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 | 5615.41 | ||
Character | \(\chi\) | \(=\) | 6048.5615 |
Dual form | 6048.2.j.d.5615.42 |
$q$-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 | ||||||||
\(5\) | 2.90802 | 1.30051 | 0.650253 | − | 0.759718i | \(-0.274663\pi\) | ||||
0.650253 | + | 0.759718i | \(0.274663\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.28828i | − 0.388432i | −0.980959 | − | 0.194216i | \(-0.937784\pi\) | ||||
0.980959 | − | 0.194216i | \(-0.0622163\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.86999i | 0.518642i | 0.965791 | + | 0.259321i | \(0.0834988\pi\) | ||||
−0.965791 | + | 0.259321i | \(0.916501\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.87222i | 0.939151i | 0.882892 | + | 0.469576i | \(0.155593\pi\) | ||||
−0.882892 | + | 0.469576i | \(0.844407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.04228 | 0.468532 | 0.234266 | − | 0.972173i | \(-0.424731\pi\) | ||||
0.234266 | + | 0.972173i | \(0.424731\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.934839 | 0.194927 | 0.0974637 | − | 0.995239i | \(-0.468927\pi\) | ||||
0.0974637 | + | 0.995239i | \(0.468927\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.45657 | 0.691315 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.98295 | 0.553920 | 0.276960 | − | 0.960881i | \(-0.410673\pi\) | ||||
0.276960 | + | 0.960881i | \(0.410673\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.85691i | 0.333511i | 0.985998 | + | 0.166756i | \(0.0533291\pi\) | ||||
−0.985998 | + | 0.166756i | \(0.946671\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.90802i | − 0.491545i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3.85846i | − 0.634327i | −0.948371 | − | 0.317163i | \(-0.897270\pi\) | ||||
0.948371 | − | 0.317163i | \(-0.102730\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 8.72247i | − 1.36222i | −0.732181 | − | 0.681110i | \(-0.761497\pi\) | ||||
0.732181 | − | 0.681110i | \(-0.238503\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.19319 | 0.181959 | 0.0909796 | − | 0.995853i | \(-0.471000\pi\) | ||||
0.0909796 | + | 0.995853i | \(0.471000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.1537 | 1.62694 | 0.813468 | − | 0.581609i | \(-0.197577\pi\) | ||||
0.813468 | + | 0.581609i | \(0.197577\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.43885 | −0.609723 | −0.304862 | − | 0.952397i | \(-0.598610\pi\) | ||||
−0.304862 | + | 0.952397i | \(0.598610\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 3.74635i | − 0.505158i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.9714i | 1.42836i | 0.699964 | + | 0.714178i | \(0.253199\pi\) | ||||
−0.699964 | + | 0.714178i | \(0.746801\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.70930i | 0.602964i | 0.953472 | + | 0.301482i | \(0.0974813\pi\) | ||||
−0.953472 | + | 0.301482i | \(0.902519\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.43797i | 0.674497i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.41800 | −0.539745 | −0.269872 | − | 0.962896i | \(-0.586981\pi\) | ||||
−0.269872 | + | 0.962896i | \(0.586981\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.72888 | 1.15461 | 0.577303 | − | 0.816530i | \(-0.304105\pi\) | ||||
0.577303 | + | 0.816530i | \(0.304105\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.40756 | 1.10107 | 0.550536 | − | 0.834812i | \(-0.314423\pi\) | ||||
0.550536 | + | 0.834812i | \(0.314423\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.28828 | −0.146813 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.4660i | 1.85257i | 0.376822 | + | 0.926286i | \(0.377017\pi\) | ||||
−0.376822 | + | 0.926286i | \(0.622983\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.72150i | 0.408488i | 0.978920 | + | 0.204244i | \(0.0654736\pi\) | ||||
−0.978920 | + | 0.204244i | \(0.934526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2605i | 1.22137i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.2297i | 1.29635i | 0.761492 | + | 0.648174i | \(0.224467\pi\) | ||||
−0.761492 | + | 0.648174i | \(0.775533\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.86999 | 0.196028 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.93900 | 0.609329 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.8302 | 1.60731 | 0.803657 | − | 0.595093i | \(-0.202885\pi\) | ||||
0.803657 | + | 0.595093i | \(0.202885\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.737825 | −0.0734163 | −0.0367081 | − | 0.999326i | \(-0.511687\pi\) | ||||
−0.0367081 | + | 0.999326i | \(0.511687\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 16.2518i | − 1.60134i | −0.599109 | − | 0.800668i | \(-0.704478\pi\) | ||||
0.599109 | − | 0.800668i | \(-0.295522\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1.49407i | − 0.144438i | −0.997389 | − | 0.0722188i | \(-0.976992\pi\) | ||||
0.997389 | − | 0.0722188i | \(-0.0230080\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 11.8362i | − 1.13370i | −0.823821 | − | 0.566850i | \(-0.808162\pi\) | ||||
