0.941592\pi\) | |||||||
\(614\) | 14.2481i | 0.575007i | ||||||||
\(615\) | 37.0835 | − | 48.3166i | 1.49535 | − | 1.94831i | ||||
\(616\) | 2.99319 | + | 1.42857i | 0.120599 | + | 0.0575588i | ||||
\(617\) | 2.52949i | 0.101834i | 0.998703 | + | 0.0509168i | \(0.0162143\pi\) | ||||
−0.998703 | + | 0.0509168i | \(0.983786\pi\) | |||||||
\(618\) | 5.00594 | + | 3.84211i | 0.201368 | + | 0.154552i | ||||
\(619\) | 23.8636 | 0.959161 | 0.479580 | − | 0.877498i | \(-0.340789\pi\) | ||||
0.479580 | + | 0.877498i | \(0.340789\pi\) | |||||||
\(620\) | 10.2744i | 0.412628i | ||||||||
\(621\) | 4.50603 | + | 1.86828i | 0.180821 | + | 0.0749716i | ||||
\(622\) | − | 19.9015i | − | 0.797977i | ||||||
\(623\) | −0.722227 | −0.0289354 | ||||||||
\(624\) | −0.115082 | + | 0.149942i | −0.00460696 | + | 0.00600248i | ||||
\(625\) | 31.7172 | 1.26869 | ||||||||
\(626\) | 30.6797 | 1.22621 | ||||||||
\(627\) | −15.0641 | − | 29.5912i | −0.601603 | − | 1.18176i | ||||
\(628\) | −1.12491 | −0.0448887 | ||||||||
\(629\) | −50.3620 | −2.00807 | ||||||||
\(630\) | 3.04790 | + | 11.3854i | 0.121431 | + | 0.453605i | ||||
\(631\) | 5.50038 | 0.218967 | 0.109483 | − | 0.993989i | \(-0.465080\pi\) | ||||
0.109483 | + | 0.993989i | \(0.465080\pi\) | |||||||
\(632\) | − | 0.361499i | − | 0.0143797i | ||||||
\(633\) | 5.63691 | − | 7.34442i | 0.224047 | − | 0.291914i | ||||
\(634\) | 15.9925i | 0.635142i | ||||||||
\(635\) | 56.2603 | 2.23262 | ||||||||
\(636\) | 5.85450 | − | 7.62791i | 0.232146 | − | 0.302466i | ||||
\(637\) | − | 0.109128i | − | 0.00432379i | ||||||
\(638\) | −14.7827 | + | 30.9732i | −0.585252 | + | 1.22624i | ||||
\(639\) | 12.7303 | − | 3.40794i | 0.503604 | − | 0.134816i | ||||
\(640\) | 3.92876i | 0.155298i | ||||||||
\(641\) | − | 19.8911i | − | 0.785652i | −0.919613 | − | 0.392826i | \(-0.871497\pi\) | ||
0.919613 | − | 0.392826i | \(-0.128503\pi\) | |||||||
\(642\) | −14.1986 | − | 10.8976i | −0.560375 | − | 0.430093i | ||||
\(643\) | −5.96699 | −0.235315 | −0.117657 | − | 0.993054i | \(-0.537538\pi\) | ||||
−0.117657 | + | 0.993054i | \(0.537538\pi\) | |||||||
\(644\) | −0.938770 | −0.0369927 | ||||||||
\(645\) | −7.82086 | − | 6.00259i | −0.307946 | − | 0.236352i | ||||
\(646\) | − | 40.3267i | − | 1.58663i | ||||||
\(647\) | − | 2.10535i | − | 0.0827700i | −0.999143 | − | 0.0413850i | \(-0.986823\pi\) | ||
0.999143 | − | 0.0413850i | \(-0.0131770\pi\) | |||||||
\(648\) | 7.79630 | − | 4.49641i | 0.306268 | − | 0.176636i | ||||
\(649\) | 22.7637 | + | 10.8645i | 0.893552 | + | 0.426469i | ||||
\(650\) | 1.13877i | 0.0446661i | ||||||||
\(651\) | −2.75786 | + | 3.59325i | −0.108089 | + | 0.140831i | ||||
\(652\) | −2.94048 | −0.115158 | ||||||||
\(653\) | 28.1561i | 1.10183i | 0.834561 | + | 0.550916i | \(0.185722\pi\) | ||||
−0.834561 | + | 0.550916i | \(0.814278\pi\) | |||||||
\(654\) | 14.4570 | − | 18.8363i | 0.565314 | − | 0.736556i | ||||
\(655\) | 70.0680i | 2.73778i | ||||||||
\(656\) | 8.95059 | 0.349462 | ||||||||
\(657\) | 9.60865 | − | 2.57226i | 0.374869 | − | 0.100353i | ||||
\(658\) | −11.4115 | −0.444865 | ||||||||
\(659\) | −49.3012 | −1.92050 | −0.960251 | − | 0.279138i | \(-0.909951\pi\) | ||||
−0.960251 | + | 0.279138i | \(0.909951\pi\) | |||||||
\(660\) | −10.2389 | − | 20.1128i | −0.398550 | − | 0.782890i | ||||
