Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(0\) |
Dimension: | \(259\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64523 | −1.87046 | −0.935232 | − | 0.354036i | \(-0.884809\pi\) | ||||
−0.935232 | + | 0.354036i | \(0.884809\pi\) | |||||||
\(3\) | 1.84208 | 1.06353 | 0.531764 | − | 0.846893i | \(-0.321529\pi\) | ||||
0.531764 | + | 0.846893i | \(0.321529\pi\) | |||||||
\(4\) | 4.99727 | 2.49863 | ||||||||
\(5\) | 3.41959 | 1.52929 | 0.764644 | − | 0.644453i | \(-0.222915\pi\) | ||||
0.764644 | + | 0.644453i | \(0.222915\pi\) | |||||||
\(6\) | −4.87275 | −1.98929 | ||||||||
\(7\) | 2.32041 | 0.877033 | 0.438517 | − | 0.898723i | \(-0.355504\pi\) | ||||
0.438517 | + | 0.898723i | \(0.355504\pi\) | |||||||
\(8\) | −7.92847 | −2.80314 | ||||||||
\(9\) | 0.393274 | 0.131091 | ||||||||
\(10\) | −9.04562 | −2.86048 | ||||||||
\(11\) | 5.19178 | 1.56538 | 0.782690 | − | 0.622412i | \(-0.213847\pi\) | ||||
0.782690 | + | 0.622412i | \(0.213847\pi\) | |||||||
\(12\) | 9.20539 | 2.65737 | ||||||||
\(13\) | −0.0581155 | −0.0161183 | −0.00805917 | − | 0.999968i | \(-0.502565\pi\) | ||||
−0.00805917 | + | 0.999968i | \(0.502565\pi\) | |||||||
\(14\) | −6.13803 | −1.64046 | ||||||||
\(15\) | 6.29918 | 1.62644 | ||||||||
\(16\) | 10.9781 | 2.74454 | ||||||||
\(17\) | 2.10063 | 0.509478 | 0.254739 | − | 0.967010i | \(-0.418010\pi\) | ||||
0.254739 | + | 0.967010i | \(0.418010\pi\) | |||||||
\(18\) | −1.04030 | −0.245202 | ||||||||
\(19\) | −0.713359 | −0.163656 | −0.0818279 | − | 0.996646i | \(-0.526076\pi\) | ||||
−0.0818279 | + | 0.996646i | \(0.526076\pi\) | |||||||
\(20\) | 17.0886 | 3.82113 | ||||||||
\(21\) | 4.27439 | 0.932749 | ||||||||
\(22\) | −13.7335 | −2.92799 | ||||||||
\(23\) | −6.51049 | −1.35753 | −0.678766 | − | 0.734355i | \(-0.737485\pi\) | ||||
−0.678766 | + | 0.734355i | \(0.737485\pi\) | |||||||
\(24\) | −14.6049 | −2.98122 | ||||||||
\(25\) | 6.69361 | 1.33872 | ||||||||
\(26\) | 0.153729 | 0.0301488 | ||||||||
\(27\) | −4.80181 | −0.924108 | ||||||||
\(28\) | 11.5957 | 2.19138 | ||||||||
\(29\) | 6.22765 | 1.15645 | 0.578223 | − | 0.815879i | \(-0.303746\pi\) | ||||
0.578223 | + | 0.815879i | \(0.303746\pi\) | |||||||
\(30\) | −16.6628 | −3.04220 | ||||||||
\(31\) | 4.81404 | 0.864627 | 0.432313 | − | 0.901723i | \(-0.357697\pi\) | ||||
0.432313 | + | 0.901723i | \(0.357697\pi\) | |||||||
\(32\) | −13.1828 | −2.33041 | ||||||||
\(33\) | 9.56369 | 1.66483 | ||||||||
\(34\) | −5.55667 | −0.952961 | ||||||||
\(35\) | 7.93486 | 1.34124 | ||||||||
\(36\) | 1.96530 | 0.327549 | ||||||||
\(37\) | 1.73351 | 0.284987 | 0.142494 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142494 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(38\) | 1.88700 | 0.306112 | ||||||||
\(39\) | −0.107054 | −0.0171423 | ||||||||
\(40\) | −27.1121 | −4.28681 | ||||||||
\(41\) | −1.43097 | −0.223480 | −0.111740 | − | 0.993737i | \(-0.535642\pi\) | ||||
−0.111740 | + | 0.993737i | \(0.535642\pi\) | |||||||
\(42\) | −11.3068 | −1.74467 | ||||||||
\(43\) | 1.24497 | 0.189856 | 0.0949279 | − | 0.995484i | \(-0.469738\pi\) | ||||
0.0949279 | + | 0.995484i | \(0.469738\pi\) | |||||||
\(44\) | 25.9447 | 3.91131 | ||||||||
\(45\) | 1.34484 | 0.200476 | ||||||||
\(46\) | 17.2218 | 2.53921 | ||||||||
\(47\) | −0.930089 | −0.135667 | −0.0678337 | − | 0.997697i | \(-0.521609\pi\) | ||||
−0.0678337 | + | 0.997697i | \(0.521609\pi\) | |||||||
\(48\) | 20.2227 | 2.91889 | ||||||||
\(49\) | −1.61569 | −0.230813 | ||||||||
\(50\) | −17.7062 | −2.50403 | ||||||||
\(51\) | 3.86954 | 0.541844 | ||||||||
\(52\) | −0.290419 | −0.0402738 | ||||||||
\(53\) | 7.34647 | 1.00911 | 0.504557 | − | 0.863378i | \(-0.331656\pi\) | ||||
0.504557 | + | 0.863378i | \(0.331656\pi\) | |||||||
\(54\) | 12.7019 | 1.72851 | ||||||||
\(55\) | 17.7538 | 2.39392 | ||||||||
\(56\) | −18.3973 | −2.45845 | ||||||||
\(57\) | −1.31407 | −0.174053 | ||||||||
\(58\) | −16.4736 | −2.16309 | ||||||||
\(59\) | 2.49443 | 0.324747 | 0.162374 | − | 0.986729i | \(-0.448085\pi\) | ||||
0.162374 | + | 0.986729i | \(0.448085\pi\) | |||||||
\(60\) | 31.4787 | 4.06388 | ||||||||
\(61\) | −4.42290 | −0.566294 | −0.283147 | − | 0.959076i | \(-0.591378\pi\) | ||||
−0.283147 | + | 0.959076i | \(0.591378\pi\) | |||||||
\(62\) | −12.7343 | −1.61725 | ||||||||
\(63\) | 0.912558 | 0.114971 | ||||||||
\(64\) | 12.9154 | 1.61442 | ||||||||
\(65\) | −0.198731 | −0.0246496 | ||||||||
\(66\) | −25.2982 | −3.11399 | ||||||||
\(67\) | 12.8794 | 1.57347 | 0.786733 | − | 0.617294i | \(-0.211771\pi\) | ||||
0.786733 | + | 0.617294i | \(0.211771\pi\) | |||||||
\(68\) | 10.4974 | 1.27300 | ||||||||
\(69\) | −11.9929 | −1.44377 | ||||||||
\(70\) | −20.9896 | −2.50873 | ||||||||
\(71\) | −13.6439 | −1.61924 | −0.809619 | − | 0.586956i | \(-0.800326\pi\) | ||||
−0.809619 | + | 0.586956i | \(0.800326\pi\) | |||||||
\(72\) | −3.11806 | −0.367467 | ||||||||
\(73\) | −4.24298 | −0.496603 | −0.248301 | − | 0.968683i | \(-0.579872\pi\) | ||||
−0.248301 | + | 0.968683i | \(0.579872\pi\) | |||||||
\(74\) | −4.58554 | −0.533058 | ||||||||
\(75\) | 12.3302 | 1.42377 | ||||||||
\(76\) | −3.56485 | −0.408916 | ||||||||
\(77\) | 12.0471 | 1.37289 | ||||||||
\(78\) | 0.283182 | 0.0320641 | ||||||||
\(79\) | −1.43461 | −0.161406 | −0.0807031 | − | 0.996738i | \(-0.525717\pi\) | ||||
−0.0807031 | + | 0.996738i | \(0.525717\pi\) | |||||||
\(80\) | 37.5408 | 4.19719 | ||||||||
\(81\) | −10.0252 | −1.11391 | ||||||||
\(82\) | 3.78526 | 0.418012 | ||||||||
\(83\) | 7.23231 | 0.793849 | 0.396925 | − | 0.917851i | \(-0.370077\pi\) | ||||
0.396925 | + | 0.917851i | \(0.370077\pi\) | |||||||
\(84\) | 21.3603 | 2.33060 | ||||||||
\(85\) | 7.18331 | 0.779139 | ||||||||
\(86\) | −3.29323 | −0.355118 | ||||||||
\(87\) | 11.4719 | 1.22991 | ||||||||
\(88\) | −41.1629 | −4.38798 | ||||||||
\(89\) | −12.8322 | −1.36021 | −0.680103 | − | 0.733116i | \(-0.738065\pi\) | ||||
−0.680103 | + | 0.733116i | \(0.738065\pi\) | |||||||
\(90\) | −3.55741 | −0.374984 | ||||||||
\(91\) | −0.134852 | −0.0141363 | ||||||||
\(92\) | −32.5347 | −3.39197 | ||||||||
\(93\) | 8.86786 | 0.919555 | ||||||||
\(94\) | 2.46031 | 0.253761 | ||||||||
\(95\) | −2.43940 | −0.250277 | ||||||||
\(96\) | −24.2839 | −2.47846 | ||||||||
\(97\) | 3.69283 | 0.374950 | 0.187475 | − | 0.982269i | \(-0.439970\pi\) | ||||
0.187475 | + | 0.982269i | \(0.439970\pi\) | |||||||
\(98\) | 4.27388 | 0.431727 | ||||||||
\(99\) | 2.04179 | 0.205208 | ||||||||
\(100\) | 33.4498 | 3.34498 | ||||||||
\(101\) | −3.59853 | −0.358067 | −0.179034 | − | 0.983843i | \(-0.557297\pi\) | ||||
−0.179034 | + | 0.983843i | \(0.557297\pi\) | |||||||
\(102\) | −10.2359 | −1.01350 | ||||||||
\(103\) | −9.80860 | −0.966470 | −0.483235 | − | 0.875491i | \(-0.660538\pi\) | ||||
−0.483235 | + | 0.875491i | \(0.660538\pi\) | |||||||
\(104\) | 0.460767 | 0.0451820 | ||||||||
\(105\) | 14.6167 | 1.42644 | ||||||||
\(106\) | −19.4331 | −1.88751 | ||||||||
\(107\) | 3.02709 | 0.292640 | 0.146320 | − | 0.989237i | \(-0.453257\pi\) | ||||
0.146320 | + | 0.989237i | \(0.453257\pi\) | |||||||
\(108\) | −23.9959 | −2.30901 | ||||||||
\(109\) | −6.80667 | −0.651960 | −0.325980 | − | 0.945377i | \(-0.605694\pi\) | ||||
