Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4400,2,Mod(1,4400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, 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("4400.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4400 = 2^{4} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4400.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: | \(35.1341768894\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.837.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 6x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2200) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.167449\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4400.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.16745 | −0.674027 | −0.337014 | − | 0.941500i | \(-0.609417\pi\) | ||||
−0.337014 | + | 0.941500i | \(0.609417\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.97196 | −1.87922 | −0.939612 | − | 0.342241i | \(-0.888814\pi\) | ||||
−0.939612 | + | 0.342241i | \(0.888814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.63706 | −0.545687 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.665102 | −0.184466 | −0.0922330 | − | 0.995737i | \(-0.529400\pi\) | ||||
−0.0922330 | + | 0.995737i | \(0.529400\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.77647 | 1.64354 | 0.821768 | − | 0.569822i | \(-0.192988\pi\) | ||||
0.821768 | + | 0.569822i | \(0.192988\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.80451 | 1.26665 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.16745 | −0.451944 | −0.225972 | − | 0.974134i | \(-0.572556\pi\) | ||||
−0.225972 | + | 0.974134i | \(0.572556\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.41353 | 1.04184 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.97196 | 1.48036 | 0.740178 | − | 0.672411i | \(-0.234741\pi\) | ||||
0.740178 | + | 0.672411i | \(0.234741\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.94392 | 1.60638 | 0.803188 | − | 0.595726i | \(-0.203136\pi\) | ||||
0.803188 | + | 0.595726i | \(0.203136\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.16745 | −0.203227 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.139410 | −0.0229189 | −0.0114594 | − | 0.999934i | \(-0.503648\pi\) | ||||
−0.0114594 | + | 0.999934i | \(0.503648\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.776472 | 0.124335 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.80451 | −0.281817 | −0.140909 | − | 0.990023i | \(-0.545002\pi\) | ||||
−0.140909 | + | 0.990023i | \(0.545002\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.80451 | −0.427684 | −0.213842 | − | 0.976868i | \(-0.568598\pi\) | ||||
−0.213842 | + | 0.976868i | \(0.568598\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.530387 | −0.0773649 | −0.0386824 | − | 0.999252i | \(-0.512316\pi\) | ||||
−0.0386824 | + | 0.999252i | \(0.512316\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.7204 | 2.53148 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.91119 | −1.10779 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.30216 | −0.865669 | −0.432834 | − | 0.901473i | \(-0.642487\pi\) | ||||
−0.432834 | + | 0.901473i | \(0.642487\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.16745 | 0.154632 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.4696 | −1.49322 | −0.746608 | − | 0.665264i | \(-0.768319\pi\) | ||||
−0.746608 | + | 0.665264i | \(0.768319\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5810 | 1.35476 | 0.677378 | − | 0.735635i | \(-0.263116\pi\) | ||||
0.677378 | + | 0.735635i | \(0.263116\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.13941 | 1.02547 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.60902 | −1.17393 | −0.586965 | − | 0.809613i | \(-0.699677\pi\) | ||||
−0.586965 | + | 0.809613i | \(0.699677\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.53039 | 0.304623 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.80921 | 1.16414 | 0.582069 | − | 0.813139i | \(-0.302243\pi\) | ||||
0.582069 | + | 0.813139i | \(0.302243\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.02804 | −0.822570 | −0.411285 | − | 0.911507i | \(-0.634920\pi\) | ||||
−0.411285 | + | 0.911507i | \(0.634920\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.97196 | −0.566608 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50235 | −0.619062 | −0.309531 | − | 0.950889i | \(-0.600172\pi\) | ||||
−0.309531 | + | 0.950889i | \(0.600172\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.40884 | −0.156538 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.5810 | −1.49071 | −0.745353 | − | 0.666670i | \(-0.767719\pi\) | ||||
−0.745353 | + | 0.666670i | \(0.767719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −9.30686 | −0.997800 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.58098 | −1.01558 | −0.507791 | − | 0.861480i | \(-0.669538\pi\) | ||||
−0.507791 | + | 0.861480i | \(0.669538\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.30686 | 0.346653 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.4416 | −1.08274 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7812 | −1.50080 | −0.750400 | − | 0.660984i | \(-0.770139\pi\) | ||||
−0.750400 | + | 0.660984i | \(0.770139\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.63706 | −0.164531 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.22353 | 0.420257 | 0.210128 | − | 0.977674i | \(-0.432612\pi\) | ||||
0.210128 | + | 0.977674i | \(0.432612\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9206 | 1.66723 | 0.833617 | − | 0.552343i | \(-0.186266\pi\) | ||||
