Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [722,2,Mod(1,722)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(722, 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("722.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 722 = 2 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 722.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: | \(5.76519902594\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{20})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.90211\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 722.1 |
$q$-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 | ||||||||
\(3\) | −0.442463 | −0.255456 | −0.127728 | − | 0.991809i | \(-0.540769\pi\) | ||||
−0.127728 | + | 0.991809i | \(0.540769\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.891491 | −0.398687 | −0.199344 | − | 0.979930i | \(-0.563881\pi\) | ||||
−0.199344 | + | 0.979930i | \(0.563881\pi\) | |||||||
\(6\) | 0.442463 | 0.180635 | ||||||||
\(7\) | 2.52015 | 0.952526 | 0.476263 | − | 0.879303i | \(-0.341991\pi\) | ||||
0.476263 | + | 0.879303i | \(0.341991\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.80423 | −0.934742 | ||||||||
\(10\) | 0.891491 | 0.281914 | ||||||||
\(11\) | 1.95199 | 0.588547 | 0.294273 | − | 0.955721i | \(-0.404922\pi\) | ||||
0.294273 | + | 0.955721i | \(0.404922\pi\) | |||||||
\(12\) | −0.442463 | −0.127728 | ||||||||
\(13\) | −6.45965 | −1.79158 | −0.895792 | − | 0.444473i | \(-0.853391\pi\) | ||||
−0.895792 | + | 0.444473i | \(0.853391\pi\) | |||||||
\(14\) | −2.52015 | −0.673538 | ||||||||
\(15\) | 0.394452 | 0.101847 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.42226 | −0.830020 | −0.415010 | − | 0.909817i | \(-0.636222\pi\) | ||||
−0.415010 | + | 0.909817i | \(0.636222\pi\) | |||||||
\(18\) | 2.80423 | 0.660962 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.891491 | −0.199344 | ||||||||
\(21\) | −1.11507 | −0.243329 | ||||||||
\(22\) | −1.95199 | −0.416165 | ||||||||
\(23\) | 8.18504 | 1.70670 | 0.853349 | − | 0.521339i | \(-0.174567\pi\) | ||||
0.853349 | + | 0.521339i | \(0.174567\pi\) | |||||||
\(24\) | 0.442463 | 0.0903175 | ||||||||
\(25\) | −4.20524 | −0.841049 | ||||||||
\(26\) | 6.45965 | 1.26684 | ||||||||
\(27\) | 2.56816 | 0.494242 | ||||||||
\(28\) | 2.52015 | 0.476263 | ||||||||
\(29\) | 4.58064 | 0.850604 | 0.425302 | − | 0.905051i | \(-0.360168\pi\) | ||||
0.425302 | + | 0.905051i | \(0.360168\pi\) | |||||||
\(30\) | −0.394452 | −0.0720168 | ||||||||
\(31\) | −8.79360 | −1.57938 | −0.789689 | − | 0.613507i | \(-0.789758\pi\) | ||||
−0.789689 | + | 0.613507i | \(0.789758\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.863684 | −0.150348 | ||||||||
\(34\) | 3.42226 | 0.586913 | ||||||||
\(35\) | −2.24669 | −0.379760 | ||||||||
\(36\) | −2.80423 | −0.467371 | ||||||||
\(37\) | −5.97980 | −0.983073 | −0.491536 | − | 0.870857i | \(-0.663564\pi\) | ||||
−0.491536 | + | 0.870857i | \(0.663564\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.85816 | 0.457672 | ||||||||
\(40\) | 0.891491 | 0.140957 | ||||||||
\(41\) | −3.48932 | −0.544941 | −0.272470 | − | 0.962164i | \(-0.587841\pi\) | ||||
−0.272470 | + | 0.962164i | \(0.587841\pi\) | |||||||
\(42\) | 1.11507 | 0.172060 | ||||||||
\(43\) | −6.24669 | −0.952611 | −0.476306 | − | 0.879280i | \(-0.658024\pi\) | ||||
−0.476306 | + | 0.879280i | \(0.658024\pi\) | |||||||
\(44\) | 1.95199 | 0.294273 | ||||||||
\(45\) | 2.49994 | 0.372670 | ||||||||
\(46\) | −8.18504 | −1.20682 | ||||||||
\(47\) | −10.5498 | −1.53885 | −0.769425 | − | 0.638738i | \(-0.779457\pi\) | ||||
−0.769425 | + | 0.638738i | \(0.779457\pi\) | |||||||
\(48\) | −0.442463 | −0.0638641 | ||||||||
\(49\) | −0.648859 | −0.0926941 | ||||||||
\(50\) | 4.20524 | 0.594711 | ||||||||
\(51\) | 1.51423 | 0.212034 | ||||||||
\(52\) | −6.45965 | −0.895792 | ||||||||
\(53\) | 3.76278 | 0.516858 | 0.258429 | − | 0.966030i | \(-0.416795\pi\) | ||||
0.258429 | + | 0.966030i | \(0.416795\pi\) | |||||||
\(54\) | −2.56816 | −0.349482 | ||||||||
\(55\) | −1.74018 | −0.234646 | ||||||||
\(56\) | −2.52015 | −0.336769 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.58064 | −0.601468 | ||||||||
\(59\) | 2.84162 | 0.369947 | 0.184973 | − | 0.982744i | \(-0.440780\pi\) | ||||
0.184973 | + | 0.982744i | \(0.440780\pi\) | |||||||
\(60\) | 0.394452 | 0.0509236 | ||||||||
\(61\) | −2.45495 | −0.314324 | −0.157162 | − | 0.987573i | \(-0.550235\pi\) | ||||
−0.157162 | + | 0.987573i | \(0.550235\pi\) | |||||||
\(62\) | 8.79360 | 1.11679 | ||||||||
\(63\) | −7.06706 | −0.890366 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.75872 | 0.714282 | ||||||||
\(66\) | 0.863684 | 0.106312 | ||||||||
\(67\) | −2.67261 | −0.326511 | −0.163256 | − | 0.986584i | \(-0.552200\pi\) | ||||
−0.163256 | + | 0.986584i | \(0.552200\pi\) | |||||||
\(68\) | −3.42226 | −0.415010 | ||||||||
\(69\) | −3.62158 | −0.435987 | ||||||||
\(70\) | 2.24669 | 0.268531 | ||||||||
\(71\) | 0.0564404 | 0.00669824 | 0.00334912 | − | 0.999994i | \(-0.498934\pi\) | ||||
0.00334912 | + | 0.999994i | \(0.498934\pi\) | |||||||
\(72\) | 2.80423 | 0.330481 | ||||||||
\(73\) | −6.96917 | −0.815680 | −0.407840 | − | 0.913053i | \(-0.633718\pi\) | ||||
−0.407840 | + | 0.913053i | \(0.633718\pi\) | |||||||
\(74\) | 5.97980 | 0.695137 | ||||||||
\(75\) | 1.86067 | 0.214851 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.91930 | 0.560606 | ||||||||
\(78\) | −2.85816 | −0.323623 | ||||||||
\(79\) | −9.13162 | −1.02739 | −0.513694 | − | 0.857974i | \(-0.671723\pi\) | ||||
−0.513694 | + | 0.857974i | \(0.671723\pi\) | |||||||
\(80\) | −0.891491 | −0.0996718 | ||||||||
\(81\) | 7.27636 | 0.808485 | ||||||||
\(82\) | 3.48932 | 0.385331 | ||||||||
\(83\) | −14.1239 | −1.55030 | −0.775150 | − | 0.631778i | \(-0.782326\pi\) | ||||
−0.775150 | + | 0.631778i | \(0.782326\pi\) | |||||||
\(84\) | −1.11507 | −0.121664 | ||||||||
\(85\) | 3.05092 | 0.330918 | ||||||||
\(86\) | 6.24669 | 0.673598 | ||||||||
\(87\) | −2.02677 | −0.217292 | ||||||||
\(88\) | −1.95199 | −0.208083 | ||||||||
\(89\) | 1.86774 | 0.197980 | 0.0989901 | − | 0.995088i | \(-0.468439\pi\) | ||||
0.0989901 | + | 0.995088i | \(0.468439\pi\) | |||||||
\(90\) | −2.49994 | −0.263517 | ||||||||
\(91\) | −16.2793 | −1.70653 | ||||||||
\(92\) | 8.18504 | 0.853349 | ||||||||
\(93\) | 3.89085 | 0.403462 | ||||||||
\(94\) | 10.5498 | 1.08813 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.442463 | 0.0451587 | ||||||||
\(97\) | 7.82432 | 0.794439 | 0.397219 | − | 0.917724i | \(-0.369975\pi\) | ||||
0.397219 | + | 0.917724i | \(0.369975\pi\) | |||||||
\(98\) | 0.648859 | 0.0655447 | ||||||||
\(99\) | −5.47382 | −0.550139 | ||||||||
\(100\) | −4.20524 | −0.420524 | ||||||||
\(101\) | −5.38487 | −0.535815 | −0.267907 | − | 0.963445i | \(-0.586332\pi\) | ||||
−0.267907 | + | 0.963445i | \(0.586332\pi\) | |||||||
\(102\) | −1.51423 | −0.149931 | ||||||||
\(103\) | −4.69468 | −0.462580 | −0.231290 | − | 0.972885i | \(-0.574295\pi\) | ||||
−0.231290 | + | 0.972885i | \(0.574295\pi\) | |||||||
\(104\) | 6.45965 | 0.633421 | ||||||||
\(105\) | 0.994078 | 0.0970121 | ||||||||
\(106\) | −3.76278 | −0.365473 | ||||||||
\(107\) | 16.0373 | 1.55038 | 0.775191 | − | 0.631727i | \(-0.217654\pi\) | ||||
0.775191 | + | 0.631727i | \(0.217654\pi\) | |||||||
\(108\) | 2.56816 | 0.247121 | ||||||||
\(109\) | 14.1008 | 1.35061 | 0.675305 | − | 0.737538i | \(-0.264012\pi\) | ||||
