Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
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: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65190 | −1.87517 | −0.937587 | − | 0.347750i | \(-0.886946\pi\) | ||||
−0.937587 | + | 0.347750i | \(0.886946\pi\) | |||||||
\(3\) | 1.08303 | 0.625286 | 0.312643 | − | 0.949871i | \(-0.398786\pi\) | ||||
0.312643 | + | 0.949871i | \(0.398786\pi\) | |||||||
\(4\) | 5.03256 | 2.51628 | ||||||||
\(5\) | 0.484312 | 0.216591 | 0.108295 | − | 0.994119i | \(-0.465461\pi\) | ||||
0.108295 | + | 0.994119i | \(0.465461\pi\) | |||||||
\(6\) | −2.87208 | −1.17252 | ||||||||
\(7\) | 1.56821 | 0.592728 | 0.296364 | − | 0.955075i | \(-0.404226\pi\) | ||||
0.296364 | + | 0.955075i | \(0.404226\pi\) | |||||||
\(8\) | −8.04203 | −2.84329 | ||||||||
\(9\) | −1.82705 | −0.609017 | ||||||||
\(10\) | −1.28435 | −0.406146 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 5.45040 | 1.57339 | ||||||||
\(13\) | 1.02036 | 0.282998 | 0.141499 | − | 0.989938i | \(-0.454808\pi\) | ||||
0.141499 | + | 0.989938i | \(0.454808\pi\) | |||||||
\(14\) | −4.15873 | −1.11147 | ||||||||
\(15\) | 0.524523 | 0.135431 | ||||||||
\(16\) | 11.2615 | 2.81538 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 4.84515 | 1.14201 | ||||||||
\(19\) | −7.33635 | −1.68307 | −0.841537 | − | 0.540200i | \(-0.818349\pi\) | ||||
−0.841537 | + | 0.540200i | \(0.818349\pi\) | |||||||
\(20\) | 2.43733 | 0.545003 | ||||||||
\(21\) | 1.69842 | 0.370625 | ||||||||
\(22\) | −2.65190 | −0.565386 | ||||||||
\(23\) | 4.79280 | 0.999367 | 0.499684 | − | 0.866208i | \(-0.333450\pi\) | ||||
0.499684 | + | 0.866208i | \(0.333450\pi\) | |||||||
\(24\) | −8.70974 | −1.77787 | ||||||||
\(25\) | −4.76544 | −0.953088 | ||||||||
\(26\) | −2.70590 | −0.530670 | ||||||||
\(27\) | −5.22783 | −1.00610 | ||||||||
\(28\) | 7.89211 | 1.49147 | ||||||||
\(29\) | −6.14051 | −1.14026 | −0.570132 | − | 0.821553i | \(-0.693108\pi\) | ||||
−0.570132 | + | 0.821553i | \(0.693108\pi\) | |||||||
\(30\) | −1.39098 | −0.253957 | ||||||||
\(31\) | −8.14245 | −1.46243 | −0.731214 | − | 0.682148i | \(-0.761046\pi\) | ||||
−0.731214 | + | 0.682148i | \(0.761046\pi\) | |||||||
\(32\) | −13.7803 | −2.43604 | ||||||||
\(33\) | 1.08303 | 0.188531 | ||||||||
\(34\) | −2.65190 | −0.454797 | ||||||||
\(35\) | 0.759504 | 0.128380 | ||||||||
\(36\) | −9.19474 | −1.53246 | ||||||||
\(37\) | 7.46703 | 1.22757 | 0.613786 | − | 0.789472i | \(-0.289646\pi\) | ||||
0.613786 | + | 0.789472i | \(0.289646\pi\) | |||||||
\(38\) | 19.4552 | 3.15606 | ||||||||
\(39\) | 1.10508 | 0.176955 | ||||||||
\(40\) | −3.89485 | −0.615830 | ||||||||
\(41\) | −10.1278 | −1.58170 | −0.790852 | − | 0.612008i | \(-0.790362\pi\) | ||||
−0.790852 | + | 0.612008i | \(0.790362\pi\) | |||||||
\(42\) | −4.50402 | −0.694986 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 5.03256 | 0.758687 | ||||||||
\(45\) | −0.884863 | −0.131908 | ||||||||
\(46\) | −12.7100 | −1.87399 | ||||||||
\(47\) | 1.41818 | 0.206863 | 0.103432 | − | 0.994637i | \(-0.467018\pi\) | ||||
0.103432 | + | 0.994637i | \(0.467018\pi\) | |||||||
\(48\) | 12.1965 | 1.76042 | ||||||||
\(49\) | −4.54071 | −0.648673 | ||||||||
\(50\) | 12.6375 | 1.78721 | ||||||||
\(51\) | 1.08303 | 0.151654 | ||||||||
\(52\) | 5.13504 | 0.712102 | ||||||||
\(53\) | 10.8066 | 1.48441 | 0.742203 | − | 0.670175i | \(-0.233781\pi\) | ||||
0.742203 | + | 0.670175i | \(0.233781\pi\) | |||||||
\(54\) | 13.8637 | 1.88661 | ||||||||
\(55\) | 0.484312 | 0.0653046 | ||||||||
\(56\) | −12.6116 | −1.68530 | ||||||||
\(57\) | −7.94547 | −1.05240 | ||||||||
\(58\) | 16.2840 | 2.13819 | ||||||||
\(59\) | −1.27321 | −0.165758 | −0.0828792 | − | 0.996560i | \(-0.526412\pi\) | ||||
−0.0828792 | + | 0.996560i | \(0.526412\pi\) | |||||||
\(60\) | 2.63969 | 0.340783 | ||||||||
\(61\) | 5.68853 | 0.728342 | 0.364171 | − | 0.931332i | \(-0.381352\pi\) | ||||
0.364171 | + | 0.931332i | \(0.381352\pi\) | |||||||
\(62\) | 21.5929 | 2.74231 | ||||||||
\(63\) | −2.86520 | −0.360982 | ||||||||
\(64\) | 14.0210 | 1.75263 | ||||||||
\(65\) | 0.494174 | 0.0612948 | ||||||||
\(66\) | −2.87208 | −0.353528 | ||||||||
\(67\) | 11.3268 | 1.38379 | 0.691893 | − | 0.722000i | \(-0.256777\pi\) | ||||
0.691893 | + | 0.722000i | \(0.256777\pi\) | |||||||
\(68\) | 5.03256 | 0.610287 | ||||||||
\(69\) | 5.19073 | 0.624891 | ||||||||
\(70\) | −2.01413 | −0.240734 | ||||||||
\(71\) | 4.89737 | 0.581211 | 0.290605 | − | 0.956843i | \(-0.406143\pi\) | ||||
0.290605 | + | 0.956843i | \(0.406143\pi\) | |||||||
\(72\) | 14.6932 | 1.73161 | ||||||||
\(73\) | 1.41558 | 0.165682 | 0.0828408 | − | 0.996563i | \(-0.473601\pi\) | ||||
0.0828408 | + | 0.996563i | \(0.473601\pi\) | |||||||
\(74\) | −19.8018 | −2.30191 | ||||||||
\(75\) | −5.16110 | −0.595953 | ||||||||
\(76\) | −36.9206 | −4.23508 | ||||||||
\(77\) | 1.56821 | 0.178714 | ||||||||
\(78\) | −2.93056 | −0.331821 | ||||||||
\(79\) | −8.10888 | −0.912320 | −0.456160 | − | 0.889898i | \(-0.650775\pi\) | ||||
−0.456160 | + | 0.889898i | \(0.650775\pi\) | |||||||
\(80\) | 5.45409 | 0.609786 | ||||||||
\(81\) | −0.180729 | −0.0200810 | ||||||||
\(82\) | 26.8580 | 2.96597 | ||||||||
\(83\) | 6.65886 | 0.730905 | 0.365452 | − | 0.930830i | \(-0.380914\pi\) | ||||
0.365452 | + | 0.930830i | \(0.380914\pi\) | |||||||
\(84\) | 8.54738 | 0.932595 | ||||||||
\(85\) | 0.484312 | 0.0525310 | ||||||||
\(86\) | −2.65190 | −0.285961 | ||||||||
\(87\) | −6.65034 | −0.712991 | ||||||||
\(88\) | −8.04203 | −0.857284 | ||||||||
\(89\) | 11.4605 | 1.21481 | 0.607405 | − | 0.794392i | \(-0.292210\pi\) | ||||
0.607405 | + | 0.794392i | \(0.292210\pi\) | |||||||
\(90\) | 2.34657 | 0.247350 | ||||||||
\(91\) | 1.60015 | 0.167741 | ||||||||
\(92\) | 24.1200 | 2.51469 | ||||||||
\(93\) | −8.81850 | −0.914436 | ||||||||
\(94\) | −3.76087 | −0.387905 | ||||||||
\(95\) | −3.55308 | −0.364538 | ||||||||
\(96\) | −14.9245 | −1.52322 | ||||||||
\(97\) | 1.82310 | 0.185107 | 0.0925537 | − | 0.995708i | \(-0.470497\pi\) | ||||
0.0925537 | + | 0.995708i | \(0.470497\pi\) | |||||||
\(98\) | 12.0415 | 1.21638 | ||||||||
\(99\) | −1.82705 | −0.183626 | ||||||||
\(100\) | −23.9824 | −2.39824 | ||||||||
\(101\) | 14.2470 | 1.41763 | 0.708813 | − | 0.705396i | \(-0.249231\pi\) | ||||
0.708813 | + | 0.705396i | \(0.249231\pi\) | |||||||
\(102\) | −2.87208 | −0.284378 | ||||||||
\(103\) | −3.92423 | −0.386666 | −0.193333 | − | 0.981133i | \(-0.561930\pi\) | ||||
−0.193333 | + | 0.981133i | \(0.561930\pi\) | |||||||
\(104\) | −8.20580 | −0.804645 | ||||||||
\(105\) | 0.822563 | 0.0802740 | ||||||||
\(106\) | −28.6581 | −2.78352 | ||||||||
\(107\) | 6.86098 | 0.663276 | 0.331638 | − | 0.943407i | \(-0.392399\pi\) | ||||
0.331638 | + | 0.943407i | \(0.392399\pi\) | |||||||
\(108\) | −26.3094 | −2.53162 | ||||||||
\(109\) | −2.06549 | −0.197838 | −0.0989188 | − | 0.995096i | \(-0.531538\pi\) | ||||
−0.0989188 | + | 0.995096i | \(0.531538\pi\) | |||||||
\(110\) | −1.28435 | −0.122458 | ||||||||
\(111\) | 8.08700 | 0.767584 | ||||||||
\(112\) | 17.6605 | 1.66876 | ||||||||
\(113\) | −12.9132 | −1.21477 | −0.607386 | − | 0.794407i | \(-0.707782\pi\) | ||||
