Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(97,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 26 x^{14} - 16 x^{13} + 469 x^{12} + 144 x^{11} - 4526 x^{10} + 4440 x^{9} + 32608 x^{8} + \cdots + 208849 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{28}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.11 | ||
Root | \(1.20279 + 1.51093i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.97 |
Dual form | 1568.3.c.g.97.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.54150i | 0.847168i | 0.905857 | + | 0.423584i | \(0.139228\pi\) | ||||
−0.905857 | + | 0.423584i | \(0.860772\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 4.11878i | − 0.823756i | −0.911239 | − | 0.411878i | \(-0.864873\pi\) | ||||
0.911239 | − | 0.411878i | \(-0.135127\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.54076 | 0.282306 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.26783 | −0.297076 | −0.148538 | − | 0.988907i | \(-0.547457\pi\) | ||||
−0.148538 | + | 0.988907i | \(0.547457\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.88759i | − 0.452892i | −0.974024 | − | 0.226446i | \(-0.927289\pi\) | ||||
0.974024 | − | 0.226446i | \(-0.0727107\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.4679 | 0.697859 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 13.8800i | − 0.816469i | −0.912877 | − | 0.408234i | \(-0.866145\pi\) | ||||
0.912877 | − | 0.408234i | \(-0.133855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 15.8261i | − 0.832951i | −0.909147 | − | 0.416476i | \(-0.863265\pi\) | ||||
0.909147 | − | 0.416476i | \(-0.136735\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −36.5036 | −1.58711 | −0.793557 | − | 0.608496i | \(-0.791773\pi\) | ||||
−0.793557 | + | 0.608496i | \(0.791773\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.03567 | 0.321427 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.3309i | 1.08633i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −28.4655 | −0.981568 | −0.490784 | − | 0.871281i | \(-0.663290\pi\) | ||||
−0.490784 | + | 0.871281i | \(0.663290\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 41.8017i | 1.34844i | 0.738529 | + | 0.674222i | \(0.235521\pi\) | ||||
−0.738529 | + | 0.674222i | \(0.764479\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 8.30521i | − 0.251673i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14.2857 | 0.386100 | 0.193050 | − | 0.981189i | \(-0.438162\pi\) | ||||
0.193050 | + | 0.981189i | \(0.438162\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.9633 | 0.383675 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 21.3515i | − 0.520769i | −0.965505 | − | 0.260385i | \(-0.916151\pi\) | ||||
0.965505 | − | 0.260385i | \(-0.0838493\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −55.3992 | −1.28835 | −0.644177 | − | 0.764877i | \(-0.722800\pi\) | ||||
−0.644177 | + | 0.764877i | \(0.722800\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 10.4648i | − 0.232551i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 33.8533i | 0.720282i | 0.932898 | + | 0.360141i | \(0.117271\pi\) | ||||
−0.932898 | + | 0.360141i | \(0.882729\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 35.2760 | 0.691686 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −84.8542 | −1.60102 | −0.800512 | − | 0.599317i | \(-0.795439\pi\) | ||||
−0.800512 | + | 0.599317i | \(0.795439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13.4595i | 0.244718i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 40.2220 | 0.705649 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 67.5572i | − 1.14504i | −0.819892 | − | 0.572518i | \(-0.805967\pi\) | ||||
0.819892 | − | 0.572518i | \(-0.194033\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 29.5759i | 0.484851i | 0.970170 | + | 0.242425i | \(0.0779429\pi\) | ||||
−0.970170 | + | 0.242425i | \(0.922057\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −24.2497 | −0.373072 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 54.9578 | 0.820266 | 0.410133 | − | 0.912026i | \(-0.365482\pi\) | ||||
0.410133 | + | 0.912026i | \(0.365482\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 92.7741i | − 1.34455i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −83.8102 | −1.18043 | −0.590213 | − | 0.807248i | \(-0.700956\pi\) | ||||
−0.590213 | + | 0.807248i | \(0.700956\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 125.613i | − 1.72073i | −0.509682 | − | 0.860363i | \(-0.670237\pi\) | ||||
0.509682 | − | 0.860363i | \(-0.329763\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 20.4227i | 0.272303i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −70.3910 | −0.891025 | −0.445512 | − | 0.895276i | \(-0.646978\pi\) | ||||
−0.445512 | + | 0.895276i | \(0.646978\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −51.6777 | −0.637997 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 27.1264i | 0.326824i | 0.986558 | + | 0.163412i | \(0.0522500\pi\) | ||||
−0.986558 | + | 0.163412i | \(0.947750\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −57.1685 | −0.672571 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 72.3451i | − 0.831553i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 146.131i | 1.64192i | 0.570987 | + | 0.820959i | \(0.306561\pi\) | ||||
−0.570987 | + | 0.820959i | \(0.693439\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −106.239 | −1.14236 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −65.1841 | −0.686148 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3574i | 0.117086i | 0.998285 | + | 0.0585431i | \(0.0186455\pi\) | ||||
−0.998285 | + | 0.0585431i | \(0.981354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.30278 | −0.0838664 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 41.8984i | − 0.414836i | −0.978252 | − | 0.207418i | \(-0.933494\pi\) | ||||
0.978252 | − | 0.207418i | \(-0.0665060\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 97.1798i | 0.943493i | 0.881734 | + | 0.471746i | \(0.156376\pi\) | ||||
−0.881734 | + | 0.471746i | \(0.843624\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 83.4437 | 0.779847 | 0.389924 | − | 0.920847i | \(-0.372501\pi\) | ||||