0.675305 | + | 0.737538i | \(0.264012\pi\) | |||||||
\(110\) | 1.74018 | 0.165920 | ||||||||
\(111\) | 2.64584 | 0.251132 | ||||||||
\(112\) | 2.52015 | 0.238132 | ||||||||
\(113\) | −12.7224 | −1.19682 | −0.598410 | − | 0.801190i | \(-0.704201\pi\) | ||||
−0.598410 | + | 0.801190i | \(0.704201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.29689 | −0.680439 | ||||||||
\(116\) | 4.58064 | 0.425302 | ||||||||
\(117\) | 18.1143 | 1.67467 | ||||||||
\(118\) | −2.84162 | −0.261592 | ||||||||
\(119\) | −8.62460 | −0.790616 | ||||||||
\(120\) | −0.394452 | −0.0360084 | ||||||||
\(121\) | −7.18974 | −0.653613 | ||||||||
\(122\) | 2.45495 | 0.222261 | ||||||||
\(123\) | 1.54390 | 0.139209 | ||||||||
\(124\) | −8.79360 | −0.789689 | ||||||||
\(125\) | 8.20640 | 0.734002 | ||||||||
\(126\) | 7.06706 | 0.629584 | ||||||||
\(127\) | 7.17442 | 0.636627 | 0.318313 | − | 0.947986i | \(-0.396884\pi\) | ||||
0.318313 | + | 0.947986i | \(0.396884\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.76393 | 0.243351 | ||||||||
\(130\) | −5.75872 | −0.505073 | ||||||||
\(131\) | −3.52265 | −0.307776 | −0.153888 | − | 0.988088i | \(-0.549179\pi\) | ||||
−0.153888 | + | 0.988088i | \(0.549179\pi\) | |||||||
\(132\) | −0.863684 | −0.0751740 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.67261 | 0.230878 | ||||||||
\(135\) | −2.28949 | −0.197048 | ||||||||
\(136\) | 3.42226 | 0.293456 | ||||||||
\(137\) | −11.0035 | −0.940096 | −0.470048 | − | 0.882641i | \(-0.655763\pi\) | ||||
−0.470048 | + | 0.882641i | \(0.655763\pi\) | |||||||
\(138\) | 3.62158 | 0.308289 | ||||||||
\(139\) | 21.7586 | 1.84554 | 0.922771 | − | 0.385350i | \(-0.125919\pi\) | ||||
0.922771 | + | 0.385350i | \(0.125919\pi\) | |||||||
\(140\) | −2.24669 | −0.189880 | ||||||||
\(141\) | 4.66791 | 0.393109 | ||||||||
\(142\) | −0.0564404 | −0.00473637 | ||||||||
\(143\) | −12.6092 | −1.05443 | ||||||||
\(144\) | −2.80423 | −0.233686 | ||||||||
\(145\) | −4.08361 | −0.339125 | ||||||||
\(146\) | 6.96917 | 0.576773 | ||||||||
\(147\) | 0.287096 | 0.0236793 | ||||||||
\(148\) | −5.97980 | −0.491536 | ||||||||
\(149\) | 14.3896 | 1.17884 | 0.589420 | − | 0.807827i | \(-0.299356\pi\) | ||||
0.589420 | + | 0.807827i | \(0.299356\pi\) | |||||||
\(150\) | −1.86067 | −0.151923 | ||||||||
\(151\) | 12.4068 | 1.00965 | 0.504824 | − | 0.863222i | \(-0.331557\pi\) | ||||
0.504824 | + | 0.863222i | \(0.331557\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.59679 | 0.775855 | ||||||||
\(154\) | −4.91930 | −0.396408 | ||||||||
\(155\) | 7.83942 | 0.629678 | ||||||||
\(156\) | 2.85816 | 0.228836 | ||||||||
\(157\) | −0.451220 | −0.0360113 | −0.0180056 | − | 0.999838i | \(-0.505732\pi\) | ||||
−0.0180056 | + | 0.999838i | \(0.505732\pi\) | |||||||
\(158\) | 9.13162 | 0.726472 | ||||||||
\(159\) | −1.66489 | −0.132035 | ||||||||
\(160\) | 0.891491 | 0.0704786 | ||||||||
\(161\) | 20.6275 | 1.62567 | ||||||||
\(162\) | −7.27636 | −0.571685 | ||||||||
\(163\) | −0.0692542 | −0.00542441 | −0.00271220 | − | 0.999996i | \(-0.500863\pi\) | ||||
−0.00271220 | + | 0.999996i | \(0.500863\pi\) | |||||||
\(164\) | −3.48932 | −0.272470 | ||||||||
\(165\) | 0.769967 | 0.0599418 | ||||||||
\(166\) | 14.1239 | 1.09623 | ||||||||
\(167\) | 2.17371 | 0.168206 | 0.0841032 | − | 0.996457i | \(-0.473197\pi\) | ||||
0.0841032 | + | 0.996457i | \(0.473197\pi\) | |||||||
\(168\) | 1.11507 | 0.0860298 | ||||||||
\(169\) | 28.7271 | 2.20977 | ||||||||
\(170\) | −3.05092 | −0.233995 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.24669 | −0.476306 | ||||||||
\(173\) | −16.8493 | −1.28103 | −0.640514 | − | 0.767947i | \(-0.721279\pi\) | ||||
−0.640514 | + | 0.767947i | \(0.721279\pi\) | |||||||
\(174\) | 2.02677 | 0.153649 | ||||||||
\(175\) | −10.5978 | −0.801121 | ||||||||
\(176\) | 1.95199 | 0.147137 | ||||||||
\(177\) | −1.25731 | −0.0945053 | ||||||||
\(178\) | −1.86774 | −0.139993 | ||||||||
\(179\) | 18.9655 | 1.41755 | 0.708775 | − | 0.705435i | \(-0.249248\pi\) | ||||
0.708775 | + | 0.705435i | \(0.249248\pi\) | |||||||
\(180\) | 2.49994 | 0.186335 | ||||||||
\(181\) | −1.98687 | −0.147683 | −0.0738415 | − | 0.997270i | \(-0.523526\pi\) | ||||
−0.0738415 | + | 0.997270i | \(0.523526\pi\) | |||||||
\(182\) | 16.2793 | 1.20670 | ||||||||
\(183\) | 1.08623 | 0.0802961 | ||||||||
\(184\) | −8.18504 | −0.603409 | ||||||||
\(185\) | 5.33094 | 0.391938 | ||||||||
\(186\) | −3.89085 | −0.285291 | ||||||||
\(187\) | −6.68021 | −0.488506 | ||||||||
\(188\) | −10.5498 | −0.769425 | ||||||||
\(189\) | 6.47214 | 0.470779 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.9259 | −1.51415 | −0.757074 | − | 0.653329i | \(-0.773372\pi\) | ||||
−0.757074 | + | 0.653329i | \(0.773372\pi\) | |||||||
\(192\) | −0.442463 | −0.0319321 | ||||||||
\(193\) | 7.78879 | 0.560650 | 0.280325 | − | 0.959905i | \(-0.409558\pi\) | ||||
0.280325 | + | 0.959905i | \(0.409558\pi\) | |||||||
\(194\) | −7.82432 | −0.561753 | ||||||||
\(195\) | −2.54802 | −0.182468 | ||||||||
\(196\) | −0.648859 | −0.0463471 | ||||||||
\(197\) | 1.82514 | 0.130036 | 0.0650180 | − | 0.997884i | \(-0.479290\pi\) | ||||
0.0650180 | + | 0.997884i | \(0.479290\pi\) | |||||||
\(198\) | 5.47382 | 0.389007 | ||||||||
\(199\) | 2.35926 | 0.167243 | 0.0836216 | − | 0.996498i | \(-0.473351\pi\) | ||||
0.0836216 | + | 0.996498i | \(0.473351\pi\) | |||||||
\(200\) | 4.20524 | 0.297356 | ||||||||
\(201\) | 1.18253 | 0.0834094 | ||||||||
\(202\) | 5.38487 | 0.378878 | ||||||||
\(203\) | 11.5439 | 0.810223 | ||||||||
\(204\) | 1.51423 | 0.106017 | ||||||||
\(205\) | 3.11070 | 0.217261 | ||||||||
\(206\) | 4.69468 | 0.327094 | ||||||||
\(207\) | −22.9527 | −1.59532 | ||||||||
\(208\) | −6.45965 | −0.447896 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.994078 | −0.0685979 | ||||||||
\(211\) | −0.361050 | −0.0248557 | −0.0124279 | − | 0.999923i | \(-0.503956\pi\) | ||||
−0.0124279 | + | 0.999923i | \(0.503956\pi\) | |||||||
\(212\) | 3.76278 | 0.258429 | ||||||||
\(213\) | −0.0249728 | −0.00171111 | ||||||||
\(214\) | −16.0373 | −1.09629 | ||||||||
\(215\) | 5.56887 | 0.379794 | ||||||||
\(216\) | −2.56816 | −0.174741 | ||||||||
\(217\) | −22.1612 | −1.50440 | ||||||||
\(218\) | −14.1008 | −0.955026 | ||||||||
\(219\) | 3.08361 | 0.208371 | ||||||||
\(220\) | −1.74018 | −0.117323 | ||||||||
\(221\) | 22.1066 | 1.48705 | ||||||||
\(222\) | −2.64584 | −0.177577 | ||||||||
\(223\) | 18.0486 | 1.20862 | 0.604312 | − | 0.796748i | \(-0.293448\pi\) | ||||
0.604312 | + | 0.796748i | \(0.293448\pi\) | |||||||
\(224\) | −2.52015 | −0.168384 | ||||||||
\(225\) | 11.7925 | 0.786163 | ||||||||
\(226\) | 12.7224 | 0.846280 | ||||||||
\(227\) | 12.2845 | 0.815349 | 0.407675 | − | 0.913127i | \(-0.366340\pi\) | ||||
0.407675 | + | 0.913127i | \(0.366340\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.79174 | 0.448811 | 0.224405 | − | 0.974496i | \(-0.427956\pi\) | ||||
0.224405 | + | 0.974496i | \(0.427956\pi\) | |||||||
\(230\) | 7.29689 | 0.481143 | ||||||||
\(231\) | −2.17661 | −0.143210 | ||||||||
\(232\) | −4.58064 | −0.300734 | ||||||||
\(233\) | 21.4294 | 1.40388 | 0.701942 | − | 0.712234i | \(-0.252317\pi\) | ||||
0.701942 | + | 0.712234i | \(0.252317\pi\) | |||||||
\(234\) | −18.1143 | −1.18417 | ||||||||
\(235\) | 9.40507 | 0.613519 | ||||||||
\(236\) | 2.84162 | 0.184973 | ||||||||
\(237\) | 4.04041 | 0.262453 | ||||||||
\(238\) | 8.62460 | 0.559050 | ||||||||
