Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5472,2,Mod(1,5472)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5472, 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("5472.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5472 = 2^{5} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5472.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: | \(43.6941399860\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 608) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.329727\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5472.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.40617 | −1.52328 | −0.761642 | − | 0.647998i | \(-0.775606\pi\) | ||||
−0.761642 | + | 0.647998i | \(0.775606\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50407 | −0.946449 | −0.473224 | − | 0.880942i | \(-0.656910\pi\) | ||||
−0.473224 | + | 0.880942i | \(0.656910\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.40617 | −0.423975 | −0.211988 | − | 0.977272i | \(-0.567994\pi\) | ||||
−0.211988 | + | 0.977272i | \(0.567994\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.22101 | 1.72540 | 0.862698 | − | 0.505719i | \(-0.168773\pi\) | ||||
0.862698 | + | 0.505719i | \(0.168773\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.16352 | 0.767267 | 0.383633 | − | 0.923485i | \(-0.374673\pi\) | ||||
0.383633 | + | 0.923485i | \(0.374673\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.91023 | −1.64940 | −0.824699 | − | 0.565572i | \(-0.808655\pi\) | ||||
−0.824699 | + | 0.565572i | \(0.808655\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.60197 | 1.32039 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.22101 | −1.15521 | −0.577606 | − | 0.816316i | \(-0.696013\pi\) | ||||
−0.577606 | + | 0.816316i | \(0.696013\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.13124 | −1.46041 | −0.730207 | − | 0.683226i | \(-0.760576\pi\) | ||||
−0.730207 | + | 0.683226i | \(0.760576\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.52927 | 1.44171 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.13124 | −1.00797 | −0.503985 | − | 0.863712i | \(-0.668133\pi\) | ||||
−0.503985 | + | 0.863712i | \(0.668133\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.68923 | −0.263813 | −0.131906 | − | 0.991262i | \(-0.542110\pi\) | ||||
−0.131906 | + | 0.991262i | \(0.542110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.71694 | −0.261831 | −0.130915 | − | 0.991394i | \(-0.541792\pi\) | ||||
−0.130915 | + | 0.991394i | \(0.541792\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.84818 | 1.43650 | 0.718252 | − | 0.695783i | \(-0.244942\pi\) | ||||
0.718252 | + | 0.695783i | \(0.244942\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.729644 | −0.104235 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.78713 | −0.382842 | −0.191421 | − | 0.981508i | \(-0.561310\pi\) | ||||
−0.191421 | + | 0.981508i | \(0.561310\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.78964 | 0.645834 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.25078 | 1.20435 | 0.602174 | − | 0.798365i | \(-0.294301\pi\) | ||||
0.602174 | + | 0.798365i | \(0.294301\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.52927 | 0.835988 | 0.417994 | − | 0.908450i | \(-0.362733\pi\) | ||||
0.417994 | + | 0.908450i | \(0.362733\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21.1898 | −2.62827 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.87233 | −0.228741 | −0.114370 | − | 0.993438i | \(-0.536485\pi\) | ||||
−0.114370 | + | 0.993438i | \(0.536485\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.0081 | −1.54378 | −0.771891 | − | 0.635755i | \(-0.780689\pi\) | ||||
−0.771891 | + | 0.635755i | \(0.780689\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.28663 | −0.735794 | −0.367897 | − | 0.929867i | \(-0.619922\pi\) | ||||
−0.367897 | + | 0.929867i | \(0.619922\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.52114 | 0.401271 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.2543 | 1.26621 | 0.633106 | − | 0.774065i | \(-0.281780\pi\) | ||||
0.633106 | + | 0.774065i | \(0.281780\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.80420 | 0.198036 | 0.0990182 | − | 0.995086i | \(-0.468430\pi\) | ||||
0.0990182 | + | 0.995086i | \(0.468430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.7755 | −1.16877 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.57426 | 0.802870 | 0.401435 | − | 0.915888i | \(-0.368512\pi\) | ||||
0.401435 | + | 0.915888i | \(0.368512\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.5778 | −1.63300 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.40617 | 0.349465 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.81233 | 0.488618 | 0.244309 | − | 0.969697i | \(-0.421439\pi\) | ||||
0.244309 | + | 0.969697i | \(0.421439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.2462 | 1.61656 | 0.808279 | − | 0.588799i | \(-0.200399\pi\) | ||||
