Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8112,2,Mod(1,8112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8112, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8112.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8112 = 2^{4} \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8112.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.7746461197\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{14})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1014) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.24698\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8112.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.692021 | 0.309481 | 0.154741 | − | 0.987955i | \(-0.450546\pi\) | ||||
0.154741 | + | 0.987955i | \(0.450546\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.356896 | 0.134894 | 0.0674470 | − | 0.997723i | \(-0.478515\pi\) | ||||
0.0674470 | + | 0.997723i | \(0.478515\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.93900 | 0.886142 | 0.443071 | − | 0.896486i | \(-0.353889\pi\) | ||||
0.443071 | + | 0.896486i | \(0.353889\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.692021 | −0.178679 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.71379 | 1.62833 | 0.814167 | − | 0.580631i | \(-0.197194\pi\) | ||||
0.814167 | + | 0.580631i | \(0.197194\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.20775 | −1.65357 | −0.826786 | − | 0.562517i | \(-0.809833\pi\) | ||||
−0.826786 | + | 0.562517i | \(0.809833\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.356896 | −0.0778811 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.39612 | −0.499627 | −0.249813 | − | 0.968294i | \(-0.580369\pi\) | ||||
−0.249813 | + | 0.968294i | \(0.580369\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.52111 | −0.904221 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.82908 | 1.45382 | 0.726912 | − | 0.686730i | \(-0.240955\pi\) | ||||
0.726912 | + | 0.686730i | \(0.240955\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.76271 | −0.496197 | −0.248099 | − | 0.968735i | \(-0.579806\pi\) | ||||
−0.248099 | + | 0.968735i | \(0.579806\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.93900 | −0.511614 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.246980 | 0.0417472 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0978 | −1.66007 | −0.830037 | − | 0.557708i | \(-0.811681\pi\) | ||||
−0.830037 | + | 0.557708i | \(0.811681\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.89008 | −0.763703 | −0.381851 | − | 0.924224i | \(-0.624713\pi\) | ||||
−0.381851 | + | 0.924224i | \(0.624713\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.59179 | −1.00524 | −0.502620 | − | 0.864508i | \(-0.667630\pi\) | ||||
−0.502620 | + | 0.864508i | \(0.667630\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.692021 | 0.103160 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.98792 | 0.727563 | 0.363781 | − | 0.931484i | \(-0.381486\pi\) | ||||
0.363781 | + | 0.931484i | \(0.381486\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.87263 | −0.981804 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.71379 | −0.940119 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.88769 | −1.22082 | −0.610409 | − | 0.792086i | \(-0.708995\pi\) | ||||
−0.610409 | + | 0.792086i | \(0.708995\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.03385 | 0.274245 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.20775 | 0.954690 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.64310 | 0.213914 | 0.106957 | − | 0.994264i | \(-0.465889\pi\) | ||||
0.106957 | + | 0.994264i | \(0.465889\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.49396 | −0.831466 | −0.415733 | − | 0.909487i | \(-0.636475\pi\) | ||||
−0.415733 | + | 0.909487i | \(0.636475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.356896 | 0.0449647 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.5254 | 1.65239 | 0.826196 | − | 0.563382i | \(-0.190500\pi\) | ||||
0.826196 | + | 0.563382i | \(0.190500\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.39612 | 0.288459 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.81163 | 0.808391 | 0.404196 | − | 0.914673i | \(-0.367551\pi\) | ||||
0.404196 | + | 0.914673i | \(0.367551\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.18598 | −0.372891 | −0.186445 | − | 0.982465i | \(-0.559697\pi\) | ||||
−0.186445 | + | 0.982465i | \(0.559697\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.52111 | 0.522052 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.04892 | 0.119535 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0465 | −1.69287 | −0.846433 | − | 0.532495i | \(-0.821255\pi\) | ||||
−0.846433 | + | 0.532495i | \(0.821255\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.8267 | −1.62744 | −0.813720 | − | 0.581256i | \(-0.802561\pi\) | ||||
−0.813720 | + | 0.581256i | \(0.802561\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.64609 | 0.503939 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.82908 | −0.839366 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.396125 | −0.0419891 | −0.0209946 | − | 0.999780i | \(-0.506683\pi\) | ||||
−0.0209946 | + | 0.999780i | \(0.506683\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.76271 | 0.286480 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.98792 | −0.511750 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.417895 | 0.0424308 | 0.0212154 | − | 0.999775i | \(-0.493246\pi\) | ||||
0.0212154 | + | 0.999775i | \(0.493246\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.93900 | 0.295381 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0151 | 0.996536 | 0.498268 | − | 0.867023i | \(-0.333970\pi\) | ||||
0.498268 | + | 0.867023i | \(0.333970\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.62565 | 0.948443 | 0.474222 | − | 0.880406i | \(-0.342730\pi\) | ||||
0.474222 | + | 0.880406i | \(0.342730\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.246980 | −0.0241027 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.63102 | 0.641045 | 0.320523 | − | 0.947241i | \(-0.396141\pi\) | ||||
0.320523 | + | 0.947241i | \(0.396141\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.9879 | −1.24402 | −0.622008 | − | 0.783011i | \(-0.713683\pi\) | ||||
