Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.23 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.10 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.44015i | 1.01834i | 0.860666 | + | 0.509170i | \(0.170048\pi\) | ||||
−0.860666 | + | 0.509170i | \(0.829952\pi\) | |||||||
\(3\) | −2.79139 | −1.61161 | −0.805804 | − | 0.592182i | \(-0.798267\pi\) | ||||
−0.805804 | + | 0.592182i | \(0.798267\pi\) | |||||||
\(4\) | −0.0740342 | −0.0370171 | ||||||||
\(5\) | − | 2.61757i | − | 1.17061i | −0.810813 | − | 0.585306i | \(-0.800975\pi\) | ||
0.810813 | − | 0.585306i | \(-0.199025\pi\) | |||||||
\(6\) | − | 4.02002i | − | 1.64117i | ||||||
\(7\) | 4.99660i | 1.88854i | 0.329173 | + | 0.944269i | \(0.393230\pi\) | ||||
−0.329173 | + | 0.944269i | \(0.606770\pi\) | |||||||
\(8\) | 2.77368i | 0.980644i | ||||||||
\(9\) | 4.79185 | 1.59728 | ||||||||
\(10\) | 3.76969 | 1.19208 | ||||||||
\(11\) | 0.0546038i | 0.0164637i | 0.999966 | + | 0.00823183i | \(0.00262030\pi\) | ||||
−0.999966 | + | 0.00823183i | \(0.997380\pi\) | |||||||
\(12\) | 0.206658 | 0.0596571 | ||||||||
\(13\) | −1.72882 | − | 3.16404i | −0.479489 | − | 0.877548i | ||||
\(14\) | −7.19586 | −1.92318 | ||||||||
\(15\) | 7.30664i | 1.88657i | ||||||||
\(16\) | −4.14259 | −1.03565 | ||||||||
\(17\) | −5.08006 | −1.23209 | −0.616047 | − | 0.787709i | \(-0.711267\pi\) | ||||
−0.616047 | + | 0.787709i | \(0.711267\pi\) | |||||||
\(18\) | 6.90098i | 1.62658i | ||||||||
\(19\) | 1.17518i | 0.269604i | 0.990873 | + | 0.134802i | \(0.0430399\pi\) | ||||
−0.990873 | + | 0.134802i | \(0.956960\pi\) | |||||||
\(20\) | 0.193789i | 0.0433326i | ||||||||
\(21\) | − | 13.9475i | − | 3.04359i | ||||||
\(22\) | −0.0786376 | −0.0167656 | ||||||||
\(23\) | −7.81207 | −1.62893 | −0.814464 | − | 0.580213i | \(-0.802969\pi\) | ||||
−0.814464 | + | 0.580213i | \(0.802969\pi\) | |||||||
\(24\) | − | 7.74242i | − | 1.58041i | ||||||
\(25\) | −1.85165 | −0.370331 | ||||||||
\(26\) | 4.55670 | − | 2.48976i | 0.893643 | − | 0.488283i | ||||
\(27\) | −5.00174 | −0.962586 | ||||||||
\(28\) | − | 0.369920i | − | 0.0699082i | ||||||
\(29\) | −7.02474 | −1.30446 | −0.652231 | − | 0.758020i | \(-0.726167\pi\) | ||||
−0.652231 | + | 0.758020i | \(0.726167\pi\) | |||||||
\(30\) | −10.5227 | −1.92117 | ||||||||
\(31\) | 1.00000i | 0.179605i | ||||||||
\(32\) | − | 0.418588i | − | 0.0739966i | ||||||
\(33\) | − | 0.152420i | − | 0.0265330i | ||||||
\(34\) | − | 7.31605i | − | 1.25469i | ||||||
\(35\) | 13.0789 | 2.21075 | ||||||||
\(36\) | −0.354761 | −0.0591268 | ||||||||
\(37\) | 6.75099i | 1.10986i | 0.831899 | + | 0.554928i | \(0.187254\pi\) | ||||
−0.831899 | + | 0.554928i | \(0.812746\pi\) | |||||||
\(38\) | −1.69243 | −0.274549 | ||||||||
\(39\) | 4.82581 | + | 8.83208i | 0.772748 | + | 1.41426i | ||||
\(40\) | 7.26030 | 1.14795 | ||||||||
\(41\) | − | 1.55918i | − | 0.243503i | −0.992561 | − | 0.121751i | \(-0.961149\pi\) | ||
0.992561 | − | 0.121751i | \(-0.0388511\pi\) | |||||||
\(42\) | 20.0864 | 3.09941 | ||||||||
\(43\) | −3.02644 | −0.461528 | −0.230764 | − | 0.973010i | \(-0.574123\pi\) | ||||
−0.230764 | + | 0.973010i | \(0.574123\pi\) | |||||||
\(44\) | − | 0.00404255i | − | 0.000609437i | ||||||
\(45\) | − | 12.5430i | − | 1.86980i | ||||||
\(46\) | − | 11.2506i | − | 1.65880i | ||||||
\(47\) | 0.191499i | 0.0279330i | 0.999902 | + | 0.0139665i | \(0.00444582\pi\) | ||||
−0.999902 | + | 0.0139665i | \(0.995554\pi\) | |||||||
\(48\) | 11.5636 | 1.66906 | ||||||||
\(49\) | −17.9661 | −2.56658 | ||||||||
\(50\) | − | 2.66666i | − | 0.377123i | ||||||
\(51\) | 14.1804 | 1.98565 | ||||||||
\(52\) | 0.127992 | + | 0.234248i | 0.0177493 | + | 0.0324843i | ||||
\(53\) | 8.59226 | 1.18024 | 0.590119 | − | 0.807317i | \(-0.299081\pi\) | ||||
0.590119 | + | 0.807317i | \(0.299081\pi\) | |||||||
\(54\) | − | 7.20326i | − | 0.980240i | ||||||
\(55\) | 0.142929 | 0.0192725 | ||||||||
\(56\) | −13.8590 | −1.85199 | ||||||||
\(57\) | − | 3.28038i | − | 0.434497i | ||||||
\(58\) | − | 10.1167i | − | 1.32839i | ||||||
\(59\) | − | 2.91407i | − | 0.379379i | −0.981844 | − | 0.189690i | \(-0.939252\pi\) | ||
0.981844 | − | 0.189690i | \(-0.0607482\pi\) | |||||||
\(60\) | − | 0.540942i | − | 0.0698353i | ||||||
\(61\) | 5.96368 | 0.763571 | 0.381786 | − | 0.924251i | \(-0.375309\pi\) | ||||
0.381786 | + | 0.924251i | \(0.375309\pi\) | |||||||
\(62\) | −1.44015 | −0.182899 | ||||||||
\(63\) | 23.9430i | 3.01653i | ||||||||
\(64\) | −7.68234 | −0.960293 | ||||||||
\(65\) | −8.28210 | + | 4.52530i | −1.02727 | + | 0.561295i | ||||
\(66\) | 0.219508 | 0.0270196 | ||||||||
\(67\) | 1.50321i | 0.183646i | 0.995775 | + | 0.0918231i | \(0.0292694\pi\) | ||||
−0.995775 | + | 0.0918231i | \(0.970731\pi\) | |||||||
\(68\) | 0.376098 | 0.0456086 | ||||||||
\(69\) | 21.8065 | 2.62520 | ||||||||
\(70\) | 18.8357i | 2.25129i | ||||||||
\(71\) | 1.44037i | 0.170940i | 0.996341 | + | 0.0854701i | \(0.0272392\pi\) | ||||
−0.996341 | + | 0.0854701i | \(0.972761\pi\) | |||||||
\(72\) | 13.2911i | 1.56637i | ||||||||
\(73\) | 13.9550i | 1.63331i | 0.577124 | + | 0.816656i | \(0.304175\pi\) | ||||
−0.577124 | + | 0.816656i | \(0.695825\pi\) | |||||||
\(74\) | −9.72244 | −1.13021 | ||||||||
\(75\) | 5.16869 | 0.596829 | ||||||||
\(76\) | − | 0.0870034i | − | 0.00997997i | ||||||
\(77\) | −0.272833 | −0.0310922 | ||||||||
\(78\) | −12.7195 | + | 6.94989i | −1.44020 | + | 0.786920i | ||||
\(79\) | 1.10819 | 0.124681 | 0.0623404 | − | 0.998055i | \(-0.480144\pi\) | ||||
0.0623404 | + | 0.998055i | \(0.480144\pi\) | |||||||
\(80\) | 10.8435i | 1.21234i | ||||||||
\(81\) | −0.413740 | −0.0459711 | ||||||||
\(82\) | 2.24545 | 0.247969 | ||||||||
\(83\) | 1.74923i | 0.192003i | 0.995381 | + | 0.0960015i | \(0.0306054\pi\) | ||||
−0.995381 | + | 0.0960015i | \(0.969395\pi\) | |||||||
\(84\) | 1.03259i | 0.112665i | ||||||||
\(85\) | 13.2974i | 1.44230i | ||||||||
\(86\) | − | 4.35854i | − | 0.469993i | ||||||
\(87\) | 19.6088 | 2.10228 | ||||||||
\(88\) | −0.151453 | −0.0161450 | ||||||||
\(89\) | 2.35995i | 0.250154i | 0.992147 | + | 0.125077i | \(0.0399179\pi\) | ||||
−0.992147 | + | 0.125077i | \(0.960082\pi\) | |||||||
\(90\) | 18.0638 | 1.90409 | ||||||||
\(91\) | 15.8095 | − | 8.63823i | 1.65728 | − | 0.905533i | ||||
\(92\) | 0.578360 | 0.0602982 | ||||||||
\(93\) | − | 2.79139i | − | 0.289453i | ||||||
\(94\) | −0.275787 | −0.0284453 | ||||||||
\(95\) | 3.07611 | 0.315602 | ||||||||
\(96\) | 1.16844i | 0.119254i | ||||||||
\(97\) | − | 12.1357i | − | 1.23220i | −0.787670 | − | 0.616098i | \(-0.788713\pi\) | ||
0.787670 | − | 0.616098i | \(-0.211287\pi\) | |||||||
\(98\) | − | 25.8738i | − | 2.61365i | ||||||
\(99\) | 0.261653i | 0.0262971i | ||||||||
\(100\) | 0.137086 | 0.0137086 | ||||||||
\(101\) | 11.6128 | 1.15552 | 0.577758 | − | 0.816208i | \(-0.303928\pi\) | ||||
0.577758 | + | 0.816208i | \(0.303928\pi\) | |||||||
\(102\) | 20.4219i | 2.02207i | ||||||||
\(103\) | −12.7238 | −1.25371 | −0.626857 | − | 0.779134i | \(-0.715659\pi\) | ||||
−0.626857 | + | 0.779134i | \(0.715659\pi\) | |||||||
\(104\) | 8.77605 | − | 4.79520i | 0.860563 | − | 0.470208i | ||||
\(105\) | −36.5084 | −3.56286 | ||||||||
\(106\) | 12.3741i | 1.20188i | ||||||||
\(107\) | −2.95463 | −0.285635 | −0.142817 | − | 0.989749i | \(-0.545616\pi\) | ||||
−0.142817 | + | 0.989749i | \(0.545616\pi\) | |||||||
\(108\) | 0.370300 | 0.0356321 | ||||||||
\(109\) | 19.9084i | 1.90688i | 0.301587 | + | 0.953439i | \(0.402484\pi\) | ||||
−0.301587 | + | 0.953439i | \(0.597516\pi\) | |||||||
\(110\) | 0.205839i | 0.0196260i | ||||||||
\(111\) | − | 18.8446i | − | 1.78865i | ||||||
\(112\) | − | 20.6989i | − | 1.95586i | ||||||
\(113\) | 0.926163 | 0.0871261 | 0.0435630 | − | 0.999051i | \(-0.486129\pi\) | ||||