−0.325980 | + | 0.945377i | \(0.605694\pi\) | |||||||
\(110\) | −46.9629 | −4.47773 | ||||||||
\(111\) | 3.19327 | 0.303092 | ||||||||
\(112\) | 25.4738 | 2.40705 | ||||||||
\(113\) | 7.21078 | 0.678333 | 0.339167 | − | 0.940726i | \(-0.389855\pi\) | ||||
0.339167 | + | 0.940726i | \(0.389855\pi\) | |||||||
\(114\) | 3.47602 | 0.325559 | ||||||||
\(115\) | −22.2632 | −2.07606 | ||||||||
\(116\) | 31.1212 | 2.88953 | ||||||||
\(117\) | −0.0228553 | −0.00211298 | ||||||||
\(118\) | −6.59835 | −0.607428 | ||||||||
\(119\) | 4.87433 | 0.446829 | ||||||||
\(120\) | −49.9429 | −4.55914 | ||||||||
\(121\) | 15.9546 | 1.45041 | ||||||||
\(122\) | 11.6996 | 1.05923 | ||||||||
\(123\) | −2.63597 | −0.237677 | ||||||||
\(124\) | 24.0570 | 2.16039 | ||||||||
\(125\) | 5.79145 | 0.518003 | ||||||||
\(126\) | −2.41393 | −0.215050 | ||||||||
\(127\) | 13.3896 | 1.18813 | 0.594066 | − | 0.804416i | \(-0.297522\pi\) | ||||
0.594066 | + | 0.804416i | \(0.297522\pi\) | |||||||
\(128\) | −7.79851 | −0.689298 | ||||||||
\(129\) | 2.29333 | 0.201917 | ||||||||
\(130\) | 0.525691 | 0.0461062 | ||||||||
\(131\) | 15.9538 | 1.39389 | 0.696945 | − | 0.717125i | \(-0.254542\pi\) | ||||
0.696945 | + | 0.717125i | \(0.254542\pi\) | |||||||
\(132\) | 47.7923 | 4.15979 | ||||||||
\(133\) | −1.65529 | −0.143532 | ||||||||
\(134\) | −34.0690 | −2.94311 | ||||||||
\(135\) | −16.4202 | −1.41323 | ||||||||
\(136\) | −16.6548 | −1.42814 | ||||||||
\(137\) | 8.97426 | 0.766722 | 0.383361 | − | 0.923598i | \(-0.374766\pi\) | ||||
0.383361 | + | 0.923598i | \(0.374766\pi\) | |||||||
\(138\) | 31.7240 | 2.70052 | ||||||||
\(139\) | −3.49221 | −0.296205 | −0.148103 | − | 0.988972i | \(-0.547317\pi\) | ||||
−0.148103 | + | 0.988972i | \(0.547317\pi\) | |||||||
\(140\) | 39.6526 | 3.35126 | ||||||||
\(141\) | −1.71330 | −0.144286 | ||||||||
\(142\) | 36.0914 | 3.02873 | ||||||||
\(143\) | −0.301723 | −0.0252313 | ||||||||
\(144\) | 4.31742 | 0.359785 | ||||||||
\(145\) | 21.2960 | 1.76854 | ||||||||
\(146\) | 11.2237 | 0.928878 | ||||||||
\(147\) | −2.97624 | −0.245476 | ||||||||
\(148\) | 8.66280 | 0.712078 | ||||||||
\(149\) | 12.9567 | 1.06145 | 0.530726 | − | 0.847543i | \(-0.321919\pi\) | ||||
0.530726 | + | 0.847543i | \(0.321919\pi\) | |||||||
\(150\) | −32.6163 | −2.66311 | ||||||||
\(151\) | −4.51215 | −0.367194 | −0.183597 | − | 0.983002i | \(-0.558774\pi\) | ||||
−0.183597 | + | 0.983002i | \(0.558774\pi\) | |||||||
\(152\) | 5.65585 | 0.458750 | ||||||||
\(153\) | 0.826125 | 0.0667882 | ||||||||
\(154\) | −31.8673 | −2.56794 | ||||||||
\(155\) | 16.4620 | 1.32226 | ||||||||
\(156\) | −0.534976 | −0.0428323 | ||||||||
\(157\) | 14.4989 | 1.15714 | 0.578569 | − | 0.815634i | \(-0.303611\pi\) | ||||
0.578569 | + | 0.815634i | \(0.303611\pi\) | |||||||
\(158\) | 3.79488 | 0.301904 | ||||||||
\(159\) | 13.5328 | 1.07322 | ||||||||
\(160\) | −45.0798 | −3.56387 | ||||||||
\(161\) | −15.1070 | −1.19060 | ||||||||
\(162\) | 26.5189 | 2.08352 | ||||||||
\(163\) | −23.4553 | −1.83716 | −0.918582 | − | 0.395230i | \(-0.870665\pi\) | ||||
−0.918582 | + | 0.395230i | \(0.870665\pi\) | |||||||
\(164\) | −7.15095 | −0.558395 | ||||||||
\(165\) | 32.7039 | 2.54600 | ||||||||
\(166\) | −19.1312 | −1.48487 | ||||||||
\(167\) | −0.0685580 | −0.00530518 | −0.00265259 | − | 0.999996i | \(-0.500844\pi\) | ||||
−0.00265259 | + | 0.999996i | \(0.500844\pi\) | |||||||
\(168\) | −33.8894 | −2.61463 | ||||||||
\(169\) | −12.9966 | −0.999740 | ||||||||
\(170\) | −19.0015 | −1.45735 | ||||||||
\(171\) | −0.280546 | −0.0214539 | ||||||||
\(172\) | 6.22143 | 0.474380 | ||||||||
\(173\) | −10.2040 | −0.775799 | −0.387900 | − | 0.921702i | \(-0.626799\pi\) | ||||
−0.387900 | + | 0.921702i | \(0.626799\pi\) | |||||||
\(174\) | −30.3458 | −2.30051 | ||||||||
\(175\) | 15.5319 | 1.17410 | ||||||||
\(176\) | 56.9961 | 4.29624 | ||||||||
\(177\) | 4.59495 | 0.345378 | ||||||||
\(178\) | 33.9441 | 2.54422 | ||||||||
\(179\) | 18.5912 | 1.38957 | 0.694785 | − | 0.719217i | \(-0.255499\pi\) | ||||
0.694785 | + | 0.719217i | \(0.255499\pi\) | |||||||
\(180\) | 6.72051 | 0.500917 | ||||||||
\(181\) | −4.17063 | −0.310001 | −0.155000 | − | 0.987914i | \(-0.549538\pi\) | ||||
−0.155000 | + | 0.987914i | \(0.549538\pi\) | |||||||
\(182\) | 0.356715 | 0.0264415 | ||||||||
\(183\) | −8.14735 | −0.602270 | ||||||||
\(184\) | 51.6183 | 3.80535 | ||||||||
\(185\) | 5.92789 | 0.435827 | ||||||||
\(186\) | −23.4576 | −1.71999 | ||||||||
\(187\) | 10.9060 | 0.797527 | ||||||||
\(188\) | −4.64791 | −0.338983 | ||||||||
\(189\) | −11.1422 | −0.810474 | ||||||||
\(190\) | 6.45278 | 0.468134 | ||||||||
\(191\) | 14.1651 | 1.02495 | 0.512476 | − | 0.858701i | \(-0.328728\pi\) | ||||
0.512476 | + | 0.858701i | \(0.328728\pi\) | |||||||
\(192\) | 23.7912 | 1.71698 | ||||||||
\(193\) | 19.1396 | 1.37770 | 0.688848 | − | 0.724906i | \(-0.258117\pi\) | ||||
0.688848 | + | 0.724906i | \(0.258117\pi\) | |||||||
\(194\) | −9.76840 | −0.701330 | ||||||||
\(195\) | −0.366080 | −0.0262155 | ||||||||
\(196\) | −8.07404 | −0.576717 | ||||||||
\(197\) | 19.9650 | 1.42245 | 0.711223 | − | 0.702966i | \(-0.248141\pi\) | ||||
0.711223 | + | 0.702966i | \(0.248141\pi\) | |||||||
\(198\) | −5.40102 | −0.383834 | ||||||||
\(199\) | −6.35378 | −0.450408 | −0.225204 | − | 0.974312i | \(-0.572305\pi\) | ||||
−0.225204 | + | 0.974312i | \(0.572305\pi\) | |||||||
\(200\) | −53.0701 | −3.75262 | ||||||||
\(201\) | 23.7249 | 1.67342 | ||||||||
\(202\) | 9.51896 | 0.669752 | ||||||||
\(203\) | 14.4507 | 1.01424 | ||||||||
\(204\) | 19.3371 | 1.35387 | ||||||||
\(205\) | −4.89334 | −0.341766 | ||||||||
\(206\) | 25.9461 | 1.80775 | ||||||||
\(207\) | −2.56041 | −0.177961 | ||||||||
\(208\) | −0.638000 | −0.0442374 | ||||||||
\(209\) | −3.70360 | −0.256184 | ||||||||
\(210\) | −38.6646 | −2.66811 | ||||||||
\(211\) | −7.81369 | −0.537917 | −0.268958 | − | 0.963152i | \(-0.586679\pi\) | ||||
−0.268958 | + | 0.963152i | \(0.586679\pi\) | |||||||
\(212\) | 36.7123 | 2.52141 | ||||||||
\(213\) | −25.1333 | −1.72211 | ||||||||
\(214\) | −8.00738 | −0.547373 | ||||||||
\(215\) | 4.25728 | 0.290344 | ||||||||
\(216\) | 38.0710 | 2.59040 | ||||||||
\(217\) | 11.1705 | 0.758306 | ||||||||
\(218\) | 18.0052 | 1.21947 | ||||||||
\(219\) | −7.81592 | −0.528151 | ||||||||
\(220\) | 88.7203 | 5.98152 | ||||||||
\(221\) | −0.122079 | −0.00821195 | ||||||||
\(222\) | −8.44694 | −0.566922 | ||||||||
\(223\) | 12.3591 | 0.827630 | 0.413815 | − | 0.910361i | \(-0.364196\pi\) | ||||
0.413815 | + | 0.910361i | \(0.364196\pi\) | |||||||
\(224\) | −30.5896 | −2.04385 | ||||||||
\(225\) | 2.63242 | 0.175495 | ||||||||
\(226\) | −19.0742 | −1.26880 | ||||||||
\(227\) | −7.75973 | −0.515031 | −0.257516 | − | 0.966274i | \(-0.582904\pi\) | ||||
−0.257516 | + | 0.966274i | \(0.582904\pi\) | |||||||
\(228\) | −6.56675 | −0.434894 | ||||||||
\(229\) | −18.1275 | −1.19790 | −0.598949 | − | 0.800787i | \(-0.704415\pi\) | ||||
−0.598949 | + | 0.800787i | \(0.704415\pi\) | |||||||
\(230\) | 58.8915 | 3.88319 | ||||||||
\(231\) | 22.1917 | 1.46011 | ||||||||
\(232\) | −49.3758 | −3.24168 | ||||||||