−0.622008 | + | 0.783011i | \(0.713683\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.0978 | 0.958444 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.792249 | 0.0745285 | 0.0372643 | − | 0.999305i | \(-0.488136\pi\) | ||||
0.0372643 | + | 0.999305i | \(0.488136\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.65817 | −0.154625 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.39612 | 0.219652 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.36227 | −0.214752 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.89008 | 0.440924 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.58881 | −0.589321 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.2174 | 1.61654 | 0.808268 | − | 0.588815i | \(-0.200405\pi\) | ||||
0.808268 | + | 0.588815i | \(0.200405\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.59179 | 0.580375 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.73556 | −0.239007 | −0.119504 | − | 0.992834i | \(-0.538130\pi\) | ||||
−0.119504 | + | 0.992834i | \(0.538130\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.57242 | −0.223057 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.692021 | −0.0595597 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.64742 | 0.653363 | 0.326681 | − | 0.945135i | \(-0.394070\pi\) | ||||
0.326681 | + | 0.945135i | \(0.394070\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.38404 | −0.287031 | −0.143515 | − | 0.989648i | \(-0.545841\pi\) | ||||
−0.143515 | + | 0.989648i | \(0.545841\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.98792 | −0.420059 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.41789 | 0.449932 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.87263 | 0.566845 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.8170 | −1.70540 | −0.852698 | − | 0.522405i | \(-0.825035\pi\) | ||||
−0.852698 | + | 0.522405i | \(0.825035\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.895461 | 0.0728715 | 0.0364358 | − | 0.999336i | \(-0.488400\pi\) | ||||
0.0364358 | + | 0.999336i | \(0.488400\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.71379 | 0.542778 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.91185 | −0.153564 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.59179 | 0.685700 | 0.342850 | − | 0.939390i | \(-0.388608\pi\) | ||||
0.342850 | + | 0.939390i | \(0.388608\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.88769 | 0.704840 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.855167 | −0.0673966 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.72587 | −0.135181 | −0.0675904 | − | 0.997713i | \(-0.521531\pi\) | ||||
−0.0675904 | + | 0.997713i | \(0.521531\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.03385 | −0.158335 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.1400 | −1.63587 | −0.817933 | − | 0.575314i | \(-0.804880\pi\) | ||||
−0.817933 | + | 0.575314i | \(0.804880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.20775 | −0.551190 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.35450 | 0.711210 | 0.355605 | − | 0.934636i | \(-0.384275\pi\) | ||||
0.355605 | + | 0.934636i | \(0.384275\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.61356 | −0.121974 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.64310 | −0.123503 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.17523 | −0.237328 | −0.118664 | − | 0.992934i | \(-0.537861\pi\) | ||||
−0.118664 | + | 0.992934i | \(0.537861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.7995 | −1.47169 | −0.735844 | − | 0.677151i | \(-0.763214\pi\) | ||||
−0.735844 | + | 0.677151i | \(0.763214\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.49396 | 0.480047 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.98792 | −0.513762 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.7318 | 1.44294 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.356896 | −0.0259604 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.2620 | −1.10432 | −0.552161 | − | 0.833737i | \(-0.686197\pi\) | ||||
−0.552161 | + | 0.833737i | \(0.686197\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.76809 | 0.343214 | 0.171607 | − | 0.985165i | \(-0.445104\pi\) | ||||
0.171607 | + | 0.985165i | \(0.445104\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.2349 | 0.871700 | 0.435850 | − | 0.900019i | \(-0.356448\pi\) | ||||
0.435850 | + | 0.900019i | \(0.356448\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.8485 | 0.839915 | 0.419958 | − | 0.907544i | \(-0.362045\pi\) | ||||
0.419958 | + | 0.907544i | \(0.362045\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.5254 | −0.954009 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.79417 | 0.196112 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.38404 | −0.236352 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.39612 | −0.166542 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −21.1836 | −1.46530 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2620 | 1.18837 | 0.594184 | − | 0.804329i | \(-0.297475\pi\) | ||||
0.594184 | + | 0.804329i | \(0.297475\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.81163 | −0.466725 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.56166 | −0.311103 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.985999 | −0.0669340 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.18598 | 0.215289 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.76809 | −0.453225 | −0.226612 | − | 0.973985i | \(-0.572765\pi\) | ||||
−0.226612 | + | 0.973985i | \(0.572765\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.52111 | −0.301407 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.6799 | −1.57169 | −0.785846 | − | 0.618422i | \(-0.787772\pi\) | ||||
−0.785846 | + | 0.618422i | \(0.787772\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.29829 | −0.548366 | −0.274183 | − | 0.961677i | \(-0.588407\pi\) | ||||
−0.274183 | + | 0.961677i | \(0.588407\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.04892 | −0.0690137 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.9651 | −1.57000 | −0.785002 | − | 0.619493i | \(-0.787338\pi\) | ||||
−0.785002 | + | 0.619493i | \(0.787338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.45175 | 0.225167 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.0465 | 0.977377 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.6160 | −0.816058 | −0.408029 | − | 0.912969i | \(-0.633784\pi\) | ||||