0.808279 | + | 0.588799i | \(0.200399\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.68923 | −0.757642 | −0.378821 | − | 0.925470i | \(-0.623670\pi\) | ||||
−0.378821 | + | 0.925470i | \(0.623670\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.8886 | −1.14931 | −0.574657 | − | 0.818394i | \(-0.694865\pi\) | ||||
−0.574657 | + | 0.818394i | \(0.694865\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.65489 | −0.541640 | −0.270820 | − | 0.962630i | \(-0.587295\pi\) | ||||
−0.270820 | + | 0.962630i | \(0.587295\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.81233 | 0.828995 | 0.414497 | − | 0.910051i | \(-0.363957\pi\) | ||||
0.414497 | + | 0.910051i | \(0.363957\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.9436 | 2.51250 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.92167 | −0.726179 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.02270 | −0.820245 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.45657 | −0.488051 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0504 | −1.06930 | −0.534650 | − | 0.845073i | \(-0.679557\pi\) | ||||
−0.534650 | + | 0.845073i | \(0.679557\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.920878 | 0.0804575 | 0.0402287 | − | 0.999190i | \(-0.487191\pi\) | ||||
0.0402287 | + | 0.999190i | \(0.487191\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.50407 | 0.217130 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.525705 | 0.0449140 | 0.0224570 | − | 0.999748i | \(-0.492851\pi\) | ||||
0.0224570 | + | 0.999748i | \(0.492851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.52927 | 0.384168 | 0.192084 | − | 0.981379i | \(-0.438475\pi\) | ||||
0.192084 | + | 0.981379i | \(0.438475\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.74777 | −0.731525 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 21.1898 | 1.75972 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.9713 | 1.55419 | 0.777094 | − | 0.629384i | \(-0.216693\pi\) | ||||
0.777094 | + | 0.629384i | \(0.216693\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.55698 | −0.533600 | −0.266800 | − | 0.963752i | \(-0.585966\pi\) | ||||
−0.266800 | + | 0.963752i | \(0.585966\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.6964 | 2.22463 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.5651 | 1.40185 | 0.700925 | − | 0.713235i | \(-0.252771\pi\) | ||||
0.700925 | + | 0.713235i | \(0.252771\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 19.8078 | 1.56107 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.9436 | 1.79708 | 0.898540 | − | 0.438892i | \(-0.144629\pi\) | ||||
0.898540 | + | 0.438892i | \(0.144629\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.24621 | 0.483346 | 0.241673 | − | 0.970358i | \(-0.422304\pi\) | ||||
0.241673 | + | 0.970358i | \(0.422304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.7009 | 1.97699 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.9436 | 1.28820 | 0.644098 | − | 0.764943i | \(-0.277233\pi\) | ||||
0.644098 | + | 0.764943i | \(0.277233\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.5318 | −1.24969 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.2462 | 1.36379 | 0.681893 | − | 0.731452i | \(-0.261157\pi\) | ||||
0.681893 | + | 0.731452i | \(0.261157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9273 | 0.812220 | 0.406110 | − | 0.913824i | \(-0.366885\pi\) | ||||
0.406110 | + | 0.913824i | \(0.366885\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.8840 | 1.53542 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.44844 | −0.325302 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.5122 | −1.12242 | −0.561212 | − | 0.827672i | \(-0.689665\pi\) | ||||
−0.561212 | + | 0.827672i | \(0.689665\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.56512 | −0.688512 | −0.344256 | − | 0.938876i | \(-0.611869\pi\) | ||||
−0.344256 | + | 0.938876i | \(0.611869\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.1394 | −1.36362 | −0.681812 | − | 0.731527i | \(-0.738808\pi\) | ||||
−0.681812 | + | 0.731527i | \(0.738808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.133749 | 0.00948125 | 0.00474062 | − | 0.999989i | \(-0.498491\pi\) | ||||
0.00474062 | + | 0.999989i | \(0.498491\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.5778 | 1.09335 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.75379 | 0.401862 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.40617 | 0.0972666 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0117 | 1.58419 | 0.792095 | − | 0.610397i | \(-0.208990\pi\) | ||||
0.792095 | + | 0.610397i | \(0.208990\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.84818 | 0.398843 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.3612 | 1.38221 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.6803 | 1.32384 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.51471 | −0.503222 | −0.251611 | − | 0.967828i | \(-0.580960\pi\) | ||||
−0.251611 | + | 0.967828i | \(0.580960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.81690 | 0.386081 | 0.193041 | − | 0.981191i | \(-0.438165\pi\) | ||||