−0.607386 | + | 0.794407i | \(0.707782\pi\) | |||||||
\(114\) | 21.0706 | 1.97344 | ||||||||
\(115\) | 2.32121 | 0.216454 | ||||||||
\(116\) | −30.9025 | −2.86922 | ||||||||
\(117\) | −1.86426 | −0.172351 | ||||||||
\(118\) | 3.37643 | 0.310826 | ||||||||
\(119\) | 1.56821 | 0.143758 | ||||||||
\(120\) | −4.21823 | −0.385070 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −15.0854 | −1.36577 | ||||||||
\(123\) | −10.9687 | −0.989017 | ||||||||
\(124\) | −40.9774 | −3.67988 | ||||||||
\(125\) | −4.72952 | −0.423021 | ||||||||
\(126\) | 7.59822 | 0.676903 | ||||||||
\(127\) | 12.5242 | 1.11134 | 0.555672 | − | 0.831402i | \(-0.312461\pi\) | ||||
0.555672 | + | 0.831402i | \(0.312461\pi\) | |||||||
\(128\) | −9.62157 | −0.850435 | ||||||||
\(129\) | 1.08303 | 0.0953553 | ||||||||
\(130\) | −1.31050 | −0.114938 | ||||||||
\(131\) | 9.19874 | 0.803698 | 0.401849 | − | 0.915706i | \(-0.368368\pi\) | ||||
0.401849 | + | 0.915706i | \(0.368368\pi\) | |||||||
\(132\) | 5.45040 | 0.474396 | ||||||||
\(133\) | −11.5049 | −0.997605 | ||||||||
\(134\) | −30.0375 | −2.59484 | ||||||||
\(135\) | −2.53190 | −0.217911 | ||||||||
\(136\) | −8.04203 | −0.689599 | ||||||||
\(137\) | 20.3360 | 1.73742 | 0.868710 | − | 0.495322i | \(-0.164950\pi\) | ||||
0.868710 | + | 0.495322i | \(0.164950\pi\) | |||||||
\(138\) | −13.7653 | −1.17178 | ||||||||
\(139\) | 17.2386 | 1.46216 | 0.731081 | − | 0.682290i | \(-0.239016\pi\) | ||||
0.731081 | + | 0.682290i | \(0.239016\pi\) | |||||||
\(140\) | 3.82225 | 0.323039 | ||||||||
\(141\) | 1.53593 | 0.129349 | ||||||||
\(142\) | −12.9873 | −1.08987 | ||||||||
\(143\) | 1.02036 | 0.0853271 | ||||||||
\(144\) | −20.5754 | −1.71462 | ||||||||
\(145\) | −2.97392 | −0.246971 | ||||||||
\(146\) | −3.75399 | −0.310682 | ||||||||
\(147\) | −4.91772 | −0.405607 | ||||||||
\(148\) | 37.5783 | 3.08891 | ||||||||
\(149\) | −7.08661 | −0.580558 | −0.290279 | − | 0.956942i | \(-0.593748\pi\) | ||||
−0.290279 | + | 0.956942i | \(0.593748\pi\) | |||||||
\(150\) | 13.6867 | 1.11752 | ||||||||
\(151\) | 4.13116 | 0.336189 | 0.168095 | − | 0.985771i | \(-0.446239\pi\) | ||||
0.168095 | + | 0.985771i | \(0.446239\pi\) | |||||||
\(152\) | 58.9991 | 4.78546 | ||||||||
\(153\) | −1.82705 | −0.147708 | ||||||||
\(154\) | −4.15873 | −0.335120 | ||||||||
\(155\) | −3.94349 | −0.316749 | ||||||||
\(156\) | 5.56139 | 0.445267 | ||||||||
\(157\) | 11.0556 | 0.882333 | 0.441167 | − | 0.897425i | \(-0.354565\pi\) | ||||
0.441167 | + | 0.897425i | \(0.354565\pi\) | |||||||
\(158\) | 21.5039 | 1.71076 | ||||||||
\(159\) | 11.7039 | 0.928179 | ||||||||
\(160\) | −6.67399 | −0.527625 | ||||||||
\(161\) | 7.51612 | 0.592353 | ||||||||
\(162\) | 0.479274 | 0.0376553 | ||||||||
\(163\) | 18.9901 | 1.48742 | 0.743708 | − | 0.668504i | \(-0.233065\pi\) | ||||
0.743708 | + | 0.668504i | \(0.233065\pi\) | |||||||
\(164\) | −50.9690 | −3.98001 | ||||||||
\(165\) | 0.524523 | 0.0408341 | ||||||||
\(166\) | −17.6586 | −1.37057 | ||||||||
\(167\) | −15.6790 | −1.21328 | −0.606640 | − | 0.794976i | \(-0.707483\pi\) | ||||
−0.606640 | + | 0.794976i | \(0.707483\pi\) | |||||||
\(168\) | −13.6587 | −1.05379 | ||||||||
\(169\) | −11.9589 | −0.919912 | ||||||||
\(170\) | −1.28435 | −0.0985048 | ||||||||
\(171\) | 13.4039 | 1.02502 | ||||||||
\(172\) | 5.03256 | 0.383729 | ||||||||
\(173\) | 13.5295 | 1.02863 | 0.514316 | − | 0.857601i | \(-0.328046\pi\) | ||||
0.514316 | + | 0.857601i | \(0.328046\pi\) | |||||||
\(174\) | 17.6360 | 1.33698 | ||||||||
\(175\) | −7.47322 | −0.564922 | ||||||||
\(176\) | 11.2615 | 0.848870 | ||||||||
\(177\) | −1.37893 | −0.103646 | ||||||||
\(178\) | −30.3921 | −2.27798 | ||||||||
\(179\) | 25.8414 | 1.93148 | 0.965739 | − | 0.259514i | \(-0.0835625\pi\) | ||||
0.965739 | + | 0.259514i | \(0.0835625\pi\) | |||||||
\(180\) | −4.45313 | −0.331916 | ||||||||
\(181\) | 17.7521 | 1.31950 | 0.659750 | − | 0.751485i | \(-0.270662\pi\) | ||||
0.659750 | + | 0.751485i | \(0.270662\pi\) | |||||||
\(182\) | −4.24342 | −0.314543 | ||||||||
\(183\) | 6.16084 | 0.455422 | ||||||||
\(184\) | −38.5438 | −2.84149 | ||||||||
\(185\) | 3.61637 | 0.265881 | ||||||||
\(186\) | 23.3858 | 1.71473 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 7.13709 | 0.520526 | ||||||||
\(189\) | −8.19834 | −0.596342 | ||||||||
\(190\) | 9.42241 | 0.683573 | ||||||||
\(191\) | 12.6545 | 0.915647 | 0.457824 | − | 0.889043i | \(-0.348629\pi\) | ||||
0.457824 | + | 0.889043i | \(0.348629\pi\) | |||||||
\(192\) | 15.1851 | 1.09589 | ||||||||
\(193\) | −6.34203 | −0.456509 | −0.228255 | − | 0.973601i | \(-0.573302\pi\) | ||||
−0.228255 | + | 0.973601i | \(0.573302\pi\) | |||||||
\(194\) | −4.83466 | −0.347109 | ||||||||
\(195\) | 0.535204 | 0.0383268 | ||||||||
\(196\) | −22.8514 | −1.63224 | ||||||||
\(197\) | 21.3012 | 1.51765 | 0.758823 | − | 0.651297i | \(-0.225775\pi\) | ||||
0.758823 | + | 0.651297i | \(0.225775\pi\) | |||||||
\(198\) | 4.84515 | 0.344330 | ||||||||
\(199\) | −15.1294 | −1.07249 | −0.536247 | − | 0.844061i | \(-0.680158\pi\) | ||||
−0.536247 | + | 0.844061i | \(0.680158\pi\) | |||||||
\(200\) | 38.3238 | 2.70990 | ||||||||
\(201\) | 12.2672 | 0.865262 | ||||||||
\(202\) | −37.7815 | −2.65830 | ||||||||
\(203\) | −9.62961 | −0.675866 | ||||||||
\(204\) | 5.45040 | 0.381604 | ||||||||
\(205\) | −4.90504 | −0.342583 | ||||||||
\(206\) | 10.4066 | 0.725065 | ||||||||
\(207\) | −8.75669 | −0.608632 | ||||||||
\(208\) | 11.4909 | 0.796747 | ||||||||
\(209\) | −7.33635 | −0.507466 | ||||||||
\(210\) | −2.18135 | −0.150528 | ||||||||
\(211\) | −17.8984 | −1.23218 | −0.616090 | − | 0.787676i | \(-0.711284\pi\) | ||||
−0.616090 | + | 0.787676i | \(0.711284\pi\) | |||||||
\(212\) | 54.3851 | 3.73518 | ||||||||
\(213\) | 5.30399 | 0.363423 | ||||||||
\(214\) | −18.1946 | −1.24376 | ||||||||
\(215\) | 0.484312 | 0.0330298 | ||||||||
\(216\) | 42.0424 | 2.86062 | ||||||||
\(217\) | −12.7691 | −0.866822 | ||||||||
\(218\) | 5.47745 | 0.370980 | ||||||||
\(219\) | 1.53312 | 0.103598 | ||||||||
\(220\) | 2.43733 | 0.164325 | ||||||||
\(221\) | 1.02036 | 0.0686371 | ||||||||
\(222\) | −21.4459 | −1.43935 | ||||||||
\(223\) | 15.5531 | 1.04151 | 0.520757 | − | 0.853705i | \(-0.325650\pi\) | ||||
0.520757 | + | 0.853705i | \(0.325650\pi\) | |||||||
\(224\) | −21.6105 | −1.44391 | ||||||||
\(225\) | 8.70671 | 0.580447 | ||||||||
\(226\) | 34.2445 | 2.27791 | ||||||||
\(227\) | 11.9457 | 0.792863 | 0.396431 | − | 0.918064i | \(-0.370249\pi\) | ||||
0.396431 | + | 0.918064i | \(0.370249\pi\) | |||||||
\(228\) | −39.9860 | −2.64814 | ||||||||
\(229\) | 9.02160 | 0.596164 | 0.298082 | − | 0.954540i | \(-0.403653\pi\) | ||||
0.298082 | + | 0.954540i | \(0.403653\pi\) | |||||||
\(230\) | −6.15561 | −0.405889 | ||||||||
\(231\) | 1.69842 | 0.111748 | ||||||||
\(232\) | 49.3821 | 3.24210 | ||||||||
\(233\) | −10.0158 | −0.656155 | −0.328078 | − | 0.944651i | \(-0.606401\pi\) | ||||
−0.328078 | + | 0.944651i | \(0.606401\pi\) | |||||||
\(234\) | 4.94382 | 0.323187 | ||||||||
\(235\) | 0.686843 | 0.0448047 | ||||||||
\(236\) | −6.40753 | −0.417094 | ||||||||