\(233\) | 7.17043 | 0.469750 | 0.234875 | − | 0.972026i | \(-0.424532\pi\) | ||||
0.234875 | + | 0.972026i | \(0.424532\pi\) | |||||||
\(234\) | 0.0604577 | 0.00395224 | ||||||||
\(235\) | −3.18053 | −0.207475 | ||||||||
\(236\) | 12.4653 | 0.811424 | ||||||||
\(237\) | −2.64267 | −0.171660 | ||||||||
\(238\) | −12.8938 | −0.835778 | ||||||||
\(239\) | 7.95581 | 0.514619 | 0.257309 | − | 0.966329i | \(-0.417164\pi\) | ||||
0.257309 | + | 0.966329i | \(0.417164\pi\) | |||||||
\(240\) | 69.1533 | 4.46382 | ||||||||
\(241\) | −0.143103 | −0.00921810 | −0.00460905 | − | 0.999989i | \(-0.501467\pi\) | ||||
−0.00460905 | + | 0.999989i | \(0.501467\pi\) | |||||||
\(242\) | −42.2036 | −2.71295 | ||||||||
\(243\) | −4.06176 | −0.260562 | ||||||||
\(244\) | −22.1024 | −1.41496 | ||||||||
\(245\) | −5.52500 | −0.352979 | ||||||||
\(246\) | 6.97276 | 0.444567 | ||||||||
\(247\) | 0.0414572 | 0.00263786 | ||||||||
\(248\) | −38.1680 | −2.42367 | ||||||||
\(249\) | 13.3225 | 0.844281 | ||||||||
\(250\) | −15.3198 | −0.968906 | ||||||||
\(251\) | 9.42872 | 0.595135 | 0.297568 | − | 0.954701i | \(-0.403825\pi\) | ||||
0.297568 | + | 0.954701i | \(0.403825\pi\) | |||||||
\(252\) | 4.56029 | 0.287272 | ||||||||
\(253\) | −33.8010 | −2.12505 | ||||||||
\(254\) | −35.4185 | −2.22236 | ||||||||
\(255\) | 13.2323 | 0.828636 | ||||||||
\(256\) | −5.20181 | −0.325113 | ||||||||
\(257\) | 3.94320 | 0.245970 | 0.122985 | − | 0.992409i | \(-0.460753\pi\) | ||||
0.122985 | + | 0.992409i | \(0.460753\pi\) | |||||||
\(258\) | −6.06641 | −0.377678 | ||||||||
\(259\) | 4.02245 | 0.249943 | ||||||||
\(260\) | −0.993114 | −0.0615903 | ||||||||
\(261\) | 2.44917 | 0.151600 | ||||||||
\(262\) | −42.2015 | −2.60722 | ||||||||
\(263\) | 1.55944 | 0.0961590 | 0.0480795 | − | 0.998844i | \(-0.484690\pi\) | ||||
0.0480795 | + | 0.998844i | \(0.484690\pi\) | |||||||
\(264\) | −75.8255 | −4.66674 | ||||||||
\(265\) | 25.1219 | 1.54323 | ||||||||
\(266\) | 4.37862 | 0.268471 | ||||||||
\(267\) | −23.6379 | −1.44662 | ||||||||
\(268\) | 64.3617 | 3.93151 | ||||||||
\(269\) | −17.6451 | −1.07584 | −0.537919 | − | 0.842996i | \(-0.680790\pi\) | ||||
−0.537919 | + | 0.842996i | \(0.680790\pi\) | |||||||
\(270\) | 43.4354 | 2.64339 | ||||||||
\(271\) | −18.2237 | −1.10701 | −0.553505 | − | 0.832846i | \(-0.686710\pi\) | ||||
−0.553505 | + | 0.832846i | \(0.686710\pi\) | |||||||
\(272\) | 23.0611 | 1.39828 | ||||||||
\(273\) | −0.248409 | −0.0150344 | ||||||||
\(274\) | −23.7390 | −1.43413 | ||||||||
\(275\) | 34.7517 | 2.09561 | ||||||||
\(276\) | −59.9316 | −3.60746 | ||||||||
\(277\) | 10.4162 | 0.625848 | 0.312924 | − | 0.949778i | \(-0.398691\pi\) | ||||
0.312924 | + | 0.949778i | \(0.398691\pi\) | |||||||
\(278\) | 9.23770 | 0.554041 | ||||||||
\(279\) | 1.89324 | 0.113345 | ||||||||
\(280\) | −62.9113 | −3.75967 | ||||||||
\(281\) | −20.8411 | −1.24328 | −0.621639 | − | 0.783304i | \(-0.713533\pi\) | ||||
−0.621639 | + | 0.783304i | \(0.713533\pi\) | |||||||
\(282\) | 4.53209 | 0.269882 | ||||||||
\(283\) | 12.9470 | 0.769619 | 0.384810 | − | 0.922996i | \(-0.374267\pi\) | ||||
0.384810 | + | 0.922996i | \(0.374267\pi\) | |||||||
\(284\) | −68.1824 | −4.04588 | ||||||||
\(285\) | −4.49358 | −0.266176 | ||||||||
\(286\) | 0.798128 | 0.0471943 | ||||||||
\(287\) | −3.32044 | −0.196000 | ||||||||
\(288\) | −5.18446 | −0.305497 | ||||||||
\(289\) | −12.5873 | −0.740432 | ||||||||
\(290\) | −56.3330 | −3.30799 | ||||||||
\(291\) | 6.80250 | 0.398770 | ||||||||
\(292\) | −21.2033 | −1.24083 | ||||||||
\(293\) | −22.1695 | −1.29516 | −0.647578 | − | 0.761999i | \(-0.724218\pi\) | ||||
−0.647578 | + | 0.761999i | \(0.724218\pi\) | |||||||
\(294\) | 7.87285 | 0.459154 | ||||||||
\(295\) | 8.52993 | 0.496632 | ||||||||
\(296\) | −13.7441 | −0.798858 | ||||||||
\(297\) | −24.9299 | −1.44658 | ||||||||
\(298\) | −34.2735 | −1.98541 | ||||||||
\(299\) | 0.378361 | 0.0218812 | ||||||||
\(300\) | 61.6173 | 3.55747 | ||||||||
\(301\) | 2.88884 | 0.166510 | ||||||||
\(302\) | 11.9357 | 0.686822 | ||||||||
\(303\) | −6.62880 | −0.380815 | ||||||||
\(304\) | −7.83136 | −0.449159 | ||||||||
\(305\) | −15.1245 | −0.866027 | ||||||||
\(306\) | −2.18529 | −0.124925 | ||||||||
\(307\) | −33.1302 | −1.89084 | −0.945421 | − | 0.325852i | \(-0.894349\pi\) | ||||
−0.945421 | + | 0.325852i | \(0.894349\pi\) | |||||||
\(308\) | 60.2024 | 3.43035 | ||||||||
\(309\) | −18.0683 | −1.02787 | ||||||||
\(310\) | −43.5460 | −2.47325 | ||||||||
\(311\) | −6.99237 | −0.396501 | −0.198251 | − | 0.980151i | \(-0.563526\pi\) | ||||
−0.198251 | + | 0.980151i | \(0.563526\pi\) | |||||||
\(312\) | 0.848772 | 0.0480523 | ||||||||
\(313\) | −15.4922 | −0.875671 | −0.437836 | − | 0.899055i | \(-0.644255\pi\) | ||||
−0.437836 | + | 0.899055i | \(0.644255\pi\) | |||||||
\(314\) | −38.3530 | −2.16438 | ||||||||
\(315\) | 3.12057 | 0.175824 | ||||||||
\(316\) | −7.16913 | −0.403295 | ||||||||
\(317\) | 23.4067 | 1.31465 | 0.657325 | − | 0.753607i | \(-0.271688\pi\) | ||||
0.657325 | + | 0.753607i | \(0.271688\pi\) | |||||||
\(318\) | −35.7975 | −2.00742 | ||||||||
\(319\) | 32.3326 | 1.81028 | ||||||||
\(320\) | 44.1652 | 2.46891 | ||||||||
\(321\) | 5.57616 | 0.311231 | ||||||||
\(322\) | 39.9616 | 2.22697 | ||||||||
\(323\) | −1.49851 | −0.0833791 | ||||||||
\(324\) | −50.0984 | −2.78324 | ||||||||
\(325\) | −0.389003 | −0.0215780 | ||||||||
\(326\) | 62.0449 | 3.43635 | ||||||||
\(327\) | −12.5385 | −0.693378 | ||||||||
\(328\) | 11.3454 | 0.626446 | ||||||||
\(329\) | −2.15819 | −0.118985 | ||||||||
\(330\) | −86.5096 | −4.76219 | ||||||||
\(331\) | −0.400810 | −0.0220305 | −0.0110153 | − | 0.999939i | \(-0.503506\pi\) | ||||
−0.0110153 | + | 0.999939i | \(0.503506\pi\) | |||||||
\(332\) | 36.1418 | 1.98354 | ||||||||
\(333\) | 0.681744 | 0.0373593 | ||||||||
\(334\) | 0.181352 | 0.00992314 | ||||||||
\(335\) | 44.0422 | 2.40628 | ||||||||
\(336\) | 46.9249 | 2.55996 | ||||||||
\(337\) | −5.56005 | −0.302875 | −0.151438 | − | 0.988467i | \(-0.548390\pi\) | ||||
−0.151438 | + | 0.988467i | \(0.548390\pi\) | |||||||
\(338\) | 34.3791 | 1.86998 | ||||||||
\(339\) | 13.2829 | 0.721426 | ||||||||
\(340\) | 35.8969 | 1.94678 | ||||||||
\(341\) | 24.9934 | 1.35347 | ||||||||
\(342\) | 0.742109 | 0.0401287 | ||||||||
\(343\) | −19.9919 | −1.07946 | ||||||||
\(344\) | −9.87069 | −0.532192 | ||||||||
\(345\) | −41.0107 | −2.20794 | ||||||||
\(346\) | 26.9921 | 1.45110 | ||||||||
\(347\) | 11.8695 | 0.637187 | 0.318593 | − | 0.947892i | \(-0.396790\pi\) | ||||
0.318593 | + | 0.947892i | \(0.396790\pi\) | |||||||
\(348\) | 57.3279 | 3.07310 | ||||||||
\(349\) | 4.90896 | 0.262771 | 0.131385 | − | 0.991331i | \(-0.458057\pi\) | ||||
0.131385 | + | 0.991331i | \(0.458057\pi\) | |||||||
\(350\) | −41.0856 | −2.19612 | ||||||||
\(351\) | 0.279060 | 0.0148951 | ||||||||
\(352\) | −68.4422 | −3.64798 | ||||||||
\(353\) | −9.40347 | −0.500496 | −0.250248 | − | 0.968182i | \(-0.580512\pi\) | ||||
−0.250248 | + | 0.968182i | \(0.580512\pi\) | |||||||
\(354\) | −12.1547 | −0.646016 | ||||||||
\(355\) | −46.6567 | −2.47628 | ||||||||
\(356\) | −64.1257 | −3.39866 | ||||||||
\(357\) | 8.97893 | 0.475216 | ||||||||
\(358\) | −49.1781 | −2.59914 | ||||||||
