Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(5615,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 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("6048.5615");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.j (of order \(2\), degree \(1\), 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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5615.9 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.d.5615.10 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | −2.85878 | −1.27849 | −0.639244 | − | 0.769004i | \(-0.720753\pi\) | ||||
−0.639244 | + | 0.769004i | \(0.720753\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.98479i | 1.50297i | 0.659749 | + | 0.751486i | \(0.270663\pi\) | ||||
−0.659749 | + | 0.751486i | \(0.729337\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.35304i | 0.652615i | 0.945264 | + | 0.326308i | \(0.105805\pi\) | ||||
−0.945264 | + | 0.326308i | \(0.894195\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8.19706i | 1.98808i | 0.109021 | + | 0.994039i | \(0.465228\pi\) | ||||
−0.109021 | + | 0.994039i | \(0.534772\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.90589 | −1.35491 | −0.677453 | − | 0.735566i | \(-0.736916\pi\) | ||||
−0.677453 | + | 0.735566i | \(0.736916\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.43848 | 0.925487 | 0.462744 | − | 0.886492i | \(-0.346865\pi\) | ||||
0.462744 | + | 0.886492i | \(0.346865\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.17265 | 0.634530 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.41440 | −1.19112 | −0.595562 | − | 0.803309i | \(-0.703071\pi\) | ||||
−0.595562 | + | 0.803309i | \(0.703071\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.31678i | 0.595710i | 0.954611 | + | 0.297855i | \(0.0962713\pi\) | ||||
−0.954611 | + | 0.297855i | \(0.903729\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.85878i | 0.483223i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 5.51080i | − 0.905970i | −0.891518 | − | 0.452985i | \(-0.850359\pi\) | ||||
0.891518 | − | 0.452985i | \(-0.149641\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 3.41549i | − 0.533410i | −0.963778 | − | 0.266705i | \(-0.914065\pi\) | ||||
0.963778 | − | 0.266705i | \(-0.0859349\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.37638 | −0.209895 | −0.104948 | − | 0.994478i | \(-0.533468\pi\) | ||||
−0.104948 | + | 0.994478i | \(0.533468\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.60102 | 0.379398 | 0.189699 | − | 0.981842i | \(-0.439249\pi\) | ||||
0.189699 | + | 0.981842i | \(0.439249\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3184 | 1.82942 | 0.914710 | − | 0.404110i | \(-0.132419\pi\) | ||||
0.914710 | + | 0.404110i | \(0.132419\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 14.2505i | − 1.92153i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.6485i | 1.38631i | 0.720788 | + | 0.693156i | \(0.243780\pi\) | ||||
−0.720788 | + | 0.693156i | \(0.756220\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.41211i | − 0.180802i | −0.995905 | − | 0.0904011i | \(-0.971185\pi\) | ||||
0.995905 | − | 0.0904011i | \(-0.0288149\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 6.72683i | − 0.834361i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.221252 | −0.0270303 | −0.0135151 | − | 0.999909i | \(-0.504302\pi\) | ||||
−0.0135151 | + | 0.999909i | \(0.504302\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.398786 | −0.0473271 | −0.0236636 | − | 0.999720i | \(-0.507533\pi\) | ||||
−0.0236636 | + | 0.999720i | \(0.507533\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7893 | −1.26279 | −0.631397 | − | 0.775460i | \(-0.717518\pi\) | ||||
−0.631397 | + | 0.775460i | \(0.717518\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.98479 | 0.568070 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.76133i | 1.09824i | 0.835745 | + | 0.549118i | \(0.185036\pi\) | ||||
−0.835745 | + | 0.549118i | \(0.814964\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 2.06831i | − 0.227027i | −0.993536 | − | 0.113513i | \(-0.963789\pi\) | ||||
0.993536 | − | 0.113513i | \(-0.0362105\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 23.4336i | − 2.54173i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 17.6684i | − 1.87284i | −0.350875 | − | 0.936422i | \(-0.614116\pi\) | ||||
0.350875 | − | 0.936422i | \(-0.385884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.35304 | 0.246665 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.8837 | 1.73223 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.62651 | −0.368217 | −0.184108 | − | 0.982906i | \(-0.558940\pi\) | ||||
−0.184108 | + | 0.982906i | \(0.558940\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4729 | 1.04209 | 0.521047 | − | 0.853528i | \(-0.325541\pi\) | ||||
0.521047 | + | 0.853528i | \(0.325541\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.50892i | 0.444277i | 0.975015 | + | 0.222139i | \(0.0713037\pi\) | ||||
−0.975015 | + | 0.222139i | \(0.928696\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.82640i | 0.659933i | 0.943993 | + | 0.329966i | \(0.107037\pi\) | ||||
