Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5760,2,Mod(1151,5760)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5760, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5760.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5760 = 2^{7} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5760.h (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: | \(45.9938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1534132224.8 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 107x^{4} + 210x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.1 | ||
Root | \(2.63019i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5760.1151 |
Dual form | 5760.2.h.h.1151.7 |
$q$-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 \(\left(\mathbb{Z}/5760\mathbb{Z}\right)^\times\).
\(n\) | \(641\) | \(901\) | \(2431\) | \(3457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.41421i | − 0.534522i | −0.963624 | − | 0.267261i | \(-0.913881\pi\) | ||||
0.963624 | − | 0.267261i | \(-0.0861187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.84616 | −1.15966 | −0.579831 | − | 0.814737i | \(-0.696881\pi\) | ||||
−0.579831 | + | 0.814737i | \(0.696881\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.406868 | 0.112845 | 0.0564224 | − | 0.998407i | \(-0.482031\pi\) | ||||
0.0564224 | + | 0.998407i | \(0.482031\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.43195i | 1.07491i | 0.843294 | + | 0.537453i | \(0.180613\pi\) | ||||
−0.843294 | + | 0.537453i | \(0.819387\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.26038i | 1.20681i | 0.797434 | + | 0.603406i | \(0.206190\pi\) | ||||
−0.797434 | + | 0.603406i | \(0.793810\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.992654 | 0.206983 | 0.103491 | − | 0.994630i | \(-0.466999\pi\) | ||||
0.103491 | + | 0.994630i | \(0.466999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.26772i | − 1.53528i | −0.640883 | − | 0.767639i | \(-0.721432\pi\) | ||||
0.640883 | − | 0.767639i | \(-0.278568\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.00735i | 0.899346i | 0.893193 | + | 0.449673i | \(0.148459\pi\) | ||||
−0.893193 | + | 0.449673i | \(0.851541\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.41421 | −0.239046 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.01773 | −0.167315 | −0.0836573 | − | 0.996495i | \(-0.526660\pi\) | ||||
−0.0836573 | + | 0.996495i | \(0.526660\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 7.68193i | − 1.19972i | −0.800106 | − | 0.599858i | \(-0.795224\pi\) | ||||
0.800106 | − | 0.599858i | \(-0.204776\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.42460i | − 0.217250i | −0.994083 | − | 0.108625i | \(-0.965355\pi\) | ||||
0.994083 | − | 0.108625i | \(-0.0346447\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.66420 | 0.972073 | 0.486037 | − | 0.873938i | \(-0.338442\pi\) | ||||
0.486037 | + | 0.873938i | \(0.338442\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.78244i | 0.244837i | 0.992479 | + | 0.122418i | \(0.0390650\pi\) | ||||
−0.992479 | + | 0.122418i | \(0.960935\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.84616i | 0.518616i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.45703 | 1.10101 | 0.550506 | − | 0.834831i | \(-0.314435\pi\) | ||||
0.550506 | + | 0.834831i | \(0.314435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.8431 | 1.38832 | 0.694160 | − | 0.719821i | \(-0.255776\pi\) | ||||
0.694160 | + | 0.719821i | \(0.255776\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 0.406868i | − 0.0504657i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.61087i | − 1.05198i | −0.850489 | − | 0.525992i | \(-0.823694\pi\) | ||||
0.850489 | − | 0.525992i | \(-0.176306\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.40383 | 0.641316 | 0.320658 | − | 0.947195i | \(-0.396096\pi\) | ||||
0.320658 | + | 0.947195i | \(0.396096\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.69232 | 1.13440 | 0.567200 | − | 0.823580i | \(-0.308027\pi\) | ||||
0.567200 | + | 0.823580i | \(0.308027\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.43929i | 0.619865i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.64951i | 0.973146i | 0.873640 | + | 0.486573i | \(0.161753\pi\) | ||||
−0.873640 | + | 0.486573i | \(0.838247\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.4853 | −1.37044 | −0.685219 | − | 0.728337i | \(-0.740293\pi\) | ||||
−0.685219 | + | 0.728337i | \(0.740293\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.43195 | 0.480712 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.19665i | 0.338845i | 0.985544 | + | 0.169422i | \(0.0541902\pi\) | ||||
−0.985544 | + | 0.169422i | \(0.945810\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 0.575398i | − 0.0603181i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.26038 | 0.539703 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.575398 | 0.0584228 | 0.0292114 | − | 0.999573i | \(-0.490700\pi\) | ||||
0.0292114 | + | 0.999573i | \(0.490700\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 0.828427i | − 0.0824316i | −0.999150 | − | 0.0412158i | \(-0.986877\pi\) | ||||
