Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1336.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1336 = 2^{3} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1336.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: | \(10.6680137100\) |
Analytic rank: | \(1\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 13x^{7} + 8x^{6} + 56x^{5} - 15x^{4} - 81x^{3} + 2x^{2} + 13x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.76335\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1336.1 |
$q$-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 | ||||||||
\(3\) | 1.76335 | 1.01807 | 0.509036 | − | 0.860745i | \(-0.330002\pi\) | ||||
0.509036 | + | 0.860745i | \(0.330002\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.14065 | −0.957328 | −0.478664 | − | 0.877998i | \(-0.658879\pi\) | ||||
−0.478664 | + | 0.877998i | \(0.658879\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.31472 | −0.874881 | −0.437440 | − | 0.899247i | \(-0.644115\pi\) | ||||
−0.437440 | + | 0.899247i | \(0.644115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.109415 | 0.0364718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.602850 | 0.181766 | 0.0908831 | − | 0.995862i | \(-0.471031\pi\) | ||||
0.0908831 | + | 0.995862i | \(0.471031\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.31508 | 0.642087 | 0.321044 | − | 0.947064i | \(-0.395966\pi\) | ||||
0.321044 | + | 0.947064i | \(0.395966\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.77473 | −0.974630 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.36219 | −1.05799 | −0.528993 | − | 0.848626i | \(-0.677430\pi\) | ||||
−0.528993 | + | 0.848626i | \(0.677430\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.77368 | 0.865741 | 0.432871 | − | 0.901456i | \(-0.357501\pi\) | ||||
0.432871 | + | 0.901456i | \(0.357501\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.08166 | −0.890692 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.45921 | −1.55535 | −0.777677 | − | 0.628665i | \(-0.783602\pi\) | ||||
−0.777677 | + | 0.628665i | \(0.783602\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.417611 | −0.0835222 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.09712 | −0.980942 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.78791 | 1.63187 | 0.815937 | − | 0.578141i | \(-0.196222\pi\) | ||||
0.815937 | + | 0.578141i | \(0.196222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.26991 | −0.946505 | −0.473252 | − | 0.880927i | \(-0.656920\pi\) | ||||
−0.473252 | + | 0.880927i | \(0.656920\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.06304 | 0.185051 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.95500 | 0.837548 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.89738 | −1.29832 | −0.649161 | − | 0.760651i | \(-0.724880\pi\) | ||||
−0.649161 | + | 0.760651i | \(0.724880\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.08230 | 0.653691 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.11012 | −1.42276 | −0.711381 | − | 0.702807i | \(-0.751930\pi\) | ||||
−0.711381 | + | 0.702807i | \(0.751930\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.06676 | 0.315178 | 0.157589 | − | 0.987505i | \(-0.449628\pi\) | ||||
0.157589 | + | 0.987505i | \(0.449628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.234220 | −0.0349155 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.53507 | −1.39083 | −0.695416 | − | 0.718607i | \(-0.744780\pi\) | ||||
−0.695416 | + | 0.718607i | \(0.744780\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.64209 | −0.234584 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.69209 | −1.07711 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.21424 | −0.304150 | −0.152075 | − | 0.988369i | \(-0.548595\pi\) | ||||
−0.152075 | + | 0.988369i | \(0.548595\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.29049 | −0.174010 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.65433 | 0.881388 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.79683 | −0.754682 | −0.377341 | − | 0.926074i | \(-0.623162\pi\) | ||||
−0.377341 | + | 0.926074i | \(0.623162\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.9341 | −1.78407 | −0.892037 | − | 0.451961i | \(-0.850724\pi\) | ||||
−0.892037 | + | 0.451961i | \(0.850724\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.253266 | −0.0319085 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.95578 | −0.614688 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8800 | 1.57354 | 0.786769 | − | 0.617247i | \(-0.211752\pi\) | ||||
0.786769 | + | 0.617247i | \(0.211752\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.1532 | −1.58346 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.93032 | −0.941156 | −0.470578 | − | 0.882358i | \(-0.655955\pi\) | ||||
−0.470578 | + | 0.882358i | \(0.655955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.6124 | 1.94433 | 0.972166 | − | 0.234295i | \(-0.0752782\pi\) | ||||
0.972166 | + | 0.234295i | \(0.0752782\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.736396 | −0.0850317 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.39543 | −0.159024 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.75232 | −0.309661 | −0.154830 | − | 0.987941i | \(-0.549483\pi\) | ||||
−0.154830 | + | 0.987941i | \(0.549483\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.31627 | −1.03514 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.18217 | 0.788346 | 0.394173 | − | 0.919036i | \(-0.371031\pi\) | ||||
0.394173 | + | 0.919036i | \(0.371031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.33793 | 1.01284 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.4962 | 1.66137 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.33737 | 0.777759 | 0.388880 | − | 0.921289i | \(-0.372862\pi\) | ||||
0.388880 | + | 0.921289i | \(0.372862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.35875 | −0.561750 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9.29272 | −0.963610 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.07813 | −0.828799 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.4665 | 1.57039 | 0.785193 | − | 0.619251i | \(-0.212564\pi\) | ||||
0.785193 | + | 0.619251i | \(0.212564\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0659611 | 0.00662934 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.27579 | 0.723968 | 0.361984 | − | 0.932184i | \(-0.382099\pi\) | ||||
