Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.219326 | −0.126628 | −0.0633139 | − | 0.997994i | \(-0.520167\pi\) | ||||
−0.0633139 | + | 0.997994i | \(0.520167\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.27443 | 1.01716 | 0.508578 | − | 0.861016i | \(-0.330171\pi\) | ||||
0.508578 | + | 0.861016i | \(0.330171\pi\) | |||||||
\(6\) | −0.219326 | −0.0895393 | ||||||||
\(7\) | −3.32577 | −1.25702 | −0.628511 | − | 0.777801i | \(-0.716335\pi\) | ||||
−0.628511 | + | 0.777801i | \(0.716335\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.95190 | −0.983965 | ||||||||
\(10\) | 2.27443 | 0.719237 | ||||||||
\(11\) | 3.87014 | 1.16689 | 0.583446 | − | 0.812152i | \(-0.301704\pi\) | ||||
0.583446 | + | 0.812152i | \(0.301704\pi\) | |||||||
\(12\) | −0.219326 | −0.0633139 | ||||||||
\(13\) | −1.48964 | −0.413150 | −0.206575 | − | 0.978431i | \(-0.566232\pi\) | ||||
−0.206575 | + | 0.978431i | \(0.566232\pi\) | |||||||
\(14\) | −3.32577 | −0.888849 | ||||||||
\(15\) | −0.498840 | −0.128800 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.776211 | 0.188259 | 0.0941294 | − | 0.995560i | \(-0.469993\pi\) | ||||
0.0941294 | + | 0.995560i | \(0.469993\pi\) | |||||||
\(18\) | −2.95190 | −0.695769 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.27443 | 0.508578 | ||||||||
\(21\) | 0.729426 | 0.159174 | ||||||||
\(22\) | 3.87014 | 0.825117 | ||||||||
\(23\) | −8.89752 | −1.85526 | −0.927631 | − | 0.373498i | \(-0.878158\pi\) | ||||
−0.927631 | + | 0.373498i | \(0.878158\pi\) | |||||||
\(24\) | −0.219326 | −0.0447697 | ||||||||
\(25\) | 0.173023 | 0.0346047 | ||||||||
\(26\) | −1.48964 | −0.292141 | ||||||||
\(27\) | 1.30540 | 0.251225 | ||||||||
\(28\) | −3.32577 | −0.628511 | ||||||||
\(29\) | 4.85906 | 0.902305 | 0.451153 | − | 0.892447i | \(-0.351013\pi\) | ||||
0.451153 | + | 0.892447i | \(0.351013\pi\) | |||||||
\(30\) | −0.498840 | −0.0910754 | ||||||||
\(31\) | 2.88048 | 0.517349 | 0.258674 | − | 0.965965i | \(-0.416714\pi\) | ||||
0.258674 | + | 0.965965i | \(0.416714\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.848822 | −0.147761 | ||||||||
\(34\) | 0.776211 | 0.133119 | ||||||||
\(35\) | −7.56422 | −1.27859 | ||||||||
\(36\) | −2.95190 | −0.491983 | ||||||||
\(37\) | −7.10422 | −1.16793 | −0.583964 | − | 0.811780i | \(-0.698499\pi\) | ||||
−0.583964 | + | 0.811780i | \(0.698499\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0.326715 | 0.0523163 | ||||||||
\(40\) | 2.27443 | 0.359619 | ||||||||
\(41\) | −7.81788 | −1.22095 | −0.610474 | − | 0.792036i | \(-0.709021\pi\) | ||||
−0.610474 | + | 0.792036i | \(0.709021\pi\) | |||||||
\(42\) | 0.729426 | 0.112553 | ||||||||
\(43\) | 0.180535 | 0.0275314 | 0.0137657 | − | 0.999905i | \(-0.495618\pi\) | ||||
0.0137657 | + | 0.999905i | \(0.495618\pi\) | |||||||
\(44\) | 3.87014 | 0.583446 | ||||||||
\(45\) | −6.71388 | −1.00085 | ||||||||
\(46\) | −8.89752 | −1.31187 | ||||||||
\(47\) | 3.93186 | 0.573521 | 0.286761 | − | 0.958002i | \(-0.407422\pi\) | ||||
0.286761 | + | 0.958002i | \(0.407422\pi\) | |||||||
\(48\) | −0.219326 | −0.0316569 | ||||||||
\(49\) | 4.06072 | 0.580103 | ||||||||
\(50\) | 0.173023 | 0.0244692 | ||||||||
\(51\) | −0.170243 | −0.0238388 | ||||||||
\(52\) | −1.48964 | −0.206575 | ||||||||
\(53\) | 2.43017 | 0.333809 | 0.166905 | − | 0.985973i | \(-0.446623\pi\) | ||||
0.166905 | + | 0.985973i | \(0.446623\pi\) | |||||||
\(54\) | 1.30540 | 0.177643 | ||||||||
\(55\) | 8.80236 | 1.18691 | ||||||||
\(56\) | −3.32577 | −0.444424 | ||||||||
\(57\) | −0.219326 | −0.0290504 | ||||||||
\(58\) | 4.85906 | 0.638026 | ||||||||
\(59\) | −9.44317 | −1.22940 | −0.614698 | − | 0.788763i | \(-0.710722\pi\) | ||||
−0.614698 | + | 0.788763i | \(0.710722\pi\) | |||||||
\(60\) | −0.498840 | −0.0644000 | ||||||||
\(61\) | −5.88140 | −0.753036 | −0.376518 | − | 0.926409i | \(-0.622879\pi\) | ||||
−0.376518 | + | 0.926409i | \(0.622879\pi\) | |||||||
\(62\) | 2.88048 | 0.365821 | ||||||||
\(63\) | 9.81732 | 1.23687 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.38807 | −0.420238 | ||||||||
\(66\) | −0.848822 | −0.104483 | ||||||||
\(67\) | −0.157168 | −0.0192011 | −0.00960056 | − | 0.999954i | \(-0.503056\pi\) | ||||
−0.00960056 | + | 0.999954i | \(0.503056\pi\) | |||||||
\(68\) | 0.776211 | 0.0941294 | ||||||||
\(69\) | 1.95145 | 0.234928 | ||||||||
\(70\) | −7.56422 | −0.904097 | ||||||||
\(71\) | 4.50788 | 0.534987 | 0.267494 | − | 0.963560i | \(-0.413805\pi\) | ||||
0.267494 | + | 0.963560i | \(0.413805\pi\) | |||||||
\(72\) | −2.95190 | −0.347884 | ||||||||
\(73\) | −8.65662 | −1.01318 | −0.506590 | − | 0.862187i | \(-0.669094\pi\) | ||||
−0.506590 | + | 0.862187i | \(0.669094\pi\) | |||||||
\(74\) | −7.10422 | −0.825849 | ||||||||
\(75\) | −0.0379485 | −0.00438191 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −12.8712 | −1.46681 | ||||||||
\(78\) | 0.326715 | 0.0369932 | ||||||||
\(79\) | −7.31318 | −0.822797 | −0.411399 | − | 0.911455i | \(-0.634960\pi\) | ||||
−0.411399 | + | 0.911455i | \(0.634960\pi\) | |||||||
\(80\) | 2.27443 | 0.254289 | ||||||||
\(81\) | 8.56938 | 0.952153 | ||||||||
\(82\) | −7.81788 | −0.863341 | ||||||||
\(83\) | −11.8891 | −1.30500 | −0.652498 | − | 0.757790i | \(-0.726279\pi\) | ||||
−0.652498 | + | 0.757790i | \(0.726279\pi\) | |||||||
\(84\) | 0.729426 | 0.0795869 | ||||||||
\(85\) | 1.76544 | 0.191488 | ||||||||
\(86\) | 0.180535 | 0.0194676 | ||||||||
\(87\) | −1.06572 | −0.114257 | ||||||||
\(88\) | 3.87014 | 0.412559 | ||||||||
\(89\) | 6.08863 | 0.645393 | 0.322697 | − | 0.946502i | \(-0.395411\pi\) | ||||
0.322697 | + | 0.946502i | \(0.395411\pi\) | |||||||
\(90\) | −6.71388 | −0.707705 | ||||||||
\(91\) | 4.95418 | 0.519339 | ||||||||
\(92\) | −8.89752 | −0.927631 | ||||||||
\(93\) | −0.631762 | −0.0655107 | ||||||||
\(94\) | 3.93186 | 0.405541 | ||||||||
\(95\) | 2.27443 | 0.233351 | ||||||||
\(96\) | −0.219326 | −0.0223848 | ||||||||
\(97\) | −0.915773 | −0.0929826 | −0.0464913 | − | 0.998919i | \(-0.514804\pi\) | ||||
−0.0464913 | + | 0.998919i | \(0.514804\pi\) | |||||||
\(98\) | 4.06072 | 0.410195 | ||||||||
\(99\) | −11.4243 | −1.14818 | ||||||||
\(100\) | 0.173023 | 0.0173023 | ||||||||
\(101\) | 13.9362 | 1.38670 | 0.693352 | − | 0.720599i | \(-0.256133\pi\) | ||||
0.693352 | + | 0.720599i | \(0.256133\pi\) | |||||||
\(102\) | −0.170243 | −0.0168566 | ||||||||
\(103\) | 0.216189 | 0.0213018 | 0.0106509 | − | 0.999943i | \(-0.496610\pi\) | ||||
0.0106509 | + | 0.999943i | \(0.496610\pi\) | |||||||
\(104\) | −1.48964 | −0.146071 | ||||||||
\(105\) | 1.65903 | 0.161904 | ||||||||
\(106\) | 2.43017 | 0.236039 | ||||||||
\(107\) | −8.87146 | −0.857636 | −0.428818 | − | 0.903391i | \(-0.641070\pi\) | ||||
−0.428818 | + | 0.903391i | \(0.641070\pi\) | |||||||
\(108\) | 1.30540 | 0.125613 | ||||||||
\(109\) | −14.8224 | −1.41973 | −0.709866 | − | 0.704336i | \(-0.751245\pi\) | ||||
−0.709866 | + | 0.704336i | \(0.751245\pi\) | |||||||
\(110\) | 8.80236 | 0.839272 | ||||||||
\(111\) | 1.55814 | 0.147892 | ||||||||
\(112\) | −3.32577 | −0.314255 | ||||||||
\(113\) | 8.48491 | 0.798193 | 0.399096 | − | 0.916909i | \(-0.369324\pi\) | ||||
0.399096 | + | 0.916909i | \(0.369324\pi\) | |||||||
