Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(161,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.j (of order \(4\), degree \(2\), not 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: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.2 | ||
Character | \(\chi\) | \(=\) | 1152.737 |
Dual form | 1152.3.j.a.161.2 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(5\) | −5.52702 | + | 5.52702i | −1.10540 | + | 1.10540i | −0.111658 | + | 0.993747i | \(0.535616\pi\) |
−0.993747 | + | 0.111658i | \(0.964384\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.79421i | 1.11346i | 0.830694 | + | 0.556729i | \(0.187944\pi\) | ||||
−0.830694 | + | 0.556729i | \(0.812056\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.48521 | − | 2.48521i | 0.225929 | − | 0.225929i | −0.585061 | − | 0.810989i | \(-0.698929\pi\) |
0.810989 | + | 0.585061i | \(0.198929\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.3242 | + | 13.3242i | −1.02494 | + | 1.02494i | −0.0252590 | + | 0.999681i | \(0.508041\pi\) |
−0.999681 | + | 0.0252590i | \(0.991959\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.86338i | 0.344905i | 0.985018 | + | 0.172452i | \(0.0551691\pi\) | ||||
−0.985018 | + | 0.172452i | \(0.944831\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.5712 | + | 18.5712i | −0.977433 | + | 0.977433i | −0.999751 | − | 0.0223177i | \(-0.992895\pi\) |
0.0223177 | + | 0.999751i | \(0.492895\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 34.3136 | 1.49190 | 0.745948 | − | 0.666004i | \(-0.231997\pi\) | ||||
0.745948 | + | 0.666004i | \(0.231997\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 36.0959i | − | 1.44384i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 21.4872 | + | 21.4872i | 0.740939 | + | 0.740939i | 0.972759 | − | 0.231820i | \(-0.0744679\pi\) |
−0.231820 | + | 0.972759i | \(0.574468\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −30.6117 | −0.987473 | −0.493737 | − | 0.869612i | \(-0.664369\pi\) | ||||
−0.493737 | + | 0.869612i | \(0.664369\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −43.0788 | − | 43.0788i | −1.23082 | − | 1.23082i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −30.3274 | − | 30.3274i | −0.819661 | − | 0.819661i | 0.166398 | − | 0.986059i | \(-0.446786\pi\) |
−0.986059 | + | 0.166398i | \(0.946786\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.12709 | −0.0762704 | −0.0381352 | − | 0.999273i | \(-0.512142\pi\) | ||||
−0.0381352 | + | 0.999273i | \(0.512142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.94981 | + | 9.94981i | 0.231391 | + | 0.231391i | 0.813273 | − | 0.581882i | \(-0.197684\pi\) |
−0.581882 | + | 0.813273i | \(0.697684\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 38.4052i | 0.817132i | 0.912729 | + | 0.408566i | \(0.133971\pi\) | ||||
−0.912729 | + | 0.408566i | \(0.866029\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11.7497 | −0.239790 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 61.1826 | − | 61.1826i | 1.15439 | − | 1.15439i | 0.168725 | − | 0.985663i | \(-0.446035\pi\) |
0.985663 | − | 0.168725i | \(-0.0539651\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 27.4717i | 0.499485i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.98892 | − | 2.98892i | 0.0506596 | − | 0.0506596i | −0.681323 | − | 0.731983i | \(-0.738595\pi\) |
0.731983 | + | 0.681323i | \(0.238595\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.88659 | + | 3.88659i | −0.0637146 | + | 0.0637146i | −0.738246 | − | 0.674531i | \(-0.764346\pi\) |
0.674531 | + | 0.738246i | \(0.264346\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 147.287i | − | 2.26595i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 47.0242 | − | 47.0242i | 0.701853 | − | 0.701853i | −0.262955 | − | 0.964808i | \(-0.584697\pi\) |
0.964808 | + | 0.262955i | \(0.0846970\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −97.5416 | −1.37383 | −0.686913 | − | 0.726740i | \(-0.741035\pi\) | ||||
−0.686913 | + | 0.726740i | \(0.741035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 106.904i | − | 1.46444i | −0.681069 | − | 0.732219i | \(-0.738485\pi\) | ||
0.681069 | − | 0.732219i | \(-0.261515\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 19.3703 | + | 19.3703i | 0.251562 | + | 0.251562i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −96.8255 | −1.22564 | −0.612820 | − | 0.790223i | \(-0.709965\pi\) | ||||
−0.612820 | + | 0.790223i | \(0.709965\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −88.8242 | − | 88.8242i | −1.07017 | − | 1.07017i | −0.997345 | − | 0.0728268i | \(-0.976798\pi\) |
−0.0728268 | − | 0.997345i | \(-0.523202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −32.4070 | − | 32.4070i | −0.381259 | − | 0.381259i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 54.8651 | 0.616462 | 0.308231 | − | 0.951311i | \(-0.400263\pi\) | ||||
0.308231 | + | 0.951311i | \(0.400263\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −103.852 | − | 103.852i | −1.14123 | − | 1.14123i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 205.287i | − | 2.16092i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00194 | −0.0515664 | −0.0257832 | − | 0.999668i | \(-0.508208\pi\) | ||||
−0.0257832 | + | 0.999668i | \(0.508208\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 37.2481 | − | 37.2481i | 0.368793 | − | 0.368793i | −0.498244 | − | 0.867037i | \(-0.666022\pi\) |
0.867037 | + | 0.498244i | \(0.166022\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 188.028i | 1.82551i | 0.408505 | + | 0.912756i | \(0.366050\pi\) | ||||
−0.408505 | + | 0.912756i | \(0.633950\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −35.2253 | + | 35.2253i | −0.329208 | + | 0.329208i | −0.852285 | − | 0.523077i | \(-0.824784\pi\) |
