Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(694,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1155.694");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15210 x^{12} + 40640 x^{10} + 63865 x^{8} + 55281 x^{6} + 22984 x^{4} + 3428 x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.13 | ||
Root | \(0.792050i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.f.694.8 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.792050i | 0.560064i | 0.959991 | + | 0.280032i | \(0.0903451\pi\) | ||||
−0.959991 | + | 0.280032i | \(0.909655\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.37266 | 0.686328 | ||||||||
\(5\) | −0.199975 | − | 2.22711i | −0.0894316 | − | 0.995993i | ||||
\(6\) | 0.792050 | 0.323353 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 2.67131i | 0.944452i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.76398 | − | 0.158390i | 0.557820 | − | 0.0500874i | ||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − | 1.37266i | − | 0.396252i | ||||||
\(13\) | − | 6.97648i | − | 1.93493i | −0.253010 | − | 0.967464i | \(-0.581421\pi\) | ||
0.253010 | − | 0.967464i | \(-0.418579\pi\) | |||||||
\(14\) | 0.792050 | 0.211684 | ||||||||
\(15\) | −2.22711 | + | 0.199975i | −0.575037 | + | 0.0516333i | ||||
\(16\) | 0.629499 | 0.157375 | ||||||||
\(17\) | − | 2.01100i | − | 0.487738i | −0.969808 | − | 0.243869i | \(-0.921583\pi\) | ||
0.969808 | − | 0.243869i | \(-0.0784167\pi\) | |||||||
\(18\) | − | 0.792050i | − | 0.186688i | ||||||
\(19\) | −6.64274 | −1.52395 | −0.761974 | − | 0.647607i | \(-0.775770\pi\) | ||||
−0.761974 | + | 0.647607i | \(0.775770\pi\) | |||||||
\(20\) | −0.274497 | − | 3.05705i | −0.0613794 | − | 0.683578i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0.792050i | 0.168866i | ||||||||
\(23\) | 2.05588i | 0.428680i | 0.976759 | + | 0.214340i | \(0.0687600\pi\) | ||||
−0.976759 | + | 0.214340i | \(0.931240\pi\) | |||||||
\(24\) | 2.67131 | 0.545280 | ||||||||
\(25\) | −4.92002 | + | 0.890732i | −0.984004 | + | 0.178146i | ||||
\(26\) | 5.52572 | 1.08368 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 1.37266i | − | 0.259408i | ||||||
\(29\) | 6.58029 | 1.22193 | 0.610965 | − | 0.791658i | \(-0.290782\pi\) | ||||
0.610965 | + | 0.791658i | \(0.290782\pi\) | |||||||
\(30\) | −0.158390 | − | 1.76398i | −0.0289180 | − | 0.322057i | ||||
\(31\) | −6.71609 | −1.20625 | −0.603123 | − | 0.797648i | \(-0.706077\pi\) | ||||
−0.603123 | + | 0.797648i | \(0.706077\pi\) | |||||||
\(32\) | 5.84122i | 1.03259i | ||||||||
\(33\) | − | 1.00000i | − | 0.174078i | ||||||
\(34\) | 1.59281 | 0.273165 | ||||||||
\(35\) | −2.22711 | + | 0.199975i | −0.376450 | + | 0.0338020i | ||||
\(36\) | −1.37266 | −0.228776 | ||||||||
\(37\) | − | 4.53927i | − | 0.746251i | −0.927781 | − | 0.373125i | \(-0.878286\pi\) | ||
0.927781 | − | 0.373125i | \(-0.121714\pi\) | |||||||
\(38\) | − | 5.26138i | − | 0.853509i | ||||||
\(39\) | −6.97648 | −1.11713 | ||||||||
\(40\) | 5.94930 | − | 0.534196i | 0.940667 | − | 0.0844638i | ||||
\(41\) | 10.5891 | 1.65375 | 0.826873 | − | 0.562389i | \(-0.190118\pi\) | ||||
0.826873 | + | 0.562389i | \(0.190118\pi\) | |||||||
\(42\) | − | 0.792050i | − | 0.122216i | ||||||
\(43\) | 5.38354i | 0.820982i | 0.911865 | + | 0.410491i | \(0.134643\pi\) | ||||
−0.911865 | + | 0.410491i | \(0.865357\pi\) | |||||||
\(44\) | 1.37266 | 0.206936 | ||||||||
\(45\) | 0.199975 | + | 2.22711i | 0.0298105 | + | 0.331998i | ||||
\(46\) | −1.62836 | −0.240088 | ||||||||
\(47\) | − | 1.71761i | − | 0.250540i | −0.992123 | − | 0.125270i | \(-0.960020\pi\) | ||
0.992123 | − | 0.125270i | \(-0.0399796\pi\) | |||||||
\(48\) | − | 0.629499i | − | 0.0908603i | ||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −0.705505 | − | 3.89690i | −0.0997734 | − | 0.551105i | ||||
\(51\) | −2.01100 | −0.281596 | ||||||||
\(52\) | − | 9.57631i | − | 1.32800i | ||||||
\(53\) | − | 5.42564i | − | 0.745268i | −0.927978 | − | 0.372634i | \(-0.878455\pi\) | ||
0.927978 | − | 0.372634i | \(-0.121545\pi\) | |||||||
\(54\) | −0.792050 | −0.107784 | ||||||||
\(55\) | −0.199975 | − | 2.22711i | −0.0269646 | − | 0.300303i | ||||
\(56\) | 2.67131 | 0.356969 | ||||||||
\(57\) | 6.64274i | 0.879852i | ||||||||
\(58\) | 5.21192i | 0.684359i | ||||||||
\(59\) | −7.79524 | −1.01485 | −0.507427 | − | 0.861695i | \(-0.669403\pi\) | ||||
−0.507427 | + | 0.861695i | \(0.669403\pi\) | |||||||
\(60\) | −3.05705 | + | 0.274497i | −0.394664 | + | 0.0354374i | ||||
\(61\) | −2.21899 | −0.284113 | −0.142057 | − | 0.989859i | \(-0.545372\pi\) | ||||
−0.142057 | + | 0.989859i | \(0.545372\pi\) | |||||||
\(62\) | − | 5.31948i | − | 0.675575i | ||||||
\(63\) | 1.00000i | 0.125988i | ||||||||
\(64\) | −3.36754 | −0.420943 | ||||||||
\(65\) | −15.5374 | + | 1.39512i | −1.92717 | + | 0.173044i | ||||
\(66\) | 0.792050 | 0.0974946 | ||||||||
\(67\) | − | 2.45990i | − | 0.300525i | −0.988646 | − | 0.150263i | \(-0.951988\pi\) | ||
0.988646 | − | 0.150263i | \(-0.0480119\pi\) | |||||||
\(68\) | − | 2.76041i | − | 0.334749i | ||||||
\(69\) | 2.05588 | 0.247498 | ||||||||
\(70\) | −0.158390 | − | 1.76398i | −0.0189313 | − | 0.210836i | ||||
\(71\) | 6.95053 | 0.824876 | 0.412438 | − | 0.910986i | \(-0.364677\pi\) | ||||
0.412438 | + | 0.910986i | \(0.364677\pi\) | |||||||
\(72\) | − | 2.67131i | − | 0.314817i | ||||||
\(73\) | − | 9.73428i | − | 1.13931i | −0.821883 | − | 0.569656i | \(-0.807077\pi\) | ||
0.821883 | − | 0.569656i | \(-0.192923\pi\) | |||||||
\(74\) | 3.59533 | 0.417948 | ||||||||
\(75\) | 0.890732 | + | 4.92002i | 0.102853 | + | 0.568115i | ||||
\(76\) | −9.11820 | −1.04593 | ||||||||
\(77\) | − | 1.00000i | − | 0.113961i | ||||||
\(78\) | − | 5.52572i | − | 0.625665i | ||||||
\(79\) | 6.67029 | 0.750466 | 0.375233 | − | 0.926931i | \(-0.377563\pi\) | ||||
0.375233 | + | 0.926931i | \(0.377563\pi\) | |||||||
\(80\) | −0.125884 | − | 1.40196i | −0.0140743 | − | 0.156744i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.38713i | 0.926203i | ||||||||
\(83\) | − | 4.69895i | − | 0.515777i | −0.966175 | − | 0.257888i | \(-0.916973\pi\) | ||
0.966175 | − | 0.257888i | \(-0.0830267\pi\) | |||||||
\(84\) | −1.37266 | −0.149769 | ||||||||
\(85\) | −4.47871 | + | 0.402149i | −0.485784 | + | 0.0436192i | ||||
\(86\) | −4.26403 | −0.459802 | ||||||||
\(87\) | − | 6.58029i | − | 0.705482i | ||||||
\(88\) | 2.67131i | 0.284763i | ||||||||
\(89\) | −6.34225 | −0.672277 | −0.336138 | − | 0.941813i | \(-0.609121\pi\) | ||||
−0.336138 | + | 0.941813i | \(0.609121\pi\) | |||||||
\(90\) | −1.76398 | + | 0.158390i | −0.185940 | + | 0.0166958i | ||||
\(91\) | −6.97648 | −0.731334 | ||||||||
\(92\) | 2.82201i | 0.294215i | ||||||||
\(93\) | 6.71609i | 0.696426i | ||||||||
\(94\) | 1.36044 | 0.140318 | ||||||||
\(95\) | 1.32838 | + | 14.7941i | 0.136289 | + | 1.51784i | ||||
\(96\) | 5.84122 | 0.596167 | ||||||||
\(97\) | 15.0556i | 1.52866i | 0.644824 | + | 0.764331i | \(0.276931\pi\) | ||||
−0.644824 | + | 0.764331i | \(0.723069\pi\) | |||||||
\(98\) | − | 0.792050i | − | 0.0800092i | ||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −6.75350 | + | 1.22267i | −0.675350 | + | 0.122267i | ||||
\(101\) | 8.60162 | 0.855894 | 0.427947 | − | 0.903804i | \(-0.359237\pi\) | ||||
0.427947 | + | 0.903804i | \(0.359237\pi\) | |||||||
\(102\) | − | 1.59281i | − | 0.157712i | ||||||
\(103\) | − | 4.50360i | − | 0.443753i | −0.975075 | − | 0.221877i | \(-0.928782\pi\) | ||
0.975075 | − | 0.221877i | \(-0.0712182\pi\) | |||||||
\(104\) | 18.6364 | 1.82745 | ||||||||
\(105\) | 0.199975 | + | 2.22711i | 0.0195156 | + | 0.217343i | ||||
\(106\) | 4.29738 | 0.417398 | ||||||||
\(107\) | − | 2.90533i | − | 0.280868i | −0.990090 | − | 0.140434i | \(-0.955150\pi\) | ||
0.990090 | − | 0.140434i | \(-0.0448498\pi\) | |||||||
\(108\) | 1.37266i | 0.132084i | ||||||||
\(109\) | 20.5935 | 1.97250 | 0.986251 | − | 0.165255i | \(-0.0528446\pi\) | ||||
0.986251 | + | 0.165255i | \(0.0528446\pi\) | |||||||
\(110\) | 1.76398 | − | 0.158390i | 0.168189 | − | 0.0151019i | ||||
\(111\) | −4.53927 | −0.430848 | ||||||||
\(112\) | − | 0.629499i | − | 0.0594820i | ||||||