\(237\) | −8.78213 | −0.570461 | ||||||||
\(238\) | −4.15873 | −0.269571 | ||||||||
\(239\) | 10.3697 | 0.670762 | 0.335381 | − | 0.942083i | \(-0.391135\pi\) | ||||
0.335381 | + | 0.942083i | \(0.391135\pi\) | |||||||
\(240\) | 5.90693 | 0.381291 | ||||||||
\(241\) | 7.73951 | 0.498546 | 0.249273 | − | 0.968433i | \(-0.419808\pi\) | ||||
0.249273 | + | 0.968433i | \(0.419808\pi\) | |||||||
\(242\) | −2.65190 | −0.170470 | ||||||||
\(243\) | 15.4878 | 0.993540 | ||||||||
\(244\) | 28.6279 | 1.83271 | ||||||||
\(245\) | −2.19912 | −0.140497 | ||||||||
\(246\) | 29.0879 | 1.85458 | ||||||||
\(247\) | −7.48574 | −0.476306 | ||||||||
\(248\) | 65.4819 | 4.15810 | ||||||||
\(249\) | 7.21173 | 0.457025 | ||||||||
\(250\) | 12.5422 | 0.793239 | ||||||||
\(251\) | 0.232469 | 0.0146733 | 0.00733665 | − | 0.999973i | \(-0.497665\pi\) | ||||
0.00733665 | + | 0.999973i | \(0.497665\pi\) | |||||||
\(252\) | −14.4193 | −0.908330 | ||||||||
\(253\) | 4.79280 | 0.301321 | ||||||||
\(254\) | −33.2129 | −2.08396 | ||||||||
\(255\) | 0.524523 | 0.0328469 | ||||||||
\(256\) | −2.52660 | −0.157912 | ||||||||
\(257\) | 16.7108 | 1.04239 | 0.521196 | − | 0.853437i | \(-0.325486\pi\) | ||||
0.521196 | + | 0.853437i | \(0.325486\pi\) | |||||||
\(258\) | −2.87208 | −0.178808 | ||||||||
\(259\) | 11.7099 | 0.727616 | ||||||||
\(260\) | 2.48696 | 0.154235 | ||||||||
\(261\) | 11.2190 | 0.694440 | ||||||||
\(262\) | −24.3941 | −1.50707 | ||||||||
\(263\) | −21.4264 | −1.32121 | −0.660604 | − | 0.750734i | \(-0.729700\pi\) | ||||
−0.660604 | + | 0.750734i | \(0.729700\pi\) | |||||||
\(264\) | −8.70974 | −0.536048 | ||||||||
\(265\) | 5.23379 | 0.321509 | ||||||||
\(266\) | 30.5099 | 1.87068 | ||||||||
\(267\) | 12.4120 | 0.759604 | ||||||||
\(268\) | 57.0027 | 3.48199 | ||||||||
\(269\) | 8.20255 | 0.500118 | 0.250059 | − | 0.968231i | \(-0.419550\pi\) | ||||
0.250059 | + | 0.968231i | \(0.419550\pi\) | |||||||
\(270\) | 6.71434 | 0.408622 | ||||||||
\(271\) | −6.08472 | −0.369621 | −0.184810 | − | 0.982774i | \(-0.559167\pi\) | ||||
−0.184810 | + | 0.982774i | \(0.559167\pi\) | |||||||
\(272\) | 11.2615 | 0.682830 | ||||||||
\(273\) | 1.73300 | 0.104886 | ||||||||
\(274\) | −53.9289 | −3.25796 | ||||||||
\(275\) | −4.76544 | −0.287367 | ||||||||
\(276\) | 26.1227 | 1.57240 | ||||||||
\(277\) | −24.3509 | −1.46310 | −0.731552 | − | 0.681786i | \(-0.761204\pi\) | ||||
−0.731552 | + | 0.681786i | \(0.761204\pi\) | |||||||
\(278\) | −45.7151 | −2.74181 | ||||||||
\(279\) | 14.8767 | 0.890643 | ||||||||
\(280\) | −6.10795 | −0.365020 | ||||||||
\(281\) | 30.4146 | 1.81438 | 0.907191 | − | 0.420719i | \(-0.138222\pi\) | ||||
0.907191 | + | 0.420719i | \(0.138222\pi\) | |||||||
\(282\) | −4.07313 | −0.242551 | ||||||||
\(283\) | −6.60928 | −0.392881 | −0.196440 | − | 0.980516i | \(-0.562938\pi\) | ||||
−0.196440 | + | 0.980516i | \(0.562938\pi\) | |||||||
\(284\) | 24.6463 | 1.46249 | ||||||||
\(285\) | −3.84808 | −0.227941 | ||||||||
\(286\) | −2.70590 | −0.160003 | ||||||||
\(287\) | −15.8826 | −0.937520 | ||||||||
\(288\) | 25.1774 | 1.48359 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 7.88653 | 0.463113 | ||||||||
\(291\) | 1.97446 | 0.115745 | ||||||||
\(292\) | 7.12401 | 0.416901 | ||||||||
\(293\) | 26.9491 | 1.57439 | 0.787193 | − | 0.616707i | \(-0.211534\pi\) | ||||
0.787193 | + | 0.616707i | \(0.211534\pi\) | |||||||
\(294\) | 13.0413 | 0.760583 | ||||||||
\(295\) | −0.616633 | −0.0359018 | ||||||||
\(296\) | −60.0501 | −3.49034 | ||||||||
\(297\) | −5.22783 | −0.303349 | ||||||||
\(298\) | 18.7930 | 1.08865 | ||||||||
\(299\) | 4.89040 | 0.282819 | ||||||||
\(300\) | −25.9736 | −1.49958 | ||||||||
\(301\) | 1.56821 | 0.0903902 | ||||||||
\(302\) | −10.9554 | −0.630413 | ||||||||
\(303\) | 15.4299 | 0.886423 | ||||||||
\(304\) | −82.6185 | −4.73849 | ||||||||
\(305\) | 2.75502 | 0.157752 | ||||||||
\(306\) | 4.84515 | 0.276979 | ||||||||
\(307\) | 32.9525 | 1.88070 | 0.940349 | − | 0.340212i | \(-0.110499\pi\) | ||||
0.940349 | + | 0.340212i | \(0.110499\pi\) | |||||||
\(308\) | 7.89211 | 0.449695 | ||||||||
\(309\) | −4.25005 | −0.241777 | ||||||||
\(310\) | 10.4577 | 0.593959 | ||||||||
\(311\) | 5.88050 | 0.333453 | 0.166726 | − | 0.986003i | \(-0.446680\pi\) | ||||
0.166726 | + | 0.986003i | \(0.446680\pi\) | |||||||
\(312\) | −8.88710 | −0.503133 | ||||||||
\(313\) | −29.2161 | −1.65139 | −0.825695 | − | 0.564117i | \(-0.809217\pi\) | ||||
−0.825695 | + | 0.564117i | \(0.809217\pi\) | |||||||
\(314\) | −29.3183 | −1.65453 | ||||||||
\(315\) | −1.38765 | −0.0781853 | ||||||||
\(316\) | −40.8084 | −2.29565 | ||||||||
\(317\) | 25.6428 | 1.44024 | 0.720121 | − | 0.693848i | \(-0.244086\pi\) | ||||
0.720121 | + | 0.693848i | \(0.244086\pi\) | |||||||
\(318\) | −31.0375 | −1.74050 | ||||||||
\(319\) | −6.14051 | −0.343802 | ||||||||
\(320\) | 6.79054 | 0.379603 | ||||||||
\(321\) | 7.43063 | 0.414737 | ||||||||
\(322\) | −19.9320 | −1.11077 | ||||||||
\(323\) | −7.33635 | −0.408205 | ||||||||
\(324\) | −0.909527 | −0.0505293 | ||||||||
\(325\) | −4.86248 | −0.269722 | ||||||||
\(326\) | −50.3597 | −2.78917 | ||||||||
\(327\) | −2.23698 | −0.123705 | ||||||||
\(328\) | 81.4484 | 4.49724 | ||||||||
\(329\) | 2.22401 | 0.122614 | ||||||||
\(330\) | −1.39098 | −0.0765710 | ||||||||
\(331\) | 31.2118 | 1.71556 | 0.857779 | − | 0.514019i | \(-0.171844\pi\) | ||||
0.857779 | + | 0.514019i | \(0.171844\pi\) | |||||||
\(332\) | 33.5111 | 1.83916 | ||||||||
\(333\) | −13.6426 | −0.747612 | ||||||||
\(334\) | 41.5792 | 2.27511 | ||||||||
\(335\) | 5.48570 | 0.299716 | ||||||||
\(336\) | 19.1268 | 1.04345 | ||||||||
\(337\) | −31.9453 | −1.74017 | −0.870087 | − | 0.492899i | \(-0.835937\pi\) | ||||
−0.870087 | + | 0.492899i | \(0.835937\pi\) | |||||||
\(338\) | 31.7137 | 1.72500 | ||||||||
\(339\) | −13.9853 | −0.759580 | ||||||||
\(340\) | 2.43733 | 0.132183 | ||||||||
\(341\) | −8.14245 | −0.440938 | ||||||||
\(342\) | −35.5457 | −1.92209 | ||||||||
\(343\) | −18.0983 | −0.977215 | ||||||||
\(344\) | −8.04203 | −0.433597 | ||||||||
\(345\) | 2.51393 | 0.135346 | ||||||||
\(346\) | −35.8790 | −1.92887 | ||||||||
\(347\) | −0.821024 | −0.0440749 | −0.0220374 | − | 0.999757i | \(-0.507015\pi\) | ||||
−0.0220374 | + | 0.999757i | \(0.507015\pi\) | |||||||
\(348\) | −33.4682 | −1.79408 | ||||||||
\(349\) | −25.0895 | −1.34301 | −0.671505 | − | 0.741000i | \(-0.734352\pi\) | ||||
−0.671505 | + | 0.741000i | \(0.734352\pi\) | |||||||
\(350\) | 19.8182 | 1.05933 | ||||||||
\(351\) | −5.33429 | −0.284723 | ||||||||
\(352\) | −13.7803 | −0.734495 | ||||||||
\(353\) | −8.68853 | −0.462444 | −0.231222 | − | 0.972901i | \(-0.574272\pi\) | ||||
−0.231222 | + | 0.972901i | \(0.574272\pi\) | |||||||
\(354\) | 3.65677 | 0.194355 | ||||||||
\(355\) | 2.37185 | 0.125885 | ||||||||
\(356\) | 57.6756 | 3.05680 | ||||||||
\(357\) | 1.69842 | 0.0898897 | ||||||||
\(358\) | −68.5288 | −3.62186 | ||||||||
\(359\) | 12.1388 | 0.640660 | 0.320330 | − | 0.947306i | \(-0.396206\pi\) | ||||
0.320330 | + | 0.947306i | \(0.396206\pi\) | |||||||
\(360\) | 7.11610 | 0.375051 | ||||||||