0.523077 | + | 0.852285i | \(0.324784\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 93.0073 | − | 93.0073i | 0.853278 | − | 0.853278i | −0.137257 | − | 0.990535i | \(-0.543829\pi\) |
0.990535 | + | 0.137257i | \(0.0438287\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.80833i | − | 0.0337021i | −0.999858 | − | 0.0168510i | \(-0.994636\pi\) | ||
0.999858 | − | 0.0168510i | \(-0.00536410\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −189.652 | + | 189.652i | −1.64915 | + | 1.64915i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −45.7004 | −0.384037 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 108.647i | 0.897913i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 61.3275 | + | 61.3275i | 0.490620 | + | 0.490620i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −173.704 | −1.36775 | −0.683875 | − | 0.729600i | \(-0.739706\pi\) | ||||
−0.683875 | + | 0.729600i | \(0.739706\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 59.8594 | + | 59.8594i | 0.456942 | + | 0.456942i | 0.897650 | − | 0.440708i | \(-0.145273\pi\) |
−0.440708 | + | 0.897650i | \(0.645273\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −144.748 | − | 144.748i | −1.08833 | − | 1.08833i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.0602 | −0.0953299 | −0.0476649 | − | 0.998863i | \(-0.515178\pi\) | ||||
−0.0476649 | + | 0.998863i | \(0.515178\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 132.497 | + | 132.497i | 0.953219 | + | 0.953219i | 0.998954 | − | 0.0457344i | \(-0.0145628\pi\) |
−0.0457344 | + | 0.998954i | \(0.514563\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 66.2271i | 0.463126i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −237.521 | −1.63807 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.4768 | + | 10.4768i | −0.0703142 | + | 0.0703142i | −0.741389 | − | 0.671075i | \(-0.765833\pi\) |
0.671075 | + | 0.741389i | \(0.265833\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 181.207i | − | 1.20005i | −0.799982 | − | 0.600024i | \(-0.795158\pi\) | ||
0.799982 | − | 0.600024i | \(-0.204842\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 169.191 | − | 169.191i | 1.09156 | − | 1.09156i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −57.9518 | + | 57.9518i | −0.369120 | + | 0.369120i | −0.867156 | − | 0.498036i | \(-0.834055\pi\) |
0.498036 | + | 0.867156i | \(0.334055\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 267.447i | 1.66116i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −87.8044 | + | 87.8044i | −0.538677 | + | 0.538677i | −0.923140 | − | 0.384463i | \(-0.874387\pi\) |
0.384463 | + | 0.923140i | \(0.374387\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 86.9131 | 0.520438 | 0.260219 | − | 0.965550i | \(-0.416205\pi\) | ||||
0.260219 | + | 0.965550i | \(0.416205\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 186.070i | − | 1.10100i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −216.007 | − | 216.007i | −1.24860 | − | 1.24860i | −0.956339 | − | 0.292258i | \(-0.905593\pi\) |
−0.292258 | − | 0.956339i | \(-0.594407\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 281.339 | 1.60765 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 86.1380 | + | 86.1380i | 0.481218 | + | 0.481218i | 0.905520 | − | 0.424303i | \(-0.139481\pi\) |
−0.424303 | + | 0.905520i | \(0.639481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.84265 | − | 1.84265i | −0.0101804 | − | 0.0101804i | 0.701998 | − | 0.712179i | \(-0.252291\pi\) |
−0.712179 | + | 0.701998i | \(0.752291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 335.241 | 1.81211 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.5718 | + | 14.5718i | 0.0779238 | + | 0.0779238i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 82.0328i | − | 0.429491i | −0.976670 | − | 0.214746i | \(-0.931108\pi\) | ||
0.976670 | − | 0.214746i | \(-0.0688922\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −91.2193 | −0.472639 | −0.236319 | − | 0.971675i | \(-0.575941\pi\) | ||||
−0.236319 | + | 0.971675i | \(0.575941\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.74282 | + | 8.74282i | −0.0443798 | + | 0.0443798i | −0.728948 | − | 0.684569i | \(-0.759991\pi\) |
0.684569 | + | 0.728948i | \(0.259991\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 128.824i | 0.647357i | 0.946167 | + | 0.323679i | \(0.104920\pi\) | ||||
−0.946167 | + | 0.323679i | \(0.895080\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −167.476 | + | 167.476i | −0.825005 | + | 0.825005i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 17.2835 | − | 17.2835i | 0.0843096 | − | 0.0843096i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 92.3070i | 0.441660i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −96.2826 | + | 96.2826i | −0.456316 | + | 0.456316i | −0.897444 | − | 0.441128i | \(-0.854578\pi\) |
0.441128 | + | 0.897444i | \(0.354578\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −109.986 | −0.511561 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 238.594i | − | 1.09951i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −78.1250 | − | 78.1250i | −0.353507 | − | 0.353507i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.9317 | −0.0714424 | −0.0357212 | − | 0.999362i | \(-0.511373\pi\) | ||||
−0.0357212 | + | 0.999362i | \(0.511373\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 66.7298 | + | 66.7298i | 0.293964 | + | 0.293964i | 0.838644 | − | 0.544680i | \(-0.183349\pi\) |
−0.544680 | + | 0.838644i | \(0.683349\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 109.514 | + | 109.514i | 0.478229 | + | 0.478229i | 0.904565 | − | 0.426336i | \(-0.140196\pi\) |
−0.426336 | + | 0.904565i | \(0.640196\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 85.9062 | 0.368696 | 0.184348 | − | 0.982861i | \(-0.440983\pi\) | ||||
