Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [460,2,Mod(91,460)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(460, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("460.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 460 = 2^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 460.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.67311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.7465802011608416256.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{14} + x^{12} + 8x^{10} - 20x^{8} + 32x^{6} + 16x^{4} - 64x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.10 | ||
Root | \(-1.37379 + 0.335728i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 460.91 |
Dual form | 460.2.e.a.91.11 |
$q$-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 \(\left(\mathbb{Z}/460\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(277\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.637910 | − | 1.26217i | 0.451071 | − | 0.892488i | ||||
\(3\) | − | 0.348132i | − | 0.200994i | −0.994937 | − | 0.100497i | \(-0.967957\pi\) | ||
0.994937 | − | 0.100497i | \(-0.0320433\pi\) | |||||||
\(4\) | −1.18614 | − | 1.61030i | −0.593070 | − | 0.805151i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −0.439402 | − | 0.222077i | −0.179385 | − | 0.0906627i | ||||
\(7\) | 4.89140 | 1.84878 | 0.924388 | − | 0.381454i | \(-0.124577\pi\) | ||||
0.924388 | + | 0.381454i | \(0.124577\pi\) | |||||||
\(8\) | −2.78912 | + | 0.469882i | −0.986104 | + | 0.166128i | ||||
\(9\) | 2.87880 | 0.959601 | ||||||||
\(10\) | 1.26217 | + | 0.637910i | 0.399133 | + | 0.201725i | ||||
\(11\) | 2.68161 | 0.808537 | 0.404268 | − | 0.914640i | \(-0.367526\pi\) | ||||
0.404268 | + | 0.914640i | \(0.367526\pi\) | |||||||
\(12\) | −0.560598 | + | 0.412934i | −0.161831 | + | 0.119204i | ||||
\(13\) | −3.09987 | −0.859750 | −0.429875 | − | 0.902888i | \(-0.641442\pi\) | ||||
−0.429875 | + | 0.902888i | \(0.641442\pi\) | |||||||
\(14\) | 3.12027 | − | 6.17377i | 0.833929 | − | 1.65001i | ||||
\(15\) | 0.348132 | 0.0898874 | ||||||||
\(16\) | −1.18614 | + | 3.82009i | −0.296535 | + | 0.955022i | ||||
\(17\) | 0.769298i | 0.186582i | 0.995639 | + | 0.0932911i | \(0.0297387\pi\) | ||||
−0.995639 | + | 0.0932911i | \(0.970261\pi\) | |||||||
\(18\) | 1.83642 | − | 3.63354i | 0.432848 | − | 0.856433i | ||||
\(19\) | −4.89140 | −1.12216 | −0.561082 | − | 0.827760i | \(-0.689615\pi\) | ||||
−0.561082 | + | 0.827760i | \(0.689615\pi\) | |||||||
\(20\) | 1.61030 | − | 1.18614i | 0.360074 | − | 0.265229i | ||||
\(21\) | − | 1.70285i | − | 0.371593i | ||||||
\(22\) | 1.71063 | − | 3.38465i | 0.364707 | − | 0.721610i | ||||
\(23\) | 2.20979 | − | 4.25639i | 0.460772 | − | 0.887518i | ||||
\(24\) | 0.163581 | + | 0.970984i | 0.0333909 | + | 0.198201i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −1.97744 | + | 3.91256i | −0.387808 | + | 0.767317i | ||||
\(27\) | − | 2.04660i | − | 0.393869i | ||||||
\(28\) | −5.80189 | − | 7.87663i | −1.09645 | − | 1.48854i | ||||
\(29\) | −1.72418 | −0.320172 | −0.160086 | − | 0.987103i | \(-0.551177\pi\) | ||||
−0.160086 | + | 0.987103i | \(0.551177\pi\) | |||||||
\(30\) | 0.222077 | − | 0.439402i | 0.0405456 | − | 0.0802234i | ||||
\(31\) | − | 8.95574i | − | 1.60850i | −0.594292 | − | 0.804250i | \(-0.702568\pi\) | ||
0.594292 | − | 0.804250i | \(-0.297432\pi\) | |||||||
\(32\) | 4.06494 | + | 3.93398i | 0.718587 | + | 0.695437i | ||||
\(33\) | − | 0.933557i | − | 0.162511i | ||||||
\(34\) | 0.970984 | + | 0.490743i | 0.166522 | + | 0.0841618i | ||||
\(35\) | 4.89140i | 0.826797i | ||||||||
\(36\) | −3.41467 | − | 4.63574i | −0.569111 | − | 0.772624i | ||||
\(37\) | 2.12461i | 0.349283i | 0.984632 | + | 0.174642i | \(0.0558767\pi\) | ||||
−0.984632 | + | 0.174642i | \(0.944123\pi\) | |||||||
\(38\) | −3.12027 | + | 6.17377i | −0.506175 | + | 1.00152i | ||||
\(39\) | 1.07917i | 0.172805i | ||||||||
\(40\) | −0.469882 | − | 2.78912i | −0.0742949 | − | 0.440999i | ||||
\(41\) | −5.04512 | −0.787915 | −0.393958 | − | 0.919129i | \(-0.628894\pi\) | ||||
−0.393958 | + | 0.919129i | \(0.628894\pi\) | |||||||
\(42\) | −2.14929 | − | 1.08627i | −0.331643 | − | 0.167615i | ||||
\(43\) | −0.739645 | −0.112795 | −0.0563974 | − | 0.998408i | \(-0.517961\pi\) | ||||
−0.0563974 | + | 0.998408i | \(0.517961\pi\) | |||||||
\(44\) | −3.18077 | − | 4.31821i | −0.479519 | − | 0.650994i | ||||
\(45\) | 2.87880i | 0.429147i | ||||||||
\(46\) | −3.96264 | − | 5.50432i | −0.584259 | − | 0.811567i | ||||
\(47\) | 9.51433i | 1.38781i | 0.720068 | + | 0.693904i | \(0.244111\pi\) | ||||
−0.720068 | + | 0.693904i | \(0.755889\pi\) | |||||||
\(48\) | 1.32990 | + | 0.412934i | 0.191954 | + | 0.0596019i | ||||
\(49\) | 16.9258 | 2.41797 | ||||||||
\(50\) | −0.637910 | + | 1.26217i | −0.0902142 | + | 0.178498i | ||||
\(51\) | 0.267818 | 0.0375020 | ||||||||
\(52\) | 3.67688 | + | 4.99173i | 0.509892 | + | 0.692228i | ||||
\(53\) | 11.1565i | 1.53246i | 0.642565 | + | 0.766231i | \(0.277870\pi\) | ||||
−0.642565 | + | 0.766231i | \(0.722130\pi\) | |||||||
\(54\) | −2.58316 | − | 1.30555i | −0.351523 | − | 0.177663i | ||||
\(55\) | 2.68161i | 0.361589i | ||||||||
\(56\) | −13.6427 | + | 2.29838i | −1.82309 | + | 0.307134i | ||||
\(57\) | 1.70285i | 0.225549i | ||||||||
\(58\) | −1.09987 | + | 2.17621i | −0.144420 | + | 0.285750i | ||||
\(59\) | − | 1.87953i | − | 0.244694i | −0.992487 | − | 0.122347i | \(-0.960958\pi\) | ||
0.992487 | − | 0.122347i | \(-0.0390420\pi\) | |||||||
\(60\) | −0.412934 | − | 0.560598i | −0.0533096 | − | 0.0723729i | ||||
\(61\) | 8.05040i | 1.03075i | 0.856965 | + | 0.515374i | \(0.172347\pi\) | ||||
−0.856965 | + | 0.515374i | \(0.827653\pi\) | |||||||
\(62\) | −11.3037 | − | 5.71296i | −1.43557 | − | 0.725547i | ||||
\(63\) | 14.0814 | 1.77409 | ||||||||
\(64\) | 7.55842 | − | 2.62112i | 0.944803 | − | 0.327640i | ||||
\(65\) | − | 3.09987i | − | 0.384492i | ||||||
\(66\) | −1.17831 | − | 0.595525i | −0.145039 | − | 0.0733041i | ||||
\(67\) | −5.76872 | −0.704762 | −0.352381 | − | 0.935857i | \(-0.614628\pi\) | ||||
−0.352381 | + | 0.935857i | \(0.614628\pi\) | |||||||
\(68\) | 1.23880 | − | 0.912496i | 0.150227 | − | 0.110656i | ||||
\(69\) | −1.48179 | − | 0.769298i | −0.178386 | − | 0.0926126i | ||||
\(70\) | 6.17377 | + | 3.12027i | 0.737907 | + | 0.372944i | ||||
\(71\) | 0.619304i | 0.0734978i | 0.999325 | + | 0.0367489i | \(0.0117002\pi\) | ||||
−0.999325 | + | 0.0367489i | \(0.988300\pi\) | |||||||
\(72\) | −8.02934 | + | 1.35270i | −0.946267 | + | 0.159417i | ||||
\(73\) | −12.6534 | −1.48097 | −0.740483 | − | 0.672075i | \(-0.765403\pi\) | ||||
−0.740483 | + | 0.672075i | \(0.765403\pi\) | |||||||
\(74\) | 2.68161 | + | 1.35531i | 0.311731 | + | 0.157551i | ||||
\(75\) | 0.348132i | 0.0401989i | ||||||||
\(76\) | 5.80189 | + | 7.87663i | 0.665522 | + | 0.903511i | ||||
\(77\) | 13.1168 | 1.49480 | ||||||||
\(78\) | 1.36209 | + | 0.688411i | 0.154226 | + | 0.0779472i | ||||
\(79\) | 6.71238 | 0.755201 | 0.377601 | − | 0.925969i | \(-0.376749\pi\) | ||||
0.377601 | + | 0.925969i | \(0.376749\pi\) | |||||||
\(80\) | −3.82009 | − | 1.18614i | −0.427099 | − | 0.132615i | ||||
\(81\) | 7.92392 | 0.880436 | ||||||||
\(82\) | −3.21833 | + | 6.36779i | −0.355406 | + | 0.703205i | ||||
\(83\) | −4.75372 | −0.521789 | −0.260894 | − | 0.965367i | \(-0.584017\pi\) | ||||
−0.260894 | + | 0.965367i | \(0.584017\pi\) | |||||||
\(84\) | −2.74211 | + | 2.01983i | −0.299189 | + | 0.220381i | ||||
\(85\) | −0.769298 | −0.0834421 | ||||||||
\(86\) | −0.471827 | + | 0.933557i | −0.0508784 | + | 0.100668i | ||||
\(87\) | 0.600243i | 0.0643528i | ||||||||
\(88\) | −7.47935 | + | 1.26004i | −0.797302 | + | 0.134321i | ||||
\(89\) | 9.87539i | 1.04679i | 0.852090 | + | 0.523395i | \(0.175335\pi\) | ||||
−0.852090 | + | 0.523395i | \(0.824665\pi\) | |||||||
\(90\) | 3.63354 | + | 1.83642i | 0.383008 | + | 0.193576i | ||||
\(91\) | −15.1627 | −1.58948 | ||||||||
\(92\) | −9.47519 | + | 1.49025i | −0.987856 | + | 0.155370i | ||||
\(93\) | −3.11778 | −0.323299 | ||||||||
\(94\) | 12.0087 | + | 6.06929i | 1.23860 | + | 0.626000i | ||||
\(95\) | − | 4.89140i | − | 0.501847i | ||||||
\(96\) | 1.36955 | − | 1.41514i | 0.139779 | − | 0.144432i | ||||
\(97\) | − | 15.8012i | − | 1.60437i | −0.597077 | − | 0.802184i | \(-0.703671\pi\) | ||
0.597077 | − | 0.802184i | \(-0.296329\pi\) | |||||||
\(98\) | 10.7971 | − | 21.3632i | 1.09068 | − | 2.15801i | ||||
\(99\) | 7.71984 | 0.775873 | ||||||||
\(100\) | 1.18614 | + | 1.61030i | 0.118614 | + | 0.161030i | ||||
\(101\) | 12.6951 | 1.26321 | 0.631604 | − | 0.775291i | \(-0.282397\pi\) | ||||
0.631604 | + | 0.775291i | \(0.282397\pi\) | |||||||
\(102\) | 0.170844 | − | 0.338031i | 0.0169160 | − | 0.0334701i | ||||
\(103\) | −15.2929 | −1.50685 | −0.753425 | − | 0.657534i | \(-0.771600\pi\) | ||||
−0.753425 | + | 0.657534i | \(0.771600\pi\) | |||||||
\(104\) | 8.64593 | − | 1.45657i | 0.847803 | − | 0.142829i | ||||
\(105\) | 1.70285 | 0.166182 | ||||||||
\(106\) | 14.0814 | + | 7.11684i | 1.36770 | + | 0.691249i | ||||
\(107\) | 0.739645 | 0.0715042 | 0.0357521 | − | 0.999361i | \(-0.488617\pi\) | ||||
0.0357521 | + | 0.999361i | \(0.488617\pi\) | |||||||