0.999150 | − | 0.0412158i | \(-0.0131231\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 13.3388i | − 1.31431i | −0.753756 | − | 0.657155i | \(-0.771760\pi\) | ||||
0.753756 | − | 0.657155i | \(-0.228240\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.84312 | −0.468202 | −0.234101 | − | 0.972212i | \(-0.575215\pi\) | ||||
−0.234101 | + | 0.972212i | \(0.575215\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.03547 | 0.386528 | 0.193264 | − | 0.981147i | \(-0.438093\pi\) | ||||
0.193264 | + | 0.981147i | \(0.438093\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 13.7811i | − 1.29642i | −0.761462 | − | 0.648210i | \(-0.775518\pi\) | ||||
0.761462 | − | 0.648210i | \(-0.224482\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 0.992654i | − 0.0925655i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.26772 | 0.574561 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.79296 | 0.344814 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.803347i | 0.0712855i | 0.999365 | + | 0.0356428i | \(0.0113478\pi\) | ||||
−0.999365 | + | 0.0356428i | \(0.988652\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.8254 | −1.03319 | −0.516594 | − | 0.856230i | \(-0.672800\pi\) | ||||
−0.516594 | + | 0.856230i | \(0.672800\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.43929 | 0.645069 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 16.9172i | − 1.44534i | −0.691195 | − | 0.722668i | \(-0.742915\pi\) | ||||
0.691195 | − | 0.722668i | \(-0.257085\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 17.1495i | − 1.45460i | −0.686320 | − | 0.727300i | \(-0.740775\pi\) | ||||
0.686320 | − | 0.727300i | \(-0.259225\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.56488 | −0.130862 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.26772 | −0.686597 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 20.7530i | − 1.70015i | −0.526660 | − | 0.850076i | \(-0.676556\pi\) | ||||
0.526660 | − | 0.850076i | \(-0.323444\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 6.35652i | − 0.517287i | −0.965973 | − | 0.258643i | \(-0.916725\pi\) | ||||
0.965973 | − | 0.258643i | \(-0.0832754\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.00735 | 0.402200 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.32541 | 0.425014 | 0.212507 | − | 0.977160i | \(-0.431837\pi\) | ||||
0.212507 | + | 0.977160i | \(0.431837\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 1.40383i | − 0.110637i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 0.378615i | − 0.0296554i | −0.999890 | − | 0.0148277i | \(-0.995280\pi\) | ||||
0.999890 | − | 0.0148277i | \(-0.00471997\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.1703 | 1.32867 | 0.664337 | − | 0.747433i | \(-0.268714\pi\) | ||||
0.664337 | + | 0.747433i | \(0.268714\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8345 | −0.987266 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 12.7383i | − 0.968476i | −0.874936 | − | 0.484238i | \(-0.839097\pi\) | ||||
0.874936 | − | 0.484238i | \(-0.160903\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.41421i | 0.106904i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.1452 | −0.982517 | −0.491258 | − | 0.871014i | \(-0.663463\pi\) | ||||
−0.491258 | + | 0.871014i | \(0.663463\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.70701 | −0.572858 | −0.286429 | − | 0.958101i | \(-0.592468\pi\) | ||||
−0.286429 | + | 0.958101i | \(0.592468\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.01773i | 0.0748253i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 17.0460i | − 1.24653i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1863 | −0.809410 | −0.404705 | − | 0.914447i | \(-0.632626\pi\) | ||||
−0.404705 | + | 0.914447i | \(0.632626\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.8952 | 1.00020 | 0.500099 | − | 0.865968i | \(-0.333297\pi\) | ||||
0.500099 | + | 0.865968i | \(0.333297\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 14.5354i | − 1.03561i | −0.855499 | − | 0.517804i | \(-0.826750\pi\) | ||||
0.855499 | − | 0.517804i | \(-0.173250\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7144i | 1.32663i | 0.748342 | + | 0.663313i | \(0.230850\pi\) | ||||
−0.748342 | + | 0.663313i | \(0.769150\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.6923 | −0.820640 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.68193 | −0.536530 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 20.2323i | − 1.39949i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.49263i | 0.240442i | 0.992747 | + | 0.120221i | \(0.0383604\pi\) | ||||
−0.992747 | + | 0.120221i | \(0.961640\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.42460 | −0.0971571 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.08146 | 0.480721 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.80322i | 0.121297i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 27.9350i | 1.87066i | 0.353772 | + | 0.935332i | \(0.384899\pi\) | ||||
−0.353772 | + | 0.935332i | \(0.615101\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.5061 | −0.830056 | −0.415028 | − | 0.909809i | \(-0.636228\pi\) | ||||