\(114\) | −0.219326 | −0.0205417 | ||||||||
\(115\) | −20.2368 | −1.88709 | ||||||||
\(116\) | 4.85906 | 0.451153 | ||||||||
\(117\) | 4.39725 | 0.406526 | ||||||||
\(118\) | −9.44317 | −0.869314 | ||||||||
\(119\) | −2.58150 | −0.236645 | ||||||||
\(120\) | −0.498840 | −0.0455377 | ||||||||
\(121\) | 3.97800 | 0.361637 | ||||||||
\(122\) | −5.88140 | −0.532477 | ||||||||
\(123\) | 1.71466 | 0.154606 | ||||||||
\(124\) | 2.88048 | 0.258674 | ||||||||
\(125\) | −10.9786 | −0.981957 | ||||||||
\(126\) | 9.81732 | 0.874596 | ||||||||
\(127\) | −5.31550 | −0.471675 | −0.235837 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235837 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.0395960 | −0.00348623 | ||||||||
\(130\) | −3.38807 | −0.297153 | ||||||||
\(131\) | 2.03558 | 0.177849 | 0.0889245 | − | 0.996038i | \(-0.471657\pi\) | ||||
0.0889245 | + | 0.996038i | \(0.471657\pi\) | |||||||
\(132\) | −0.848822 | −0.0738804 | ||||||||
\(133\) | −3.32577 | −0.288381 | ||||||||
\(134\) | −0.157168 | −0.0135772 | ||||||||
\(135\) | 2.96905 | 0.255535 | ||||||||
\(136\) | 0.776211 | 0.0665595 | ||||||||
\(137\) | 0.269241 | 0.0230028 | 0.0115014 | − | 0.999934i | \(-0.496339\pi\) | ||||
0.0115014 | + | 0.999934i | \(0.496339\pi\) | |||||||
\(138\) | 1.95145 | 0.166119 | ||||||||
\(139\) | 13.5163 | 1.14644 | 0.573221 | − | 0.819401i | \(-0.305694\pi\) | ||||
0.573221 | + | 0.819401i | \(0.305694\pi\) | |||||||
\(140\) | −7.56422 | −0.639293 | ||||||||
\(141\) | −0.862358 | −0.0726237 | ||||||||
\(142\) | 4.50788 | 0.378293 | ||||||||
\(143\) | −5.76510 | −0.482102 | ||||||||
\(144\) | −2.95190 | −0.245991 | ||||||||
\(145\) | 11.0516 | 0.917784 | ||||||||
\(146\) | −8.65662 | −0.716427 | ||||||||
\(147\) | −0.890621 | −0.0734572 | ||||||||
\(148\) | −7.10422 | −0.583964 | ||||||||
\(149\) | 16.1543 | 1.32342 | 0.661708 | − | 0.749762i | \(-0.269832\pi\) | ||||
0.661708 | + | 0.749762i | \(0.269832\pi\) | |||||||
\(150\) | −0.0379485 | −0.00309848 | ||||||||
\(151\) | −2.60227 | −0.211770 | −0.105885 | − | 0.994378i | \(-0.533768\pi\) | ||||
−0.105885 | + | 0.994378i | \(0.533768\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −2.29129 | −0.185240 | ||||||||
\(154\) | −12.8712 | −1.03719 | ||||||||
\(155\) | 6.55143 | 0.526224 | ||||||||
\(156\) | 0.326715 | 0.0261581 | ||||||||
\(157\) | −22.9956 | −1.83525 | −0.917623 | − | 0.397452i | \(-0.869895\pi\) | ||||
−0.917623 | + | 0.397452i | \(0.869895\pi\) | |||||||
\(158\) | −7.31318 | −0.581806 | ||||||||
\(159\) | −0.532998 | −0.0422695 | ||||||||
\(160\) | 2.27443 | 0.179809 | ||||||||
\(161\) | 29.5911 | 2.33210 | ||||||||
\(162\) | 8.56938 | 0.673274 | ||||||||
\(163\) | −0.813102 | −0.0636870 | −0.0318435 | − | 0.999493i | \(-0.510138\pi\) | ||||
−0.0318435 | + | 0.999493i | \(0.510138\pi\) | |||||||
\(164\) | −7.81788 | −0.610474 | ||||||||
\(165\) | −1.93058 | −0.150296 | ||||||||
\(166\) | −11.8891 | −0.922772 | ||||||||
\(167\) | −0.224287 | −0.0173558 | −0.00867791 | − | 0.999962i | \(-0.502762\pi\) | ||||
−0.00867791 | + | 0.999962i | \(0.502762\pi\) | |||||||
\(168\) | 0.729426 | 0.0562764 | ||||||||
\(169\) | −10.7810 | −0.829307 | ||||||||
\(170\) | 1.76544 | 0.135403 | ||||||||
\(171\) | −2.95190 | −0.225737 | ||||||||
\(172\) | 0.180535 | 0.0137657 | ||||||||
\(173\) | −3.97111 | −0.301918 | −0.150959 | − | 0.988540i | \(-0.548236\pi\) | ||||
−0.150959 | + | 0.988540i | \(0.548236\pi\) | |||||||
\(174\) | −1.06572 | −0.0807918 | ||||||||
\(175\) | −0.575435 | −0.0434988 | ||||||||
\(176\) | 3.87014 | 0.291723 | ||||||||
\(177\) | 2.07113 | 0.155676 | ||||||||
\(178\) | 6.08863 | 0.456362 | ||||||||
\(179\) | −1.17036 | −0.0874768 | −0.0437384 | − | 0.999043i | \(-0.513927\pi\) | ||||
−0.0437384 | + | 0.999043i | \(0.513927\pi\) | |||||||
\(180\) | −6.71388 | −0.500423 | ||||||||
\(181\) | −8.51244 | −0.632725 | −0.316362 | − | 0.948638i | \(-0.602462\pi\) | ||||
−0.316362 | + | 0.948638i | \(0.602462\pi\) | |||||||
\(182\) | 4.95418 | 0.367228 | ||||||||
\(183\) | 1.28994 | 0.0953553 | ||||||||
\(184\) | −8.89752 | −0.655934 | ||||||||
\(185\) | −16.1580 | −1.18796 | ||||||||
\(186\) | −0.631762 | −0.0463230 | ||||||||
\(187\) | 3.00405 | 0.219678 | ||||||||
\(188\) | 3.93186 | 0.286761 | ||||||||
\(189\) | −4.34147 | −0.315795 | ||||||||
\(190\) | 2.27443 | 0.165004 | ||||||||
\(191\) | −26.5812 | −1.92335 | −0.961674 | − | 0.274196i | \(-0.911588\pi\) | ||||
−0.961674 | + | 0.274196i | \(0.911588\pi\) | |||||||
\(192\) | −0.219326 | −0.0158285 | ||||||||
\(193\) | 2.02726 | 0.145925 | 0.0729627 | − | 0.997335i | \(-0.476755\pi\) | ||||
0.0729627 | + | 0.997335i | \(0.476755\pi\) | |||||||
\(194\) | −0.915773 | −0.0657486 | ||||||||
\(195\) | 0.743090 | 0.0532138 | ||||||||
\(196\) | 4.06072 | 0.290052 | ||||||||
\(197\) | −23.4024 | −1.66735 | −0.833676 | − | 0.552254i | \(-0.813768\pi\) | ||||
−0.833676 | + | 0.552254i | \(0.813768\pi\) | |||||||
\(198\) | −11.4243 | −0.811887 | ||||||||
\(199\) | 12.2850 | 0.870860 | 0.435430 | − | 0.900223i | \(-0.356596\pi\) | ||||
0.435430 | + | 0.900223i | \(0.356596\pi\) | |||||||
\(200\) | 0.173023 | 0.0122346 | ||||||||
\(201\) | 0.0344710 | 0.00243139 | ||||||||
\(202\) | 13.9362 | 0.980547 | ||||||||
\(203\) | −16.1601 | −1.13422 | ||||||||
\(204\) | −0.170243 | −0.0119194 | ||||||||
\(205\) | −17.7812 | −1.24189 | ||||||||
\(206\) | 0.216189 | 0.0150626 | ||||||||
\(207\) | 26.2646 | 1.82551 | ||||||||
\(208\) | −1.48964 | −0.103288 | ||||||||
\(209\) | 3.87014 | 0.267703 | ||||||||
\(210\) | 1.65903 | 0.114484 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 2.43017 | 0.166905 | ||||||||
\(213\) | −0.988694 | −0.0677442 | ||||||||
\(214\) | −8.87146 | −0.606440 | ||||||||
\(215\) | 0.410614 | 0.0280037 | ||||||||
\(216\) | 1.30540 | 0.0888215 | ||||||||
\(217\) | −9.57979 | −0.650318 | ||||||||
\(218\) | −14.8224 | −1.00390 | ||||||||
\(219\) | 1.89862 | 0.128297 | ||||||||
\(220\) | 8.80236 | 0.593455 | ||||||||
\(221\) | −1.15627 | −0.0777792 | ||||||||
\(222\) | 1.55814 | 0.104575 | ||||||||
\(223\) | 9.42269 | 0.630990 | 0.315495 | − | 0.948927i | \(-0.397829\pi\) | ||||
0.315495 | + | 0.948927i | \(0.397829\pi\) | |||||||
\(224\) | −3.32577 | −0.222212 | ||||||||
\(225\) | −0.510747 | −0.0340498 | ||||||||
\(226\) | 8.48491 | 0.564408 | ||||||||
\(227\) | −23.2406 | −1.54254 | −0.771268 | − | 0.636511i | \(-0.780377\pi\) | ||||
−0.771268 | + | 0.636511i | \(0.780377\pi\) | |||||||
\(228\) | −0.219326 | −0.0145252 | ||||||||
\(229\) | 5.04393 | 0.333312 | 0.166656 | − | 0.986015i | \(-0.446703\pi\) | ||||
0.166656 | + | 0.986015i | \(0.446703\pi\) | |||||||
\(230\) | −20.2368 | −1.33437 | ||||||||
\(231\) | 2.82298 | 0.185739 | ||||||||
\(232\) | 4.85906 | 0.319013 | ||||||||
\(233\) | 0.0399453 | 0.00261690 | 0.00130845 | − | 0.999999i | \(-0.499584\pi\) | ||||
0.00130845 | + | 0.999999i | \(0.499584\pi\) | |||||||
\(234\) | 4.39725 | 0.287457 | ||||||||
\(235\) | 8.94274 | 0.583360 | ||||||||
\(236\) | −9.44317 | −0.614698 | ||||||||
\(237\) | 1.60397 | 0.104189 | ||||||||
\(238\) | −2.58150 | −0.167334 | ||||||||
\(239\) | 18.8370 | 1.21847 | 0.609233 | − | 0.792992i | \(-0.291478\pi\) | ||||