−0.408029 | + | 0.912969i | \(0.633784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.3937 | 1.70017 | 0.850085 | − | 0.526646i | \(-0.176551\pi\) | ||||
0.850085 | + | 0.526646i | \(0.176551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.75600 | −0.303850 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.8267 | 0.939603 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.0344 | 1.89576 | 0.947879 | − | 0.318632i | \(-0.103223\pi\) | ||||
0.947879 | + | 0.318632i | \(0.103223\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.04221 | −0.442740 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.64609 | −0.290949 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.2620 | 0.702507 | 0.351254 | − | 0.936280i | \(-0.385756\pi\) | ||||
0.351254 | + | 0.936280i | \(0.385756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.60388 | −0.223934 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.82908 | 0.484608 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.54958 | 0.342202 | 0.171101 | − | 0.985254i | \(-0.445268\pi\) | ||||
0.171101 | + | 0.985254i | \(0.445268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.15047 | −0.377821 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.396125 | 0.0242424 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.6872 | 1.01744 | 0.508719 | − | 0.860932i | \(-0.330119\pi\) | ||||
0.508719 | + | 0.860932i | \(0.330119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.61356 | 0.401745 | 0.200873 | − | 0.979617i | \(-0.435622\pi\) | ||||
0.200873 | + | 0.979617i | \(0.435622\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.2875 | −0.801269 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.7995 | −1.30981 | −0.654904 | − | 0.755712i | \(-0.727291\pi\) | ||||
−0.654904 | + | 0.755712i | \(0.727291\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.76271 | −0.165399 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.5918 | 1.22840 | 0.614202 | − | 0.789149i | \(-0.289478\pi\) | ||||
0.614202 | + | 0.789149i | \(0.289478\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0121 | 0.773488 | 0.386744 | − | 0.922187i | \(-0.373600\pi\) | ||||
0.386744 | + | 0.922187i | \(0.373600\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.98792 | 0.295459 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.74525 | −0.103019 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.0750 | 1.65147 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.417895 | −0.0244974 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.9390 | −0.872746 | −0.436373 | − | 0.899766i | \(-0.643737\pi\) | ||||
−0.436373 | + | 0.899766i | \(0.643737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.13706 | 0.0662024 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.93900 | −0.170538 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.35258 | −0.135601 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.0151 | −0.575350 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.49396 | −0.257323 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.0301 | −1.48562 | −0.742809 | − | 0.669503i | \(-0.766507\pi\) | ||||
−0.742809 | + | 0.669503i | \(0.766507\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.62565 | −0.547584 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.81163 | 0.272842 | 0.136421 | − | 0.990651i | \(-0.456440\pi\) | ||||
0.136421 | + | 0.990651i | \(0.456440\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.0411 | −1.47193 | −0.735966 | − | 0.677018i | \(-0.763272\pi\) | ||||
−0.735966 | + | 0.677018i | \(0.763272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.246980 | 0.0139157 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.5211 | −0.647090 | −0.323545 | − | 0.946213i | \(-0.604875\pi\) | ||||
−0.323545 | + | 0.946213i | \(0.604875\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.0097 | 1.28830 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.63102 | −0.370108 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −48.3913 | −2.69257 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.9879 | 0.718234 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.78017 | 0.0981438 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.43834 | −0.188988 | −0.0944940 | − | 0.995525i | \(-0.530123\pi\) | ||||
−0.0944940 | + | 0.995525i | \(0.530123\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.0978 | −0.553358 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.35988 | 0.511385 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.20105 | 0.446739 | 0.223370 | − | 0.974734i | \(-0.428294\pi\) | ||||
0.223370 | + | 0.974734i | \(0.428294\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.792249 | −0.0430291 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.11960 | −0.439701 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.95108 | −0.267333 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.65817 | 0.0892729 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.86294 | −0.422105 | −0.211052 | − | 0.977475i | \(-0.567689\pi\) | ||||
−0.211052 | + | 0.977475i | \(0.567689\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.7245 | −1.00230 | −0.501151 | − | 0.865360i | \(-0.667090\pi\) | ||||
−0.501151 | + | 0.865360i | \(0.667090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.5448 | −1.67896 | −0.839480 | − | 0.543391i | \(-0.817140\pi\) | ||||
−0.839480 | + | 0.543391i | \(0.817140\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.71379 | 0.250182 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.39612 | −0.126816 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.39612 | −0.126463 | −0.0632313 | − | 0.997999i | \(-0.520141\pi\) | ||||
−0.0632313 | + | 0.997999i | \(0.520141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 32.9517 | 1.73430 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.36227 | 0.123987 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.20477 | −0.115403 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.00431187 | 0.000225078 0 | 0.000112539 | − | 1.00000i | \(-0.499964\pi\) | ||||