\(108\) | −3.29565 | + | 2.42756i | −0.317124 | + | 0.233592i | ||||
\(109\) | − | 14.4722i | − | 1.38618i | −0.720851 | − | 0.693090i | \(-0.756249\pi\) | ||
0.720851 | − | 0.693090i | \(-0.243751\pi\) | |||||||
\(110\) | 3.38465 | + | 1.71063i | 0.322714 | + | 0.163102i | ||||
\(111\) | 0.739645 | 0.0702040 | ||||||||
\(112\) | −5.80189 | + | 18.6856i | −0.548227 | + | 1.76562i | ||||
\(113\) | 14.8197i | 1.39412i | 0.717013 | + | 0.697060i | \(0.245509\pi\) | ||||
−0.717013 | + | 0.697060i | \(0.754491\pi\) | |||||||
\(114\) | 2.14929 | + | 1.08627i | 0.201299 | + | 0.101738i | ||||
\(115\) | 4.25639 | + | 2.20979i | 0.396910 | + | 0.206064i | ||||
\(116\) | 2.04512 | + | 2.77645i | 0.189885 | + | 0.257787i | ||||
\(117\) | −8.92392 | −0.825017 | ||||||||
\(118\) | −2.37228 | − | 1.19897i | −0.218386 | − | 0.110374i | ||||
\(119\) | 3.76295i | 0.344949i | ||||||||
\(120\) | −0.970984 | + | 0.163581i | −0.0886383 | + | 0.0149328i | ||||
\(121\) | −3.80895 | −0.346268 | ||||||||
\(122\) | 10.1610 | + | 5.13543i | 0.919931 | + | 0.464940i | ||||
\(123\) | 1.75637i | 0.158367i | ||||||||
\(124\) | −14.4214 | + | 10.6228i | −1.29508 | + | 0.953953i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 8.98266 | − | 17.7731i | 0.800239 | − | 1.58335i | ||||
\(127\) | − | 7.80725i | − | 0.692781i | −0.938090 | − | 0.346391i | \(-0.887407\pi\) | ||
0.938090 | − | 0.346391i | \(-0.112593\pi\) | |||||||
\(128\) | 1.51330 | − | 11.2120i | 0.133758 | − | 0.991014i | ||||
\(129\) | 0.257494i | 0.0226711i | ||||||||
\(130\) | −3.91256 | − | 1.97744i | −0.343154 | − | 0.173433i | ||||
\(131\) | − | 13.1943i | − | 1.15279i | −0.817172 | − | 0.576394i | \(-0.804459\pi\) | ||
0.817172 | − | 0.576394i | \(-0.195541\pi\) | |||||||
\(132\) | −1.50331 | + | 1.10733i | −0.130846 | + | 0.0963807i | ||||
\(133\) | −23.9258 | −2.07463 | ||||||||
\(134\) | −3.67993 | + | 7.28110i | −0.317897 | + | 0.628991i | ||||
\(135\) | 2.04660 | 0.176143 | ||||||||
\(136\) | −0.361479 | − | 2.14567i | −0.0309966 | − | 0.183990i | ||||
\(137\) | 10.8089i | 0.923471i | 0.887018 | + | 0.461735i | \(0.152773\pi\) | ||||
−0.887018 | + | 0.461735i | \(0.847227\pi\) | |||||||
\(138\) | −1.91623 | + | 1.37952i | −0.163120 | + | 0.117433i | ||||
\(139\) | 2.31388i | 0.196261i | 0.995174 | + | 0.0981305i | \(0.0312863\pi\) | ||||
−0.995174 | + | 0.0981305i | \(0.968714\pi\) | |||||||
\(140\) | 7.87663 | − | 5.80189i | 0.665697 | − | 0.490349i | ||||
\(141\) | 3.31225 | 0.278942 | ||||||||
\(142\) | 0.781666 | + | 0.395060i | 0.0655960 | + | 0.0331527i | ||||
\(143\) | −8.31266 | −0.695139 | ||||||||
\(144\) | −3.41467 | + | 10.9973i | −0.284556 | + | 0.916440i | ||||
\(145\) | − | 1.72418i | − | 0.143185i | ||||||
\(146\) | −8.07172 | + | 15.9707i | −0.668021 | + | 1.32175i | ||||
\(147\) | − | 5.89242i | − | 0.485998i | ||||||
\(148\) | 3.42126 | − | 2.52008i | 0.281226 | − | 0.207150i | ||||
\(149\) | − | 4.69262i | − | 0.384434i | −0.981352 | − | 0.192217i | \(-0.938432\pi\) | ||
0.981352 | − | 0.192217i | \(-0.0615678\pi\) | |||||||
\(150\) | 0.439402 | + | 0.222077i | 0.0358770 | + | 0.0181325i | ||||
\(151\) | 4.65716i | 0.378995i | 0.981881 | + | 0.189497i | \(0.0606858\pi\) | ||||
−0.981881 | + | 0.189497i | \(0.939314\pi\) | |||||||
\(152\) | 13.6427 | − | 2.29838i | 1.10657 | − | 0.186423i | ||||
\(153\) | 2.21466i | 0.179045i | ||||||||
\(154\) | 8.36737 | − | 16.5557i | 0.674262 | − | 1.33409i | ||||
\(155\) | 8.95574 | 0.719343 | ||||||||
\(156\) | 1.73778 | − | 1.28004i | 0.139134 | − | 0.102485i | ||||
\(157\) | 16.5705i | 1.32247i | 0.750179 | + | 0.661234i | \(0.229967\pi\) | ||||
−0.750179 | + | 0.661234i | \(0.770033\pi\) | |||||||
\(158\) | 4.28189 | − | 8.47215i | 0.340649 | − | 0.674008i | ||||
\(159\) | 3.88394 | 0.308016 | ||||||||
\(160\) | −3.93398 | + | 4.06494i | −0.311009 | + | 0.321362i | ||||
\(161\) | 10.8089 | − | 20.8197i | 0.851865 | − | 1.64082i | ||||
\(162\) | 5.05475 | − | 10.0013i | 0.397139 | − | 0.785779i | ||||
\(163\) | 14.7245i | 1.15331i | 0.816988 | + | 0.576655i | \(0.195642\pi\) | ||||
−0.816988 | + | 0.576655i | \(0.804358\pi\) | |||||||
\(164\) | 5.98422 | + | 8.12416i | 0.467289 | + | 0.634390i | ||||
\(165\) | 0.933557 | 0.0726773 | ||||||||
\(166\) | −3.03245 | + | 6.00000i | −0.235364 | + | 0.465690i | ||||
\(167\) | 1.87953i | 0.145442i | 0.997352 | + | 0.0727211i | \(0.0231683\pi\) | ||||
−0.997352 | + | 0.0727211i | \(0.976832\pi\) | |||||||
\(168\) | 0.800141 | + | 4.74947i | 0.0617322 | + | 0.366430i | ||||
\(169\) | −3.39079 | −0.260830 | ||||||||
\(170\) | −0.490743 | + | 0.970984i | −0.0376383 | + | 0.0744711i | ||||
\(171\) | −14.0814 | −1.07683 | ||||||||
\(172\) | 0.877323 | + | 1.19105i | 0.0668952 | + | 0.0908168i | ||||
\(173\) | 0.769298 | 0.0584887 | 0.0292443 | − | 0.999572i | \(-0.490690\pi\) | ||||
0.0292443 | + | 0.999572i | \(0.490690\pi\) | |||||||
\(174\) | 0.757608 | + | 0.382901i | 0.0574341 | + | 0.0290277i | ||||
\(175\) | −4.89140 | −0.369755 | ||||||||
\(176\) | −3.18077 | + | 10.2440i | −0.239760 | + | 0.772170i | ||||
\(177\) | −0.654324 | −0.0491820 | ||||||||
\(178\) | 12.4644 | + | 6.29962i | 0.934247 | + | 0.472176i | ||||
\(179\) | 13.1943i | 0.986185i | 0.869977 | + | 0.493093i | \(0.164134\pi\) | ||||
−0.869977 | + | 0.493093i | \(0.835866\pi\) | |||||||
\(180\) | 4.63574 | − | 3.41467i | 0.345528 | − | 0.254514i | ||||
\(181\) | − | 11.8779i | − | 0.882875i | −0.897292 | − | 0.441437i | \(-0.854469\pi\) | ||
0.897292 | − | 0.441437i | \(-0.145531\pi\) | |||||||
\(182\) | −9.67245 | + | 19.1379i | −0.716970 | + | 1.41860i | ||||
\(183\) | 2.80261 | 0.207175 | ||||||||
\(184\) | −4.16337 | + | 12.9099i | −0.306928 | + | 0.951733i | ||||
\(185\) | −2.12461 | −0.156204 | ||||||||
\(186\) | −1.98887 | + | 3.93517i | −0.145831 | + | 0.288541i | ||||
\(187\) | 2.06296i | 0.150859i | ||||||||
\(188\) | 15.3209 | − | 11.2853i | 1.11739 | − | 0.823068i | ||||
\(189\) | − | 10.0107i | − | 0.728175i | ||||||
\(190\) | −6.17377 | − | 3.12027i | −0.447893 | − | 0.226369i | ||||
\(191\) | 4.75372 | 0.343967 | 0.171984 | − | 0.985100i | \(-0.444982\pi\) | ||||
0.171984 | + | 0.985100i | \(0.444982\pi\) | |||||||
\(192\) | −0.912496 | − | 2.63133i | −0.0658537 | − | 0.189900i | ||||
\(193\) | −6.85313 | −0.493299 | −0.246649 | − | 0.969105i | \(-0.579330\pi\) | ||||
−0.246649 | + | 0.969105i | \(0.579330\pi\) | |||||||
\(194\) | −19.9438 | − | 10.0797i | −1.43188 | − | 0.723683i | ||||
\(195\) | −1.07917 | −0.0772807 | ||||||||
\(196\) | −20.0764 | − | 27.2556i | −1.43403 | − | 1.94683i | ||||
\(197\) | 10.6181 | 0.756507 | 0.378254 | − | 0.925702i | \(-0.376525\pi\) | ||||
0.378254 | + | 0.925702i | \(0.376525\pi\) | |||||||
\(198\) | 4.92457 | − | 9.74374i | 0.349974 | − | 0.692458i | ||||
\(199\) | −1.01500 | −0.0719515 | −0.0359757 | − | 0.999353i | \(-0.511454\pi\) | ||||
−0.0359757 | + | 0.999353i | \(0.511454\pi\) | |||||||
\(200\) | 2.78912 | − | 0.469882i | 0.197221 | − | 0.0332257i | ||||
\(201\) | 2.00828i | 0.141653i | ||||||||
\(202\) | 8.09833 | − | 16.0233i | 0.569797 | − | 1.12740i | ||||
\(203\) | −8.43365 | −0.591926 | ||||||||
\(204\) | −0.317669 | − | 0.431267i | −0.0222413 | − | 0.0301947i | ||||
\(205\) | − | 5.04512i | − | 0.352366i | ||||||
\(206\) | −9.75547 | + | 19.3022i | −0.679696 | + | 1.34485i | ||||
\(207\) | 6.36154 | − | 12.2533i | 0.442158 | − | 0.851664i | ||||
\(208\) | 3.67688 | − | 11.8418i | 0.254946 | − | 0.821080i | ||||
\(209\) | −13.1168 | −0.907311 | ||||||||
\(210\) | 1.08627 | − | 2.14929i | 0.0749597 | − | 0.148315i | ||||
\(211\) | 10.9279i | 0.752310i | 0.926557 | + | 0.376155i | \(0.122754\pi\) | ||||
−0.926557 | + | 0.376155i | \(0.877246\pi\) | |||||||
\(212\) | 17.9653 | − | 13.2332i | 1.23386 | − | 0.908858i | ||||
\(213\) | 0.215600 | 0.0147727 | ||||||||
\(214\) | 0.471827 | − | 0.933557i | 0.0322534 | − | 0.0638166i | ||||
\(215\) | − | 0.739645i | − | 0.0504434i | ||||||
\(216\) | 0.961661 | + | 5.70823i | 0.0654328 | + | 0.388396i | ||||
\(217\) | − | 43.8061i | − | 2.97375i | ||||||
\(218\) | −18.2663 | − | 9.23194i | −1.23715 | − | 0.625266i | ||||
\(219\) | 4.40505i | 0.297666i | ||||||||
\(220\) | 4.31821 | − | 3.18077i | 0.291133 | − | 0.214448i | ||||
\(221\) | − | 2.38473i | − | 0.160414i | ||||||
\(222\) | 0.471827 | − | 0.933557i | 0.0316670 | − | 0.0626562i | ||||
\(223\) | 22.2639i | 1.49090i | 0.666561 | + | 0.745450i | \(0.267766\pi\) | ||||
−0.666561 | + | 0.745450i | \(0.732234\pi\) | |||||||
\(224\) | 19.8833 | + | 19.2427i | 1.32851 | + | 1.28571i | ||||
\(225\) | −2.87880 | −0.191920 | ||||||||
\(226\) | 18.7050 | + | 9.45364i | 1.24424 | + | 0.628847i | ||||
\(227\) | −28.9763 | −1.92322 | −0.961611 | − | 0.274415i | \(-0.911516\pi\) | ||||
−0.961611 | + | 0.274415i | \(0.911516\pi\) | |||||||
\(228\) | 2.74211 | − | 2.01983i | 0.181601 | − | 0.133766i | ||||
\(229\) | − | 26.8197i | − | 1.77230i | −0.463403 | − | 0.886148i | \(-0.653372\pi\) | ||
0.463403 | − | 0.886148i | \(-0.346628\pi\) | |||||||
\(230\) | 5.50432 | − | 3.96264i | 0.362944 | − | 0.261288i | ||||
\(231\) | − | 4.56640i | − | 0.300447i | ||||||
\(232\) | 4.80895 | − | 0.810161i | 0.315723 | − | 0.0531897i | ||||