\(239\) | −11.8376 | −0.765713 | −0.382856 | − | 0.923808i | \(-0.625060\pi\) | ||||
−0.382856 | + | 0.923808i | \(0.625060\pi\) | |||||||
\(240\) | 0.394452 | 0.0254618 | ||||||||
\(241\) | −21.7463 | −1.40080 | −0.700401 | − | 0.713749i | \(-0.746996\pi\) | ||||
−0.700401 | + | 0.713749i | \(0.746996\pi\) | |||||||
\(242\) | 7.18974 | 0.462174 | ||||||||
\(243\) | −10.9240 | −0.700775 | ||||||||
\(244\) | −2.45495 | −0.157162 | ||||||||
\(245\) | 0.578452 | 0.0369560 | ||||||||
\(246\) | −1.54390 | −0.0984353 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.79360 | 0.558394 | ||||||||
\(249\) | 6.24931 | 0.396034 | ||||||||
\(250\) | −8.20640 | −0.519018 | ||||||||
\(251\) | 23.6410 | 1.49221 | 0.746104 | − | 0.665829i | \(-0.231922\pi\) | ||||
0.746104 | + | 0.665829i | \(0.231922\pi\) | |||||||
\(252\) | −7.06706 | −0.445183 | ||||||||
\(253\) | 15.9771 | 1.00447 | ||||||||
\(254\) | −7.17442 | −0.450163 | ||||||||
\(255\) | −1.34992 | −0.0845352 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.923469 | −0.0576044 | −0.0288022 | − | 0.999585i | \(-0.509169\pi\) | ||||
−0.0288022 | + | 0.999585i | \(0.509169\pi\) | |||||||
\(258\) | −2.76393 | −0.172075 | ||||||||
\(259\) | −15.0700 | −0.936402 | ||||||||
\(260\) | 5.75872 | 0.357141 | ||||||||
\(261\) | −12.8452 | −0.795096 | ||||||||
\(262\) | 3.52265 | 0.217630 | ||||||||
\(263\) | 4.31967 | 0.266362 | 0.133181 | − | 0.991092i | \(-0.457481\pi\) | ||||
0.133181 | + | 0.991092i | \(0.457481\pi\) | |||||||
\(264\) | 0.863684 | 0.0531561 | ||||||||
\(265\) | −3.35449 | −0.206064 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.826407 | −0.0505753 | ||||||||
\(268\) | −2.67261 | −0.163256 | ||||||||
\(269\) | −10.7954 | −0.658205 | −0.329102 | − | 0.944294i | \(-0.606746\pi\) | ||||
−0.329102 | + | 0.944294i | \(0.606746\pi\) | |||||||
\(270\) | 2.28949 | 0.139334 | ||||||||
\(271\) | 0.807243 | 0.0490365 | 0.0245183 | − | 0.999699i | \(-0.492195\pi\) | ||||
0.0245183 | + | 0.999699i | \(0.492195\pi\) | |||||||
\(272\) | −3.42226 | −0.207505 | ||||||||
\(273\) | 7.20298 | 0.435944 | ||||||||
\(274\) | 11.0035 | 0.664749 | ||||||||
\(275\) | −8.20859 | −0.494996 | ||||||||
\(276\) | −3.62158 | −0.217994 | ||||||||
\(277\) | −9.14869 | −0.549691 | −0.274846 | − | 0.961488i | \(-0.588627\pi\) | ||||
−0.274846 | + | 0.961488i | \(0.588627\pi\) | |||||||
\(278\) | −21.7586 | −1.30499 | ||||||||
\(279\) | 24.6593 | 1.47631 | ||||||||
\(280\) | 2.24669 | 0.134265 | ||||||||
\(281\) | 21.2158 | 1.26563 | 0.632813 | − | 0.774305i | \(-0.281900\pi\) | ||||
0.632813 | + | 0.774305i | \(0.281900\pi\) | |||||||
\(282\) | −4.66791 | −0.277970 | ||||||||
\(283\) | 5.18985 | 0.308505 | 0.154252 | − | 0.988031i | \(-0.450703\pi\) | ||||
0.154252 | + | 0.988031i | \(0.450703\pi\) | |||||||
\(284\) | 0.0564404 | 0.00334912 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.6092 | 0.745596 | ||||||||
\(287\) | −8.79360 | −0.519070 | ||||||||
\(288\) | 2.80423 | 0.165241 | ||||||||
\(289\) | −5.28814 | −0.311067 | ||||||||
\(290\) | 4.08361 | 0.239798 | ||||||||
\(291\) | −3.46197 | −0.202945 | ||||||||
\(292\) | −6.96917 | −0.407840 | ||||||||
\(293\) | −17.5660 | −1.02621 | −0.513107 | − | 0.858324i | \(-0.671506\pi\) | ||||
−0.513107 | + | 0.858324i | \(0.671506\pi\) | |||||||
\(294\) | −0.287096 | −0.0167438 | ||||||||
\(295\) | −2.53328 | −0.147493 | ||||||||
\(296\) | 5.97980 | 0.347569 | ||||||||
\(297\) | 5.01302 | 0.290885 | ||||||||
\(298\) | −14.3896 | −0.833565 | ||||||||
\(299\) | −52.8725 | −3.05769 | ||||||||
\(300\) | 1.86067 | 0.107426 | ||||||||
\(301\) | −15.7426 | −0.907387 | ||||||||
\(302\) | −12.4068 | −0.713929 | ||||||||
\(303\) | 2.38261 | 0.136877 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.18857 | 0.125317 | ||||||||
\(306\) | −9.59679 | −0.548612 | ||||||||
\(307\) | −21.5684 | −1.23097 | −0.615486 | − | 0.788148i | \(-0.711040\pi\) | ||||
−0.615486 | + | 0.788148i | \(0.711040\pi\) | |||||||
\(308\) | 4.91930 | 0.280303 | ||||||||
\(309\) | 2.07722 | 0.118169 | ||||||||
\(310\) | −7.83942 | −0.445249 | ||||||||
\(311\) | −2.57368 | −0.145940 | −0.0729701 | − | 0.997334i | \(-0.523248\pi\) | ||||
−0.0729701 | + | 0.997334i | \(0.523248\pi\) | |||||||
\(312\) | −2.85816 | −0.161811 | ||||||||
\(313\) | −5.18389 | −0.293011 | −0.146505 | − | 0.989210i | \(-0.546803\pi\) | ||||
−0.146505 | + | 0.989210i | \(0.546803\pi\) | |||||||
\(314\) | 0.451220 | 0.0254638 | ||||||||
\(315\) | 6.30023 | 0.354977 | ||||||||
\(316\) | −9.13162 | −0.513694 | ||||||||
\(317\) | −20.2562 | −1.13770 | −0.568850 | − | 0.822442i | \(-0.692611\pi\) | ||||
−0.568850 | + | 0.822442i | \(0.692611\pi\) | |||||||
\(318\) | 1.66489 | 0.0933625 | ||||||||
\(319\) | 8.94137 | 0.500620 | ||||||||
\(320\) | −0.891491 | −0.0498359 | ||||||||
\(321\) | −7.09591 | −0.396055 | ||||||||
\(322\) | −20.6275 | −1.14953 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.27636 | 0.404242 | ||||||||
\(325\) | 27.1644 | 1.50681 | ||||||||
\(326\) | 0.0692542 | 0.00383564 | ||||||||
\(327\) | −6.23909 | −0.345022 | ||||||||
\(328\) | 3.48932 | 0.192666 | ||||||||
\(329\) | −26.5871 | −1.46579 | ||||||||
\(330\) | −0.769967 | −0.0423853 | ||||||||
\(331\) | −21.3280 | −1.17229 | −0.586146 | − | 0.810205i | \(-0.699356\pi\) | ||||
−0.586146 | + | 0.810205i | \(0.699356\pi\) | |||||||
\(332\) | −14.1239 | −0.775150 | ||||||||
\(333\) | 16.7687 | 0.918919 | ||||||||
\(334\) | −2.17371 | −0.118940 | ||||||||
\(335\) | 2.38261 | 0.130176 | ||||||||
\(336\) | −1.11507 | −0.0608322 | ||||||||
\(337\) | −22.7275 | −1.23804 | −0.619022 | − | 0.785374i | \(-0.712471\pi\) | ||||
−0.619022 | + | 0.785374i | \(0.712471\pi\) | |||||||
\(338\) | −28.7271 | −1.56255 | ||||||||
\(339\) | 5.62919 | 0.305735 | ||||||||
\(340\) | 3.05092 | 0.165459 | ||||||||
\(341\) | −17.1650 | −0.929538 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.2762 | −1.04082 | ||||||||
\(344\) | 6.24669 | 0.336799 | ||||||||
\(345\) | 3.22861 | 0.173822 | ||||||||
\(346\) | 16.8493 | 0.905823 | ||||||||
\(347\) | −4.92855 | −0.264579 | −0.132289 | − | 0.991211i | \(-0.542233\pi\) | ||||
−0.132289 | + | 0.991211i | \(0.542233\pi\) | |||||||
\(348\) | −2.02677 | −0.108646 | ||||||||
\(349\) | 26.1615 | 1.40039 | 0.700197 | − | 0.713950i | \(-0.253096\pi\) | ||||
0.700197 | + | 0.713950i | \(0.253096\pi\) | |||||||
\(350\) | 10.5978 | 0.566478 | ||||||||
\(351\) | −16.5894 | −0.885477 | ||||||||
\(352\) | −1.95199 | −0.104041 | ||||||||
\(353\) | 2.70813 | 0.144139 | 0.0720697 | − | 0.997400i | \(-0.477040\pi\) | ||||
0.0720697 | + | 0.997400i | \(0.477040\pi\) | |||||||
\(354\) | 1.25731 | 0.0668253 | ||||||||
\(355\) | −0.0503161 | −0.00267050 | ||||||||
\(356\) | 1.86774 | 0.0989901 | ||||||||
\(357\) | 3.81607 | 0.201968 | ||||||||
\(358\) | −18.9655 | −1.00236 | ||||||||
\(359\) | −9.31002 | −0.491364 | −0.245682 | − | 0.969350i | \(-0.579012\pi\) | ||||
−0.245682 | + | 0.969350i | \(0.579012\pi\) | |||||||
\(360\) | −2.49994 | −0.131759 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 1.98687 | 0.104428 | ||||||||
\(363\) | 3.18120 | 0.166970 | ||||||||
\(364\) | −16.2793 | −0.853265 | ||||||||
\(365\) | 6.21296 | 0.325201 | ||||||||
\(366\) | −1.08623 | −0.0567779 | ||||||||
\(367\) | 7.75442 | 0.404777 | 0.202389 | − | 0.979305i | \(-0.435130\pi\) | ||||
0.202389 | + | 0.979305i | \(0.435130\pi\) | |||||||
