Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8712,2,Mod(1,8712)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8712, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8712.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8712 = 2^{3} \cdot 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8712.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: | \(69.5656702409\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 968) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8712.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.73205 | 1.66902 | 0.834512 | − | 0.550990i | \(-0.185750\pi\) | ||||
0.834512 | + | 0.550990i | \(0.185750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.73205 | −1.03262 | −0.516309 | − | 0.856402i | \(-0.672694\pi\) | ||||
−0.516309 | + | 0.856402i | \(0.672694\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.46410 | −1.23812 | −0.619060 | − | 0.785344i | \(-0.712486\pi\) | ||||
−0.619060 | + | 0.785344i | \(0.712486\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.26795 | 0.550058 | 0.275029 | − | 0.961436i | \(-0.411312\pi\) | ||||
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.26795 | −0.749719 | −0.374859 | − | 0.927082i | \(-0.622309\pi\) | ||||
−0.374859 | + | 0.927082i | \(0.622309\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.19615 | 0.457929 | 0.228965 | − | 0.973435i | \(-0.426466\pi\) | ||||
0.228965 | + | 0.973435i | \(0.426466\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.92820 | 1.78564 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.46410 | −0.828963 | −0.414481 | − | 0.910058i | \(-0.636037\pi\) | ||||
−0.414481 | + | 0.910058i | \(0.636037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.73205 | −0.849901 | −0.424951 | − | 0.905216i | \(-0.639709\pi\) | ||||
−0.424951 | + | 0.905216i | \(0.639709\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.1962 | −1.72346 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.73205 | 0.942343 | 0.471172 | − | 0.882042i | \(-0.343831\pi\) | ||||
0.471172 | + | 0.882042i | \(0.343831\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.73205 | 1.20754 | 0.603772 | − | 0.797157i | \(-0.293664\pi\) | ||||
0.603772 | + | 0.797157i | \(0.293664\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.26795 | 0.476679 | 0.238340 | − | 0.971182i | \(-0.423397\pi\) | ||||
0.238340 | + | 0.971182i | \(0.423397\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.464102 | 0.0663002 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.19615 | −0.164304 | −0.0821521 | − | 0.996620i | \(-0.526179\pi\) | ||||
−0.0821521 | + | 0.996620i | \(0.526179\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.4641 | −1.75288 | −0.876438 | − | 0.481514i | \(-0.840087\pi\) | ||||
−0.876438 | + | 0.481514i | \(0.840087\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.53590 | −0.836836 | −0.418418 | − | 0.908255i | \(-0.637415\pi\) | ||||
−0.418418 | + | 0.908255i | \(0.637415\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.6603 | −2.06645 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.196152 | −0.0239638 | −0.0119819 | − | 0.999928i | \(-0.503814\pi\) | ||||
−0.0119819 | + | 0.999928i | \(0.503814\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.53590 | −0.300956 | −0.150478 | − | 0.988613i | \(-0.548081\pi\) | ||||
−0.150478 | + | 0.988613i | \(0.548081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.92820 | 1.04497 | 0.522484 | − | 0.852649i | \(-0.325006\pi\) | ||||
0.522484 | + | 0.852649i | \(0.325006\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.5885 | 1.86635 | 0.933174 | − | 0.359426i | \(-0.117027\pi\) | ||||
0.933174 | + | 0.359426i | \(0.117027\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.19615 | 0.241059 | 0.120530 | − | 0.992710i | \(-0.461541\pi\) | ||||
0.120530 | + | 0.992710i | \(0.461541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.46410 | 0.918061 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.4641 | 1.74519 | 0.872596 | − | 0.488443i | \(-0.162435\pi\) | ||||
0.872596 | + | 0.488443i | \(0.162435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.1962 | 1.27850 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.1962 | −1.25130 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.9282 | −1.21113 | −0.605563 | − | 0.795798i | \(-0.707052\pi\) | ||||
−0.605563 | + | 0.795798i | \(0.707052\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.4641 | −1.73774 | −0.868872 | − | 0.495038i | \(-0.835154\pi\) | ||||
−0.868872 | + | 0.495038i | \(0.835154\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.53590 | −0.644001 | −0.322001 | − | 0.946739i | \(-0.604355\pi\) | ||||
