Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1121,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 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("2240.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.3534400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 3x^{4} + 16x^{3} + x^{2} - 12x + 40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.3 | ||
Root | \(-1.81837 - 0.301352i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1121 |
Dual form | 2240.2.b.f.1121.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 0.602705i | − 0.347972i | −0.984748 | − | 0.173986i | \(-0.944335\pi\) | ||||
0.984748 | − | 0.173986i | \(-0.0556647\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.63675 | 0.878916 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.63675i | − 1.69954i | −0.527151 | − | 0.849772i | \(-0.676740\pi\) | ||||
0.527151 | − | 0.849772i | \(-0.323260\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.43134i | − 1.22903i | −0.788904 | − | 0.614516i | \(-0.789351\pi\) | ||||
0.788904 | − | 0.614516i | \(-0.210649\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.602705 | −0.155618 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.46538 | −1.81062 | −0.905310 | − | 0.424751i | \(-0.860362\pi\) | ||||
−0.905310 | + | 0.424751i | \(0.860362\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.20541i | − 0.276540i | −0.990395 | − | 0.138270i | \(-0.955846\pi\) | ||||
0.990395 | − | 0.138270i | \(-0.0441542\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 0.602705i | − 0.131521i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.27349 | 1.51663 | 0.758314 | − | 0.651889i | \(-0.226023\pi\) | ||||
0.758314 | + | 0.651889i | \(0.226023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 3.39730i | − 0.653810i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.67079i | 1.23873i | 0.785101 | + | 0.619367i | \(0.212611\pi\) | ||||
−0.785101 | + | 0.619367i | \(0.787389\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.0681 | −1.80828 | −0.904141 | − | 0.427235i | \(-0.859488\pi\) | ||||
−0.904141 | + | 0.427235i | \(0.859488\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.39730 | −0.591393 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 1.00000i | − 0.169031i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.86267i | 0.799419i | 0.916642 | + | 0.399709i | \(0.130889\pi\) | ||||
−0.916642 | + | 0.399709i | \(0.869111\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.67079 | −0.427668 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.79459 | −0.748789 | −0.374395 | − | 0.927269i | \(-0.622149\pi\) | ||||
−0.374395 | + | 0.927269i | \(0.622149\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.00000i | − 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 2.63675i | − 0.393063i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.43134 | 0.938107 | 0.469053 | − | 0.883170i | \(-0.344595\pi\) | ||||
0.469053 | + | 0.883170i | \(0.344595\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.49942i | 0.630045i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.06808i | − 0.284073i | −0.989861 | − | 0.142037i | \(-0.954635\pi\) | ||||
0.989861 | − | 0.142037i | \(-0.0453651\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.63675 | −0.760059 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.726506 | −0.0962281 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.06808i | 0.269242i | 0.990897 | + | 0.134621i | \(0.0429816\pi\) | ||||
−0.990897 | + | 0.134621i | \(0.957018\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.27349i | − 0.163054i | −0.996671 | − | 0.0815271i | \(-0.974020\pi\) | ||||
0.996671 | − | 0.0815271i | \(-0.0259797\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.63675 | 0.332199 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.43134 | −0.549640 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 7.20541i | − 0.880281i | −0.897929 | − | 0.440140i | \(-0.854929\pi\) | ||||
0.897929 | − | 0.440140i | \(-0.145071\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 4.38377i | − 0.527744i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.79459 | −0.806369 | −0.403185 | − | 0.915119i | \(-0.632097\pi\) | ||||
−0.403185 | + | 0.915119i | \(0.632097\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.27349 | 0.149051 | 0.0745256 | − | 0.997219i | \(-0.476256\pi\) | ||||
0.0745256 | + | 0.997219i | \(0.476256\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.602705i | 0.0695944i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 5.63675i | − 0.642367i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.0816 | 1.47180 | 0.735898 | − | 0.677092i | \(-0.236760\pi\) | ||||
0.735898 | + | 0.677092i | \(0.236760\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.86267 | 0.651408 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.20541i | − 0.132311i | −0.997809 | − | 0.0661555i | \(-0.978927\pi\) | ||||
0.997809 | − | 0.0661555i | \(-0.0210733\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.46538i | 0.809734i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.02052 | 0.431045 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.2735 | −1.83099 | −0.915493 | − | 0.402333i | \(-0.868199\pi\) | ||||
−0.915493 | + | 0.402333i | \(0.868199\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 4.43134i | − 0.464530i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.06808i | 0.629231i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.20541 | −0.123672 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.4654 | 1.16413 | 0.582066 | − | 0.813141i | \(-0.302244\pi\) | ||||
0.582066 | + | 0.813141i | \(0.302244\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 14.8627i | − 1.49375i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.41082i | 0.438893i | 0.975625 | + | 0.219446i | \(0.0704251\pi\) | ||||
−0.975625 | + | 0.219446i | \(0.929575\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.56866 | 0.548697 | 0.274348 | − | 0.961630i | \(-0.411538\pi\) | ||||
0.274348 | + | 0.961630i | \(0.411538\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.602705 | −0.0588180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 18.1362i | − 1.75329i | −0.481138 | − | 0.876645i | \(-0.659776\pi\) | ||||
0.481138 | − | 0.876645i | \(-0.340224\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.0816i | 1.63612i | 0.575132 | + | 0.818061i | \(0.304951\pi\) | ||||