0.361984 | + | 0.932184i | \(0.382099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.1140 | 1.48923 | 0.744615 | − | 0.667494i | \(-0.232633\pi\) | ||||
0.744615 | + | 0.667494i | \(0.232633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.73742 | 0.852685 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.69621 | 0.647348 | 0.323674 | − | 0.946169i | \(-0.395082\pi\) | ||||
0.323674 | + | 0.946169i | \(0.395082\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.7429 | −1.79524 | −0.897620 | − | 0.440770i | \(-0.854705\pi\) | ||||
−0.897620 | + | 0.440770i | \(0.854705\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.9259 | −1.32179 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.44430 | −0.324012 | −0.162006 | − | 0.986790i | \(-0.551796\pi\) | ||||
−0.162006 | + | 0.986790i | \(0.551796\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.9676 | 1.48898 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.253305 | 0.0234181 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0972 | 0.925612 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6366 | −0.966961 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −16.0644 | −1.44848 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5972 | 1.03729 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.9612 | 1.06139 | 0.530693 | − | 0.847564i | \(-0.321932\pi\) | ||||
0.530693 | + | 0.847564i | \(0.321932\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.64443 | 0.320875 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.3596 | 0.905124 | 0.452562 | − | 0.891733i | \(-0.350510\pi\) | ||||
0.452562 | + | 0.891733i | \(0.350510\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.73500 | −0.757420 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.9112 | 0.939083 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.58902 | −0.648373 | −0.324187 | − | 0.945993i | \(-0.605091\pi\) | ||||
−0.324187 | + | 0.945993i | \(0.605091\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.3794 | 1.55892 | 0.779459 | − | 0.626453i | \(-0.215494\pi\) | ||||
0.779459 | + | 0.626453i | \(0.215494\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.8137 | −1.41597 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.39565 | 0.116710 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.8118 | −1.56224 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.89558 | −0.238823 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.8525 | −1.05292 | −0.526460 | − | 0.850200i | \(-0.676481\pi\) | ||||
−0.526460 | + | 0.850200i | \(0.676481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.6877 | 1.84630 | 0.923148 | − | 0.384445i | \(-0.125607\pi\) | ||||
0.923148 | + | 0.384445i | \(0.125607\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.477291 | −0.0385867 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.2811 | 0.906116 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.90630 | −0.391565 | −0.195783 | − | 0.980647i | \(-0.562725\pi\) | ||||
−0.195783 | + | 0.980647i | \(0.562725\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.90449 | −0.309647 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.2660 | 1.36075 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.2900 | 1.04095 | 0.520476 | − | 0.853876i | \(-0.325754\pi\) | ||||
0.520476 | + | 0.853876i | \(0.325754\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.27559 | −0.177155 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.64041 | −0.587724 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.412898 | 0.0315751 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.46160 | 0.111123 | 0.0555616 | − | 0.998455i | \(-0.482305\pi\) | ||||
0.0555616 | + | 0.998455i | \(0.482305\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.966651 | 0.0730720 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.2219 | −0.768321 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.13991 | −0.384175 | −0.192087 | − | 0.981378i | \(-0.561526\pi\) | ||||
−0.192087 | + | 0.981378i | \(0.561526\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.6366 | −1.68257 | −0.841283 | − | 0.540596i | \(-0.818199\pi\) | ||||
−0.841283 | + | 0.540596i | \(0.818199\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.5707 | −1.81632 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.9055 | 1.24292 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.62975 | −0.192306 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.7984 | 0.858207 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.6449 | 0.987309 | 0.493655 | − | 0.869658i | \(-0.335661\pi\) | ||||
0.493655 | + | 0.869658i | \(0.335661\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.9607 | −0.860951 | −0.430476 | − | 0.902602i | \(-0.641654\pi\) | ||||
−0.430476 | + | 0.902602i | \(0.641654\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.73878 | −0.625797 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.35883 | 0.239307 | 0.119653 | − | 0.992816i | \(-0.461822\pi\) | ||||
0.119653 | + | 0.992816i | \(0.461822\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.2433 | −1.43501 | −0.717506 | − | 0.696552i | \(-0.754716\pi\) | ||||
−0.717506 | + | 0.696552i | \(0.754716\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 22.7119 | 1.60198 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.3415 | −1.42769 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.5016 | 1.36205 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.816152 | −0.0567265 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.27496 | 0.157362 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00805 | −0.275926 | −0.137963 | − | 0.990437i | \(-0.544055\pi\) | ||||
−0.137963 | + | 0.990437i | \(0.544055\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.9840 | −0.958166 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.42422 | −0.301729 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.1984 | 0.828079 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 29.2935 | 1.97947 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.0988 | −0.679320 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.8926 | −1.13122 | −0.565608 | − | 0.824674i | \(-0.691358\pi\) | ||||
−0.565608 | + | 0.824674i | \(0.691358\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.0456931 | −0.00304620 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.8277 | −1.44875 | −0.724377 | − | 0.689404i | \(-0.757873\pi\) | ||||
−0.724377 | + | 0.689404i | \(0.757873\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.80083 | −0.647657 | −0.323829 | − | 0.946116i | \(-0.604970\pi\) | ||||