\(359\) | 14.4132 | 0.760697 | 0.380349 | − | 0.924843i | \(-0.375804\pi\) | ||||
0.380349 | + | 0.924843i | \(0.375804\pi\) | |||||||
\(360\) | −10.6625 | −0.561963 | ||||||||
\(361\) | −18.4911 | −0.973217 | ||||||||
\(362\) | 11.0323 | 0.579845 | ||||||||
\(363\) | 29.3896 | 1.54256 | ||||||||
\(364\) | −0.673891 | −0.0353215 | ||||||||
\(365\) | −14.5093 | −0.759449 | ||||||||
\(366\) | 21.5517 | 1.12652 | ||||||||
\(367\) | 25.9169 | 1.35285 | 0.676425 | − | 0.736511i | \(-0.263528\pi\) | ||||
0.676425 | + | 0.736511i | \(0.263528\pi\) | |||||||
\(368\) | −71.4731 | −3.72579 | ||||||||
\(369\) | −0.562764 | −0.0292963 | ||||||||
\(370\) | −15.6807 | −0.815199 | ||||||||
\(371\) | 17.0468 | 0.885027 | ||||||||
\(372\) | 44.3151 | 2.29763 | ||||||||
\(373\) | −22.6577 | −1.17317 | −0.586585 | − | 0.809888i | \(-0.699528\pi\) | ||||
−0.586585 | + | 0.809888i | \(0.699528\pi\) | |||||||
\(374\) | −28.8490 | −1.49175 | ||||||||
\(375\) | 10.6683 | 0.550911 | ||||||||
\(376\) | 7.37419 | 0.380295 | ||||||||
\(377\) | −0.361923 | −0.0186400 | ||||||||
\(378\) | 29.4737 | 1.51596 | ||||||||
\(379\) | −19.4114 | −0.997098 | −0.498549 | − | 0.866862i | \(-0.666134\pi\) | ||||
−0.498549 | + | 0.866862i | \(0.666134\pi\) | |||||||
\(380\) | −12.1903 | −0.625350 | ||||||||
\(381\) | 24.6647 | 1.26361 | ||||||||
\(382\) | −37.4701 | −1.91714 | ||||||||
\(383\) | −22.3188 | −1.14044 | −0.570220 | − | 0.821492i | \(-0.693142\pi\) | ||||
−0.570220 | + | 0.821492i | \(0.693142\pi\) | |||||||
\(384\) | −14.3655 | −0.733087 | ||||||||
\(385\) | 41.1960 | 2.09954 | ||||||||
\(386\) | −50.6286 | −2.57693 | ||||||||
\(387\) | 0.489613 | 0.0248884 | ||||||||
\(388\) | 18.4541 | 0.936863 | ||||||||
\(389\) | 5.03268 | 0.255167 | 0.127584 | − | 0.991828i | \(-0.459278\pi\) | ||||
0.127584 | + | 0.991828i | \(0.459278\pi\) | |||||||
\(390\) | 0.968367 | 0.0490352 | ||||||||
\(391\) | −13.6762 | −0.691633 | ||||||||
\(392\) | 12.8100 | 0.647001 | ||||||||
\(393\) | 29.3882 | 1.48244 | ||||||||
\(394\) | −52.8121 | −2.66063 | ||||||||
\(395\) | −4.90578 | −0.246837 | ||||||||
\(396\) | 10.2034 | 0.512739 | ||||||||
\(397\) | −38.7478 | −1.94470 | −0.972349 | − | 0.233535i | \(-0.924971\pi\) | ||||
−0.972349 | + | 0.233535i | \(0.924971\pi\) | |||||||
\(398\) | 16.8073 | 0.842471 | ||||||||
\(399\) | −3.04918 | −0.152650 | ||||||||
\(400\) | 73.4834 | 3.67417 | ||||||||
\(401\) | −8.43229 | −0.421089 | −0.210544 | − | 0.977584i | \(-0.567524\pi\) | ||||
−0.210544 | + | 0.977584i | \(0.567524\pi\) | |||||||
\(402\) | −62.7579 | −3.13008 | ||||||||
\(403\) | −0.279770 | −0.0139364 | ||||||||
\(404\) | −17.9828 | −0.894679 | ||||||||
\(405\) | −34.2819 | −1.70348 | ||||||||
\(406\) | −38.2255 | −1.89710 | ||||||||
\(407\) | 8.99999 | 0.446113 | ||||||||
\(408\) | −30.6796 | −1.51887 | ||||||||
\(409\) | 13.9214 | 0.688371 | 0.344186 | − | 0.938902i | \(-0.388155\pi\) | ||||
0.344186 | + | 0.938902i | \(0.388155\pi\) | |||||||
\(410\) | 12.9440 | 0.639260 | ||||||||
\(411\) | 16.5313 | 0.815431 | ||||||||
\(412\) | −49.0162 | −2.41486 | ||||||||
\(413\) | 5.78810 | 0.284814 | ||||||||
\(414\) | 6.77288 | 0.332869 | ||||||||
\(415\) | 24.7315 | 1.21402 | ||||||||
\(416\) | 0.766126 | 0.0375624 | ||||||||
\(417\) | −6.43294 | −0.315022 | ||||||||
\(418\) | 9.79690 | 0.479182 | ||||||||
\(419\) | −26.7345 | −1.30606 | −0.653032 | − | 0.757330i | \(-0.726503\pi\) | ||||
−0.653032 | + | 0.757330i | \(0.726503\pi\) | |||||||
\(420\) | 73.0435 | 3.56416 | ||||||||
\(421\) | −32.9303 | −1.60492 | −0.802462 | − | 0.596704i | \(-0.796477\pi\) | ||||
−0.802462 | + | 0.596704i | \(0.796477\pi\) | |||||||
\(422\) | 20.6691 | 1.00615 | ||||||||
\(423\) | −0.365780 | −0.0177848 | ||||||||
\(424\) | −58.2463 | −2.82869 | ||||||||
\(425\) | 14.0608 | 0.682050 | ||||||||
\(426\) | 66.4835 | 3.22113 | ||||||||
\(427\) | −10.2629 | −0.496659 | ||||||||
\(428\) | 15.1272 | 0.731201 | ||||||||
\(429\) | −0.555799 | −0.0268342 | ||||||||
\(430\) | −11.2615 | −0.543078 | ||||||||
\(431\) | −20.4037 | −0.982813 | −0.491407 | − | 0.870930i | \(-0.663517\pi\) | ||||
−0.491407 | + | 0.870930i | \(0.663517\pi\) | |||||||
\(432\) | −52.7149 | −2.53625 | ||||||||
\(433\) | 31.9531 | 1.53557 | 0.767783 | − | 0.640709i | \(-0.221360\pi\) | ||||
0.767783 | + | 0.640709i | \(0.221360\pi\) | |||||||
\(434\) | −29.5487 | −1.41838 | ||||||||
\(435\) | 39.2291 | 1.88089 | ||||||||
\(436\) | −34.0147 | −1.62901 | ||||||||
\(437\) | 4.64432 | 0.222168 | ||||||||
\(438\) | 20.6749 | 0.987887 | ||||||||
\(439\) | −4.54105 | −0.216733 | −0.108366 | − | 0.994111i | \(-0.534562\pi\) | ||||
−0.108366 | + | 0.994111i | \(0.534562\pi\) | |||||||
\(440\) | −140.760 | −6.71048 | ||||||||
\(441\) | −0.635409 | −0.0302576 | ||||||||
\(442\) | 0.322929 | 0.0153601 | ||||||||
\(443\) | −1.49264 | −0.0709175 | −0.0354588 | − | 0.999371i | \(-0.511289\pi\) | ||||
−0.0354588 | + | 0.999371i | \(0.511289\pi\) | |||||||
\(444\) | 15.9576 | 0.757315 | ||||||||
\(445\) | −43.8808 | −2.08015 | ||||||||
\(446\) | −32.6928 | −1.54805 | ||||||||
\(447\) | 23.8673 | 1.12888 | ||||||||
\(448\) | 29.9689 | 1.41590 | ||||||||
\(449\) | 19.3172 | 0.911635 | 0.455817 | − | 0.890073i | \(-0.349347\pi\) | ||||
0.455817 | + | 0.890073i | \(0.349347\pi\) | |||||||
\(450\) | −6.96338 | −0.328257 | ||||||||
\(451\) | −7.42929 | −0.349832 | ||||||||
\(452\) | 36.0342 | 1.69491 | ||||||||
\(453\) | −8.31176 | −0.390521 | ||||||||
\(454\) | 20.5263 | 0.963347 | ||||||||
\(455\) | −0.461139 | −0.0216185 | ||||||||
\(456\) | 10.4186 | 0.487893 | ||||||||
\(457\) | 15.8292 | 0.740457 | 0.370229 | − | 0.928941i | \(-0.379279\pi\) | ||||
0.370229 | + | 0.928941i | \(0.379279\pi\) | |||||||
\(458\) | 47.9515 | 2.24062 | ||||||||
\(459\) | −10.0868 | −0.470813 | ||||||||
\(460\) | −111.255 | −5.18731 | ||||||||
\(461\) | 41.8837 | 1.95072 | 0.975359 | − | 0.220625i | \(-0.0708098\pi\) | ||||
0.975359 | + | 0.220625i | \(0.0708098\pi\) | |||||||
\(462\) | −58.7023 | −2.73108 | ||||||||
\(463\) | −4.56067 | −0.211952 | −0.105976 | − | 0.994369i | \(-0.533797\pi\) | ||||
−0.105976 | + | 0.994369i | \(0.533797\pi\) | |||||||
\(464\) | 68.3681 | 3.17391 | ||||||||
\(465\) | 30.3245 | 1.40626 | ||||||||
\(466\) | −18.9675 | −0.878651 | ||||||||
\(467\) | −29.8059 | −1.37925 | −0.689627 | − | 0.724164i | \(-0.742226\pi\) | ||||
−0.689627 | + | 0.724164i | \(0.742226\pi\) | |||||||
\(468\) | −0.114214 | −0.00527955 | ||||||||
\(469\) | 29.8854 | 1.37998 | ||||||||
\(470\) | 8.41324 | 0.388074 | ||||||||
\(471\) | 26.7082 | 1.23065 | ||||||||
\(472\) | −19.7770 | −0.910311 | ||||||||
\(473\) | 6.46359 | 0.297196 | ||||||||
\(474\) | 6.99049 | 0.321084 | ||||||||
\(475\) | −4.77495 | −0.219090 | ||||||||
\(476\) | 24.3583 | 1.11646 | ||||||||
\(477\) | 2.88917 | 0.132286 | ||||||||
\(478\) | −21.0450 | −0.962575 | ||||||||
\(479\) | −11.2690 | −0.514895 | −0.257447 | − | 0.966292i | \(-0.582881\pi\) | ||||
−0.257447 | + | 0.966292i | \(0.582881\pi\) | |||||||
\(480\) | −83.0409 | −3.79028 | ||||||||
\(481\) | −0.100744 | −0.00459352 | ||||||||
\(482\) | 0.378542 | 0.0172421 | ||||||||
\(483\) | −27.8284 | −1.26624 | ||||||||
