Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1122,2,Mod(1055,1122)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1122, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1122.1055");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1122.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.95921510679\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 18x^{14} + 124x^{12} + 420x^{10} + 746x^{8} + 681x^{6} + 288x^{4} + 42x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1055.5 | ||
Root | \(0.886946i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1122.1055 |
Dual form | 1122.2.b.c.1055.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times\).
\(n\) | \(409\) | \(749\) | \(1057\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.423385 | − | 1.67951i | −0.244441 | − | 0.969664i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 4.07146i | 1.82081i | 0.413715 | + | 0.910407i | \(0.364231\pi\) | ||||
−0.413715 | + | 0.910407i | \(0.635769\pi\) | |||||||
\(6\) | −0.423385 | − | 1.67951i | −0.172846 | − | 0.685656i | ||||
\(7\) | − | 4.79476i | − | 1.81225i | −0.423013 | − | 0.906124i | \(-0.639027\pi\) | ||
0.423013 | − | 0.906124i | \(-0.360973\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.64149 | + | 1.42216i | −0.880497 | + | 0.474052i | ||||
\(10\) | 4.07146i | 1.28751i | ||||||||
\(11\) | −2.78151 | − | 1.80643i | −0.838657 | − | 0.544660i | ||||
\(12\) | −0.423385 | − | 1.67951i | −0.122221 | − | 0.484832i | ||||
\(13\) | − | 2.57431i | − | 0.713986i | −0.934107 | − | 0.356993i | \(-0.883802\pi\) | ||
0.934107 | − | 0.356993i | \(-0.116198\pi\) | |||||||
\(14\) | − | 4.79476i | − | 1.28145i | ||||||
\(15\) | 6.83805 | − | 1.72380i | 1.76558 | − | 0.445082i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.64149 | + | 1.42216i | −0.622605 | + | 0.335206i | ||||
\(19\) | − | 4.54838i | − | 1.04347i | −0.853108 | − | 0.521735i | \(-0.825285\pi\) | ||
0.853108 | − | 0.521735i | \(-0.174715\pi\) | |||||||
\(20\) | 4.07146i | 0.910407i | ||||||||
\(21\) | −8.05283 | + | 2.03003i | −1.75727 | + | 0.442988i | ||||
\(22\) | −2.78151 | − | 1.80643i | −0.593020 | − | 0.385133i | ||||
\(23\) | − | 5.62472i | − | 1.17283i | −0.810009 | − | 0.586417i | \(-0.800538\pi\) | ||
0.810009 | − | 0.586417i | \(-0.199462\pi\) | |||||||
\(24\) | −0.423385 | − | 1.67951i | −0.0864231 | − | 0.342828i | ||||
\(25\) | −11.5768 | −2.31536 | ||||||||
\(26\) | − | 2.57431i | − | 0.504864i | ||||||
\(27\) | 3.50689 | + | 3.83428i | 0.674901 | + | 0.737908i | ||||
\(28\) | − | 4.79476i | − | 0.906124i | ||||||
\(29\) | 7.91832 | 1.47040 | 0.735198 | − | 0.677853i | \(-0.237089\pi\) | ||||
0.735198 | + | 0.677853i | \(0.237089\pi\) | |||||||
\(30\) | 6.83805 | − | 1.72380i | 1.24845 | − | 0.314721i | ||||
\(31\) | −0.355300 | −0.0638137 | −0.0319069 | − | 0.999491i | \(-0.510158\pi\) | ||||
−0.0319069 | + | 0.999491i | \(0.510158\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.85627 | + | 5.43638i | −0.323135 | + | 0.946353i | ||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | 19.5217 | 3.29976 | ||||||||
\(36\) | −2.64149 | + | 1.42216i | −0.440248 | + | 0.237026i | ||||
\(37\) | 5.35573 | 0.880477 | 0.440239 | − | 0.897881i | \(-0.354894\pi\) | ||||
0.440239 | + | 0.897881i | \(0.354894\pi\) | |||||||
\(38\) | − | 4.54838i | − | 0.737844i | ||||||
\(39\) | −4.32358 | + | 1.08993i | −0.692326 | + | 0.174528i | ||||
\(40\) | 4.07146i | 0.643755i | ||||||||
\(41\) | 1.52886 | 0.238767 | 0.119384 | − | 0.992848i | \(-0.461908\pi\) | ||||
0.119384 | + | 0.992848i | \(0.461908\pi\) | |||||||
\(42\) | −8.05283 | + | 2.03003i | −1.24258 | + | 0.313240i | ||||
\(43\) | − | 4.45168i | − | 0.678874i | −0.940629 | − | 0.339437i | \(-0.889763\pi\) | ||
0.940629 | − | 0.339437i | \(-0.110237\pi\) | |||||||
\(44\) | −2.78151 | − | 1.80643i | −0.419328 | − | 0.272330i | ||||
\(45\) | −5.79026 | − | 10.7547i | −0.863160 | − | 1.60322i | ||||
\(46\) | − | 5.62472i | − | 0.829319i | ||||||
\(47\) | − | 9.23503i | − | 1.34707i | −0.739157 | − | 0.673534i | \(-0.764776\pi\) | ||
0.739157 | − | 0.673534i | \(-0.235224\pi\) | |||||||
\(48\) | −0.423385 | − | 1.67951i | −0.0611104 | − | 0.242416i | ||||
\(49\) | −15.9897 | −2.28424 | ||||||||
\(50\) | −11.5768 | −1.63721 | ||||||||
\(51\) | 0.423385 | + | 1.67951i | 0.0592858 | + | 0.235178i | ||||
\(52\) | − | 2.57431i | − | 0.356993i | ||||||
\(53\) | − | 9.72335i | − | 1.33560i | −0.744339 | − | 0.667802i | \(-0.767235\pi\) | ||
0.744339 | − | 0.667802i | \(-0.232765\pi\) | |||||||
\(54\) | 3.50689 | + | 3.83428i | 0.477227 | + | 0.521780i | ||||
\(55\) | 7.35482 | − | 11.3248i | 0.991724 | − | 1.52704i | ||||
\(56\) | − | 4.79476i | − | 0.640726i | ||||||
\(57\) | −7.63903 | + | 1.92571i | −1.01181 | + | 0.255067i | ||||
\(58\) | 7.91832 | 1.03973 | ||||||||
\(59\) | 11.6299i | 1.51408i | 0.653366 | + | 0.757042i | \(0.273356\pi\) | ||||
−0.653366 | + | 0.757042i | \(0.726644\pi\) | |||||||
\(60\) | 6.83805 | − | 1.72380i | 0.882788 | − | 0.222541i | ||||
\(61\) | 4.09863i | 0.524776i | 0.964962 | + | 0.262388i | \(0.0845100\pi\) | ||||
−0.964962 | + | 0.262388i | \(0.915490\pi\) | |||||||
\(62\) | −0.355300 | −0.0451231 | ||||||||
\(63\) | 6.81889 | + | 12.6653i | 0.859100 | + | 1.59568i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.4812 | 1.30003 | ||||||||
\(66\) | −1.85627 | + | 5.43638i | −0.228491 | + | 0.669173i | ||||
\(67\) | −5.11830 | −0.625299 | −0.312650 | − | 0.949868i | \(-0.601217\pi\) | ||||
−0.312650 | + | 0.949868i | \(0.601217\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −9.44676 | + | 2.38142i | −1.13726 | + | 0.286689i | ||||
\(70\) | 19.5217 | 2.33329 | ||||||||
\(71\) | 7.91292i | 0.939091i | 0.882908 | + | 0.469546i | \(0.155582\pi\) | ||||
−0.882908 | + | 0.469546i | \(0.844418\pi\) | |||||||
\(72\) | −2.64149 | + | 1.42216i | −0.311303 | + | 0.167603i | ||||
\(73\) | − | 4.26429i | − | 0.499097i | −0.968362 | − | 0.249549i | \(-0.919718\pi\) | ||
0.968362 | − | 0.249549i | \(-0.0802823\pi\) | |||||||
\(74\) | 5.35573 | 0.622591 | ||||||||
\(75\) | 4.90144 | + | 19.4433i | 0.565970 | + | 2.24512i | ||||
\(76\) | − | 4.54838i | − | 0.521735i | ||||||
\(77\) | −8.66141 | + | 13.3367i | −0.987059 | + | 1.51985i | ||||
\(78\) | −4.32358 | + | 1.08993i | −0.489549 | + | 0.123410i | ||||
\(79\) | 9.05706i | 1.01900i | 0.860471 | + | 0.509500i | \(0.170169\pi\) | ||||
−0.860471 | + | 0.509500i | \(0.829831\pi\) | |||||||
\(80\) | 4.07146i | 0.455203i | ||||||||
\(81\) | 4.95494 | − | 7.51323i | 0.550549 | − | 0.834803i | ||||
\(82\) | 1.52886 | 0.168834 | ||||||||
\(83\) | −7.26631 | −0.797581 | −0.398791 | − | 0.917042i | \(-0.630570\pi\) | ||||
−0.398791 | + | 0.917042i | \(0.630570\pi\) | |||||||
\(84\) | −8.05283 | + | 2.03003i | −0.878636 | + | 0.221494i | ||||
\(85\) | − | 4.07146i | − | 0.441612i | ||||||
\(86\) | − | 4.45168i | − | 0.480037i | ||||||
\(87\) | −3.35250 | − | 13.2989i | −0.359426 | − | 1.42579i | ||||
\(88\) | −2.78151 | − | 1.80643i | −0.296510 | − | 0.192566i | ||||
\(89\) | 12.2301i | 1.29639i | 0.761473 | + | 0.648197i | \(0.224477\pi\) | ||||
−0.761473 | + | 0.648197i | \(0.775523\pi\) | |||||||
\(90\) | −5.79026 | − | 10.7547i | −0.610347 | − | 1.13365i | ||||
\(91\) | −12.3432 | −1.29392 | ||||||||
\(92\) | − | 5.62472i | − | 0.586417i | ||||||
\(93\) | 0.150429 | + | 0.596728i | 0.0155987 | + | 0.0618779i | ||||
\(94\) | − | 9.23503i | − | 0.952520i | ||||||
\(95\) | 18.5185 | 1.89996 | ||||||||
\(96\) | −0.423385 | − | 1.67951i | −0.0432116 | − | 0.171414i | ||||
\(97\) | 0.0605836 | 0.00615133 | 0.00307567 | − | 0.999995i | \(-0.499021\pi\) | ||||
0.00307567 | + | 0.999995i | \(0.499021\pi\) | |||||||
\(98\) | −15.9897 | −1.61520 | ||||||||
\(99\) | 9.91636 | + | 0.815933i | 0.996632 | + | 0.0820044i | ||||
\(100\) | −11.5768 | −1.15768 | ||||||||
\(101\) | −10.6605 | −1.06076 | −0.530380 | − | 0.847760i | \(-0.677951\pi\) | ||||
−0.530380 | + | 0.847760i | \(0.677951\pi\) | |||||||
\(102\) | 0.423385 | + | 1.67951i | 0.0419214 | + | 0.166296i | ||||
\(103\) | 1.38499 | 0.136467 | 0.0682334 | − | 0.997669i | \(-0.478264\pi\) | ||||
0.0682334 | + | 0.997669i | \(0.478264\pi\) | |||||||
\(104\) | − | 2.57431i | − | 0.252432i | ||||||
\(105\) | −8.26518 | − | 32.7868i | −0.806599 | − | 3.19966i | ||||
\(106\) | − | 9.72335i | − | 0.944415i | ||||||
\(107\) | −4.25253 | −0.411108 | −0.205554 | − | 0.978646i | \(-0.565900\pi\) | ||||
−0.205554 | + | 0.978646i | \(0.565900\pi\) | |||||||
\(108\) | 3.50689 | + | 3.83428i | 0.337451 | + | 0.368954i | ||||
\(109\) | 5.49088i | 0.525931i | 0.964805 | + | 0.262966i | \(0.0847005\pi\) | ||||
−0.964805 | + | 0.262966i | \(0.915299\pi\) | |||||||