0.0435630 | + | 0.999051i | \(0.486129\pi\) | |||||||
\(114\) | 4.72424 | 0.442465 | ||||||||
\(115\) | 20.4486i | 1.90684i | ||||||||
\(116\) | 0.520071 | 0.0482874 | ||||||||
\(117\) | −8.28425 | − | 15.1616i | −0.765879 | − | 1.40169i | ||||
\(118\) | 4.19670 | 0.386337 | ||||||||
\(119\) | − | 25.3830i | − | 2.32686i | ||||||
\(120\) | −20.2663 | −1.85005 | ||||||||
\(121\) | 10.9970 | 0.999729 | ||||||||
\(122\) | 8.58860i | 0.777575i | ||||||||
\(123\) | 4.35227i | 0.392431i | ||||||||
\(124\) | − | 0.0740342i | − | 0.00664847i | ||||||
\(125\) | − | 8.24100i | − | 0.737098i | ||||||
\(126\) | −34.4815 | −3.07185 | ||||||||
\(127\) | 16.3194 | 1.44812 | 0.724058 | − | 0.689739i | \(-0.242275\pi\) | ||||
0.724058 | + | 0.689739i | \(0.242275\pi\) | |||||||
\(128\) | − | 11.9009i | − | 1.05190i | ||||||
\(129\) | 8.44798 | 0.743803 | ||||||||
\(130\) | −6.51712 | − | 11.9275i | −0.571589 | − | 1.04611i | ||||
\(131\) | 15.1689 | 1.32532 | 0.662658 | − | 0.748922i | \(-0.269428\pi\) | ||||
0.662658 | + | 0.748922i | \(0.269428\pi\) | |||||||
\(132\) | 0.0112843i | 0.000982174i | ||||||||
\(133\) | −5.87190 | −0.509158 | ||||||||
\(134\) | −2.16485 | −0.187014 | ||||||||
\(135\) | 13.0924i | 1.12681i | ||||||||
\(136\) | − | 14.0905i | − | 1.20825i | ||||||
\(137\) | − | 11.4877i | − | 0.981463i | −0.871311 | − | 0.490732i | \(-0.836730\pi\) | ||
0.871311 | − | 0.490732i | \(-0.163270\pi\) | |||||||
\(138\) | 31.4047i | 2.67334i | ||||||||
\(139\) | −6.64791 | −0.563869 | −0.281934 | − | 0.959434i | \(-0.590976\pi\) | ||||
−0.281934 | + | 0.959434i | \(0.590976\pi\) | |||||||
\(140\) | −0.968289 | −0.0818354 | ||||||||
\(141\) | − | 0.534548i | − | 0.0450170i | ||||||
\(142\) | −2.07435 | −0.174075 | ||||||||
\(143\) | 0.172769 | − | 0.0944001i | 0.0144476 | − | 0.00789413i | ||||
\(144\) | −19.8506 | −1.65422 | ||||||||
\(145\) | 18.3877i | 1.52702i | ||||||||
\(146\) | −20.0973 | −1.66327 | ||||||||
\(147\) | 50.1502 | 4.13632 | ||||||||
\(148\) | − | 0.499804i | − | 0.0410836i | ||||||
\(149\) | − | 1.35792i | − | 0.111245i | −0.998452 | − | 0.0556224i | \(-0.982286\pi\) | ||
0.998452 | − | 0.0556224i | \(-0.0177143\pi\) | |||||||
\(150\) | 7.44369i | 0.607775i | ||||||||
\(151\) | 12.4451i | 1.01277i | 0.862308 | + | 0.506384i | \(0.169018\pi\) | ||||
−0.862308 | + | 0.506384i | \(0.830982\pi\) | |||||||
\(152\) | −3.25957 | −0.264386 | ||||||||
\(153\) | −24.3429 | −1.96800 | ||||||||
\(154\) | − | 0.392921i | − | 0.0316625i | ||||||
\(155\) | 2.61757 | 0.210248 | ||||||||
\(156\) | −0.357275 | − | 0.653876i | −0.0286049 | − | 0.0523520i | ||||
\(157\) | 15.5894 | 1.24417 | 0.622086 | − | 0.782949i | \(-0.286286\pi\) | ||||
0.622086 | + | 0.782949i | \(0.286286\pi\) | |||||||
\(158\) | 1.59596i | 0.126968i | ||||||||
\(159\) | −23.9843 | −1.90208 | ||||||||
\(160\) | −1.09568 | −0.0866213 | ||||||||
\(161\) | − | 39.0338i | − | 3.07630i | ||||||
\(162\) | − | 0.595848i | − | 0.0468143i | ||||||
\(163\) | − | 2.52440i | − | 0.197726i | −0.995101 | − | 0.0988632i | \(-0.968479\pi\) | ||
0.995101 | − | 0.0988632i | \(-0.0315206\pi\) | |||||||
\(164\) | 0.115433i | 0.00901377i | ||||||||
\(165\) | −0.398970 | −0.0310598 | ||||||||
\(166\) | −2.51916 | −0.195524 | ||||||||
\(167\) | 9.92382i | 0.767928i | 0.923348 | + | 0.383964i | \(0.125441\pi\) | ||||
−0.923348 | + | 0.383964i | \(0.874559\pi\) | |||||||
\(168\) | 38.6858 | 2.98468 | ||||||||
\(169\) | −7.02236 | + | 10.9401i | −0.540181 | + | 0.841549i | ||||
\(170\) | −19.1502 | −1.46876 | ||||||||
\(171\) | 5.63127i | 0.430634i | ||||||||
\(172\) | 0.224060 | 0.0170844 | ||||||||
\(173\) | −20.3536 | −1.54745 | −0.773726 | − | 0.633520i | \(-0.781609\pi\) | ||||
−0.773726 | + | 0.633520i | \(0.781609\pi\) | |||||||
\(174\) | 28.2396i | 2.14084i | ||||||||
\(175\) | − | 9.25199i | − | 0.699385i | ||||||
\(176\) | − | 0.226201i | − | 0.0170505i | ||||||
\(177\) | 8.13429i | 0.611411i | ||||||||
\(178\) | −3.39869 | −0.254742 | ||||||||
\(179\) | 4.85781 | 0.363090 | 0.181545 | − | 0.983383i | \(-0.441890\pi\) | ||||
0.181545 | + | 0.983383i | \(0.441890\pi\) | |||||||
\(180\) | 0.928610i | 0.0692145i | ||||||||
\(181\) | 6.82673 | 0.507427 | 0.253713 | − | 0.967279i | \(-0.418348\pi\) | ||||
0.253713 | + | 0.967279i | \(0.418348\pi\) | |||||||
\(182\) | 12.4404 | + | 22.7680i | 0.922141 | + | 1.68768i | ||||
\(183\) | −16.6469 | −1.23058 | ||||||||
\(184\) | − | 21.6682i | − | 1.59740i | ||||||
\(185\) | 17.6712 | 1.29921 | ||||||||
\(186\) | 4.02002 | 0.294762 | ||||||||
\(187\) | − | 0.277390i | − | 0.0202848i | ||||||
\(188\) | − | 0.0141775i | − | 0.00103400i | ||||||
\(189\) | − | 24.9917i | − | 1.81788i | ||||||
\(190\) | 4.43006i | 0.321390i | ||||||||
\(191\) | −13.8071 | −0.999043 | −0.499522 | − | 0.866301i | \(-0.666491\pi\) | ||||
−0.499522 | + | 0.866301i | \(0.666491\pi\) | |||||||
\(192\) | 21.4444 | 1.54762 | ||||||||
\(193\) | 8.92165i | 0.642194i | 0.947046 | + | 0.321097i | \(0.104052\pi\) | ||||
−0.947046 | + | 0.321097i | \(0.895948\pi\) | |||||||
\(194\) | 17.4773 | 1.25479 | ||||||||
\(195\) | 23.1185 | − | 12.6319i | 1.65555 | − | 0.904588i | ||||
\(196\) | 1.33010 | 0.0950073 | ||||||||
\(197\) | − | 8.13765i | − | 0.579783i | −0.957059 | − | 0.289892i | \(-0.906381\pi\) | ||
0.957059 | − | 0.289892i | \(-0.0936193\pi\) | |||||||
\(198\) | −0.376820 | −0.0267794 | ||||||||
\(199\) | 12.4940 | 0.885678 | 0.442839 | − | 0.896601i | \(-0.353971\pi\) | ||||
0.442839 | + | 0.896601i | \(0.353971\pi\) | |||||||
\(200\) | − | 5.13590i | − | 0.363163i | ||||||
\(201\) | − | 4.19604i | − | 0.295966i | ||||||
\(202\) | 16.7242i | 1.17671i | ||||||||
\(203\) | − | 35.0999i | − | 2.46353i | ||||||
\(204\) | −1.04984 | −0.0735032 | ||||||||
\(205\) | −4.08126 | −0.285047 | ||||||||
\(206\) | − | 18.3242i | − | 1.27671i | ||||||
\(207\) | −37.4342 | −2.60186 | ||||||||
\(208\) | 7.16179 | + | 13.1073i | 0.496581 | + | 0.908830i | ||||
\(209\) | −0.0641691 | −0.00443867 | ||||||||
\(210\) | − | 52.5776i | − | 3.62820i | ||||||
\(211\) | −20.8611 | −1.43614 | −0.718068 | − | 0.695973i | \(-0.754973\pi\) | ||||
−0.718068 | + | 0.695973i | \(0.754973\pi\) | |||||||
\(212\) | −0.636121 | −0.0436890 | ||||||||
\(213\) | − | 4.02063i | − | 0.275489i | ||||||
\(214\) | − | 4.25511i | − | 0.290873i | ||||||
\(215\) | 7.92192i | 0.540270i | ||||||||
\(216\) | − | 13.8732i | − | 0.943954i | ||||||
\(217\) | −4.99660 | −0.339192 | ||||||||
\(218\) | −28.6711 | −1.94185 | ||||||||
\(219\) | − | 38.9539i | − | 2.63226i | ||||||
\(220\) | −0.0105816 | −0.000713414 | ||||||||
\(221\) | 8.78251 | + | 16.0735i | 0.590775 | + | 1.08122i | ||||
\(222\) | 27.1391 | 1.82146 | ||||||||
\(223\) | 18.6577i | 1.24941i | 0.780859 | + | 0.624707i | \(0.214782\pi\) | ||||
−0.780859 | + | 0.624707i | \(0.785218\pi\) | |||||||
\(224\) | 2.09152 | 0.139746 | ||||||||
\(225\) | −8.87285 | −0.591523 | ||||||||
\(226\) | 1.33381i | 0.0887240i | ||||||||
\(227\) | 27.9915i | 1.85786i | 0.370251 | + | 0.928932i | \(0.379272\pi\) | ||||
−0.370251 | + | 0.928932i | \(0.620728\pi\) | |||||||
\(228\) | 0.242860i | 0.0160838i | ||||||||
\(229\) | − | 9.20943i | − | 0.608576i | −0.952580 | − | 0.304288i | \(-0.901581\pi\) | ||
0.952580 | − | 0.304288i | \(-0.0984186\pi\) | |||||||
\(230\) | −29.4491 | −1.94181 | ||||||||
\(231\) | 0.761584 | 0.0501085 | ||||||||
\(232\) | − | 19.4844i | − | 1.27921i | ||||||
\(233\) | 19.5339 | 1.27971 | 0.639854 | − | 0.768497i | \(-0.278995\pi\) | ||||
0.639854 | + | 0.768497i | \(0.278995\pi\) | |||||||
\(234\) | 21.8350 | − | 11.9306i | 1.42740 | − | 0.779925i | ||||
\(235\) | 0.501261 | 0.0326987 | ||||||||
\(236\) | 0.215741i | 0.0140435i | ||||||||