−0.415028 | + | 0.909809i | \(0.636228\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.65685 | −0.241652 | −0.120826 | − | 0.992674i | \(-0.538554\pi\) | ||||
−0.120826 | + | 0.992674i | \(0.538554\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 0.361010i | − 0.0236506i | −0.999930 | − | 0.0118253i | \(-0.996236\pi\) | ||||
0.999930 | − | 0.0118253i | \(-0.00376419\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 6.66420i | − 0.434724i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.36387 | 0.476329 | 0.238165 | − | 0.971225i | \(-0.423454\pi\) | ||||
0.238165 | + | 0.971225i | \(0.423454\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.7425 | 1.52939 | 0.764694 | − | 0.644394i | \(-0.222890\pi\) | ||||
0.764694 | + | 0.644394i | \(0.222890\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 5.00000i | − 0.319438i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.14028i | 0.136183i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.279424 | 0.0176371 | 0.00881854 | − | 0.999961i | \(-0.497193\pi\) | ||||
0.00881854 | + | 0.999961i | \(0.497193\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.81791 | −0.240030 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 14.5741i | − 0.909106i | −0.890720 | − | 0.454553i | \(-0.849799\pi\) | ||||
0.890720 | − | 0.454553i | \(-0.150201\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.43929i | 0.0894334i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0073 | 0.678742 | 0.339371 | − | 0.940653i | \(-0.389786\pi\) | ||||
0.339371 | + | 0.940653i | \(0.389786\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.78244 | 0.109494 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 7.04599i | − 0.429601i | −0.976658 | − | 0.214801i | \(-0.931090\pi\) | ||||
0.976658 | − | 0.214801i | \(-0.0689102\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.49263i | 0.0906706i | 0.998972 | + | 0.0453353i | \(0.0144356\pi\) | ||||
−0.998972 | + | 0.0453353i | \(0.985564\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.84616 | 0.231932 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.5385 | 1.65463 | 0.827314 | − | 0.561740i | \(-0.189868\pi\) | ||||
0.827314 | + | 0.561740i | \(0.189868\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.77205i | 0.105712i | 0.998602 | + | 0.0528558i | \(0.0168324\pi\) | ||||
−0.998602 | + | 0.0528558i | \(0.983168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.46007i | 0.443455i | 0.975109 | + | 0.221728i | \(0.0711696\pi\) | ||||
−0.975109 | + | 0.221728i | \(0.928830\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.8639 | −0.641275 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.64216 | −0.155421 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.5208i | 1.19884i | 0.800437 | + | 0.599418i | \(0.204601\pi\) | ||||
−0.800437 | + | 0.599418i | \(0.795399\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 8.45703i | − 0.492387i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.403879 | 0.0233569 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.01469 | −0.116125 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 10.8431i | − 0.620875i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.1776i | 1.37989i | 0.723862 | + | 0.689944i | \(0.242365\pi\) | ||||
−0.723862 | + | 0.689944i | \(0.757635\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.1421 | 1.48238 | 0.741192 | − | 0.671293i | \(-0.234261\pi\) | ||||
0.741192 | + | 0.671293i | \(0.234261\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.7322 | 1.62404 | 0.812021 | − | 0.583629i | \(-0.198368\pi\) | ||||
0.812021 | + | 0.583629i | \(0.198368\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 13.3137i | − 0.747772i | −0.927475 | − | 0.373886i | \(-0.878025\pi\) | ||||
0.927475 | − | 0.373886i | \(-0.121975\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.7990i | 1.78040i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.3137 | −1.29721 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.406868 | −0.0225690 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 9.42460i | − 0.519595i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 31.7811i | − 1.74685i | −0.486960 | − | 0.873424i | \(-0.661894\pi\) | ||||
0.486960 | − | 0.873424i | \(-0.338106\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.61087 | −0.470462 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.03547 | 0.219826 | 0.109913 | − | 0.993941i | \(-0.464943\pi\) | ||||
0.109913 | + | 0.993941i | \(0.464943\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 19.2591i | − 1.04294i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 16.9706i | − 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.435121 | −0.0233585 | −0.0116793 | − | 0.999932i | \(-0.503718\pi\) | ||||
−0.0116793 | + | 0.999932i | \(0.503718\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.6629 | −1.21312 | −0.606558 | − | 0.795039i | \(-0.707450\pi\) | ||||
−0.606558 | + | 0.795039i | \(0.707450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.2812i | 1.02623i | 0.858319 | + | 0.513116i | \(0.171509\pi\) | ||||