\(661\) | 4.68898 | 0.182380 | 0.0911900 | − | 0.995834i | \(-0.470933\pi\) | ||||
0.0911900 | + | 0.995834i | \(0.470933\pi\) | |||||||
\(662\) | 0.500933 | 0.0194693 | ||||||||
\(663\) | 0.802888 | − | 1.04609i | 0.0311816 | − | 0.0406269i | ||||
\(664\) | 1.48034 | 0.0574485 | ||||||||
\(665\) | 22.7092i | 0.880623i | ||||||||
\(666\) | −5.60015 | − | 20.9193i | −0.217002 | − | 0.810607i | ||||
\(667\) | − | 9.71428i | − | 0.376139i | ||||||
\(668\) | −21.5860 | −0.835186 | ||||||||
\(669\) | 26.1855 | + | 20.0976i | 1.01239 | + | 0.777018i | ||||
\(670\) | 22.0225i | 0.850802i | ||||||||
\(671\) | 19.0171 | + | 9.07636i | 0.734147 | + | 0.350389i | ||||
\(672\) | −1.05456 | + | 1.37401i | −0.0406807 | + | 0.0530035i | ||||
\(673\) | − | 40.7322i | − | 1.57011i | −0.619426 | − | 0.785055i | \(-0.712635\pi\) | ||
0.619426 | − | 0.785055i | \(-0.287365\pi\) | |||||||
\(674\) | − | 11.7562i | − | 0.452833i | ||||||
\(675\) | 20.7675 | − | 50.0882i | 0.799340 | − | 1.92789i | ||||
\(676\) | 12.9881 | 0.499542 | ||||||||
\(677\) | −16.1261 | −0.619776 | −0.309888 | − | 0.950773i | \(-0.600292\pi\) | ||||
−0.309888 | + | 0.950773i | \(0.600292\pi\) | |||||||
\(678\) | −0.847717 | + | 1.10450i | −0.0325564 | + | 0.0424182i | ||||
\(679\) | 3.48997i | 0.133933i | ||||||||
\(680\) | − | 27.4097i | − | 1.05111i | ||||||
\(681\) | −23.6530 | − | 18.1539i | −0.906386 | − | 0.695660i | ||||
\(682\) | 3.73594 | − | 7.82768i | 0.143057 | − | 0.299737i | ||||
\(683\) | − | 35.6615i | − | 1.36455i | −0.731095 | − | 0.682276i | \(-0.760990\pi\) | ||
0.731095 | − | 0.682276i | \(-0.239010\pi\) | |||||||
\(684\) | 16.7508 | − | 4.48425i | 0.640485 | − | 0.171459i | ||||
\(685\) | 26.4131 | 1.00919 | ||||||||
\(686\) | − | 1.00000i | − | 0.0381802i | ||||||
\(687\) | 28.1220 | + | 21.5839i | 1.07292 | + | 0.823476i | ||||
\(688\) | − | 1.44880i | − | 0.0552352i | ||||||
\(689\) | 0.605830 | 0.0230803 | ||||||||
\(690\) | 5.06762 | + | 3.88945i | 0.192921 | + | 0.148069i | ||||
\(691\) | −35.8799 | −1.36494 | −0.682468 | − | 0.730916i | \(-0.739093\pi\) | ||||
−0.682468 | + | 0.730916i | \(0.739093\pi\) | |||||||
\(692\) | −5.10422 | −0.194033 | ||||||||
\(693\) | 1.81785 | − | 9.78240i | 0.0690543 | − | 0.371603i | ||||
\(694\) | 31.2589 | 1.18657 | ||||||||
\(695\) | 23.7715 | 0.901705 | ||||||||
\(696\) | −14.2181 | − | 10.9125i | −0.538934 | − | 0.413637i | ||||
\(697\) | −62.4452 | −2.36528 | ||||||||
\(698\) | 26.8168i | 1.01503i | ||||||||
\(699\) | 23.5933 | + | 18.1081i | 0.892381 | + | 0.684911i | ||||
\(700\) | 10.4352i | 0.394413i | ||||||||
\(701\) | −22.3303 | −0.843405 | −0.421702 | − | 0.906734i | \(-0.638567\pi\) | ||||
−0.421702 | + | 0.906734i | \(0.638567\pi\) | |||||||
\(702\) | 0.523805 | + | 0.217179i | 0.0197697 | + | 0.00819688i | ||||
\(703\) | − | 41.7254i | − | 1.57370i | ||||||
\(704\) | 1.42857 | − | 2.99319i | 0.0538413 | − | 0.112810i | ||||
\(705\) | 61.6008 | + | 47.2792i | 2.32002 | + | 1.78064i | ||||
\(706\) | 30.7700i | 1.15804i | ||||||||
\(707\) | − | 10.2648i | − | 0.386049i | ||||||
\(708\) | −8.02012 | + | 10.4495i | −0.301415 | + | 0.392718i | ||||
\(709\) | 22.2230 | 0.834601 | 0.417300 | − | 0.908769i | \(-0.362976\pi\) | ||||
0.417300 | + | 0.908769i | \(0.362976\pi\) | |||||||
\(710\) | 17.2585 | 0.647701 | ||||||||