\(237\) | −3.09338 | −0.200937 | ||||||||
\(238\) | 36.5554 | 2.36953 | ||||||||
\(239\) | 16.9297i | 1.09509i | 0.836776 | + | 0.547546i | \(0.184438\pi\) | ||||
−0.836776 | + | 0.547546i | \(0.815562\pi\) | |||||||
\(240\) | − | 30.2684i | − | 1.95382i | ||||||
\(241\) | 14.6063i | 0.940875i | 0.882433 | + | 0.470438i | \(0.155904\pi\) | ||||
−0.882433 | + | 0.470438i | \(0.844096\pi\) | |||||||
\(242\) | 15.8374i | 1.01806i | ||||||||
\(243\) | 16.1601 | 1.03667 | ||||||||
\(244\) | −0.441516 | −0.0282652 | ||||||||
\(245\) | 47.0273i | 3.00447i | ||||||||
\(246\) | −6.26793 | −0.399629 | ||||||||
\(247\) | 3.71832 | − | 2.03167i | 0.236591 | − | 0.129272i | ||||
\(248\) | −2.77368 | −0.176129 | ||||||||
\(249\) | − | 4.88278i | − | 0.309434i | ||||||
\(250\) | 11.8683 | 0.750616 | ||||||||
\(251\) | −28.9232 | −1.82561 | −0.912807 | − | 0.408391i | \(-0.866090\pi\) | ||||
−0.912807 | + | 0.408391i | \(0.866090\pi\) | |||||||
\(252\) | − | 1.77260i | − | 0.111663i | ||||||
\(253\) | − | 0.426568i | − | 0.0268181i | ||||||
\(254\) | 23.5025i | 1.47468i | ||||||||
\(255\) | − | 37.1182i | − | 2.32443i | ||||||
\(256\) | 1.77442 | 0.110901 | ||||||||
\(257\) | −19.4544 | −1.21353 | −0.606767 | − | 0.794880i | \(-0.707534\pi\) | ||||
−0.606767 | + | 0.794880i | \(0.707534\pi\) | |||||||
\(258\) | 12.1664i | 0.757445i | ||||||||
\(259\) | −33.7320 | −2.09601 | ||||||||
\(260\) | 0.613159 | − | 0.335027i | 0.0380265 | − | 0.0207775i | ||||
\(261\) | −33.6615 | −2.08359 | ||||||||
\(262\) | 21.8456i | 1.34962i | ||||||||
\(263\) | 20.2310 | 1.24750 | 0.623750 | − | 0.781624i | \(-0.285608\pi\) | ||||
0.623750 | + | 0.781624i | \(0.285608\pi\) | |||||||
\(264\) | 0.422765 | 0.0260194 | ||||||||
\(265\) | − | 22.4908i | − | 1.38160i | ||||||
\(266\) | − | 8.45642i | − | 0.518496i | ||||||
\(267\) | − | 6.58754i | − | 0.403151i | ||||||
\(268\) | − | 0.111289i | − | 0.00679805i | ||||||
\(269\) | −8.30420 | −0.506316 | −0.253158 | − | 0.967425i | \(-0.581469\pi\) | ||||
−0.253158 | + | 0.967425i | \(0.581469\pi\) | |||||||
\(270\) | −18.8550 | −1.14748 | ||||||||
\(271\) | − | 14.7486i | − | 0.895912i | −0.894056 | − | 0.447956i | \(-0.852152\pi\) | ||
0.894056 | − | 0.447956i | \(-0.147848\pi\) | |||||||
\(272\) | 21.0446 | 1.27601 | ||||||||
\(273\) | −44.1304 | + | 24.1127i | −2.67089 | + | 1.45936i | ||||
\(274\) | 16.5441 | 0.999464 | ||||||||
\(275\) | − | 0.101107i | − | 0.00609700i | ||||||
\(276\) | −1.61443 | −0.0971772 | ||||||||
\(277\) | −15.4228 | −0.926664 | −0.463332 | − | 0.886185i | \(-0.653346\pi\) | ||||
−0.463332 | + | 0.886185i | \(0.653346\pi\) | |||||||
\(278\) | − | 9.57400i | − | 0.574210i | ||||||
\(279\) | 4.79185i | 0.286880i | ||||||||
\(280\) | 36.2768i | 2.16795i | ||||||||
\(281\) | 17.2595i | 1.02962i | 0.857306 | + | 0.514808i | \(0.172137\pi\) | ||||
−0.857306 | + | 0.514808i | \(0.827863\pi\) | |||||||
\(282\) | 0.769829 | 0.0458427 | ||||||||
\(283\) | 12.2230 | 0.726583 | 0.363291 | − | 0.931676i | \(-0.381653\pi\) | ||||
0.363291 | + | 0.931676i | \(0.381653\pi\) | |||||||
\(284\) | − | 0.106636i | − | 0.00632771i | ||||||
\(285\) | −8.58661 | −0.508627 | ||||||||
\(286\) | 0.135950 | + | 0.248813i | 0.00803891 | + | 0.0147126i | ||||
\(287\) | 7.79060 | 0.459865 | ||||||||
\(288\) | − | 2.00581i | − | 0.118194i | ||||||
\(289\) | 8.80698 | 0.518057 | ||||||||
\(290\) | −26.4811 | −1.55502 | ||||||||
\(291\) | 33.8755i | 1.98582i | ||||||||
\(292\) | − | 1.03315i | − | 0.0604605i | ||||||
\(293\) | − | 11.5516i | − | 0.674850i | −0.941352 | − | 0.337425i | \(-0.890444\pi\) | ||
0.941352 | − | 0.337425i | \(-0.109556\pi\) | |||||||
\(294\) | 72.2239i | 4.21218i | ||||||||
\(295\) | −7.62776 | −0.444106 | ||||||||
\(296\) | −18.7251 | −1.08837 | ||||||||
\(297\) | − | 0.273114i | − | 0.0158477i | ||||||
\(298\) | 1.95560 | 0.113285 | ||||||||
\(299\) | 13.5057 | + | 24.7177i | 0.781053 | + | 1.42946i | ||||
\(300\) | −0.382660 | −0.0220929 | ||||||||
\(301\) | − | 15.1219i | − | 0.871614i | ||||||
\(302\) | −17.9228 | −1.03134 | ||||||||
\(303\) | −32.4158 | −1.86224 | ||||||||
\(304\) | − | 4.86828i | − | 0.279215i | ||||||
\(305\) | − | 15.6103i | − | 0.893845i | ||||||
\(306\) | − | 35.0574i | − | 2.00410i | ||||||
\(307\) | − | 22.1226i | − | 1.26260i | −0.775537 | − | 0.631302i | \(-0.782521\pi\) | ||
0.775537 | − | 0.631302i | \(-0.217479\pi\) | |||||||
\(308\) | 0.0201990 | 0.00115095 | ||||||||
\(309\) | 35.5171 | 2.02050 | ||||||||
\(310\) | 3.76969i | 0.214104i | ||||||||
\(311\) | −17.1273 | −0.971203 | −0.485601 | − | 0.874180i | \(-0.661399\pi\) | ||||
−0.485601 | + | 0.874180i | \(0.661399\pi\) | |||||||
\(312\) | −24.4974 | + | 13.3853i | −1.38689 | + | 0.757791i | ||||
\(313\) | −28.9822 | −1.63817 | −0.819086 | − | 0.573670i | \(-0.805519\pi\) | ||||
−0.819086 | + | 0.573670i | \(0.805519\pi\) | |||||||
\(314\) | 22.4511i | 1.26699i | ||||||||
\(315\) | 62.6723 | 3.53118 | ||||||||
\(316\) | −0.0820438 | −0.00461532 | ||||||||
\(317\) | − | 6.22426i | − | 0.349590i | −0.984605 | − | 0.174795i | \(-0.944074\pi\) | ||
0.984605 | − | 0.174795i | \(-0.0559262\pi\) | |||||||
\(318\) | − | 34.5410i | − | 1.93697i | ||||||
\(319\) | − | 0.383577i | − | 0.0214762i | ||||||
\(320\) | 20.1090i | 1.12413i | ||||||||
\(321\) | 8.24751 | 0.460331 | ||||||||
\(322\) | 56.2146 | 3.13272 | ||||||||
\(323\) | − | 5.96997i | − | 0.332178i | ||||||
\(324\) | 0.0306309 | 0.00170172 | ||||||||
\(325\) | 3.20118 | + | 5.85872i | 0.177569 | + | 0.324983i | ||||
\(326\) | 3.63552 | 0.201353 | ||||||||
\(327\) | − | 55.5720i | − | 3.07314i | ||||||
\(328\) | 4.32467 | 0.238790 | ||||||||
\(329\) | −0.956844 | −0.0527525 | ||||||||
\(330\) | − | 0.574577i | − | 0.0316294i | ||||||
\(331\) | − | 5.28437i | − | 0.290455i | −0.989398 | − | 0.145228i | \(-0.953609\pi\) | ||
0.989398 | − | 0.145228i | \(-0.0463915\pi\) | |||||||
\(332\) | − | 0.129503i | − | 0.00710740i | ||||||
\(333\) | 32.3497i | 1.77275i | ||||||||
\(334\) | −14.2918 | −0.782012 | ||||||||
\(335\) | 3.93475 | 0.214978 | ||||||||
\(336\) | 57.7786i | 3.15208i | ||||||||
\(337\) | −7.23845 | −0.394304 | −0.197152 | − | 0.980373i | \(-0.563169\pi\) | ||||
−0.197152 | + | 0.980373i | \(0.563169\pi\) | |||||||
\(338\) | −15.7554 | − | 10.1133i | −0.856983 | − | 0.550089i | ||||
\(339\) | −2.58528 | −0.140413 | ||||||||
\(340\) | − | 0.984462i | − | 0.0533899i | ||||||
\(341\) | −0.0546038 | −0.00295696 | ||||||||
\(342\) | −8.10988 | −0.438532 | ||||||||
\(343\) | − | 54.7930i | − | 2.95855i | ||||||
\(344\) | − | 8.39439i | − | 0.452595i | ||||||
\(345\) | − | 57.0800i | − | 3.07308i | ||||||
\(346\) | − | 29.3122i | − | 1.57583i | ||||||
\(347\) | 33.0880 | 1.77626 | 0.888128 | − | 0.459597i | \(-0.152006\pi\) | ||||
0.888128 | + | 0.459597i | \(0.152006\pi\) | |||||||
\(348\) | −1.45172 | −0.0778204 | ||||||||
\(349\) | − | 6.94086i | − | 0.371536i | −0.982594 | − | 0.185768i | \(-0.940523\pi\) | ||
0.982594 | − | 0.185768i | \(-0.0594772\pi\) | |||||||
\(350\) | 13.3243 | 0.712211 | ||||||||
\(351\) | 8.64711 | + | 15.8257i | 0.461549 | + | 0.844715i | ||||
\(352\) | 0.0228565 | 0.00121825 | ||||||||
\(353\) | − | 30.0813i | − | 1.60107i | −0.599288 | − | 0.800534i | \(-0.704550\pi\) | ||
0.599288 | − | 0.800534i | \(-0.295450\pi\) | |||||||
\(354\) | −11.7146 | −0.622624 | ||||||||
\(355\) | 3.77026 | 0.200105 | ||||||||
\(356\) | − | 0.174717i | − | 0.00925999i | ||||||
\(357\) | 70.8539i | 3.74999i | ||||||||
\(358\) | 6.99598i | 0.369749i | ||||||||
\(359\) | − | 3.73997i | − | 0.197388i | −0.995118 | − | 0.0986940i | \(-0.968534\pi\) | ||
0.995118 | − | 0.0986940i | \(-0.0314665\pi\) | |||||||
\(360\) | 34.7902 | 1.83361 | ||||||||