\(361\) | 34.8220 | 1.83274 | ||||||||
\(362\) | −47.0766 | −2.47429 | ||||||||
\(363\) | 1.08303 | 0.0568442 | ||||||||
\(364\) | 8.05283 | 0.422083 | ||||||||
\(365\) | 0.685585 | 0.0358851 | ||||||||
\(366\) | −16.3379 | −0.853996 | ||||||||
\(367\) | −11.1331 | −0.581141 | −0.290571 | − | 0.956854i | \(-0.593845\pi\) | ||||
−0.290571 | + | 0.956854i | \(0.593845\pi\) | |||||||
\(368\) | 53.9742 | 2.81360 | ||||||||
\(369\) | 18.5041 | 0.963284 | ||||||||
\(370\) | −9.59025 | −0.498573 | ||||||||
\(371\) | 16.9471 | 0.879850 | ||||||||
\(372\) | −44.3796 | −2.30098 | ||||||||
\(373\) | −14.6057 | −0.756255 | −0.378127 | − | 0.925754i | \(-0.623432\pi\) | ||||
−0.378127 | + | 0.925754i | \(0.623432\pi\) | |||||||
\(374\) | −2.65190 | −0.137126 | ||||||||
\(375\) | −5.12220 | −0.264509 | ||||||||
\(376\) | −11.4051 | −0.588172 | ||||||||
\(377\) | −6.26555 | −0.322692 | ||||||||
\(378\) | 21.7412 | 1.11824 | ||||||||
\(379\) | 3.50121 | 0.179845 | 0.0899226 | − | 0.995949i | \(-0.471338\pi\) | ||||
0.0899226 | + | 0.995949i | \(0.471338\pi\) | |||||||
\(380\) | −17.8811 | −0.917281 | ||||||||
\(381\) | 13.5641 | 0.694908 | ||||||||
\(382\) | −33.5584 | −1.71700 | ||||||||
\(383\) | −22.2719 | −1.13804 | −0.569019 | − | 0.822324i | \(-0.692677\pi\) | ||||
−0.569019 | + | 0.822324i | \(0.692677\pi\) | |||||||
\(384\) | −10.4204 | −0.531765 | ||||||||
\(385\) | 0.759504 | 0.0387079 | ||||||||
\(386\) | 16.8184 | 0.856034 | ||||||||
\(387\) | −1.82705 | −0.0928742 | ||||||||
\(388\) | 9.17484 | 0.465782 | ||||||||
\(389\) | −4.82631 | −0.244704 | −0.122352 | − | 0.992487i | \(-0.539044\pi\) | ||||
−0.122352 | + | 0.992487i | \(0.539044\pi\) | |||||||
\(390\) | −1.41931 | −0.0718694 | ||||||||
\(391\) | 4.79280 | 0.242382 | ||||||||
\(392\) | 36.5166 | 1.84437 | ||||||||
\(393\) | 9.96249 | 0.502541 | ||||||||
\(394\) | −56.4885 | −2.84585 | ||||||||
\(395\) | −3.92723 | −0.197600 | ||||||||
\(396\) | −9.19474 | −0.462053 | ||||||||
\(397\) | −5.16985 | −0.259468 | −0.129734 | − | 0.991549i | \(-0.541412\pi\) | ||||
−0.129734 | + | 0.991549i | \(0.541412\pi\) | |||||||
\(398\) | 40.1216 | 2.01111 | ||||||||
\(399\) | −12.4602 | −0.623789 | ||||||||
\(400\) | −53.6661 | −2.68331 | ||||||||
\(401\) | 11.5195 | 0.575256 | 0.287628 | − | 0.957742i | \(-0.407133\pi\) | ||||
0.287628 | + | 0.957742i | \(0.407133\pi\) | |||||||
\(402\) | −32.5314 | −1.62252 | ||||||||
\(403\) | −8.30826 | −0.413864 | ||||||||
\(404\) | 71.6987 | 3.56715 | ||||||||
\(405\) | −0.0875291 | −0.00434935 | ||||||||
\(406\) | 25.5367 | 1.26737 | ||||||||
\(407\) | 7.46703 | 0.370127 | ||||||||
\(408\) | −8.70974 | −0.431197 | ||||||||
\(409\) | −13.5590 | −0.670449 | −0.335224 | − | 0.942138i | \(-0.608812\pi\) | ||||
−0.335224 | + | 0.942138i | \(0.608812\pi\) | |||||||
\(410\) | 13.0077 | 0.642402 | ||||||||
\(411\) | 22.0244 | 1.08638 | ||||||||
\(412\) | −19.7489 | −0.972958 | ||||||||
\(413\) | −1.99667 | −0.0982497 | ||||||||
\(414\) | 23.2218 | 1.14129 | ||||||||
\(415\) | 3.22497 | 0.158307 | ||||||||
\(416\) | −14.0610 | −0.689395 | ||||||||
\(417\) | 18.6699 | 0.914270 | ||||||||
\(418\) | 19.4552 | 0.951587 | ||||||||
\(419\) | 1.91395 | 0.0935028 | 0.0467514 | − | 0.998907i | \(-0.485113\pi\) | ||||
0.0467514 | + | 0.998907i | \(0.485113\pi\) | |||||||
\(420\) | 4.13960 | 0.201992 | ||||||||
\(421\) | 10.6250 | 0.517832 | 0.258916 | − | 0.965900i | \(-0.416635\pi\) | ||||
0.258916 | + | 0.965900i | \(0.416635\pi\) | |||||||
\(422\) | 47.4648 | 2.31055 | ||||||||
\(423\) | −2.59109 | −0.125983 | ||||||||
\(424\) | −86.9074 | −4.22060 | ||||||||
\(425\) | −4.76544 | −0.231158 | ||||||||
\(426\) | −14.0656 | −0.681482 | ||||||||
\(427\) | 8.92082 | 0.431709 | ||||||||
\(428\) | 34.5283 | 1.66899 | ||||||||
\(429\) | 1.10508 | 0.0533538 | ||||||||
\(430\) | −1.28435 | −0.0619367 | ||||||||
\(431\) | −36.9115 | −1.77797 | −0.888983 | − | 0.457940i | \(-0.848588\pi\) | ||||
−0.888983 | + | 0.457940i | \(0.848588\pi\) | |||||||
\(432\) | −58.8733 | −2.83254 | ||||||||
\(433\) | 7.31761 | 0.351662 | 0.175831 | − | 0.984420i | \(-0.443739\pi\) | ||||
0.175831 | + | 0.984420i | \(0.443739\pi\) | |||||||
\(434\) | 33.8623 | 1.62544 | ||||||||
\(435\) | −3.22084 | −0.154427 | ||||||||
\(436\) | −10.3947 | −0.497815 | ||||||||
\(437\) | −35.1616 | −1.68201 | ||||||||
\(438\) | −4.06567 | −0.194265 | ||||||||
\(439\) | −10.9146 | −0.520924 | −0.260462 | − | 0.965484i | \(-0.583875\pi\) | ||||
−0.260462 | + | 0.965484i | \(0.583875\pi\) | |||||||
\(440\) | −3.89485 | −0.185680 | ||||||||
\(441\) | 8.29612 | 0.395053 | ||||||||
\(442\) | −2.70590 | −0.128706 | ||||||||
\(443\) | 22.9347 | 1.08966 | 0.544831 | − | 0.838546i | \(-0.316594\pi\) | ||||
0.544831 | + | 0.838546i | \(0.316594\pi\) | |||||||
\(444\) | 40.6983 | 1.93146 | ||||||||
\(445\) | 5.55046 | 0.263117 | ||||||||
\(446\) | −41.2453 | −1.95302 | ||||||||
\(447\) | −7.67499 | −0.363015 | ||||||||
\(448\) | 21.9879 | 1.03883 | ||||||||
\(449\) | 14.4872 | 0.683693 | 0.341846 | − | 0.939756i | \(-0.388948\pi\) | ||||
0.341846 | + | 0.939756i | \(0.388948\pi\) | |||||||
\(450\) | −23.0893 | −1.08844 | ||||||||
\(451\) | −10.1278 | −0.476902 | ||||||||
\(452\) | −64.9864 | −3.05670 | ||||||||
\(453\) | 4.47416 | 0.210214 | ||||||||
\(454\) | −31.6787 | −1.48676 | ||||||||
\(455\) | 0.774970 | 0.0363311 | ||||||||
\(456\) | 63.8977 | 2.99228 | ||||||||
\(457\) | −9.74970 | −0.456072 | −0.228036 | − | 0.973653i | \(-0.573230\pi\) | ||||
−0.228036 | + | 0.973653i | \(0.573230\pi\) | |||||||
\(458\) | −23.9244 | −1.11791 | ||||||||
\(459\) | −5.22783 | −0.244014 | ||||||||
\(460\) | 11.6816 | 0.544659 | ||||||||
\(461\) | −6.42711 | −0.299340 | −0.149670 | − | 0.988736i | \(-0.547821\pi\) | ||||
−0.149670 | + | 0.988736i | \(0.547821\pi\) | |||||||
\(462\) | −4.50402 | −0.209546 | ||||||||
\(463\) | −25.6703 | −1.19300 | −0.596501 | − | 0.802612i | \(-0.703443\pi\) | ||||
−0.596501 | + | 0.802612i | \(0.703443\pi\) | |||||||
\(464\) | −69.1515 | −3.21028 | ||||||||
\(465\) | −4.27091 | −0.198059 | ||||||||
\(466\) | 26.5608 | 1.23041 | ||||||||
\(467\) | −13.8491 | −0.640858 | −0.320429 | − | 0.947272i | \(-0.603827\pi\) | ||||
−0.320429 | + | 0.947272i | \(0.603827\pi\) | |||||||
\(468\) | −9.38198 | −0.433682 | ||||||||
\(469\) | 17.7628 | 0.820209 | ||||||||
\(470\) | −1.82144 | −0.0840166 | ||||||||
\(471\) | 11.9735 | 0.551711 | ||||||||
\(472\) | 10.2392 | 0.471299 | ||||||||
\(473\) | 1.00000 | 0.0459800 | ||||||||
\(474\) | 23.2893 | 1.06971 | ||||||||
\(475\) | 34.9609 | 1.60412 | ||||||||
\(476\) | 7.89211 | 0.361734 | ||||||||
\(477\) | −19.7443 | −0.904029 | ||||||||
\(478\) | −27.4995 | −1.25780 | ||||||||
\(479\) | −23.6330 | −1.07982 | −0.539910 | − | 0.841723i | \(-0.681542\pi\) | ||||
−0.539910 | + | 0.841723i | \(0.681542\pi\) | |||||||
\(480\) | −7.22811 | −0.329917 | ||||||||
\(481\) | 7.61908 | 0.347400 | ||||||||
\(482\) | −20.5244 | −0.934860 | ||||||||
\(483\) | 8.14016 | 0.370390 | ||||||||
\(484\) | 5.03256 | 0.228753 | ||||||||
\(485\) | 0.882948 | 0.0400926 | ||||||||
\(486\) | −41.0719 | −1.86306 | ||||||||