\(368\) | 8.18504 | 0.426675 | ||||||||
\(369\) | 9.78485 | 0.509379 | ||||||||
\(370\) | −5.33094 | −0.277142 | ||||||||
\(371\) | 9.48276 | 0.492320 | ||||||||
\(372\) | 3.89085 | 0.201731 | ||||||||
\(373\) | −25.0124 | −1.29509 | −0.647546 | − | 0.762027i | \(-0.724205\pi\) | ||||
−0.647546 | + | 0.762027i | \(0.724205\pi\) | |||||||
\(374\) | 6.68021 | 0.345426 | ||||||||
\(375\) | −3.63103 | −0.187506 | ||||||||
\(376\) | 10.5498 | 0.544065 | ||||||||
\(377\) | −29.5894 | −1.52393 | ||||||||
\(378\) | −6.47214 | −0.332891 | ||||||||
\(379\) | 19.1802 | 0.985222 | 0.492611 | − | 0.870250i | \(-0.336043\pi\) | ||||
0.492611 | + | 0.870250i | \(0.336043\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.17442 | −0.162630 | ||||||||
\(382\) | 20.9259 | 1.07066 | ||||||||
\(383\) | −4.83319 | −0.246964 | −0.123482 | − | 0.992347i | \(-0.539406\pi\) | ||||
−0.123482 | + | 0.992347i | \(0.539406\pi\) | |||||||
\(384\) | 0.442463 | 0.0225794 | ||||||||
\(385\) | −4.38551 | −0.223506 | ||||||||
\(386\) | −7.78879 | −0.396439 | ||||||||
\(387\) | 17.5171 | 0.890446 | ||||||||
\(388\) | 7.82432 | 0.397219 | ||||||||
\(389\) | 21.7291 | 1.10171 | 0.550855 | − | 0.834601i | \(-0.314302\pi\) | ||||
0.550855 | + | 0.834601i | \(0.314302\pi\) | |||||||
\(390\) | 2.54802 | 0.129024 | ||||||||
\(391\) | −28.0113 | −1.41659 | ||||||||
\(392\) | 0.648859 | 0.0327723 | ||||||||
\(393\) | 1.55865 | 0.0786233 | ||||||||
\(394\) | −1.82514 | −0.0919493 | ||||||||
\(395\) | 8.14076 | 0.409606 | ||||||||
\(396\) | −5.47382 | −0.275070 | ||||||||
\(397\) | 11.7140 | 0.587909 | 0.293955 | − | 0.955819i | \(-0.405029\pi\) | ||||
0.293955 | + | 0.955819i | \(0.405029\pi\) | |||||||
\(398\) | −2.35926 | −0.118259 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.20524 | −0.210262 | ||||||||
\(401\) | −11.8123 | −0.589880 | −0.294940 | − | 0.955516i | \(-0.595300\pi\) | ||||
−0.294940 | + | 0.955516i | \(0.595300\pi\) | |||||||
\(402\) | −1.18253 | −0.0589793 | ||||||||
\(403\) | 56.8036 | 2.82959 | ||||||||
\(404\) | −5.38487 | −0.267907 | ||||||||
\(405\) | −6.48681 | −0.322332 | ||||||||
\(406\) | −11.5439 | −0.572914 | ||||||||
\(407\) | −11.6725 | −0.578584 | ||||||||
\(408\) | −1.51423 | −0.0749653 | ||||||||
\(409\) | 25.2663 | 1.24934 | 0.624668 | − | 0.780890i | \(-0.285234\pi\) | ||||
0.624668 | + | 0.780890i | \(0.285234\pi\) | |||||||
\(410\) | −3.11070 | −0.153627 | ||||||||
\(411\) | 4.86867 | 0.240154 | ||||||||
\(412\) | −4.69468 | −0.231290 | ||||||||
\(413\) | 7.16129 | 0.352384 | ||||||||
\(414\) | 22.9527 | 1.12806 | ||||||||
\(415\) | 12.5913 | 0.618084 | ||||||||
\(416\) | 6.45965 | 0.316710 | ||||||||
\(417\) | −9.62739 | −0.471455 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.6143 | 1.54446 | 0.772229 | − | 0.635344i | \(-0.219142\pi\) | ||||
0.772229 | + | 0.635344i | \(0.219142\pi\) | |||||||
\(420\) | 0.994078 | 0.0485060 | ||||||||
\(421\) | −2.18972 | −0.106720 | −0.0533602 | − | 0.998575i | \(-0.516993\pi\) | ||||
−0.0533602 | + | 0.998575i | \(0.516993\pi\) | |||||||
\(422\) | 0.361050 | 0.0175757 | ||||||||
\(423\) | 29.5841 | 1.43843 | ||||||||
\(424\) | −3.76278 | −0.182737 | ||||||||
\(425\) | 14.3914 | 0.698087 | ||||||||
\(426\) | 0.0249728 | 0.00120994 | ||||||||
\(427\) | −6.18683 | −0.299402 | ||||||||
\(428\) | 16.0373 | 0.775191 | ||||||||
\(429\) | 5.57909 | 0.269361 | ||||||||
\(430\) | −5.56887 | −0.268555 | ||||||||
\(431\) | −1.80372 | −0.0868819 | −0.0434410 | − | 0.999056i | \(-0.513832\pi\) | ||||
−0.0434410 | + | 0.999056i | \(0.513832\pi\) | |||||||
\(432\) | 2.56816 | 0.123561 | ||||||||
\(433\) | −6.57233 | −0.315846 | −0.157923 | − | 0.987451i | \(-0.550480\pi\) | ||||
−0.157923 | + | 0.987451i | \(0.550480\pi\) | |||||||
\(434\) | 22.1612 | 1.06377 | ||||||||
\(435\) | 1.80685 | 0.0866316 | ||||||||
\(436\) | 14.1008 | 0.675305 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.08361 | −0.147340 | ||||||||
\(439\) | −9.13060 | −0.435780 | −0.217890 | − | 0.975973i | \(-0.569917\pi\) | ||||
−0.217890 | + | 0.975973i | \(0.569917\pi\) | |||||||
\(440\) | 1.74018 | 0.0829599 | ||||||||
\(441\) | 1.81955 | 0.0866451 | ||||||||
\(442\) | −22.1066 | −1.05150 | ||||||||
\(443\) | −27.4686 | −1.30507 | −0.652536 | − | 0.757757i | \(-0.726295\pi\) | ||||
−0.652536 | + | 0.757757i | \(0.726295\pi\) | |||||||
\(444\) | 2.64584 | 0.125566 | ||||||||
\(445\) | −1.66508 | −0.0789321 | ||||||||
\(446\) | −18.0486 | −0.854626 | ||||||||
\(447\) | −6.36686 | −0.301142 | ||||||||
\(448\) | 2.52015 | 0.119066 | ||||||||
\(449\) | −7.57293 | −0.357389 | −0.178694 | − | 0.983905i | \(-0.557187\pi\) | ||||
−0.178694 | + | 0.983905i | \(0.557187\pi\) | |||||||
\(450\) | −11.7925 | −0.555902 | ||||||||
\(451\) | −6.81112 | −0.320723 | ||||||||
\(452\) | −12.7224 | −0.598410 | ||||||||
\(453\) | −5.48954 | −0.257921 | ||||||||
\(454\) | −12.2845 | −0.576539 | ||||||||
\(455\) | 14.5128 | 0.680372 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.7675 | −1.01824 | −0.509120 | − | 0.860696i | \(-0.670029\pi\) | ||||
−0.509120 | + | 0.860696i | \(0.670029\pi\) | |||||||
\(458\) | −6.79174 | −0.317357 | ||||||||
\(459\) | −8.78890 | −0.410231 | ||||||||
\(460\) | −7.29689 | −0.340219 | ||||||||
\(461\) | 11.9444 | 0.556305 | 0.278153 | − | 0.960537i | \(-0.410278\pi\) | ||||
0.278153 | + | 0.960537i | \(0.410278\pi\) | |||||||
\(462\) | 2.17661 | 0.101265 | ||||||||
\(463\) | −8.75371 | −0.406819 | −0.203410 | − | 0.979094i | \(-0.565202\pi\) | ||||
−0.203410 | + | 0.979094i | \(0.565202\pi\) | |||||||
\(464\) | 4.58064 | 0.212651 | ||||||||
\(465\) | −3.46866 | −0.160855 | ||||||||
\(466\) | −21.4294 | −0.992696 | ||||||||
\(467\) | 29.3568 | 1.35847 | 0.679236 | − | 0.733920i | \(-0.262311\pi\) | ||||
0.679236 | + | 0.733920i | \(0.262311\pi\) | |||||||
\(468\) | 18.1143 | 0.837335 | ||||||||
\(469\) | −6.73537 | −0.311010 | ||||||||
\(470\) | −9.40507 | −0.433824 | ||||||||
\(471\) | 0.199648 | 0.00919932 | ||||||||
\(472\) | −2.84162 | −0.130796 | ||||||||
\(473\) | −12.1935 | −0.560656 | ||||||||
\(474\) | −4.04041 | −0.185582 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.62460 | −0.395308 | ||||||||
\(477\) | −10.5517 | −0.483128 | ||||||||
\(478\) | 11.8376 | 0.541441 | ||||||||
\(479\) | −24.8705 | −1.13636 | −0.568180 | − | 0.822904i | \(-0.692352\pi\) | ||||
−0.568180 | + | 0.822904i | \(0.692352\pi\) | |||||||
\(480\) | −0.394452 | −0.0180042 | ||||||||
\(481\) | 38.6274 | 1.76126 | ||||||||
\(482\) | 21.7463 | 0.990517 | ||||||||
\(483\) | −9.12692 | −0.415289 | ||||||||
\(484\) | −7.18974 | −0.326806 | ||||||||
\(485\) | −6.97531 | −0.316733 | ||||||||
\(486\) | 10.9240 | 0.495523 | ||||||||
\(487\) | −8.53766 | −0.386878 | −0.193439 | − | 0.981112i | \(-0.561964\pi\) | ||||
−0.193439 | + | 0.981112i | \(0.561964\pi\) | |||||||
\(488\) | 2.45495 | 0.111130 | ||||||||
\(489\) | 0.0306425 | 0.00138570 | ||||||||
\(490\) | −0.578452 | −0.0261318 | ||||||||
\(491\) | −11.5397 | −0.520780 | −0.260390 | − | 0.965504i | \(-0.583851\pi\) | ||||
−0.260390 | + | 0.965504i | \(0.583851\pi\) | |||||||
\(492\) | 1.54390 | 0.0696043 | ||||||||
\(493\) | −15.6762 | −0.706019 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.87986 | 0.219333 | ||||||||
\(496\) | −8.79360 | −0.394844 | ||||||||
\(497\) | 0.142238 | 0.00638025 | ||||||||
\(498\) | −6.24931 | −0.280038 | ||||||||