\(110\) | 7.35482 | − | 11.3248i | 0.701255 | − | 1.07978i | ||||
\(111\) | −2.26754 | − | 8.99499i | −0.215225 | − | 0.853767i | ||||
\(112\) | − | 4.79476i | − | 0.453062i | ||||||
\(113\) | 17.3599i | 1.63308i | 0.577286 | + | 0.816542i | \(0.304112\pi\) | ||||
−0.577286 | + | 0.816542i | \(0.695888\pi\) | |||||||
\(114\) | −7.63903 | + | 1.92571i | −0.715461 | + | 0.180360i | ||||
\(115\) | 22.9008 | 2.13551 | ||||||||
\(116\) | 7.91832 | 0.735198 | ||||||||
\(117\) | 3.66108 | + | 6.80002i | 0.338467 | + | 0.628662i | ||||
\(118\) | 11.6299i | 1.07062i | ||||||||
\(119\) | 4.79476i | 0.439535i | ||||||||
\(120\) | 6.83805 | − | 1.72380i | 0.624226 | − | 0.157360i | ||||
\(121\) | 4.47360 | + | 10.0492i | 0.406691 | + | 0.913566i | ||||
\(122\) | 4.09863i | 0.371073i | ||||||||
\(123\) | −0.647295 | − | 2.56773i | −0.0583646 | − | 0.231524i | ||||
\(124\) | −0.355300 | −0.0319069 | ||||||||
\(125\) | − | 26.7772i | − | 2.39502i | ||||||
\(126\) | 6.81889 | + | 12.6653i | 0.607475 | + | 1.12831i | ||||
\(127\) | − | 3.35314i | − | 0.297543i | −0.988872 | − | 0.148772i | \(-0.952468\pi\) | ||
0.988872 | − | 0.148772i | \(-0.0475319\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −7.47662 | + | 1.88477i | −0.658280 | + | 0.165945i | ||||
\(130\) | 10.4812 | 0.919263 | ||||||||
\(131\) | 14.6947 | 1.28388 | 0.641939 | − | 0.766755i | \(-0.278130\pi\) | ||||
0.641939 | + | 0.766755i | \(0.278130\pi\) | |||||||
\(132\) | −1.85627 | + | 5.43638i | −0.161567 | + | 0.473176i | ||||
\(133\) | −21.8084 | −1.89102 | ||||||||
\(134\) | −5.11830 | −0.442153 | ||||||||
\(135\) | −15.6111 | + | 14.2782i | −1.34359 | + | 1.22887i | ||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | − | 21.6014i | − | 1.84553i | −0.385361 | − | 0.922766i | \(-0.625923\pi\) | ||
0.385361 | − | 0.922766i | \(-0.374077\pi\) | |||||||
\(138\) | −9.44676 | + | 2.38142i | −0.804161 | + | 0.202720i | ||||
\(139\) | − | 8.89537i | − | 0.754496i | −0.926112 | − | 0.377248i | \(-0.876870\pi\) | ||
0.926112 | − | 0.377248i | \(-0.123130\pi\) | |||||||
\(140\) | 19.5217 | 1.64988 | ||||||||
\(141\) | −15.5103 | + | 3.90997i | −1.30620 | + | 0.329279i | ||||
\(142\) | 7.91292i | 0.664038i | ||||||||
\(143\) | −4.65032 | + | 7.16048i | −0.388880 | + | 0.598789i | ||||
\(144\) | −2.64149 | + | 1.42216i | −0.220124 | + | 0.118513i | ||||
\(145\) | 32.2391i | 2.67731i | ||||||||
\(146\) | − | 4.26429i | − | 0.352915i | ||||||
\(147\) | 6.76979 | + | 26.8548i | 0.558363 | + | 2.21495i | ||||
\(148\) | 5.35573 | 0.440239 | ||||||||
\(149\) | 18.8204 | 1.54183 | 0.770914 | − | 0.636940i | \(-0.219800\pi\) | ||||
0.770914 | + | 0.636940i | \(0.219800\pi\) | |||||||
\(150\) | 4.90144 | + | 19.4433i | 0.400201 | + | 1.58754i | ||||
\(151\) | − | 16.6132i | − | 1.35196i | −0.736920 | − | 0.675980i | \(-0.763721\pi\) | ||
0.736920 | − | 0.675980i | \(-0.236279\pi\) | |||||||
\(152\) | − | 4.54838i | − | 0.368922i | ||||||
\(153\) | 2.64149 | − | 1.42216i | 0.213552 | − | 0.114975i | ||||
\(154\) | −8.66141 | + | 13.3367i | −0.697956 | + | 1.07470i | ||||
\(155\) | − | 1.44659i | − | 0.116193i | ||||||
\(156\) | −4.32358 | + | 1.08993i | −0.346163 | + | 0.0872639i | ||||
\(157\) | 13.0711 | 1.04318 | 0.521592 | − | 0.853195i | \(-0.325338\pi\) | ||||
0.521592 | + | 0.853195i | \(0.325338\pi\) | |||||||
\(158\) | 9.05706i | 0.720541i | ||||||||
\(159\) | −16.3304 | + | 4.11672i | −1.29509 | + | 0.326477i | ||||
\(160\) | 4.07146i | 0.321877i | ||||||||
\(161\) | −26.9692 | −2.12547 | ||||||||
\(162\) | 4.95494 | − | 7.51323i | 0.389297 | − | 0.590295i | ||||
\(163\) | 1.55929 | 0.122133 | 0.0610665 | − | 0.998134i | \(-0.480550\pi\) | ||||
0.0610665 | + | 0.998134i | \(0.480550\pi\) | |||||||
\(164\) | 1.52886 | 0.119384 | ||||||||
\(165\) | −22.1340 | − | 7.55773i | −1.72313 | − | 0.588368i | ||||
\(166\) | −7.26631 | −0.563975 | ||||||||
\(167\) | 2.47630 | 0.191622 | 0.0958111 | − | 0.995400i | \(-0.469456\pi\) | ||||
0.0958111 | + | 0.995400i | \(0.469456\pi\) | |||||||
\(168\) | −8.05283 | + | 2.03003i | −0.621289 | + | 0.156620i | ||||
\(169\) | 6.37292 | 0.490224 | ||||||||
\(170\) | − | 4.07146i | − | 0.312267i | ||||||
\(171\) | 6.46851 | + | 12.0145i | 0.494659 | + | 0.918771i | ||||
\(172\) | − | 4.45168i | − | 0.339437i | ||||||
\(173\) | 5.92606 | 0.450550 | 0.225275 | − | 0.974295i | \(-0.427672\pi\) | ||||
0.225275 | + | 0.974295i | \(0.427672\pi\) | |||||||
\(174\) | −3.35250 | − | 13.2989i | −0.254152 | − | 1.00819i | ||||
\(175\) | 55.5079i | 4.19601i | ||||||||
\(176\) | −2.78151 | − | 1.80643i | −0.209664 | − | 0.136165i | ||||
\(177\) | 19.5325 | − | 4.92393i | 1.46815 | − | 0.370105i | ||||
\(178\) | 12.2301i | 0.916688i | ||||||||
\(179\) | − | 7.57467i | − | 0.566158i | −0.959097 | − | 0.283079i | \(-0.908644\pi\) | ||
0.959097 | − | 0.283079i | \(-0.0913558\pi\) | |||||||
\(180\) | −5.79026 | − | 10.7547i | −0.431580 | − | 0.801610i | ||||
\(181\) | 2.71865 | 0.202076 | 0.101038 | − | 0.994883i | \(-0.467784\pi\) | ||||
0.101038 | + | 0.994883i | \(0.467784\pi\) | |||||||
\(182\) | −12.3432 | −0.914939 | ||||||||
\(183\) | 6.88368 | − | 1.73530i | 0.508856 | − | 0.128277i | ||||
\(184\) | − | 5.62472i | − | 0.414660i | ||||||
\(185\) | 21.8057i | 1.60318i | ||||||||
\(186\) | 0.150429 | + | 0.596728i | 0.0110300 | + | 0.0437542i | ||||
\(187\) | 2.78151 | + | 1.80643i | 0.203404 | + | 0.132099i | ||||
\(188\) | − | 9.23503i | − | 0.673534i | ||||||
\(189\) | 18.3844 | − | 16.8147i | 1.33727 | − | 1.22309i | ||||
\(190\) | 18.5185 | 1.34348 | ||||||||
\(191\) | 20.5365i | 1.48597i | 0.669310 | + | 0.742983i | \(0.266590\pi\) | ||||
−0.669310 | + | 0.742983i | \(0.733410\pi\) | |||||||
\(192\) | −0.423385 | − | 1.67951i | −0.0305552 | − | 0.121208i | ||||
\(193\) | 3.45941i | 0.249014i | 0.992219 | + | 0.124507i | \(0.0397349\pi\) | ||||
−0.992219 | + | 0.124507i | \(0.960265\pi\) | |||||||
\(194\) | 0.0605836 | 0.00434965 | ||||||||
\(195\) | −4.43759 | − | 17.6033i | −0.317782 | − | 1.26060i | ||||
\(196\) | −15.9897 | −1.14212 | ||||||||
\(197\) | 6.31827 | 0.450158 | 0.225079 | − | 0.974340i | \(-0.427736\pi\) | ||||
0.225079 | + | 0.974340i | \(0.427736\pi\) | |||||||
\(198\) | 9.91636 | + | 0.815933i | 0.704725 | + | 0.0579858i | ||||
\(199\) | 0.756526 | 0.0536287 | 0.0268143 | − | 0.999640i | \(-0.491464\pi\) | ||||
0.0268143 | + | 0.999640i | \(0.491464\pi\) | |||||||
\(200\) | −11.5768 | −0.818603 | ||||||||
\(201\) | 2.16701 | + | 8.59622i | 0.152849 | + | 0.606330i | ||||
\(202\) | −10.6605 | −0.750070 | ||||||||
\(203\) | − | 37.9664i | − | 2.66472i | ||||||
\(204\) | 0.423385 | + | 1.67951i | 0.0296429 | + | 0.117589i | ||||
\(205\) | 6.22468i | 0.434751i | ||||||||
\(206\) | 1.38499 | 0.0964967 | ||||||||
\(207\) | 7.99923 | + | 14.8576i | 0.555985 | + | 1.03268i | ||||
\(208\) | − | 2.57431i | − | 0.178496i | ||||||
\(209\) | −8.21634 | + | 12.6514i | −0.568336 | + | 0.875113i | ||||
\(210\) | −8.26518 | − | 32.7868i | −0.570352 | − | 2.26250i | ||||
\(211\) | − | 11.6543i | − | 0.802313i | −0.916010 | − | 0.401156i | \(-0.868608\pi\) | ||
0.916010 | − | 0.401156i | \(-0.131392\pi\) | |||||||
\(212\) | − | 9.72335i | − | 0.667802i | ||||||
\(213\) | 13.2898 | − | 3.35021i | 0.910603 | − | 0.229553i | ||||
\(214\) | −4.25253 | −0.290697 | ||||||||
\(215\) | 18.1248 | 1.23610 | ||||||||
\(216\) | 3.50689 | + | 3.83428i | 0.238614 | + | 0.260890i | ||||
\(217\) | 1.70358i | 0.115646i | ||||||||
\(218\) | 5.49088i | 0.371889i | ||||||||
\(219\) | −7.16191 | + | 1.80544i | −0.483957 | + | 0.122000i | ||||
\(220\) | 7.35482 | − | 11.3248i | 0.495862 | − | 0.763519i | ||||
\(221\) | 2.57431i | 0.173167i | ||||||||
\(222\) | −2.26754 | − | 8.99499i | −0.152187 | − | 0.603705i | ||||
\(223\) | −0.142411 | −0.00953654 | −0.00476827 | − | 0.999989i | \(-0.501518\pi\) | ||||
−0.00476827 | + | 0.999989i | \(0.501518\pi\) | |||||||
\(224\) | − | 4.79476i | − | 0.320363i | ||||||
\(225\) | 30.5800 | − | 16.4640i | 2.03867 | − | 1.09760i | ||||
\(226\) | 17.3599i | 1.15476i | ||||||||
\(227\) | 6.24693 | 0.414623 | 0.207312 | − | 0.978275i | \(-0.433529\pi\) | ||||
0.207312 | + | 0.978275i | \(0.433529\pi\) | |||||||
\(228\) | −7.63903 | + | 1.92571i | −0.505907 | + | 0.127534i | ||||
\(229\) | 10.0198 | 0.662128 | 0.331064 | − | 0.943608i | \(-0.392592\pi\) | ||||
0.331064 | + | 0.943608i | \(0.392592\pi\) | |||||||
\(230\) | 22.9008 | 1.51004 | ||||||||
\(231\) | 26.0661 | + | 8.90036i | 1.71503 | + | 0.585600i | ||||
\(232\) | 7.91832 | 0.519863 | ||||||||
\(233\) | 27.9235 | 1.82933 | 0.914666 | − | 0.404211i | \(-0.132454\pi\) | ||||
0.914666 | + | 0.404211i | \(0.132454\pi\) | |||||||
\(234\) | 3.66108 | + | 6.80002i | 0.239332 | + | 0.444531i | ||||
