Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.561553 | −0.212247 | −0.106124 | − | 0.994353i | \(-0.533844\pi\) | ||||
−0.106124 | + | 0.994353i | \(0.533844\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 4.12311 | 1.24316 | 0.621582 | − | 0.783349i | \(-0.286490\pi\) | ||||
0.621582 | + | 0.783349i | \(0.286490\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.561553 | −0.150081 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.12311 | −0.757464 | −0.378732 | − | 0.925506i | \(-0.623640\pi\) | ||||
−0.378732 | + | 0.925506i | \(0.623640\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0.561553 | 0.128829 | 0.0644145 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644145 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −0.561553 | −0.122541 | ||||||||
\(22\) | 4.12311 | 0.879049 | ||||||||
\(23\) | 4.68466 | 0.976819 | 0.488409 | − | 0.872615i | \(-0.337577\pi\) | ||||
0.488409 | + | 0.872615i | \(0.337577\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.561553 | −0.106124 | ||||||||
\(29\) | 2.43845 | 0.452808 | 0.226404 | − | 0.974033i | \(-0.427303\pi\) | ||||
0.226404 | + | 0.974033i | \(0.427303\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | −6.68466 | −1.20060 | −0.600300 | − | 0.799775i | \(-0.704952\pi\) | ||||
−0.600300 | + | 0.799775i | \(0.704952\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.12311 | 0.717741 | ||||||||
\(34\) | −3.12311 | −0.535608 | ||||||||
\(35\) | −0.561553 | −0.0949197 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.12311 | −0.677834 | −0.338917 | − | 0.940816i | \(-0.610061\pi\) | ||||
−0.338917 | + | 0.940816i | \(0.610061\pi\) | |||||||
\(38\) | 0.561553 | 0.0910959 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 12.2462 | 1.91254 | 0.956268 | − | 0.292490i | \(-0.0944840\pi\) | ||||
0.956268 | + | 0.292490i | \(0.0944840\pi\) | |||||||
\(42\) | −0.561553 | −0.0866495 | ||||||||
\(43\) | 0.438447 | 0.0668626 | 0.0334313 | − | 0.999441i | \(-0.489357\pi\) | ||||
0.0334313 | + | 0.999441i | \(0.489357\pi\) | |||||||
\(44\) | 4.12311 | 0.621582 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 4.68466 | 0.690715 | ||||||||
\(47\) | 7.00000 | 1.02105 | 0.510527 | − | 0.859861i | \(-0.329450\pi\) | ||||
0.510527 | + | 0.859861i | \(0.329450\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.68466 | −0.954951 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −3.12311 | −0.437322 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.56155 | 1.17602 | 0.588010 | − | 0.808854i | \(-0.299912\pi\) | ||||
0.588010 | + | 0.808854i | \(0.299912\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 4.12311 | 0.555959 | ||||||||
\(56\) | −0.561553 | −0.0750407 | ||||||||
\(57\) | 0.561553 | 0.0743795 | ||||||||
\(58\) | 2.43845 | 0.320184 | ||||||||
\(59\) | 6.43845 | 0.838214 | 0.419107 | − | 0.907937i | \(-0.362343\pi\) | ||||
0.419107 | + | 0.907937i | \(0.362343\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | −6.68466 | −0.848952 | ||||||||
\(63\) | −0.561553 | −0.0707490 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.12311 | 0.507519 | ||||||||
\(67\) | −2.24621 | −0.274418 | −0.137209 | − | 0.990542i | \(-0.543813\pi\) | ||||
−0.137209 | + | 0.990542i | \(0.543813\pi\) | |||||||
\(68\) | −3.12311 | −0.378732 | ||||||||
\(69\) | 4.68466 | 0.563967 | ||||||||
\(70\) | −0.561553 | −0.0671184 | ||||||||
\(71\) | −13.1231 | −1.55743 | −0.778713 | − | 0.627380i | \(-0.784127\pi\) | ||||
−0.778713 | + | 0.627380i | \(0.784127\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 9.36932 | 1.09660 | 0.548298 | − | 0.836283i | \(-0.315276\pi\) | ||||
0.548298 | + | 0.836283i | \(0.315276\pi\) | |||||||
\(74\) | −4.12311 | −0.479301 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0.561553 | 0.0644145 | ||||||||
\(77\) | −2.31534 | −0.263858 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.5616 | 1.30078 | 0.650388 | − | 0.759602i | \(-0.274606\pi\) | ||||
0.650388 | + | 0.759602i | \(0.274606\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.2462 | 1.35237 | ||||||||
\(83\) | −7.12311 | −0.781862 | −0.390931 | − | 0.920420i | \(-0.627847\pi\) | ||||
−0.390931 | + | 0.920420i | \(0.627847\pi\) | |||||||
\(84\) | −0.561553 | −0.0612704 | ||||||||
\(85\) | −3.12311 | −0.338748 | ||||||||
\(86\) | 0.438447 | 0.0472790 | ||||||||
\(87\) | 2.43845 | 0.261429 | ||||||||
\(88\) | 4.12311 | 0.439525 | ||||||||
\(89\) | −18.8078 | −1.99362 | −0.996810 | − | 0.0798174i | \(-0.974566\pi\) | ||||
−0.996810 | + | 0.0798174i | \(0.974566\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.68466 | 0.488409 | ||||||||
\(93\) | −6.68466 | −0.693167 | ||||||||
\(94\) | 7.00000 | 0.721995 | ||||||||
\(95\) | 0.561553 | 0.0576141 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −7.12311 | −0.723242 | −0.361621 | − | 0.932325i | \(-0.617777\pi\) | ||||
−0.361621 | + | 0.932325i | \(0.617777\pi\) | |||||||
\(98\) | −6.68466 | −0.675252 | ||||||||
\(99\) | 4.12311 | 0.414388 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −8.87689 | −0.883284 | −0.441642 | − | 0.897191i | \(-0.645604\pi\) | ||||
−0.441642 | + | 0.897191i | \(0.645604\pi\) | |||||||
\(102\) | −3.12311 | −0.309234 | ||||||||
\(103\) | 4.56155 | 0.449463 | 0.224732 | − | 0.974421i | \(-0.427849\pi\) | ||||
0.224732 | + | 0.974421i | \(0.427849\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.561553 | −0.0548019 | ||||||||
\(106\) | 8.56155 | 0.831572 | ||||||||
\(107\) | 2.00000 | 0.193347 | 0.0966736 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966736 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −3.75379 | −0.359548 | −0.179774 | − | 0.983708i | \(-0.557537\pi\) | ||||
−0.179774 | + | 0.983708i | \(0.557537\pi\) | |||||||
\(110\) | 4.12311 | 0.393123 | ||||||||
\(111\) | −4.12311 | −0.391348 | ||||||||
\(112\) | −0.561553 | −0.0530618 | ||||||||
\(113\) | 8.68466 | 0.816984 | 0.408492 | − | 0.912762i | \(-0.366055\pi\) | ||||
0.408492 | + | 0.912762i | \(0.366055\pi\) | |||||||
\(114\) | 0.561553 | 0.0525942 | ||||||||
\(115\) | 4.68466 | 0.436847 | ||||||||
\(116\) | 2.43845 | 0.226404 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.43845 | 0.592707 | ||||||||
\(119\) | 1.75379 | 0.160770 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 6.00000 | 0.545455 | ||||||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | 12.2462 | 1.10420 | ||||||||
\(124\) | −6.68466 | −0.600300 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −0.561553 | −0.0500271 | ||||||||
\(127\) | −8.56155 | −0.759715 | −0.379857 | − | 0.925045i | \(-0.624027\pi\) | ||||
−0.379857 | + | 0.925045i | \(0.624027\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.438447 | 0.0386031 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.12311 | −0.185497 | −0.0927483 | − | 0.995690i | \(-0.529565\pi\) | ||||
−0.0927483 | + | 0.995690i | \(0.529565\pi\) | |||||||