\(484\) | 79.7292 | 3.62405 | ||||||||
\(485\) | 12.6280 | 0.573407 | ||||||||
\(486\) | 10.7443 | 0.487372 | ||||||||
\(487\) | 16.0998 | 0.729554 | 0.364777 | − | 0.931095i | \(-0.381145\pi\) | ||||
0.364777 | + | 0.931095i | \(0.381145\pi\) | |||||||
\(488\) | 35.0668 | 1.58740 | ||||||||
\(489\) | −43.2067 | −1.95388 | ||||||||
\(490\) | 14.6149 | 0.660235 | ||||||||
\(491\) | −4.27274 | −0.192826 | −0.0964130 | − | 0.995341i | \(-0.530737\pi\) | ||||
−0.0964130 | + | 0.995341i | \(0.530737\pi\) | |||||||
\(492\) | −13.1726 | −0.593869 | ||||||||
\(493\) | 13.0820 | 0.589184 | ||||||||
\(494\) | −0.109664 | −0.00493402 | ||||||||
\(495\) | 6.98209 | 0.313822 | ||||||||
\(496\) | 52.8492 | 2.37300 | ||||||||
\(497\) | −31.6596 | −1.42013 | ||||||||
\(498\) | −35.2412 | −1.57920 | ||||||||
\(499\) | 9.35834 | 0.418937 | 0.209468 | − | 0.977815i | \(-0.432827\pi\) | ||||
0.209468 | + | 0.977815i | \(0.432827\pi\) | |||||||
\(500\) | 28.9414 | 1.29430 | ||||||||
\(501\) | −0.126290 | −0.00564220 | ||||||||
\(502\) | −24.9412 | −1.11318 | ||||||||
\(503\) | 30.3031 | 1.35115 | 0.675575 | − | 0.737291i | \(-0.263895\pi\) | ||||
0.675575 | + | 0.737291i | \(0.263895\pi\) | |||||||
\(504\) | −7.23519 | −0.322281 | ||||||||
\(505\) | −12.3055 | −0.547588 | ||||||||
\(506\) | 89.4117 | 3.97483 | ||||||||
\(507\) | −23.9409 | −1.06325 | ||||||||
\(508\) | 66.9112 | 2.96871 | ||||||||
\(509\) | 10.7840 | 0.477990 | 0.238995 | − | 0.971021i | \(-0.423182\pi\) | ||||
0.238995 | + | 0.971021i | \(0.423182\pi\) | |||||||
\(510\) | −35.0024 | −1.54993 | ||||||||
\(511\) | −9.84545 | −0.435537 | ||||||||
\(512\) | 29.3570 | 1.29741 | ||||||||
\(513\) | 3.42541 | 0.151236 | ||||||||
\(514\) | −10.4307 | −0.460077 | ||||||||
\(515\) | −33.5414 | −1.47801 | ||||||||
\(516\) | 11.4604 | 0.504516 | ||||||||
\(517\) | −4.82882 | −0.212371 | ||||||||
\(518\) | −10.6403 | −0.467509 | ||||||||
\(519\) | −18.7967 | −0.825084 | ||||||||
\(520\) | 1.57564 | 0.0690962 | ||||||||
\(521\) | −25.4407 | −1.11458 | −0.557289 | − | 0.830318i | \(-0.688159\pi\) | ||||
−0.557289 | + | 0.830318i | \(0.688159\pi\) | |||||||
\(522\) | −6.47864 | −0.283562 | ||||||||
\(523\) | −39.9406 | −1.74648 | −0.873239 | − | 0.487292i | \(-0.837985\pi\) | ||||
−0.873239 | + | 0.487292i | \(0.837985\pi\) | |||||||
\(524\) | 79.7254 | 3.48282 | ||||||||
\(525\) | 28.6111 | 1.24869 | ||||||||
\(526\) | −4.12508 | −0.179862 | ||||||||
\(527\) | 10.1125 | 0.440509 | ||||||||
\(528\) | 104.992 | 4.56917 | ||||||||
\(529\) | 19.3865 | 0.842892 | ||||||||
\(530\) | −66.4534 | −2.88655 | ||||||||
\(531\) | 0.980995 | 0.0425715 | ||||||||
\(532\) | −8.27191 | −0.358633 | ||||||||
\(533\) | 0.0831617 | 0.00360213 | ||||||||
\(534\) | 62.5278 | 2.70584 | ||||||||
\(535\) | 10.3514 | 0.447531 | ||||||||
\(536\) | −102.114 | −4.41064 | ||||||||
\(537\) | 34.2465 | 1.47785 | ||||||||
\(538\) | 46.6754 | 2.01232 | ||||||||
\(539\) | −8.38831 | −0.361310 | ||||||||
\(540\) | −82.0563 | −3.53114 | ||||||||
\(541\) | −27.5899 | −1.18618 | −0.593090 | − | 0.805136i | \(-0.702092\pi\) | ||||
−0.593090 | + | 0.805136i | \(0.702092\pi\) | |||||||
\(542\) | 48.2059 | 2.07062 | ||||||||
\(543\) | −7.68265 | −0.329694 | ||||||||
\(544\) | −27.6923 | −1.18730 | ||||||||
\(545\) | −23.2760 | −0.997035 | ||||||||
\(546\) | 0.657099 | 0.0281212 | ||||||||
\(547\) | −23.9891 | −1.02570 | −0.512850 | − | 0.858478i | \(-0.671410\pi\) | ||||
−0.512850 | + | 0.858478i | \(0.671410\pi\) | |||||||
\(548\) | 44.8468 | 1.91576 | ||||||||
\(549\) | −1.73941 | −0.0742363 | ||||||||
\(550\) | −91.9265 | −3.91976 | ||||||||
\(551\) | −4.44255 | −0.189259 | ||||||||
\(552\) | 95.0852 | 4.04710 | ||||||||
\(553\) | −3.32888 | −0.141559 | ||||||||
\(554\) | −27.5533 | −1.17063 | ||||||||
\(555\) | 10.9197 | 0.463514 | ||||||||
\(556\) | −17.4515 | −0.740108 | ||||||||
\(557\) | 40.0814 | 1.69830 | 0.849152 | − | 0.528148i | \(-0.177113\pi\) | ||||
0.849152 | + | 0.528148i | \(0.177113\pi\) | |||||||
\(558\) | −5.00805 | −0.212008 | ||||||||
\(559\) | −0.0723519 | −0.00306016 | ||||||||
\(560\) | 87.1100 | 3.68107 | ||||||||
\(561\) | 20.0898 | 0.848192 | ||||||||
\(562\) | 55.1297 | 2.32551 | ||||||||
\(563\) | 20.4006 | 0.859781 | 0.429891 | − | 0.902881i | \(-0.358552\pi\) | ||||
0.429891 | + | 0.902881i | \(0.358552\pi\) | |||||||
\(564\) | −8.56183 | −0.360518 | ||||||||
\(565\) | 24.6579 | 1.03737 | ||||||||
\(566\) | −34.2478 | −1.43954 | ||||||||
\(567\) | −23.2625 | −0.976933 | ||||||||
\(568\) | 108.176 | 4.53895 | ||||||||
\(569\) | 25.5676 | 1.07185 | 0.535925 | − | 0.844266i | \(-0.319963\pi\) | ||||
0.535925 | + | 0.844266i | \(0.319963\pi\) | |||||||
\(570\) | 11.8866 | 0.497873 | ||||||||
\(571\) | 46.8061 | 1.95877 | 0.979386 | − | 0.201997i | \(-0.0647430\pi\) | ||||
0.979386 | + | 0.201997i | \(0.0647430\pi\) | |||||||
\(572\) | −1.50779 | −0.0630439 | ||||||||
\(573\) | 26.0934 | 1.09007 | ||||||||
\(574\) | 8.78335 | 0.366610 | ||||||||
\(575\) | −43.5787 | −1.81736 | ||||||||
\(576\) | 5.07927 | 0.211636 | ||||||||
\(577\) | −34.6628 | −1.44303 | −0.721515 | − | 0.692399i | \(-0.756554\pi\) | ||||
−0.721515 | + | 0.692399i | \(0.756554\pi\) | |||||||
\(578\) | 33.2965 | 1.38495 | ||||||||
\(579\) | 35.2567 | 1.46522 | ||||||||
\(580\) | 106.422 | 4.41893 | ||||||||
\(581\) | 16.7819 | 0.696232 | ||||||||
\(582\) | −17.9942 | −0.745884 | ||||||||
\(583\) | 38.1412 | 1.57965 | ||||||||
\(584\) | 33.6403 | 1.39205 | ||||||||
\(585\) | −0.0781559 | −0.00323135 | ||||||||
\(586\) | 58.6435 | 2.42254 | ||||||||
\(587\) | −18.6552 | −0.769984 | −0.384992 | − | 0.922920i | \(-0.625796\pi\) | ||||
−0.384992 | + | 0.922920i | \(0.625796\pi\) | |||||||
\(588\) | −14.8731 | −0.613354 | ||||||||
\(589\) | −3.43414 | −0.141501 | ||||||||
\(590\) | −22.5637 | −0.928932 | ||||||||
\(591\) | 36.7772 | 1.51281 | ||||||||
\(592\) | 19.0307 | 0.782157 | ||||||||
\(593\) | 16.0408 | 0.658715 | 0.329358 | − | 0.944205i | \(-0.393168\pi\) | ||||
0.329358 | + | 0.944205i | \(0.393168\pi\) | |||||||
\(594\) | 65.9455 | 2.70578 | ||||||||
\(595\) | 16.6682 | 0.683331 | ||||||||
\(596\) | 64.7480 | 2.65218 | ||||||||
\(597\) | −11.7042 | −0.479021 | ||||||||
\(598\) | −1.00085 | −0.0409279 | ||||||||
\(599\) | −25.6413 | −1.04767 | −0.523837 | − | 0.851819i | \(-0.675500\pi\) | ||||
−0.523837 | + | 0.851819i | \(0.675500\pi\) | |||||||
\(600\) | −97.7596 | −3.99102 | ||||||||
\(601\) | −30.9986 | −1.26446 | −0.632230 | − | 0.774781i | \(-0.717860\pi\) | ||||
−0.632230 | + | 0.774781i | \(0.717860\pi\) | |||||||
\(602\) | −7.64165 | −0.311450 | ||||||||
\(603\) | 5.06512 | 0.206268 | ||||||||
\(604\) | −22.5484 | −0.917482 | ||||||||
\(605\) | 54.5581 | 2.21810 | ||||||||
\(606\) | 17.5347 | 0.712300 | ||||||||
\(607\) | −25.7761 | −1.04622 | −0.523111 | − | 0.852265i | \(-0.675229\pi\) | ||||
−0.523111 | + | 0.852265i | \(0.675229\pi\) | |||||||
\(608\) | 9.40408 | 0.381386 | ||||||||
\(609\) | 26.6194 | 1.07867 | ||||||||
\(610\) | 40.0079 | 1.61987 | ||||||||
\(611\) | 0.0540526 | 0.00218674 | ||||||||
\(612\) | 4.12836 | 0.166879 | ||||||||
\(613\) | 14.1549 | 0.571709 | 0.285855 | − | 0.958273i | \(-0.407723\pi\) | ||||
