Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, 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("1216.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(9.70980888579\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 608) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.56155 | 1.47891 | 0.739457 | − | 0.673204i | \(-0.235083\pi\) | ||||
0.739457 | + | 0.673204i | \(0.235083\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.56155 | −0.698348 | −0.349174 | − | 0.937058i | \(-0.613538\pi\) | ||||
−0.349174 | + | 0.937058i | \(0.613538\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.56155 | −1.07385 | −0.536924 | − | 0.843630i | \(-0.680414\pi\) | ||||
−0.536924 | + | 0.843630i | \(0.680414\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.56155 | −0.710447 | −0.355223 | − | 0.934781i | \(-0.615595\pi\) | ||||
−0.355223 | + | 0.934781i | \(0.615595\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.00000 | −1.03280 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.12311 | −1.97014 | −0.985071 | − | 0.172147i | \(-0.944930\pi\) | ||||
−0.985071 | + | 0.172147i | \(0.944930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.68466 | −1.67693 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.43845 | −0.299937 | −0.149968 | − | 0.988691i | \(-0.547917\pi\) | ||||
−0.149968 | + | 0.988691i | \(0.547917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.56155 | −0.512311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43845 | 0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.68466 | 1.42701 | 0.713503 | − | 0.700653i | \(-0.247108\pi\) | ||||
0.713503 | + | 0.700653i | \(0.247108\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.876894 | −0.157495 | −0.0787474 | − | 0.996895i | \(-0.525092\pi\) | ||||
−0.0787474 | + | 0.996895i | \(0.525092\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.12311 | −1.58813 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.68466 | 0.791852 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.12311 | 0.184637 | 0.0923187 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923187 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.56155 | −1.05069 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | 0.624695 | 0.312348 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312348 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.56155 | 1.45812 | 0.729062 | − | 0.684448i | \(-0.239957\pi\) | ||||
0.729062 | + | 0.684448i | \(0.239957\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.56155 | −0.829067 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.68466 | −1.26679 | −0.633394 | − | 0.773830i | \(-0.718339\pi\) | ||||
−0.633394 | + | 0.773830i | \(0.718339\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −20.8078 | −2.91367 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.56155 | 1.17602 | 0.588010 | − | 0.808854i | \(-0.299912\pi\) | ||||
0.588010 | + | 0.808854i | \(0.299912\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.56155 | 0.749920 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.56155 | 0.339286 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.56155 | −1.11462 | −0.557310 | − | 0.830305i | \(-0.688166\pi\) | ||||
−0.557310 | + | 0.830305i | \(0.688166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.80776 | 0.743608 | 0.371804 | − | 0.928311i | \(-0.378739\pi\) | ||||
0.371804 | + | 0.928311i | \(0.378739\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.6847 | −1.34614 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.56155 | −0.557282 | −0.278641 | − | 0.960395i | \(-0.589884\pi\) | ||||
−0.278641 | + | 0.960395i | \(0.589884\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.68466 | −0.443581 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.2462 | −1.45336 | −0.726679 | − | 0.686977i | \(-0.758937\pi\) | ||||
−0.726679 | + | 0.686977i | \(0.758937\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.24621 | 0.848105 | 0.424052 | − | 0.905638i | \(-0.360607\pi\) | ||||
0.424052 | + | 0.905638i | \(0.360607\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.56155 | −0.757663 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.6847 | 1.21763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.36932 | 0.808888 | 0.404444 | − | 0.914563i | \(-0.367465\pi\) | ||||
0.404444 | + | 0.914563i | \(0.367465\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.6847 | 1.37584 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.6847 | 2.11042 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.36932 | 0.993146 | 0.496573 | − | 0.867995i | \(-0.334592\pi\) | ||||
0.496573 | + | 0.867995i | \(0.334592\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.68466 | 0.805571 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.24621 | −0.232921 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.56155 | −0.160212 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.12311 | −0.114034 | −0.0570170 | − | 0.998373i | \(-0.518159\pi\) | ||||
−0.0570170 | + | 0.998373i | \(0.518159\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.6847 | −1.27486 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.2462 | −1.61656 | −0.808279 | − | 0.588799i | \(-0.799601\pi\) | ||||
−0.808279 | + | 0.588799i | \(0.799601\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.4924 | 1.82211 | 0.911056 | − | 0.412282i | \(-0.135268\pi\) | ||||
0.911056 | + | 0.412282i | \(0.135268\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.0000 | 1.17108 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.9309 | −1.15340 | −0.576700 | − | 0.816956i | \(-0.695660\pi\) | ||||
−0.576700 | + | 0.816956i | \(0.695660\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.561553 | −0.0537870 | −0.0268935 | − | 0.999638i | \(-0.508561\pi\) | ||||
−0.0268935 | + | 0.999638i | \(0.508561\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.87689 | 0.273063 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.1231 | 1.23452 | 0.617259 | − | 0.786760i | \(-0.288243\pi\) | ||||