0.389924 | + | 0.920847i | \(0.372501\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −161.993 | −1.48618 | −0.743088 | − | 0.669194i | \(-0.766639\pi\) | ||||
−0.743088 | + | 0.669194i | \(0.766639\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 36.3072i | 0.327092i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 27.2503 | 0.241153 | 0.120576 | − | 0.992704i | \(-0.461526\pi\) | ||||
0.120576 | + | 0.992704i | \(0.461526\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 150.350i | 1.30739i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 14.9590i | − 0.127854i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −110.321 | −0.911746 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 54.2650 | 0.441179 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 136.067i | − 1.08853i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 232.457 | 1.83037 | 0.915183 | − | 0.403038i | \(-0.132046\pi\) | ||||
0.915183 | + | 0.403038i | \(0.132046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 140.797i | − 1.09145i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 176.102i | − 1.34429i | −0.740418 | − | 0.672146i | \(-0.765373\pi\) | ||||
0.740418 | − | 0.672146i | \(-0.234627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 120.807 | 0.894869 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −264.925 | −1.93376 | −0.966879 | − | 0.255234i | \(-0.917847\pi\) | ||||
−0.966879 | + | 0.255234i | \(0.917847\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 267.680i | − 1.92576i | −0.269935 | − | 0.962878i | \(-0.587002\pi\) | ||||
0.269935 | − | 0.962878i | \(-0.412998\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −86.0382 | −0.610200 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.2397i | 0.134543i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 117.243i | 0.808572i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.94540 | −0.0130564 | −0.00652820 | − | 0.999979i | \(-0.502078\pi\) | ||||
−0.00652820 | + | 0.999979i | \(0.502078\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −100.305 | −0.664270 | −0.332135 | − | 0.943232i | \(-0.607769\pi\) | ||||
−0.332135 | + | 0.943232i | \(0.607769\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 35.2656i | − 0.230494i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 172.172 | 1.11079 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 135.277i | − 0.861638i | −0.902438 | − | 0.430819i | \(-0.858225\pi\) | ||||
0.902438 | − | 0.430819i | \(-0.141775\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 215.657i | − 1.35634i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −254.706 | −1.56261 | −0.781307 | − | 0.624146i | \(-0.785447\pi\) | ||||
−0.781307 | + | 0.624146i | \(0.785447\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −34.2073 | −0.207317 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 50.9246i | 0.304938i | 0.988308 | + | 0.152469i | \(0.0487224\pi\) | ||||
−0.988308 | + | 0.152469i | \(0.951278\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 134.336 | 0.794889 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 40.2102i | − 0.235147i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 70.4200i | − 0.407052i | −0.979070 | − | 0.203526i | \(-0.934760\pi\) | ||||
0.979070 | − | 0.203526i | \(-0.0652401\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 171.697 | 0.970038 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −147.440 | −0.823689 | −0.411845 | − | 0.911254i | \(-0.635115\pi\) | ||||
−0.411845 | + | 0.911254i | \(0.635115\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 294.491i | − 1.62702i | −0.581550 | − | 0.813511i | \(-0.697553\pi\) | ||||
0.581550 | − | 0.813511i | \(-0.302447\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −75.1672 | −0.410750 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 58.8396i | − 0.318052i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 45.3574i | 0.242553i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 112.519 | 0.589105 | 0.294553 | − | 0.955635i | \(-0.404829\pi\) | ||||
0.294553 | + | 0.955635i | \(0.404829\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 127.487 | 0.660554 | 0.330277 | − | 0.943884i | \(-0.392858\pi\) | ||||
0.330277 | + | 0.943884i | \(0.392858\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 61.6307i | − 0.316055i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −293.140 | −1.48802 | −0.744011 | − | 0.668167i | \(-0.767079\pi\) | ||||
−0.744011 | + | 0.668167i | \(0.767079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.74194i | 0.0489545i | 0.999700 | + | 0.0244772i | \(0.00779212\pi\) | ||||
−0.999700 | + | 0.0244772i | \(0.992208\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 139.676i | 0.694903i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −87.9422 | −0.428986 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −92.7469 | −0.448052 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 51.7170i | 0.247450i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 139.516 | 0.661214 | 0.330607 | − | 0.943769i | \(-0.392747\pi\) | ||||
0.330607 | + | 0.943769i | \(0.392747\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 213.004i | − 1.00002i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 228.177i | 1.06129i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 319.246 | 1.45774 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −81.7196 | −0.369772 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 273.426i | − 1.22612i | −0.790035 | − | 0.613062i | \(-0.789938\pi\) | ||||
0.790035 | − | 0.613062i | \(-0.210062\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 20.4167 | 0.0907409 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 67.5444i | − 0.297552i | −0.988871 | − | 0.148776i | \(-0.952467\pi\) | ||||
0.988871 | − | 0.148776i | \(-0.0475334\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 192.563i | − 0.840888i | −0.907319 | − | 0.420444i | \(-0.861874\pi\) | ||||
