Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3360,2,Mod(1,3360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3360.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(26.8297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3360.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.12311 | 1.54467 | 0.772337 | − | 0.635213i | \(-0.219088\pi\) | ||||
0.772337 | + | 0.635213i | \(0.219088\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.12311 | −0.866194 | −0.433097 | − | 0.901347i | \(-0.642579\pi\) | ||||
−0.433097 | + | 0.901347i | \(0.642579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.12311 | −0.257658 | −0.128829 | − | 0.991667i | \(-0.541122\pi\) | ||||
−0.128829 | + | 0.991667i | \(0.541122\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.12311 | 0.920137 | 0.460068 | − | 0.887883i | \(-0.347825\pi\) | ||||
0.460068 | + | 0.887883i | \(0.347825\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.12311 | 0.891818 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.12311 | −0.500097 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.2462 | 1.56253 | 0.781266 | − | 0.624198i | \(-0.214574\pi\) | ||||
0.781266 | + | 0.624198i | \(0.214574\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3693 | 1.83642 | 0.918208 | − | 0.396098i | \(-0.129636\pi\) | ||||
0.918208 | + | 0.396098i | \(0.129636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.12311 | −0.690799 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.12311 | −0.148759 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.24621 | −1.05582 | −0.527910 | − | 0.849301i | \(-0.677024\pi\) | ||||
−0.527910 | + | 0.849301i | \(0.677024\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.12311 | 0.387374 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.24621 | −0.274418 | −0.137209 | − | 0.990542i | \(-0.543813\pi\) | ||||
−0.137209 | + | 0.990542i | \(0.543813\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.12311 | −0.608001 | −0.304000 | − | 0.952672i | \(-0.598322\pi\) | ||||
−0.304000 | + | 0.952672i | \(0.598322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.1231 | 1.77003 | 0.885013 | − | 0.465567i | \(-0.154149\pi\) | ||||
0.885013 | + | 0.465567i | \(0.154149\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.12311 | 0.583832 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.24621 | −0.252719 | −0.126359 | − | 0.991985i | \(-0.540329\pi\) | ||||
−0.126359 | + | 0.991985i | \(0.540329\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.00000 | −0.439057 | −0.219529 | − | 0.975606i | \(-0.570452\pi\) | ||||
−0.219529 | + | 0.975606i | \(0.570452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.246211 | −0.0260983 | −0.0130492 | − | 0.999915i | \(-0.504154\pi\) | ||||
−0.0130492 | + | 0.999915i | \(0.504154\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.12311 | −0.327390 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.12311 | 0.531241 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.12311 | 0.115228 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.87689 | 0.495174 | 0.247587 | − | 0.968866i | \(-0.420362\pi\) | ||||
0.247587 | + | 0.968866i | \(0.420362\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.12311 | 0.514891 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.246211 | −0.0244989 | −0.0122495 | − | 0.999925i | \(-0.503899\pi\) | ||||
−0.0122495 | + | 0.999925i | \(0.503899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.00000 | −0.773389 | −0.386695 | − | 0.922208i | \(-0.626383\pi\) | ||||
−0.386695 | + | 0.922208i | \(0.626383\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.24621 | 0.789844 | 0.394922 | − | 0.918715i | \(-0.370772\pi\) | ||||
0.394922 | + | 0.918715i | \(0.370772\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.00000 | −0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.36932 | −0.505103 | −0.252551 | − | 0.967583i | \(-0.581270\pi\) | ||||
−0.252551 | + | 0.967583i | \(0.581270\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.12311 | −0.288731 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2462 | 1.38602 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.4924 | 1.81841 | 0.909204 | − | 0.416350i | \(-0.136691\pi\) | ||||
0.909204 | + | 0.416350i | \(0.136691\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.2462 | 0.902129 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.75379 | 0.153229 | 0.0766146 | − | 0.997061i | \(-0.475589\pi\) | ||||
0.0766146 | + | 0.997061i | \(0.475589\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.12311 | −0.0973856 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.8769 | 1.10015 | 0.550074 | − | 0.835116i | \(-0.314600\pi\) | ||||
0.550074 | + | 0.835116i | \(0.314600\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.12311 | −0.773812 | −0.386906 | − | 0.922119i | \(-0.626456\pi\) | ||||
−0.386906 | + | 0.922119i | \(0.626456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.0000 | −1.33799 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.2462 | −1.00325 | −0.501624 | − | 0.865086i | \(-0.667264\pi\) | ||||
−0.501624 | + | 0.865086i | \(0.667264\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4924 | 1.66765 | 0.833825 | − | 0.552029i | \(-0.186146\pi\) | ||||