\(235\) | 37.6001 | 2.45276 | ||||||||
\(236\) | 11.6299i | 0.757042i | ||||||||
\(237\) | 15.2114 | − | 3.83462i | 0.988087 | − | 0.249086i | ||||
\(238\) | 4.79476i | 0.310798i | ||||||||
\(239\) | −16.6886 | −1.07949 | −0.539747 | − | 0.841828i | \(-0.681480\pi\) | ||||
−0.539747 | + | 0.841828i | \(0.681480\pi\) | |||||||
\(240\) | 6.83805 | − | 1.72380i | 0.441394 | − | 0.111271i | ||||
\(241\) | 14.9599i | 0.963652i | 0.876267 | + | 0.481826i | \(0.160026\pi\) | ||||
−0.876267 | + | 0.481826i | \(0.839974\pi\) | |||||||
\(242\) | 4.47360 | + | 10.0492i | 0.287574 | + | 0.645989i | ||||
\(243\) | −14.7164 | − | 5.14087i | −0.944055 | − | 0.329787i | ||||
\(244\) | 4.09863i | 0.262388i | ||||||||
\(245\) | − | 65.1014i | − | 4.15918i | ||||||
\(246\) | −0.647295 | − | 2.56773i | −0.0412700 | − | 0.163712i | ||||
\(247\) | −11.7089 | −0.745022 | ||||||||
\(248\) | −0.355300 | −0.0225616 | ||||||||
\(249\) | 3.07645 | + | 12.2038i | 0.194962 | + | 0.773386i | ||||
\(250\) | − | 26.7772i | − | 1.69354i | ||||||
\(251\) | 11.2495i | 0.710063i | 0.934854 | + | 0.355032i | \(0.115530\pi\) | ||||
−0.934854 | + | 0.355032i | \(0.884470\pi\) | |||||||
\(252\) | 6.81889 | + | 12.6653i | 0.429550 | + | 0.797839i | ||||
\(253\) | −10.1607 | + | 15.6452i | −0.638796 | + | 0.983606i | ||||
\(254\) | − | 3.35314i | − | 0.210395i | ||||||
\(255\) | −6.83805 | + | 1.72380i | −0.428215 | + | 0.107948i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.3690i | 1.14583i | 0.819616 | + | 0.572913i | \(0.194187\pi\) | ||||
−0.819616 | + | 0.572913i | \(0.805813\pi\) | |||||||
\(258\) | −7.47662 | + | 1.88477i | −0.465474 | + | 0.117341i | ||||
\(259\) | − | 25.6794i | − | 1.59564i | ||||||
\(260\) | 10.4812 | 0.650017 | ||||||||
\(261\) | −20.9162 | + | 11.2611i | −1.29468 | + | 0.697044i | ||||
\(262\) | 14.6947 | 0.907839 | ||||||||
\(263\) | −7.76831 | −0.479015 | −0.239507 | − | 0.970895i | \(-0.576986\pi\) | ||||
−0.239507 | + | 0.970895i | \(0.576986\pi\) | |||||||
\(264\) | −1.85627 | + | 5.43638i | −0.114245 | + | 0.334586i | ||||
\(265\) | 39.5882 | 2.43189 | ||||||||
\(266\) | −21.8084 | −1.33716 | ||||||||
\(267\) | 20.5406 | − | 5.17806i | 1.25707 | − | 0.316892i | ||||
\(268\) | −5.11830 | −0.312650 | ||||||||
\(269\) | 6.64285i | 0.405022i | 0.979280 | + | 0.202511i | \(0.0649102\pi\) | ||||
−0.979280 | + | 0.202511i | \(0.935090\pi\) | |||||||
\(270\) | −15.6111 | + | 14.2782i | −0.950063 | + | 0.868942i | ||||
\(271\) | − | 11.5920i | − | 0.704162i | −0.935969 | − | 0.352081i | \(-0.885474\pi\) | ||
0.935969 | − | 0.352081i | \(-0.114526\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 5.22593 | + | 20.7305i | 0.316287 | + | 1.25467i | ||||
\(274\) | − | 21.6014i | − | 1.30499i | ||||||
\(275\) | 32.2010 | + | 20.9127i | 1.94179 | + | 1.26108i | ||||
\(276\) | −9.44676 | + | 2.38142i | −0.568628 | + | 0.143345i | ||||
\(277\) | − | 14.4698i | − | 0.869406i | −0.900574 | − | 0.434703i | \(-0.856853\pi\) | ||
0.900574 | − | 0.434703i | \(-0.143147\pi\) | |||||||
\(278\) | − | 8.89537i | − | 0.533509i | ||||||
\(279\) | 0.938521 | − | 0.505292i | 0.0561878 | − | 0.0302510i | ||||
\(280\) | 19.5217 | 1.16664 | ||||||||
\(281\) | 12.0617 | 0.719541 | 0.359770 | − | 0.933041i | \(-0.382855\pi\) | ||||
0.359770 | + | 0.933041i | \(0.382855\pi\) | |||||||
\(282\) | −15.5103 | + | 3.90997i | −0.923625 | + | 0.232836i | ||||
\(283\) | − | 3.34479i | − | 0.198827i | −0.995046 | − | 0.0994135i | \(-0.968303\pi\) | ||
0.995046 | − | 0.0994135i | \(-0.0316967\pi\) | |||||||
\(284\) | 7.91292i | 0.469546i | ||||||||
\(285\) | −7.84047 | − | 31.1020i | −0.464430 | − | 1.84233i | ||||
\(286\) | −4.65032 | + | 7.16048i | −0.274979 | + | 0.423408i | ||||
\(287\) | − | 7.33049i | − | 0.432705i | ||||||
\(288\) | −2.64149 | + | 1.42216i | −0.155651 | + | 0.0838014i | ||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 32.2391i | 1.89315i | ||||||||
\(291\) | −0.0256502 | − | 0.101751i | −0.00150364 | − | 0.00596473i | ||||
\(292\) | − | 4.26429i | − | 0.249549i | ||||||
\(293\) | −1.72105 | −0.100545 | −0.0502724 | − | 0.998736i | \(-0.516009\pi\) | ||||
−0.0502724 | + | 0.998736i | \(0.516009\pi\) | |||||||
\(294\) | 6.76979 | + | 26.8548i | 0.394822 | + | 1.56620i | ||||
\(295\) | −47.3507 | −2.75686 | ||||||||
\(296\) | 5.35573 | 0.311296 | ||||||||
\(297\) | −2.82807 | − | 17.0001i | −0.164102 | − | 0.986443i | ||||
\(298\) | 18.8204 | 1.09024 | ||||||||
\(299\) | −14.4798 | −0.837387 | ||||||||
\(300\) | 4.90144 | + | 19.4433i | 0.282985 | + | 1.12256i | ||||
\(301\) | −21.3447 | −1.23029 | ||||||||
\(302\) | − | 16.6132i | − | 0.955980i | ||||||
\(303\) | 4.51350 | + | 17.9044i | 0.259294 | + | 1.02858i | ||||
\(304\) | − | 4.54838i | − | 0.260867i | ||||||
\(305\) | −16.6874 | −0.955519 | ||||||||
\(306\) | 2.64149 | − | 1.42216i | 0.151004 | − | 0.0812993i | ||||
\(307\) | 15.5925i | 0.889913i | 0.895552 | + | 0.444957i | \(0.146781\pi\) | ||||
−0.895552 | + | 0.444957i | \(0.853219\pi\) | |||||||
\(308\) | −8.66141 | + | 13.3367i | −0.493530 | + | 0.759927i | ||||
\(309\) | −0.586383 | − | 2.32610i | −0.0333582 | − | 0.132327i | ||||
\(310\) | − | 1.44659i | − | 0.0821607i | ||||||
\(311\) | 28.3662i | 1.60850i | 0.594291 | + | 0.804250i | \(0.297433\pi\) | ||||
−0.594291 | + | 0.804250i | \(0.702567\pi\) | |||||||
\(312\) | −4.32358 | + | 1.08993i | −0.244774 | + | 0.0617049i | ||||
\(313\) | 6.39671 | 0.361564 | 0.180782 | − | 0.983523i | \(-0.442137\pi\) | ||||
0.180782 | + | 0.983523i | \(0.442137\pi\) | |||||||
\(314\) | 13.0711 | 0.737643 | ||||||||
\(315\) | −51.5663 | + | 27.7629i | −2.90543 | + | 1.56426i | ||||
\(316\) | 9.05706i | 0.509500i | ||||||||
\(317\) | − | 29.7857i | − | 1.67293i | −0.548019 | − | 0.836466i | \(-0.684618\pi\) | ||
0.548019 | − | 0.836466i | \(-0.315382\pi\) | |||||||
\(318\) | −16.3304 | + | 4.11672i | −0.915765 | + | 0.230854i | ||||
\(319\) | −22.0249 | − | 14.3039i | −1.23316 | − | 0.800866i | ||||
\(320\) | 4.07146i | 0.227602i | ||||||||
\(321\) | 1.80046 | + | 7.14215i | 0.100492 | + | 0.398636i | ||||
\(322\) | −26.9692 | −1.50293 | ||||||||
\(323\) | 4.54838i | 0.253078i | ||||||||
\(324\) | 4.95494 | − | 7.51323i | 0.275274 | − | 0.417401i | ||||
\(325\) | 29.8023i | 1.65313i | ||||||||
\(326\) | 1.55929 | 0.0863610 | ||||||||
\(327\) | 9.22198 | − | 2.32476i | 0.509976 | − | 0.128559i | ||||
\(328\) | 1.52886 | 0.0844170 | ||||||||
\(329\) | −44.2797 | −2.44122 | ||||||||
\(330\) | −22.1340 | − | 7.55773i | −1.21844 | − | 0.416039i | ||||
\(331\) | −12.4742 | −0.685644 | −0.342822 | − | 0.939400i | \(-0.611383\pi\) | ||||
−0.342822 | + | 0.939400i | \(0.611383\pi\) | |||||||
\(332\) | −7.26631 | −0.398791 | ||||||||
\(333\) | −14.1471 | + | 7.61669i | −0.775257 | + | 0.417392i | ||||
\(334\) | 2.47630 | 0.135497 | ||||||||
\(335\) | − | 20.8389i | − | 1.13855i | ||||||
\(336\) | −8.05283 | + | 2.03003i | −0.439318 | + | 0.110747i | ||||
\(337\) | − | 14.7125i | − | 0.801440i | −0.916201 | − | 0.400720i | \(-0.868760\pi\) | ||
0.916201 | − | 0.400720i | \(-0.131240\pi\) | |||||||
\(338\) | 6.37292 | 0.346641 | ||||||||
\(339\) | 29.1561 | − | 7.34993i | 1.58354 | − | 0.399193i | ||||
\(340\) | − | 4.07146i | − | 0.220806i | ||||||
\(341\) | 0.988270 | + | 0.641825i | 0.0535178 | + | 0.0347568i | ||||
\(342\) | 6.46851 | + | 12.0145i | 0.349777 | + | 0.649669i | ||||
\(343\) | 43.1034i | 2.32736i | ||||||||
\(344\) | − | 4.45168i | − | 0.240018i | ||||||
\(345\) | −9.69587 | − | 38.4621i | −0.522008 | − | 2.07073i | ||||
\(346\) | 5.92606 | 0.318587 | ||||||||
\(347\) | −25.1368 | −1.34941 | −0.674707 | − | 0.738086i | \(-0.735730\pi\) | ||||
−0.674707 | + | 0.738086i | \(0.735730\pi\) | |||||||
\(348\) | −3.35250 | − | 13.2989i | −0.179713 | − | 0.712895i | ||||
\(349\) | − | 7.45414i | − | 0.399011i | −0.979897 | − | 0.199505i | \(-0.936066\pi\) | ||
0.979897 | − | 0.199505i | \(-0.0639336\pi\) | |||||||
\(350\) | 55.5079i | 2.96702i | ||||||||
\(351\) | 9.87064 | − | 9.02783i | 0.526856 | − | 0.481870i | ||||
\(352\) | −2.78151 | − | 1.80643i | −0.148255 | − | 0.0962832i | ||||
\(353\) | − | 2.60469i | − | 0.138634i | −0.997595 | − | 0.0693168i | \(-0.977918\pi\) | ||
0.997595 | − | 0.0693168i | \(-0.0220819\pi\) | |||||||
\(354\) | 19.5325 | − | 4.92393i | 1.03814 | − | 0.261704i | ||||
\(355\) | −32.2172 | −1.70991 | ||||||||
\(356\) | 12.2301i | 0.648197i | ||||||||
\(357\) | 8.05283 | − | 2.03003i | 0.426201 | − | 0.107440i | ||||
\(358\) | − | 7.57467i | − | 0.400334i | ||||||
\(359\) | −7.37005 | −0.388977 | −0.194488 | − | 0.980905i | \(-0.562305\pi\) | ||||
−0.194488 | + | 0.980905i | \(0.562305\pi\) | |||||||
\(360\) | −5.79026 | − | 10.7547i | −0.305173 | − | 0.566824i | ||||