0.000112539 | 1.00000i | \(0.499964\pi\) | ||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.89008 | −0.254568 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.17198 | −0.164681 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.3129 | −1.67310 | −0.836549 | − | 0.547892i | \(-0.815430\pi\) | ||||
−0.836549 | + | 0.547892i | \(0.815430\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.58881 | 0.340245 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.7560 | −1.01480 | −0.507399 | − | 0.861711i | \(-0.669393\pi\) | ||||
−0.507399 | + | 0.861711i | \(0.669393\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.2174 | −0.933308 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.8116 | −1.47221 | −0.736103 | − | 0.676870i | \(-0.763336\pi\) | ||||
−0.736103 | + | 0.676870i | \(0.763336\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.725873 | 0.0369939 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.59179 | −0.335080 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.7821 | 1.76352 | 0.881761 | − | 0.471697i | \(-0.156358\pi\) | ||||
0.881761 | + | 0.471697i | \(0.156358\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16.0871 | −0.813559 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.73556 | 0.137991 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.4125 | −0.523911 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.15346 | −0.258645 | −0.129322 | − | 0.991603i | \(-0.541280\pi\) | ||||
−0.129322 | + | 0.991603i | \(0.541280\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.57242 | 0.128782 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.3250 | 0.665417 | 0.332708 | − | 0.943030i | \(-0.392038\pi\) | ||||
0.332708 | + | 0.943030i | \(0.392038\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.692021 | 0.0343868 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.6775 | −1.47106 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.0237 | −1.18789 | −0.593947 | − | 0.804504i | \(-0.702431\pi\) | ||||
−0.593947 | + | 0.804504i | \(0.702431\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.64742 | −0.377219 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.586417 | 0.0288557 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.2604 | −0.503663 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.38404 | 0.165717 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.8049 | −0.674415 | −0.337207 | − | 0.941430i | \(-0.609482\pi\) | ||||
−0.337207 | + | 0.941430i | \(0.609482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.72587 | 0.376536 | 0.188268 | − | 0.982118i | \(-0.439713\pi\) | ||||
0.188268 | + | 0.982118i | \(0.439713\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.98792 | 0.242521 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −30.3538 | −1.47237 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.31767 | −0.112160 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.640120 | −0.0308335 | −0.0154168 | − | 0.999881i | \(-0.504907\pi\) | ||||
−0.0154168 | + | 0.999881i | \(0.504907\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.2760 | 1.02246 | 0.511231 | − | 0.859443i | \(-0.329190\pi\) | ||||
0.511231 | + | 0.859443i | \(0.329190\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.41789 | −0.259768 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.2707 | 0.826168 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.7181 | −0.607002 | −0.303501 | − | 0.952831i | \(-0.598156\pi\) | ||||
−0.303501 | + | 0.952831i | \(0.598156\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.87263 | −0.327268 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.5972 | −1.07362 | −0.536812 | − | 0.843702i | \(-0.680372\pi\) | ||||
−0.536812 | + | 0.843702i | \(0.680372\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.274127 | −0.0129949 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.8170 | 0.984610 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.6474 | 0.549676 | 0.274838 | − | 0.961491i | \(-0.411376\pi\) | ||||
0.274838 | + | 0.961491i | \(0.411376\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.3720 | −0.676749 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.895461 | −0.0420724 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.1890 | −0.991178 | −0.495589 | − | 0.868557i | \(-0.665048\pi\) | ||||
−0.495589 | + | 0.868557i | \(0.665048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.71379 | −0.313373 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.0694 | 1.12102 | 0.560511 | − | 0.828147i | \(-0.310605\pi\) | ||||
0.560511 | + | 0.828147i | \(0.310605\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1715 | 0.844502 | 0.422251 | − | 0.906479i | \(-0.361240\pi\) | ||||
0.422251 | + | 0.906479i | \(0.361240\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.91185 | 0.0886601 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.93123 | 0.135641 | 0.0678206 | − | 0.997698i | \(-0.478395\pi\) | ||||
0.0678206 | + | 0.997698i | \(0.478395\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.82717 | 0.222898 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.59179 | −0.395889 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.3733 | −0.890785 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 32.5870 | 1.49519 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.88769 | −0.406939 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.7090 | 1.40313 | 0.701565 | − | 0.712605i | \(-0.252485\pi\) | ||||
0.701565 | + | 0.712605i | \(0.252485\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.855167 | 0.0389114 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.289192 | 0.0131315 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.1497 | −1.09433 | −0.547164 | − | 0.837025i | \(-0.684293\pi\) | ||||
−0.547164 | + | 0.837025i | \(0.684293\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.72587 | 0.0780467 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.5972 | −0.658761 | −0.329381 | − | 0.944197i | \(-0.606840\pi\) | ||||
−0.329381 | + | 0.944197i | \(0.606840\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 52.5628 | 2.36731 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.03385 | 0.0914148 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.43104 | 0.109047 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.85517 | −0.306879 | −0.153440 | − | 0.988158i | \(-0.549035\pi\) | ||||