\(487\) | −18.1556 | −0.822710 | −0.411355 | − | 0.911475i | \(-0.634944\pi\) | ||||
−0.411355 | + | 0.911475i | \(0.634944\pi\) | |||||||
\(488\) | −45.7474 | −2.07089 | ||||||||
\(489\) | 20.5668 | 0.930061 | ||||||||
\(490\) | 5.83185 | 0.263456 | ||||||||
\(491\) | −23.5022 | −1.06064 | −0.530321 | − | 0.847797i | \(-0.677928\pi\) | ||||
−0.530321 | + | 0.847797i | \(0.677928\pi\) | |||||||
\(492\) | −55.2008 | −2.48864 | ||||||||
\(493\) | −6.14051 | −0.276554 | ||||||||
\(494\) | 19.8514 | 0.893157 | ||||||||
\(495\) | −0.884863 | −0.0397716 | ||||||||
\(496\) | −91.6964 | −4.11729 | ||||||||
\(497\) | 7.68011 | 0.344500 | ||||||||
\(498\) | −19.1248 | −0.857001 | ||||||||
\(499\) | −30.8475 | −1.38093 | −0.690463 | − | 0.723368i | \(-0.742593\pi\) | ||||
−0.690463 | + | 0.723368i | \(0.742593\pi\) | |||||||
\(500\) | −23.8016 | −1.06444 | ||||||||
\(501\) | −16.9808 | −0.758648 | ||||||||
\(502\) | −0.616483 | −0.0275150 | ||||||||
\(503\) | 8.04226 | 0.358587 | 0.179293 | − | 0.983796i | \(-0.442619\pi\) | ||||
0.179293 | + | 0.983796i | \(0.442619\pi\) | |||||||
\(504\) | 23.0421 | 1.02637 | ||||||||
\(505\) | 6.89998 | 0.307045 | ||||||||
\(506\) | −12.7100 | −0.565029 | ||||||||
\(507\) | −12.9518 | −0.575208 | ||||||||
\(508\) | 63.0288 | 2.79645 | ||||||||
\(509\) | 9.35402 | 0.414610 | 0.207305 | − | 0.978276i | \(-0.433531\pi\) | ||||
0.207305 | + | 0.978276i | \(0.433531\pi\) | |||||||
\(510\) | −1.39098 | −0.0615937 | ||||||||
\(511\) | 2.21994 | 0.0982042 | ||||||||
\(512\) | 25.9434 | 1.14655 | ||||||||
\(513\) | 38.3532 | 1.69333 | ||||||||
\(514\) | −44.3154 | −1.95467 | ||||||||
\(515\) | −1.90055 | −0.0837483 | ||||||||
\(516\) | 5.45040 | 0.239940 | ||||||||
\(517\) | 1.41818 | 0.0623716 | ||||||||
\(518\) | −31.0534 | −1.36441 | ||||||||
\(519\) | 14.6529 | 0.643190 | ||||||||
\(520\) | −3.97417 | −0.174279 | ||||||||
\(521\) | −5.30658 | −0.232486 | −0.116243 | − | 0.993221i | \(-0.537085\pi\) | ||||
−0.116243 | + | 0.993221i | \(0.537085\pi\) | |||||||
\(522\) | −29.7517 | −1.30220 | ||||||||
\(523\) | 1.93256 | 0.0845048 | 0.0422524 | − | 0.999107i | \(-0.486547\pi\) | ||||
0.0422524 | + | 0.999107i | \(0.486547\pi\) | |||||||
\(524\) | 46.2932 | 2.02233 | ||||||||
\(525\) | −8.09370 | −0.353238 | ||||||||
\(526\) | 56.8206 | 2.47750 | ||||||||
\(527\) | −8.14245 | −0.354691 | ||||||||
\(528\) | 12.1965 | 0.530786 | ||||||||
\(529\) | −0.0290886 | −0.00126472 | ||||||||
\(530\) | −13.8795 | −0.602886 | ||||||||
\(531\) | 2.32623 | 0.100950 | ||||||||
\(532\) | −57.8993 | −2.51025 | ||||||||
\(533\) | −10.3341 | −0.447619 | ||||||||
\(534\) | −32.9154 | −1.42439 | ||||||||
\(535\) | 3.32286 | 0.143660 | ||||||||
\(536\) | −91.0903 | −3.93450 | ||||||||
\(537\) | 27.9870 | 1.20773 | ||||||||
\(538\) | −21.7523 | −0.937809 | ||||||||
\(539\) | −4.54071 | −0.195582 | ||||||||
\(540\) | −12.7419 | −0.548326 | ||||||||
\(541\) | −36.2145 | −1.55698 | −0.778491 | − | 0.627656i | \(-0.784015\pi\) | ||||
−0.778491 | + | 0.627656i | \(0.784015\pi\) | |||||||
\(542\) | 16.1361 | 0.693103 | ||||||||
\(543\) | 19.2260 | 0.825065 | ||||||||
\(544\) | −13.7803 | −0.590827 | ||||||||
\(545\) | −1.00034 | −0.0428498 | ||||||||
\(546\) | −4.59574 | −0.196680 | ||||||||
\(547\) | 17.5984 | 0.752454 | 0.376227 | − | 0.926528i | \(-0.377221\pi\) | ||||
0.376227 | + | 0.926528i | \(0.377221\pi\) | |||||||
\(548\) | 102.342 | 4.37183 | ||||||||
\(549\) | −10.3932 | −0.443573 | ||||||||
\(550\) | 12.6375 | 0.538863 | ||||||||
\(551\) | 45.0489 | 1.91915 | ||||||||
\(552\) | −41.7440 | −1.77674 | ||||||||
\(553\) | −12.7164 | −0.540758 | ||||||||
\(554\) | 64.5761 | 2.74357 | ||||||||
\(555\) | 3.91663 | 0.166252 | ||||||||
\(556\) | 86.7545 | 3.67921 | ||||||||
\(557\) | −27.6812 | −1.17289 | −0.586444 | − | 0.809990i | \(-0.699473\pi\) | ||||
−0.586444 | + | 0.809990i | \(0.699473\pi\) | |||||||
\(558\) | −39.4514 | −1.67011 | ||||||||
\(559\) | 1.02036 | 0.0431568 | ||||||||
\(560\) | 8.55317 | 0.361437 | ||||||||
\(561\) | 1.08303 | 0.0457255 | ||||||||
\(562\) | −80.6563 | −3.40228 | ||||||||
\(563\) | 27.8477 | 1.17364 | 0.586820 | − | 0.809718i | \(-0.300380\pi\) | ||||
0.586820 | + | 0.809718i | \(0.300380\pi\) | |||||||
\(564\) | 7.72966 | 0.325477 | ||||||||
\(565\) | −6.25402 | −0.263108 | ||||||||
\(566\) | 17.5271 | 0.736720 | ||||||||
\(567\) | −0.283421 | −0.0119025 | ||||||||
\(568\) | −39.3848 | −1.65255 | ||||||||
\(569\) | −13.4866 | −0.565386 | −0.282693 | − | 0.959210i | \(-0.591228\pi\) | ||||
−0.282693 | + | 0.959210i | \(0.591228\pi\) | |||||||
\(570\) | 10.2047 | 0.427429 | ||||||||
\(571\) | −29.9641 | −1.25396 | −0.626979 | − | 0.779036i | \(-0.715709\pi\) | ||||
−0.626979 | + | 0.779036i | \(0.715709\pi\) | |||||||
\(572\) | 5.13504 | 0.214707 | ||||||||
\(573\) | 13.7052 | 0.572542 | ||||||||
\(574\) | 42.1190 | 1.75801 | ||||||||
\(575\) | −22.8398 | −0.952485 | ||||||||
\(576\) | −25.6171 | −1.06738 | ||||||||
\(577\) | 37.3022 | 1.55291 | 0.776456 | − | 0.630171i | \(-0.217015\pi\) | ||||
0.776456 | + | 0.630171i | \(0.217015\pi\) | |||||||
\(578\) | −2.65190 | −0.110304 | ||||||||
\(579\) | −6.86859 | −0.285449 | ||||||||
\(580\) | −14.9664 | −0.621447 | ||||||||
\(581\) | 10.4425 | 0.433228 | ||||||||
\(582\) | −5.23607 | −0.217042 | ||||||||
\(583\) | 10.8066 | 0.447565 | ||||||||
\(584\) | −11.3842 | −0.471081 | ||||||||
\(585\) | −0.902882 | −0.0373296 | ||||||||
\(586\) | −71.4664 | −2.95225 | ||||||||
\(587\) | −28.8806 | −1.19203 | −0.596016 | − | 0.802973i | \(-0.703250\pi\) | ||||
−0.596016 | + | 0.802973i | \(0.703250\pi\) | |||||||
\(588\) | −24.7487 | −1.02062 | ||||||||
\(589\) | 59.7359 | 2.46137 | ||||||||
\(590\) | 1.63525 | 0.0673221 | ||||||||
\(591\) | 23.0698 | 0.948963 | ||||||||
\(592\) | 84.0901 | 3.45608 | ||||||||
\(593\) | −21.6510 | −0.889100 | −0.444550 | − | 0.895754i | \(-0.646636\pi\) | ||||
−0.444550 | + | 0.895754i | \(0.646636\pi\) | |||||||
\(594\) | 13.8637 | 0.568833 | ||||||||
\(595\) | 0.759504 | 0.0311366 | ||||||||
\(596\) | −35.6638 | −1.46085 | ||||||||
\(597\) | −16.3855 | −0.670615 | ||||||||
\(598\) | −12.9688 | −0.530335 | ||||||||
\(599\) | 23.0256 | 0.940802 | 0.470401 | − | 0.882453i | \(-0.344109\pi\) | ||||
0.470401 | + | 0.882453i | \(0.344109\pi\) | |||||||
\(600\) | 41.5058 | 1.69447 | ||||||||
\(601\) | 0.612719 | 0.0249933 | 0.0124967 | − | 0.999922i | \(-0.496022\pi\) | ||||
0.0124967 | + | 0.999922i | \(0.496022\pi\) | |||||||
\(602\) | −4.15873 | −0.169497 | ||||||||
\(603\) | −20.6946 | −0.842750 | ||||||||
\(604\) | 20.7903 | 0.845946 | ||||||||
\(605\) | 0.484312 | 0.0196901 | ||||||||
\(606\) | −40.9184 | −1.66220 | ||||||||
\(607\) | 5.55922 | 0.225642 | 0.112821 | − | 0.993615i | \(-0.464011\pi\) | ||||
0.112821 | + | 0.993615i | \(0.464011\pi\) | |||||||
\(608\) | 101.097 | 4.10004 | ||||||||
\(609\) | −10.4291 | −0.422610 | ||||||||
\(610\) | −7.30604 | −0.295813 | ||||||||
\(611\) | 1.44706 | 0.0585419 | ||||||||
\(612\) | −9.19474 | −0.371675 | ||||||||
\(613\) | 18.0912 | 0.730695 | 0.365347 | − | 0.930871i | \(-0.380950\pi\) | ||||