0.617259 | + | 0.786760i | \(0.288243\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.24621 | 0.209460 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.12311 | −0.843431 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 24.3693 | 2.23393 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.68466 | 0.153151 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.2462 | 0.923870 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8078 | 1.05612 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.87689 | −0.610226 | −0.305113 | − | 0.952316i | \(-0.598694\pi\) | ||||
−0.305113 | + | 0.952316i | \(0.598694\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 24.4924 | 2.15644 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.5616 | −1.53436 | −0.767180 | − | 0.641432i | \(-0.778341\pi\) | ||||
−0.767180 | + | 0.641432i | \(0.778341\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | −0.260133 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.24621 | −0.193323 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3693 | −0.885911 | −0.442955 | − | 0.896544i | \(-0.646070\pi\) | ||||
−0.442955 | + | 0.896544i | \(0.646070\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.56155 | 0.811000 | 0.405500 | − | 0.914095i | \(-0.367097\pi\) | ||||
0.405500 | + | 0.914095i | \(0.367097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22.2462 | −1.87347 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.12311 | 0.762912 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0000 | −0.996546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.12311 | 0.422547 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.43845 | −0.527458 | −0.263729 | − | 0.964597i | \(-0.584952\pi\) | ||||
−0.263729 | + | 0.964597i | \(0.584952\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4924 | −0.853861 | −0.426931 | − | 0.904284i | \(-0.640405\pi\) | ||||
−0.426931 | + | 0.904284i | \(0.640405\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −28.9309 | −2.33892 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.36932 | 0.109986 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.2462 | 1.93506 | 0.967529 | − | 0.252759i | \(-0.0813381\pi\) | ||||
0.967529 | + | 0.252759i | \(0.0813381\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 21.9309 | 1.73923 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.31534 | 0.340097 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.4924 | −1.29179 | −0.645893 | − | 0.763428i | \(-0.723515\pi\) | ||||
−0.645893 | + | 0.763428i | \(0.723515\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.2462 | 1.10907 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.43845 | −0.495265 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.56155 | 0.272359 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.75379 | 0.285395 | 0.142698 | − | 0.989766i | \(-0.454422\pi\) | ||||
0.142698 | + | 0.989766i | \(0.454422\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.68466 | 0.580906 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.9309 | −1.64843 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.2462 | −1.06481 | −0.532406 | − | 0.846489i | \(-0.678712\pi\) | ||||
−0.532406 | + | 0.846489i | \(0.678712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.2462 | −1.20757 | −0.603786 | − | 0.797147i | \(-0.706342\pi\) | ||||
−0.603786 | + | 0.797147i | \(0.706342\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.8769 | 1.09973 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.75379 | −0.128941 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.9309 | 2.11563 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.31534 | −0.313895 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.00000 | 0.0723575 | 0.0361787 | − | 0.999345i | \(-0.488481\pi\) | ||||
0.0361787 | + | 0.999345i | \(0.488481\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.4924 | −1.04319 | −0.521594 | − | 0.853194i | \(-0.674662\pi\) | ||||
−0.521594 | + | 0.853194i | \(0.674662\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.2462 | 0.733746 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.3693 | 0.952524 | 0.476262 | − | 0.879303i | \(-0.341991\pi\) | ||||
0.476262 | + | 0.879303i | \(0.341991\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.7386 | −1.82456 | −0.912282 | − | 0.409563i | \(-0.865681\pi\) | ||||
−0.912282 | + | 0.409563i | \(0.865681\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.6847 | −0.824172 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.0540 | −1.61807 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.24621 | −0.436254 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.12311 | −0.356080 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.56155 | −0.246358 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.4384 | 0.787455 | 0.393728 | − | 0.919227i | \(-0.371185\pi\) | ||||
0.393728 | + | 0.919227i | \(0.371185\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −31.3693 | −2.14939 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.9309 | −1.01828 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.63068 | 0.178582 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.5616 | 1.25427 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.8078 | 1.39968 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.3693 | −1.56493 | −0.782463 | − | 0.622698i | \(-0.786037\pi\) | ||||
−0.782463 | + | 0.622698i | \(0.786037\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.12311 | −0.608207 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.31534 | 0.286419 | 0.143210 | − | 0.989692i | \(-0.454258\pi\) | ||||
0.143210 | + | 0.989692i | \(0.454258\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.43845 | 0.557628 | 0.278814 | − | 0.960345i | \(-0.410059\pi\) | ||||
0.278814 | + | 0.960345i | \(0.410059\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 27.3693 | 1.80077 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.93087 | 0.585081 | 0.292540 | − | 0.956253i | \(-0.405499\pi\) | ||||
0.292540 | + | 0.956253i | \(0.405499\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.5616 | 0.884658 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −25.6155 | −1.66391 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.0000 | −0.970269 | −0.485135 | − | 0.874439i | \(-0.661229\pi\) | ||||
−0.485135 | + | 0.874439i | \(0.661229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.24621 | 0.144691 | 0.0723456 | − | 0.997380i | \(-0.476952\pi\) | ||||