0.609233 | + | 0.792992i | \(0.291478\pi\) | |||||||
\(240\) | −0.498840 | −0.0322000 | ||||||||
\(241\) | −17.3048 | −1.11470 | −0.557352 | − | 0.830277i | \(-0.688182\pi\) | ||||
−0.557352 | + | 0.830277i | \(0.688182\pi\) | |||||||
\(242\) | 3.97800 | 0.255716 | ||||||||
\(243\) | −5.79570 | −0.371794 | ||||||||
\(244\) | −5.88140 | −0.376518 | ||||||||
\(245\) | 9.23582 | 0.590055 | ||||||||
\(246\) | 1.71466 | 0.109323 | ||||||||
\(247\) | −1.48964 | −0.0947832 | ||||||||
\(248\) | 2.88048 | 0.182910 | ||||||||
\(249\) | 2.60758 | 0.165249 | ||||||||
\(250\) | −10.9786 | −0.694348 | ||||||||
\(251\) | 0.183589 | 0.0115880 | 0.00579402 | − | 0.999983i | \(-0.498156\pi\) | ||||
0.00579402 | + | 0.999983i | \(0.498156\pi\) | |||||||
\(252\) | 9.81732 | 0.618433 | ||||||||
\(253\) | −34.4347 | −2.16489 | ||||||||
\(254\) | −5.31550 | −0.333524 | ||||||||
\(255\) | −0.387205 | −0.0242477 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −28.6461 | −1.78690 | −0.893448 | − | 0.449166i | \(-0.851721\pi\) | ||||
−0.893448 | + | 0.449166i | \(0.851721\pi\) | |||||||
\(258\) | −0.0395960 | −0.00246514 | ||||||||
\(259\) | 23.6270 | 1.46811 | ||||||||
\(260\) | −3.38807 | −0.210119 | ||||||||
\(261\) | −14.3434 | −0.887837 | ||||||||
\(262\) | 2.03558 | 0.125758 | ||||||||
\(263\) | −13.6178 | −0.839710 | −0.419855 | − | 0.907591i | \(-0.637919\pi\) | ||||
−0.419855 | + | 0.907591i | \(0.637919\pi\) | |||||||
\(264\) | −0.848822 | −0.0522414 | ||||||||
\(265\) | 5.52724 | 0.339536 | ||||||||
\(266\) | −3.32577 | −0.203916 | ||||||||
\(267\) | −1.33539 | −0.0817247 | ||||||||
\(268\) | −0.157168 | −0.00960056 | ||||||||
\(269\) | −3.95941 | −0.241410 | −0.120705 | − | 0.992688i | \(-0.538515\pi\) | ||||
−0.120705 | + | 0.992688i | \(0.538515\pi\) | |||||||
\(270\) | 2.96905 | 0.180690 | ||||||||
\(271\) | −4.17077 | −0.253356 | −0.126678 | − | 0.991944i | \(-0.540432\pi\) | ||||
−0.126678 | + | 0.991944i | \(0.540432\pi\) | |||||||
\(272\) | 0.776211 | 0.0470647 | ||||||||
\(273\) | −1.08658 | −0.0657627 | ||||||||
\(274\) | 0.269241 | 0.0162655 | ||||||||
\(275\) | 0.669625 | 0.0403799 | ||||||||
\(276\) | 1.95145 | 0.117464 | ||||||||
\(277\) | 17.6128 | 1.05825 | 0.529126 | − | 0.848543i | \(-0.322520\pi\) | ||||
0.529126 | + | 0.848543i | \(0.322520\pi\) | |||||||
\(278\) | 13.5163 | 0.810656 | ||||||||
\(279\) | −8.50286 | −0.509053 | ||||||||
\(280\) | −7.56422 | −0.452048 | ||||||||
\(281\) | −15.1516 | −0.903866 | −0.451933 | − | 0.892052i | \(-0.649265\pi\) | ||||
−0.451933 | + | 0.892052i | \(0.649265\pi\) | |||||||
\(282\) | −0.862358 | −0.0513527 | ||||||||
\(283\) | 32.2846 | 1.91912 | 0.959559 | − | 0.281506i | \(-0.0908339\pi\) | ||||
0.959559 | + | 0.281506i | \(0.0908339\pi\) | |||||||
\(284\) | 4.50788 | 0.267494 | ||||||||
\(285\) | −0.498840 | −0.0295488 | ||||||||
\(286\) | −5.76510 | −0.340898 | ||||||||
\(287\) | 26.0005 | 1.53476 | ||||||||
\(288\) | −2.95190 | −0.173942 | ||||||||
\(289\) | −16.3975 | −0.964559 | ||||||||
\(290\) | 11.0516 | 0.648972 | ||||||||
\(291\) | 0.200852 | 0.0117742 | ||||||||
\(292\) | −8.65662 | −0.506590 | ||||||||
\(293\) | 26.6325 | 1.55589 | 0.777945 | − | 0.628332i | \(-0.216262\pi\) | ||||
0.777945 | + | 0.628332i | \(0.216262\pi\) | |||||||
\(294\) | −0.890621 | −0.0519421 | ||||||||
\(295\) | −21.4778 | −1.25049 | ||||||||
\(296\) | −7.10422 | −0.412925 | ||||||||
\(297\) | 5.05210 | 0.293152 | ||||||||
\(298\) | 16.1543 | 0.935796 | ||||||||
\(299\) | 13.2541 | 0.766502 | ||||||||
\(300\) | −0.0379485 | −0.00219096 | ||||||||
\(301\) | −0.600418 | −0.0346075 | ||||||||
\(302\) | −2.60227 | −0.149744 | ||||||||
\(303\) | −3.05657 | −0.175595 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −13.3768 | −0.765955 | ||||||||
\(306\) | −2.29129 | −0.130985 | ||||||||
\(307\) | 17.8341 | 1.01784 | 0.508922 | − | 0.860813i | \(-0.330044\pi\) | ||||
0.508922 | + | 0.860813i | \(0.330044\pi\) | |||||||
\(308\) | −12.8712 | −0.733404 | ||||||||
\(309\) | −0.0474159 | −0.00269739 | ||||||||
\(310\) | 6.55143 | 0.372096 | ||||||||
\(311\) | −23.3430 | −1.32366 | −0.661830 | − | 0.749654i | \(-0.730220\pi\) | ||||
−0.661830 | + | 0.749654i | \(0.730220\pi\) | |||||||
\(312\) | 0.326715 | 0.0184966 | ||||||||
\(313\) | 0.540099 | 0.0305282 | 0.0152641 | − | 0.999883i | \(-0.495141\pi\) | ||||
0.0152641 | + | 0.999883i | \(0.495141\pi\) | |||||||
\(314\) | −22.9956 | −1.29771 | ||||||||
\(315\) | 22.3288 | 1.25808 | ||||||||
\(316\) | −7.31318 | −0.411399 | ||||||||
\(317\) | 17.0554 | 0.957925 | 0.478963 | − | 0.877835i | \(-0.341013\pi\) | ||||
0.478963 | + | 0.877835i | \(0.341013\pi\) | |||||||
\(318\) | −0.532998 | −0.0298890 | ||||||||
\(319\) | 18.8053 | 1.05289 | ||||||||
\(320\) | 2.27443 | 0.127144 | ||||||||
\(321\) | 1.94574 | 0.108600 | ||||||||
\(322\) | 29.5911 | 1.64905 | ||||||||
\(323\) | 0.776211 | 0.0431895 | ||||||||
\(324\) | 8.56938 | 0.476077 | ||||||||
\(325\) | −0.257742 | −0.0142969 | ||||||||
\(326\) | −0.813102 | −0.0450335 | ||||||||
\(327\) | 3.25094 | 0.179777 | ||||||||
\(328\) | −7.81788 | −0.431670 | ||||||||
\(329\) | −13.0765 | −0.720929 | ||||||||
\(330\) | −1.93058 | −0.106275 | ||||||||
\(331\) | 34.0474 | 1.87142 | 0.935708 | − | 0.352776i | \(-0.114762\pi\) | ||||
0.935708 | + | 0.352776i | \(0.114762\pi\) | |||||||
\(332\) | −11.8891 | −0.652498 | ||||||||
\(333\) | 20.9709 | 1.14920 | ||||||||
\(334\) | −0.224287 | −0.0122724 | ||||||||
\(335\) | −0.357467 | −0.0195305 | ||||||||
\(336\) | 0.729426 | 0.0397934 | ||||||||
\(337\) | −9.48533 | −0.516699 | −0.258350 | − | 0.966052i | \(-0.583179\pi\) | ||||
−0.258350 | + | 0.966052i | \(0.583179\pi\) | |||||||
\(338\) | −10.7810 | −0.586408 | ||||||||
\(339\) | −1.86096 | −0.101073 | ||||||||
\(340\) | 1.76544 | 0.0957442 | ||||||||
\(341\) | 11.1478 | 0.603690 | ||||||||
\(342\) | −2.95190 | −0.159620 | ||||||||
\(343\) | 9.77535 | 0.527819 | ||||||||
\(344\) | 0.180535 | 0.00973381 | ||||||||
\(345\) | 4.43844 | 0.238958 | ||||||||
\(346\) | −3.97111 | −0.213488 | ||||||||
\(347\) | −36.5159 | −1.96028 | −0.980139 | − | 0.198313i | \(-0.936454\pi\) | ||||
−0.980139 | + | 0.198313i | \(0.936454\pi\) | |||||||
\(348\) | −1.06572 | −0.0571284 | ||||||||
\(349\) | 5.10461 | 0.273243 | 0.136622 | − | 0.990623i | \(-0.456376\pi\) | ||||
0.136622 | + | 0.990623i | \(0.456376\pi\) | |||||||
\(350\) | −0.575435 | −0.0307583 | ||||||||
\(351\) | −1.94457 | −0.103794 | ||||||||
\(352\) | 3.87014 | 0.206279 | ||||||||
\(353\) | −9.06775 | −0.482628 | −0.241314 | − | 0.970447i | \(-0.577578\pi\) | ||||
−0.241314 | + | 0.970447i | \(0.577578\pi\) | |||||||
\(354\) | 2.07113 | 0.110079 | ||||||||
\(355\) | 10.2529 | 0.544165 | ||||||||
\(356\) | 6.08863 | 0.322697 | ||||||||
\(357\) | 0.566188 | 0.0299659 | ||||||||
\(358\) | −1.17036 | −0.0618554 | ||||||||
\(359\) | 15.4124 | 0.813434 | 0.406717 | − | 0.913554i | \(-0.366673\pi\) | ||||
0.406717 | + | 0.913554i | \(0.366673\pi\) | |||||||
\(360\) | −6.71388 | −0.353852 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −8.51244 | −0.447404 | ||||||||
\(363\) | −0.872478 | −0.0457932 | ||||||||