0.823821 | − | 0.566850i | \(-0.191838\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 15.3287i | − 1.44200i | −0.692934 | − | 0.721001i | \(-0.743682\pi\) | ||||
0.692934 | − | 0.721001i | \(-0.256318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.71853 | 0.253504 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.87222 | 0.354966 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.34033 | 0.849121 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.48831 | −0.401447 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 6.55275i | − 0.581462i | −0.956805 | − | 0.290731i | \(-0.906101\pi\) | ||||
0.956805 | − | 0.290731i | \(-0.0938985\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 11.6893i | − 1.02130i | −0.859790 | − | 0.510648i | \(-0.829405\pi\) | ||||
0.859790 | − | 0.510648i | \(-0.170595\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.04228i | − 0.177088i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 7.35868i | − 0.628694i | −0.949308 | − | 0.314347i | \(-0.898214\pi\) | ||||
0.949308 | − | 0.314347i | \(-0.101786\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.2683 | 1.29504 | 0.647520 | − | 0.762048i | \(-0.275806\pi\) | ||||
0.647520 | + | 0.762048i | \(0.275806\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.40908 | 0.201457 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.67448 | 0.720376 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.6778 | −1.36630 | −0.683148 | − | 0.730280i | \(-0.739389\pi\) | ||||
−0.683148 | + | 0.730280i | \(0.739389\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.4838i | 1.34143i | 0.741714 | + | 0.670716i | \(0.234013\pi\) | ||||
−0.741714 | + | 0.670716i | \(0.765987\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.39994i | 0.433733i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.0196i | 1.27851i | 0.768997 | + | 0.639253i | \(0.220756\pi\) | ||||
−0.768997 | + | 0.639253i | \(0.779244\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 0.934839i | − 0.0736756i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.18368 | −0.484343 | −0.242172 | − | 0.970233i | \(-0.577860\pi\) | ||||
−0.242172 | + | 0.970233i | \(0.577860\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.7232 | 0.984549 | 0.492275 | − | 0.870440i | \(-0.336166\pi\) | ||||
0.492275 | + | 0.870440i | \(0.336166\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.50313 | 0.731010 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.2579 | −0.855925 | −0.427963 | − | 0.903796i | \(-0.640769\pi\) | ||||
−0.427963 | + | 0.903796i | \(0.640769\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.45657i | − 0.261292i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 8.68048i | − 0.648809i | −0.945918 | − | 0.324405i | \(-0.894836\pi\) | ||||
0.945918 | − | 0.324405i | \(-0.105164\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2.48587i | − 0.184773i | −0.995723 | − | 0.0923866i | \(-0.970550\pi\) | ||||
0.995723 | − | 0.0923866i | \(-0.0294496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 11.2205i | − 0.824945i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.98851 | 0.364796 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.40263 | −0.246206 | −0.123103 | − | 0.992394i | \(-0.539285\pi\) | ||||
−0.123103 | + | 0.992394i | \(0.539285\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.7031 | 1.49024 | 0.745121 | − | 0.666929i | \(-0.232392\pi\) | ||||
0.745121 | + | 0.666929i | \(0.232392\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.3546 | −1.16521 | −0.582607 | − | 0.812754i | \(-0.697967\pi\) | ||||
−0.582607 | + | 0.812754i | \(0.697967\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 11.3717i | − 0.806121i | −0.915173 | − | 0.403061i | \(-0.867946\pi\) | ||||
0.915173 | − | 0.403061i | \(-0.132054\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 2.98295i | − 0.209362i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 25.3651i | − 1.77158i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 2.63104i | − 0.181993i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.56405 | 0.176517 | 0.0882583 | − | 0.996098i | \(-0.471870\pi\) | ||||
0.0882583 | + | 0.996098i | \(0.471870\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.46981 | 0.236639 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.85691 | 0.126055 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.24102 | −0.487083 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.37584i | − 0.0921329i | −0.998938 | − | 0.0460665i | \(-0.985331\pi\) | ||||
0.998938 | − | 0.0460665i | \(-0.0146686\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.3740i | 1.81688i | 0.418020 | + | 0.908438i | \(0.362724\pi\) | ||||
−0.418020 | + | 0.908438i | \(0.637276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.3066i | 0.813243i | 0.913597 | + | 0.406621i | \(0.133293\pi\) | ||||
−0.913597 | + | 0.406621i | \(0.866707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.0829i | 1.57772i | 0.614571 | + | 0.788862i | \(0.289329\pi\) | ||||