0.184348 | + | 0.982861i | \(0.440983\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −212.266 | − | 212.266i | −0.903261 | − | 0.903261i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 47.0157i | − | 0.196718i | −0.995151 | − | 0.0983592i | \(-0.968641\pi\) | ||
0.995151 | − | 0.0983592i | \(-0.0313594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 312.627 | 1.29721 | 0.648603 | − | 0.761127i | \(-0.275354\pi\) | ||||
0.648603 | + | 0.761127i | \(0.275354\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 64.9408 | − | 64.9408i | 0.265064 | − | 0.265064i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 494.894i | − | 2.00362i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 125.339 | − | 125.339i | 0.499360 | − | 0.499360i | −0.411878 | − | 0.911239i | \(-0.635127\pi\) |
0.911239 | + | 0.411878i | \(0.135127\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 85.2767 | − | 85.2767i | 0.337062 | − | 0.337062i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 341.153i | − | 1.32744i | −0.747980 | − | 0.663722i | \(-0.768976\pi\) | ||
0.747980 | − | 0.663722i | \(-0.231024\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 236.378 | − | 236.378i | 0.912658 | − | 0.912658i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −161.903 | −0.615599 | −0.307799 | − | 0.951451i | \(-0.599593\pi\) | ||||
−0.307799 | + | 0.951451i | \(0.599593\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 676.315i | 2.55213i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 65.6610 | + | 65.6610i | 0.244093 | + | 0.244093i | 0.818541 | − | 0.574448i | \(-0.194783\pi\) |
−0.574448 | + | 0.818541i | \(0.694783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 200.090 | 0.738339 | 0.369170 | − | 0.929362i | \(-0.379642\pi\) | ||||
0.369170 | + | 0.929362i | \(0.379642\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −89.7061 | − | 89.7061i | −0.326204 | − | 0.326204i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 70.7882 | + | 70.7882i | 0.255553 | + | 0.255553i | 0.823243 | − | 0.567690i | \(-0.192163\pi\) |
−0.567690 | + | 0.823243i | \(0.692163\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −448.021 | −1.59438 | −0.797190 | − | 0.603729i | \(-0.793681\pi\) | ||||
−0.797190 | + | 0.603729i | \(0.793681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 187.254 | + | 187.254i | 0.661676 | + | 0.661676i | 0.955775 | − | 0.294099i | \(-0.0950196\pi\) |
−0.294099 | + | 0.955775i | \(0.595020\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 24.3732i | − | 0.0849239i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 254.621 | 0.881041 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −200.350 | + | 200.350i | −0.683788 | + | 0.683788i | −0.960852 | − | 0.277063i | \(-0.910639\pi\) |
0.277063 | + | 0.960852i | \(0.410639\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 33.0396i | 0.111999i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −457.202 | + | 457.202i | −1.52910 | + | 1.52910i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −77.5509 | + | 77.5509i | −0.257644 | + | 0.257644i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 42.9625i | − | 0.140861i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 118.542 | − | 118.542i | 0.386130 | − | 0.386130i | −0.487174 | − | 0.873305i | \(-0.661972\pi\) |
0.873305 | + | 0.487174i | \(0.161972\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.29491 | 0.0105946 | 0.00529729 | − | 0.999986i | \(-0.498314\pi\) | ||||
0.00529729 | + | 0.999986i | \(0.498314\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 492.839i | 1.57457i | 0.616592 | + | 0.787283i | \(0.288513\pi\) | ||||
−0.616592 | + | 0.787283i | \(0.711487\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −118.311 | − | 118.311i | −0.373222 | − | 0.373222i | 0.495427 | − | 0.868649i | \(-0.335012\pi\) |
−0.868649 | + | 0.495427i | \(0.835012\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 106.801 | 0.334799 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −108.890 | − | 108.890i | −0.337121 | − | 0.337121i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 480.950 | + | 480.950i | 1.47985 | + | 1.47985i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −299.338 | −0.909843 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 52.2818 | + | 52.2818i | 0.157951 | + | 0.157951i | 0.781658 | − | 0.623707i | \(-0.214374\pi\) |
−0.623707 | + | 0.781658i | \(0.714374\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 519.807i | 1.55166i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 104.504 | 0.310100 | 0.155050 | − | 0.987907i | \(-0.450446\pi\) | ||||
0.155050 | + | 0.987907i | \(0.450446\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −76.0765 | + | 76.0765i | −0.223098 | + | 0.223098i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 290.337i | 0.846463i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 312.769 | − | 312.769i | 0.901351 | − | 0.901351i | −0.0942021 | − | 0.995553i | \(-0.530030\pi\) |
0.995553 | + | 0.0942021i | \(0.0300300\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 114.172 | − | 114.172i | 0.327141 | − | 0.327141i | −0.524357 | − | 0.851498i | \(-0.675694\pi\) |
0.851498 | + | 0.524357i | \(0.175694\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 312.848i | 0.886255i | 0.896459 | + | 0.443127i | \(0.146131\pi\) | ||||
−0.896459 | + | 0.443127i | \(0.853869\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 539.115 | − | 539.115i | 1.51863 | − | 1.51863i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 670.421 | 1.86747 | 0.933734 | − | 0.357967i | \(-0.116530\pi\) | ||||
0.933734 | + | 0.357967i | \(0.116530\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 328.781i | − | 0.910751i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 590.861 | + | 590.861i | 1.61880 | + | 1.61880i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −531.445 | −1.44808 | −0.724039 | − | 0.689759i | \(-0.757717\pi\) | ||||