\(499\) | −29.6091 | −1.32548 | −0.662742 | − | 0.748848i | \(-0.730607\pi\) | ||||
−0.662742 | + | 0.748848i | \(0.730607\pi\) | |||||||
\(500\) | 8.20640 | 0.367001 | ||||||||
\(501\) | −0.961785 | −0.0429694 | ||||||||
\(502\) | −23.6410 | −1.05515 | ||||||||
\(503\) | 5.86827 | 0.261653 | 0.130827 | − | 0.991405i | \(-0.458237\pi\) | ||||
0.130827 | + | 0.991405i | \(0.458237\pi\) | |||||||
\(504\) | 7.06706 | 0.314792 | ||||||||
\(505\) | 4.80057 | 0.213622 | ||||||||
\(506\) | −15.9771 | −0.710269 | ||||||||
\(507\) | −12.7107 | −0.564501 | ||||||||
\(508\) | 7.17442 | 0.318313 | ||||||||
\(509\) | 25.5687 | 1.13331 | 0.566656 | − | 0.823954i | \(-0.308237\pi\) | ||||
0.566656 | + | 0.823954i | \(0.308237\pi\) | |||||||
\(510\) | 1.34992 | 0.0597754 | ||||||||
\(511\) | −17.5633 | −0.776957 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.923469 | 0.0407325 | ||||||||
\(515\) | 4.18527 | 0.184425 | ||||||||
\(516\) | 2.76393 | 0.121675 | ||||||||
\(517\) | −20.5931 | −0.905685 | ||||||||
\(518\) | 15.0700 | 0.662136 | ||||||||
\(519\) | 7.45520 | 0.327247 | ||||||||
\(520\) | −5.75872 | −0.252537 | ||||||||
\(521\) | 14.0332 | 0.614807 | 0.307403 | − | 0.951579i | \(-0.400540\pi\) | ||||
0.307403 | + | 0.951579i | \(0.400540\pi\) | |||||||
\(522\) | 12.8452 | 0.562217 | ||||||||
\(523\) | −31.0784 | −1.35896 | −0.679482 | − | 0.733692i | \(-0.737795\pi\) | ||||
−0.679482 | + | 0.733692i | \(0.737795\pi\) | |||||||
\(524\) | −3.52265 | −0.153888 | ||||||||
\(525\) | 4.68915 | 0.204651 | ||||||||
\(526\) | −4.31967 | −0.188347 | ||||||||
\(527\) | 30.0940 | 1.31092 | ||||||||
\(528\) | −0.863684 | −0.0375870 | ||||||||
\(529\) | 43.9949 | 1.91282 | ||||||||
\(530\) | 3.35449 | 0.145710 | ||||||||
\(531\) | −7.96853 | −0.345805 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.5398 | 0.976307 | ||||||||
\(534\) | 0.826407 | 0.0357621 | ||||||||
\(535\) | −14.2971 | −0.618117 | ||||||||
\(536\) | 2.67261 | 0.115439 | ||||||||
\(537\) | −8.39155 | −0.362122 | ||||||||
\(538\) | 10.7954 | 0.465421 | ||||||||
\(539\) | −1.26657 | −0.0545548 | ||||||||
\(540\) | −2.28949 | −0.0985240 | ||||||||
\(541\) | 2.89608 | 0.124512 | 0.0622561 | − | 0.998060i | \(-0.480170\pi\) | ||||
0.0622561 | + | 0.998060i | \(0.480170\pi\) | |||||||
\(542\) | −0.807243 | −0.0346741 | ||||||||
\(543\) | 0.879118 | 0.0377266 | ||||||||
\(544\) | 3.42226 | 0.146728 | ||||||||
\(545\) | −12.5707 | −0.538471 | ||||||||
\(546\) | −7.20298 | −0.308259 | ||||||||
\(547\) | −30.3861 | −1.29922 | −0.649608 | − | 0.760269i | \(-0.725067\pi\) | ||||
−0.649608 | + | 0.760269i | \(0.725067\pi\) | |||||||
\(548\) | −11.0035 | −0.470048 | ||||||||
\(549\) | 6.88423 | 0.293812 | ||||||||
\(550\) | 8.20859 | 0.350015 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 3.62158 | 0.154145 | ||||||||
\(553\) | −23.0130 | −0.978613 | ||||||||
\(554\) | 9.14869 | 0.388691 | ||||||||
\(555\) | −2.35875 | −0.100123 | ||||||||
\(556\) | 21.7586 | 0.922771 | ||||||||
\(557\) | −6.13412 | −0.259911 | −0.129956 | − | 0.991520i | \(-0.541483\pi\) | ||||
−0.129956 | + | 0.991520i | \(0.541483\pi\) | |||||||
\(558\) | −24.6593 | −1.04391 | ||||||||
\(559\) | 40.3514 | 1.70668 | ||||||||
\(560\) | −2.24669 | −0.0949400 | ||||||||
\(561\) | 2.95575 | 0.124792 | ||||||||
\(562\) | −21.2158 | −0.894932 | ||||||||
\(563\) | 28.1917 | 1.18814 | 0.594069 | − | 0.804414i | \(-0.297521\pi\) | ||||
0.594069 | + | 0.804414i | \(0.297521\pi\) | |||||||
\(564\) | 4.66791 | 0.196554 | ||||||||
\(565\) | 11.3419 | 0.477157 | ||||||||
\(566\) | −5.18985 | −0.218146 | ||||||||
\(567\) | 18.3375 | 0.770103 | ||||||||
\(568\) | −0.0564404 | −0.00236819 | ||||||||
\(569\) | 42.1145 | 1.76553 | 0.882766 | − | 0.469812i | \(-0.155678\pi\) | ||||
0.882766 | + | 0.469812i | \(0.155678\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.166927 | 0.00698566 | 0.00349283 | − | 0.999994i | \(-0.498888\pi\) | ||||
0.00349283 | + | 0.999994i | \(0.498888\pi\) | |||||||
\(572\) | −12.6092 | −0.527216 | ||||||||
\(573\) | 9.25896 | 0.386799 | ||||||||
\(574\) | 8.79360 | 0.367038 | ||||||||
\(575\) | −34.4201 | −1.43542 | ||||||||
\(576\) | −2.80423 | −0.116843 | ||||||||
\(577\) | −19.9631 | −0.831076 | −0.415538 | − | 0.909576i | \(-0.636407\pi\) | ||||
−0.415538 | + | 0.909576i | \(0.636407\pi\) | |||||||
\(578\) | 5.28814 | 0.219957 | ||||||||
\(579\) | −3.44626 | −0.143222 | ||||||||
\(580\) | −4.08361 | −0.169562 | ||||||||
\(581\) | −35.5943 | −1.47670 | ||||||||
\(582\) | 3.46197 | 0.143503 | ||||||||
\(583\) | 7.34490 | 0.304195 | ||||||||
\(584\) | 6.96917 | 0.288387 | ||||||||
\(585\) | −16.1488 | −0.667669 | ||||||||
\(586\) | 17.5660 | 0.725643 | ||||||||
\(587\) | 10.1440 | 0.418689 | 0.209345 | − | 0.977842i | \(-0.432867\pi\) | ||||
0.209345 | + | 0.977842i | \(0.432867\pi\) | |||||||
\(588\) | 0.287096 | 0.0118397 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 2.53328 | 0.104293 | ||||||||
\(591\) | −0.807559 | −0.0332185 | ||||||||
\(592\) | −5.97980 | −0.245768 | ||||||||
\(593\) | 7.45315 | 0.306064 | 0.153032 | − | 0.988221i | \(-0.451096\pi\) | ||||
0.153032 | + | 0.988221i | \(0.451096\pi\) | |||||||
\(594\) | −5.01302 | −0.205687 | ||||||||
\(595\) | 7.68876 | 0.315208 | ||||||||
\(596\) | 14.3896 | 0.589420 | ||||||||
\(597\) | −1.04388 | −0.0427233 | ||||||||
\(598\) | 52.8725 | 2.16212 | ||||||||
\(599\) | 6.37141 | 0.260329 | 0.130164 | − | 0.991492i | \(-0.458449\pi\) | ||||
0.130164 | + | 0.991492i | \(0.458449\pi\) | |||||||
\(600\) | −1.86067 | −0.0759614 | ||||||||
\(601\) | −1.74631 | −0.0712333 | −0.0356166 | − | 0.999366i | \(-0.511340\pi\) | ||||
−0.0356166 | + | 0.999366i | \(0.511340\pi\) | |||||||
\(602\) | 15.7426 | 0.641620 | ||||||||
\(603\) | 7.49460 | 0.305204 | ||||||||
\(604\) | 12.4068 | 0.504824 | ||||||||
\(605\) | 6.40959 | 0.260587 | ||||||||
\(606\) | −2.38261 | −0.0967869 | ||||||||
\(607\) | −32.1612 | −1.30538 | −0.652691 | − | 0.757624i | \(-0.726360\pi\) | ||||
−0.652691 | + | 0.757624i | \(0.726360\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.10775 | −0.206977 | ||||||||
\(610\) | −2.18857 | −0.0886125 | ||||||||
\(611\) | 68.1481 | 2.75698 | ||||||||
\(612\) | 9.59679 | 0.387927 | ||||||||
\(613\) | 12.7645 | 0.515552 | 0.257776 | − | 0.966205i | \(-0.417010\pi\) | ||||
0.257776 | + | 0.966205i | \(0.417010\pi\) | |||||||
\(614\) | 21.5684 | 0.870428 | ||||||||
\(615\) | −1.37637 | −0.0555007 | ||||||||
\(616\) | −4.91930 | −0.198204 | ||||||||
\(617\) | −1.68323 | −0.0677643 | −0.0338822 | − | 0.999426i | \(-0.510787\pi\) | ||||
−0.0338822 | + | 0.999426i | \(0.510787\pi\) | |||||||
\(618\) | −2.07722 | −0.0835582 | ||||||||
\(619\) | 31.5285 | 1.26724 | 0.633618 | − | 0.773646i | \(-0.281569\pi\) | ||||
0.633618 | + | 0.773646i | \(0.281569\pi\) | |||||||
\(620\) | 7.83942 | 0.314839 | ||||||||
\(621\) | 21.0205 | 0.843523 | ||||||||
\(622\) | 2.57368 | 0.103195 | ||||||||
\(623\) | 4.70698 | 0.188581 | ||||||||
\(624\) | 2.85816 | 0.114418 | ||||||||
\(625\) | 13.7103 | 0.548411 | ||||||||
\(626\) | 5.18389 | 0.207190 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.451220 | −0.0180056 | ||||||||
\(629\) | 20.4644 | 0.815970 | ||||||||
\(630\) | −6.30023 | −0.251007 | ||||||||
\(631\) | −31.7662 | −1.26459 | −0.632297 | − | 0.774726i | \(-0.717888\pi\) | ||||
−0.632297 | + | 0.774726i | \(0.717888\pi\) | |||||||