\(711\) | −1.04761 | + | 0.280448i | −0.0392884 | + | 0.0105176i | ||||
\(712\) | 0.722227i | 0.0270666i | ||||||||
\(713\) | 2.45504i | 0.0919419i | ||||||||
\(714\) | 7.35733 | − | 9.58598i | 0.275341 | − | 0.358746i | ||||
\(715\) | 0.612480 | − | 1.28329i | 0.0229055 | − | 0.0479923i | ||||
\(716\) | − | 17.2258i | − | 0.643759i | ||||||
\(717\) | 12.9015 | + | 9.90201i | 0.481814 | + | 0.369797i | ||||
\(718\) | 14.7885 | 0.551904 | ||||||||
\(719\) | − | 14.2388i | − | 0.531017i | −0.964109 | − | 0.265508i | \(-0.914460\pi\) | ||
0.964109 | − | 0.265508i | \(-0.0855398\pi\) | |||||||
\(720\) | 11.3854 | − | 3.04790i | 0.424308 | − | 0.113588i | ||||
\(721\) | 3.64331i | 0.135684i | ||||||||
\(722\) | 14.4110 | 0.536324 | ||||||||
\(723\) | 10.9437 | − | 14.2587i | 0.407000 | − | 0.530286i | ||||
\(724\) | 11.9832 | 0.445350 | ||||||||
\(725\) | −107.982 | −4.01035 | ||||||||
\(726\) | 0.487296 | + | 19.0463i | 0.0180852 | + | 0.706875i | ||||
\(727\) | −0.772552 | −0.0286524 | −0.0143262 | − | 0.999897i | \(-0.504560\pi\) | ||||
−0.0143262 | + | 0.999897i | \(0.504560\pi\) | |||||||
\(728\) | −0.109128 | −0.00404453 | ||||||||
\(729\) | −19.0787 | − | 19.1051i | −0.706619 | − | 0.707595i | ||||
\(730\) | 13.0265 | 0.482131 | ||||||||
\(731\) | 10.1078i | 0.373851i | ||||||||
\(732\) | −6.70013 | + | 8.72970i | −0.247644 | + | 0.322659i | ||||
\(733\) | 20.9468i | 0.773687i | 0.922145 | + | 0.386844i | \(0.126435\pi\) | ||||
−0.922145 | + | 0.386844i | \(0.873565\pi\) | |||||||
\(734\) | 16.5826 | 0.612076 | ||||||||
\(735\) | −4.14313 | + | 5.39815i | −0.152822 | + | 0.199114i | ||||
\(736\) | 0.938770i | 0.0346035i | ||||||||
\(737\) | 8.00777 | − | 16.7782i | 0.294970 | − | 0.618031i | ||||
\(738\) | −6.94378 | − | 25.9384i | −0.255604 | − | 0.954806i | ||||
\(739\) | − | 31.8490i | − | 1.17159i | −0.810461 | − | 0.585793i | \(-0.800783\pi\) | ||
0.810461 | − | 0.585793i | \(-0.199217\pi\) | |||||||
\(740\) | − | 28.3603i | − | 1.04255i | ||||||
\(741\) | 0.866699 | + | 0.665200i | 0.0318390 | + | 0.0244367i | ||||
\(742\) | 5.55158 | 0.203805 | ||||||||
\(743\) | −2.95393 | −0.108369 | −0.0541847 | − | 0.998531i | \(-0.517256\pi\) | ||||
−0.0541847 | + | 0.998531i | \(0.517256\pi\) | |||||||
\(744\) | 3.59325 | + | 2.75786i | 0.131735 | + | 0.101108i | ||||
\(745\) | 26.1316i | 0.957386i | ||||||||
\(746\) | − | 18.1538i | − | 0.664659i | ||||||
\(747\) | −1.14844 | − | 4.28997i | −0.0420191 | − | 0.156962i | ||||
\(748\) | −9.96665 | + | 20.8825i | −0.364417 | + | 0.763539i | ||||
\(749\) | − | 10.3337i | − | 0.377586i | ||||||
\(750\) | 22.5187 | − | 29.3399i | 0.822266 | − | 1.07134i | ||||
\(751\) | −7.94197 | −0.289807 | −0.144903 | − | 0.989446i | \(-0.546287\pi\) | ||||
−0.144903 | + | 0.989446i | \(0.546287\pi\) | |||||||
\(752\) | 11.4115i | 0.416133i | ||||||||
\(753\) | 8.17676 | − | 10.6536i | 0.297978 | − | 0.388240i | ||||
\(754\) | − | 1.12924i | − | 0.0411244i | ||||||
\(755\) | 3.84190 | 0.139821 | ||||||||
\(756\) | 4.79993 | + | 1.99014i | 0.174572 | + | 0.0723806i | ||||
\(757\) | −22.0057 | −0.799810 | −0.399905 | − | 0.916557i | \(-0.630957\pi\) | ||||
−0.399905 | + | 0.916557i | \(0.630957\pi\) | |||||||
\(758\) | 12.5603 | 0.456211 | ||||||||
\(759\) | −2.44657 | − | 4.80592i | −0.0888049 | − | 0.174444i | ||||