\(132\) | 4.12311 | 0.358870 | ||||||||
\(133\) | −0.315342 | −0.0273436 | ||||||||
\(134\) | −2.24621 | −0.194043 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −3.12311 | −0.267804 | ||||||||
\(137\) | 11.8078 | 1.00881 | 0.504403 | − | 0.863469i | \(-0.331713\pi\) | ||||
0.504403 | + | 0.863469i | \(0.331713\pi\) | |||||||
\(138\) | 4.68466 | 0.398785 | ||||||||
\(139\) | 12.5616 | 1.06546 | 0.532729 | − | 0.846286i | \(-0.321167\pi\) | ||||
0.532729 | + | 0.846286i | \(0.321167\pi\) | |||||||
\(140\) | −0.561553 | −0.0474599 | ||||||||
\(141\) | 7.00000 | 0.589506 | ||||||||
\(142\) | −13.1231 | −1.10127 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.43845 | 0.202502 | ||||||||
\(146\) | 9.36932 | 0.775410 | ||||||||
\(147\) | −6.68466 | −0.551341 | ||||||||
\(148\) | −4.12311 | −0.338917 | ||||||||
\(149\) | −2.19224 | −0.179595 | −0.0897975 | − | 0.995960i | \(-0.528622\pi\) | ||||
−0.0897975 | + | 0.995960i | \(0.528622\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −15.3693 | −1.25074 | −0.625369 | − | 0.780329i | \(-0.715051\pi\) | ||||
−0.625369 | + | 0.780329i | \(0.715051\pi\) | |||||||
\(152\) | 0.561553 | 0.0455479 | ||||||||
\(153\) | −3.12311 | −0.252488 | ||||||||
\(154\) | −2.31534 | −0.186576 | ||||||||
\(155\) | −6.68466 | −0.536925 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.8769 | 1.10750 | 0.553748 | − | 0.832684i | \(-0.313197\pi\) | ||||
0.553748 | + | 0.832684i | \(0.313197\pi\) | |||||||
\(158\) | 11.5616 | 0.919788 | ||||||||
\(159\) | 8.56155 | 0.678975 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −2.63068 | −0.207327 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −14.4384 | −1.13091 | −0.565453 | − | 0.824780i | \(-0.691299\pi\) | ||||
−0.565453 | + | 0.824780i | \(0.691299\pi\) | |||||||
\(164\) | 12.2462 | 0.956268 | ||||||||
\(165\) | 4.12311 | 0.320983 | ||||||||
\(166\) | −7.12311 | −0.552860 | ||||||||
\(167\) | 4.36932 | 0.338108 | 0.169054 | − | 0.985607i | \(-0.445929\pi\) | ||||
0.169054 | + | 0.985607i | \(0.445929\pi\) | |||||||
\(168\) | −0.561553 | −0.0433247 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3.12311 | −0.239531 | ||||||||
\(171\) | 0.561553 | 0.0429430 | ||||||||
\(172\) | 0.438447 | 0.0334313 | ||||||||
\(173\) | 20.1771 | 1.53404 | 0.767018 | − | 0.641626i | \(-0.221740\pi\) | ||||
0.767018 | + | 0.641626i | \(0.221740\pi\) | |||||||
\(174\) | 2.43845 | 0.184858 | ||||||||
\(175\) | −0.561553 | −0.0424494 | ||||||||
\(176\) | 4.12311 | 0.310791 | ||||||||
\(177\) | 6.43845 | 0.483943 | ||||||||
\(178\) | −18.8078 | −1.40970 | ||||||||
\(179\) | −12.6847 | −0.948096 | −0.474048 | − | 0.880499i | \(-0.657208\pi\) | ||||
−0.474048 | + | 0.880499i | \(0.657208\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | 2.87689 | 0.213838 | 0.106919 | − | 0.994268i | \(-0.465901\pi\) | ||||
0.106919 | + | 0.994268i | \(0.465901\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | 4.68466 | 0.345358 | ||||||||
\(185\) | −4.12311 | −0.303137 | ||||||||
\(186\) | −6.68466 | −0.490143 | ||||||||
\(187\) | −12.8769 | −0.941652 | ||||||||
\(188\) | 7.00000 | 0.510527 | ||||||||
\(189\) | −0.561553 | −0.0408470 | ||||||||
\(190\) | 0.561553 | 0.0407393 | ||||||||
\(191\) | 10.8769 | 0.787024 | 0.393512 | − | 0.919319i | \(-0.371260\pi\) | ||||
0.393512 | + | 0.919319i | \(0.371260\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(194\) | −7.12311 | −0.511409 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.68466 | −0.477476 | ||||||||
\(197\) | 12.8078 | 0.912515 | 0.456258 | − | 0.889848i | \(-0.349190\pi\) | ||||
0.456258 | + | 0.889848i | \(0.349190\pi\) | |||||||
\(198\) | 4.12311 | 0.293016 | ||||||||
\(199\) | 2.87689 | 0.203938 | 0.101969 | − | 0.994788i | \(-0.467486\pi\) | ||||
0.101969 | + | 0.994788i | \(0.467486\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −2.24621 | −0.158436 | ||||||||
\(202\) | −8.87689 | −0.624576 | ||||||||
\(203\) | −1.36932 | −0.0961072 | ||||||||
\(204\) | −3.12311 | −0.218661 | ||||||||
\(205\) | 12.2462 | 0.855312 | ||||||||
\(206\) | 4.56155 | 0.317818 | ||||||||
\(207\) | 4.68466 | 0.325606 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.31534 | 0.160156 | ||||||||
\(210\) | −0.561553 | −0.0387508 | ||||||||
\(211\) | −21.9309 | −1.50978 | −0.754892 | − | 0.655850i | \(-0.772311\pi\) | ||||
−0.754892 | + | 0.655850i | \(0.772311\pi\) | |||||||
\(212\) | 8.56155 | 0.588010 | ||||||||
\(213\) | −13.1231 | −0.899180 | ||||||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | 0.438447 | 0.0299018 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 3.75379 | 0.254824 | ||||||||
\(218\) | −3.75379 | −0.254239 | ||||||||
\(219\) | 9.36932 | 0.633120 | ||||||||
\(220\) | 4.12311 | 0.277980 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.12311 | −0.276725 | ||||||||
\(223\) | 27.3002 | 1.82816 | 0.914078 | − | 0.405539i | \(-0.132916\pi\) | ||||
0.914078 | + | 0.405539i | \(0.132916\pi\) | |||||||
\(224\) | −0.561553 | −0.0375203 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 8.68466 | 0.577695 | ||||||||
\(227\) | −20.0000 | −1.32745 | −0.663723 | − | 0.747978i | \(-0.731025\pi\) | ||||
−0.663723 | + | 0.747978i | \(0.731025\pi\) | |||||||
\(228\) | 0.561553 | 0.0371897 | ||||||||
\(229\) | −24.2462 | −1.60223 | −0.801117 | − | 0.598507i | \(-0.795761\pi\) | ||||
−0.801117 | + | 0.598507i | \(0.795761\pi\) | |||||||
\(230\) | 4.68466 | 0.308897 | ||||||||
\(231\) | −2.31534 | −0.152338 | ||||||||
\(232\) | 2.43845 | 0.160092 | ||||||||
\(233\) | −5.31534 | −0.348220 | −0.174110 | − | 0.984726i | \(-0.555705\pi\) | ||||
−0.174110 | + | 0.984726i | \(0.555705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.00000 | 0.456630 | ||||||||
\(236\) | 6.43845 | 0.419107 | ||||||||
\(237\) | 11.5616 | 0.751004 | ||||||||
\(238\) | 1.75379 | 0.113681 | ||||||||
\(239\) | −11.3693 | −0.735420 | −0.367710 | − | 0.929941i | \(-0.619858\pi\) | ||||
−0.367710 | + | 0.929941i | \(0.619858\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −28.1231 | −1.81157 | −0.905784 | − | 0.423739i | \(-0.860717\pi\) | ||||
−0.905784 | + | 0.423739i | \(0.860717\pi\) | |||||||
\(242\) | 6.00000 | 0.385695 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | −6.68466 | −0.427067 | ||||||||
\(246\) | 12.2462 | 0.780790 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.68466 | −0.424476 | ||||||||
\(249\) | −7.12311 | −0.451408 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −8.12311 | −0.512726 | −0.256363 | − | 0.966581i | \(-0.582524\pi\) | ||||
−0.256363 | + | 0.966581i | \(0.582524\pi\) | |||||||
\(252\) | −0.561553 | −0.0353745 | ||||||||
\(253\) | 19.3153 | 1.21435 | ||||||||
\(254\) | −8.56155 | −0.537200 | ||||||||
\(255\) | −3.12311 | −0.195576 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.56155 | −0.346920 | −0.173460 | − | 0.984841i | \(-0.555495\pi\) | ||||