−0.322001 | + | 0.946739i | \(0.604355\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.1244 | −1.65547 | −0.827737 | − | 0.561116i | \(-0.810372\pi\) | ||||
−0.827737 | + | 0.561116i | \(0.810372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.4641 | −1.19384 | −0.596922 | − | 0.802299i | \(-0.703610\pi\) | ||||
−0.596922 | + | 0.802299i | \(0.703610\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.00000 | −0.470360 | −0.235180 | − | 0.971952i | \(-0.575568\pi\) | ||||
−0.235180 | + | 0.971952i | \(0.575568\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.19615 | 0.764295 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.19615 | −0.568000 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 14.6603 | 1.31125 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.92820 | 0.774173 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.53590 | 0.216656 | 0.108328 | − | 0.994115i | \(-0.465450\pi\) | ||||
0.108328 | + | 0.994115i | \(0.465450\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.19615 | −0.525551 | −0.262775 | − | 0.964857i | \(-0.584638\pi\) | ||||
−0.262775 | + | 0.964857i | \(0.584638\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.6603 | −1.38356 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.53590 | −0.453518 | −0.226759 | − | 0.973951i | \(-0.572813\pi\) | ||||
−0.226759 | + | 0.973951i | \(0.572813\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.5359 | 0.857399 | 0.428700 | − | 0.903447i | \(-0.358972\pi\) | ||||
0.428700 | + | 0.903447i | \(0.358972\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.6603 | −1.41851 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.7846 | −1.65879 | −0.829396 | − | 0.558661i | \(-0.811315\pi\) | ||||
−0.829396 | + | 0.558661i | \(0.811315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.5167 | −1.84197 | −0.920984 | − | 0.389602i | \(-0.872613\pi\) | ||||
−0.920984 | + | 0.389602i | \(0.872613\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.53590 | 0.505763 | 0.252882 | − | 0.967497i | \(-0.418622\pi\) | ||||
0.252882 | + | 0.967497i | \(0.418622\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.92820 | 0.532939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.53590 | −0.192801 | −0.0964004 | − | 0.995343i | \(-0.530733\pi\) | ||||
−0.0964004 | + | 0.995343i | \(0.530733\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.3923 | −1.84388 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0000 | −1.19590 | −0.597948 | − | 0.801535i | \(-0.704017\pi\) | ||||
−0.597948 | + | 0.801535i | \(0.704017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.80385 | −0.208408 | −0.104204 | − | 0.994556i | \(-0.533230\pi\) | ||||
−0.104204 | + | 0.994556i | \(0.533230\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.3923 | 1.57279 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.39230 | −0.317816 | −0.158908 | − | 0.987293i | \(-0.550797\pi\) | ||||
−0.158908 | + | 0.987293i | \(0.550797\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.6603 | −1.19923 | −0.599616 | − | 0.800288i | \(-0.704680\pi\) | ||||
−0.599616 | + | 0.800288i | \(0.704680\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.92820 | 0.422367 | 0.211183 | − | 0.977446i | \(-0.432268\pi\) | ||||
0.211183 | + | 0.977446i | \(0.432268\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.53590 | −0.463318 | −0.231659 | − | 0.972797i | \(-0.574415\pi\) | ||||
−0.231659 | + | 0.972797i | \(0.574415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.1962 | 0.856002 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.8564 | 2.01542 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8564 | −1.22929 | −0.614643 | − | 0.788806i | \(-0.710700\pi\) | ||||
−0.614643 | + | 0.788806i | \(0.710700\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −29.8564 | −2.03619 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.9282 | 0.877624 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.1244 | −0.681038 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.39230 | −0.561990 | −0.280995 | − | 0.959709i | \(-0.590664\pi\) | ||||
−0.280995 | + | 0.959709i | \(0.590664\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.60770 | 0.239451 | 0.119726 | − | 0.992807i | \(-0.461799\pi\) | ||||
0.119726 | + | 0.992807i | \(0.461799\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.8038 | 0.846102 | 0.423051 | − | 0.906106i | \(-0.360959\pi\) | ||||
0.423051 | + | 0.906106i | \(0.360959\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.19615 | −0.0783626 | −0.0391813 | − | 0.999232i | \(-0.512475\pi\) | ||||
−0.0391813 | + | 0.999232i | \(0.512475\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1962 | 0.795589 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.5167 | 1.26243 | 0.631214 | − | 0.775609i | \(-0.282557\pi\) | ||||