0.193041 | + | 0.981191i | \(0.438165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.1702 | −1.72938 | −0.864688 | − | 0.502309i | \(-0.832484\pi\) | ||||
−0.864688 | + | 0.502309i | \(0.832484\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.22352 | −0.145667 | −0.0728337 | − | 0.997344i | \(-0.523204\pi\) | ||||
−0.0728337 | + | 0.997344i | \(0.523204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −33.5445 | −2.18820 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.12873 | 0.525804 | 0.262902 | − | 0.964823i | \(-0.415320\pi\) | ||||
0.262902 | + | 0.964823i | \(0.415320\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.9517 | 1.67170 | 0.835848 | − | 0.548960i | \(-0.184976\pi\) | ||||
0.835848 | + | 0.548960i | \(0.184976\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.48529 | 0.158779 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.22101 | −0.395833 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.53741 | −0.0970403 | −0.0485202 | − | 0.998822i | \(-0.515451\pi\) | ||||
−0.0485202 | + | 0.998822i | \(0.515451\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.1231 | 0.699304 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.370318 | 0.0230998 | 0.0115499 | − | 0.999933i | \(-0.496323\pi\) | ||||
0.0115499 | + | 0.999933i | \(0.496323\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.3530 | 0.953992 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.9067 | −1.16584 | −0.582919 | − | 0.812530i | \(-0.698090\pi\) | ||||
−0.582919 | + | 0.812530i | \(0.698090\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.49342 | 0.583176 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.1898 | 0.926138 | 0.463069 | − | 0.886322i | \(-0.346748\pi\) | ||||
0.463069 | + | 0.886322i | \(0.346748\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.4027 | 1.72534 | 0.862669 | − | 0.505768i | \(-0.168791\pi\) | ||||
0.862669 | + | 0.505768i | \(0.168791\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.28347 | −0.559814 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.4647 | 1.71028 | 0.855139 | − | 0.518398i | \(-0.173471\pi\) | ||||
0.855139 | + | 0.518398i | \(0.173471\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.1394 | 1.61900 | 0.809500 | − | 0.587120i | \(-0.199738\pi\) | ||||
0.809500 | + | 0.587120i | \(0.199738\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.9117 | 1.59974 | 0.799868 | − | 0.600175i | \(-0.204903\pi\) | ||||
0.799868 | + | 0.600175i | \(0.204903\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.22994 | 0.249685 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.99213 | −0.411302 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.2714 | −0.600062 | −0.300031 | − | 0.953929i | \(-0.596997\pi\) | ||||
−0.300031 | + | 0.953929i | \(0.596997\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.5097 | −1.83457 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −49.2096 | −2.84587 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.29933 | 0.247809 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.2398 | −1.27345 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.05854 | −0.288706 | −0.144353 | − | 0.989526i | \(-0.546110\pi\) | ||||
−0.144353 | + | 0.989526i | \(0.546110\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.4222 | −0.761105 | −0.380553 | − | 0.924759i | \(-0.624266\pi\) | ||||
−0.380553 | + | 0.924759i | \(0.624266\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.94001 | 0.392272 | 0.196136 | − | 0.980577i | \(-0.437161\pi\) | ||||
0.196136 | + | 0.980577i | \(0.437161\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.60448 | −0.314779 | −0.157389 | − | 0.987537i | \(-0.550308\pi\) | ||||
−0.157389 | + | 0.987537i | \(0.550308\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.74777 | 0.489781 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.16352 | −0.176023 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 41.0709 | 2.27820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.6605 | −1.35958 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.11140 | −0.225983 | −0.112992 | − | 0.993596i | \(-0.536043\pi\) | ||||
−0.112992 | + | 0.993596i | \(0.536043\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.37745 | 0.348437 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.632801 | −0.0344709 | −0.0172354 | − | 0.999851i | \(-0.505486\pi\) | ||||
−0.0172354 | + | 0.999851i | \(0.505486\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.4339 | 0.619179 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3556 | 1.04510 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.02871 | −0.162590 | −0.0812949 | − | 0.996690i | \(-0.525906\pi\) | ||||
−0.0812949 | + | 0.996690i | \(0.525906\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.0954 | 1.02215 | 0.511076 | − | 0.859535i | \(-0.329247\pi\) | ||||