0.907319 | − | 0.420444i | \(-0.138126\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 81.4048 | 0.349377 | 0.174689 | − | 0.984624i | \(-0.444108\pi\) | ||||
0.174689 | + | 0.984624i | \(0.444108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 139.434 | 0.593336 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 178.899i | − 0.754848i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.6152 | −0.0946244 | −0.0473122 | − | 0.998880i | \(-0.515066\pi\) | ||||
−0.0473122 | + | 0.998880i | \(0.515066\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 94.1663i | − 0.390732i | −0.980730 | − | 0.195366i | \(-0.937411\pi\) | ||||
0.980730 | − | 0.195366i | \(-0.0625894\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 132.639i | 0.545839i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −93.1775 | −0.377237 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −68.9419 | −0.276875 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 316.694i | 1.26173i | 0.775892 | + | 0.630865i | \(0.217300\pi\) | ||||
−0.775892 | + | 0.630865i | \(0.782700\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 119.288 | 0.471493 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 145.294i | − 0.569780i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 47.0598i | − 0.183112i | −0.995800 | − | 0.0915560i | \(-0.970816\pi\) | ||||
0.995800 | − | 0.0915560i | \(-0.0291840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −72.3239 | −0.277103 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 406.504 | 1.54564 | 0.772822 | − | 0.634623i | \(-0.218845\pi\) | ||||
0.772822 | + | 0.634623i | \(0.218845\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 349.496i | 1.31885i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −371.392 | −1.39098 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 332.504i | 1.23608i | 0.786148 | + | 0.618038i | \(0.212072\pi\) | ||||
−0.786148 | + | 0.618038i | \(0.787928\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 71.3242i | − 0.263189i | −0.991304 | − | 0.131595i | \(-0.957990\pi\) | ||||
0.991304 | − | 0.131595i | \(-0.0420097\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −26.2592 | −0.0954881 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.7147 | −0.107273 | −0.0536367 | − | 0.998561i | \(-0.517081\pi\) | ||||
−0.0536367 | + | 0.998561i | \(0.517081\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 106.208i | 0.380674i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.06447 | 0.0322579 | 0.0161289 | − | 0.999870i | \(-0.494866\pi\) | ||||
0.0161289 | + | 0.999870i | \(0.494866\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 184.738i | − 0.652784i | −0.945235 | − | 0.326392i | \(-0.894167\pi\) | ||||
0.945235 | − | 0.326392i | \(-0.105833\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 165.666i | − 0.581283i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 96.3464 | 0.333379 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.8648 | −0.0991917 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 300.389i | − 1.02522i | −0.858622 | − | 0.512609i | \(-0.828679\pi\) | ||||
0.858622 | − | 0.512609i | \(-0.171321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −278.253 | −0.943230 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 95.8485i | − 0.322722i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 214.918i | 0.718791i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 106.485 | 0.351436 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 121.817 | 0.399398 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 390.385i | 1.27161i | 0.771848 | + | 0.635807i | \(0.219333\pi\) | ||||
−0.771848 | + | 0.635807i | \(0.780667\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −246.983 | −0.799297 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 96.0768i | 0.308929i | 0.987998 | + | 0.154464i | \(0.0493652\pi\) | ||||
−0.987998 | + | 0.154464i | \(0.950635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 484.883i | 1.54915i | 0.632484 | + | 0.774574i | \(0.282036\pi\) | ||||
−0.632484 | + | 0.774574i | \(0.717964\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 67.9427 | 0.214330 | 0.107165 | − | 0.994241i | \(-0.465823\pi\) | ||||
0.107165 | + | 0.994241i | \(0.465823\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 93.0205 | 0.291600 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 212.072i | 0.660662i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −219.665 | −0.680079 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 47.3108i | − 0.145572i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 411.706i | − 1.25904i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −265.268 | −0.801415 | −0.400707 | − | 0.916206i | \(-0.631236\pi\) | ||||
−0.400707 | + | 0.916206i | \(0.631236\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 36.2965 | 0.108999 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 226.359i | − 0.675699i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 549.980 | 1.63199 | 0.815993 | − | 0.578061i | \(-0.196191\pi\) | ||||
0.815993 | + | 0.578061i | \(0.196191\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 69.2566i | 0.204297i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 136.601i | − 0.400590i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −382.116 | −1.10758 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −678.750 | −1.95605 | −0.978026 | − | 0.208481i | \(-0.933148\pi\) | ||||
−0.978026 | + | 0.208481i | \(0.933148\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 170.081i | 0.487339i | 0.969858 | + | 0.243669i | \(0.0783511\pi\) | ||||
−0.969858 | + | 0.243669i | \(0.921649\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 172.688 | 0.491990 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 236.047i | 0.668689i | 0.942451 | + | 0.334345i | \(0.108515\pi\) | ||||
−0.942451 | + | 0.334345i | \(0.891485\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 345.196i | 0.972382i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −458.116 | −1.27609 | −0.638044 | − | 0.770000i | \(-0.720256\pi\) | ||||
