Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, 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("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.621.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - 6x - 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 418) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.14510\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-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 | ||||||||
\(3\) | 2.14510 | 1.23848 | 0.619238 | − | 0.785204i | \(-0.287442\pi\) | ||||
0.619238 | + | 0.785204i | \(0.287442\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.60147 | −0.716197 | −0.358099 | − | 0.933684i | \(-0.616575\pi\) | ||||
−0.358099 | + | 0.933684i | \(0.616575\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.89167 | −1.09295 | −0.546474 | − | 0.837476i | \(-0.684030\pi\) | ||||
−0.546474 | + | 0.837476i | \(0.684030\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.60147 | 0.533822 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.89167 | 1.35671 | 0.678353 | − | 0.734736i | \(-0.262694\pi\) | ||||
0.678353 | + | 0.734736i | \(0.262694\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.43531 | −0.886993 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.74657 | −1.39375 | −0.696874 | − | 0.717194i | \(-0.745426\pi\) | ||||
−0.696874 | + | 0.717194i | \(0.745426\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.20293 | −1.35359 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.74657 | 1.61527 | 0.807636 | − | 0.589682i | \(-0.200747\pi\) | ||||
0.807636 | + | 0.589682i | \(0.200747\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.43531 | −0.487062 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.00000 | −0.577350 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.34803 | 0.993105 | 0.496552 | − | 0.868007i | \(-0.334599\pi\) | ||||
0.496552 | + | 0.868007i | \(0.334599\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.43531 | 1.33542 | 0.667710 | − | 0.744421i | \(-0.267274\pi\) | ||||
0.667710 | + | 0.744421i | \(0.267274\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.14510 | 0.373414 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.63091 | 0.782767 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.49314 | −1.23186 | −0.615932 | − | 0.787799i | \(-0.711220\pi\) | ||||
−0.615932 | + | 0.787799i | \(0.711220\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.4931 | 1.68025 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.05783 | −0.321379 | −0.160689 | − | 0.987005i | \(-0.551372\pi\) | ||||
−0.160689 | + | 0.987005i | \(0.551372\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.6887 | 1.63002 | 0.815009 | − | 0.579449i | \(-0.196732\pi\) | ||||
0.815009 | + | 0.579449i | \(0.196732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.56469 | −0.382322 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.08727 | 1.03379 | 0.516893 | − | 0.856050i | \(-0.327089\pi\) | ||||
0.516893 | + | 0.856050i | \(0.327089\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.36176 | 0.194537 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.3270 | −1.72612 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.32698 | 1.14380 | 0.571899 | − | 0.820324i | \(-0.306207\pi\) | ||||
0.571899 | + | 0.820324i | \(0.306207\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.60147 | −0.215942 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.14510 | 0.284126 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.54364 | 0.331153 | 0.165577 | − | 0.986197i | \(-0.447051\pi\) | ||||
0.165577 | + | 0.986197i | \(0.447051\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.4931 | 1.72762 | 0.863810 | − | 0.503818i | \(-0.168072\pi\) | ||||
0.863810 | + | 0.503818i | \(0.168072\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.63091 | −0.583440 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.83384 | −0.971669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3848 | 1.26871 | 0.634353 | − | 0.773043i | \(-0.281267\pi\) | ||||
0.634353 | + | 0.773043i | \(0.281267\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16.6172 | 2.00047 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.9789 | −1.77767 | −0.888837 | − | 0.458224i | \(-0.848486\pi\) | ||||
−0.888837 | + | 0.458224i | \(0.848486\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.74657 | −0.438503 | −0.219251 | − | 0.975668i | \(-0.570361\pi\) | ||||
−0.219251 | + | 0.975668i | \(0.570361\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.22399 | −0.603214 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.89167 | −0.329536 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.69607 | 0.978384 | 0.489192 | − | 0.872176i | \(-0.337292\pi\) | ||||
0.489192 | + | 0.872176i | \(0.337292\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2397 | −1.24886 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.10833 | 0.670476 | 0.335238 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335238 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.20293 | 0.998198 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.4721 | 1.22994 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.20293 | 0.339510 | 0.169755 | − | 0.985486i | \(-0.445702\pi\) | ||||
0.169755 | + | 0.985486i | \(0.445702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.1451 | −1.48281 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.9495 | 1.65389 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.60147 | −0.164307 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.98627 | −0.709349 | −0.354674 | − | 0.934990i | \(-0.615408\pi\) | ||||
−0.354674 | + | 0.934990i | \(0.615408\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.60147 | 0.160953 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.20293 | −0.119696 | −0.0598481 | − | 0.998207i | \(-0.519062\pi\) | ||||
−0.0598481 | + | 0.998207i | \(0.519062\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.8779 | −1.66303 | −0.831517 | − | 0.555500i | \(-0.812527\pi\) | ||||
−0.831517 | + | 0.555500i | \(0.812527\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.93378 | 0.969438 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.03677 | 0.776944 | 0.388472 | − | 0.921460i | \(-0.373003\pi\) | ||||
0.388472 | + | 0.921460i | \(0.373003\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.5299 | 1.10437 | 0.552183 | − | 0.833723i | \(-0.313795\pi\) | ||||