\(113\) | − | 17.8285i | − | 1.67716i | −0.544777 | − | 0.838581i | \(-0.683386\pi\) | ||
0.544777 | − | 0.838581i | \(-0.316614\pi\) | |||||||
\(114\) | −5.26138 | −0.492774 | ||||||||
\(115\) | 4.57866 | − | 0.411124i | 0.426962 | − | 0.0383375i | ||||
\(116\) | 9.03248 | 0.838645 | ||||||||
\(117\) | 6.97648i | 0.644976i | ||||||||
\(118\) | − | 6.17422i | − | 0.568383i | ||||||
\(119\) | −2.01100 | −0.184348 | ||||||||
\(120\) | −0.534196 | − | 5.94930i | −0.0487652 | − | 0.543095i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 1.75756i | − | 0.159122i | ||||||
\(123\) | − | 10.5891i | − | 0.954790i | ||||||
\(124\) | −9.21889 | −0.827881 | ||||||||
\(125\) | 2.96764 | + | 10.7793i | 0.265434 | + | 0.964129i | ||||
\(126\) | −0.792050 | −0.0705614 | ||||||||
\(127\) | − | 14.2017i | − | 1.26020i | −0.776516 | − | 0.630098i | \(-0.783015\pi\) | ||
0.776516 | − | 0.630098i | \(-0.216985\pi\) | |||||||
\(128\) | 9.01518i | 0.796837i | ||||||||
\(129\) | 5.38354 | 0.473994 | ||||||||
\(130\) | −1.10501 | − | 12.3064i | −0.0969155 | − | 1.07934i | ||||
\(131\) | 16.7427 | 1.46281 | 0.731406 | − | 0.681942i | \(-0.238864\pi\) | ||||
0.731406 | + | 0.681942i | \(0.238864\pi\) | |||||||
\(132\) | − | 1.37266i | − | 0.119474i | ||||||
\(133\) | 6.64274i | 0.575998i | ||||||||
\(134\) | 1.94837 | 0.168313 | ||||||||
\(135\) | 2.22711 | − | 0.199975i | 0.191679 | − | 0.0172111i | ||||
\(136\) | 5.37200 | 0.460645 | ||||||||
\(137\) | 16.4926i | 1.40905i | 0.709677 | + | 0.704527i | \(0.248841\pi\) | ||||
−0.709677 | + | 0.704527i | \(0.751159\pi\) | |||||||
\(138\) | 1.62836i | 0.138615i | ||||||||
\(139\) | −1.65018 | −0.139966 | −0.0699831 | − | 0.997548i | \(-0.522295\pi\) | ||||
−0.0699831 | + | 0.997548i | \(0.522295\pi\) | |||||||
\(140\) | −3.05705 | + | 0.274497i | −0.258368 | + | 0.0231992i | ||||
\(141\) | −1.71761 | −0.144649 | ||||||||
\(142\) | 5.50517i | 0.461984i | ||||||||
\(143\) | − | 6.97648i | − | 0.583402i | ||||||
\(144\) | −0.629499 | −0.0524582 | ||||||||
\(145\) | −1.31589 | − | 14.6550i | −0.109279 | − | 1.21703i | ||||
\(146\) | 7.71004 | 0.638087 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | − | 6.23085i | − | 0.512173i | ||||||
\(149\) | 6.27969 | 0.514452 | 0.257226 | − | 0.966351i | \(-0.417192\pi\) | ||||
0.257226 | + | 0.966351i | \(0.417192\pi\) | |||||||
\(150\) | −3.89690 | + | 0.705505i | −0.318181 | + | 0.0576042i | ||||
\(151\) | 15.0368 | 1.22368 | 0.611839 | − | 0.790983i | \(-0.290430\pi\) | ||||
0.611839 | + | 0.790983i | \(0.290430\pi\) | |||||||
\(152\) | − | 17.7448i | − | 1.43930i | ||||||
\(153\) | 2.01100i | 0.162579i | ||||||||
\(154\) | 0.792050 | 0.0638252 | ||||||||
\(155\) | 1.34305 | + | 14.9575i | 0.107876 | + | 1.20141i | ||||
\(156\) | −9.57631 | −0.766718 | ||||||||
\(157\) | − | 1.00596i | − | 0.0802845i | −0.999194 | − | 0.0401422i | \(-0.987219\pi\) | ||
0.999194 | − | 0.0401422i | \(-0.0127811\pi\) | |||||||
\(158\) | 5.28320i | 0.420309i | ||||||||
\(159\) | −5.42564 | −0.430281 | ||||||||
\(160\) | 13.0090 | − | 1.16810i | 1.02845 | − | 0.0923463i | ||||
\(161\) | 2.05588 | 0.162026 | ||||||||
\(162\) | 0.792050i | 0.0622293i | ||||||||
\(163\) | − | 7.18836i | − | 0.563036i | −0.959556 | − | 0.281518i | \(-0.909162\pi\) | ||
0.959556 | − | 0.281518i | \(-0.0908379\pi\) | |||||||
\(164\) | 14.5352 | 1.13501 | ||||||||
\(165\) | −2.22711 | + | 0.199975i | −0.173380 | + | 0.0155680i | ||||
\(166\) | 3.72180 | 0.288868 | ||||||||
\(167\) | 25.3518i | 1.96178i | 0.194569 | + | 0.980889i | \(0.437669\pi\) | ||||
−0.194569 | + | 0.980889i | \(0.562331\pi\) | |||||||
\(168\) | − | 2.67131i | − | 0.206096i | ||||||
\(169\) | −35.6713 | −2.74394 | ||||||||
\(170\) | −0.318522 | − | 3.54736i | −0.0244295 | − | 0.272070i | ||||
\(171\) | 6.64274 | 0.507983 | ||||||||
\(172\) | 7.38975i | 0.563463i | ||||||||
\(173\) | 23.6325i | 1.79674i | 0.439236 | + | 0.898372i | \(0.355249\pi\) | ||||
−0.439236 | + | 0.898372i | \(0.644751\pi\) | |||||||
\(174\) | 5.21192 | 0.395115 | ||||||||
\(175\) | 0.890732 | + | 4.92002i | 0.0673330 | + | 0.371919i | ||||
\(176\) | 0.629499 | 0.0474502 | ||||||||
\(177\) | 7.79524i | 0.585926i | ||||||||
\(178\) | − | 5.02338i | − | 0.376518i | ||||||
\(179\) | −4.63413 | −0.346371 | −0.173185 | − | 0.984889i | \(-0.555406\pi\) | ||||
−0.173185 | + | 0.984889i | \(0.555406\pi\) | |||||||
\(180\) | 0.274497 | + | 3.05705i | 0.0204598 | + | 0.227859i | ||||
\(181\) | 20.1523 | 1.49791 | 0.748954 | − | 0.662622i | \(-0.230556\pi\) | ||||
0.748954 | + | 0.662622i | \(0.230556\pi\) | |||||||
\(182\) | − | 5.52572i | − | 0.409594i | ||||||
\(183\) | 2.21899i | 0.164033i | ||||||||
\(184\) | −5.49189 | −0.404867 | ||||||||
\(185\) | −10.1094 | + | 0.907740i | −0.743260 | + | 0.0667384i | ||||
\(186\) | −5.31948 | −0.390043 | ||||||||
\(187\) | − | 2.01100i | − | 0.147059i | ||||||
\(188\) | − | 2.35769i | − | 0.171952i | ||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −11.7177 | + | 1.05215i | −0.850089 | + | 0.0763306i | ||||
\(191\) | −17.0974 | −1.23712 | −0.618562 | − | 0.785736i | \(-0.712284\pi\) | ||||
−0.618562 | + | 0.785736i | \(0.712284\pi\) | |||||||
\(192\) | 3.36754i | 0.243032i | ||||||||
\(193\) | 7.66253i | 0.551561i | 0.961221 | + | 0.275780i | \(0.0889363\pi\) | ||||
−0.961221 | + | 0.275780i | \(0.911064\pi\) | |||||||
\(194\) | −11.9248 | −0.856149 | ||||||||
\(195\) | 1.39512 | + | 15.5374i | 0.0999067 | + | 1.11265i | ||||
\(196\) | −1.37266 | −0.0980469 | ||||||||
\(197\) | 12.1159i | 0.863220i | 0.902060 | + | 0.431610i | \(0.142054\pi\) | ||||
−0.902060 | + | 0.431610i | \(0.857946\pi\) | |||||||
\(198\) | − | 0.792050i | − | 0.0562886i | ||||||
\(199\) | −14.8587 | −1.05330 | −0.526652 | − | 0.850081i | \(-0.676553\pi\) | ||||
−0.526652 | + | 0.850081i | \(0.676553\pi\) | |||||||
\(200\) | −2.37942 | − | 13.1429i | −0.168251 | − | 0.929344i | ||||
\(201\) | −2.45990 | −0.173508 | ||||||||
\(202\) | 6.81292i | 0.479355i | ||||||||
\(203\) | − | 6.58029i | − | 0.461846i | ||||||
\(204\) | −2.76041 | −0.193267 | ||||||||
\(205\) | −2.11756 | − | 23.5831i | −0.147897 | − | 1.64712i | ||||
\(206\) | 3.56708 | 0.248530 | ||||||||
\(207\) | − | 2.05588i | − | 0.142893i | ||||||
\(208\) | − | 4.39168i | − | 0.304508i | ||||||
\(209\) | −6.64274 | −0.459488 | ||||||||
\(210\) | −1.76398 | + | 0.158390i | −0.121726 | + | 0.0109300i | ||||
\(211\) | 5.59506 | 0.385180 | 0.192590 | − | 0.981279i | \(-0.438311\pi\) | ||||
0.192590 | + | 0.981279i | \(0.438311\pi\) | |||||||
\(212\) | − | 7.44753i | − | 0.511499i | ||||||
\(213\) | − | 6.95053i | − | 0.476243i | ||||||
\(214\) | 2.30116 | 0.157304 | ||||||||
\(215\) | 11.9897 | − | 1.07657i | 0.817692 | − | 0.0734217i | ||||
\(216\) | −2.67131 | −0.181760 | ||||||||
\(217\) | 6.71609i | 0.455918i | ||||||||
\(218\) | 16.3111i | 1.10473i | ||||||||
\(219\) | −9.73428 | −0.657782 | ||||||||
\(220\) | −0.274497 | − | 3.05705i | −0.0185066 | − | 0.206107i | ||||
\(221\) | −14.0297 | −0.943738 | ||||||||
\(222\) | − | 3.59533i | − | 0.241302i | ||||||
\(223\) | 14.9290i | 0.999721i | 0.866106 | + | 0.499860i | \(0.166615\pi\) | ||||
−0.866106 | + | 0.499860i | \(0.833385\pi\) | |||||||
\(224\) | 5.84122 | 0.390283 | ||||||||
\(225\) | 4.92002 | − | 0.890732i | 0.328001 | − | 0.0593821i | ||||
\(226\) | 14.1210 | 0.939318 | ||||||||
\(227\) | 12.4673i | 0.827486i | 0.910394 | + | 0.413743i | \(0.135779\pi\) | ||||
−0.910394 | + | 0.413743i | \(0.864221\pi\) | |||||||
\(228\) | 9.11820i | 0.603867i | ||||||||
\(229\) | −11.3408 | −0.749420 | −0.374710 | − | 0.927142i | \(-0.622258\pi\) | ||||
−0.374710 | + | 0.927142i | \(0.622258\pi\) | |||||||
\(230\) | 0.325631 | + | 3.62653i | 0.0214715 | + | 0.239126i | ||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 17.5780i | 1.15405i | ||||||||
\(233\) | − | 15.4252i | − | 1.01054i | −0.862962 | − | 0.505269i | \(-0.831393\pi\) | ||
0.862962 | − | 0.505269i | \(-0.168607\pi\) | |||||||
\(234\) | −5.52572 | −0.361228 | ||||||||
\(235\) | −3.82531 | + | 0.343480i | −0.249536 | + | 0.0224061i | ||||
\(236\) | −10.7002 | −0.696523 | ||||||||