\(632\) | 9.13162 | 0.363236 | ||||||||
\(633\) | 0.159752 | 0.00634955 | ||||||||
\(634\) | 20.2562 | 0.804475 | ||||||||
\(635\) | −6.39593 | −0.253815 | ||||||||
\(636\) | −1.66489 | −0.0660173 | ||||||||
\(637\) | 4.19140 | 0.166069 | ||||||||
\(638\) | −8.94137 | −0.353992 | ||||||||
\(639\) | −0.158272 | −0.00626113 | ||||||||
\(640\) | 0.891491 | 0.0352393 | ||||||||
\(641\) | 40.4437 | 1.59743 | 0.798715 | − | 0.601709i | \(-0.205513\pi\) | ||||
0.798715 | + | 0.601709i | \(0.205513\pi\) | |||||||
\(642\) | 7.09591 | 0.280053 | ||||||||
\(643\) | −26.1033 | −1.02941 | −0.514706 | − | 0.857367i | \(-0.672099\pi\) | ||||
−0.514706 | + | 0.857367i | \(0.672099\pi\) | |||||||
\(644\) | 20.6275 | 0.812837 | ||||||||
\(645\) | −2.46402 | −0.0970208 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.7713 | −1.91740 | −0.958699 | − | 0.284423i | \(-0.908198\pi\) | ||||
−0.958699 | + | 0.284423i | \(0.908198\pi\) | |||||||
\(648\) | −7.27636 | −0.285842 | ||||||||
\(649\) | 5.54680 | 0.217731 | ||||||||
\(650\) | −27.1644 | −1.06548 | ||||||||
\(651\) | 9.80551 | 0.384308 | ||||||||
\(652\) | −0.0692542 | −0.00271220 | ||||||||
\(653\) | −43.1831 | −1.68988 | −0.844942 | − | 0.534858i | \(-0.820365\pi\) | ||||
−0.844942 | + | 0.534858i | \(0.820365\pi\) | |||||||
\(654\) | 6.23909 | 0.243968 | ||||||||
\(655\) | 3.14042 | 0.122706 | ||||||||
\(656\) | −3.48932 | −0.136235 | ||||||||
\(657\) | 19.5431 | 0.762451 | ||||||||
\(658\) | 26.5871 | 1.03647 | ||||||||
\(659\) | 14.2769 | 0.556148 | 0.278074 | − | 0.960560i | \(-0.410304\pi\) | ||||
0.278074 | + | 0.960560i | \(0.410304\pi\) | |||||||
\(660\) | 0.769967 | 0.0299709 | ||||||||
\(661\) | −35.7497 | −1.39050 | −0.695251 | − | 0.718768i | \(-0.744707\pi\) | ||||
−0.695251 | + | 0.718768i | \(0.744707\pi\) | |||||||
\(662\) | 21.3280 | 0.828936 | ||||||||
\(663\) | −9.78136 | −0.379877 | ||||||||
\(664\) | 14.1239 | 0.548114 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.7687 | −0.649774 | ||||||||
\(667\) | 37.4928 | 1.45173 | ||||||||
\(668\) | 2.17371 | 0.0841032 | ||||||||
\(669\) | −7.98585 | −0.308751 | ||||||||
\(670\) | −2.38261 | −0.0920482 | ||||||||
\(671\) | −4.79204 | −0.184994 | ||||||||
\(672\) | 1.11507 | 0.0430149 | ||||||||
\(673\) | −10.3574 | −0.399248 | −0.199624 | − | 0.979873i | \(-0.563972\pi\) | ||||
−0.199624 | + | 0.979873i | \(0.563972\pi\) | |||||||
\(674\) | 22.7275 | 0.875429 | ||||||||
\(675\) | −10.7997 | −0.415682 | ||||||||
\(676\) | 28.7271 | 1.10489 | ||||||||
\(677\) | 10.7171 | 0.411891 | 0.205945 | − | 0.978564i | \(-0.433973\pi\) | ||||
0.205945 | + | 0.978564i | \(0.433973\pi\) | |||||||
\(678\) | −5.62919 | −0.216188 | ||||||||
\(679\) | 19.7184 | 0.756724 | ||||||||
\(680\) | −3.05092 | −0.116997 | ||||||||
\(681\) | −5.43543 | −0.208286 | ||||||||
\(682\) | 17.1650 | 0.657283 | ||||||||
\(683\) | −0.122930 | −0.00470377 | −0.00235188 | − | 0.999997i | \(-0.500749\pi\) | ||||
−0.00235188 | + | 0.999997i | \(0.500749\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.80957 | 0.374804 | ||||||||
\(686\) | 19.2762 | 0.735971 | ||||||||
\(687\) | −3.00510 | −0.114652 | ||||||||
\(688\) | −6.24669 | −0.238153 | ||||||||
\(689\) | −24.3062 | −0.925994 | ||||||||
\(690\) | −3.22861 | −0.122911 | ||||||||
\(691\) | −25.2815 | −0.961752 | −0.480876 | − | 0.876789i | \(-0.659681\pi\) | ||||
−0.480876 | + | 0.876789i | \(0.659681\pi\) | |||||||
\(692\) | −16.8493 | −0.640514 | ||||||||
\(693\) | −13.7948 | −0.524022 | ||||||||
\(694\) | 4.92855 | 0.187085 | ||||||||
\(695\) | −19.3976 | −0.735793 | ||||||||
\(696\) | 2.02677 | 0.0768244 | ||||||||
\(697\) | 11.9414 | 0.452312 | ||||||||
\(698\) | −26.1615 | −0.990228 | ||||||||
\(699\) | −9.48171 | −0.358631 | ||||||||
\(700\) | −10.5978 | −0.400560 | ||||||||
\(701\) | −5.17287 | −0.195377 | −0.0976883 | − | 0.995217i | \(-0.531145\pi\) | ||||
−0.0976883 | + | 0.995217i | \(0.531145\pi\) | |||||||
\(702\) | 16.5894 | 0.626127 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.95199 | 0.0735684 | ||||||||
\(705\) | −4.16140 | −0.156727 | ||||||||
\(706\) | −2.70813 | −0.101922 | ||||||||
\(707\) | −13.5707 | −0.510377 | ||||||||
\(708\) | −1.25731 | −0.0472526 | ||||||||
\(709\) | −29.9907 | −1.12632 | −0.563162 | − | 0.826346i | \(-0.690415\pi\) | ||||
−0.563162 | + | 0.826346i | \(0.690415\pi\) | |||||||
\(710\) | 0.0503161 | 0.00188833 | ||||||||
\(711\) | 25.6071 | 0.960342 | ||||||||
\(712\) | −1.86774 | −0.0699965 | ||||||||
\(713\) | −71.9760 | −2.69552 | ||||||||
\(714\) | −3.81607 | −0.142813 | ||||||||
\(715\) | 11.2410 | 0.420388 | ||||||||
\(716\) | 18.9655 | 0.708775 | ||||||||
\(717\) | 5.23772 | 0.195606 | ||||||||
\(718\) | 9.31002 | 0.347447 | ||||||||
\(719\) | −22.7033 | −0.846688 | −0.423344 | − | 0.905969i | \(-0.639144\pi\) | ||||
−0.423344 | + | 0.905969i | \(0.639144\pi\) | |||||||
\(720\) | 2.49994 | 0.0931674 | ||||||||
\(721\) | −11.8313 | −0.440620 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.62195 | 0.357844 | ||||||||
\(724\) | −1.98687 | −0.0738415 | ||||||||
\(725\) | −19.2627 | −0.715400 | ||||||||
\(726\) | −3.18120 | −0.118065 | ||||||||
\(727\) | 36.5937 | 1.35719 | 0.678593 | − | 0.734514i | \(-0.262590\pi\) | ||||
0.678593 | + | 0.734514i | \(0.262590\pi\) | |||||||
\(728\) | 16.2793 | 0.603350 | ||||||||
\(729\) | −16.9956 | −0.629467 | ||||||||
\(730\) | −6.21296 | −0.229952 | ||||||||
\(731\) | 21.3778 | 0.790686 | ||||||||
\(732\) | 1.08623 | 0.0401481 | ||||||||
\(733\) | 21.1522 | 0.781275 | 0.390637 | − | 0.920545i | \(-0.372255\pi\) | ||||
0.390637 | + | 0.920545i | \(0.372255\pi\) | |||||||
\(734\) | −7.75442 | −0.286221 | ||||||||
\(735\) | −0.255944 | −0.00944064 | ||||||||
\(736\) | −8.18504 | −0.301705 | ||||||||
\(737\) | −5.21690 | −0.192167 | ||||||||
\(738\) | −9.78485 | −0.360185 | ||||||||
\(739\) | 48.3066 | 1.77699 | 0.888494 | − | 0.458888i | \(-0.151752\pi\) | ||||
0.888494 | + | 0.458888i | \(0.151752\pi\) | |||||||
\(740\) | 5.33094 | 0.195969 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.48276 | −0.348123 | ||||||||
\(743\) | −31.8598 | −1.16882 | −0.584412 | − | 0.811457i | \(-0.698675\pi\) | ||||
−0.584412 | + | 0.811457i | \(0.698675\pi\) | |||||||
\(744\) | −3.89085 | −0.142645 | ||||||||
\(745\) | −12.8282 | −0.469988 | ||||||||
\(746\) | 25.0124 | 0.915768 | ||||||||
\(747\) | 39.6066 | 1.44913 | ||||||||
\(748\) | −6.68021 | −0.244253 | ||||||||
\(749\) | 40.4163 | 1.47678 | ||||||||
\(750\) | 3.63103 | 0.132586 | ||||||||
\(751\) | 40.9962 | 1.49597 | 0.747987 | − | 0.663713i | \(-0.231020\pi\) | ||||
0.747987 | + | 0.663713i | \(0.231020\pi\) | |||||||
\(752\) | −10.5498 | −0.384712 | ||||||||
\(753\) | −10.4603 | −0.381194 | ||||||||
\(754\) | 29.5894 | 1.07758 | ||||||||
\(755\) | −11.0605 | −0.402533 | ||||||||
\(756\) | 6.47214 | 0.235389 | ||||||||
\(757\) | −12.8215 | −0.466006 | −0.233003 | − | 0.972476i | \(-0.574855\pi\) | ||||
−0.233003 | + | 0.972476i | \(0.574855\pi\) | |||||||
\(758\) | −19.1802 | −0.696657 | ||||||||
\(759\) | −7.06929 | −0.256599 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.6382 | 1.29188 | 0.645942 | − | 0.763386i | \(-0.276465\pi\) | ||||
0.645942 | + | 0.763386i | \(0.276465\pi\) | |||||||
\(762\) | 3.17442 | 0.114997 | ||||||||
\(763\) | 35.5361 | 1.28649 | ||||||||
\(764\) | −20.9259 | −0.757074 | ||||||||
\(765\) | −8.55546 | −0.309323 | ||||||||