0.552183 | + | 0.833723i | \(0.313795\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.0735 | −1.52563 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.00000 | −0.752577 | −0.376288 | − | 0.926503i | \(-0.622800\pi\) | ||||
−0.376288 | + | 0.926503i | \(0.622800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.4059 | −1.15685 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.83384 | 0.724239 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.6172 | 1.52329 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.41425 | −0.398020 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.9074 | 1.06503 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.2765 | 1.88798 | 0.943991 | − | 0.329971i | \(-0.107039\pi\) | ||||
0.943991 | + | 0.329971i | \(0.107039\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 22.9284 | 2.01874 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.43531 | 0.300144 | 0.150072 | − | 0.988675i | \(-0.452049\pi\) | ||||
0.150072 | + | 0.988675i | \(0.452049\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.89167 | −0.250740 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.80440 | 0.413497 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.5877 | 1.16088 | 0.580439 | − | 0.814303i | \(-0.302881\pi\) | ||||
0.580439 | + | 0.814303i | \(0.302881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.19560 | −0.271048 | −0.135524 | − | 0.990774i | \(-0.543272\pi\) | ||||
−0.135524 | + | 0.990774i | \(0.543272\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.2029 | 1.28032 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.89167 | 0.409062 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.56469 | −0.711259 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.92112 | 0.240930 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0735 | −0.989104 | −0.494552 | − | 0.869148i | \(-0.664668\pi\) | ||||
−0.494552 | + | 0.869148i | \(0.664668\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.91273 | 0.399792 | 0.199896 | − | 0.979817i | \(-0.435940\pi\) | ||||
0.199896 | + | 0.979817i | \(0.435940\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.20293 | −0.744013 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.9074 | −0.956425 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.00733 | 0.639054 | 0.319527 | − | 0.947577i | \(-0.396476\pi\) | ||||
0.319527 | + | 0.947577i | \(0.396476\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.8622 | 1.41657 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.4005 | −1.76541 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.88434 | −0.147593 | −0.0737966 | − | 0.997273i | \(-0.523512\pi\) | ||||
−0.0737966 | + | 0.997273i | \(0.523512\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.43531 | −0.267438 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.98627 | 0.385849 | 0.192925 | − | 0.981214i | \(-0.438203\pi\) | ||||
0.192925 | + | 0.981214i | \(0.438203\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.9284 | 0.840650 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.60147 | 0.122467 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.51419 | 0.495265 | 0.247632 | − | 0.968854i | \(-0.420347\pi\) | ||||
0.247632 | + | 0.968854i | \(0.420347\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.04211 | 0.532333 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.45636 | 0.410125 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.55096 | 0.414899 | 0.207449 | − | 0.978246i | \(-0.433484\pi\) | ||||
0.207449 | + | 0.978246i | \(0.433484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.88434 | 0.140062 | 0.0700311 | − | 0.997545i | \(-0.477690\pi\) | ||||
0.0700311 | + | 0.997545i | \(0.477690\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.9442 | 2.13961 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.0000 | 0.882258 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.74657 | −0.420231 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.67501 | 0.631014 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.44264 | −0.176743 | −0.0883715 | − | 0.996088i | \(-0.528166\pi\) | ||||
−0.0883715 | + | 0.996088i | \(0.528166\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.67501 | −0.696423 | −0.348211 | − | 0.937416i | \(-0.613211\pi\) | ||||
−0.348211 | + | 0.937416i | \(0.613211\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.8044 | −1.20339 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.4931 | −1.24633 | −0.623167 | − | 0.782089i | \(-0.714154\pi\) | ||||
−0.623167 | + | 0.782089i | \(0.714154\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.2397 | 1.78920 | 0.894598 | − | 0.446873i | \(-0.147462\pi\) | ||||
0.894598 | + | 0.446873i | \(0.147462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.2765 | 1.57126 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.4648 | −1.08541 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.29554 | 0.230171 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.4059 | 0.862267 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.8338 | 1.02120 | 0.510602 | − | 0.859817i | \(-0.329423\pi\) | ||||
0.510602 | + | 0.859817i | \(0.329423\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −32.1314 | −2.20161 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.1176 | −1.16741 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.5005 | −1.45955 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.03677 | −0.543075 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.1103 | −1.89090 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.4931 | −0.769637 | −0.384819 | − | 0.922992i | \(-0.625736\pi\) | ||||
−0.384819 | + | 0.922992i | \(0.625736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.90006 | −0.260004 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.73284 | −0.579619 | −0.289810 | − | 0.957084i | \(-0.593592\pi\) | ||||
−0.289810 | + | 0.957084i | \(0.593592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.84117 | 0.518159 | 0.259080 | − | 0.965856i | \(-0.416581\pi\) | ||||
0.259080 | + | 0.965856i | \(0.416581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.20293 | −0.408123 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.5069 | −0.819352 | −0.409676 | − | 0.912231i | \(-0.634358\pi\) | ||||