−0.943993 | + | 0.329966i | \(0.892963\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 13.1273i | − 1.25737i | −0.777660 | − | 0.628685i | \(-0.783593\pi\) | ||||
0.777660 | − | 0.628685i | \(-0.216407\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 5.30759i | − 0.499297i | −0.968337 | − | 0.249648i | \(-0.919685\pi\) | ||||
0.968337 | − | 0.249648i | \(-0.0803150\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.6887 | −1.18322 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.19706 | 0.751423 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.8482 | −1.25892 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.22400 | 0.467248 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.80347i | 0.160032i | 0.996794 | + | 0.0800160i | \(0.0254972\pi\) | ||||
−0.996794 | + | 0.0800160i | \(0.974503\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.93535i | 0.868056i | 0.900899 | + | 0.434028i | \(0.142908\pi\) | ||||
−0.900899 | + | 0.434028i | \(0.857092\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.90589i | 0.512106i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1.16258i | − 0.0993261i | −0.998766 | − | 0.0496630i | \(-0.984185\pi\) | ||||
0.998766 | − | 0.0496630i | \(-0.0158147\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.0996 | −1.45037 | −0.725186 | − | 0.688553i | \(-0.758246\pi\) | ||||
−0.725186 | + | 0.688553i | \(0.758246\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.7294 | −0.980863 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.3374 | 1.52284 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.1689 | −1.89807 | −0.949034 | − | 0.315173i | \(-0.897937\pi\) | ||||
−0.949034 | + | 0.315173i | \(0.897937\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 1.67795i | − 0.136549i | −0.997667 | − | 0.0682747i | \(-0.978251\pi\) | ||||
0.997667 | − | 0.0682747i | \(-0.0217494\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 9.48195i | − 0.761608i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.22459i | 0.177542i | 0.996052 | + | 0.0887710i | \(0.0282939\pi\) | ||||
−0.996052 | + | 0.0887710i | \(0.971706\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 4.43848i | − 0.349801i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.3358 | 1.35785 | 0.678924 | − | 0.734209i | \(-0.262447\pi\) | ||||
0.678924 | + | 0.734209i | \(0.262447\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.4429 | −1.65930 | −0.829650 | − | 0.558284i | \(-0.811460\pi\) | ||||
−0.829650 | + | 0.558284i | \(0.811460\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.46321 | 0.574093 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.70545 | −0.737892 | −0.368946 | − | 0.929451i | \(-0.620281\pi\) | ||||
−0.368946 | + | 0.929451i | \(0.620281\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.17265i | − 0.239830i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 14.7350i | − 1.10134i | −0.834722 | − | 0.550671i | \(-0.814372\pi\) | ||||
0.834722 | − | 0.550671i | \(-0.185628\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 17.7055i | − 1.31604i | −0.753001 | − | 0.658019i | \(-0.771395\pi\) | ||||
0.753001 | − | 0.658019i | \(-0.228605\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.7542i | 1.15827i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −40.8606 | −2.98803 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.9941 | −1.30201 | −0.651003 | − | 0.759075i | \(-0.725652\pi\) | ||||
−0.651003 | + | 0.759075i | \(0.725652\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.8594 | −1.78942 | −0.894709 | − | 0.446649i | \(-0.852617\pi\) | ||||
−0.894709 | + | 0.446649i | \(0.852617\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.4145 | 1.24073 | 0.620367 | − | 0.784312i | \(-0.286984\pi\) | ||||
0.620367 | + | 0.784312i | \(0.286984\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 20.0065i | − 1.41823i | −0.705095 | − | 0.709113i | \(-0.749096\pi\) | ||||
0.705095 | − | 0.709113i | \(-0.250904\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.41440i | 0.450203i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.76415i | 0.681958i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 29.4397i | − 2.03638i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.0542 | 1.03637 | 0.518186 | − | 0.855268i | \(-0.326608\pi\) | ||||
0.518186 | + | 0.855268i | \(0.326608\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.93476 | 0.268349 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.31678 | 0.225157 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.2880 | −1.29745 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.7615i | 0.854570i | 0.904117 | + | 0.427285i | \(0.140530\pi\) | ||||
−0.904117 | + | 0.427285i | \(0.859470\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.7167i | 1.70688i | 0.521194 | + | 0.853438i | \(0.325487\pi\) | ||||
−0.521194 | + | 0.853438i | \(0.674513\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.7033i | 0.707293i | 0.935379 | + | 0.353647i | \(0.115058\pi\) | ||||