\(361\) | −1.68773 | −0.0888281 | ||||||||
\(362\) | 2.71865 | 0.142889 | ||||||||
\(363\) | 14.9837 | − | 11.7681i | 0.786440 | − | 0.617667i | ||||
\(364\) | −12.3432 | −0.646959 | ||||||||
\(365\) | 17.3619 | 0.908763 | ||||||||
\(366\) | 6.88368 | − | 1.73530i | 0.359816 | − | 0.0907055i | ||||
\(367\) | 3.43567 | 0.179340 | 0.0896702 | − | 0.995972i | \(-0.471419\pi\) | ||||
0.0896702 | + | 0.995972i | \(0.471419\pi\) | |||||||
\(368\) | − | 5.62472i | − | 0.293209i | ||||||
\(369\) | −4.03846 | + | 2.17427i | −0.210234 | + | 0.113188i | ||||
\(370\) | 21.8057i | 1.13362i | ||||||||
\(371\) | −46.6211 | −2.42045 | ||||||||
\(372\) | 0.150429 | + | 0.596728i | 0.00779936 | + | 0.0309389i | ||||
\(373\) | 30.6755i | 1.58832i | 0.607711 | + | 0.794158i | \(0.292088\pi\) | ||||
−0.607711 | + | 0.794158i | \(0.707912\pi\) | |||||||
\(374\) | 2.78151 | + | 1.80643i | 0.143828 | + | 0.0934085i | ||||
\(375\) | −44.9725 | + | 11.3371i | −2.32237 | + | 0.585443i | ||||
\(376\) | − | 9.23503i | − | 0.476260i | ||||||
\(377\) | − | 20.3842i | − | 1.04984i | ||||||
\(378\) | 18.3844 | − | 16.8147i | 0.945594 | − | 0.864854i | ||||
\(379\) | −6.90631 | −0.354753 | −0.177377 | − | 0.984143i | \(-0.556761\pi\) | ||||
−0.177377 | + | 0.984143i | \(0.556761\pi\) | |||||||
\(380\) | 18.5185 | 0.949981 | ||||||||
\(381\) | −5.63163 | + | 1.41967i | −0.288517 | + | 0.0727319i | ||||
\(382\) | 20.5365i | 1.05074i | ||||||||
\(383\) | 8.94380i | 0.457007i | 0.973543 | + | 0.228503i | \(0.0733832\pi\) | ||||
−0.973543 | + | 0.228503i | \(0.926617\pi\) | |||||||
\(384\) | −0.423385 | − | 1.67951i | −0.0216058 | − | 0.0857070i | ||||
\(385\) | −54.2997 | − | 35.2646i | −2.76737 | − | 1.79725i | ||||
\(386\) | 3.45941i | 0.176079i | ||||||||
\(387\) | 6.33098 | + | 11.7591i | 0.321822 | + | 0.597747i | ||||
\(388\) | 0.0605836 | 0.00307567 | ||||||||
\(389\) | − | 37.7077i | − | 1.91186i | −0.293598 | − | 0.955929i | \(-0.594853\pi\) | ||
0.293598 | − | 0.955929i | \(-0.405147\pi\) | |||||||
\(390\) | −4.43759 | − | 17.6033i | −0.224706 | − | 0.891377i | ||||
\(391\) | 5.62472i | 0.284454i | ||||||||
\(392\) | −15.9897 | −0.807601 | ||||||||
\(393\) | −6.22150 | − | 24.6798i | −0.313833 | − | 1.24493i | ||||
\(394\) | 6.31827 | 0.318310 | ||||||||
\(395\) | −36.8755 | −1.85541 | ||||||||
\(396\) | 9.91636 | + | 0.815933i | 0.498316 | + | 0.0410022i | ||||
\(397\) | 30.7172 | 1.54165 | 0.770826 | − | 0.637045i | \(-0.219844\pi\) | ||||
0.770826 | + | 0.637045i | \(0.219844\pi\) | |||||||
\(398\) | 0.756526 | 0.0379212 | ||||||||
\(399\) | 9.23333 | + | 36.6273i | 0.462245 | + | 1.83366i | ||||
\(400\) | −11.5768 | −0.578840 | ||||||||
\(401\) | − | 1.35005i | − | 0.0674184i | −0.999432 | − | 0.0337092i | \(-0.989268\pi\) | ||
0.999432 | − | 0.0337092i | \(-0.0107320\pi\) | |||||||
\(402\) | 2.16701 | + | 8.59622i | 0.108081 | + | 0.428740i | ||||
\(403\) | 0.914652i | 0.0455621i | ||||||||
\(404\) | −10.6605 | −0.530380 | ||||||||
\(405\) | 30.5898 | + | 20.1739i | 1.52002 | + | 1.00245i | ||||
\(406\) | − | 37.9664i | − | 1.88424i | ||||||
\(407\) | −14.8970 | − | 9.67478i | −0.738418 | − | 0.479561i | ||||
\(408\) | 0.423385 | + | 1.67951i | 0.0209607 | + | 0.0831480i | ||||
\(409\) | − | 31.8859i | − | 1.57666i | −0.615254 | − | 0.788329i | \(-0.710946\pi\) | ||
0.615254 | − | 0.788329i | \(-0.289054\pi\) | |||||||
\(410\) | 6.22468i | 0.307415i | ||||||||
\(411\) | −36.2797 | + | 9.14571i | −1.78955 | + | 0.451125i | ||||
\(412\) | 1.38499 | 0.0682334 | ||||||||
\(413\) | 55.7625 | 2.74390 | ||||||||
\(414\) | 7.99923 | + | 14.8576i | 0.393141 | + | 0.730213i | ||||
\(415\) | − | 29.5845i | − | 1.45225i | ||||||
\(416\) | − | 2.57431i | − | 0.126216i | ||||||
\(417\) | −14.9398 | + | 3.76617i | −0.731607 | + | 0.184430i | ||||
\(418\) | −8.21634 | + | 12.6514i | −0.401874 | + | 0.618798i | ||||
\(419\) | 6.43054i | 0.314152i | 0.987587 | + | 0.157076i | \(0.0502068\pi\) | ||||
−0.987587 | + | 0.157076i | \(0.949793\pi\) | |||||||
\(420\) | −8.26518 | − | 32.7868i | −0.403300 | − | 1.59983i | ||||
\(421\) | −0.960351 | −0.0468046 | −0.0234023 | − | 0.999726i | \(-0.507450\pi\) | ||||
−0.0234023 | + | 0.999726i | \(0.507450\pi\) | |||||||
\(422\) | − | 11.6543i | − | 0.567321i | ||||||
\(423\) | 13.1337 | + | 24.3942i | 0.638580 | + | 1.18609i | ||||
\(424\) | − | 9.72335i | − | 0.472208i | ||||||
\(425\) | 11.5768 | 0.561557 | ||||||||
\(426\) | 13.2898 | − | 3.35021i | 0.643894 | − | 0.162318i | ||||
\(427\) | 19.6519 | 0.951024 | ||||||||
\(428\) | −4.25253 | −0.205554 | ||||||||
\(429\) | 13.9949 | + | 4.77861i | 0.675682 | + | 0.230714i | ||||
\(430\) | 18.1248 | 0.874057 | ||||||||
\(431\) | −1.91773 | −0.0923738 | −0.0461869 | − | 0.998933i | \(-0.514707\pi\) | ||||
−0.0461869 | + | 0.998933i | \(0.514707\pi\) | |||||||
\(432\) | 3.50689 | + | 3.83428i | 0.168725 | + | 0.184477i | ||||
\(433\) | 10.0096 | 0.481031 | 0.240516 | − | 0.970645i | \(-0.422683\pi\) | ||||
0.240516 | + | 0.970645i | \(0.422683\pi\) | |||||||
\(434\) | 1.70358i | 0.0817742i | ||||||||
\(435\) | 54.1459 | − | 13.6496i | 2.59610 | − | 0.654447i | ||||
\(436\) | 5.49088i | 0.262966i | ||||||||
\(437\) | −25.5833 | −1.22382 | ||||||||
\(438\) | −7.16191 | + | 1.80544i | −0.342209 | + | 0.0862671i | ||||
\(439\) | 23.1549i | 1.10512i | 0.833472 | + | 0.552562i | \(0.186350\pi\) | ||||
−0.833472 | + | 0.552562i | \(0.813650\pi\) | |||||||
\(440\) | 7.35482 | − | 11.3248i | 0.350628 | − | 0.539889i | ||||
\(441\) | 42.2366 | − | 22.7398i | 2.01127 | − | 1.08285i | ||||
\(442\) | 2.57431i | 0.122448i | ||||||||
\(443\) | − | 10.9209i | − | 0.518869i | −0.965761 | − | 0.259435i | \(-0.916464\pi\) | ||
0.965761 | − | 0.259435i | \(-0.0835362\pi\) | |||||||
\(444\) | −2.26754 | − | 8.99499i | −0.107613 | − | 0.426884i | ||||
\(445\) | −49.7946 | −2.36049 | ||||||||
\(446\) | −0.142411 | −0.00674335 | ||||||||
\(447\) | −7.96828 | − | 31.6090i | −0.376887 | − | 1.49505i | ||||
\(448\) | − | 4.79476i | − | 0.226531i | ||||||
\(449\) | 13.2072i | 0.623286i | 0.950199 | + | 0.311643i | \(0.100879\pi\) | ||||
−0.950199 | + | 0.311643i | \(0.899121\pi\) | |||||||
\(450\) | 30.5800 | − | 16.4640i | 1.44156 | − | 0.776122i | ||||
\(451\) | −4.25253 | − | 2.76178i | −0.200244 | − | 0.130047i | ||||
\(452\) | 17.3599i | 0.816542i | ||||||||
\(453\) | −27.9019 | + | 7.03376i | −1.31095 | + | 0.330475i | ||||
\(454\) | 6.24693 | 0.293183 | ||||||||
\(455\) | − | 50.2549i | − | 2.35598i | ||||||
\(456\) | −7.63903 | + | 1.92571i | −0.357730 | + | 0.0901799i | ||||
\(457\) | − | 21.3501i | − | 0.998717i | −0.866395 | − | 0.499359i | \(-0.833569\pi\) | ||
0.866395 | − | 0.499359i | \(-0.166431\pi\) | |||||||
\(458\) | 10.0198 | 0.468195 | ||||||||
\(459\) | −3.50689 | − | 3.83428i | −0.163688 | − | 0.178969i | ||||
\(460\) | 22.9008 | 1.06776 | ||||||||
\(461\) | −4.75396 | −0.221414 | −0.110707 | − | 0.993853i | \(-0.535312\pi\) | ||||
−0.110707 | + | 0.993853i | \(0.535312\pi\) | |||||||
\(462\) | 26.0661 | + | 8.90036i | 1.21271 | + | 0.414082i | ||||
\(463\) | 34.9504 | 1.62428 | 0.812142 | − | 0.583460i | \(-0.198301\pi\) | ||||
0.812142 | + | 0.583460i | \(0.198301\pi\) | |||||||
\(464\) | 7.91832 | 0.367599 | ||||||||
\(465\) | −2.42956 | + | 0.612464i | −0.112668 | + | 0.0284023i | ||||
\(466\) | 27.9235 | 1.29353 | ||||||||
\(467\) | − | 17.6209i | − | 0.815400i | −0.913116 | − | 0.407700i | \(-0.866331\pi\) | ||
0.913116 | − | 0.407700i | \(-0.133669\pi\) | |||||||
\(468\) | 3.66108 | + | 6.80002i | 0.169233 | + | 0.314331i | ||||
\(469\) | 24.5410i | 1.13320i | ||||||||
\(470\) | 37.6001 | 1.73436 | ||||||||
\(471\) | −5.53409 | − | 21.9529i | −0.254997 | − | 1.01154i | ||||
\(472\) | 11.6299i | 0.535310i | ||||||||
\(473\) | −8.04166 | + | 12.3824i | −0.369756 | + | 0.569343i | ||||
\(474\) | 15.2114 | − | 3.83462i | 0.698683 | − | 0.176130i | ||||
\(475\) | 52.6557i | 2.41601i | ||||||||
\(476\) | 4.79476i | 0.219767i | ||||||||
\(477\) | 13.8281 | + | 25.6841i | 0.633146 | + | 1.17600i | ||||
\(478\) | −16.6886 | −0.763317 | ||||||||
\(479\) | 21.9110 | 1.00114 | 0.500569 | − | 0.865696i | \(-0.333124\pi\) | ||||
0.500569 | + | 0.865696i | \(0.333124\pi\) | |||||||
\(480\) | 6.83805 | − | 1.72380i | 0.312113 | − | 0.0786802i | ||||
\(481\) | − | 13.7873i | − | 0.628648i | ||||||
\(482\) | 14.9599i | 0.681405i | ||||||||
\(483\) | 11.4183 | + | 45.2949i | 0.519552 | + | 2.06099i | ||||
\(484\) | 4.47360 | + | 10.0492i | 0.203345 | + | 0.456783i | ||||
\(485\) | 0.246664i | 0.0112004i | ||||||||
\(486\) | −14.7164 | − | 5.14087i | −0.667548 | − | 0.233195i | ||||
\(487\) | −18.5751 | −0.841716 | −0.420858 | − | 0.907127i | \(-0.638271\pi\) | ||||
−0.420858 | + | 0.907127i | \(0.638271\pi\) | |||||||