−0.724039 | + | 0.689759i | \(0.757717\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 476.870 | + | 476.870i | 1.28536 | + | 1.28536i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.9291 | − | 25.9291i | −0.0695151 | − | 0.0695151i | 0.671494 | − | 0.741010i | \(-0.265653\pi\) |
−0.741010 | + | 0.671494i | \(0.765653\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −572.601 | −1.51884 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −109.268 | − | 109.268i | −0.288307 | − | 0.288307i | 0.548103 | − | 0.836411i | \(-0.315350\pi\) |
−0.836411 | + | 0.548103i | \(0.815350\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 93.3821i | 0.243818i | 0.992541 | + | 0.121909i | \(0.0389015\pi\) | ||||
−0.992541 | + | 0.121909i | \(0.961098\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −214.120 | −0.556156 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 66.8268 | − | 66.8268i | 0.171791 | − | 0.171791i | −0.615975 | − | 0.787766i | \(-0.711238\pi\) |
0.787766 | + | 0.615975i | \(0.211238\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 201.194i | 0.514562i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 535.157 | − | 535.157i | 1.35483 | − | 1.35483i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −329.309 | + | 329.309i | −0.829494 | + | 0.829494i | −0.987447 | − | 0.157953i | \(-0.949511\pi\) |
0.157953 | + | 0.987447i | \(0.449511\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 129.336i | 0.322534i | 0.986911 | + | 0.161267i | \(0.0515581\pi\) | ||||
−0.986911 | + | 0.161267i | \(0.948442\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 407.877 | − | 407.877i | 1.01210 | − | 1.01210i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −150.740 | −0.370369 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 567.479i | − | 1.38748i | −0.720226 | − | 0.693739i | \(-0.755962\pi\) | ||
0.720226 | − | 0.693739i | \(-0.244038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 23.2962 | + | 23.2962i | 0.0564074 | + | 0.0564074i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 981.867 | 2.36594 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.9979 | − | 11.9979i | −0.0286346 | − | 0.0286346i | 0.692645 | − | 0.721279i | \(-0.256445\pi\) |
−0.721279 | + | 0.692645i | \(0.756445\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −301.310 | − | 301.310i | −0.715700 | − | 0.715700i | 0.252022 | − | 0.967722i | \(-0.418905\pi\) |
−0.967722 | + | 0.252022i | \(0.918905\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 211.644 | 0.497987 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.2929 | − | 30.2929i | −0.0709436 | − | 0.0709436i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 700.273i | 1.62476i | 0.583126 | + | 0.812382i | \(0.301829\pi\) | ||||
−0.583126 | + | 0.812382i | \(0.698171\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −93.2906 | −0.215452 | −0.107726 | − | 0.994181i | \(-0.534357\pi\) | ||||
−0.107726 | + | 0.994181i | \(0.534357\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −637.246 | + | 637.246i | −1.45823 | + | 1.45823i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 98.5794i | − | 0.224554i | −0.993677 | − | 0.112277i | \(-0.964186\pi\) | ||
0.993677 | − | 0.112277i | \(-0.0358145\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −574.790 | + | 574.790i | −1.29749 | + | 1.29749i | −0.367450 | + | 0.930043i | \(0.619769\pi\) |
−0.930043 | + | 0.367450i | \(0.880231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −303.241 | + | 303.241i | −0.681440 | + | 0.681440i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 79.1258i | 0.176227i | 0.996110 | + | 0.0881133i | \(0.0280838\pi\) | ||||
−0.996110 | + | 0.0881133i | \(0.971916\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.77148 | + | 7.77148i | −0.0172317 | + | 0.0172317i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1147.98 | 2.52304 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 721.867i | 1.57958i | 0.613380 | + | 0.789788i | \(0.289810\pi\) | ||||
−0.613380 | + | 0.789788i | \(0.710190\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −57.6748 | − | 57.6748i | −0.125108 | − | 0.125108i | 0.641780 | − | 0.766888i | \(-0.278196\pi\) |
−0.766888 | + | 0.641780i | \(0.778196\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −469.888 | −1.01488 | −0.507438 | − | 0.861688i | \(-0.669407\pi\) | ||||
−0.507438 | + | 0.861688i | \(0.669407\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 284.381 | + | 284.381i | 0.608954 | + | 0.608954i | 0.942673 | − | 0.333719i | \(-0.108304\pi\) |
−0.333719 | + | 0.942673i | \(0.608304\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 366.516 | + | 366.516i | 0.781485 | + | 0.781485i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 49.4548 | 0.104556 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 670.346 | + | 670.346i | 1.41126 | + | 1.41126i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 74.7175i | 0.155986i | 0.996954 | + | 0.0779932i | \(0.0248512\pi\) | ||||
−0.996954 | + | 0.0779932i | \(0.975149\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 808.179 | 1.68021 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.6458 | − | 27.6458i | 0.0570017 | − | 0.0570017i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 465.139i | − | 0.955111i | −0.878602 | − | 0.477555i | \(-0.841523\pi\) | ||
0.878602 | − | 0.477555i | \(-0.158477\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −165.364 | + | 165.364i | −0.336791 | + | 0.336791i | −0.855158 | − | 0.518367i | \(-0.826540\pi\) |