−0.638044 | + | 0.770000i | \(0.720256\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 110.535 | 0.306193 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 280.382i | − 0.772402i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −517.372 | −1.41746 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 411.437i | 1.12108i | 0.828127 | + | 0.560541i | \(0.189407\pi\) | ||||
−0.828127 | + | 0.560541i | \(0.810593\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 54.2491i | − 0.147016i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.7971 | 0.0423514 | 0.0211757 | − | 0.999776i | \(-0.493259\pi\) | ||||
0.0211757 | + | 0.999776i | \(0.493259\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 345.814 | 0.922170 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 167.593i | 0.444544i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 455.384 | 1.20154 | 0.600770 | − | 0.799422i | \(-0.294861\pi\) | ||||
0.600770 | + | 0.799422i | \(0.294861\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 590.789i | 1.55063i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 183.288i | 0.478558i | 0.970951 | + | 0.239279i | \(0.0769111\pi\) | ||||
−0.970951 | + | 0.239279i | \(0.923089\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −140.756 | −0.363710 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −185.494 | −0.476849 | −0.238424 | − | 0.971161i | \(-0.576631\pi\) | ||||
−0.238424 | + | 0.971161i | \(0.576631\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 506.669i | 1.29583i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 447.565 | 1.13884 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 289.925i | 0.733987i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 45.6707i | 0.115039i | 0.998344 | + | 0.0575197i | \(0.0183192\pi\) | ||||
−0.998344 | + | 0.0575197i | \(0.981681\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 38.4623 | 0.0959160 | 0.0479580 | − | 0.998849i | \(-0.484729\pi\) | ||||
0.0479580 | + | 0.998849i | \(0.484729\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 246.112 | 0.610699 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 212.849i | 0.525553i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −46.6833 | −0.114701 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 167.737i | − 0.410114i | −0.978750 | − | 0.205057i | \(-0.934262\pi\) | ||||
0.978750 | − | 0.205057i | \(-0.0657380\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 673.308i | − 1.63822i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 111.728 | 0.269223 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 680.310 | 1.63144 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 300.318i | 0.716751i | 0.933578 | + | 0.358375i | \(0.116669\pi\) | ||||
−0.933578 | + | 0.358375i | \(0.883331\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 280.567 | 0.666430 | 0.333215 | − | 0.942851i | \(-0.391867\pi\) | ||||
0.333215 | + | 0.942851i | \(0.391867\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 86.0129i | 0.203340i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 111.535i | − 0.262435i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −48.8977 | −0.113981 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −224.764 | −0.521495 | −0.260747 | − | 0.965407i | \(-0.583969\pi\) | ||||
−0.260747 | + | 0.965407i | \(0.583969\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 731.236i | 1.68877i | 0.535739 | + | 0.844383i | \(0.320033\pi\) | ||||
−0.535739 | + | 0.844383i | \(0.679967\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −297.973 | −0.684996 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 577.709i | 1.32199i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 299.439i | − 0.682094i | −0.940046 | − | 0.341047i | \(-0.889218\pi\) | ||||
0.940046 | − | 0.341047i | \(-0.110782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −396.155 | −0.894255 | −0.447127 | − | 0.894470i | \(-0.647553\pi\) | ||||
−0.447127 | + | 0.894470i | \(0.647553\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 601.880 | 1.35254 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 4.94425i | − 0.0110610i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 128.183 | 0.285486 | 0.142743 | − | 0.989760i | \(-0.454408\pi\) | ||||
0.142743 | + | 0.989760i | \(0.454408\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 69.7733i | 0.154708i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 254.925i | − 0.562748i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 405.147 | 0.886537 | 0.443268 | − | 0.896389i | \(-0.353819\pi\) | ||||
0.443268 | + | 0.896389i | \(0.353819\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 407.112 | 0.886954 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 312.620i | 0.678134i | 0.940762 | + | 0.339067i | \(0.110111\pi\) | ||||
−0.940762 | + | 0.339067i | \(0.889889\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −246.396 | −0.532173 | −0.266087 | − | 0.963949i | \(-0.585731\pi\) | ||||
−0.266087 | + | 0.963949i | \(0.585731\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 437.576i | 0.941024i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.7706i | 0.0466180i | 0.999728 | + | 0.0233090i | \(0.00742015\pi\) | ||||
−0.999728 | + | 0.0233090i | \(0.992580\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 343.807 | 0.729952 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 181.035 | 0.382739 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 127.173i | − 0.267733i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −215.594 | −0.451979 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 522.490i | − 1.09079i | −0.838178 | − | 0.545397i | \(-0.816379\pi\) | ||||
0.838178 | − | 0.545397i | \(-0.183621\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 84.1084i | − 0.174862i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 46.7785 | 0.0964505 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −818.134 | −1.67995 | −0.839974 | − | 0.542627i | \(-0.817430\pi\) | ||||
−0.839974 | + | 0.542627i | \(0.817430\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 647.337i | − 1.32380i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 762.002 | 1.55194 | 0.775969 | − | 0.630771i | \(-0.217261\pi\) | ||||