−0.173460 | + | 0.984841i | \(0.555495\pi\) | |||||||
\(258\) | 0.438447 | 0.0272965 | ||||||||
\(259\) | 2.31534 | 0.143868 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.43845 | 0.150936 | ||||||||
\(262\) | −2.12311 | −0.131166 | ||||||||
\(263\) | −13.0000 | −0.801614 | −0.400807 | − | 0.916162i | \(-0.631270\pi\) | ||||
−0.400807 | + | 0.916162i | \(0.631270\pi\) | |||||||
\(264\) | 4.12311 | 0.253760 | ||||||||
\(265\) | 8.56155 | 0.525932 | ||||||||
\(266\) | −0.315342 | −0.0193348 | ||||||||
\(267\) | −18.8078 | −1.15102 | ||||||||
\(268\) | −2.24621 | −0.137209 | ||||||||
\(269\) | 21.3693 | 1.30291 | 0.651455 | − | 0.758687i | \(-0.274159\pi\) | ||||
0.651455 | + | 0.758687i | \(0.274159\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −13.1771 | −0.800451 | −0.400225 | − | 0.916417i | \(-0.631068\pi\) | ||||
−0.400225 | + | 0.916417i | \(0.631068\pi\) | |||||||
\(272\) | −3.12311 | −0.189366 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.8078 | 0.713333 | ||||||||
\(275\) | 4.12311 | 0.248633 | ||||||||
\(276\) | 4.68466 | 0.281983 | ||||||||
\(277\) | −1.00000 | −0.0600842 | −0.0300421 | − | 0.999549i | \(-0.509564\pi\) | ||||
−0.0300421 | + | 0.999549i | \(0.509564\pi\) | |||||||
\(278\) | 12.5616 | 0.753392 | ||||||||
\(279\) | −6.68466 | −0.400200 | ||||||||
\(280\) | −0.561553 | −0.0335592 | ||||||||
\(281\) | 16.2462 | 0.969168 | 0.484584 | − | 0.874745i | \(-0.338971\pi\) | ||||
0.484584 | + | 0.874745i | \(0.338971\pi\) | |||||||
\(282\) | 7.00000 | 0.416844 | ||||||||
\(283\) | 15.5616 | 0.925038 | 0.462519 | − | 0.886609i | \(-0.346946\pi\) | ||||
0.462519 | + | 0.886609i | \(0.346946\pi\) | |||||||
\(284\) | −13.1231 | −0.778713 | ||||||||
\(285\) | 0.561553 | 0.0332635 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.87689 | −0.405930 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −7.24621 | −0.426248 | ||||||||
\(290\) | 2.43845 | 0.143191 | ||||||||
\(291\) | −7.12311 | −0.417564 | ||||||||
\(292\) | 9.36932 | 0.548298 | ||||||||
\(293\) | 3.93087 | 0.229644 | 0.114822 | − | 0.993386i | \(-0.463370\pi\) | ||||
0.114822 | + | 0.993386i | \(0.463370\pi\) | |||||||
\(294\) | −6.68466 | −0.389857 | ||||||||
\(295\) | 6.43845 | 0.374861 | ||||||||
\(296\) | −4.12311 | −0.239651 | ||||||||
\(297\) | 4.12311 | 0.239247 | ||||||||
\(298\) | −2.19224 | −0.126993 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −0.246211 | −0.0141914 | ||||||||
\(302\) | −15.3693 | −0.884405 | ||||||||
\(303\) | −8.87689 | −0.509964 | ||||||||
\(304\) | 0.561553 | 0.0322073 | ||||||||
\(305\) | 6.00000 | 0.343559 | ||||||||
\(306\) | −3.12311 | −0.178536 | ||||||||
\(307\) | 25.6155 | 1.46196 | 0.730978 | − | 0.682401i | \(-0.239064\pi\) | ||||
0.730978 | + | 0.682401i | \(0.239064\pi\) | |||||||
\(308\) | −2.31534 | −0.131929 | ||||||||
\(309\) | 4.56155 | 0.259498 | ||||||||
\(310\) | −6.68466 | −0.379663 | ||||||||
\(311\) | 30.7386 | 1.74303 | 0.871514 | − | 0.490371i | \(-0.163139\pi\) | ||||
0.871514 | + | 0.490371i | \(0.163139\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.3693 | 1.77310 | 0.886549 | − | 0.462634i | \(-0.153096\pi\) | ||||
0.886549 | + | 0.462634i | \(0.153096\pi\) | |||||||
\(314\) | 13.8769 | 0.783118 | ||||||||
\(315\) | −0.561553 | −0.0316399 | ||||||||
\(316\) | 11.5616 | 0.650388 | ||||||||
\(317\) | −24.8078 | −1.39334 | −0.696671 | − | 0.717390i | \(-0.745336\pi\) | ||||
−0.696671 | + | 0.717390i | \(0.745336\pi\) | |||||||
\(318\) | 8.56155 | 0.480108 | ||||||||
\(319\) | 10.0540 | 0.562915 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 2.00000 | 0.111629 | ||||||||
\(322\) | −2.63068 | −0.146602 | ||||||||
\(323\) | −1.75379 | −0.0975834 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.4384 | −0.799672 | ||||||||
\(327\) | −3.75379 | −0.207585 | ||||||||
\(328\) | 12.2462 | 0.676184 | ||||||||
\(329\) | −3.93087 | −0.216716 | ||||||||
\(330\) | 4.12311 | 0.226969 | ||||||||
\(331\) | 30.7386 | 1.68955 | 0.844774 | − | 0.535123i | \(-0.179735\pi\) | ||||
0.844774 | + | 0.535123i | \(0.179735\pi\) | |||||||
\(332\) | −7.12311 | −0.390931 | ||||||||
\(333\) | −4.12311 | −0.225945 | ||||||||
\(334\) | 4.36932 | 0.239078 | ||||||||
\(335\) | −2.24621 | −0.122724 | ||||||||
\(336\) | −0.561553 | −0.0306352 | ||||||||
\(337\) | −6.00000 | −0.326841 | −0.163420 | − | 0.986557i | \(-0.552253\pi\) | ||||
−0.163420 | + | 0.986557i | \(0.552253\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.68466 | 0.471686 | ||||||||
\(340\) | −3.12311 | −0.169374 | ||||||||
\(341\) | −27.5616 | −1.49254 | ||||||||
\(342\) | 0.561553 | 0.0303653 | ||||||||
\(343\) | 7.68466 | 0.414933 | ||||||||
\(344\) | 0.438447 | 0.0236395 | ||||||||
\(345\) | 4.68466 | 0.252214 | ||||||||
\(346\) | 20.1771 | 1.08473 | ||||||||
\(347\) | 0.876894 | 0.0470742 | 0.0235371 | − | 0.999723i | \(-0.492507\pi\) | ||||
0.0235371 | + | 0.999723i | \(0.492507\pi\) | |||||||
\(348\) | 2.43845 | 0.130714 | ||||||||
\(349\) | 8.49242 | 0.454589 | 0.227294 | − | 0.973826i | \(-0.427012\pi\) | ||||
0.227294 | + | 0.973826i | \(0.427012\pi\) | |||||||
\(350\) | −0.561553 | −0.0300163 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.12311 | 0.219762 | ||||||||
\(353\) | −25.8617 | −1.37648 | −0.688241 | − | 0.725482i | \(-0.741617\pi\) | ||||
−0.688241 | + | 0.725482i | \(0.741617\pi\) | |||||||
\(354\) | 6.43845 | 0.342200 | ||||||||
\(355\) | −13.1231 | −0.696502 | ||||||||
\(356\) | −18.8078 | −0.996810 | ||||||||
\(357\) | 1.75379 | 0.0928203 | ||||||||
\(358\) | −12.6847 | −0.670405 | ||||||||
\(359\) | 13.1231 | 0.692611 | 0.346306 | − | 0.938122i | \(-0.387436\pi\) | ||||
0.346306 | + | 0.938122i | \(0.387436\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −18.6847 | −0.983403 | ||||||||
\(362\) | 2.87689 | 0.151206 | ||||||||
\(363\) | 6.00000 | 0.314918 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.36932 | 0.490412 | ||||||||
\(366\) | 6.00000 | 0.313625 | ||||||||
\(367\) | 12.4924 | 0.652099 | 0.326050 | − | 0.945353i | \(-0.394282\pi\) | ||||
0.326050 | + | 0.945353i | \(0.394282\pi\) | |||||||
\(368\) | 4.68466 | 0.244205 | ||||||||
\(369\) | 12.2462 | 0.637512 | ||||||||
\(370\) | −4.12311 | −0.214350 | ||||||||
\(371\) | −4.80776 | −0.249607 | ||||||||
\(372\) | −6.68466 | −0.346583 | ||||||||
\(373\) | −25.8078 | −1.33628 | −0.668138 | − | 0.744038i | \(-0.732908\pi\) | ||||
−0.668138 | + | 0.744038i | \(0.732908\pi\) | |||||||
\(374\) | −12.8769 | −0.665848 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.561553 | −0.0288832 | ||||||||
\(379\) | −17.6847 | −0.908400 | −0.454200 | − | 0.890900i | \(-0.650075\pi\) | ||||
−0.454200 | + | 0.890900i | \(0.650075\pi\) | |||||||
\(380\) | 0.561553 | 0.0288071 | ||||||||
\(381\) | −8.56155 | −0.438622 | ||||||||
\(382\) | 10.8769 | 0.556510 | ||||||||
\(383\) | 0.192236 | 0.00982280 | 0.00491140 | − | 0.999988i | \(-0.498437\pi\) | ||||