−0.153440 | + | 0.988158i | \(0.549035\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.1400 | 0.944468 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.7332 | 1.19197 | 0.595987 | − | 0.802994i | \(-0.296761\pi\) | ||||
0.595987 | + | 0.802994i | \(0.296761\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.93064 | 0.308409 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.6595 | −0.915716 | −0.457858 | − | 0.889025i | \(-0.651383\pi\) | ||||
−0.457858 | + | 0.889025i | \(0.651383\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.13706 | −0.0503007 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.20775 | 0.318230 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.66115 | 0.293525 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.6595 | 0.644724 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.35450 | −0.410617 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0965 | −0.661390 | −0.330695 | − | 0.943738i | \(-0.607283\pi\) | ||||
−0.330695 | + | 0.943738i | \(0.607283\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.0349168 | −0.00152680 | −0.000763402 | − | 1.00000i | \(-0.500243\pi\) | ||||
−0.000763402 | 1.00000i | \(0.500243\pi\) | ||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.61356 | 0.0704217 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.5483 | −0.807975 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.2586 | −0.750373 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.64310 | 0.0713046 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.58881 | 0.198392 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.17523 | 0.137021 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.1987 | −0.870018 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0858 | 0.562600 | 0.281300 | − | 0.959620i | \(-0.409234\pi\) | ||||
0.281300 | + | 0.959620i | \(0.409234\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19.7995 | 0.849680 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.98792 | −0.385000 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.97584 | 0.255508 | 0.127754 | − | 0.991806i | \(-0.459223\pi\) | ||||
0.127754 | + | 0.991806i | \(0.459223\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.49396 | −0.277155 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −56.4301 | −2.40400 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.37004 | −0.228357 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.98792 | 0.296621 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.4397 | −0.442343 | −0.221171 | − | 0.975235i | \(-0.570988\pi\) | ||||
−0.221171 | + | 0.975235i | \(0.570988\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.7318 | −0.833079 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.66056 | 0.238564 | 0.119282 | − | 0.992860i | \(-0.461941\pi\) | ||||
0.119282 | + | 0.992860i | \(0.461941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.548253 | 0.0230652 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.356896 | 0.0149882 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.6568 | 0.865980 | 0.432990 | − | 0.901399i | \(-0.357459\pi\) | ||||
0.432990 | + | 0.901399i | \(0.357459\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.3672 | −1.85671 | −0.928354 | − | 0.371697i | \(-0.878776\pi\) | ||||
−0.928354 | + | 0.371697i | \(0.878776\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.2620 | 0.637581 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.8331 | 0.451773 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.4426 | 1.22571 | 0.612857 | − | 0.790194i | \(-0.290020\pi\) | ||||
0.612857 | + | 0.790194i | \(0.290020\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.76809 | −0.198155 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.29159 | −0.219532 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.1209 | −1.08182 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.5636 | 0.807475 | 0.403738 | − | 0.914875i | \(-0.367711\pi\) | ||||
0.403738 | + | 0.914875i | \(0.367711\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 19.9129 | 0.820498 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.2349 | −0.503276 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.8793 | −0.446761 | −0.223380 | − | 0.974731i | \(-0.571709\pi\) | ||||
−0.223380 | + | 0.974731i | \(0.571709\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.65817 | 0.0679783 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.8485 | −0.484925 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.0543 | −0.655961 | −0.327980 | − | 0.944685i | \(-0.606368\pi\) | ||||
−0.327980 | + | 0.944685i | \(0.606368\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.8955 | 0.526017 | 0.263008 | − | 0.964794i | \(-0.415285\pi\) | ||||
0.263008 | + | 0.964794i | \(0.415285\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.5254 | 0.550798 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.63474 | −0.0664618 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.4741 | −1.80515 | −0.902574 | − | 0.430534i | \(-0.858325\pi\) | ||||
−0.902574 | + | 0.430534i | \(0.858325\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.79417 | −0.113225 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.0253 | 1.69739 | 0.848694 | − | 0.528884i | \(-0.177390\pi\) | ||||
0.848694 | + | 0.528884i | \(0.177390\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.38404 | 0.136458 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.6655 | −0.670926 | −0.335463 | − | 0.942053i | \(-0.608893\pi\) | ||||
−0.335463 | + | 0.942053i | \(0.608893\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.7512 | −1.59774 | −0.798868 | − | 0.601506i | \(-0.794568\pi\) | ||||
−0.798868 | + | 0.601506i | \(0.794568\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.39612 | 0.0961532 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.141375 | −0.00566408 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.0459 | 0.721837 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.1836 | 0.845991 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −67.7948 | −2.70315 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.5767 | −0.580290 | −0.290145 | − | 0.956983i | \(-0.593704\pi\) | ||||