−0.323829 | + | 0.946116i | \(0.604970\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.46063 | −0.161898 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.4242 | −1.14150 | −0.570749 | − | 0.821125i | \(-0.693347\pi\) | ||||
−0.570749 | + | 0.821125i | \(0.693347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.4113 | 1.33148 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.85332 | −0.315257 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.238358 | −0.0154181 | −0.00770905 | − | 0.999970i | \(-0.502454\pi\) | ||||
−0.00770905 | + | 0.999970i | \(0.502454\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.7271 | 1.14190 | 0.570951 | − | 0.820984i | \(-0.306575\pi\) | ||||
0.570951 | + | 0.820984i | \(0.306575\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.13652 | −0.0729076 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.51513 | 0.224574 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.73636 | 0.555881 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.6647 | 0.802593 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.15416 | 0.262208 | 0.131104 | − | 0.991369i | \(-0.458148\pi\) | ||||
0.131104 | + | 0.991369i | \(0.458148\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.49679 | −0.282711 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.4661 | 1.03115 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.11780 | −0.506374 | −0.253187 | − | 0.967417i | \(-0.581479\pi\) | ||||
−0.253187 | + | 0.967417i | \(0.581479\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.2802 | 1.13588 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.961532 | 0.0595173 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.194729 | −0.0120075 | −0.00600376 | − | 0.999982i | \(-0.501911\pi\) | ||||
−0.00600376 | + | 0.999982i | \(0.501911\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.73992 | 0.291171 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.9384 | 0.791816 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.6456 | −0.953932 | −0.476966 | − | 0.878922i | \(-0.658264\pi\) | ||||
−0.476966 | + | 0.878922i | \(0.658264\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.69848 | 0.467650 | 0.233825 | − | 0.972279i | \(-0.424876\pi\) | ||||
0.233825 | + | 0.972279i | \(0.424876\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.44937 | −0.571902 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.251757 | −0.0151815 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.0696 | 1.20586 | 0.602932 | − | 0.797793i | \(-0.293999\pi\) | ||||
0.602932 | + | 0.797793i | \(0.293999\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.576610 | −0.0345207 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.54093 | −0.211234 | −0.105617 | − | 0.994407i | \(-0.533682\pi\) | ||||
−0.105617 | + | 0.994407i | \(0.533682\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.22156 | −0.369833 | −0.184917 | − | 0.982754i | \(-0.559201\pi\) | ||||
−0.184917 | + | 0.982754i | \(0.559201\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.2446 | −0.843777 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.0874 | 1.24475 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.02872 | 0.119336 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 27.2729 | 1.59877 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.1746 | −0.769667 | −0.384834 | − | 0.922986i | \(-0.625741\pi\) | ||||
−0.384834 | + | 0.922986i | \(0.625741\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.4090 | 0.722479 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.07280 | −0.178302 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.2687 | −0.998672 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.78397 | −0.275744 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.8298 | 0.737052 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.8280 | 1.70795 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.5356 | 0.772519 | 0.386260 | − | 0.922390i | \(-0.373767\pi\) | ||||
0.386260 | + | 0.922390i | \(0.373767\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.6514 | 1.51614 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.9439 | −1.35774 | −0.678868 | − | 0.734261i | \(-0.737529\pi\) | ||||
−0.678868 | + | 0.734261i | \(0.737529\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.22216 | −0.521267 | −0.260634 | − | 0.965438i | \(-0.583931\pi\) | ||||
−0.260634 | + | 0.965438i | \(0.583931\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.542153 | 0.0305469 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.95458 | 0.446774 | 0.223387 | − | 0.974730i | \(-0.428289\pi\) | ||||
0.223387 | + | 0.974730i | \(0.428289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.29779 | 0.296619 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.8078 | 0.659047 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.4615 | −0.915943 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.966802 | −0.0536285 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −33.0503 | −1.82768 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 22.0710 | 1.21681 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.4389 | −1.50818 | −0.754089 | − | 0.656772i | \(-0.771921\pi\) | ||||
−0.754089 | + | 0.656772i | \(0.771921\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.864095 | −0.0473521 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −27.5715 | −1.50639 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.751936 | 0.0409606 | 0.0204803 | − | 0.999790i | \(-0.493480\pi\) | ||||
0.0204803 | + | 0.999790i | \(0.493480\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.07352 | −0.329868 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.17697 | −0.172043 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0040 | 1.08011 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 28.1565 | 1.51589 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.02151 | −0.215886 | −0.107943 | − | 0.994157i | \(-0.534426\pi\) | ||||
−0.107943 | + | 0.994157i | \(0.534426\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.2514 | 1.83344 | 0.916719 | − | 0.399533i | \(-0.130828\pi\) | ||||
0.916719 | + | 0.399533i | \(0.130828\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.8002 | −0.629850 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.1247 | −1.65660 | −0.828299 | − | 0.560286i | \(-0.810691\pi\) | ||||