\(488\) | 4.09863i | 0.185536i | ||||||||
\(489\) | −0.660180 | − | 2.61884i | −0.0298544 | − | 0.118428i | ||||
\(490\) | − | 65.1014i | − | 2.94098i | ||||||
\(491\) | 8.75916 | 0.395295 | 0.197648 | − | 0.980273i | \(-0.436670\pi\) | ||||
0.197648 | + | 0.980273i | \(0.436670\pi\) | |||||||
\(492\) | −0.647295 | − | 2.56773i | −0.0291823 | − | 0.115762i | ||||
\(493\) | −7.91832 | −0.356623 | ||||||||
\(494\) | −11.7089 | −0.526810 | ||||||||
\(495\) | −3.32204 | + | 40.3741i | −0.149315 | + | 1.81468i | ||||
\(496\) | −0.355300 | −0.0159534 | ||||||||
\(497\) | 37.9405 | 1.70187 | ||||||||
\(498\) | 3.07645 | + | 12.2038i | 0.137859 | + | 0.546866i | ||||
\(499\) | 1.95828 | 0.0876645 | 0.0438323 | − | 0.999039i | \(-0.486043\pi\) | ||||
0.0438323 | + | 0.999039i | \(0.486043\pi\) | |||||||
\(500\) | − | 26.7772i | − | 1.19751i | ||||||
\(501\) | −1.04843 | − | 4.15897i | −0.0468404 | − | 0.185809i | ||||
\(502\) | 11.2495i | 0.502090i | ||||||||
\(503\) | −3.41142 | −0.152108 | −0.0760538 | − | 0.997104i | \(-0.524232\pi\) | ||||
−0.0760538 | + | 0.997104i | \(0.524232\pi\) | |||||||
\(504\) | 6.81889 | + | 12.6653i | 0.303738 | + | 0.564157i | ||||
\(505\) | − | 43.4038i | − | 1.93144i | ||||||
\(506\) | −10.1607 | + | 15.6452i | −0.451697 | + | 0.695514i | ||||
\(507\) | −2.69820 | − | 10.7034i | −0.119831 | − | 0.475353i | ||||
\(508\) | − | 3.35314i | − | 0.148772i | ||||||
\(509\) | 4.69659i | 0.208173i | 0.994568 | + | 0.104086i | \(0.0331918\pi\) | ||||
−0.994568 | + | 0.104086i | \(0.966808\pi\) | |||||||
\(510\) | −6.83805 | + | 1.72380i | −0.302794 | + | 0.0763310i | ||||
\(511\) | −20.4462 | −0.904488 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 17.4398 | − | 15.9507i | 0.769984 | − | 0.704239i | ||||
\(514\) | 18.3690i | 0.810222i | ||||||||
\(515\) | 5.63892i | 0.248481i | ||||||||
\(516\) | −7.47662 | + | 1.88477i | −0.329140 | + | 0.0829725i | ||||
\(517\) | −16.6825 | + | 25.6873i | −0.733694 | + | 1.12973i | ||||
\(518\) | − | 25.6794i | − | 1.12829i | ||||||
\(519\) | −2.50901 | − | 9.95287i | −0.110133 | − | 0.436882i | ||||
\(520\) | 10.4812 | 0.459632 | ||||||||
\(521\) | 3.32317i | 0.145591i | 0.997347 | + | 0.0727953i | \(0.0231920\pi\) | ||||
−0.997347 | + | 0.0727953i | \(0.976808\pi\) | |||||||
\(522\) | −20.9162 | + | 11.2611i | −0.915476 | + | 0.492885i | ||||
\(523\) | − | 8.02106i | − | 0.350737i | −0.984503 | − | 0.175368i | \(-0.943888\pi\) | ||
0.984503 | − | 0.175368i | \(-0.0561116\pi\) | |||||||
\(524\) | 14.6947 | 0.641939 | ||||||||
\(525\) | 93.2260 | − | 23.5012i | 4.06872 | − | 1.02568i | ||||
\(526\) | −7.76831 | −0.338715 | ||||||||
\(527\) | 0.355300 | 0.0154771 | ||||||||
\(528\) | −1.85627 | + | 5.43638i | −0.0807837 | + | 0.236588i | ||||
\(529\) | −8.63745 | −0.375541 | ||||||||
\(530\) | 39.5882 | 1.71960 | ||||||||
\(531\) | −16.5395 | − | 30.7203i | −0.717755 | − | 1.33315i | ||||
\(532\) | −21.8084 | −0.945512 | ||||||||
\(533\) | − | 3.93575i | − | 0.170476i | ||||||
\(534\) | 20.5406 | − | 5.17806i | 0.888880 | − | 0.224077i | ||||
\(535\) | − | 17.3140i | − | 0.748550i | ||||||
\(536\) | −5.11830 | −0.221077 | ||||||||
\(537\) | −12.7217 | + | 3.20700i | −0.548983 | + | 0.138392i | ||||
\(538\) | 6.64285i | 0.286394i | ||||||||
\(539\) | 44.4755 | + | 28.8843i | 1.91569 | + | 1.24414i | ||||
\(540\) | −15.6111 | + | 14.2782i | −0.671796 | + | 0.614435i | ||||
\(541\) | − | 41.8224i | − | 1.79809i | −0.437860 | − | 0.899043i | \(-0.644263\pi\) | ||
0.437860 | − | 0.899043i | \(-0.355737\pi\) | |||||||
\(542\) | − | 11.5920i | − | 0.497918i | ||||||
\(543\) | −1.15104 | − | 4.56599i | −0.0493957 | − | 0.195946i | ||||
\(544\) | −1.00000 | −0.0428746 | ||||||||
\(545\) | −22.3559 | −0.957622 | ||||||||
\(546\) | 5.22593 | + | 20.7305i | 0.223649 | + | 0.887183i | ||||
\(547\) | − | 33.5931i | − | 1.43634i | −0.695869 | − | 0.718169i | \(-0.744981\pi\) | ||
0.695869 | − | 0.718169i | \(-0.255019\pi\) | |||||||
\(548\) | − | 21.6014i | − | 0.922766i | ||||||
\(549\) | −5.82890 | − | 10.8265i | −0.248771 | − | 0.462063i | ||||
\(550\) | 32.2010 | + | 20.9127i | 1.37305 | + | 0.891721i | ||||
\(551\) | − | 36.0155i | − | 1.53431i | ||||||
\(552\) | −9.44676 | + | 2.38142i | −0.402081 | + | 0.101360i | ||||
\(553\) | 43.4264 | 1.84668 | ||||||||
\(554\) | − | 14.4698i | − | 0.614763i | ||||||
\(555\) | 36.6228 | − | 9.23219i | 1.55455 | − | 0.391885i | ||||
\(556\) | − | 8.89537i | − | 0.377248i | ||||||
\(557\) | −44.9677 | −1.90534 | −0.952671 | − | 0.304002i | \(-0.901677\pi\) | ||||
−0.952671 | + | 0.304002i | \(0.901677\pi\) | |||||||
\(558\) | 0.938521 | − | 0.505292i | 0.0397307 | − | 0.0213907i | ||||
\(559\) | −11.4600 | −0.484707 | ||||||||
\(560\) | 19.5217 | 0.824941 | ||||||||
\(561\) | 1.85627 | − | 5.43638i | 0.0783717 | − | 0.229524i | ||||
\(562\) | 12.0617 | 0.508792 | ||||||||
\(563\) | −3.48936 | −0.147059 | −0.0735296 | − | 0.997293i | \(-0.523426\pi\) | ||||
−0.0735296 | + | 0.997293i | \(0.523426\pi\) | |||||||
\(564\) | −15.5103 | + | 3.90997i | −0.653101 | + | 0.164640i | ||||
\(565\) | −70.6802 | −2.97354 | ||||||||
\(566\) | − | 3.34479i | − | 0.140592i | ||||||
\(567\) | −36.0241 | − | 23.7577i | −1.51287 | − | 0.997731i | ||||
\(568\) | 7.91292i | 0.332019i | ||||||||
\(569\) | 12.7550 | 0.534717 | 0.267359 | − | 0.963597i | \(-0.413849\pi\) | ||||
0.267359 | + | 0.963597i | \(0.413849\pi\) | |||||||
\(570\) | −7.84047 | − | 31.1020i | −0.328401 | − | 1.30272i | ||||
\(571\) | − | 23.8987i | − | 1.00013i | −0.865988 | − | 0.500065i | \(-0.833309\pi\) | ||
0.865988 | − | 0.500065i | \(-0.166691\pi\) | |||||||
\(572\) | −4.65032 | + | 7.16048i | −0.194440 | + | 0.299395i | ||||
\(573\) | 34.4911 | − | 8.69483i | 1.44089 | − | 0.363232i | ||||
\(574\) | − | 7.33049i | − | 0.305969i | ||||||
\(575\) | 65.1162i | 2.71553i | ||||||||
\(576\) | −2.64149 | + | 1.42216i | −0.110062 | + | 0.0592565i | ||||
\(577\) | −10.8405 | −0.451296 | −0.225648 | − | 0.974209i | \(-0.572450\pi\) | ||||
−0.225648 | + | 0.974209i | \(0.572450\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 5.81011 | − | 1.46466i | 0.241460 | − | 0.0608693i | ||||
\(580\) | 32.2391i | 1.33866i | ||||||||
\(581\) | 34.8402i | 1.44541i | ||||||||
\(582\) | −0.0256502 | − | 0.101751i | −0.00106323 | − | 0.00421770i | ||||
\(583\) | −17.5646 | + | 27.0456i | −0.727451 | + | 1.12011i | ||||
\(584\) | − | 4.26429i | − | 0.176458i | ||||||
\(585\) | −27.6860 | + | 14.9059i | −1.14468 | + | 0.616284i | ||||
\(586\) | −1.72105 | −0.0710959 | ||||||||
\(587\) | − | 14.2826i | − | 0.589506i | −0.955573 | − | 0.294753i | \(-0.904763\pi\) | ||
0.955573 | − | 0.294753i | \(-0.0952374\pi\) | |||||||
\(588\) | 6.76979 | + | 26.8548i | 0.279182 | + | 1.10747i | ||||
\(589\) | 1.61604i | 0.0665876i | ||||||||
\(590\) | −47.3507 | −1.94940 | ||||||||
\(591\) | −2.67506 | − | 10.6116i | −0.110037 | − | 0.436502i | ||||
\(592\) | 5.35573 | 0.220119 | ||||||||
\(593\) | 9.31428 | 0.382491 | 0.191246 | − | 0.981542i | \(-0.438747\pi\) | ||||
0.191246 | + | 0.981542i | \(0.438747\pi\) | |||||||
\(594\) | −2.82807 | − | 17.0001i | −0.116037 | − | 0.697521i | ||||
\(595\) | −19.5217 | −0.800310 | ||||||||
\(596\) | 18.8204 | 0.770914 | ||||||||
\(597\) | −0.320302 | − | 1.27059i | −0.0131091 | − | 0.0520018i | ||||
\(598\) | −14.4798 | −0.592122 | ||||||||
\(599\) | − | 12.4153i | − | 0.507275i | −0.967299 | − | 0.253638i | \(-0.918373\pi\) | ||
0.967299 | − | 0.253638i | \(-0.0816270\pi\) | |||||||
\(600\) | 4.90144 | + | 19.4433i | 0.200101 | + | 0.793770i | ||||
\(601\) | − | 16.2793i | − | 0.664047i | −0.943271 | − | 0.332024i | \(-0.892269\pi\) | ||
0.943271 | − | 0.332024i | \(-0.107731\pi\) | |||||||
\(602\) | −21.3447 | −0.869945 | ||||||||
\(603\) | 13.5199 | − | 7.27902i | 0.550574 | − | 0.296425i | ||||
\(604\) | − | 16.6132i | − | 0.675980i | ||||||
\(605\) | −40.9150 | + | 18.2141i | −1.66343 | + | 0.740507i | ||||
\(606\) | 4.51350 | + | 17.9044i | 0.183348 | + | 0.727316i | ||||
\(607\) | 20.2972i | 0.823840i | 0.911220 | + | 0.411920i | \(0.135142\pi\) | ||||
−0.911220 | + | 0.411920i | \(0.864858\pi\) | |||||||
\(608\) | − | 4.54838i | − | 0.184461i | ||||||
\(609\) | −63.7649 | + | 16.0744i | −2.58388 | + | 0.651368i | ||||
\(610\) | −16.6874 | −0.675654 | ||||||||
\(611\) | −23.7738 | −0.961787 | ||||||||
\(612\) | 2.64149 | − | 1.42216i | 0.106776 | − | 0.0574873i | ||||
\(613\) | 42.1895i | 1.70402i | 0.523527 | + | 0.852009i | \(0.324616\pi\) | ||||
−0.523527 | + | 0.852009i | \(0.675384\pi\) | |||||||
\(614\) | 15.5925i | 0.629264i | ||||||||
\(615\) | 10.4544 | − | 2.63544i | 0.421562 | − | 0.106271i | ||||
\(616\) | −8.66141 | + | 13.3367i | −0.348978 | + | 0.537349i | ||||
