Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(13,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.i (of order \(11\), degree \(10\), 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: | \(2.20387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{11})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.302381 - 2.10310i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 276.121 |
Dual form | 276.2.i.a.73.1 |
$q$-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 \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(e\left(\frac{9}{11}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −0.959493 | − | 0.281733i | −0.553964 | − | 0.162658i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.52130 | + | 0.977682i | −0.680348 | + | 0.437233i | −0.834643 | − | 0.550792i | \(-0.814326\pi\) |
0.154295 | + | 0.988025i | \(0.450689\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.485296 | − | 3.37531i | 0.183425 | − | 1.27575i | −0.665165 | − | 0.746696i | \(-0.731639\pi\) |
0.848590 | − | 0.529051i | \(-0.177452\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.841254 | + | 0.540641i | 0.280418 | + | 0.180214i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.800715 | − | 1.75332i | −0.241425 | − | 0.528646i | 0.749669 | − | 0.661813i | \(-0.230213\pi\) |
−0.991094 | + | 0.133167i | \(0.957485\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.753988 | − | 5.24410i | −0.209119 | − | 1.45445i | −0.776042 | − | 0.630682i | \(-0.782775\pi\) |
0.566923 | − | 0.823771i | \(-0.308134\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73512 | − | 0.509479i | 0.448007 | − | 0.131547i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.496392 | − | 0.572867i | 0.120393 | − | 0.138941i | −0.692354 | − | 0.721558i | \(-0.743426\pi\) |
0.812746 | + | 0.582618i | \(0.197972\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.10335 | − | 3.58146i | −0.711958 | − | 0.821643i | 0.278358 | − | 0.960477i | \(-0.410210\pi\) |
−0.990316 | + | 0.138834i | \(0.955664\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.41657 | + | 3.10186i | −0.309122 | + | 0.676882i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.36166 | − | 3.42041i | 0.700955 | − | 0.713206i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.718574 | + | 1.57346i | −0.143715 | + | 0.314691i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.654861 | − | 0.755750i | −0.126028 | − | 0.145444i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.79381 | + | 3.22422i | −0.518797 | + | 0.598723i | −0.953329 | − | 0.301933i | \(-0.902368\pi\) |
0.434532 | + | 0.900656i | \(0.356914\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.28356 | − | 0.964142i | 0.589746 | − | 0.173165i | 0.0267745 | − | 0.999641i | \(-0.491476\pi\) |
0.562971 | + | 0.826477i | \(0.309658\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.274313 | + | 1.90789i | 0.0477517 | + | 0.332120i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.56170 | + | 5.60934i | 0.433006 | + | 0.948151i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.09318 | − | 1.98787i | −0.508516 | − | 0.326803i | 0.261099 | − | 0.965312i | \(-0.415915\pi\) |
−0.769614 | + | 0.638509i | \(0.779552\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.753988 | + | 5.24410i | −0.120735 | + | 0.839728i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.92232 | + | 3.80604i | −0.924911 | + | 0.594404i | −0.914079 | − | 0.405537i | \(-0.867084\pi\) |
−0.0108322 | + | 0.999941i | \(0.503448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.52444 | + | 1.03487i | 0.537472 | + | 0.157816i | 0.539192 | − | 0.842183i | \(-0.318730\pi\) |
−0.00172068 | + | 0.999999i | \(0.500548\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.80838 | −0.269577 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.3519 | 1.50998 | 0.754989 | − | 0.655738i | \(-0.227642\pi\) | ||||
0.754989 | + | 0.655738i | \(0.227642\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.44075 | − | 1.30392i | −0.634393 | − | 0.186275i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.637680 | + | 0.409812i | −0.0892930 | + | 0.0573851i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.11911 | + | 7.78361i | −0.153722 | + | 1.06916i | 0.756187 | + | 0.654355i | \(0.227060\pi\) |
−0.909910 | + | 0.414806i | \(0.863849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.93232 | + | 1.88449i | 0.395394 | + | 0.254104i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.96863 | + | 4.31070i | 0.260751 | + | 0.570966i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.53778 | − | 10.6955i | −0.200202 | − | 1.39244i | −0.803682 | − | 0.595059i | \(-0.797129\pi\) |
0.603480 | − | 0.797378i | \(-0.293780\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.3748 | − | 3.63356i | 1.58443 | − | 0.465229i | 0.633268 | − | 0.773933i | \(-0.281713\pi\) |
0.951158 | + | 0.308704i | \(0.0998951\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.23309 | − | 2.57712i | 0.281343 | − | 0.324687i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.27411 | + | 7.24071i | 0.778208 | + | 0.898100i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.57750 | + | 5.64394i | −0.314892 | + | 0.689517i | −0.999213 | − | 0.0396637i | \(-0.987371\pi\) |
0.684321 | + | 0.729181i | \(0.260099\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.18913 | + | 2.33477i | −0.504312 | + | 0.281074i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.14490 | + | 13.4555i | −0.729266 | + | 1.59687i | 0.0711790 | + | 0.997464i | \(0.477324\pi\) |
−0.800445 | + | 0.599406i | \(0.795403\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.97621 | + | 5.74285i | 0.582421 | + | 0.672150i | 0.968124 | − | 0.250473i | \(-0.0805862\pi\) |
−0.385702 | + | 0.922623i | \(0.626041\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.13276 | − | 1.30728i | 0.130800 | − | 0.150951i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.30658 | + | 1.85178i | −0.718702 | + | 0.211030i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.905219 | − | 6.29594i | −0.101845 | − | 0.708348i | −0.975210 | − | 0.221282i | \(-0.928976\pi\) |
0.873365 | − | 0.487067i | \(-0.161933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.415415 | + | 0.909632i | 0.0461572 | + | 0.101070i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.22677 | − | 5.28702i | −0.903005 | − | 0.580326i | 0.00467489 | − | 0.999989i | \(-0.498512\pi\) |
−0.907680 | + | 0.419663i | \(0.862148\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.195081 | + | 1.35682i | −0.0211595 | + | 0.147168i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.58901 | − | 2.30651i | 0.384782 | − | 0.247284i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.6954 | − | 3.14044i | −1.13371 | − | 0.332886i | −0.339543 | − | 0.940591i | \(-0.610272\pi\) |
−0.794163 | + | 0.607704i | \(0.792091\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.0664 | −1.89387 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.42219 | −0.354864 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.22267 | + | 2.41439i | 0.843628 | + | 0.247712i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.41054 | − | 4.11980i | 0.650892 | − | 0.418303i | −0.173100 | − | 0.984904i | \(-0.555378\pi\) |
0.823992 | + | 0.566601i | \(0.191742\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.274313 | − | 1.90789i | 0.0275695 | − | 0.191750i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.49704 | + | 4.81805i | 0.745983 | + | 0.479414i | 0.857587 | − | 0.514339i | \(-0.171963\pi\) |
−0.111604 | + | 0.993753i | \(0.535599\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.367699 | − | 0.805149i | −0.0362305 | − | 0.0793337i | 0.890651 | − | 0.454687i | \(-0.150249\pi\) |
−0.926882 | + | 0.375353i | \(0.877521\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.877598 | − | 6.10383i | −0.0856448 | − | 0.595673i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.59185 | − | 2.22917i | 0.733932 | − | 0.215502i | 0.106653 | − | 0.994296i | \(-0.465987\pi\) |
0.627279 | + | 0.778794i | \(0.284168\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.15251 | − | 1.33007i | 0.110391 | − | 0.127398i | −0.697865 | − | 0.716229i | \(-0.745866\pi\) |