−0.409676 | + | 0.912231i | \(0.634358\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.3500 | −0.740394 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.6540 | 1.21170 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.6245 | −1.59283 | −0.796414 | − | 0.604752i | \(-0.793272\pi\) | ||||
−0.796414 | + | 0.604752i | \(0.793272\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.0809 | 1.03586 | 0.517930 | − | 0.855423i | \(-0.326703\pi\) | ||||
0.517930 | + | 0.855423i | \(0.326703\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.1103 | −0.969328 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.18081 | −0.139327 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.89167 | 0.311250 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.1030 | 0.830368 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.0873 | −0.826061 | −0.413031 | − | 0.910717i | \(-0.635530\pi\) | ||||
−0.413031 | + | 0.910717i | \(0.635530\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.74657 | 0.487023 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 19.7412 | 1.23624 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.723522 | 0.0451320 | 0.0225660 | − | 0.999745i | \(-0.492816\pi\) | ||||
0.0225660 | + | 0.999745i | \(0.492816\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.6677 | 1.34636 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.56469 | 0.530141 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.7760 | −0.849465 | −0.424733 | − | 0.905319i | \(-0.639632\pi\) | ||||
−0.424733 | + | 0.905319i | \(0.639632\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.3354 | −0.819185 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.87062 | 0.420475 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.9579 | −1.21685 | −0.608427 | − | 0.793610i | \(-0.708199\pi\) | ||||
−0.608427 | + | 0.793610i | \(0.708199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.7486 | −1.74635 | −0.873175 | − | 0.487406i | \(-0.837943\pi\) | ||||
−0.873175 | + | 0.487406i | \(0.837943\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −30.3427 | −1.83642 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.43531 | −0.146855 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.08727 | 0.185496 | 0.0927482 | − | 0.995690i | \(-0.470435\pi\) | ||||
0.0927482 | + | 0.995690i | \(0.470435\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.9074 | 0.712877 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.09460 | 0.542538 | 0.271269 | − | 0.962504i | \(-0.412557\pi\) | ||||
0.271269 | + | 0.962504i | \(0.412557\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.1451 | −0.781395 | −0.390698 | − | 0.920519i | \(-0.627766\pi\) | ||||
−0.390698 | + | 0.920519i | \(0.627766\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.43531 | −0.203490 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.95056 | 0.351251 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.0230 | 0.942532 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.9863 | −0.878511 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.10833 | 0.181591 | 0.0907953 | − | 0.995870i | \(-0.471059\pi\) | ||||
0.0907953 | + | 0.995870i | \(0.471059\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.07355 | −0.237171 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.00000 | −0.174078 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 37.8937 | 2.19145 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.9083 | −1.78153 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.58041 | −0.148241 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.6088 | −1.23732 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.18920 | −0.124944 | −0.0624722 | − | 0.998047i | \(-0.519898\pi\) | ||||
−0.0624722 | + | 0.998047i | \(0.519898\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −36.2049 | −2.05963 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.92112 | −0.222346 | −0.111173 | − | 0.993801i | \(-0.535461\pi\) | ||||
−0.111173 | + | 0.993801i | \(0.535461\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.7118 | −1.22722 | −0.613611 | − | 0.789608i | \(-0.710284\pi\) | ||||
−0.613611 | + | 0.789608i | \(0.710284\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.41625 | 0.417858 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.90739 | 0.387958 | 0.193979 | − | 0.981006i | \(-0.437861\pi\) | ||||
0.193979 | + | 0.981006i | \(0.437861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.34803 | 0.299432 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.2397 | 0.962226 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.74657 | −0.319748 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.9127 | −0.660799 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.7328 | 1.36773 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.4941 | −1.12987 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.1030 | −1.76454 | −0.882270 | − | 0.470744i | \(-0.843986\pi\) | ||||
−0.882270 | + | 0.470744i | \(0.843986\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.0000 | −0.657596 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.6309 | −0.908644 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.55096 | −0.0844864 | −0.0422432 | − | 0.999107i | \(-0.513450\pi\) | ||||
−0.0422432 | + | 0.999107i | \(0.513450\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.1608 | −0.932048 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.43531 | 0.402645 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.3039 | 0.880330 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −26.6118 | −1.43273 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.506864 | 0.0272099 | 0.0136049 | − | 0.999907i | \(-0.495669\pi\) | ||||
0.0136049 | + | 0.999907i | \(0.495669\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.8117 | 0.578738 | 0.289369 | − | 0.957218i | \(-0.406554\pi\) | ||||
0.289369 | + | 0.957218i | \(0.406554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.6750 | −0.783294 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.0966 | 1.44221 | 0.721103 | − | 0.692828i | \(-0.243635\pi\) | ||||
0.721103 | + | 0.692828i | \(0.243635\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.9883 | 1.27316 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 35.6456 | 1.88656 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.7486 | 1.09507 | 0.547534 | − | 0.836784i | \(-0.315567\pi\) | ||||