0.285855 | + | 0.958273i | \(0.407723\pi\) | |||||||
\(614\) | 87.6372 | 3.53675 | ||||||||
\(615\) | −9.01394 | −0.363477 | ||||||||
\(616\) | −95.5148 | −3.84840 | ||||||||
\(617\) | 0.762338 | 0.0306906 | 0.0153453 | − | 0.999882i | \(-0.495115\pi\) | ||||
0.0153453 | + | 0.999882i | \(0.495115\pi\) | |||||||
\(618\) | 47.7948 | 1.92259 | ||||||||
\(619\) | 47.3150 | 1.90175 | 0.950876 | − | 0.309572i | \(-0.100186\pi\) | ||||
0.950876 | + | 0.309572i | \(0.100186\pi\) | |||||||
\(620\) | 82.2652 | 3.30385 | ||||||||
\(621\) | 31.2621 | 1.25451 | ||||||||
\(622\) | 18.4965 | 0.741641 | ||||||||
\(623\) | −29.7759 | −1.19295 | ||||||||
\(624\) | −1.17525 | −0.0470477 | ||||||||
\(625\) | −13.6636 | −0.546546 | ||||||||
\(626\) | 40.9805 | 1.63791 | ||||||||
\(627\) | −6.82235 | −0.272458 | ||||||||
\(628\) | 72.4548 | 2.89126 | ||||||||
\(629\) | 3.64147 | 0.145195 | ||||||||
\(630\) | −8.25465 | −0.328873 | ||||||||
\(631\) | −41.5514 | −1.65414 | −0.827068 | − | 0.562102i | \(-0.809993\pi\) | ||||
−0.827068 | + | 0.562102i | \(0.809993\pi\) | |||||||
\(632\) | 11.3743 | 0.452444 | ||||||||
\(633\) | −14.3935 | −0.572089 | ||||||||
\(634\) | −61.9161 | −2.45900 | ||||||||
\(635\) | 45.7869 | 1.81700 | ||||||||
\(636\) | 67.6271 | 2.68159 | ||||||||
\(637\) | 0.0938967 | 0.00372032 | ||||||||
\(638\) | −85.5273 | −3.38606 | ||||||||
\(639\) | −5.36581 | −0.212268 | ||||||||
\(640\) | −26.6677 | −1.05413 | ||||||||
\(641\) | 3.09194 | 0.122124 | 0.0610621 | − | 0.998134i | \(-0.480551\pi\) | ||||
0.0610621 | + | 0.998134i | \(0.480551\pi\) | |||||||
\(642\) | −14.7503 | −0.582146 | ||||||||
\(643\) | 10.2815 | 0.405461 | 0.202731 | − | 0.979235i | \(-0.435018\pi\) | ||||
0.202731 | + | 0.979235i | \(0.435018\pi\) | |||||||
\(644\) | −75.4938 | −2.97487 | ||||||||
\(645\) | 7.84227 | 0.308789 | ||||||||
\(646\) | 3.96390 | 0.155958 | ||||||||
\(647\) | −9.41355 | −0.370085 | −0.185042 | − | 0.982731i | \(-0.559242\pi\) | ||||
−0.185042 | + | 0.982731i | \(0.559242\pi\) | |||||||
\(648\) | 79.4842 | 3.12243 | ||||||||
\(649\) | 12.9505 | 0.508353 | ||||||||
\(650\) | 1.02900 | 0.0403608 | ||||||||
\(651\) | 20.5771 | 0.806480 | ||||||||
\(652\) | −117.213 | −4.59040 | ||||||||
\(653\) | −2.29527 | −0.0898208 | −0.0449104 | − | 0.998991i | \(-0.514300\pi\) | ||||
−0.0449104 | + | 0.998991i | \(0.514300\pi\) | |||||||
\(654\) | 33.1672 | 1.29694 | ||||||||
\(655\) | 54.5555 | 2.13166 | ||||||||
\(656\) | −15.7094 | −0.613350 | ||||||||
\(657\) | −1.66865 | −0.0651004 | ||||||||
\(658\) | 5.70892 | 0.222557 | ||||||||
\(659\) | −9.80371 | −0.381898 | −0.190949 | − | 0.981600i | \(-0.561157\pi\) | ||||
−0.190949 | + | 0.981600i | \(0.561157\pi\) | |||||||
\(660\) | 163.430 | 6.36151 | ||||||||
\(661\) | −33.6238 | −1.30782 | −0.653908 | − | 0.756574i | \(-0.726872\pi\) | ||||
−0.653908 | + | 0.756574i | \(0.726872\pi\) | |||||||
\(662\) | 1.06024 | 0.0412072 | ||||||||
\(663\) | −0.224881 | −0.00873364 | ||||||||
\(664\) | −57.3412 | −2.22527 | ||||||||
\(665\) | −5.66041 | −0.219501 | ||||||||
\(666\) | −1.80337 | −0.0698793 | ||||||||
\(667\) | −40.5451 | −1.56991 | ||||||||
\(668\) | −0.342603 | −0.0132557 | ||||||||
\(669\) | 22.7666 | 0.880207 | ||||||||
\(670\) | −116.502 | −4.50086 | ||||||||
\(671\) | −22.9627 | −0.886466 | ||||||||
\(672\) | −56.3485 | −2.17369 | ||||||||
\(673\) | 5.07110 | 0.195476 | 0.0977382 | − | 0.995212i | \(-0.468839\pi\) | ||||
0.0977382 | + | 0.995212i | \(0.468839\pi\) | |||||||
\(674\) | 14.7076 | 0.566517 | ||||||||
\(675\) | −32.1414 | −1.23712 | ||||||||
\(676\) | −64.9476 | −2.49798 | ||||||||
\(677\) | −9.78191 | −0.375949 | −0.187975 | − | 0.982174i | \(-0.560192\pi\) | ||||
−0.187975 | + | 0.982174i | \(0.560192\pi\) | |||||||
\(678\) | −35.1363 | −1.34940 | ||||||||
\(679\) | 8.56888 | 0.328844 | ||||||||
\(680\) | −56.9527 | −2.18404 | ||||||||
\(681\) | −14.2941 | −0.547750 | ||||||||
\(682\) | −66.1135 | −2.53161 | ||||||||
\(683\) | 30.9517 | 1.18433 | 0.592166 | − | 0.805816i | \(-0.298273\pi\) | ||||
0.592166 | + | 0.805816i | \(0.298273\pi\) | |||||||
\(684\) | −1.40196 | −0.0536053 | ||||||||
\(685\) | 30.6883 | 1.17254 | ||||||||
\(686\) | 52.8834 | 2.01910 | ||||||||
\(687\) | −33.3924 | −1.27400 | ||||||||
\(688\) | 13.6674 | 0.521066 | ||||||||
\(689\) | −0.426944 | −0.0162653 | ||||||||
\(690\) | 108.483 | 4.12988 | ||||||||
\(691\) | −7.88528 | −0.299970 | −0.149985 | − | 0.988688i | \(-0.547923\pi\) | ||||
−0.149985 | + | 0.988688i | \(0.547923\pi\) | |||||||
\(692\) | −50.9923 | −1.93844 | ||||||||
\(693\) | 4.73780 | 0.179974 | ||||||||
\(694\) | −31.3975 | −1.19183 | ||||||||
\(695\) | −11.9419 | −0.452983 | ||||||||
\(696\) | −90.9543 | −3.44762 | ||||||||
\(697\) | −3.00595 | −0.113858 | ||||||||
\(698\) | −12.9854 | −0.491503 | ||||||||
\(699\) | 13.2085 | 0.499592 | ||||||||
\(700\) | 77.6172 | 2.93365 | ||||||||
\(701\) | 42.5856 | 1.60844 | 0.804218 | − | 0.594335i | \(-0.202585\pi\) | ||||
0.804218 | + | 0.594335i | \(0.202585\pi\) | |||||||
\(702\) | −0.738178 | −0.0278607 | ||||||||
\(703\) | −1.23661 | −0.0466398 | ||||||||
\(704\) | 67.0537 | 2.52718 | ||||||||
\(705\) | −5.85880 | −0.220655 | ||||||||
\(706\) | 24.8744 | 0.936160 | ||||||||
\(707\) | −8.35007 | −0.314037 | ||||||||
\(708\) | 22.9622 | 0.862972 | ||||||||
\(709\) | 37.1217 | 1.39413 | 0.697067 | − | 0.717006i | \(-0.254488\pi\) | ||||
0.697067 | + | 0.717006i | \(0.254488\pi\) | |||||||
\(710\) | 123.418 | 4.63179 | ||||||||
\(711\) | −0.564195 | −0.0211590 | ||||||||
\(712\) | 101.739 | 3.81285 | ||||||||
\(713\) | −31.3418 | −1.17376 | ||||||||
\(714\) | −23.7514 | −0.888873 | ||||||||
\(715\) | −1.03177 | −0.0385860 | ||||||||
\(716\) | 92.9051 | 3.47203 | ||||||||
\(717\) | 14.6553 | 0.547311 | ||||||||
\(718\) | −38.1262 | −1.42286 | ||||||||
\(719\) | 11.2596 | 0.419911 | 0.209955 | − | 0.977711i | \(-0.432668\pi\) | ||||
0.209955 | + | 0.977711i | \(0.432668\pi\) | |||||||
\(720\) | 14.7638 | 0.550215 | ||||||||
\(721\) | −22.7600 | −0.847627 | ||||||||
\(722\) | 48.9133 | 1.82037 | ||||||||
\(723\) | −0.263609 | −0.00980371 | ||||||||
\(724\) | −20.8418 | −0.774578 | ||||||||
\(725\) | 41.6855 | 1.54816 | ||||||||
\(726\) | −77.7425 | −2.88530 | ||||||||
\(727\) | −36.2194 | −1.34330 | −0.671652 | − | 0.740867i | \(-0.734415\pi\) | ||||
−0.671652 | + | 0.740867i | \(0.734415\pi\) | |||||||
\(728\) | 1.06917 | 0.0396261 | ||||||||
\(729\) | 22.5934 | 0.836792 | ||||||||
\(730\) | 38.3804 | 1.42052 | ||||||||
\(731\) | 2.61522 | 0.0967274 | ||||||||
\(732\) | −40.7145 | −1.50485 | ||||||||
\(733\) | 2.36474 | 0.0873438 | 0.0436719 | − | 0.999046i | \(-0.486094\pi\) | ||||
0.0436719 | + | 0.999046i | \(0.486094\pi\) | |||||||
\(734\) | −68.5563 | −2.53046 | ||||||||
\(735\) | −10.1775 | −0.375403 | ||||||||
\(736\) | 85.8266 | 3.16361 | ||||||||
\(737\) | 66.8668 | 2.46307 | ||||||||
\(738\) | 1.48864 | 0.0547977 | ||||||||
\(739\) | −2.64267 | −0.0972124 | −0.0486062 | − | 0.998818i | \(-0.515478\pi\) | ||||
−0.0486062 | + | 0.998818i | \(0.515478\pi\) | |||||||
\(740\) | 29.6233 | 1.08897 | ||||||||
\(741\) | 0.0763677 | 0.00280544 | ||||||||