0.808256 | + | 0.588832i | \(0.200412\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.40784 | + | 2.77879i | 0.228542 | + | 0.263751i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.94750 | − | 15.2129i | 0.653566 | − | 1.43111i | −0.234832 | − | 0.972036i | \(-0.575454\pi\) |
0.888398 | − | 0.459074i | \(-0.151819\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.77003 | + | 8.49012i | −0.165056 | + | 0.791708i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.20088 | − | 4.81926i | 0.203471 | − | 0.445540i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.69271 | − | 1.95349i | −0.155170 | − | 0.179076i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.77048 | − | 5.50543i | 0.433680 | − | 0.500493i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.75471 | − | 1.98336i | 0.609052 | − | 0.178834i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.73197 | − | 12.0461i | −0.154912 | − | 1.07744i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.531324 | + | 1.16344i | 0.0471473 | + | 0.103238i | 0.931740 | − | 0.363126i | \(-0.118291\pi\) |
−0.884593 | + | 0.466365i | \(0.845563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.09012 | − | 1.98590i | −0.272070 | − | 0.174849i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.43523 | − | 9.98224i | 0.125397 | − | 0.872152i | −0.825887 | − | 0.563835i | \(-0.809325\pi\) |
0.951284 | − | 0.308317i | \(-0.0997657\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.5946 | + | 8.73670i | −1.17880 | + | 0.757568i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.73512 | + | 0.509479i | 0.149336 | + | 0.0438489i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.53140 | 0.558015 | 0.279007 | − | 0.960289i | \(-0.409995\pi\) | ||||
0.279007 | + | 0.960289i | \(0.409995\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.55305 | −0.725461 | −0.362730 | − | 0.931894i | \(-0.618155\pi\) | ||||
−0.362730 | + | 0.931894i | \(0.618155\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.93256 | − | 2.91646i | −0.836473 | − | 0.245610i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.59086 | + | 5.52101i | −0.718404 | + | 0.461690i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.09796 | − | 7.63648i | 0.0911806 | − | 0.634175i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.89351 | + | 2.50221i | 0.321132 | + | 0.206379i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.34464 | + | 2.94435i | 0.110157 | + | 0.241211i | 0.956680 | − | 0.291142i | \(-0.0940352\pi\) |
−0.846523 | + | 0.532353i | \(0.821308\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.00038 | − | 6.95781i | −0.0814100 | − | 0.566219i | −0.989175 | − | 0.146740i | \(-0.953122\pi\) |
0.907765 | − | 0.419479i | \(-0.137787\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.727307 | − | 0.213556i | 0.0587993 | − | 0.0172650i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.05267 | + | 4.67704i | −0.325519 | + | 0.375668i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.1324 | + | 15.1556i | 1.04808 | + | 1.20955i | 0.977257 | + | 0.212058i | \(0.0680167\pi\) |
0.0708217 | + | 0.997489i | \(0.477438\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.26668 | − | 7.15303i | 0.259065 | − | 0.567272i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.91356 | − | 13.0066i | −0.781298 | − | 1.02506i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.16725 | + | 13.5044i | −0.483056 | + | 1.05775i | 0.498556 | + | 0.866858i | \(0.333864\pi\) |
−0.981612 | + | 0.190888i | \(0.938863\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.28262 | − | 2.63428i | −0.177702 | − | 0.205079i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.1307 | − | 18.6159i | 1.24823 | − | 1.44054i | 0.395272 | − | 0.918564i | \(-0.370650\pi\) |
0.852961 | − | 0.521974i | \(-0.174804\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.4587 | + | 4.24546i | −1.11221 | + | 0.326574i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.674423 | − | 4.69071i | −0.0515744 | − | 0.358708i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.48345 | − | 14.1968i | −0.492928 | − | 1.07936i | −0.978704 | − | 0.205278i | \(-0.934190\pi\) |
0.485776 | − | 0.874083i | \(-0.338537\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.96218 | + | 3.18900i | 0.375106 | + | 0.241066i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.53778 | + | 10.6955i | −0.115587 | + | 0.803924i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.2621 | + | 9.80838i | −1.14075 | + | 0.733113i | −0.967775 | − | 0.251815i | \(-0.918973\pi\) |
−0.172970 | + | 0.984927i | \(0.555336\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.5232 | + | 7.49429i | 1.89712 | + | 0.557046i | 0.990967 | + | 0.134103i | \(0.0428154\pi\) |
0.906157 | + | 0.422942i | \(0.139003\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.8972 | −0.953388 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.64917 | 0.488856 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.40189 | − | 0.411631i | −0.102516 | − | 0.0301015i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.86869 | + | 1.84360i | −0.208667 | + | 0.134102i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.52838 | − | 24.5404i | 0.255305 | − | 1.77568i | −0.309935 | − | 0.950758i | \(-0.600307\pi\) |
0.565240 | − | 0.824927i | \(-0.308784\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.96991 | − | 2.55131i | −0.285761 | − | 0.183647i | 0.389906 | − | 0.920855i | \(-0.372508\pi\) |
−0.675666 | + | 0.737208i | \(0.736144\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.98002 | − | 8.71503i | −0.285015 | − | 0.624096i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.58426 | + | 11.0188i | 0.112874 | + | 0.785055i | 0.965100 | + | 0.261882i | \(0.0843430\pi\) |
−0.852226 | + | 0.523174i | \(0.824748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.56852 | − | 2.22232i | 0.536518 | − | 0.157536i | −0.00223844 | − | 0.999997i | \(-0.500713\pi\) |
0.538756 | + | 0.842462i | \(0.318894\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.06318 | − | 4.68915i | 0.286594 | − | 0.330747i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.52693 | + | 10.9947i | 0.668660 | + | 0.771674i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.28854 | − | 11.5803i | 0.369368 | − | 0.808803i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.67722 | − | 1.05999i | 0.325090 | − | 0.0736741i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.79455 | + | 8.30890i | −0.262474 | + | 0.574738i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2185 | + | 14.1009i | 0.841159 | + | 0.970749i | 0.999863 | − | 0.0165774i | \(-0.00527698\pi\) |
−0.158704 | + | 0.987326i | \(0.550732\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.68683 | − | 11.1792i | 0.663731 | − | 0.765986i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.37351 | + | 1.87143i | −0.434670 | + | 0.127631i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.66077 | − | 11.5509i | −0.112741 | − | 0.784129i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.15669 | − | 6.91219i | −0.213309 | − | 0.467082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.37845 | − | 2.17120i | −0.227259 | − | 0.146050i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.29264 | + | 22.9008i | −0.220491 | + | 1.53355i | 0.515694 | + | 0.856773i | \(0.327534\pi\) |
−0.736186 | + | 0.676779i | \(0.763375\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.45518 | + | 0.935186i | −0.0970119 | + | 0.0623457i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.8332 | − | 3.47453i | −0.785394 | − | 0.230613i | −0.135641 | − | 0.990758i | \(-0.543309\pi\) |
−0.649753 | + | 0.760145i | \(0.725128\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.4857 | −0.758998 | −0.379499 | − | 0.925192i | \(-0.623904\pi\) | ||||
−0.379499 | + | 0.925192i | \(0.623904\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.57283 | 0.432460 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.13434 | + | 1.50758i | 0.336362 | + | 0.0987647i | 0.445552 | − | 0.895256i | \(-0.353008\pi\) |