0.833617 | + | 0.552343i | \(0.186266\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.66980 | 0.548120 | 0.274060 | − | 0.961713i | \(-0.411633\pi\) | ||||
0.274060 | + | 0.961713i | \(0.411633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.2508 | −1.55654 | −0.778271 | − | 0.627928i | \(-0.783903\pi\) | ||||
−0.778271 | + | 0.627928i | \(0.783903\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.162754 | 0.0154479 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.86059 | −0.175030 | −0.0875148 | − | 0.996163i | \(-0.527893\pi\) | ||||
−0.0875148 | + | 0.996163i | \(0.527893\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.08881 | 0.100661 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −33.6924 | −3.08857 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.10668 | 0.189953 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1674 | −0.990951 | −0.495475 | − | 0.868622i | \(-0.665006\pi\) | ||||
−0.495475 | + | 0.868622i | \(0.665006\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.27412 | 0.288271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.7812 | −1.29144 | −0.645718 | − | 0.763576i | \(-0.723442\pi\) | ||||
−0.645718 | + | 0.763576i | \(0.723442\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.97196 | 0.431124 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.63706 | −0.652478 | −0.326239 | − | 0.945287i | \(-0.605781\pi\) | ||||
−0.326239 | + | 0.945287i | \(0.605781\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.27882 | 0.447744 | 0.223872 | − | 0.974619i | \(-0.428130\pi\) | ||||
0.223872 | + | 0.974619i | \(0.428130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.619200 | 0.0521460 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.665102 | −0.0556186 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −20.6877 | −1.70629 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.60902 | 0.459509 | 0.229755 | − | 0.973249i | \(-0.426208\pi\) | ||||
0.229755 | + | 0.973249i | \(0.426208\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.86059 | 0.314170 | 0.157085 | − | 0.987585i | \(-0.449790\pi\) | ||||
0.157085 | + | 0.987585i | \(0.449790\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.0935 | −0.896857 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.5482 | 1.32069 | 0.660347 | − | 0.750961i | \(-0.270409\pi\) | ||||
0.660347 | + | 0.750961i | \(0.270409\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.35746 | 0.583484 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.7765 | 0.849305 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.8598 | 1.63387 | 0.816933 | − | 0.576733i | \(-0.195673\pi\) | ||||
0.816933 | + | 0.576733i | \(0.195673\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.0226 | −1.62677 | −0.813387 | − | 0.581723i | \(-0.802379\pi\) | ||||
−0.813387 | + | 0.581723i | \(0.802379\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5576 | −0.965972 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.63706 | 0.125189 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.33020 | 0.329219 | 0.164610 | − | 0.986359i | \(-0.447364\pi\) | ||||
0.164610 | + | 0.986359i | \(0.447364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.3902 | 1.00647 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.6371 | −1.09403 | −0.547013 | − | 0.837124i | \(-0.684235\pi\) | ||||
−0.547013 | + | 0.837124i | \(0.684235\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.9112 | 0.885352 | 0.442676 | − | 0.896682i | \(-0.354029\pi\) | ||||
0.442676 | + | 0.896682i | \(0.354029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.3528 | −0.913142 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.77647 | 0.495545 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −26.9159 | −1.95784 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.2508 | −1.46530 | −0.732648 | − | 0.680608i | \(-0.761716\pi\) | ||||
−0.732648 | + | 0.680608i | \(0.761716\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.2180 | −1.38335 | −0.691673 | − | 0.722211i | \(-0.743126\pi\) | ||||
−0.691673 | + | 0.722211i | \(0.743126\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.9945 | 1.49580 | 0.747899 | − | 0.663813i | \(-0.231063\pi\) | ||||
0.747899 | + | 0.663813i | \(0.231063\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.64176 | −0.329045 | −0.164523 | − | 0.986373i | \(-0.552608\pi\) | ||||
−0.164523 | + | 0.986373i | \(0.552608\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.2180 | 0.791260 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −39.6363 | −2.78192 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.54825 | 0.246620 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.19079 | 0.219663 | 0.109832 | − | 0.993950i | \(-0.464969\pi\) | ||||
0.109832 | + | 0.993950i | \(0.464969\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.4518 | −0.784661 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −44.4688 | −3.01874 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.20488 | 0.554434 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.50704 | −0.303177 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.46961 | 0.500202 | 0.250101 | − | 0.968220i | \(-0.419536\pi\) | ||||
0.250101 | + | 0.968220i | \(0.419536\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.1947 | 1.47311 | 0.736557 | − | 0.676375i | \(-0.236450\pi\) | ||||
0.736557 | + | 0.676375i | \(0.236450\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.50235 | 0.231442 | 0.115721 | − | 0.993282i | \(-0.463082\pi\) | ||||