\(361\) | 17.6190 | 0.927314 | ||||||||
\(362\) | 9.83152i | 0.516733i | ||||||||
\(363\) | −30.6969 | −1.61117 | ||||||||
\(364\) | −1.17044 | + | 0.639525i | −0.0613478 | + | 0.0335202i | ||||
\(365\) | 36.5282 | 1.91197 | ||||||||
\(366\) | − | 23.9741i | − | 1.25315i | ||||||
\(367\) | 4.57778 | 0.238958 | 0.119479 | − | 0.992837i | \(-0.461878\pi\) | ||||
0.119479 | + | 0.992837i | \(0.461878\pi\) | |||||||
\(368\) | 32.3622 | 1.68700 | ||||||||
\(369\) | − | 7.47135i | − | 0.388943i | ||||||
\(370\) | 25.4491i | 1.32304i | ||||||||
\(371\) | 42.9321i | 2.22892i | ||||||||
\(372\) | 0.206658i | 0.0107147i | ||||||||
\(373\) | −11.9473 | −0.618607 | −0.309303 | − | 0.950963i | \(-0.600096\pi\) | ||||
−0.309303 | + | 0.950963i | \(0.600096\pi\) | |||||||
\(374\) | 0.399484 | 0.0206568 | ||||||||
\(375\) | 23.0038i | 1.18791i | ||||||||
\(376\) | −0.531157 | −0.0273923 | ||||||||
\(377\) | 12.1445 | + | 22.2266i | 0.625475 | + | 1.14473i | ||||
\(378\) | 35.9919 | 1.85122 | ||||||||
\(379\) | 0.620093i | 0.0318521i | 0.999873 | + | 0.0159260i | \(0.00506963\pi\) | ||||
−0.999873 | + | 0.0159260i | \(0.994930\pi\) | |||||||
\(380\) | −0.227737 | −0.0116827 | ||||||||
\(381\) | −45.5539 | −2.33380 | ||||||||
\(382\) | − | 19.8842i | − | 1.01737i | ||||||
\(383\) | 27.8945i | 1.42534i | 0.701498 | + | 0.712671i | \(0.252515\pi\) | ||||
−0.701498 | + | 0.712671i | \(0.747485\pi\) | |||||||
\(384\) | 33.2201i | 1.69525i | ||||||||
\(385\) | 0.714160i | 0.0363969i | ||||||||
\(386\) | −12.8485 | −0.653972 | ||||||||
\(387\) | −14.5023 | −0.737191 | ||||||||
\(388\) | 0.898459i | 0.0456123i | ||||||||
\(389\) | 12.8614 | 0.652097 | 0.326048 | − | 0.945353i | \(-0.394283\pi\) | ||||
0.326048 | + | 0.945353i | \(0.394283\pi\) | |||||||
\(390\) | 18.1918 | + | 33.2942i | 0.921178 | + | 1.68592i | ||||
\(391\) | 39.6858 | 2.00699 | ||||||||
\(392\) | − | 49.8321i | − | 2.51690i | ||||||
\(393\) | −42.3424 | −2.13589 | ||||||||
\(394\) | 11.7194 | 0.590417 | ||||||||
\(395\) | − | 2.90075i | − | 0.145953i | ||||||
\(396\) | − | 0.0193713i | − | 0.000973443i | ||||||
\(397\) | − | 24.6396i | − | 1.23663i | −0.785931 | − | 0.618314i | \(-0.787816\pi\) | ||
0.785931 | − | 0.618314i | \(-0.212184\pi\) | |||||||
\(398\) | 17.9933i | 0.901922i | ||||||||
\(399\) | 16.3907 | 0.820564 | ||||||||
\(400\) | 7.67064 | 0.383532 | ||||||||
\(401\) | 20.3020i | 1.01383i | 0.861995 | + | 0.506917i | \(0.169215\pi\) | ||||
−0.861995 | + | 0.506917i | \(0.830785\pi\) | |||||||
\(402\) | 6.04293 | 0.301394 | ||||||||
\(403\) | 3.16404 | − | 1.72882i | 0.157612 | − | 0.0861187i | ||||
\(404\) | −0.859744 | −0.0427739 | ||||||||
\(405\) | 1.08299i | 0.0538143i | ||||||||
\(406\) | 50.5491 | 2.50871 | ||||||||
\(407\) | −0.368629 | −0.0182723 | ||||||||
\(408\) | 39.3319i | 1.94722i | ||||||||
\(409\) | − | 7.67595i | − | 0.379551i | −0.981827 | − | 0.189776i | \(-0.939224\pi\) | ||
0.981827 | − | 0.189776i | \(-0.0607761\pi\) | |||||||
\(410\) | − | 5.87762i | − | 0.290275i | ||||||
\(411\) | 32.0667i | 1.58174i | ||||||||
\(412\) | 0.941997 | 0.0464089 | ||||||||
\(413\) | 14.5604 | 0.716472 | ||||||||
\(414\) | − | 53.9110i | − | 2.64958i | ||||||
\(415\) | 4.57873 | 0.224761 | ||||||||
\(416\) | −1.32443 | + | 0.723664i | −0.0649356 | + | 0.0354805i | ||||
\(417\) | 18.5569 | 0.908736 | ||||||||
\(418\) | − | 0.0924132i | − | 0.00452008i | ||||||
\(419\) | −24.4074 | −1.19238 | −0.596189 | − | 0.802844i | \(-0.703319\pi\) | ||||
−0.596189 | + | 0.802844i | \(0.703319\pi\) | |||||||
\(420\) | 2.70287 | 0.131887 | ||||||||
\(421\) | 7.83588i | 0.381898i | 0.981600 | + | 0.190949i | \(0.0611564\pi\) | ||||
−0.981600 | + | 0.190949i | \(0.938844\pi\) | |||||||
\(422\) | − | 30.0431i | − | 1.46248i | ||||||
\(423\) | 0.917633i | 0.0446169i | ||||||||
\(424\) | 23.8322i | 1.15739i | ||||||||
\(425\) | 9.40651 | 0.456283 | ||||||||
\(426\) | 5.79031 | 0.280541 | ||||||||
\(427\) | 29.7982i | 1.44203i | ||||||||
\(428\) | 0.218744 | 0.0105734 | ||||||||
\(429\) | −0.482265 | + | 0.263507i | −0.0232840 | + | 0.0127223i | ||||
\(430\) | −11.4088 | −0.550179 | ||||||||
\(431\) | 7.77841i | 0.374673i | 0.982296 | + | 0.187337i | \(0.0599855\pi\) | ||||
−0.982296 | + | 0.187337i | \(0.940015\pi\) | |||||||
\(432\) | 20.7202 | 0.996899 | ||||||||
\(433\) | 26.6655 | 1.28146 | 0.640732 | − | 0.767765i | \(-0.278631\pi\) | ||||
0.640732 | + | 0.767765i | \(0.278631\pi\) | |||||||
\(434\) | − | 7.19586i | − | 0.345413i | ||||||
\(435\) | − | 51.3273i | − | 2.46096i | ||||||
\(436\) | − | 1.47390i | − | 0.0705871i | ||||||
\(437\) | − | 9.18057i | − | 0.439166i | ||||||
\(438\) | 56.0995 | 2.68054 | ||||||||
\(439\) | 14.4283 | 0.688626 | 0.344313 | − | 0.938855i | \(-0.388112\pi\) | ||||
0.344313 | + | 0.938855i | \(0.388112\pi\) | |||||||
\(440\) | 0.396439i | 0.0188995i | ||||||||
\(441\) | −86.0906 | −4.09955 | ||||||||
\(442\) | −23.1483 | + | 12.6481i | −1.10105 | + | 0.601610i | ||||
\(443\) | 5.19341 | 0.246746 | 0.123373 | − | 0.992360i | \(-0.460629\pi\) | ||||
0.123373 | + | 0.992360i | \(0.460629\pi\) | |||||||
\(444\) | 1.39515i | 0.0662108i | ||||||||
\(445\) | 6.17733 | 0.292834 | ||||||||
\(446\) | −26.8699 | −1.27233 | ||||||||
\(447\) | 3.79047i | 0.179283i | ||||||||
\(448\) | − | 38.3856i | − | 1.81355i | ||||||
\(449\) | 14.9729i | 0.706615i | 0.935507 | + | 0.353308i | \(0.114943\pi\) | ||||
−0.935507 | + | 0.353308i | \(0.885057\pi\) | |||||||
\(450\) | − | 12.7782i | − | 0.602372i | ||||||
\(451\) | 0.0851371 | 0.00400895 | ||||||||
\(452\) | −0.0685677 | −0.00322516 | ||||||||
\(453\) | − | 34.7391i | − | 1.63218i | ||||||
\(454\) | −40.3120 | −1.89194 | ||||||||
\(455\) | −22.6112 | − | 41.3824i | −1.06003 | − | 1.94004i | ||||
\(456\) | 9.09872 | 0.426087 | ||||||||
\(457\) | − | 42.0543i | − | 1.96722i | −0.180316 | − | 0.983609i | \(-0.557712\pi\) | ||
0.180316 | − | 0.983609i | \(-0.442288\pi\) | |||||||
\(458\) | 13.2630 | 0.619738 | ||||||||
\(459\) | 25.4091 | 1.18600 | ||||||||
\(460\) | − | 1.51390i | − | 0.0705858i | ||||||
\(461\) | − | 9.31370i | − | 0.433782i | −0.976196 | − | 0.216891i | \(-0.930408\pi\) | ||
0.976196 | − | 0.216891i | \(-0.0695917\pi\) | |||||||
\(462\) | 1.09680i | 0.0510275i | ||||||||
\(463\) | 10.3203i | 0.479625i | 0.970819 | + | 0.239813i | \(0.0770860\pi\) | ||||
−0.970819 | + | 0.239813i | \(0.922914\pi\) | |||||||
\(464\) | 29.1006 | 1.35096 | ||||||||
\(465\) | −7.30664 | −0.338838 | ||||||||
\(466\) | 28.1318i | 1.30318i | ||||||||
\(467\) | −0.661824 | −0.0306255 | −0.0153128 | − | 0.999883i | \(-0.504874\pi\) | ||||
−0.0153128 | + | 0.999883i | \(0.504874\pi\) | |||||||
\(468\) | 0.613318 | + | 1.12248i | 0.0283506 | + | 0.0518866i | ||||
\(469\) | −7.51094 | −0.346823 | ||||||||
\(470\) | 0.721891i | 0.0332984i | ||||||||
\(471\) | −43.5161 | −2.00512 | ||||||||
\(472\) | 8.08269 | 0.372036 | ||||||||
\(473\) | − | 0.165255i | − | 0.00759844i | ||||||
\(474\) | − | 4.45493i | − | 0.204622i | ||||||
\(475\) | − | 2.17602i | − | 0.0998428i | ||||||
\(476\) | 1.87921i | 0.0861336i | ||||||||
\(477\) | 41.1728 | 1.88517 | ||||||||
\(478\) | −24.3813 | −1.11518 | ||||||||
\(479\) | − | 3.63440i | − | 0.166060i | −0.996547 | − | 0.0830300i | \(-0.973540\pi\) | ||
0.996547 | − | 0.0830300i | \(-0.0264597\pi\) | |||||||
\(480\) | 3.05847 | 0.139600 | ||||||||
\(481\) | 21.3604 | − | 11.6712i | 0.973952 | − | 0.532163i | ||||
\(482\) | −21.0353 | −0.958131 | ||||||||
\(483\) | 108.959i | 4.95778i | ||||||||
\(484\) | −0.814156 | −0.0370071 | ||||||||
\(485\) | −31.7661 | −1.44242 | ||||||||
\(486\) | 23.2730i | 1.05569i | ||||||||
\(487\) | 31.1232i | 1.41033i | 0.709045 | + | 0.705163i | \(0.249126\pi\) | ||||
−0.709045 | + | 0.705163i | \(0.750874\pi\) | |||||||