\(364\) | 4.95418 | 0.259670 | ||||||||
\(365\) | −19.6889 | −1.03056 | ||||||||
\(366\) | 1.28994 | 0.0674264 | ||||||||
\(367\) | −23.5461 | −1.22910 | −0.614548 | − | 0.788880i | \(-0.710661\pi\) | ||||
−0.614548 | + | 0.788880i | \(0.710661\pi\) | |||||||
\(368\) | −8.89752 | −0.463815 | ||||||||
\(369\) | 23.0776 | 1.20137 | ||||||||
\(370\) | −16.1580 | −0.840017 | ||||||||
\(371\) | −8.08217 | −0.419605 | ||||||||
\(372\) | −0.631762 | −0.0327553 | ||||||||
\(373\) | 18.0439 | 0.934280 | 0.467140 | − | 0.884183i | \(-0.345284\pi\) | ||||
0.467140 | + | 0.884183i | \(0.345284\pi\) | |||||||
\(374\) | 3.00405 | 0.155336 | ||||||||
\(375\) | 2.40789 | 0.124343 | ||||||||
\(376\) | 3.93186 | 0.202770 | ||||||||
\(377\) | −7.23823 | −0.372788 | ||||||||
\(378\) | −4.34147 | −0.223301 | ||||||||
\(379\) | 25.5307 | 1.31143 | 0.655713 | − | 0.755010i | \(-0.272368\pi\) | ||||
0.655713 | + | 0.755010i | \(0.272368\pi\) | |||||||
\(380\) | 2.27443 | 0.116676 | ||||||||
\(381\) | 1.16583 | 0.0597271 | ||||||||
\(382\) | −26.5812 | −1.36001 | ||||||||
\(383\) | 10.9443 | 0.559226 | 0.279613 | − | 0.960113i | \(-0.409794\pi\) | ||||
0.279613 | + | 0.960113i | \(0.409794\pi\) | |||||||
\(384\) | −0.219326 | −0.0111924 | ||||||||
\(385\) | −29.2746 | −1.49197 | ||||||||
\(386\) | 2.02726 | 0.103185 | ||||||||
\(387\) | −0.532921 | −0.0270899 | ||||||||
\(388\) | −0.915773 | −0.0464913 | ||||||||
\(389\) | 11.8152 | 0.599054 | 0.299527 | − | 0.954088i | \(-0.403171\pi\) | ||||
0.299527 | + | 0.954088i | \(0.403171\pi\) | |||||||
\(390\) | 0.743090 | 0.0376278 | ||||||||
\(391\) | −6.90635 | −0.349269 | ||||||||
\(392\) | 4.06072 | 0.205098 | ||||||||
\(393\) | −0.446454 | −0.0225206 | ||||||||
\(394\) | −23.4024 | −1.17900 | ||||||||
\(395\) | −16.6333 | −0.836913 | ||||||||
\(396\) | −11.4243 | −0.574091 | ||||||||
\(397\) | −25.4826 | −1.27893 | −0.639467 | − | 0.768819i | \(-0.720845\pi\) | ||||
−0.639467 | + | 0.768819i | \(0.720845\pi\) | |||||||
\(398\) | 12.2850 | 0.615791 | ||||||||
\(399\) | 0.729426 | 0.0365170 | ||||||||
\(400\) | 0.173023 | 0.00865117 | ||||||||
\(401\) | −26.9100 | −1.34382 | −0.671911 | − | 0.740632i | \(-0.734526\pi\) | ||||
−0.671911 | + | 0.740632i | \(0.734526\pi\) | |||||||
\(402\) | 0.0344710 | 0.00171926 | ||||||||
\(403\) | −4.29086 | −0.213743 | ||||||||
\(404\) | 13.9362 | 0.693352 | ||||||||
\(405\) | 19.4904 | 0.968488 | ||||||||
\(406\) | −16.1601 | −0.802013 | ||||||||
\(407\) | −27.4944 | −1.36284 | ||||||||
\(408\) | −0.170243 | −0.00842828 | ||||||||
\(409\) | −17.8779 | −0.884007 | −0.442003 | − | 0.897013i | \(-0.645732\pi\) | ||||
−0.442003 | + | 0.897013i | \(0.645732\pi\) | |||||||
\(410\) | −17.7812 | −0.878152 | ||||||||
\(411\) | −0.0590515 | −0.00291280 | ||||||||
\(412\) | 0.216189 | 0.0106509 | ||||||||
\(413\) | 31.4058 | 1.54538 | ||||||||
\(414\) | 26.2646 | 1.29083 | ||||||||
\(415\) | −27.0409 | −1.32738 | ||||||||
\(416\) | −1.48964 | −0.0730354 | ||||||||
\(417\) | −2.96448 | −0.145171 | ||||||||
\(418\) | 3.87014 | 0.189295 | ||||||||
\(419\) | 1.95105 | 0.0953150 | 0.0476575 | − | 0.998864i | \(-0.484824\pi\) | ||||
0.0476575 | + | 0.998864i | \(0.484824\pi\) | |||||||
\(420\) | 1.65903 | 0.0809522 | ||||||||
\(421\) | 7.76004 | 0.378201 | 0.189101 | − | 0.981958i | \(-0.439443\pi\) | ||||
0.189101 | + | 0.981958i | \(0.439443\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −11.6065 | −0.564325 | ||||||||
\(424\) | 2.43017 | 0.118019 | ||||||||
\(425\) | 0.134303 | 0.00651464 | ||||||||
\(426\) | −0.988694 | −0.0479024 | ||||||||
\(427\) | 19.5602 | 0.946583 | ||||||||
\(428\) | −8.87146 | −0.428818 | ||||||||
\(429\) | 1.26443 | 0.0610475 | ||||||||
\(430\) | 0.410614 | 0.0198016 | ||||||||
\(431\) | −12.2312 | −0.589156 | −0.294578 | − | 0.955627i | \(-0.595179\pi\) | ||||
−0.294578 | + | 0.955627i | \(0.595179\pi\) | |||||||
\(432\) | 1.30540 | 0.0628063 | ||||||||
\(433\) | 18.6933 | 0.898342 | 0.449171 | − | 0.893446i | \(-0.351719\pi\) | ||||
0.449171 | + | 0.893446i | \(0.351719\pi\) | |||||||
\(434\) | −9.57979 | −0.459845 | ||||||||
\(435\) | −2.42390 | −0.116217 | ||||||||
\(436\) | −14.8224 | −0.709866 | ||||||||
\(437\) | −8.89752 | −0.425626 | ||||||||
\(438\) | 1.89862 | 0.0907195 | ||||||||
\(439\) | −10.4972 | −0.501005 | −0.250502 | − | 0.968116i | \(-0.580596\pi\) | ||||
−0.250502 | + | 0.968116i | \(0.580596\pi\) | |||||||
\(440\) | 8.80236 | 0.419636 | ||||||||
\(441\) | −11.9868 | −0.570802 | ||||||||
\(442\) | −1.15627 | −0.0549982 | ||||||||
\(443\) | 38.5842 | 1.83319 | 0.916596 | − | 0.399814i | \(-0.130925\pi\) | ||||
0.916596 | + | 0.399814i | \(0.130925\pi\) | |||||||
\(444\) | 1.55814 | 0.0739460 | ||||||||
\(445\) | 13.8481 | 0.656465 | ||||||||
\(446\) | 9.42269 | 0.446178 | ||||||||
\(447\) | −3.54306 | −0.167581 | ||||||||
\(448\) | −3.32577 | −0.157128 | ||||||||
\(449\) | −30.0086 | −1.41619 | −0.708096 | − | 0.706116i | \(-0.750446\pi\) | ||||
−0.708096 | + | 0.706116i | \(0.750446\pi\) | |||||||
\(450\) | −0.510747 | −0.0240769 | ||||||||
\(451\) | −30.2563 | −1.42471 | ||||||||
\(452\) | 8.48491 | 0.399096 | ||||||||
\(453\) | 0.570745 | 0.0268159 | ||||||||
\(454\) | −23.2406 | −1.09074 | ||||||||
\(455\) | 11.2679 | 0.528248 | ||||||||
\(456\) | −0.219326 | −0.0102709 | ||||||||
\(457\) | 34.4348 | 1.61079 | 0.805397 | − | 0.592736i | \(-0.201952\pi\) | ||||
0.805397 | + | 0.592736i | \(0.201952\pi\) | |||||||
\(458\) | 5.04393 | 0.235687 | ||||||||
\(459\) | 1.01327 | 0.0472953 | ||||||||
\(460\) | −20.2368 | −0.943545 | ||||||||
\(461\) | −8.96726 | −0.417647 | −0.208823 | − | 0.977953i | \(-0.566963\pi\) | ||||
−0.208823 | + | 0.977953i | \(0.566963\pi\) | |||||||
\(462\) | 2.82298 | 0.131337 | ||||||||
\(463\) | −12.2753 | −0.570480 | −0.285240 | − | 0.958456i | \(-0.592073\pi\) | ||||
−0.285240 | + | 0.958456i | \(0.592073\pi\) | |||||||
\(464\) | 4.85906 | 0.225576 | ||||||||
\(465\) | −1.43690 | −0.0666345 | ||||||||
\(466\) | 0.0399453 | 0.00185043 | ||||||||
\(467\) | 37.4755 | 1.73416 | 0.867079 | − | 0.498171i | \(-0.165995\pi\) | ||||
0.867079 | + | 0.498171i | \(0.165995\pi\) | |||||||
\(468\) | 4.39725 | 0.203263 | ||||||||
\(469\) | 0.522704 | 0.0241362 | ||||||||
\(470\) | 8.94274 | 0.412498 | ||||||||
\(471\) | 5.04352 | 0.232393 | ||||||||
\(472\) | −9.44317 | −0.434657 | ||||||||
\(473\) | 0.698697 | 0.0321261 | ||||||||
\(474\) | 1.60397 | 0.0736727 | ||||||||
\(475\) | 0.173023 | 0.00793886 | ||||||||
\(476\) | −2.58150 | −0.118323 | ||||||||
\(477\) | −7.17360 | −0.328457 | ||||||||
\(478\) | 18.8370 | 0.861585 | ||||||||
\(479\) | −0.888395 | −0.0405918 | −0.0202959 | − | 0.999794i | \(-0.506461\pi\) | ||||
−0.0202959 | + | 0.999794i | \(0.506461\pi\) | |||||||
\(480\) | −0.498840 | −0.0227688 | ||||||||
\(481\) | 10.5827 | 0.482530 | ||||||||
\(482\) | −17.3048 | −0.788214 | ||||||||
\(483\) | −6.49008 | −0.295309 | ||||||||
\(484\) | 3.97800 | 0.180818 | ||||||||
\(485\) | −2.08286 | −0.0945777 | ||||||||
\(486\) | −5.79570 | −0.262898 | ||||||||
\(487\) | −22.8576 | −1.03578 | −0.517888 | − | 0.855448i | \(-0.673282\pi\) | ||||
−0.517888 | + | 0.855448i | \(0.673282\pi\) | |||||||