0.631214 | + | 0.775609i | \(0.282557\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.92820 | 0.575116 | 0.287558 | − | 0.957763i | \(-0.407157\pi\) | ||||
0.287558 | + | 0.957763i | \(0.407157\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.73205 | 0.110657 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.5885 | 0.928241 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.2679 | −1.08994 | −0.544972 | − | 0.838454i | \(-0.683460\pi\) | ||||
−0.544972 | + | 0.838454i | \(0.683460\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.46410 | 0.278463 | 0.139232 | − | 0.990260i | \(-0.455537\pi\) | ||||
0.139232 | + | 0.990260i | \(0.455537\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −15.6603 | −0.973081 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.33975 | −0.144275 | −0.0721375 | − | 0.997395i | \(-0.522982\pi\) | ||||
−0.0721375 | + | 0.997395i | \(0.522982\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.46410 | −0.274228 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.0526 | 1.16166 | 0.580828 | − | 0.814027i | \(-0.302729\pi\) | ||||
0.580828 | + | 0.814027i | \(0.302729\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.53590 | 0.397028 | 0.198514 | − | 0.980098i | \(-0.436389\pi\) | ||||
0.198514 | + | 0.980098i | \(0.436389\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.7846 | 0.828237 | 0.414118 | − | 0.910223i | \(-0.364090\pi\) | ||||
0.414118 | + | 0.910223i | \(0.364090\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.85641 | 0.468674 | 0.234337 | − | 0.972155i | \(-0.424708\pi\) | ||||
0.234337 | + | 0.972155i | \(0.424708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −30.9282 | −1.83849 | −0.919245 | − | 0.393685i | \(-0.871200\pi\) | ||||
−0.919245 | + | 0.393685i | \(0.871200\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.1244 | −1.24693 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.8564 | −0.697436 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.3205 | 1.30398 | 0.651989 | − | 0.758228i | \(-0.273935\pi\) | ||||
0.651989 | + | 0.758228i | \(0.273935\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −50.2487 | −2.92559 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.80385 | −0.566971 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.8564 | 1.25978 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.3923 | −1.39670 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.4449 | 1.85173 | 0.925863 | − | 0.377859i | \(-0.123340\pi\) | ||||
0.925863 | + | 0.377859i | \(0.123340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.7846 | −0.951768 | −0.475884 | − | 0.879508i | \(-0.657872\pi\) | ||||
−0.475884 | + | 0.879508i | \(0.657872\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.00000 | −0.395663 | −0.197832 | − | 0.980236i | \(-0.563390\pi\) | ||||
−0.197832 | + | 0.980236i | \(0.563390\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.85641 | −0.216597 | −0.108299 | − | 0.994118i | \(-0.534540\pi\) | ||||
−0.108299 | + | 0.994118i | \(0.534540\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.41154 | −0.412389 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −39.8564 | −2.21084 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.92820 | −0.492228 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.07180 | −0.0589113 | −0.0294556 | − | 0.999566i | \(-0.509377\pi\) | ||||
−0.0294556 | + | 0.999566i | \(0.509377\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.732051 | −0.0399962 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.19615 | −0.391999 | −0.196000 | − | 0.980604i | \(-0.562795\pi\) | ||||
−0.196000 | + | 0.980604i | \(0.562795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8564 | 0.964155 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.3923 | −1.30945 | −0.654724 | − | 0.755868i | \(-0.727215\pi\) | ||||
−0.654724 | + | 0.755868i | \(0.727215\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.3923 | −0.930989 | −0.465494 | − | 0.885051i | \(-0.654123\pi\) | ||||
−0.465494 | + | 0.885051i | \(0.654123\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.92820 | 0.421976 | 0.210988 | − | 0.977489i | \(-0.432332\pi\) | ||||
0.210988 | + | 0.977489i | \(0.432332\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.46410 | −0.502302 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.2679 | 1.33359 | 0.666796 | − | 0.745241i | \(-0.267665\pi\) | ||||
0.666796 | + | 0.745241i | \(0.267665\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.32051 | −0.437921 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 33.3205 | 1.74408 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.5167 | 1.12316 | 0.561580 | − | 0.827422i | \(-0.310194\pi\) | ||||