\(742\) | −45.0929 | −1.65541 | ||||||||
\(743\) | −28.1565 | −1.03296 | −0.516481 | − | 0.856299i | \(-0.672758\pi\) | ||||
−0.516481 | + | 0.856299i | \(0.672758\pi\) | |||||||
\(744\) | −70.3086 | −2.57764 | ||||||||
\(745\) | 44.3066 | 1.62327 | ||||||||
\(746\) | 59.9349 | 2.19437 | ||||||||
\(747\) | 2.84428 | 0.104067 | ||||||||
\(748\) | 54.5003 | 1.99273 | ||||||||
\(749\) | 7.02411 | 0.256655 | ||||||||
\(750\) | −28.2203 | −1.03046 | ||||||||
\(751\) | 17.8849 | 0.652628 | 0.326314 | − | 0.945261i | \(-0.394193\pi\) | ||||
0.326314 | + | 0.945261i | \(0.394193\pi\) | |||||||
\(752\) | −10.2107 | −0.372344 | ||||||||
\(753\) | 17.3685 | 0.632943 | ||||||||
\(754\) | 0.957372 | 0.0348654 | ||||||||
\(755\) | −15.4297 | −0.561545 | ||||||||
\(756\) | −55.6804 | −2.02508 | ||||||||
\(757\) | −7.08973 | −0.257681 | −0.128840 | − | 0.991665i | \(-0.541125\pi\) | ||||
−0.128840 | + | 0.991665i | \(0.541125\pi\) | |||||||
\(758\) | 51.3478 | 1.86504 | ||||||||
\(759\) | −62.2644 | −2.26005 | ||||||||
\(760\) | 19.3407 | 0.701561 | ||||||||
\(761\) | 16.7001 | 0.605379 | 0.302689 | − | 0.953089i | \(-0.402116\pi\) | ||||
0.302689 | + | 0.953089i | \(0.402116\pi\) | |||||||
\(762\) | −65.2439 | −2.36354 | ||||||||
\(763\) | −15.7943 | −0.571791 | ||||||||
\(764\) | 70.7869 | 2.56098 | ||||||||
\(765\) | 2.82501 | 0.102138 | ||||||||
\(766\) | 59.0386 | 2.13315 | ||||||||
\(767\) | −0.144965 | −0.00523439 | ||||||||
\(768\) | −9.58216 | −0.345767 | ||||||||
\(769\) | −6.03331 | −0.217567 | −0.108783 | − | 0.994065i | \(-0.534695\pi\) | ||||
−0.108783 | + | 0.994065i | \(0.534695\pi\) | |||||||
\(770\) | −108.973 | −3.92712 | ||||||||
\(771\) | 7.26370 | 0.261596 | ||||||||
\(772\) | 95.6454 | 3.44236 | ||||||||
\(773\) | −27.6703 | −0.995230 | −0.497615 | − | 0.867398i | \(-0.665791\pi\) | ||||
−0.497615 | + | 0.867398i | \(0.665791\pi\) | |||||||
\(774\) | −1.29514 | −0.0465529 | ||||||||
\(775\) | 32.2233 | 1.15749 | ||||||||
\(776\) | −29.2785 | −1.05104 | ||||||||
\(777\) | 7.40970 | 0.265821 | ||||||||
\(778\) | −13.3126 | −0.477281 | ||||||||
\(779\) | 1.02080 | 0.0365739 | ||||||||
\(780\) | −1.82940 | −0.0655030 | ||||||||
\(781\) | −70.8363 | −2.53472 | ||||||||
\(782\) | 36.1766 | 1.29367 | ||||||||
\(783\) | −29.9040 | −1.06868 | ||||||||
\(784\) | −17.7373 | −0.633474 | ||||||||
\(785\) | 49.5803 | 1.76960 | ||||||||
\(786\) | −77.7388 | −2.77285 | ||||||||
\(787\) | −8.18533 | −0.291775 | −0.145888 | − | 0.989301i | \(-0.546604\pi\) | ||||
−0.145888 | + | 0.989301i | \(0.546604\pi\) | |||||||
\(788\) | 99.7704 | 3.55417 | ||||||||
\(789\) | 2.87262 | 0.102268 | ||||||||
\(790\) | 12.9769 | 0.461699 | ||||||||
\(791\) | 16.7320 | 0.594921 | ||||||||
\(792\) | −16.1883 | −0.575226 | ||||||||
\(793\) | 0.257039 | 0.00912773 | ||||||||
\(794\) | 102.497 | 3.63748 | ||||||||
\(795\) | 46.2767 | 1.64126 | ||||||||
\(796\) | −31.7516 | −1.12540 | ||||||||
\(797\) | −29.7002 | −1.05203 | −0.526017 | − | 0.850474i | \(-0.676315\pi\) | ||||
−0.526017 | + | 0.850474i | \(0.676315\pi\) | |||||||
\(798\) | 8.06579 | 0.285526 | ||||||||
\(799\) | −1.95378 | −0.0691197 | ||||||||
\(800\) | −88.2406 | −3.11978 | ||||||||
\(801\) | −5.04656 | −0.178311 | ||||||||
\(802\) | 22.3054 | 0.787631 | ||||||||
\(803\) | −22.0286 | −0.777372 | ||||||||
\(804\) | 118.560 | 4.18127 | ||||||||
\(805\) | −51.6599 | −1.82077 | ||||||||
\(806\) | 0.740058 | 0.0260674 | ||||||||
\(807\) | −32.5037 | −1.14418 | ||||||||
\(808\) | 28.5309 | 1.00371 | ||||||||
\(809\) | 37.8009 | 1.32901 | 0.664504 | − | 0.747284i | \(-0.268643\pi\) | ||||
0.664504 | + | 0.747284i | \(0.268643\pi\) | |||||||
\(810\) | 90.6838 | 3.18630 | ||||||||
\(811\) | −6.57643 | −0.230930 | −0.115465 | − | 0.993312i | \(-0.536836\pi\) | ||||
−0.115465 | + | 0.993312i | \(0.536836\pi\) | |||||||
\(812\) | 72.2141 | 2.53422 | ||||||||
\(813\) | −33.5696 | −1.17734 | ||||||||
\(814\) | −23.8071 | −0.834438 | ||||||||
\(815\) | −80.2077 | −2.80955 | ||||||||
\(816\) | 42.4804 | 1.48711 | ||||||||
\(817\) | −0.888109 | −0.0310710 | ||||||||
\(818\) | −36.8255 | −1.28757 | ||||||||
\(819\) | −0.0530338 | −0.00185315 | ||||||||
\(820\) | −24.4533 | −0.853947 | ||||||||
\(821\) | −15.6248 | −0.545308 | −0.272654 | − | 0.962112i | \(-0.587901\pi\) | ||||
−0.272654 | + | 0.962112i | \(0.587901\pi\) | |||||||
\(822\) | −43.7293 | −1.52523 | ||||||||
\(823\) | −14.6905 | −0.512078 | −0.256039 | − | 0.966666i | \(-0.582418\pi\) | ||||
−0.256039 | + | 0.966666i | \(0.582418\pi\) | |||||||
\(824\) | 77.7673 | 2.70915 | ||||||||
\(825\) | 64.0156 | 2.22874 | ||||||||
\(826\) | −15.3109 | −0.532734 | ||||||||
\(827\) | −28.5293 | −0.992060 | −0.496030 | − | 0.868305i | \(-0.665209\pi\) | ||||
−0.496030 | + | 0.868305i | \(0.665209\pi\) | |||||||
\(828\) | −12.7950 | −0.444658 | ||||||||
\(829\) | −12.2428 | −0.425212 | −0.212606 | − | 0.977138i | \(-0.568195\pi\) | ||||
−0.212606 | + | 0.977138i | \(0.568195\pi\) | |||||||
\(830\) | −65.4208 | −2.27079 | ||||||||
\(831\) | 19.1875 | 0.665607 | ||||||||
\(832\) | −0.750583 | −0.0260218 | ||||||||
\(833\) | −3.39397 | −0.117594 | ||||||||
\(834\) | 17.0166 | 0.589238 | ||||||||
\(835\) | −0.234440 | −0.00811314 | ||||||||
\(836\) | −18.5079 | −0.640109 | ||||||||
\(837\) | −23.1161 | −0.799009 | ||||||||
\(838\) | 70.7189 | 2.44294 | ||||||||
\(839\) | −5.15144 | −0.177847 | −0.0889237 | − | 0.996038i | \(-0.528343\pi\) | ||||
−0.0889237 | + | 0.996038i | \(0.528343\pi\) | |||||||
\(840\) | −115.888 | −3.99852 | ||||||||
\(841\) | 9.78366 | 0.337367 | ||||||||
\(842\) | 87.1083 | 3.00195 | ||||||||
\(843\) | −38.3911 | −1.32226 | ||||||||
\(844\) | −39.0471 | −1.34406 | ||||||||
\(845\) | −44.4431 | −1.52889 | ||||||||
\(846\) | 0.967574 | 0.0332659 | ||||||||
\(847\) | 37.0211 | 1.27206 | ||||||||
\(848\) | 80.6505 | 2.76955 | ||||||||
\(849\) | 23.8495 | 0.818511 | ||||||||
\(850\) | −37.1942 | −1.27575 | ||||||||
\(851\) | −11.2860 | −0.386879 | ||||||||
\(852\) | −125.598 | −4.30291 | ||||||||
\(853\) | 16.5114 | 0.565338 | 0.282669 | − | 0.959218i | \(-0.408780\pi\) | ||||
0.282669 | + | 0.959218i | \(0.408780\pi\) | |||||||
\(854\) | 27.1479 | 0.928982 | ||||||||
\(855\) | −0.959352 | −0.0328091 | ||||||||
\(856\) | −24.0002 | −0.820311 | ||||||||
\(857\) | 23.6615 | 0.808260 | 0.404130 | − | 0.914702i | \(-0.367574\pi\) | ||||
0.404130 | + | 0.914702i | \(0.367574\pi\) | |||||||
\(858\) | 1.47022 | 0.0501924 | ||||||||
\(859\) | 18.0175 | 0.614748 | 0.307374 | − | 0.951589i | \(-0.400550\pi\) | ||||
0.307374 | + | 0.951589i | \(0.400550\pi\) | |||||||
\(860\) | 21.2748 | 0.725463 | ||||||||
\(861\) | −6.11654 | −0.208451 | ||||||||
\(862\) | 53.9727 | 1.83832 | ||||||||
\(863\) | −47.0214 | −1.60063 | −0.800314 | − | 0.599581i | \(-0.795334\pi\) | ||||
−0.800314 | + | 0.599581i | \(0.795334\pi\) | |||||||
\(864\) | 63.3014 | 2.15356 | ||||||||
\(865\) | −34.8937 | −1.18642 | ||||||||
\(866\) | −84.5234 | −2.87222 | ||||||||
\(867\) | −23.1869 | −0.787470 | ||||||||
\(868\) | 55.8222 | 1.89473 | ||||||||
\(869\) | −7.44817 | −0.252662 | ||||||||
\(870\) | −103.770 | −3.51814 | ||||||||
\(871\) | −0.748491 | −0.0253617 | ||||||||