0.547534 | + | 0.836784i | \(0.315567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.14510 | 0.112589 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.6402 | −1.33841 | −0.669205 | − | 0.743078i | \(-0.733365\pi\) | ||||
−0.669205 | + | 0.743078i | \(0.733365\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.29554 | −0.171559 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.0789 | −1.25011 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.2049 | 1.30506 | 0.652531 | − | 0.757762i | \(-0.273707\pi\) | ||||
0.652531 | + | 0.757762i | \(0.273707\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.5426 | 1.31901 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.1608 | 1.34735 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.47208 | −0.178349 | −0.0891744 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891744 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 45.6402 | 2.33822 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.1176 | −1.18126 | −0.590628 | − | 0.806944i | \(-0.701120\pi\) | ||||
−0.590628 | + | 0.806944i | \(0.701120\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.63091 | 0.236013 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.1176 | 0.870139 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.7623 | −1.35690 | −0.678451 | − | 0.734646i | \(-0.737348\pi\) | ||||
−0.678451 | + | 0.734646i | \(0.737348\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −44.5162 | −2.25128 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.36909 | 0.371721 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.9265 | −0.700716 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.1030 | −1.56101 | −0.780507 | − | 0.625147i | \(-0.785039\pi\) | ||||
−0.780507 | + | 0.625147i | \(0.785039\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.20293 | −0.310535 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.3500 | 1.46567 | 0.732835 | − | 0.680406i | \(-0.238197\pi\) | ||||
0.732835 | + | 0.680406i | \(0.238197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.3711 | 1.81177 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | 0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.49314 | −0.371421 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.58774 | 0.424636 | 0.212318 | − | 0.977201i | \(-0.431899\pi\) | ||||
0.212318 | + | 0.977201i | \(0.431899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 29.1471 | 1.43772 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.35536 | −0.361934 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.78228 | −0.480193 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.85490 | −0.335686 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.59414 | −0.370998 | −0.185499 | − | 0.982644i | \(-0.559390\pi\) | ||||
−0.185499 | + | 0.982644i | \(0.559390\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.76030 | 0.426951 | 0.213475 | − | 0.976948i | \(-0.431522\pi\) | ||||
0.213475 | + | 0.976948i | \(0.431522\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.3500 | 0.551857 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.9947 | 0.678841 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −39.0177 | −1.88820 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.4931 | 0.506613 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.6677 | 1.62172 | 0.810858 | − | 0.585243i | \(-0.199001\pi\) | ||||
0.810858 | + | 0.585243i | \(0.199001\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.5383 | 1.46758 | 0.733789 | − | 0.679378i | \(-0.237750\pi\) | ||||
0.733789 | + | 0.679378i | \(0.237750\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.3721 | −0.880877 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.74657 | 0.370569 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.5069 | 0.596920 | 0.298460 | − | 0.954422i | \(-0.403527\pi\) | ||||
0.298460 | + | 0.954422i | \(0.403527\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.18081 | 0.103848 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.6677 | 0.839417 | 0.419709 | − | 0.907659i | \(-0.362132\pi\) | ||||
0.419709 | + | 0.907659i | \(0.362132\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.12938 | −0.243156 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.8990 | −1.22498 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.7098 | −0.835777 | −0.417888 | − | 0.908498i | \(-0.637230\pi\) | ||||
−0.417888 | + | 0.908498i | \(0.637230\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.05783 | −0.0968994 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.5383 | 0.495133 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 22.6529 | 1.06198 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.8064 | −1.16039 | −0.580197 | − | 0.814476i | \(-0.697024\pi\) | ||||
−0.580197 | + | 0.814476i | \(0.697024\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.2397 | 0.804681 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.98627 | −0.139085 | −0.0695423 | − | 0.997579i | \(-0.522154\pi\) | ||||
−0.0695423 | + | 0.997579i | \(0.522154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.5667 | 1.83882 | 0.919410 | − | 0.393301i | \(-0.128667\pi\) | ||||
0.919410 | + | 0.393301i | \(0.128667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −25.5426 | −1.18451 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.46475 | −0.206604 | −0.103302 | − | 0.994650i | \(-0.532941\pi\) | ||||
−0.103302 | + | 0.994650i | \(0.532941\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −30.0294 | −1.38663 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.1765 | 0.791453 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.6887 | 0.491469 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.43531 | −0.111740 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.3354 | 0.610585 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.8863 | 0.954321 | 0.477161 | − | 0.878816i | \(-0.341666\pi\) | ||||
0.477161 | + | 0.878816i | \(0.341666\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.6540 | −1.67128 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −48.0514 | −2.18642 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.1883 | 0.508033 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.2838 | −0.692575 | −0.346288 | − | 0.938128i | \(-0.612558\pi\) | ||||