−0.575132 | + | 0.818061i | \(0.695049\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.93076 | 0.278175 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.4789 | −0.985772 | −0.492886 | − | 0.870094i | \(-0.664058\pi\) | ||||
−0.492886 | + | 0.870094i | \(0.664058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 7.27349i | − 0.678257i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 11.6843i | − 1.08022i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.46538 | −0.684350 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −20.7729 | −1.88845 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.88972i | 0.260558i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.06808 | −0.538455 | −0.269228 | − | 0.963077i | \(-0.586768\pi\) | ||||
−0.269228 | + | 0.963077i | \(0.586768\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.20541 | −0.106130 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 12.8627i | − 1.12382i | −0.827199 | − | 0.561909i | \(-0.810067\pi\) | ||||
0.827199 | − | 0.561909i | \(-0.189933\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.20541i | − 0.104522i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.39730 | −0.292393 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.2735 | −1.13403 | −0.567016 | − | 0.823707i | \(-0.691902\pi\) | ||||
−0.567016 | + | 0.823707i | \(0.691902\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.86267i | − 0.412447i | −0.978505 | − | 0.206223i | \(-0.933883\pi\) | ||||
0.978505 | − | 0.206223i | \(-0.0661173\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 3.87620i | − 0.326435i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −24.9783 | −2.08879 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.67079 | 0.553979 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 0.602705i | − 0.0497103i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 20.1362i | − 1.64962i | −0.565411 | − | 0.824810i | \(-0.691282\pi\) | ||||
0.565411 | − | 0.824810i | \(-0.308718\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.25997 | 0.672187 | 0.336093 | − | 0.941829i | \(-0.390894\pi\) | ||||
0.336093 | + | 0.941829i | \(0.390894\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.6843 | −1.59138 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.0681i | 0.808688i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 16.4108i | − 1.30973i | −0.755748 | − | 0.654863i | \(-0.772726\pi\) | ||||
0.755748 | − | 0.654863i | \(-0.227274\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.24644 | −0.0988495 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.27349 | 0.573232 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 10.4789i | − 0.820771i | −0.911912 | − | 0.410386i | \(-0.865394\pi\) | ||||
0.911912 | − | 0.410386i | \(-0.134606\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.39730i | 0.264479i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.39030 | −0.184967 | −0.0924836 | − | 0.995714i | \(-0.529481\pi\) | ||||
−0.0924836 | + | 0.995714i | \(0.529481\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.63675 | −0.510519 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 3.17836i | − 0.243055i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.5675i | 1.56372i | 0.623455 | + | 0.781859i | \(0.285728\pi\) | ||||
−0.623455 | + | 0.781859i | \(0.714272\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.24644 | 0.0936885 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.8627i | 0.811914i | 0.913892 | + | 0.405957i | \(0.133062\pi\) | ||||
−0.913892 | + | 0.405957i | \(0.866938\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.7524i | 1.61684i | 0.588604 | + | 0.808421i | \(0.299678\pi\) | ||||
−0.588604 | + | 0.808421i | \(0.700322\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.767541 | −0.0567383 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.86267 | 0.357511 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 42.0804i | 3.07723i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 3.39730i | − 0.247117i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.05456 | −0.510450 | −0.255225 | − | 0.966882i | \(-0.582150\pi\) | ||||
−0.255225 | + | 0.966882i | \(0.582150\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.54815 | 0.255401 | 0.127701 | − | 0.991813i | \(-0.459240\pi\) | ||||
0.127701 | + | 0.991813i | \(0.459240\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.67079i | 0.191259i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 22.8897i | − 1.63083i | −0.578880 | − | 0.815413i | \(-0.696510\pi\) | ||||
0.578880 | − | 0.815413i | \(-0.303490\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.6151 | 1.46136 | 0.730682 | − | 0.682718i | \(-0.239202\pi\) | ||||
0.730682 | + | 0.682718i | \(0.239202\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.34274 | −0.306313 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.67079i | 0.468198i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.79459i | 0.334869i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.1784 | 1.33299 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.79459 | −0.469992 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.95243i | 0.272097i | 0.990702 | + | 0.136048i | \(0.0434403\pi\) | ||||
−0.990702 | + | 0.136048i | \(0.956560\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.09513i | 0.280594i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.00000 | −0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0681 | −0.683466 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 0.767541i | − 0.0518656i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 33.0816i | 2.22531i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.39030 | −0.160066 | −0.0800332 | − | 0.996792i | \(-0.525503\pi\) | ||||
−0.0800332 | + | 0.996792i | \(0.525503\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.63675 | −0.175783 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.738872i | 0.0490407i | 0.999699 | + | 0.0245203i | \(0.00780585\pi\) | ||||
−0.999699 | + | 0.0245203i | \(0.992194\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 12.9308i | − 0.854489i | −0.904136 | − | 0.427244i | \(-0.859484\pi\) | ||||
0.904136 | − | 0.427244i | \(-0.140516\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.39730 | −0.223526 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.9988 | 1.24466 | 0.622328 | − | 0.782757i | \(-0.286187\pi\) | ||||
0.622328 | + | 0.782757i | \(0.286187\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 6.43134i | − 0.419534i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 7.88435i | − 0.512144i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.6708 | 1.20771 | 0.603856 | − | 0.797093i | \(-0.293630\pi\) | ||||