0.518367 | + | 0.855158i | \(0.326540\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −125.988 | + | 125.988i | −0.255553 | + | 0.255553i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 760.260i | − | 1.52970i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −502.645 | + | 502.645i | −1.00730 | + | 1.00730i | −0.00733057 | + | 0.999973i | \(0.502333\pi\) |
−0.999973 | + | 0.00733057i | \(0.997667\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.2713 | −0.0383127 | −0.0191563 | − | 0.999817i | \(-0.506098\pi\) | ||||
−0.0191563 | + | 0.999817i | \(0.506098\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 411.742i | 0.815330i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 136.252 | + | 136.252i | 0.267686 | + | 0.267686i | 0.828167 | − | 0.560481i | \(-0.189384\pi\) |
−0.560481 | + | 0.828167i | \(0.689384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 833.232 | 1.63059 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1039.23 | − | 1039.23i | −2.01793 | − | 2.01793i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 95.4452 | + | 95.4452i | 0.184613 | + | 0.184613i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −196.906 | −0.377939 | −0.188969 | − | 0.981983i | \(-0.560515\pi\) | ||||
−0.188969 | + | 0.981983i | \(0.560515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −481.313 | − | 481.313i | −0.920293 | − | 0.920293i | 0.0767569 | − | 0.997050i | \(-0.475543\pi\) |
−0.997050 | + | 0.0767569i | \(0.975543\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 179.488i | − | 0.340584i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 648.424 | 1.22575 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 41.6660 | − | 41.6660i | 0.0781726 | − | 0.0781726i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 389.382i | − | 0.727817i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −29.2005 | + | 29.2005i | −0.0541753 | + | 0.0541753i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.4319 | − | 38.4319i | 0.0710387 | − | 0.0710387i | −0.670695 | − | 0.741733i | \(-0.734004\pi\) |
0.741733 | + | 0.670695i | \(0.234004\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1028.11i | 1.88643i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −249.883 | + | 249.883i | −0.456824 | + | 0.456824i | −0.897611 | − | 0.440788i | \(-0.854699\pi\) |
0.440788 | + | 0.897611i | \(0.354699\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −798.089 | −1.44844 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 754.678i | − | 1.36470i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −561.819 | − | 561.819i | −1.00865 | − | 1.00865i | −0.999962 | − | 0.00868977i | \(-0.997234\pi\) |
−0.00868977 | − | 0.999962i | \(-0.502766\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −265.147 | −0.474323 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 512.028 | + | 512.028i | 0.909464 | + | 0.909464i | 0.996229 | − | 0.0867652i | \(-0.0276530\pi\) |
−0.0867652 | + | 0.996229i | \(0.527653\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.0487 | + | 21.0487i | 0.0372544 | + | 0.0372544i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −278.458 | −0.489382 | −0.244691 | − | 0.969601i | \(-0.578686\pi\) | ||||
−0.244691 | + | 0.969601i | \(0.578686\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −83.1512 | − | 83.1512i | −0.145624 | − | 0.145624i | 0.630536 | − | 0.776160i | \(-0.282835\pi\) |
−0.776160 | + | 0.630536i | \(0.782835\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1238.58i | − | 2.15406i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1079.23 | −1.87042 | −0.935208 | − | 0.354098i | \(-0.884788\pi\) | ||||
−0.935208 | + | 0.354098i | \(0.884788\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 692.315 | − | 692.315i | 1.19159 | − | 1.19159i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 304.104i | − | 0.521619i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −197.819 | + | 197.819i | −0.337000 | + | 0.337000i | −0.855237 | − | 0.518237i | \(-0.826588\pi\) |
0.518237 | + | 0.855237i | \(0.326588\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 568.496 | − | 568.496i | 0.965189 | − | 0.965189i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 313.761i | − | 0.529108i | −0.964371 | − | 0.264554i | \(-0.914775\pi\) | ||
0.964371 | − | 0.264554i | \(-0.0852248\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 252.587 | − | 252.587i | 0.424516 | − | 0.424516i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1076.31 | −1.79684 | −0.898422 | − | 0.439133i | \(-0.855286\pi\) | ||||
−0.898422 | + | 0.439133i | \(0.855286\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.5949i | 0.0425873i | 0.999773 | + | 0.0212936i | \(0.00677848\pi\) | ||||
−0.999773 | + | 0.0212936i | \(0.993222\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −600.497 | − | 600.497i | −0.992557 | − | 0.992557i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −576.415 | −0.949612 | −0.474806 | − | 0.880090i | \(-0.657482\pi\) | ||||
−0.474806 | + | 0.880090i | \(0.657482\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −511.719 | − | 511.719i | −0.837511 | − | 0.837511i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 478.265 | + | 478.265i | 0.780205 | + | 0.780205i | 0.979865 | − | 0.199660i | \(-0.0639839\pi\) |
−0.199660 | + | 0.979865i | \(0.563984\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1106.10 | 1.79271 | 0.896357 | − | 0.443334i | \(-0.146204\pi\) | ||||
0.896357 | + | 0.443334i | \(0.146204\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −592.514 | − | 592.514i | −0.957212 | − | 0.957212i | 0.0419094 | − | 0.999121i | \(-0.486656\pi\) |
−0.999121 | + | 0.0419094i | \(0.986656\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 427.630i | 0.686405i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 224.481 | 0.359170 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 177.821 | − | 177.821i | 0.282705 | − | 0.282705i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 845.724i | 1.34029i | 0.742229 | + | 0.670146i | \(0.233769\pi\) | ||||