0.115721 | + | 0.993282i | \(0.463082\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.80451 | 0.381909 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.637062 | 0.0417353 | 0.0208677 | − | 0.999782i | \(-0.493357\pi\) | ||||
0.0208677 | + | 0.999782i | \(0.493357\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.42371 | 0.417265 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.35824 | 0.540650 | 0.270325 | − | 0.962769i | \(-0.412869\pi\) | ||||
0.270325 | + | 0.962769i | \(0.412869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.0506 | 0.647416 | 0.323708 | − | 0.946157i | \(-0.395070\pi\) | ||||
0.323708 | + | 0.946157i | \(0.395070\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.5959 | −0.936325 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.665102 | 0.0423194 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.8551 | 1.00478 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.44627 | 0.217527 | 0.108763 | − | 0.994068i | \(-0.465311\pi\) | ||||
0.108763 | + | 0.994068i | \(0.465311\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.16745 | −0.136266 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.4743 | −0.715748 | −0.357874 | − | 0.933770i | \(-0.616498\pi\) | ||||
−0.357874 | + | 0.933770i | \(0.616498\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.693141 | 0.0430697 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.0506 | −0.807812 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.41823 | 0.272440 | 0.136220 | − | 0.990679i | \(-0.456505\pi\) | ||||
0.136220 | + | 0.990679i | \(0.456505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.1853 | 0.684530 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.11607 | 0.372903 | 0.186452 | − | 0.982464i | \(-0.440301\pi\) | ||||
0.186452 | + | 0.982464i | \(0.440301\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.3014 | 1.65844 | 0.829220 | − | 0.558922i | \(-0.188785\pi\) | ||||
0.829220 | + | 0.558922i | \(0.188785\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.86059 | −0.233654 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.14411 | 0.0687426 | 0.0343713 | − | 0.999409i | \(-0.489057\pi\) | ||||
0.0343713 | + | 0.999409i | \(0.489057\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.6418 | −0.876579 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.6410 | −1.82789 | −0.913944 | − | 0.405841i | \(-0.866979\pi\) | ||||
−0.913944 | + | 0.405841i | \(0.866979\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.16275 | −0.247450 | −0.123725 | − | 0.992317i | \(-0.539484\pi\) | ||||
−0.123725 | + | 0.992317i | \(0.539484\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.97196 | 0.529598 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.9206 | 1.70121 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.2563 | 1.01158 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −25.7757 | −1.50583 | −0.752916 | − | 0.658117i | \(-0.771353\pi\) | ||||
−0.752916 | + | 0.658117i | \(0.771353\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.41353 | 0.314125 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.44157 | 0.0833684 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.9439 | 0.803714 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.93075 | −0.283264 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.7859 | 0.729728 | 0.364864 | − | 0.931061i | \(-0.381116\pi\) | ||||
0.364864 | + | 0.931061i | \(0.381116\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.7539 | −1.12376 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.39098 | −0.192285 | −0.0961423 | − | 0.995368i | \(-0.530650\pi\) | ||||
−0.0961423 | + | 0.995368i | \(0.530650\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.32551 | −0.357539 | −0.178769 | − | 0.983891i | \(-0.557212\pi\) | ||||
−0.178769 | + | 0.983891i | \(0.557212\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −18.4510 | −1.03631 | −0.518155 | − | 0.855287i | \(-0.673381\pi\) | ||||
−0.518155 | + | 0.855287i | \(0.673381\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.97196 | 0.446344 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.61920 | −0.369448 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.77647 | −0.377053 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.9720 | 1.04915 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.63706 | 0.145386 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.19549 | 0.120675 | 0.0603375 | − | 0.998178i | \(-0.480782\pi\) | ||||
0.0603375 | + | 0.998178i | \(0.480782\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.228223 | 0.0125065 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.8878 | 0.974413 | 0.487206 | − | 0.873287i | \(-0.338016\pi\) | ||||
0.487206 | + | 0.873287i | \(0.338016\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.17214 | 0.117975 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.94392 | 0.484341 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −53.3014 | −2.87800 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.0280 | 1.02148 | 0.510739 | − | 0.859736i | \(-0.329372\pi\) | ||||
0.510739 | + | 0.859736i | \(0.329372\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.6090 | −1.53141 | −0.765703 | − | 0.643194i | \(-0.777609\pi\) | ||||
−0.765703 | + | 0.643194i | \(0.777609\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.60055 | −0.192183 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.6698 | 1.04692 | 0.523459 | − | 0.852051i | \(-0.324641\pi\) | ||||
0.523459 | + | 0.852051i | \(0.324641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 39.3341 | 2.08178 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.8271 | 0.571431 | 0.285715 | − | 0.958315i | \(-0.407769\pi\) | ||||