0.833825 | + | 0.552029i | \(0.186146\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.12311 | −0.411498 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.12311 | 0.568486 | 0.284243 | − | 0.958752i | \(-0.408258\pi\) | ||||
0.284243 | + | 0.958752i | \(0.408258\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.3693 | 1.06026 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2462 | 0.802545 | 0.401273 | − | 0.915959i | \(-0.368568\pi\) | ||||
0.401273 | + | 0.915959i | \(0.368568\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.12311 | −0.398833 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0000 | −1.23812 | −0.619059 | − | 0.785345i | \(-0.712486\pi\) | ||||
−0.619059 | + | 0.785345i | \(0.712486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.24621 | −0.249709 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.12311 | −0.0858860 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.246211 | −0.0187191 | −0.00935955 | − | 0.999956i | \(-0.502979\pi\) | ||||
−0.00935955 | + | 0.999956i | \(0.502979\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.87689 | −0.215029 | −0.107515 | − | 0.994204i | \(-0.534289\pi\) | ||||
−0.107515 | + | 0.994204i | \(0.534289\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.4924 | 1.67185 | 0.835924 | − | 0.548845i | \(-0.184932\pi\) | ||||
0.835924 | + | 0.548845i | \(0.184932\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.24621 | −0.609577 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | 0.147043 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.2462 | 0.749277 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.12311 | 0.370695 | 0.185347 | − | 0.982673i | \(-0.440659\pi\) | ||||
0.185347 | + | 0.982673i | \(0.440659\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.0000 | 1.29567 | 0.647834 | − | 0.761781i | \(-0.275675\pi\) | ||||
0.647834 | + | 0.761781i | \(0.275675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.12311 | 0.223650 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.6155 | 1.68254 | 0.841268 | − | 0.540618i | \(-0.181809\pi\) | ||||
0.841268 | + | 0.540618i | \(0.181809\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.12311 | 0.363167 | 0.181584 | − | 0.983375i | \(-0.441878\pi\) | ||||
0.181584 | + | 0.983375i | \(0.441878\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.24621 | −0.158436 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | −0.140372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.75379 | −0.397998 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.75379 | 0.396107 | 0.198054 | − | 0.980191i | \(-0.436538\pi\) | ||||
0.198054 | + | 0.980191i | \(0.436538\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.12311 | −0.351029 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.2462 | −0.698786 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.12311 | 0.347779 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.1231 | 1.02192 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.24621 | −0.420166 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.2462 | −1.22186 | −0.610928 | − | 0.791686i | \(-0.709204\pi\) | ||||
−0.610928 | + | 0.791686i | \(0.709204\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.75379 | −0.248057 | −0.124029 | − | 0.992279i | \(-0.539581\pi\) | ||||
−0.124029 | + | 0.992279i | \(0.539581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.12311 | 0.337076 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.1231 | 1.51485 | 0.757423 | − | 0.652925i | \(-0.226458\pi\) | ||||
0.757423 | + | 0.652925i | \(0.226458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.24621 | −0.145907 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.1231 | −0.848863 | −0.424432 | − | 0.905460i | \(-0.639526\pi\) | ||||
−0.424432 | + | 0.905460i | \(0.639526\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.2462 | 1.30417 | 0.652087 | − | 0.758145i | \(-0.273894\pi\) | ||||
0.652087 | + | 0.758145i | \(0.273894\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.50758 | 0.223182 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.00000 | −0.125245 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.2462 | 1.26292 | 0.631462 | − | 0.775407i | \(-0.282455\pi\) | ||||
0.631462 | + | 0.775407i | \(0.282455\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.2462 | −1.12511 | −0.562555 | − | 0.826760i | \(-0.690181\pi\) | ||||
−0.562555 | + | 0.826760i | \(0.690181\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.3693 | −0.821271 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.246211 | −0.0150679 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.2462 | −0.990549 | −0.495274 | − | 0.868737i | \(-0.664933\pi\) | ||||
−0.495274 | + | 0.868737i | \(0.664933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.6155 | −1.07007 | −0.535034 | − | 0.844831i | \(-0.679701\pi\) | ||||
−0.535034 | + | 0.844831i | \(0.679701\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.12311 | −0.189019 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.12311 | 0.308935 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.4924 | −0.870765 | −0.435383 | − | 0.900245i | \(-0.643387\pi\) | ||||