\(233\) | −23.4406 | −1.53564 | −0.767822 | − | 0.640663i | \(-0.778660\pi\) | ||||
−0.767822 | + | 0.640663i | \(0.778660\pi\) | |||||||
\(234\) | −5.69266 | + | 11.2635i | −0.372141 | + | 0.736318i | ||||
\(235\) | −9.51433 | −0.620647 | ||||||||
\(236\) | −3.02661 | + | 2.22938i | −0.197015 | + | 0.145121i | ||||
\(237\) | − | 2.33680i | − | 0.151791i | ||||||
\(238\) | 4.74947 | + | 2.40042i | 0.307863 | + | 0.155596i | ||||
\(239\) | − | 7.29540i | − | 0.471900i | −0.971765 | − | 0.235950i | \(-0.924180\pi\) | ||
0.971765 | − | 0.235950i | \(-0.0758202\pi\) | |||||||
\(240\) | −0.412934 | + | 1.32990i | −0.0266548 | + | 0.0858444i | ||||
\(241\) | − | 14.4459i | − | 0.930541i | −0.885169 | − | 0.465270i | \(-0.845957\pi\) | ||
0.885169 | − | 0.465270i | \(-0.154043\pi\) | |||||||
\(242\) | −2.42977 | + | 4.80754i | −0.156191 | + | 0.309040i | ||||
\(243\) | − | 8.89838i | − | 0.570831i | ||||||
\(244\) | 12.9636 | − | 9.54891i | 0.829908 | − | 0.611306i | ||||
\(245\) | 16.9258i | 1.08135i | ||||||||
\(246\) | 2.21683 | + | 1.12041i | 0.141340 | + | 0.0714345i | ||||
\(247\) | 15.1627 | 0.964780 | ||||||||
\(248\) | 4.20814 | + | 24.9787i | 0.267217 | + | 1.58615i | ||||
\(249\) | 1.65492i | 0.104877i | ||||||||
\(250\) | −1.26217 | − | 0.637910i | −0.0798266 | − | 0.0403450i | ||||
\(251\) | 16.3575 | 1.03248 | 0.516238 | − | 0.856445i | \(-0.327332\pi\) | ||||
0.516238 | + | 0.856445i | \(0.327332\pi\) | |||||||
\(252\) | −16.7025 | − | 22.6753i | −1.05216 | − | 1.42841i | ||||
\(253\) | 5.92579 | − | 11.4140i | 0.372551 | − | 0.717591i | ||||
\(254\) | −9.85407 | − | 4.98033i | −0.618299 | − | 0.312493i | ||||
\(255\) | 0.267818i | 0.0167714i | ||||||||
\(256\) | −13.1861 | − | 9.06232i | −0.824134 | − | 0.566395i | ||||
\(257\) | −13.2545 | −0.826793 | −0.413396 | − | 0.910551i | \(-0.635658\pi\) | ||||
−0.413396 | + | 0.910551i | \(0.635658\pi\) | |||||||
\(258\) | 0.325001 | + | 0.164258i | 0.0202337 | + | 0.0102263i | ||||
\(259\) | 10.3923i | 0.645746i | ||||||||
\(260\) | −4.99173 | + | 3.67688i | −0.309574 | + | 0.228031i | ||||
\(261\) | −4.96357 | −0.307237 | ||||||||
\(262\) | −16.6534 | − | 8.41676i | −1.02885 | − | 0.519989i | ||||
\(263\) | 23.4662 | 1.44699 | 0.723495 | − | 0.690330i | \(-0.242535\pi\) | ||||
0.723495 | + | 0.690330i | \(0.242535\pi\) | |||||||
\(264\) | 0.438661 | + | 2.60380i | 0.0269977 | + | 0.160253i | ||||
\(265\) | −11.1565 | −0.685338 | ||||||||
\(266\) | −15.2625 | + | 30.1984i | −0.935805 | + | 1.85158i | ||||
\(267\) | 3.43794 | 0.210399 | ||||||||
\(268\) | 6.84252 | + | 9.28938i | 0.417973 | + | 0.567439i | ||||
\(269\) | 11.8144 | 0.720338 | 0.360169 | − | 0.932887i | \(-0.382719\pi\) | ||||
0.360169 | + | 0.932887i | \(0.382719\pi\) | |||||||
\(270\) | 1.30555 | − | 2.58316i | 0.0794532 | − | 0.157206i | ||||
\(271\) | − | 15.4138i | − | 0.936324i | −0.883643 | − | 0.468162i | \(-0.844916\pi\) | ||
0.883643 | − | 0.468162i | \(-0.155084\pi\) | |||||||
\(272\) | −2.93879 | − | 0.912496i | −0.178190 | − | 0.0553282i | ||||
\(273\) | 5.27863i | 0.319477i | ||||||||
\(274\) | 13.6427 | + | 6.89514i | 0.824187 | + | 0.416551i | ||||
\(275\) | −2.68161 | −0.161707 | ||||||||
\(276\) | 0.518806 | + | 3.29862i | 0.0312284 | + | 0.198554i | ||||
\(277\) | −9.94277 | −0.597403 | −0.298701 | − | 0.954347i | \(-0.596553\pi\) | ||||
−0.298701 | + | 0.954347i | \(0.596553\pi\) | |||||||
\(278\) | 2.92051 | + | 1.47605i | 0.175161 | + | 0.0885276i | ||||
\(279\) | − | 25.7818i | − | 1.54352i | ||||||
\(280\) | −2.29838 | − | 13.6427i | −0.137354 | − | 0.815308i | ||||
\(281\) | 26.9360i | 1.60687i | 0.595393 | + | 0.803434i | \(0.296996\pi\) | ||||
−0.595393 | + | 0.803434i | \(0.703004\pi\) | |||||||
\(282\) | 2.11292 | − | 4.18062i | 0.125822 | − | 0.248952i | ||||
\(283\) | 2.08879 | 0.124166 | 0.0620830 | − | 0.998071i | \(-0.480226\pi\) | ||||
0.0620830 | + | 0.998071i | \(0.480226\pi\) | |||||||
\(284\) | 0.997266 | − | 0.734582i | 0.0591768 | − | 0.0435894i | ||||
\(285\) | −1.70285 | −0.100868 | ||||||||
\(286\) | −5.30273 | + | 10.4920i | −0.313557 | + | 0.620404i | ||||
\(287\) | −24.6777 | −1.45668 | ||||||||
\(288\) | 11.7022 | + | 11.3252i | 0.689557 | + | 0.667342i | ||||
\(289\) | 16.4082 | 0.965187 | ||||||||
\(290\) | −2.17621 | − | 1.09987i | −0.127791 | − | 0.0645867i | ||||
\(291\) | −5.50090 | −0.322469 | ||||||||
\(292\) | 15.0087 | + | 20.3758i | 0.878317 | + | 1.19240i | ||||
\(293\) | − | 6.11633i | − | 0.357320i | −0.983911 | − | 0.178660i | \(-0.942824\pi\) | ||
0.983911 | − | 0.178660i | \(-0.0571762\pi\) | |||||||
\(294\) | −7.43723 | − | 3.75883i | −0.433748 | − | 0.219220i | ||||
\(295\) | 1.87953 | 0.109430 | ||||||||
\(296\) | −0.998315 | − | 5.92579i | −0.0580259 | − | 0.344430i | ||||
\(297\) | − | 5.48820i | − | 0.318457i | ||||||
\(298\) | −5.92288 | − | 2.99347i | −0.343103 | − | 0.173407i | ||||
\(299\) | −6.85005 | + | 13.1943i | −0.396149 | + | 0.763044i | ||||
\(300\) | 0.560598 | − | 0.412934i | 0.0323661 | − | 0.0238408i | ||||
\(301\) | −3.61790 | −0.208532 | ||||||||
\(302\) | 5.87813 | + | 2.97085i | 0.338248 | + | 0.170953i | ||||
\(303\) | − | 4.41957i | − | 0.253898i | ||||||
\(304\) | 5.80189 | − | 18.6856i | 0.332761 | − | 1.07169i | ||||
\(305\) | −8.05040 | −0.460965 | ||||||||
\(306\) | 2.79527 | + | 1.41275i | 0.159795 | + | 0.0807618i | ||||
\(307\) | − | 9.32012i | − | 0.531927i | −0.963983 | − | 0.265964i | \(-0.914310\pi\) | ||
0.963983 | − | 0.265964i | \(-0.0856901\pi\) | |||||||
\(308\) | −15.5584 | − | 21.1221i | −0.886523 | − | 1.20354i | ||||
\(309\) | 5.32394i | 0.302868i | ||||||||
\(310\) | 5.71296 | − | 11.3037i | 0.324474 | − | 0.642005i | ||||
\(311\) | − | 9.31162i | − | 0.528014i | −0.964521 | − | 0.264007i | \(-0.914956\pi\) | ||
0.964521 | − | 0.264007i | \(-0.0850442\pi\) | |||||||
\(312\) | −0.507081 | − | 3.00993i | −0.0287078 | − | 0.170404i | ||||
\(313\) | − | 10.8089i | − | 0.610958i | −0.952199 | − | 0.305479i | \(-0.901183\pi\) | ||
0.952199 | − | 0.305479i | \(-0.0988166\pi\) | |||||||
\(314\) | 20.9147 | + | 10.5705i | 1.18029 | + | 0.596527i | ||||
\(315\) | 14.0814i | 0.793396i | ||||||||
\(316\) | −7.96182 | − | 10.8089i | −0.447888 | − | 0.608051i | ||||
\(317\) | 31.0426 | 1.74353 | 0.871764 | − | 0.489926i | \(-0.162976\pi\) | ||||
0.871764 | + | 0.489926i | \(0.162976\pi\) | |||||||
\(318\) | 2.47760 | − | 4.90219i | 0.138937 | − | 0.274901i | ||||
\(319\) | −4.62358 | −0.258871 | ||||||||
\(320\) | 2.62112 | + | 7.55842i | 0.146525 | + | 0.422529i | ||||
\(321\) | − | 0.257494i | − | 0.0143719i | ||||||
\(322\) | −19.3828 | − | 26.9238i | −1.08016 | − | 1.50041i | ||||
\(323\) | − | 3.76295i | − | 0.209376i | ||||||
\(324\) | −9.39889 | − | 12.7599i | −0.522160 | − | 0.708884i | ||||
\(325\) | 3.09987 | 0.171950 | ||||||||
\(326\) | 18.5848 | + | 9.39289i | 1.02931 | + | 0.520224i | ||||
\(327\) | −5.03823 | −0.278615 | ||||||||
\(328\) | 14.0715 | − | 2.37061i | 0.776966 | − | 0.130895i | ||||
\(329\) | 46.5384i | 2.56574i | ||||||||
\(330\) | 0.595525 | − | 1.17831i | 0.0327826 | − | 0.0648636i | ||||
\(331\) | − | 24.6366i | − | 1.35415i | −0.735915 | − | 0.677074i | \(-0.763248\pi\) | ||
0.735915 | − | 0.677074i | \(-0.236752\pi\) | |||||||
\(332\) | 5.63858 | + | 7.65492i | 0.309457 | + | 0.420119i | ||||
\(333\) | 6.11633i | 0.335173i | ||||||||
\(334\) | 2.37228 | + | 1.19897i | 0.129805 | + | 0.0656047i | ||||
\(335\) | − | 5.76872i | − | 0.315179i | ||||||
\(336\) | 6.50506 | + | 2.01983i | 0.354880 | + | 0.110191i | ||||
\(337\) | 10.4351i | 0.568438i | 0.958759 | + | 0.284219i | \(0.0917342\pi\) | ||||
−0.958759 | + | 0.284219i | \(0.908266\pi\) | |||||||
\(338\) | −2.16302 | + | 4.27976i | −0.117653 | + | 0.232788i | ||||
\(339\) | 5.15922 | 0.280210 | ||||||||
\(340\) | 0.912496 | + | 1.23880i | 0.0494870 | + | 0.0671835i | ||||
\(341\) | − | 24.0158i | − | 1.30053i | ||||||
\(342\) | −8.98266 | + | 17.7731i | −0.485727 | + | 0.961058i | ||||
\(343\) | 48.5510 | 2.62151 | ||||||||
\(344\) | 2.06296 | − | 0.347546i | 0.111227 | − | 0.0187384i | ||||
\(345\) | 0.769298 | − | 1.48179i | 0.0414176 | − | 0.0797767i | ||||
\(346\) | 0.490743 | − | 0.970984i | 0.0263825 | − | 0.0522004i | ||||
\(347\) | − | 32.9279i | − | 1.76766i | −0.467805 | − | 0.883831i | \(-0.654955\pi\) | ||
0.467805 | − | 0.883831i | \(-0.345045\pi\) | |||||||
\(348\) | 0.966572 | − | 0.711972i | 0.0518137 | − | 0.0381657i | ||||
\(349\) | 1.02721 | 0.0549851 | 0.0274925 | − | 0.999622i | \(-0.491248\pi\) | ||||
0.0274925 | + | 0.999622i | \(0.491248\pi\) | |||||||
\(350\) | −3.12027 | + | 6.17377i | −0.166786 | + | 0.330002i | ||||
\(351\) | 6.34420i | 0.338629i | ||||||||
\(352\) | 10.9006 | + | 10.5494i | 0.581004 | + | 0.562286i | ||||
\(353\) | 10.0183 | 0.533222 | 0.266611 | − | 0.963804i | \(-0.414096\pi\) | ||||
0.266611 | + | 0.963804i | \(0.414096\pi\) | |||||||
\(354\) | −0.417400 | + | 0.825868i | −0.0221846 | + | 0.0438944i | ||||
\(355\) | −0.619304 | −0.0328692 | ||||||||
\(356\) | 15.9024 | − | 11.7136i | 0.842823 | − | 0.620820i | ||||
\(357\) | 1.31000 | 0.0693327 | ||||||||
\(358\) | 16.6534 | + | 8.41676i | 0.880159 | + | 0.444839i | ||||
\(359\) | 15.3095 | 0.808007 | 0.404003 | − | 0.914758i | \(-0.367618\pi\) | ||||