0.0723456 | + | 0.997380i | \(0.476952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.2462 | −1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.12311 | −0.199528 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.56155 | −0.162988 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.8769 | 1.19627 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.68466 | −0.421932 | −0.210966 | − | 0.977493i | \(-0.567661\pi\) | ||||
−0.210966 | + | 0.977493i | \(0.567661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.12311 | 0.322087 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 32.4924 | 2.03475 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.75379 | 0.608425 | 0.304212 | − | 0.952604i | \(-0.401607\pi\) | ||||
0.304212 | + | 0.952604i | \(0.401607\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.36932 | −0.209359 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.3693 | 1.69412 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 26.0540 | 1.60656 | 0.803278 | − | 0.595604i | \(-0.203087\pi\) | ||||
0.803278 | + | 0.595604i | \(0.203087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.3693 | −0.821271 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.0000 | 1.46878 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.4924 | −0.883619 | −0.441809 | − | 0.897109i | \(-0.645663\pi\) | ||||
−0.441809 | + | 0.897109i | \(0.645663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.0540 | 1.64341 | 0.821706 | − | 0.569912i | \(-0.193023\pi\) | ||||
0.821706 | + | 0.569912i | \(0.193023\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 19.6847 | 1.19137 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.12311 | 0.550144 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.684658 | −0.0411371 | −0.0205686 | − | 0.999788i | \(-0.506548\pi\) | ||||
−0.0205686 | + | 0.999788i | \(0.506548\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.12311 | −0.186975 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.3693 | −1.51341 | −0.756703 | − | 0.653758i | \(-0.773191\pi\) | ||||
−0.756703 | + | 0.653758i | \(0.773191\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.4384 | 1.45271 | 0.726357 | − | 0.687317i | \(-0.241212\pi\) | ||||
0.726357 | + | 0.687317i | \(0.241212\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.00000 | −0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | −0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 48.9848 | 2.88146 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.87689 | −0.168647 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.6847 | −1.61736 | −0.808678 | − | 0.588252i | \(-0.799816\pi\) | ||||
−0.808678 | + | 0.588252i | \(0.799816\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.3693 | 0.778392 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.12311 | −0.297273 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.68466 | 0.213089 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.6847 | −1.65336 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −41.6155 | −2.39075 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.06913 | −0.519297 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.3693 | 1.67620 | 0.838098 | − | 0.545520i | \(-0.183668\pi\) | ||||
0.838098 | + | 0.545520i | \(0.183668\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 47.3693 | 2.69475 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.12311 | −0.120390 | −0.0601951 | − | 0.998187i | \(-0.519172\pi\) | ||||
−0.0601951 | + | 0.998187i | \(0.519172\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.9309 | 1.57875 | 0.789373 | − | 0.613914i | \(-0.210406\pi\) | ||||
0.789373 | + | 0.613914i | \(0.210406\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.6847 | 0.940074 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.5616 | −1.15485 | −0.577426 | − | 0.816443i | \(-0.695943\pi\) | ||||
−0.577426 | + | 0.816443i | \(0.695943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.3693 | −1.53239 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.5616 | −1.70578 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.12311 | −0.451982 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.56155 | 0.363969 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.43845 | −0.0795463 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 26.0540 | 1.43640 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.56155 | 0.470586 | 0.235293 | − | 0.971925i | \(-0.424395\pi\) | ||||
0.235293 | + | 0.971925i | \(0.424395\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.00000 | 0.219199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.12311 | 0.389177 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.4924 | 0.680506 | 0.340253 | − | 0.940334i | \(-0.389487\pi\) | ||||
0.340253 | + | 0.940334i | \(0.389487\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 33.6155 | 1.82574 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.12311 | 0.169126 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.75379 | 0.309774 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.438447 | −0.0235371 | −0.0117685 | − | 0.999931i | \(-0.503746\pi\) | ||||
−0.0117685 | + | 0.999931i | \(0.503746\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.31534 | −0.0704086 | −0.0352043 | − | 0.999380i | \(-0.511208\pi\) | ||||
−0.0352043 | + | 0.999380i | \(0.511208\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.68466 | −0.196673 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.0691303 | −0.00367944 | −0.00183972 | − | 0.999998i | \(-0.500586\pi\) | ||||
−0.00183972 | + | 0.999998i | \(0.500586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.1231 | 1.01495 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 62.4233 | 3.30379 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −36.1231 | −1.90650 | −0.953252 | − | 0.302176i | \(-0.902287\pi\) | ||||
−0.953252 | + | 0.302176i | \(0.902287\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.31534 | 0.226497 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.3153 | −0.592272 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.0000 | 1.04399 | 0.521996 | − | 0.852948i | \(-0.325188\pi\) | ||||