−0.435383 | + | 0.900245i | \(0.643387\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.12311 | 0.306712 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.7386 | 1.47578 | 0.737892 | − | 0.674919i | \(-0.235822\pi\) | ||||
0.737892 | + | 0.674919i | \(0.235822\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.0000 | −1.18888 | −0.594438 | − | 0.804141i | \(-0.702626\pi\) | ||||
−0.594438 | + | 0.804141i | \(0.702626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.12311 | 0.0665270 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.00000 | 0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.87689 | 0.285889 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.2462 | −0.949114 | −0.474557 | − | 0.880225i | \(-0.657392\pi\) | ||||
−0.474557 | + | 0.880225i | \(0.657392\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.12311 | 0.297273 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.2462 | 0.590582 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.246211 | −0.0141445 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.24621 | 0.472177 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.75379 | −0.556678 | −0.278339 | − | 0.960483i | \(-0.589784\pi\) | ||||
−0.278339 | + | 0.960483i | \(0.589784\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.0000 | −0.907277 | −0.453638 | − | 0.891186i | \(-0.649874\pi\) | ||||
−0.453638 | + | 0.891186i | \(0.649874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.3693 | 1.88615 | 0.943073 | − | 0.332587i | \(-0.107921\pi\) | ||||
0.943073 | + | 0.332587i | \(0.107921\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.1231 | −0.849398 | −0.424699 | − | 0.905335i | \(-0.639620\pi\) | ||||
−0.424699 | + | 0.905335i | \(0.639620\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.2462 | −0.573678 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.00000 | −0.446516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.24621 | −0.124983 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.12311 | −0.173239 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.24621 | 0.456017 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.24621 | 0.123463 | 0.0617315 | − | 0.998093i | \(-0.480338\pi\) | ||||
0.0617315 | + | 0.998093i | \(0.480338\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.24621 | 0.122724 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.36932 | −0.291621 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 26.2462 | 1.42131 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.2462 | −1.40897 | −0.704485 | − | 0.709719i | \(-0.748822\pi\) | ||||
−0.704485 | + | 0.709719i | \(0.748822\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.7538 | −0.629166 | −0.314583 | − | 0.949230i | \(-0.601865\pi\) | ||||
−0.314583 | + | 0.949230i | \(0.601865\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.12311 | −0.166699 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4924 | −0.558455 | −0.279228 | − | 0.960225i | \(-0.590078\pi\) | ||||
−0.279228 | + | 0.960225i | \(0.590078\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.12311 | 0.271906 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.00000 | 0.105851 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.6155 | 1.77416 | 0.887080 | − | 0.461616i | \(-0.152730\pi\) | ||||
0.887080 | + | 0.461616i | \(0.152730\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.2462 | 0.800219 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.1231 | −0.791580 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.7538 | 0.717942 | 0.358971 | − | 0.933349i | \(-0.383128\pi\) | ||||
0.358971 | + | 0.933349i | \(0.383128\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.3693 | 0.694100 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.2462 | −1.04831 | −0.524155 | − | 0.851623i | \(-0.675619\pi\) | ||||
−0.524155 | + | 0.851623i | \(0.675619\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.24621 | 0.321696 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4924 | 0.641693 | 0.320846 | − | 0.947131i | \(-0.396033\pi\) | ||||
0.320846 | + | 0.947131i | \(0.396033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.4924 | 1.04986 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.49242 | 0.229552 | 0.114776 | − | 0.993391i | \(-0.463385\pi\) | ||||
0.114776 | + | 0.993391i | \(0.463385\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.12311 | −0.261098 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.2462 | 0.520844 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.2462 | −1.02652 | −0.513262 | − | 0.858232i | \(-0.671563\pi\) | ||||
−0.513262 | + | 0.858232i | \(0.671563\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.75379 | 0.0884669 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.24621 | 0.113019 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.1231 | −0.959761 | −0.479881 | − | 0.877334i | \(-0.659320\pi\) | ||||
−0.479881 | + | 0.877334i | \(0.659320\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.12311 | −0.0562256 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.9848 | −1.94681 | −0.973405 | − | 0.229090i | \(-0.926425\pi\) | ||||
−0.973405 | + | 0.229090i | \(0.926425\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.0000 | −0.797017 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.2462 | −0.507886 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.0000 | −0.692255 | −0.346128 | − | 0.938187i | \(-0.612504\pi\) | ||||