−0.828299 | + | 0.560286i | \(0.810691\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.9761 | 0.900996 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 17.8050 | 0.942341 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.8992 | −0.575237 | −0.287618 | − | 0.957745i | \(-0.592863\pi\) | ||||
−0.287618 | + | 0.957745i | \(0.592863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.75935 | −0.250492 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.7560 | −0.984437 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −35.5613 | −1.86136 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.47211 | 0.494440 | 0.247220 | − | 0.968959i | \(-0.420483\pi\) | ||||
0.247220 | + | 0.968959i | \(0.420483\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.996787 | −0.0518907 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.12535 | 0.266095 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.8698 | 0.614593 | 0.307297 | − | 0.951614i | \(-0.400576\pi\) | ||||
0.307297 | + | 0.951614i | \(0.400576\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.4500 | 1.05603 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.3447 | 1.04780 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.91179 | 0.355035 | 0.177517 | − | 0.984118i | \(-0.443193\pi\) | ||||
0.177517 | + | 0.984118i | \(0.443193\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21.0918 | 1.08057 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.5500 | 0.845666 | 0.422833 | − | 0.906208i | \(-0.361036\pi\) | ||||
0.422833 | + | 0.906208i | \(0.361036\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.98712 | 0.152238 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.226136 | 0.0114951 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.0288 | 0.609884 | 0.304942 | − | 0.952371i | \(-0.401363\pi\) | ||||
0.304942 | + | 0.952371i | \(0.401363\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.5385 | 1.64554 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.2677 | 0.921482 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.89177 | 0.296447 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.2217 | 1.56697 | 0.783487 | − | 0.621409i | \(-0.213439\pi\) | ||||
0.783487 | + | 0.621409i | \(0.213439\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.4029 | −0.771109 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.4271 | −1.26977 | −0.634885 | − | 0.772607i | \(-0.718953\pi\) | ||||
−0.634885 | + | 0.772607i | \(0.718953\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.2003 | −0.607738 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.9429 | 0.990971 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.76094 | −0.235991 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.95783 | −0.0968086 | −0.0484043 | − | 0.998828i | \(-0.515414\pi\) | ||||
−0.0484043 | + | 0.998828i | \(0.515414\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.3821 | −0.660091 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.4180 | 0.660257 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.3745 | −0.754706 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.4093 | 1.58709 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.7504 | −0.916016 | −0.458008 | − | 0.888948i | \(-0.651437\pi\) | ||||
−0.458008 | + | 0.888948i | \(0.651437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.1681 | 0.982934 | 0.491467 | − | 0.870896i | \(-0.336461\pi\) | ||||
0.491467 | + | 0.870896i | \(0.336461\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.04328 | −0.0507261 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.82170 | 0.0883654 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.2534 | 1.56085 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.46102 | 0.118819 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.3780 | −1.02974 | −0.514872 | − | 0.857267i | \(-0.672161\pi\) | ||||
−0.514872 | + | 0.857267i | \(0.672161\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.303474 | 0.0145841 | 0.00729203 | − | 0.999973i | \(-0.497679\pi\) | ||||
0.00729203 | + | 0.999973i | \(0.497679\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −33.1719 | −1.59047 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −28.1487 | −1.34653 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.21788 | 0.201308 | 0.100654 | − | 0.994921i | \(-0.467906\pi\) | ||||
0.100654 | + | 0.994921i | \(0.467906\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.179669 | −0.00855569 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.4183 | 1.54024 | 0.770121 | − | 0.637898i | \(-0.220196\pi\) | ||||
0.770121 | + | 0.637898i | \(0.220196\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.7067 | −0.744571 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.6636 | −1.07195 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.4412 | 0.917485 | 0.458742 | − | 0.888569i | \(-0.348300\pi\) | ||||
0.458742 | + | 0.888569i | \(0.348300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.49204 | −0.258610 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 40.0064 | 1.87966 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.4712 | 0.537779 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.33537 | −0.109244 | −0.0546219 | − | 0.998507i | \(-0.517395\pi\) | ||||
−0.0546219 | + | 0.998507i | \(0.517395\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.2346 | 1.03782 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.2317 | 1.59433 | 0.797165 | − | 0.603762i | \(-0.206332\pi\) | ||||
0.797165 | + | 0.603762i | \(0.206332\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.3015 | 1.08291 | 0.541457 | − | 0.840729i | \(-0.317873\pi\) | ||||
0.541457 | + | 0.840729i | \(0.317873\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.8925 | 0.922492 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.0070 | −1.15718 | −0.578592 | − | 0.815617i | \(-0.696398\pi\) | ||||
−0.578592 | + | 0.815617i | \(0.696398\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.8135 | −1.37666 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.65153 | −0.398642 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.24595 | 0.0572888 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.57593 | −0.0723086 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.242272 | −0.0110929 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.8036 | −0.722085 | −0.361042 | − | 0.932549i | \(-0.617579\pi\) | ||||