−0.935379 | + | 0.353647i | \(0.884942\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 5.55917i | − 0.364194i | −0.983281 | − | 0.182097i | \(-0.941712\pi\) | ||||
0.983281 | − | 0.182097i | \(-0.0582884\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.43577 | −0.485056 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.7187 | −1.34018 | −0.670092 | − | 0.742278i | \(-0.733745\pi\) | ||||
−0.670092 | + | 0.742278i | \(0.733745\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.03091 | 0.388485 | 0.194242 | − | 0.980954i | \(-0.437775\pi\) | ||||
0.194242 | + | 0.980954i | \(0.437775\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.85878 | 0.182641 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 13.8968i | − 0.884232i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.01117i | 0.505660i | 0.967511 | + | 0.252830i | \(0.0813614\pi\) | ||||
−0.967511 | + | 0.252830i | \(0.918639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.1249i | 1.39098i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.1009i | 0.879590i | 0.898098 | + | 0.439795i | \(0.144949\pi\) | ||||
−0.898098 | + | 0.439795i | \(0.855051\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.51080 | −0.342424 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.6348 | 1.51905 | 0.759524 | − | 0.650479i | \(-0.225432\pi\) | ||||
0.759524 | + | 0.650479i | \(0.225432\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.0744 | −2.33889 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.64498 | −0.588065 | −0.294032 | − | 0.955795i | \(-0.594997\pi\) | ||||
−0.294032 | + | 0.955795i | \(0.594997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 13.3466i | − 0.810751i | −0.914150 | − | 0.405375i | \(-0.867141\pi\) | ||||
0.914150 | − | 0.405375i | \(-0.132859\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.8150i | 0.953681i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 18.5217i | − 1.11286i | −0.830895 | − | 0.556429i | \(-0.812171\pi\) | ||||
0.830895 | − | 0.556429i | \(-0.187829\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 18.7455i | − 1.11826i | −0.829079 | − | 0.559131i | \(-0.811135\pi\) | ||||
0.829079 | − | 0.559131i | \(-0.188865\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.32063 | 0.137947 | 0.0689736 | − | 0.997618i | \(-0.478028\pi\) | ||||
0.0689736 | + | 0.997618i | \(0.478028\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.41549 | −0.201610 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −50.1918 | −2.95246 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.61125 | −0.210972 | −0.105486 | − | 0.994421i | \(-0.533640\pi\) | ||||
−0.105486 | + | 0.994421i | \(0.533640\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 30.4417i | − 1.77238i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10.4439i | 0.603987i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.37638i | 0.0793330i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.03692i | 0.231153i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.9273 | 1.13731 | 0.568656 | − | 0.822576i | \(-0.307464\pi\) | ||||
0.568656 | + | 0.822576i | \(0.307464\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.68722 | −0.265788 | −0.132894 | − | 0.991130i | \(-0.542427\pi\) | ||||
−0.132894 | + | 0.991130i | \(0.542427\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.2179 | −0.747118 | −0.373559 | − | 0.927606i | \(-0.621863\pi\) | ||||
−0.373559 | + | 0.927606i | \(0.621863\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.8162 | −0.775995 | −0.387997 | − | 0.921660i | \(-0.626833\pi\) | ||||
−0.387997 | + | 0.921660i | \(0.626833\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 31.9745i | − 1.79023i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 48.4110i | − 2.69366i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.46537i | 0.414104i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 2.60102i | − 0.143399i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.70429 | −0.533396 | −0.266698 | − | 0.963780i | \(-0.585933\pi\) | ||||
−0.266698 | + | 0.963780i | \(0.585933\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.632513 | 0.0345579 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.04484 | 0.274810 | 0.137405 | − | 0.990515i | \(-0.456124\pi\) | ||||
0.137405 | + | 0.990515i | \(0.456124\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.5334 | −0.895336 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2.01718i | − 0.108288i | −0.998533 | − | 0.0541440i | \(-0.982757\pi\) | ||||
0.998533 | − | 0.0541440i | \(-0.0172430\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.528557i | 0.0282930i | 0.999900 | + | 0.0141465i | \(0.00450312\pi\) | ||||
−0.999900 | + | 0.0141465i | \(0.995497\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.3448i | 0.550600i | 0.961358 | + | 0.275300i | \(0.0887772\pi\) | ||||
−0.961358 | + | 0.275300i | \(0.911223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.14004 | 0.0605072 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.62306 | −0.0856618 | −0.0428309 | − | 0.999082i | \(-0.513638\pi\) | ||||