0.603856 | + | 0.797093i | \(0.293630\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5892 | 0.746525 | 0.373262 | − | 0.927726i | \(-0.378239\pi\) | ||||
0.373262 | + | 0.927726i | \(0.378239\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 13.7253i | − 0.880481i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.00000i | − 0.0638877i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.34158 | −0.339876 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.726506 | −0.0460405 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.86267i | 0.306929i | 0.988154 | + | 0.153465i | \(0.0490431\pi\) | ||||
−0.988154 | + | 0.153465i | \(0.950957\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 40.9988i | − 2.57758i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.49942 | 0.281765 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.6843 | 0.978361 | 0.489180 | − | 0.872183i | \(-0.337296\pi\) | ||||
0.489180 | + | 0.872183i | \(0.337296\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.86267i | 0.302152i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.5892i | 1.08874i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.2054 | 1.06093 | 0.530466 | − | 0.847707i | \(-0.322017\pi\) | ||||
0.530466 | + | 0.847707i | \(0.322017\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.06808 | −0.127041 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.4108i | 0.637132i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 14.4789i | − 0.882794i | −0.897312 | − | 0.441397i | \(-0.854483\pi\) | ||||
0.897312 | − | 0.441397i | \(-0.145517\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.58918 | −0.339519 | −0.169759 | − | 0.985486i | \(-0.554299\pi\) | ||||
−0.169759 | + | 0.985486i | \(0.554299\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.67079 | −0.161643 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.63675i | 0.339909i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 3.27349i | − 0.196685i | −0.995153 | − | 0.0983426i | \(-0.968646\pi\) | ||||
0.995153 | − | 0.0983426i | \(-0.0313541\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.5470 | −1.58933 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.95243 | −0.235782 | −0.117891 | − | 0.993027i | \(-0.537613\pi\) | ||||
−0.117891 | + | 0.993027i | \(0.537613\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 18.0804i | − 1.07477i | −0.843337 | − | 0.537386i | \(-0.819412\pi\) | ||||
0.843337 | − | 0.537386i | \(-0.180588\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.726506i | 0.0430345i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.79459 | −0.283016 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.7319 | 2.27835 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 6.91024i | − 0.405085i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.84216i | 0.166041i | 0.996548 | + | 0.0830203i | \(0.0264566\pi\) | ||||
−0.996548 | + | 0.0830203i | \(0.973543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.06808 | 0.120408 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −19.1497 | −1.11118 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 32.2313i | − 1.86398i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 2.00000i | − 0.115278i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.65842 | 0.152722 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.27349 | −0.0729200 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 8.73887i | − 0.498754i | −0.968407 | − | 0.249377i | \(-0.919774\pi\) | ||||
0.968407 | − | 0.249377i | \(-0.0802258\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 3.35626i | − 0.190931i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.1373 | −0.858359 | −0.429180 | − | 0.903219i | \(-0.641197\pi\) | ||||
−0.429180 | + | 0.903219i | \(0.641197\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.150851 | 0.00852659 | 0.00426330 | − | 0.999991i | \(-0.498643\pi\) | ||||
0.00426330 | + | 0.999991i | \(0.498643\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 2.63675i | − 0.148564i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 22.1632i | − 1.24481i | −0.782695 | − | 0.622405i | \(-0.786156\pi\) | ||||
0.782695 | − | 0.622405i | \(-0.213844\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.6015 | 2.10528 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.9308 | −0.610095 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.99884i | 0.500709i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.43134i | 0.245806i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.2952 | 0.569324 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.43134 | 0.354571 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.5880i | 1.79120i | 0.444861 | + | 0.895600i | \(0.353253\pi\) | ||||
−0.444861 | + | 0.895600i | \(0.646747\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.8216i | 0.702622i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.20541 | −0.393674 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.4789 | 1.22450 | 0.612252 | − | 0.790663i | \(-0.290264\pi\) | ||||
0.612252 | + | 0.790663i | \(0.290264\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.31569i | 0.343021i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 56.7512i | 3.07325i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.38377 | −0.236014 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 25.0259i | − 1.34346i | −0.740796 | − | 0.671730i | \(-0.765551\pi\) | ||||
0.740796 | − | 0.671730i | \(-0.234449\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 13.3145i | − 0.712710i | −0.934351 | − | 0.356355i | \(-0.884019\pi\) | ||||
0.934351 | − | 0.356355i | \(-0.115981\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.0546 | −0.803553 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.8340 | 1.85403 | 0.927014 | − | 0.375028i | \(-0.122367\pi\) | ||||
0.927014 | + | 0.375028i | \(0.122367\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.79459i | 0.360619i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.49942i | 0.238135i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.51994 | −0.449665 | −0.224833 | − | 0.974397i | \(-0.572184\pi\) | ||||
−0.224833 | + | 0.974397i | \(0.572184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.5470 | 0.923526 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.5199i | 0.657126i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.27349i | − 0.0666577i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.02052 | −0.418668 | −0.209334 | − | 0.977844i | \(-0.567130\pi\) | ||||