−0.346288 | + | 0.938128i | \(0.612558\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.04211 | −0.182791 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.31965 | −0.149814 | −0.0749069 | − | 0.997191i | \(-0.523866\pi\) | ||||
−0.0749069 | + | 0.997191i | \(0.523866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.7328 | −1.38414 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.56469 | −0.115274 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 43.3142 | 1.94291 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.07355 | 0.0928247 | 0.0464124 | − | 0.998922i | \(-0.485221\pi\) | ||||
0.0464124 | + | 0.998922i | \(0.485221\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.6961 | 0.477865 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.11672 | 0.0497921 | 0.0248960 | − | 0.999690i | \(-0.492075\pi\) | ||||
0.0248960 | + | 0.999690i | \(0.492075\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.92645 | 0.0857260 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.4426 | 1.04112 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.2481 | −1.69532 | −0.847659 | − | 0.530542i | \(-0.821988\pi\) | ||||
−0.847659 | + | 0.530542i | \(0.821988\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8338 | 0.479261 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.00000 | −0.132453 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 27.0294 | 1.19106 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.08727 | 0.311698 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.9736 | 0.613373 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.8853 | 0.476892 | 0.238446 | − | 0.971156i | \(-0.423362\pi\) | ||||
0.238446 | + | 0.971156i | \(0.423362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.7191 | 0.687349 | 0.343674 | − | 0.939089i | \(-0.388328\pi\) | ||||
0.343674 | + | 0.939089i | \(0.388328\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.1060 | 0.659282 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −42.7275 | −1.86124 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 37.0093 | 1.60910 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.07355 | 0.176777 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.0662 | −0.436016 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.8706 | −0.556445 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.9074 | 0.513842 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.36176 | 0.0586552 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.4373 | −1.13663 | −0.568314 | − | 0.822812i | \(-0.692404\pi\) | ||||
−0.568314 | + | 0.822812i | \(0.692404\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.04211 | 0.173464 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.4648 | −0.790943 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.9588 | 1.06716 | 0.533581 | − | 0.845749i | \(-0.320846\pi\) | ||||
0.533581 | + | 0.845749i | \(0.320846\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 21.6088 | 0.922241 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.34803 | 0.227834 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.1462 | −1.06932 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 25.7412 | 1.09265 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.30486 | 0.351888 | 0.175944 | − | 0.984400i | \(-0.443702\pi\) | ||||
0.175944 | + | 0.984400i | \(0.443702\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 52.2858 | 2.21145 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.3270 | −0.520445 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.6402 | −1.75493 | −0.877463 | − | 0.479644i | \(-0.840766\pi\) | ||||
−0.877463 | + | 0.479644i | \(0.840766\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.8117 | 0.538993 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 32.5015 | 1.36494 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.9138 | −0.625219 | −0.312609 | − | 0.949882i | \(-0.601203\pi\) | ||||
−0.312609 | + | 0.949882i | \(0.601203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.0020 | 0.962603 | 0.481302 | − | 0.876555i | \(-0.340164\pi\) | ||||
0.481302 | + | 0.876555i | \(0.340164\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.23970 | −0.218892 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.8653 | −0.786737 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.6613 | −1.40134 | −0.700669 | − | 0.713487i | \(-0.747115\pi\) | ||||
−0.700669 | + | 0.713487i | \(0.747115\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20.7539 | −0.862502 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.6633 | −0.732796 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.32698 | 0.344868 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.5456 | −0.518698 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.00000 | −0.165098 | −0.0825488 | − | 0.996587i | \(-0.526306\pi\) | ||||
−0.0825488 | + | 0.996587i | \(0.526306\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.43531 | 0.306367 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −37.5246 | −1.54355 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.9588 | −1.27133 | −0.635663 | − | 0.771967i | \(-0.719273\pi\) | ||||
−0.635663 | + | 0.771967i | \(0.719273\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −26.6118 | −1.09098 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 54.1418 | 2.21587 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.93378 | −0.160730 | −0.0803650 | − | 0.996766i | \(-0.525609\pi\) | ||||
−0.0803650 | + | 0.996766i | \(0.525609\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.1451 | 0.944108 | 0.472054 | − | 0.881570i | \(-0.343513\pi\) | ||||
0.472054 | + | 0.881570i | \(0.343513\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.6309 | 0.677263 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.60147 | −0.0651088 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.78334 | 0.0723836 | 0.0361918 | − | 0.999345i | \(-0.488477\pi\) | ||||
0.0361918 | + | 0.999345i | \(0.488477\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −33.1735 | −1.34426 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.6686 | 1.40254 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.0598 | −1.33527 | −0.667637 | − | 0.744487i | \(-0.732694\pi\) | ||||
−0.667637 | + | 0.744487i | \(0.732694\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.06927 | 0.285061 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.8412 | −0.879292 | −0.439646 | − | 0.898171i | \(-0.644896\pi\) | ||||