−0.0428309 | + | 0.999082i | \(0.513638\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.8796 | 0.835768 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.8443 | 1.61447 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 33.5635i | − 1.75200i | −0.482312 | − | 0.875999i | \(-0.660203\pi\) | ||||
0.482312 | − | 0.875999i | \(-0.339797\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 13.3184i | − 0.691456i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 20.4199i | − 1.05730i | −0.848840 | − | 0.528650i | \(-0.822698\pi\) | ||||
0.848840 | − | 0.528650i | \(-0.177302\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 15.0933i | − 0.777346i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.6529 | −1.52317 | −0.761583 | − | 0.648068i | \(-0.775577\pi\) | ||||
−0.761583 | + | 0.648068i | \(0.775577\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.82347 | −0.246468 | −0.123234 | − | 0.992378i | \(-0.539327\pi\) | ||||
−0.123234 | + | 0.992378i | \(0.539327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.2505 | −0.726270 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.5242 | −0.939214 | −0.469607 | − | 0.882876i | \(-0.655604\pi\) | ||||
−0.469607 | + | 0.882876i | \(0.655604\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.3825i | 1.83994i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 27.9056i | − 1.40408i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 2.91585i | − 0.146342i | −0.997319 | − | 0.0731712i | \(-0.976688\pi\) | ||||
0.997319 | − | 0.0731712i | \(-0.0233119\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 2.62856i | − 0.131264i | −0.997844 | − | 0.0656319i | \(-0.979094\pi\) | ||||
0.997844 | − | 0.0656319i | \(-0.0209063\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.80450 | −0.388770 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.4702 | 1.36165 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0556 | 1.28836 | 0.644182 | − | 0.764872i | \(-0.277198\pi\) | ||||
0.644182 | + | 0.764872i | \(0.277198\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.6485 | 0.523977 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.91286i | 0.290251i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 9.43185i | − 0.460776i | −0.973099 | − | 0.230388i | \(-0.926000\pi\) | ||||
0.973099 | − | 0.230388i | \(-0.0739995\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 22.3767i | − 1.09057i | −0.838249 | − | 0.545287i | \(-0.816421\pi\) | ||||
0.838249 | − | 0.545287i | \(-0.183579\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.0064i | 1.26150i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.41211 | −0.0683368 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.1600 | 0.682061 | 0.341030 | − | 0.940052i | \(-0.389224\pi\) | ||||
0.341030 | + | 0.940052i | \(0.389224\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.47617 | 0.455396 | 0.227698 | − | 0.973732i | \(-0.426880\pi\) | ||||
0.227698 | + | 0.973732i | \(0.426880\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.2132 | −1.25395 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 5.40493i | − 0.257963i | −0.991647 | − | 0.128982i | \(-0.958829\pi\) | ||||
0.991647 | − | 0.128982i | \(-0.0411709\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 28.2417i | − 1.34180i | −0.741546 | − | 0.670902i | \(-0.765907\pi\) | ||||
0.741546 | − | 0.670902i | \(-0.234093\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 50.5101i | 2.39441i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.0885i | 1.46716i | 0.679605 | + | 0.733578i | \(0.262151\pi\) | ||||
−0.679605 | + | 0.733578i | \(0.737849\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.0255 | 0.801700 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.72683 | −0.315359 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.4214 | 0.721383 | 0.360691 | − | 0.932685i | \(-0.382541\pi\) | ||||
0.360691 | + | 0.932685i | \(0.382541\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.7699 | 1.01392 | 0.506962 | − | 0.861968i | \(-0.330768\pi\) | ||||
0.506962 | + | 0.861968i | \(0.330768\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 33.1540i | − 1.54080i | −0.637563 | − | 0.770398i | \(-0.720057\pi\) | ||||
0.637563 | − | 0.770398i | \(-0.279943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.3233i | 1.07927i | 0.841898 | + | 0.539637i | \(0.181439\pi\) | ||||
−0.841898 | + | 0.539637i | \(0.818561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.221252i | 0.0102165i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 6.86095i | − 0.315467i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −18.7373 | −0.859728 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.7837 | −1.36085 | −0.680426 | − | 0.732817i | \(-0.738205\pi\) | ||||
−0.680426 | + | 0.732817i | \(0.738205\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.9671 | 0.591250 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.3674 | 0.470761 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.61251i | 0.344956i | 0.985013 | + | 0.172478i | \(0.0551773\pi\) | ||||