−0.109190 | + | 0.994021i | \(0.534826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.7484 | + | 10.1209i | −1.02731 | + | 0.660212i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.905219 | + | 6.29594i | −0.0588003 | + | 0.408965i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.62507 | + | 6.18565i | 0.622594 | + | 0.400117i | 0.813561 | − | 0.581480i | \(-0.197526\pi\) |
−0.190967 | + | 0.981596i | \(0.561162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.45687 | + | 3.19010i | 0.0938452 | + | 0.205492i | 0.950733 | − | 0.310010i | \(-0.100333\pi\) |
−0.856888 | + | 0.515503i | \(0.827605\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.142315 | − | 0.989821i | −0.00912950 | − | 0.0634971i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.03055 | − | 2.35798i | 0.513053 | − | 0.150646i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.4416 | + | 18.9747i | −1.04616 | + | 1.20733i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.40400 | + | 7.39061i | 0.405837 | + | 0.468361i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.91943 | + | 10.7720i | −0.310512 | + | 0.679925i | −0.998971 | − | 0.0453492i | \(-0.985560\pi\) |
0.688460 | + | 0.725275i | \(0.258287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.68881 | − | 3.15529i | −0.546261 | − | 0.198371i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.569439 | − | 1.24690i | 0.0356596 | − | 0.0780837i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.7144 | + | 19.2895i | 1.04262 | + | 1.20324i | 0.978702 | + | 0.205287i | \(0.0658129\pi\) |
0.0639142 | + | 0.997955i | \(0.479642\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.21077 | + | 9.47573i | −0.510192 | + | 0.588794i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.09345 | + | 1.20194i | −0.253378 | + | 0.0743985i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.511613 | + | 3.55835i | 0.0315474 | + | 0.219417i | 0.999496 | − | 0.0317294i | \(-0.0101015\pi\) |
−0.967949 | + | 0.251147i | \(0.919192\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.90739 | − | 12.9354i | −0.362888 | − | 0.794614i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.37736 | + | 6.02646i | 0.573885 | + | 0.368814i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.30719 | + | 16.0468i | −0.140672 | + | 0.978393i | 0.790148 | + | 0.612915i | \(0.210003\pi\) |
−0.930820 | + | 0.365478i | \(0.880906\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.65183 | + | 2.34689i | −0.221833 | + | 0.142563i | −0.646838 | − | 0.762628i | \(-0.723909\pi\) |
0.425005 | + | 0.905191i | \(0.360272\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.3346 | + | 5.08989i | 1.04914 | + | 0.308054i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.33415 | 0.201057 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.6009 | 1.71846 | 0.859230 | − | 0.511589i | \(-0.170943\pi\) | ||||
0.859230 | + | 0.511589i | \(0.170943\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.28356 | + | 0.964142i | 0.196582 | + | 0.0577216i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.53062 | + | 6.12496i | −0.568549 | + | 0.365384i | −0.793113 | − | 0.609075i | \(-0.791541\pi\) |
0.224563 | + | 0.974459i | \(0.427904\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.759137 | − | 5.27992i | 0.0451260 | − | 0.313858i | −0.954739 | − | 0.297444i | \(-0.903866\pi\) |
0.999865 | − | 0.0164143i | \(-0.00522508\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.20938 | − | 4.63319i | −0.427047 | − | 0.274446i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.97249 | + | 21.8367i | 0.588658 | + | 1.28898i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.33758 | + | 16.2582i | 0.137505 | + | 0.956367i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.31155 | + | 2.14687i | −0.428611 | + | 0.125851i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.4905 | − | 17.8770i | 0.904963 | − | 1.04438i | −0.0938455 | − | 0.995587i | \(-0.529916\pi\) |
0.998809 | − | 0.0487965i | \(-0.0155386\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.7963 | + | 14.7677i | 0.745027 | + | 0.859806i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.800715 | + | 1.75332i | −0.0464622 | + | 0.101738i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.4717 | − | 15.0499i | −1.18391 | − | 0.870361i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.20340 | − | 11.3939i | 0.299919 | − | 0.656731i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.83595 | − | 6.73505i | −0.335267 | − | 0.386918i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.2733 | + | 17.6263i | −0.874547 | + | 1.00928i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.7890 | − | 5.51696i | 1.07235 | − | 0.314870i | 0.302534 | − | 0.953139i | \(-0.402167\pi\) |
0.769813 | + | 0.638269i | \(0.220349\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.125968 | + | 0.876128i | 0.00716608 | + | 0.0498412i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.797463 | − | 1.74620i | −0.0452200 | − | 0.0990179i | 0.885674 | − | 0.464308i | \(-0.153697\pi\) |
−0.930894 | + | 0.365290i | \(0.880970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.6720 | − | 6.85849i | −0.603219 | − | 0.387665i | 0.203090 | − | 0.979160i | \(-0.434902\pi\) |
−0.806309 | + | 0.591495i | \(0.798538\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.877598 | + | 6.10383i | −0.0494471 | + | 0.343912i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.62869 | − | 1.68936i | 0.147642 | − | 0.0948838i | −0.464734 | − | 0.885450i | \(-0.653850\pi\) |
0.612376 | + | 0.790566i | \(0.290214\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.89014 | + | 2.31675i | 0.441763 | + | 0.129713i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.91236 | −0.441625 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.59218 | −0.199874 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.79317 | + | 2.58191i | 0.487757 | + | 0.143218i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.48055 | + | 0.951493i | −0.0818747 | + | 0.0526177i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.02373 | − | 34.9408i | 0.276967 | − | 1.92635i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.8260 | − | 6.95744i | −0.595050 | − | 0.382415i | 0.208175 | − | 0.978092i | \(-0.433248\pi\) |
−0.803225 | + | 0.595676i | \(0.796884\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.52743 | − | 3.34460i | −0.0837025 | − | 0.183283i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.59682 | − | 11.1061i | −0.0872436 | − | 0.606792i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8281 | − | 4.35393i | 0.807739 | − | 0.237174i | 0.148311 | − | 0.988941i | \(-0.452616\pi\) |
0.659429 | + | 0.751767i | \(0.270798\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.9520 | + | 12.6393i | −0.594834 | + | 0.686475i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.31965 | − | 4.98514i | −0.233922 | − | 0.269960i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.35979 | − | 7.35691i | 0.181412 | − | 0.397236i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.09027 | − | 7.64754i | 0.220213 | − | 0.411730i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.54167 | + | 16.5140i | −0.404858 | + | 0.886516i | 0.591896 | + | 0.806014i | \(0.298380\pi\) |
−0.996754 | + | 0.0805017i | \(0.974348\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.3287 | − | 16.5361i | −0.766995 | − | 0.885160i | 0.229104 | − | 0.973402i | \(-0.426420\pi\) |
−0.996099 | + | 0.0882423i | \(0.971875\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.46947 | + | 4.00398i | −0.185187 | + | 0.213717i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.6096 | + | 3.40888i | −0.617916 | + | 0.181436i | −0.575685 | − | 0.817672i | \(-0.695265\pi\) |
−0.0422305 | + | 0.999108i | \(0.513446\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.80691 | − | 26.4776i | −0.202050 | − | 1.40529i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.07378 | + | 2.35125i | 0.0568304 | + | 0.124441i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.98260 | − | 1.91680i | −0.157415 | − | 0.101165i | 0.459562 | − | 0.888146i | \(-0.348007\pi\) |