−0.361042 | + | 0.932549i | \(0.617579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.2831 | −0.833636 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30.4460 | 1.38534 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −33.1084 | −1.50337 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.4205 | 0.653456 | 0.326728 | − | 0.945118i | \(-0.394054\pi\) | ||||
0.326728 | + | 0.945118i | \(0.394054\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.4349 | 1.05976 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.85762 | 0.354610 | 0.177305 | − | 0.984156i | \(-0.443262\pi\) | ||||
0.177305 | + | 0.984156i | \(0.443262\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.3345 | −1.72650 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.141200 | −0.00634645 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.3565 | 0.823400 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.0143 | −0.851196 | −0.425598 | − | 0.904912i | \(-0.639936\pi\) | ||||
−0.425598 | + | 0.904912i | \(0.639936\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.76335 | 0.0787808 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.6269 | 0.696768 | 0.348384 | − | 0.937352i | \(-0.386731\pi\) | ||||
0.348384 | + | 0.937352i | \(0.386731\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.5749 | −0.693076 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.4728 | −0.598346 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.0033 | −1.41852 | −0.709261 | − | 0.704946i | \(-0.750971\pi\) | ||||
−0.709261 | + | 0.704946i | \(0.750971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −38.4529 | −1.70106 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.2349 | −0.849242 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −32.3539 | −1.42568 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.74822 | −0.252806 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.57731 | 0.113131 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.6637 | −1.69389 | −0.846943 | − | 0.531684i | \(-0.821559\pi\) | ||||
−0.846943 | + | 0.531684i | \(0.821559\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.8532 | −1.43657 | −0.718285 | − | 0.695749i | \(-0.755073\pi\) | ||||
−0.718285 | + | 0.695749i | \(0.755073\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.70455 | 0.0743926 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.9884 | 1.00139 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.6398 | 1.41912 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.634262 | −0.0275246 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.0906 | −0.913537 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14.3343 | −0.619724 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.06348 | −0.391118 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.989932 | −0.0426394 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.89302 | −0.124381 | −0.0621904 | − | 0.998064i | \(-0.519809\pi\) | ||||
−0.0621904 | + | 0.998064i | \(0.519809\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −39.9163 | −1.71297 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 40.1219 | 1.71863 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.4045 | −1.38552 | −0.692758 | − | 0.721170i | \(-0.743605\pi\) | ||||
−0.692758 | + | 0.721170i | \(0.743605\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.52460 | −0.0650684 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.1627 | 1.41278 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.37085 | 0.270916 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 29.8105 | 1.26538 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.0178 | 0.721068 | 0.360534 | − | 0.932746i | \(-0.382595\pi\) | ||||
0.360534 | + | 0.932746i | \(0.382595\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.78472 | 0.202372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.63718 | −0.195782 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.04420 | 0.170443 | 0.0852214 | − | 0.996362i | \(-0.472840\pi\) | ||||
0.0852214 | + | 0.996362i | \(0.472840\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.37304 | 0.310186 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.5645 | 0.905625 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.4572 | −1.57029 | −0.785143 | − | 0.619315i | \(-0.787411\pi\) | ||||
−0.785143 | + | 0.619315i | \(0.787411\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.5962 | −1.15486 | −0.577432 | − | 0.816439i | \(-0.695945\pi\) | ||||
−0.577432 | + | 0.816439i | \(0.695945\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.0608 | 1.00515 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.11505 | 0.129907 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.00542 | 0.208378 | 0.104189 | − | 0.994558i | \(-0.466775\pi\) | ||||
0.104189 | + | 0.994558i | \(0.466775\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.0910 | −0.876511 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.6247 | −0.689708 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.33486 | −0.0552841 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.542238 | −0.0224188 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.4526 | −0.885444 | −0.442722 | − | 0.896659i | \(-0.645987\pi\) | ||||
−0.442722 | + | 0.896659i | \(0.645987\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.8870 | −0.819428 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.92281 | 0.243632 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.5505 | −0.967105 | −0.483552 | − | 0.875315i | \(-0.660654\pi\) | ||||
−0.483552 | + | 0.875315i | \(0.660654\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −21.6147 | −0.886115 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −35.6962 | −1.46095 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.2263 | 1.15329 | 0.576647 | − | 0.816994i | \(-0.304361\pi\) | ||||
0.576647 | + | 0.816994i | \(0.304361\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.4269 | 0.751649 | 0.375825 | − | 0.926691i | \(-0.377359\pi\) | ||||
0.375825 | + | 0.926691i | \(0.377359\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.40927 | 0.0573898 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.7692 | 0.925699 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.58224 | 0.307753 | 0.153877 | − | 0.988090i | \(-0.450824\pi\) | ||||
0.153877 | + | 0.988090i | \(0.450824\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −35.8693 | −1.45350 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.0744 | −0.893035 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.9490 | −1.20963 | −0.604813 | − | 0.796367i | \(-0.706752\pi\) | ||||