−0.346128 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.8769 | 0.635170 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.00000 | 0.196352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.12311 | −0.446760 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.7538 | −0.867329 | −0.433665 | − | 0.901074i | \(-0.642780\pi\) | ||||
−0.433665 | + | 0.901074i | \(0.642780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.49242 | −0.316421 | −0.158211 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158211 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.24621 | −0.399062 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.0000 | −0.772487 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.6155 | −1.61920 | −0.809602 | − | 0.586980i | \(-0.800317\pi\) | ||||
−0.809602 | + | 0.586980i | \(0.800317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.87689 | 0.234369 | 0.117184 | − | 0.993110i | \(-0.462613\pi\) | ||||
0.117184 | + | 0.993110i | \(0.462613\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.00000 | 0.0958927 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.6155 | 1.60438 | 0.802191 | − | 0.597068i | \(-0.203668\pi\) | ||||
0.802191 | + | 0.597068i | \(0.203668\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.7386 | −1.08035 | −0.540173 | − | 0.841554i | \(-0.681641\pi\) | ||||
−0.540173 | + | 0.841554i | \(0.681641\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.246211 | 0.0116715 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.2462 | −0.579226 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.0000 | −0.660701 | −0.330350 | − | 0.943858i | \(-0.607167\pi\) | ||||
−0.330350 | + | 0.943858i | \(0.607167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.2462 | 0.482475 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.4924 | 0.962818 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.12311 | 0.146413 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.24621 | 0.198629 | 0.0993147 | − | 0.995056i | \(-0.468335\pi\) | ||||
0.0993147 | + | 0.995056i | \(0.468335\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.4924 | 0.674979 | 0.337490 | − | 0.941329i | \(-0.390422\pi\) | ||||
0.337490 | + | 0.941329i | \(0.390422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.12311 | −0.237578 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.9848 | 1.71145 | 0.855727 | − | 0.517427i | \(-0.173110\pi\) | ||||
0.855727 | + | 0.517427i | \(0.173110\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.24621 | −0.103720 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.12311 | 0.328215 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 52.4924 | 2.41360 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.12311 | −0.0515316 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.3693 | 0.612139 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00000 | 0.365529 | 0.182765 | − | 0.983157i | \(-0.441495\pi\) | ||||
0.182765 | + | 0.983157i | \(0.441495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.24621 | 0.284803 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.87689 | −0.221448 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.0000 | 1.45006 | 0.725029 | − | 0.688718i | \(-0.241826\pi\) | ||||
0.725029 | + | 0.688718i | \(0.241826\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.2462 | 0.463350 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.1231 | 0.592237 | 0.296119 | − | 0.955151i | \(-0.404308\pi\) | ||||
0.296119 | + | 0.955151i | \(0.404308\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.00000 | −0.180151 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.12311 | −0.230266 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.12311 | −0.229803 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.4924 | −0.917367 | −0.458683 | − | 0.888600i | \(-0.651679\pi\) | ||||
−0.458683 | + | 0.888600i | \(0.651679\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.0000 | −0.714827 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.50758 | −0.156395 | −0.0781976 | − | 0.996938i | \(-0.524916\pi\) | ||||
−0.0781976 | + | 0.996938i | \(0.524916\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.246211 | 0.0109563 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.24621 | −0.144169 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.7538 | −0.520978 | −0.260489 | − | 0.965477i | \(-0.583884\pi\) | ||||
−0.260489 | + | 0.965477i | \(0.583884\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.1231 | 0.669007 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.12311 | −0.0495863 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.246211 | −0.0108075 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.4924 | 0.985411 | 0.492705 | − | 0.870196i | \(-0.336008\pi\) | ||||
0.492705 | + | 0.870196i | \(0.336008\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.7386 | −1.51901 | −0.759507 | − | 0.650499i | \(-0.774560\pi\) | ||||