0.404003 | + | 0.914758i | \(0.367618\pi\) | |||||||
\(360\) | −1.35270 | − | 8.02934i | −0.0712934 | − | 0.423183i | ||||
\(361\) | 4.92579 | 0.259252 | ||||||||
\(362\) | −14.9919 | − | 7.57701i | −0.787955 | − | 0.398239i | ||||
\(363\) | 1.32602i | 0.0695979i | ||||||||
\(364\) | 17.9851 | + | 24.4165i | 0.942676 | + | 1.27977i | ||||
\(365\) | − | 12.6534i | − | 0.662308i | ||||||
\(366\) | 1.78781 | − | 3.53736i | 0.0934504 | − | 0.184901i | ||||
\(367\) | 25.2963 | 1.32046 | 0.660229 | − | 0.751064i | \(-0.270459\pi\) | ||||
0.660229 | + | 0.751064i | \(0.270459\pi\) | |||||||
\(368\) | 13.6387 | + | 13.4903i | 0.710964 | + | 0.703228i | ||||
\(369\) | −14.5239 | −0.756084 | ||||||||
\(370\) | −1.35531 | + | 2.68161i | −0.0704592 | + | 0.139410i | ||||
\(371\) | 54.5709i | 2.83318i | ||||||||
\(372\) | 3.69813 | + | 5.02057i | 0.191739 | + | 0.260305i | ||||
\(373\) | 8.71062i | 0.451019i | 0.974241 | + | 0.225509i | \(0.0724046\pi\) | ||||
−0.974241 | + | 0.225509i | \(0.927595\pi\) | |||||||
\(374\) | 2.60380 | + | 1.31598i | 0.134640 | + | 0.0680479i | ||||
\(375\) | −0.348132 | −0.0179775 | ||||||||
\(376\) | −4.47061 | − | 26.5366i | −0.230554 | − | 1.36852i | ||||
\(377\) | 5.34473 | 0.275268 | ||||||||
\(378\) | −12.6353 | − | 6.38596i | −0.649887 | − | 0.328458i | ||||
\(379\) | −26.6288 | −1.36783 | −0.683915 | − | 0.729562i | \(-0.739724\pi\) | ||||
−0.683915 | + | 0.729562i | \(0.739724\pi\) | |||||||
\(380\) | −7.87663 | + | 5.80189i | −0.404062 | + | 0.297631i | ||||
\(381\) | −2.71796 | −0.139245 | ||||||||
\(382\) | 3.03245 | − | 6.00000i | 0.155154 | − | 0.306987i | ||||
\(383\) | −6.10287 | −0.311842 | −0.155921 | − | 0.987770i | \(-0.549835\pi\) | ||||
−0.155921 | + | 0.987770i | \(0.549835\pi\) | |||||||
\(384\) | −3.90328 | − | 0.526830i | −0.199188 | − | 0.0268847i | ||||
\(385\) | 13.1168i | 0.668496i | ||||||||
\(386\) | −4.37168 | + | 8.64980i | −0.222513 | + | 0.440263i | ||||
\(387\) | −2.12929 | −0.108238 | ||||||||
\(388\) | −25.4447 | + | 18.7424i | −1.29176 | + | 0.951503i | ||||
\(389\) | 22.9660i | 1.16442i | 0.813038 | + | 0.582210i | \(0.197812\pi\) | ||||
−0.813038 | + | 0.582210i | \(0.802188\pi\) | |||||||
\(390\) | −0.688411 | + | 1.36209i | −0.0348591 | + | 0.0689721i | ||||
\(391\) | 3.27443 | + | 1.69998i | 0.165595 | + | 0.0859719i | ||||
\(392\) | −47.2081 | + | 7.95312i | −2.38437 | + | 0.401693i | ||||
\(393\) | −4.59335 | −0.231704 | ||||||||
\(394\) | 6.77339 | − | 13.4018i | 0.341238 | − | 0.675174i | ||||
\(395\) | 6.71238i | 0.337736i | ||||||||
\(396\) | −9.15682 | − | 12.4313i | −0.460147 | − | 0.624695i | ||||
\(397\) | 13.8346 | 0.694339 | 0.347170 | − | 0.937802i | \(-0.387143\pi\) | ||||
0.347170 | + | 0.937802i | \(0.387143\pi\) | |||||||
\(398\) | −0.647479 | + | 1.28110i | −0.0324552 | + | 0.0642159i | ||||
\(399\) | 8.32934i | 0.416989i | ||||||||
\(400\) | 1.18614 | − | 3.82009i | 0.0593070 | − | 0.191004i | ||||
\(401\) | − | 0.116328i | − | 0.00580915i | −0.999996 | − | 0.00290457i | \(-0.999075\pi\) | ||
0.999996 | − | 0.00290457i | \(-0.000924556\pi\) | |||||||
\(402\) | 2.53479 | + | 1.28110i | 0.126424 | + | 0.0638956i | ||||
\(403\) | 27.7617i | 1.38291i | ||||||||
\(404\) | −15.0582 | − | 20.4429i | −0.749172 | − | 1.01707i | ||||
\(405\) | 7.92392i | 0.393743i | ||||||||
\(406\) | −5.37991 | + | 10.6447i | −0.267001 | + | 0.528287i | ||||
\(407\) | 5.69738i | 0.282408i | ||||||||
\(408\) | −0.746977 | + | 0.125843i | −0.0369809 | + | 0.00623014i | ||||
\(409\) | 9.27395 | 0.458567 | 0.229284 | − | 0.973360i | \(-0.426362\pi\) | ||||
0.229284 | + | 0.973360i | \(0.426362\pi\) | |||||||
\(410\) | −6.36779 | − | 3.21833i | −0.314483 | − | 0.158942i | ||||
\(411\) | 3.76295 | 0.185612 | ||||||||
\(412\) | 18.1395 | + | 24.6261i | 0.893668 | + | 1.21324i | ||||
\(413\) | − | 9.19352i | − | 0.452384i | ||||||
\(414\) | −11.4077 | − | 15.8459i | −0.560655 | − | 0.778781i | ||||
\(415\) | − | 4.75372i | − | 0.233351i | ||||||
\(416\) | −12.6008 | − | 12.1948i | −0.617805 | − | 0.597901i | ||||
\(417\) | 0.805538 | 0.0394474 | ||||||||
\(418\) | −8.36737 | + | 16.5557i | −0.409261 | + | 0.809764i | ||||
\(419\) | −34.5998 | −1.69031 | −0.845155 | − | 0.534521i | \(-0.820492\pi\) | ||||
−0.845155 | + | 0.534521i | \(0.820492\pi\) | |||||||
\(420\) | −2.01983 | − | 2.74211i | −0.0985574 | − | 0.133801i | ||||
\(421\) | 24.5730i | 1.19761i | 0.800894 | + | 0.598806i | \(0.204358\pi\) | ||||
−0.800894 | + | 0.598806i | \(0.795642\pi\) | |||||||
\(422\) | 13.7929 | + | 6.97105i | 0.671428 | + | 0.339345i | ||||
\(423\) | 27.3899i | 1.33174i | ||||||||
\(424\) | −5.24224 | − | 31.1168i | −0.254585 | − | 1.51117i | ||||
\(425\) | − | 0.769298i | − | 0.0373164i | ||||||
\(426\) | 0.137533 | − | 0.272123i | 0.00666351 | − | 0.0131844i | ||||
\(427\) | 39.3777i | 1.90562i | ||||||||
\(428\) | −0.877323 | − | 1.19105i | −0.0424070 | − | 0.0575716i | ||||
\(429\) | 2.89391i | 0.139719i | ||||||||
\(430\) | −0.933557 | − | 0.471827i | −0.0450201 | − | 0.0227535i | ||||
\(431\) | 35.8188 | 1.72533 | 0.862665 | − | 0.505775i | \(-0.168794\pi\) | ||||
0.862665 | + | 0.505775i | \(0.168794\pi\) | |||||||
\(432\) | 7.81820 | + | 2.42756i | 0.376153 | + | 0.116796i | ||||
\(433\) | 27.5411i | 1.32354i | 0.749707 | + | 0.661770i | \(0.230194\pi\) | ||||
−0.749707 | + | 0.661770i | \(0.769806\pi\) | |||||||
\(434\) | −55.2907 | − | 27.9444i | −2.65404 | − | 1.34137i | ||||
\(435\) | −0.600243 | −0.0287794 | ||||||||
\(436\) | −23.3045 | + | 17.1660i | −1.11608 | + | 0.822103i | ||||
\(437\) | −10.8089 | + | 20.8197i | −0.517062 | + | 0.995941i | ||||
\(438\) | 5.55992 | + | 2.81003i | 0.265663 | + | 0.134268i | ||||
\(439\) | − | 17.7949i | − | 0.849304i | −0.905357 | − | 0.424652i | \(-0.860396\pi\) | ||
0.905357 | − | 0.424652i | \(-0.139604\pi\) | |||||||
\(440\) | −1.26004 | − | 7.47935i | −0.0600701 | − | 0.356564i | ||||
\(441\) | 48.7260 | 2.32029 | ||||||||
\(442\) | −3.00993 | − | 1.52124i | −0.143168 | − | 0.0723581i | ||||
\(443\) | − | 22.1711i | − | 1.05338i | −0.850057 | − | 0.526690i | \(-0.823433\pi\) | ||
0.850057 | − | 0.526690i | \(-0.176567\pi\) | |||||||
\(444\) | −0.877323 | − | 1.19105i | −0.0416359 | − | 0.0565248i | ||||
\(445\) | −9.87539 | −0.468139 | ||||||||
\(446\) | 28.1008 | + | 14.2024i | 1.33061 | + | 0.672502i | ||||
\(447\) | −1.63365 | −0.0772692 | ||||||||
\(448\) | 36.9713 | − | 12.8209i | 1.74673 | − | 0.605732i | ||||
\(449\) | −0.495960 | −0.0234058 | −0.0117029 | − | 0.999932i | \(-0.503725\pi\) | ||||
−0.0117029 | + | 0.999932i | \(0.503725\pi\) | |||||||
\(450\) | −1.83642 | + | 3.63354i | −0.0865696 | + | 0.171287i | ||||
\(451\) | −13.5291 | −0.637059 | ||||||||
\(452\) | 23.8642 | − | 17.5782i | 1.12248 | − | 0.826811i | ||||
\(453\) | 1.62131 | 0.0761758 | ||||||||
\(454\) | −18.4843 | + | 36.5730i | −0.867510 | + | 1.71645i | ||||
\(455\) | − | 15.1627i | − | 0.710839i | ||||||
\(456\) | −0.800141 | − | 4.74947i | −0.0374700 | − | 0.222414i | ||||
\(457\) | − | 16.8280i | − | 0.787180i | −0.919286 | − | 0.393590i | \(-0.871233\pi\) | ||
0.919286 | − | 0.393590i | \(-0.128767\pi\) | |||||||
\(458\) | −33.8510 | − | 17.1086i | −1.58175 | − | 0.799431i | ||||
\(459\) | 1.57445 | 0.0734889 | ||||||||
\(460\) | −1.49025 | − | 9.47519i | −0.0694834 | − | 0.441783i | ||||
\(461\) | 33.3266 | 1.55217 | 0.776086 | − | 0.630627i | \(-0.217202\pi\) | ||||
0.776086 | + | 0.630627i | \(0.217202\pi\) | |||||||
\(462\) | −5.76357 | − | 2.91295i | −0.268145 | − | 0.135523i | ||||
\(463\) | − | 29.8840i | − | 1.38883i | −0.719575 | − | 0.694414i | \(-0.755663\pi\) | ||
0.719575 | − | 0.694414i | \(-0.244337\pi\) | |||||||
\(464\) | 2.04512 | − | 6.58652i | 0.0949423 | − | 0.305771i | ||||
\(465\) | − | 3.11778i | − | 0.144584i | ||||||
\(466\) | −14.9530 | + | 29.5860i | −0.692684 | + | 1.37054i | ||||
\(467\) | −6.17422 | −0.285709 | −0.142854 | − | 0.989744i | \(-0.545628\pi\) | ||||
−0.142854 | + | 0.989744i | \(0.545628\pi\) | |||||||
\(468\) | 10.5850 | + | 14.3702i | 0.489293 | + | 0.664263i | ||||
\(469\) | −28.2171 | −1.30295 | ||||||||
\(470\) | −6.06929 | + | 12.0087i | −0.279956 | + | 0.553920i | ||||
\(471\) | 5.76872 | 0.265809 | ||||||||
\(472\) | 0.883156 | + | 5.24224i | 0.0406506 | + | 0.241293i | ||||
\(473\) | −1.98344 | −0.0911987 | ||||||||
\(474\) | −2.94943 | − | 1.49067i | −0.135472 | − | 0.0684686i | ||||
\(475\) | 4.89140 | 0.224433 | ||||||||
\(476\) | 6.05948 | − | 4.46338i | 0.277736 | − | 0.204579i | ||||
\(477\) | 32.1174i | 1.47055i | ||||||||
\(478\) | −9.20802 | − | 4.65381i | −0.421165 | − | 0.212860i | ||||
\(479\) | −24.0773 | −1.10012 | −0.550061 | − | 0.835125i | \(-0.685395\pi\) | ||||
−0.550061 | + | 0.835125i | \(0.685395\pi\) | |||||||
\(480\) | 1.41514 | + | 1.36955i | 0.0645920 | + | 0.0625110i | ||||
\(481\) | − | 6.58601i | − | 0.300296i | ||||||
\(482\) | −18.2331 | − | 9.21517i | −0.830497 | − | 0.419740i | ||||
\(483\) | −7.24801 | − | 3.76295i | −0.329796 | − | 0.171220i | ||||
\(484\) | 4.51795 | + | 6.13356i | 0.205361 | + | 0.278798i | ||||
\(485\) | 15.8012 | 0.717495 | ||||||||
\(486\) | −11.2313 | − | 5.67637i | −0.509460 | − | 0.257485i | ||||