\(766\) | 4.83319 | 0.174630 | ||||||||
\(767\) | −18.3558 | −0.662791 | ||||||||
\(768\) | −0.442463 | −0.0159660 | ||||||||
\(769\) | −5.57401 | −0.201004 | −0.100502 | − | 0.994937i | \(-0.532045\pi\) | ||||
−0.100502 | + | 0.994937i | \(0.532045\pi\) | |||||||
\(770\) | 4.38551 | 0.158043 | ||||||||
\(771\) | 0.408601 | 0.0147154 | ||||||||
\(772\) | 7.78879 | 0.280325 | ||||||||
\(773\) | 36.4119 | 1.30965 | 0.654823 | − | 0.755782i | \(-0.272743\pi\) | ||||
0.654823 | + | 0.755782i | \(0.272743\pi\) | |||||||
\(774\) | −17.5171 | −0.629640 | ||||||||
\(775\) | 36.9792 | 1.32833 | ||||||||
\(776\) | −7.82432 | −0.280877 | ||||||||
\(777\) | 6.66791 | 0.239210 | ||||||||
\(778\) | −21.7291 | −0.779027 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −2.54802 | −0.0912339 | ||||||||
\(781\) | 0.110171 | 0.00394223 | ||||||||
\(782\) | 28.0113 | 1.00168 | ||||||||
\(783\) | 11.7638 | 0.420405 | ||||||||
\(784\) | −0.648859 | −0.0231735 | ||||||||
\(785\) | 0.402259 | 0.0143572 | ||||||||
\(786\) | −1.55865 | −0.0555951 | ||||||||
\(787\) | 31.9046 | 1.13728 | 0.568638 | − | 0.822588i | \(-0.307471\pi\) | ||||
0.568638 | + | 0.822588i | \(0.307471\pi\) | |||||||
\(788\) | 1.82514 | 0.0650180 | ||||||||
\(789\) | −1.91130 | −0.0680440 | ||||||||
\(790\) | −8.14076 | −0.289635 | ||||||||
\(791\) | −32.0622 | −1.14000 | ||||||||
\(792\) | 5.47382 | 0.194504 | ||||||||
\(793\) | 15.8581 | 0.563138 | ||||||||
\(794\) | −11.7140 | −0.415715 | ||||||||
\(795\) | 1.48424 | 0.0526405 | ||||||||
\(796\) | 2.35926 | 0.0836216 | ||||||||
\(797\) | −2.09165 | −0.0740900 | −0.0370450 | − | 0.999314i | \(-0.511794\pi\) | ||||
−0.0370450 | + | 0.999314i | \(0.511794\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.1042 | 1.27728 | ||||||||
\(800\) | 4.20524 | 0.148678 | ||||||||
\(801\) | −5.23757 | −0.185060 | ||||||||
\(802\) | 11.8123 | 0.417108 | ||||||||
\(803\) | −13.6038 | −0.480066 | ||||||||
\(804\) | 1.18253 | 0.0417047 | ||||||||
\(805\) | −18.3892 | −0.648136 | ||||||||
\(806\) | −56.8036 | −2.00082 | ||||||||
\(807\) | 4.77655 | 0.168143 | ||||||||
\(808\) | 5.38487 | 0.189439 | ||||||||
\(809\) | −30.0719 | −1.05727 | −0.528636 | − | 0.848849i | \(-0.677296\pi\) | ||||
−0.528636 | + | 0.848849i | \(0.677296\pi\) | |||||||
\(810\) | 6.48681 | 0.227923 | ||||||||
\(811\) | 0.823592 | 0.0289202 | 0.0144601 | − | 0.999895i | \(-0.495397\pi\) | ||||
0.0144601 | + | 0.999895i | \(0.495397\pi\) | |||||||
\(812\) | 11.5439 | 0.405111 | ||||||||
\(813\) | −0.357176 | −0.0125267 | ||||||||
\(814\) | 11.6725 | 0.409121 | ||||||||
\(815\) | 0.0617395 | 0.00216264 | ||||||||
\(816\) | 1.51423 | 0.0530085 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −25.2663 | −0.883414 | ||||||||
\(819\) | 45.6507 | 1.59517 | ||||||||
\(820\) | 3.11070 | 0.108630 | ||||||||
\(821\) | 7.71124 | 0.269124 | 0.134562 | − | 0.990905i | \(-0.457037\pi\) | ||||
0.134562 | + | 0.990905i | \(0.457037\pi\) | |||||||
\(822\) | −4.86867 | −0.169814 | ||||||||
\(823\) | −24.8120 | −0.864893 | −0.432447 | − | 0.901660i | \(-0.642350\pi\) | ||||
−0.432447 | + | 0.901660i | \(0.642350\pi\) | |||||||
\(824\) | 4.69468 | 0.163547 | ||||||||
\(825\) | 3.63200 | 0.126450 | ||||||||
\(826\) | −7.16129 | −0.249173 | ||||||||
\(827\) | 10.6285 | 0.369588 | 0.184794 | − | 0.982777i | \(-0.440838\pi\) | ||||
0.184794 | + | 0.982777i | \(0.440838\pi\) | |||||||
\(828\) | −22.9527 | −0.797662 | ||||||||
\(829\) | 21.4710 | 0.745718 | 0.372859 | − | 0.927888i | \(-0.378377\pi\) | ||||
0.372859 | + | 0.927888i | \(0.378377\pi\) | |||||||
\(830\) | −12.5913 | −0.437052 | ||||||||
\(831\) | 4.04796 | 0.140422 | ||||||||
\(832\) | −6.45965 | −0.223948 | ||||||||
\(833\) | 2.22056 | 0.0769380 | ||||||||
\(834\) | 9.62739 | 0.333369 | ||||||||
\(835\) | −1.93784 | −0.0670617 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.5834 | −0.780595 | ||||||||
\(838\) | −31.6143 | −1.09210 | ||||||||
\(839\) | −48.8239 | −1.68559 | −0.842794 | − | 0.538237i | \(-0.819091\pi\) | ||||
−0.842794 | + | 0.538237i | \(0.819091\pi\) | |||||||
\(840\) | −0.994078 | −0.0342990 | ||||||||
\(841\) | −8.01770 | −0.276472 | ||||||||
\(842\) | 2.18972 | 0.0754627 | ||||||||
\(843\) | −9.38720 | −0.323312 | ||||||||
\(844\) | −0.361050 | −0.0124279 | ||||||||
\(845\) | −25.6099 | −0.881009 | ||||||||
\(846\) | −29.5841 | −1.01712 | ||||||||
\(847\) | −18.1192 | −0.622583 | ||||||||
\(848\) | 3.76278 | 0.129214 | ||||||||
\(849\) | −2.29632 | −0.0788095 | ||||||||
\(850\) | −14.3914 | −0.493622 | ||||||||
\(851\) | −48.9449 | −1.67781 | ||||||||
\(852\) | −0.0249728 | −0.000855554 0 | ||||||||
\(853\) | −21.0110 | −0.719404 | −0.359702 | − | 0.933067i | \(-0.617122\pi\) | ||||
−0.359702 | + | 0.933067i | \(0.617122\pi\) | |||||||
\(854\) | 6.18683 | 0.211709 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16.0373 | −0.548143 | ||||||||
\(857\) | 32.2392 | 1.10127 | 0.550635 | − | 0.834746i | \(-0.314386\pi\) | ||||
0.550635 | + | 0.834746i | \(0.314386\pi\) | |||||||
\(858\) | −5.57909 | −0.190467 | ||||||||
\(859\) | −41.2274 | −1.40666 | −0.703331 | − | 0.710863i | \(-0.748305\pi\) | ||||
−0.703331 | + | 0.710863i | \(0.748305\pi\) | |||||||
\(860\) | 5.56887 | 0.189897 | ||||||||
\(861\) | 3.89085 | 0.132600 | ||||||||
\(862\) | 1.80372 | 0.0614348 | ||||||||
\(863\) | −42.0649 | −1.43191 | −0.715953 | − | 0.698148i | \(-0.754008\pi\) | ||||
−0.715953 | + | 0.698148i | \(0.754008\pi\) | |||||||
\(864\) | −2.56816 | −0.0873705 | ||||||||
\(865\) | 15.0210 | 0.510729 | ||||||||
\(866\) | 6.57233 | 0.223337 | ||||||||
\(867\) | 2.33981 | 0.0794640 | ||||||||
\(868\) | −22.1612 | −0.752199 | ||||||||
\(869\) | −17.8248 | −0.604665 | ||||||||
\(870\) | −1.80685 | −0.0612578 | ||||||||
\(871\) | 17.2641 | 0.584972 | ||||||||
\(872\) | −14.1008 | −0.477513 | ||||||||
\(873\) | −21.9412 | −0.742596 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.6813 | 0.699156 | ||||||||
\(876\) | 3.08361 | 0.104185 | ||||||||
\(877\) | −2.35551 | −0.0795400 | −0.0397700 | − | 0.999209i | \(-0.512663\pi\) | ||||
−0.0397700 | + | 0.999209i | \(0.512663\pi\) | |||||||
\(878\) | 9.13060 | 0.308143 | ||||||||
\(879\) | 7.77230 | 0.262153 | ||||||||
\(880\) | −1.74018 | −0.0586615 | ||||||||
\(881\) | 23.1354 | 0.779450 | 0.389725 | − | 0.920931i | \(-0.372570\pi\) | ||||
0.389725 | + | 0.920931i | \(0.372570\pi\) | |||||||
\(882\) | −1.81955 | −0.0612673 | ||||||||
\(883\) | 7.01191 | 0.235969 | 0.117985 | − | 0.993015i | \(-0.462357\pi\) | ||||
0.117985 | + | 0.993015i | \(0.462357\pi\) | |||||||
\(884\) | 22.1066 | 0.743525 | ||||||||
\(885\) | 1.12088 | 0.0376780 | ||||||||
\(886\) | 27.4686 | 0.922826 | ||||||||
\(887\) | −48.9293 | −1.64289 | −0.821443 | − | 0.570291i | \(-0.806830\pi\) | ||||
−0.821443 | + | 0.570291i | \(0.806830\pi\) | |||||||
\(888\) | −2.64584 | −0.0887886 | ||||||||
\(889\) | 18.0806 | 0.606403 | ||||||||
\(890\) | 1.66508 | 0.0558134 | ||||||||
\(891\) | 14.2034 | 0.475831 | ||||||||
\(892\) | 18.0486 | 0.604312 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 6.36686 | 0.212940 | ||||||||
\(895\) | −16.9076 | −0.565159 | ||||||||
\(896\) | −2.52015 | −0.0841922 | ||||||||
\(897\) | 23.3941 | 0.781108 | ||||||||
\(898\) | 7.57293 | 0.252712 | ||||||||
\(899\) | −40.2804 | −1.34343 | ||||||||
\(900\) | 11.7925 | 0.393082 | ||||||||
\(901\) | −12.8772 | −0.429002 | ||||||||