0.365347 | + | 0.930871i | \(0.380950\pi\) | |||||||
\(614\) | −87.3866 | −3.52664 | ||||||||
\(615\) | −5.31229 | −0.214212 | ||||||||
\(616\) | −12.6116 | −0.508136 | ||||||||
\(617\) | −36.5000 | −1.46943 | −0.734717 | − | 0.678374i | \(-0.762685\pi\) | ||||
−0.734717 | + | 0.678374i | \(0.762685\pi\) | |||||||
\(618\) | 11.2707 | 0.453373 | ||||||||
\(619\) | 39.7950 | 1.59950 | 0.799748 | − | 0.600336i | \(-0.204967\pi\) | ||||
0.799748 | + | 0.600336i | \(0.204967\pi\) | |||||||
\(620\) | −19.8458 | −0.797028 | ||||||||
\(621\) | −25.0559 | −1.00546 | ||||||||
\(622\) | −15.5945 | −0.625282 | ||||||||
\(623\) | 17.9725 | 0.720052 | ||||||||
\(624\) | 12.4449 | 0.498195 | ||||||||
\(625\) | 21.5366 | 0.861466 | ||||||||
\(626\) | 77.4780 | 3.09664 | ||||||||
\(627\) | −7.94547 | −0.317311 | ||||||||
\(628\) | 55.6380 | 2.22020 | ||||||||
\(629\) | 7.46703 | 0.297730 | ||||||||
\(630\) | 3.67991 | 0.146611 | ||||||||
\(631\) | −13.1475 | −0.523394 | −0.261697 | − | 0.965150i | \(-0.584282\pi\) | ||||
−0.261697 | + | 0.965150i | \(0.584282\pi\) | |||||||
\(632\) | 65.2118 | 2.59399 | ||||||||
\(633\) | −19.3845 | −0.770465 | ||||||||
\(634\) | −68.0020 | −2.70071 | ||||||||
\(635\) | 6.06563 | 0.240707 | ||||||||
\(636\) | 58.9005 | 2.33556 | ||||||||
\(637\) | −4.63318 | −0.183573 | ||||||||
\(638\) | 16.2840 | 0.644689 | ||||||||
\(639\) | −8.94775 | −0.353967 | ||||||||
\(640\) | −4.65984 | −0.184196 | ||||||||
\(641\) | 19.1939 | 0.758113 | 0.379056 | − | 0.925374i | \(-0.376249\pi\) | ||||
0.379056 | + | 0.925374i | \(0.376249\pi\) | |||||||
\(642\) | −19.7053 | −0.777705 | ||||||||
\(643\) | −40.2102 | −1.58573 | −0.792867 | − | 0.609395i | \(-0.791413\pi\) | ||||
−0.792867 | + | 0.609395i | \(0.791413\pi\) | |||||||
\(644\) | 37.8253 | 1.49053 | ||||||||
\(645\) | 0.524523 | 0.0206531 | ||||||||
\(646\) | 19.4552 | 0.765456 | ||||||||
\(647\) | 4.58287 | 0.180171 | 0.0900855 | − | 0.995934i | \(-0.471286\pi\) | ||||
0.0900855 | + | 0.995934i | \(0.471286\pi\) | |||||||
\(648\) | 1.45343 | 0.0570959 | ||||||||
\(649\) | −1.27321 | −0.0499780 | ||||||||
\(650\) | 12.8948 | 0.505776 | ||||||||
\(651\) | −13.8293 | −0.542012 | ||||||||
\(652\) | 95.5686 | 3.74276 | ||||||||
\(653\) | 12.2990 | 0.481298 | 0.240649 | − | 0.970612i | \(-0.422640\pi\) | ||||
0.240649 | + | 0.970612i | \(0.422640\pi\) | |||||||
\(654\) | 5.93223 | 0.231969 | ||||||||
\(655\) | 4.45506 | 0.174074 | ||||||||
\(656\) | −114.055 | −4.45310 | ||||||||
\(657\) | −2.58635 | −0.100903 | ||||||||
\(658\) | −5.89785 | −0.229922 | ||||||||
\(659\) | 13.4355 | 0.523371 | 0.261686 | − | 0.965153i | \(-0.415722\pi\) | ||||
0.261686 | + | 0.965153i | \(0.415722\pi\) | |||||||
\(660\) | 2.63969 | 0.102750 | ||||||||
\(661\) | 17.7966 | 0.692206 | 0.346103 | − | 0.938196i | \(-0.387505\pi\) | ||||
0.346103 | + | 0.938196i | \(0.387505\pi\) | |||||||
\(662\) | −82.7706 | −3.21697 | ||||||||
\(663\) | 1.10508 | 0.0429178 | ||||||||
\(664\) | −53.5508 | −2.07817 | ||||||||
\(665\) | −5.57198 | −0.216072 | ||||||||
\(666\) | 36.1789 | 1.40190 | ||||||||
\(667\) | −29.4302 | −1.13954 | ||||||||
\(668\) | −78.9057 | −3.05295 | ||||||||
\(669\) | 16.8445 | 0.651245 | ||||||||
\(670\) | −14.5475 | −0.562019 | ||||||||
\(671\) | 5.68853 | 0.219603 | ||||||||
\(672\) | −23.4048 | −0.902858 | ||||||||
\(673\) | 26.6423 | 1.02699 | 0.513493 | − | 0.858094i | \(-0.328351\pi\) | ||||
0.513493 | + | 0.858094i | \(0.328351\pi\) | |||||||
\(674\) | 84.7157 | 3.26313 | ||||||||
\(675\) | 24.9129 | 0.958899 | ||||||||
\(676\) | −60.1837 | −2.31476 | ||||||||
\(677\) | 23.2799 | 0.894720 | 0.447360 | − | 0.894354i | \(-0.352364\pi\) | ||||
0.447360 | + | 0.894354i | \(0.352364\pi\) | |||||||
\(678\) | 37.0877 | 1.42434 | ||||||||
\(679\) | 2.85900 | 0.109718 | ||||||||
\(680\) | −3.89485 | −0.149361 | ||||||||
\(681\) | 12.9375 | 0.495766 | ||||||||
\(682\) | 21.5929 | 0.826837 | ||||||||
\(683\) | 12.8161 | 0.490396 | 0.245198 | − | 0.969473i | \(-0.421147\pi\) | ||||
0.245198 | + | 0.969473i | \(0.421147\pi\) | |||||||
\(684\) | 67.4558 | 2.57924 | ||||||||
\(685\) | 9.84895 | 0.376309 | ||||||||
\(686\) | 47.9948 | 1.83245 | ||||||||
\(687\) | 9.77065 | 0.372773 | ||||||||
\(688\) | 11.2615 | 0.429342 | ||||||||
\(689\) | 11.0267 | 0.420084 | ||||||||
\(690\) | −6.66669 | −0.253797 | ||||||||
\(691\) | 31.9623 | 1.21590 | 0.607951 | − | 0.793974i | \(-0.291992\pi\) | ||||
0.607951 | + | 0.793974i | \(0.291992\pi\) | |||||||
\(692\) | 68.0882 | 2.58833 | ||||||||
\(693\) | −2.86520 | −0.108840 | ||||||||
\(694\) | 2.17727 | 0.0826481 | ||||||||
\(695\) | 8.34888 | 0.316691 | ||||||||
\(696\) | 53.4822 | 2.02724 | ||||||||
\(697\) | −10.1278 | −0.383619 | ||||||||
\(698\) | 66.5348 | 2.51838 | ||||||||
\(699\) | −10.8474 | −0.410285 | ||||||||
\(700\) | −37.6094 | −1.42150 | ||||||||
\(701\) | −36.7874 | −1.38944 | −0.694720 | − | 0.719280i | \(-0.744472\pi\) | ||||
−0.694720 | + | 0.719280i | \(0.744472\pi\) | |||||||
\(702\) | 14.1460 | 0.533906 | ||||||||
\(703\) | −54.7807 | −2.06609 | ||||||||
\(704\) | 14.0210 | 0.528436 | ||||||||
\(705\) | 0.743870 | 0.0280158 | ||||||||
\(706\) | 23.0411 | 0.867163 | ||||||||
\(707\) | 22.3423 | 0.840267 | ||||||||
\(708\) | −6.93953 | −0.260803 | ||||||||
\(709\) | 17.7689 | 0.667324 | 0.333662 | − | 0.942693i | \(-0.391716\pi\) | ||||
0.333662 | + | 0.942693i | \(0.391716\pi\) | |||||||
\(710\) | −6.28992 | −0.236056 | ||||||||
\(711\) | 14.8153 | 0.555618 | ||||||||
\(712\) | −92.1657 | −3.45406 | ||||||||
\(713\) | −39.0251 | −1.46150 | ||||||||
\(714\) | −4.50402 | −0.168559 | ||||||||
\(715\) | 0.494174 | 0.0184811 | ||||||||
\(716\) | 130.048 | 4.86014 | ||||||||
\(717\) | 11.2307 | 0.419418 | ||||||||
\(718\) | −32.1908 | −1.20135 | ||||||||
\(719\) | −18.0141 | −0.671811 | −0.335906 | − | 0.941896i | \(-0.609042\pi\) | ||||
−0.335906 | + | 0.941896i | \(0.609042\pi\) | |||||||
\(720\) | −9.96491 | −0.371370 | ||||||||
\(721\) | −6.15402 | −0.229188 | ||||||||
\(722\) | −92.3443 | −3.43670 | ||||||||
\(723\) | 8.38210 | 0.311734 | ||||||||
\(724\) | 89.3383 | 3.32023 | ||||||||
\(725\) | 29.2622 | 1.08677 | ||||||||
\(726\) | −2.87208 | −0.106593 | ||||||||
\(727\) | 3.40152 | 0.126155 | 0.0630776 | − | 0.998009i | \(-0.479908\pi\) | ||||
0.0630776 | + | 0.998009i | \(0.479908\pi\) | |||||||
\(728\) | −12.8684 | −0.476935 | ||||||||
\(729\) | 17.3158 | 0.641328 | ||||||||
\(730\) | −1.81810 | −0.0672909 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 31.0048 | 1.14597 | ||||||||
\(733\) | 23.0184 | 0.850205 | 0.425102 | − | 0.905145i | \(-0.360238\pi\) | ||||
0.425102 | + | 0.905145i | \(0.360238\pi\) | |||||||
\(734\) | 29.5237 | 1.08974 | ||||||||
\(735\) | −2.38171 | −0.0878507 | ||||||||
\(736\) | −66.0464 | −2.43450 | ||||||||
\(737\) | 11.3268 | 0.417227 | ||||||||
\(738\) | −49.0709 | −1.80633 | ||||||||
\(739\) | −40.3901 | −1.48578 | −0.742888 | − | 0.669416i | \(-0.766544\pi\) | ||||
−0.742888 | + | 0.669416i | \(0.766544\pi\) | |||||||
\(740\) | 18.1996 | 0.669031 | ||||||||
\(741\) | −8.10726 | −0.297828 | ||||||||
\(742\) | −44.9420 | −1.64987 | ||||||||