0.561580 | + | 0.827422i | \(0.310194\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.26795 | 0.169663 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.46410 | 0.0758083 | 0.0379042 | − | 0.999281i | \(-0.487932\pi\) | ||||
0.0379042 | + | 0.999281i | \(0.487932\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.9282 | 1.02635 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.1769 | 1.70418 | 0.852092 | − | 0.523392i | \(-0.175334\pi\) | ||||
0.852092 | + | 0.523392i | \(0.175334\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.3205 | −0.987232 | −0.493616 | − | 0.869680i | \(-0.664325\pi\) | ||||
−0.493616 | + | 0.869680i | \(0.664325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 30.1244 | 1.52737 | 0.763683 | − | 0.645592i | \(-0.223389\pi\) | ||||
0.763683 | + | 0.645592i | \(0.223389\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.98076 | 0.251888 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 61.9090 | 3.11498 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.8756 | 0.596022 | 0.298011 | − | 0.954563i | \(-0.403677\pi\) | ||||
0.298011 | + | 0.954563i | \(0.403677\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.24871 | 0.461859 | 0.230929 | − | 0.972971i | \(-0.425823\pi\) | ||||
0.230929 | + | 0.972971i | \(0.425823\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.1244 | 1.05228 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.7321 | −1.37126 | −0.685631 | − | 0.727949i | \(-0.740474\pi\) | ||||
−0.685631 | + | 0.727949i | \(0.740474\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.7846 | 1.81005 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.19615 | 0.402333 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.66025 | 0.276522 | 0.138261 | − | 0.990396i | \(-0.455849\pi\) | ||||
0.138261 | + | 0.990396i | \(0.455849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5167 | 0.610025 | 0.305012 | − | 0.952348i | \(-0.401339\pi\) | ||||
0.305012 | + | 0.952348i | \(0.401339\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.2487 | 0.982207 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.8564 | 0.864132 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.39230 | 0.211570 | 0.105785 | − | 0.994389i | \(-0.466264\pi\) | ||||
0.105785 | + | 0.994389i | \(0.466264\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.00000 | −0.432512 | −0.216256 | − | 0.976337i | \(-0.569385\pi\) | ||||
−0.216256 | + | 0.976337i | \(0.569385\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.17691 | −0.343318 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.5885 | −1.74627 | −0.873136 | − | 0.487477i | \(-0.837917\pi\) | ||||
−0.873136 | + | 0.487477i | \(0.837917\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.9282 | −0.709260 | −0.354630 | − | 0.935007i | \(-0.615393\pi\) | ||||
−0.354630 | + | 0.935007i | \(0.615393\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 61.4449 | 2.91277 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.14359 | 0.0539695 | 0.0269848 | − | 0.999636i | \(-0.491409\pi\) | ||||
0.0269848 | + | 0.999636i | \(0.491409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 45.5167 | 2.13385 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.58846 | 0.167861 | 0.0839305 | − | 0.996472i | \(-0.473253\pi\) | ||||
0.0839305 | + | 0.996472i | \(0.473253\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.3205 | −1.03957 | −0.519785 | − | 0.854297i | \(-0.673988\pi\) | ||||
−0.519785 | + | 0.854297i | \(0.673988\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.7846 | −1.70953 | −0.854763 | − | 0.519019i | \(-0.826298\pi\) | ||||
−0.854763 | + | 0.519019i | \(0.826298\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.3923 | 1.31384 | 0.656920 | − | 0.753961i | \(-0.271859\pi\) | ||||
0.656920 | + | 0.753961i | \(0.271859\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.535898 | 0.0247455 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.1769 | −1.33873 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.0718 | 0.597266 | 0.298633 | − | 0.954368i | \(-0.403469\pi\) | ||||
0.298633 | + | 0.954368i | \(0.403469\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.5885 | −1.16673 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −44.5167 | −2.02140 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.1962 | −0.824546 | −0.412273 | − | 0.911060i | \(-0.635265\pi\) | ||||
−0.412273 | + | 0.911060i | \(0.635265\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.6603 | −1.24829 | −0.624145 | − | 0.781309i | \(-0.714553\pi\) | ||||