−0.759507 | + | 0.650499i | \(0.774560\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.2462 | 0.446332 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.24621 | −0.270553 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.00000 | 0.345870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.87689 | −0.124147 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.12311 | 0.220668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.4924 | −0.623078 | −0.311539 | − | 0.950233i | \(-0.600844\pi\) | ||||
−0.311539 | + | 0.950233i | \(0.600844\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.4924 | 0.965242 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.24621 | −0.353229 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.7538 | 0.930125 | 0.465062 | − | 0.885278i | \(-0.346032\pi\) | ||||
0.465062 | + | 0.885278i | \(0.346032\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.24621 | −0.351940 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.24621 | 0.0956918 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.24621 | −0.0955186 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.00000 | 0.0848953 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.1231 | −0.640787 | −0.320393 | − | 0.947285i | \(-0.603815\pi\) | ||||
−0.320393 | + | 0.947285i | \(0.603815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.0000 | −1.35346 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.2462 | 0.432595 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −16.4924 | −0.695073 | −0.347536 | − | 0.937667i | \(-0.612982\pi\) | ||||
−0.347536 | + | 0.937667i | \(0.612982\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.36932 | 0.225889 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.50758 | −0.146788 | −0.0733938 | − | 0.997303i | \(-0.523383\pi\) | ||||
−0.0733938 | + | 0.997303i | \(0.523383\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.12311 | 0.214021 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.6155 | −0.983127 | −0.491564 | − | 0.870842i | \(-0.663574\pi\) | ||||
−0.491564 | + | 0.870842i | \(0.663574\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18.0000 | 0.748054 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.00000 | −0.165948 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 68.4924 | 2.83667 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.12311 | 0.129125 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.4924 | −1.34111 | −0.670553 | − | 0.741862i | \(-0.733943\pi\) | ||||
−0.670553 | + | 0.741862i | \(0.733943\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.75379 | −0.237081 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.6155 | 0.971413 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 30.4924 | 1.25217 | 0.626087 | − | 0.779753i | \(-0.284656\pi\) | ||||
0.626087 | + | 0.779753i | \(0.284656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.00000 | −0.0819920 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.12311 | 0.209675 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.12311 | 0.209324 | 0.104662 | − | 0.994508i | \(-0.466624\pi\) | ||||
0.104662 | + | 0.994508i | \(0.466624\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.2462 | −0.662697 | −0.331348 | − | 0.943508i | \(-0.607504\pi\) | ||||
−0.331348 | + | 0.943508i | \(0.607504\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.24621 | −0.0914728 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.2462 | −0.619847 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.7538 | 0.558249 | 0.279125 | − | 0.960255i | \(-0.409956\pi\) | ||||
0.279125 | + | 0.960255i | \(0.409956\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.00000 | −0.0810441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.9848 | 0.928349 | 0.464175 | − | 0.885744i | \(-0.346351\pi\) | ||||
0.464175 | + | 0.885744i | \(0.346351\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.00000 | −0.0806478 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.3693 | −0.538228 | −0.269114 | − | 0.963108i | \(-0.586731\pi\) | ||||
−0.269114 | + | 0.963108i | \(0.586731\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.1231 | −0.688236 | −0.344118 | − | 0.938926i | \(-0.611822\pi\) | ||||
−0.344118 | + | 0.938926i | \(0.611822\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.246211 | −0.00986425 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.75379 | −0.229784 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.00000 | −0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.24621 | −0.0894203 | −0.0447101 | − | 0.999000i | \(-0.514236\pi\) | ||||
−0.0447101 | + | 0.999000i | \(0.514236\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.75379 | 0.228693 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.4924 | −0.813217 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.12311 | −0.123742 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.12311 | −0.202667 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.24621 | −0.325706 | −0.162853 | − | 0.986650i | \(-0.552070\pi\) | ||||
−0.162853 | + | 0.986650i | \(0.552070\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.2462 | −0.877305 | −0.438652 | − | 0.898657i | \(-0.644544\pi\) | ||||
−0.438652 | + | 0.898657i | \(0.644544\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.2462 | −0.403444 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.9848 | −1.61128 | −0.805640 | − | 0.592405i | \(-0.798179\pi\) | ||||