−0.209334 | + | 0.977844i | \(0.567130\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.6421 | −0.658122 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 2.06808i | − 0.107370i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.58918i | 0.496509i | 0.968695 | + | 0.248254i | \(0.0798569\pi\) | ||||
−0.968695 | + | 0.248254i | \(0.920143\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.602705 | 0.0311235 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.5605 | 1.52244 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4519i | 0.639609i | 0.947484 | + | 0.319804i | \(0.103617\pi\) | ||||
−0.947484 | + | 0.319804i | \(0.896383\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.65726i | 0.187367i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.8615 | 1.11707 | 0.558536 | − | 0.829481i | \(-0.311363\pi\) | ||||
0.558536 | + | 0.829481i | \(0.311363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.63675 | −0.287275 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 5.27349i | − 0.268067i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.46538i | 0.277106i | 0.990355 | + | 0.138553i | \(0.0442451\pi\) | ||||
−0.990355 | + | 0.138553i | \(0.955755\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −54.2994 | −2.74604 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.75240 | −0.391057 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 13.0816i | − 0.658207i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2518i | 1.11679i | 0.829576 | + | 0.558393i | \(0.188582\pi\) | ||||
−0.829576 | + | 0.558393i | \(0.811418\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.726506 | −0.0363708 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.910240 | −0.0454552 | −0.0227276 | − | 0.999742i | \(-0.507235\pi\) | ||||
−0.0227276 | + | 0.999742i | \(0.507235\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 44.6151i | 2.22243i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 5.86267i | − 0.291319i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.4097 | 1.35865 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.47890 | −0.320361 | −0.160181 | − | 0.987088i | \(-0.551208\pi\) | ||||
−0.160181 | + | 0.987088i | \(0.551208\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.00000i | 0.394611i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.06808i | 0.101764i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.20541 | −0.0591712 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.93076 | −0.143520 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.4789i | 1.39129i | 0.718388 | + | 0.695643i | \(0.244880\pi\) | ||||
−0.718388 | + | 0.695643i | \(0.755120\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 9.46538i | − 0.461314i | −0.973035 | − | 0.230657i | \(-0.925912\pi\) | ||||
0.973035 | − | 0.230657i | \(-0.0740876\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 16.9578 | 0.824517 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.46538 | 0.362124 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.27349i | − 0.0616287i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 15.0546i | 0.726841i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.7799 | −1.19361 | −0.596803 | − | 0.802388i | \(-0.703563\pi\) | ||||
−0.596803 | + | 0.802388i | \(0.703563\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.4519 | 1.36731 | 0.683654 | − | 0.729806i | \(-0.260390\pi\) | ||||
0.683654 | + | 0.729806i | \(0.260390\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 4.02052i | − 0.192769i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 8.76754i | − 0.419408i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.7946 | 0.897017 | 0.448508 | − | 0.893779i | \(-0.351955\pi\) | ||||
0.448508 | + | 0.893779i | \(0.351955\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.63675 | 0.125559 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 5.23246i | − 0.248602i | −0.992245 | − | 0.124301i | \(-0.960331\pi\) | ||||
0.992245 | − | 0.124301i | \(-0.0396688\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.2735i | 0.818842i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.1362 | −0.574021 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.4584 | 0.682333 | 0.341167 | − | 0.940003i | \(-0.389178\pi\) | ||||
0.341167 | + | 0.940003i | \(0.389178\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.0259i | 1.27260i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 4.97832i | − 0.233902i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.43134 | −0.207744 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.9308 | −1.35332 | −0.676662 | − | 0.736294i | \(-0.736574\pi\) | ||||
−0.676662 | + | 0.736294i | \(0.736574\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.3621i | 1.18380i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 35.1350i | − 1.63640i | −0.574933 | − | 0.818200i | \(-0.694972\pi\) | ||||
0.574933 | − | 0.818200i | \(-0.305028\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.9578 | −1.15989 | −0.579944 | − | 0.814656i | \(-0.696926\pi\) | ||||
−0.579944 | + | 0.814656i | \(0.696926\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.06808 | 0.281401 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.8081i | 0.638963i | 0.947592 | + | 0.319482i | \(0.103509\pi\) | ||||
−0.947592 | + | 0.319482i | \(0.896491\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 7.20541i | − 0.332715i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.89088 | −0.455748 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.2735 | −0.518356 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.20541i | 0.0553080i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 5.45301i | − 0.249676i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.7524 | −0.902510 | −0.451255 | − | 0.892395i | \(-0.649024\pi\) | ||||
−0.451255 | + | 0.892395i | \(0.649024\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.5481 | 0.982511 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 4.38377i | − 0.199468i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 11.4654i | − 0.520616i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.6843 | 1.52638 | 0.763191 | − | 0.646173i | \(-0.223632\pi\) | ||||
0.763191 | + | 0.646173i | \(0.223632\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.31569 | −0.285605 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 21.7729i | − 0.982598i | −0.870991 | − | 0.491299i | \(-0.836522\pi\) | ||||