−0.742229 | + | 0.670146i | \(0.766231\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 960.067 | − | 960.067i | 1.51192 | − | 1.51192i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 156.555 | − | 156.555i | 0.245770 | − | 0.245770i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1167.54i | − | 1.82143i | −0.413035 | − | 0.910715i | \(-0.635531\pi\) | ||
0.413035 | − | 0.910715i | \(-0.364469\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −296.182 | + | 296.182i | −0.460626 | + | 0.460626i | −0.898861 | − | 0.438235i | \(-0.855604\pi\) |
0.438235 | + | 0.898861i | \(0.355604\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 113.278 | 0.175082 | 0.0875412 | − | 0.996161i | \(-0.472099\pi\) | ||||
0.0875412 | + | 0.996161i | \(0.472099\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.8562i | − | 0.0228909i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.6005 | − | 24.6005i | −0.0376730 | − | 0.0376730i | 0.688019 | − | 0.725692i | \(-0.258480\pi\) |
−0.725692 | + | 0.688019i | \(0.758480\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −661.689 | −1.01021 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 430.149 | + | 430.149i | 0.652730 | + | 0.652730i | 0.953650 | − | 0.300919i | \(-0.0972935\pi\) |
−0.300919 | + | 0.953650i | \(0.597293\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −755.093 | − | 755.093i | −1.14235 | − | 1.14235i | −0.988019 | − | 0.154330i | \(-0.950678\pi\) |
−0.154330 | − | 0.988019i | \(-0.549322\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1600.05 | 2.40609 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 737.305 | + | 737.305i | 1.10540 | + | 1.10540i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.3180i | 0.0287899i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −148.466 | −0.220604 | −0.110302 | − | 0.993898i | \(-0.535182\pi\) | ||||
−0.110302 | + | 0.993898i | \(0.535182\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −422.759 | + | 422.759i | −0.624459 | + | 0.624459i | −0.946668 | − | 0.322209i | \(-0.895575\pi\) |
0.322209 | + | 0.946668i | \(0.395575\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 38.9862i | − | 0.0574171i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −473.364 | + | 473.364i | −0.693066 | + | 0.693066i | −0.962905 | − | 0.269839i | \(-0.913029\pi\) |
0.269839 | + | 0.962905i | \(0.413029\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 72.1840 | − | 72.1840i | 0.105378 | − | 0.105378i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1630.42i | 2.36636i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −286.969 | + | 286.969i | −0.415295 | + | 0.415295i | −0.883579 | − | 0.468283i | \(-0.844873\pi\) |
0.468283 | + | 0.883579i | \(0.344873\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1464.63 | −2.10739 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 18.3353i | − | 0.0263060i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 490.554 | + | 490.554i | 0.699791 | + | 0.699791i | 0.964365 | − | 0.264574i | \(-0.0852314\pi\) |
−0.264574 | + | 0.964365i | \(0.585231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1126.44 | 1.60233 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 290.319 | + | 290.319i | 0.410635 | + | 0.410635i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −471.995 | − | 471.995i | −0.665719 | − | 0.665719i | 0.291003 | − | 0.956722i | \(-0.406011\pi\) |
−0.956722 | + | 0.291003i | \(0.906011\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1050.40 | −1.47321 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −366.038 | − | 366.038i | −0.511942 | − | 0.511942i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1035.64i | − | 1.44040i | −0.693769 | − | 0.720198i | \(-0.744051\pi\) | ||
0.693769 | − | 0.720198i | \(-0.255949\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1465.53 | −2.03263 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 775.602 | − | 775.602i | 1.06980 | − | 1.06980i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 172.311i | − | 0.237016i | −0.992953 | − | 0.118508i | \(-0.962189\pi\) | ||
0.992953 | − | 0.118508i | \(-0.0378112\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −58.3395 | + | 58.3395i | −0.0798078 | + | 0.0798078i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 729.510 | − | 729.510i | 0.995239 | − | 0.995239i | −0.00474987 | − | 0.999989i | \(-0.501512\pi\) |
0.999989 | + | 0.00474987i | \(0.00151193\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 233.730i | − | 0.317137i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −183.822 | + | 183.822i | −0.248745 | + | 0.248745i | −0.820455 | − | 0.571711i | \(-0.806280\pi\) |
0.571711 | + | 0.820455i | \(0.306280\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1276.92 | 1.71860 | 0.859300 | − | 0.511471i | \(-0.170899\pi\) | ||||
0.859300 | + | 0.511471i | \(0.170899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 115.811i | − | 0.155451i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −274.553 | − | 274.553i | −0.366560 | − | 0.366560i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −841.133 | −1.12002 | −0.560009 | − | 0.828487i | \(-0.689202\pi\) | ||||
−0.560009 | + | 0.828487i | \(0.689202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1001.54 | + | 1001.54i | 1.32654 | + | 1.32654i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −695.488 | − | 695.488i | −0.918743 | − | 0.918743i | 0.0781952 | − | 0.996938i | \(-0.475084\pi\) |
−0.996938 | + | 0.0781952i | \(0.975084\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −449.501 | −0.590671 | −0.295335 | − | 0.955394i | \(-0.595431\pi\) | ||||