\(743\) | −15.2934 | −0.561059 | −0.280530 | − | 0.959845i | \(-0.590510\pi\) | ||||
−0.280530 | + | 0.959845i | \(0.590510\pi\) | |||||||
\(744\) | 70.9187 | 2.60000 | ||||||||
\(745\) | −3.43213 | −0.125744 | ||||||||
\(746\) | 38.7328 | 1.41811 | ||||||||
\(747\) | −12.1661 | −0.445134 | ||||||||
\(748\) | 5.03256 | 0.184009 | ||||||||
\(749\) | 10.7595 | 0.393142 | ||||||||
\(750\) | 13.5836 | 0.496001 | ||||||||
\(751\) | 12.6008 | 0.459808 | 0.229904 | − | 0.973213i | \(-0.426159\pi\) | ||||
0.229904 | + | 0.973213i | \(0.426159\pi\) | |||||||
\(752\) | 15.9709 | 0.582399 | ||||||||
\(753\) | 0.251770 | 0.00917501 | ||||||||
\(754\) | 16.6156 | 0.605104 | ||||||||
\(755\) | 2.00077 | 0.0728155 | ||||||||
\(756\) | −41.2586 | −1.50056 | ||||||||
\(757\) | 1.42839 | 0.0519157 | 0.0259579 | − | 0.999663i | \(-0.491736\pi\) | ||||
0.0259579 | + | 0.999663i | \(0.491736\pi\) | |||||||
\(758\) | −9.28486 | −0.337241 | ||||||||
\(759\) | 5.19073 | 0.188412 | ||||||||
\(760\) | 28.5740 | 1.03649 | ||||||||
\(761\) | −29.8787 | −1.08310 | −0.541550 | − | 0.840668i | \(-0.682162\pi\) | ||||
−0.541550 | + | 0.840668i | \(0.682162\pi\) | |||||||
\(762\) | −35.9705 | −1.30307 | ||||||||
\(763\) | −3.23912 | −0.117264 | ||||||||
\(764\) | 63.6845 | 2.30402 | ||||||||
\(765\) | −0.884863 | −0.0319923 | ||||||||
\(766\) | 59.0627 | 2.13402 | ||||||||
\(767\) | −1.29914 | −0.0469093 | ||||||||
\(768\) | −2.73637 | −0.0987404 | ||||||||
\(769\) | 27.3343 | 0.985700 | 0.492850 | − | 0.870114i | \(-0.335955\pi\) | ||||
0.492850 | + | 0.870114i | \(0.335955\pi\) | |||||||
\(770\) | −2.01413 | −0.0725840 | ||||||||
\(771\) | 18.0983 | 0.651793 | ||||||||
\(772\) | −31.9166 | −1.14870 | ||||||||
\(773\) | 16.4424 | 0.591393 | 0.295696 | − | 0.955282i | \(-0.404448\pi\) | ||||
0.295696 | + | 0.955282i | \(0.404448\pi\) | |||||||
\(774\) | 4.84515 | 0.174155 | ||||||||
\(775\) | 38.8024 | 1.39382 | ||||||||
\(776\) | −14.6614 | −0.526314 | ||||||||
\(777\) | 12.6821 | 0.454969 | ||||||||
\(778\) | 12.7989 | 0.458862 | ||||||||
\(779\) | 74.3014 | 2.66212 | ||||||||
\(780\) | 2.69345 | 0.0964409 | ||||||||
\(781\) | 4.89737 | 0.175242 | ||||||||
\(782\) | −12.7100 | −0.454509 | ||||||||
\(783\) | 32.1015 | 1.14721 | ||||||||
\(784\) | −51.1354 | −1.82626 | ||||||||
\(785\) | 5.35436 | 0.191105 | ||||||||
\(786\) | −26.4195 | −0.942352 | ||||||||
\(787\) | −33.9183 | −1.20906 | −0.604528 | − | 0.796584i | \(-0.706638\pi\) | ||||
−0.604528 | + | 0.796584i | \(0.706638\pi\) | |||||||
\(788\) | 107.199 | 3.81882 | ||||||||
\(789\) | −23.2054 | −0.826134 | ||||||||
\(790\) | 10.4146 | 0.370535 | ||||||||
\(791\) | −20.2506 | −0.720029 | ||||||||
\(792\) | 14.6932 | 0.522100 | ||||||||
\(793\) | 5.80437 | 0.206119 | ||||||||
\(794\) | 13.7099 | 0.486547 | ||||||||
\(795\) | 5.66834 | 0.201035 | ||||||||
\(796\) | −76.1395 | −2.69869 | ||||||||
\(797\) | 34.9331 | 1.23739 | 0.618697 | − | 0.785629i | \(-0.287661\pi\) | ||||
0.618697 | + | 0.785629i | \(0.287661\pi\) | |||||||
\(798\) | 33.0431 | 1.16971 | ||||||||
\(799\) | 1.41818 | 0.0501717 | ||||||||
\(800\) | 65.6694 | 2.32176 | ||||||||
\(801\) | −20.9389 | −0.739840 | ||||||||
\(802\) | −30.5485 | −1.07871 | ||||||||
\(803\) | 1.41558 | 0.0499549 | ||||||||
\(804\) | 61.7355 | 2.17724 | ||||||||
\(805\) | 3.64015 | 0.128298 | ||||||||
\(806\) | 22.0327 | 0.776067 | ||||||||
\(807\) | 8.88359 | 0.312717 | ||||||||
\(808\) | −114.575 | −4.03072 | ||||||||
\(809\) | −52.0232 | −1.82904 | −0.914518 | − | 0.404544i | \(-0.867430\pi\) | ||||
−0.914518 | + | 0.404544i | \(0.867430\pi\) | |||||||
\(810\) | 0.232118 | 0.00815580 | ||||||||
\(811\) | −46.4867 | −1.63237 | −0.816184 | − | 0.577792i | \(-0.803915\pi\) | ||||
−0.816184 | + | 0.577792i | \(0.803915\pi\) | |||||||
\(812\) | −48.4616 | −1.70067 | ||||||||
\(813\) | −6.58992 | −0.231119 | ||||||||
\(814\) | −19.8018 | −0.694052 | ||||||||
\(815\) | 9.19712 | 0.322161 | ||||||||
\(816\) | 12.1965 | 0.426964 | ||||||||
\(817\) | −7.33635 | −0.256666 | ||||||||
\(818\) | 35.9570 | 1.25721 | ||||||||
\(819\) | −2.92355 | −0.102157 | ||||||||
\(820\) | −24.6849 | −0.862034 | ||||||||
\(821\) | 13.2659 | 0.462982 | 0.231491 | − | 0.972837i | \(-0.425640\pi\) | ||||
0.231491 | + | 0.972837i | \(0.425640\pi\) | |||||||
\(822\) | −58.4065 | −2.03716 | ||||||||
\(823\) | −47.4929 | −1.65550 | −0.827748 | − | 0.561099i | \(-0.810379\pi\) | ||||
−0.827748 | + | 0.561099i | \(0.810379\pi\) | |||||||
\(824\) | 31.5588 | 1.09940 | ||||||||
\(825\) | −5.16110 | −0.179687 | ||||||||
\(826\) | 5.29496 | 0.184235 | ||||||||
\(827\) | 38.7721 | 1.34824 | 0.674119 | − | 0.738623i | \(-0.264524\pi\) | ||||
0.674119 | + | 0.738623i | \(0.264524\pi\) | |||||||
\(828\) | −44.0685 | −1.53149 | ||||||||
\(829\) | −43.9338 | −1.52588 | −0.762942 | − | 0.646467i | \(-0.776246\pi\) | ||||
−0.762942 | + | 0.646467i | \(0.776246\pi\) | |||||||
\(830\) | −8.55228 | −0.296854 | ||||||||
\(831\) | −26.3727 | −0.914859 | ||||||||
\(832\) | 14.3065 | 0.495989 | ||||||||
\(833\) | −4.54071 | −0.157326 | ||||||||
\(834\) | −49.5107 | −1.71442 | ||||||||
\(835\) | −7.59355 | −0.262786 | ||||||||
\(836\) | −36.9206 | −1.27693 | ||||||||
\(837\) | 42.5673 | 1.47134 | ||||||||
\(838\) | −5.07561 | −0.175334 | ||||||||
\(839\) | 12.1994 | 0.421170 | 0.210585 | − | 0.977576i | \(-0.432463\pi\) | ||||
0.210585 | + | 0.977576i | \(0.432463\pi\) | |||||||
\(840\) | −6.61508 | −0.228242 | ||||||||
\(841\) | 8.70581 | 0.300200 | ||||||||
\(842\) | −28.1765 | −0.971026 | ||||||||
\(843\) | 32.9398 | 1.13451 | ||||||||
\(844\) | −90.0749 | −3.10051 | ||||||||
\(845\) | −5.79182 | −0.199245 | ||||||||
\(846\) | 6.87131 | 0.236241 | ||||||||
\(847\) | 1.56821 | 0.0538844 | ||||||||
\(848\) | 121.699 | 4.17917 | ||||||||
\(849\) | −7.15803 | −0.245663 | ||||||||
\(850\) | 12.6375 | 0.433461 | ||||||||
\(851\) | 35.7880 | 1.22680 | ||||||||
\(852\) | 26.6926 | 0.914474 | ||||||||
\(853\) | −31.2174 | −1.06886 | −0.534432 | − | 0.845211i | \(-0.679475\pi\) | ||||
−0.534432 | + | 0.845211i | \(0.679475\pi\) | |||||||
\(854\) | −23.6571 | −0.809529 | ||||||||
\(855\) | 6.49166 | 0.222010 | ||||||||
\(856\) | −55.1762 | −1.88588 | ||||||||
\(857\) | −30.7427 | −1.05015 | −0.525075 | − | 0.851056i | \(-0.675963\pi\) | ||||
−0.525075 | + | 0.851056i | \(0.675963\pi\) | |||||||
\(858\) | −2.93056 | −0.100048 | ||||||||
\(859\) | 42.7205 | 1.45760 | 0.728802 | − | 0.684725i | \(-0.240078\pi\) | ||||
0.728802 | + | 0.684725i | \(0.240078\pi\) | |||||||
\(860\) | 2.43733 | 0.0831122 | ||||||||
\(861\) | −17.2013 | −0.586218 | ||||||||
\(862\) | 97.8856 | 3.33400 | ||||||||
\(863\) | 11.2589 | 0.383259 | 0.191629 | − | 0.981467i | \(-0.438623\pi\) | ||||
0.191629 | + | 0.981467i | \(0.438623\pi\) | |||||||
\(864\) | 72.0413 | 2.45089 | ||||||||
\(865\) | 6.55252 | 0.222792 | ||||||||
\(866\) | −19.4055 | −0.659427 | ||||||||
\(867\) | 1.08303 | 0.0367815 | ||||||||
\(868\) | −64.2612 | −2.18117 | ||||||||
\(869\) | −8.10888 | −0.275075 | ||||||||
\(870\) | 8.54133 | 0.289578 | ||||||||
\(871\) | 11.5574 | 0.391609 | ||||||||