−0.604813 | + | 0.796367i | \(0.706752\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 34.3882 | 1.38667 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.9020 | 0.881743 | 0.440871 | − | 0.897570i | \(-0.354669\pi\) | ||||
0.440871 | + | 0.897570i | \(0.354669\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.7587 | 1.71862 | 0.859308 | − | 0.511459i | \(-0.170895\pi\) | ||||
0.859308 | + | 0.511459i | \(0.170895\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 38.0205 | 1.52571 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.9839 | −0.680447 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.7375 | −0.909502 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.01156 | 0.160206 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.4499 | 1.37361 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.2171 | −1.24273 | −0.621366 | − | 0.783521i | \(-0.713422\pi\) | ||||
−0.621366 | + | 0.783521i | \(0.713422\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.06761 | −0.280912 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −25.6048 | −1.01610 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.80156 | −0.150623 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.867699 | −0.0343257 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.411286 | 0.0162448 | 0.00812241 | − | 0.999967i | \(-0.497415\pi\) | ||||
0.00812241 | + | 0.999967i | \(0.497415\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8285 | 0.900267 | 0.450134 | − | 0.892961i | \(-0.351376\pi\) | ||||
0.450134 | + | 0.892961i | \(0.351376\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.80146 | −0.307182 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.5055 | 1.90695 | 0.953475 | − | 0.301473i | \(-0.0974783\pi\) | ||||
0.953475 | + | 0.301473i | \(0.0974783\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.49462 | −0.137176 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.5100 | 0.843044 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.3576 | −1.22712 | −0.613558 | − | 0.789649i | \(-0.710262\pi\) | ||||
−0.613558 | + | 0.789649i | \(0.710262\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.1763 | −0.866501 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.81765 | 0.0709132 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.5454 | −0.410792 | −0.205396 | − | 0.978679i | \(-0.565848\pi\) | ||||
−0.205396 | + | 0.978679i | \(0.565848\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.0755 | 0.936429 | 0.468215 | − | 0.883615i | \(-0.344897\pi\) | ||||
0.468215 | + | 0.883615i | \(0.344897\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.8078 | −0.691597 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.6986 | 0.725100 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −65.5509 | −2.53814 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.7877 | −1.15166 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.40016 | −0.324284 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.3524 | −1.63257 | −0.816283 | − | 0.577652i | \(-0.803969\pi\) | ||||
−0.816283 | + | 0.577652i | \(0.803969\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.12861 | 0.0819304 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.0861 | −1.27160 | −0.635801 | − | 0.771853i | \(-0.719330\pi\) | ||||
−0.635801 | + | 0.771853i | \(0.719330\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.8006 | −1.37390 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −38.4899 | −1.47494 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.9254 | 1.22159 | 0.610796 | − | 0.791788i | \(-0.290850\pi\) | ||||
0.610796 | + | 0.791788i | \(0.290850\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.2454 | 0.620706 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −17.2823 | −0.659362 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.12615 | −0.195291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31.5093 | −1.19867 | −0.599336 | − | 0.800498i | \(-0.704569\pi\) | ||||
−0.599336 | + | 0.800498i | \(0.704569\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.152681 | −0.00579988 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −39.3438 | −1.49240 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.7401 | 1.50526 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.7250 | −1.16213 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.352719 | 0.0133220 | 0.00666100 | − | 0.999978i | \(-0.497880\pi\) | ||||
0.00666100 | + | 0.999978i | \(0.497880\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −29.8022 | −1.12401 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 35.9923 | 1.35555 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.8414 | −0.633386 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.1858 | −0.607870 | −0.303935 | − | 0.952693i | \(-0.598301\pi\) | ||||
−0.303935 | + | 0.952693i | \(0.598301\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.301147 | −0.0112939 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39.3094 | 1.47215 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.98759 | −0.111730 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.420310 | −0.0156968 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.9403 | −1.34035 | −0.670174 | − | 0.742204i | \(-0.733780\pi\) | ||||
−0.670174 | + | 0.742204i | \(0.733780\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −34.9847 | −1.30290 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.2591 | 1.16254 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.66993 | −0.136298 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.13113 | −0.227391 | −0.113696 | − | 0.993516i | \(-0.536269\pi\) | ||||
−0.113696 | + | 0.993516i | \(0.536269\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.9447 | 0.960916 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.01562 | −0.333455 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.2168 | 0.783660 | 0.391830 | − | 0.920038i | \(-0.371842\pi\) | ||||
0.391830 | + | 0.920038i | \(0.371842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.19842 | 0.228632 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.76469 | 0.286016 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.35371 | 0.233725 | 0.116862 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116862 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.4053 | 0.565928 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.1390 | 0.592082 | 0.296041 | − | 0.955175i | \(-0.404333\pi\) | ||||