\(237\) | − | 6.67029i | − | 0.433282i | ||||||
\(238\) | − | 1.59281i | − | 0.103247i | ||||||
\(239\) | 15.6157 | 1.01009 | 0.505047 | − | 0.863092i | \(-0.331475\pi\) | ||||
0.505047 | + | 0.863092i | \(0.331475\pi\) | |||||||
\(240\) | −1.40196 | + | 0.125884i | −0.0904962 | + | 0.00812578i | ||||
\(241\) | 23.5767 | 1.51871 | 0.759353 | − | 0.650679i | \(-0.225516\pi\) | ||||
0.759353 | + | 0.650679i | \(0.225516\pi\) | |||||||
\(242\) | 0.792050i | 0.0509149i | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −3.04592 | −0.194995 | ||||||||
\(245\) | 0.199975 | + | 2.22711i | 0.0127759 | + | 0.142285i | ||||
\(246\) | 8.38713 | 0.534744 | ||||||||
\(247\) | 46.3429i | 2.94873i | ||||||||
\(248\) | − | 17.9408i | − | 1.13924i | ||||||
\(249\) | −4.69895 | −0.297784 | ||||||||
\(250\) | −8.53774 | + | 2.35052i | −0.539974 | + | 0.148660i | ||||
\(251\) | 20.6569 | 1.30385 | 0.651925 | − | 0.758284i | \(-0.273962\pi\) | ||||
0.651925 | + | 0.758284i | \(0.273962\pi\) | |||||||
\(252\) | 1.37266i | 0.0864692i | ||||||||
\(253\) | 2.05588i | 0.129252i | ||||||||
\(254\) | 11.2484 | 0.705790 | ||||||||
\(255\) | 0.402149 | + | 4.47871i | 0.0251836 | + | 0.280467i | ||||
\(256\) | −13.8756 | −0.867223 | ||||||||
\(257\) | 0.652452i | 0.0406988i | 0.999793 | + | 0.0203494i | \(0.00647787\pi\) | ||||
−0.999793 | + | 0.0203494i | \(0.993522\pi\) | |||||||
\(258\) | 4.26403i | 0.265467i | ||||||||
\(259\) | −4.53927 | −0.282056 | ||||||||
\(260\) | −21.3275 | + | 1.91502i | −1.32267 | + | 0.118765i | ||||
\(261\) | −6.58029 | −0.407310 | ||||||||
\(262\) | 13.2610i | 0.819269i | ||||||||
\(263\) | 25.3131i | 1.56087i | 0.625236 | + | 0.780436i | \(0.285003\pi\) | ||||
−0.625236 | + | 0.780436i | \(0.714997\pi\) | |||||||
\(264\) | 2.67131 | 0.164408 | ||||||||
\(265\) | −12.0835 | + | 1.08499i | −0.742282 | + | 0.0666505i | ||||
\(266\) | −5.26138 | −0.322596 | ||||||||
\(267\) | 6.34225i | 0.388139i | ||||||||
\(268\) | − | 3.37660i | − | 0.206259i | ||||||
\(269\) | −4.53171 | −0.276303 | −0.138151 | − | 0.990411i | \(-0.544116\pi\) | ||||
−0.138151 | + | 0.990411i | \(0.544116\pi\) | |||||||
\(270\) | 0.158390 | + | 1.76398i | 0.00963933 | + | 0.107352i | ||||
\(271\) | −13.1341 | −0.797841 | −0.398920 | − | 0.916986i | \(-0.630615\pi\) | ||||
−0.398920 | + | 0.916986i | \(0.630615\pi\) | |||||||
\(272\) | − | 1.26592i | − | 0.0767576i | ||||||
\(273\) | 6.97648i | 0.422236i | ||||||||
\(274\) | −13.0629 | −0.789161 | ||||||||
\(275\) | −4.92002 | + | 0.890732i | −0.296688 | + | 0.0537132i | ||||
\(276\) | 2.82201 | 0.169865 | ||||||||
\(277\) | − | 25.2114i | − | 1.51481i | −0.652947 | − | 0.757403i | \(-0.726468\pi\) | ||
0.652947 | − | 0.757403i | \(-0.273532\pi\) | |||||||
\(278\) | − | 1.30702i | − | 0.0783901i | ||||||
\(279\) | 6.71609 | 0.402082 | ||||||||
\(280\) | −0.534196 | − | 5.94930i | −0.0319243 | − | 0.355539i | ||||
\(281\) | −11.6960 | −0.697725 | −0.348862 | − | 0.937174i | \(-0.613432\pi\) | ||||
−0.348862 | + | 0.937174i | \(0.613432\pi\) | |||||||
\(282\) | − | 1.36044i | − | 0.0810128i | ||||||
\(283\) | 18.7140i | 1.11243i | 0.831038 | + | 0.556216i | \(0.187747\pi\) | ||||
−0.831038 | + | 0.556216i | \(0.812253\pi\) | |||||||
\(284\) | 9.54069 | 0.566136 | ||||||||
\(285\) | 14.7941 | − | 1.32838i | 0.876327 | − | 0.0786866i | ||||
\(286\) | 5.52572 | 0.326743 | ||||||||
\(287\) | − | 10.5891i | − | 0.625057i | ||||||
\(288\) | − | 5.84122i | − | 0.344197i | ||||||
\(289\) | 12.9559 | 0.762111 | ||||||||
\(290\) | 11.6075 | − | 1.04225i | 0.681617 | − | 0.0612033i | ||||
\(291\) | 15.0556 | 0.882574 | ||||||||
\(292\) | − | 13.3618i | − | 0.781942i | ||||||
\(293\) | − | 18.1044i | − | 1.05767i | −0.848724 | − | 0.528836i | \(-0.822629\pi\) | ||
0.848724 | − | 0.528836i | \(-0.177371\pi\) | |||||||
\(294\) | −0.792050 | −0.0461933 | ||||||||
\(295\) | 1.55885 | + | 17.3608i | 0.0907600 | + | 1.01079i | ||||
\(296\) | 12.1258 | 0.704798 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | 4.97383i | 0.288126i | ||||||||
\(299\) | 14.3428 | 0.829464 | ||||||||
\(300\) | 1.22267 | + | 6.75350i | 0.0705908 | + | 0.389913i | ||||
\(301\) | 5.38354 | 0.310302 | ||||||||
\(302\) | 11.9099i | 0.685338i | ||||||||
\(303\) | − | 8.60162i | − | 0.494150i | ||||||
\(304\) | −4.18159 | −0.239831 | ||||||||
\(305\) | 0.443744 | + | 4.94194i | 0.0254087 | + | 0.282975i | ||||
\(306\) | −1.59281 | −0.0910549 | ||||||||
\(307\) | 11.2076i | 0.639652i | 0.947476 | + | 0.319826i | \(0.103625\pi\) | ||||
−0.947476 | + | 0.319826i | \(0.896375\pi\) | |||||||
\(308\) | − | 1.37266i | − | 0.0782144i | ||||||
\(309\) | −4.50360 | −0.256201 | ||||||||
\(310\) | −11.8471 | + | 1.06376i | −0.672868 | + | 0.0604177i | ||||
\(311\) | 16.2770 | 0.922982 | 0.461491 | − | 0.887145i | \(-0.347315\pi\) | ||||
0.461491 | + | 0.887145i | \(0.347315\pi\) | |||||||
\(312\) | − | 18.6364i | − | 1.05508i | ||||||
\(313\) | 3.97432i | 0.224642i | 0.993672 | + | 0.112321i | \(0.0358285\pi\) | ||||
−0.993672 | + | 0.112321i | \(0.964172\pi\) | |||||||
\(314\) | 0.796772 | 0.0449644 | ||||||||
\(315\) | 2.22711 | − | 0.199975i | 0.125483 | − | 0.0112673i | ||||
\(316\) | 9.15601 | 0.515066 | ||||||||
\(317\) | 0.264616i | 0.0148623i | 0.999972 | + | 0.00743116i | \(0.00236543\pi\) | ||||
−0.999972 | + | 0.00743116i | \(0.997635\pi\) | |||||||
\(318\) | − | 4.29738i | − | 0.240985i | ||||||
\(319\) | 6.58029 | 0.368426 | ||||||||
\(320\) | 0.673425 | + | 7.49988i | 0.0376456 | + | 0.419256i | ||||
\(321\) | −2.90533 | −0.162159 | ||||||||
\(322\) | 1.62836i | 0.0907448i | ||||||||
\(323\) | 13.3585i | 0.743288i | ||||||||
\(324\) | 1.37266 | 0.0762587 | ||||||||
\(325\) | 6.21417 | + | 34.3244i | 0.344700 | + | 1.90398i | ||||
\(326\) | 5.69355 | 0.315336 | ||||||||
\(327\) | − | 20.5935i | − | 1.13882i | ||||||
\(328\) | 28.2869i | 1.56188i | ||||||||
\(329\) | −1.71761 | −0.0946951 | ||||||||
\(330\) | −0.158390 | − | 1.76398i | −0.00871910 | − | 0.0971040i | ||||
\(331\) | −7.36413 | −0.404769 | −0.202385 | − | 0.979306i | \(-0.564869\pi\) | ||||
−0.202385 | + | 0.979306i | \(0.564869\pi\) | |||||||
\(332\) | − | 6.45004i | − | 0.353992i | ||||||
\(333\) | 4.53927i | 0.248750i | ||||||||
\(334\) | −20.0799 | −1.09872 | ||||||||
\(335\) | −5.47847 | + | 0.491920i | −0.299321 | + | 0.0268764i | ||||
\(336\) | −0.629499 | −0.0343420 | ||||||||
\(337\) | − | 18.2163i | − | 0.992305i | −0.868235 | − | 0.496152i | \(-0.834746\pi\) | ||
0.868235 | − | 0.496152i | \(-0.165254\pi\) | |||||||
\(338\) | − | 28.2534i | − | 1.53678i | ||||||
\(339\) | −17.8285 | −0.968310 | ||||||||
\(340\) | −6.14772 | + | 0.552013i | −0.333407 | + | 0.0299371i | ||||
\(341\) | −6.71609 | −0.363697 | ||||||||
\(342\) | 5.26138i | 0.284503i | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −14.3811 | −0.775378 | ||||||||
\(345\) | −0.411124 | − | 4.57866i | −0.0221342 | − | 0.246507i | ||||
\(346\) | −18.7181 | −1.00629 | ||||||||
\(347\) | − | 4.83663i | − | 0.259644i | −0.991537 | − | 0.129822i | \(-0.958559\pi\) | ||
0.991537 | − | 0.129822i | \(-0.0414405\pi\) | |||||||
\(348\) | − | 9.03248i | − | 0.484192i | ||||||
\(349\) | 26.1747 | 1.40110 | 0.700550 | − | 0.713603i | \(-0.252938\pi\) | ||||
0.700550 | + | 0.713603i | \(0.252938\pi\) | |||||||
\(350\) | −3.89690 | + | 0.705505i | −0.208298 | + | 0.0377108i | ||||
\(351\) | 6.97648 | 0.372377 | ||||||||
\(352\) | 5.84122i | 0.311338i | ||||||||
\(353\) | 34.1495i | 1.81759i | 0.417240 | + | 0.908796i | \(0.362997\pi\) | ||||
−0.417240 | + | 0.908796i | \(0.637003\pi\) | |||||||
\(354\) | −6.17422 | −0.328156 | ||||||||
\(355\) | −1.38993 | − | 15.4796i | −0.0737700 | − | 0.821571i | ||||
\(356\) | −8.70573 | −0.461403 | ||||||||
\(357\) | 2.01100i | 0.106433i | ||||||||
\(358\) | − | 3.67046i | − | 0.193990i | ||||||
\(359\) | −36.6175 | −1.93260 | −0.966299 | − | 0.257422i | \(-0.917127\pi\) | ||||
−0.966299 | + | 0.257422i | \(0.917127\pi\) | |||||||
\(360\) | −5.94930 | + | 0.534196i | −0.313556 | + | 0.0281546i | ||||
\(361\) | 25.1260 | 1.32242 | ||||||||
\(362\) | 15.9616i | 0.838924i | ||||||||
\(363\) | − | 1.00000i | − | 0.0524864i | ||||||