0.511076 | + | 0.859535i | \(0.329247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.2025 | −0.809147 | −0.404573 | − | 0.914506i | \(-0.632580\pi\) | ||||
−0.404573 | + | 0.914506i | \(0.632580\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 44.3079 | 2.35162 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −34.9411 | −1.84412 | −0.922059 | − | 0.387048i | \(-0.873495\pi\) | ||||
−0.922059 | + | 0.387048i | \(0.873495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.4133 | 1.12082 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7.60839 | −0.397155 | −0.198577 | − | 0.980085i | \(-0.563632\pi\) | ||||
−0.198577 | + | 0.980085i | \(0.563632\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.97916 | 0.362340 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.38739 | 0.486060 | 0.243030 | − | 0.970019i | \(-0.421859\pi\) | ||||
0.243030 | + | 0.970019i | \(0.421859\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −38.7009 | −1.99320 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.0046 | −0.565267 | −0.282633 | − | 0.959228i | \(-0.591208\pi\) | ||||
−0.282633 | + | 0.959228i | \(0.591208\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 20.6923 | 1.05733 | 0.528665 | − | 0.848831i | \(-0.322693\pi\) | ||||
0.528665 | + | 0.848831i | \(0.322693\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.9936 | −0.611249 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.4306 | 0.731659 | 0.365830 | − | 0.930682i | \(-0.380785\pi\) | ||||
0.365830 | + | 0.930682i | \(0.380785\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.0242 | −1.26553 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −38.3342 | −1.92880 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.2739 | −0.716388 | −0.358194 | − | 0.933647i | \(-0.616607\pi\) | ||||
−0.358194 | + | 0.933647i | \(0.616607\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.38559 | −0.268943 | −0.134472 | − | 0.990917i | \(-0.542934\pi\) | ||||
−0.134472 | + | 0.990917i | \(0.542934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −50.5845 | −2.51979 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.62155 | 0.427354 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.07983 | 0.251182 | 0.125591 | − | 0.992082i | \(-0.459917\pi\) | ||||
0.125591 | + | 0.992082i | \(0.459917\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.1646 | −1.13985 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.14539 | −0.301666 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.30576 | 0.210350 | 0.105175 | − | 0.994454i | \(-0.466460\pi\) | ||||
0.105175 | + | 0.994454i | \(0.466460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.8670 | −0.870782 | −0.435391 | − | 0.900241i | \(-0.643390\pi\) | ||||
−0.435391 | + | 0.900241i | \(0.643390\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.8855 | 1.01309 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.3497 | −0.791219 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.1958 | −0.876461 | −0.438230 | − | 0.898863i | \(-0.644395\pi\) | ||||
−0.438230 | + | 0.898863i | \(0.644395\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6074 | −0.798100 | −0.399050 | − | 0.916929i | \(-0.630660\pi\) | ||||
−0.399050 | + | 0.916929i | \(0.630660\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.91023 | 0.378398 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.6084 | 0.554038 | 0.277019 | − | 0.960864i | \(-0.410653\pi\) | ||||
0.277019 | + | 0.960864i | \(0.410653\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.8140 | 1.13144 | 0.565720 | − | 0.824598i | \(-0.308598\pi\) | ||||
0.565720 | + | 0.824598i | \(0.308598\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.7992 | −1.22300 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.72336 | −0.175716 | −0.0878582 | − | 0.996133i | \(-0.528002\pi\) | ||||
−0.0878582 | + | 0.996133i | \(0.528002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.37533 | 0.111850 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 53.0607 | 2.48752 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.7719 | 1.25234 | 0.626169 | − | 0.779688i | \(-0.284622\pi\) | ||||
0.626169 | + | 0.779688i | \(0.284622\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.76735 | −0.361761 | −0.180881 | − | 0.983505i | \(-0.557895\pi\) | ||||
−0.180881 | + | 0.983505i | \(0.557895\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.7928 | 0.641004 | 0.320502 | − | 0.947248i | \(-0.396148\pi\) | ||||
0.320502 | + | 0.947248i | \(0.396148\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.7282 | 1.28311 | 0.641554 | − | 0.767078i | \(-0.278290\pi\) | ||||
0.641554 | + | 0.767078i | \(0.278290\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.68843 | 0.216492 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.41430 | 0.111010 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.60197 | −0.302919 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0163 | 0.640420 | 0.320210 | − | 0.947347i | \(-0.396247\pi\) | ||||