−0.624145 | + | 0.781309i | \(0.714553\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.1244 | −0.455978 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.92820 | 0.310772 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.5167 | 0.870205 | 0.435102 | − | 0.900381i | \(-0.356712\pi\) | ||||
0.435102 | + | 0.900381i | \(0.356712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −65.1769 | −2.90033 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −42.7846 | −1.89639 | −0.948197 | − | 0.317682i | \(-0.897095\pi\) | ||||
−0.948197 | + | 0.317682i | \(0.897095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.3923 | −1.07905 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.3923 | −1.07485 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.3205 | 1.54742 | 0.773710 | − | 0.633540i | \(-0.218399\pi\) | ||||
0.773710 | + | 0.633540i | \(0.218399\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.53590 | −0.285795 | −0.142897 | − | 0.989738i | \(-0.545642\pi\) | ||||
−0.142897 | + | 0.989738i | \(0.545642\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.7321 | −0.467495 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1769 | −0.790301 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −34.5167 | −1.49508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −63.9090 | −2.76303 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −46.5167 | −1.99255 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.7128 | 1.52697 | 0.763485 | − | 0.645826i | \(-0.223487\pi\) | ||||
0.763485 | + | 0.645826i | \(0.223487\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.5885 | 0.621489 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.3205 | −1.92722 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.3205 | 1.15761 | 0.578804 | − | 0.815467i | \(-0.303520\pi\) | ||||
0.578804 | + | 0.815467i | \(0.303520\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.7128 | 1.51049 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.1244 | 0.890285 | 0.445143 | − | 0.895460i | \(-0.353153\pi\) | ||||
0.445143 | + | 0.895460i | \(0.353153\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.6603 | −0.785043 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.14359 | 0.173708 | 0.0868542 | − | 0.996221i | \(-0.472319\pi\) | ||||
0.0868542 | + | 0.996221i | \(0.472319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.05256 | 0.336989 | 0.168495 | − | 0.985703i | \(-0.446109\pi\) | ||||
0.168495 | + | 0.985703i | \(0.446109\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 19.6077 | 0.817697 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.5359 | 0.563507 | 0.281753 | − | 0.959487i | \(-0.409084\pi\) | ||||
0.281753 | + | 0.959487i | \(0.409084\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | −0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.7321 | −0.773154 | −0.386577 | − | 0.922257i | \(-0.626343\pi\) | ||||
−0.386577 | + | 0.922257i | \(0.626343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.4641 | 0.637187 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.3731 | −1.24727 | −0.623636 | − | 0.781715i | \(-0.714345\pi\) | ||||
−0.623636 | + | 0.781715i | \(0.714345\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.1244 | −0.948006 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.1244 | −0.863118 | −0.431559 | − | 0.902085i | \(-0.642036\pi\) | ||||
−0.431559 | + | 0.902085i | \(0.642036\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.1962 | 1.19094 | 0.595468 | − | 0.803379i | \(-0.296967\pi\) | ||||
0.595468 | + | 0.803379i | \(0.296967\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.1962 | −1.46916 | −0.734578 | − | 0.678524i | \(-0.762620\pi\) | ||||
−0.734578 | + | 0.678524i | \(0.762620\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.5885 | −0.590186 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.9282 | −0.804893 | −0.402446 | − | 0.915444i | \(-0.631840\pi\) | ||||
−0.402446 | + | 0.915444i | \(0.631840\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.3205 | 1.78428 | 0.892138 | − | 0.451763i | \(-0.149205\pi\) | ||||
0.892138 | + | 0.451763i | \(0.149205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.6603 | 1.35292 | 0.676460 | − | 0.736479i | \(-0.263513\pi\) | ||||
0.676460 | + | 0.736479i | \(0.263513\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −44.9808 | −1.80212 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.0718 | 0.402872 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.0000 | 0.518344 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.0526 | 1.27599 | 0.637996 | − | 0.770040i | \(-0.279764\pi\) | ||||
0.637996 | + | 0.770040i | \(0.279764\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.07180 | −0.0820876 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.4641 | 0.413307 | 0.206654 | − | 0.978414i | \(-0.433743\pi\) | ||||