\(364\) | −9.57631 | −0.501935 | ||||||||
\(365\) | −21.6793 | + | 1.94661i | −1.13475 | + | 0.101890i | ||||
\(366\) | −1.75756 | −0.0918689 | ||||||||
\(367\) | − | 29.1290i | − | 1.52052i | −0.649618 | − | 0.760260i | \(-0.725071\pi\) | ||
0.649618 | − | 0.760260i | \(-0.274929\pi\) | |||||||
\(368\) | 1.29417i | 0.0674633i | ||||||||
\(369\) | −10.5891 | −0.551248 | ||||||||
\(370\) | −0.718976 | − | 8.00718i | −0.0373778 | − | 0.416273i | ||||
\(371\) | −5.42564 | −0.281685 | ||||||||
\(372\) | 9.21889i | 0.477977i | ||||||||
\(373\) | 0.177939i | 0.00921334i | 0.999989 | + | 0.00460667i | \(0.00146635\pi\) | ||||
−0.999989 | + | 0.00460667i | \(0.998534\pi\) | |||||||
\(374\) | 1.59281 | 0.0823623 | ||||||||
\(375\) | 10.7793 | − | 2.96764i | 0.556640 | − | 0.153248i | ||||
\(376\) | 4.58828 | 0.236623 | ||||||||
\(377\) | − | 45.9073i | − | 2.36435i | ||||||
\(378\) | 0.792050i | 0.0407387i | ||||||||
\(379\) | −0.0707006 | −0.00363164 | −0.00181582 | − | 0.999998i | \(-0.500578\pi\) | ||||
−0.00181582 | + | 0.999998i | \(0.500578\pi\) | |||||||
\(380\) | 1.82341 | + | 20.3072i | 0.0935391 | + | 1.04174i | ||||
\(381\) | −14.2017 | −0.727574 | ||||||||
\(382\) | − | 13.5420i | − | 0.692869i | ||||||
\(383\) | 2.25388i | 0.115168i | 0.998341 | + | 0.0575840i | \(0.0183397\pi\) | ||||
−0.998341 | + | 0.0575840i | \(0.981660\pi\) | |||||||
\(384\) | 9.01518 | 0.460054 | ||||||||
\(385\) | −2.22711 | + | 0.199975i | −0.113504 | + | 0.0101917i | ||||
\(386\) | −6.06911 | −0.308909 | ||||||||
\(387\) | − | 5.38354i | − | 0.273661i | ||||||
\(388\) | 20.6661i | 1.04916i | ||||||||
\(389\) | 0.181295 | 0.00919203 | 0.00459602 | − | 0.999989i | \(-0.498537\pi\) | ||||
0.00459602 | + | 0.999989i | \(0.498537\pi\) | |||||||
\(390\) | −12.3064 | + | 1.10501i | −0.623158 | + | 0.0559542i | ||||
\(391\) | 4.13436 | 0.209084 | ||||||||
\(392\) | − | 2.67131i | − | 0.134922i | ||||||
\(393\) | − | 16.7427i | − | 0.844555i | ||||||
\(394\) | −9.59638 | −0.483458 | ||||||||
\(395\) | −1.33389 | − | 14.8555i | −0.0671153 | − | 0.747459i | ||||
\(396\) | −1.37266 | −0.0689786 | ||||||||
\(397\) | 9.73781i | 0.488726i | 0.969684 | + | 0.244363i | \(0.0785789\pi\) | ||||
−0.969684 | + | 0.244363i | \(0.921421\pi\) | |||||||
\(398\) | − | 11.7688i | − | 0.589918i | ||||||
\(399\) | 6.64274 | 0.332553 | ||||||||
\(400\) | −3.09715 | + | 0.560715i | −0.154857 | + | 0.0280357i | ||||
\(401\) | −10.7003 | −0.534348 | −0.267174 | − | 0.963648i | \(-0.586090\pi\) | ||||
−0.267174 | + | 0.963648i | \(0.586090\pi\) | |||||||
\(402\) | − | 1.94837i | − | 0.0971758i | ||||||
\(403\) | 46.8547i | 2.33400i | ||||||||
\(404\) | 11.8071 | 0.587424 | ||||||||
\(405\) | −0.199975 | − | 2.22711i | −0.00993684 | − | 0.110666i | ||||
\(406\) | 5.21192 | 0.258663 | ||||||||
\(407\) | − | 4.53927i | − | 0.225003i | ||||||
\(408\) | − | 5.37200i | − | 0.265954i | ||||||
\(409\) | −31.1485 | −1.54020 | −0.770098 | − | 0.637926i | \(-0.779793\pi\) | ||||
−0.770098 | + | 0.637926i | \(0.779793\pi\) | |||||||
\(410\) | 18.6790 | − | 1.67722i | 0.922492 | − | 0.0828318i | ||||
\(411\) | 16.4926 | 0.813518 | ||||||||
\(412\) | − | 6.18190i | − | 0.304560i | ||||||
\(413\) | 7.79524i | 0.383579i | ||||||||
\(414\) | 1.62836 | 0.0800294 | ||||||||
\(415\) | −10.4651 | + | 0.939673i | −0.513710 | + | 0.0461267i | ||||
\(416\) | 40.7512 | 1.99799 | ||||||||
\(417\) | 1.65018i | 0.0808096i | ||||||||
\(418\) | − | 5.26138i | − | 0.257343i | ||||||
\(419\) | 25.2282 | 1.23248 | 0.616239 | − | 0.787559i | \(-0.288655\pi\) | ||||
0.616239 | + | 0.787559i | \(0.288655\pi\) | |||||||
\(420\) | 0.274497 | + | 3.05705i | 0.0133941 | + | 0.149169i | ||||
\(421\) | 9.09604 | 0.443314 | 0.221657 | − | 0.975125i | \(-0.428853\pi\) | ||||
0.221657 | + | 0.975125i | \(0.428853\pi\) | |||||||
\(422\) | 4.43157i | 0.215725i | ||||||||
\(423\) | 1.71761i | 0.0835132i | ||||||||
\(424\) | 14.4936 | 0.703870 | ||||||||
\(425\) | 1.79126 | + | 9.89414i | 0.0868888 | + | 0.479936i | ||||
\(426\) | 5.50517 | 0.266726 | ||||||||
\(427\) | 2.21899i | 0.107385i | ||||||||
\(428\) | − | 3.98801i | − | 0.192768i | ||||||
\(429\) | −6.97648 | −0.336828 | ||||||||
\(430\) | 0.852700 | + | 9.49646i | 0.0411208 | + | 0.457960i | ||||
\(431\) | 28.0128 | 1.34933 | 0.674665 | − | 0.738124i | \(-0.264288\pi\) | ||||
0.674665 | + | 0.738124i | \(0.264288\pi\) | |||||||
\(432\) | 0.629499i | 0.0302868i | ||||||||
\(433\) | 19.2478i | 0.924988i | 0.886622 | + | 0.462494i | \(0.153045\pi\) | ||||
−0.886622 | + | 0.462494i | \(0.846955\pi\) | |||||||
\(434\) | −5.31948 | −0.255343 | ||||||||
\(435\) | −14.6550 | + | 1.31589i | −0.702655 | + | 0.0630923i | ||||
\(436\) | 28.2678 | 1.35378 | ||||||||
\(437\) | − | 13.6566i | − | 0.653286i | ||||||
\(438\) | − | 7.71004i | − | 0.368400i | ||||||
\(439\) | −31.8121 | −1.51831 | −0.759154 | − | 0.650911i | \(-0.774387\pi\) | ||||
−0.759154 | + | 0.650911i | \(0.774387\pi\) | |||||||
\(440\) | 5.94930 | − | 0.534196i | 0.283622 | − | 0.0254668i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | − | 11.1122i | − | 0.528554i | ||||||
\(443\) | − | 4.63304i | − | 0.220122i | −0.993925 | − | 0.110061i | \(-0.964895\pi\) | ||
0.993925 | − | 0.110061i | \(-0.0351047\pi\) | |||||||
\(444\) | −6.23085 | −0.295703 | ||||||||
\(445\) | 1.26829 | + | 14.1249i | 0.0601228 | + | 0.669583i | ||||
\(446\) | −11.8245 | −0.559908 | ||||||||
\(447\) | − | 6.27969i | − | 0.297019i | ||||||
\(448\) | 3.36754i | 0.159101i | ||||||||
\(449\) | −29.2903 | −1.38230 | −0.691148 | − | 0.722714i | \(-0.742895\pi\) | ||||
−0.691148 | + | 0.722714i | \(0.742895\pi\) | |||||||
\(450\) | 0.705505 | + | 3.89690i | 0.0332578 | + | 0.183702i | ||||
\(451\) | 10.5891 | 0.498623 | ||||||||
\(452\) | − | 24.4724i | − | 1.15108i | ||||||
\(453\) | − | 15.0368i | − | 0.706490i | ||||||
\(454\) | −9.87475 | −0.463445 | ||||||||
\(455\) | 1.39512 | + | 15.5374i | 0.0654043 | + | 0.728403i | ||||
\(456\) | −17.7448 | −0.830978 | ||||||||
\(457\) | − | 31.1481i | − | 1.45704i | −0.685022 | − | 0.728522i | \(-0.740207\pi\) | ||
0.685022 | − | 0.728522i | \(-0.259793\pi\) | |||||||
\(458\) | − | 8.98248i | − | 0.419723i | ||||||
\(459\) | 2.01100 | 0.0938653 | ||||||||
\(460\) | 6.28492 | − | 0.564332i | 0.293036 | − | 0.0263121i | ||||
\(461\) | 5.07279 | 0.236263 | 0.118132 | − | 0.992998i | \(-0.462310\pi\) | ||||
0.118132 | + | 0.992998i | \(0.462310\pi\) | |||||||
\(462\) | − | 0.792050i | − | 0.0368495i | ||||||
\(463\) | 26.6104i | 1.23669i | 0.785906 | + | 0.618346i | \(0.212197\pi\) | ||||
−0.785906 | + | 0.618346i | \(0.787803\pi\) | |||||||
\(464\) | 4.14229 | 0.192301 | ||||||||
\(465\) | 14.9575 | − | 1.34305i | 0.693636 | − | 0.0622825i | ||||
\(466\) | 12.2175 | 0.565966 | ||||||||
\(467\) | − | 14.2806i | − | 0.660828i | −0.943836 | − | 0.330414i | \(-0.892812\pi\) | ||
0.943836 | − | 0.330414i | \(-0.107188\pi\) | |||||||
\(468\) | 9.57631i | 0.442665i | ||||||||
\(469\) | −2.45990 | −0.113588 | ||||||||
\(470\) | −0.272053 | − | 3.02984i | −0.0125489 | − | 0.139756i | ||||
\(471\) | −1.00596 | −0.0463523 | ||||||||
\(472\) | − | 20.8235i | − | 0.958481i | ||||||
\(473\) | 5.38354i | 0.247535i | ||||||||
\(474\) | 5.28320 | 0.242666 | ||||||||
\(475\) | 32.6824 | − | 5.91690i | 1.49957 | − | 0.271486i | ||||
\(476\) | −2.76041 | −0.126523 | ||||||||
\(477\) | 5.42564i | 0.248423i | ||||||||
\(478\) | 12.3684i | 0.565718i | ||||||||
\(479\) | −18.8608 | −0.861773 | −0.430887 | − | 0.902406i | \(-0.641799\pi\) | ||||
−0.430887 | + | 0.902406i | \(0.641799\pi\) | |||||||
\(480\) | −1.16810 | − | 13.0090i | −0.0533162 | − | 0.593778i | ||||
\(481\) | −31.6681 | −1.44394 | ||||||||
\(482\) | 18.6739i | 0.850573i | ||||||||
\(483\) | − | 2.05588i | − | 0.0935456i | ||||||
\(484\) | 1.37266 | 0.0623935 | ||||||||
\(485\) | 33.5304 | − | 3.01074i | 1.52254 | − | 0.136711i | ||||
\(486\) | 0.792050 | 0.0359281 | ||||||||
\(487\) | − | 39.5539i | − | 1.79236i | −0.443691 | − | 0.896180i | \(-0.646331\pi\) | ||
0.443691 | − | 0.896180i | \(-0.353669\pi\) | |||||||
\(488\) | − | 5.92763i | − | 0.268331i | ||||||