−0.858319 | + | 0.513116i | \(0.828491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 5.40383i | − 0.286805i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.66103 | −0.457112 | −0.228556 | − | 0.973531i | \(-0.573400\pi\) | ||||
−0.228556 | + | 0.973531i | \(0.573400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.67155 | −0.456397 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 9.69232i | − 0.507319i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.8595i | 1.24546i | 0.782438 | + | 0.622729i | \(0.213976\pi\) | ||||
−0.782438 | + | 0.622729i | \(0.786024\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.52075 | 0.130871 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.5177 | 1.21770 | 0.608850 | − | 0.793285i | \(-0.291631\pi\) | ||||
0.608850 | + | 0.793285i | \(0.291631\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 3.36387i | − 0.173248i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 23.6408i | − 1.21435i | −0.794569 | − | 0.607174i | \(-0.792303\pi\) | ||||
0.794569 | − | 0.607174i | \(-0.207697\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.2143 | 1.69717 | 0.848587 | − | 0.529057i | \(-0.177454\pi\) | ||||
0.848587 | + | 0.529057i | \(0.177454\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.43929 | 0.277212 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 5.46456i | − 0.277064i | −0.990358 | − | 0.138532i | \(-0.955762\pi\) | ||||
0.990358 | − | 0.138532i | \(-0.0442384\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.39939i | 0.222487i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.64951 | 0.435204 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.6493 | 0.935983 | 0.467991 | − | 0.883733i | \(-0.344978\pi\) | ||||
0.467991 | + | 0.883733i | \(0.344978\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.2113i | 0.659743i | 0.944026 | + | 0.329872i | \(0.107005\pi\) | ||||
−0.944026 | + | 0.329872i | \(0.892995\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.03733i | 0.101487i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.91437 | 0.194028 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.84920 | 0.239778 | 0.119889 | − | 0.992787i | \(-0.461746\pi\) | ||||
0.119889 | + | 0.992787i | \(0.461746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 11.9600i | − 0.588515i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.4853i | 0.612878i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.22060 | 0.255043 | 0.127522 | − | 0.991836i | \(-0.459298\pi\) | ||||
0.127522 | + | 0.991836i | \(0.459298\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.3137 | 0.648870 | 0.324435 | − | 0.945908i | \(-0.394826\pi\) | ||||
0.324435 | + | 0.945908i | \(0.394826\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 4.43195i | − 0.214981i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 15.3345i | − 0.742088i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 21.1671 | 1.01958 | 0.509791 | − | 0.860298i | \(-0.329723\pi\) | ||||
0.509791 | + | 0.860298i | \(0.329723\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.9262 | −1.72650 | −0.863251 | − | 0.504775i | \(-0.831575\pi\) | ||||
−0.863251 | + | 0.504775i | \(0.831575\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.22173i | 0.249789i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.927802i | 0.0442816i | 0.999755 | + | 0.0221408i | \(0.00704821\pi\) | ||||
−0.999755 | + | 0.0221408i | \(0.992952\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.5061 | 0.784227 | 0.392113 | − | 0.919917i | \(-0.371744\pi\) | ||||
0.392113 | + | 0.919917i | \(0.371744\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.19665 | 0.151536 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 16.7695i | − 0.791401i | −0.918380 | − | 0.395700i | \(-0.870502\pi\) | ||||
0.918380 | − | 0.395700i | \(-0.129498\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 29.5460i | 1.39126i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.575398 | −0.0269751 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.6169 | −0.824084 | −0.412042 | − | 0.911165i | \(-0.635184\pi\) | ||||
−0.412042 | + | 0.911165i | \(0.635184\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 16.2885i | − 0.758631i | −0.925267 | − | 0.379315i | \(-0.876160\pi\) | ||||
0.925267 | − | 0.379315i | \(-0.123840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 13.0519i | − 0.606573i | −0.952899 | − | 0.303286i | \(-0.901916\pi\) | ||||
0.952899 | − | 0.303286i | \(-0.0980839\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.665514 | −0.0307963 | −0.0153982 | − | 0.999881i | \(-0.504902\pi\) | ||||
−0.0153982 | + | 0.999881i | \(0.504902\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.1776 | −0.562310 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.47925i | 0.251936i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 5.26038i | − 0.241363i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.1316 | −1.78797 | −0.893985 | − | 0.448098i | \(-0.852102\pi\) | ||||