0.206654 | + | 0.978414i | \(0.433743\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.0526 | 1.34290 | 0.671451 | − | 0.741049i | \(-0.265671\pi\) | ||||
0.671451 | + | 0.741049i | \(0.265671\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.3923 | −0.644448 | −0.322224 | − | 0.946663i | \(-0.604430\pi\) | ||||
−0.322224 | + | 0.946663i | \(0.604430\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.92820 | −0.271122 | −0.135561 | − | 0.990769i | \(-0.543284\pi\) | ||||
−0.135561 | + | 0.990769i | \(0.543284\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.8564 | −1.16659 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.98076 | 0.116114 | 0.0580570 | − | 0.998313i | \(-0.481509\pi\) | ||||
0.0580570 | + | 0.998313i | \(0.481509\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.3397 | −0.674438 | −0.337219 | − | 0.941426i | \(-0.609486\pi\) | ||||
−0.337219 | + | 0.941426i | \(0.609486\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33.3205 | 1.29211 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.80385 | −0.379606 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.9282 | 1.11510 | 0.557550 | − | 0.830143i | \(-0.311741\pi\) | ||||
0.557550 | + | 0.830143i | \(0.311741\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.8564 | −0.647844 | −0.323922 | − | 0.946084i | \(-0.605002\pi\) | ||||
−0.323922 | + | 0.946084i | \(0.605002\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.5885 | 1.25063 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.1244 | 0.884829 | 0.442414 | − | 0.896811i | \(-0.354122\pi\) | ||||
0.442414 | + | 0.896811i | \(0.354122\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.46410 | 0.361605 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.33975 | 0.203428 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.1769 | −0.805608 | −0.402804 | − | 0.915286i | \(-0.631964\pi\) | ||||
−0.402804 | + | 0.915286i | \(0.631964\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.1244 | −0.877157 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.5359 | 0.664220 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.6077 | −0.476186 | −0.238093 | − | 0.971242i | \(-0.576522\pi\) | ||||
−0.238093 | + | 0.971242i | \(0.576522\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.7321 | −0.706493 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 47.7128 | 1.79443 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.143594 | −0.00539277 | −0.00269638 | − | 0.999996i | \(-0.500858\pi\) | ||||
−0.00269638 | + | 0.999996i | \(0.500858\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.3923 | −0.389195 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.1962 | −0.380252 | −0.190126 | − | 0.981760i | \(-0.560890\pi\) | ||||
−0.190126 | + | 0.981760i | \(0.560890\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.8564 | 0.665007 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −39.8564 | −1.48023 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.19615 | −0.0814508 | −0.0407254 | − | 0.999170i | \(-0.512967\pi\) | ||||
−0.0407254 | + | 0.999170i | \(0.512967\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.1436 | −0.671065 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.0000 | −1.21888 | −0.609441 | − | 0.792831i | \(-0.708606\pi\) | ||||
−0.609441 | + | 0.792831i | \(0.708606\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.7321 | −0.615498 | −0.307749 | − | 0.951468i | \(-0.599576\pi\) | ||||
−0.307749 | + | 0.951468i | \(0.599576\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 41.3731 | 1.51783 | 0.758915 | − | 0.651189i | \(-0.225730\pi\) | ||||
0.758915 | + | 0.651189i | \(0.225730\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.6603 | −0.756933 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 46.7846 | 1.70947 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.8564 | −1.23544 | −0.617719 | − | 0.786399i | \(-0.711943\pi\) | ||||
−0.617719 | + | 0.786399i | \(0.711943\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.3205 | 1.43102 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.1244 | −1.38565 | −0.692827 | − | 0.721104i | \(-0.743635\pi\) | ||||
−0.692827 | + | 0.721104i | \(0.743635\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23.1962 | −0.840860 | −0.420430 | − | 0.907325i | \(-0.638121\pi\) | ||||
−0.420430 | + | 0.907325i | \(0.638121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.0526 | 1.23279 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 60.1051 | 2.17027 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.2679 | −0.514515 | −0.257258 | − | 0.966343i | \(-0.582819\pi\) | ||||