\(489\) | −7.18836 | −0.325069 | ||||||||
\(490\) | −1.76398 | + | 0.158390i | −0.0796886 | + | 0.00715534i | ||||
\(491\) | −9.52713 | −0.429953 | −0.214977 | − | 0.976619i | \(-0.568968\pi\) | ||||
−0.214977 | + | 0.976619i | \(0.568968\pi\) | |||||||
\(492\) | − | 14.5352i | − | 0.655299i | ||||||
\(493\) | − | 13.2329i | − | 0.595982i | ||||||
\(494\) | −36.7059 | −1.65148 | ||||||||
\(495\) | 0.199975 | + | 2.22711i | 0.00898821 | + | 0.100101i | ||||
\(496\) | −4.22777 | −0.189833 | ||||||||
\(497\) | − | 6.95053i | − | 0.311774i | ||||||
\(498\) | − | 3.72180i | − | 0.166778i | ||||||
\(499\) | 14.3007 | 0.640187 | 0.320094 | − | 0.947386i | \(-0.396286\pi\) | ||||
0.320094 | + | 0.947386i | \(0.396286\pi\) | |||||||
\(500\) | 4.07355 | + | 14.7963i | 0.182175 | + | 0.661709i | ||||
\(501\) | 25.3518 | 1.13263 | ||||||||
\(502\) | 16.3613i | 0.730239i | ||||||||
\(503\) | − | 3.16460i | − | 0.141102i | −0.997508 | − | 0.0705512i | \(-0.977524\pi\) | ||
0.997508 | − | 0.0705512i | \(-0.0224758\pi\) | |||||||
\(504\) | −2.67131 | −0.118990 | ||||||||
\(505\) | −1.72011 | − | 19.1567i | −0.0765439 | − | 0.852464i | ||||
\(506\) | −1.62836 | −0.0723893 | ||||||||
\(507\) | 35.6713i | 1.58422i | ||||||||
\(508\) | − | 19.4940i | − | 0.864908i | ||||||
\(509\) | 16.5587 | 0.733952 | 0.366976 | − | 0.930231i | \(-0.380393\pi\) | ||||
0.366976 | + | 0.930231i | \(0.380393\pi\) | |||||||
\(510\) | −3.54736 | + | 0.318522i | −0.157080 | + | 0.0141044i | ||||
\(511\) | −9.73428 | −0.430619 | ||||||||
\(512\) | 7.04022i | 0.311137i | ||||||||
\(513\) | − | 6.64274i | − | 0.293284i | ||||||
\(514\) | −0.516775 | −0.0227940 | ||||||||
\(515\) | −10.0300 | + | 0.900608i | −0.441975 | + | 0.0396855i | ||||
\(516\) | 7.38975 | 0.325315 | ||||||||
\(517\) | − | 1.71761i | − | 0.0755405i | ||||||
\(518\) | − | 3.59533i | − | 0.157970i | ||||||
\(519\) | 23.6325 | 1.03735 | ||||||||
\(520\) | −3.72681 | − | 41.5052i | −0.163431 | − | 1.82012i | ||||
\(521\) | 0.0943128 | 0.00413192 | 0.00206596 | − | 0.999998i | \(-0.499342\pi\) | ||||
0.00206596 | + | 0.999998i | \(0.499342\pi\) | |||||||
\(522\) | − | 5.21192i | − | 0.228120i | ||||||
\(523\) | 39.1138i | 1.71033i | 0.518358 | + | 0.855164i | \(0.326544\pi\) | ||||
−0.518358 | + | 0.855164i | \(0.673456\pi\) | |||||||
\(524\) | 22.9819 | 1.00397 | ||||||||
\(525\) | 4.92002 | − | 0.890732i | 0.214727 | − | 0.0388747i | ||||
\(526\) | −20.0492 | −0.874188 | ||||||||
\(527\) | 13.5060i | 0.588332i | ||||||||
\(528\) | − | 0.629499i | − | 0.0273954i | ||||||
\(529\) | 18.7734 | 0.816234 | ||||||||
\(530\) | −0.859368 | − | 9.57072i | −0.0373286 | − | 0.415726i | ||||
\(531\) | 7.79524 | 0.338285 | ||||||||
\(532\) | 9.11820i | 0.395324i | ||||||||
\(533\) | − | 73.8749i | − | 3.19988i | ||||||
\(534\) | −5.02338 | −0.217383 | ||||||||
\(535\) | −6.47047 | + | 0.580993i | −0.279743 | + | 0.0251185i | ||||
\(536\) | 6.57118 | 0.283832 | ||||||||
\(537\) | 4.63413i | 0.199977i | ||||||||
\(538\) | − | 3.58934i | − | 0.154747i | ||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 3.05705 | − | 0.274497i | 0.131555 | − | 0.0118125i | ||||
\(541\) | −4.25392 | −0.182890 | −0.0914451 | − | 0.995810i | \(-0.529149\pi\) | ||||
−0.0914451 | + | 0.995810i | \(0.529149\pi\) | |||||||
\(542\) | − | 10.4029i | − | 0.446842i | ||||||
\(543\) | − | 20.1523i | − | 0.864817i | ||||||
\(544\) | 11.7467 | 0.503635 | ||||||||
\(545\) | −4.11819 | − | 45.8640i | −0.176404 | − | 1.96460i | ||||
\(546\) | −5.52572 | −0.236479 | ||||||||
\(547\) | − | 0.274019i | − | 0.0117162i | −0.999983 | − | 0.00585810i | \(-0.998135\pi\) | ||
0.999983 | − | 0.00585810i | \(-0.00186470\pi\) | |||||||
\(548\) | 22.6386i | 0.967074i | ||||||||
\(549\) | 2.21899 | 0.0947044 | ||||||||
\(550\) | −0.705505 | − | 3.89690i | −0.0300828 | − | 0.166165i | ||||
\(551\) | −43.7112 | −1.86216 | ||||||||
\(552\) | 5.49189i | 0.233750i | ||||||||
\(553\) | − | 6.67029i | − | 0.283649i | ||||||
\(554\) | 19.9687 | 0.848389 | ||||||||
\(555\) | 0.907740 | + | 10.1094i | 0.0385314 | + | 0.429122i | ||||
\(556\) | −2.26513 | −0.0960628 | ||||||||
\(557\) | 23.2359i | 0.984538i | 0.870443 | + | 0.492269i | \(0.163832\pi\) | ||||
−0.870443 | + | 0.492269i | \(0.836168\pi\) | |||||||
\(558\) | 5.31948i | 0.225192i | ||||||||
\(559\) | 37.5581 | 1.58854 | ||||||||
\(560\) | −1.40196 | + | 0.125884i | −0.0592437 | + | 0.00531957i | ||||
\(561\) | −2.01100 | −0.0849043 | ||||||||
\(562\) | − | 9.26382i | − | 0.390771i | ||||||
\(563\) | − | 26.3095i | − | 1.10881i | −0.832246 | − | 0.554407i | \(-0.812945\pi\) | ||
0.832246 | − | 0.554407i | \(-0.187055\pi\) | |||||||
\(564\) | −2.35769 | −0.0992768 | ||||||||
\(565\) | −39.7059 | + | 3.56525i | −1.67044 | + | 0.149991i | ||||
\(566\) | −14.8224 | −0.623033 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 18.5670i | 0.779056i | ||||||||
\(569\) | −11.5720 | −0.485123 | −0.242562 | − | 0.970136i | \(-0.577988\pi\) | ||||
−0.242562 | + | 0.970136i | \(0.577988\pi\) | |||||||
\(570\) | 1.05215 | + | 11.7177i | 0.0440695 | + | 0.490799i | ||||
\(571\) | −16.6267 | −0.695804 | −0.347902 | − | 0.937531i | \(-0.613106\pi\) | ||||
−0.347902 | + | 0.937531i | \(0.613106\pi\) | |||||||
\(572\) | − | 9.57631i | − | 0.400406i | ||||||
\(573\) | 17.0974i | 0.714254i | ||||||||
\(574\) | 8.38713 | 0.350072 | ||||||||
\(575\) | −1.83123 | − | 10.1150i | −0.0763678 | − | 0.421823i | ||||
\(576\) | 3.36754 | 0.140314 | ||||||||
\(577\) | − | 26.8828i | − | 1.11915i | −0.828781 | − | 0.559573i | \(-0.810965\pi\) | ||
0.828781 | − | 0.559573i | \(-0.189035\pi\) | |||||||
\(578\) | 10.2617i | 0.426831i | ||||||||
\(579\) | 7.66253 | 0.318444 | ||||||||
\(580\) | −1.80627 | − | 20.1163i | −0.0750013 | − | 0.835284i | ||||
\(581\) | −4.69895 | −0.194945 | ||||||||
\(582\) | 11.9248i | 0.494298i | ||||||||
\(583\) | − | 5.42564i | − | 0.224707i | ||||||
\(584\) | 26.0033 | 1.07602 | ||||||||
\(585\) | 15.5374 | − | 1.39512i | 0.642391 | − | 0.0576812i | ||||
\(586\) | 14.3396 | 0.592364 | ||||||||
\(587\) | − | 9.63552i | − | 0.397701i | −0.980030 | − | 0.198850i | \(-0.936279\pi\) | ||
0.980030 | − | 0.198850i | \(-0.0637208\pi\) | |||||||
\(588\) | 1.37266i | 0.0566074i | ||||||||
\(589\) | 44.6132 | 1.83826 | ||||||||
\(590\) | −13.7507 | + | 1.23469i | −0.566106 | + | 0.0508314i | ||||
\(591\) | 12.1159 | 0.498380 | ||||||||
\(592\) | − | 2.85746i | − | 0.117441i | ||||||
\(593\) | 5.93289i | 0.243635i | 0.992553 | + | 0.121817i | \(0.0388722\pi\) | ||||
−0.992553 | + | 0.121817i | \(0.961128\pi\) | |||||||
\(594\) | −0.792050 | −0.0324982 | ||||||||
\(595\) | 0.402149 | + | 4.47871i | 0.0164865 | + | 0.183609i | ||||
\(596\) | 8.61985 | 0.353083 | ||||||||
\(597\) | 14.8587i | 0.608126i | ||||||||
\(598\) | 11.3602i | 0.464553i | ||||||||
\(599\) | 24.2153 | 0.989411 | 0.494705 | − | 0.869061i | \(-0.335276\pi\) | ||||
0.494705 | + | 0.869061i | \(0.335276\pi\) | |||||||
\(600\) | −13.1429 | + | 2.37942i | −0.536557 | + | 0.0971396i | ||||
\(601\) | 43.6346 | 1.77989 | 0.889947 | − | 0.456065i | \(-0.150741\pi\) | ||||
0.889947 | + | 0.456065i | \(0.150741\pi\) | |||||||
\(602\) | 4.26403i | 0.173789i | ||||||||
\(603\) | 2.45990i | 0.100175i | ||||||||
\(604\) | 20.6404 | 0.839844 | ||||||||
\(605\) | −0.199975 | − | 2.22711i | −0.00813014 | − | 0.0905448i | ||||
\(606\) | 6.81292 | 0.276756 | ||||||||
\(607\) | 11.0521i | 0.448592i | 0.974521 | + | 0.224296i | \(0.0720082\pi\) | ||||
−0.974521 | + | 0.224296i | \(0.927992\pi\) | |||||||
\(608\) | − | 38.8017i | − | 1.57362i | ||||||
\(609\) | −6.58029 | −0.266647 | ||||||||
\(610\) | −3.91427 | + | 0.351467i | −0.158484 | + | 0.0142305i | ||||
\(611\) | −11.9829 | −0.484776 | ||||||||
\(612\) | 2.76041i | 0.111583i | ||||||||
\(613\) | − | 9.26989i | − | 0.374407i | −0.982321 | − | 0.187204i | \(-0.940058\pi\) | ||
0.982321 | − | 0.187204i | \(-0.0599424\pi\) | |||||||
\(614\) | −8.87699 | −0.358246 | ||||||||
\(615\) | −23.5831 | + | 2.11756i | −0.950964 | + | 0.0853884i | ||||
\(616\) | 2.67131 | 0.107630 | ||||||||
\(617\) | − | 14.8200i | − | 0.596630i | −0.954467 | − | 0.298315i | \(-0.903575\pi\) | ||