−0.616977 | + | 0.786981i | \(0.711643\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.492073 | + | 3.42244i | −0.0258986 | + | 0.180129i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.12830 | + | 3.93842i | −0.321652 | + | 0.206713i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.1850 | − | 3.87147i | −0.690135 | − | 0.202642i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.1379 | −1.36439 | −0.682194 | − | 0.731171i | \(-0.738974\pi\) | ||||
−0.682194 | + | 0.731171i | \(0.738974\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.03987 | −0.366481 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.7290 | + | 7.55472i | 1.33578 | + | 0.392221i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.1660 | − | 7.81858i | 0.629929 | − | 0.404831i | −0.186354 | − | 0.982483i | \(-0.559667\pi\) |
0.816283 | + | 0.577652i | \(0.196031\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.73197 | + | 12.0461i | −0.0894384 | + | 0.622058i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.0147 | + | 12.2200i | 0.979305 | + | 0.629361i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.6229 | − | 25.4505i | −0.597026 | − | 1.30730i | −0.931102 | − | 0.364758i | \(-0.881152\pi\) |
0.334076 | − | 0.942546i | \(-0.391576\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.182023 | − | 1.26600i | −0.00932534 | − | 0.0648592i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.7316 | − | 5.20645i | 0.906040 | − | 0.266037i | 0.204667 | − | 0.978832i | \(-0.434389\pi\) |
0.701373 | + | 0.712794i | \(0.252571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.78377 | − | 8.98295i | 0.396698 | − | 0.457814i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.40545 | + | 2.77604i | 0.122276 | + | 0.141114i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.6824 | − | 23.3913i | 0.541621 | − | 1.18598i | −0.418965 | − | 0.908002i | \(-0.637607\pi\) |
0.960586 | − | 0.277982i | \(-0.0896656\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.290741 | − | 3.62365i | −0.0147034 | − | 0.183256i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.18941 | + | 9.17354i | −0.211328 | + | 0.462744i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.53254 | + | 8.69302i | 0.379003 | + | 0.437393i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2955 | − | 21.1141i | 0.918225 | − | 1.05969i | −0.0797958 | − | 0.996811i | \(-0.525427\pi\) |
0.998021 | − | 0.0628775i | \(-0.0200277\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.5053 | − | 4.55277i | 0.776237 | − | 0.227924i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.47619 | − | 24.1775i | −0.173593 | − | 1.20737i | −0.871216 | − | 0.490900i | \(-0.836668\pi\) |
0.697623 | − | 0.716465i | \(-0.254241\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.53183 | − | 16.4924i | −0.375187 | − | 0.821545i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.52130 | − | 0.977682i | −0.0755942 | − | 0.0485814i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.00861 | + | 7.01505i | −0.0499950 | + | 0.347723i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.4357 | + | 19.5599i | −1.50495 | + | 0.967173i | −0.510738 | + | 0.859736i | \(0.670628\pi\) |
−0.994212 | + | 0.107437i | \(0.965736\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.26683 | − | 1.84011i | −0.309120 | − | 0.0907658i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −36.8470 | −1.81312 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.6844 | 0.868095 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.20660 | + | 2.40967i | 0.401879 | + | 0.118002i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.96574 | − | 4.47661i | 0.340299 | − | 0.218697i | −0.359318 | − | 0.933215i | \(-0.616991\pi\) |
0.699617 | + | 0.714519i | \(0.253354\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.08820 | + | 35.3892i | −0.247984 | + | 1.72476i | 0.361852 | + | 0.932236i | \(0.382145\pi\) |
−0.609836 | + | 0.792528i | \(0.708765\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.70856 | + | 5.59665i | 0.423425 | + | 0.272119i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.544687 | + | 1.19270i | 0.0264212 | + | 0.0578544i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.25896 | − | 43.5320i | −0.302892 | − | 2.10666i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.79832 | − | 2.87705i | 0.473067 | − | 0.138905i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.2907 | + | 16.4924i | −0.688361 | + | 0.794411i | −0.987131 | − | 0.159914i | \(-0.948878\pi\) |
0.298770 | + | 0.954325i | \(0.403424\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.9066 | − | 22.9735i | −0.956651 | − | 1.10403i | −0.994499 | − | 0.104751i | \(-0.966596\pi\) |
0.0378476 | − | 0.999284i | \(-0.487950\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.20493 | + | 7.01782i | −0.153665 | + | 0.336479i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.6825 | − | 1.42490i | −1.08505 | − | 0.0681621i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.60356 | − | 18.8392i | 0.410626 | − | 0.899145i | −0.585456 | − | 0.810704i | \(-0.699084\pi\) |
0.996081 | − | 0.0884405i | \(-0.0281883\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.03084 | − | 3.49778i | −0.144326 | − | 0.166561i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.1133 | + | 18.5958i | −0.765567 | + | 0.883512i | −0.995980 | − | 0.0895812i | \(-0.971447\pi\) |
0.230412 | + | 0.973093i | \(0.425993\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.3412 | − | 5.67910i | 0.916863 | − | 0.269215i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.460654 | − | 3.20392i | −0.0217882 | − | 0.151540i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.3387 | + | 35.7767i | 0.771070 | + | 1.68841i | 0.724283 | + | 0.689502i | \(0.242171\pi\) |
0.0467864 | + | 0.998905i | \(0.485102\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.4153 | + | 7.33617i | 0.537525 | + | 0.345447i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.00038 | + | 6.95781i | −0.0470021 | + | 0.326907i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.4844 | − | 17.6632i | 1.28849 | − | 0.828063i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.4781 | − | 4.83841i | −0.770814 | − | 0.226331i | −0.127401 | − | 0.991851i | \(-0.540664\pi\) |
−0.643412 | + | 0.765520i | \(0.722482\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.758011 | −0.0353809 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.59212 | 0.0741524 | 0.0370762 | − | 0.999312i | \(-0.488196\pi\) | ||||
0.0370762 | + | 0.999312i | \(0.488196\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0004 | + | 4.11088i | 0.650653 | + | 0.191049i | 0.590371 | − | 0.807132i | \(-0.298982\pi\) |
0.0602827 | + | 0.998181i | \(0.480800\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.20619 | − | 3.34581i | 0.241431 | − | 0.155158i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.20501 | − | 29.2465i | 0.194585 | − | 1.35337i | −0.625097 | − | 0.780547i | \(-0.714940\pi\) |
0.819681 | − | 0.572820i | \(-0.194150\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.7992 | + | 11.4388i | 0.821890 | + | 0.528197i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.33061 | − | 18.2415i | −0.383854 | − | 0.840524i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.00761 | − | 7.00810i | −0.0463301 | − | 0.322233i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.86526 | − | 2.30945i | 0.360883 | − | 0.105965i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.14960 | + | 5.94295i | −0.235784 | + | 0.272109i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.07544 | − | 2.39519i | −0.0948293 | − | 0.109439i | 0.706351 | − | 0.707861i | \(-0.250340\pi\) |
−0.801181 | + | 0.598423i | \(0.795794\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.09235 | + | 17.7198i | −0.368979 | + | 0.807952i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.84762 | + | 15.2727i | 0.266076 | + | 0.694931i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.72452 | + | 12.5349i | −0.259937 | + | 0.569183i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.8452 | − | 24.0567i | −0.944586 | − | 1.09011i | −0.995812 | − | 0.0914238i | \(-0.970858\pi\) |