0.320210 | + | 0.947347i | \(0.396247\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.1425 | −1.73915 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.3916 | −0.744304 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.5764 | 1.70275 | 0.851374 | − | 0.524559i | \(-0.175770\pi\) | ||||
0.851374 | + | 0.524559i | \(0.175770\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.24309 | 0.236617 | 0.118309 | − | 0.992977i | \(-0.462253\pi\) | ||||
0.118309 | + | 0.992977i | \(0.462253\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.6803 | −0.886356 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.5733 | 1.46111 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.0542 | −1.30065 | −0.650323 | − | 0.759658i | \(-0.725367\pi\) | ||||
−0.650323 | + | 0.759658i | \(0.725367\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −31.5512 | −1.40680 | −0.703399 | − | 0.710796i | \(-0.748335\pi\) | ||||
−0.703399 | + | 0.710796i | \(0.748335\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −55.3373 | −2.46248 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.5097 | −0.776104 | −0.388052 | − | 0.921638i | \(-0.626852\pi\) | ||||
−0.388052 | + | 0.921638i | \(0.626852\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.7421 | 0.696391 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.1908 | 1.15410 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.8482 | −0.609042 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.8780 | 1.65947 | 0.829733 | − | 0.558161i | \(-0.188493\pi\) | ||||
0.829733 | + | 0.558161i | \(0.188493\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.3739 | −1.24070 | −0.620352 | − | 0.784324i | \(-0.713010\pi\) | ||||
−0.620352 | + | 0.784324i | \(0.713010\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.7234 | −1.12053 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.5718 | 1.72051 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.5087 | −0.455182 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 40.4945 | 1.75073 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.02600 | 0.0441930 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.5868 | 1.65898 | 0.829488 | − | 0.558524i | \(-0.188632\pi\) | ||||
0.829488 | + | 0.558524i | \(0.188632\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.2615 | 0.825071 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.3947 | 0.572717 | 0.286359 | − | 0.958123i | \(-0.407555\pi\) | ||||
0.286359 | + | 0.958123i | \(0.407555\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.22101 | 0.265024 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.1816 | −1.19841 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.46471 | −0.189176 | −0.0945879 | − | 0.995517i | \(-0.530153\pi\) | ||||
−0.0945879 | + | 0.995517i | \(0.530153\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.6811 | −0.451762 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.1171 | −0.932124 | −0.466062 | − | 0.884752i | \(-0.654328\pi\) | ||||
−0.466062 | + | 0.884752i | \(0.654328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.0163 | −1.26279 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.70238 | −0.280978 | −0.140489 | − | 0.990082i | \(-0.544868\pi\) | ||||
−0.140489 | + | 0.990082i | \(0.544868\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.37533 | 0.266799 | 0.133400 | − | 0.991062i | \(-0.457411\pi\) | ||||
0.133400 | + | 0.991062i | \(0.457411\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −52.2231 | −2.17785 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.5654 | 1.85528 | 0.927641 | − | 0.373474i | \(-0.121834\pi\) | ||||
0.927641 | + | 0.373474i | \(0.121834\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.51783 | −0.187431 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.91917 | 0.162315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.6311 | −1.22301 | −0.611503 | − | 0.791242i | \(-0.709435\pi\) | ||||
−0.611503 | + | 0.791242i | \(0.709435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.13124 | 0.335042 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −43.6572 | −1.79279 | −0.896393 | − | 0.443259i | \(-0.853822\pi\) | ||||
−0.896393 | + | 0.443259i | \(0.853822\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.9825 | 1.10618 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.5661 | −0.513438 | −0.256719 | − | 0.966486i | \(-0.582641\pi\) | ||||
−0.256719 | + | 0.966486i | \(0.582641\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.9213 | −1.54684 | −0.773421 | − | 0.633893i | \(-0.781456\pi\) | ||||
−0.773421 | + | 0.633893i | \(0.781456\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.7328 | 1.24947 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.93332 | −0.0784710 | −0.0392355 | − | 0.999230i | \(-0.512492\pi\) | ||||
−0.0392355 | + | 0.999230i | \(0.512492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 61.2656 | 2.47854 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.4306 | 0.744404 | 0.372202 | − | 0.928152i | \(-0.378603\pi\) | ||||