\(760\) | 22.7092 | 0.823748 | ||||||||
\(761\) | −32.8592 | −1.19114 | −0.595572 | − | 0.803302i | \(-0.703075\pi\) | ||||
−0.595572 | + | 0.803302i | \(0.703075\pi\) | |||||||
\(762\) | 15.1014 | − | 19.6759i | 0.547068 | − | 0.712783i | ||||
\(763\) | 13.7090 | 0.496299 | ||||||||
\(764\) | 13.1345i | 0.475191i | ||||||||
\(765\) | −79.4320 | + | 21.2642i | −2.87187 | + | 0.768807i | ||||
\(766\) | 3.12388i | 0.112870i | ||||||||
\(767\) | −0.829932 | −0.0299671 | ||||||||
\(768\) | 1.37401 | + | 1.05456i | 0.0495802 | + | 0.0380533i | ||||
\(769\) | 8.41547i | 0.303470i | 0.988421 | + | 0.151735i | \(0.0484860\pi\) | ||||
−0.988421 | + | 0.151735i | \(0.951514\pi\) | |||||||
\(770\) | 5.61252 | − | 11.7595i | 0.202261 | − | 0.423784i | ||||
\(771\) | −23.4349 | + | 30.5337i | −0.843988 | + | 1.09964i | ||||
\(772\) | 7.13624i | 0.256839i | ||||||||
\(773\) | 38.4899i | 1.38438i | 0.721713 | + | 0.692192i | \(0.243355\pi\) | ||||
−0.721713 | + | 0.692192i | \(0.756645\pi\) | |||||||
\(774\) | −4.19857 | + | 1.12397i | −0.150915 | + | 0.0404002i | ||||
\(775\) | 27.2897 | 0.980275 | ||||||||
\(776\) | 3.48997 | 0.125282 | ||||||||
\(777\) | 7.61252 | − | 9.91846i | 0.273098 | − | 0.355823i | ||||
\(778\) | 25.8114i | 0.925383i | ||||||||
\(779\) | − | 51.7364i | − | 1.85365i | ||||||
\(780\) | 0.589087 | + | 0.452130i | 0.0210927 | + | 0.0161888i | ||||
\(781\) | −13.1487 | − | 6.27552i | −0.470497 | − | 0.224556i | ||||
\(782\) | − | 6.54948i | − | 0.234209i | ||||||
\(783\) | −20.5937 | + | 49.6691i | −0.735959 | + | 1.77503i | ||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 4.41950i | 0.157739i | ||||||||
\(786\) | 24.5049 | + | 18.8077i | 0.874060 | + | 0.670850i | ||||
\(787\) | − | 23.4784i | − | 0.836916i | −0.908236 | − | 0.418458i | \(-0.862571\pi\) | ||
0.908236 | − | 0.418458i | \(-0.137429\pi\) | |||||||
\(788\) | −1.57331 | −0.0560467 | ||||||||
\(789\) | 26.0082 | + | 19.9616i | 0.925917 | + | 0.710650i | ||||
\(790\) | −1.42025 | −0.0505301 | ||||||||
\(791\) | −0.803856 | −0.0285818 | ||||||||
\(792\) | −9.78240 | − | 1.81785i | −0.347603 | − | 0.0645944i | ||||
\(793\) | −0.693337 | −0.0246211 | ||||||||
\(794\) | −26.4518 | −0.938739 | ||||||||
\(795\) | −29.9683 | − | 23.0009i | −1.06286 | − | 0.815759i | ||||
\(796\) | −4.38353 | −0.155370 | ||||||||
\(797\) | − | 19.4036i | − | 0.687311i | −0.939096 | − | 0.343655i | \(-0.888335\pi\) | ||
0.939096 | − | 0.343655i | \(-0.111665\pi\) | |||||||
\(798\) | 7.94207 | + | 6.09562i | 0.281146 | + | 0.215783i | ||||
\(799\) | − | 79.6139i | − | 2.81654i | ||||||
\(800\) | 10.4352 | 0.368939 | ||||||||
\(801\) | 2.09298 | − | 0.560297i | 0.0739519 | − | 0.0197971i | ||||
\(802\) | − | 28.0552i | − | 0.990662i | ||||||
\(803\) | −9.92441 | − | 4.73666i | −0.350225 | − | 0.167153i | ||||
\(804\) | 7.70192 | + | 5.91130i | 0.271626 | + | 0.208475i | ||||
\(805\) | 3.68821i | 0.129992i | ||||||||
\(806\) | 0.285386i | 0.0100523i | ||||||||
\(807\) | 18.3969 | − | 23.9696i | 0.647600 | − | 0.843768i | ||||
\(808\) | −10.2648 | −0.361115 | ||||||||
\(809\) | −11.7416 | −0.412814 | −0.206407 | − | 0.978466i | \(-0.566177\pi\) | ||||
−0.206407 | + | 0.978466i | \(0.566177\pi\) | |||||||
\(810\) | −17.6653 | − | 30.6298i | −0.620697 | − | 1.07622i | ||||