−0.985013 | + | 0.172478i | \(0.944823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.4249i | 0.470471i | 0.971938 | + | 0.235236i | \(0.0755862\pi\) | ||||
−0.971938 | + | 0.235236i | \(0.924414\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 52.5792i | − 2.36805i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.398786i | 0.0178880i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.3685 | 1.09088 | 0.545441 | − | 0.838149i | \(-0.316362\pi\) | ||||
0.545441 | + | 0.838149i | \(0.316362\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 38.3668 | 1.71069 | 0.855345 | − | 0.518058i | \(-0.173345\pi\) | ||||
0.855345 | + | 0.518058i | \(0.173345\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.9398 | −1.33231 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.6708 | 0.517298 | 0.258649 | − | 0.965971i | \(-0.416723\pi\) | ||||
0.258649 | + | 0.965971i | \(0.416723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.7893i | 0.477291i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 12.8900i | − 0.568003i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.9656i | 0.570225i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 8.09319i | − 0.354569i | −0.984160 | − | 0.177284i | \(-0.943269\pi\) | ||||
0.984160 | − | 0.177284i | \(-0.0567313\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.5864 | 0.550363 | 0.275181 | − | 0.961392i | \(-0.411262\pi\) | ||||
0.275181 | + | 0.961392i | \(0.411262\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.1878 | −1.18432 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.29989 | −0.143473 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.03678 | 0.348112 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 19.5152i | − 0.843716i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 4.98479i | − 0.214710i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 33.6824i | − 1.44812i | −0.689738 | − | 0.724059i | \(-0.742274\pi\) | ||||
0.689738 | − | 0.724059i | \(-0.257726\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 37.5282i | 1.60753i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.7087 | 1.35576 | 0.677882 | − | 0.735170i | \(-0.262898\pi\) | ||||
0.677882 | + | 0.735170i | \(0.262898\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.8828 | 1.61386 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.76133 | 0.415094 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.0418 | −1.23054 | −0.615270 | − | 0.788316i | \(-0.710953\pi\) | ||||
−0.615270 | + | 0.788316i | \(0.710953\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 3.23867i | − 0.136981i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.5955i | 1.45803i | 0.684499 | + | 0.729013i | \(0.260021\pi\) | ||||
−0.684499 | + | 0.729013i | \(0.739979\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.1733i | 0.638344i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 44.7913i | 1.87775i | 0.344258 | + | 0.938875i | \(0.388131\pi\) | ||||
−0.344258 | + | 0.938875i | \(0.611869\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.8182 | 0.578276 | 0.289138 | − | 0.957287i | \(-0.406631\pi\) | ||||
0.289138 | + | 0.957287i | \(0.406631\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.0818 | 0.587250 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.53927 | −0.105711 | −0.0528557 | − | 0.998602i | \(-0.516832\pi\) | ||||
−0.0528557 | + | 0.998602i | \(0.516832\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.06831 | −0.0858081 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 66.3894i | 2.74957i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.23636i | 0.0510300i | 0.999674 | + | 0.0255150i | \(0.00812256\pi\) | ||||
−0.999674 | + | 0.0255150i | \(0.991877\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 19.5885i | − 0.807131i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 2.47202i | − 0.101514i | −0.998711 | − | 0.0507568i | \(-0.983837\pi\) | ||||
0.998711 | − | 0.0507568i | \(-0.0161633\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.4336 | −0.960685 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.80798 | 0.278166 | 0.139083 | − | 0.990281i | \(-0.455584\pi\) | ||||
0.139083 | + | 0.990281i | \(0.455584\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.857050 | −0.0349598 | −0.0174799 | − | 0.999847i | \(-0.505564\pi\) | ||||
−0.0174799 | + | 0.999847i | \(0.505564\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 39.5889 | 1.60952 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.9929i | 0.933252i | 0.884455 | + | 0.466626i | \(0.154531\pi\) | ||||
−0.884455 | + | 0.466626i | \(0.845469\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.12031i | 0.247601i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.9605i | 0.442691i | 0.975195 | + | 0.221346i | \(0.0710449\pi\) | ||||
−0.975195 | + | 0.221346i | \(0.928955\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.9140i | 0.640675i | 0.947304 | + | 0.320337i | \(0.103796\pi\) | ||||
−0.947304 | + | 0.320337i | \(0.896204\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.1115 | −0.969124 | −0.484562 | − | 0.874757i | \(-0.661021\pi\) | ||||