0.775969 | + | 0.630771i | \(0.217261\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 395.100i | 0.801420i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 34.1973i | 0.0690854i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 50.9869 | 0.102178 | 0.0510891 | − | 0.998694i | \(-0.483731\pi\) | ||||
0.0510891 | + | 0.998694i | \(0.483731\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −129.425 | −0.258334 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 305.233i | − 0.606825i | −0.952859 | − | 0.303413i | \(-0.901874\pi\) | ||||
0.952859 | − | 0.303413i | \(-0.0981260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −172.570 | −0.341723 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 341.416i | 0.673404i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 180.752i | − 0.355112i | −0.984111 | − | 0.177556i | \(-0.943181\pi\) | ||||
0.984111 | − | 0.177556i | \(-0.0568191\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 464.193 | 0.904859 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 400.262 | 0.777207 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 110.627i | − 0.213978i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 178.973 | 0.344841 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 361.152i | − 0.693190i | −0.938015 | − | 0.346595i | \(-0.887338\pi\) | ||||
0.938015 | − | 0.346595i | \(-0.112662\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 654.144i | 1.25075i | 0.780323 | + | 0.625377i | \(0.215055\pi\) | ||||
−0.780323 | + | 0.625377i | \(0.784945\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 580.207 | 1.10096 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 803.514 | 1.51893 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 171.646i | − 0.323251i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −125.709 | −0.235852 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 343.686i | − 0.642404i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 374.720i | − 0.697803i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 603.284 | 1.11513 | 0.557564 | − | 0.830134i | \(-0.311736\pi\) | ||||
0.557564 | + | 0.830134i | \(0.311736\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 748.450 | 1.37836 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 667.214i | 1.22424i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −686.167 | −1.25442 | −0.627209 | − | 0.778851i | \(-0.715803\pi\) | ||||
−0.627209 | + | 0.778851i | \(0.715803\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 75.1452i | 0.136876i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 450.497i | 0.817598i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 149.541 | 0.269443 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 785.321 | 1.40991 | 0.704956 | − | 0.709251i | \(-0.250967\pi\) | ||||
0.704956 | + | 0.709251i | \(0.250967\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 326.168i | 0.583485i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −115.276 | −0.205483 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 454.058i | − 0.806498i | −0.915090 | − | 0.403249i | \(-0.867881\pi\) | ||||
0.915090 | − | 0.403249i | \(-0.132119\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 112.238i | − 0.198651i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −71.4274 | −0.125532 | −0.0627658 | − | 0.998028i | \(-0.519992\pi\) | ||||
−0.0627658 | + | 0.998028i | \(0.519992\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −718.067 | −1.25756 | −0.628780 | − | 0.777583i | \(-0.716445\pi\) | ||||
−0.628780 | + | 0.777583i | \(0.716445\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 285.968i | 0.499071i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −293.331 | −0.510141 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 907.985i | 1.57363i | 0.617188 | + | 0.786815i | \(0.288272\pi\) | ||||
−0.617188 | + | 0.786815i | \(0.711728\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 324.009i | 0.559600i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 277.290 | 0.475625 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −61.6126 | −0.105321 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 862.870i | − 1.46997i | −0.678086 | − | 0.734983i | \(-0.737190\pi\) | ||||
0.678086 | − | 0.734983i | \(-0.262810\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 661.557 | 1.12319 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 745.017i | − 1.26060i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 542.856i | − 0.915440i | −0.889096 | − | 0.457720i | \(-0.848666\pi\) | ||||
0.889096 | − | 0.457720i | \(-0.151334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.7592 | −0.0414727 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −78.6147 | −0.131243 | −0.0656216 | − | 0.997845i | \(-0.520903\pi\) | ||||
−0.0656216 | + | 0.997845i | \(0.520903\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 851.603i | 1.41698i | 0.705722 | + | 0.708489i | \(0.250623\pi\) | ||||
−0.705722 | + | 0.708489i | \(0.749377\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 139.635 | 0.231566 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 454.389i | 0.751056i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 233.575i | 0.384802i | 0.981316 | + | 0.192401i | \(0.0616275\pi\) | ||||
−0.981316 | + | 0.192401i | \(0.938373\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 199.314 | 0.326210 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 81.1241 | 0.132339 | 0.0661697 | − | 0.997808i | \(-0.478922\pi\) | ||||
0.0661697 | + | 0.997808i | \(0.478922\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 223.505i | − 0.363424i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 47.2962 | 0.0766552 | 0.0383276 | − | 0.999265i | \(-0.487797\pi\) | ||||
0.0383276 | + | 0.999265i | \(0.487797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 657.406i | − 1.06205i | −0.847357 | − | 0.531023i | \(-0.821808\pi\) | ||||