0.285715 | + | 0.958315i | \(0.407769\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.16745 | −0.0612752 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.50235 | −0.339420 | −0.169710 | − | 0.985494i | \(-0.554283\pi\) | ||||
−0.169710 | + | 0.985494i | \(0.554283\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.95410 | 0.153784 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 31.3341 | 1.62679 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.14880 | −0.421929 | −0.210964 | − | 0.977494i | \(-0.567660\pi\) | ||||
−0.210964 | + | 0.977494i | \(0.567660\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.30216 | −0.273075 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.14411 | −0.0587687 | −0.0293844 | − | 0.999568i | \(-0.509355\pi\) | ||||
−0.0293844 | + | 0.999568i | \(0.509355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.0374 | 0.667928 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.53508 | 0.129537 | 0.0647683 | − | 0.997900i | \(-0.479369\pi\) | ||||
0.0647683 | + | 0.997900i | \(0.479369\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.59116 | 0.233382 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.6698 | −0.642384 | −0.321192 | − | 0.947014i | \(-0.604084\pi\) | ||||
−0.321192 | + | 0.947014i | \(0.604084\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.6877 | −0.742787 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.2563 | 0.870463 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.9945 | −1.60576 | −0.802879 | − | 0.596141i | \(-0.796700\pi\) | ||||
−0.802879 | + | 0.596141i | \(0.796700\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.80451 | −0.290589 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.19549 | 0.459201 | 0.229600 | − | 0.973285i | \(-0.426258\pi\) | ||||
0.229600 | + | 0.973285i | \(0.426258\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.94862 | −0.296322 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.139410 | −0.00691030 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.4790 | −1.25986 | −0.629928 | − | 0.776654i | \(-0.716916\pi\) | ||||
−0.629928 | + | 0.776654i | \(0.716916\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.91588 | 0.439788 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 57.0265 | 2.80609 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.16275 | −0.301791 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.0132 | 1.22197 | 0.610987 | − | 0.791641i | \(-0.290773\pi\) | ||||
0.610987 | + | 0.791641i | \(0.290773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.8084 | −1.55025 | −0.775124 | − | 0.631809i | \(-0.782313\pi\) | ||||
−0.775124 | + | 0.631809i | \(0.782313\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.868276 | 0.0422170 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −52.6082 | −2.54589 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.776472 | 0.0374884 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.9712 | −1.44366 | −0.721830 | − | 0.692070i | \(-0.756699\pi\) | ||||
−0.721830 | + | 0.692070i | \(0.756699\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.8271 | −1.91397 | −0.956983 | − | 0.290143i | \(-0.906297\pi\) | ||||
−0.956983 | + | 0.290143i | \(0.906297\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.16745 | 0.103683 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.4369 | 0.832217 | 0.416108 | − | 0.909315i | \(-0.363394\pi\) | ||||
0.416108 | + | 0.909315i | \(0.363394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.0094 | −1.38140 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.21335 | 0.200182 | 0.100091 | − | 0.994978i | \(-0.468087\pi\) | ||||
0.100091 | + | 0.994978i | \(0.468087\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.54825 | −0.309722 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13.6643 | −0.644859 | −0.322429 | − | 0.946593i | \(-0.604500\pi\) | ||||
−0.322429 | + | 0.946593i | \(0.604500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.80451 | −0.0849711 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.50704 | −0.211759 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.25078 | 0.245621 | 0.122811 | − | 0.992430i | \(-0.460809\pi\) | ||||
0.122811 | + | 0.992430i | \(0.460809\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 36.6847 | 1.71229 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.74843 | −0.267731 | −0.133866 | − | 0.990999i | \(-0.542739\pi\) | ||||
−0.133866 | + | 0.990999i | \(0.542739\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.7710 | −1.29063 | −0.645314 | − | 0.763918i | \(-0.723273\pi\) | ||||
−0.645314 | + | 0.763918i | \(0.723273\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.3575 | −0.618109 | −0.309055 | − | 0.951044i | \(-0.600013\pi\) | ||||
−0.309055 | + | 0.951044i | \(0.600013\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 47.7757 | 2.20608 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.3192 | −0.890184 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.80451 | −0.128952 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.3170 | 0.472385 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.7578 | −0.537229 | −0.268614 | − | 0.963248i | \(-0.586566\pi\) | ||||
−0.268614 | + | 0.963248i | \(0.586566\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0927218 | 0.00422775 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.5810 | −0.572455 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.6651 | −0.845796 | −0.422898 | − | 0.906177i | \(-0.638987\pi\) | ||||