\(872\) | 16.6107 | 0.562509 | ||||||||
\(873\) | −3.33089 | −0.112734 | ||||||||
\(874\) | 93.2450 | 3.15406 | ||||||||
\(875\) | −7.41689 | −0.250737 | ||||||||
\(876\) | 7.71550 | 0.260683 | ||||||||
\(877\) | 3.08997 | 0.104341 | 0.0521704 | − | 0.998638i | \(-0.483386\pi\) | ||||
0.0521704 | + | 0.998638i | \(0.483386\pi\) | |||||||
\(878\) | 28.9443 | 0.976824 | ||||||||
\(879\) | 29.1867 | 0.984442 | ||||||||
\(880\) | 5.45409 | 0.183857 | ||||||||
\(881\) | −36.8348 | −1.24100 | −0.620498 | − | 0.784208i | \(-0.713070\pi\) | ||||
−0.620498 | + | 0.784208i | \(0.713070\pi\) | |||||||
\(882\) | −22.0004 | −0.740794 | ||||||||
\(883\) | 1.84452 | 0.0620730 | 0.0310365 | − | 0.999518i | \(-0.490119\pi\) | ||||
0.0310365 | + | 0.999518i | \(0.490119\pi\) | |||||||
\(884\) | 5.13504 | 0.172710 | ||||||||
\(885\) | −0.667831 | −0.0224489 | ||||||||
\(886\) | −60.8206 | −2.04331 | ||||||||
\(887\) | −10.8252 | −0.363476 | −0.181738 | − | 0.983347i | \(-0.558172\pi\) | ||||
−0.181738 | + | 0.983347i | \(0.558172\pi\) | |||||||
\(888\) | −65.0359 | −2.18246 | ||||||||
\(889\) | 19.6406 | 0.658725 | ||||||||
\(890\) | −14.7192 | −0.493390 | ||||||||
\(891\) | −0.180729 | −0.00605464 | ||||||||
\(892\) | 78.2720 | 2.62074 | ||||||||
\(893\) | −10.4043 | −0.348166 | ||||||||
\(894\) | 20.3533 | 0.680716 | ||||||||
\(895\) | 12.5153 | 0.418341 | ||||||||
\(896\) | −15.0887 | −0.504076 | ||||||||
\(897\) | 5.29643 | 0.176843 | ||||||||
\(898\) | −38.4185 | −1.28204 | ||||||||
\(899\) | 49.9988 | 1.66755 | ||||||||
\(900\) | 43.8170 | 1.46057 | ||||||||
\(901\) | 10.8066 | 0.360022 | ||||||||
\(902\) | 26.8580 | 0.894274 | ||||||||
\(903\) | 1.69842 | 0.0565197 | ||||||||
\(904\) | 103.848 | 3.45394 | ||||||||
\(905\) | 8.59753 | 0.285792 | ||||||||
\(906\) | −11.8650 | −0.394189 | ||||||||
\(907\) | 25.7796 | 0.855998 | 0.427999 | − | 0.903779i | \(-0.359219\pi\) | ||||
0.427999 | + | 0.903779i | \(0.359219\pi\) | |||||||
\(908\) | 60.1173 | 1.99506 | ||||||||
\(909\) | −26.0300 | −0.863359 | ||||||||
\(910\) | −2.05514 | −0.0681272 | ||||||||
\(911\) | 27.2784 | 0.903774 | 0.451887 | − | 0.892075i | \(-0.350751\pi\) | ||||
0.451887 | + | 0.892075i | \(0.350751\pi\) | |||||||
\(912\) | −89.4781 | −2.96291 | ||||||||
\(913\) | 6.65886 | 0.220376 | ||||||||
\(914\) | 25.8552 | 0.855214 | ||||||||
\(915\) | 2.98377 | 0.0986403 | ||||||||
\(916\) | 45.4017 | 1.50012 | ||||||||
\(917\) | 14.4256 | 0.476374 | ||||||||
\(918\) | 13.8637 | 0.457569 | ||||||||
\(919\) | 33.1425 | 1.09327 | 0.546635 | − | 0.837371i | \(-0.315909\pi\) | ||||
0.546635 | + | 0.837371i | \(0.315909\pi\) | |||||||
\(920\) | −18.6672 | −0.615441 | ||||||||
\(921\) | 35.6884 | 1.17597 | ||||||||
\(922\) | 17.0440 | 0.561315 | ||||||||
\(923\) | 4.99710 | 0.164481 | ||||||||
\(924\) | 8.54738 | 0.281188 | ||||||||
\(925\) | −35.5837 | −1.16998 | ||||||||
\(926\) | 68.0751 | 2.23709 | ||||||||
\(927\) | 7.16976 | 0.235486 | ||||||||
\(928\) | 84.6183 | 2.77773 | ||||||||
\(929\) | −0.0748777 | −0.00245666 | −0.00122833 | − | 0.999999i | \(-0.500391\pi\) | ||||
−0.00122833 | + | 0.999999i | \(0.500391\pi\) | |||||||
\(930\) | 11.3260 | 0.371394 | ||||||||
\(931\) | 33.3123 | 1.09176 | ||||||||
\(932\) | −50.4050 | −1.65107 | ||||||||
\(933\) | 6.36875 | 0.208503 | ||||||||
\(934\) | 36.7263 | 1.20172 | ||||||||
\(935\) | 0.484312 | 0.0158387 | ||||||||
\(936\) | 14.9924 | 0.490042 | ||||||||
\(937\) | 60.6074 | 1.97996 | 0.989979 | − | 0.141214i | \(-0.0451007\pi\) | ||||
0.989979 | + | 0.141214i | \(0.0451007\pi\) | |||||||
\(938\) | −47.1051 | −1.53804 | ||||||||
\(939\) | −31.6418 | −1.03259 | ||||||||
\(940\) | 3.45658 | 0.112741 | ||||||||
\(941\) | 31.7439 | 1.03482 | 0.517410 | − | 0.855737i | \(-0.326896\pi\) | ||||
0.517410 | + | 0.855737i | \(0.326896\pi\) | |||||||
\(942\) | −31.7525 | −1.03455 | ||||||||
\(943\) | −48.5407 | −1.58070 | ||||||||
\(944\) | −14.3383 | −0.466673 | ||||||||
\(945\) | −3.97056 | −0.129162 | ||||||||
\(946\) | −2.65190 | −0.0862206 | ||||||||
\(947\) | 43.7339 | 1.42116 | 0.710581 | − | 0.703616i | \(-0.248432\pi\) | ||||
0.710581 | + | 0.703616i | \(0.248432\pi\) | |||||||
\(948\) | −44.1966 | −1.43544 | ||||||||
\(949\) | 1.44441 | 0.0468876 | ||||||||
\(950\) | −92.7128 | −3.00800 | ||||||||
\(951\) | 27.7718 | 0.900564 | ||||||||
\(952\) | −12.6116 | −0.408744 | ||||||||
\(953\) | −38.8015 | −1.25690 | −0.628452 | − | 0.777848i | \(-0.716311\pi\) | ||||
−0.628452 | + | 0.777848i | \(0.716311\pi\) | |||||||
\(954\) | 52.3598 | 1.69521 | ||||||||
\(955\) | 6.12873 | 0.198321 | ||||||||
\(956\) | 52.1863 | 1.68783 | ||||||||
\(957\) | −6.65034 | −0.214975 | ||||||||
\(958\) | 62.6723 | 2.02485 | ||||||||
\(959\) | 31.8911 | 1.02982 | ||||||||
\(960\) | 7.35434 | 0.237360 | ||||||||
\(961\) | 35.2995 | 1.13869 | ||||||||
\(962\) | −20.2050 | −0.651436 | ||||||||
\(963\) | −12.5354 | −0.403947 | ||||||||
\(964\) | 38.9495 | 1.25448 | ||||||||
\(965\) | −3.07152 | −0.0988758 | ||||||||
\(966\) | −21.5869 | −0.694546 | ||||||||
\(967\) | 55.5641 | 1.78682 | 0.893411 | − | 0.449240i | \(-0.148305\pi\) | ||||
0.893411 | + | 0.449240i | \(0.148305\pi\) | |||||||
\(968\) | −8.04203 | −0.258481 | ||||||||
\(969\) | −7.94547 | −0.255245 | ||||||||
\(970\) | −2.34149 | −0.0751806 | ||||||||
\(971\) | −34.5549 | −1.10892 | −0.554459 | − | 0.832211i | \(-0.687075\pi\) | ||||
−0.554459 | + | 0.832211i | \(0.687075\pi\) | |||||||
\(972\) | 77.9430 | 2.50002 | ||||||||
\(973\) | 27.0338 | 0.866665 | ||||||||
\(974\) | 48.1469 | 1.54273 | ||||||||
\(975\) | −5.26620 | −0.168653 | ||||||||
\(976\) | 64.0615 | 2.05056 | ||||||||
\(977\) | 34.5407 | 1.10506 | 0.552528 | − | 0.833495i | \(-0.313663\pi\) | ||||
0.552528 | + | 0.833495i | \(0.313663\pi\) | |||||||
\(978\) | −54.5409 | −1.74403 | ||||||||
\(979\) | 11.4605 | 0.366279 | ||||||||
\(980\) | −11.0672 | −0.353529 | ||||||||
\(981\) | 3.77375 | 0.120487 | ||||||||
\(982\) | 62.3255 | 1.98889 | ||||||||
\(983\) | −30.1136 | −0.960476 | −0.480238 | − | 0.877138i | \(-0.659450\pi\) | ||||
−0.480238 | + | 0.877138i | \(0.659450\pi\) | |||||||
\(984\) | 88.2109 | 2.81206 | ||||||||
\(985\) | 10.3164 | 0.328708 | ||||||||
\(986\) | 16.2840 | 0.518588 | ||||||||
\(987\) | 2.40866 | 0.0766686 | ||||||||
\(988\) | −37.6724 | −1.19852 | ||||||||
\(989\) | 4.79280 | 0.152402 | ||||||||
\(990\) | 2.34657 | 0.0745788 | ||||||||
\(991\) | −53.3869 | −1.69589 | −0.847946 | − | 0.530083i | \(-0.822161\pi\) | ||||
−0.847946 | + | 0.530083i | \(0.822161\pi\) | |||||||
\(992\) | 112.206 | 3.56254 | ||||||||
\(993\) | 33.8033 | 1.07271 | ||||||||
\(994\) | −20.3669 | −0.645998 | ||||||||
\(995\) | −7.32734 | −0.232292 | ||||||||
\(996\) | 36.2934 | 1.15000 | ||||||||
\(997\) | 7.11891 | 0.225458 | 0.112729 | − | 0.993626i | \(-0.464041\pi\) | ||||
0.112729 | + | 0.993626i | \(0.464041\pi\) | |||||||
\(998\) | 81.8045 | 2.58948 | ||||||||
\(999\) | −39.0364 | −1.23506 |
(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 | 8041.2.a.j.1.3 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.j.1.3 | ✓ | 82 | 1.1 | even | 1 | trivial |