0.0512256 | − | 0.998687i | \(-0.483687\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.72205 | − | 11.2198i | 0.439647 | − | 0.507379i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.7015 | + | 3.14225i | −0.482953 | + | 0.141808i | −0.514141 | − | 0.857706i | \(-0.671889\pi\) |
0.0311880 | + | 0.999514i | \(0.490071\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.460228 | + | 3.20096i | 0.0207276 | + | 0.144164i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.44799 | + | 3.17066i | 0.0650825 | + | 0.142511i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 42.4343 | + | 27.2708i | 1.90344 | + | 1.22326i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.553581 | + | 3.85024i | −0.0247817 | + | 0.172360i | −0.998453 | − | 0.0555942i | \(-0.982295\pi\) |
0.973672 | + | 0.227955i | \(0.0732038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.7220 | + | 13.3172i | −0.925791 | + | 0.594970i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.0920 | − | 10.5976i | −1.60926 | − | 0.472523i | −0.651160 | − | 0.758940i | \(-0.725717\pi\) |
−0.958105 | + | 0.286418i | \(0.907536\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.1158 | −0.717143 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.0691 | 0.669243 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.9608 | − | 5.56740i | −0.840424 | − | 0.246771i | −0.166935 | − | 0.985968i | \(-0.553387\pi\) |
−0.673489 | + | 0.739197i | \(0.735205\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.7988 | − | 14.0093i | 0.964324 | − | 0.619733i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.674423 | + | 4.69071i | −0.0297765 | + | 0.207100i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.34656 | + | 0.865383i | 0.0593366 | + | 0.0381333i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.28891 | − | 18.1502i | −0.364546 | − | 0.798244i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.22113 | + | 15.4483i | 0.0974969 | + | 0.678106i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.3779 | + | 7.74525i | −1.15564 | + | 0.339326i | −0.802736 | − | 0.596335i | \(-0.796623\pi\) |
−0.352901 | + | 0.935660i | \(0.614805\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.32266 | − | 6.14267i | 0.232744 | − | 0.268600i | −0.627349 | − | 0.778738i | \(-0.715860\pi\) |
0.860093 | + | 0.510138i | \(0.170406\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.86274 | − | 4.45783i | −0.168584 | − | 0.194556i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.07761 | − | 2.35964i | 0.0469414 | − | 0.102787i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.398477 | − | 22.9965i | −0.0173251 | − | 0.999850i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.48877 | − | 9.82903i | 0.194796 | − | 0.426544i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.4246 | + | 28.1875i | 1.05795 | + | 1.22094i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.37009 | + | 10.8137i | −0.405104 | + | 0.467515i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.4072 | − | 5.11123i | 0.751178 | − | 0.220566i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.26958 | + | 8.83013i | 0.0546847 | + | 0.380341i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.72352 | + | 21.2915i | 0.418047 | + | 0.915395i | 0.995117 | + | 0.0987006i | \(0.0314686\pi\) |
−0.577070 | + | 0.816695i | \(0.695804\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.3779 | − | 14.3814i | −0.960329 | − | 0.617166i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.452935 | + | 3.15023i | −0.0194016 | + | 0.134941i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.7794 | − | 8.85546i | 0.589163 | − | 0.378632i | −0.211829 | − | 0.977307i | \(-0.567942\pi\) |
0.800992 | + | 0.598675i | \(0.204306\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.3748 | + | 3.63356i | 0.528142 | + | 0.155076i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.2176 | 0.861298 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.6900 | −0.922354 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.37983 | − | 1.87329i | −0.270809 | − | 0.0795166i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.0768 | − | 10.3319i | 0.681196 | − | 0.437778i | −0.153750 | − | 0.988110i | \(-0.549135\pi\) |
0.834946 | + | 0.550332i | \(0.185499\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.76957 | − | 19.2628i | 0.117140 | − | 0.814729i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.22913 | + | 0.789915i | 0.0518940 | + | 0.0333502i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.42062 | + | 18.4386i | 0.354887 | + | 0.777094i | 0.999916 | + | 0.0129360i | \(0.00411778\pi\) |
−0.645030 | + | 0.764158i | \(0.723155\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.30413 | + | 29.9359i | 0.181076 | + | 1.25941i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.27189 | − | 0.960713i | 0.137406 | − | 0.0403462i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.1549 | − | 14.0276i | 0.509562 | − | 0.588066i | −0.441425 | − | 0.897298i | \(-0.645527\pi\) |
0.950986 | + | 0.309233i | \(0.100072\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.6110 | + | 35.3269i | 1.28103 | + | 1.47839i | 0.797838 | + | 0.602872i | \(0.205977\pi\) |
0.483191 | + | 0.875515i | \(0.339478\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.2993 | + | 22.5523i | −0.430260 | + | 0.942137i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.96628 | + | 7.74725i | 0.123702 | + | 0.323083i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.8811 | + | 32.5851i | −0.619509 | + | 1.35653i | 0.296368 | + | 0.955074i | \(0.404225\pi\) |
−0.915876 | + | 0.401461i | \(0.868503\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.09032 | + | 3.56642i | 0.128429 | + | 0.148215i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.8378 | + | 25.2021i | −0.905983 | + | 1.04556i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.5433 | − | 4.27029i | 0.602320 | − | 0.176857i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.36349 | + | 9.48331i | 0.0563736 | + | 0.392087i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.00770622 | + | 0.0168743i | 0.000318070 | + | 0.000696476i | 0.909791 | − | 0.415067i | \(-0.136242\pi\) |
−0.909473 | + | 0.415763i | \(0.863515\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.6431 | − | 8.76788i | −0.562154 | − | 0.361274i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.58426 | − | 11.0188i | 0.0651678 | − | 0.453252i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.46726 | + | 3.51359i | −0.224513 | + | 0.144286i | −0.648063 | − | 0.761587i | \(-0.724420\pi\) |
0.423549 | + | 0.905873i | \(0.360784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.48501 | + | 1.31692i | 0.183867 | + | 0.0539883i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.88804 | −0.322836 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.49989 | −0.306437 | −0.153219 | − | 0.988192i | \(-0.548964\pi\) | ||||
−0.153219 | + | 0.988192i | \(0.548964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.6872 | − | 7.24882i | −1.00701 | − | 0.295686i | −0.263682 | − | 0.964610i | \(-0.584937\pi\) |
−0.743331 | + | 0.668924i | \(0.766755\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.21968 | + | 3.35448i | −0.212562 | + | 0.136605i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.87479 | + | 13.0394i | −0.0762210 | + | 0.530129i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.3740 | + | 15.6642i | 0.989309 | + | 0.635790i | 0.931959 | − | 0.362564i | \(-0.118098\pi\) |
0.0573502 | + | 0.998354i | \(0.481735\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.04347 | − | 13.2334i | −0.244894 | − | 0.536242i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.80520 | − | 54.2863i | −0.315765 | − | 2.19619i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.25859 | + | 0.663181i | −0.0912235 | + | 0.0267856i | −0.327026 | − | 0.945015i | \(-0.606046\pi\) |
0.235802 | + | 0.971801i | \(0.424228\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.33686 | + | 9.62125i | −0.336175 | + | 0.387966i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.99989 | − | 11.5405i | −0.402580 | − | 0.464603i | 0.517871 | − | 0.855458i | \(-0.326725\pi\) |