0.954467 | − | 0.298315i | \(-0.0964246\pi\) | |||||||
\(618\) | − | 3.56708i | − | 0.143489i | ||||||
\(619\) | −8.04117 | −0.323202 | −0.161601 | − | 0.986856i | \(-0.551666\pi\) | ||||
−0.161601 | + | 0.986856i | \(0.551666\pi\) | |||||||
\(620\) | 1.84355 | + | 20.5315i | 0.0740387 | + | 0.824563i | ||||
\(621\) | −2.05588 | −0.0824995 | ||||||||
\(622\) | 12.8922i | 0.516929i | ||||||||
\(623\) | 6.34225i | 0.254097i | ||||||||
\(624\) | −4.39168 | −0.175808 | ||||||||
\(625\) | 23.4132 | − | 8.76484i | 0.936528 | − | 0.350594i | ||||
\(626\) | −3.14786 | −0.125814 | ||||||||
\(627\) | 6.64274i | 0.265285i | ||||||||
\(628\) | − | 1.38084i | − | 0.0551015i | ||||||
\(629\) | −9.12845 | −0.363975 | ||||||||
\(630\) | 0.158390 | + | 1.76398i | 0.00631042 | + | 0.0702787i | ||||
\(631\) | 28.2050 | 1.12283 | 0.561413 | − | 0.827536i | \(-0.310258\pi\) | ||||
0.561413 | + | 0.827536i | \(0.310258\pi\) | |||||||
\(632\) | 17.8184i | 0.708779i | ||||||||
\(633\) | − | 5.59506i | − | 0.222384i | ||||||
\(634\) | −0.209589 | −0.00832385 | ||||||||
\(635\) | −31.6287 | + | 2.83998i | −1.25515 | + | 0.112701i | ||||
\(636\) | −7.44753 | −0.295314 | ||||||||
\(637\) | 6.97648i | 0.276418i | ||||||||
\(638\) | 5.21192i | 0.206342i | ||||||||
\(639\) | −6.95053 | −0.274959 | ||||||||
\(640\) | 20.0778 | − | 1.80281i | 0.793644 | − | 0.0712624i | ||||
\(641\) | 2.00498 | 0.0791919 | 0.0395959 | − | 0.999216i | \(-0.487393\pi\) | ||||
0.0395959 | + | 0.999216i | \(0.487393\pi\) | |||||||
\(642\) | − | 2.30116i | − | 0.0908197i | ||||||
\(643\) | − | 7.10193i | − | 0.280073i | −0.990146 | − | 0.140036i | \(-0.955278\pi\) | ||
0.990146 | − | 0.140036i | \(-0.0447220\pi\) | |||||||
\(644\) | 2.82201 | 0.111203 | ||||||||
\(645\) | −1.07657 | − | 11.9897i | −0.0423900 | − | 0.472095i | ||||
\(646\) | −10.5806 | −0.416289 | ||||||||
\(647\) | 6.36568i | 0.250261i | 0.992140 | + | 0.125130i | \(0.0399349\pi\) | ||||
−0.992140 | + | 0.125130i | \(0.960065\pi\) | |||||||
\(648\) | 2.67131i | 0.104939i | ||||||||
\(649\) | −7.79524 | −0.305990 | ||||||||
\(650\) | −27.1867 | + | 4.92194i | −1.06635 | + | 0.193054i | ||||
\(651\) | 6.71609 | 0.263224 | ||||||||
\(652\) | − | 9.86715i | − | 0.386428i | ||||||
\(653\) | 2.88871i | 0.113044i | 0.998401 | + | 0.0565220i | \(0.0180011\pi\) | ||||
−0.998401 | + | 0.0565220i | \(0.981999\pi\) | |||||||
\(654\) | 16.3111 | 0.637815 | ||||||||
\(655\) | −3.34811 | − | 37.2877i | −0.130822 | − | 1.45695i | ||||
\(656\) | 6.66585 | 0.260258 | ||||||||
\(657\) | 9.73428i | 0.379770i | ||||||||
\(658\) | − | 1.36044i | − | 0.0530353i | ||||||
\(659\) | 5.34350 | 0.208153 | 0.104077 | − | 0.994569i | \(-0.466811\pi\) | ||||
0.104077 | + | 0.994569i | \(0.466811\pi\) | |||||||
\(660\) | −3.05705 | + | 0.274497i | −0.118996 | + | 0.0106848i | ||||
\(661\) | 24.6815 | 0.959997 | 0.479999 | − | 0.877269i | \(-0.340637\pi\) | ||||
0.479999 | + | 0.877269i | \(0.340637\pi\) | |||||||
\(662\) | − | 5.83276i | − | 0.226697i | ||||||
\(663\) | 14.0297i | 0.544867i | ||||||||
\(664\) | 12.5524 | 0.487126 | ||||||||
\(665\) | 14.7941 | − | 1.32838i | 0.573690 | − | 0.0515124i | ||||
\(666\) | −3.59533 | −0.139316 | ||||||||
\(667\) | 13.5283i | 0.523817i | ||||||||
\(668\) | 34.7993i | 1.34642i | ||||||||
\(669\) | 14.9290 | 0.577189 | ||||||||
\(670\) | −0.389625 | − | 4.33923i | −0.0150525 | − | 0.167639i | ||||
\(671\) | −2.21899 | −0.0856633 | ||||||||
\(672\) | − | 5.84122i | − | 0.225330i | ||||||
\(673\) | − | 7.79045i | − | 0.300300i | −0.988663 | − | 0.150150i | \(-0.952024\pi\) | ||
0.988663 | − | 0.150150i | \(-0.0479756\pi\) | |||||||
\(674\) | 14.4282 | 0.555754 | ||||||||
\(675\) | −0.890732 | − | 4.92002i | −0.0342843 | − | 0.189372i | ||||
\(676\) | −48.9644 | −1.88325 | ||||||||
\(677\) | 7.81878i | 0.300500i | 0.988648 | + | 0.150250i | \(0.0480079\pi\) | ||||
−0.988648 | + | 0.150250i | \(0.951992\pi\) | |||||||
\(678\) | − | 14.1210i | − | 0.542315i | ||||||
\(679\) | 15.0556 | 0.577780 | ||||||||
\(680\) | −1.07427 | − | 11.9640i | −0.0411962 | − | 0.458799i | ||||
\(681\) | 12.4673 | 0.477749 | ||||||||
\(682\) | − | 5.31948i | − | 0.203694i | ||||||
\(683\) | 35.5185i | 1.35908i | 0.733640 | + | 0.679538i | \(0.237820\pi\) | ||||
−0.733640 | + | 0.679538i | \(0.762180\pi\) | |||||||
\(684\) | 9.11820 | 0.348643 | ||||||||
\(685\) | 36.7307 | − | 3.29810i | 1.40341 | − | 0.126014i | ||||
\(686\) | −0.792050 | −0.0302406 | ||||||||
\(687\) | 11.3408i | 0.432678i | ||||||||
\(688\) | 3.38893i | 0.129202i | ||||||||
\(689\) | −37.8518 | −1.44204 | ||||||||
\(690\) | 3.62653 | − | 0.325631i | 0.138060 | − | 0.0123966i | ||||
\(691\) | 37.5400 | 1.42809 | 0.714045 | − | 0.700100i | \(-0.246861\pi\) | ||||
0.714045 | + | 0.700100i | \(0.246861\pi\) | |||||||
\(692\) | 32.4393i | 1.23316i | ||||||||
\(693\) | 1.00000i | 0.0379869i | ||||||||
\(694\) | 3.83085 | 0.145417 | ||||||||
\(695\) | 0.329994 | + | 3.67512i | 0.0125174 | + | 0.139405i | ||||
\(696\) | 17.5780 | 0.666293 | ||||||||
\(697\) | − | 21.2947i | − | 0.806595i | ||||||
\(698\) | 20.7317i | 0.784706i | ||||||||
\(699\) | −15.4252 | −0.583435 | ||||||||
\(700\) | 1.22267 | + | 6.75350i | 0.0462125 | + | 0.255258i | ||||
\(701\) | 11.3900 | 0.430194 | 0.215097 | − | 0.976593i | \(-0.430993\pi\) | ||||
0.215097 | + | 0.976593i | \(0.430993\pi\) | |||||||
\(702\) | 5.52572i | 0.208555i | ||||||||
\(703\) | 30.1532i | 1.13725i | ||||||||
\(704\) | −3.36754 | −0.126919 | ||||||||
\(705\) | 0.343480 | + | 3.82531i | 0.0129362 | + | 0.144069i | ||||
\(706\) | −27.0481 | −1.01797 | ||||||||
\(707\) | − | 8.60162i | − | 0.323497i | ||||||
\(708\) | 10.7002i | 0.402138i | ||||||||
\(709\) | −43.6935 | −1.64094 | −0.820471 | − | 0.571688i | \(-0.806289\pi\) | ||||
−0.820471 | + | 0.571688i | \(0.806289\pi\) | |||||||
\(710\) | 12.2606 | − | 1.10090i | 0.460132 | − | 0.0413159i | ||||
\(711\) | −6.67029 | −0.250155 | ||||||||
\(712\) | − | 16.9421i | − | 0.634933i | ||||||
\(713\) | − | 13.8075i | − | 0.517093i | ||||||
\(714\) | −1.59281 | −0.0596094 | ||||||||
\(715\) | −15.5374 | + | 1.39512i | −0.581065 | + | 0.0521746i | ||||
\(716\) | −6.36106 | −0.237724 | ||||||||
\(717\) | − | 15.6157i | − | 0.583178i | ||||||
\(718\) | − | 29.0029i | − | 1.08238i | ||||||
\(719\) | 32.3812 | 1.20761 | 0.603807 | − | 0.797130i | \(-0.293650\pi\) | ||||
0.603807 | + | 0.797130i | \(0.293650\pi\) | |||||||
\(720\) | 0.125884 | + | 1.40196i | 0.00469142 | + | 0.0522480i | ||||
\(721\) | −4.50360 | −0.167723 | ||||||||
\(722\) | 19.9010i | 0.740640i | ||||||||
\(723\) | − | 23.5767i | − | 0.876825i | ||||||
\(724\) | 27.6622 | 1.02806 | ||||||||
\(725\) | −32.3752 | + | 5.86128i | −1.20238 | + | 0.217682i | ||||
\(726\) | 0.792050 | 0.0293957 | ||||||||
\(727\) | − | 0.0109599i | − | 0.000406481i | −1.00000 | 0.000203240i | \(-0.999935\pi\) | |||
1.00000 | 0.000203240i | \(-6.46934e-5\pi\) | ||||||||
\(728\) | − | 18.6364i | − | 0.690710i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −1.54182 | − | 17.1711i | −0.0570651 | − | 0.635531i | ||||
\(731\) | 10.8263 | 0.400424 | ||||||||
\(732\) | 3.04592i | 0.112580i | ||||||||
\(733\) | − | 42.6165i | − | 1.57408i | −0.616903 | − | 0.787039i | \(-0.711613\pi\) | ||
0.616903 | − | 0.787039i | \(-0.288387\pi\) | |||||||
\(734\) | 23.0716 | 0.851589 | ||||||||
\(735\) | 2.22711 | − | 0.199975i | 0.0821481 | − | 0.00737619i | ||||
\(736\) | −12.0088 | −0.442651 | ||||||||
\(737\) | − | 2.45990i | − | 0.0906118i | ||||||
\(738\) | − | 8.38713i | − | 0.308734i | ||||||
\(739\) | −13.4478 | −0.494685 | −0.247343 | − | 0.968928i | \(-0.579557\pi\) | ||||
−0.247343 | + | 0.968928i | \(0.579557\pi\) | |||||||
\(740\) | −13.8768 | + | 1.24601i | −0.510121 | + | 0.0458044i | ||||
\(741\) | 46.3429 | 1.70245 | ||||||||
\(742\) | − | 4.29738i | − | 0.157762i | ||||||
\(743\) | − | 31.3424i | − | 1.14984i | −0.818209 | − | 0.574921i | \(-0.805033\pi\) | ||
0.818209 | − | 0.574921i | \(-0.194967\pi\) | |||||||
\(744\) | −17.9408 | −0.657741 | ||||||||
\(745\) | −1.25578 | − | 13.9855i | −0.0460082 | − | 0.512390i | ||||