\(487\) | − | 19.4857i | − | 0.882983i | −0.897266 | − | 0.441491i | \(-0.854450\pi\) | ||
0.897266 | − | 0.441491i | \(-0.145550\pi\) | |||||||
\(488\) | −3.78274 | − | 22.4536i | −0.171236 | − | 1.01643i | ||||
\(489\) | 5.12606 | 0.231809 | ||||||||
\(490\) | 21.3632 | + | 10.7971i | 0.965091 | + | 0.487765i | ||||
\(491\) | − | 8.73549i | − | 0.394227i | −0.980381 | − | 0.197114i | \(-0.936843\pi\) | ||
0.980381 | − | 0.197114i | \(-0.0631568\pi\) | |||||||
\(492\) | 2.82828 | − | 2.08330i | 0.127509 | − | 0.0939225i | ||||
\(493\) | − | 1.32641i | − | 0.0597384i | ||||||
\(494\) | 9.67245 | − | 19.1379i | 0.435184 | − | 0.861055i | ||||
\(495\) | 7.71984i | 0.346981i | ||||||||
\(496\) | 34.2117 | + | 10.6228i | 1.53615 | + | 0.476977i | ||||
\(497\) | 3.02926i | 0.135881i | ||||||||
\(498\) | 2.08879 | + | 1.05569i | 0.0936011 | + | 0.0473068i | ||||
\(499\) | − | 25.9227i | − | 1.16046i | −0.814452 | − | 0.580231i | \(-0.802962\pi\) | ||
0.814452 | − | 0.580231i | \(-0.197038\pi\) | |||||||
\(500\) | −1.61030 | + | 1.18614i | −0.0720149 | + | 0.0530458i | ||||
\(501\) | 0.654324 | 0.0292331 | ||||||||
\(502\) | 10.4346 | − | 20.6459i | 0.465720 | − | 0.921473i | ||||
\(503\) | −9.84913 | −0.439151 | −0.219576 | − | 0.975596i | \(-0.570467\pi\) | ||||
−0.219576 | + | 0.975596i | \(0.570467\pi\) | |||||||
\(504\) | −39.2747 | + | 6.61659i | −1.74943 | + | 0.294726i | ||||
\(505\) | 12.6951i | 0.564924i | ||||||||
\(506\) | −10.6263 | − | 14.7605i | −0.472395 | − | 0.656182i | ||||
\(507\) | 1.18045i | 0.0524254i | ||||||||
\(508\) | −12.5720 | + | 9.26050i | −0.557793 | + | 0.410868i | ||||
\(509\) | −41.5701 | −1.84256 | −0.921282 | − | 0.388895i | \(-0.872857\pi\) | ||||
−0.921282 | + | 0.388895i | \(0.872857\pi\) | |||||||
\(510\) | 0.338031 | + | 0.170844i | 0.0149683 | + | 0.00756509i | ||||
\(511\) | −61.8928 | −2.73797 | ||||||||
\(512\) | −19.8498 | + | 10.8622i | −0.877244 | + | 0.480045i | ||||
\(513\) | 10.0107i | 0.441985i | ||||||||
\(514\) | −8.45518 | + | 16.7294i | −0.372942 | + | 0.737903i | ||||
\(515\) | − | 15.2929i | − | 0.673884i | ||||||
\(516\) | 0.414643 | − | 0.305424i | 0.0182537 | − | 0.0134456i | ||||
\(517\) | 25.5138i | 1.12209i | ||||||||
\(518\) | 13.1168 | + | 6.62936i | 0.576321 | + | 0.291277i | ||||
\(519\) | − | 0.267818i | − | 0.0117559i | ||||||
\(520\) | 1.45657 | + | 8.64593i | 0.0638750 | + | 0.379149i | ||||
\(521\) | 17.2728i | 0.756736i | 0.925655 | + | 0.378368i | \(0.123515\pi\) | ||||
−0.925655 | + | 0.378368i | \(0.876485\pi\) | |||||||
\(522\) | −3.16632 | + | 6.26487i | −0.138586 | + | 0.274206i | ||||
\(523\) | −9.24464 | −0.404240 | −0.202120 | − | 0.979361i | \(-0.564783\pi\) | ||||
−0.202120 | + | 0.979361i | \(0.564783\pi\) | |||||||
\(524\) | −21.2467 | + | 15.6502i | −0.928168 | + | 0.683684i | ||||
\(525\) | 1.70285i | 0.0743187i | ||||||||
\(526\) | 14.9693 | − | 29.6183i | 0.652695 | − | 1.29142i | ||||
\(527\) | 6.88964 | 0.300117 | ||||||||
\(528\) | 3.56627 | + | 1.10733i | 0.155202 | + | 0.0481903i | ||||
\(529\) | −13.2337 | − | 18.8114i | −0.575378 | − | 0.817888i | ||||
\(530\) | −7.11684 | + | 14.0814i | −0.309136 | + | 0.611656i | ||||
\(531\) | − | 5.41079i | − | 0.234808i | ||||||
\(532\) | 28.3794 | + | 38.5277i | 1.23040 | + | 1.67039i | ||||
\(533\) | 15.6392 | 0.677410 | ||||||||
\(534\) | 2.19310 | − | 4.33927i | 0.0949047 | − | 0.187778i | ||||
\(535\) | 0.739645i | 0.0319776i | ||||||||
\(536\) | 16.0897 | − | 2.71062i | 0.694968 | − | 0.117081i | ||||
\(537\) | 4.59335 | 0.198218 | ||||||||
\(538\) | 7.53654 | − | 14.9118i | 0.324923 | − | 0.642893i | ||||
\(539\) | 45.3884 | 1.95502 | ||||||||
\(540\) | −2.42756 | − | 3.29565i | −0.104465 | − | 0.141822i | ||||
\(541\) | −15.7687 | −0.677949 | −0.338974 | − | 0.940796i | \(-0.610080\pi\) | ||||
−0.338974 | + | 0.940796i | \(0.610080\pi\) | |||||||
\(542\) | −19.4549 | − | 9.83265i | −0.835658 | − | 0.422349i | ||||
\(543\) | −4.13507 | −0.177453 | ||||||||
\(544\) | −3.02641 | + | 3.12715i | −0.129756 | + | 0.134076i | ||||
\(545\) | 14.4722 | 0.619919 | ||||||||
\(546\) | 6.66252 | + | 3.36729i | 0.285130 | + | 0.144107i | ||||
\(547\) | 12.5618i | 0.537104i | 0.963265 | + | 0.268552i | \(0.0865451\pi\) | ||||
−0.963265 | + | 0.268552i | \(0.913455\pi\) | |||||||
\(548\) | 17.4057 | − | 12.8209i | 0.743533 | − | 0.547683i | ||||
\(549\) | 23.1755i | 0.989107i | ||||||||
\(550\) | −1.71063 | + | 3.38465i | −0.0729415 | + | 0.144322i | ||||
\(551\) | 8.43365 | 0.359286 | ||||||||
\(552\) | 4.49437 | + | 1.44940i | 0.191293 | + | 0.0616907i | ||||
\(553\) | 32.8329 | 1.39620 | ||||||||
\(554\) | −6.34259 | + | 12.5494i | −0.269471 | + | 0.533175i | ||||
\(555\) | 0.739645i | 0.0313962i | ||||||||
\(556\) | 3.72605 | − | 2.74459i | 0.158020 | − | 0.116397i | ||||
\(557\) | − | 29.2656i | − | 1.24002i | −0.784593 | − | 0.620011i | \(-0.787128\pi\) | ||
0.784593 | − | 0.620011i | \(-0.212872\pi\) | |||||||
\(558\) | −32.5410 | − | 16.4465i | −1.37757 | − | 0.696236i | ||||
\(559\) | 2.29280 | 0.0969753 | ||||||||
\(560\) | −18.6856 | − | 5.80189i | −0.789610 | − | 0.245175i | ||||
\(561\) | 0.718183 | 0.0303217 | ||||||||
\(562\) | 33.9978 | + | 17.1828i | 1.43411 | + | 0.724811i | ||||
\(563\) | 1.47929 | 0.0623446 | 0.0311723 | − | 0.999514i | \(-0.490076\pi\) | ||||
0.0311723 | + | 0.999514i | \(0.490076\pi\) | |||||||
\(564\) | −3.92879 | − | 5.33372i | −0.165432 | − | 0.224590i | ||||
\(565\) | −14.8197 | −0.623469 | ||||||||
\(566\) | 1.33246 | − | 2.63641i | 0.0560076 | − | 0.110817i | ||||
\(567\) | 38.7591 | 1.62773 | ||||||||
\(568\) | −0.291000 | − | 1.72732i | −0.0122101 | − | 0.0724765i | ||||
\(569\) | − | 30.9277i | − | 1.29656i | −0.761403 | − | 0.648279i | \(-0.775489\pi\) | ||
0.761403 | − | 0.648279i | \(-0.224511\pi\) | |||||||
\(570\) | −1.08627 | + | 2.14929i | −0.0454988 | + | 0.0900239i | ||||
\(571\) | −0.388810 | −0.0162712 | −0.00813559 | − | 0.999967i | \(-0.502590\pi\) | ||||
−0.00813559 | + | 0.999967i | \(0.502590\pi\) | |||||||
\(572\) | 9.85998 | + | 13.3859i | 0.412267 | + | 0.559692i | ||||
\(573\) | − | 1.65492i | − | 0.0691355i | ||||||
\(574\) | −15.7422 | + | 31.1474i | −0.657065 | + | 1.30007i | ||||
\(575\) | −2.20979 | + | 4.25639i | −0.0921545 | + | 0.177504i | ||||
\(576\) | 21.7592 | − | 7.54568i | 0.906634 | − | 0.314403i | ||||
\(577\) | 32.8871 | 1.36911 | 0.684553 | − | 0.728963i | \(-0.259997\pi\) | ||||
0.684553 | + | 0.728963i | \(0.259997\pi\) | |||||||
\(578\) | 10.4669 | − | 20.7099i | 0.435368 | − | 0.861418i | ||||
\(579\) | 2.38580i | 0.0991503i | ||||||||
\(580\) | −2.77645 | + | 2.04512i | −0.115286 | + | 0.0849189i | ||||
\(581\) | −23.2524 | −0.964670 | ||||||||
\(582\) | −3.50908 | + | 6.94307i | −0.145456 | + | 0.287800i | ||||
\(583\) | 29.9174i | 1.23905i | ||||||||
\(584\) | 35.2919 | − | 5.94560i | 1.46039 | − | 0.246031i | ||||
\(585\) | − | 8.92392i | − | 0.368959i | ||||||
\(586\) | −7.71984 | − | 3.90167i | −0.318904 | − | 0.161176i | ||||
\(587\) | 24.5665i | 1.01397i | 0.861955 | + | 0.506984i | \(0.169240\pi\) | ||||
−0.861955 | + | 0.506984i | \(0.830760\pi\) | |||||||
\(588\) | −9.48857 | + | 6.98924i | −0.391302 | + | 0.288231i | ||||
\(589\) | 43.8061i | 1.80500i | ||||||||
\(590\) | 1.19897 | − | 2.37228i | 0.0493608 | − | 0.0976653i | ||||
\(591\) | − | 3.69650i | − | 0.152054i | ||||||
\(592\) | −8.11619 | − | 2.52008i | −0.333573 | − | 0.103575i | ||||
\(593\) | 35.8516 | 1.47225 | 0.736124 | − | 0.676847i | \(-0.236654\pi\) | ||||
0.736124 | + | 0.676847i | \(0.236654\pi\) | |||||||
\(594\) | −6.92703 | − | 3.50098i | −0.284219 | − | 0.143647i | ||||
\(595\) | −3.76295 | −0.154266 | ||||||||
\(596\) | −7.55653 | + | 5.56611i | −0.309528 | + | 0.227997i | ||||
\(597\) | 0.353355i | 0.0144618i | ||||||||
\(598\) | 12.2837 | + | 17.0627i | 0.502316 | + | 0.697745i | ||||
\(599\) | − | 33.8638i | − | 1.38364i | −0.722072 | − | 0.691818i | \(-0.756810\pi\) | ||
0.722072 | − | 0.691818i | \(-0.243190\pi\) | |||||||
\(600\) | −0.163581 | − | 0.970984i | −0.00667817 | − | 0.0396403i | ||||
\(601\) | 12.5633 | 0.512469 | 0.256235 | − | 0.966615i | \(-0.417518\pi\) | ||||
0.256235 | + | 0.966615i | \(0.417518\pi\) | |||||||
\(602\) | −2.30789 | + | 4.56640i | −0.0940628 | + | 0.186113i | ||||
\(603\) | −16.6070 | −0.676290 | ||||||||
\(604\) | 7.49944 | − | 5.52405i | 0.305148 | − | 0.224770i | ||||
\(605\) | − | 3.80895i | − | 0.154856i | ||||||
\(606\) | −5.57825 | − | 2.81929i | −0.226601 | − | 0.114526i | ||||
\(607\) | 19.8410i | 0.805320i | 0.915350 | + | 0.402660i | \(0.131914\pi\) | ||||
−0.915350 | + | 0.402660i | \(0.868086\pi\) | |||||||
\(608\) | −19.8833 | − | 19.2427i | −0.806373 | − | 0.780394i | ||||
\(609\) | 2.93603i | 0.118974i | ||||||||
\(610\) | −5.13543 | + | 10.1610i | −0.207928 | + | 0.411405i | ||||
\(611\) | − | 29.4932i | − | 1.19317i | ||||||
\(612\) | 3.56627 | − | 2.62690i | 0.144158 | − | 0.106186i | ||||
\(613\) | − | 31.7187i | − | 1.28111i | −0.767914 | − | 0.640553i | \(-0.778705\pi\) | ||
0.767914 | − | 0.640553i | \(-0.221295\pi\) | |||||||
\(614\) | −11.7636 | − | 5.94540i | −0.474739 | − | 0.239937i | ||||
\(615\) | −1.75637 | −0.0708237 | ||||||||