0.847357 | − | 0.531023i | \(-0.178192\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 1070.68i | − 1.72413i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −359.536 | −0.575258 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −131.439 | −0.209631 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 198.285i | − 0.315239i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 270.276 | 0.428330 | 0.214165 | − | 0.976797i | \(-0.431297\pi\) | ||||
0.214165 | + | 0.976797i | \(0.431297\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 354.581i | 0.560159i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 957.437i | − 1.50777i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −212.941 | −0.333242 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 244.610 | 0.381606 | 0.190803 | − | 0.981628i | \(-0.438891\pi\) | ||||
0.190803 | + | 0.981628i | \(0.438891\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 358.233i | − 0.557128i | −0.960418 | − | 0.278564i | \(-0.910142\pi\) | ||||
0.960418 | − | 0.278564i | \(-0.0898584\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −579.913 | −0.899089 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1182.75i | 1.82806i | 0.405647 | + | 0.914030i | \(0.367046\pi\) | ||||
−0.405647 | + | 0.914030i | \(0.632954\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 220.766i | 0.340163i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 215.295 | 0.329701 | 0.164850 | − | 0.986319i | \(-0.447286\pi\) | ||||
0.164850 | + | 0.986319i | \(0.447286\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −725.327 | −1.10737 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 319.152i | − 0.485772i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 254.983 | 0.386925 | 0.193462 | − | 0.981108i | \(-0.438028\pi\) | ||||
0.193462 | + | 0.981108i | \(0.438028\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1243.66i | − 1.88148i | −0.339126 | − | 0.940741i | \(-0.610131\pi\) | ||||
0.339126 | − | 0.940741i | \(-0.389869\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 207.691i | − 0.313259i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1039.09 | 1.55786 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 694.912 | 1.03873 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 96.6491i | − 0.144037i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −63.0354 | −0.0936633 | −0.0468317 | − | 0.998903i | \(-0.514912\pi\) | ||||
−0.0468317 | + | 0.998903i | \(0.514912\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 235.693i | 0.349175i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 987.456i | 1.45858i | 0.684207 | + | 0.729288i | \(0.260149\pi\) | ||||
−0.684207 | + | 0.729288i | \(0.739851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 171.664 | 0.252077 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 934.895 | 1.36881 | 0.684403 | − | 0.729104i | \(-0.260063\pi\) | ||||
0.684403 | + | 0.729104i | \(0.260063\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1091.17i | 1.59294i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 489.400 | 0.712373 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 499.587i | 0.725090i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 972.480i | − 1.40735i | −0.710521 | − | 0.703676i | \(-0.751541\pi\) | ||||
0.710521 | − | 0.703676i | \(-0.248459\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1102.52 | −1.58635 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −296.359 | −0.425192 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 206.891i | 0.295981i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 695.549 | 0.992224 | 0.496112 | − | 0.868259i | \(-0.334761\pi\) | ||||
0.496112 | + | 0.868259i | \(0.334761\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 226.086i | − 0.321602i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 354.372i | 0.502656i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −157.264 | −0.221811 | −0.110905 | − | 0.993831i | \(-0.535375\pi\) | ||||
−0.110905 | + | 0.993831i | \(0.535375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −178.846 | −0.251542 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1525.91i | − 2.14013i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 79.2440 | 0.110831 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 57.4767i | − 0.0801628i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 211.949i | 0.294783i | 0.989078 | + | 0.147392i | \(0.0470878\pi\) | ||||
−0.989078 | + | 0.147392i | \(0.952912\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 239.324 | 0.331015 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −228.739 | −0.315502 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 271.507i | 0.373462i | 0.982411 | + | 0.186731i | \(0.0597893\pi\) | ||||
−0.982411 | + | 0.186731i | \(0.940211\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −802.202 | −1.10041 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 768.939i | 1.05190i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 510.429i | 0.696357i | 0.937428 | + | 0.348178i | \(0.113200\pi\) | ||||
−0.937428 | + | 0.348178i | \(0.886800\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −179.593 | −0.243681 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 374.168 | 0.506317 | 0.253158 | − | 0.967425i | \(-0.418531\pi\) | ||||
0.253158 | + | 0.967425i | \(0.418531\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 236.811i | − 0.319583i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 792.307 | 1.06636 | 0.533181 | − | 0.846001i | \(-0.320996\pi\) | ||||
0.533181 | + | 0.846001i | \(0.320996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.01268i | 0.0107553i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 68.9217i | 0.0922646i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.2964 | 0.0350152 | 0.0175076 | − | 0.999847i | \(-0.494427\pi\) | ||||
0.0175076 | + | 0.999847i | \(0.494427\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −804.880 | −1.06890 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 413.133i | 0.547196i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1287.30 | 1.70053 | 0.850264 | − | 0.526356i | \(-0.176442\pi\) | ||||