0.296041 | + | 0.955175i | \(0.404333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.5128 | 1.00799 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.785840 | 0.0287524 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.4998 | −0.566352 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.0766 | −0.659626 | −0.329813 | − | 0.944046i | \(-0.606986\pi\) | ||||
−0.329813 | + | 0.944046i | \(0.606986\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.32526 | 0.266947 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −48.5664 | −1.76751 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.73240 | −0.281039 | −0.140519 | − | 0.990078i | \(-0.544877\pi\) | ||||
−0.140519 | + | 0.990078i | \(0.544877\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.92943 | −0.287820 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.3809 | −0.521307 | −0.260653 | − | 0.965432i | \(-0.583938\pi\) | ||||
−0.260653 | + | 0.965432i | \(0.583938\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.3844 | 1.57062 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.02171 | 0.0369401 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.4201 | −0.484572 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.8199 | 1.00321 | 0.501606 | − | 0.865096i | \(-0.332743\pi\) | ||||
0.501606 | + | 0.865096i | \(0.332743\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.3145 | −0.515526 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −50.1686 | −1.80444 | −0.902220 | − | 0.431276i | \(-0.858063\pi\) | ||||
−0.902220 | + | 0.431276i | \(0.858063\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.20077 | 0.0790542 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.2345 | 1.15641 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −34.3787 | −1.23174 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.78080 | −0.171070 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −44.7930 | −1.60077 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.5027 | 0.374856 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.18585 | 0.113563 | 0.0567816 | − | 0.998387i | \(-0.481916\pi\) | ||||
0.0567816 | + | 0.998387i | \(0.481916\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.343376 | −0.0122245 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.97258 | 0.283472 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.2585 | −1.14553 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.35816 | 0.296433 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.9946 | −1.52295 | −0.761473 | − | 0.648197i | \(-0.775523\pi\) | ||||
−0.761473 | + | 0.648197i | \(0.775523\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.5938 | 1.47148 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.802821 | 0.0283663 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.0148 | 0.353414 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.9604 | −1.30268 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.5888 | −0.971172 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.74852 | 0.237265 | 0.118633 | − | 0.992938i | \(-0.462149\pi\) | ||||
0.118633 | + | 0.992938i | \(0.462149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.5200 | 1.66865 | 0.834326 | − | 0.551271i | \(-0.185857\pi\) | ||||
0.834326 | + | 0.551271i | \(0.185857\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.5751 | 0.476101 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.4492 | −0.996533 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.79930 | 0.272863 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.586330 | −0.0204880 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.64018 | −0.301544 | −0.150772 | − | 0.988569i | \(-0.548176\pi\) | ||||
−0.150772 | + | 0.988569i | \(0.548176\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.5776 | 1.72817 | 0.864084 | − | 0.503348i | \(-0.167899\pi\) | ||||
0.864084 | + | 0.503348i | \(0.167899\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.443936 | −0.0154559 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.5098 | −1.44344 | −0.721718 | − | 0.692187i | \(-0.756647\pi\) | ||||
−0.721718 | + | 0.692187i | \(0.756647\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.3918 | −1.19448 | −0.597238 | − | 0.802064i | \(-0.703735\pi\) | ||||
−0.597238 | + | 0.802064i | \(0.703735\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 35.3897 | 1.22766 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.16309 | 0.248186 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.14065 | −0.0740803 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 26.8614 | 0.928466 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.9413 | −0.757499 | −0.378749 | − | 0.925499i | \(-0.623646\pi\) | ||||
−0.378749 | + | 0.925499i | \(0.623646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48.2273 | 1.66301 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.24391 | −0.215052 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.3555 | 0.562645 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24.6207 | 0.845976 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.9708 | −0.376517 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58.9083 | 2.01935 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.6049 | −1.01365 | −0.506826 | − | 0.862048i | \(-0.669181\pi\) | ||||
−0.506826 | + | 0.862048i | \(0.669181\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.883872 | −0.0302278 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.9376 | 1.53504 | 0.767519 | − | 0.641026i | \(-0.221491\pi\) | ||||
0.767519 | + | 0.641026i | \(0.221491\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.8861 | 1.12206 | 0.561029 | − | 0.827796i | \(-0.310406\pi\) | ||||
0.561029 | + | 0.827796i | \(0.310406\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.1845 | 1.26724 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 35.2095 | 1.19855 | 0.599273 | − | 0.800545i | \(-0.295457\pi\) | ||||
0.599273 | + | 0.800545i | \(0.295457\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.12877 | −0.106381 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.57734 | 0.121493 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.65924 | −0.0562858 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.8181 | 1.01035 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.69227 | 0.0572748 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −26.8443 | −0.907502 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.3650 | 1.02535 | 0.512676 | − | 0.858582i | \(-0.328654\pi\) | ||||