0.521996 | + | 0.852948i | \(0.325188\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.2462 | 0.741628 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.6847 | −1.33348 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.9309 | −0.721313 | −0.360657 | − | 0.932699i | \(-0.617447\pi\) | ||||
−0.360657 | + | 0.932699i | \(0.617447\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 30.2462 | 1.56191 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.6847 | −1.01381 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.0540 | −1.08147 | −0.540735 | − | 0.841193i | \(-0.681854\pi\) | ||||
−0.540735 | + | 0.841193i | \(0.681854\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.6155 | −0.902471 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.75379 | −0.396200 | −0.198100 | − | 0.980182i | \(-0.563477\pi\) | ||||
−0.198100 | + | 0.980182i | \(0.563477\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.6847 | −0.850329 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 34.0540 | 1.73106 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.19224 | −0.313959 | −0.156979 | − | 0.987602i | \(-0.550176\pi\) | ||||
−0.156979 | + | 0.987602i | \(0.550176\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.6847 | 0.590919 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −44.9848 | −2.26919 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.6155 | 0.785702 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.56155 | 0.479881 | 0.239940 | − | 0.970788i | \(-0.422872\pi\) | ||||
0.239940 | + | 0.970788i | \(0.422872\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.68466 | −0.384714 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.36932 | −0.0683804 | −0.0341902 | − | 0.999415i | \(-0.510885\pi\) | ||||
−0.0341902 | + | 0.999415i | \(0.510885\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.24621 | 0.111892 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.9309 | 0.543159 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.1231 | 1.34115 | 0.670576 | − | 0.741841i | \(-0.266047\pi\) | ||||
0.670576 | + | 0.741841i | \(0.266047\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −26.5616 | −1.31018 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 25.6847 | 1.26386 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.5076 | −0.564885 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 24.4924 | 1.19940 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.75379 | −0.476504 | −0.238252 | − | 0.971203i | \(-0.576574\pi\) | ||||
−0.238252 | + | 0.971203i | \(0.576574\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0540 | 0.831160 | 0.415580 | − | 0.909557i | \(-0.363579\pi\) | ||||
0.415580 | + | 0.909557i | \(0.363579\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.9309 | −1.50391 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.8078 | 1.00932 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.4233 | −0.843172 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 23.3693 | 1.12828 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.8769 | 1.10194 | 0.550971 | − | 0.834525i | \(-0.314258\pi\) | ||||
0.550971 | + | 0.834525i | \(0.314258\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.61553 | −0.0776373 | −0.0388187 | − | 0.999246i | \(-0.512359\pi\) | ||||
−0.0388187 | + | 0.999246i | \(0.512359\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −30.7386 | −1.47380 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.43845 | −0.0688103 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.2462 | −0.870844 | −0.435422 | − | 0.900226i | \(-0.643401\pi\) | ||||
−0.435422 | + | 0.900226i | \(0.643401\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.12311 | 0.339196 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.6847 | −0.507643 | −0.253822 | − | 0.967251i | \(-0.581688\pi\) | ||||
−0.253822 | + | 0.967251i | \(0.581688\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.6307 | −0.693561 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.4924 | −0.780065 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.87689 | −0.324541 | −0.162270 | − | 0.986746i | \(-0.551882\pi\) | ||||
−0.162270 | + | 0.986746i | \(0.551882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.2462 | −0.670828 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −26.8769 | −1.26279 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.0000 | −0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.8769 | −1.30403 | −0.652013 | − | 0.758208i | \(-0.726075\pi\) | ||||
−0.652013 | + | 0.758208i | \(0.726075\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.6847 | −0.545393 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.06913 | 0.236093 | 0.118046 | − | 0.993008i | \(-0.462337\pi\) | ||||
0.118046 | + | 0.993008i | \(0.462337\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0540 | 1.02494 | 0.512468 | − | 0.858707i | \(-0.328731\pi\) | ||||
0.512468 | + | 0.858707i | \(0.328731\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.50758 | 0.162660 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.31534 | 0.245965 | 0.122982 | − | 0.992409i | \(-0.460754\pi\) | ||||
0.122982 | + | 0.992409i | \(0.460754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.6847 | 0.631899 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 62.1080 | 2.86178 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34.0540 | −1.56580 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.56155 | −0.117532 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.4924 | 1.39615 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.24621 | −0.102632 | −0.0513160 | − | 0.998682i | \(-0.516342\pi\) | ||||
−0.0513160 | + | 0.998682i | \(0.516342\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.87689 | −0.131175 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.0540 | 0.502973 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.75379 | 0.0796354 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.4924 | −1.20049 | −0.600243 | − | 0.799818i | \(-0.704930\pi\) | ||||
−0.600243 | + | 0.799818i | \(0.704930\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −42.2462 | −1.91044 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.492423 | 0.0222227 | 0.0111114 | − | 0.999938i | \(-0.496463\pi\) | ||||