−0.920452 | + | 0.390856i | \(0.872179\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.77631 | + | 10.4587i | −0.191976 | + | 0.420369i | −0.981004 | − | 0.193988i | \(-0.937858\pi\) |
0.789028 | + | 0.614358i | \(0.210585\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.78640 | − | 0.300678i | −0.192071 | − | 0.0120658i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.7904 | + | 34.5761i | −0.632628 | + | 1.38526i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.74830 | + | 10.0961i | 0.349932 | + | 0.403843i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.98173 | − | 6.90328i | 0.238887 | − | 0.275690i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.67421 | + | 0.785219i | −0.106628 | + | 0.0313087i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.01067 | + | 13.9845i | 0.0800436 | + | 0.556715i | 0.989897 | + | 0.141786i | \(0.0452845\pi\) |
−0.909854 | + | 0.414929i | \(0.863806\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.75090 | − | 16.9721i | −0.308071 | − | 0.674581i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.94578 | − | 1.25047i | −0.0772158 | − | 0.0496235i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.48963 | + | 24.2709i | −0.138264 | + | 0.961648i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.4440 | + | 7.99727i | −0.492277 | + | 0.316367i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.8830 | + | 7.01267i | 0.943320 | + | 0.276984i | 0.717003 | − | 0.697070i | \(-0.245513\pi\) |
0.226317 | + | 0.974054i | \(0.427331\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.5235 | 0.927678 | 0.463839 | − | 0.885919i | \(-0.346472\pi\) | ||||
0.463839 | + | 0.885919i | \(0.346472\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.64258 | 0.261551 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.2110 | + | 5.64087i | 0.755264 | + | 0.221766i | 0.636627 | − | 0.771172i | \(-0.280329\pi\) |
0.118637 | + | 0.992938i | \(0.462147\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.5213 | + | 11.2603i | −0.687773 | + | 0.442005i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.66077 | + | 11.5509i | −0.0650909 | + | 0.452717i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.28245 | − | 4.03749i | −0.245851 | − | 0.157999i | 0.411912 | − | 0.911224i | \(-0.364861\pi\) |
−0.657764 | + | 0.753224i | \(0.728497\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.57604 | + | 16.5892i | 0.296020 | + | 0.648194i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.08143 | + | 7.52154i | 0.0421907 | + | 0.293443i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.4634 | + | 3.07234i | −0.407597 | + | 0.119681i | −0.479102 | − | 0.877759i | \(-0.659038\pi\) |
0.0715057 | + | 0.997440i | \(0.477220\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.3039 | + | 13.0454i | −0.439672 | + | 0.507409i | −0.931729 | − | 0.363154i | \(-0.881700\pi\) |
0.492057 | + | 0.870563i | \(0.336245\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.62990 | + | 3.03506i | 0.102137 | + | 0.117872i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.1398 | − | 26.5824i | 0.470759 | − | 1.03082i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.63636 | + | 20.3947i | 0.0633600 | + | 0.789687i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.61117 | − | 21.0455i | 0.371589 | − | 0.813667i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.2794 | − | 18.7875i | −0.628461 | − | 0.725283i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.61892 | − | 5.33051i | 0.178046 | − | 0.205476i | −0.659711 | − | 0.751520i | \(-0.729321\pi\) |
0.837757 | + | 0.546043i | \(0.183867\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.65971 | − | 0.487333i | 0.0638821 | − | 0.0187575i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.71912 | − | 25.8671i | −0.142937 | − | 0.994152i | −0.927426 | − | 0.374008i | \(-0.877983\pi\) |
0.784488 | − | 0.620144i | \(-0.212926\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7946 | − | 23.6369i | −0.414259 | − | 0.907100i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.3749 | + | 6.66757i | 0.397569 | + | 0.255502i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.601211 | − | 4.18151i | 0.0230047 | − | 0.160001i | −0.975081 | − | 0.221850i | \(-0.928791\pi\) |
0.998086 | + | 0.0618487i | \(0.0196996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.93623 | + | 6.38563i | −0.379644 | + | 0.243982i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.0205 | + | 3.23590i | 0.420457 | + | 0.123457i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 41.6619 | 1.58719 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.2154 | 1.33966 | 0.669829 | − | 0.742516i | \(-0.266367\pi\) | ||||
0.669829 | + | 0.742516i | \(0.266367\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.30658 | − | 1.85178i | −0.239567 | − | 0.0703433i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.0118 | − | 8.36217i | 0.493565 | − | 0.317195i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.759435 | + | 5.28199i | −0.0287657 | + | 0.200070i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.50163 | − | 2.89302i | −0.170267 | − | 0.109424i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.0954 | + | 35.2441i | 0.607917 | + | 1.33115i | 0.923990 | + | 0.382417i | \(0.124908\pi\) |
−0.316073 | + | 0.948735i | \(0.602365\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.47976 | + | 17.2471i | 0.0935261 | + | 0.650488i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.9618 | − | 5.27406i | 0.676481 | − | 0.198633i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.9007 | − | 22.9666i | 0.748443 | − | 0.863749i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.24611 | + | 10.6706i | 0.347245 | + | 0.400742i | 0.902326 | − | 0.431054i | \(-0.141858\pi\) |
−0.555081 | + | 0.831796i | \(0.687313\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.64232 | − | 5.78588i | 0.0990948 | − | 0.216987i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.74047 | − | 14.4723i | 0.289883 | − | 0.541991i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.67151 | − | 16.7983i | 0.286898 | − | 0.628220i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.49248 | − | 8.64679i | −0.279812 | − | 0.322920i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.2454 | + | 36.0591i | −1.16526 | + | 1.34478i | −0.237590 | + | 0.971365i | \(0.576358\pi\) |
−0.927666 | + | 0.373412i | \(0.878188\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.89607 | + | 0.850363i | −0.107855 | + | 0.0316692i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.499101 | − | 3.47132i | −0.0185618 | − | 0.129100i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.06562 | − | 6.71278i | −0.113854 | − | 0.249306i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.9527 | − | 19.8921i | −1.14797 | − | 0.737756i | −0.178736 | − | 0.983897i | \(-0.557201\pi\) |
−0.969234 | + | 0.246141i | \(0.920837\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.142315 | + | 0.989821i | −0.00527092 | + | 0.0366601i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.34234 | − | 1.50533i | 0.0866347 | − | 0.0556768i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.7585 | − | 6.97613i | −0.877541 | − | 0.257669i | −0.188221 | − | 0.982127i | \(-0.560272\pi\) |
−0.689320 | + | 0.724457i | \(0.742090\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.36958 | −0.308717 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.9595 | 0.440533 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.0128 | − | 5.28903i | −0.662611 | − | 0.194560i | −0.0669010 | − | 0.997760i | \(-0.521311\pi\) |
−0.595710 | + | 0.803199i | \(0.703129\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.1214 | − | 13.5739i | 0.775915 | − | 0.498650i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.33086 | − | 30.1218i | 0.158884 | − | 1.10506i | −0.741811 | − | 0.670609i | \(-0.766033\pi\) |
0.900695 | − | 0.434452i | \(-0.143058\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.92425 | − | 3.16462i | −0.180411 | − | 0.115943i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.06242 | − | 8.89545i | −0.148636 | − | 0.325468i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.83984 | − | 26.7067i | −0.140305 | − | 0.975840i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.7928 | + | 10.2161i | −1.26961 | + | 0.372790i | −0.846062 | − | 0.533085i | \(-0.821033\pi\) |