0.850264 | + | 0.526356i | \(0.176442\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 303.170i | 0.399434i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 969.451i | − 1.27392i | −0.770898 | − | 0.636959i | \(-0.780192\pi\) | ||||
0.770898 | − | 0.636959i | \(-0.219808\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −145.251 | −0.189871 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −397.749 | −0.518578 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 499.204i | 0.649160i | 0.945858 | + | 0.324580i | \(0.105223\pi\) | ||||
−0.945858 | + | 0.324580i | \(0.894777\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 119.603 | 0.155127 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 145.343i | − 0.188024i | −0.995571 | − | 0.0940120i | \(-0.970031\pi\) | ||||
0.995571 | − | 0.0940120i | \(-0.0299692\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 335.905i | 0.433426i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −337.911 | −0.433775 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 273.878 | 0.350676 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 834.918i | − 1.06631i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −557.176 | −0.709779 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 384.668i | − 0.488778i | −0.969677 | − | 0.244389i | \(-0.921413\pi\) | ||||
0.969677 | − | 0.244389i | \(-0.0785873\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1033.13i | 1.30942i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 174.131 | 0.219585 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −888.245 | −1.11729 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 9.29571i | − 0.0116634i | −0.999983 | − | 0.00583169i | \(-0.998144\pi\) | ||||
0.999983 | − | 0.00583169i | \(-0.00185629\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 469.882 | 0.588088 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 371.283i | 0.463524i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 410.482i | 0.511186i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −845.061 | −1.04716 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −815.391 | −1.00790 | −0.503950 | − | 0.863733i | \(-0.668120\pi\) | ||||
−0.503950 | + | 0.863733i | \(0.668120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 762.398i | 0.940071i | 0.882647 | + | 0.470036i | \(0.155759\pi\) | ||||
−0.882647 | + | 0.470036i | \(0.844241\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 181.271 | 0.222965 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1049.08i | 1.28721i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 876.751i | 1.07314i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1123.94 | −1.36899 | −0.684493 | − | 0.729020i | \(-0.739976\pi\) | ||||
−0.684493 | + | 0.729020i | \(0.739976\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 332.822 | 0.404401 | 0.202200 | − | 0.979344i | \(-0.435191\pi\) | ||||
0.202200 | + | 0.979344i | \(0.435191\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 66.7380i | − 0.0808945i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −451.741 | −0.546241 | −0.273120 | − | 0.961980i | \(-0.588056\pi\) | ||||
−0.273120 | + | 0.961980i | \(0.588056\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 457.296i | 0.551624i | 0.961212 | + | 0.275812i | \(0.0889467\pi\) | ||||
−0.961212 | + | 0.275812i | \(0.911053\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 75.5202i | − 0.0908786i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 209.747 | 0.251194 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1226.08 | −1.46485 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 97.6089i | − 0.116340i | −0.998307 | − | 0.0581698i | \(-0.981474\pi\) | ||||
0.998307 | − | 0.0581698i | \(-0.0185265\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.7167 | −0.0365240 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.0374i | 0.0273278i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 553.301i | − 0.654794i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 469.512 | 0.553017 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −521.480 | −0.612785 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 832.329i | 0.975766i | 0.872909 | + | 0.487883i | \(0.162231\pi\) | ||||
−0.872909 | + | 0.487883i | \(0.837769\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −165.617 | −0.193704 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 976.964i | − 1.13998i | −0.821651 | − | 0.569991i | \(-0.806947\pi\) | ||||
0.821651 | − | 0.569991i | \(-0.193053\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 697.938i | − 0.812500i | −0.913762 | − | 0.406250i | \(-0.866836\pi\) | ||||
0.913762 | − | 0.406250i | \(-0.133164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −843.036 | −0.976867 | −0.488434 | − | 0.872601i | \(-0.662432\pi\) | ||||
−0.488434 | + | 0.872601i | \(0.662432\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −290.044 | −0.335311 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 244.865i | 0.282428i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 230.026 | 0.264702 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 323.569i | − 0.371492i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 28.8563i | 0.0330542i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 58.1145 | 0.0662651 | 0.0331326 | − | 0.999451i | \(-0.489452\pi\) | ||||
0.0331326 | + | 0.999451i | \(0.489452\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 763.440 | 0.868532 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1034.35i | − 1.17406i | −0.809565 | − | 0.587030i | \(-0.800297\pi\) | ||||
0.809565 | − | 0.587030i | \(-0.199703\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −483.067 | −0.547075 | −0.273538 | − | 0.961861i | \(-0.588194\pi\) | ||||
−0.273538 | + | 0.961861i | \(0.588194\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 707.181i | − 0.799075i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 440.647i | − 0.496783i | −0.968660 | − | 0.248392i | \(-0.920098\pi\) | ||||