\(617\) | − | 16.9281i | − | 0.681499i | −0.940154 | − | 0.340749i | \(-0.889319\pi\) | ||
0.940154 | − | 0.340749i | \(-0.110681\pi\) | |||||||
\(618\) | −0.586383 | − | 2.32610i | −0.0235878 | − | 0.0935693i | ||||
\(619\) | 18.3615 | 0.738009 | 0.369005 | − | 0.929428i | \(-0.379699\pi\) | ||||
0.369005 | + | 0.929428i | \(0.379699\pi\) | |||||||
\(620\) | − | 1.44659i | − | 0.0580964i | ||||||
\(621\) | 21.5668 | − | 19.7253i | 0.865444 | − | 0.791548i | ||||
\(622\) | 28.3662i | 1.13738i | ||||||||
\(623\) | 58.6406 | 2.34939 | ||||||||
\(624\) | −4.32358 | + | 1.08993i | −0.173082 | + | 0.0436319i | ||||
\(625\) | 51.1383 | 2.04553 | ||||||||
\(626\) | 6.39671 | 0.255664 | ||||||||
\(627\) | 24.7267 | + | 8.44301i | 0.987490 | + | 0.337181i | ||||
\(628\) | 13.0711 | 0.521592 | ||||||||
\(629\) | −5.35573 | −0.213547 | ||||||||
\(630\) | −51.5663 | + | 27.7629i | −2.05445 | + | 1.10610i | ||||
\(631\) | 11.3092 | 0.450214 | 0.225107 | − | 0.974334i | \(-0.427727\pi\) | ||||
0.225107 | + | 0.974334i | \(0.427727\pi\) | |||||||
\(632\) | 9.05706i | 0.360271i | ||||||||
\(633\) | −19.5734 | + | 4.93424i | −0.777974 | + | 0.196118i | ||||
\(634\) | − | 29.7857i | − | 1.18294i | ||||||
\(635\) | 13.6522 | 0.541771 | ||||||||
\(636\) | −16.3304 | + | 4.11672i | −0.647544 | + | 0.163239i | ||||
\(637\) | 41.1624i | 1.63092i | ||||||||
\(638\) | −22.0249 | − | 14.3039i | −0.871974 | − | 0.566298i | ||||
\(639\) | −11.2534 | − | 20.9019i | −0.445178 | − | 0.826867i | ||||
\(640\) | 4.07146i | 0.160939i | ||||||||
\(641\) | 37.8476i | 1.49489i | 0.664323 | + | 0.747446i | \(0.268720\pi\) | ||||
−0.664323 | + | 0.747446i | \(0.731280\pi\) | |||||||
\(642\) | 1.80046 | + | 7.14215i | 0.0710584 | + | 0.281878i | ||||
\(643\) | 29.5912 | 1.16696 | 0.583481 | − | 0.812127i | \(-0.301690\pi\) | ||||
0.583481 | + | 0.812127i | \(0.301690\pi\) | |||||||
\(644\) | −26.9692 | −1.06273 | ||||||||
\(645\) | −7.67378 | − | 30.4408i | −0.302155 | − | 1.19861i | ||||
\(646\) | 4.54838i | 0.178954i | ||||||||
\(647\) | 19.4975i | 0.766525i | 0.923640 | + | 0.383262i | \(0.125199\pi\) | ||||
−0.923640 | + | 0.383262i | \(0.874801\pi\) | |||||||
\(648\) | 4.95494 | − | 7.51323i | 0.194648 | − | 0.295147i | ||||
\(649\) | 21.0086 | − | 32.3487i | 0.824661 | − | 1.26980i | ||||
\(650\) | 29.8023i | 1.16894i | ||||||||
\(651\) | 2.86117 | − | 0.721268i | 0.112138 | − | 0.0282687i | ||||
\(652\) | 1.55929 | 0.0610665 | ||||||||
\(653\) | 48.5131i | 1.89846i | 0.314578 | + | 0.949232i | \(0.398137\pi\) | ||||
−0.314578 | + | 0.949232i | \(0.601863\pi\) | |||||||
\(654\) | 9.22198 | − | 2.32476i | 0.360608 | − | 0.0909052i | ||||
\(655\) | 59.8288i | 2.33770i | ||||||||
\(656\) | 1.52886 | 0.0596918 | ||||||||
\(657\) | 6.06449 | + | 11.2641i | 0.236598 | + | 0.439454i | ||||
\(658\) | −44.2797 | −1.72620 | ||||||||
\(659\) | −22.5480 | −0.878346 | −0.439173 | − | 0.898402i | \(-0.644728\pi\) | ||||
−0.439173 | + | 0.898402i | \(0.644728\pi\) | |||||||
\(660\) | −22.1340 | − | 7.55773i | −0.861566 | − | 0.294184i | ||||
\(661\) | 40.1237 | 1.56063 | 0.780316 | − | 0.625386i | \(-0.215058\pi\) | ||||
0.780316 | + | 0.625386i | \(0.215058\pi\) | |||||||
\(662\) | −12.4742 | −0.484824 | ||||||||
\(663\) | 4.32358 | − | 1.08993i | 0.167914 | − | 0.0423292i | ||||
\(664\) | −7.26631 | −0.281988 | ||||||||
\(665\) | − | 88.7919i | − | 3.44320i | ||||||
\(666\) | −14.1471 | + | 7.61669i | −0.548190 | + | 0.295141i | ||||
\(667\) | − | 44.5383i | − | 1.72453i | ||||||
\(668\) | 2.47630 | 0.0958111 | ||||||||
\(669\) | 0.0602946 | + | 0.239180i | 0.00233113 | + | 0.00924724i | ||||
\(670\) | − | 20.8389i | − | 0.805079i | ||||||
\(671\) | 7.40390 | − | 11.4004i | 0.285825 | − | 0.440107i | ||||
\(672\) | −8.05283 | + | 2.03003i | −0.310645 | + | 0.0783100i | ||||
\(673\) | − | 16.1708i | − | 0.623338i | −0.950191 | − | 0.311669i | \(-0.899112\pi\) | ||
0.950191 | − | 0.311669i | \(-0.100888\pi\) | |||||||
\(674\) | − | 14.7125i | − | 0.566704i | ||||||
\(675\) | −40.5986 | − | 44.3887i | −1.56264 | − | 1.70852i | ||||
\(676\) | 6.37292 | 0.245112 | ||||||||
\(677\) | −9.65140 | −0.370933 | −0.185467 | − | 0.982651i | \(-0.559380\pi\) | ||||
−0.185467 | + | 0.982651i | \(0.559380\pi\) | |||||||
\(678\) | 29.1561 | − | 7.34993i | 1.11973 | − | 0.282272i | ||||
\(679\) | − | 0.290484i | − | 0.0111477i | ||||||
\(680\) | − | 4.07146i | − | 0.156133i | ||||||
\(681\) | −2.64486 | − | 10.4918i | −0.101351 | − | 0.402045i | ||||
\(682\) | 0.988270 | + | 0.641825i | 0.0378428 | + | 0.0245768i | ||||
\(683\) | 26.8700i | 1.02815i | 0.857745 | + | 0.514075i | \(0.171865\pi\) | ||||
−0.857745 | + | 0.514075i | \(0.828135\pi\) | |||||||
\(684\) | 6.46851 | + | 12.0145i | 0.247329 | + | 0.459386i | ||||
\(685\) | 87.9493 | 3.36037 | ||||||||
\(686\) | 43.1034i | 1.64569i | ||||||||
\(687\) | −4.24224 | − | 16.8284i | −0.161852 | − | 0.642042i | ||||
\(688\) | − | 4.45168i | − | 0.169719i | ||||||
\(689\) | −25.0309 | −0.953603 | ||||||||
\(690\) | −9.69587 | − | 38.4621i | −0.369115 | − | 1.46423i | ||||
\(691\) | 24.7811 | 0.942719 | 0.471360 | − | 0.881941i | \(-0.343763\pi\) | ||||
0.471360 | + | 0.881941i | \(0.343763\pi\) | |||||||
\(692\) | 5.92606 | 0.225275 | ||||||||
\(693\) | 3.91220 | − | 47.5465i | 0.148612 | − | 1.80614i | ||||
\(694\) | −25.1368 | −0.954180 | ||||||||
\(695\) | 36.2172 | 1.37380 | ||||||||
\(696\) | −3.35250 | − | 13.2989i | −0.127076 | − | 0.504093i | ||||
\(697\) | −1.52886 | −0.0579096 | ||||||||
\(698\) | − | 7.45414i | − | 0.282143i | ||||||
\(699\) | −11.8224 | − | 46.8978i | −0.447165 | − | 1.77384i | ||||
\(700\) | 55.5079i | 2.09800i | ||||||||
\(701\) | −29.9252 | −1.13026 | −0.565130 | − | 0.825002i | \(-0.691174\pi\) | ||||
−0.565130 | + | 0.825002i | \(0.691174\pi\) | |||||||
\(702\) | 9.87064 | − | 9.02783i | 0.372543 | − | 0.340734i | ||||
\(703\) | − | 24.3599i | − | 0.918751i | ||||||
\(704\) | −2.78151 | − | 1.80643i | −0.104832 | − | 0.0680825i | ||||
\(705\) | −15.9193 | − | 63.1496i | −0.599556 | − | 2.37835i | ||||
\(706\) | − | 2.60469i | − | 0.0980287i | ||||||
\(707\) | 51.1145i | 1.92236i | ||||||||
\(708\) | 19.5325 | − | 4.92393i | 0.734077 | − | 0.185053i | ||||
\(709\) | −6.10968 | −0.229454 | −0.114727 | − | 0.993397i | \(-0.536599\pi\) | ||||
−0.114727 | + | 0.993397i | \(0.536599\pi\) | |||||||
\(710\) | −32.2172 | −1.20909 | ||||||||
\(711\) | −12.8806 | − | 23.9241i | −0.483059 | − | 0.897225i | ||||
\(712\) | 12.2301i | 0.458344i | ||||||||
\(713\) | 1.99846i | 0.0748429i | ||||||||
\(714\) | 8.05283 | − | 2.03003i | 0.301370 | − | 0.0759719i | ||||
\(715\) | −29.1536 | − | 18.9336i | −1.09028 | − | 0.708077i | ||||
\(716\) | − | 7.57467i | − | 0.283079i | ||||||
\(717\) | 7.06569 | + | 28.0286i | 0.263873 | + | 1.04675i | ||||
\(718\) | −7.37005 | −0.275048 | ||||||||
\(719\) | 17.3107i | 0.645579i | 0.946471 | + | 0.322790i | \(0.104621\pi\) | ||||
−0.946471 | + | 0.322790i | \(0.895379\pi\) | |||||||
\(720\) | −5.79026 | − | 10.7547i | −0.215790 | − | 0.400805i | ||||
\(721\) | − | 6.64068i | − | 0.247312i | ||||||
\(722\) | −1.68773 | −0.0628110 | ||||||||
\(723\) | 25.1253 | − | 6.33380i | 0.934419 | − | 0.235557i | ||||
\(724\) | 2.71865 | 0.101038 | ||||||||
\(725\) | −91.6688 | −3.40449 | ||||||||
\(726\) | 14.9837 | − | 11.7681i | 0.556097 | − | 0.436756i | ||||
\(727\) | −4.20516 | −0.155961 | −0.0779803 | − | 0.996955i | \(-0.524847\pi\) | ||||
−0.0779803 | + | 0.996955i | \(0.524847\pi\) | |||||||
\(728\) | −12.3432 | −0.457469 | ||||||||
\(729\) | −2.40344 | + | 26.8928i | −0.0890164 | + | 0.996030i | ||||
\(730\) | 17.3619 | 0.642593 | ||||||||
\(731\) | 4.45168i | 0.164651i | ||||||||
\(732\) | 6.88368 | − | 1.73530i | 0.254428 | − | 0.0641385i | ||||
\(733\) | − | 27.8143i | − | 1.02734i | −0.857987 | − | 0.513672i | \(-0.828285\pi\) | ||
0.857987 | − | 0.513672i | \(-0.171715\pi\) | |||||||
\(734\) | 3.43567 | 0.126813 | ||||||||
\(735\) | −109.338 | + | 27.5630i | −4.03300 | + | 1.01668i | ||||
\(736\) | − | 5.62472i | − | 0.207330i | ||||||
\(737\) | 14.2366 | + | 9.24586i | 0.524412 | + | 0.340576i | ||||
\(738\) | −4.03846 | + | 2.17427i | −0.148658 | + | 0.0800361i | ||||
\(739\) | − | 35.6113i | − | 1.30998i | −0.755636 | − | 0.654991i | \(-0.772672\pi\) | ||
0.755636 | − | 0.654991i | \(-0.227328\pi\) | |||||||
\(740\) | 21.8057i | 0.801592i | ||||||||
\(741\) | 4.95739 | + | 19.6653i | 0.182114 | + | 0.722421i | ||||
\(742\) | −46.6211 | −1.71151 | ||||||||
\(743\) | −35.6074 | −1.30631 | −0.653154 | − | 0.757225i | \(-0.726554\pi\) | ||||
−0.653154 | + | 0.757225i | \(0.726554\pi\) | |||||||
\(744\) | 0.150429 | + | 0.596728i | 0.00551498 | + | 0.0218771i | ||||