\(811\) | − | 12.4057i | − | 0.435622i | −0.975991 | − | 0.217811i | \(-0.930108\pi\) | ||
0.975991 | − | 0.217811i | \(-0.0698917\pi\) | |||||||
\(812\) | − | 10.3479i | − | 0.363139i | ||||||
\(813\) | −9.37752 | + | 12.2181i | −0.328884 | + | 0.428508i | ||||
\(814\) | −10.3123 | + | 21.6068i | −0.361447 | + | 0.757317i | ||||
\(815\) | 11.5525i | 0.404665i | ||||||||
\(816\) | −9.58598 | − | 7.35733i | −0.335576 | − | 0.257558i | ||||
\(817\) | −8.37442 | −0.292984 | ||||||||
\(818\) | 1.22795i | 0.0429343i | ||||||||
\(819\) | 0.0846601 | + | 0.316247i | 0.00295826 | + | 0.0110506i | ||||
\(820\) | − | 35.1647i | − | 1.22801i | ||||||
\(821\) | 26.3947 | 0.921182 | 0.460591 | − | 0.887612i | \(-0.347637\pi\) | ||||
0.460591 | + | 0.887612i | \(0.347637\pi\) | |||||||
\(822\) | 7.08983 | − | 9.23745i | 0.247286 | − | 0.322193i | ||||
\(823\) | −28.8057 | −1.00410 | −0.502052 | − | 0.864837i | \(-0.667421\pi\) | ||||
−0.502052 | + | 0.864837i | \(0.667421\pi\) | |||||||
\(824\) | 3.64331 | 0.126921 | ||||||||
\(825\) | −53.4216 | + | 27.1956i | −1.85990 | + | 0.946829i | ||||
\(826\) | −7.60516 | −0.264617 | ||||||||
\(827\) | 30.8632 | 1.07322 | 0.536609 | − | 0.843831i | \(-0.319705\pi\) | ||||
0.536609 | + | 0.843831i | \(0.319705\pi\) | |||||||
\(828\) | 2.72052 | − | 0.728289i | 0.0945444 | − | 0.0253098i | ||||
\(829\) | 3.62488 | 0.125897 | 0.0629486 | − | 0.998017i | \(-0.479950\pi\) | ||||
0.0629486 | + | 0.998017i | \(0.479950\pi\) | |||||||
\(830\) | − | 5.81593i | − | 0.201874i | ||||||
\(831\) | −12.2731 | + | 15.9908i | −0.425750 | + | 0.554716i | ||||
\(832\) | 0.109128i | 0.00378332i | ||||||||
\(833\) | 6.97666 | 0.241727 | ||||||||
\(834\) | 6.38078 | − | 8.31362i | 0.220948 | − | 0.287877i | ||||
\(835\) | 84.8061i | 2.93484i | ||||||||
\(836\) | −17.3013 | − | 8.25747i | −0.598379 | − | 0.285590i | ||||
\(837\) | 5.20453 | − | 12.5526i | 0.179895 | − | 0.433881i | ||||
\(838\) | 10.5048i | 0.362882i | ||||||||
\(839\) | − | 26.1251i | − | 0.901939i | −0.892539 | − | 0.450969i | \(-0.851078\pi\) | ||
0.892539 | − | 0.450969i | \(-0.148922\pi\) | |||||||
\(840\) | 5.39815 | + | 4.14313i | 0.186254 | + | 0.142952i | ||||
\(841\) | 78.0786 | 2.69237 | ||||||||
\(842\) | 14.6003 | 0.503159 | ||||||||
\(843\) | 23.2163 | + | 17.8188i | 0.799613 | + | 0.613711i | ||||
\(844\) | − | 5.34526i | − | 0.183991i | ||||||
\(845\) | − | 51.0271i | − | 1.75539i | ||||||
\(846\) | 33.0699 | − | 8.85290i | 1.13697 | − | 0.304369i | ||||
\(847\) | −8.55197 | + | 6.91837i | −0.293849 | + | 0.237718i | ||||
\(848\) | − | 5.55158i | − | 0.190642i | ||||||
\(849\) | −6.51754 | + | 8.49181i | −0.223682 | + | 0.291438i | ||||
\(850\) | −72.8028 | −2.49711 | ||||||||
\(851\) | − | 6.77665i | − | 0.232300i | ||||||
\(852\) | 4.63256 | − | 6.03583i | 0.158709 | − | 0.206784i | ||||
\(853\) | − | 31.5638i | − | 1.08073i | −0.841432 | − | 0.540363i | \(-0.818287\pi\) | ||
0.841432 | − | 0.540363i | \(-0.181713\pi\) | |||||||
\(854\) | −6.35346 | −0.217411 | ||||||||
\(855\) | −17.6175 | − | 65.8101i | −0.602507 | − | 2.25066i | ||||
\(856\) | −10.3337 | −0.353200 | ||||||||
\(857\) | 20.8294 | 0.711519 | 0.355760 | − | 0.934577i | \(-0.384222\pi\) | ||||
0.355760 | + | 0.934577i | \(0.384222\pi\) | |||||||