−0.295335 | + | 0.955394i | \(0.595431\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 724.918 | + | 724.918i | 0.950090 | + | 0.950090i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 79.6500i | 0.103846i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1445.97 | −1.88033 | −0.940163 | − | 0.340725i | \(-0.889328\pi\) | ||||
−0.940163 | + | 0.340725i | \(0.889328\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −186.543 | + | 186.543i | −0.241323 | + | 0.241323i | −0.817397 | − | 0.576074i | \(-0.804584\pi\) |
0.576074 | + | 0.817397i | \(0.304584\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1104.96i | 1.42575i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58.0738 | − | 58.0738i | 0.0745492 | − | 0.0745492i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −242.412 | + | 242.412i | −0.310386 | + | 0.310386i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 640.602i | − | 0.816053i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −753.754 | + | 753.754i | −0.957756 | + | 0.957756i | −0.999143 | − | 0.0413871i | \(-0.986822\pi\) |
0.0413871 | + | 0.999143i | \(0.486822\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.6829 | 0.0375258 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 103.572i | − | 0.130607i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 531.870 | + | 531.870i | 0.667340 | + | 0.667340i | 0.957100 | − | 0.289759i | \(-0.0935752\pi\) |
−0.289759 | + | 0.957100i | \(0.593575\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −225.184 | −0.281833 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −265.679 | − | 265.679i | −0.330858 | − | 0.330858i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1478.19 | − | 1478.19i | −1.83626 | − | 1.83626i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 540.279 | 0.667836 | 0.333918 | − | 0.942602i | \(-0.391629\pi\) | ||||
0.333918 | + | 0.942602i | \(0.391629\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −702.871 | − | 702.871i | −0.866672 | − | 0.866672i | 0.125430 | − | 0.992102i | \(-0.459969\pi\) |
−0.992102 | + | 0.125430i | \(0.959969\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 970.594i | − | 1.19091i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −369.560 | −0.452338 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 286.031 | − | 286.031i | 0.348393 | − | 0.348393i | −0.511117 | − | 0.859511i | \(-0.670768\pi\) |
0.859511 | + | 0.511117i | \(0.170768\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 215.600i | 0.261969i | 0.991384 | + | 0.130984i | \(0.0418138\pi\) | ||||
−0.991384 | + | 0.130984i | \(0.958186\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 375.162 | − | 375.162i | 0.453642 | − | 0.453642i | −0.442920 | − | 0.896561i | \(-0.646057\pi\) |
0.896561 | + | 0.442920i | \(0.146057\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.5151 | + | 22.5151i | −0.0271594 | + | 0.0271594i | −0.720556 | − | 0.693397i | \(-0.756113\pi\) |
0.693397 | + | 0.720556i | \(0.256113\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 68.8929i | − | 0.0827046i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −480.370 | + | 480.370i | −0.575294 | + | 0.575294i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1139.61 | 1.35830 | 0.679151 | − | 0.733999i | \(-0.262348\pi\) | ||||
0.679151 | + | 0.733999i | \(0.262348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 82.4023i | 0.0979814i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1028.41 | + | 1028.41i | 1.21705 | + | 1.21705i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −846.821 | −0.999788 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1040.64 | − | 1040.64i | −1.22285 | − | 1.22285i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 405.464 | + | 405.464i | 0.475339 | + | 0.475339i | 0.903637 | − | 0.428298i | \(-0.140887\pi\) |
−0.428298 | + | 0.903637i | \(0.640887\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1006.21 | 1.17411 | 0.587056 | − | 0.809546i | \(-0.300287\pi\) | ||||
0.587056 | + | 0.809546i | \(0.300287\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −626.283 | − | 626.283i | −0.729083 | − | 0.729083i | 0.241354 | − | 0.970437i | \(-0.422409\pi\) |
−0.970437 | + | 0.241354i | \(0.922409\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 926.795i | − | 1.07392i | −0.843607 | − | 0.536961i | \(-0.819572\pi\) | ||
0.843607 | − | 0.536961i | \(-0.180428\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2387.76 | 2.76041 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −240.632 | + | 240.632i | −0.276907 | + | 0.276907i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1253.12i | 1.43872i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −478.000 | + | 478.000i | −0.546285 | + | 0.546285i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 558.537 | − | 558.537i | 0.636872 | − | 0.636872i | −0.312911 | − | 0.949783i | \(-0.601304\pi\) |
0.949783 | + | 0.312911i | \(0.101304\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 969.827i | 1.10083i | 0.834893 | + | 0.550413i | \(0.185530\pi\) | ||||
−0.834893 | + | 0.550413i | \(0.814470\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −549.585 | + | 549.585i | −0.622407 | + | 0.622407i | −0.946146 | − | 0.323739i | \(-0.895060\pi\) |
0.323739 | + | 0.946146i | \(0.395060\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1552.40 | −1.75017 | −0.875086 | − | 0.483968i | \(-0.839195\pi\) | ||||
−0.875086 | + | 0.483968i | \(0.839195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1353.89i | − | 1.52293i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −713.232 | − | 713.232i | −0.798692 | − | 0.798692i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −952.173 | −1.06388 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −657.760 | − | 657.760i | −0.731657 | − | 0.731657i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 358.737 | + | 358.737i | 0.398154 | + | 0.398154i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.3687 | 0.0225069 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 451.019 | + | 451.019i | 0.497265 | + | 0.497265i | 0.910586 | − | 0.413321i | \(-0.135631\pi\) |