0.870991 | − | 0.491299i | \(-0.163478\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 49.8000i | − 2.24288i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.8627 | −0.668028 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.79459 | −0.304779 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.8692i | 0.934234i | 0.884196 | + | 0.467117i | \(0.154707\pi\) | ||||
−0.884196 | + | 0.467117i | \(0.845293\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.44065i | 0.0643634i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.1578 | −0.675855 | −0.337927 | − | 0.941172i | \(-0.609726\pi\) | ||||
−0.337927 | + | 0.941172i | \(0.609726\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.41082 | 0.196279 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.00000i | 0.177646i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.4789i | 0.464469i | 0.972660 | + | 0.232235i | \(0.0746037\pi\) | ||||
−0.972660 | + | 0.232235i | \(0.925396\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.27349 | 0.0563360 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.09513 | −0.180805 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 5.56866i | − 0.245385i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 36.2518i | − 1.59435i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.3961 | 0.544130 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.7934 | −0.954788 | −0.477394 | − | 0.878689i | \(-0.658418\pi\) | ||||
−0.477394 | + | 0.878689i | \(0.658418\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.79459i | 0.122199i | 0.998132 | + | 0.0610994i | \(0.0194607\pi\) | ||||
−0.998132 | + | 0.0610994i | \(0.980539\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.602705i | 0.0263042i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 75.1621 | 3.27411 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.9037 | 1.30016 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.45301i | 0.236641i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.2464i | 0.920286i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.1362 | −0.784095 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.54699 | 0.282523 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.63675i | − 0.242792i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.0546i | 0.991193i | 0.868553 | + | 0.495596i | \(0.165050\pi\) | ||||
−0.868553 | + | 0.495596i | \(0.834950\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.1103 | 0.562616 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.0816 | 0.731696 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.7265i | 0.629660i | 0.949148 | + | 0.314830i | \(0.101947\pi\) | ||||
−0.949148 | + | 0.314830i | \(0.898053\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 3.35788i | − 0.143311i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.04103 | 0.342560 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.0816 | 0.556287 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 2.93076i | − 0.124404i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.9578i | 1.22698i | 0.789702 | + | 0.613491i | \(0.210235\pi\) | ||||
−0.789702 | + | 0.613491i | \(0.789765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.86267 | −0.374851 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.3621 | 1.07079 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.6162i | 0.995305i | 0.867376 | + | 0.497653i | \(0.165805\pi\) | ||||
−0.867376 | + | 0.497653i | \(0.834195\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.4789i | 0.440851i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.86267 | 0.246209 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.2325 | 0.554734 | 0.277367 | − | 0.960764i | \(-0.410538\pi\) | ||||
0.277367 | + | 0.960764i | \(0.410538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.13733i | 0.214990i | 0.994206 | + | 0.107495i | \(0.0342830\pi\) | ||||
−0.994206 | + | 0.107495i | \(0.965717\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.25182i | 0.177622i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.27349 | −0.303326 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.7400 | 0.905049 | 0.452525 | − | 0.891752i | \(-0.350523\pi\) | ||||
0.452525 | + | 0.891752i | \(0.350523\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 2.13849i | − 0.0888724i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 1.20541i | − 0.0500088i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.6573 | −0.482795 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.6843 | −0.483087 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 18.6584i | − 0.770116i | −0.922892 | − | 0.385058i | \(-0.874182\pi\) | ||||
0.922892 | − | 0.385058i | \(-0.125818\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.1362i | 0.500062i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.7957 | −0.567481 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.67079 | 0.356067 | 0.178033 | − | 0.984024i | \(-0.443027\pi\) | ||||
0.178033 | + | 0.984024i | \(0.443027\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.46538i | 0.306051i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 12.4248i | − 0.508513i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.3292 | 1.19836 | 0.599180 | − | 0.800615i | \(-0.295494\pi\) | ||||
0.599180 | + | 0.800615i | \(0.295494\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.5188 | 1.61200 | 0.806002 | − | 0.591912i | \(-0.201627\pi\) | ||||
0.806002 | + | 0.591912i | \(0.201627\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 18.9988i | − 0.773693i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.7729i | 0.844539i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.3891 | 1.43640 | 0.718201 | − | 0.695836i | \(-0.244966\pi\) | ||||
0.718201 | + | 0.695836i | \(0.244966\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.02052 | 0.162920 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 28.4994i | − 1.15296i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.6561i | 1.80364i | 0.432109 | + | 0.901822i | \(0.357770\pi\) | ||||
−0.432109 | + | 0.901822i | \(0.642230\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.88972 | 0.116525 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.16438 | −0.127393 | −0.0636965 | − | 0.997969i | \(-0.520289\pi\) | ||||
−0.0636965 | + | 0.997969i | \(0.520289\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 44.3134i | 1.78110i | 0.454881 | + | 0.890552i | \(0.349682\pi\) | ||||