0.00491140 | + | 0.999988i | \(0.498437\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −2.31534 | −0.118001 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.438447 | 0.0222875 | ||||||||
\(388\) | −7.12311 | −0.361621 | ||||||||
\(389\) | −18.0540 | −0.915373 | −0.457686 | − | 0.889114i | \(-0.651322\pi\) | ||||
−0.457686 | + | 0.889114i | \(0.651322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.6307 | −0.739905 | ||||||||
\(392\) | −6.68466 | −0.337626 | ||||||||
\(393\) | −2.12311 | −0.107097 | ||||||||
\(394\) | 12.8078 | 0.645246 | ||||||||
\(395\) | 11.5616 | 0.581725 | ||||||||
\(396\) | 4.12311 | 0.207194 | ||||||||
\(397\) | −20.1231 | −1.00995 | −0.504975 | − | 0.863134i | \(-0.668498\pi\) | ||||
−0.504975 | + | 0.863134i | \(0.668498\pi\) | |||||||
\(398\) | 2.87689 | 0.144206 | ||||||||
\(399\) | −0.315342 | −0.0157868 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 0.315342 | 0.0157474 | 0.00787370 | − | 0.999969i | \(-0.497494\pi\) | ||||
0.00787370 | + | 0.999969i | \(0.497494\pi\) | |||||||
\(402\) | −2.24621 | −0.112031 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8.87689 | −0.441642 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −1.36932 | −0.0679581 | ||||||||
\(407\) | −17.0000 | −0.842659 | ||||||||
\(408\) | −3.12311 | −0.154617 | ||||||||
\(409\) | −18.8078 | −0.929984 | −0.464992 | − | 0.885315i | \(-0.653943\pi\) | ||||
−0.464992 | + | 0.885315i | \(0.653943\pi\) | |||||||
\(410\) | 12.2462 | 0.604797 | ||||||||
\(411\) | 11.8078 | 0.582434 | ||||||||
\(412\) | 4.56155 | 0.224732 | ||||||||
\(413\) | −3.61553 | −0.177909 | ||||||||
\(414\) | 4.68466 | 0.230238 | ||||||||
\(415\) | −7.12311 | −0.349660 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.5616 | 0.615142 | ||||||||
\(418\) | 2.31534 | 0.113247 | ||||||||
\(419\) | 32.4924 | 1.58736 | 0.793679 | − | 0.608336i | \(-0.208163\pi\) | ||||
0.793679 | + | 0.608336i | \(0.208163\pi\) | |||||||
\(420\) | −0.561553 | −0.0274010 | ||||||||
\(421\) | −32.4924 | −1.58358 | −0.791792 | − | 0.610791i | \(-0.790852\pi\) | ||||
−0.791792 | + | 0.610791i | \(0.790852\pi\) | |||||||
\(422\) | −21.9309 | −1.06758 | ||||||||
\(423\) | 7.00000 | 0.340352 | ||||||||
\(424\) | 8.56155 | 0.415786 | ||||||||
\(425\) | −3.12311 | −0.151493 | ||||||||
\(426\) | −13.1231 | −0.635817 | ||||||||
\(427\) | −3.36932 | −0.163053 | ||||||||
\(428\) | 2.00000 | 0.0966736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.438447 | 0.0211438 | ||||||||
\(431\) | −22.7386 | −1.09528 | −0.547641 | − | 0.836714i | \(-0.684474\pi\) | ||||
−0.547641 | + | 0.836714i | \(0.684474\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −18.7386 | −0.900521 | −0.450261 | − | 0.892897i | \(-0.648669\pi\) | ||||
−0.450261 | + | 0.892897i | \(0.648669\pi\) | |||||||
\(434\) | 3.75379 | 0.180188 | ||||||||
\(435\) | 2.43845 | 0.116915 | ||||||||
\(436\) | −3.75379 | −0.179774 | ||||||||
\(437\) | 2.63068 | 0.125843 | ||||||||
\(438\) | 9.36932 | 0.447683 | ||||||||
\(439\) | 25.1231 | 1.19906 | 0.599530 | − | 0.800352i | \(-0.295354\pi\) | ||||
0.599530 | + | 0.800352i | \(0.295354\pi\) | |||||||
\(440\) | 4.12311 | 0.196561 | ||||||||
\(441\) | −6.68466 | −0.318317 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.1231 | −0.623498 | −0.311749 | − | 0.950165i | \(-0.600915\pi\) | ||||
−0.311749 | + | 0.950165i | \(0.600915\pi\) | |||||||
\(444\) | −4.12311 | −0.195674 | ||||||||
\(445\) | −18.8078 | −0.891574 | ||||||||
\(446\) | 27.3002 | 1.29270 | ||||||||
\(447\) | −2.19224 | −0.103689 | ||||||||
\(448\) | −0.561553 | −0.0265309 | ||||||||
\(449\) | −20.1771 | −0.952215 | −0.476108 | − | 0.879387i | \(-0.657953\pi\) | ||||
−0.476108 | + | 0.879387i | \(0.657953\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 50.4924 | 2.37760 | ||||||||
\(452\) | 8.68466 | 0.408492 | ||||||||
\(453\) | −15.3693 | −0.722113 | ||||||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.561553 | 0.0262971 | ||||||||
\(457\) | 20.2462 | 0.947078 | 0.473539 | − | 0.880773i | \(-0.342976\pi\) | ||||
0.473539 | + | 0.880773i | \(0.342976\pi\) | |||||||
\(458\) | −24.2462 | −1.13295 | ||||||||
\(459\) | −3.12311 | −0.145774 | ||||||||
\(460\) | 4.68466 | 0.218423 | ||||||||
\(461\) | −30.0540 | −1.39975 | −0.699877 | − | 0.714264i | \(-0.746762\pi\) | ||||
−0.699877 | + | 0.714264i | \(0.746762\pi\) | |||||||
\(462\) | −2.31534 | −0.107719 | ||||||||
\(463\) | −7.61553 | −0.353924 | −0.176962 | − | 0.984218i | \(-0.556627\pi\) | ||||
−0.176962 | + | 0.984218i | \(0.556627\pi\) | |||||||
\(464\) | 2.43845 | 0.113202 | ||||||||
\(465\) | −6.68466 | −0.309994 | ||||||||
\(466\) | −5.31534 | −0.246228 | ||||||||
\(467\) | −17.8617 | −0.826543 | −0.413271 | − | 0.910608i | \(-0.635614\pi\) | ||||
−0.413271 | + | 0.910608i | \(0.635614\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.26137 | 0.0582445 | ||||||||
\(470\) | 7.00000 | 0.322886 | ||||||||
\(471\) | 13.8769 | 0.639414 | ||||||||
\(472\) | 6.43845 | 0.296354 | ||||||||
\(473\) | 1.80776 | 0.0831211 | ||||||||
\(474\) | 11.5616 | 0.531040 | ||||||||
\(475\) | 0.561553 | 0.0257658 | ||||||||
\(476\) | 1.75379 | 0.0803848 | ||||||||
\(477\) | 8.56155 | 0.392007 | ||||||||
\(478\) | −11.3693 | −0.520020 | ||||||||
\(479\) | −38.2462 | −1.74751 | −0.873757 | − | 0.486363i | \(-0.838323\pi\) | ||||
−0.873757 | + | 0.486363i | \(0.838323\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −28.1231 | −1.28097 | ||||||||
\(483\) | −2.63068 | −0.119700 | ||||||||
\(484\) | 6.00000 | 0.272727 | ||||||||
\(485\) | −7.12311 | −0.323444 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 13.0540 | 0.591532 | 0.295766 | − | 0.955260i | \(-0.404425\pi\) | ||||
0.295766 | + | 0.955260i | \(0.404425\pi\) | |||||||
\(488\) | 6.00000 | 0.271607 | ||||||||
\(489\) | −14.4384 | −0.652929 | ||||||||
\(490\) | −6.68466 | −0.301982 | ||||||||
\(491\) | −17.4384 | −0.786986 | −0.393493 | − | 0.919328i | \(-0.628733\pi\) | ||||
−0.393493 | + | 0.919328i | \(0.628733\pi\) | |||||||
\(492\) | 12.2462 | 0.552102 | ||||||||
\(493\) | −7.61553 | −0.342986 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.12311 | 0.185320 | ||||||||
\(496\) | −6.68466 | −0.300150 | ||||||||
\(497\) | 7.36932 | 0.330559 | ||||||||
\(498\) | −7.12311 | −0.319194 | ||||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 4.36932 | 0.195207 | ||||||||
\(502\) | −8.12311 | −0.362552 | ||||||||
\(503\) | −43.0540 | −1.91968 | −0.959841 | − | 0.280545i | \(-0.909485\pi\) | ||||
−0.959841 | + | 0.280545i | \(0.909485\pi\) | |||||||
\(504\) | −0.561553 | −0.0250136 | ||||||||
\(505\) | −8.87689 | −0.395017 | ||||||||
\(506\) | 19.3153 | 0.858672 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.56155 | −0.379857 | ||||||||
\(509\) | 40.5464 | 1.79719 | 0.898594 | − | 0.438782i | \(-0.144590\pi\) | ||||
0.898594 | + | 0.438782i | \(0.144590\pi\) | |||||||
\(510\) | −3.12311 | −0.138293 | ||||||||