\(858\) | −0.284402 | − | 0.558665i | −0.00970933 | − | 0.0190725i | ||||
\(859\) | −22.4198 | −0.764952 | −0.382476 | − | 0.923965i | \(-0.624929\pi\) | ||||
−0.382476 | + | 0.923965i | \(0.624929\pi\) | |||||||
\(860\) | −5.69201 | −0.194096 | ||||||||
\(861\) | 9.43896 | − | 12.2982i | 0.321679 | − | 0.419120i | ||||
\(862\) | −15.1801 | −0.517035 | ||||||||
\(863\) | 23.5284i | 0.800915i | 0.916315 | + | 0.400457i | \(0.131149\pi\) | ||||
−0.916315 | + | 0.400457i | \(0.868851\pi\) | |||||||
\(864\) | 1.99014 | − | 4.79993i | 0.0677059 | − | 0.163297i | ||||
\(865\) | 20.0533i | 0.681832i | ||||||||
\(866\) | −17.1583 | −0.583064 | ||||||||
\(867\) | 43.5200 | + | 33.4020i | 1.47802 | + | 1.13439i | ||||
\(868\) | 2.61516i | 0.0887644i | ||||||||
\(869\) | 1.08204 | + | 0.516427i | 0.0367056 | + | 0.0175186i | ||||
\(870\) | −42.8726 | + | 55.8594i | −1.45352 | + | 1.89381i | ||||
\(871\) | 0.611708i | 0.0207269i | ||||||||
\(872\) | − | 13.7090i | − | 0.464245i | ||||||
\(873\) | −2.70748 | − | 10.1138i | −0.0916344 | − | 0.342299i | ||||
\(874\) | 5.42631 | 0.183548 | ||||||||
\(875\) | 21.3536 | 0.721882 | ||||||||
\(876\) | 3.49658 | − | 4.55575i | 0.118138 | − | 0.153924i | ||||
\(877\) | − | 4.71771i | − | 0.159306i | −0.996823 | − | 0.0796528i | \(-0.974619\pi\) | ||
0.996823 | − | 0.0796528i | \(-0.0253812\pi\) | |||||||
\(878\) | 17.7286i | 0.598312i | ||||||||
\(879\) | 17.8874 | + | 13.7288i | 0.603327 | + | 0.463059i | ||||
\(880\) | −11.7595 | − | 5.61252i | −0.396414 | − | 0.189198i | ||||
\(881\) | − | 41.4868i | − | 1.39773i | −0.715256 | − | 0.698863i | \(-0.753690\pi\) | ||
0.715256 | − | 0.698863i | \(-0.246310\pi\) | |||||||
\(882\) | 0.775791 | + | 2.89796i | 0.0261222 | + | 0.0975793i | ||||
\(883\) | 15.8632 | 0.533839 | 0.266920 | − | 0.963719i | \(-0.413994\pi\) | ||||
0.266920 | + | 0.963719i | \(0.413994\pi\) | |||||||
\(884\) | − | 0.761346i | − | 0.0256068i | ||||||
\(885\) | 41.0538 | + | 31.5092i | 1.38001 | + | 1.05917i | ||||
\(886\) | 6.70808i | 0.225362i | ||||||||
\(887\) | −51.9855 | −1.74550 | −0.872750 | − | 0.488167i | \(-0.837666\pi\) | ||||
−0.872750 | + | 0.488167i | \(0.837666\pi\) | |||||||
\(888\) | −9.91846 | − | 7.61252i | −0.332842 | − | 0.255459i | ||||
\(889\) | 14.3201 | 0.480280 | ||||||||
\(890\) | 2.83746 | 0.0951118 | ||||||||
\(891\) | 2.32106 | + | 29.7592i | 0.0777584 | + | 0.996972i | ||||
\(892\) | 19.0577 | 0.638100 | ||||||||
\(893\) | 65.9609 | 2.20730 | ||||||||
\(894\) | 9.13899 | + | 7.01426i | 0.305654 | + | 0.234592i | ||||
\(895\) | −67.6761 | −2.26216 | ||||||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 0.140761 | + | 0.108035i | 0.00469988 | + | 0.00360720i | ||||
\(898\) | − | 2.86960i | − | 0.0957597i | ||||||
\(899\) | −27.0614 | −0.902548 | ||||||||
\(900\) | −8.09552 | − | 30.2407i | −0.269851 | − | 1.00802i | ||||
\(901\) | 38.7315i | 1.29033i | ||||||||
\(902\) | −12.7865 | + | 26.7908i | −0.425745 | + | 0.892036i | ||||
\(903\) | −1.99067 | − | 1.52786i | −0.0662453 | − | 0.0508439i | ||||
\(904\) | 0.803856i | 0.0267358i | ||||||||
\(905\) | − | 47.0790i | − | 1.56496i | ||||||
\(906\) | 1.03125 | − | 1.34363i | 0.0342609 | − | 0.0446390i | ||||
\(907\) | −19.0347 | −0.632038 | −0.316019 | − | 0.948753i | \(-0.602346\pi\) | ||||
−0.316019 | + | 0.948753i | \(0.602346\pi\) | |||||||