−0.454881 | + | 0.890552i | \(0.650318\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 24.7102i | − 0.991586i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.2735 | −0.692048 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.09513i | 0.163544i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 36.3017i | − 1.44744i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.6708 | −1.69870 | −0.849349 | − | 0.527832i | \(-0.823005\pi\) | ||||
−0.849349 | + | 0.527832i | \(0.823005\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.38215 | 0.0946820 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.06808i | 0.240805i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 4.43134i | − 0.175576i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.9156 | −0.708731 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.1784 | −0.520514 | −0.260257 | − | 0.965539i | \(-0.583807\pi\) | ||||
−0.260257 | + | 0.965539i | \(0.583807\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 6.71182i | − 0.264688i | −0.991204 | − | 0.132344i | \(-0.957750\pi\) | ||||
0.991204 | − | 0.132344i | \(-0.0422504\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.20541i | 0.0474630i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.8615 | −0.702209 | −0.351104 | − | 0.936336i | \(-0.614194\pi\) | ||||
−0.351104 | + | 0.936336i | \(0.614194\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.6573 | 0.457588 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.06808i | 0.237827i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 26.1632i | − 1.02385i | −0.859031 | − | 0.511923i | \(-0.828933\pi\) | ||||
0.859031 | − | 0.511923i | \(-0.171067\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.8627 | −0.502586 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.35788 | 0.131003 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 30.6766i | − 1.19499i | −0.801872 | − | 0.597496i | \(-0.796162\pi\) | ||||
0.801872 | − | 0.597496i | \(-0.203838\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 14.9988i | − 0.583387i | −0.956512 | − | 0.291694i | \(-0.905781\pi\) | ||||
0.956512 | − | 0.291694i | \(-0.0942188\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.9384 | 0.774345 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.20541 | −0.0467438 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.5199i | 1.87870i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.44065i | 0.0556986i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.17836 | −0.277118 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.3157 | 0.628924 | 0.314462 | − | 0.949270i | \(-0.398176\pi\) | ||||
0.314462 | + | 0.949270i | \(0.398176\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.39730i | 0.130762i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2.88319i | − 0.110810i | −0.998464 | − | 0.0554050i | \(-0.982355\pi\) | ||||
0.998464 | − | 0.0554050i | \(-0.0176450\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.4654 | 0.440001 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.445322 | 0.0170648 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 2.86267i | − 0.109537i | −0.998499 | − | 0.0547686i | \(-0.982558\pi\) | ||||
0.998499 | − | 0.0547686i | \(-0.0174421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.2735i | 0.507154i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.79343 | −0.297338 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.16438 | −0.349135 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.9578i | 0.949440i | 0.880137 | + | 0.474720i | \(0.157451\pi\) | ||||
−0.880137 | + | 0.474720i | \(0.842549\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 14.8627i | − 0.564586i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.86267 | −0.184452 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.7934 | 1.35577 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 11.4507i | − 0.433105i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.0394i | 1.28565i | 0.766013 | + | 0.642825i | \(0.222238\pi\) | ||||
−0.766013 | + | 0.642825i | \(0.777762\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.86151 | 0.221071 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.87620 | −0.145986 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.41082i | 0.165886i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.7648i | 1.34317i | 0.740926 | + | 0.671587i | \(0.234387\pi\) | ||||
−0.740926 | + | 0.671587i | \(0.765613\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 34.4929 | 1.29358 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −73.2301 | −2.74249 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.9783i | 0.934136i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 11.2530i | − 0.420250i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.97295 | 0.222753 | 0.111377 | − | 0.993778i | \(-0.464474\pi\) | ||||
0.111377 | + | 0.993778i | \(0.464474\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.56866 | 0.207388 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 6.98486i | − 0.259770i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 6.67079i | − 0.247747i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.5048 | 1.31680 | 0.658400 | − | 0.752668i | \(-0.271234\pi\) | ||||
0.658400 | + | 0.752668i | \(0.271234\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.31569 | 0.345025 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.9308i | 0.552234i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 22.2518i | − 0.821890i | −0.911660 | − | 0.410945i | \(-0.865199\pi\) | ||||
0.911660 | − | 0.410945i | \(-0.134801\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.602705 | −0.0222311 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −40.6151 | −1.49608 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 34.0452i | − 1.25237i | −0.779673 | − | 0.626187i | \(-0.784615\pi\) | ||||
0.779673 | − | 0.626187i | \(-0.215385\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.21939i | 0.118267i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.4367 | −1.22667 | −0.613337 | − | 0.789821i | \(-0.710173\pi\) | ||||
−0.613337 | + | 0.789821i | \(0.710173\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.1362 | −0.737732 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 3.17836i | − 0.116290i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 18.1362i | − 0.662681i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.8340 | 1.34409 | 0.672046 | − | 0.740509i | \(-0.265416\pi\) | ||||