\(745\) | 76.6265i | 2.80738i | ||||||||
\(746\) | 30.6755i | 1.12311i | ||||||||
\(747\) | 19.1939 | − | 10.3338i | 0.702268 | − | 0.378095i | ||||
\(748\) | 2.78151 | + | 1.80643i | 0.101702 | + | 0.0660497i | ||||
\(749\) | 20.3898i | 0.745029i | ||||||||
\(750\) | −44.9725 | + | 11.3371i | −1.64216 | + | 0.413971i | ||||
\(751\) | 1.60225 | 0.0584669 | 0.0292334 | − | 0.999573i | \(-0.490693\pi\) | ||||
0.0292334 | + | 0.999573i | \(0.490693\pi\) | |||||||
\(752\) | − | 9.23503i | − | 0.336767i | ||||||
\(753\) | 18.8936 | − | 4.76288i | 0.688523 | − | 0.173569i | ||||
\(754\) | − | 20.3842i | − | 0.742350i | ||||||
\(755\) | 67.6399 | 2.46167 | ||||||||
\(756\) | 18.3844 | − | 16.8147i | 0.668636 | − | 0.611544i | ||||
\(757\) | −30.4905 | −1.10820 | −0.554098 | − | 0.832452i | \(-0.686937\pi\) | ||||
−0.554098 | + | 0.832452i | \(0.686937\pi\) | |||||||
\(758\) | −6.90631 | −0.250848 | ||||||||
\(759\) | 30.5781 | + | 10.4410i | 1.10992 | + | 0.378984i | ||||
\(760\) | 18.5185 | 0.671738 | ||||||||
\(761\) | −33.3992 | −1.21072 | −0.605360 | − | 0.795952i | \(-0.706971\pi\) | ||||
−0.605360 | + | 0.795952i | \(0.706971\pi\) | |||||||
\(762\) | −5.63163 | + | 1.41967i | −0.204012 | + | 0.0514292i | ||||
\(763\) | 26.3274 | 0.953117 | ||||||||
\(764\) | 20.5365i | 0.742983i | ||||||||
\(765\) | 5.79026 | + | 10.7547i | 0.209347 | + | 0.388838i | ||||
\(766\) | 8.94380i | 0.323153i | ||||||||
\(767\) | 29.9390 | 1.08103 | ||||||||
\(768\) | −0.423385 | − | 1.67951i | −0.0152776 | − | 0.0606040i | ||||
\(769\) | − | 1.31668i | − | 0.0474806i | −0.999718 | − | 0.0237403i | \(-0.992443\pi\) | ||
0.999718 | − | 0.0237403i | \(-0.00755749\pi\) | |||||||
\(770\) | −54.2997 | − | 35.2646i | −1.95683 | − | 1.27085i | ||||
\(771\) | 30.8509 | − | 7.77716i | 1.11107 | − | 0.280088i | ||||
\(772\) | 3.45941i | 0.124507i | ||||||||
\(773\) | 16.6818i | 0.600003i | 0.953939 | + | 0.300001i | \(0.0969871\pi\) | ||||
−0.953939 | + | 0.300001i | \(0.903013\pi\) | |||||||
\(774\) | 6.33098 | + | 11.7591i | 0.227562 | + | 0.422671i | ||||
\(775\) | 4.11323 | 0.147752 | ||||||||
\(776\) | 0.0605836 | 0.00217483 | ||||||||
\(777\) | −43.1288 | + | 10.8723i | −1.54724 | + | 0.390041i | ||||
\(778\) | − | 37.7077i | − | 1.35189i | ||||||
\(779\) | − | 6.95382i | − | 0.249146i | ||||||
\(780\) | −4.43759 | − | 17.6033i | −0.158891 | − | 0.630298i | ||||
\(781\) | 14.2942 | − | 22.0099i | 0.511486 | − | 0.787575i | ||||
\(782\) | 5.62472i | 0.201139i | ||||||||
\(783\) | 27.7687 | + | 30.3611i | 0.992372 | + | 1.08502i | ||||
\(784\) | −15.9897 | −0.571060 | ||||||||
\(785\) | 53.2183i | 1.89944i | ||||||||
\(786\) | −6.22150 | − | 24.6798i | −0.221914 | − | 0.880299i | ||||
\(787\) | − | 14.2557i | − | 0.508159i | −0.967183 | − | 0.254080i | \(-0.918227\pi\) | ||
0.967183 | − | 0.254080i | \(-0.0817726\pi\) | |||||||
\(788\) | 6.31827 | 0.225079 | ||||||||
\(789\) | 3.28899 | + | 13.0469i | 0.117091 | + | 0.464483i | ||||
\(790\) | −36.8755 | −1.31197 | ||||||||
\(791\) | 83.2366 | 2.95955 | ||||||||
\(792\) | 9.91636 | + | 0.815933i | 0.352363 | + | 0.0289929i | ||||
\(793\) | 10.5512 | 0.374683 | ||||||||
\(794\) | 30.7172 | 1.09011 | ||||||||
\(795\) | −16.7611 | − | 66.4887i | −0.594454 | − | 2.35811i | ||||
\(796\) | 0.756526 | 0.0268143 | ||||||||
\(797\) | − | 35.1548i | − | 1.24525i | −0.782521 | − | 0.622624i | \(-0.786067\pi\) | ||
0.782521 | − | 0.622624i | \(-0.213933\pi\) | |||||||
\(798\) | 9.23333 | + | 36.6273i | 0.326856 | + | 1.29659i | ||||
\(799\) | 9.23503i | 0.326712i | ||||||||
\(800\) | −11.5768 | −0.409302 | ||||||||
\(801\) | −17.3932 | − | 32.3058i | −0.614558 | − | 1.14147i | ||||
\(802\) | − | 1.35005i | − | 0.0476720i | ||||||
\(803\) | −7.70316 | + | 11.8612i | −0.271839 | + | 0.418572i | ||||
\(804\) | 2.16701 | + | 8.59622i | 0.0764246 | + | 0.303165i | ||||
\(805\) | − | 109.804i | − | 3.87008i | ||||||
\(806\) | 0.914652i | 0.0322173i | ||||||||
\(807\) | 11.1567 | − | 2.81249i | 0.392735 | − | 0.0990042i | ||||
\(808\) | −10.6605 | −0.375035 | ||||||||
\(809\) | 47.1237 | 1.65678 | 0.828391 | − | 0.560151i | \(-0.189257\pi\) | ||||
0.828391 | + | 0.560151i | \(0.189257\pi\) | |||||||
\(810\) | 30.5898 | + | 20.1739i | 1.07482 | + | 0.708837i | ||||
\(811\) | 14.2763i | 0.501310i | 0.968077 | + | 0.250655i | \(0.0806459\pi\) | ||||
−0.968077 | + | 0.250655i | \(0.919354\pi\) | |||||||
\(812\) | − | 37.9664i | − | 1.33236i | ||||||
\(813\) | −19.4688 | + | 4.90787i | −0.682801 | + | 0.172127i | ||||
\(814\) | −14.8970 | − | 9.67478i | −0.522141 | − | 0.339101i | ||||
\(815\) | 6.34858i | 0.222381i | ||||||||
\(816\) | 0.423385 | + | 1.67951i | 0.0148214 | + | 0.0587945i | ||||
\(817\) | −20.2479 | −0.708385 | ||||||||
\(818\) | − | 31.8859i | − | 1.11487i | ||||||
\(819\) | 32.6044 | − | 17.5540i | 1.13929 | − | 0.613385i | ||||
\(820\) | 6.22468i | 0.217375i | ||||||||
\(821\) | 16.8744 | 0.588922 | 0.294461 | − | 0.955664i | \(-0.404860\pi\) | ||||
0.294461 | + | 0.955664i | \(0.404860\pi\) | |||||||
\(822\) | −36.2797 | + | 9.14571i | −1.26540 | + | 0.318993i | ||||
\(823\) | 6.12550 | 0.213522 | 0.106761 | − | 0.994285i | \(-0.465952\pi\) | ||||
0.106761 | + | 0.994285i | \(0.465952\pi\) | |||||||
\(824\) | 1.38499 | 0.0482483 | ||||||||
\(825\) | 21.4897 | − | 62.9359i | 0.748174 | − | 2.19115i | ||||
\(826\) | 55.7625 | 1.94023 | ||||||||
\(827\) | −11.1077 | −0.386252 | −0.193126 | − | 0.981174i | \(-0.561863\pi\) | ||||
−0.193126 | + | 0.981174i | \(0.561863\pi\) | |||||||
\(828\) | 7.99923 | + | 14.8576i | 0.277992 | + | 0.516339i | ||||
\(829\) | −46.9752 | −1.63152 | −0.815758 | − | 0.578393i | \(-0.803680\pi\) | ||||
−0.815758 | + | 0.578393i | \(0.803680\pi\) | |||||||
\(830\) | − | 29.5845i | − | 1.02689i | ||||||
\(831\) | −24.3021 | + | 6.12630i | −0.843032 | + | 0.212519i | ||||
\(832\) | − | 2.57431i | − | 0.0892482i | ||||||
\(833\) | 15.9897 | 0.554010 | ||||||||
\(834\) | −14.9398 | + | 3.76617i | −0.517324 | + | 0.130412i | ||||
\(835\) | 10.0822i | 0.348908i | ||||||||
\(836\) | −8.21634 | + | 12.6514i | −0.284168 | + | 0.437556i | ||||
\(837\) | −1.24600 | − | 1.36232i | −0.0430680 | − | 0.0470886i | ||||
\(838\) | 6.43054i | 0.222139i | ||||||||
\(839\) | 25.1642i | 0.868765i | 0.900728 | + | 0.434383i | \(0.143033\pi\) | ||||
−0.900728 | + | 0.434383i | \(0.856967\pi\) | |||||||
\(840\) | −8.26518 | − | 32.7868i | −0.285176 | − | 1.13125i | ||||
\(841\) | 33.6998 | 1.16206 | ||||||||
\(842\) | −0.960351 | −0.0330959 | ||||||||
\(843\) | −5.10675 | − | 20.2577i | −0.175886 | − | 0.697713i | ||||
\(844\) | − | 11.6543i | − | 0.401156i | ||||||
\(845\) | 25.9471i | 0.892607i | ||||||||
\(846\) | 13.1337 | + | 24.3942i | 0.451544 | + | 0.838691i | ||||
\(847\) | 48.1836 | − | 21.4498i | 1.65561 | − | 0.737024i | ||||
\(848\) | − | 9.72335i | − | 0.333901i | ||||||
\(849\) | −5.61760 | + | 1.41613i | −0.192795 | + | 0.0486016i | ||||
\(850\) | 11.5768 | 0.397081 | ||||||||
\(851\) | − | 30.1245i | − | 1.03265i | ||||||
\(852\) | 13.2898 | − | 3.35021i | 0.455302 | − | 0.114776i | ||||
\(853\) | 25.5957i | 0.876379i | 0.898883 | + | 0.438189i | \(0.144380\pi\) | ||||
−0.898883 | + | 0.438189i | \(0.855620\pi\) | |||||||
\(854\) | 19.6519 | 0.672475 | ||||||||
\(855\) | −48.9165 | + | 26.3363i | −1.67291 | + | 0.900681i | ||||
\(856\) | −4.25253 | −0.145348 | ||||||||
\(857\) | 36.7932 | 1.25683 | 0.628415 | − | 0.777878i | \(-0.283704\pi\) | ||||
0.628415 | + | 0.777878i | \(0.283704\pi\) | |||||||
\(858\) | 13.9949 | + | 4.77861i | 0.477780 | + | 0.163139i | ||||
\(859\) | 30.2778 | 1.03306 | 0.516532 | − | 0.856268i | \(-0.327223\pi\) | ||||
0.516532 | + | 0.856268i | \(0.327223\pi\) | |||||||
\(860\) | 18.1248 | 0.618052 | ||||||||
\(861\) | −12.3116 | + | 3.10362i | −0.419579 | + | 0.105771i | ||||
\(862\) | −1.91773 | −0.0653182 | ||||||||
\(863\) | − | 5.71212i | − | 0.194443i | −0.995263 | − | 0.0972214i | \(-0.969005\pi\) | ||
0.995263 | − | 0.0972214i | \(-0.0309955\pi\) | |||||||
\(864\) | 3.50689 | + | 3.83428i | 0.119307 | + | 0.130445i | ||||
\(865\) | 24.1277i | 0.820368i | ||||||||
\(866\) | 10.0096 | 0.340141 | ||||||||
\(867\) | −0.423385 | − | 1.67951i | −0.0143789 | − | 0.0570391i | ||||
\(868\) | 1.70358i | 0.0578231i | ||||||||
\(869\) | 16.3610 | − | 25.1923i | 0.555008 | − | 0.854591i | ||||
\(870\) | 54.1459 | − | 13.6496i | 1.83572 | − | 0.462764i | ||||
\(871\) | 13.1761i | 0.446455i | ||||||||
\(872\) | 5.49088i | 0.185945i | ||||||||
\(873\) | −0.160031 | + | 0.0861594i | −0.00541623 | + | 0.00291605i | ||||
\(874\) | −25.5833 | −0.865369 | ||||||||
\(875\) | −128.390 | −4.34038 | ||||||||
\(876\) | −7.16191 | + | 1.80544i | −0.241978 | + | 0.0610001i | ||||