−0.423545 | + | 0.905875i | \(0.639215\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.75499 | − | 8.94974i | 0.282608 | − | 0.326147i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.32442 | + | 9.60689i | 0.302957 | + | 0.349631i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.1304 | + | 39.7001i | −0.658961 | + | 1.44292i | 0.224526 | + | 0.974468i | \(0.427917\pi\) |
−0.883487 | + | 0.468456i | \(0.844811\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.44791 | + | 5.47540i | 0.270342 | + | 0.198744i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.29149 | + | 2.82797i | −0.0468164 | + | 0.102514i | −0.931595 | − | 0.363498i | \(-0.881582\pi\) |
0.884779 | + | 0.466012i | \(0.154310\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.93009 | − | 4.53557i | −0.142279 | − | 0.164198i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.897664 | + | 1.03596i | −0.0324551 | + | 0.0374552i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −54.9289 | + | 16.1286i | −1.98337 | + | 0.582369i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.34944 | + | 44.1613i | 0.228967 | + | 1.59250i | 0.702475 | + | 0.711709i | \(0.252078\pi\) |
−0.473508 | + | 0.880790i | \(0.657012\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.6029 | − | 23.2171i | −0.381854 | − | 0.836143i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.3965 | + | 9.25209i | 0.517807 | + | 0.332774i | 0.773304 | − | 0.634035i | \(-0.218603\pi\) |
−0.255497 | + | 0.966810i | \(0.582239\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.842448 | + | 5.85936i | −0.0302616 | + | 0.210474i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.5478 | − | 6.77866i | 0.378400 | − | 0.243183i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.0102 | + | 9.39905i | 1.14689 | + | 0.336756i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.5121 | 1.02024 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.26626 | 0.152464 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −34.7957 | − | 10.2169i | −1.24191 | − | 0.364658i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.8248 | + | 23.6658i | −1.31266 | + | 0.843596i | −0.994530 | − | 0.104451i | \(-0.966692\pi\) |
−0.318131 | + | 0.948047i | \(0.603055\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.511613 | − | 3.55835i | 0.0182139 | − | 0.126681i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −47.9767 | − | 30.8327i | −1.70585 | − | 1.09629i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.3852 | − | 62.1549i | −1.00799 | − | 2.20718i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.02378 | + | 14.0757i | 0.0717761 | + | 0.499214i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.6054 | + | 8.10566i | −0.977832 | + | 0.287117i | −0.731329 | − | 0.682025i | \(-0.761100\pi\) |
−0.246503 | + | 0.969142i | \(0.579281\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.13859 | − | 5.93025i | 0.181790 | − | 0.209797i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.29966 | − | 8.42426i | −0.257921 | − | 0.297657i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.08454 | − | 13.3233i | 0.214719 | − | 0.470168i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.7978 | + | 10.0946i | 0.979744 | + | 0.355788i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.73465 | − | 14.7468i | 0.237071 | − | 0.519113i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.71151 | + | 10.0536i | 0.306280 | + | 0.353466i | 0.887935 | − | 0.459970i | \(-0.152140\pi\) |
−0.581654 | + | 0.813436i | \(0.697594\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0940 | − | 34.7303i | 1.05674 | − | 1.21955i | 0.0819035 | − | 0.996640i | \(-0.473900\pi\) |
0.974840 | − | 0.222907i | \(-0.0715545\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.16510 | − | 1.22298i | 0.146077 | − | 0.0428919i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.82075 | − | 26.5739i | −0.133835 | − | 0.930842i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.23123 | − | 15.8342i | −0.252989 | − | 0.553968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.1984 | − | 9.76742i | −0.531075 | − | 0.341301i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.84569 | − | 47.6128i | 0.238916 | − | 1.66170i | −0.418534 | − | 0.908201i | \(-0.637456\pi\) |
0.657451 | − | 0.753498i | \(-0.271635\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.2085 | − | 15.5579i | 0.843856 | − | 0.542313i | −0.0457968 | − | 0.998951i | \(-0.514583\pi\) |
0.889653 | + | 0.456637i | \(0.150946\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.19909 | − | 0.939338i | −0.111378 | − | 0.0327035i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.0915 | 1.63753 | 0.818766 | − | 0.574128i | \(-0.194659\pi\) | ||||
0.818766 | + | 0.574128i | \(0.194659\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.9669 | −0.971330 | −0.485665 | − | 0.874145i | \(-0.661423\pi\) | ||||
−0.485665 | + | 0.874145i | \(0.661423\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.4423 | − | 8.05780i | −0.951964 | − | 0.279522i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.95133 | + | 1.89670i | −0.102257 | + | 0.0657169i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.33934 | + | 44.0911i | −0.219382 | + | 1.52584i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.87893 | − | 1.85017i | −0.0995103 | − | 0.0639514i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.71830 | + | 16.9007i | 0.266465 | + | 0.583477i | 0.994812 | − | 0.101731i | \(-0.0324382\pi\) |
−0.728347 | + | 0.685209i | \(0.759711\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.53686 | + | 10.6891i | 0.0529952 | + | 0.368590i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.8702 | − | 3.19177i | 0.374388 | − | 0.109930i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.8454 | − | 20.5947i | 0.613899 | − | 0.708478i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.2674 | − | 18.7736i | −0.558955 | − | 0.645069i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.21591 | + | 4.85217i | −0.0760499 | + | 0.166526i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.1975 | + | 3.89743i | −0.589524 | + | 0.133602i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.1531 | − | 39.7498i | 0.621551 | − | 1.36101i | −0.292834 | − | 0.956163i | \(-0.594598\pi\) |
0.914386 | − | 0.404844i | \(-0.132674\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.61203 | + | 6.47663i | 0.191927 | + | 0.221496i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.5393 | − | 27.1658i | 0.804087 | − | 0.927966i | −0.194511 | − | 0.980900i | \(-0.562312\pi\) |
0.998598 | + | 0.0529347i | \(0.0168575\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.6711 | − | 7.83135i | 0.910008 | − | 0.267202i | 0.206964 | − | 0.978349i | \(-0.433642\pi\) |
0.703044 | + | 0.711146i | \(0.251824\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.41642 | − | 23.7618i | −0.116431 | − | 0.809798i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.79661 | − | 6.12373i | −0.0951979 | − | 0.208454i | 0.856042 | − | 0.516906i | \(-0.172916\pi\) |
−0.951240 | + | 0.308452i | \(0.900189\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.7432 | + | 15.2589i | 0.807294 | + | 0.518817i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.33758 | − | 16.2582i | 0.0793884 | − | 0.552158i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.3140 | + | 6.62839i | −0.349878 | + | 0.224853i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.5408 | + | 9.26122i | 1.06872 | + | 0.313804i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.62022 | 0.257906 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −41.4998 | −1.40295 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.0177 | − | 3.52871i | −0.405808 | − | 0.119156i | 0.0724571 | − | 0.997372i | \(-0.476916\pi\) |