\(511\) | −5.26137 | −0.232749 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.561553 | 0.0247932 | ||||||||
\(514\) | −5.56155 | −0.245310 | ||||||||
\(515\) | 4.56155 | 0.201006 | ||||||||
\(516\) | 0.438447 | 0.0193016 | ||||||||
\(517\) | 28.8617 | 1.26934 | ||||||||
\(518\) | 2.31534 | 0.101730 | ||||||||
\(519\) | 20.1771 | 0.885676 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.31534 | −0.276680 | −0.138340 | − | 0.990385i | \(-0.544177\pi\) | ||||
−0.138340 | + | 0.990385i | \(0.544177\pi\) | |||||||
\(522\) | 2.43845 | 0.106728 | ||||||||
\(523\) | −29.8078 | −1.30340 | −0.651701 | − | 0.758476i | \(-0.725944\pi\) | ||||
−0.651701 | + | 0.758476i | \(0.725944\pi\) | |||||||
\(524\) | −2.12311 | −0.0927483 | ||||||||
\(525\) | −0.561553 | −0.0245082 | ||||||||
\(526\) | −13.0000 | −0.566827 | ||||||||
\(527\) | 20.8769 | 0.909412 | ||||||||
\(528\) | 4.12311 | 0.179435 | ||||||||
\(529\) | −1.05398 | −0.0458250 | ||||||||
\(530\) | 8.56155 | 0.371890 | ||||||||
\(531\) | 6.43845 | 0.279405 | ||||||||
\(532\) | −0.315342 | −0.0136718 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −18.8078 | −0.813892 | ||||||||
\(535\) | 2.00000 | 0.0864675 | ||||||||
\(536\) | −2.24621 | −0.0970215 | ||||||||
\(537\) | −12.6847 | −0.547383 | ||||||||
\(538\) | 21.3693 | 0.921297 | ||||||||
\(539\) | −27.5616 | −1.18716 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −27.3693 | −1.17670 | −0.588349 | − | 0.808607i | \(-0.700222\pi\) | ||||
−0.588349 | + | 0.808607i | \(0.700222\pi\) | |||||||
\(542\) | −13.1771 | −0.566004 | ||||||||
\(543\) | 2.87689 | 0.123459 | ||||||||
\(544\) | −3.12311 | −0.133902 | ||||||||
\(545\) | −3.75379 | −0.160795 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.61553 | −0.240103 | −0.120051 | − | 0.992768i | \(-0.538306\pi\) | ||||
−0.120051 | + | 0.992768i | \(0.538306\pi\) | |||||||
\(548\) | 11.8078 | 0.504403 | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 4.12311 | 0.175810 | ||||||||
\(551\) | 1.36932 | 0.0583349 | ||||||||
\(552\) | 4.68466 | 0.199392 | ||||||||
\(553\) | −6.49242 | −0.276086 | ||||||||
\(554\) | −1.00000 | −0.0424859 | ||||||||
\(555\) | −4.12311 | −0.175016 | ||||||||
\(556\) | 12.5616 | 0.532729 | ||||||||
\(557\) | −8.56155 | −0.362765 | −0.181382 | − | 0.983413i | \(-0.558057\pi\) | ||||
−0.181382 | + | 0.983413i | \(0.558057\pi\) | |||||||
\(558\) | −6.68466 | −0.282984 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.561553 | −0.0237299 | ||||||||
\(561\) | −12.8769 | −0.543663 | ||||||||
\(562\) | 16.2462 | 0.685305 | ||||||||
\(563\) | −32.9848 | −1.39015 | −0.695073 | − | 0.718939i | \(-0.744628\pi\) | ||||
−0.695073 | + | 0.718939i | \(0.744628\pi\) | |||||||
\(564\) | 7.00000 | 0.294753 | ||||||||
\(565\) | 8.68466 | 0.365366 | ||||||||
\(566\) | 15.5616 | 0.654101 | ||||||||
\(567\) | −0.561553 | −0.0235830 | ||||||||
\(568\) | −13.1231 | −0.550633 | ||||||||
\(569\) | 26.1771 | 1.09740 | 0.548700 | − | 0.836019i | \(-0.315123\pi\) | ||||
0.548700 | + | 0.836019i | \(0.315123\pi\) | |||||||
\(570\) | 0.561553 | 0.0235209 | ||||||||
\(571\) | 23.6847 | 0.991172 | 0.495586 | − | 0.868559i | \(-0.334953\pi\) | ||||
0.495586 | + | 0.868559i | \(0.334953\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.8769 | 0.454389 | ||||||||
\(574\) | −6.87689 | −0.287036 | ||||||||
\(575\) | 4.68466 | 0.195364 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −40.7386 | −1.69597 | −0.847986 | − | 0.530019i | \(-0.822185\pi\) | ||||
−0.847986 | + | 0.530019i | \(0.822185\pi\) | |||||||
\(578\) | −7.24621 | −0.301403 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.43845 | 0.101251 | ||||||||
\(581\) | 4.00000 | 0.165948 | ||||||||
\(582\) | −7.12311 | −0.295262 | ||||||||
\(583\) | 35.3002 | 1.46198 | ||||||||
\(584\) | 9.36932 | 0.387705 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.93087 | 0.162383 | ||||||||
\(587\) | −40.2462 | −1.66114 | −0.830569 | − | 0.556915i | \(-0.811985\pi\) | ||||
−0.830569 | + | 0.556915i | \(0.811985\pi\) | |||||||
\(588\) | −6.68466 | −0.275671 | ||||||||
\(589\) | −3.75379 | −0.154672 | ||||||||
\(590\) | 6.43845 | 0.265067 | ||||||||
\(591\) | 12.8078 | 0.526841 | ||||||||
\(592\) | −4.12311 | −0.169459 | ||||||||
\(593\) | 33.1771 | 1.36242 | 0.681210 | − | 0.732088i | \(-0.261454\pi\) | ||||
0.681210 | + | 0.732088i | \(0.261454\pi\) | |||||||
\(594\) | 4.12311 | 0.169173 | ||||||||
\(595\) | 1.75379 | 0.0718983 | ||||||||
\(596\) | −2.19224 | −0.0897975 | ||||||||
\(597\) | 2.87689 | 0.117743 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.0000 | −0.572024 | −0.286012 | − | 0.958226i | \(-0.592330\pi\) | ||||
−0.286012 | + | 0.958226i | \(0.592330\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 29.9848 | 1.22311 | 0.611554 | − | 0.791203i | \(-0.290545\pi\) | ||||
0.611554 | + | 0.791203i | \(0.290545\pi\) | |||||||
\(602\) | −0.246211 | −0.0100348 | ||||||||
\(603\) | −2.24621 | −0.0914728 | ||||||||
\(604\) | −15.3693 | −0.625369 | ||||||||
\(605\) | 6.00000 | 0.243935 | ||||||||
\(606\) | −8.87689 | −0.360599 | ||||||||
\(607\) | 32.4233 | 1.31602 | 0.658010 | − | 0.753009i | \(-0.271398\pi\) | ||||
0.658010 | + | 0.753009i | \(0.271398\pi\) | |||||||
\(608\) | 0.561553 | 0.0227740 | ||||||||
\(609\) | −1.36932 | −0.0554875 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.12311 | −0.126244 | ||||||||
\(613\) | 19.8769 | 0.802820 | 0.401410 | − | 0.915898i | \(-0.368520\pi\) | ||||
0.401410 | + | 0.915898i | \(0.368520\pi\) | |||||||
\(614\) | 25.6155 | 1.03376 | ||||||||
\(615\) | 12.2462 | 0.493815 | ||||||||
\(616\) | −2.31534 | −0.0932878 | ||||||||
\(617\) | −29.3153 | −1.18019 | −0.590096 | − | 0.807333i | \(-0.700910\pi\) | ||||
−0.590096 | + | 0.807333i | \(0.700910\pi\) | |||||||
\(618\) | 4.56155 | 0.183493 | ||||||||
\(619\) | −20.5616 | −0.826439 | −0.413219 | − | 0.910632i | \(-0.635596\pi\) | ||||
−0.413219 | + | 0.910632i | \(0.635596\pi\) | |||||||
\(620\) | −6.68466 | −0.268462 | ||||||||
\(621\) | 4.68466 | 0.187989 | ||||||||
\(622\) | 30.7386 | 1.23251 | ||||||||
\(623\) | 10.5616 | 0.423140 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 31.3693 | 1.25377 | ||||||||
\(627\) | 2.31534 | 0.0924658 | ||||||||
\(628\) | 13.8769 | 0.553748 | ||||||||
\(629\) | 12.8769 | 0.513435 | ||||||||
\(630\) | −0.561553 | −0.0223728 | ||||||||
\(631\) | −13.7538 | −0.547530 | −0.273765 | − | 0.961797i | \(-0.588269\pi\) | ||||
−0.273765 | + | 0.961797i | \(0.588269\pi\) | |||||||
\(632\) | 11.5616 | 0.459894 | ||||||||
\(633\) | −21.9309 | −0.871674 | ||||||||
\(634\) | −24.8078 | −0.985242 | ||||||||
\(635\) | −8.56155 | −0.339755 | ||||||||
\(636\) | 8.56155 | 0.339488 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.0540 | 0.398041 | ||||||||
\(639\) | −13.1231 | −0.519142 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −11.4384 | −0.451792 | −0.225896 | − | 0.974151i | \(-0.572531\pi\) | ||||