−0.614571 | + | 0.788862i | \(0.710671\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.4352 | 2.11584 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.0426 | −1.16708 | −0.583540 | − | 0.812085i | \(-0.698333\pi\) | ||||
−0.583540 | + | 0.812085i | \(0.698333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.8541 | −0.699174 | −0.349587 | − | 0.936904i | \(-0.613678\pi\) | ||||
−0.349587 | + | 0.936904i | \(0.613678\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.90802 | −0.185787 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.81905i | 0.243001i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 6.63032i | − 0.418502i | −0.977862 | − | 0.209251i | \(-0.932897\pi\) | ||||
0.977862 | − | 0.209251i | \(-0.0671025\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.20434i | − 0.0757160i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.2398i | 0.763497i | 0.924266 | + | 0.381748i | \(0.124678\pi\) | ||||
−0.924266 | + | 0.381748i | \(0.875322\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.85846 | −0.239753 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.87474 | −0.177264 | −0.0886320 | − | 0.996064i | \(-0.528250\pi\) | ||||
−0.0886320 | + | 0.996064i | \(0.528250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.9083 | −0.792948 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.17565 | −0.376536 | −0.188268 | − | 0.982118i | \(-0.560287\pi\) | ||||
−0.188268 | + | 0.982118i | \(0.560287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 19.5103i | − 1.18517i | −0.805510 | − | 0.592583i | \(-0.798108\pi\) | ||||
0.805510 | − | 0.592583i | \(-0.201892\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 4.45305i | − 0.268529i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.82757i | 0.169892i | 0.996386 | + | 0.0849460i | \(0.0270718\pi\) | ||||
−0.996386 | + | 0.0849460i | \(0.972928\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 29.7569i | − 1.77515i | −0.460663 | − | 0.887575i | \(-0.652388\pi\) | ||||
0.460663 | − | 0.887575i | \(-0.347612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.7427 | 1.82746 | 0.913731 | − | 0.406319i | \(-0.133188\pi\) | ||||
0.913731 | + | 0.406319i | \(0.133188\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.72247 | −0.514871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.00592 | 0.117995 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.70430 | −0.333249 | −0.166624 | − | 0.986020i | \(-0.553287\pi\) | ||||
−0.166624 | + | 0.986020i | \(0.553287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 31.9051i | 1.85758i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.74814i | 0.101098i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.19319i | − 0.0687741i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.6947i | 0.784158i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.47411 | 0.369497 | 0.184748 | − | 0.982786i | \(-0.440853\pi\) | ||||
0.184748 | + | 0.982786i | \(0.440853\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.44723 | 0.138770 | 0.0693848 | − | 0.997590i | \(-0.477896\pi\) | ||||
0.0693848 | + | 0.997590i | \(0.477896\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.03434 | −0.454128 | −0.227064 | − | 0.973880i | \(-0.572913\pi\) | ||||
−0.227064 | + | 0.973880i | \(0.572913\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.0098 | −1.06770 | −0.533850 | − | 0.845579i | \(-0.679255\pi\) | ||||
−0.533850 | + | 0.845579i | \(0.679255\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 3.84289i | − 0.215160i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.90817i | 0.440022i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.46376i | 0.358545i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 11.1537i | − 0.614924i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.8597 | 1.97103 | 0.985515 | − | 0.169588i | \(-0.0542438\pi\) | ||||
0.985515 | + | 0.169588i | \(0.0542438\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.8476 | −0.701941 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.90274 | −0.376016 | −0.188008 | − | 0.982168i | \(-0.560203\pi\) | ||||
−0.188008 | + | 0.982168i | \(0.560203\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.39223 | 0.129546 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 36.6932i | − 1.96980i | −0.173135 | − | 0.984898i | \(-0.555390\pi\) | ||||
0.173135 | − | 0.984898i | \(-0.444610\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 28.2560i | − 1.51251i | −0.654278 | − | 0.756254i | \(-0.727027\pi\) | ||||
0.654278 | − | 0.756254i | \(-0.272973\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.3138i | 1.29410i | 0.762450 | + | 0.647048i | \(0.223997\pi\) | ||||
−0.762450 | + | 0.647048i | \(0.776003\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.2918 | 1.50157 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.95382 | 0.103119 | 0.0515594 | − | 0.998670i | \(-0.483581\pi\) | ||||