0.0111114 | + | 0.999938i | \(0.496463\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −62.4233 | −2.81140 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 19.8078 | 0.890293 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 36.7386 | 1.64795 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.68466 | 0.388779 | 0.194389 | − | 0.980924i | \(-0.437727\pi\) | ||||
0.194389 | + | 0.980924i | \(0.437727\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.56155 | 0.292565 | 0.146283 | − | 0.989243i | \(-0.453269\pi\) | ||||
0.146283 | + | 0.989243i | \(0.453269\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.3693 | 1.12892 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.4924 | −0.732454 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.6155 | −0.958091 | −0.479046 | − | 0.877790i | \(-0.659017\pi\) | ||||
−0.479046 | + | 0.877790i | \(0.659017\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.7386 | −0.961661 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.43845 | 0.0635090 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28.8769 | −1.27247 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.9309 | 1.36034 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.61553 | 0.422075 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.36932 | −0.0599909 | −0.0299954 | − | 0.999550i | \(-0.509549\pi\) | ||||
−0.0299954 | + | 0.999550i | \(0.509549\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.5464 | 1.64179 | 0.820895 | − | 0.571080i | \(-0.193475\pi\) | ||||
0.820895 | + | 0.571080i | \(0.193475\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.6847 | 0.859109 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.12311 | 0.310287 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.9309 | −0.910038 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.4924 | −1.32326 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.2462 | −0.443813 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.6307 | 0.805475 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.4924 | −1.57476 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.12311 | −0.306814 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.5616 | 1.70088 | 0.850442 | − | 0.526069i | \(-0.176335\pi\) | ||||
0.850442 | + | 0.526069i | \(0.176335\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −41.6155 | −1.78589 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.876894 | 0.0375620 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.49242 | −0.363110 | −0.181555 | − | 0.983381i | \(-0.558113\pi\) | ||||
−0.181555 | + | 0.983381i | \(0.558113\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 20.6847 | 0.882800 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.68466 | 0.327377 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.0000 | 1.27573 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.49242 | −0.190693 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.9309 | −0.463156 | −0.231578 | − | 0.972816i | \(-0.574389\pi\) | ||||
−0.231578 | + | 0.972816i | \(0.574389\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.4924 | −1.03592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 74.1080 | 3.12884 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.7538 | −0.579653 | −0.289827 | − | 0.957079i | \(-0.593598\pi\) | ||||
−0.289827 | + | 0.957079i | \(0.593598\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.4924 | −0.862123 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.0000 | 0.881917 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.7386 | 0.953253 | 0.476627 | − | 0.879106i | \(-0.341859\pi\) | ||||
0.476627 | + | 0.879106i | \(0.341859\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.00000 | −0.334790 | −0.167395 | − | 0.985890i | \(-0.553535\pi\) | ||||
−0.167395 | + | 0.985890i | \(0.553535\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.56155 | 0.107010 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.68466 | 0.153661 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.2462 | −0.468186 | −0.234093 | − | 0.972214i | \(-0.575212\pi\) | ||||
−0.234093 | + | 0.972214i | \(0.575212\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −37.1231 | −1.54278 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.1080 | −0.917192 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.4924 | −1.26287 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.2462 | 0.589008 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.06913 | −0.209225 | −0.104613 | − | 0.994513i | \(-0.533360\pi\) | ||||
−0.104613 | + | 0.994513i | \(0.533360\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.876894 | −0.0361318 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 34.2462 | 1.40870 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.7386 | −0.687373 | −0.343687 | − | 0.939084i | \(-0.611676\pi\) | ||||
−0.343687 | + | 0.939084i | \(0.611676\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −38.0540 | −1.56006 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −65.9309 | −2.69837 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.8617 | 0.566375 | 0.283188 | − | 0.959065i | \(-0.408608\pi\) | ||||
0.283188 | + | 0.959065i | \(0.408608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.3693 | −1.19800 | −0.599000 | − | 0.800749i | \(-0.704435\pi\) | ||||
−0.599000 | + | 0.800749i | \(0.704435\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.2462 | −0.661597 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.63068 | −0.106952 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.1231 | 0.857360 | 0.428680 | − | 0.903456i | \(-0.358979\pi\) | ||||
0.428680 | + | 0.903456i | \(0.358979\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −59.0540 | −2.39299 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.2462 | 0.899985 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.5464 | −1.15298 | −0.576489 | − | 0.817105i | \(-0.695578\pi\) | ||||
−0.576489 | + | 0.817105i | \(0.695578\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.0000 | −0.645182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.31534 | 0.375022 | 0.187511 | − | 0.982263i | \(-0.439958\pi\) | ||||
0.187511 | + | 0.982263i | \(0.439958\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.8769 | −1.56259 | −0.781297 | − | 0.624159i | \(-0.785442\pi\) | ||||