−0.422898 | + | 0.906177i | \(0.638987\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −24.3528 | −1.10127 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.4969 | −1.46656 | −0.733282 | − | 0.679925i | \(-0.762012\pi\) | ||||
−0.733282 | + | 0.679925i | \(0.762012\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 54.0218 | 2.43302 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −48.7710 | −2.18768 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.6884 | −0.523247 | −0.261623 | − | 0.965170i | \(-0.584258\pi\) | ||||
−0.261623 | + | 0.965170i | \(0.584258\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.5428 | 1.09649 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.67449 | 0.253013 | 0.126507 | − | 0.991966i | \(-0.459624\pi\) | ||||
0.126507 | + | 0.991966i | \(0.459624\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14.6604 | 0.651092 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.5857 | −0.779472 | −0.389736 | − | 0.920927i | \(-0.627434\pi\) | ||||
−0.389736 | + | 0.920927i | \(0.627434\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.9431 | 1.54579 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.41353 | −0.239013 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.530387 | −0.0233264 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.05529 | −0.221903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.1300 | 0.575237 | 0.287618 | − | 0.957745i | \(-0.407137\pi\) | ||||
0.287618 | + | 0.957745i | \(0.407137\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.0226 | 1.83752 | 0.918759 | − | 0.394819i | \(-0.129193\pi\) | ||||
0.918759 | + | 0.394819i | \(0.129193\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 60.6082 | 2.64014 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.3022 | −0.795746 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 18.7765 | 0.814829 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.20018 | 0.0519857 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 17.0880 | 0.737403 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.7204 | 0.763271 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.9992 | −1.20378 | −0.601890 | − | 0.798579i | \(-0.705585\pi\) | ||||
−0.601890 | + | 0.798579i | \(0.705585\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −13.9057 | −0.596751 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.05999 | −0.387377 | −0.193689 | − | 0.981063i | \(-0.562045\pi\) | ||||
−0.193689 | + | 0.981063i | \(0.562045\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.3217 | −0.739273 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.97196 | −0.339617 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.3575 | 1.16336 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.8224 | 1.30599 | 0.652993 | − | 0.757364i | \(-0.273513\pi\) | ||||
0.652993 | + | 0.757364i | \(0.273513\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.86529 | 0.0788932 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.91119 | −0.334011 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.13862 | 0.385147 | 0.192574 | − | 0.981283i | \(-0.438317\pi\) | ||||
0.192574 | + | 0.981283i | \(0.438317\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.00470 | 0.294170 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.9720 | −1.04688 | −0.523440 | − | 0.852063i | \(-0.675351\pi\) | ||||
−0.523440 | + | 0.852063i | \(0.675351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.9898 | 0.752851 | 0.376425 | − | 0.926447i | \(-0.377153\pi\) | ||||
0.376425 | + | 0.926447i | \(0.377153\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.6418 | 0.987649 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.7812 | −1.65611 | −0.828056 | − | 0.560646i | \(-0.810553\pi\) | ||||
−0.828056 | + | 0.560646i | \(0.810553\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.4361 | 0.932412 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 67.5241 | 2.80137 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.30216 | −0.261009 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.72509 | 0.153751 | 0.0768754 | − | 0.997041i | \(-0.475506\pi\) | ||||
0.0768754 | + | 0.997041i | \(0.475506\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.94392 | −0.368528 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.5100 | −1.00821 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.7017 | −0.891184 | −0.445592 | − | 0.895236i | \(-0.647007\pi\) | ||||
−0.445592 | + | 0.895236i | \(0.647007\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.41902 | 0.221786 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.7157 | −1.05071 | −0.525357 | − | 0.850882i | \(-0.676068\pi\) | ||||
−0.525357 | + | 0.850882i | \(0.676068\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.8551 | −1.54414 | −0.772071 | − | 0.635536i | \(-0.780779\pi\) | ||||
−0.772071 | + | 0.635536i | \(0.780779\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.7306 | 0.640598 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.4361 | 0.667120 | 0.333560 | − | 0.942729i | \(-0.391750\pi\) | ||||
0.333560 | + | 0.942729i | \(0.391750\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 46.2733 | 1.87509 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.352761 | 0.0142712 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.1674 | 0.854945 | 0.427473 | − | 0.904028i | \(-0.359404\pi\) | ||||
0.427473 | + | 0.904028i | \(0.359404\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.3575 | −1.86628 | −0.933140 | − | 0.359512i | \(-0.882943\pi\) | ||||