0.0515594 | + | 0.998670i | \(0.483581\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.8291 | −0.780478 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.3574 | 1.43195 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.3819i | 1.11613i | 0.829798 | + | 0.558064i | \(0.188456\pi\) | ||||
−0.829798 | + | 0.558064i | \(0.811544\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.43885i | 0.230454i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 33.0682i | − 1.71221i | −0.516804 | − | 0.856104i | \(-0.672878\pi\) | ||||
0.516804 | − | 0.856104i | \(-0.327122\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.57809i | 0.287286i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.0331 | 0.874934 | 0.437467 | − | 0.899235i | \(-0.355876\pi\) | ||||
0.437467 | + | 0.899235i | \(0.355876\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.7372 | −0.804132 | −0.402066 | − | 0.915611i | \(-0.631708\pi\) | ||||
−0.402066 | + | 0.915611i | \(0.631708\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.74635 | −0.190932 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.7854 | 1.15527 | 0.577634 | − | 0.816296i | \(-0.303976\pi\) | ||||
0.577634 | + | 0.816296i | \(0.303976\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.61990i | 0.183066i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 47.8835i | 2.40928i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.6829i | 1.18861i | 0.804239 | + | 0.594306i | \(0.202573\pi\) | ||||
−0.804239 | + | 0.594306i | \(0.797427\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 1.51029i | − 0.0754204i | −0.999289 | − | 0.0377102i | \(-0.987994\pi\) | ||||
0.999289 | − | 0.0377102i | \(-0.0120064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.47241 | −0.172973 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.97079 | −0.246393 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.86160 | 0.487625 | 0.243812 | − | 0.969822i | \(-0.421602\pi\) | ||||
0.243812 | + | 0.969822i | \(0.421602\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.9714 | 0.539868 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.8222i | 0.531241i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 20.8183i | − 1.01704i | −0.861050 | − | 0.508520i | \(-0.830193\pi\) | ||||
0.861050 | − | 0.508520i | \(-0.169807\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.5459i | 1.39124i | 0.718409 | + | 0.695621i | \(0.244871\pi\) | ||||
−0.718409 | + | 0.695621i | \(0.755129\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.3846i | 0.649249i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.70930 | 0.227899 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.53111 | −0.314593 | −0.157296 | − | 0.987551i | \(-0.550278\pi\) | ||||
−0.157296 | + | 0.987551i | \(0.550278\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.2151 | 0.683136 | 0.341568 | − | 0.939857i | \(-0.389042\pi\) | ||||
0.341568 | + | 0.939857i | \(0.389042\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.90921 | 0.0913297 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 22.5811i | − 1.07773i | −0.842391 | − | 0.538867i | \(-0.818852\pi\) | ||||
0.842391 | − | 0.538867i | \(-0.181148\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.7932i | 0.750359i | 0.926952 | + | 0.375179i | \(0.122419\pi\) | ||||
−0.926952 | + | 0.375179i | \(0.877581\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 35.5643i | 1.68591i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 26.9861i | − 1.27355i | −0.771049 | − | 0.636776i | \(-0.780267\pi\) | ||||
0.771049 | − | 0.636776i | \(-0.219733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.2370 | −0.529130 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.43797 | 0.254936 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.9588 | 1.77564 | 0.887818 | − | 0.460195i | \(-0.152220\pi\) | ||||
0.887818 | + | 0.460195i | \(0.152220\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.35921 | 0.389327 | 0.194664 | − | 0.980870i | \(-0.437638\pi\) | ||||
0.194664 | + | 0.980870i | \(0.437638\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.4723i | 0.858483i | 0.903190 | + | 0.429241i | \(0.141219\pi\) | ||||
−0.903190 | + | 0.429241i | \(0.858781\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.34051i | 0.200855i | 0.994944 | + | 0.100427i | \(0.0320210\pi\) | ||||
−0.994944 | + | 0.100427i | \(0.967979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.41800i | 0.204004i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1.53716i | − 0.0706788i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.05931 | 0.323903 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.7292 | −1.54113 | −0.770564 | − | 0.637363i | \(-0.780025\pi\) | ||||
−0.770564 | + | 0.637363i | \(0.780025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.21528 | 0.328989 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 46.0345 | 2.09032 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 6.00662i | − 0.272186i | −0.990696 | − | 0.136093i | \(-0.956545\pi\) | ||||