\(902\) | 6.81112 | 0.226785 | ||||||||
\(903\) | 6.96552 | 0.231798 | ||||||||
\(904\) | 12.7224 | 0.423140 | ||||||||
\(905\) | 1.77128 | 0.0588793 | ||||||||
\(906\) | 5.48954 | 0.182378 | ||||||||
\(907\) | 1.19304 | 0.0396143 | 0.0198071 | − | 0.999804i | \(-0.493695\pi\) | ||||
0.0198071 | + | 0.999804i | \(0.493695\pi\) | |||||||
\(908\) | 12.2845 | 0.407675 | ||||||||
\(909\) | 15.1004 | 0.500848 | ||||||||
\(910\) | −14.5128 | −0.481096 | ||||||||
\(911\) | −37.6344 | −1.24688 | −0.623442 | − | 0.781870i | \(-0.714266\pi\) | ||||
−0.623442 | + | 0.781870i | \(0.714266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −27.5697 | −0.912424 | ||||||||
\(914\) | 21.7675 | 0.720004 | ||||||||
\(915\) | −0.968361 | −0.0320130 | ||||||||
\(916\) | 6.79174 | 0.224405 | ||||||||
\(917\) | −8.87761 | −0.293164 | ||||||||
\(918\) | 8.78890 | 0.290077 | ||||||||
\(919\) | 26.9476 | 0.888921 | 0.444460 | − | 0.895799i | \(-0.353395\pi\) | ||||
0.444460 | + | 0.895799i | \(0.353395\pi\) | |||||||
\(920\) | 7.29689 | 0.240571 | ||||||||
\(921\) | 9.54321 | 0.314460 | ||||||||
\(922\) | −11.9444 | −0.393367 | ||||||||
\(923\) | −0.364585 | −0.0120005 | ||||||||
\(924\) | −2.17661 | −0.0716052 | ||||||||
\(925\) | 25.1465 | 0.826812 | ||||||||
\(926\) | 8.75371 | 0.287665 | ||||||||
\(927\) | 13.1649 | 0.432393 | ||||||||
\(928\) | −4.58064 | −0.150367 | ||||||||
\(929\) | −17.8550 | −0.585804 | −0.292902 | − | 0.956142i | \(-0.594621\pi\) | ||||
−0.292902 | + | 0.956142i | \(0.594621\pi\) | |||||||
\(930\) | 3.46866 | 0.113742 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21.4294 | 0.701942 | ||||||||
\(933\) | 1.13876 | 0.0372814 | ||||||||
\(934\) | −29.3568 | −0.960585 | ||||||||
\(935\) | 5.95535 | 0.194761 | ||||||||
\(936\) | −18.1143 | −0.592085 | ||||||||
\(937\) | −23.8326 | −0.778576 | −0.389288 | − | 0.921116i | \(-0.627279\pi\) | ||||
−0.389288 | + | 0.921116i | \(0.627279\pi\) | |||||||
\(938\) | 6.73537 | 0.219918 | ||||||||
\(939\) | 2.29368 | 0.0748514 | ||||||||
\(940\) | 9.40507 | 0.306760 | ||||||||
\(941\) | −20.3651 | −0.663882 | −0.331941 | − | 0.943300i | \(-0.607704\pi\) | ||||
−0.331941 | + | 0.943300i | \(0.607704\pi\) | |||||||
\(942\) | −0.199648 | −0.00650490 | ||||||||
\(943\) | −28.5602 | −0.930049 | ||||||||
\(944\) | 2.84162 | 0.0924867 | ||||||||
\(945\) | −5.76985 | −0.187693 | ||||||||
\(946\) | 12.1935 | 0.396444 | ||||||||
\(947\) | −3.41590 | −0.111002 | −0.0555009 | − | 0.998459i | \(-0.517676\pi\) | ||||
−0.0555009 | + | 0.998459i | \(0.517676\pi\) | |||||||
\(948\) | 4.04041 | 0.131226 | ||||||||
\(949\) | 45.0184 | 1.46136 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.96261 | 0.290633 | ||||||||
\(952\) | 8.62460 | 0.279525 | ||||||||
\(953\) | 17.7393 | 0.574634 | 0.287317 | − | 0.957836i | \(-0.407237\pi\) | ||||
0.287317 | + | 0.957836i | \(0.407237\pi\) | |||||||
\(954\) | 10.5517 | 0.341623 | ||||||||
\(955\) | 18.6553 | 0.603671 | ||||||||
\(956\) | −11.8376 | −0.382856 | ||||||||
\(957\) | −3.95623 | −0.127887 | ||||||||
\(958\) | 24.8705 | 0.803528 | ||||||||
\(959\) | −27.7306 | −0.895466 | ||||||||
\(960\) | 0.394452 | 0.0127309 | ||||||||
\(961\) | 46.3275 | 1.49443 | ||||||||
\(962\) | −38.6274 | −1.24540 | ||||||||
\(963\) | −44.9721 | −1.44921 | ||||||||
\(964\) | −21.7463 | −0.700401 | ||||||||
\(965\) | −6.94364 | −0.223524 | ||||||||
\(966\) | 9.12692 | 0.293654 | ||||||||
\(967\) | −42.7551 | −1.37491 | −0.687456 | − | 0.726226i | \(-0.741273\pi\) | ||||
−0.687456 | + | 0.726226i | \(0.741273\pi\) | |||||||
\(968\) | 7.18974 | 0.231087 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.97531 | 0.223964 | ||||||||
\(971\) | −53.0487 | −1.70241 | −0.851207 | − | 0.524830i | \(-0.824129\pi\) | ||||
−0.851207 | + | 0.524830i | \(0.824129\pi\) | |||||||
\(972\) | −10.9240 | −0.350387 | ||||||||
\(973\) | 54.8349 | 1.75793 | ||||||||
\(974\) | 8.53766 | 0.273564 | ||||||||
\(975\) | −12.0193 | −0.384924 | ||||||||
\(976\) | −2.45495 | −0.0785810 | ||||||||
\(977\) | 12.3264 | 0.394356 | 0.197178 | − | 0.980368i | \(-0.436822\pi\) | ||||
0.197178 | + | 0.980368i | \(0.436822\pi\) | |||||||
\(978\) | −0.0306425 | −0.000979838 0 | ||||||||
\(979\) | 3.64581 | 0.116521 | ||||||||
\(980\) | 0.578452 | 0.0184780 | ||||||||
\(981\) | −39.5418 | −1.26247 | ||||||||
\(982\) | 11.5397 | 0.368247 | ||||||||
\(983\) | 32.2554 | 1.02879 | 0.514394 | − | 0.857554i | \(-0.328017\pi\) | ||||
0.514394 | + | 0.857554i | \(0.328017\pi\) | |||||||
\(984\) | −1.54390 | −0.0492177 | ||||||||
\(985\) | −1.62710 | −0.0518437 | ||||||||
\(986\) | 15.6762 | 0.499231 | ||||||||
\(987\) | 11.7638 | 0.374446 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51.1294 | −1.62582 | ||||||||
\(990\) | −4.87986 | −0.155092 | ||||||||
\(991\) | −27.8366 | −0.884258 | −0.442129 | − | 0.896951i | \(-0.645777\pi\) | ||||
−0.442129 | + | 0.896951i | \(0.645777\pi\) | |||||||
\(992\) | 8.79360 | 0.279197 | ||||||||
\(993\) | 9.43686 | 0.299470 | ||||||||
\(994\) | −0.142238 | −0.00451152 | ||||||||
\(995\) | −2.10326 | −0.0666777 | ||||||||
\(996\) | 6.24931 | 0.198017 | ||||||||
\(997\) | −43.3313 | −1.37232 | −0.686159 | − | 0.727452i | \(-0.740704\pi\) | ||||
−0.686159 | + | 0.727452i | \(0.740704\pi\) | |||||||
\(998\) | 29.6091 | 0.937258 | ||||||||
\(999\) | −15.3571 | −0.485876 |
(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 | 722.2.a.m.1.3 | ✓ | 4 | |
3.2 | odd | 2 | 6498.2.a.ca.1.2 | 4 | |||
4.3 | odd | 2 | 5776.2.a.bv.1.2 | 4 | |||
19.2 | odd | 18 | 722.2.e.r.99.2 | 24 | |||
19.3 | odd | 18 | 722.2.e.r.389.2 | 24 | |||
19.4 | even | 9 | 722.2.e.s.415.2 | 24 | |||
19.5 | even | 9 | 722.2.e.s.595.2 | 24 | |||
19.6 | even | 9 | 722.2.e.s.245.3 | 24 | |||
19.7 | even | 3 | 722.2.c.n.429.2 | 8 | |||
19.8 | odd | 6 | 722.2.c.m.653.3 | 8 | |||
19.9 | even | 9 | 722.2.e.s.423.3 | 24 | |||
19.10 | odd | 18 | 722.2.e.r.423.2 | 24 | |||
19.11 | even | 3 | 722.2.c.n.653.2 | 8 | |||
19.12 | odd | 6 | 722.2.c.m.429.3 | 8 | |||
19.13 | odd | 18 | 722.2.e.r.245.2 | 24 | |||
19.14 | odd | 18 | 722.2.e.r.595.3 | 24 | |||
19.15 | odd | 18 | 722.2.e.r.415.3 | 24 | |||
19.16 | even | 9 | 722.2.e.s.389.3 | 24 | |||
19.17 | even | 9 | 722.2.e.s.99.3 | 24 | |||
19.18 | odd | 2 | 722.2.a.n.1.2 | yes | 4 | ||
57.56 | even | 2 | 6498.2.a.bx.1.2 | 4 | |||
76.75 | even | 2 | 5776.2.a.bt.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
722.2.a.m.1.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
722.2.a.n.1.2 | yes | 4 | 19.18 | odd | 2 | ||
722.2.c.m.429.3 | 8 | 19.12 | odd | 6 | |||
722.2.c.m.653.3 | 8 | 19.8 | odd | 6 | |||
722.2.c.n.429.2 | 8 | 19.7 | even | 3 | |||
722.2.c.n.653.2 | 8 | 19.11 | even | 3 | |||
722.2.e.r.99.2 | 24 | 19.2 | odd | 18 | |||
722.2.e.r.245.2 | 24 | 19.13 | odd | 18 | |||
722.2.e.r.389.2 | 24 | 19.3 | odd | 18 | |||
722.2.e.r.415.3 | 24 | 19.15 | odd | 18 | |||
722.2.e.r.423.2 | 24 | 19.10 | odd | 18 | |||
722.2.e.r.595.3 | 24 | 19.14 | odd | 18 | |||
722.2.e.s.99.3 | 24 | 19.17 | even | 9 | |||
722.2.e.s.245.3 | 24 | 19.6 | even | 9 | |||
722.2.e.s.389.3 | 24 | 19.16 | even | 9 | |||
722.2.e.s.415.2 | 24 | 19.4 | even | 9 | |||
722.2.e.s.423.3 | 24 | 19.9 | even | 9 | |||
722.2.e.s.595.2 | 24 | 19.5 | even | 9 | |||
5776.2.a.bt.1.3 | 4 | 76.75 | even | 2 | |||
5776.2.a.bv.1.2 | 4 | 4.3 | odd | 2 | |||
6498.2.a.bx.1.2 | 4 | 57.56 | even | 2 | |||
6498.2.a.ca.1.2 | 4 | 3.2 | odd | 2 |