\(616\) | −36.5845 | + | 6.16337i | −1.47403 | + | 0.248329i | ||||
\(617\) | 31.1431i | 1.25377i | 0.779110 | + | 0.626887i | \(0.215671\pi\) | ||||
−0.779110 | + | 0.626887i | \(0.784329\pi\) | |||||||
\(618\) | 6.71971 | + | 3.39620i | 0.270306 | + | 0.136615i | ||||
\(619\) | 43.2425 | 1.73806 | 0.869031 | − | 0.494758i | \(-0.164743\pi\) | ||||
0.869031 | + | 0.494758i | \(0.164743\pi\) | |||||||
\(620\) | −10.6228 | − | 14.4214i | −0.426621 | − | 0.579179i | ||||
\(621\) | −8.71113 | − | 4.52255i | −0.349566 | − | 0.181484i | ||||
\(622\) | −11.7528 | − | 5.93998i | −0.471246 | − | 0.238172i | ||||
\(623\) | 48.3045i | 1.93528i | ||||||||
\(624\) | −4.12251 | − | 1.28004i | −0.165032 | − | 0.0512427i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −13.6427 | − | 6.89514i | −0.545273 | − | 0.275585i | ||||
\(627\) | 4.56640i | 0.182364i | ||||||||
\(628\) | 26.6835 | − | 19.6549i | 1.06479 | − | 0.784317i | ||||
\(629\) | −1.63446 | −0.0651701 | ||||||||
\(630\) | 17.7731 | + | 8.98266i | 0.708096 | + | 0.357878i | ||||
\(631\) | 43.9563 | 1.74987 | 0.874936 | − | 0.484239i | \(-0.160904\pi\) | ||||
0.874936 | + | 0.484239i | \(0.160904\pi\) | |||||||
\(632\) | −18.7216 | + | 3.15402i | −0.744707 | + | 0.125460i | ||||
\(633\) | 3.80437 | 0.151210 | ||||||||
\(634\) | 19.8024 | − | 39.1811i | 0.786455 | − | 1.55608i | ||||
\(635\) | 7.80725 | 0.309821 | ||||||||
\(636\) | −4.60690 | − | 6.25431i | −0.182675 | − | 0.248000i | ||||
\(637\) | −52.4678 | −2.07885 | ||||||||
\(638\) | −2.94943 | + | 5.83574i | −0.116769 | + | 0.231039i | ||||
\(639\) | 1.78285i | 0.0705286i | ||||||||
\(640\) | 11.2120 | + | 1.51330i | 0.443195 | + | 0.0598185i | ||||
\(641\) | − | 19.7640i | − | 0.780631i | −0.920681 | − | 0.390316i | \(-0.872366\pi\) | ||
0.920681 | − | 0.390316i | \(-0.127634\pi\) | |||||||
\(642\) | −0.325001 | − | 0.164258i | −0.0128268 | − | 0.00648276i | ||||
\(643\) | −9.44865 | −0.372618 | −0.186309 | − | 0.982491i | \(-0.559653\pi\) | ||||
−0.186309 | + | 0.982491i | \(0.559653\pi\) | |||||||
\(644\) | −46.3469 | + | 7.28943i | −1.82632 | + | 0.287244i | ||||
\(645\) | −0.257494 | −0.0101388 | ||||||||
\(646\) | −4.74947 | − | 2.40042i | −0.186866 | − | 0.0944433i | ||||
\(647\) | 0.950541i | 0.0373696i | 0.999825 | + | 0.0186848i | \(0.00594791\pi\) | ||||
−0.999825 | + | 0.0186848i | \(0.994052\pi\) | |||||||
\(648\) | −22.1008 | + | 3.72331i | −0.868201 | + | 0.146265i | ||||
\(649\) | − | 5.04017i | − | 0.197844i | ||||||
\(650\) | 1.97744 | − | 3.91256i | 0.0775616 | − | 0.153463i | ||||
\(651\) | −15.2503 | −0.597708 | ||||||||
\(652\) | 23.7108 | − | 17.4653i | 0.928588 | − | 0.683993i | ||||
\(653\) | −5.83079 | −0.228176 | −0.114088 | − | 0.993471i | \(-0.536395\pi\) | ||||
−0.114088 | + | 0.993471i | \(0.536395\pi\) | |||||||
\(654\) | −3.21394 | + | 6.35909i | −0.125675 | + | 0.248660i | ||||
\(655\) | 13.1943 | 0.515542 | ||||||||
\(656\) | 5.98422 | − | 19.2728i | 0.233645 | − | 0.752476i | ||||
\(657\) | −36.4266 | −1.42114 | ||||||||
\(658\) | 58.7393 | + | 29.6873i | 2.28990 | + | 1.15733i | ||||
\(659\) | 1.14514 | 0.0446083 | 0.0223042 | − | 0.999751i | \(-0.492900\pi\) | ||||
0.0223042 | + | 0.999751i | \(0.492900\pi\) | |||||||
\(660\) | −1.10733 | − | 1.50331i | −0.0431027 | − | 0.0585162i | ||||
\(661\) | − | 17.1348i | − | 0.666468i | −0.942844 | − | 0.333234i | \(-0.891860\pi\) | ||
0.942844 | − | 0.333234i | \(-0.108140\pi\) | |||||||
\(662\) | −31.0955 | − | 15.7159i | −1.20856 | − | 0.610817i | ||||
\(663\) | −0.830200 | −0.0322423 | ||||||||
\(664\) | 13.2587 | − | 2.23369i | 0.514538 | − | 0.0866839i | ||||
\(665\) | − | 23.9258i | − | 0.927802i | ||||||
\(666\) | 7.71984 | + | 3.90167i | 0.299138 | + | 0.151187i | ||||
\(667\) | −3.81007 | + | 7.33878i | −0.147526 | + | 0.284159i | ||||
\(668\) | 3.02661 | − | 2.22938i | 0.117103 | − | 0.0862575i | ||||
\(669\) | 7.75079 | 0.299663 | ||||||||
\(670\) | −7.28110 | − | 3.67993i | −0.281294 | − | 0.142168i | ||||
\(671\) | 21.5881i | 0.833398i | ||||||||
\(672\) | 6.69900 | − | 6.92201i | 0.258420 | − | 0.267022i | ||||
\(673\) | 26.3083 | 1.01411 | 0.507055 | − | 0.861913i | \(-0.330734\pi\) | ||||
0.507055 | + | 0.861913i | \(0.330734\pi\) | |||||||
\(674\) | 13.1709 | + | 6.65668i | 0.507324 | + | 0.256406i | ||||
\(675\) | 2.04660i | 0.0787738i | ||||||||
\(676\) | 4.02196 | + | 5.46020i | 0.154691 | + | 0.210008i | ||||
\(677\) | − | 37.5386i | − | 1.44273i | −0.692557 | − | 0.721363i | \(-0.743516\pi\) | ||
0.692557 | − | 0.721363i | \(-0.256484\pi\) | |||||||
\(678\) | 3.29112 | − | 6.51180i | 0.126395 | − | 0.250084i | ||||
\(679\) | − | 77.2899i | − | 2.96611i | ||||||
\(680\) | 2.14567 | − | 0.361479i | 0.0822826 | − | 0.0138621i | ||||
\(681\) | 10.0876i | 0.386557i | ||||||||
\(682\) | −30.3121 | − | 15.3200i | −1.16071 | − | 0.586631i | ||||
\(683\) | − | 33.5658i | − | 1.28436i | −0.766553 | − | 0.642180i | \(-0.778030\pi\) | ||
0.766553 | − | 0.642180i | \(-0.221970\pi\) | |||||||
\(684\) | 16.7025 | + | 22.6753i | 0.638636 | + | 0.867010i | ||||
\(685\) | −10.8089 | −0.412989 | ||||||||
\(686\) | 30.9712 | − | 61.2796i | 1.18249 | − | 2.33967i | ||||
\(687\) | −9.33681 | −0.356221 | ||||||||
\(688\) | 0.877323 | − | 2.82551i | 0.0334476 | − | 0.107721i | ||||
\(689\) | − | 34.5837i | − | 1.31753i | ||||||
\(690\) | −1.37952 | − | 1.91623i | −0.0525175 | − | 0.0729497i | ||||
\(691\) | 8.91302i | 0.339067i | 0.985524 | + | 0.169534i | \(0.0542261\pi\) | ||||
−0.985524 | + | 0.169534i | \(0.945774\pi\) | |||||||
\(692\) | −0.912496 | − | 1.23880i | −0.0346879 | − | 0.0470922i | ||||
\(693\) | 37.7608 | 1.43441 | ||||||||
\(694\) | −41.5606 | − | 21.0051i | −1.57762 | − | 0.797341i | ||||
\(695\) | −2.31388 | −0.0877706 | ||||||||
\(696\) | −0.282043 | − | 1.67415i | −0.0106908 | − | 0.0634585i | ||||
\(697\) | − | 3.88120i | − | 0.147011i | ||||||
\(698\) | 0.655265 | − | 1.29651i | 0.0248022 | − | 0.0490735i | ||||
\(699\) | 8.16043i | 0.308656i | ||||||||
\(700\) | 5.80189 | + | 7.87663i | 0.219291 | + | 0.297709i | ||||
\(701\) | 19.6286i | 0.741364i | 0.928760 | + | 0.370682i | \(0.120876\pi\) | ||||
−0.928760 | + | 0.370682i | \(0.879124\pi\) | |||||||
\(702\) | 8.00746 | + | 4.04703i | 0.302222 | + | 0.152745i | ||||
\(703\) | − | 10.3923i | − | 0.391953i | ||||||
\(704\) | 20.2688 | − | 7.02882i | 0.763908 | − | 0.264909i | ||||
\(705\) | 3.31225i | 0.124746i | ||||||||
\(706\) | 6.39079 | − | 12.6448i | 0.240521 | − | 0.475894i | ||||
\(707\) | 62.0968 | 2.33539 | ||||||||
\(708\) | 0.776121 | + | 1.05366i | 0.0291684 | + | 0.0395990i | ||||
\(709\) | − | 30.9947i | − | 1.16403i | −0.813178 | − | 0.582015i | \(-0.802264\pi\) | ||
0.813178 | − | 0.582015i | \(-0.197736\pi\) | |||||||
\(710\) | −0.395060 | + | 0.781666i | −0.0148264 | + | 0.0293354i | ||||
\(711\) | 19.3236 | 0.724692 | ||||||||
\(712\) | −4.64027 | − | 27.5437i | −0.173901 | − | 1.03224i | ||||
\(713\) | −38.1191 | − | 19.7903i | −1.42757 | − | 0.741152i | ||||
\(714\) | 0.835665 | − | 1.65345i | 0.0312740 | − | 0.0618786i | ||||
\(715\) | − | 8.31266i | − | 0.310876i | ||||||
\(716\) | 21.2467 | − | 15.6502i | 0.794028 | − | 0.584877i | ||||
\(717\) | −2.53976 | −0.0948492 | ||||||||
\(718\) | 9.76611 | − | 19.3232i | 0.364468 | − | 0.721136i | ||||
\(719\) | − | 6.45760i | − | 0.240828i | −0.992724 | − | 0.120414i | \(-0.961578\pi\) | ||
0.992724 | − | 0.120414i | \(-0.0384222\pi\) | |||||||
\(720\) | −10.9973 | − | 3.41467i | −0.409845 | − | 0.127257i | ||||
\(721\) | −74.8035 | −2.78583 | ||||||||
\(722\) | 3.14221 | − | 6.21718i | 0.116941 | − | 0.231380i | ||||
\(723\) | −5.02908 | −0.187033 | ||||||||
\(724\) | −19.1269 | + | 14.0888i | −0.710847 | + | 0.523607i | ||||
\(725\) | 1.72418 | 0.0640344 | ||||||||
\(726\) | 1.67366 | + | 0.845881i | 0.0621153 | + | 0.0313936i | ||||
\(727\) | −16.4785 | −0.611153 | −0.305577 | − | 0.952167i | \(-0.598849\pi\) | ||||
−0.305577 | + | 0.952167i | \(0.598849\pi\) | |||||||
\(728\) | 42.2907 | − | 7.12468i | 1.56740 | − | 0.264058i | ||||
\(729\) | 20.6740 | 0.765702 | ||||||||
\(730\) | −15.9707 | − | 8.07172i | −0.591102 | − | 0.298748i | ||||
\(731\) | − | 0.569007i | − | 0.0210455i | ||||||
\(732\) | −3.32428 | − | 4.51304i | −0.122869 | − | 0.166807i | ||||
\(733\) | − | 16.1329i | − | 0.595882i | −0.954584 | − | 0.297941i | \(-0.903700\pi\) | ||
0.954584 | − | 0.297941i | \(-0.0962998\pi\) | |||||||
\(734\) | 16.1368 | − | 31.9283i | 0.595620 | − | 1.17849i | ||||
\(735\) | 5.89242 | 0.217345 | ||||||||
\(736\) | 25.7272 | − | 8.60872i | 0.948318 | − | 0.317322i | ||||
\(737\) | −15.4695 | −0.569826 | ||||||||
\(738\) | −9.26495 | + | 18.3316i | −0.341048 | + | 0.674796i | ||||
\(739\) | 33.9931i | 1.25045i | 0.780443 | + | 0.625227i | \(0.214994\pi\) | ||||
−0.780443 | + | 0.625227i | \(0.785006\pi\) | |||||||
\(740\) | 2.52008 | + | 3.42126i | 0.0926401 | + | 0.125768i | ||||
\(741\) | − | 5.27863i | − | 0.193915i | ||||||
\(742\) | 68.8777 | + | 34.8113i | 2.52858 | + | 1.27796i | ||||
\(743\) | 14.8782 | 0.545829 | 0.272914 | − | 0.962038i | \(-0.412012\pi\) | ||||
0.272914 | + | 0.962038i | \(0.412012\pi\) | |||||||
\(744\) | 8.69589 | − | 1.46499i | 0.318807 | − | 0.0537092i | ||||