0.990696 | − | 0.136093i | \(-0.0434546\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 26.2731i | − 1.18569i | −0.805318 | − | 0.592844i | \(-0.798005\pi\) | ||||
0.805318 | − | 0.592844i | \(-0.201995\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.5506i | 0.520215i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 9.72888i | − 0.436400i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.9974 | −1.61147 | −0.805733 | − | 0.592279i | \(-0.798228\pi\) | ||||
−0.805733 | + | 0.592279i | \(0.798228\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.7775 | −0.703485 | −0.351743 | − | 0.936097i | \(-0.614411\pi\) | ||||
−0.351743 | + | 0.936097i | \(0.614411\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.14561 | −0.0954783 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.09029 | 0.269947 | 0.134974 | − | 0.990849i | \(-0.456905\pi\) | ||||
0.134974 | + | 0.990849i | \(0.456905\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 9.40756i | − 0.416166i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 47.2605i | − 2.08255i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 14.3691i | − 0.631954i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.1215i | 0.793916i | 0.917837 | + | 0.396958i | \(0.129934\pi\) | ||||
−0.917837 | + | 0.396958i | \(0.870066\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.00317 | −0.175046 | −0.0875232 | − | 0.996162i | \(-0.527895\pi\) | ||||
−0.0875232 | + | 0.996162i | \(0.527895\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.19037 | −0.313217 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1261 | −0.962003 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.3109 | 0.706505 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 4.34480i | − 0.187842i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.28828i | 0.0554903i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 4.52777i | − 0.194664i | −0.995252 | − | 0.0973320i | \(-0.968969\pi\) | ||||
0.995252 | − | 0.0973320i | \(-0.0310309\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 34.4198i | − 1.47438i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.99785 | −0.0854218 | −0.0427109 | − | 0.999087i | \(-0.513599\pi\) | ||||
−0.0427109 | + | 0.999087i | \(0.513599\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.09203 | 0.259529 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.4660 | 0.700206 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.9242 | −0.632360 | −0.316180 | − | 0.948699i | \(-0.602400\pi\) | ||||
−0.316180 | + | 0.948699i | \(0.602400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.23125i | 0.0943717i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 0.157861i | − 0.00665305i | −0.999994 | − | 0.00332653i | \(-0.998941\pi\) | ||||
0.999994 | − | 0.00332653i | \(-0.00105887\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 44.5761i | − 1.87533i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.8914i | 0.498514i | 0.968437 | + | 0.249257i | \(0.0801864\pi\) | ||||
−0.968437 | + | 0.249257i | \(0.919814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0748 | −0.589013 | −0.294507 | − | 0.955649i | \(-0.595155\pi\) | ||||
−0.294507 | + | 0.955649i | \(0.595155\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.23134 | 0.134756 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.5261 | 1.06267 | 0.531333 | − | 0.847163i | \(-0.321691\pi\) | ||||
0.531333 | + | 0.847163i | \(0.321691\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.72150 | 0.154394 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.71850i | 0.236836i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.47422i | 0.391043i | 0.980699 | + | 0.195521i | \(0.0626399\pi\) | ||||
−0.980699 | + | 0.195521i | \(0.937360\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.79234i | 0.156261i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.9405i | 0.777792i | 0.921282 | + | 0.388896i | \(0.127143\pi\) | ||||
−0.921282 | + | 0.388896i | \(0.872857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.2605 | 0.461635 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.9184 | 1.42673 | 0.713364 | − | 0.700794i | \(-0.247171\pi\) | ||||
0.713364 | + | 0.700794i | \(0.247171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.8342 | 1.05380 | 0.526899 | − | 0.849928i | \(-0.323355\pi\) | ||||
0.526899 | + | 0.849928i | \(0.323355\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.1618 | 1.10429 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 14.4361i | − 0.585943i | −0.956121 | − | 0.292972i | \(-0.905356\pi\) | ||||
0.956121 | − | 0.292972i | \(-0.0946442\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.8574i | 0.843798i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.3647i | 1.87265i | 0.351133 | + | 0.936325i | \(0.385796\pi\) | ||||
−0.351133 | + | 0.936325i | \(0.614204\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 29.3648i | − 1.18218i | −0.806605 | − | 0.591091i | \(-0.798697\pi\) | ||||