−0.781297 | + | 0.624159i | \(0.785442\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.06913 | −0.0830313 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −28.1080 | −1.12612 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.63068 | −0.225227 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.12311 | −0.364342 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.12311 | −0.363762 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.30019 | −0.330425 | −0.165213 | − | 0.986258i | \(-0.552831\pi\) | ||||
−0.165213 | + | 0.986258i | \(0.552831\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 29.3002 | 1.16458 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.7386 | 0.426150 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.12311 | −0.202985 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −43.6155 | −1.72540 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −50.1080 | −1.97915 | −0.989573 | − | 0.144035i | \(-0.953992\pi\) | ||||
−0.989573 | + | 0.144035i | \(0.953992\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.3002 | −1.03718 | −0.518589 | − | 0.855024i | \(-0.673543\pi\) | ||||
−0.518589 | + | 0.855024i | \(0.673543\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −38.2462 | −1.50594 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −47.0000 | −1.84776 | −0.923880 | − | 0.382682i | \(-0.875001\pi\) | ||||
−0.923880 | + | 0.382682i | \(0.875001\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.4924 | 1.19693 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.73863 | 0.264108 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.8078 | 0.462074 | 0.231037 | − | 0.972945i | \(-0.425788\pi\) | ||||
0.231037 | + | 0.972945i | \(0.425788\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27.4233 | 1.07152 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.8078 | 1.00686 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.5464 | 1.46260 | 0.731300 | − | 0.682056i | \(-0.238914\pi\) | ||||
0.731300 | + | 0.682056i | \(0.238914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.1771 | −0.940379 | −0.470190 | − | 0.882565i | \(-0.655815\pi\) | ||||
−0.470190 | + | 0.882565i | \(0.655815\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 53.3002 | 2.07001 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.68466 | 0.181663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.0540 | −0.428012 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −59.8617 | −2.31439 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.6847 | −0.798522 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.8769 | −0.496368 | −0.248184 | − | 0.968713i | \(-0.579834\pi\) | ||||
−0.248184 | + | 0.968713i | \(0.579834\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.68466 | −0.141823 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.56155 | 0.252181 | 0.126090 | − | 0.992019i | \(-0.459757\pi\) | ||||
0.126090 | + | 0.992019i | \(0.459757\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.36932 | 0.129303 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0540 | 0.423589 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.2462 | −1.31039 | −0.655197 | − | 0.755458i | \(-0.727415\pi\) | ||||
−0.655197 | + | 0.755458i | \(0.727415\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.1922 | 0.618674 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.6155 | 0.824684 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21.9309 | −0.835500 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.94602 | −0.302281 | −0.151141 | − | 0.988512i | \(-0.548295\pi\) | ||||
−0.151141 | + | 0.988512i | \(0.548295\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 38.0540 | 1.44555 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.9309 | −0.566360 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.4924 | −1.23074 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.8769 | 0.865284 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.6155 | 1.04302 | 0.521512 | − | 0.853244i | \(-0.325368\pi\) | ||||
0.521512 | + | 0.853244i | \(0.325368\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.12311 | 0.0423587 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 34.7386 | 1.30833 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 48.7386 | 1.83300 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.5076 | −0.657511 | −0.328755 | − | 0.944415i | \(-0.606629\pi\) | ||||
−0.328755 | + | 0.944415i | \(0.606629\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −35.6155 | −1.33569 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.26137 | 0.0472385 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.2462 | −0.532778 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −38.4233 | −1.43494 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.49242 | 0.354008 | 0.177004 | − | 0.984210i | \(-0.443360\pi\) | ||||
0.177004 | + | 0.984210i | \(0.443360\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −55.4773 | −2.06608 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.75379 | 0.213986 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −19.6847 | −0.731070 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.36932 | 0.0878731 | 0.0439365 | − | 0.999034i | \(-0.486010\pi\) | ||||
0.0439365 | + | 0.999034i | \(0.486010\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −77.6695 | −2.87271 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.3693 | 0.789294 | 0.394647 | − | 0.918833i | \(-0.370867\pi\) | ||||
0.394647 | + | 0.918833i | \(0.370867\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.00000 | −0.295084 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.2462 | 0.598437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.56155 | 0.204585 | 0.102293 | − | 0.994754i | \(-0.467382\pi\) | ||||
0.102293 | + | 0.994754i | \(0.467382\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.56155 | −0.241045 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.1231 | −1.14180 | −0.570898 | − | 0.821021i | \(-0.693405\pi\) | ||||
−0.570898 | + | 0.821021i | \(0.693405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0540 | 0.368349 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.2462 | 0.960299 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.7926 | 1.30783 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000 | 0.437886 | 0.218943 | − | 0.975738i | \(-0.429739\pi\) | ||||