−0.893985 | + | 0.448098i | \(0.852102\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.414083 | −0.0188806 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 0.575398i | − 0.0261275i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 40.7528i | − 1.84669i | −0.383976 | − | 0.923343i | \(-0.625445\pi\) | ||||
0.383976 | − | 0.923343i | \(-0.374555\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.3627 | −1.23486 | −0.617432 | − | 0.786625i | \(-0.711827\pi\) | ||||
−0.617432 | + | 0.786625i | \(0.711827\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.6421 | 1.65028 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 7.64216i | − 0.342798i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 30.6597i | − 1.37252i | −0.727358 | − | 0.686259i | \(-0.759252\pi\) | ||||
0.727358 | − | 0.686259i | \(-0.240748\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.0930 | 1.38637 | 0.693184 | − | 0.720761i | \(-0.256207\pi\) | ||||
0.693184 | + | 0.720761i | \(0.256207\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.828427 | −0.0368645 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.70701i | 0.341607i | 0.985305 | + | 0.170804i | \(0.0546364\pi\) | ||||
−0.985305 | + | 0.170804i | \(0.945364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 13.7070i | − 0.606363i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.3388 | −0.587777 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25.6316 | −1.12728 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 13.4142i | − 0.587687i | −0.955853 | − | 0.293844i | \(-0.905065\pi\) | ||||
0.955853 | − | 0.293844i | \(-0.0949345\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.4853i | 0.545943i | 0.962022 | + | 0.272972i | \(0.0880065\pi\) | ||||
−0.962022 | + | 0.272972i | \(0.911993\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.1923 | −0.966712 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0146 | −0.957158 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3.12553i | − 0.135382i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.84312i | 0.209386i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.2308 | −0.828330 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.2546 | 1.42973 | 0.714863 | − | 0.699265i | \(-0.246489\pi\) | ||||
0.714863 | + | 0.699265i | \(0.246489\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 4.03547i | − 0.172860i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.9306i | 1.49352i | 0.665091 | + | 0.746762i | \(0.268393\pi\) | ||||
−0.665091 | + | 0.746762i | \(0.731607\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 43.4913 | 1.85279 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.2323 | 0.520168 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.7089i | 0.538495i | 0.963071 | + | 0.269247i | \(0.0867749\pi\) | ||||
−0.963071 | + | 0.269247i | \(0.913225\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 0.579625i | − 0.0245155i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.3137 | −0.982556 | −0.491278 | − | 0.871003i | \(-0.663470\pi\) | ||||
−0.491278 | + | 0.871003i | \(0.663470\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.7811 | −0.579776 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 14.8976i | − 0.624539i | −0.949994 | − | 0.312270i | \(-0.898911\pi\) | ||||
0.949994 | − | 0.312270i | \(-0.101089\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.73962i | − 0.114650i | −0.998356 | − | 0.0573249i | \(-0.981743\pi\) | ||||
0.998356 | − | 0.0573249i | \(-0.0182571\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.992654 | −0.0413965 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.5875 | 0.565656 | 0.282828 | − | 0.959171i | \(-0.408727\pi\) | ||||
0.282828 | + | 0.959171i | \(0.408727\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.6569i | 0.732530i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 6.85555i | − 0.283928i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.0649 | 1.24091 | 0.620455 | − | 0.784242i | \(-0.286948\pi\) | ||||
0.620455 | + | 0.784242i | \(0.286948\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.3405 | −1.08534 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.4259i | 0.920920i | 0.887681 | + | 0.460460i | \(0.152315\pi\) | ||||
−0.887681 | + | 0.460460i | \(0.847685\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 6.26772i | − 0.256952i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.60221 | 0.392336 | 0.196168 | − | 0.980570i | \(-0.437150\pi\) | ||||
0.196168 | + | 0.980570i | \(0.437150\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 44.8613 | 1.82993 | 0.914965 | − | 0.403534i | \(-0.132218\pi\) | ||||
0.914965 | + | 0.403534i | \(0.132218\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.79296i | − 0.154206i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 5.46437i | − 0.221792i | −0.993832 | − | 0.110896i | \(-0.964628\pi\) | ||||
0.993832 | − | 0.110896i | \(-0.0353721\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.71145 | 0.109693 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.20586 | 0.331431 | 0.165716 | − | 0.986174i | \(-0.447007\pi\) | ||||