−0.805640 | + | 0.592405i | \(0.798179\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.4924 | −0.804398 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.12311 | 0.200790 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.61553 | 0.298019 | 0.149009 | − | 0.988836i | \(-0.452392\pi\) | ||||
0.149009 | + | 0.988836i | \(0.452392\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.75379 | −0.0685262 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.1231 | 0.590009 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.61553 | −0.374568 | −0.187284 | − | 0.982306i | \(-0.559968\pi\) | ||||
−0.187284 | + | 0.982306i | \(0.559968\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.7538 | 1.23508 | 0.617540 | − | 0.786540i | \(-0.288130\pi\) | ||||
0.617540 | + | 0.786540i | \(0.288130\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.24621 | −0.242583 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.12311 | 0.0435522 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.2462 | −0.705439 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −42.2462 | −1.63090 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.2311 | 1.43515 | 0.717576 | − | 0.696480i | \(-0.245252\pi\) | ||||
0.717576 | + | 0.696480i | \(0.245252\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.75379 | 0.298002 | 0.149001 | − | 0.988837i | \(-0.452394\pi\) | ||||
0.149001 | + | 0.988837i | \(0.452394\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.87689 | 0.187158 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.00000 | −0.153280 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.7538 | −0.526274 | −0.263137 | − | 0.964758i | \(-0.584757\pi\) | ||||
−0.263137 | + | 0.964758i | \(0.584757\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.8769 | −0.492001 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.75379 | −0.143216 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.7538 | −1.59069 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.6307 | 0.784828 | 0.392414 | − | 0.919789i | \(-0.371640\pi\) | ||||
0.392414 | + | 0.919789i | \(0.371640\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.12311 | 0.194611 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.12311 | 0.346059 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.1231 | 0.874596 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.4924 | −1.45384 | −0.726919 | − | 0.686723i | \(-0.759049\pi\) | ||||
−0.726919 | + | 0.686723i | \(0.759049\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.24621 | 0.0847175 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.246211 | −0.00925973 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.0000 | −0.976450 | −0.488225 | − | 0.872718i | \(-0.662356\pi\) | ||||
−0.488225 | + | 0.872718i | \(0.662356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.24621 | −0.0842395 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.0000 | 0.598366 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −13.1231 | −0.490091 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −43.2311 | −1.61225 | −0.806123 | − | 0.591748i | \(-0.798438\pi\) | ||||
−0.806123 | + | 0.591748i | \(0.798438\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.2462 | 0.752965 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.00000 | −0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.7386 | 1.14003 | 0.570016 | − | 0.821633i | \(-0.306937\pi\) | ||||
0.570016 | + | 0.821633i | \(0.306937\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.4924 | 0.757940 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.6155 | −1.75872 | −0.879360 | − | 0.476158i | \(-0.842029\pi\) | ||||
−0.879360 | + | 0.476158i | \(0.842029\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.5076 | −0.423887 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.0000 | −1.47142 | −0.735712 | − | 0.677295i | \(-0.763152\pi\) | ||||
−0.735712 | + | 0.677295i | \(0.763152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.50758 | 0.128854 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.7386 | 0.540708 | 0.270354 | − | 0.962761i | \(-0.412859\pi\) | ||||
0.270354 | + | 0.962761i | \(0.412859\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.2462 | 0.448666 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.00000 | −0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.2462 | 0.373890 | 0.186945 | − | 0.982370i | \(-0.440141\pi\) | ||||
0.186945 | + | 0.982370i | \(0.440141\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.4924 | −0.745796 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.7538 | 1.29949 | 0.649747 | − | 0.760151i | \(-0.274875\pi\) | ||||
0.649747 | + | 0.760151i | \(0.274875\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.7386 | −1.04177 | −0.520887 | − | 0.853625i | \(-0.674399\pi\) | ||||
−0.520887 | + | 0.853625i | \(0.674399\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.24621 | 0.298533 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.00000 | −0.0723102 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.4924 | 0.451075 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.2462 | −1.16283 | −0.581414 | − | 0.813608i | \(-0.697500\pi\) | ||||