0.218943 | + | 0.975738i | \(0.429739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.1231 | −0.624001 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.3845 | 0.596292 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.0540 | 0.583492 | 0.291746 | − | 0.956496i | \(-0.405764\pi\) | ||||
0.291746 | + | 0.956496i | \(0.405764\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 13.1231 | 0.476339 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.8617 | 0.611238 | 0.305619 | − | 0.952154i | \(-0.401137\pi\) | ||||
0.305619 | + | 0.952154i | \(0.401137\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.68466 | 0.0609887 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 45.1771 | 1.63338 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.9309 | 0.791878 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.3693 | −0.446049 | −0.223024 | − | 0.974813i | \(-0.571593\pi\) | ||||
−0.223024 | + | 0.974813i | \(0.571593\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.9848 | 0.899807 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.05398 | −0.181779 | −0.0908894 | − | 0.995861i | \(-0.528971\pi\) | ||||
−0.0908894 | + | 0.995861i | \(0.528971\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.24621 | 0.0806863 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.63068 | −0.309624 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.00000 | 0.143315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.6155 | 1.56069 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.0540 | 0.395037 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −37.8617 | −1.35134 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.5616 | 0.946817 | 0.473409 | − | 0.880843i | \(-0.343023\pi\) | ||||
0.473409 | + | 0.880843i | \(0.343023\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 66.7386 | 2.37596 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −39.3693 | −1.39981 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.8769 | −0.528294 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −34.2462 | −1.21459 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.68466 | −0.343048 | −0.171524 | − | 0.985180i | \(-0.554869\pi\) | ||||
−0.171524 | + | 0.985180i | \(0.554869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 70.5464 | 2.49575 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.3693 | 1.17905 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.8078 | −0.910736 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.73863 | −0.237506 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.1231 | −1.30680 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.12311 | −0.0746444 | −0.0373222 | − | 0.999303i | \(-0.511883\pi\) | ||||
−0.0373222 | + | 0.999303i | \(0.511883\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.4233 | 1.77060 | 0.885301 | − | 0.465019i | \(-0.153953\pi\) | ||||
0.885301 | + | 0.465019i | \(0.153953\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 69.3002 | 2.43046 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 25.7538 | 0.902116 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.56155 | 0.334516 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.3693 | 0.956361 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.6847 | −0.582299 | −0.291149 | − | 0.956678i | \(-0.594038\pi\) | ||||
−0.291149 | + | 0.956678i | \(0.594038\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.36932 | 0.152305 | 0.0761524 | − | 0.997096i | \(-0.475736\pi\) | ||||
0.0761524 | + | 0.997096i | \(0.475736\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 23.3693 | 0.813615 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.4384 | 0.536847 | 0.268424 | − | 0.963301i | \(-0.413497\pi\) | ||||
0.268424 | + | 0.963301i | \(0.413497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.5464 | 1.79028 | 0.895140 | − | 0.445785i | \(-0.147075\pi\) | ||||
0.895140 | + | 0.445785i | \(0.147075\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.75379 | −0.0608383 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.2462 | −0.562898 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.26137 | −0.0435992 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.6155 | 0.401013 | 0.200506 | − | 0.979692i | \(-0.435741\pi\) | ||||
0.200506 | + | 0.979692i | \(0.435741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.0540 | 1.03634 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −64.9848 | −2.23820 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.0540 | 0.345867 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.05398 | −0.173657 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 62.6004 | 2.14844 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.61553 | −0.0553796 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.7538 | −0.539399 | −0.269700 | − | 0.962944i | \(-0.586924\pi\) | ||||
−0.269700 | + | 0.962944i | \(0.586924\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.56155 | −0.190201 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.3693 | 1.27651 | 0.638256 | − | 0.769824i | \(-0.279656\pi\) | ||||
0.638256 | + | 0.769824i | \(0.279656\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.06913 | −0.241196 | −0.120598 | − | 0.992701i | \(-0.538481\pi\) | ||||
−0.120598 | + | 0.992701i | \(0.538481\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.7386 | −1.04757 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −47.3693 | −1.61247 | −0.806235 | − | 0.591595i | \(-0.798498\pi\) | ||||
−0.806235 | + | 0.591595i | \(0.798498\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.86174 | −0.199305 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 125.477 | 4.26143 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.6155 | 1.20817 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6847 | 0.395920 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.00000 | −0.135379 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −35.4233 | −1.19753 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.68466 | 0.327028 | 0.163514 | − | 0.986541i | \(-0.447717\pi\) | ||||
0.163514 | + | 0.986541i | \(0.447717\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −70.9157 | −2.39193 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.3153 | 1.25719 | 0.628593 | − | 0.777735i | \(-0.283631\pi\) | ||||