0.165716 | + | 0.986174i | \(0.447007\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.4881i | 0.784563i | 0.919845 | + | 0.392281i | \(0.128314\pi\) | ||||
−0.919845 | + | 0.392281i | \(0.871686\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 19.0932i | − 0.767422i | −0.923453 | − | 0.383711i | \(-0.874646\pi\) | ||||
0.923453 | − | 0.383711i | \(-0.125354\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.52075 | 0.181120 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 4.51055i | − 0.179847i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 11.0993i | − 0.441857i | −0.975290 | − | 0.220928i | \(-0.929091\pi\) | ||||
0.975290 | − | 0.220928i | \(-0.0709087\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.803347 | 0.0318798 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.03434 | 0.0806034 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 6.74261i | − 0.266317i | −0.991095 | − | 0.133159i | \(-0.957488\pi\) | ||||
0.991095 | − | 0.133159i | \(-0.0425120\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.7338i | 1.64582i | 0.568172 | + | 0.822910i | \(0.307651\pi\) | ||||
−0.568172 | + | 0.822910i | \(0.692349\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.2853 | 1.62309 | 0.811546 | − | 0.584289i | \(-0.198626\pi\) | ||||
0.811546 | + | 0.584289i | \(0.198626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.5271 | −1.27680 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.1482i | 0.866727i | 0.901219 | + | 0.433363i | \(0.142673\pi\) | ||||
−0.901219 | + | 0.433363i | \(0.857327\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.8254i | 0.462056i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5490 | 0.410931 | 0.205465 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205465 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.0207 | 0.895402 | 0.447701 | − | 0.894183i | \(-0.352243\pi\) | ||||
0.447701 | + | 0.894183i | \(0.352243\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 7.43929i | − 0.288483i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 8.20699i | − 0.317776i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.7044 | −1.60998 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.9766 | 1.61808 | 0.809039 | − | 0.587754i | \(-0.199988\pi\) | ||||
0.809039 | + | 0.587754i | \(0.199988\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.0441i | 0.616624i | 0.951285 | + | 0.308312i | \(0.0997641\pi\) | ||||
−0.951285 | + | 0.308312i | \(0.900236\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 0.813735i | − 0.0312283i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.0769 | 1.68656 | 0.843278 | − | 0.537477i | \(-0.180623\pi\) | ||||
0.843278 | + | 0.537477i | \(0.180623\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16.9172 | −0.646374 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.725217i | 0.0276286i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.3524i | 1.19270i | 0.802725 | + | 0.596350i | \(0.203383\pi\) | ||||
−0.802725 | + | 0.596350i | \(0.796617\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.1495 | −0.650517 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.0459 | 1.28958 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.5147i | 0.850367i | 0.905107 | + | 0.425184i | \(0.139790\pi\) | ||||
−0.905107 | + | 0.425184i | \(0.860210\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 5.35366i | − 0.201917i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.17157 | −0.0440615 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.1214 | −0.605450 | −0.302725 | − | 0.953078i | \(-0.597896\pi\) | ||||
−0.302725 | + | 0.953078i | \(0.597896\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.97056i | 0.186149i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.56488i | 0.0585232i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.9894 | −1.41677 | −0.708383 | − | 0.705828i | \(-0.750575\pi\) | ||||
−0.708383 | + | 0.705828i | \(0.750575\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.8639 | −0.702528 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.26772i | 0.307055i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.9746i | 1.37131i | 0.727926 | + | 0.685656i | \(0.240485\pi\) | ||||
−0.727926 | + | 0.685656i | \(0.759515\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.31376 | 0.233523 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.8877 | 1.21473 | 0.607367 | − | 0.794422i | \(-0.292226\pi\) | ||||
0.607367 | + | 0.794422i | \(0.292226\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.1188i | 1.21995i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 13.1095i | − 0.482242i | −0.970495 | − | 0.241121i | \(-0.922485\pi\) | ||||
0.970495 | − | 0.241121i | \(-0.0775150\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −52.4187 | −1.92306 | −0.961529 | − | 0.274705i | \(-0.911420\pi\) | ||||
−0.961529 | + | 0.274705i | \(0.911420\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.7530 | −0.760331 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.84920i | 0.250264i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.0904i | 0.806090i | 0.915180 | + | 0.403045i | \(0.132048\pi\) | ||||