0.672046 | + | 0.740509i | \(0.265416\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.93076 | 0.106803 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 8.25997i | − 0.300611i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 8.76754i | − 0.318662i | −0.987225 | − | 0.159331i | \(-0.949066\pi\) | ||||
0.987225 | − | 0.159331i | \(-0.0509337\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.7102 | −0.896924 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.2723 | −0.517372 | −0.258686 | − | 0.965962i | \(-0.583289\pi\) | ||||
−0.258686 | + | 0.965962i | \(0.583289\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.0816i | 0.618396i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19.6843i | 0.711688i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.16438 | 0.330906 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.9718 | −1.04475 | −0.522375 | − | 0.852716i | \(-0.674954\pi\) | ||||
−0.522375 | + | 0.852716i | \(0.674954\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 9.45301i | − 0.340442i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.88435i | 0.355515i | 0.984074 | + | 0.177758i | \(0.0568843\pi\) | ||||
−0.984074 | + | 0.177758i | \(0.943116\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.0681 | 0.361656 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.93076 | 0.105140 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.77945i | 0.207070i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.2994i | 1.37046i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 22.6626 | 0.809897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.4108 | −0.585727 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 3.91723i | − 0.139634i | −0.997560 | − | 0.0698171i | \(-0.977758\pi\) | ||||
0.997560 | − | 0.0698171i | \(-0.0222416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 10.3698i | − 0.369174i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.4789 | −0.372587 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.64328 | −0.200399 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.24644i | 0.0442068i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 26.0205i | − 0.921694i | −0.887480 | − | 0.460847i | \(-0.847546\pi\) | ||||
0.887480 | − | 0.460847i | \(-0.152454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.0124 | −1.69856 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −45.5458 | −1.60928 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 7.17836i | − 0.253319i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 7.27349i | − 0.256357i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.72651 | −0.307188 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.7729 | −1.60929 | −0.804645 | − | 0.593756i | \(-0.797644\pi\) | ||||
−0.804645 | + | 0.593756i | \(0.797644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 28.2313i | − 0.991335i | −0.868512 | − | 0.495668i | \(-0.834923\pi\) | ||||
0.868512 | − | 0.495668i | \(-0.165077\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.36863i | 0.118143i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.4789 | −0.367060 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.41082 | −0.0843439 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 11.6843i | − 0.408283i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.56167i | 0.159203i | 0.996827 | + | 0.0796017i | \(0.0253648\pi\) | ||||
−0.996827 | + | 0.0796017i | \(0.974635\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.4789 | 0.853281 | 0.426640 | − | 0.904421i | \(-0.359697\pi\) | ||||
0.426640 | + | 0.904421i | \(0.359697\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.39730 | 0.118279 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.3826i | 0.813093i | 0.913630 | + | 0.406547i | \(0.133267\pi\) | ||||
−0.913630 | + | 0.406547i | \(0.866733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.69830i | 0.336836i | 0.985716 | + | 0.168418i | \(0.0538658\pi\) | ||||
−0.985716 | + | 0.168418i | \(0.946134\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.97295 | −0.0684409 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.46538 | −0.258660 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.39030i | 0.0827198i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.2043i | 1.18227i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.2031 | 1.21535 | 0.607673 | − | 0.794187i | \(-0.292103\pi\) | ||||
0.607673 | + | 0.794187i | \(0.292103\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.4994 | −0.534463 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.38215i | 0.0820456i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.63675i | 0.228311i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.7729 | −0.713766 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.8972 | −0.373990 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.3686i | 1.21242i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 19.6433i | − 0.672573i | −0.941760 | − | 0.336287i | \(-0.890829\pi\) | ||||
0.941760 | − | 0.336287i | \(-0.109171\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.17836 | −0.108698 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.0410 | 0.479633 | 0.239816 | − | 0.970818i | \(-0.422913\pi\) | ||||
0.239816 | + | 0.970818i | \(0.422913\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 53.3663i | − 1.82083i | −0.413691 | − | 0.910417i | \(-0.635761\pi\) | ||||
0.413691 | − | 0.910417i | \(-0.364239\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.88972i | 0.0984815i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.5188 | 1.14099 | 0.570496 | − | 0.821300i | \(-0.306751\pi\) | ||||
0.570496 | + | 0.821300i | \(0.306751\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.5675 | 0.699316 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 23.3439i | − 0.792800i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 73.7377i | − 2.50138i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.9296 | −1.08189 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.2313 | 1.02317 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000i | 0.0338062i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.97295i | − 0.0666218i | −0.999445 | − | 0.0333109i | \(-0.989395\pi\) | ||||
0.999445 | − | 0.0333109i | \(-0.0106052\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.71298 | 0.0577774 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.9590 | −0.470290 | −0.235145 | − | 0.971960i | \(-0.575556\pi\) | ||||
−0.235145 | + | 0.971960i | \(0.575556\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.5458i | 0.859686i | 0.902904 | + | 0.429843i | \(0.141431\pi\) | ||||