0.628593 | + | 0.777735i | \(0.283631\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.9309 | 0.973601 | 0.486801 | − | 0.873513i | \(-0.338164\pi\) | ||||
0.486801 | + | 0.873513i | \(0.338164\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 34.2462 | 1.15117 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.2311 | −1.51871 | −0.759355 | − | 0.650676i | \(-0.774485\pi\) | ||||
−0.759355 | + | 0.650676i | \(0.774485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.6307 | 0.691931 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.9309 | 0.835216 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.68466 | −0.290621 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.2462 | 0.743609 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.43845 | 0.315141 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.73863 | −0.224746 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −69.5464 | −2.31693 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −73.4773 | −2.44517 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.3693 | 0.843305 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.4384 | −0.379807 | −0.189904 | − | 0.981803i | \(-0.560818\pi\) | ||||
−0.189904 | + | 0.981803i | \(0.560818\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −57.8617 | −1.91915 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.876894 | 0.0290528 | 0.0145264 | − | 0.999894i | \(-0.495376\pi\) | ||||
0.0145264 | + | 0.999894i | \(0.495376\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.2462 | −0.868623 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.2311 | −0.767995 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 52.6847 | 1.73980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.3002 | −0.966524 | −0.483262 | − | 0.875476i | \(-0.660548\pi\) | ||||
−0.483262 | + | 0.875476i | \(0.660548\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 75.2311 | 2.47895 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.3693 | 1.03253 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.87689 | −0.0945917 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 65.8617 | 2.16318 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.82292 | −0.322280 | −0.161140 | − | 0.986932i | \(-0.551517\pi\) | ||||
−0.161140 | + | 0.986932i | \(0.551517\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.43845 | −0.178047 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −45.1771 | −1.47745 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.2462 | −0.955432 | −0.477716 | − | 0.878514i | \(-0.658535\pi\) | ||||
−0.477716 | + | 0.878514i | \(0.658535\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 71.5464 | 2.33483 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.3002 | 1.15075 | 0.575377 | − | 0.817889i | \(-0.304856\pi\) | ||||
0.575377 | + | 0.817889i | \(0.304856\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.75379 | −0.187369 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.73863 | 0.219208 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.9848 | −0.941881 | −0.470940 | − | 0.882165i | \(-0.656085\pi\) | ||||
−0.470940 | + | 0.882165i | \(0.656085\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.5616 | −0.602534 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −52.6695 | −1.70793 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.24621 | 0.267121 | 0.133560 | − | 0.991041i | \(-0.457359\pi\) | ||||
0.133560 | + | 0.991041i | \(0.457359\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.56155 | −0.0505307 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −70.1080 | −2.26627 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.1080 | 1.00453 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2311 | −0.975195 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42.4924 | −1.36930 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.6307 | 0.728507 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.0000 | 0.771788 | 0.385894 | − | 0.922543i | \(-0.373893\pi\) | ||||
0.385894 | + | 0.922543i | \(0.373893\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.8078 | −0.668442 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.4924 | −1.81293 | −0.906464 | − | 0.422283i | \(-0.861229\pi\) | ||||
−0.906464 | + | 0.422283i | \(0.861229\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.6847 | −0.919588 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 16.8078 | 0.538279 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.3845 | −0.396214 | −0.198107 | − | 0.980180i | \(-0.563479\pi\) | ||||
−0.198107 | + | 0.980180i | \(0.563479\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.3693 | −1.06649 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.6155 | 0.944589 | 0.472294 | − | 0.881441i | \(-0.343426\pi\) | ||||
0.472294 | + | 0.881441i | \(0.343426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.8769 | −0.665193 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 66.7386 | 2.12431 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.7538 | −0.437345 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.75379 | 0.0557109 | 0.0278555 | − | 0.999612i | \(-0.491132\pi\) | ||||
0.0278555 | + | 0.999612i | \(0.491132\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.9309 | 0.695955 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.1922 | 1.27418 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47.9157 | −1.51751 | −0.758753 | − | 0.651379i | \(-0.774191\pi\) | ||||
−0.758753 | + | 0.651379i | \(0.774191\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.61553 | 0.0511130 |
(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 | 1216.2.a.t.1.2 | 2 | ||
4.3 | odd | 2 | 1216.2.a.s.1.1 | 2 | |||
8.3 | odd | 2 | 608.2.a.h.1.2 | yes | 2 | ||
8.5 | even | 2 | 608.2.a.g.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 5472.2.a.bc.1.1 | 2 | |||
24.11 | even | 2 | 5472.2.a.bf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.a.g.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
608.2.a.h.1.2 | yes | 2 | 8.3 | odd | 2 | ||
1216.2.a.s.1.1 | 2 | 4.3 | odd | 2 | |||
1216.2.a.t.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5472.2.a.bc.1.1 | 2 | 24.5 | odd | 2 | |||
5472.2.a.bf.1.1 | 2 | 24.11 | even | 2 |