−0.225896 | + | 0.974151i | \(0.572531\pi\) | |||||||
\(642\) | 2.00000 | 0.0789337 | ||||||||
\(643\) | 21.7538 | 0.857886 | 0.428943 | − | 0.903332i | \(-0.358886\pi\) | ||||
0.428943 | + | 0.903332i | \(0.358886\pi\) | |||||||
\(644\) | −2.63068 | −0.103663 | ||||||||
\(645\) | 0.438447 | 0.0172638 | ||||||||
\(646\) | −1.75379 | −0.0690019 | ||||||||
\(647\) | 35.0540 | 1.37811 | 0.689057 | − | 0.724707i | \(-0.258025\pi\) | ||||
0.689057 | + | 0.724707i | \(0.258025\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 26.5464 | 1.04204 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.75379 | 0.147123 | ||||||||
\(652\) | −14.4384 | −0.565453 | ||||||||
\(653\) | −44.5616 | −1.74383 | −0.871914 | − | 0.489659i | \(-0.837121\pi\) | ||||
−0.871914 | + | 0.489659i | \(0.837121\pi\) | |||||||
\(654\) | −3.75379 | −0.146785 | ||||||||
\(655\) | −2.12311 | −0.0829566 | ||||||||
\(656\) | 12.2462 | 0.478134 | ||||||||
\(657\) | 9.36932 | 0.365532 | ||||||||
\(658\) | −3.93087 | −0.153241 | ||||||||
\(659\) | −6.05398 | −0.235829 | −0.117915 | − | 0.993024i | \(-0.537621\pi\) | ||||
−0.117915 | + | 0.993024i | \(0.537621\pi\) | |||||||
\(660\) | 4.12311 | 0.160492 | ||||||||
\(661\) | 29.6155 | 1.15191 | 0.575955 | − | 0.817481i | \(-0.304630\pi\) | ||||
0.575955 | + | 0.817481i | \(0.304630\pi\) | |||||||
\(662\) | 30.7386 | 1.19469 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.12311 | −0.276430 | ||||||||
\(665\) | −0.315342 | −0.0122284 | ||||||||
\(666\) | −4.12311 | −0.159767 | ||||||||
\(667\) | 11.4233 | 0.442312 | ||||||||
\(668\) | 4.36932 | 0.169054 | ||||||||
\(669\) | 27.3002 | 1.05549 | ||||||||
\(670\) | −2.24621 | −0.0867787 | ||||||||
\(671\) | 24.7386 | 0.955024 | ||||||||
\(672\) | −0.561553 | −0.0216624 | ||||||||
\(673\) | 25.7538 | 0.992736 | 0.496368 | − | 0.868112i | \(-0.334667\pi\) | ||||
0.496368 | + | 0.868112i | \(0.334667\pi\) | |||||||
\(674\) | −6.00000 | −0.231111 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.1231 | −1.42676 | −0.713378 | − | 0.700779i | \(-0.752836\pi\) | ||||
−0.713378 | + | 0.700779i | \(0.752836\pi\) | |||||||
\(678\) | 8.68466 | 0.333532 | ||||||||
\(679\) | 4.00000 | 0.153506 | ||||||||
\(680\) | −3.12311 | −0.119766 | ||||||||
\(681\) | −20.0000 | −0.766402 | ||||||||
\(682\) | −27.5616 | −1.05539 | ||||||||
\(683\) | 17.1231 | 0.655197 | 0.327599 | − | 0.944817i | \(-0.393761\pi\) | ||||
0.327599 | + | 0.944817i | \(0.393761\pi\) | |||||||
\(684\) | 0.561553 | 0.0214715 | ||||||||
\(685\) | 11.8078 | 0.451151 | ||||||||
\(686\) | 7.68466 | 0.293402 | ||||||||
\(687\) | −24.2462 | −0.925051 | ||||||||
\(688\) | 0.438447 | 0.0167156 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 4.68466 | 0.178342 | ||||||||
\(691\) | −20.5616 | −0.782198 | −0.391099 | − | 0.920349i | \(-0.627905\pi\) | ||||
−0.391099 | + | 0.920349i | \(0.627905\pi\) | |||||||
\(692\) | 20.1771 | 0.767018 | ||||||||
\(693\) | −2.31534 | −0.0879526 | ||||||||
\(694\) | 0.876894 | 0.0332865 | ||||||||
\(695\) | 12.5616 | 0.476487 | ||||||||
\(696\) | 2.43845 | 0.0924291 | ||||||||
\(697\) | −38.2462 | −1.44868 | ||||||||
\(698\) | 8.49242 | 0.321443 | ||||||||
\(699\) | −5.31534 | −0.201045 | ||||||||
\(700\) | −0.561553 | −0.0212247 | ||||||||
\(701\) | −36.3002 | −1.37104 | −0.685520 | − | 0.728054i | \(-0.740425\pi\) | ||||
−0.685520 | + | 0.728054i | \(0.740425\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.31534 | −0.0873248 | ||||||||
\(704\) | 4.12311 | 0.155395 | ||||||||
\(705\) | 7.00000 | 0.263635 | ||||||||
\(706\) | −25.8617 | −0.973319 | ||||||||
\(707\) | 4.98485 | 0.187474 | ||||||||
\(708\) | 6.43845 | 0.241972 | ||||||||
\(709\) | 34.2462 | 1.28614 | 0.643072 | − | 0.765806i | \(-0.277660\pi\) | ||||
0.643072 | + | 0.765806i | \(0.277660\pi\) | |||||||
\(710\) | −13.1231 | −0.492501 | ||||||||
\(711\) | 11.5616 | 0.433592 | ||||||||
\(712\) | −18.8078 | −0.704851 | ||||||||
\(713\) | −31.3153 | −1.17277 | ||||||||
\(714\) | 1.75379 | 0.0656339 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.6847 | −0.474048 | ||||||||
\(717\) | −11.3693 | −0.424595 | ||||||||
\(718\) | 13.1231 | 0.489750 | ||||||||
\(719\) | 44.9848 | 1.67765 | 0.838826 | − | 0.544400i | \(-0.183243\pi\) | ||||
0.838826 | + | 0.544400i | \(0.183243\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −2.56155 | −0.0953972 | ||||||||
\(722\) | −18.6847 | −0.695371 | ||||||||
\(723\) | −28.1231 | −1.04591 | ||||||||
\(724\) | 2.87689 | 0.106919 | ||||||||
\(725\) | 2.43845 | 0.0905617 | ||||||||
\(726\) | 6.00000 | 0.222681 | ||||||||
\(727\) | 38.4233 | 1.42504 | 0.712521 | − | 0.701651i | \(-0.247554\pi\) | ||||
0.712521 | + | 0.701651i | \(0.247554\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 9.36932 | 0.346774 | ||||||||
\(731\) | −1.36932 | −0.0506460 | ||||||||
\(732\) | 6.00000 | 0.221766 | ||||||||
\(733\) | 20.0691 | 0.741270 | 0.370635 | − | 0.928779i | \(-0.379140\pi\) | ||||
0.370635 | + | 0.928779i | \(0.379140\pi\) | |||||||
\(734\) | 12.4924 | 0.461104 | ||||||||
\(735\) | −6.68466 | −0.246567 | ||||||||
\(736\) | 4.68466 | 0.172679 | ||||||||
\(737\) | −9.26137 | −0.341147 | ||||||||
\(738\) | 12.2462 | 0.450789 | ||||||||
\(739\) | −27.5464 | −1.01331 | −0.506655 | − | 0.862149i | \(-0.669118\pi\) | ||||
−0.506655 | + | 0.862149i | \(0.669118\pi\) | |||||||
\(740\) | −4.12311 | −0.151568 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.80776 | −0.176499 | ||||||||
\(743\) | 13.1771 | 0.483420 | 0.241710 | − | 0.970349i | \(-0.422292\pi\) | ||||
0.241710 | + | 0.970349i | \(0.422292\pi\) | |||||||
\(744\) | −6.68466 | −0.245071 | ||||||||
\(745\) | −2.19224 | −0.0803173 | ||||||||
\(746\) | −25.8078 | −0.944889 | ||||||||
\(747\) | −7.12311 | −0.260621 | ||||||||
\(748\) | −12.8769 | −0.470826 | ||||||||
\(749\) | −1.12311 | −0.0410374 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −23.8078 | −0.868758 | −0.434379 | − | 0.900730i | \(-0.643032\pi\) | ||||
−0.434379 | + | 0.900730i | \(0.643032\pi\) | |||||||
\(752\) | 7.00000 | 0.255264 | ||||||||
\(753\) | −8.12311 | −0.296022 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.3693 | −0.559347 | ||||||||
\(756\) | −0.561553 | −0.0204235 | ||||||||
\(757\) | −28.4233 | −1.03306 | −0.516531 | − | 0.856268i | \(-0.672777\pi\) | ||||
−0.516531 | + | 0.856268i | \(0.672777\pi\) | |||||||
\(758\) | −17.6847 | −0.642336 | ||||||||
\(759\) | 19.3153 | 0.701102 | ||||||||
\(760\) | 0.561553 | 0.0203697 | ||||||||
\(761\) | −17.9309 | −0.649994 | −0.324997 | − | 0.945715i | \(-0.605363\pi\) | ||||
−0.324997 | + | 0.945715i | \(0.605363\pi\) | |||||||
\(762\) | −8.56155 | −0.310152 | ||||||||
\(763\) | 2.10795 | 0.0763129 | ||||||||
\(764\) | 10.8769 | 0.393512 | ||||||||
\(765\) | −3.12311 | −0.112916 | ||||||||