−0.933140 | + | 0.359512i | \(0.882943\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.52100 | 0.262101 | 0.131050 | − | 0.991376i | \(-0.458165\pi\) | ||||
0.131050 | + | 0.991376i | \(0.458165\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.7336 | −0.470852 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 47.6363 | 1.90851 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.16745 | 0.0466234 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.944708 | −0.0376680 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.8645 | −0.950031 | −0.475015 | − | 0.879978i | \(-0.657557\pi\) | ||||
−0.475015 | + | 0.879978i | \(0.657557\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.72509 | −0.148059 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.7859 | −0.466973 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.0583 | −0.635256 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.1153 | 1.50546 | 0.752732 | − | 0.658328i | \(-0.228736\pi\) | ||||
0.752732 | + | 0.658328i | \(0.228736\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.2694 | −1.19371 | −0.596855 | − | 0.802349i | \(-0.703583\pi\) | ||||
−0.596855 | + | 0.802349i | \(0.703583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.18610 | 0.164572 | 0.0822862 | − | 0.996609i | \(-0.473778\pi\) | ||||
0.0822862 | + | 0.996609i | \(0.473778\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.4696 | −0.450222 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 51.9151 | 2.03471 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.3949 | −0.719848 | −0.359924 | − | 0.932982i | \(-0.617197\pi\) | ||||
−0.359924 | + | 0.932982i | \(0.617197\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.5053 | 0.448866 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.92058 | 0.113770 | 0.0568848 | − | 0.998381i | \(-0.481883\pi\) | ||||
0.0568848 | + | 0.998381i | \(0.481883\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.5304 | −0.954121 | −0.477061 | − | 0.878870i | \(-0.658298\pi\) | ||||
−0.477061 | + | 0.878870i | \(0.658298\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.26174 | 0.204349 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.2788 | −0.669039 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.72039 | −0.337150 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.5810 | 0.408474 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.91667 | −0.228071 | −0.114035 | − | 0.993477i | \(-0.536378\pi\) | ||||
−0.114035 | + | 0.993477i | \(0.536378\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.80921 | −0.146400 | −0.0731999 | − | 0.997317i | \(-0.523321\pi\) | ||||
−0.0731999 | + | 0.997317i | \(0.523321\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 73.4914 | 2.82034 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.9112 | −0.992919 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.5241 | 1.20624 | 0.603118 | − | 0.797652i | \(-0.293925\pi\) | ||||
0.603118 | + | 0.797652i | \(0.293925\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.08881 | −0.155998 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.19158 | 0.159686 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.9253 | 0.491701 | 0.245850 | − | 0.969308i | \(-0.420933\pi\) | ||||
0.245850 | + | 0.969308i | \(0.420933\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.13941 | 0.309191 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.2282 | −0.463177 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.743738 | −0.0281308 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.6504 | 1.42203 | 0.711017 | − | 0.703175i | \(-0.248235\pi\) | ||||
0.711017 | + | 0.703175i | \(0.248235\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.139410 | 0.00525795 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.9992 | −0.789757 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.1059 | −1.31843 | −0.659215 | − | 0.751955i | \(-0.729111\pi\) | ||||
−0.659215 | + | 0.751955i | \(0.729111\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.00769 | 0.337815 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.3855 | −0.725993 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.75782 | −0.364413 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.0833 | −1.42027 | −0.710134 | − | 0.704066i | \(-0.751366\pi\) | ||||
−0.710134 | + | 0.704066i | \(0.751366\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −84.1284 | −3.13311 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.7336 | −0.436376 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.6465 | 0.876998 | 0.438499 | − | 0.898732i | \(-0.355510\pi\) | ||||
0.438499 | + | 0.898732i | \(0.355510\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.2664 | 0.787646 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.0047 | −0.702914 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.3847 | 1.63939 | 0.819693 | − | 0.572803i | \(-0.194144\pi\) | ||||
0.819693 | + | 0.572803i | \(0.194144\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.60902 | −0.353953 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.2959 | −1.59267 | −0.796333 | − | 0.604859i | \(-0.793229\pi\) | ||||
−0.796333 | + | 0.604859i | \(0.793229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.776472 | −0.0285244 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.0327344 | −0.00120091 | −0.000600454 | − | 1.00000i | \(-0.500191\pi\) | ||||
−0.000600454 | 1.00000i | \(0.500191\pi\) | ||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.2329 | 0.813460 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −28.1900 | −1.03004 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.1292 | −1.53732 | −0.768659 | − | 0.639659i | \(-0.779076\pi\) | ||||