\(745\) | 4.69262 | 0.171924 | ||||||||
\(746\) | 10.9943 | + | 5.55659i | 0.402529 | + | 0.203441i | ||||
\(747\) | −13.6850 | −0.500709 | ||||||||
\(748\) | 3.32199 | − | 2.44696i | 0.121464 | − | 0.0894698i | ||||
\(749\) | 3.61790 | 0.132195 | ||||||||
\(750\) | −0.222077 | + | 0.439402i | −0.00810912 | + | 0.0160447i | ||||
\(751\) | −1.07379 | −0.0391833 | −0.0195916 | − | 0.999808i | \(-0.506237\pi\) | ||||
−0.0195916 | + | 0.999808i | \(0.506237\pi\) | |||||||
\(752\) | −36.3456 | − | 11.2853i | −1.32539 | − | 0.411534i | ||||
\(753\) | − | 5.69458i | − | 0.207522i | ||||||
\(754\) | 3.40946 | − | 6.74596i | 0.124165 | − | 0.245673i | ||||
\(755\) | −4.65716 | −0.169492 | ||||||||
\(756\) | −16.1203 | + | 11.8742i | −0.586290 | + | 0.431859i | ||||
\(757\) | − | 49.0368i | − | 1.78227i | −0.453735 | − | 0.891137i | \(-0.649909\pi\) | ||
0.453735 | − | 0.891137i | \(-0.350091\pi\) | |||||||
\(758\) | −16.9868 | + | 33.6101i | −0.616988 | + | 1.22077i | ||||
\(759\) | −3.97358 | − | 2.06296i | −0.144232 | − | 0.0748807i | ||||
\(760\) | 2.29838 | + | 13.6427i | 0.0833710 | + | 0.494873i | ||||
\(761\) | 15.4133 | 0.558731 | 0.279366 | − | 0.960185i | \(-0.409876\pi\) | ||||
0.279366 | + | 0.960185i | \(0.409876\pi\) | |||||||
\(762\) | −1.73381 | + | 3.43052i | −0.0628094 | + | 0.124275i | ||||
\(763\) | − | 70.7891i | − | 2.56274i | ||||||
\(764\) | −5.63858 | − | 7.65492i | −0.203997 | − | 0.276945i | ||||
\(765\) | −2.21466 | −0.0800712 | ||||||||
\(766\) | −3.89309 | + | 7.70285i | −0.140663 | + | 0.278315i | ||||
\(767\) | 5.82629i | 0.210375i | ||||||||
\(768\) | −3.15489 | + | 4.59052i | −0.113842 | + | 0.165646i | ||||
\(769\) | 31.8146i | 1.14726i | 0.819114 | + | 0.573631i | \(0.194466\pi\) | ||||
−0.819114 | + | 0.573631i | \(0.805534\pi\) | |||||||
\(770\) | 16.5557 | + | 8.36737i | 0.596625 | + | 0.301539i | ||||
\(771\) | 4.61432i | 0.166181i | ||||||||
\(772\) | 8.12877 | + | 11.0356i | 0.292561 | + | 0.397180i | ||||
\(773\) | 41.4024i | 1.48914i | 0.667545 | + | 0.744570i | \(0.267345\pi\) | ||||
−0.667545 | + | 0.744570i | \(0.732655\pi\) | |||||||
\(774\) | −1.35830 | + | 2.68753i | −0.0488230 | + | 0.0966011i | ||||
\(775\) | 8.95574i | 0.321700i | ||||||||
\(776\) | 7.42469 | + | 44.0715i | 0.266531 | + | 1.58207i | ||||
\(777\) | 3.61790 | 0.129791 | ||||||||
\(778\) | 28.9869 | + | 14.6502i | 1.03923 | + | 0.525236i | ||||
\(779\) | 24.6777 | 0.884170 | ||||||||
\(780\) | 1.28004 | + | 1.73778i | 0.0458329 | + | 0.0622226i | ||||
\(781\) | 1.66073i | 0.0594257i | ||||||||
\(782\) | 4.23446 | − | 3.04845i | 0.151424 | − | 0.109012i | ||||
\(783\) | 3.52871i | 0.126106i | ||||||||
\(784\) | −20.0764 | + | 64.6580i | −0.717013 | + | 2.30921i | ||||
\(785\) | −16.5705 | −0.591426 | ||||||||
\(786\) | −2.93015 | + | 5.79758i | −0.104515 | + | 0.206793i | ||||
\(787\) | −52.5560 | −1.87342 | −0.936709 | − | 0.350110i | \(-0.886144\pi\) | ||||
−0.936709 | + | 0.350110i | \(0.886144\pi\) | |||||||
\(788\) | −12.5945 | − | 17.0983i | −0.448662 | − | 0.609102i | ||||
\(789\) | − | 8.16935i | − | 0.290837i | ||||||
\(790\) | 8.47215 | + | 4.28189i | 0.301426 | + | 0.152343i | ||||
\(791\) | 72.4891i | 2.57741i | ||||||||
\(792\) | −21.5316 | + | 3.62741i | −0.765092 | + | 0.128894i | ||||
\(793\) | − | 24.9552i | − | 0.886185i | ||||||
\(794\) | 8.82524 | − | 17.4616i | 0.313196 | − | 0.619690i | ||||
\(795\) | 3.88394i | 0.137749i | ||||||||
\(796\) | 1.20393 | + | 1.63446i | 0.0426723 | + | 0.0579318i | ||||
\(797\) | 31.5518i | 1.11762i | 0.829295 | + | 0.558811i | \(0.188742\pi\) | ||||
−0.829295 | + | 0.558811i | \(0.811258\pi\) | |||||||
\(798\) | 10.5130 | + | 5.31338i | 0.372158 | + | 0.188091i | ||||
\(799\) | −7.31936 | −0.258940 | ||||||||
\(800\) | −4.06494 | − | 3.93398i | −0.143717 | − | 0.139087i | ||||
\(801\) | 28.4293i | 1.00450i | ||||||||
\(802\) | −0.146826 | − | 0.0742069i | −0.00518460 | − | 0.00262034i | ||||
\(803\) | −33.9315 | −1.19742 | ||||||||
\(804\) | 3.23393 | − | 2.38210i | 0.114052 | − | 0.0840103i | ||||
\(805\) | 20.8197 | + | 10.8089i | 0.733798 | + | 0.380965i | ||||
\(806\) | 35.0399 | + | 17.7095i | 1.23423 | + | 0.623789i | ||||
\(807\) | − | 4.11298i | − | 0.144784i | ||||||
\(808\) | −35.4082 | + | 5.96519i | −1.24566 | + | 0.209855i | ||||
\(809\) | −44.2553 | −1.55593 | −0.777967 | − | 0.628305i | \(-0.783749\pi\) | ||||
−0.777967 | + | 0.628305i | \(0.783749\pi\) | |||||||
\(810\) | 10.0013 | + | 5.05475i | 0.351411 | + | 0.177606i | ||||
\(811\) | − | 20.1920i | − | 0.709037i | −0.935049 | − | 0.354519i | \(-0.884645\pi\) | ||
0.935049 | − | 0.354519i | \(-0.115355\pi\) | |||||||
\(812\) | 10.0035 | + | 13.5807i | 0.351054 | + | 0.476590i | ||||
\(813\) | −5.36606 | −0.188196 | ||||||||
\(814\) | 7.19105 | + | 3.63442i | 0.252046 | + | 0.127386i | ||||
\(815\) | −14.7245 | −0.515776 | ||||||||
\(816\) | −0.317669 | + | 1.02309i | −0.0111207 | + | 0.0358152i | ||||
\(817\) | 3.61790 | 0.126574 | ||||||||
\(818\) | 5.91595 | − | 11.7053i | 0.206846 | − | 0.409266i | ||||
\(819\) | −43.6505 | −1.52527 | ||||||||
\(820\) | −8.12416 | + | 5.98422i | −0.283708 | + | 0.208978i | ||||
\(821\) | −23.0606 | −0.804822 | −0.402411 | − | 0.915459i | \(-0.631828\pi\) | ||||
−0.402411 | + | 0.915459i | \(0.631828\pi\) | |||||||
\(822\) | 2.40042 | − | 4.74947i | 0.0837243 | − | 0.165657i | ||||
\(823\) | − | 16.1779i | − | 0.563927i | −0.959425 | − | 0.281963i | \(-0.909014\pi\) | ||
0.959425 | − | 0.281963i | \(-0.0909857\pi\) | |||||||
\(824\) | 42.6537 | − | 7.18583i | 1.48591 | − | 0.250330i | ||||
\(825\) | 0.933557i | 0.0325023i | ||||||||
\(826\) | −11.6038 | − | 5.86464i | −0.403747 | − | 0.204057i | ||||
\(827\) | 21.0266 | 0.731166 | 0.365583 | − | 0.930779i | \(-0.380870\pi\) | ||||
0.365583 | + | 0.930779i | \(0.380870\pi\) | |||||||
\(828\) | −27.2772 | + | 4.29015i | −0.947948 | + | 0.149093i | ||||
\(829\) | 6.23369 | 0.216505 | 0.108252 | − | 0.994123i | \(-0.465475\pi\) | ||||
0.108252 | + | 0.994123i | \(0.465475\pi\) | |||||||
\(830\) | −6.00000 | − | 3.03245i | −0.208263 | − | 0.105258i | ||||
\(831\) | 3.46140i | 0.120075i | ||||||||
\(832\) | −23.4301 | + | 8.12513i | −0.812294 | + | 0.281688i | ||||
\(833\) | 13.0210i | 0.451150i | ||||||||
\(834\) | 0.513861 | − | 1.01672i | 0.0177935 | − | 0.0352063i | ||||
\(835\) | −1.87953 | −0.0650437 | ||||||||
\(836\) | 15.5584 | + | 21.1221i | 0.538099 | + | 0.730522i | ||||
\(837\) | −18.3288 | −0.633538 | ||||||||
\(838\) | −22.0716 | + | 43.6708i | −0.762449 | + | 1.50858i | ||||
\(839\) | −19.3616 | −0.668436 | −0.334218 | − | 0.942496i | \(-0.608472\pi\) | ||||
−0.334218 | + | 0.942496i | \(0.608472\pi\) | |||||||
\(840\) | −4.74947 | + | 0.800141i | −0.163872 | + | 0.0276075i | ||||
\(841\) | −26.0272 | −0.897490 | ||||||||
\(842\) | 31.0152 | + | 15.6753i | 1.06886 | + | 0.540208i | ||||
\(843\) | 9.37730 | 0.322972 | ||||||||
\(844\) | 17.5973 | − | 12.9621i | 0.605723 | − | 0.446173i | ||||
\(845\) | − | 3.39079i | − | 0.116647i | ||||||
\(846\) | 34.5707 | + | 17.4723i | 1.18856 | + | 0.600710i | ||||
\(847\) | −18.6311 | −0.640172 | ||||||||
\(848\) | −42.6188 | − | 13.2332i | −1.46354 | − | 0.454429i | ||||
\(849\) | − | 0.727177i | − | 0.0249567i | ||||||
\(850\) | −0.970984 | − | 0.490743i | −0.0333045 | − | 0.0168324i | ||||
\(851\) | 9.04316 | + | 4.69493i | 0.309995 | + | 0.160940i | ||||
\(852\) | −0.255732 | − | 0.347181i | −0.00876122 | − | 0.0118942i | ||||
\(853\) | 39.7903 | 1.36239 | 0.681197 | − | 0.732100i | \(-0.261460\pi\) | ||||
0.681197 | + | 0.732100i | \(0.261460\pi\) | |||||||
\(854\) | 49.7013 | + | 25.1195i | 1.70074 | + | 0.859570i | ||||
\(855\) | − | 14.0814i | − | 0.481573i | ||||||
\(856\) | −2.06296 | + | 0.347546i | −0.0705105 | + | 0.0118789i | ||||
\(857\) | 23.1378 | 0.790372 | 0.395186 | − | 0.918601i | \(-0.370680\pi\) | ||||
0.395186 | + | 0.918601i | \(0.370680\pi\) | |||||||
\(858\) | 3.65260 | + | 1.84605i | 0.124698 | + | 0.0630232i | ||||
\(859\) | 44.7107i | 1.52551i | 0.646687 | + | 0.762755i | \(0.276154\pi\) | ||||
−0.646687 | + | 0.762755i | \(0.723846\pi\) | |||||||
\(860\) | −1.19105 | + | 0.877323i | −0.0406145 | + | 0.0299165i | ||||
\(861\) | 8.59111i | 0.292784i | ||||||||
\(862\) | 22.8492 | − | 45.2094i | 0.778246 | − | 1.53984i | ||||
\(863\) | − | 3.39308i | − | 0.115502i | −0.998331 | − | 0.0577509i | \(-0.981607\pi\) | ||
0.998331 | − | 0.0577509i | \(-0.0183929\pi\) | |||||||
\(864\) | 8.05130 | − | 8.31932i | 0.273911 | − | 0.283029i | ||||
\(865\) | 0.769298i | 0.0261569i | ||||||||
\(866\) | 34.7615 | + | 17.5687i | 1.18124 | + | 0.597010i | ||||
\(867\) | − | 5.71222i | − | 0.193997i | ||||||
\(868\) | −70.5411 | + | 51.9602i | −2.39432 | + | 1.76365i | ||||
\(869\) | 18.0000 | 0.610608 | ||||||||
\(870\) | −0.382901 | + | 0.757608i | −0.0129816 | + | 0.0256853i | ||||
\(871\) | 17.8823 | 0.605919 | ||||||||
\(872\) | 6.80020 | + | 40.3646i | 0.230284 | + | 1.36692i | ||||
\(873\) | − | 45.4885i | − | 1.53955i | ||||||
\(874\) | 19.3828 | + | 26.9238i | 0.655634 | + | 0.910712i | ||||
\(875\) | − | 4.89140i | − | 0.165359i | ||||||
\(876\) | 7.09346 | − | 5.22501i | 0.239666 | − | 0.176537i | ||||