−0.290145 | + | 0.956983i | \(0.593704\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.2620 | −0.686105 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.6069 | 0.500288 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.81163 | 0.269464 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.4349 | 1.51809 | 0.759043 | − | 0.651040i | \(-0.225667\pi\) | ||||
0.759043 | + | 0.651040i | \(0.225667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.04221 | 0.0411009 | 0.0205504 | − | 0.999789i | \(-0.493458\pi\) | ||||
0.0205504 | + | 0.999789i | \(0.493458\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.56166 | 0.179615 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.1608 | 1.10711 | 0.553557 | − | 0.832811i | \(-0.313270\pi\) | ||||
0.553557 | + | 0.832811i | \(0.313270\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.82908 | 0.189558 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.985999 | 0.0386444 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.6203 | 0.415603 | 0.207802 | − | 0.978171i | \(-0.433369\pi\) | ||||
0.207802 | + | 0.978171i | \(0.433369\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.89307 | −0.0739683 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.18598 | −0.124297 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.3629 | 1.57231 | 0.786157 | − | 0.618027i | \(-0.212068\pi\) | ||||
0.786157 | + | 0.618027i | \(0.212068\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −31.9168 | −1.24142 | −0.620709 | − | 0.784041i | \(-0.713155\pi\) | ||||
−0.620709 | + | 0.784041i | \(0.713155\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.78017 | −0.0690319 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.7595 | −0.726369 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.76809 | 0.261669 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.0858 | −0.736797 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.82802 | 0.147559 | 0.0737797 | − | 0.997275i | \(-0.476494\pi\) | ||||
0.0737797 | + | 0.997275i | \(0.476494\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.52111 | 0.174017 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.78927 | 0.0687670 | 0.0343835 | − | 0.999409i | \(-0.489053\pi\) | ||||
0.0343835 | + | 0.999409i | \(0.489053\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.149145 | 0.00572366 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.6799 | 0.907417 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.759725 | −0.0290701 | −0.0145350 | − | 0.999894i | \(-0.504627\pi\) | ||||
−0.0145350 | + | 0.999894i | \(0.504627\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.29218 | 0.202204 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.29829 | 0.316600 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.65950 | −0.177256 | −0.0886278 | − | 0.996065i | \(-0.528248\pi\) | ||||
−0.0886278 | + | 0.996065i | \(0.528248\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.04892 | 0.0398451 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.34183 | −0.0888307 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.8310 | −1.24356 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.9651 | 0.906443 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.3284 | −0.918872 | −0.459436 | − | 0.888211i | \(-0.651948\pi\) | ||||
−0.459436 | + | 0.888211i | \(0.651948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 72.7827 | 2.74505 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.45175 | −0.130000 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.57434 | 0.134427 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.3927 | −1.10386 | −0.551932 | − | 0.833889i | \(-0.686109\pi\) | ||||
−0.551932 | + | 0.833889i | \(0.686109\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.0465 | −0.564289 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.61979 | 0.247913 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.6160 | 0.471152 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 51.4878 | 1.92017 | 0.960086 | − | 0.279704i | \(-0.0902363\pi\) | ||||
0.960086 | + | 0.279704i | \(0.0902363\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.43535 | 0.127939 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −26.3937 | −0.981593 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −35.3961 | −1.31458 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.67324 | 0.136233 | 0.0681164 | − | 0.997677i | \(-0.478301\pi\) | ||||
0.0681164 | + | 0.997677i | \(0.478301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.2559 | −1.63686 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.3612 | 0.678187 | 0.339093 | − | 0.940753i | \(-0.389880\pi\) | ||||
0.339093 | + | 0.940753i | \(0.389880\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.75600 | 0.175428 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.7512 | 1.46425 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.68233 | −0.0618856 | −0.0309428 | − | 0.999521i | \(-0.509851\pi\) | ||||
−0.0309428 | + | 0.999521i | \(0.509851\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.2935 | −1.77172 | −0.885858 | − | 0.463956i | \(-0.846430\pi\) | ||||
−0.885858 | + | 0.463956i | \(0.846430\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.4058 | −0.527788 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.8267 | −0.542480 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.36658 | 0.0864731 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.7011 | −0.426980 | −0.213490 | − | 0.976945i | \(-0.568483\pi\) | ||||
−0.213490 | + | 0.976945i | \(0.568483\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −30.0344 | −1.09452 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.619678 | 0.0225524 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.1836 | 0.915313 | 0.457657 | − | 0.889129i | \(-0.348689\pi\) | ||||
0.457657 | + | 0.889129i | \(0.348689\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.04221 | 0.255616 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.4155 | 0.812561 | 0.406281 | − | 0.913748i | \(-0.366826\pi\) | ||||
0.406281 | + | 0.913748i | \(0.366826\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.63533 | −0.167810 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.64609 | 0.167980 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.132751 | −0.00478714 | −0.00239357 | − | 0.999997i | \(-0.500762\pi\) | ||||