\(766\) | 0.192236 | 0.00694577 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −33.3153 | −1.20138 | −0.600691 | − | 0.799481i | \(-0.705108\pi\) | ||||
−0.600691 | + | 0.799481i | \(0.705108\pi\) | |||||||
\(770\) | −2.31534 | −0.0834391 | ||||||||
\(771\) | −5.56155 | −0.200294 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.1771 | 0.869589 | 0.434795 | − | 0.900530i | \(-0.356821\pi\) | ||||
0.434795 | + | 0.900530i | \(0.356821\pi\) | |||||||
\(774\) | 0.438447 | 0.0157597 | ||||||||
\(775\) | −6.68466 | −0.240120 | ||||||||
\(776\) | −7.12311 | −0.255705 | ||||||||
\(777\) | 2.31534 | 0.0830624 | ||||||||
\(778\) | −18.0540 | −0.647266 | ||||||||
\(779\) | 6.87689 | 0.246390 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.1080 | −1.93613 | ||||||||
\(782\) | −14.6307 | −0.523192 | ||||||||
\(783\) | 2.43845 | 0.0871430 | ||||||||
\(784\) | −6.68466 | −0.238738 | ||||||||
\(785\) | 13.8769 | 0.495288 | ||||||||
\(786\) | −2.12311 | −0.0757287 | ||||||||
\(787\) | 31.3153 | 1.11627 | 0.558136 | − | 0.829750i | \(-0.311517\pi\) | ||||
0.558136 | + | 0.829750i | \(0.311517\pi\) | |||||||
\(788\) | 12.8078 | 0.456258 | ||||||||
\(789\) | −13.0000 | −0.462812 | ||||||||
\(790\) | 11.5616 | 0.411342 | ||||||||
\(791\) | −4.87689 | −0.173402 | ||||||||
\(792\) | 4.12311 | 0.146508 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.1231 | −0.714142 | ||||||||
\(795\) | 8.56155 | 0.303647 | ||||||||
\(796\) | 2.87689 | 0.101969 | ||||||||
\(797\) | 13.1231 | 0.464844 | 0.232422 | − | 0.972615i | \(-0.425335\pi\) | ||||
0.232422 | + | 0.972615i | \(0.425335\pi\) | |||||||
\(798\) | −0.315342 | −0.0111630 | ||||||||
\(799\) | −21.8617 | −0.773413 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −18.8078 | −0.664540 | ||||||||
\(802\) | 0.315342 | 0.0111351 | ||||||||
\(803\) | 38.6307 | 1.36325 | ||||||||
\(804\) | −2.24621 | −0.0792178 | ||||||||
\(805\) | −2.63068 | −0.0927194 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.3693 | 0.752236 | ||||||||
\(808\) | −8.87689 | −0.312288 | ||||||||
\(809\) | −14.4924 | −0.509526 | −0.254763 | − | 0.967003i | \(-0.581998\pi\) | ||||
−0.254763 | + | 0.967003i | \(0.581998\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 47.5464 | 1.66958 | 0.834790 | − | 0.550569i | \(-0.185589\pi\) | ||||
0.834790 | + | 0.550569i | \(0.185589\pi\) | |||||||
\(812\) | −1.36932 | −0.0480536 | ||||||||
\(813\) | −13.1771 | −0.462140 | ||||||||
\(814\) | −17.0000 | −0.595850 | ||||||||
\(815\) | −14.4384 | −0.505757 | ||||||||
\(816\) | −3.12311 | −0.109331 | ||||||||
\(817\) | 0.246211 | 0.00861384 | ||||||||
\(818\) | −18.8078 | −0.657598 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.2462 | 0.427656 | ||||||||
\(821\) | −8.43845 | −0.294504 | −0.147252 | − | 0.989099i | \(-0.547043\pi\) | ||||
−0.147252 | + | 0.989099i | \(0.547043\pi\) | |||||||
\(822\) | 11.8078 | 0.411843 | ||||||||
\(823\) | 5.05398 | 0.176171 | 0.0880853 | − | 0.996113i | \(-0.471925\pi\) | ||||
0.0880853 | + | 0.996113i | \(0.471925\pi\) | |||||||
\(824\) | 4.56155 | 0.158909 | ||||||||
\(825\) | 4.12311 | 0.143548 | ||||||||
\(826\) | −3.61553 | −0.125800 | ||||||||
\(827\) | −28.2462 | −0.982217 | −0.491109 | − | 0.871098i | \(-0.663408\pi\) | ||||
−0.491109 | + | 0.871098i | \(0.663408\pi\) | |||||||
\(828\) | 4.68466 | 0.162803 | ||||||||
\(829\) | 12.3845 | 0.430130 | 0.215065 | − | 0.976600i | \(-0.431004\pi\) | ||||
0.215065 | + | 0.976600i | \(0.431004\pi\) | |||||||
\(830\) | −7.12311 | −0.247247 | ||||||||
\(831\) | −1.00000 | −0.0346896 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.8769 | 0.723342 | ||||||||
\(834\) | 12.5616 | 0.434971 | ||||||||
\(835\) | 4.36932 | 0.151206 | ||||||||
\(836\) | 2.31534 | 0.0800778 | ||||||||
\(837\) | −6.68466 | −0.231056 | ||||||||
\(838\) | 32.4924 | 1.12243 | ||||||||
\(839\) | 36.7386 | 1.26836 | 0.634179 | − | 0.773186i | \(-0.281338\pi\) | ||||
0.634179 | + | 0.773186i | \(0.281338\pi\) | |||||||
\(840\) | −0.561553 | −0.0193754 | ||||||||
\(841\) | −23.0540 | −0.794965 | ||||||||
\(842\) | −32.4924 | −1.11976 | ||||||||
\(843\) | 16.2462 | 0.559549 | ||||||||
\(844\) | −21.9309 | −0.754892 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.00000 | 0.240665 | ||||||||
\(847\) | −3.36932 | −0.115771 | ||||||||
\(848\) | 8.56155 | 0.294005 | ||||||||
\(849\) | 15.5616 | 0.534071 | ||||||||
\(850\) | −3.12311 | −0.107122 | ||||||||
\(851\) | −19.3153 | −0.662121 | ||||||||
\(852\) | −13.1231 | −0.449590 | ||||||||
\(853\) | 2.30019 | 0.0787569 | 0.0393784 | − | 0.999224i | \(-0.487462\pi\) | ||||
0.0393784 | + | 0.999224i | \(0.487462\pi\) | |||||||
\(854\) | −3.36932 | −0.115296 | ||||||||
\(855\) | 0.561553 | 0.0192047 | ||||||||
\(856\) | 2.00000 | 0.0683586 | ||||||||
\(857\) | −6.19224 | −0.211523 | −0.105761 | − | 0.994392i | \(-0.533728\pi\) | ||||
−0.105761 | + | 0.994392i | \(0.533728\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.7926 | 1.35771 | 0.678853 | − | 0.734274i | \(-0.262477\pi\) | ||||
0.678853 | + | 0.734274i | \(0.262477\pi\) | |||||||
\(860\) | 0.438447 | 0.0149509 | ||||||||
\(861\) | −6.87689 | −0.234364 | ||||||||
\(862\) | −22.7386 | −0.774481 | ||||||||
\(863\) | 2.43845 | 0.0830057 | 0.0415029 | − | 0.999138i | \(-0.486785\pi\) | ||||
0.0415029 | + | 0.999138i | \(0.486785\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 20.1771 | 0.686041 | ||||||||
\(866\) | −18.7386 | −0.636765 | ||||||||
\(867\) | −7.24621 | −0.246094 | ||||||||
\(868\) | 3.75379 | 0.127412 | ||||||||
\(869\) | 47.6695 | 1.61708 | ||||||||
\(870\) | 2.43845 | 0.0826711 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.75379 | −0.127119 | ||||||||
\(873\) | −7.12311 | −0.241081 | ||||||||
\(874\) | 2.63068 | 0.0889842 | ||||||||
\(875\) | −0.561553 | −0.0189839 | ||||||||
\(876\) | 9.36932 | 0.316560 | ||||||||
\(877\) | 8.43845 | 0.284946 | 0.142473 | − | 0.989799i | \(-0.454495\pi\) | ||||
0.142473 | + | 0.989799i | \(0.454495\pi\) | |||||||
\(878\) | 25.1231 | 0.847864 | ||||||||
\(879\) | 3.93087 | 0.132585 | ||||||||
\(880\) | 4.12311 | 0.138990 | ||||||||
\(881\) | −24.5616 | −0.827500 | −0.413750 | − | 0.910391i | \(-0.635781\pi\) | ||||
−0.413750 | + | 0.910391i | \(0.635781\pi\) | |||||||
\(882\) | −6.68466 | −0.225084 | ||||||||
\(883\) | −19.1771 | −0.645360 | −0.322680 | − | 0.946508i | \(-0.604584\pi\) | ||||
−0.322680 | + | 0.946508i | \(0.604584\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.43845 | 0.216426 | ||||||||
\(886\) | −13.1231 | −0.440879 | ||||||||
\(887\) | −33.1080 | −1.11166 | −0.555828 | − | 0.831297i | \(-0.687599\pi\) | ||||
−0.555828 | + | 0.831297i | \(0.687599\pi\) | |||||||
\(888\) | −4.12311 | −0.138362 | ||||||||
\(889\) | 4.80776 | 0.161247 | ||||||||
\(890\) | −18.8078 | −0.630438 | ||||||||
\(891\) | 4.12311 | 0.138129 | ||||||||
\(892\) | 27.3002 | 0.914078 | ||||||||
\(893\) | 3.93087 | 0.131542 | ||||||||
\(894\) | −2.19224 | −0.0733193 | ||||||||