−0.439646 | + | 0.898171i | \(0.644896\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.2206 | 1.85776 | 0.928882 | − | 0.370375i | \(-0.120771\pi\) | ||||
0.928882 | + | 0.370375i | \(0.120771\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −23.2397 | −0.932577 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.26182 | −0.371067 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.89273 | −0.275709 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.14510 | 0.0856671 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 43.0598 | 1.71691 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.317659 | −0.0126458 | −0.00632291 | − | 0.999980i | \(-0.502013\pi\) | ||||
−0.00632291 | + | 0.999980i | \(0.502013\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31.8201 | 1.26474 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.0735 | −1.35217 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.66129 | 0.263930 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.9883 | −0.948961 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.5246 | −1.64012 | −0.820061 | − | 0.572276i | \(-0.806061\pi\) | ||||
−0.820061 | + | 0.572276i | \(0.806061\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.26182 | −0.286378 | −0.143189 | − | 0.989695i | \(-0.545736\pi\) | ||||
−0.143189 | + | 0.989695i | \(0.545736\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −36.7191 | −1.44581 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.0819 | −1.14333 | −0.571664 | − | 0.820487i | \(-0.693702\pi\) | ||||
−0.571664 | + | 0.820487i | \(0.693702\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.54364 | 0.0998465 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −46.1207 | −1.80761 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.6529 | 0.495146 | 0.247573 | − | 0.968869i | \(-0.420367\pi\) | ||||
0.247573 | + | 0.968869i | \(0.420367\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.50153 | −0.214962 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −49.4878 | −1.92777 | −0.963886 | − | 0.266317i | \(-0.914193\pi\) | ||||
−0.963886 | + | 0.266317i | \(0.914193\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.94950 | 0.192513 | 0.0962566 | − | 0.995357i | \(-0.469313\pi\) | ||||
0.0962566 | + | 0.995357i | \(0.469313\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −60.2995 | −2.34184 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.63091 | 0.179579 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 41.4289 | 1.60413 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.6540 | −0.953177 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.4931 | 0.520897 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.9001 | 0.844185 | 0.422093 | − | 0.906553i | \(-0.361296\pi\) | ||||
0.422093 | + | 0.906553i | \(0.361296\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.30592 | 0.281205 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.4353 | 1.01599 | 0.507996 | − | 0.861360i | \(-0.330387\pi\) | ||||
0.507996 | + | 0.861360i | \(0.330387\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.2020 | 0.775282 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.7328 | −0.717844 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.82545 | −0.375960 | −0.187980 | − | 0.982173i | \(-0.560194\pi\) | ||||
−0.187980 | + | 0.982173i | \(0.560194\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.7603 | −0.831418 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.8201 | 0.641727 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.7328 | 1.55180 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.8255 | 0.754196 | 0.377098 | − | 0.926173i | \(-0.376922\pi\) | ||||
0.377098 | + | 0.926173i | \(0.376922\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.63091 | −0.175914 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.11765 | 0.194123 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.8255 | 0.447921 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −26.8285 | −1.01475 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.7550 | −0.406209 | −0.203105 | − | 0.979157i | \(-0.565103\pi\) | ||||
−0.203105 | + | 0.979157i | \(0.565103\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.49314 | −0.282609 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24.3470 | −0.916960 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.47848 | 0.130822 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.82651 | −0.0685962 | −0.0342981 | − | 0.999412i | \(-0.510920\pi\) | ||||
−0.0342981 | + | 0.999412i | \(0.510920\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.9265 | 0.522283 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 57.5981 | 2.15707 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.83384 | −0.292969 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −52.8221 | −1.97268 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.65929 | 0.173762 | 0.0868812 | − | 0.996219i | \(-0.472310\pi\) | ||||
0.0868812 | + | 0.996219i | \(0.472310\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48.8055 | 1.81761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.4951 | 1.28289 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.0241 | −0.483703 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.9358 | −0.739377 | −0.369688 | − | 0.929156i | \(-0.620536\pi\) | ||||
−0.369688 | + | 0.929156i | \(0.620536\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.30592 | 0.0483676 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −61.4236 | −2.27183 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.7687 | 0.508558 | 0.254279 | − | 0.967131i | \(-0.418162\pi\) | ||||
0.254279 | + | 0.967131i | \(0.418162\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.67807 | −0.172553 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.3848 | 0.382529 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.4867 | −0.827188 | −0.413594 | − | 0.910461i | \(-0.635727\pi\) | ||||
−0.413594 | + | 0.910461i | \(0.635727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.4931 | 0.385475 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 50.6540 | 1.85831 | 0.929157 | − | 0.369686i | \(-0.120535\pi\) | ||||
0.929157 | + | 0.369686i | \(0.120535\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.3354 | 0.708393 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.78228 | 0.357915 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −23.2397 | −0.849160 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.9127 | 1.41995 | 0.709973 | − | 0.704229i | \(-0.248707\pi\) | ||||