\(908\) | −17.2146 | −0.571288 | ||||||||
\(909\) | 7.96336 | + | 29.7470i | 0.264128 | + | 0.986646i | ||||
\(910\) | 0.428736i | 0.0142125i | ||||||||
\(911\) | 33.2014i | 1.10001i | 0.835160 | + | 0.550006i | \(0.185375\pi\) | ||||
−0.835160 | + | 0.550006i | \(0.814625\pi\) | |||||||
\(912\) | 6.09562 | − | 7.94207i | 0.201846 | − | 0.262988i | ||||
\(913\) | −2.11478 | + | 4.43095i | −0.0699889 | + | 0.146643i | ||||
\(914\) | 10.7141i | 0.354390i | ||||||||
\(915\) | 34.2969 | + | 26.3232i | 1.13382 | + | 0.870219i | ||||
\(916\) | 20.4671 | 0.676252 | ||||||||
\(917\) | 17.8346i | 0.588951i | ||||||||
\(918\) | −13.8845 | + | 33.4875i | −0.458257 | + | 1.10525i | ||||
\(919\) | − | 16.5613i | − | 0.546306i | −0.961971 | − | 0.273153i | \(-0.911933\pi\) | ||
0.961971 | − | 0.273153i | \(-0.0880666\pi\) | |||||||
\(920\) | 3.68821 | 0.121597 | ||||||||
\(921\) | 15.0255 | − | 19.5770i | 0.495108 | − | 0.645084i | ||||
\(922\) | −5.60949 | −0.184739 | ||||||||
\(923\) | 0.479382 | 0.0157791 | ||||||||
\(924\) | −2.60614 | − | 5.11938i | −0.0857359 | − | 0.168415i | ||||
\(925\) | −75.3278 | −2.47676 | ||||||||
\(926\) | 3.97144 | 0.130510 | ||||||||
\(927\) | −2.82645 | − | 10.5582i | −0.0928328 | − | 0.346776i | ||||
\(928\) | −10.3479 | −0.339686 | ||||||||
\(929\) | − | 4.32333i | − | 0.141844i | −0.997482 | − | 0.0709219i | \(-0.977406\pi\) | ||
0.997482 | − | 0.0709219i | \(-0.0225941\pi\) | |||||||
\(930\) | 10.8350 | − | 14.1170i | 0.355292 | − | 0.462916i | ||||
\(931\) | 5.78023i | 0.189439i | ||||||||
\(932\) | 17.1712 | 0.562460 | ||||||||
\(933\) | −20.9874 | + | 27.3448i | −0.687096 | + | 0.895228i | ||||
\(934\) | − | 6.98066i | − | 0.228414i | ||||||
\(935\) | 82.0423 | + | 39.1566i | 2.68307 | + | 1.28056i | ||||
\(936\) | 0.316247 | − | 0.0846601i | 0.0103368 | − | 0.00276720i | ||||
\(937\) | 0.667158i | 0.0217951i | 0.999941 | + | 0.0108975i | \(0.00346887\pi\) | ||||
−0.999941 | + | 0.0108975i | \(0.996531\pi\) | |||||||
\(938\) | 5.60544i | 0.183024i | ||||||||
\(939\) | −42.1541 | − | 32.3537i | −1.37565 | − | 1.05582i | ||||
\(940\) | 44.8329 | 1.46229 | ||||||||
\(941\) | 33.6358 | 1.09650 | 0.548248 | − | 0.836316i | \(-0.315295\pi\) | ||||
0.548248 | + | 0.836316i | \(0.315295\pi\) | |||||||
\(942\) | 1.54563 | + | 1.18629i | 0.0503594 | + | 0.0386513i | ||||
\(943\) | − | 8.40255i | − | 0.273625i | ||||||
\(944\) | 7.60516i | 0.247527i | ||||||||
\(945\) | 7.81878 | − | 18.8578i | 0.254345 | − | 0.613444i | ||||
\(946\) | 4.33655 | + | 2.06972i | 0.140993 | + | 0.0672924i | ||||
\(947\) | 54.3038i | 1.76464i | 0.470652 | + | 0.882319i | \(0.344019\pi\) | ||||
−0.470652 | + | 0.882319i | \(0.655981\pi\) | |||||||
\(948\) | −0.381224 | + | 0.496703i | −0.0123816 | + | 0.0161322i | ||||
\(949\) | 0.361830 | 0.0117455 | ||||||||
\(950\) | − | 60.3178i | − | 1.95697i | ||||||
\(951\) | 16.8651 | − | 21.9738i | 0.546887 | − | 0.712548i | ||||
\(952\) | − | 6.97666i | − | 0.226115i | ||||||
\(953\) | 8.99829 | 0.291483 | 0.145742 | − | 0.989323i | \(-0.453443\pi\) | ||||
0.145742 | + | 0.989323i | \(0.453443\pi\) | |||||||
\(954\) | −16.0882 | + | 4.30686i | −0.520876 | + | 0.139440i | ||||
\(955\) | 51.6025 | 1.66982 | ||||||||
\(956\) | 9.38967 | 0.303684 | ||||||||