\(488\) | 16.5413i | 0.748792i | ||||||||
\(489\) | 7.04659i | 0.318658i | ||||||||
\(490\) | −67.7265 | −3.05957 | ||||||||
\(491\) | 17.9607 | 0.810555 | 0.405277 | − | 0.914194i | \(-0.367175\pi\) | ||||
0.405277 | + | 0.914194i | \(0.367175\pi\) | |||||||
\(492\) | − | 0.322217i | − | 0.0145267i | ||||||
\(493\) | 35.6861 | 1.60722 | ||||||||
\(494\) | 2.92591 | + | 5.35493i | 0.131643 | + | 0.240930i | ||||
\(495\) | 0.684894 | 0.0307837 | ||||||||
\(496\) | − | 4.14259i | − | 0.186008i | ||||||
\(497\) | −7.19695 | −0.322827 | ||||||||
\(498\) | 7.03194 | 0.315109 | ||||||||
\(499\) | − | 8.12403i | − | 0.363681i | −0.983328 | − | 0.181841i | \(-0.941794\pi\) | ||
0.983328 | − | 0.181841i | \(-0.0582055\pi\) | |||||||
\(500\) | 0.610116i | 0.0272852i | ||||||||
\(501\) | − | 27.7012i | − | 1.23760i | ||||||
\(502\) | − | 41.6537i | − | 1.85910i | ||||||
\(503\) | −38.6811 | −1.72471 | −0.862354 | − | 0.506307i | \(-0.831010\pi\) | ||||
−0.862354 | + | 0.506307i | \(0.831010\pi\) | |||||||
\(504\) | −66.4102 | −2.95814 | ||||||||
\(505\) | − | 30.3973i | − | 1.35266i | ||||||
\(506\) | 0.614323 | 0.0273100 | ||||||||
\(507\) | 19.6021 | − | 30.5382i | 0.870561 | − | 1.35625i | ||||
\(508\) | −1.20820 | −0.0536051 | ||||||||
\(509\) | 16.1272i | 0.714826i | 0.933946 | + | 0.357413i | \(0.116341\pi\) | ||||
−0.933946 | + | 0.357413i | \(0.883659\pi\) | |||||||
\(510\) | 53.4558 | 2.36706 | ||||||||
\(511\) | −69.7278 | −3.08458 | ||||||||
\(512\) | − | 21.2464i | − | 0.938967i | ||||||
\(513\) | − | 5.87794i | − | 0.259517i | ||||||
\(514\) | − | 28.0173i | − | 1.23579i | ||||||
\(515\) | 33.3054i | 1.46761i | ||||||||
\(516\) | −0.625439 | −0.0275334 | ||||||||
\(517\) | −0.0104566 | −0.000459879 | ||||||||
\(518\) | − | 48.5792i | − | 2.13445i | ||||||
\(519\) | 56.8147 | 2.49389 | ||||||||
\(520\) | −12.5517 | − | 22.9719i | −0.550431 | − | 1.00738i | ||||
\(521\) | 5.58342 | 0.244614 | 0.122307 | − | 0.992492i | \(-0.460971\pi\) | ||||
0.122307 | + | 0.992492i | \(0.460971\pi\) | |||||||
\(522\) | − | 48.4776i | − | 2.12181i | ||||||
\(523\) | −24.8140 | −1.08504 | −0.542520 | − | 0.840043i | \(-0.682530\pi\) | ||||
−0.542520 | + | 0.840043i | \(0.682530\pi\) | |||||||
\(524\) | −1.12302 | −0.0490594 | ||||||||
\(525\) | 25.8259i | 1.12713i | ||||||||
\(526\) | 29.1358i | 1.27038i | ||||||||
\(527\) | − | 5.08006i | − | 0.221291i | ||||||
\(528\) | 0.631414i | 0.0274788i | ||||||||
\(529\) | 38.0284 | 1.65341 | ||||||||
\(530\) | 32.3901 | 1.40694 | ||||||||
\(531\) | − | 13.9638i | − | 0.605976i | ||||||
\(532\) | 0.434721 | 0.0188476 | ||||||||
\(533\) | −4.93331 | + | 2.69554i | −0.213686 | + | 0.116757i | ||||
\(534\) | 9.48705 | 0.410545 | ||||||||
\(535\) | 7.73394i | 0.334367i | ||||||||
\(536\) | −4.16942 | −0.180092 | ||||||||
\(537\) | −13.5600 | −0.585159 | ||||||||
\(538\) | − | 11.9593i | − | 0.515602i | ||||||
\(539\) | − | 0.981014i | − | 0.0422553i | ||||||
\(540\) | − | 0.969285i | − | 0.0417114i | ||||||
\(541\) | 30.2928i | 1.30239i | 0.758911 | + | 0.651195i | \(0.225732\pi\) | ||||
−0.758911 | + | 0.651195i | \(0.774268\pi\) | |||||||
\(542\) | 21.2402 | 0.912344 | ||||||||
\(543\) | −19.0560 | −0.817773 | ||||||||
\(544\) | 2.12645i | 0.0911709i | ||||||||
\(545\) | 52.1115 | 2.23221 | ||||||||
\(546\) | −34.7259 | − | 63.5544i | −1.48613 | − | 2.71988i | ||||
\(547\) | −0.782832 | −0.0334715 | −0.0167357 | − | 0.999860i | \(-0.505327\pi\) | ||||
−0.0167357 | + | 0.999860i | \(0.505327\pi\) | |||||||
\(548\) | 0.850485i | 0.0363309i | ||||||||
\(549\) | 28.5770 | 1.21964 | ||||||||
\(550\) | 0.145610 | 0.00620882 | ||||||||
\(551\) | − | 8.25532i | − | 0.351688i | ||||||
\(552\) | 60.4843i | 2.57438i | ||||||||
\(553\) | 5.53717i | 0.235465i | ||||||||
\(554\) | − | 22.2111i | − | 0.943659i | ||||||
\(555\) | −49.3271 | −2.09382 | ||||||||
\(556\) | 0.492173 | 0.0208728 | ||||||||
\(557\) | 12.1105i | 0.513140i | 0.966526 | + | 0.256570i | \(0.0825924\pi\) | ||||
−0.966526 | + | 0.256570i | \(0.917408\pi\) | |||||||
\(558\) | −6.90098 | −0.292142 | ||||||||
\(559\) | 5.23218 | + | 9.57580i | 0.221298 | + | 0.405013i | ||||
\(560\) | −54.1807 | −2.28955 | ||||||||
\(561\) | 0.774304i | 0.0326911i | ||||||||
\(562\) | −24.8563 | −1.04850 | ||||||||
\(563\) | 11.9218 | 0.502446 | 0.251223 | − | 0.967929i | \(-0.419167\pi\) | ||||
0.251223 | + | 0.967929i | \(0.419167\pi\) | |||||||
\(564\) | 0.0395748i | 0.00166640i | ||||||||
\(565\) | − | 2.42429i | − | 0.101991i | ||||||
\(566\) | 17.6030i | 0.739908i | ||||||||
\(567\) | − | 2.06730i | − | 0.0868183i | ||||||
\(568\) | −3.99512 | −0.167632 | ||||||||
\(569\) | −14.4513 | −0.605831 | −0.302916 | − | 0.953017i | \(-0.597960\pi\) | ||||
−0.302916 | + | 0.953017i | \(0.597960\pi\) | |||||||
\(570\) | − | 12.3660i | − | 0.517955i | ||||||
\(571\) | −22.3002 | −0.933233 | −0.466616 | − | 0.884460i | \(-0.654527\pi\) | ||||
−0.466616 | + | 0.884460i | \(0.654527\pi\) | |||||||
\(572\) | −0.0127908 | + | 0.00698884i | −0.000534810 | + | 0.000292218i | ||||
\(573\) | 38.5408 | 1.61007 | ||||||||
\(574\) | 11.2196i | 0.468299i | ||||||||
\(575\) | 14.4653 | 0.603243 | ||||||||
\(576\) | −36.8126 | −1.53386 | ||||||||
\(577\) | 34.1283i | 1.42078i | 0.703808 | + | 0.710390i | \(0.251481\pi\) | ||||
−0.703808 | + | 0.710390i | \(0.748519\pi\) | |||||||
\(578\) | 12.6834i | 0.527559i | ||||||||
\(579\) | − | 24.9038i | − | 1.03497i | ||||||
\(580\) | − | 1.36132i | − | 0.0565258i | ||||||
\(581\) | −8.74022 | −0.362605 | ||||||||
\(582\) | −48.7858 | −2.02224 | ||||||||
\(583\) | 0.469169i | 0.0194310i | ||||||||
\(584\) | −38.7068 | −1.60170 | ||||||||
\(585\) | −39.6865 | + | 21.6846i | −1.64084 | + | 0.896546i | ||||
\(586\) | 16.6360 | 0.687227 | ||||||||
\(587\) | 17.1675i | 0.708579i | 0.935136 | + | 0.354290i | \(0.115277\pi\) | ||||
−0.935136 | + | 0.354290i | \(0.884723\pi\) | |||||||
\(588\) | −3.71283 | −0.153115 | ||||||||
\(589\) | −1.17518 | −0.0484224 | ||||||||
\(590\) | − | 10.9851i | − | 0.452251i | ||||||
\(591\) | 22.7153i | 0.934384i | ||||||||
\(592\) | − | 27.9666i | − | 1.14942i | ||||||
\(593\) | 23.3023i | 0.956909i | 0.878112 | + | 0.478455i | \(0.158803\pi\) | ||||
−0.878112 | + | 0.478455i | \(0.841197\pi\) | |||||||
\(594\) | 0.393325 | 0.0161383 | ||||||||
\(595\) | −66.4418 | −2.72385 | ||||||||
\(596\) | 0.100532i | 0.00411796i | ||||||||
\(597\) | −34.8757 | −1.42737 | ||||||||
\(598\) | −35.5973 | + | 19.4502i | −1.45568 | + | 0.795378i | ||||
\(599\) | −12.7509 | −0.520986 | −0.260493 | − | 0.965476i | \(-0.583885\pi\) | ||||
−0.260493 | + | 0.965476i | \(0.583885\pi\) | |||||||
\(600\) | 14.3363i | 0.585277i | ||||||||
\(601\) | 21.0313 | 0.857886 | 0.428943 | − | 0.903332i | \(-0.358886\pi\) | ||||
0.428943 | + | 0.903332i | \(0.358886\pi\) | |||||||
\(602\) | 21.7779 | 0.887600 | ||||||||
\(603\) | 7.20315i | 0.293335i | ||||||||
\(604\) | − | 0.921363i | − | 0.0374897i | ||||||
\(605\) | − | 28.7854i | − | 1.17029i | ||||||
\(606\) | − | 46.6837i | − | 1.89639i | ||||||
\(607\) | −28.5285 | −1.15793 | −0.578967 | − | 0.815351i | \(-0.696544\pi\) | ||||
−0.578967 | + | 0.815351i | \(0.696544\pi\) | |||||||
\(608\) | 0.491915 | 0.0199498 | ||||||||
\(609\) | 97.9773i | 3.97024i | ||||||||
\(610\) | 22.4812 | 0.910238 | ||||||||
\(611\) | 0.605911 | − | 0.331067i | 0.0245125 | − | 0.0133935i | ||||
\(612\) | 1.80220 | 0.0728498 | ||||||||
\(613\) | − | 20.0076i | − | 0.808099i | −0.914737 | − | 0.404050i | \(-0.867602\pi\) | ||
0.914737 | − | 0.404050i | \(-0.132398\pi\) | |||||||
\(614\) | 31.8599 | 1.28576 | ||||||||
\(615\) | 11.3924 | 0.459385 | ||||||||
\(616\) | − | 0.756753i | − | 0.0304904i | ||||||