\(746\) | −0.140937 | −0.00516006 | ||||||||
\(747\) | 4.69895i | 0.171926i | ||||||||
\(748\) | − | 2.76041i | − | 0.100930i | ||||||
\(749\) | −2.90533 | −0.106158 | ||||||||
\(750\) | 2.35052 | + | 8.53774i | 0.0858288 | + | 0.311754i | ||||
\(751\) | −43.3436 | −1.58163 | −0.790816 | − | 0.612054i | \(-0.790343\pi\) | ||||
−0.790816 | + | 0.612054i | \(0.790343\pi\) | |||||||
\(752\) | − | 1.08123i | − | 0.0394286i | ||||||
\(753\) | − | 20.6569i | − | 0.752778i | ||||||
\(754\) | 36.3609 | 1.32418 | ||||||||
\(755\) | −3.00698 | − | 33.4886i | −0.109435 | − | 1.21877i | ||||
\(756\) | 1.37266 | 0.0499230 | ||||||||
\(757\) | − | 37.9384i | − | 1.37890i | −0.724336 | − | 0.689448i | \(-0.757853\pi\) | ||
0.724336 | − | 0.689448i | \(-0.242147\pi\) | |||||||
\(758\) | − | 0.0559984i | − | 0.00203395i | ||||||
\(759\) | 2.05588 | 0.0746236 | ||||||||
\(760\) | −39.5197 | + | 3.54852i | −1.43353 | + | 0.128719i | ||||
\(761\) | −26.3508 | −0.955215 | −0.477607 | − | 0.878573i | \(-0.658496\pi\) | ||||
−0.477607 | + | 0.878573i | \(0.658496\pi\) | |||||||
\(762\) | − | 11.2484i | − | 0.407488i | ||||||
\(763\) | − | 20.5935i | − | 0.745536i | ||||||
\(764\) | −23.4688 | −0.849073 | ||||||||
\(765\) | 4.47871 | − | 0.402149i | 0.161928 | − | 0.0145397i | ||||
\(766\) | −1.78519 | −0.0645014 | ||||||||
\(767\) | 54.3833i | 1.96367i | ||||||||
\(768\) | 13.8756i | 0.500691i | ||||||||
\(769\) | −13.3491 | −0.481381 | −0.240690 | − | 0.970602i | \(-0.577374\pi\) | ||||
−0.240690 | + | 0.970602i | \(0.577374\pi\) | |||||||
\(770\) | −0.158390 | − | 1.76398i | −0.00570799 | − | 0.0635695i | ||||
\(771\) | 0.652452 | 0.0234975 | ||||||||
\(772\) | 10.5180i | 0.378552i | ||||||||
\(773\) | 4.65893i | 0.167570i | 0.996484 | + | 0.0837851i | \(0.0267009\pi\) | ||||
−0.996484 | + | 0.0837851i | \(0.973299\pi\) | |||||||
\(774\) | 4.26403 | 0.153267 | ||||||||
\(775\) | 33.0433 | − | 5.98224i | 1.18695 | − | 0.214888i | ||||
\(776\) | −40.2182 | −1.44375 | ||||||||
\(777\) | 4.53927i | 0.162845i | ||||||||
\(778\) | 0.143595i | 0.00514813i | ||||||||
\(779\) | −70.3409 | −2.52022 | ||||||||
\(780\) | 1.91502 | + | 21.3275i | 0.0685688 | + | 0.763646i | ||||
\(781\) | 6.95053 | 0.248710 | ||||||||
\(782\) | 3.27462i | 0.117100i | ||||||||
\(783\) | 6.58029i | 0.235161i | ||||||||
\(784\) | −0.629499 | −0.0224821 | ||||||||
\(785\) | −2.24038 | + | 0.201167i | −0.0799628 | + | 0.00717997i | ||||
\(786\) | 13.2610 | 0.473005 | ||||||||
\(787\) | 18.0636i | 0.643897i | 0.946757 | + | 0.321948i | \(0.104338\pi\) | ||||
−0.946757 | + | 0.321948i | \(0.895662\pi\) | |||||||
\(788\) | 16.6309i | 0.592452i | ||||||||
\(789\) | 25.3131 | 0.901170 | ||||||||
\(790\) | 11.7663 | − | 1.05651i | 0.418625 | − | 0.0375889i | ||||
\(791\) | −17.8285 | −0.633908 | ||||||||
\(792\) | − | 2.67131i | − | 0.0949210i | ||||||
\(793\) | 15.4808i | 0.549738i | ||||||||
\(794\) | −7.71283 | −0.273718 | ||||||||
\(795\) | 1.08499 | + | 12.0835i | 0.0384807 | + | 0.428557i | ||||
\(796\) | −20.3959 | −0.722913 | ||||||||
\(797\) | 30.8679i | 1.09340i | 0.837330 | + | 0.546698i | \(0.184115\pi\) | ||||
−0.837330 | + | 0.546698i | \(0.815885\pi\) | |||||||
\(798\) | 5.26138i | 0.186251i | ||||||||
\(799\) | −3.45411 | −0.122198 | ||||||||
\(800\) | −5.20296 | − | 28.7389i | −0.183953 | − | 1.01607i | ||||
\(801\) | 6.34225 | 0.224092 | ||||||||
\(802\) | − | 8.47519i | − | 0.299269i | ||||||
\(803\) | − | 9.73428i | − | 0.343515i | ||||||
\(804\) | −3.37660 | −0.119084 | ||||||||
\(805\) | −0.411124 | − | 4.57866i | −0.0144902 | − | 0.161376i | ||||
\(806\) | −37.1113 | −1.30719 | ||||||||
\(807\) | 4.53171i | 0.159524i | ||||||||
\(808\) | 22.9776i | 0.808350i | ||||||||
\(809\) | −3.33569 | −0.117276 | −0.0586382 | − | 0.998279i | \(-0.518676\pi\) | ||||
−0.0586382 | + | 0.998279i | \(0.518676\pi\) | |||||||
\(810\) | 1.76398 | − | 0.158390i | 0.0619800 | − | 0.00556527i | ||||
\(811\) | −28.9946 | −1.01814 | −0.509068 | − | 0.860726i | \(-0.670010\pi\) | ||||
−0.509068 | + | 0.860726i | \(0.670010\pi\) | |||||||
\(812\) | − | 9.03248i | − | 0.316978i | ||||||
\(813\) | 13.1341i | 0.460634i | ||||||||
\(814\) | 3.59533 | 0.126016 | ||||||||
\(815\) | −16.0093 | + | 1.43749i | −0.560780 | + | 0.0503532i | ||||
\(816\) | −1.26592 | −0.0443160 | ||||||||
\(817\) | − | 35.7614i | − | 1.25113i | ||||||
\(818\) | − | 24.6712i | − | 0.862609i | ||||||
\(819\) | 6.97648 | 0.243778 | ||||||||
\(820\) | −2.90669 | − | 32.3716i | −0.101506 | − | 1.13046i | ||||
\(821\) | −5.47236 | −0.190987 | −0.0954934 | − | 0.995430i | \(-0.530443\pi\) | ||||
−0.0954934 | + | 0.995430i | \(0.530443\pi\) | |||||||
\(822\) | 13.0629i | 0.455622i | ||||||||
\(823\) | 8.28403i | 0.288763i | 0.989522 | + | 0.144382i | \(0.0461193\pi\) | ||||
−0.989522 | + | 0.144382i | \(0.953881\pi\) | |||||||
\(824\) | 12.0305 | 0.419103 | ||||||||
\(825\) | 0.890732 | + | 4.92002i | 0.0310113 | + | 0.171293i | ||||
\(826\) | −6.17422 | −0.214829 | ||||||||
\(827\) | − | 18.6467i | − | 0.648409i | −0.945987 | − | 0.324204i | \(-0.894903\pi\) | ||
0.945987 | − | 0.324204i | \(-0.105097\pi\) | |||||||
\(828\) | − | 2.82201i | − | 0.0980717i | ||||||
\(829\) | −20.1059 | −0.698307 | −0.349153 | − | 0.937066i | \(-0.613531\pi\) | ||||
−0.349153 | + | 0.937066i | \(0.613531\pi\) | |||||||
\(830\) | −0.744268 | − | 8.28886i | −0.0258339 | − | 0.287711i | ||||
\(831\) | −25.2114 | −0.874574 | ||||||||
\(832\) | 23.4936i | 0.814494i | ||||||||
\(833\) | 2.01100i | 0.0696769i | ||||||||
\(834\) | −1.30702 | −0.0452585 | ||||||||
\(835\) | 56.4611 | − | 5.06972i | 1.95392 | − | 0.175445i | ||||
\(836\) | −9.11820 | −0.315359 | ||||||||
\(837\) | − | 6.71609i | − | 0.232142i | ||||||
\(838\) | 19.9820i | 0.690267i | ||||||||
\(839\) | −8.85969 | −0.305871 | −0.152935 | − | 0.988236i | \(-0.548873\pi\) | ||||
−0.152935 | + | 0.988236i | \(0.548873\pi\) | |||||||
\(840\) | −5.94930 | + | 0.534196i | −0.205270 | + | 0.0184315i | ||||
\(841\) | 14.3003 | 0.493113 | ||||||||
\(842\) | 7.20452i | 0.248284i | ||||||||
\(843\) | 11.6960i | 0.402832i | ||||||||
\(844\) | 7.68009 | 0.264360 | ||||||||
\(845\) | 7.13336 | + | 79.4437i | 0.245395 | + | 2.73295i | ||||
\(846\) | −1.36044 | −0.0467727 | ||||||||
\(847\) | − | 1.00000i | − | 0.0343604i | ||||||
\(848\) | − | 3.41543i | − | 0.117286i | ||||||
\(849\) | 18.7140 | 0.642263 | ||||||||
\(850\) | −7.83666 | + | 1.41877i | −0.268795 | + | 0.0486633i | ||||
\(851\) | 9.33217 | 0.319903 | ||||||||
\(852\) | − | 9.54069i | − | 0.326859i | ||||||
\(853\) | − | 1.18696i | − | 0.0406409i | −0.999794 | − | 0.0203204i | \(-0.993531\pi\) | ||
0.999794 | − | 0.0203204i | \(-0.00646864\pi\) | |||||||
\(854\) | −1.75756 | −0.0601423 | ||||||||
\(855\) | −1.32838 | − | 14.7941i | −0.0454297 | − | 0.505947i | ||||
\(856\) | 7.76103 | 0.265267 | ||||||||
\(857\) | − | 42.4639i | − | 1.45054i | −0.688466 | − | 0.725269i | \(-0.741715\pi\) | ||
0.688466 | − | 0.725269i | \(-0.258285\pi\) | |||||||
\(858\) | − | 5.52572i | − | 0.188645i | ||||||
\(859\) | 7.06518 | 0.241061 | 0.120530 | − | 0.992710i | \(-0.461540\pi\) | ||||
0.120530 | + | 0.992710i | \(0.461540\pi\) | |||||||
\(860\) | 16.4578 | − | 1.47777i | 0.561205 | − | 0.0503914i | ||||
\(861\) | −10.5891 | −0.360877 | ||||||||
\(862\) | 22.1876i | 0.755711i | ||||||||
\(863\) | 44.1199i | 1.50186i | 0.660382 | + | 0.750930i | \(0.270395\pi\) | ||||
−0.660382 | + | 0.750930i | \(0.729605\pi\) | |||||||
\(864\) | −5.84122 | −0.198722 | ||||||||
\(865\) | 52.6321 | − | 4.72591i | 1.78954 | − | 0.160686i | ||||
\(866\) | −15.2452 | −0.518053 | ||||||||
\(867\) | − | 12.9559i | − | 0.440005i | ||||||
\(868\) | 9.21889i | 0.312909i | ||||||||
\(869\) | 6.67029 | 0.226274 | ||||||||
\(870\) | −1.04225 | − | 11.6075i | −0.0353357 | − | 0.393532i | ||||
\(871\) | −17.1615 | −0.581494 | ||||||||
\(872\) | 55.0118i | 1.86293i | ||||||||
\(873\) | − | 15.0556i | − | 0.509554i | ||||||
\(874\) | 10.8167 | 0.365882 | ||||||||
\(875\) | 10.7793 | − | 2.96764i | 0.364407 | − | 0.100324i | ||||
\(876\) | −13.3618 | −0.451454 | ||||||||