0.709973 | + | 0.704229i | \(0.248707\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.0735 | −1.02306 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.86756 | −0.286330 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.5877 | −0.748274 | −0.374137 | − | 0.927373i | \(-0.622061\pi\) | ||||
−0.374137 | + | 0.927373i | \(0.622061\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.6172 | 0.603166 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.6025 | 0.384341 | 0.192171 | − | 0.981362i | \(-0.438447\pi\) | ||||
0.192171 | + | 0.981362i | \(0.438447\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.3407 | −1.20701 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.7382 | 0.532860 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.4426 | 0.449278 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.77495 | −0.316433 | −0.158216 | − | 0.987404i | \(-0.550574\pi\) | ||||
−0.158216 | + | 0.987404i | \(0.550574\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.55203 | 0.0558949 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.8653 | −1.68563 | −0.842813 | − | 0.538206i | \(-0.819102\pi\) | ||||
−0.842813 | + | 0.538206i | \(0.819102\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.1073 | −0.650432 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 46.4794 | 1.66744 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.05783 | −0.0737294 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.9789 | −0.535989 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.0441 | −0.573369 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.8235 | −0.457689 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.4143 | 0.977213 | 0.488606 | − | 0.872504i | \(-0.337505\pi\) | ||||
0.488606 | + | 0.872504i | \(0.337505\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.5510 | −1.05204 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.1334 | 0.822528 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 66.0040 | 2.34387 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −28.6057 | −1.01454 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.16616 | −0.324682 | −0.162341 | − | 0.986735i | \(-0.551904\pi\) | ||||
−0.162341 | + | 0.986735i | \(0.551904\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.7275 | −1.44084 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.12938 | 0.181238 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.74657 | −0.132214 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.8737 | 1.26438 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −42.8117 | −1.50704 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.0829 | 1.69050 | 0.845252 | − | 0.534368i | \(-0.179450\pi\) | ||||
0.845252 | + | 0.534368i | \(0.179450\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.67395 | 0.0938951 | 0.0469475 | − | 0.998897i | \(-0.485051\pi\) | ||||
0.0469475 | + | 0.998897i | \(0.485051\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −61.6686 | −2.16281 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.01771 | 0.105706 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.6887 | 0.373952 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.6529 | −0.791556 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.5078 | 1.02983 | 0.514915 | − | 0.857242i | \(-0.327824\pi\) | ||||
0.514915 | + | 0.857242i | \(0.327824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.39654 | 0.0835382 | 0.0417691 | − | 0.999127i | \(-0.486701\pi\) | ||||
0.0417691 | + | 0.999127i | \(0.486701\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.22399 | −0.181876 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.78868 | −0.270839 | −0.135419 | − | 0.990788i | \(-0.543238\pi\) | ||||
−0.135419 | + | 0.990788i | \(0.543238\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.2818 | 0.461296 | 0.230648 | − | 0.973037i | \(-0.425915\pi\) | ||||
0.230648 | + | 0.973037i | \(0.425915\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.62252 | 0.229733 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.82545 | −0.271136 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.98534 | −0.276344 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −22.3059 | −0.771006 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.9063 | 1.17058 | 0.585288 | − | 0.810825i | \(-0.300981\pi\) | ||||
0.585288 | + | 0.810825i | \(0.300981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.398534 | −0.0137426 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.5089 | 0.671921 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.5015 | −0.602071 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.89167 | −0.0993590 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.1976 | −0.967739 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −58.0461 | −1.98979 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.0735 | 1.37209 | 0.686046 | − | 0.727558i | \(-0.259345\pi\) | ||||
0.686046 | + | 0.727558i | \(0.259345\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.56469 | −0.0877106 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.665693 | 0.0227396 | 0.0113698 | − | 0.999935i | \(-0.496381\pi\) | ||||
0.0113698 | + | 0.999935i | \(0.496381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.8990 | −0.474228 | −0.237114 | − | 0.971482i | \(-0.576201\pi\) | ||||
−0.237114 | + | 0.971482i | \(0.576201\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.7646 | 0.435015 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.3941 | 1.37503 | 0.687516 | − | 0.726169i | \(-0.258701\pi\) | ||||
0.687516 | + | 0.726169i | \(0.258701\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.4323 | −0.354707 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 34.3711 | 1.16730 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.69607 | 0.294994 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.7991 | 1.72126 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.1883 | −0.378666 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −34.4323 | −1.16402 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.6108 | 0.527139 | 0.263569 | − | 0.964640i | \(-0.415100\pi\) | ||||