0.372202 | + | 0.928152i | \(0.378603\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.5314 | −1.22915 | −0.614574 | − | 0.788859i | \(-0.710672\pi\) | ||||
−0.614574 | + | 0.788859i | \(0.710672\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.9094 | −1.16197 | −0.580984 | − | 0.813915i | \(-0.697332\pi\) | ||||
−0.580984 | + | 0.813915i | \(0.697332\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.9665 | −0.759875 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.4238 | −0.576954 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.3963 | −0.773382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.5314 | −1.29505 | −0.647527 | − | 0.762042i | \(-0.724197\pi\) | ||||
−0.647527 | + | 0.762042i | \(0.724197\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 41.0457 | 1.62885 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.53912 | −0.179846 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.1312 | 1.19011 | 0.595056 | − | 0.803684i | \(-0.297130\pi\) | ||||
0.595056 | + | 0.803684i | \(0.297130\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.1752 | −0.795633 | −0.397817 | − | 0.917465i | \(-0.630232\pi\) | ||||
−0.397817 | + | 0.917465i | \(0.630232\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.2741 | 0.561174 | 0.280587 | − | 0.959829i | \(-0.409471\pi\) | ||||
0.280587 | + | 0.959829i | \(0.409471\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.0081 | −0.510614 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.21538 | −0.360626 | −0.180313 | − | 0.983609i | \(-0.557711\pi\) | ||||
−0.180313 | + | 0.983609i | \(0.557711\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.13666 | −0.122560 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.1511 | −0.473339 | −0.236669 | − | 0.971590i | \(-0.576056\pi\) | ||||
−0.236669 | + | 0.971590i | \(0.576056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6924 | 0.532574 | 0.266287 | − | 0.963894i | \(-0.414203\pi\) | ||||
0.266287 | + | 0.963894i | \(0.414203\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.52927 | −0.330751 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 49.2096 | 1.90540 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.18124 | −0.354438 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.5341 | 1.56247 | 0.781237 | − | 0.624234i | \(-0.214589\pi\) | ||||
0.781237 | + | 0.624234i | \(0.214589\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.5653 | −0.444492 | −0.222246 | − | 0.974991i | \(-0.571339\pi\) | ||||
−0.222246 | + | 0.974991i | \(0.571339\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0504 | −0.462452 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.2625 | 1.69366 | 0.846828 | − | 0.531866i | \(-0.178509\pi\) | ||||
0.846828 | + | 0.531866i | \(0.178509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.79064 | −0.0684168 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.3387 | −0.660554 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.6676 | 1.24274 | 0.621368 | − | 0.783519i | \(-0.286577\pi\) | ||||
0.621368 | + | 0.783519i | \(0.286577\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.4275 | −0.585197 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.34391 | −0.202415 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.73150 | 0.329784 | 0.164892 | − | 0.986312i | \(-0.447272\pi\) | ||||
0.164892 | + | 0.986312i | \(0.447272\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.13124 | 0.231244 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40.6816 | −1.52999 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.3058 | 0.537264 | 0.268632 | − | 0.963243i | \(-0.413428\pi\) | ||||
0.268632 | + | 0.963243i | \(0.413428\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 64.3200 | 2.40880 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.7964 | 1.11432 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21.4959 | −0.801663 | −0.400831 | − | 0.916152i | \(-0.631279\pi\) | ||||
−0.400831 | + | 0.916152i | \(0.631279\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.2543 | 0.717069 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −41.0709 | −1.52533 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 47.6002 | 1.76539 | 0.882696 | − | 0.469944i | \(-0.155726\pi\) | ||||
0.882696 | + | 0.469944i | \(0.155726\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.43158 | −0.200894 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −49.7239 | −1.83659 | −0.918297 | − | 0.395892i | \(-0.870435\pi\) | ||||
−0.918297 | + | 0.395892i | \(0.870435\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.63280 | 0.0969805 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.5283 | −1.30693 | −0.653464 | − | 0.756957i | \(-0.726685\pi\) | ||||
−0.653464 | + | 0.756957i | \(0.726685\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.3612 | 0.746979 | 0.373490 | − | 0.927634i | \(-0.378161\pi\) | ||||