−0.915180 | + | 0.403045i | \(0.867952\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.35652 | −0.231338 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.6954 | −1.40641 | −0.703203 | − | 0.710989i | \(-0.748248\pi\) | ||||
−0.703203 | + | 0.710989i | \(0.748248\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.4142i | 1.06626i | 0.846032 | + | 0.533132i | \(0.178985\pi\) | ||||
−0.846032 | + | 0.533132i | \(0.821015\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 5.70701i | − 0.206608i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.44089 | 0.124243 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.06259 | −0.0743790 | −0.0371895 | − | 0.999308i | \(-0.511841\pi\) | ||||
−0.0371895 | + | 0.999308i | \(0.511841\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 3.72779i | − 0.134079i | −0.997750 | − | 0.0670397i | \(-0.978645\pi\) | ||||
0.997750 | − | 0.0670397i | \(-0.0213554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 5.00735i | − 0.179869i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 40.4099 | 1.44783 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.7840 | −0.743709 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 5.32541i | − 0.190072i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 15.4054i | − 0.549144i | −0.961567 | − | 0.274572i | \(-0.911464\pi\) | ||||
0.961567 | − | 0.274572i | \(-0.0885362\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.4895 | −0.692965 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.41172 | 0.156665 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 49.8507i | − 1.76580i | −0.469557 | − | 0.882902i | \(-0.655586\pi\) | ||||
0.469557 | − | 0.882902i | \(-0.344414\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.5354i | 1.04489i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.2782 | −1.31552 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.40383 | −0.0494783 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 52.4410i | − 1.84373i | −0.387513 | − | 0.921864i | \(-0.626666\pi\) | ||||
0.387513 | − | 0.921864i | \(-0.373334\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.1284i | 0.812150i | 0.913840 | + | 0.406075i | \(0.133103\pi\) | ||||
−0.913840 | + | 0.406075i | \(0.866897\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.378615 | −0.0132623 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.49394 | 0.262180 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.0581i | 0.700033i | 0.936744 | + | 0.350016i | \(0.113824\pi\) | ||||
−0.936744 | + | 0.350016i | \(0.886176\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 53.6212i | − 1.86912i | −0.355809 | − | 0.934559i | \(-0.615795\pi\) | ||||
0.355809 | − | 0.934559i | \(-0.384205\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −55.1565 | −1.91798 | −0.958990 | − | 0.283440i | \(-0.908524\pi\) | ||||
−0.958990 | + | 0.283440i | \(0.908524\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −41.8284 | −1.45276 | −0.726380 | − | 0.687294i | \(-0.758799\pi\) | ||||
−0.726380 | + | 0.687294i | \(0.758799\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.1597i | 0.767789i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 17.1703i | − 0.594201i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.57282 | −0.330491 | −0.165245 | − | 0.986253i | \(-0.552842\pi\) | ||||
−0.165245 | + | 0.986253i | \(0.552842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −39.3552 | −1.35708 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.8345i | 0.441519i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 5.36405i | − 0.184311i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.01026 | −0.0346312 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.67042 | 0.125673 | 0.0628363 | − | 0.998024i | \(-0.479985\pi\) | ||||
0.0628363 | + | 0.998024i | \(0.479985\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.6536i | 1.59366i | 0.604205 | + | 0.796829i | \(0.293491\pi\) | ||||
−0.604205 | + | 0.796829i | \(0.706509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 34.9546i | − 1.19263i | −0.802749 | − | 0.596317i | \(-0.796630\pi\) | ||||
0.802749 | − | 0.596317i | \(-0.203370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.3332 | 1.61124 | 0.805620 | − | 0.592433i | \(-0.201832\pi\) | ||||
0.805620 | + | 0.592433i | \(0.201832\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.7383 | −0.433116 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 33.2674i | − 1.12852i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 3.50348i | − 0.118711i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.41421 | 0.0478091 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.2456 | −0.683644 | −0.341822 | − | 0.939765i | \(-0.611044\pi\) | ||||
−0.341822 | + | 0.939765i | \(0.611044\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.09628i | 0.272771i | 0.990656 | + | 0.136385i | \(0.0435485\pi\) | ||||
−0.990656 | + | 0.136385i | \(0.956451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.6923i | 1.36940i | 0.728823 | + | 0.684702i | \(0.240068\pi\) | ||||