−0.768659 | + | 0.639659i | \(0.779076\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.02334 | −0.146619 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.5257 | 1.07313 | 0.536565 | − | 0.843859i | \(-0.319722\pi\) | ||||
0.536565 | + | 0.843859i | \(0.319722\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.53039 | 0.0918472 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.66041 | 0.0964397 | 0.0482198 | − | 0.998837i | \(-0.484645\pi\) | ||||
0.0482198 | + | 0.998837i | \(0.484645\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 80.7982 | 2.92509 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.62846 | 0.275448 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.3108 | 1.63395 | 0.816974 | − | 0.576674i | \(-0.195650\pi\) | ||||
0.816974 | + | 0.576674i | \(0.195650\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.3957 | 0.482433 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.52021 | −0.270483 | −0.135242 | − | 0.990813i | \(-0.543181\pi\) | ||||
−0.135242 | + | 0.990813i | \(0.543181\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.809207 | −0.0290301 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.80451 | 0.0646533 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.80921 | 0.351001 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 43.1565 | 1.54229 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.30765 | −0.0822587 | −0.0411293 | − | 0.999154i | \(-0.513096\pi\) | ||||
−0.0411293 | + | 0.999154i | \(0.513096\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.15806 | −0.183632 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.25078 | 0.328920 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.03743 | −0.249906 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.3902 | −0.757679 | −0.378840 | − | 0.925462i | \(-0.623677\pi\) | ||||
−0.378840 | + | 0.925462i | \(0.623677\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.59415 | −0.127152 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.6847 | 0.554191 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.02804 | −0.248014 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.14020 | −0.251347 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.8177 | 1.36476 | 0.682378 | − | 0.730999i | \(-0.260946\pi\) | ||||
0.682378 | + | 0.730999i | \(0.260946\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.6877 | −1.49897 | −0.749483 | − | 0.662023i | \(-0.769698\pi\) | ||||
−0.749483 | + | 0.662023i | \(0.769698\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.8730 | −1.11783 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.80451 | 0.0981174 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.41353 | −0.189164 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.4649 | 1.09813 | 0.549067 | − | 0.835779i | \(-0.314983\pi\) | ||||
0.549067 | + | 0.835779i | \(0.314983\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.1122 | 0.422203 | 0.211102 | − | 0.977464i | \(-0.432295\pi\) | ||||
0.211102 | + | 0.977464i | \(0.432295\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.2359 | 1.81642 | 0.908210 | − | 0.418514i | \(-0.137449\pi\) | ||||
0.908210 | + | 0.418514i | \(0.137449\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.3808 | 1.57614 | 0.788070 | − | 0.615585i | \(-0.211080\pi\) | ||||
0.788070 | + | 0.615585i | \(0.211080\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.33568 | −0.0463344 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 120.082 | 4.16059 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 48.4182 | 1.67358 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.01865 | −0.311358 | −0.155679 | − | 0.987808i | \(-0.549757\pi\) | ||||
−0.155679 | + | 0.987808i | \(0.549757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.5522 | 1.19145 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 35.7718 | 1.23205 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.97196 | −0.170839 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.85980 | 0.166788 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.302164 | 0.0103580 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.2780 | −0.660067 | −0.330034 | − | 0.943969i | \(-0.607060\pi\) | ||||
−0.330034 | + | 0.943969i | \(0.607060\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.6269 | −0.738760 | −0.369380 | − | 0.929278i | \(-0.620430\pi\) | ||||
−0.369380 | + | 0.929278i | \(0.620430\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.6557 | 0.602405 | 0.301203 | − | 0.953560i | \(-0.402612\pi\) | ||||
0.301203 | + | 0.953560i | \(0.402612\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.4743 | −0.356963 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.21805 | −0.143584 | −0.0717920 | − | 0.997420i | \(-0.522872\pi\) | ||||
−0.0717920 | + | 0.997420i | \(0.522872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −33.7633 | −1.14666 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.50235 | −0.186654 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.39098 | 0.216550 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.1977 | 0.818968 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.7982 | 1.61403 | 0.807016 | − | 0.590530i | \(-0.201081\pi\) | ||||
0.807016 | + | 0.590530i | \(0.201081\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.0918 | 1.01497 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.3761 | −0.787561 | −0.393780 | − | 0.919205i | \(-0.628833\pi\) | ||||
−0.393780 | + | 0.919205i | \(0.628833\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.1955 | 0.746938 | 0.373469 | − | 0.927643i | \(-0.378168\pi\) | ||||