−0.413321 | + | 0.910586i | \(0.635631\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1490.19i | 1.63578i | 0.575378 | + | 0.817888i | \(0.304855\pi\) | ||||
−0.575378 | + | 0.817888i | \(0.695145\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −441.494 | −0.483565 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −466.557 | + | 466.557i | −0.508786 | + | 0.508786i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 949.287i | − | 1.03296i | −0.856300 | − | 0.516478i | \(-0.827243\pi\) | ||
0.856300 | − | 0.516478i | \(-0.172757\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1299.67 | − | 1299.67i | 1.40809 | − | 1.40809i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1094.70 | + | 1094.70i | −1.18346 | + | 1.18346i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1078.41i | − | 1.16083i | −0.814322 | − | 0.580413i | \(-0.802891\pi\) | ||
0.814322 | − | 0.580413i | \(-0.197109\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 218.206 | − | 218.206i | 0.234378 | − | 0.234378i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −161.077 | −0.172275 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1158.42i | − | 1.23631i | −0.786056 | − | 0.618155i | \(-0.787880\pi\) | ||
0.786056 | − | 0.618155i | \(-0.212120\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1027.40 | − | 1027.40i | −1.09181 | − | 1.09181i | −0.995335 | − | 0.0964770i | \(-0.969243\pi\) |
−0.0964770 | − | 0.995335i | \(-0.530757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −107.302 | −0.113788 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −890.208 | − | 890.208i | −0.940030 | − | 0.940030i | 0.0582710 | − | 0.998301i | \(-0.481441\pi\) |
−0.998301 | + | 0.0582710i | \(0.981441\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1424.41 | + | 1424.41i | 1.50096 | + | 1.50096i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −566.070 | −0.593987 | −0.296994 | − | 0.954879i | \(-0.595984\pi\) | ||||
−0.296994 | + | 0.954879i | \(0.595984\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 453.397 | + | 453.397i | 0.474761 | + | 0.474761i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 101.794i | − | 0.106146i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.9259 | −0.0248968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 504.171 | − | 504.171i | 0.522457 | − | 0.522457i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 461.918i | 0.477682i | 0.971059 | + | 0.238841i | \(0.0767674\pi\) | ||||
−0.971059 | + | 0.238841i | \(0.923233\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −703.059 | + | 703.059i | −0.724057 | + | 0.724057i | −0.969429 | − | 0.245372i | \(-0.921090\pi\) |
0.245372 | + | 0.969429i | \(0.421090\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1032.71 | + | 1032.71i | −1.06137 | + | 1.06137i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1020.60i | − | 1.04462i | −0.852755 | − | 0.522311i | \(-0.825070\pi\) | ||
0.852755 | − | 0.522311i | \(-0.174930\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 136.352 | − | 136.352i | 0.139276 | − | 0.139276i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −837.639 | −0.852125 | −0.426063 | − | 0.904694i | \(-0.640100\pi\) | ||||
−0.426063 | + | 0.904694i | \(0.640100\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 96.6435i | − | 0.0981152i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 341.414 | + | 341.414i | 0.345211 | + | 0.345211i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 273.535 | 0.276019 | 0.138009 | − | 0.990431i | \(-0.455930\pi\) | ||||
0.138009 | + | 0.990431i | \(0.455930\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −712.013 | − | 712.013i | −0.715591 | − | 0.715591i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −77.9043 | − | 77.9043i | −0.0781387 | − | 0.0781387i | 0.666957 | − | 0.745096i | \(-0.267596\pi\) |
−0.745096 | + | 0.666957i | \(0.767596\pi\) | |||||||
\(998\) | 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 | 1152.3.j.a.737.2 | 32 | ||
3.2 | odd | 2 | inner | 1152.3.j.a.737.15 | 32 | ||
4.3 | odd | 2 | 1152.3.j.b.737.2 | 32 | |||
8.3 | odd | 2 | 576.3.j.a.305.15 | 32 | |||
8.5 | even | 2 | 144.3.j.a.53.2 | ✓ | 32 | ||
12.11 | even | 2 | 1152.3.j.b.737.15 | 32 | |||
16.3 | odd | 4 | 1152.3.j.b.161.15 | 32 | |||
16.5 | even | 4 | 144.3.j.a.125.15 | yes | 32 | ||
16.11 | odd | 4 | 576.3.j.a.17.2 | 32 | |||
16.13 | even | 4 | inner | 1152.3.j.a.161.15 | 32 | ||
24.5 | odd | 2 | 144.3.j.a.53.15 | yes | 32 | ||
24.11 | even | 2 | 576.3.j.a.305.2 | 32 | |||
48.5 | odd | 4 | 144.3.j.a.125.2 | yes | 32 | ||
48.11 | even | 4 | 576.3.j.a.17.15 | 32 | |||
48.29 | odd | 4 | inner | 1152.3.j.a.161.2 | 32 | ||
48.35 | even | 4 | 1152.3.j.b.161.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.j.a.53.2 | ✓ | 32 | 8.5 | even | 2 | ||
144.3.j.a.53.15 | yes | 32 | 24.5 | odd | 2 | ||
144.3.j.a.125.2 | yes | 32 | 48.5 | odd | 4 | ||
144.3.j.a.125.15 | yes | 32 | 16.5 | even | 4 | ||
576.3.j.a.17.2 | 32 | 16.11 | odd | 4 | |||
576.3.j.a.17.15 | 32 | 48.11 | even | 4 | |||
576.3.j.a.305.2 | 32 | 24.11 | even | 2 | |||
576.3.j.a.305.15 | 32 | 8.3 | odd | 2 | |||
1152.3.j.a.161.2 | 32 | 48.29 | odd | 4 | inner | ||
1152.3.j.a.161.15 | 32 | 16.13 | even | 4 | inner | ||
1152.3.j.a.737.2 | 32 | 1.1 | even | 1 | trivial | ||
1152.3.j.a.737.15 | 32 | 3.2 | odd | 2 | inner | ||
1152.3.j.b.161.2 | 32 | 48.35 | even | 4 | |||
1152.3.j.b.161.15 | 32 | 16.3 | odd | 4 | |||
1152.3.j.b.737.2 | 32 | 4.3 | odd | 2 | |||
1152.3.j.b.737.15 | 32 | 12.11 | even | 2 |