−0.728823 | + | 0.684702i | \(0.759932\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.2265 | −0.779870 | −0.389935 | − | 0.920842i | \(-0.627502\pi\) | ||||
−0.389935 | + | 0.920842i | \(0.627502\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.13610 | 0.0381037 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.0562i | 1.17311i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.1452i | 0.439395i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41.3993 | 1.38075 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.89968 | −0.263176 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.70701i | 0.256190i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.1083i | 0.468457i | 0.972182 | + | 0.234229i | \(0.0752564\pi\) | ||||
−0.972182 | + | 0.234229i | \(0.924744\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.3111 | −1.13678 | −0.568389 | − | 0.822760i | \(-0.692433\pi\) | ||||
−0.568389 | + | 0.822760i | \(0.692433\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48.0204 | 1.58924 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.7236i | 0.552263i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 52.0278i | − 1.71624i | −0.513450 | − | 0.858120i | \(-0.671633\pi\) | ||||
0.513450 | − | 0.858120i | \(-0.328367\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.19864 | 0.0723692 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.01773 | 0.0334629 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 15.1836i | − 0.498156i | −0.968483 | − | 0.249078i | \(-0.919872\pi\) | ||||
0.968483 | − | 0.249078i | \(-0.0801276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.3019i | 0.862009i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.0460 | −0.557463 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.4057 | −0.895305 | −0.447652 | − | 0.894208i | \(-0.647740\pi\) | ||||
−0.447652 | + | 0.894208i | \(0.647740\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.1214i | 0.362548i | 0.983433 | + | 0.181274i | \(0.0580220\pi\) | ||||
−0.983433 | + | 0.181274i | \(0.941978\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 7.62550i | − 0.248321i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.6863 | −0.412249 | −0.206125 | − | 0.978526i | \(-0.566085\pi\) | ||||
−0.206125 | + | 0.978526i | \(0.566085\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.94349 | 0.128011 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.7543i | 1.12580i | 0.826524 | + | 0.562901i | \(0.190315\pi\) | ||||
−0.826524 | + | 0.562901i | \(0.809685\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.1863i | 0.361979i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.9246 | −0.772565 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.92649 | 0.191177 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 13.8952i | − 0.447302i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 8.70080i | − 0.279799i | −0.990166 | − | 0.139899i | \(-0.955322\pi\) | ||||
0.990166 | − | 0.139899i | \(-0.0446779\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.82379 | −0.0585281 | −0.0292640 | − | 0.999572i | \(-0.509316\pi\) | ||||
−0.0292640 | + | 0.999572i | \(0.509316\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −24.2530 | −0.777516 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 23.7099i | − 0.758548i | −0.925284 | − | 0.379274i | \(-0.876174\pi\) | ||||
0.925284 | − | 0.379274i | \(-0.123826\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 12.2948i | − 0.392945i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.06988 | −0.257389 | −0.128695 | − | 0.991684i | \(-0.541079\pi\) | ||||
−0.128695 | + | 0.991684i | \(0.541079\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.5354 | −0.463138 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.41414i | − 0.0449669i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 53.5636i | − 1.70150i | −0.525568 | − | 0.850751i | \(-0.676147\pi\) | ||||
0.525568 | − | 0.850751i | \(-0.323853\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18.7144 | 0.593285 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.9985 | 1.39345 | 0.696723 | − | 0.717340i | \(-0.254641\pi\) | ||||
0.696723 | + | 0.717340i | \(0.254641\pi\) | |||||||
\(998\) | 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 | 5760.2.h.h.1151.1 | yes | 8 | |
3.2 | odd | 2 | 5760.2.h.c.1151.6 | yes | 8 | ||
4.3 | odd | 2 | 5760.2.h.c.1151.4 | yes | 8 | ||
8.3 | odd | 2 | 5760.2.h.e.1151.7 | yes | 8 | ||
8.5 | even | 2 | 5760.2.h.b.1151.6 | yes | 8 | ||
12.11 | even | 2 | inner | 5760.2.h.h.1151.7 | yes | 8 | |
24.5 | odd | 2 | 5760.2.h.e.1151.1 | yes | 8 | ||
24.11 | even | 2 | 5760.2.h.b.1151.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5760.2.h.b.1151.4 | ✓ | 8 | 24.11 | even | 2 | ||
5760.2.h.b.1151.6 | yes | 8 | 8.5 | even | 2 | ||
5760.2.h.c.1151.4 | yes | 8 | 4.3 | odd | 2 | ||
5760.2.h.c.1151.6 | yes | 8 | 3.2 | odd | 2 | ||
5760.2.h.e.1151.1 | yes | 8 | 24.5 | odd | 2 | ||
5760.2.h.e.1151.7 | yes | 8 | 8.3 | odd | 2 | ||
5760.2.h.h.1151.1 | yes | 8 | 1.1 | even | 1 | trivial | |
5760.2.h.h.1151.7 | yes | 8 | 12.11 | even | 2 | inner |