0.263569 | + | 0.964640i | \(0.415100\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.66769 | 0.224895 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.9843 | 0.673288 | 0.336644 | − | 0.941632i | \(-0.390708\pi\) | ||||
0.336644 | + | 0.941632i | \(0.390708\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.2167 | −0.680345 | −0.340172 | − | 0.940363i | \(-0.610485\pi\) | ||||
−0.340172 | + | 0.940363i | \(0.610485\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.73818 | −0.293731 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.1471 | −0.676473 | −0.338237 | − | 0.941061i | \(-0.609830\pi\) | ||||
−0.338237 | + | 0.941061i | \(0.609830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −61.5246 | −2.06347 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.2397 | −0.376544 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.08727 | 0.237167 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.88968 | −0.297149 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 81.2858 | 2.71405 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.7643 | 1.32621 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47.8516 | −1.59417 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −66.3015 | −2.20638 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.01771 | −0.100312 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.57109 | −0.151781 | −0.0758903 | − | 0.997116i | \(-0.524180\pi\) | ||||
−0.0758903 | + | 0.997116i | \(0.524180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.92645 | −0.0638964 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.6402 | −1.71092 | −0.855459 | − | 0.517871i | \(-0.826725\pi\) | ||||
−0.855459 | + | 0.517871i | \(0.826725\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.10833 | 0.202156 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −46.3531 | −1.53239 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.93378 | −0.328042 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.8412 | 1.61112 | 0.805561 | − | 0.592513i | \(-0.201864\pi\) | ||||
0.805561 | + | 0.592513i | \(0.201864\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.69607 | −0.154741 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −73.2721 | −2.41178 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.2481 | 0.599994 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −27.0294 | −0.887763 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −57.8819 | −1.89904 | −0.949522 | − | 0.313700i | \(-0.898431\pi\) | ||||
−0.949522 | + | 0.313700i | \(0.898431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.36176 | 0.0446299 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.41120 | −0.275370 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.20293 | 0.300968 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −57.6496 | −1.88333 | −0.941664 | − | 0.336553i | \(-0.890739\pi\) | ||||
−0.941664 | + | 0.336553i | \(0.890739\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −46.5740 | −1.51989 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.0966 | −0.492135 | −0.246067 | − | 0.969253i | \(-0.579138\pi\) | ||||
−0.246067 | + | 0.969253i | \(0.579138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.9411 | −0.519114 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.8927 | −0.451931 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.3775 | −1.08462 | −0.542311 | − | 0.840178i | \(-0.682451\pi\) | ||||
−0.542311 | + | 0.840178i | \(0.682451\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.3270 | −0.594919 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.8171 | 0.480476 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.4794 | −0.404248 | −0.202124 | − | 0.979360i | \(-0.564784\pi\) | ||||
−0.202124 | + | 0.979360i | \(0.564784\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.91180 | 0.126583 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.4721 | 0.370840 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −39.2913 | −1.26878 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.2838 | 0.783349 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.8706 | 0.414750 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.4942 | 0.498776 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.5804 | 0.404559 | 0.202279 | − | 0.979328i | \(-0.435165\pi\) | ||||
0.202279 | + | 0.979328i | \(0.435165\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.3270 | −0.396000 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.79067 | 0.0574653 | 0.0287327 | − | 0.999587i | \(-0.490853\pi\) | ||||
0.0287327 | + | 0.999587i | \(0.490853\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.24063 | 0.296241 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.5540 | −0.818384 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.40586 | 0.204942 | 0.102471 | − | 0.994736i | \(-0.467325\pi\) | ||||
0.102471 | + | 0.994736i | \(0.467325\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.20293 | 0.102366 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.4648 | 0.589534 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.5647 | 0.655912 | 0.327956 | − | 0.944693i | \(-0.393640\pi\) | ||||
0.327956 | + | 0.944693i | \(0.393640\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.0147 | 0.892621 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −43.9619 | −1.39932 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 82.8011 | 2.63292 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.0166 | 0.921744 | 0.460872 | − | 0.887467i | \(-0.347537\pi\) | ||||
0.460872 | + | 0.887467i | \(0.347537\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −68.8642 | −2.18534 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.4205 | −1.28142 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.3638 | 1.34167 | 0.670837 | − | 0.741605i | \(-0.265935\pi\) | ||||
0.670837 | + | 0.741605i | \(0.265935\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.4794 | 0.711217 |
(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 | 3344.2.a.q.1.3 | 3 | ||
4.3 | odd | 2 | 418.2.a.g.1.1 | ✓ | 3 | ||
12.11 | even | 2 | 3762.2.a.bg.1.2 | 3 | |||
44.43 | even | 2 | 4598.2.a.bo.1.1 | 3 | |||
76.75 | even | 2 | 7942.2.a.bi.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.a.g.1.1 | ✓ | 3 | 4.3 | odd | 2 | ||
3344.2.a.q.1.3 | 3 | 1.1 | even | 1 | trivial | ||
3762.2.a.bg.1.2 | 3 | 12.11 | even | 2 | |||
4598.2.a.bo.1.1 | 3 | 44.43 | even | 2 | |||
7942.2.a.bi.1.3 | 3 | 76.75 | even | 2 |