−0.484562 | + | 0.874757i | \(0.661021\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.6684 | −0.707869 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7975 | −1.23190 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 45.1723 | 1.80114 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0647i | 0.758955i | 0.925201 | + | 0.379477i | \(0.123896\pi\) | ||||
−0.925201 | + | 0.379477i | \(0.876104\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 5.15573i | − 0.204599i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.35304i | − 0.0932308i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 16.6996i | − 0.659595i | −0.944052 | − | 0.329797i | \(-0.893020\pi\) | ||||
0.944052 | − | 0.329797i | \(-0.106980\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.2897 | −0.602966 | −0.301483 | − | 0.953472i | \(-0.597482\pi\) | ||||
−0.301483 | + | 0.953472i | \(0.597482\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.6300 | −1.67596 | −0.837979 | − | 0.545702i | \(-0.816263\pi\) | ||||
−0.837979 | + | 0.545702i | \(0.816263\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −53.0804 | −2.08359 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.14973 | 0.201524 | 0.100762 | − | 0.994911i | \(-0.467872\pi\) | ||||
0.100762 | + | 0.994911i | \(0.467872\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 28.4030i | − 1.10980i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 0.965465i | − 0.0376092i | −0.999823 | − | 0.0188046i | \(-0.994014\pi\) | ||||
0.999823 | − | 0.0188046i | \(-0.00598604\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.54386i | 0.332318i | 0.986099 | + | 0.166159i | \(0.0531365\pi\) | ||||
−0.986099 | + | 0.166159i | \(0.946864\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 16.8837i | − 0.654721i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.4702 | −1.10237 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.03908 | 0.271741 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.8364 | 1.38139 | 0.690695 | − | 0.723146i | \(-0.257305\pi\) | ||||
0.690695 | + | 0.723146i | \(0.257305\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.3770 | 0.590985 | 0.295493 | − | 0.955345i | \(-0.404516\pi\) | ||||
0.295493 | + | 0.955345i | \(0.404516\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.62651i | 0.139173i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 31.3038i | − 1.19781i | −0.800822 | − | 0.598903i | \(-0.795604\pi\) | ||||
0.800822 | − | 0.598903i | \(-0.204396\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.32357i | 0.126987i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 31.3387i | 1.19391i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.1921 | −1.45289 | −0.726447 | − | 0.687222i | \(-0.758830\pi\) | ||||
−0.726447 | + | 0.687222i | \(0.758830\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 48.8842 | 1.85428 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.9970 | 1.06046 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.5040 | 1.71866 | 0.859331 | − | 0.511419i | \(-0.170880\pi\) | ||||
0.859331 | + | 0.511419i | \(0.170880\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.5462i | 1.22750i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 10.4729i | − 0.393875i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.7256i | 0.665698i | 0.942980 | + | 0.332849i | \(0.108010\pi\) | ||||
−0.942980 | + | 0.332849i | \(0.891990\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.7214i | 0.551322i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.5319 | 1.25402 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.0561 | 1.15820 | 0.579098 | − | 0.815258i | \(-0.303405\pi\) | ||||
0.579098 | + | 0.815258i | \(0.303405\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.50892 | 0.167921 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −20.3507 | −0.755804 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 7.88096i | − 0.292289i | −0.989263 | − | 0.146144i | \(-0.953314\pi\) | ||||
0.989263 | − | 0.146144i | \(-0.0466864\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 11.2822i | − 0.417288i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 31.2981i | − 1.15602i | −0.816029 | − | 0.578011i | \(-0.803829\pi\) | ||||
0.816029 | − | 0.578011i | \(-0.196171\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 1.10290i | − 0.0406257i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.91989 | −0.364909 | −0.182455 | − | 0.983214i | \(-0.558404\pi\) | ||||
−0.182455 | + | 0.983214i | \(0.558404\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.2085 | −0.778065 | −0.389032 | − | 0.921224i | \(-0.627191\pi\) | ||||
−0.389032 | + | 0.921224i | \(0.627191\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 66.2348 | 2.42666 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.82640 | 0.249431 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 31.2986i | − 1.14210i | −0.820915 | − | 0.571051i | \(-0.806536\pi\) | ||||