−0.00239357 | + | 0.999997i | \(0.500762\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.2620 | −0.405593 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.0694 | −1.72893 | −0.864467 | − | 0.502689i | \(-0.832344\pi\) | ||||
−0.864467 | + | 0.502689i | \(0.832344\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.4905 | 0.448672 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.60388 | 0.129288 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.2465 | 1.26284 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.0194 | 0.716350 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.82908 | −0.279789 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.94571 | 0.212211 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.20908 | −0.221330 | −0.110665 | − | 0.993858i | \(-0.535298\pi\) | ||||
−0.110665 | + | 0.993858i | \(0.535298\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.54958 | −0.197570 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.282750 | 0.0100534 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.15047 | 0.218135 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.327830 | 0.0116123 | 0.00580616 | − | 0.999983i | \(-0.498152\pi\) | ||||
0.00580616 | + | 0.999983i | \(0.498152\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.4878 | 1.18471 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.396125 | −0.0139964 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.36360 | −0.330434 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.591794 | −0.0208580 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.6872 | −0.587419 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.4383 | −1.31626 | −0.658131 | − | 0.752904i | \(-0.728653\pi\) | ||||
−0.658131 | + | 0.752904i | \(0.728653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.1448 | −0.602037 | −0.301018 | − | 0.953618i | \(-0.597327\pi\) | ||||
−0.301018 | + | 0.953618i | \(0.597327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.61356 | −0.231948 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.19434 | −0.0418360 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47.5120 | 1.66223 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.7885 | −0.620824 | −0.310412 | − | 0.950602i | \(-0.600467\pi\) | ||||
−0.310412 | + | 0.950602i | \(0.600467\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2301 | −0.426315 | −0.213157 | − | 0.977018i | \(-0.568375\pi\) | ||||
−0.213157 | + | 0.977018i | \(0.568375\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.2875 | 0.462613 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.5623 | −0.715020 | −0.357510 | − | 0.933909i | \(-0.616374\pi\) | ||||
−0.357510 | + | 0.933909i | \(0.616374\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.4470 | −0.883809 | −0.441905 | − | 0.897062i | \(-0.645697\pi\) | ||||
−0.441905 | + | 0.897062i | \(0.645697\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.7995 | 0.756218 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −46.1414 | −1.59870 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.6294 | −0.506270 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.76271 | 0.0954932 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −5.76676 | −0.199091 | −0.0995453 | − | 0.995033i | \(-0.531739\pi\) | ||||
−0.0995453 | + | 0.995033i | \(0.531739\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.2946 | 1.11361 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −20.5918 | −0.709219 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.843085 | −0.0289688 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.0121 | −0.446573 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.1957 | 0.829417 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.1728 | −0.724944 | −0.362472 | − | 0.931995i | \(-0.618067\pi\) | ||||
−0.362472 | + | 0.931995i | \(0.618067\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.98792 | −0.170583 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0086 | 0.410207 | 0.205103 | − | 0.978740i | \(-0.434247\pi\) | ||||
0.205103 | + | 0.978740i | \(0.434247\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.66296 | 0.0567393 | 0.0283697 | − | 0.999598i | \(-0.490968\pi\) | ||||
0.0283697 | + | 0.999598i | \(0.490968\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.74525 | 0.0594780 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.8323 | 0.811262 | 0.405631 | − | 0.914037i | \(-0.367052\pi\) | ||||
0.405631 | + | 0.914037i | \(0.367052\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.47352 | 0.220106 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −28.0750 | −0.953477 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −44.2218 | −1.50012 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.417895 | 0.0141436 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.35152 | −0.0794959 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.3177 | −1.42897 | −0.714483 | − | 0.699653i | \(-0.753338\pi\) | ||||
−0.714483 | + | 0.699653i | \(0.753338\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.9390 | 0.503880 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.2741 | 0.750434 | 0.375217 | − | 0.926937i | \(-0.377568\pi\) | ||||
0.375217 | + | 0.926937i | \(0.377568\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.54229 | 0.287471 | 0.143735 | − | 0.989616i | \(-0.454089\pi\) | ||||
0.143735 | + | 0.989616i | \(0.454089\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.13706 | −0.0382220 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.9142 | 0.635078 | 0.317539 | − | 0.948245i | \(-0.397144\pi\) | ||||
0.317539 | + | 0.948245i | \(0.397144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.50173 | 0.218061 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.93900 | 0.0984602 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35.9517 | −1.20308 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.19733 | −0.0734485 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.6295 | −0.721384 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −59.6701 | −1.98790 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.35258 | 0.0782891 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.7017 | −0.455460 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.9517 | −0.463258 | −0.231629 | − | 0.972804i | \(-0.574405\pi\) | ||||