\(877\) | −1.69211 | −0.0571383 | −0.0285692 | − | 0.999592i | \(-0.509095\pi\) | ||||
−0.0285692 | + | 0.999592i | \(0.509095\pi\) | |||||||
\(878\) | −22.4602 | − | 11.3515i | −0.757994 | − | 0.383096i | ||||
\(879\) | −2.12929 | −0.0718192 | ||||||||
\(880\) | −10.2440 | − | 3.18077i | −0.345325 | − | 0.107224i | ||||
\(881\) | − | 7.53860i | − | 0.253982i | −0.991904 | − | 0.126991i | \(-0.959468\pi\) | ||
0.991904 | − | 0.126991i | \(-0.0405319\pi\) | |||||||
\(882\) | 31.0828 | − | 61.5005i | 1.04661 | − | 2.07083i | ||||
\(883\) | − | 8.23718i | − | 0.277203i | −0.990348 | − | 0.138602i | \(-0.955739\pi\) | ||
0.990348 | − | 0.138602i | \(-0.0442607\pi\) | |||||||
\(884\) | −3.84013 | + | 2.82862i | −0.129157 | + | 0.0951368i | ||||
\(885\) | − | 0.654324i | − | 0.0219949i | ||||||
\(886\) | −27.9837 | − | 14.1432i | −0.940129 | − | 0.475149i | ||||
\(887\) | − | 9.60780i | − | 0.322598i | −0.986906 | − | 0.161299i | \(-0.948432\pi\) | ||
0.986906 | − | 0.161299i | \(-0.0515684\pi\) | |||||||
\(888\) | −2.06296 | + | 0.347546i | −0.0692284 | + | 0.0116629i | ||||
\(889\) | − | 38.1884i | − | 1.28080i | ||||||
\(890\) | −6.29962 | + | 12.4644i | −0.211164 | + | 0.417808i | ||||
\(891\) | 21.2489 | 0.711865 | ||||||||
\(892\) | 35.8516 | − | 26.4081i | 1.20040 | − | 0.884209i | ||||
\(893\) | − | 46.5384i | − | 1.55735i | ||||||
\(894\) | −1.04212 | + | 2.06195i | −0.0348539 | + | 0.0689618i | ||||
\(895\) | −13.1943 | −0.441035 | ||||||||
\(896\) | 7.40217 | − | 54.8426i | 0.247289 | − | 1.83216i | ||||
\(897\) | 4.59335 | + | 2.38473i | 0.153367 | + | 0.0796237i | ||||
\(898\) | −0.316378 | + | 0.625985i | −0.0105577 | + | 0.0208894i | ||||
\(899\) | 15.4413i | 0.514996i | ||||||||
\(900\) | 3.41467 | + | 4.63574i | 0.113822 | + | 0.154525i | ||||
\(901\) | −8.58267 | −0.285930 | ||||||||
\(902\) | −8.63033 | + | 17.0760i | −0.287358 | + | 0.568567i | ||||
\(903\) | 1.25951i | 0.0419138i | ||||||||
\(904\) | −6.96351 | − | 41.3340i | −0.231603 | − | 1.37475i | ||||
\(905\) | 11.8779 | 0.394834 | ||||||||
\(906\) | 1.03425 | − | 2.04637i | 0.0343607 | − | 0.0679860i | ||||
\(907\) | 31.5673 | 1.04818 | 0.524088 | − | 0.851664i | \(-0.324406\pi\) | ||||
0.524088 | + | 0.851664i | \(0.324406\pi\) | |||||||
\(908\) | 34.3699 | + | 46.6605i | 1.14061 | + | 1.54848i | ||||
\(909\) | 36.5467 | 1.21218 | ||||||||
\(910\) | −19.1379 | − | 9.67245i | −0.634415 | − | 0.320639i | ||||
\(911\) | −28.9429 | −0.958921 | −0.479461 | − | 0.877563i | \(-0.659168\pi\) | ||||
−0.479461 | + | 0.877563i | \(0.659168\pi\) | |||||||
\(912\) | −6.50506 | − | 2.01983i | −0.215404 | − | 0.0668831i | ||||
\(913\) | −12.7476 | −0.421885 | ||||||||
\(914\) | −21.2398 | − | 10.7347i | −0.702549 | − | 0.355074i | ||||
\(915\) | 2.80261i | 0.0926513i | ||||||||
\(916\) | −43.1878 | + | 31.8119i | −1.42696 | + | 1.05110i | ||||
\(917\) | − | 64.5384i | − | 2.13125i | ||||||
\(918\) | 1.00436 | − | 1.98722i | 0.0331487 | − | 0.0655880i | ||||
\(919\) | −49.9290 | −1.64701 | −0.823503 | − | 0.567312i | \(-0.807983\pi\) | ||||
−0.823503 | + | 0.567312i | \(0.807983\pi\) | |||||||
\(920\) | −12.9099 | − | 4.16337i | −0.425628 | − | 0.137262i | ||||
\(921\) | −3.24464 | −0.106914 | ||||||||
\(922\) | 21.2594 | − | 42.0637i | 0.700139 | − | 1.38530i | ||||
\(923\) | − | 1.91976i | − | 0.0631898i | ||||||
\(924\) | −7.35328 | + | 5.41639i | −0.241905 | + | 0.178186i | ||||
\(925\) | − | 2.12461i | − | 0.0698567i | ||||||
\(926\) | −37.7187 | − | 19.0633i | −1.23951 | − | 0.626460i | ||||
\(927\) | −44.0251 | −1.44597 | ||||||||
\(928\) | −7.00869 | − | 6.78289i | −0.230072 | − | 0.222659i | ||||
\(929\) | −10.8751 | −0.356799 | −0.178399 | − | 0.983958i | \(-0.557092\pi\) | ||||
−0.178399 | + | 0.983958i | \(0.557092\pi\) | |||||||
\(930\) | −3.93517 | − | 1.98887i | −0.129039 | − | 0.0652175i | ||||
\(931\) | −82.7908 | −2.71336 | ||||||||
\(932\) | 27.8038 | + | 37.7464i | 0.910745 | + | 1.23643i | ||||
\(933\) | −3.24168 | −0.106128 | ||||||||
\(934\) | −3.93860 | + | 7.79291i | −0.128875 | + | 0.254992i | ||||
\(935\) | −2.06296 | −0.0674660 | ||||||||
\(936\) | 24.8899 | − | 4.19319i | 0.813553 | − | 0.137059i | ||||
\(937\) | 48.0375i | 1.56932i | 0.619928 | + | 0.784658i | \(0.287162\pi\) | ||||
−0.619928 | + | 0.784658i | \(0.712838\pi\) | |||||||
\(938\) | −18.0000 | + | 35.6148i | −0.587721 | + | 1.16286i | ||||
\(939\) | −3.76295 | −0.122799 | ||||||||
\(940\) | 11.2853 | + | 15.3209i | 0.368087 | + | 0.499714i | ||||
\(941\) | 29.2945i | 0.954973i | 0.878639 | + | 0.477486i | \(0.158452\pi\) | ||||
−0.878639 | + | 0.477486i | \(0.841548\pi\) | |||||||
\(942\) | 3.67993 | − | 7.28110i | 0.119899 | − | 0.237231i | ||||
\(943\) | −11.1486 | + | 21.4740i | −0.363050 | + | 0.699289i | ||||
\(944\) | 7.17996 | + | 2.22938i | 0.233688 | + | 0.0725603i | ||||
\(945\) | 10.0107 | 0.325650 | ||||||||
\(946\) | −1.26526 | + | 2.50344i | −0.0411371 | + | 0.0813938i | ||||
\(947\) | 4.93626i | 0.160407i | 0.996779 | + | 0.0802035i | \(0.0255570\pi\) | ||||
−0.996779 | + | 0.0802035i | \(0.974443\pi\) | |||||||
\(948\) | −3.76295 | + | 2.77177i | −0.122215 | + | 0.0900229i | ||||
\(949\) | 39.2239 | 1.27326 | ||||||||
\(950\) | 3.12027 | − | 6.17377i | 0.101235 | − | 0.200304i | ||||
\(951\) | − | 10.8069i | − | 0.350439i | ||||||
\(952\) | −1.76814 | − | 10.4953i | −0.0573057 | − | 0.340155i | ||||
\(953\) | − | 20.8691i | − | 0.676015i | −0.941143 | − | 0.338008i | \(-0.890247\pi\) | ||
0.941143 | − | 0.338008i | \(-0.109753\pi\) | |||||||
\(954\) | 40.5375 | + | 20.4880i | 1.31245 | + | 0.663323i | ||||
\(955\) | 4.75372i | 0.153827i | ||||||||
\(956\) | −11.7478 | + | 8.65337i | −0.379951 | + | 0.279870i | ||||
\(957\) | 1.60962i | 0.0520316i | ||||||||
\(958\) | −15.3592 | + | 30.3897i | −0.496233 | + | 0.981846i | ||||
\(959\) | 52.8709i | 1.70729i | ||||||||
\(960\) | 2.63133 | − | 0.912496i | 0.0849259 | − | 0.0294507i | ||||
\(961\) | −49.2054 | −1.58727 | ||||||||
\(962\) | −8.31266 | − | 4.20128i | −0.268011 | − | 0.135455i | ||||
\(963\) | 2.12929 | 0.0686155 | ||||||||
\(964\) | −23.2622 | + | 17.1348i | −0.749225 | + | 0.551876i | ||||
\(965\) | − | 6.85313i | − | 0.220610i | ||||||
\(966\) | −9.37306 | + | 6.74779i | −0.301573 | + | 0.217107i | ||||
\(967\) | 58.1918i | 1.87132i | 0.352902 | + | 0.935660i | \(0.385195\pi\) | ||||
−0.352902 | + | 0.935660i | \(0.614805\pi\) | |||||||
\(968\) | 10.6236 | − | 1.78976i | 0.341456 | − | 0.0575249i | ||||
\(969\) | −1.31000 | −0.0420834 | ||||||||
\(970\) | 10.0797 | − | 19.9438i | 0.323641 | − | 0.640356i | ||||
\(971\) | 14.4231 | 0.462858 | 0.231429 | − | 0.972852i | \(-0.425660\pi\) | ||||
0.231429 | + | 0.972852i | \(0.425660\pi\) | |||||||
\(972\) | −14.3291 | + | 10.5547i | −0.459605 | + | 0.338543i | ||||
\(973\) | 11.3181i | 0.362843i | ||||||||
\(974\) | −24.5943 | − | 12.4301i | −0.788052 | − | 0.398288i | ||||
\(975\) | − | 1.07917i | − | 0.0345610i | ||||||
\(976\) | −30.7532 | − | 9.54891i | −0.984387 | − | 0.305653i | ||||
\(977\) | 11.4330i | 0.365775i | 0.983134 | + | 0.182887i | \(0.0585444\pi\) | ||||
−0.983134 | + | 0.182887i | \(0.941456\pi\) | |||||||
\(978\) | 3.26997 | − | 6.46996i | 0.104562 | − | 0.206886i | ||||
\(979\) | 26.4820i | 0.846368i | ||||||||
\(980\) | 27.2556 | − | 20.0764i | 0.870649 | − | 0.641316i | ||||
\(981\) | − | 41.6625i | − | 1.33018i | ||||||
\(982\) | −11.0257 | − | 5.57246i | −0.351843 | − | 0.177824i | ||||
\(983\) | 30.0714 | 0.959127 | 0.479564 | − | 0.877507i | \(-0.340795\pi\) | ||||
0.479564 | + | 0.877507i | \(0.340795\pi\) | |||||||
\(984\) | −0.825286 | − | 4.89873i | −0.0263092 | − | 0.156166i | ||||
\(985\) | 10.6181i | 0.338320i | ||||||||
\(986\) | −1.67415 | − | 0.846130i | −0.0533158 | − | 0.0269463i | ||||
\(987\) | 16.2015 | 0.515700 | ||||||||
\(988\) | −17.9851 | − | 24.4165i | −0.572183 | − | 0.776794i | ||||
\(989\) | −1.63446 | + | 3.14822i | −0.0519727 | + | 0.100107i | ||||
\(990\) | 9.74374 | + | 4.92457i | 0.309676 | + | 0.156513i | ||||
\(991\) | 17.2895i | 0.549218i | 0.961556 | + | 0.274609i | \(0.0885485\pi\) | ||||
−0.961556 | + | 0.274609i | \(0.911452\pi\) | |||||||
\(992\) | 35.2318 | − | 36.4046i | 1.11861 | − | 1.15585i | ||||
\(993\) | −8.57679 | −0.272176 | ||||||||
\(994\) | 3.82344 | + | 1.93240i | 0.121272 | + | 0.0612920i | ||||
\(995\) | − | 1.01500i | − | 0.0321777i | ||||||
\(996\) | 2.66493 | − | 1.96297i | 0.0844415 | − | 0.0621992i | ||||
\(997\) | 33.7032 | 1.06739 | 0.533695 | − | 0.845677i | \(-0.320803\pi\) | ||||
0.533695 | + | 0.845677i | \(0.320803\pi\) | |||||||
\(998\) | −32.7189 | − | 16.5364i | −1.03570 | − | 0.523450i | ||||
\(999\) | 4.34823 | 0.137572 |
(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 | 460.2.e.a.91.10 | yes | 16 | |
4.3 | odd | 2 | inner | 460.2.e.a.91.12 | yes | 16 | |
23.22 | odd | 2 | inner | 460.2.e.a.91.9 | ✓ | 16 | |
92.91 | even | 2 | inner | 460.2.e.a.91.11 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.2.e.a.91.9 | ✓ | 16 | 23.22 | odd | 2 | inner | |
460.2.e.a.91.10 | yes | 16 | 1.1 | even | 1 | trivial | |
460.2.e.a.91.11 | yes | 16 | 92.91 | even | 2 | inner | |
460.2.e.a.91.12 | yes | 16 | 4.3 | odd | 2 | inner |