0.373490 | + | 0.927634i | \(0.378161\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −64.6194 | −2.36747 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.7699 | 1.08777 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.9868 | −0.692840 | −0.346420 | − | 0.938080i | \(-0.612603\pi\) | ||||
−0.346420 | + | 0.938080i | \(0.612603\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.3342 | 0.812824 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.4738 | −0.816826 | −0.408413 | − | 0.912797i | \(-0.633918\pi\) | ||||
−0.408413 | + | 0.912797i | \(0.633918\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.40973 | 0.0511028 | 0.0255514 | − | 0.999674i | \(-0.491866\pi\) | ||||
0.0255514 | + | 0.999674i | \(0.491866\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.1602 | 0.512634 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 57.5492 | 2.07798 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.114116 | −0.00411512 | −0.00205756 | − | 0.999998i | \(-0.500655\pi\) | ||||
−0.00205756 | + | 0.999998i | \(0.500655\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 46.1799 | 1.66097 | 0.830487 | − | 0.557038i | \(-0.188062\pi\) | ||||
0.830487 | + | 0.557038i | \(0.188062\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −53.6822 | −1.92832 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.68923 | 0.0605228 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.2916 | 0.654525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −59.8297 | −2.13541 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.6847 | −0.452159 | −0.226080 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226080 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.0667 | −0.784601 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 40.6186 | 1.44241 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.2796 | −1.39135 | −0.695677 | − | 0.718355i | \(-0.744895\pi\) | ||||
−0.695677 | + | 0.718355i | \(0.744895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.1549 | 1.10218 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.84004 | 0.311958 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −67.4685 | −2.37795 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.09896 | 0.0386374 | 0.0193187 | − | 0.999813i | \(-0.493850\pi\) | ||||
0.0193187 | + | 0.999813i | \(0.493850\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.5627 | −1.28389 | −0.641944 | − | 0.766751i | \(-0.721872\pi\) | ||||
−0.641944 | + | 0.766751i | \(0.721872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −78.1496 | −2.73746 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.71694 | 0.0600681 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.8823 | 0.624097 | 0.312049 | − | 0.950066i | \(-0.398985\pi\) | ||||
0.312049 | + | 0.950066i | \(0.398985\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.31328 | 0.289783 | 0.144891 | − | 0.989448i | \(-0.453717\pi\) | ||||
0.144891 | + | 0.989448i | \(0.453717\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.280204 | 0.00974363 | 0.00487182 | − | 0.999988i | \(-0.498449\pi\) | ||||
0.00487182 | + | 0.999988i | \(0.498449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.04148 | 0.209829 | 0.104915 | − | 0.994481i | \(-0.466543\pi\) | ||||
0.104915 | + | 0.994481i | \(0.466543\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.30824 | −0.0799759 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.2756 | −0.736274 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.5942 | 1.02171 | 0.510853 | − | 0.859668i | \(-0.329330\pi\) | ||||
0.510853 | + | 0.859668i | \(0.329330\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.70093 | 0.334515 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −87.5416 | −3.01152 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.5934 | 0.776320 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.4996 | 1.66254 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.2331 | 0.521570 | 0.260785 | − | 0.965397i | \(-0.416019\pi\) | ||||
0.260785 | + | 0.965397i | \(0.416019\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.25535 | 0.0770412 | 0.0385206 | − | 0.999258i | \(-0.487735\pi\) | ||||
0.0385206 | + | 0.999258i | \(0.487735\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.91686 | 0.0654025 | 0.0327013 | − | 0.999465i | \(-0.489589\pi\) | ||||
0.0327013 | + | 0.999465i | \(0.489589\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.8530 | −1.22045 | −0.610225 | − | 0.792228i | \(-0.708921\pi\) | ||||
−0.610225 | + | 0.792228i | \(0.708921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.7126 | −1.96229 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.8255 | −0.536843 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.6478 | −0.394669 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.6636 | 0.461915 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.2323 | 1.62869 | 0.814344 | − | 0.580383i | \(-0.197097\pi\) | ||||