\(488\) | −5.88140 | −0.266239 | ||||||||
\(489\) | 0.178334 | 0.00806454 | ||||||||
\(490\) | 9.23582 | 0.417232 | ||||||||
\(491\) | 12.6592 | 0.571303 | 0.285652 | − | 0.958334i | \(-0.407790\pi\) | ||||
0.285652 | + | 0.958334i | \(0.407790\pi\) | |||||||
\(492\) | 1.71466 | 0.0773030 | ||||||||
\(493\) | 3.77166 | 0.169867 | ||||||||
\(494\) | −1.48964 | −0.0670218 | ||||||||
\(495\) | −25.9837 | −1.16788 | ||||||||
\(496\) | 2.88048 | 0.129337 | ||||||||
\(497\) | −14.9922 | −0.672490 | ||||||||
\(498\) | 2.60758 | 0.116849 | ||||||||
\(499\) | 43.5023 | 1.94743 | 0.973715 | − | 0.227768i | \(-0.0731427\pi\) | ||||
0.973715 | + | 0.227768i | \(0.0731427\pi\) | |||||||
\(500\) | −10.9786 | −0.490978 | ||||||||
\(501\) | 0.0491918 | 0.00219773 | ||||||||
\(502\) | 0.183589 | 0.00819398 | ||||||||
\(503\) | 3.62671 | 0.161707 | 0.0808534 | − | 0.996726i | \(-0.474235\pi\) | ||||
0.0808534 | + | 0.996726i | \(0.474235\pi\) | |||||||
\(504\) | 9.81732 | 0.437298 | ||||||||
\(505\) | 31.6969 | 1.41049 | ||||||||
\(506\) | −34.4347 | −1.53081 | ||||||||
\(507\) | 2.36455 | 0.105013 | ||||||||
\(508\) | −5.31550 | −0.235837 | ||||||||
\(509\) | −24.9347 | −1.10521 | −0.552606 | − | 0.833443i | \(-0.686366\pi\) | ||||
−0.552606 | + | 0.833443i | \(0.686366\pi\) | |||||||
\(510\) | −0.387205 | −0.0171457 | ||||||||
\(511\) | 28.7899 | 1.27359 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.30540 | 0.0576350 | ||||||||
\(514\) | −28.6461 | −1.26353 | ||||||||
\(515\) | 0.491707 | 0.0216672 | ||||||||
\(516\) | −0.0395960 | −0.00174312 | ||||||||
\(517\) | 15.2169 | 0.669237 | ||||||||
\(518\) | 23.6270 | 1.03811 | ||||||||
\(519\) | 0.870965 | 0.0382311 | ||||||||
\(520\) | −3.38807 | −0.148577 | ||||||||
\(521\) | 3.44440 | 0.150902 | 0.0754510 | − | 0.997150i | \(-0.475960\pi\) | ||||
0.0754510 | + | 0.997150i | \(0.475960\pi\) | |||||||
\(522\) | −14.3434 | −0.627796 | ||||||||
\(523\) | 18.8977 | 0.826341 | 0.413170 | − | 0.910654i | \(-0.364421\pi\) | ||||
0.413170 | + | 0.910654i | \(0.364421\pi\) | |||||||
\(524\) | 2.03558 | 0.0889245 | ||||||||
\(525\) | 0.126208 | 0.00550816 | ||||||||
\(526\) | −13.6178 | −0.593765 | ||||||||
\(527\) | 2.23586 | 0.0973954 | ||||||||
\(528\) | −0.848822 | −0.0369402 | ||||||||
\(529\) | 56.1659 | 2.44200 | ||||||||
\(530\) | 5.52724 | 0.240088 | ||||||||
\(531\) | 27.8753 | 1.20968 | ||||||||
\(532\) | −3.32577 | −0.144190 | ||||||||
\(533\) | 11.6458 | 0.504435 | ||||||||
\(534\) | −1.33539 | −0.0577881 | ||||||||
\(535\) | −20.1775 | −0.872349 | ||||||||
\(536\) | −0.157168 | −0.00678862 | ||||||||
\(537\) | 0.256690 | 0.0110770 | ||||||||
\(538\) | −3.95941 | −0.170702 | ||||||||
\(539\) | 15.7156 | 0.676918 | ||||||||
\(540\) | 2.96905 | 0.127767 | ||||||||
\(541\) | 16.7703 | 0.721011 | 0.360505 | − | 0.932757i | \(-0.382604\pi\) | ||||
0.360505 | + | 0.932757i | \(0.382604\pi\) | |||||||
\(542\) | −4.17077 | −0.179150 | ||||||||
\(543\) | 1.86700 | 0.0801205 | ||||||||
\(544\) | 0.776211 | 0.0332798 | ||||||||
\(545\) | −33.7126 | −1.44409 | ||||||||
\(546\) | −1.08658 | −0.0465013 | ||||||||
\(547\) | −25.6690 | −1.09753 | −0.548764 | − | 0.835977i | \(-0.684902\pi\) | ||||
−0.548764 | + | 0.835977i | \(0.684902\pi\) | |||||||
\(548\) | 0.269241 | 0.0115014 | ||||||||
\(549\) | 17.3613 | 0.740962 | ||||||||
\(550\) | 0.669625 | 0.0285529 | ||||||||
\(551\) | 4.85906 | 0.207003 | ||||||||
\(552\) | 1.95145 | 0.0830594 | ||||||||
\(553\) | 24.3219 | 1.03427 | ||||||||
\(554\) | 17.6128 | 0.748297 | ||||||||
\(555\) | 3.54387 | 0.150429 | ||||||||
\(556\) | 13.5163 | 0.573221 | ||||||||
\(557\) | −30.3522 | −1.28607 | −0.643033 | − | 0.765838i | \(-0.722324\pi\) | ||||
−0.643033 | + | 0.765838i | \(0.722324\pi\) | |||||||
\(558\) | −8.50286 | −0.359955 | ||||||||
\(559\) | −0.268932 | −0.0113746 | ||||||||
\(560\) | −7.56422 | −0.319647 | ||||||||
\(561\) | −0.658865 | −0.0278173 | ||||||||
\(562\) | −15.1516 | −0.639130 | ||||||||
\(563\) | −15.3643 | −0.647528 | −0.323764 | − | 0.946138i | \(-0.604948\pi\) | ||||
−0.323764 | + | 0.946138i | \(0.604948\pi\) | |||||||
\(564\) | −0.862358 | −0.0363118 | ||||||||
\(565\) | 19.2983 | 0.811886 | ||||||||
\(566\) | 32.2846 | 1.35702 | ||||||||
\(567\) | −28.4998 | −1.19688 | ||||||||
\(568\) | 4.50788 | 0.189147 | ||||||||
\(569\) | 2.41097 | 0.101073 | 0.0505366 | − | 0.998722i | \(-0.483907\pi\) | ||||
0.0505366 | + | 0.998722i | \(0.483907\pi\) | |||||||
\(570\) | −0.498840 | −0.0208941 | ||||||||
\(571\) | 13.9963 | 0.585725 | 0.292863 | − | 0.956155i | \(-0.405392\pi\) | ||||
0.292863 | + | 0.956155i | \(0.405392\pi\) | |||||||
\(572\) | −5.76510 | −0.241051 | ||||||||
\(573\) | 5.82994 | 0.243549 | ||||||||
\(574\) | 26.0005 | 1.08524 | ||||||||
\(575\) | −1.53948 | −0.0642007 | ||||||||
\(576\) | −2.95190 | −0.122996 | ||||||||
\(577\) | 6.63098 | 0.276051 | 0.138026 | − | 0.990429i | \(-0.455924\pi\) | ||||
0.138026 | + | 0.990429i | \(0.455924\pi\) | |||||||
\(578\) | −16.3975 | −0.682046 | ||||||||
\(579\) | −0.444630 | −0.0184782 | ||||||||
\(580\) | 11.0516 | 0.458892 | ||||||||
\(581\) | 39.5403 | 1.64041 | ||||||||
\(582\) | 0.200852 | 0.00832560 | ||||||||
\(583\) | 9.40509 | 0.389519 | ||||||||
\(584\) | −8.65662 | −0.358213 | ||||||||
\(585\) | 10.0012 | 0.413500 | ||||||||
\(586\) | 26.6325 | 1.10018 | ||||||||
\(587\) | −37.7032 | −1.55618 | −0.778088 | − | 0.628155i | \(-0.783810\pi\) | ||||
−0.778088 | + | 0.628155i | \(0.783810\pi\) | |||||||
\(588\) | −0.890621 | −0.0367286 | ||||||||
\(589\) | 2.88048 | 0.118688 | ||||||||
\(590\) | −21.4778 | −0.884227 | ||||||||
\(591\) | 5.13275 | 0.211133 | ||||||||
\(592\) | −7.10422 | −0.291982 | ||||||||
\(593\) | −2.24240 | −0.0920845 | −0.0460422 | − | 0.998939i | \(-0.514661\pi\) | ||||
−0.0460422 | + | 0.998939i | \(0.514661\pi\) | |||||||
\(594\) | 5.05210 | 0.207290 | ||||||||
\(595\) | −5.87143 | −0.240705 | ||||||||
\(596\) | 16.1543 | 0.661708 | ||||||||
\(597\) | −2.69441 | −0.110275 | ||||||||
\(598\) | 13.2541 | 0.541999 | ||||||||
\(599\) | 37.6138 | 1.53686 | 0.768430 | − | 0.639934i | \(-0.221038\pi\) | ||||
0.768430 | + | 0.639934i | \(0.221038\pi\) | |||||||
\(600\) | −0.0379485 | −0.00154924 | ||||||||
\(601\) | −21.9816 | −0.896650 | −0.448325 | − | 0.893871i | \(-0.647979\pi\) | ||||
−0.448325 | + | 0.893871i | \(0.647979\pi\) | |||||||
\(602\) | −0.600418 | −0.0244712 | ||||||||
\(603\) | 0.463943 | 0.0188932 | ||||||||
\(604\) | −2.60227 | −0.105885 | ||||||||
\(605\) | 9.04768 | 0.367841 | ||||||||
\(606\) | −3.05657 | −0.124164 | ||||||||
\(607\) | 18.8259 | 0.764118 | 0.382059 | − | 0.924138i | \(-0.375215\pi\) | ||||
0.382059 | + | 0.924138i | \(0.375215\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 3.54433 | 0.143623 | ||||||||
\(610\) | −13.3768 | −0.541612 | ||||||||
\(611\) | −5.85704 | −0.236951 | ||||||||
\(612\) | −2.29129 | −0.0926201 | ||||||||
\(613\) | −34.1263 | −1.37835 | −0.689174 | − | 0.724596i | \(-0.742027\pi\) | ||||
−0.689174 | + | 0.724596i | \(0.742027\pi\) | |||||||
\(614\) | 17.8341 | 0.719725 | ||||||||
\(615\) | 3.89988 | 0.157258 | ||||||||
\(616\) | −12.8712 | −0.518595 | ||||||||