\(872\) | 53.9665 | 1.82754 | ||||||||
\(873\) | 1.45229 | 0.0491527 | ||||||||
\(874\) | −12.2853 | −0.415557 | ||||||||
\(875\) | 13.4386 | 0.454306 | ||||||||
\(876\) | −39.0582 | −1.31966 | ||||||||
\(877\) | 22.7645 | 0.768703 | 0.384351 | − | 0.923187i | \(-0.374425\pi\) | ||||
0.384351 | + | 0.923187i | \(0.374425\pi\) | |||||||
\(878\) | 12.0122 | 0.405391 | ||||||||
\(879\) | −40.8381 | −1.37743 | ||||||||
\(880\) | 194.903 | 6.57019 | ||||||||
\(881\) | −24.2189 | −0.815956 | −0.407978 | − | 0.912992i | \(-0.633766\pi\) | ||||
−0.407978 | + | 0.912992i | \(0.633766\pi\) | |||||||
\(882\) | 1.68081 | 0.0565957 | ||||||||
\(883\) | 21.6653 | 0.729095 | 0.364548 | − | 0.931185i | \(-0.381224\pi\) | ||||
0.364548 | + | 0.931185i | \(0.381224\pi\) | |||||||
\(884\) | −0.610063 | −0.0205186 | ||||||||
\(885\) | 15.7129 | 0.528182 | ||||||||
\(886\) | 3.94839 | 0.132649 | ||||||||
\(887\) | 9.10194 | 0.305613 | 0.152807 | − | 0.988256i | \(-0.451169\pi\) | ||||
0.152807 | + | 0.988256i | \(0.451169\pi\) | |||||||
\(888\) | −25.3177 | −0.849608 | ||||||||
\(889\) | 31.0693 | 1.04203 | ||||||||
\(890\) | 116.075 | 3.89084 | ||||||||
\(891\) | −52.0484 | −1.74369 | ||||||||
\(892\) | 61.7620 | 2.06794 | ||||||||
\(893\) | 0.663488 | 0.0222028 | ||||||||
\(894\) | −63.1346 | −2.11154 | ||||||||
\(895\) | 63.5743 | 2.12505 | ||||||||
\(896\) | −18.0958 | −0.604537 | ||||||||
\(897\) | 0.696972 | 0.0232712 | ||||||||
\(898\) | −51.0985 | −1.70518 | ||||||||
\(899\) | 29.9802 | 0.999894 | ||||||||
\(900\) | 13.1549 | 0.438497 | ||||||||
\(901\) | 15.4322 | 0.514122 | ||||||||
\(902\) | 19.6522 | 0.654347 | ||||||||
\(903\) | 5.32148 | 0.177088 | ||||||||
\(904\) | −57.1705 | −1.90146 | ||||||||
\(905\) | −14.2619 | −0.474080 | ||||||||
\(906\) | 21.9866 | 0.730454 | ||||||||
\(907\) | 4.68005 | 0.155398 | 0.0776992 | − | 0.996977i | \(-0.475243\pi\) | ||||
0.0776992 | + | 0.996977i | \(0.475243\pi\) | |||||||
\(908\) | −38.7774 | −1.28687 | ||||||||
\(909\) | −1.41521 | −0.0469395 | ||||||||
\(910\) | 1.21982 | 0.0404366 | ||||||||
\(911\) | −15.5766 | −0.516077 | −0.258039 | − | 0.966135i | \(-0.583076\pi\) | ||||
−0.258039 | + | 0.966135i | \(0.583076\pi\) | |||||||
\(912\) | −14.4260 | −0.477693 | ||||||||
\(913\) | 37.5485 | 1.24268 | ||||||||
\(914\) | −41.8719 | −1.38500 | ||||||||
\(915\) | −27.8606 | −0.921044 | ||||||||
\(916\) | −90.5879 | −2.99311 | ||||||||
\(917\) | 37.0194 | 1.22249 | ||||||||
\(918\) | 26.6821 | 0.880639 | ||||||||
\(919\) | 32.5815 | 1.07477 | 0.537383 | − | 0.843339i | \(-0.319413\pi\) | ||||
0.537383 | + | 0.843339i | \(0.319413\pi\) | |||||||
\(920\) | 176.513 | 5.81948 | ||||||||
\(921\) | −61.0287 | −2.01096 | ||||||||
\(922\) | −110.792 | −3.64875 | ||||||||
\(923\) | 0.792925 | 0.0260994 | ||||||||
\(924\) | 110.898 | 3.64827 | ||||||||
\(925\) | 11.6034 | 0.381518 | ||||||||
\(926\) | 12.0640 | 0.396449 | ||||||||
\(927\) | −3.85747 | −0.126696 | ||||||||
\(928\) | −82.0980 | −2.69500 | ||||||||
\(929\) | −5.89176 | −0.193302 | −0.0966512 | − | 0.995318i | \(-0.530813\pi\) | ||||
−0.0966512 | + | 0.995318i | \(0.530813\pi\) | |||||||
\(930\) | −80.2153 | −2.63036 | ||||||||
\(931\) | 1.15257 | 0.0377739 | ||||||||
\(932\) | 35.8325 | 1.17373 | ||||||||
\(933\) | −12.8805 | −0.421690 | ||||||||
\(934\) | 78.8437 | 2.57985 | ||||||||
\(935\) | 37.2941 | 1.21965 | ||||||||
\(936\) | 0.181208 | 0.00592296 | ||||||||
\(937\) | −6.43083 | −0.210086 | −0.105043 | − | 0.994468i | \(-0.533498\pi\) | ||||
−0.105043 | + | 0.994468i | \(0.533498\pi\) | |||||||
\(938\) | −79.0540 | −2.58121 | ||||||||
\(939\) | −28.5380 | −0.931301 | ||||||||
\(940\) | −15.8939 | −0.518403 | ||||||||
\(941\) | −22.5880 | −0.736349 | −0.368175 | − | 0.929757i | \(-0.620017\pi\) | ||||
−0.368175 | + | 0.929757i | \(0.620017\pi\) | |||||||
\(942\) | −70.6494 | −2.30188 | ||||||||
\(943\) | 9.31633 | 0.303382 | ||||||||
\(944\) | 27.3842 | 0.891280 | ||||||||
\(945\) | −38.1017 | −1.23945 | ||||||||
\(946\) | −17.0977 | −0.555895 | ||||||||
\(947\) | 7.90199 | 0.256780 | 0.128390 | − | 0.991724i | \(-0.459019\pi\) | ||||
0.128390 | + | 0.991724i | \(0.459019\pi\) | |||||||
\(948\) | −13.2061 | −0.428915 | ||||||||
\(949\) | 0.246583 | 0.00800442 | ||||||||
\(950\) | 12.6309 | 0.409799 | ||||||||
\(951\) | 43.1171 | 1.39817 | ||||||||
\(952\) | −38.6460 | −1.25253 | ||||||||
\(953\) | 3.70593 | 0.120047 | 0.0600235 | − | 0.998197i | \(-0.480882\pi\) | ||||
0.0600235 | + | 0.998197i | \(0.480882\pi\) | |||||||
\(954\) | −7.64254 | −0.247437 | ||||||||
\(955\) | 48.4390 | 1.56745 | ||||||||
\(956\) | 39.7573 | 1.28584 | ||||||||
\(957\) | 59.5594 | 1.92528 | ||||||||
\(958\) | 29.8092 | 0.963092 | ||||||||
\(959\) | 20.8240 | 0.672441 | ||||||||
\(960\) | 81.3561 | 2.62576 | ||||||||
\(961\) | −7.82504 | −0.252421 | ||||||||
\(962\) | 0.266491 | 0.00859201 | ||||||||
\(963\) | 1.19048 | 0.0383626 | ||||||||
\(964\) | −0.715126 | −0.0230327 | ||||||||
\(965\) | 65.4495 | 2.10689 | ||||||||
\(966\) | 73.6127 | 2.36845 | ||||||||
\(967\) | 59.0925 | 1.90029 | 0.950143 | − | 0.311815i | \(-0.100937\pi\) | ||||
0.950143 | + | 0.311815i | \(0.100937\pi\) | |||||||
\(968\) | −126.495 | −4.06571 | ||||||||
\(969\) | −2.76037 | −0.0886760 | ||||||||
\(970\) | −33.4039 | −1.07254 | ||||||||
\(971\) | −28.4465 | −0.912892 | −0.456446 | − | 0.889751i | \(-0.650878\pi\) | ||||
−0.456446 | + | 0.889751i | \(0.650878\pi\) | |||||||
\(972\) | −20.2977 | −0.651049 | ||||||||
\(973\) | −8.10335 | −0.259782 | ||||||||
\(974\) | −42.5879 | −1.36460 | ||||||||
\(975\) | −0.716575 | −0.0229488 | ||||||||
\(976\) | −48.5552 | −1.55421 | ||||||||
\(977\) | 7.38506 | 0.236269 | 0.118135 | − | 0.992998i | \(-0.462309\pi\) | ||||
0.118135 | + | 0.992998i | \(0.462309\pi\) | |||||||
\(978\) | 114.292 | 3.65465 | ||||||||
\(979\) | −66.6217 | −2.12924 | ||||||||
\(980\) | −27.6099 | −0.881966 | ||||||||
\(981\) | −2.67689 | −0.0854664 | ||||||||
\(982\) | 11.3024 | 0.360674 | ||||||||
\(983\) | −23.7948 | −0.758936 | −0.379468 | − | 0.925205i | \(-0.623893\pi\) | ||||
−0.379468 | + | 0.925205i | \(0.623893\pi\) | |||||||
\(984\) | 20.8992 | 0.666243 | ||||||||
\(985\) | 68.2721 | 2.17533 | ||||||||
\(986\) | −34.6050 | −1.10205 | ||||||||
\(987\) | −3.97557 | −0.126544 | ||||||||
\(988\) | 0.207173 | 0.00659105 | ||||||||
\(989\) | −8.10535 | −0.257735 | ||||||||
\(990\) | −18.4693 | −0.586992 | ||||||||
\(991\) | 5.56043 | 0.176633 | 0.0883164 | − | 0.996092i | \(-0.471851\pi\) | ||||
0.0883164 | + | 0.996092i | \(0.471851\pi\) | |||||||
\(992\) | −63.4626 | −2.01494 | ||||||||
\(993\) | −0.738325 | −0.0234301 | ||||||||
\(994\) | 83.7470 | 2.65629 | ||||||||
\(995\) | −21.7274 | −0.688803 | ||||||||
\(996\) | 66.5762 | 2.10955 | ||||||||
\(997\) | −4.91329 | −0.155606 | −0.0778028 | − | 0.996969i | \(-0.524790\pi\) | ||||
−0.0778028 | + | 0.996969i | \(0.524790\pi\) | |||||||
\(998\) | −24.7550 | −0.783606 | ||||||||
\(999\) | −8.32398 | −0.263359 |
(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 | 6037.2.a.b.1.5 | ✓ | 259 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.b.1.5 | ✓ | 259 | 1.1 | even | 1 | trivial |