−0.257258 | + | 0.966343i | \(0.582819\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.8564 | 1.43354 | 0.716768 | − | 0.697312i | \(-0.245621\pi\) | ||||
0.716768 | + | 0.697312i | \(0.245621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.2487 | −1.51762 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.2679 | −0.905318 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −77.5692 | −2.76856 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.78461 | −0.170553 | −0.0852765 | − | 0.996357i | \(-0.527177\pi\) | ||||
−0.0852765 | + | 0.996357i | \(0.527177\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.6603 | 0.485703 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.1769 | 1.03610 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.6410 | −1.43958 | −0.719789 | − | 0.694193i | \(-0.755762\pi\) | ||||
−0.719789 | + | 0.694193i | \(0.755762\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.41154 | 0.262202 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.3923 | −0.789225 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.7128 | 0.482117 | 0.241058 | − | 0.970511i | \(-0.422505\pi\) | ||||
0.241058 | + | 0.970511i | \(0.422505\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.0718 | 0.599472 | 0.299736 | − | 0.954022i | \(-0.403101\pi\) | ||||
0.299736 | + | 0.954022i | \(0.403101\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −87.7654 | −3.07429 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.1436 | 0.914649 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.1769 | 0.459877 | 0.229939 | − | 0.973205i | \(-0.426147\pi\) | ||||
0.229939 | + | 0.973205i | \(0.426147\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | 0.278862 | 0.139431 | − | 0.990232i | \(-0.455473\pi\) | ||||
0.139431 | + | 0.990232i | \(0.455473\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.9090 | −0.900943 | −0.450471 | − | 0.892791i | \(-0.648744\pi\) | ||||
−0.450471 | + | 0.892791i | \(0.648744\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.58846 | 0.0551694 | 0.0275847 | − | 0.999619i | \(-0.491218\pi\) | ||||
0.0275847 | + | 0.999619i | \(0.491218\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.05256 | 0.0364690 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.3923 | 0.844131 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 53.2295 | 1.83769 | 0.918843 | − | 0.394624i | \(-0.129125\pi\) | ||||
0.918843 | + | 0.394624i | \(0.129125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.07180 | −0.312821 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.8564 | 0.889487 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.5885 | 0.431527 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.4641 | 0.495241 | 0.247621 | − | 0.968857i | \(-0.420351\pi\) | ||||
0.247621 | + | 0.968857i | \(0.420351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.1436 | −0.893048 | −0.446524 | − | 0.894772i | \(-0.647338\pi\) | ||||
−0.446524 | + | 0.894772i | \(0.647338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 54.6410 | 1.86433 | 0.932164 | − | 0.362037i | \(-0.117919\pi\) | ||||
0.932164 | + | 0.362037i | \(0.117919\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.5885 | 0.496597 | 0.248298 | − | 0.968684i | \(-0.420129\pi\) | ||||
0.248298 | + | 0.968684i | \(0.420129\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.46410 | −0.321789 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.875644 | 0.0296701 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −40.0526 | −1.35402 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.7846 | −0.533008 | −0.266504 | − | 0.963834i | \(-0.585869\pi\) | ||||
−0.266504 | + | 0.963834i | \(0.585869\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.67949 | 0.326110 | 0.163055 | − | 0.986617i | \(-0.447865\pi\) | ||||
0.163055 | + | 0.986617i | \(0.447865\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.53590 | 0.219950 | 0.109975 | − | 0.993934i | \(-0.464923\pi\) | ||||
0.109975 | + | 0.993934i | \(0.464923\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43.2295 | −1.45150 | −0.725752 | − | 0.687957i | \(-0.758508\pi\) | ||||
−0.725752 | + | 0.687957i | \(0.758508\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.6795 | −0.357376 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −59.7128 | −1.99598 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.1244 | 0.704537 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.71281 | −0.0903769 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.4641 | −0.347839 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.8564 | 0.592912 | 0.296456 | − | 0.955046i | \(-0.404195\pi\) | ||||
0.296456 | + | 0.955046i | \(0.404195\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.1769 | 0.436571 | 0.218285 | − | 0.975885i | \(-0.429954\pi\) | ||||