0.820915 | − | 0.571051i | \(-0.193464\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.79689i | 0.174577i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 50.1185i | − 1.82159i | −0.412863 | − | 0.910793i | \(-0.635471\pi\) | ||||
0.412863 | − | 0.910793i | \(-0.364529\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.4522i | 1.21264i | 0.795220 | + | 0.606321i | \(0.207355\pi\) | ||||
−0.795220 | + | 0.606321i | \(0.792645\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.1273 | −0.475241 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.0562 | −0.904728 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.8586 | −1.25703 | −0.628516 | − | 0.777797i | \(-0.716337\pi\) | ||||
−0.628516 | + | 0.777797i | \(0.716337\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.819156 | −0.0294630 | −0.0147315 | − | 0.999891i | \(-0.504689\pi\) | ||||
−0.0147315 | + | 0.999891i | \(0.504689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.5230i | 0.377996i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.1715i | 0.722720i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 1.98786i | − 0.0711314i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 6.35964i | − 0.226985i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.1948 | −0.755514 | −0.377757 | − | 0.925905i | \(-0.623305\pi\) | ||||
−0.377757 | + | 0.925905i | \(0.623305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.30759 | −0.188716 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.32275 | 0.117994 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.4236 | −0.369221 | −0.184611 | − | 0.982812i | \(-0.559102\pi\) | ||||
−0.184611 | + | 0.982812i | \(0.559102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.3207i | 0.754274i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 53.7825i | − 1.89794i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.6887i | 0.447217i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 6.79289i | − 0.238825i | −0.992845 | − | 0.119413i | \(-0.961899\pi\) | ||||
0.992845 | − | 0.119413i | \(-0.0381012\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.6600 | −0.549897 | −0.274949 | − | 0.961459i | \(-0.588661\pi\) | ||||
−0.274949 | + | 0.961459i | \(0.588661\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −49.5594 | −1.73599 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.12873 | 0.284388 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.83489 | −0.343240 | −0.171620 | − | 0.985163i | \(-0.554900\pi\) | ||||
−0.171620 | + | 0.985163i | \(0.554900\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.9492i | 0.590811i | 0.955372 | + | 0.295406i | \(0.0954548\pi\) | ||||
−0.955372 | + | 0.295406i | \(0.904545\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 54.3499i | 1.88993i | 0.327169 | + | 0.944966i | \(0.393905\pi\) | ||||
−0.327169 | + | 0.944966i | \(0.606095\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.679562i | 0.0236022i | 0.999930 | + | 0.0118011i | \(0.00375649\pi\) | ||||
−0.999930 | + | 0.0118011i | \(0.996244\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 8.19706i | − 0.284011i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 61.3006 | 2.12139 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.0696 | −1.59050 | −0.795249 | − | 0.606283i | \(-0.792660\pi\) | ||||
−0.795249 | + | 0.606283i | \(0.792660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.1445 | 0.418777 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.3357 | −0.733971 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.8482i | 0.475828i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 24.4596i | − 0.838463i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.6910i | 1.22204i | 0.791617 | + | 0.611018i | \(0.209240\pi\) | ||||
−0.791617 | + | 0.611018i | \(0.790760\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 27.4542i | − 0.937818i | −0.883247 | − | 0.468909i | \(-0.844647\pi\) | ||||
0.883247 | − | 0.468909i | \(-0.155353\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.8392 | 0.711025 | 0.355512 | − | 0.934672i | \(-0.384306\pi\) | ||||
0.355512 | + | 0.934672i | \(0.384306\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.8505 | 0.879960 | 0.439980 | − | 0.898008i | \(-0.354986\pi\) | ||||
0.439980 | + | 0.898008i | \(0.354986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.7458 | 0.943385 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.6582 | −1.65062 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 0.520615i | − 0.0176404i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 5.22400i | − 0.176603i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 12.7819i | − 0.431613i | −0.976436 | − | 0.215806i | \(-0.930762\pi\) | ||||
0.976436 | − | 0.215806i | \(-0.0692380\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 9.54473i | − 0.321570i | −0.986989 | − | 0.160785i | \(-0.948597\pi\) | ||||
0.986989 | − | 0.160785i | \(-0.0514026\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.8835 | 0.635479 | 0.317740 | − | 0.948178i | \(-0.397076\pi\) | ||||