\(617\) | − | 5.04682i | − | 0.203177i | −0.994826 | − | 0.101589i | \(-0.967607\pi\) | ||
0.994826 | − | 0.101589i | \(-0.0323926\pi\) | |||||||
\(618\) | 51.1500i | 2.05755i | ||||||||
\(619\) | 27.5782i | 1.10846i | 0.832363 | + | 0.554231i | \(0.186987\pi\) | ||||
−0.832363 | + | 0.554231i | \(0.813013\pi\) | |||||||
\(620\) | −0.193789 | −0.00778277 | ||||||||
\(621\) | 39.0740 | 1.56798 | ||||||||
\(622\) | − | 24.6660i | − | 0.989015i | ||||||
\(623\) | −11.7917 | −0.472426 | ||||||||
\(624\) | −19.9913 | − | 36.5876i | −0.800294 | − | 1.46468i | ||||
\(625\) | −30.8296 | −1.23319 | ||||||||
\(626\) | − | 41.7388i | − | 1.66822i | ||||||
\(627\) | 0.179121 | 0.00715340 | ||||||||
\(628\) | −1.15415 | −0.0460556 | ||||||||
\(629\) | − | 34.2954i | − | 1.36745i | ||||||
\(630\) | 90.2576i | 3.59595i | ||||||||
\(631\) | − | 46.3626i | − | 1.84566i | −0.385202 | − | 0.922832i | \(-0.625868\pi\) | ||
0.385202 | − | 0.922832i | \(-0.374132\pi\) | |||||||
\(632\) | 3.07376i | 0.122268i | ||||||||
\(633\) | 58.2314 | 2.31449 | ||||||||
\(634\) | 8.96388 | 0.356001 | ||||||||
\(635\) | − | 42.7172i | − | 1.69518i | ||||||
\(636\) | 1.77566 | 0.0704095 | ||||||||
\(637\) | 31.0601 | + | 56.8454i | 1.23065 | + | 2.25230i | ||||
\(638\) | 0.552409 | 0.0218701 | ||||||||
\(639\) | 6.90202i | 0.273040i | ||||||||
\(640\) | −31.1514 | −1.23137 | ||||||||
\(641\) | 16.3261 | 0.644843 | 0.322422 | − | 0.946596i | \(-0.395503\pi\) | ||||
0.322422 | + | 0.946596i | \(0.395503\pi\) | |||||||
\(642\) | 11.8777i | 0.468774i | ||||||||
\(643\) | 6.80196i | 0.268243i | 0.990965 | + | 0.134122i | \(0.0428213\pi\) | ||||
−0.990965 | + | 0.134122i | \(0.957179\pi\) | |||||||
\(644\) | 2.88984i | 0.113876i | ||||||||
\(645\) | − | 22.1131i | − | 0.870704i | ||||||
\(646\) | 8.59766 | 0.338270 | ||||||||
\(647\) | −12.7863 | −0.502681 | −0.251340 | − | 0.967899i | \(-0.580871\pi\) | ||||
−0.251340 | + | 0.967899i | \(0.580871\pi\) | |||||||
\(648\) | − | 1.14758i | − | 0.0450813i | ||||||
\(649\) | 0.159119 | 0.00624597 | ||||||||
\(650\) | −8.43744 | + | 4.61018i | −0.330944 | + | 0.180826i | ||||
\(651\) | 13.9475 | 0.546644 | ||||||||
\(652\) | 0.186892i | 0.00731926i | ||||||||
\(653\) | 31.3311 | 1.22608 | 0.613041 | − | 0.790051i | \(-0.289946\pi\) | ||||
0.613041 | + | 0.790051i | \(0.289946\pi\) | |||||||
\(654\) | 80.0321 | 3.12950 | ||||||||
\(655\) | − | 39.7057i | − | 1.55143i | ||||||
\(656\) | 6.45904i | 0.252183i | ||||||||
\(657\) | 66.8704i | 2.60886i | ||||||||
\(658\) | − | 1.37800i | − | 0.0537200i | ||||||
\(659\) | −18.7431 | −0.730127 | −0.365064 | − | 0.930983i | \(-0.618953\pi\) | ||||
−0.365064 | + | 0.930983i | \(0.618953\pi\) | |||||||
\(660\) | 0.0295374 | 0.00114974 | ||||||||
\(661\) | − | 13.7249i | − | 0.533836i | −0.963719 | − | 0.266918i | \(-0.913995\pi\) | ||
0.963719 | − | 0.266918i | \(-0.0860053\pi\) | |||||||
\(662\) | 7.61029 | 0.295782 | ||||||||
\(663\) | −24.5154 | − | 44.8675i | −0.952099 | − | 1.74251i | ||||
\(664\) | −4.85181 | −0.188287 | ||||||||
\(665\) | 15.3701i | 0.596026i | ||||||||
\(666\) | −46.5885 | −1.80527 | ||||||||
\(667\) | 54.8778 | 2.12488 | ||||||||
\(668\) | − | 0.734702i | − | 0.0284265i | ||||||
\(669\) | − | 52.0810i | − | 2.01357i | ||||||
\(670\) | 5.66663i | 0.218921i | ||||||||
\(671\) | 0.325639i | 0.0125712i | ||||||||
\(672\) | −5.83824 | −0.225215 | ||||||||
\(673\) | 15.0786 | 0.581237 | 0.290619 | − | 0.956839i | \(-0.406139\pi\) | ||||
0.290619 | + | 0.956839i | \(0.406139\pi\) | |||||||
\(674\) | − | 10.4245i | − | 0.401535i | ||||||
\(675\) | 9.26150 | 0.356475 | ||||||||
\(676\) | 0.519895 | − | 0.809944i | 0.0199960 | − | 0.0311517i | ||||
\(677\) | −26.8652 | −1.03251 | −0.516257 | − | 0.856434i | \(-0.672675\pi\) | ||||
−0.516257 | + | 0.856434i | \(0.672675\pi\) | |||||||
\(678\) | − | 3.72319i | − | 0.142988i | ||||||
\(679\) | 60.6374 | 2.32705 | ||||||||
\(680\) | −36.8827 | −1.41439 | ||||||||
\(681\) | − | 78.1352i | − | 2.99415i | ||||||
\(682\) | − | 0.0786376i | − | 0.00301119i | ||||||
\(683\) | 10.6702i | 0.408285i | 0.978941 | + | 0.204143i | \(0.0654406\pi\) | ||||
−0.978941 | + | 0.204143i | \(0.934559\pi\) | |||||||
\(684\) | − | 0.416907i | − | 0.0159408i | ||||||
\(685\) | −30.0699 | −1.14891 | ||||||||
\(686\) | 78.9102 | 3.01281 | ||||||||
\(687\) | 25.7071i | 0.980787i | ||||||||
\(688\) | 12.5373 | 0.477980 | ||||||||
\(689\) | −14.8545 | − | 27.1863i | −0.565910 | − | 1.03571i | ||||
\(690\) | 82.2038 | 3.12945 | ||||||||
\(691\) | − | 0.654117i | − | 0.0248838i | −0.999923 | − | 0.0124419i | \(-0.996040\pi\) | ||
0.999923 | − | 0.0124419i | \(-0.00396048\pi\) | |||||||
\(692\) | 1.50686 | 0.0572822 | ||||||||
\(693\) | −1.30738 | −0.0496631 | ||||||||
\(694\) | 47.6517i | 1.80883i | ||||||||
\(695\) | 17.4014i | 0.660071i | ||||||||
\(696\) | 54.3885i | 2.06159i | ||||||||
\(697\) | 7.92072i | 0.300019i | ||||||||
\(698\) | 9.99588 | 0.378350 | ||||||||
\(699\) | −54.5267 | −2.06239 | ||||||||
\(700\) | 0.684964i | 0.0258892i | ||||||||
\(701\) | 20.2045 | 0.763112 | 0.381556 | − | 0.924346i | \(-0.375388\pi\) | ||||
0.381556 | + | 0.924346i | \(0.375388\pi\) | |||||||
\(702\) | −22.7914 | + | 12.4531i | −0.860208 | + | 0.470014i | ||||
\(703\) | −7.93361 | −0.299222 | ||||||||
\(704\) | − | 0.419485i | − | 0.0158099i | ||||||
\(705\) | −1.39921 | −0.0526974 | ||||||||
\(706\) | 43.3216 | 1.63043 | ||||||||
\(707\) | 58.0246i | 2.18224i | ||||||||
\(708\) | − | 0.602216i | − | 0.0226327i | ||||||
\(709\) | − | 48.7025i | − | 1.82906i | −0.404518 | − | 0.914530i | \(-0.632561\pi\) | ||
0.404518 | − | 0.914530i | \(-0.367439\pi\) | |||||||
\(710\) | 5.42974i | 0.203775i | ||||||||
\(711\) | 5.31026 | 0.199150 | ||||||||
\(712\) | −6.54575 | −0.245313 | ||||||||
\(713\) | − | 7.81207i | − | 0.292564i | ||||||
\(714\) | −102.040 | −3.81876 | ||||||||
\(715\) | −0.247099 | − | 0.452234i | −0.00924096 | − | 0.0169126i | ||||
\(716\) | −0.359644 | −0.0134405 | ||||||||
\(717\) | − | 47.2574i | − | 1.76486i | ||||||
\(718\) | 5.38612 | 0.201008 | ||||||||
\(719\) | 16.7247 | 0.623725 | 0.311862 | − | 0.950127i | \(-0.399047\pi\) | ||||
0.311862 | + | 0.950127i | \(0.399047\pi\) | |||||||
\(720\) | 51.9604i | 1.93645i | ||||||||
\(721\) | − | 63.5758i | − | 2.36769i | ||||||
\(722\) | 25.3740i | 0.944321i | ||||||||
\(723\) | − | 40.7719i | − | 1.51632i | ||||||
\(724\) | −0.505411 | −0.0187835 | ||||||||
\(725\) | 13.0074 | 0.483083 | ||||||||
\(726\) | − | 44.2082i | − | 1.64072i | ||||||
\(727\) | −20.1667 | −0.747940 | −0.373970 | − | 0.927441i | \(-0.622004\pi\) | ||||
−0.373970 | + | 0.927441i | \(0.622004\pi\) | |||||||
\(728\) | 23.9597 | + | 43.8505i | 0.888006 | + | 1.62521i | ||||
\(729\) | −43.8680 | −1.62474 | ||||||||
\(730\) | 52.6062i | 1.94704i | ||||||||
\(731\) | 15.3745 | 0.568647 | ||||||||
\(732\) | 1.23244 | 0.0455524 | ||||||||
\(733\) | 6.69141i | 0.247153i | 0.992335 | + | 0.123576i | \(0.0394364\pi\) | ||||
−0.992335 | + | 0.123576i | \(0.960564\pi\) | |||||||
\(734\) | 6.59270i | 0.243341i | ||||||||
\(735\) | − | 131.272i | − | 4.84203i | ||||||
\(736\) | 3.27004i | 0.120535i | ||||||||
\(737\) | −0.0820809 | −0.00302349 | ||||||||
\(738\) | 10.7599 | 0.396076 | ||||||||
\(739\) | 14.7948i | 0.544235i | 0.962264 | + | 0.272118i | \(0.0877240\pi\) | ||||
−0.962264 | + | 0.272118i | \(0.912276\pi\) | |||||||
\(740\) | −1.30827 | −0.0480930 | ||||||||
\(741\) | −10.3793 | + | 5.67118i | −0.381292 | + | 0.208336i | ||||
\(742\) | −61.8287 | −2.26980 | ||||||||
\(743\) | 12.2435i | 0.449170i | 0.974455 | + | 0.224585i | \(0.0721026\pi\) | ||||
−0.974455 | + | 0.224585i | \(0.927897\pi\) | |||||||
\(744\) | 7.74242 | 0.283851 | ||||||||
\(745\) | −3.55444 | −0.130224 | ||||||||