−0.478265 | + | 0.878216i | \(0.658734\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.8995 | + | 12.7886i | −0.671194 | + | 0.431350i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.25497 | − | 29.5939i | 0.143353 | − | 0.997045i | −0.783438 | − | 0.621470i | \(-0.786536\pi\) |
0.926792 | − | 0.375576i | \(-0.122555\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.2520 | + | 10.4445i | 0.546923 | + | 0.351486i | 0.784741 | − | 0.619824i | \(-0.212796\pi\) |
−0.237818 | + | 0.971310i | \(0.576432\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.11738 | − | 17.7746i | −0.272863 | − | 0.597486i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.50812 | + | 52.2201i | 0.252098 | + | 1.75338i | 0.585572 | + | 0.810620i | \(0.300870\pi\) |
−0.333474 | + | 0.942759i | \(0.608221\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.18481 | − | 1.22877i | 0.140354 | − | 0.0412116i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.26225 | − | 1.45671i | 0.0422869 | − | 0.0488017i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.1255 | − | 37.0748i | −1.07504 | − | 1.24066i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.6289 | − | 29.8430i | 0.455562 | − | 0.997543i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.4024 | + | 20.2078i | 0.514270 | + | 0.674720i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.06504 | + | 13.2806i | −0.202280 | + | 0.442932i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.90345 | + | 4.50483i | 0.130043 | + | 0.150078i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.20264 | + | 9.46636i | −0.272967 | + | 0.315021i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −46.1555 | + | 13.5525i | −1.53426 | + | 0.450500i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.829035 | − | 5.76607i | −0.0275277 | − | 0.191459i | 0.971418 | − | 0.237377i | \(-0.0762878\pi\) |
−0.998945 | + | 0.0459181i | \(0.985379\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.70207 | + | 8.10641i | 0.122790 | + | 0.268873i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.2223 | − | 19.4227i | −1.00131 | − | 0.643503i | −0.0661796 | − | 0.997808i | \(-0.521081\pi\) |
−0.935130 | + | 0.354305i | \(0.884717\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.68255 | + | 18.6576i | −0.0887795 | + | 0.617475i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 19.6205 | − | 12.6094i | 0.648635 | − | 0.416852i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −32.9966 | − | 9.68868i | −1.08964 | − | 0.319949i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.76019 | −0.190011 | −0.0950055 | − | 0.995477i | \(-0.530287\pi\) | ||||
−0.0950055 | + | 0.995477i | \(0.530287\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.5823 | −0.645257 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 75.1950 | + | 22.0792i | 2.47507 | + | 0.726747i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.35050 | − | 3.43856i | 0.175923 | − | 0.113059i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.125968 | − | 0.876128i | 0.00413734 | − | 0.0287758i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.6393 | + | 10.6934i | 0.545917 | + | 0.350839i | 0.784349 | − | 0.620320i | \(-0.212997\pi\) |
−0.238432 | + | 0.971159i | \(0.576634\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.11127 | + | 19.9509i | 0.298610 | + | 0.653864i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.273199 | + | 1.90014i | 0.00894412 | + | 0.0622077i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.53514 | − | 0.744384i | 0.0829080 | − | 0.0243440i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.359201 | + | 0.414540i | −0.0117346 | + | 0.0135424i | −0.761587 | − | 0.648063i | \(-0.775579\pi\) |
0.749852 | + | 0.661606i | \(0.230125\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.30747 | + | 9.58733i | 0.271104 | + | 0.312871i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.7468 | − | 41.0498i | 0.611129 | − | 1.33819i | −0.310670 | − | 0.950518i | \(-0.600553\pi\) |
0.921799 | − | 0.387669i | \(-0.126719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.89058 | + | 33.0514i | −0.224388 | + | 1.07630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.56170 | − | 5.60934i | 0.0833320 | − | 0.182472i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.55059 | − | 2.94354i | −0.0828832 | − | 0.0956523i | 0.712793 | − | 0.701374i | \(-0.247430\pi\) |
−0.795676 | + | 0.605722i | \(0.792884\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.3641 | − | 30.4258i | 0.855815 | − | 0.987663i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.99816 | + | 0.880339i | −0.0972220 | + | 0.0285470i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.86795 | + | 47.7677i | 0.222475 | + | 1.54735i | 0.728632 | + | 0.684905i | \(0.240157\pi\) |
−0.506157 | + | 0.862441i | \(0.668934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.6250 | + | 40.7831i | 0.602692 | + | 1.31971i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.91783 | − | 4.44582i | −0.223622 | − | 0.143713i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.16966 | − | 22.0455i | 0.102354 | − | 0.711886i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.2266 | + | 10.4282i | −0.523440 | + | 0.336394i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.59185 | + | 2.22917i | 0.244644 | + | 0.0718340i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.53381 | 0.274713 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −52.3950 | −1.68491 | −0.842456 | − | 0.538766i | \(-0.818891\pi\) | ||||
−0.842456 | + | 0.538766i | \(0.818891\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.44667 | + | 1.01203i | 0.110723 | + | 0.0325112i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.372738 | − | 0.239544i | 0.0119617 | − | 0.00768733i | −0.534646 | − | 0.845076i | \(-0.679555\pi\) |
0.546608 | + | 0.837389i | \(0.315919\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.15077 | + | 28.8692i | −0.133067 | + | 0.925504i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.70957 | − | 4.95464i | −0.246904 | − | 0.158676i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.8870 | + | 47.9259i | 0.700228 | + | 1.53329i | 0.839695 | + | 0.543058i | \(0.182734\pi\) |
−0.139467 | + | 0.990227i | \(0.544539\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.05773 | + | 21.2670i | 0.0977255 | + | 0.679696i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.68865 | − | 0.495831i | 0.0539143 | − | 0.0158307i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.4554 | + | 12.0662i | −0.333475 | + | 0.384851i | −0.897580 | − | 0.440853i | \(-0.854676\pi\) |
0.564104 | + | 0.825704i | \(0.309222\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.1830 | − | 15.2140i | −0.420046 | − | 0.484758i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.6642 | + | 32.1101i | −0.466767 | + | 1.02208i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.3876 | − | 8.57617i | 0.489299 | − | 0.272706i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.03107 | + | 19.7753i | −0.286881 | + | 0.628183i | −0.997125 | − | 0.0757732i | \(-0.975857\pi\) |
0.710244 | + | 0.703956i | \(0.248585\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.42732 | + | 9.72565i | 0.267433 | + | 0.308634i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.34129 | + | 10.7804i | −0.296139 | + | 0.341762i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.8973 | + | 9.07225i | −0.978526 | + | 0.287321i | −0.731616 | − | 0.681717i | \(-0.761233\pi\) |
−0.246910 | + | 0.969038i | \(0.579415\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.523273 | + | 3.63944i | 0.0165556 | + | 0.115147i |
(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 | 276.2.i.a.121.1 | yes | 20 | |
3.2 | odd | 2 | 828.2.q.c.397.2 | 20 | |||
23.2 | even | 11 | 6348.2.a.s.1.3 | 10 | |||
23.4 | even | 11 | inner | 276.2.i.a.73.1 | ✓ | 20 | |
23.21 | odd | 22 | 6348.2.a.t.1.8 | 10 | |||
69.50 | odd | 22 | 828.2.q.c.73.2 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.73.1 | ✓ | 20 | 23.4 | even | 11 | inner | |
276.2.i.a.121.1 | yes | 20 | 1.1 | even | 1 | trivial | |
828.2.q.c.73.2 | 20 | 69.50 | odd | 22 | |||
828.2.q.c.397.2 | 20 | 3.2 | odd | 2 | |||
6348.2.a.s.1.3 | 10 | 23.2 | even | 11 | |||
6348.2.a.t.1.8 | 10 | 23.21 | odd | 22 |