\(895\) | −12.6847 | −0.424001 | ||||||||
\(896\) | −0.561553 | −0.0187602 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −20.1771 | −0.673318 | ||||||||
\(899\) | −16.3002 | −0.543642 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −26.7386 | −0.890793 | ||||||||
\(902\) | 50.4924 | 1.68121 | ||||||||
\(903\) | −0.246211 | −0.00819340 | ||||||||
\(904\) | 8.68466 | 0.288847 | ||||||||
\(905\) | 2.87689 | 0.0956312 | ||||||||
\(906\) | −15.3693 | −0.510611 | ||||||||
\(907\) | −53.9157 | −1.79024 | −0.895121 | − | 0.445823i | \(-0.852911\pi\) | ||||
−0.895121 | + | 0.445823i | \(0.852911\pi\) | |||||||
\(908\) | −20.0000 | −0.663723 | ||||||||
\(909\) | −8.87689 | −0.294428 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.6307 | −0.617262 | −0.308631 | − | 0.951182i | \(-0.599871\pi\) | ||||
−0.308631 | + | 0.951182i | \(0.599871\pi\) | |||||||
\(912\) | 0.561553 | 0.0185949 | ||||||||
\(913\) | −29.3693 | −0.971983 | ||||||||
\(914\) | 20.2462 | 0.669685 | ||||||||
\(915\) | 6.00000 | 0.198354 | ||||||||
\(916\) | −24.2462 | −0.801117 | ||||||||
\(917\) | 1.19224 | 0.0393711 | ||||||||
\(918\) | −3.12311 | −0.103078 | ||||||||
\(919\) | 16.6307 | 0.548596 | 0.274298 | − | 0.961645i | \(-0.411555\pi\) | ||||
0.274298 | + | 0.961645i | \(0.411555\pi\) | |||||||
\(920\) | 4.68466 | 0.154449 | ||||||||
\(921\) | 25.6155 | 0.844060 | ||||||||
\(922\) | −30.0540 | −0.989775 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.31534 | −0.0761691 | ||||||||
\(925\) | −4.12311 | −0.135567 | ||||||||
\(926\) | −7.61553 | −0.250262 | ||||||||
\(927\) | 4.56155 | 0.149821 | ||||||||
\(928\) | 2.43845 | 0.0800460 | ||||||||
\(929\) | −25.1231 | −0.824262 | −0.412131 | − | 0.911125i | \(-0.635215\pi\) | ||||
−0.412131 | + | 0.911125i | \(0.635215\pi\) | |||||||
\(930\) | −6.68466 | −0.219199 | ||||||||
\(931\) | −3.75379 | −0.123025 | ||||||||
\(932\) | −5.31534 | −0.174110 | ||||||||
\(933\) | 30.7386 | 1.00634 | ||||||||
\(934\) | −17.8617 | −0.584454 | ||||||||
\(935\) | −12.8769 | −0.421119 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.2311 | 1.73898 | 0.869491 | − | 0.493948i | \(-0.164447\pi\) | ||||
0.869491 | + | 0.493948i | \(0.164447\pi\) | |||||||
\(938\) | 1.26137 | 0.0411851 | ||||||||
\(939\) | 31.3693 | 1.02370 | ||||||||
\(940\) | 7.00000 | 0.228315 | ||||||||
\(941\) | −25.3693 | −0.827016 | −0.413508 | − | 0.910500i | \(-0.635697\pi\) | ||||
−0.413508 | + | 0.910500i | \(0.635697\pi\) | |||||||
\(942\) | 13.8769 | 0.452134 | ||||||||
\(943\) | 57.3693 | 1.86820 | ||||||||
\(944\) | 6.43845 | 0.209554 | ||||||||
\(945\) | −0.561553 | −0.0182673 | ||||||||
\(946\) | 1.80776 | 0.0587755 | ||||||||
\(947\) | −43.8617 | −1.42532 | −0.712658 | − | 0.701512i | \(-0.752509\pi\) | ||||
−0.712658 | + | 0.701512i | \(0.752509\pi\) | |||||||
\(948\) | 11.5616 | 0.375502 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.561553 | 0.0182192 | ||||||||
\(951\) | −24.8078 | −0.804447 | ||||||||
\(952\) | 1.75379 | 0.0568406 | ||||||||
\(953\) | 51.1771 | 1.65779 | 0.828894 | − | 0.559406i | \(-0.188971\pi\) | ||||
0.828894 | + | 0.559406i | \(0.188971\pi\) | |||||||
\(954\) | 8.56155 | 0.277191 | ||||||||
\(955\) | 10.8769 | 0.351968 | ||||||||
\(956\) | −11.3693 | −0.367710 | ||||||||
\(957\) | 10.0540 | 0.324999 | ||||||||
\(958\) | −38.2462 | −1.23568 | ||||||||
\(959\) | −6.63068 | −0.214116 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | 13.6847 | 0.441441 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.00000 | 0.0644491 | ||||||||
\(964\) | −28.1231 | −0.905784 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.63068 | −0.0846408 | ||||||||
\(967\) | 15.6847 | 0.504385 | 0.252192 | − | 0.967677i | \(-0.418848\pi\) | ||||
0.252192 | + | 0.967677i | \(0.418848\pi\) | |||||||
\(968\) | 6.00000 | 0.192847 | ||||||||
\(969\) | −1.75379 | −0.0563398 | ||||||||
\(970\) | −7.12311 | −0.228709 | ||||||||
\(971\) | −4.31534 | −0.138486 | −0.0692430 | − | 0.997600i | \(-0.522058\pi\) | ||||
−0.0692430 | + | 0.997600i | \(0.522058\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −7.05398 | −0.226140 | ||||||||
\(974\) | 13.0540 | 0.418276 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | −48.3002 | −1.54526 | −0.772630 | − | 0.634857i | \(-0.781059\pi\) | ||||
−0.772630 | + | 0.634857i | \(0.781059\pi\) | |||||||
\(978\) | −14.4384 | −0.461691 | ||||||||
\(979\) | −77.5464 | −2.47839 | ||||||||
\(980\) | −6.68466 | −0.213534 | ||||||||
\(981\) | −3.75379 | −0.119849 | ||||||||
\(982\) | −17.4384 | −0.556483 | ||||||||
\(983\) | 32.1231 | 1.02457 | 0.512284 | − | 0.858816i | \(-0.328800\pi\) | ||||
0.512284 | + | 0.858816i | \(0.328800\pi\) | |||||||
\(984\) | 12.2462 | 0.390395 | ||||||||
\(985\) | 12.8078 | 0.408089 | ||||||||
\(986\) | −7.61553 | −0.242528 | ||||||||
\(987\) | −3.93087 | −0.125121 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.05398 | 0.0653126 | ||||||||
\(990\) | 4.12311 | 0.131041 | ||||||||
\(991\) | 49.4233 | 1.56998 | 0.784991 | − | 0.619507i | \(-0.212667\pi\) | ||||
0.784991 | + | 0.619507i | \(0.212667\pi\) | |||||||
\(992\) | −6.68466 | −0.212238 | ||||||||
\(993\) | 30.7386 | 0.975461 | ||||||||
\(994\) | 7.36932 | 0.233741 | ||||||||
\(995\) | 2.87689 | 0.0912037 | ||||||||
\(996\) | −7.12311 | −0.225704 | ||||||||
\(997\) | −37.5464 | −1.18911 | −0.594553 | − | 0.804056i | \(-0.702671\pi\) | ||||
−0.594553 | + | 0.804056i | \(0.702671\pi\) | |||||||
\(998\) | 4.00000 | 0.126618 | ||||||||
\(999\) | −4.12311 | −0.130449 |
(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 | 5070.2.a.bi.1.1 | 2 | ||
13.3 | even | 3 | 390.2.i.g.61.2 | ✓ | 4 | ||
13.5 | odd | 4 | 5070.2.b.r.1351.1 | 4 | |||
13.8 | odd | 4 | 5070.2.b.r.1351.4 | 4 | |||
13.9 | even | 3 | 390.2.i.g.211.2 | yes | 4 | ||
13.12 | even | 2 | 5070.2.a.bb.1.2 | 2 | |||
39.29 | odd | 6 | 1170.2.i.o.451.2 | 4 | |||
39.35 | odd | 6 | 1170.2.i.o.991.2 | 4 | |||
65.3 | odd | 12 | 1950.2.z.n.1699.4 | 8 | |||
65.9 | even | 6 | 1950.2.i.bi.601.1 | 4 | |||
65.22 | odd | 12 | 1950.2.z.n.1849.4 | 8 | |||
65.29 | even | 6 | 1950.2.i.bi.451.1 | 4 | |||
65.42 | odd | 12 | 1950.2.z.n.1699.1 | 8 | |||
65.48 | odd | 12 | 1950.2.z.n.1849.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.g.61.2 | ✓ | 4 | 13.3 | even | 3 | ||
390.2.i.g.211.2 | yes | 4 | 13.9 | even | 3 | ||
1170.2.i.o.451.2 | 4 | 39.29 | odd | 6 | |||
1170.2.i.o.991.2 | 4 | 39.35 | odd | 6 | |||
1950.2.i.bi.451.1 | 4 | 65.29 | even | 6 | |||
1950.2.i.bi.601.1 | 4 | 65.9 | even | 6 | |||
1950.2.z.n.1699.1 | 8 | 65.42 | odd | 12 | |||
1950.2.z.n.1699.4 | 8 | 65.3 | odd | 12 | |||
1950.2.z.n.1849.1 | 8 | 65.48 | odd | 12 | |||
1950.2.z.n.1849.4 | 8 | 65.22 | odd | 12 | |||
5070.2.a.bb.1.2 | 2 | 13.12 | even | 2 | |||
5070.2.a.bi.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5070.2.b.r.1351.1 | 4 | 13.5 | odd | 4 | |||
5070.2.b.r.1351.4 | 4 | 13.8 | odd | 4 |