0.373469 | + | 0.927643i | \(0.378168\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.46961 | −0.183652 | −0.0918258 | − | 0.995775i | \(-0.529270\pi\) | ||||
−0.0918258 | + | 0.995775i | \(0.529270\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55.5241 | 1.86222 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.40884 | −0.0471979 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.530387 | 0.0177487 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.68296 | −0.0561925 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 71.3006 | 2.37801 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.7064 | −1.42276 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.2788 | −0.541725 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.9486 | −1.42609 | −0.713043 | − | 0.701121i | \(-0.752683\pi\) | ||||
−0.713043 | + | 0.701121i | \(0.752683\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.91418 | −0.229329 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.1573 | −0.999155 | −0.499578 | − | 0.866269i | \(-0.666511\pi\) | ||||
−0.499578 | + | 0.866269i | \(0.666511\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5810 | −0.449465 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 73.4914 | 2.42690 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.6635 | 1.44033 | 0.720163 | − | 0.693804i | \(-0.244067\pi\) | ||||
0.720163 | + | 0.693804i | \(0.244067\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.9268 | −0.491856 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.52412 | −0.214744 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −27.7000 | −0.909789 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.8318 | 0.945940 | 0.472970 | − | 0.881079i | \(-0.343182\pi\) | ||||
0.472970 | + | 0.881079i | \(0.343182\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.7204 | −0.580762 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.95879 | 0.129605 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.5063 | 0.506567 | 0.253284 | − | 0.967392i | \(-0.418489\pi\) | ||||
0.253284 | + | 0.967392i | \(0.418489\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.38471 | 0.240991 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.4743 | 1.05863 | 0.529316 | − | 0.848425i | \(-0.322449\pi\) | ||||
0.529316 | + | 0.848425i | \(0.322449\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.91119 | 0.127366 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 53.3575 | 1.73388 | 0.866942 | − | 0.498409i | \(-0.166082\pi\) | ||||
0.866942 | + | 0.498409i | \(0.166082\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.67436 | 0.151736 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.5406 | 0.698501 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.54825 | −0.147332 | −0.0736661 | − | 0.997283i | \(-0.523470\pi\) | ||||
−0.0736661 | + | 0.997283i | \(0.523470\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.30686 | −0.300848 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 37.9712 | 1.22615 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.9937 | 1.58044 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.28181 | −0.299102 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.7765 | −1.31128 | −0.655641 | − | 0.755072i | \(-0.727602\pi\) | ||||
−0.655641 | + | 0.755072i | \(0.727602\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.91119 | 0.254144 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47.4641 | −1.52320 | −0.761598 | − | 0.648049i | \(-0.775585\pi\) | ||||
−0.761598 | + | 0.648049i | \(0.775585\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −26.2461 | −0.841411 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.5755 | 1.29813 | 0.649063 | − | 0.760735i | \(-0.275161\pi\) | ||||
0.649063 | + | 0.760735i | \(0.275161\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.58098 | −0.306210 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.6035 | 0.849386 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.3622 | −1.06409 | −0.532044 | − | 0.846717i | \(-0.678576\pi\) | ||||
−0.532044 | + | 0.846717i | \(0.678576\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.07864 | −0.0979941 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.07864 | 0.193289 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.6082 | 0.654642 | 0.327321 | − | 0.944913i | \(-0.393854\pi\) | ||||
0.327321 | + | 0.944913i | \(0.393854\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.56312 | −0.0813382 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.9027 | 0.440303 | 0.220152 | − | 0.975466i | \(-0.429345\pi\) | ||||
0.220152 | + | 0.975466i | \(0.429345\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.754701 | −0.0238777 |
(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 | 4400.2.a.bx.1.2 | 3 | ||
4.3 | odd | 2 | 2200.2.a.w.1.2 | yes | 3 | ||
5.2 | odd | 4 | 4400.2.b.bc.4049.4 | 6 | |||
5.3 | odd | 4 | 4400.2.b.bc.4049.3 | 6 | |||
5.4 | even | 2 | 4400.2.a.ca.1.2 | 3 | |||
20.3 | even | 4 | 2200.2.b.l.1849.4 | 6 | |||
20.7 | even | 4 | 2200.2.b.l.1849.3 | 6 | |||
20.19 | odd | 2 | 2200.2.a.t.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2200.2.a.t.1.2 | ✓ | 3 | 20.19 | odd | 2 | ||
2200.2.a.w.1.2 | yes | 3 | 4.3 | odd | 2 | ||
2200.2.b.l.1849.3 | 6 | 20.7 | even | 4 | |||
2200.2.b.l.1849.4 | 6 | 20.3 | even | 4 | |||
4400.2.a.bx.1.2 | 3 | 1.1 | even | 1 | trivial | ||
4400.2.a.ca.1.2 | 3 | 5.4 | even | 2 | |||
4400.2.b.bc.4049.3 | 6 | 5.3 | odd | 4 | |||
4400.2.b.bc.4049.4 | 6 | 5.2 | odd | 4 |