\(746\) | − | 17.2059i | − | 0.629952i | ||||||
\(747\) | 8.38205i | 0.306683i | ||||||||
\(748\) | 0.0205364i | 0.000750884i | ||||||||
\(749\) | − | 14.7631i | − | 0.539432i | ||||||
\(750\) | −33.1290 | −1.20970 | ||||||||
\(751\) | 22.4866 | 0.820548 | 0.410274 | − | 0.911962i | \(-0.365433\pi\) | ||||
0.410274 | + | 0.911962i | \(0.365433\pi\) | |||||||
\(752\) | − | 0.793301i | − | 0.0289287i | ||||||
\(753\) | 80.7358 | 2.94218 | ||||||||
\(754\) | −32.0096 | + | 17.4899i | −1.16572 | + | 0.636946i | ||||
\(755\) | 32.5759 | 1.18556 | ||||||||
\(756\) | 1.85024i | 0.0672927i | ||||||||
\(757\) | 3.82393 | 0.138983 | 0.0694915 | − | 0.997583i | \(-0.477862\pi\) | ||||
0.0694915 | + | 0.997583i | \(0.477862\pi\) | |||||||
\(758\) | −0.893028 | −0.0324362 | ||||||||
\(759\) | 1.19072i | 0.0432203i | ||||||||
\(760\) | 8.53214i | 0.309493i | ||||||||
\(761\) | 33.7254i | 1.22254i | 0.791420 | + | 0.611272i | \(0.209342\pi\) | ||||
−0.791420 | + | 0.611272i | \(0.790658\pi\) | |||||||
\(762\) | − | 65.6045i | − | 2.37660i | ||||||
\(763\) | −99.4743 | −3.60121 | ||||||||
\(764\) | 1.02219 | 0.0369817 | ||||||||
\(765\) | 63.7190i | 2.30377i | ||||||||
\(766\) | −40.1723 | −1.45148 | ||||||||
\(767\) | −9.22024 | + | 5.03790i | −0.332923 | + | 0.181908i | ||||
\(768\) | −4.95308 | −0.178729 | ||||||||
\(769\) | − | 12.5287i | − | 0.451795i | −0.974151 | − | 0.225897i | \(-0.927469\pi\) | ||
0.974151 | − | 0.225897i | \(-0.0725314\pi\) | |||||||
\(770\) | −1.02850 | −0.0370645 | ||||||||
\(771\) | 54.3048 | 1.95574 | ||||||||
\(772\) | − | 0.660507i | − | 0.0237722i | ||||||
\(773\) | − | 23.6248i | − | 0.849723i | −0.905258 | − | 0.424862i | \(-0.860323\pi\) | ||
0.905258 | − | 0.424862i | \(-0.139677\pi\) | |||||||
\(774\) | − | 20.8854i | − | 0.750711i | ||||||
\(775\) | − | 1.85165i | − | 0.0665134i | ||||||
\(776\) | 33.6606 | 1.20835 | ||||||||
\(777\) | 94.1592 | 3.37794 | ||||||||
\(778\) | 18.5223i | 0.664056i | ||||||||
\(779\) | 1.83231 | 0.0656494 | ||||||||
\(780\) | −1.71156 | + | 0.935191i | −0.0612838 | + | 0.0334852i | ||||
\(781\) | −0.0786495 | −0.00281430 | ||||||||
\(782\) | 57.1535i | 2.04380i | ||||||||
\(783\) | 35.1359 | 1.25566 | ||||||||
\(784\) | 74.4260 | 2.65807 | ||||||||
\(785\) | − | 40.8063i | − | 1.45644i | ||||||
\(786\) | − | 60.9794i | − | 2.17506i | ||||||
\(787\) | 1.20685i | 0.0430194i | 0.999769 | + | 0.0215097i | \(0.00684729\pi\) | ||||
−0.999769 | + | 0.0215097i | \(0.993153\pi\) | |||||||
\(788\) | 0.602464i | 0.0214619i | ||||||||
\(789\) | −56.4727 | −2.01048 | ||||||||
\(790\) | 4.17752 | 0.148630 | ||||||||
\(791\) | 4.62767i | 0.164541i | ||||||||
\(792\) | −0.725742 | −0.0257881 | ||||||||
\(793\) | −10.3101 | − | 18.8694i | −0.366124 | − | 0.670070i | ||||
\(794\) | 35.4848 | 1.25931 | ||||||||
\(795\) | 62.7806i | 2.22660i | ||||||||
\(796\) | −0.924985 | −0.0327852 | ||||||||
\(797\) | −28.1207 | −0.996085 | −0.498042 | − | 0.867153i | \(-0.665948\pi\) | ||||
−0.498042 | + | 0.867153i | \(0.665948\pi\) | |||||||
\(798\) | 23.6051i | 0.835613i | ||||||||
\(799\) | − | 0.972825i | − | 0.0344161i | ||||||
\(800\) | 0.775081i | 0.0274032i | ||||||||
\(801\) | 11.3085i | 0.399567i | ||||||||
\(802\) | −29.2380 | −1.03243 | ||||||||
\(803\) | −0.761997 | −0.0268903 | ||||||||
\(804\) | 0.310650i | 0.0109558i | ||||||||
\(805\) | −102.174 | −3.60115 | ||||||||
\(806\) | 2.48976 | + | 4.55670i | 0.0876981 | + | 0.160503i | ||||
\(807\) | 23.1802 | 0.815983 | ||||||||
\(808\) | 32.2102i | 1.13315i | ||||||||
\(809\) | −32.4182 | −1.13976 | −0.569881 | − | 0.821727i | \(-0.693011\pi\) | ||||
−0.569881 | + | 0.821727i | \(0.693011\pi\) | |||||||
\(810\) | −1.55967 | −0.0548013 | ||||||||
\(811\) | − | 15.1013i | − | 0.530279i | −0.964210 | − | 0.265139i | \(-0.914582\pi\) | ||
0.964210 | − | 0.265139i | \(-0.0854180\pi\) | |||||||
\(812\) | 2.59859i | 0.0911926i | ||||||||
\(813\) | 41.1690i | 1.44386i | ||||||||
\(814\) | − | 0.530882i | − | 0.0186074i | ||||||
\(815\) | −6.60779 | −0.231461 | ||||||||
\(816\) | −58.7436 | −2.05644 | ||||||||
\(817\) | − | 3.55661i | − | 0.124430i | ||||||
\(818\) | 11.0545 | 0.386513 | ||||||||
\(819\) | 75.7566 | − | 41.3931i | 2.64715 | − | 1.44639i | ||||
\(820\) | 0.302153 | 0.0105516 | ||||||||
\(821\) | − | 7.53751i | − | 0.263061i | −0.991312 | − | 0.131531i | \(-0.958011\pi\) | ||
0.991312 | − | 0.131531i | \(-0.0419891\pi\) | |||||||
\(822\) | −46.1809 | −1.61074 | ||||||||
\(823\) | −20.7098 | −0.721897 | −0.360949 | − | 0.932586i | \(-0.617547\pi\) | ||||
−0.360949 | + | 0.932586i | \(0.617547\pi\) | |||||||
\(824\) | − | 35.2918i | − | 1.22945i | ||||||
\(825\) | 0.282230i | 0.00982598i | ||||||||
\(826\) | 20.9692i | 0.729613i | ||||||||
\(827\) | − | 22.6064i | − | 0.786101i | −0.919517 | − | 0.393051i | \(-0.871420\pi\) | ||
0.919517 | − | 0.393051i | \(-0.128580\pi\) | |||||||
\(828\) | 2.77141 | 0.0963133 | ||||||||
\(829\) | 50.3014 | 1.74704 | 0.873520 | − | 0.486789i | \(-0.161832\pi\) | ||||
0.873520 | + | 0.486789i | \(0.161832\pi\) | |||||||
\(830\) | 6.59406i | 0.228883i | ||||||||
\(831\) | 43.0509 | 1.49342 | ||||||||
\(832\) | 13.2814 | + | 24.3073i | 0.460450 | + | 0.842703i | ||||
\(833\) | 91.2686 | 3.16227 | ||||||||
\(834\) | 26.7247i | 0.925402i | ||||||||
\(835\) | 25.9763 | 0.898945 | ||||||||
\(836\) | 0.00475071 | 0.000164307 | ||||||||
\(837\) | − | 5.00174i | − | 0.172885i | ||||||
\(838\) | − | 35.1503i | − | 1.21425i | ||||||
\(839\) | 27.1797i | 0.938346i | 0.883106 | + | 0.469173i | \(0.155448\pi\) | ||||
−0.883106 | + | 0.469173i | \(0.844552\pi\) | |||||||
\(840\) | − | 101.263i | − | 3.49389i | ||||||
\(841\) | 20.3470 | 0.701620 | ||||||||
\(842\) | −11.2849 | −0.388902 | ||||||||
\(843\) | − | 48.1779i | − | 1.65934i | ||||||
\(844\) | 1.54443 | 0.0531616 | ||||||||
\(845\) | 28.6365 | + | 18.3815i | 0.985126 | + | 0.632342i | ||||
\(846\) | −1.32153 | −0.0454351 | ||||||||
\(847\) | 54.9478i | 1.88803i | ||||||||
\(848\) | −35.5942 | −1.22231 | ||||||||
\(849\) | −34.1192 | −1.17097 | ||||||||
\(850\) | 13.5468i | 0.464651i | ||||||||
\(851\) | − | 52.7392i | − | 1.80788i | ||||||
\(852\) | 0.297664i | 0.0101978i | ||||||||
\(853\) | − | 7.69689i | − | 0.263536i | −0.991281 | − | 0.131768i | \(-0.957935\pi\) | ||
0.991281 | − | 0.131768i | \(-0.0420655\pi\) | |||||||
\(854\) | −42.9138 | −1.46848 | ||||||||
\(855\) | 14.7402 | 0.504105 | ||||||||
\(856\) | − | 8.19520i | − | 0.280106i | ||||||
\(857\) | −53.2084 | −1.81756 | −0.908782 | − | 0.417272i | \(-0.862986\pi\) | ||||
−0.908782 | + | 0.417272i | \(0.862986\pi\) | |||||||
\(858\) | −0.379490 | − | 0.694534i | −0.0129556 | − | 0.0237110i | ||||
\(859\) | −28.0111 | −0.955728 | −0.477864 | − | 0.878434i | \(-0.658589\pi\) | ||||
−0.477864 | + | 0.878434i | \(0.658589\pi\) | |||||||
\(860\) | − | 0.586493i | − | 0.0199992i | ||||||
\(861\) | −21.7466 | −0.741122 | ||||||||
\(862\) | −11.2021 | −0.381545 | ||||||||
\(863\) | − | 19.3779i | − | 0.659630i | −0.944046 | − | 0.329815i | \(-0.893014\pi\) | ||
0.944046 | − | 0.329815i | \(-0.106986\pi\) | |||||||
\(864\) | 2.09367i | 0.0712281i | ||||||||
\(865\) | 53.2768i | 1.81146i | ||||||||
\(866\) | 38.4024i | 1.30497i | ||||||||
\(867\) | −24.5837 | −0.834906 | ||||||||
\(868\) | 0.369920 | 0.0125559 | ||||||||
\(869\) | 0.0605112i | 0.00205270i | ||||||||
\(870\) | 73.9190 | 2.50609 | ||||||||
\(871\) | 4.75622 | − | 2.59878i | 0.161158 | − | 0.0880563i | ||||
\(872\) | −55.2195 | −1.86997 | ||||||||
\(873\) | − | 58.1525i | − | 1.96817i | ||||||
\(874\) | 13.2214 | 0.447221 | ||||||||
\(875\) | 41.1770 | 1.39204 | ||||||||
\(876\) | 2.88392i | 0.0974387i | ||||||||