\(877\) | 16.2216i | 0.547763i | 0.961763 | + | 0.273882i | \(0.0883077\pi\) | ||||
−0.961763 | + | 0.273882i | \(0.911692\pi\) | |||||||
\(878\) | − | 25.1968i | − | 0.850350i | ||||||
\(879\) | −18.1044 | −0.610647 | ||||||||
\(880\) | −0.125884 | − | 1.40196i | −0.00424355 | − | 0.0472601i | ||||
\(881\) | −36.1694 | −1.21858 | −0.609290 | − | 0.792948i | \(-0.708545\pi\) | ||||
−0.609290 | + | 0.792948i | \(0.708545\pi\) | |||||||
\(882\) | 0.792050i | 0.0266697i | ||||||||
\(883\) | − | 13.0357i | − | 0.438685i | −0.975648 | − | 0.219343i | \(-0.929609\pi\) | ||
0.975648 | − | 0.219343i | \(-0.0703912\pi\) | |||||||
\(884\) | −19.2579 | −0.647714 | ||||||||
\(885\) | 17.3608 | − | 1.55885i | 0.583578 | − | 0.0524003i | ||||
\(886\) | 3.66960 | 0.123283 | ||||||||
\(887\) | − | 35.7631i | − | 1.20081i | −0.799697 | − | 0.600403i | \(-0.795007\pi\) | ||
0.799697 | − | 0.600403i | \(-0.204993\pi\) | |||||||
\(888\) | − | 12.1258i | − | 0.406915i | ||||||
\(889\) | −14.2017 | −0.476309 | ||||||||
\(890\) | −11.1876 | + | 1.00455i | −0.375009 | + | 0.0336726i | ||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 20.4924i | 0.686137i | ||||||||
\(893\) | 11.4097i | 0.381809i | ||||||||
\(894\) | 4.97383 | 0.166350 | ||||||||
\(895\) | 0.926710 | + | 10.3207i | 0.0309765 | + | 0.344983i | ||||
\(896\) | 9.01518 | 0.301176 | ||||||||
\(897\) | − | 14.3428i | − | 0.478891i | ||||||
\(898\) | − | 23.1994i | − | 0.774174i | ||||||
\(899\) | −44.1939 | −1.47395 | ||||||||
\(900\) | 6.75350 | − | 1.22267i | 0.225117 | − | 0.0407556i | ||||
\(901\) | −10.9109 | −0.363496 | ||||||||
\(902\) | 8.38713i | 0.279261i | ||||||||
\(903\) | − | 5.38354i | − | 0.179153i | ||||||
\(904\) | 47.6254 | 1.58400 | ||||||||
\(905\) | −4.02995 | − | 44.8813i | −0.133960 | − | 1.49191i | ||||
\(906\) | 11.9099 | 0.395680 | ||||||||
\(907\) | − | 9.68421i | − | 0.321559i | −0.986990 | − | 0.160779i | \(-0.948599\pi\) | ||
0.986990 | − | 0.160779i | \(-0.0514008\pi\) | |||||||
\(908\) | 17.1134i | 0.567927i | ||||||||
\(909\) | −8.60162 | −0.285298 | ||||||||
\(910\) | −12.3064 | + | 1.10501i | −0.407953 | + | 0.0366306i | ||||
\(911\) | −12.9132 | −0.427835 | −0.213917 | − | 0.976852i | \(-0.568622\pi\) | ||||
−0.213917 | + | 0.976852i | \(0.568622\pi\) | |||||||
\(912\) | 4.18159i | 0.138466i | ||||||||
\(913\) | − | 4.69895i | − | 0.155513i | ||||||
\(914\) | 24.6708 | 0.816038 | ||||||||
\(915\) | 4.94194 | − | 0.443744i | 0.163376 | − | 0.0146697i | ||||
\(916\) | −15.5670 | −0.514348 | ||||||||
\(917\) | − | 16.7427i | − | 0.552891i | ||||||
\(918\) | 1.59281i | 0.0525706i | ||||||||
\(919\) | 20.4704 | 0.675256 | 0.337628 | − | 0.941280i | \(-0.390375\pi\) | ||||
0.337628 | + | 0.941280i | \(0.390375\pi\) | |||||||
\(920\) | 1.09824 | + | 12.2310i | 0.0362079 | + | 0.403245i | ||||
\(921\) | 11.2076 | 0.369303 | ||||||||
\(922\) | 4.01790i | 0.132323i | ||||||||
\(923\) | − | 48.4902i | − | 1.59608i | ||||||
\(924\) | −1.37266 | −0.0451571 | ||||||||
\(925\) | 4.04327 | + | 22.3333i | 0.132942 | + | 0.734314i | ||||
\(926\) | −21.0768 | −0.692627 | ||||||||
\(927\) | 4.50360i | 0.147918i | ||||||||
\(928\) | 38.4370i | 1.26175i | ||||||||
\(929\) | −18.7464 | −0.615048 | −0.307524 | − | 0.951540i | \(-0.599500\pi\) | ||||
−0.307524 | + | 0.951540i | \(0.599500\pi\) | |||||||
\(930\) | 1.06376 | + | 11.8471i | 0.0348822 | + | 0.388481i | ||||
\(931\) | 6.64274 | 0.217707 | ||||||||
\(932\) | − | 21.1735i | − | 0.693561i | ||||||
\(933\) | − | 16.2770i | − | 0.532884i | ||||||
\(934\) | 11.3110 | 0.370106 | ||||||||
\(935\) | −4.47871 | + | 0.402149i | −0.146469 | + | 0.0131517i | ||||
\(936\) | −18.6364 | −0.609149 | ||||||||
\(937\) | − | 47.9357i | − | 1.56599i | −0.622027 | − | 0.782996i | \(-0.713690\pi\) | ||
0.622027 | − | 0.782996i | \(-0.286310\pi\) | |||||||
\(938\) | − | 1.94837i | − | 0.0636165i | ||||||
\(939\) | 3.97432 | 0.129697 | ||||||||
\(940\) | −5.25084 | + | 0.471480i | −0.171263 | + | 0.0153780i | ||||
\(941\) | −40.2901 | −1.31342 | −0.656709 | − | 0.754144i | \(-0.728052\pi\) | ||||
−0.656709 | + | 0.754144i | \(0.728052\pi\) | |||||||
\(942\) | − | 0.796772i | − | 0.0259602i | ||||||
\(943\) | 21.7699i | 0.708927i | ||||||||
\(944\) | −4.90709 | −0.159712 | ||||||||
\(945\) | −0.199975 | − | 2.22711i | −0.00650519 | − | 0.0724478i | ||||
\(946\) | −4.26403 | −0.138636 | ||||||||
\(947\) | − | 3.95361i | − | 0.128475i | −0.997935 | − | 0.0642375i | \(-0.979538\pi\) | ||
0.997935 | − | 0.0642375i | \(-0.0204615\pi\) | |||||||
\(948\) | − | 9.15601i | − | 0.297374i | ||||||
\(949\) | −67.9110 | −2.20448 | ||||||||
\(950\) | 4.68648 | + | 25.8861i | 0.152050 | + | 0.839856i | ||||
\(951\) | 0.264616 | 0.00858076 | ||||||||
\(952\) | − | 5.37200i | − | 0.174108i | ||||||
\(953\) | − | 11.1167i | − | 0.360106i | −0.983657 | − | 0.180053i | \(-0.942373\pi\) | ||
0.983657 | − | 0.180053i | \(-0.0576269\pi\) | |||||||
\(954\) | −4.29738 | −0.139133 | ||||||||
\(955\) | 3.41905 | + | 38.0777i | 0.110638 | + | 1.23217i | ||||
\(956\) | 21.4350 | 0.693256 | ||||||||
\(957\) | − | 6.58029i | − | 0.212711i | ||||||
\(958\) | − | 14.9387i | − | 0.482648i | ||||||
\(959\) | 16.4926 | 0.532572 | ||||||||
\(960\) | 7.49988 | − | 0.673425i | 0.242058 | − | 0.0217347i | ||||
\(961\) | 14.1059 | 0.455029 | ||||||||
\(962\) | − | 25.0827i | − | 0.808699i | ||||||
\(963\) | 2.90533i | 0.0936228i | ||||||||
\(964\) | 32.3627 | 1.04233 | ||||||||
\(965\) | 17.0653 | − | 1.53231i | 0.549351 | − | 0.0493269i | ||||
\(966\) | 1.62836 | 0.0523915 | ||||||||
\(967\) | 23.7486i | 0.763702i | 0.924224 | + | 0.381851i | \(0.124713\pi\) | ||||
−0.924224 | + | 0.381851i | \(0.875287\pi\) | |||||||
\(968\) | 2.67131i | 0.0858593i | ||||||||
\(969\) | 13.3585 | 0.429138 | ||||||||
\(970\) | 2.38466 | + | 26.5578i | 0.0765667 | + | 0.852718i | ||||
\(971\) | −6.78652 | −0.217790 | −0.108895 | − | 0.994053i | \(-0.534731\pi\) | ||||
−0.108895 | + | 0.994053i | \(0.534731\pi\) | |||||||
\(972\) | − | 1.37266i | − | 0.0440280i | ||||||
\(973\) | 1.65018i | 0.0529023i | ||||||||
\(974\) | 31.3287 | 1.00384 | ||||||||
\(975\) | 34.3244 | − | 6.21417i | 1.09926 | − | 0.199013i | ||||
\(976\) | −1.39685 | −0.0447122 | ||||||||
\(977\) | − | 3.56837i | − | 0.114162i | −0.998370 | − | 0.0570812i | \(-0.981821\pi\) | ||
0.998370 | − | 0.0570812i | \(-0.0181794\pi\) | |||||||
\(978\) | − | 5.69355i | − | 0.182059i | ||||||
\(979\) | −6.34225 | −0.202699 | ||||||||
\(980\) | 0.274497 | + | 3.05705i | 0.00876849 | + | 0.0976540i | ||||
\(981\) | −20.5935 | −0.657501 | ||||||||
\(982\) | − | 7.54596i | − | 0.240801i | ||||||
\(983\) | − | 14.5740i | − | 0.464837i | −0.972616 | − | 0.232419i | \(-0.925336\pi\) | ||
0.972616 | − | 0.232419i | \(-0.0746639\pi\) | |||||||
\(984\) | 28.2869 | 0.901753 | ||||||||
\(985\) | 26.9833 | − | 2.42287i | 0.859761 | − | 0.0771991i | ||||
\(986\) | 10.4812 | 0.333788 | ||||||||
\(987\) | 1.71761i | 0.0546722i | ||||||||
\(988\) | 63.6129i | 2.02380i | ||||||||
\(989\) | −11.0679 | −0.351938 | ||||||||
\(990\) | −1.76398 | + | 0.158390i | −0.0560630 | + | 0.00503397i | ||||
\(991\) | −29.1681 | −0.926555 | −0.463277 | − | 0.886213i | \(-0.653327\pi\) | ||||
−0.463277 | + | 0.886213i | \(0.653327\pi\) | |||||||
\(992\) | − | 39.2302i | − | 1.24556i | ||||||
\(993\) | 7.36413i | 0.233693i | ||||||||
\(994\) | 5.50517 | 0.174613 | ||||||||
\(995\) | 2.97137 | + | 33.0919i | 0.0941987 | + | 1.04908i | ||||
\(996\) | −6.45004 | −0.204377 | ||||||||
\(997\) | 58.0260i | 1.83770i | 0.394605 | + | 0.918851i | \(0.370881\pi\) | ||||
−0.394605 | + | 0.918851i | \(0.629119\pi\) | |||||||
\(998\) | 11.3269i | 0.358546i | ||||||||
\(999\) | 4.53927 | 0.143616 |
(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 | 1155.2.c.f.694.13 | yes | 20 | |
5.2 | odd | 4 | 5775.2.a.cn.1.5 | 10 | |||
5.3 | odd | 4 | 5775.2.a.co.1.6 | 10 | |||
5.4 | even | 2 | inner | 1155.2.c.f.694.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.f.694.8 | ✓ | 20 | 5.4 | even | 2 | inner | |
1155.2.c.f.694.13 | yes | 20 | 1.1 | even | 1 | trivial | |
5775.2.a.cn.1.5 | 10 | 5.2 | odd | 4 | |||
5775.2.a.co.1.6 | 10 | 5.3 | odd | 4 |