0.968660 | − | 0.248392i | \(-0.0799020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 168.874 | 0.189533 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 535.764 | 0.599960 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 607.274i | 0.678519i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −546.216 | −0.608937 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1189.91i | − 1.32359i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1177.77i | 1.30719i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1212.94 | −1.34027 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 459.549 | 0.506669 | 0.253334 | − | 0.967379i | \(-0.418473\pi\) | ||||
0.253334 | + | 0.967379i | \(0.418473\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 106.454i | − 0.117111i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1515.03 | −1.66304 | −0.831518 | − | 0.555498i | \(-0.812528\pi\) | ||||
−0.831518 | + | 0.555498i | \(0.812528\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 88.6447i | − 0.0970916i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 309.597i | 0.338358i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 103.364 | 0.112475 | 0.0562373 | − | 0.998417i | \(-0.482090\pi\) | ||||
0.0562373 | + | 0.998417i | \(0.482090\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −992.166 | −1.07727 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 493.441i | 0.534605i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 114.795 | 0.124103 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 246.910i | 0.266354i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1353.04i | − 1.45645i | −0.685338 | − | 0.728225i | \(-0.740346\pi\) | ||||
0.685338 | − | 0.728225i | \(-0.259654\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −244.180 | −0.261715 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 186.817 | 0.199805 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1443.67i | − 1.54074i | −0.637600 | − | 0.770368i | \(-0.720073\pi\) | ||||
0.637600 | − | 0.770368i | \(-0.279927\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1232.33 | −1.31239 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1267.74i | − 1.34722i | −0.739085 | − | 0.673612i | \(-0.764742\pi\) | ||||
0.739085 | − | 0.673612i | \(-0.235258\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 779.408i | 0.826520i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 401.424 | 0.423890 | 0.211945 | − | 0.977282i | \(-0.432020\pi\) | ||||
0.211945 | + | 0.977282i | \(0.432020\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −739.558 | −0.779303 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 172.677i | 0.181574i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1544.95 | −1.62115 | −0.810573 | − | 0.585637i | \(-0.800844\pi\) | ||||
−0.810573 | + | 0.585637i | \(0.800844\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 463.441i | − 0.485279i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 236.412i | 0.247034i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −786.386 | −0.818299 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 212.010 | 0.220156 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 525.090i | − 0.544135i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1272.03 | −1.31544 | −0.657718 | − | 0.753264i | \(-0.728478\pi\) | ||||
−0.657718 | + | 0.753264i | \(0.728478\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 558.280i | − 0.576141i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1057.91i | 1.08950i | 0.838598 | + | 0.544751i | \(0.183376\pi\) | ||||
−0.838598 | + | 0.544751i | \(0.816624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 120.241 | 0.123324 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 455.290 | 0.466008 | 0.233004 | − | 0.972476i | \(-0.425144\pi\) | ||||
0.233004 | + | 0.972476i | \(0.425144\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 477.531i | − 0.487774i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −411.585 | −0.419557 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1083.26i | − 1.10199i | −0.834508 | − | 0.550995i | \(-0.814248\pi\) | ||||
0.834508 | − | 0.550995i | \(-0.185752\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1207.38i | 1.22577i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2022.27 | 2.04476 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1110.08 | 1.12016 | 0.560081 | − | 0.828438i | \(-0.310770\pi\) | ||||
0.560081 | + | 0.828438i | \(0.310770\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 674.180i | − 0.678933i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 40.1249 | 0.0403265 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1538.71i | − 1.54334i | −0.636025 | − | 0.771668i | \(-0.719423\pi\) | ||||
0.636025 | − | 0.771668i | \(-0.280577\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 419.012i | 0.419432i |
(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 | 1568.3.c.g.97.11 | 16 | ||
4.3 | odd | 2 | inner | 1568.3.c.g.97.5 | 16 | ||
7.4 | even | 3 | 224.3.s.b.33.6 | yes | 16 | ||
7.5 | odd | 6 | 224.3.s.b.129.6 | yes | 16 | ||
7.6 | odd | 2 | inner | 1568.3.c.g.97.6 | 16 | ||
28.11 | odd | 6 | 224.3.s.b.33.3 | ✓ | 16 | ||
28.19 | even | 6 | 224.3.s.b.129.3 | yes | 16 | ||
28.27 | even | 2 | inner | 1568.3.c.g.97.12 | 16 | ||
56.5 | odd | 6 | 448.3.s.h.129.3 | 16 | |||
56.11 | odd | 6 | 448.3.s.h.257.6 | 16 | |||
56.19 | even | 6 | 448.3.s.h.129.6 | 16 | |||
56.53 | even | 6 | 448.3.s.h.257.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.b.33.3 | ✓ | 16 | 28.11 | odd | 6 | ||
224.3.s.b.33.6 | yes | 16 | 7.4 | even | 3 | ||
224.3.s.b.129.3 | yes | 16 | 28.19 | even | 6 | ||
224.3.s.b.129.6 | yes | 16 | 7.5 | odd | 6 | ||
448.3.s.h.129.3 | 16 | 56.5 | odd | 6 | |||
448.3.s.h.129.6 | 16 | 56.19 | even | 6 | |||
448.3.s.h.257.3 | 16 | 56.53 | even | 6 | |||
448.3.s.h.257.6 | 16 | 56.11 | odd | 6 | |||
1568.3.c.g.97.5 | 16 | 4.3 | odd | 2 | inner | ||
1568.3.c.g.97.6 | 16 | 7.6 | odd | 2 | inner | ||
1568.3.c.g.97.11 | 16 | 1.1 | even | 1 | trivial | ||
1568.3.c.g.97.12 | 16 | 28.27 | even | 2 | inner |