0.814344 | + | 0.580383i | \(0.197097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.77336 | −0.160819 | −0.0804094 | − | 0.996762i | \(-0.525623\pi\) | ||||
−0.0804094 | + | 0.996762i | \(0.525623\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.2144 | 0.747573 | 0.373787 | − | 0.927515i | \(-0.378059\pi\) | ||||
0.373787 | + | 0.927515i | \(0.378059\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.1729 | 1.41603 | 0.708014 | − | 0.706198i | \(-0.249591\pi\) | ||||
0.708014 | + | 0.706198i | \(0.249591\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.1750 | 1.01204 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.84818 | −0.329557 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −62.1496 | −2.07743 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 50.5845 | 1.68709 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.81714 | −0.293742 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −37.2202 | −1.23724 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.7564 | 0.888430 | 0.444215 | − | 0.895920i | \(-0.353483\pi\) | ||||
0.444215 | + | 0.895920i | \(0.353483\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.1281 | −0.368691 | −0.184346 | − | 0.982861i | \(-0.559017\pi\) | ||||
−0.184346 | + | 0.982861i | \(0.559017\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.53700 | −0.0839625 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.30594 | −0.0761489 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.45195 | 0.179843 | 0.0899216 | − | 0.995949i | \(-0.471338\pi\) | ||||
0.0899216 | + | 0.995949i | \(0.471338\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −80.9237 | −2.66364 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.4783 | −1.33092 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.94402 | 0.0637813 | 0.0318906 | − | 0.999491i | \(-0.489847\pi\) | ||||
0.0318906 | + | 0.999491i | \(0.489847\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.729644 | 0.0239131 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.1521 | 0.495527 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.2897 | −0.368820 | −0.184410 | − | 0.982849i | \(-0.559037\pi\) | ||||
−0.184410 | + | 0.982849i | \(0.559037\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −51.4229 | −1.67634 | −0.838170 | − | 0.545409i | \(-0.816374\pi\) | ||||
−0.838170 | + | 0.545409i | \(0.816374\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3622 | 0.435133 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.94045 | −0.0630563 | −0.0315281 | − | 0.999503i | \(-0.510037\pi\) | ||||
−0.0315281 | + | 0.999503i | \(0.510037\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.1092 | −1.26954 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.4523 | 0.759693 | 0.379847 | − | 0.925049i | \(-0.375977\pi\) | ||||
0.379847 | + | 0.925049i | \(0.375977\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 52.8371 | 1.70977 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.31640 | −0.0425088 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.1171 | 1.13281 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.5804 | 1.04880 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −59.0194 | −1.89794 | −0.948968 | − | 0.315373i | \(-0.897870\pi\) | ||||
−0.948968 | + | 0.315373i | \(0.897870\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.7743 | 1.27642 | 0.638209 | − | 0.769863i | \(-0.279676\pi\) | ||||
0.638209 | + | 0.769863i | \(0.279676\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.3416 | −0.363595 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.9538 | 1.34222 | 0.671111 | − | 0.741357i | \(-0.265817\pi\) | ||||
0.671111 | + | 0.741357i | \(0.265817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6507 | −0.340397 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.93132 | 0.252970 | 0.126485 | − | 0.991969i | \(-0.459630\pi\) | ||||
0.126485 | + | 0.991969i | \(0.459630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 65.1919 | 2.07719 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.5814 | 0.431863 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.8408 | −0.789093 | −0.394546 | − | 0.918876i | \(-0.629098\pi\) | ||||
−0.394546 | + | 0.918876i | \(0.629098\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.455573 | −0.0144426 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.1157 | 0.890433 | 0.445216 | − | 0.895423i | \(-0.353127\pi\) | ||||
0.445216 | + | 0.895423i | \(0.353127\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 5472.2.a.bt.1.1 | 4 | ||
3.2 | odd | 2 | 608.2.a.i.1.4 | ✓ | 4 | ||
4.3 | odd | 2 | 5472.2.a.bs.1.1 | 4 | |||
12.11 | even | 2 | 608.2.a.j.1.2 | yes | 4 | ||
24.5 | odd | 2 | 1216.2.a.x.1.1 | 4 | |||
24.11 | even | 2 | 1216.2.a.w.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.a.i.1.4 | ✓ | 4 | 3.2 | odd | 2 | ||
608.2.a.j.1.2 | yes | 4 | 12.11 | even | 2 | ||
1216.2.a.w.1.3 | 4 | 24.11 | even | 2 | |||
1216.2.a.x.1.1 | 4 | 24.5 | odd | 2 | |||
5472.2.a.bs.1.1 | 4 | 4.3 | odd | 2 | |||
5472.2.a.bt.1.1 | 4 | 1.1 | even | 1 | trivial |