0.218285 | + | 0.975885i | \(0.429954\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.8564 | 0.721762 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.0000 | 0.395843 | 0.197922 | − | 0.980218i | \(-0.436581\pi\) | ||||
0.197922 | + | 0.980218i | \(0.436581\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.3205 | 0.372619 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 51.1769 | 1.68269 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.9282 | 0.653823 | 0.326912 | − | 0.945055i | \(-0.393992\pi\) | ||||
0.326912 | + | 0.945055i | \(0.393992\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.51666 | −0.0497065 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.2679 | −1.18482 | −0.592411 | − | 0.805636i | \(-0.701824\pi\) | ||||
−0.592411 | + | 0.805636i | \(0.701824\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.0000 | 0.684580 | 0.342290 | − | 0.939594i | \(-0.388797\pi\) | ||||
0.342290 | + | 0.939594i | \(0.388797\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.9808 | 0.552970 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.5167 | 0.374241 | 0.187121 | − | 0.982337i | \(-0.440084\pi\) | ||||
0.187121 | + | 0.982337i | \(0.440084\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.8564 | −1.29379 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.1962 | −0.557038 | −0.278519 | − | 0.960431i | \(-0.589844\pi\) | ||||
−0.278519 | + | 0.960431i | \(0.589844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.3923 | −0.530443 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.92820 | −0.223723 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.60770 | −0.277668 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −62.1769 | −2.00155 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.7321 | 0.602382 | 0.301191 | − | 0.953564i | \(-0.402616\pi\) | ||||
0.301191 | + | 0.953564i | \(0.402616\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.5167 | −1.26815 | −0.634075 | − | 0.773272i | \(-0.718619\pi\) | ||||
−0.634075 | + | 0.773272i | \(0.718619\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.9282 | 0.542693 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.1769 | −0.837474 | −0.418737 | − | 0.908108i | \(-0.637527\pi\) | ||||
−0.418737 | + | 0.908108i | \(0.637527\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.1051 | −1.15157 | −0.575787 | − | 0.817600i | \(-0.695304\pi\) | ||||
−0.575787 | + | 0.817600i | \(0.695304\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.1244 | 0.704941 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.5692 | −0.558669 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.8564 | 0.567227 | 0.283614 | − | 0.958939i | \(-0.408467\pi\) | ||||
0.283614 | + | 0.958939i | \(0.408467\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24.3923 | −0.773288 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57.9282 | −1.83460 | −0.917302 | − | 0.398192i | \(-0.869638\pi\) | ||||
−0.917302 | + | 0.398192i | \(0.869638\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8712.2.a.br.1.2 | 2 | ||
3.2 | odd | 2 | 968.2.a.k.1.2 | ✓ | 2 | ||
11.10 | odd | 2 | 8712.2.a.bs.1.2 | 2 | |||
12.11 | even | 2 | 1936.2.a.q.1.1 | 2 | |||
24.5 | odd | 2 | 7744.2.a.bu.1.1 | 2 | |||
24.11 | even | 2 | 7744.2.a.cx.1.2 | 2 | |||
33.2 | even | 10 | 968.2.i.n.81.2 | 8 | |||
33.5 | odd | 10 | 968.2.i.o.729.2 | 8 | |||
33.8 | even | 10 | 968.2.i.n.9.1 | 8 | |||
33.14 | odd | 10 | 968.2.i.o.9.1 | 8 | |||
33.17 | even | 10 | 968.2.i.n.729.2 | 8 | |||
33.20 | odd | 10 | 968.2.i.o.81.2 | 8 | |||
33.26 | odd | 10 | 968.2.i.o.753.1 | 8 | |||
33.29 | even | 10 | 968.2.i.n.753.1 | 8 | |||
33.32 | even | 2 | 968.2.a.l.1.2 | yes | 2 | ||
132.131 | odd | 2 | 1936.2.a.p.1.1 | 2 | |||
264.131 | odd | 2 | 7744.2.a.cw.1.2 | 2 | |||
264.197 | even | 2 | 7744.2.a.bv.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
968.2.a.k.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
968.2.a.l.1.2 | yes | 2 | 33.32 | even | 2 | ||
968.2.i.n.9.1 | 8 | 33.8 | even | 10 | |||
968.2.i.n.81.2 | 8 | 33.2 | even | 10 | |||
968.2.i.n.729.2 | 8 | 33.17 | even | 10 | |||
968.2.i.n.753.1 | 8 | 33.29 | even | 10 | |||
968.2.i.o.9.1 | 8 | 33.14 | odd | 10 | |||
968.2.i.o.81.2 | 8 | 33.20 | odd | 10 | |||
968.2.i.o.729.2 | 8 | 33.5 | odd | 10 | |||
968.2.i.o.753.1 | 8 | 33.26 | odd | 10 | |||
1936.2.a.p.1.1 | 2 | 132.131 | odd | 2 | |||
1936.2.a.q.1.1 | 2 | 12.11 | even | 2 | |||
7744.2.a.bu.1.1 | 2 | 24.5 | odd | 2 | |||
7744.2.a.bv.1.1 | 2 | 264.197 | even | 2 | |||
7744.2.a.cw.1.2 | 2 | 264.131 | odd | 2 | |||
7744.2.a.cx.1.2 | 2 | 24.11 | even | 2 | |||
8712.2.a.br.1.2 | 2 | 1.1 | even | 1 | trivial | ||
8712.2.a.bs.1.2 | 2 | 11.10 | odd | 2 |