−0.581414 | + | 0.813608i | \(0.697500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.2462 | 0.729149 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.2462 | −0.584336 | −0.292168 | − | 0.956367i | \(-0.594377\pi\) | ||||
−0.292168 | + | 0.956367i | \(0.594377\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.12311 | 0.184027 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.00000 | −0.0717496 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.24621 | −0.0804789 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.2462 | −0.939163 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.12311 | −0.254235 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.2311 | 1.11327 | 0.556633 | − | 0.830758i | \(-0.312093\pi\) | ||||
0.556633 | + | 0.830758i | \(0.312093\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.2462 | −0.649582 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.36932 | −0.190911 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.7538 | 0.914544 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.3693 | −0.474161 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.7386 | −1.30135 | −0.650675 | − | 0.759357i | \(-0.725514\pi\) | ||||
−0.650675 | + | 0.759357i | \(0.725514\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.246211 | −0.00869945 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 77.4773 | 2.73411 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.2462 | −0.571894 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.2462 | 0.711819 | 0.355909 | − | 0.934520i | \(-0.384171\pi\) | ||||
0.355909 | + | 0.934520i | \(0.384171\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.6155 | −1.88270 | −0.941348 | − | 0.337438i | \(-0.890440\pi\) | ||||
−0.941348 | + | 0.337438i | \(0.890440\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.6155 | −0.617804 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.2462 | −0.358909 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.5076 | −0.402599 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.12311 | −0.109130 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 54.9848 | 1.91898 | 0.959492 | − | 0.281735i | \(-0.0909100\pi\) | ||||
0.959492 | + | 0.281735i | \(0.0909100\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4924 | −0.435458 | −0.217729 | − | 0.976009i | \(-0.569865\pi\) | ||||
−0.217729 | + | 0.976009i | \(0.569865\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.12311 | 0.178364 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.9848 | 1.70337 | 0.851685 | − | 0.524054i | \(-0.175581\pi\) | ||||
0.851685 | + | 0.524054i | \(0.175581\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.49242 | 0.225491 | 0.112746 | − | 0.993624i | \(-0.464035\pi\) | ||||
0.112746 | + | 0.993624i | \(0.464035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.4924 | −0.502737 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000 | 0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000 | 0.553703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.12311 | 0.177080 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.7386 | −1.33741 | −0.668703 | − | 0.743530i | \(-0.733150\pi\) | ||||
−0.668703 | + | 0.743530i | \(0.733150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.7386 | 0.852044 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.24621 | 0.111673 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.2462 | 0.523866 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.0000 | −0.686398 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.384472 | 0.0131641 | 0.00658203 | − | 0.999978i | \(-0.497905\pi\) | ||||
0.00658203 | + | 0.999978i | \(0.497905\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.12311 | 0.0384094 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.2462 | −1.64806 | −0.824030 | − | 0.566547i | \(-0.808279\pi\) | ||||
−0.824030 | + | 0.566547i | \(0.808279\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.6155 | 0.737512 | 0.368756 | − | 0.929526i | \(-0.379784\pi\) | ||||
0.368756 | + | 0.929526i | \(0.379784\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.00000 | 0.0681598 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.0000 | 1.36162 | 0.680808 | − | 0.732462i | \(-0.261629\pi\) | ||||
0.680808 | + | 0.732462i | \(0.261629\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.246211 | 0.00837143 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.0000 | −0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.5076 | −0.390368 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.01515 | 0.237699 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.87689 | 0.165058 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.4924 | 0.354304 | 0.177152 | − | 0.984184i | \(-0.443312\pi\) | ||||
0.177152 | + | 0.984184i | \(0.443312\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.2462 | −0.547971 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40.2462 | −1.35593 | −0.677965 | − | 0.735095i | \(-0.737138\pi\) | ||||
−0.677965 | + | 0.735095i | \(0.737138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.2462 | 0.614034 | 0.307017 | − | 0.951704i | \(-0.400669\pi\) | ||||
0.307017 | + | 0.951704i | \(0.400669\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.00000 | 0.134459 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.0000 | −1.61168 | −0.805841 | − | 0.592132i | \(-0.798286\pi\) | ||||