\(877\) | − | 6.54713i | − | 0.221081i | −0.993872 | − | 0.110540i | \(-0.964742\pi\) | ||
0.993872 | − | 0.110540i | \(-0.0352582\pi\) | |||||||
\(878\) | 20.7790i | 0.701256i | ||||||||
\(879\) | 32.2449i | 1.08759i | ||||||||
\(880\) | −0.592096 | −0.0199595 | ||||||||
\(881\) | −50.1477 | −1.68952 | −0.844760 | − | 0.535145i | \(-0.820257\pi\) | ||||
−0.844760 | + | 0.535145i | \(0.820257\pi\) | |||||||
\(882\) | − | 123.983i | − | 4.17474i | ||||||
\(883\) | −6.21470 | −0.209141 | −0.104571 | − | 0.994517i | \(-0.533347\pi\) | ||||
−0.104571 | + | 0.994517i | \(0.533347\pi\) | |||||||
\(884\) | −0.650206 | − | 1.18999i | −0.0218688 | − | 0.0400237i | ||||
\(885\) | 21.2920 | 0.715724 | ||||||||
\(886\) | 7.47929i | 0.251272i | ||||||||
\(887\) | −0.519213 | −0.0174335 | −0.00871673 | − | 0.999962i | \(-0.502775\pi\) | ||||
−0.00871673 | + | 0.999962i | \(0.502775\pi\) | |||||||
\(888\) | 52.2690 | 1.75403 | ||||||||
\(889\) | 81.5418i | 2.73482i | ||||||||
\(890\) | 8.89629i | 0.298204i | ||||||||
\(891\) | − | 0.0225918i | − | 0.000756853i | ||||||
\(892\) | − | 1.38131i | − | 0.0462497i | ||||||
\(893\) | −0.225045 | −0.00753085 | ||||||||
\(894\) | −5.45885 | −0.182571 | ||||||||
\(895\) | − | 12.7156i | − | 0.425037i | ||||||
\(896\) | 59.4641 | 1.98656 | ||||||||
\(897\) | −37.6996 | − | 68.9968i | −1.25875 | − | 2.30374i | ||||
\(898\) | −21.5632 | −0.719575 | ||||||||
\(899\) | − | 7.02474i | − | 0.234288i | ||||||
\(900\) | 0.656894 | 0.0218965 | ||||||||
\(901\) | −43.6492 | −1.45416 | ||||||||
\(902\) | 0.122610i | 0.00408247i | ||||||||
\(903\) | 42.2112i | 1.40470i | ||||||||
\(904\) | 2.56888i | 0.0854397i | ||||||||
\(905\) | − | 17.8694i | − | 0.593999i | ||||||
\(906\) | 50.0295 | 1.66212 | ||||||||
\(907\) | −32.5497 | −1.08079 | −0.540397 | − | 0.841410i | \(-0.681726\pi\) | ||||
−0.540397 | + | 0.841410i | \(0.681726\pi\) | |||||||
\(908\) | − | 2.07233i | − | 0.0687727i | ||||||
\(909\) | 55.6468 | 1.84569 | ||||||||
\(910\) | 59.5968 | − | 32.5635i | 1.97562 | − | 1.07947i | ||||
\(911\) | 12.1736 | 0.403331 | 0.201665 | − | 0.979454i | \(-0.435365\pi\) | ||||
0.201665 | + | 0.979454i | \(0.435365\pi\) | |||||||
\(912\) | 13.5892i | 0.449985i | ||||||||
\(913\) | −0.0955146 | −0.00316107 | ||||||||
\(914\) | 60.5645 | 2.00330 | ||||||||
\(915\) | 43.5745i | 1.44053i | ||||||||
\(916\) | 0.681813i | 0.0225277i | ||||||||
\(917\) | 75.7932i | 2.50291i | ||||||||
\(918\) | 36.5930i | 1.20775i | ||||||||
\(919\) | 33.3627 | 1.10053 | 0.550266 | − | 0.834989i | \(-0.314526\pi\) | ||||
0.550266 | + | 0.834989i | \(0.314526\pi\) | |||||||
\(920\) | −56.7179 | −1.86993 | ||||||||
\(921\) | 61.7528i | 2.03482i | ||||||||
\(922\) | 13.4131 | 0.441738 | ||||||||
\(923\) | 4.55739 | − | 2.49014i | 0.150008 | − | 0.0819639i | ||||
\(924\) | −0.0563833 | −0.00185487 | ||||||||
\(925\) | − | 12.5005i | − | 0.411014i | ||||||
\(926\) | −14.8628 | −0.488422 | ||||||||
\(927\) | −60.9706 | −2.00254 | ||||||||
\(928\) | 2.94047i | 0.0965258i | ||||||||
\(929\) | 4.29919i | 0.141052i | 0.997510 | + | 0.0705259i | \(0.0224678\pi\) | ||||
−0.997510 | + | 0.0705259i | \(0.977532\pi\) | |||||||
\(930\) | − | 10.5227i | − | 0.345052i | ||||||
\(931\) | − | 21.1133i | − | 0.691961i | ||||||
\(932\) | −1.44618 | −0.0473711 | ||||||||
\(933\) | 47.8091 | 1.56520 | ||||||||
\(934\) | − | 0.953126i | − | 0.0311872i | ||||||
\(935\) | −0.726087 | −0.0237456 | ||||||||
\(936\) | 42.0535 | − | 22.9779i | 1.37456 | − | 0.751055i | ||||
\(937\) | 48.4050 | 1.58132 | 0.790662 | − | 0.612253i | \(-0.209737\pi\) | ||||
0.790662 | + | 0.612253i | \(0.209737\pi\) | |||||||
\(938\) | − | 10.8169i | − | 0.353184i | ||||||
\(939\) | 80.9006 | 2.64009 | ||||||||
\(940\) | −0.0371105 | −0.00121041 | ||||||||
\(941\) | 31.2320i | 1.01813i | 0.860727 | + | 0.509067i | \(0.170010\pi\) | ||||
−0.860727 | + | 0.509067i | \(0.829990\pi\) | |||||||
\(942\) | − | 62.6698i | − | 2.04189i | ||||||
\(943\) | 12.1804i | 0.396649i | ||||||||
\(944\) | 12.0718i | 0.392903i | ||||||||
\(945\) | −65.4175 | −2.12803 | ||||||||
\(946\) | 0.237992 | 0.00773780 | ||||||||
\(947\) | 27.4625i | 0.892410i | 0.894931 | + | 0.446205i | \(0.147225\pi\) | ||||
−0.894931 | + | 0.446205i | \(0.852775\pi\) | |||||||
\(948\) | 0.229016 | 0.00743809 | ||||||||
\(949\) | 44.1543 | − | 24.1257i | 1.43331 | − | 0.783155i | ||||
\(950\) | 3.13380 | 0.101674 | ||||||||
\(951\) | 17.3743i | 0.563401i | ||||||||
\(952\) | 70.4044 | 2.28182 | ||||||||
\(953\) | −39.5670 | −1.28170 | −0.640850 | − | 0.767666i | \(-0.721418\pi\) | ||||
−0.640850 | + | 0.767666i | \(0.721418\pi\) | |||||||
\(954\) | 59.2950i | 1.91975i | ||||||||
\(955\) | 36.1409i | 1.16949i | ||||||||
\(956\) | − | 1.25338i | − | 0.0405371i | ||||||
\(957\) | 1.07071i | 0.0346112i | ||||||||
\(958\) | 5.23409 | 0.169106 | ||||||||
\(959\) | 57.3997 | 1.85353 | ||||||||
\(960\) | − | 56.1322i | − | 1.81166i | ||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 16.8084 | + | 30.7622i | 0.541923 | + | 0.991814i | ||||
\(963\) | −14.1581 | −0.456239 | ||||||||
\(964\) | − | 1.08137i | − | 0.0348285i | ||||||
\(965\) | 23.3530 | 0.751760 | ||||||||
\(966\) | −156.917 | −5.04871 | ||||||||
\(967\) | − | 0.618915i | − | 0.0199030i | −0.999950 | − | 0.00995149i | \(-0.996832\pi\) | ||
0.999950 | − | 0.00995149i | \(-0.00316771\pi\) | |||||||
\(968\) | 30.5022i | 0.980379i | ||||||||
\(969\) | 16.6645i | 0.535341i | ||||||||
\(970\) | − | 45.7479i | − | 1.46888i | ||||||
\(971\) | 9.35978 | 0.300370 | 0.150185 | − | 0.988658i | \(-0.452013\pi\) | ||||
0.150185 | + | 0.988658i | \(0.452013\pi\) | |||||||
\(972\) | −1.19640 | −0.0383746 | ||||||||
\(973\) | − | 33.2170i | − | 1.06489i | ||||||
\(974\) | −44.8221 | −1.43619 | ||||||||
\(975\) | −8.93573 | − | 16.3540i | −0.286173 | − | 0.523746i | ||||
\(976\) | −24.7051 | −0.790790 | ||||||||
\(977\) | 21.1557i | 0.676830i | 0.940997 | + | 0.338415i | \(0.109891\pi\) | ||||
−0.940997 | + | 0.338415i | \(0.890109\pi\) | |||||||
\(978\) | −10.1481 | −0.324502 | ||||||||
\(979\) | −0.128862 | −0.00411846 | ||||||||
\(980\) | − | 3.48163i | − | 0.111217i | ||||||
\(981\) | 95.3979i | 3.04582i | ||||||||
\(982\) | 25.8661i | 0.825421i | ||||||||
\(983\) | − | 18.5493i | − | 0.591630i | −0.955245 | − | 0.295815i | \(-0.904409\pi\) | ||
0.955245 | − | 0.295815i | \(-0.0955912\pi\) | |||||||
\(984\) | −12.0718 | −0.384836 | ||||||||
\(985\) | −21.3008 | −0.678701 | ||||||||
\(986\) | 51.3933i | 1.63670i | ||||||||
\(987\) | 2.67092 | 0.0850164 | ||||||||
\(988\) | −0.275283 | + | 0.150413i | −0.00875790 | + | 0.00478528i | ||||
\(989\) | 23.6428 | 0.751797 | ||||||||
\(990\) | 0.986350i | 0.0313483i | ||||||||
\(991\) | −32.6306 | −1.03654 | −0.518272 | − | 0.855216i | \(-0.673425\pi\) | ||||
−0.518272 | + | 0.855216i | \(0.673425\pi\) | |||||||
\(992\) | 0.418588 | 0.0132902 | ||||||||
\(993\) | 14.7507i | 0.468100i | ||||||||
\(994\) | − | 10.3647i | − | 0.328748i | ||||||
\(995\) | − | 32.7039i | − | 1.03678i | ||||||
\(996\) | 0.361493i | 0.0114543i | ||||||||
\(997\) | −12.4748 | −0.395082 | −0.197541 | − | 0.980295i | \(-0.563296\pi\) | ||||
−0.197541 | + | 0.980295i | \(0.563296\pi\) | |||||||
\(998\) | 11.6998 | 0.370351 | ||||||||
\(999\) | − | 33.7667i | − | 1.06833i |
(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 | 403.2.c.b.311.23 | yes | 32 | |
13.5 | odd | 4 | 5239.2.a.k.1.13 | 16 | |||
13.8 | odd | 4 | 5239.2.a.l.1.4 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.10 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.10 | ✓ | 32 | 13.12 | even | 2 | inner | |
403.2.c.b.311.23 | yes | 32 | 1.1 | even | 1 | trivial | |
5239.2.a.k.1.13 | 16 | 13.5 | odd | 4 | |||
5239.2.a.l.1.4 | 16 | 13.8 | odd | 4 |