\(957\) | 52.9747 | − | 26.9681i | 1.71243 | − | 0.871754i | ||||
\(958\) | −22.5631 | −0.728981 | ||||||||
\(959\) | 6.72300 | 0.217097 | ||||||||
\(960\) | 4.14313 | − | 5.39815i | 0.133719 | − | 0.174225i | ||||
\(961\) | −24.1609 | −0.779385 | ||||||||
\(962\) | − | 0.787752i | − | 0.0253982i | ||||||
\(963\) | 8.01681 | + | 29.9467i | 0.258338 | + | 0.965019i | ||||
\(964\) | − | 10.3774i | − | 0.334235i | ||||||
\(965\) | 28.0366 | 0.902530 | ||||||||
\(966\) | 1.28988 | + | 0.989993i | 0.0415011 | + | 0.0318525i | ||||
\(967\) | − | 29.1744i | − | 0.938187i | −0.883149 | − | 0.469093i | \(-0.844581\pi\) | ||
0.883149 | − | 0.469093i | \(-0.155419\pi\) | |||||||
\(968\) | 6.91837 | + | 8.55197i | 0.222365 | + | 0.274871i | ||||
\(969\) | −42.5271 | + | 55.4092i | −1.36617 | + | 1.78000i | ||||
\(970\) | − | 13.7113i | − | 0.440242i | ||||||
\(971\) | 47.7488i | 1.53233i | 0.642642 | + | 0.766166i | \(0.277838\pi\) | ||||
−0.642642 | + | 0.766166i | \(0.722162\pi\) | |||||||
\(972\) | −15.4539 | − | 2.04359i | −0.495685 | − | 0.0655481i | ||||
\(973\) | 6.05064 | 0.193974 | ||||||||
\(974\) | 9.83009 | 0.314976 | ||||||||
\(975\) | 1.20090 | − | 1.56467i | 0.0384596 | − | 0.0501096i | ||||
\(976\) | 6.35346i | 0.203369i | ||||||||
\(977\) | 51.7861i | 1.65678i | 0.560150 | + | 0.828391i | \(0.310744\pi\) | ||||
−0.560150 | + | 0.828391i | \(0.689256\pi\) | |||||||
\(978\) | 4.04024 | + | 3.10093i | 0.129193 | + | 0.0991567i | ||||
\(979\) | −2.16176 | − | 1.03175i | −0.0690902 | − | 0.0329749i | ||||
\(980\) | 3.92876i | 0.125500i | ||||||||
\(981\) | −39.7281 | + | 10.6353i | −1.26842 | + | 0.339559i | ||||
\(982\) | 7.60395 | 0.242652 | ||||||||
\(983\) | 13.0802i | 0.417193i | 0.978002 | + | 0.208597i | \(0.0668896\pi\) | ||||
−0.978002 | + | 0.208597i | \(0.933110\pi\) | |||||||
\(984\) | −12.2982 | − | 9.43896i | −0.392051 | − | 0.300903i | ||||
\(985\) | 6.18115i | 0.196948i | ||||||||
\(986\) | 72.1937 | 2.29911 | ||||||||
\(987\) | 15.6794 | + | 12.0341i | 0.499082 | + | 0.383050i | ||||
\(988\) | 0.630782 | 0.0200678 | ||||||||
\(989\) | −1.36010 | −0.0432485 | ||||||||
\(990\) | −7.14189 | + | 38.4328i | −0.226984 | + | 1.22147i | ||||
\(991\) | −21.4492 | −0.681356 | −0.340678 | − | 0.940180i | \(-0.610657\pi\) | ||||
−0.340678 | + | 0.940180i | \(0.610657\pi\) | |||||||
\(992\) | 2.61516 | 0.0830315 | ||||||||
\(993\) | −0.688285 | − | 0.528265i | −0.0218421 | − | 0.0167640i | ||||
\(994\) | 4.39287 | 0.139333 | ||||||||
\(995\) | 17.2219i | 0.545970i | ||||||||
\(996\) | −2.03400 | − | 1.56112i | −0.0644499 | − | 0.0494659i | ||||
\(997\) | 35.6278i | 1.12834i | 0.825657 | + | 0.564172i | \(0.190805\pi\) | ||||
−0.825657 | + | 0.564172i | \(0.809195\pi\) | |||||||
\(998\) | 40.0276 | 1.26705 | ||||||||
\(999\) | −14.3661 | + | 34.6490i | −0.454523 | + | 1.09625i |
(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 | 462.2.c.a.197.10 | yes | 12 | |
3.2 | odd | 2 | 462.2.c.b.197.9 | yes | 12 | ||
11.10 | odd | 2 | 462.2.c.b.197.10 | yes | 12 | ||
33.32 | even | 2 | inner | 462.2.c.a.197.9 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.c.a.197.9 | ✓ | 12 | 33.32 | even | 2 | inner | |
462.2.c.a.197.10 | yes | 12 | 1.1 | even | 1 | trivial | |
462.2.c.b.197.9 | yes | 12 | 3.2 | odd | 2 | ||
462.2.c.b.197.10 | yes | 12 | 11.10 | odd | 2 |