−0.231629 | + | 0.972804i | \(0.574405\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.0151 | 0.332179 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.0422 | −1.49232 | −0.746158 | − | 0.665769i | \(-0.768103\pi\) | ||||
−0.746158 | + | 0.665769i | \(0.768103\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.5757 | −1.44214 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.49396 | 0.148566 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.976311 | −0.0322406 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.9976 | −1.31940 | −0.659700 | − | 0.751529i | \(-0.729317\pi\) | ||||
−0.659700 | + | 0.751529i | \(0.729317\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 26.0301 | 0.857722 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.6534 | 1.50107 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.62565 | 0.316148 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 34.6848 | 1.13797 | 0.568986 | − | 0.822347i | \(-0.307336\pi\) | ||||
0.568986 | + | 0.822347i | \(0.307336\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.5362 | 1.62348 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.81163 | −0.157526 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.6549 | 0.446562 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.1260 | −0.624821 | −0.312410 | − | 0.949947i | \(-0.601136\pi\) | ||||
−0.312410 | + | 0.949947i | \(0.601136\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.0411 | 0.849821 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.5972 | −0.736647 | −0.368323 | − | 0.929698i | \(-0.620068\pi\) | ||||
−0.368323 | + | 0.929698i | \(0.620068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.7172 | 0.381566 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.246980 | −0.00803425 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.4359 | 0.891548 | 0.445774 | − | 0.895145i | \(-0.352928\pi\) | ||||
0.445774 | + | 0.895145i | \(0.352928\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.5211 | 0.373597 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.84787 | −0.0598584 | −0.0299292 | − | 0.999552i | \(-0.509528\pi\) | ||||
−0.0299292 | + | 0.999552i | \(0.509528\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.5617 | −0.341767 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.0097 | −0.743798 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.72933 | 0.0881347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.3674 | −0.753788 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.63102 | 0.213682 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.29962 | 0.106218 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.88471 | 0.285713 | 0.142856 | − | 0.989743i | \(-0.454371\pi\) | ||||
0.142856 | + | 0.989743i | \(0.454371\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 48.3913 | 1.55455 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.0863 | −1.12597 | −0.562987 | − | 0.826466i | \(-0.690348\pi\) | ||||
−0.562987 | + | 0.826466i | \(0.690348\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.20775 | −0.0387187 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.33704 | −0.266726 | −0.133363 | − | 0.991067i | \(-0.542578\pi\) | ||||
−0.133363 | + | 0.991067i | \(0.542578\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.16421 | −0.0372083 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.9879 | −0.414672 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 55.6051 | 1.77353 | 0.886763 | − | 0.462224i | \(-0.152949\pi\) | ||||
0.886763 | + | 0.462224i | \(0.152949\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.46681 | 0.269775 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.78017 | −0.0566634 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.7948 | 0.502244 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.5967 | 1.38489 | 0.692447 | − | 0.721468i | \(-0.256532\pi\) | ||||
0.692447 | + | 0.721468i | \(0.256532\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.43834 | 0.109112 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.19939 | 0.259938 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.4590 | 0.711285 | 0.355643 | − | 0.934622i | \(-0.384262\pi\) | ||||
0.355643 | + | 0.934622i | \(0.384262\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.0978 | 0.319481 |
(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 | 8112.2.a.bz.1.3 | 3 | ||
4.3 | odd | 2 | 1014.2.a.o.1.3 | yes | 3 | ||
12.11 | even | 2 | 3042.2.a.bd.1.1 | 3 | |||
13.12 | even | 2 | 8112.2.a.ce.1.1 | 3 | |||
52.3 | odd | 6 | 1014.2.e.k.529.3 | 6 | |||
52.7 | even | 12 | 1014.2.i.g.361.6 | 12 | |||
52.11 | even | 12 | 1014.2.i.g.823.3 | 12 | |||
52.15 | even | 12 | 1014.2.i.g.823.4 | 12 | |||
52.19 | even | 12 | 1014.2.i.g.361.1 | 12 | |||
52.23 | odd | 6 | 1014.2.e.m.529.1 | 6 | |||
52.31 | even | 4 | 1014.2.b.g.337.1 | 6 | |||
52.35 | odd | 6 | 1014.2.e.k.991.3 | 6 | |||
52.43 | odd | 6 | 1014.2.e.m.991.1 | 6 | |||
52.47 | even | 4 | 1014.2.b.g.337.6 | 6 | |||
52.51 | odd | 2 | 1014.2.a.m.1.1 | ✓ | 3 | ||
156.47 | odd | 4 | 3042.2.b.r.1351.1 | 6 | |||
156.83 | odd | 4 | 3042.2.b.r.1351.6 | 6 | |||
156.155 | even | 2 | 3042.2.a.be.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1014.2.a.m.1.1 | ✓ | 3 | 52.51 | odd | 2 | ||
1014.2.a.o.1.3 | yes | 3 | 4.3 | odd | 2 | ||
1014.2.b.g.337.1 | 6 | 52.31 | even | 4 | |||
1014.2.b.g.337.6 | 6 | 52.47 | even | 4 | |||
1014.2.e.k.529.3 | 6 | 52.3 | odd | 6 | |||
1014.2.e.k.991.3 | 6 | 52.35 | odd | 6 | |||
1014.2.e.m.529.1 | 6 | 52.23 | odd | 6 | |||
1014.2.e.m.991.1 | 6 | 52.43 | odd | 6 | |||
1014.2.i.g.361.1 | 12 | 52.19 | even | 12 | |||
1014.2.i.g.361.6 | 12 | 52.7 | even | 12 | |||
1014.2.i.g.823.3 | 12 | 52.11 | even | 12 | |||
1014.2.i.g.823.4 | 12 | 52.15 | even | 12 | |||
3042.2.a.bd.1.1 | 3 | 12.11 | even | 2 | |||
3042.2.a.be.1.3 | 3 | 156.155 | even | 2 | |||
3042.2.b.r.1351.1 | 6 | 156.47 | odd | 4 | |||
3042.2.b.r.1351.6 | 6 | 156.83 | odd | 4 | |||
8112.2.a.bz.1.3 | 3 | 1.1 | even | 1 | trivial | ||
8112.2.a.ce.1.1 | 3 | 13.12 | even | 2 |