−0.902904 | + | 0.429843i | \(0.858569\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 1.24644i | − 0.0418988i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.8615 | −0.599731 | −0.299865 | − | 0.953981i | \(-0.596942\pi\) | ||||
−0.299865 | + | 0.953981i | \(0.596942\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.06808 | −0.203517 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 33.0464i | − 1.10710i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 7.75240i | − 0.259424i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.8627 | 0.363099 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.4260 | −0.648614 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 67.1621i | − 2.23998i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.4390i | 0.514349i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.20541 | −0.0401135 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.7524 | 0.723074 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 20.0681i | − 0.666350i | −0.942865 | − | 0.333175i | \(-0.891880\pi\) | ||||
0.942865 | − | 0.333175i | \(-0.108120\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.6302i | 0.385750i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.10912 | 0.202404 | 0.101202 | − | 0.994866i | \(-0.467731\pi\) | ||||
0.101202 | + | 0.994866i | \(0.467731\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.79459 | −0.224868 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.767541i | 0.0253741i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 12.8627i | − 0.424763i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.779907 | 0.0257267 | 0.0128634 | − | 0.999917i | \(-0.495905\pi\) | ||||
0.0128634 | + | 0.999917i | \(0.495905\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.26696 | −0.173552 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.1091i | 0.991054i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 4.86267i | − 0.159884i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.6832 | 0.482258 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.2453 | 0.532991 | 0.266495 | − | 0.963836i | \(-0.414134\pi\) | ||||
0.266495 | + | 0.963836i | \(0.414134\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.20541i | − 0.0395057i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.12334i | 0.298685i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 42.0804 | 1.37618 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.2870 | 1.31612 | 0.658060 | − | 0.752966i | \(-0.271377\pi\) | ||||
0.658060 | + | 0.752966i | \(0.271377\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 0.0909185i | − 0.00296701i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.63021i | 0.118342i | 0.998248 | + | 0.0591708i | \(0.0188457\pi\) | ||||
−0.998248 | + | 0.0591708i | \(0.981154\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.8734 | −1.13563 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.39730 | −0.110514 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.0247i | 1.49560i | 0.663922 | + | 0.747801i | \(0.268890\pi\) | ||||
−0.663922 | + | 0.747801i | \(0.731110\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 5.64328i | − 0.183189i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.3579 | −0.433159 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.75240 | 0.0567657 | 0.0283829 | − | 0.999597i | \(-0.490964\pi\) | ||||
0.0283829 | + | 0.999597i | \(0.490964\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.05456i | 0.228280i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 22.6626i | − 0.732579i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13.2735 | −0.428623 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 70.3663 | 2.26988 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 47.8205i | − 1.54099i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 3.54815i | − 0.114219i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.6162 | −0.888078 | −0.444039 | − | 0.896007i | \(-0.646455\pi\) | ||||
−0.444039 | + | 0.896007i | \(0.646455\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.42365 | 0.174233 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.615071i | 0.0197386i | 0.999951 | + | 0.00986928i | \(0.00314154\pi\) | ||||
−0.999951 | + | 0.00986928i | \(0.996858\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 4.86267i | − 0.155890i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.67079 | 0.0855337 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.0940 | 0.994784 | 0.497392 | − | 0.867526i | \(-0.334291\pi\) | ||||
0.497392 | + | 0.867526i | \(0.334291\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 97.3663i | 3.11184i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.0399i | 1.43801i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.4313 | −0.332708 | −0.166354 | − | 0.986066i | \(-0.553199\pi\) | ||||
−0.166354 | + | 0.986066i | \(0.553199\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.8897 | −0.729327 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 3.87620i | − 0.123381i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 14.5470i | − 0.462567i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.89088 | 0.0600658 | 0.0300329 | − | 0.999549i | \(-0.490439\pi\) | ||||
0.0300329 | + | 0.999549i | \(0.490439\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.6410 | 0.623287 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 20.6151i | − 0.653542i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 21.1578i | − 0.670076i | −0.942205 | − | 0.335038i | \(-0.891251\pi\) | ||||
0.942205 | − | 0.335038i | \(-0.108749\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.5199 | 0.522668 |
(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 | 2240.2.b.f.1121.3 | yes | 6 | |
4.3 | odd | 2 | 2240.2.b.e.1121.4 | yes | 6 | ||
8.3 | odd | 2 | 2240.2.b.e.1121.3 | ✓ | 6 | ||
8.5 | even | 2 | inner | 2240.2.b.f.1121.4 | yes | 6 | |
16.3 | odd | 4 | 8960.2.a.bk.1.2 | 3 | |||
16.5 | even | 4 | 8960.2.a.bn.1.2 | 3 | |||
16.11 | odd | 4 | 8960.2.a.bq.1.2 | 3 | |||
16.13 | even | 4 | 8960.2.a.bh.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.b.e.1121.3 | ✓ | 6 | 8.3 | odd | 2 | ||
2240.2.b.e.1121.4 | yes | 6 | 4.3 | odd | 2 | ||
2240.2.b.f.1121.3 | yes | 6 | 1.1 | even | 1 | trivial | |
2240.2.b.f.1121.4 | yes | 6 | 8.5 | even | 2 | inner | |
8960.2.a.bh.1.2 | 3 | 16.13 | even | 4 | |||
8960.2.a.bk.1.2 | 3 | 16.3 | odd | 4 | |||
8960.2.a.bn.1.2 | 3 | 16.5 | even | 4 | |||
8960.2.a.bq.1.2 | 3 | 16.11 | odd | 4 |