\(877\) | 41.9623i | 1.41697i | 0.705727 | + | 0.708484i | \(0.250621\pi\) | ||||
−0.705727 | + | 0.708484i | \(0.749379\pi\) | |||||||
\(878\) | 23.1549i | 0.781441i | ||||||||
\(879\) | 0.728667 | + | 2.89052i | 0.0245773 | + | 0.0974947i | ||||
\(880\) | 7.35482 | − | 11.3248i | 0.247931 | − | 0.381759i | ||||
\(881\) | − | 7.05198i | − | 0.237587i | −0.992919 | − | 0.118794i | \(-0.962097\pi\) | ||
0.992919 | − | 0.118794i | \(-0.0379027\pi\) | |||||||
\(882\) | 42.2366 | − | 22.7398i | 1.42218 | − | 0.765690i | ||||
\(883\) | −8.47204 | −0.285107 | −0.142553 | − | 0.989787i | \(-0.545531\pi\) | ||||
−0.142553 | + | 0.989787i | \(0.545531\pi\) | |||||||
\(884\) | 2.57431i | 0.0865835i | ||||||||
\(885\) | 20.0476 | + | 79.5259i | 0.673892 | + | 2.67323i | ||||
\(886\) | − | 10.9209i | − | 0.366896i | ||||||
\(887\) | −47.8035 | −1.60509 | −0.802543 | − | 0.596595i | \(-0.796520\pi\) | ||||
−0.802543 | + | 0.596595i | \(0.796520\pi\) | |||||||
\(888\) | −2.26754 | − | 8.99499i | −0.0760936 | − | 0.301852i | ||||
\(889\) | −16.0775 | −0.539222 | ||||||||
\(890\) | −49.7946 | −1.66912 | ||||||||
\(891\) | −27.3544 | + | 11.9473i | −0.916406 | + | 0.400251i | ||||
\(892\) | −0.142411 | −0.00476827 | ||||||||
\(893\) | −42.0044 | −1.40562 | ||||||||
\(894\) | −7.96828 | − | 31.6090i | −0.266499 | − | 1.05716i | ||||
\(895\) | 30.8400 | 1.03087 | ||||||||
\(896\) | − | 4.79476i | − | 0.160182i | ||||||
\(897\) | 6.13052 | + | 24.3189i | 0.204692 | + | 0.811984i | ||||
\(898\) | 13.2072i | 0.440730i | ||||||||
\(899\) | −2.81338 | −0.0938314 | ||||||||
\(900\) | 30.5800 | − | 16.4640i | 1.01933 | − | 0.548801i | ||||
\(901\) | 9.72335i | 0.323932i | ||||||||
\(902\) | −4.25253 | − | 2.76178i | −0.141594 | − | 0.0919571i | ||||
\(903\) | 9.03703 | + | 35.8486i | 0.300734 | + | 1.19297i | ||||
\(904\) | 17.3599i | 0.577382i | ||||||||
\(905\) | 11.0689i | 0.367942i | ||||||||
\(906\) | −27.9019 | + | 7.03376i | −0.926979 | + | 0.233681i | ||||
\(907\) | −8.75556 | −0.290724 | −0.145362 | − | 0.989379i | \(-0.546435\pi\) | ||||
−0.145362 | + | 0.989379i | \(0.546435\pi\) | |||||||
\(908\) | 6.24693 | 0.207312 | ||||||||
\(909\) | 28.1596 | − | 15.1609i | 0.933995 | − | 0.502855i | ||||
\(910\) | − | 50.2549i | − | 1.66593i | ||||||
\(911\) | − | 22.7770i | − | 0.754634i | −0.926084 | − | 0.377317i | \(-0.876847\pi\) | ||
0.926084 | − | 0.377317i | \(-0.123153\pi\) | |||||||
\(912\) | −7.63903 | + | 1.92571i | −0.252954 | + | 0.0637668i | ||||
\(913\) | 20.2113 | + | 13.1261i | 0.668897 | + | 0.434411i | ||||
\(914\) | − | 21.3501i | − | 0.706200i | ||||||
\(915\) | 7.06520 | + | 28.0266i | 0.233568 | + | 0.926532i | ||||
\(916\) | 10.0198 | 0.331064 | ||||||||
\(917\) | − | 70.4573i | − | 2.32671i | ||||||
\(918\) | −3.50689 | − | 3.83428i | −0.115745 | − | 0.126550i | ||||
\(919\) | − | 35.0107i | − | 1.15490i | −0.816427 | − | 0.577449i | \(-0.804048\pi\) | ||
0.816427 | − | 0.577449i | \(-0.195952\pi\) | |||||||
\(920\) | 22.9008 | 0.755018 | ||||||||
\(921\) | 26.1878 | − | 6.60165i | 0.862917 | − | 0.217532i | ||||
\(922\) | −4.75396 | −0.156563 | ||||||||
\(923\) | 20.3703 | 0.670498 | ||||||||
\(924\) | 26.0661 | + | 8.90036i | 0.857513 | + | 0.292800i | ||||
\(925\) | −62.0023 | −2.03862 | ||||||||
\(926\) | 34.9504 | 1.14854 | ||||||||
\(927\) | −3.65843 | + | 1.96967i | −0.120159 | + | 0.0646924i | ||||
\(928\) | 7.91832 | 0.259932 | ||||||||
\(929\) | 18.4339i | 0.604796i | 0.953182 | + | 0.302398i | \(0.0977872\pi\) | ||||
−0.953182 | + | 0.302398i | \(0.902213\pi\) | |||||||
\(930\) | −2.42956 | + | 0.612464i | −0.0796683 | + | 0.0200835i | ||||
\(931\) | 72.7271i | 2.38354i | ||||||||
\(932\) | 27.9235 | 0.914666 | ||||||||
\(933\) | 47.6413 | − | 12.0098i | 1.55971 | − | 0.393184i | ||||
\(934\) | − | 17.6209i | − | 0.576575i | ||||||
\(935\) | −7.35482 | + | 11.3248i | −0.240528 | + | 0.370361i | ||||
\(936\) | 3.66108 | + | 6.80002i | 0.119666 | + | 0.222266i | ||||
\(937\) | 17.0084i | 0.555640i | 0.960633 | + | 0.277820i | \(0.0896119\pi\) | ||||
−0.960633 | + | 0.277820i | \(0.910388\pi\) | |||||||
\(938\) | 24.5410i | 0.801292i | ||||||||
\(939\) | −2.70827 | − | 10.7433i | −0.0883812 | − | 0.350595i | ||||
\(940\) | 37.6001 | 1.22638 | ||||||||
\(941\) | 7.06014 | 0.230154 | 0.115077 | − | 0.993357i | \(-0.463289\pi\) | ||||
0.115077 | + | 0.993357i | \(0.463289\pi\) | |||||||
\(942\) | −5.53409 | − | 21.9529i | −0.180310 | − | 0.715265i | ||||
\(943\) | − | 8.59939i | − | 0.280035i | ||||||
\(944\) | 11.6299i | 0.378521i | ||||||||
\(945\) | 68.4603 | + | 74.8516i | 2.22702 | + | 2.43492i | ||||
\(946\) | −8.04166 | + | 12.3824i | −0.261457 | + | 0.402586i | ||||
\(947\) | − | 14.7310i | − | 0.478692i | −0.970934 | − | 0.239346i | \(-0.923067\pi\) | ||
0.970934 | − | 0.239346i | \(-0.0769331\pi\) | |||||||
\(948\) | 15.2114 | − | 3.83462i | 0.494043 | − | 0.124543i | ||||
\(949\) | −10.9776 | −0.356348 | ||||||||
\(950\) | 52.6557i | 1.70838i | ||||||||
\(951\) | −50.0253 | + | 12.6108i | −1.62218 | + | 0.408934i | ||||
\(952\) | 4.79476i | 0.155399i | ||||||||
\(953\) | 1.29427 | 0.0419255 | 0.0209628 | − | 0.999780i | \(-0.493327\pi\) | ||||
0.0209628 | + | 0.999780i | \(0.493327\pi\) | |||||||
\(954\) | 13.8281 | + | 25.6841i | 0.447702 | + | 0.831554i | ||||
\(955\) | −83.6134 | −2.70567 | ||||||||
\(956\) | −16.6886 | −0.539747 | ||||||||
\(957\) | −14.6985 | + | 43.0470i | −0.475136 | + | 1.39151i | ||||
\(958\) | 21.9110 | 0.707912 | ||||||||
\(959\) | −103.573 | −3.34456 | ||||||||
\(960\) | 6.83805 | − | 1.72380i | 0.220697 | − | 0.0556353i | ||||
\(961\) | −30.8738 | −0.995928 | ||||||||
\(962\) | − | 13.7873i | − | 0.444521i | ||||||
\(963\) | 11.2330 | − | 6.04776i | 0.361979 | − | 0.194886i | ||||
\(964\) | 14.9599i | 0.481826i | ||||||||
\(965\) | −14.0849 | −0.453408 | ||||||||
\(966\) | 11.4183 | + | 45.2949i | 0.367379 | + | 1.45734i | ||||
\(967\) | 22.1308i | 0.711680i | 0.934547 | + | 0.355840i | \(0.115805\pi\) | ||||
−0.934547 | + | 0.355840i | \(0.884195\pi\) | |||||||
\(968\) | 4.47360 | + | 10.0492i | 0.143787 | + | 0.322994i | ||||
\(969\) | 7.63903 | − | 1.92571i | 0.245401 | − | 0.0618629i | ||||
\(970\) | 0.246664i | 0.00791990i | ||||||||
\(971\) | − | 3.01415i | − | 0.0967288i | −0.998830 | − | 0.0483644i | \(-0.984599\pi\) | ||
0.998830 | − | 0.0483644i | \(-0.0154009\pi\) | |||||||
\(972\) | −14.7164 | − | 5.14087i | −0.472028 | − | 0.164894i | ||||
\(973\) | −42.6511 | −1.36733 | ||||||||
\(974\) | −18.5751 | −0.595183 | ||||||||
\(975\) | 50.0532 | − | 12.6178i | 1.60298 | − | 0.404095i | ||||
\(976\) | 4.09863i | 0.131194i | ||||||||
\(977\) | − | 12.0668i | − | 0.386050i | −0.981194 | − | 0.193025i | \(-0.938170\pi\) | ||
0.981194 | − | 0.193025i | \(-0.0618298\pi\) | |||||||
\(978\) | −0.660180 | − | 2.61884i | −0.0211102 | − | 0.0837412i | ||||
\(979\) | 22.0930 | − | 34.0183i | 0.706094 | − | 1.08723i | ||||
\(980\) | − | 65.1014i | − | 2.07959i | ||||||
\(981\) | −7.80889 | − | 14.5041i | −0.249319 | − | 0.463081i | ||||
\(982\) | 8.75916 | 0.279516 | ||||||||
\(983\) | 59.4225i | 1.89528i | 0.319334 | + | 0.947642i | \(0.396541\pi\) | ||||
−0.319334 | + | 0.947642i | \(0.603459\pi\) | |||||||
\(984\) | −0.647295 | − | 2.56773i | −0.0206350 | − | 0.0818561i | ||||
\(985\) | 25.7246i | 0.819654i | ||||||||
\(986\) | −7.91832 | −0.252171 | ||||||||
\(987\) | 18.7474 | + | 74.3681i | 0.596735 | + | 2.36716i | ||||
\(988\) | −11.7089 | −0.372511 | ||||||||
\(989\) | −25.0394 | −0.796208 | ||||||||
\(990\) | −3.32204 | + | 40.3741i | −0.105581 | + | 1.28317i | ||||
\(991\) | 16.1986 | 0.514566 | 0.257283 | − | 0.966336i | \(-0.417173\pi\) | ||||
0.257283 | + | 0.966336i | \(0.417173\pi\) | |||||||
\(992\) | −0.355300 | −0.0112808 | ||||||||
\(993\) | 5.28139 | + | 20.9505i | 0.167600 | + | 0.664845i | ||||
\(994\) | 37.9405 | 1.20340 | ||||||||
\(995\) | 3.08017i | 0.0976478i | ||||||||
\(996\) | 3.07645 | + | 12.2038i | 0.0974810 | + | 0.386693i | ||||
\(997\) | − | 18.8652i | − | 0.597468i | −0.954336 | − | 0.298734i | \(-0.903436\pi\) | ||
0.954336 | − | 0.298734i | \(-0.0965644\pi\) | |||||||
\(998\) | 1.95828 | 0.0619882 | ||||||||
\(999\) | 18.7820 | + | 20.5354i | 0.594235 | + | 0.649711i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1122.2.b.c.1055.5 | yes | 16 | |
3.2 | odd | 2 | 1122.2.b.a.1055.6 | yes | 16 | ||
11.10 | odd | 2 | 1122.2.b.a.1055.5 | ✓ | 16 | ||
33.32 | even | 2 | inner | 1122.2.b.c.1055.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1122.2.b.a.1055.5 | ✓ | 16 | 11.10 | odd | 2 | ||
1122.2.b.a.1055.6 | yes | 16 | 3.2 | odd | 2 | ||
1122.2.b.c.1055.5 | yes | 16 | 1.1 | even | 1 | trivial | |
1122.2.b.c.1055.6 | yes | 16 | 33.32 | even | 2 | inner |