\(617\) | −8.79088 | −0.353907 | −0.176954 | − | 0.984219i | \(-0.556624\pi\) | ||||
−0.176954 | + | 0.984219i | \(0.556624\pi\) | |||||||
\(618\) | −0.0474159 | −0.00190735 | ||||||||
\(619\) | −13.6216 | −0.547500 | −0.273750 | − | 0.961801i | \(-0.588264\pi\) | ||||
−0.273750 | + | 0.961801i | \(0.588264\pi\) | |||||||
\(620\) | 6.55143 | 0.263112 | ||||||||
\(621\) | −11.6149 | −0.466088 | ||||||||
\(622\) | −23.3430 | −0.935969 | ||||||||
\(623\) | −20.2494 | −0.811273 | ||||||||
\(624\) | 0.326715 | 0.0130791 | ||||||||
\(625\) | −25.8352 | −1.03341 | ||||||||
\(626\) | 0.540099 | 0.0215867 | ||||||||
\(627\) | −0.848822 | −0.0338987 | ||||||||
\(628\) | −22.9956 | −0.917623 | ||||||||
\(629\) | −5.51438 | −0.219873 | ||||||||
\(630\) | 22.3288 | 0.889600 | ||||||||
\(631\) | 16.0179 | 0.637664 | 0.318832 | − | 0.947811i | \(-0.396709\pi\) | ||||
0.318832 | + | 0.947811i | \(0.396709\pi\) | |||||||
\(632\) | −7.31318 | −0.290903 | ||||||||
\(633\) | 0.219326 | 0.00871741 | ||||||||
\(634\) | 17.0554 | 0.677356 | ||||||||
\(635\) | −12.0897 | −0.479766 | ||||||||
\(636\) | −0.532998 | −0.0211347 | ||||||||
\(637\) | −6.04900 | −0.239670 | ||||||||
\(638\) | 18.8053 | 0.744507 | ||||||||
\(639\) | −13.3068 | −0.526409 | ||||||||
\(640\) | 2.27443 | 0.0899047 | ||||||||
\(641\) | −7.21015 | −0.284784 | −0.142392 | − | 0.989810i | \(-0.545479\pi\) | ||||
−0.142392 | + | 0.989810i | \(0.545479\pi\) | |||||||
\(642\) | 1.94574 | 0.0767921 | ||||||||
\(643\) | 4.15506 | 0.163860 | 0.0819298 | − | 0.996638i | \(-0.473892\pi\) | ||||
0.0819298 | + | 0.996638i | \(0.473892\pi\) | |||||||
\(644\) | 29.5911 | 1.16605 | ||||||||
\(645\) | −0.0900583 | −0.00354604 | ||||||||
\(646\) | 0.776211 | 0.0305396 | ||||||||
\(647\) | 40.2218 | 1.58128 | 0.790642 | − | 0.612279i | \(-0.209747\pi\) | ||||
0.790642 | + | 0.612279i | \(0.209747\pi\) | |||||||
\(648\) | 8.56938 | 0.336637 | ||||||||
\(649\) | −36.5464 | −1.43457 | ||||||||
\(650\) | −0.257742 | −0.0101095 | ||||||||
\(651\) | 2.10109 | 0.0823483 | ||||||||
\(652\) | −0.813102 | −0.0318435 | ||||||||
\(653\) | −16.0758 | −0.629096 | −0.314548 | − | 0.949242i | \(-0.601853\pi\) | ||||
−0.314548 | + | 0.949242i | \(0.601853\pi\) | |||||||
\(654\) | 3.25094 | 0.127122 | ||||||||
\(655\) | 4.62977 | 0.180900 | ||||||||
\(656\) | −7.81788 | −0.305237 | ||||||||
\(657\) | 25.5534 | 0.996934 | ||||||||
\(658\) | −13.0765 | −0.509773 | ||||||||
\(659\) | −32.3698 | −1.26095 | −0.630473 | − | 0.776211i | \(-0.717139\pi\) | ||||
−0.630473 | + | 0.776211i | \(0.717139\pi\) | |||||||
\(660\) | −1.93058 | −0.0751479 | ||||||||
\(661\) | 28.3297 | 1.10190 | 0.550948 | − | 0.834539i | \(-0.314266\pi\) | ||||
0.550948 | + | 0.834539i | \(0.314266\pi\) | |||||||
\(662\) | 34.0474 | 1.32329 | ||||||||
\(663\) | 0.253600 | 0.00984900 | ||||||||
\(664\) | −11.8891 | −0.461386 | ||||||||
\(665\) | −7.56422 | −0.293328 | ||||||||
\(666\) | 20.9709 | 0.812607 | ||||||||
\(667\) | −43.2336 | −1.67401 | ||||||||
\(668\) | −0.224287 | −0.00867791 | ||||||||
\(669\) | −2.06664 | −0.0799009 | ||||||||
\(670\) | −0.357467 | −0.0138102 | ||||||||
\(671\) | −22.7619 | −0.878712 | ||||||||
\(672\) | 0.729426 | 0.0281382 | ||||||||
\(673\) | 5.58056 | 0.215115 | 0.107557 | − | 0.994199i | \(-0.465697\pi\) | ||||
0.107557 | + | 0.994199i | \(0.465697\pi\) | |||||||
\(674\) | −9.48533 | −0.365361 | ||||||||
\(675\) | 0.225865 | 0.00869356 | ||||||||
\(676\) | −10.7810 | −0.414653 | ||||||||
\(677\) | 36.5549 | 1.40492 | 0.702459 | − | 0.711724i | \(-0.252085\pi\) | ||||
0.702459 | + | 0.711724i | \(0.252085\pi\) | |||||||
\(678\) | −1.86096 | −0.0714696 | ||||||||
\(679\) | 3.04565 | 0.116881 | ||||||||
\(680\) | 1.76544 | 0.0677014 | ||||||||
\(681\) | 5.09727 | 0.195328 | ||||||||
\(682\) | 11.1478 | 0.426873 | ||||||||
\(683\) | −5.59207 | −0.213975 | −0.106987 | − | 0.994260i | \(-0.534120\pi\) | ||||
−0.106987 | + | 0.994260i | \(0.534120\pi\) | |||||||
\(684\) | −2.95190 | −0.112869 | ||||||||
\(685\) | 0.612370 | 0.0233975 | ||||||||
\(686\) | 9.77535 | 0.373224 | ||||||||
\(687\) | −1.10626 | −0.0422066 | ||||||||
\(688\) | 0.180535 | 0.00688284 | ||||||||
\(689\) | −3.62006 | −0.137913 | ||||||||
\(690\) | 4.43844 | 0.168969 | ||||||||
\(691\) | 7.35685 | 0.279868 | 0.139934 | − | 0.990161i | \(-0.455311\pi\) | ||||
0.139934 | + | 0.990161i | \(0.455311\pi\) | |||||||
\(692\) | −3.97111 | −0.150959 | ||||||||
\(693\) | 37.9944 | 1.44329 | ||||||||
\(694\) | −36.5159 | −1.38613 | ||||||||
\(695\) | 30.7420 | 1.16611 | ||||||||
\(696\) | −1.06572 | −0.0403959 | ||||||||
\(697\) | −6.06833 | −0.229854 | ||||||||
\(698\) | 5.10461 | 0.193212 | ||||||||
\(699\) | −0.00876102 | −0.000331372 0 | ||||||||
\(700\) | −0.575435 | −0.0217494 | ||||||||
\(701\) | 42.9081 | 1.62062 | 0.810308 | − | 0.586004i | \(-0.199300\pi\) | ||||
0.810308 | + | 0.586004i | \(0.199300\pi\) | |||||||
\(702\) | −1.94457 | −0.0733932 | ||||||||
\(703\) | −7.10422 | −0.267941 | ||||||||
\(704\) | 3.87014 | 0.145861 | ||||||||
\(705\) | −1.96137 | −0.0738696 | ||||||||
\(706\) | −9.06775 | −0.341269 | ||||||||
\(707\) | −46.3485 | −1.74312 | ||||||||
\(708\) | 2.07113 | 0.0778378 | ||||||||
\(709\) | 1.97574 | 0.0742004 | 0.0371002 | − | 0.999312i | \(-0.488188\pi\) | ||||
0.0371002 | + | 0.999312i | \(0.488188\pi\) | |||||||
\(710\) | 10.2529 | 0.384783 | ||||||||
\(711\) | 21.5878 | 0.809604 | ||||||||
\(712\) | 6.08863 | 0.228181 | ||||||||
\(713\) | −25.6291 | −0.959817 | ||||||||
\(714\) | 0.566188 | 0.0211891 | ||||||||
\(715\) | −13.1123 | −0.490372 | ||||||||
\(716\) | −1.17036 | −0.0437384 | ||||||||
\(717\) | −4.13144 | −0.154291 | ||||||||
\(718\) | 15.4124 | 0.575185 | ||||||||
\(719\) | 8.80075 | 0.328213 | 0.164106 | − | 0.986443i | \(-0.447526\pi\) | ||||
0.164106 | + | 0.986443i | \(0.447526\pi\) | |||||||
\(720\) | −6.71388 | −0.250211 | ||||||||
\(721\) | −0.718995 | −0.0267768 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 3.79540 | 0.141152 | ||||||||
\(724\) | −8.51244 | −0.316362 | ||||||||
\(725\) | 0.840731 | 0.0312240 | ||||||||
\(726\) | −0.872478 | −0.0323807 | ||||||||
\(727\) | −2.66065 | −0.0986782 | −0.0493391 | − | 0.998782i | \(-0.515711\pi\) | ||||
−0.0493391 | + | 0.998782i | \(0.515711\pi\) | |||||||
\(728\) | 4.95418 | 0.183614 | ||||||||
\(729\) | −24.4370 | −0.905074 | ||||||||
\(730\) | −19.6889 | −0.728717 | ||||||||
\(731\) | 0.140133 | 0.00518302 | ||||||||
\(732\) | 1.28994 | 0.0476776 | ||||||||
\(733\) | −29.0243 | −1.07204 | −0.536018 | − | 0.844207i | \(-0.680072\pi\) | ||||
−0.536018 | + | 0.844207i | \(0.680072\pi\) | |||||||
\(734\) | −23.5461 | −0.869102 | ||||||||
\(735\) | −2.02565 | −0.0747173 | ||||||||
\(736\) | −8.89752 | −0.327967 | ||||||||
\(737\) | −0.608262 | −0.0224056 | ||||||||
\(738\) | 23.0776 | 0.849498 | ||||||||
\(739\) | 33.7327 | 1.24088 | 0.620440 | − | 0.784254i | \(-0.286954\pi\) | ||||
0.620440 | + | 0.784254i | \(0.286954\pi\) | |||||||
\(740\) | −16.1580 | −0.593982 | ||||||||
\(741\) | 0.326715 | 0.0120022 | ||||||||
\(742\) | −8.08217 | −0.296706 | ||||||||
\(743\) | −33.7006 | −1.23636 | −0.618178 | − | 0.786038i | \(-0.712129\pi\) | ||||