0.317740 | + | 0.948178i | \(0.397076\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.9738 | −0.670654 | −0.335327 | − | 0.942102i | \(-0.608847\pi\) | ||||
−0.335327 | + | 0.942102i | \(0.608847\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.80347 | 0.0604864 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.3614 | −0.514049 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.1241i | 1.40805i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 21.2751i | − 0.709565i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 109.172i | 3.63703i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 50.6162i | 1.68254i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.50951 | −0.249349 | −0.124675 | − | 0.992198i | \(-0.539789\pi\) | ||||
−0.124675 | + | 0.992198i | \(0.539789\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.1774 | −1.09922 | −0.549609 | − | 0.835422i | \(-0.685223\pi\) | ||||
−0.549609 | + | 0.835422i | \(0.685223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.3101 | 0.341215 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.93535 | 0.328094 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.2043i | 0.435568i | 0.975997 | + | 0.217784i | \(0.0698829\pi\) | ||||
−0.975997 | + | 0.217784i | \(0.930117\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 0.938358i | − 0.0308864i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 17.4838i | − 0.574865i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.175426i | 0.00575553i | 0.999996 | + | 0.00287776i | \(0.000916022\pi\) | ||||
−0.999996 | + | 0.00287776i | \(0.999084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.90589 | 0.193558 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 116.812 | 3.82015 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.2203 | −0.333884 | −0.166942 | − | 0.985967i | \(-0.553389\pi\) | ||||
−0.166942 | + | 0.985967i | \(0.553389\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.9676 | −0.618327 | −0.309163 | − | 0.951009i | \(-0.600049\pi\) | ||||
−0.309163 | + | 0.951009i | \(0.600049\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 15.1596i | − 0.493664i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.01612i | 0.195497i | 0.995211 | + | 0.0977487i | \(0.0311642\pi\) | ||||
−0.995211 | + | 0.0977487i | \(0.968836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 25.3877i | − 0.824119i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 18.9690i | − 0.614468i | −0.951634 | − | 0.307234i | \(-0.900597\pi\) | ||||
0.951634 | − | 0.307234i | \(-0.0994034\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 51.4412 | 1.66460 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.16258 | −0.0375417 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.9990 | 0.645129 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 71.0677 | 2.28775 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 28.6527i | − 0.921408i | −0.887554 | − | 0.460704i | \(-0.847597\pi\) | ||||
0.887554 | − | 0.460704i | \(-0.152403\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 47.4986i | − 1.52430i | −0.647399 | − | 0.762151i | \(-0.724143\pi\) | ||||
0.647399 | − | 0.762151i | \(-0.275857\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.0996i | 0.548189i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.0015i | 1.27976i | 0.768474 | + | 0.639881i | \(0.221016\pi\) | ||||
−0.768474 | + | 0.639881i | \(0.778984\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 88.0732 | 2.81483 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.0829 | 0.704334 | 0.352167 | − | 0.935937i | \(-0.385445\pi\) | ||||
0.352167 | + | 0.935937i | \(0.385445\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −49.7844 | −1.58626 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.10902 | −0.194255 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.2351i | 0.547490i | 0.961802 | + | 0.273745i | \(0.0882625\pi\) | ||||
−0.961802 | + | 0.273745i | \(0.911738\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 57.1944i | 1.81318i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.9872i | 0.696342i | 0.937431 | + | 0.348171i | \(0.113197\pi\) | ||||
−0.937431 | + | 0.348171i | \(0.886803\pi\) | |||||||
\(998\) | 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 | 6048.2.j.d.5615.9 | 48 | ||
3.2 | odd | 2 | inner | 6048.2.j.d.5615.40 | 48 | ||
4.3 | odd | 2 | 1512.2.j.d.323.10 | yes | 48 | ||
8.3 | odd | 2 | inner | 6048.2.j.d.5615.39 | 48 | ||
8.5 | even | 2 | 1512.2.j.d.323.40 | yes | 48 | ||
12.11 | even | 2 | 1512.2.j.d.323.39 | yes | 48 | ||
24.5 | odd | 2 | 1512.2.j.d.323.9 | ✓ | 48 | ||
24.11 | even | 2 | inner | 6048.2.j.d.5615.10 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.d.323.9 | ✓ | 48 | 24.5 | odd | 2 | ||
1512.2.j.d.323.10 | yes | 48 | 4.3 | odd | 2 | ||
1512.2.j.d.323.39 | yes | 48 | 12.11 | even | 2 | ||
1512.2.j.d.323.40 | yes | 48 | 8.5 | even | 2 | ||
6048.2.j.d.5615.9 | 48 | 1.1 | even | 1 | trivial | ||
6048.2.j.d.5615.10 | 48 | 24.11 | even | 2 | inner | ||
6048.2.j.d.5615.39 | 48 | 8.3 | odd | 2 | inner | ||
6048.2.j.d.5615.40 | 48 | 3.2 | odd | 2 | inner |