−0.805841 | + | 0.592132i | \(0.798286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.4924 | 0.687294 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.12311 | 0.171630 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.87689 | 0.0961640 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.2462 | −0.341730 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.7386 | 0.890793 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.2462 | 0.340973 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.4924 | −0.747673 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −38.7386 | −1.28630 | −0.643148 | − | 0.765742i | \(-0.722372\pi\) | ||||
−0.643148 | + | 0.765742i | \(0.722372\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.246211 | −0.00816631 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.61553 | 0.0535248 | 0.0267624 | − | 0.999642i | \(-0.491480\pi\) | ||||
0.0267624 | + | 0.999642i | \(0.491480\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −20.4924 | −0.678200 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.24621 | 0.272611 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.75379 | 0.0579152 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.2462 | −0.601887 | −0.300943 | − | 0.953642i | \(-0.597302\pi\) | ||||
−0.300943 | + | 0.953642i | \(0.597302\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.75379 | −0.321398 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.0000 | 0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.00000 | −0.0657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.7538 | −0.385629 | −0.192815 | − | 0.981235i | \(-0.561762\pi\) | ||||
−0.192815 | + | 0.981235i | \(0.561762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.12311 | −0.0368083 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.0000 | −0.523816 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.2462 | −0.335087 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.1080 | 1.31027 | 0.655135 | − | 0.755512i | \(-0.272612\pi\) | ||||
0.655135 | + | 0.755512i | \(0.272612\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.3693 | 1.08897 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.9848 | 1.40127 | 0.700633 | − | 0.713522i | \(-0.252901\pi\) | ||||
0.700633 | + | 0.713522i | \(0.252901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −51.2311 | −1.66479 | −0.832393 | − | 0.554186i | \(-0.813030\pi\) | ||||
−0.832393 | + | 0.554186i | \(0.813030\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.2311 | −1.53318 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.1231 | −0.490400 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.63068 | 0.0852162 | 0.0426081 | − | 0.999092i | \(-0.486433\pi\) | ||||
0.0426081 | + | 0.999092i | \(0.486433\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.12311 | −0.165780 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.2462 | −0.331213 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.8769 | 0.415817 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.75379 | −0.153348 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.00000 | −0.257796 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18.0000 | −0.579441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0000 | 0.514525 | 0.257263 | − | 0.966342i | \(-0.417179\pi\) | ||||
0.257263 | + | 0.966342i | \(0.417179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.24621 | −0.0721587 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.0000 | 1.41203 | 0.706014 | − | 0.708198i | \(-0.250492\pi\) | ||||
0.706014 | + | 0.708198i | \(0.250492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.12311 | −0.292473 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.12311 | −0.100019 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.6307 | 0.340106 | 0.170053 | − | 0.985435i | \(-0.445606\pi\) | ||||
0.170053 | + | 0.985435i | \(0.445606\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.26137 | −0.0403134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.24621 | 0.263281 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11.5076 | −0.367035 | −0.183517 | − | 0.983016i | \(-0.558748\pi\) | ||||
−0.183517 | + | 0.983016i | \(0.558748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.6155 | −0.752453 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.26137 | −0.294197 | −0.147098 | − | 0.989122i | \(-0.546993\pi\) | ||||
−0.147098 | + | 0.989122i | \(0.546993\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.24621 | 0.0712814 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.12311 | −0.162413 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.8617 | 1.19909 | 0.599547 | − | 0.800340i | \(-0.295348\pi\) | ||||
0.599547 | + | 0.800340i | \(0.295348\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 3360.2.a.bg.1.2 | yes | 2 | |
4.3 | odd | 2 | 3360.2.a.ba.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 6720.2.a.cw.1.2 | 2 | |||
8.5 | even | 2 | 6720.2.a.ct.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3360.2.a.ba.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
3360.2.a.bg.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
6720.2.a.ct.1.1 | 2 | 8.5 | even | 2 | |||
6720.2.a.cw.1.2 | 2 | 8.3 | odd | 2 |