−0.618178 | + | 0.786038i | \(0.712129\pi\) | |||||||
\(744\) | −0.631762 | −0.0231615 | ||||||||
\(745\) | 36.7419 | 1.34612 | ||||||||
\(746\) | 18.0439 | 0.660635 | ||||||||
\(747\) | 35.0954 | 1.28407 | ||||||||
\(748\) | 3.00405 | 0.109839 | ||||||||
\(749\) | 29.5044 | 1.07807 | ||||||||
\(750\) | 2.40789 | 0.0879237 | ||||||||
\(751\) | 46.4367 | 1.69450 | 0.847250 | − | 0.531194i | \(-0.178256\pi\) | ||||
0.847250 | + | 0.531194i | \(0.178256\pi\) | |||||||
\(752\) | 3.93186 | 0.143380 | ||||||||
\(753\) | −0.0402658 | −0.00146737 | ||||||||
\(754\) | −7.23823 | −0.263601 | ||||||||
\(755\) | −5.91868 | −0.215403 | ||||||||
\(756\) | −4.34147 | −0.157898 | ||||||||
\(757\) | 14.3009 | 0.519775 | 0.259887 | − | 0.965639i | \(-0.416315\pi\) | ||||
0.259887 | + | 0.965639i | \(0.416315\pi\) | |||||||
\(758\) | 25.5307 | 0.927318 | ||||||||
\(759\) | 7.55241 | 0.274135 | ||||||||
\(760\) | 2.27443 | 0.0825022 | ||||||||
\(761\) | −16.1913 | −0.586936 | −0.293468 | − | 0.955969i | \(-0.594809\pi\) | ||||
−0.293468 | + | 0.955969i | \(0.594809\pi\) | |||||||
\(762\) | 1.16583 | 0.0422334 | ||||||||
\(763\) | 49.2960 | 1.78463 | ||||||||
\(764\) | −26.5812 | −0.961674 | ||||||||
\(765\) | −5.21138 | −0.188418 | ||||||||
\(766\) | 10.9443 | 0.395433 | ||||||||
\(767\) | 14.0669 | 0.507925 | ||||||||
\(768\) | −0.219326 | −0.00791423 | ||||||||
\(769\) | −35.2375 | −1.27070 | −0.635349 | − | 0.772225i | \(-0.719144\pi\) | ||||
−0.635349 | + | 0.772225i | \(0.719144\pi\) | |||||||
\(770\) | −29.2746 | −1.05498 | ||||||||
\(771\) | 6.28283 | 0.226271 | ||||||||
\(772\) | 2.02726 | 0.0729627 | ||||||||
\(773\) | −16.6163 | −0.597646 | −0.298823 | − | 0.954308i | \(-0.596594\pi\) | ||||
−0.298823 | + | 0.954308i | \(0.596594\pi\) | |||||||
\(774\) | −0.532921 | −0.0191555 | ||||||||
\(775\) | 0.498390 | 0.0179027 | ||||||||
\(776\) | −0.915773 | −0.0328743 | ||||||||
\(777\) | −5.18200 | −0.185903 | ||||||||
\(778\) | 11.8152 | 0.423595 | ||||||||
\(779\) | −7.81788 | −0.280105 | ||||||||
\(780\) | 0.743090 | 0.0266069 | ||||||||
\(781\) | 17.4461 | 0.624272 | ||||||||
\(782\) | −6.90635 | −0.246971 | ||||||||
\(783\) | 6.34304 | 0.226682 | ||||||||
\(784\) | 4.06072 | 0.145026 | ||||||||
\(785\) | −52.3018 | −1.86673 | ||||||||
\(786\) | −0.446454 | −0.0159245 | ||||||||
\(787\) | 55.4813 | 1.97769 | 0.988847 | − | 0.148932i | \(-0.0475835\pi\) | ||||
0.988847 | + | 0.148932i | \(0.0475835\pi\) | |||||||
\(788\) | −23.4024 | −0.833676 | ||||||||
\(789\) | 2.98674 | 0.106331 | ||||||||
\(790\) | −16.6333 | −0.591787 | ||||||||
\(791\) | −28.2188 | −1.00335 | ||||||||
\(792\) | −11.4243 | −0.405943 | ||||||||
\(793\) | 8.76114 | 0.311117 | ||||||||
\(794\) | −25.4826 | −0.904343 | ||||||||
\(795\) | −1.21227 | −0.0429946 | ||||||||
\(796\) | 12.2850 | 0.435430 | ||||||||
\(797\) | −22.0708 | −0.781786 | −0.390893 | − | 0.920436i | \(-0.627834\pi\) | ||||
−0.390893 | + | 0.920436i | \(0.627834\pi\) | |||||||
\(798\) | 0.729426 | 0.0258214 | ||||||||
\(799\) | 3.05196 | 0.107970 | ||||||||
\(800\) | 0.173023 | 0.00611730 | ||||||||
\(801\) | −17.9730 | −0.635045 | ||||||||
\(802\) | −26.9100 | −0.950226 | ||||||||
\(803\) | −33.5023 | −1.18227 | ||||||||
\(804\) | 0.0344710 | 0.00121570 | ||||||||
\(805\) | 67.3028 | 2.37211 | ||||||||
\(806\) | −4.29086 | −0.151139 | ||||||||
\(807\) | 0.868401 | 0.0305692 | ||||||||
\(808\) | 13.9362 | 0.490274 | ||||||||
\(809\) | −25.6910 | −0.903248 | −0.451624 | − | 0.892208i | \(-0.649155\pi\) | ||||
−0.451624 | + | 0.892208i | \(0.649155\pi\) | |||||||
\(810\) | 19.4904 | 0.684824 | ||||||||
\(811\) | 11.5579 | 0.405854 | 0.202927 | − | 0.979194i | \(-0.434955\pi\) | ||||
0.202927 | + | 0.979194i | \(0.434955\pi\) | |||||||
\(812\) | −16.1601 | −0.567109 | ||||||||
\(813\) | 0.914757 | 0.0320819 | ||||||||
\(814\) | −27.4944 | −0.963677 | ||||||||
\(815\) | −1.84934 | −0.0647796 | ||||||||
\(816\) | −0.170243 | −0.00595970 | ||||||||
\(817\) | 0.180535 | 0.00631613 | ||||||||
\(818\) | −17.8779 | −0.625087 | ||||||||
\(819\) | −14.6242 | −0.511012 | ||||||||
\(820\) | −17.7812 | −0.620947 | ||||||||
\(821\) | 9.87345 | 0.344586 | 0.172293 | − | 0.985046i | \(-0.444882\pi\) | ||||
0.172293 | + | 0.985046i | \(0.444882\pi\) | |||||||
\(822\) | −0.0590515 | −0.00205966 | ||||||||
\(823\) | 39.6575 | 1.38237 | 0.691186 | − | 0.722677i | \(-0.257088\pi\) | ||||
0.691186 | + | 0.722677i | \(0.257088\pi\) | |||||||
\(824\) | 0.216189 | 0.00753131 | ||||||||
\(825\) | −0.146866 | −0.00511322 | ||||||||
\(826\) | 31.4058 | 1.09275 | ||||||||
\(827\) | −28.3694 | −0.986501 | −0.493250 | − | 0.869887i | \(-0.664191\pi\) | ||||
−0.493250 | + | 0.869887i | \(0.664191\pi\) | |||||||
\(828\) | 26.2646 | 0.912757 | ||||||||
\(829\) | −4.82781 | −0.167677 | −0.0838383 | − | 0.996479i | \(-0.526718\pi\) | ||||
−0.0838383 | + | 0.996479i | \(0.526718\pi\) | |||||||
\(830\) | −27.0409 | −0.938603 | ||||||||
\(831\) | −3.86294 | −0.134004 | ||||||||
\(832\) | −1.48964 | −0.0516438 | ||||||||
\(833\) | 3.15198 | 0.109210 | ||||||||
\(834\) | −2.96448 | −0.102652 | ||||||||
\(835\) | −0.510124 | −0.0176536 | ||||||||
\(836\) | 3.87014 | 0.133852 | ||||||||
\(837\) | 3.76018 | 0.129971 | ||||||||
\(838\) | 1.95105 | 0.0673979 | ||||||||
\(839\) | −5.59719 | −0.193237 | −0.0966183 | − | 0.995322i | \(-0.530803\pi\) | ||||
−0.0966183 | + | 0.995322i | \(0.530803\pi\) | |||||||
\(840\) | 1.65903 | 0.0572419 | ||||||||
\(841\) | −5.38952 | −0.185845 | ||||||||
\(842\) | 7.76004 | 0.267429 | ||||||||
\(843\) | 3.32313 | 0.114455 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −24.5206 | −0.843534 | ||||||||
\(846\) | −11.6065 | −0.399038 | ||||||||
\(847\) | −13.2299 | −0.454585 | ||||||||
\(848\) | 2.43017 | 0.0834523 | ||||||||
\(849\) | −7.08084 | −0.243014 | ||||||||
\(850\) | 0.134303 | 0.00460654 | ||||||||
\(851\) | 63.2100 | 2.16681 | ||||||||
\(852\) | −0.988694 | −0.0338721 | ||||||||
\(853\) | 44.5474 | 1.52527 | 0.762637 | − | 0.646827i | \(-0.223904\pi\) | ||||
0.762637 | + | 0.646827i | \(0.223904\pi\) | |||||||
\(854\) | 19.5602 | 0.669335 | ||||||||
\(855\) | −6.71388 | −0.229610 | ||||||||
\(856\) | −8.87146 | −0.303220 | ||||||||
\(857\) | −17.4083 | −0.594656 | −0.297328 | − | 0.954775i | \(-0.596096\pi\) | ||||
−0.297328 | + | 0.954775i | \(0.596096\pi\) | |||||||
\(858\) | 1.26443 | 0.0431671 | ||||||||
\(859\) | −32.1652 | −1.09746 | −0.548731 | − | 0.835999i | \(-0.684889\pi\) | ||||
−0.548731 | + | 0.835999i | \(0.684889\pi\) | |||||||
\(860\) | 0.410614 | 0.0140018 | ||||||||
\(861\) | −5.70257 | −0.194343 | ||||||||
\(862\) | −12.2312 | −0.416596 | ||||||||
\(863\) | 44.8554 | 1.52689 | 0.763447 | − | 0.645870i | \(-0.223505\pi\) | ||||
0.763447 | + | 0.645870i | \(0.223505\pi\) | |||||||
\(864\) | 1.30540 | 0.0444107 | ||||||||
\(865\) | −9.03200 | −0.307097 | ||||||||
\(866\) | 18.6933 | 0.635224 | ||||||||
\(867\) | 3.59639 | 0.122140 | ||||||||
\(868\) | −9.57979 | −0.325159 | ||||||||
\(869\) | −28.3031 | −0.960116 | ||||||||
\(870\) | −2.42390 | −0.0821778 | ||||||||
\(871\) | 0.234123 | 0.00793295 | ||||||||
\(872\) | −14.8224 | −0.501951 | ||||||||