0.512676 | + | 0.858582i | \(0.328654\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.2314 | −0.783577 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.2880 | −0.582448 | −0.291224 | − | 0.956655i | \(-0.594062\pi\) | ||||
−0.291224 | + | 0.956655i | \(0.594062\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.02538 | 0.202770 | 0.101385 | − | 0.994847i | \(-0.467673\pi\) | ||||
0.101385 | + | 0.994847i | \(0.467673\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21.8814 | 0.735536 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.18060 | 0.173948 | 0.0869738 | − | 0.996211i | \(-0.472280\pi\) | ||||
0.0869738 | + | 0.996211i | \(0.472280\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.6868 | −0.928586 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.61632 | −0.188154 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35.9823 | −1.20410 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.0028 | 0.367782 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −30.4507 | −1.01672 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46.3115 | −1.54458 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.65895 | 0.321786 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.43583 | −0.280727 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 48.4571 | 1.61077 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.1119 | 1.06626 | 0.533129 | − | 0.846034i | \(-0.321016\pi\) | ||||
0.533129 | + | 0.846034i | \(0.321016\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.796084 | 0.0264044 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.93962 | −0.296183 | −0.148091 | − | 0.988974i | \(-0.547313\pi\) | ||||
−0.148091 | + | 0.988974i | \(0.547313\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.32977 | 0.143295 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 52.5973 | 1.73881 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.9796 | −0.791876 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.0469 | 0.331415 | 0.165708 | − | 0.986175i | \(-0.447009\pi\) | ||||
0.165708 | + | 0.986175i | \(0.447009\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.8681 | 0.786480 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18.3593 | −0.604304 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.29803 | 0.108439 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.65371 | 0.0543149 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.81527 | −0.125175 | −0.0625875 | − | 0.998039i | \(-0.519935\pi\) | ||||
−0.0625875 | + | 0.998039i | \(0.519935\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.19670 | −0.203089 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −42.2216 | −1.38227 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.62937 | 0.184100 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5607 | −0.345004 | −0.172502 | − | 0.985009i | \(-0.555185\pi\) | ||||
−0.172502 | + | 0.985009i | \(0.555185\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.2619 | −0.530688 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.0712 | 1.17589 | 0.587944 | − | 0.808902i | \(-0.299938\pi\) | ||||
0.587944 | + | 0.808902i | \(0.299938\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 67.9543 | 2.21290 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −25.2563 | −0.821586 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.80219 | 0.0910589 | 0.0455294 | − | 0.998963i | \(-0.485503\pi\) | ||||
0.0455294 | + | 0.998963i | \(0.485503\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 38.4589 | 1.24843 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.0267 | 0.454848 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.17253 | −0.167555 | −0.0837773 | − | 0.996485i | \(-0.526698\pi\) | ||||
−0.0837773 | + | 0.996485i | \(0.526698\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.2089 | −0.945179 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.34188 | 0.301980 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.5664 | 0.567249 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.22800 | −0.104129 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.732669 | 0.0236099 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.6037 | 0.824213 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.37994 | −0.0443760 | −0.0221880 | − | 0.999754i | \(-0.507063\pi\) | ||||
−0.0221880 | + | 0.999754i | \(0.507063\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.0275 | −0.932496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.0946 | −0.548591 | −0.274295 | − | 0.961645i | \(-0.588445\pi\) | ||||
−0.274295 | + | 0.961645i | \(0.588445\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.5431 | −1.36387 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.70481 | −0.0545977 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.2402 | 1.15943 | 0.579714 | − | 0.814820i | \(-0.303164\pi\) | ||||
0.579714 | + | 0.814820i | \(0.303164\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.42333 | 0.141370 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.05076 | −0.0654756 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.1807 | 0.611770 | 0.305885 | − | 0.952068i | \(-0.401048\pi\) | ||||
0.305885 | + | 0.952068i | \(0.401048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.19009 | −0.229095 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 38.9189 | 1.23880 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.4164 | −0.490214 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.9073 | −1.26770 | −0.633849 | − | 0.773457i | \(-0.718526\pi\) | ||||
−0.633849 | + | 0.773457i | \(0.718526\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −48.3845 | −1.53544 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.3339 | 1.37378 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.95261 | 0.0935101 | 0.0467551 | − | 0.998906i | \(-0.485112\pi\) | ||||
0.0467551 | + | 0.998906i | \(0.485112\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40.2539 | 1.27358 |
(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 | 1336.2.a.c.1.8 | ✓ | 9 | |
4.3 | odd | 2 | 2672.2.a.m.1.2 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1336.2.a.c.1.8 | ✓ | 9 | 1.1 | even | 1 | trivial | |
2672.2.a.m.1.2 | 9 | 4.3 | odd | 2 |