\(873\) | 2.70327 | 0.0914917 | ||||||||
\(874\) | −8.89752 | −0.300963 | ||||||||
\(875\) | 36.5123 | 1.23434 | ||||||||
\(876\) | 1.89862 | 0.0641484 | ||||||||
\(877\) | 32.1443 | 1.08544 | 0.542718 | − | 0.839915i | \(-0.317395\pi\) | ||||
0.542718 | + | 0.839915i | \(0.317395\pi\) | |||||||
\(878\) | −10.4972 | −0.354264 | ||||||||
\(879\) | −5.84120 | −0.197019 | ||||||||
\(880\) | 8.80236 | 0.296728 | ||||||||
\(881\) | 14.7435 | 0.496721 | 0.248361 | − | 0.968668i | \(-0.420108\pi\) | ||||
0.248361 | + | 0.968668i | \(0.420108\pi\) | |||||||
\(882\) | −11.9868 | −0.403618 | ||||||||
\(883\) | −53.3082 | −1.79396 | −0.896981 | − | 0.442068i | \(-0.854245\pi\) | ||||
−0.896981 | + | 0.442068i | \(0.854245\pi\) | |||||||
\(884\) | −1.15627 | −0.0388896 | ||||||||
\(885\) | 4.71063 | 0.158346 | ||||||||
\(886\) | 38.5842 | 1.29626 | ||||||||
\(887\) | −15.3308 | −0.514757 | −0.257379 | − | 0.966311i | \(-0.582859\pi\) | ||||
−0.257379 | + | 0.966311i | \(0.582859\pi\) | |||||||
\(888\) | 1.55814 | 0.0522877 | ||||||||
\(889\) | 17.6781 | 0.592905 | ||||||||
\(890\) | 13.8481 | 0.464191 | ||||||||
\(891\) | 33.1647 | 1.11106 | ||||||||
\(892\) | 9.42269 | 0.315495 | ||||||||
\(893\) | 3.93186 | 0.131575 | ||||||||
\(894\) | −3.54306 | −0.118498 | ||||||||
\(895\) | −2.66190 | −0.0889775 | ||||||||
\(896\) | −3.32577 | −0.111106 | ||||||||
\(897\) | −2.90696 | −0.0970604 | ||||||||
\(898\) | −30.0086 | −1.00140 | ||||||||
\(899\) | 13.9964 | 0.466806 | ||||||||
\(900\) | −0.510747 | −0.0170249 | ||||||||
\(901\) | 1.88632 | 0.0628425 | ||||||||
\(902\) | −30.2563 | −1.00743 | ||||||||
\(903\) | 0.131687 | 0.00438227 | ||||||||
\(904\) | 8.48491 | 0.282204 | ||||||||
\(905\) | −19.3609 | −0.643579 | ||||||||
\(906\) | 0.570745 | 0.0189617 | ||||||||
\(907\) | −55.8503 | −1.85448 | −0.927240 | − | 0.374467i | \(-0.877826\pi\) | ||||
−0.927240 | + | 0.374467i | \(0.877826\pi\) | |||||||
\(908\) | −23.2406 | −0.771268 | ||||||||
\(909\) | −41.1382 | −1.36447 | ||||||||
\(910\) | 11.2679 | 0.373528 | ||||||||
\(911\) | 8.85277 | 0.293305 | 0.146653 | − | 0.989188i | \(-0.453150\pi\) | ||||
0.146653 | + | 0.989188i | \(0.453150\pi\) | |||||||
\(912\) | −0.219326 | −0.00726260 | ||||||||
\(913\) | −46.0125 | −1.52279 | ||||||||
\(914\) | 34.4348 | 1.13900 | ||||||||
\(915\) | 2.93388 | 0.0969911 | ||||||||
\(916\) | 5.04393 | 0.166656 | ||||||||
\(917\) | −6.76985 | −0.223560 | ||||||||
\(918\) | 1.01327 | 0.0334428 | ||||||||
\(919\) | 42.5615 | 1.40397 | 0.701987 | − | 0.712190i | \(-0.252297\pi\) | ||||
0.701987 | + | 0.712190i | \(0.252297\pi\) | |||||||
\(920\) | −20.2368 | −0.667187 | ||||||||
\(921\) | −3.91147 | −0.128887 | ||||||||
\(922\) | −8.96726 | −0.295321 | ||||||||
\(923\) | −6.71510 | −0.221030 | ||||||||
\(924\) | 2.82298 | 0.0928693 | ||||||||
\(925\) | −1.22920 | −0.0404157 | ||||||||
\(926\) | −12.2753 | −0.403391 | ||||||||
\(927\) | −0.638168 | −0.0209602 | ||||||||
\(928\) | 4.85906 | 0.159507 | ||||||||
\(929\) | −2.58457 | −0.0847969 | −0.0423984 | − | 0.999101i | \(-0.513500\pi\) | ||||
−0.0423984 | + | 0.999101i | \(0.513500\pi\) | |||||||
\(930\) | −1.43690 | −0.0471177 | ||||||||
\(931\) | 4.06072 | 0.133085 | ||||||||
\(932\) | 0.0399453 | 0.00130845 | ||||||||
\(933\) | 5.11972 | 0.167612 | ||||||||
\(934\) | 37.4755 | 1.22623 | ||||||||
\(935\) | 6.83249 | 0.223446 | ||||||||
\(936\) | 4.39725 | 0.143729 | ||||||||
\(937\) | −41.7399 | −1.36358 | −0.681792 | − | 0.731546i | \(-0.738799\pi\) | ||||
−0.681792 | + | 0.731546i | \(0.738799\pi\) | |||||||
\(938\) | 0.522704 | 0.0170669 | ||||||||
\(939\) | −0.118457 | −0.00386571 | ||||||||
\(940\) | 8.94274 | 0.291680 | ||||||||
\(941\) | 47.6551 | 1.55351 | 0.776756 | − | 0.629801i | \(-0.216864\pi\) | ||||
0.776756 | + | 0.629801i | \(0.216864\pi\) | |||||||
\(942\) | 5.04352 | 0.164327 | ||||||||
\(943\) | 69.5598 | 2.26518 | ||||||||
\(944\) | −9.44317 | −0.307349 | ||||||||
\(945\) | −9.87436 | −0.321213 | ||||||||
\(946\) | 0.698697 | 0.0227166 | ||||||||
\(947\) | 19.9334 | 0.647747 | 0.323874 | − | 0.946100i | \(-0.395015\pi\) | ||||
0.323874 | + | 0.946100i | \(0.395015\pi\) | |||||||
\(948\) | 1.60397 | 0.0520945 | ||||||||
\(949\) | 12.8952 | 0.418596 | ||||||||
\(950\) | 0.173023 | 0.00561362 | ||||||||
\(951\) | −3.74068 | −0.121300 | ||||||||
\(952\) | −2.58150 | −0.0836668 | ||||||||
\(953\) | −8.20450 | −0.265770 | −0.132885 | − | 0.991131i | \(-0.542424\pi\) | ||||
−0.132885 | + | 0.991131i | \(0.542424\pi\) | |||||||
\(954\) | −7.17360 | −0.232254 | ||||||||
\(955\) | −60.4570 | −1.95634 | ||||||||
\(956\) | 18.8370 | 0.609233 | ||||||||
\(957\) | −4.12448 | −0.133325 | ||||||||
\(958\) | −0.888395 | −0.0287027 | ||||||||
\(959\) | −0.895434 | −0.0289151 | ||||||||
\(960\) | −0.498840 | −0.0161000 | ||||||||
\(961\) | −22.7029 | −0.732350 | ||||||||
\(962\) | 10.5827 | 0.341200 | ||||||||
\(963\) | 26.1876 | 0.843884 | ||||||||
\(964\) | −17.3048 | −0.557352 | ||||||||
\(965\) | 4.61086 | 0.148429 | ||||||||
\(966\) | −6.49008 | −0.208815 | ||||||||
\(967\) | −3.43780 | −0.110552 | −0.0552762 | − | 0.998471i | \(-0.517604\pi\) | ||||
−0.0552762 | + | 0.998471i | \(0.517604\pi\) | |||||||
\(968\) | 3.97800 | 0.127858 | ||||||||
\(969\) | −0.170243 | −0.00546899 | ||||||||
\(970\) | −2.08286 | −0.0668766 | ||||||||
\(971\) | 28.9208 | 0.928112 | 0.464056 | − | 0.885806i | \(-0.346394\pi\) | ||||
0.464056 | + | 0.885806i | \(0.346394\pi\) | |||||||
\(972\) | −5.79570 | −0.185897 | ||||||||
\(973\) | −44.9522 | −1.44110 | ||||||||
\(974\) | −22.8576 | −0.732404 | ||||||||
\(975\) | 0.0565294 | 0.00181039 | ||||||||
\(976\) | −5.88140 | −0.188259 | ||||||||
\(977\) | 8.58772 | 0.274746 | 0.137373 | − | 0.990519i | \(-0.456134\pi\) | ||||
0.137373 | + | 0.990519i | \(0.456134\pi\) | |||||||
\(978\) | 0.178334 | 0.00570249 | ||||||||
\(979\) | 23.5639 | 0.753104 | ||||||||
\(980\) | 9.23582 | 0.295028 | ||||||||
\(981\) | 43.7543 | 1.39697 | ||||||||
\(982\) | 12.6592 | 0.403972 | ||||||||
\(983\) | −19.0744 | −0.608378 | −0.304189 | − | 0.952612i | \(-0.598385\pi\) | ||||
−0.304189 | + | 0.952612i | \(0.598385\pi\) | |||||||
\(984\) | 1.71466 | 0.0546614 | ||||||||
\(985\) | −53.2271 | −1.69596 | ||||||||
\(986\) | 3.77166 | 0.120114 | ||||||||
\(987\) | 2.86800 | 0.0912895 | ||||||||
\(988\) | −1.48964 | −0.0473916 | ||||||||
\(989\) | −1.60632 | −0.0510779 | ||||||||
\(990\) | −25.9837 | −0.825815 | ||||||||
\(991\) | 54.0756 | 1.71777 | 0.858884 | − | 0.512170i | \(-0.171158\pi\) | ||||
0.858884 | + | 0.512170i | \(0.171158\pi\) | |||||||
\(992\) | 2.88048 | 0.0914552 | ||||||||
\(993\) | −7.46747 | −0.236973 | ||||||||
\(994\) | −14.9922 | −0.475523 | ||||||||
\(995\) | 27.9413 | 0.885799 | ||||||||
\(996\) | 2.60758 | 0.0826244 | ||||||||
\(997\) | −29.1666 | −0.923714 | −0.461857 | − | 0.886954i | \(-0.652817\pi\) | ||||
−0.461857 | + | 0.886954i | \(0.652817\pi\) | |||||||
\(998\) | 43.5023 | 1.37704 | ||||||||
\(999\) | −9.27388 | −0.293412 |
(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 | 8018.2.a.d.1.16 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.d.1.16 | ✓ | 30 | 1.1 | even | 1 | trivial |