0.806605 | − | 0.591091i | \(-0.201303\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.7590 | −0.553021 | −0.276510 | − | 0.961011i | \(-0.589178\pi\) | ||||
−0.276510 | + | 0.961011i | \(0.589178\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.2297 | 0.489974 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3350 | −1.21340 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.9408 | 0.595729 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.9228i | 1.31064i | 0.755352 | + | 0.655319i | \(0.227466\pi\) | ||||
−0.755352 | + | 0.655319i | \(0.772534\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 19.0555i | − 0.756195i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.86999i | − 0.0740918i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.5844i | 1.56349i | 0.623597 | + | 0.781746i | \(0.285670\pi\) | ||||
−0.623597 | + | 0.781746i | \(0.714330\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −44.0571 | −1.73744 | −0.868720 | − | 0.495303i | \(-0.835057\pi\) | ||||
−0.868720 | + | 0.495303i | \(0.835057\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.4430 | 1.55066 | 0.775331 | − | 0.631555i | \(-0.217583\pi\) | ||||
0.775331 | + | 0.631555i | \(0.217583\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.1343 | 0.554819 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.4794 | 1.70148 | 0.850741 | − | 0.525585i | \(-0.176154\pi\) | ||||
0.850741 | + | 0.525585i | \(0.176154\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 33.9926i | − 1.32820i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.8653i | 1.04652i | 0.852172 | + | 0.523262i | \(0.175285\pi\) | ||||
−0.852172 | + | 0.523262i | \(0.824715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.365746i | 0.0142259i | 0.999975 | + | 0.00711293i | \(0.00226414\pi\) | ||||
−0.999975 | + | 0.00711293i | \(0.997736\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 5.93900i | − 0.230305i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.78858 | 0.107974 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.06691 | 0.234211 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.2522 | 1.35887 | 0.679435 | − | 0.733735i | \(-0.262225\pi\) | ||||
0.679435 | + | 0.733735i | \(0.262225\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.6841 | −1.10242 | −0.551211 | − | 0.834366i | \(-0.685834\pi\) | ||||
−0.551211 | + | 0.834366i | \(0.685834\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 15.8302i | − 0.607508i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 22.7609i | − 0.870921i | −0.900208 | − | 0.435460i | \(-0.856586\pi\) | ||||
0.900208 | − | 0.435460i | \(-0.143414\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 21.3992i | − 0.817620i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 8.30061i | − 0.316228i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −36.1270 | −1.37434 | −0.687168 | − | 0.726499i | \(-0.741146\pi\) | ||||
−0.687168 | + | 0.726499i | \(0.741146\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 44.4005 | 1.68421 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.7753 | 1.27933 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.7739 | −0.935699 | −0.467849 | − | 0.883808i | \(-0.654971\pi\) | ||||
−0.467849 | + | 0.883808i | \(0.654971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 7.88007i | − 0.297202i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.737825i | 0.0277487i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 23.4819i | − 0.881881i | −0.897536 | − | 0.440941i | \(-0.854645\pi\) | ||||
0.897536 | − | 0.440941i | \(-0.145355\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.73591i | 0.0650105i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.00564 | 0.261996 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.0908 | −1.42055 | −0.710274 | − | 0.703926i | \(-0.751429\pi\) | ||||
−0.710274 | + | 0.703926i | \(0.751429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.2518 | −0.605248 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.3108 | 0.382933 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.53603i | 0.242408i | 0.992628 | + | 0.121204i | \(0.0386755\pi\) | ||||
−0.992628 | + | 0.121204i | \(0.961324\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.62028i | 0.170887i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 32.5549i | − 1.20244i | −0.799082 | − | 0.601222i | \(-0.794681\pi\) | ||||
0.799082 | − | 0.601222i | \(-0.205319\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.69163i | 0.209654i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.47095 | 0.201252 | 0.100626 | − | 0.994924i | \(-0.467915\pi\) | ||||
0.100626 | + | 0.994924i | \(0.467915\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.23548 | −0.265444 | −0.132722 | − | 0.991153i | \(-0.542372\pi\) | ||||
−0.132722 | + | 0.991153i | \(0.542372\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −48.4992 | −1.77687 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.49407 | −0.0545923 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 24.5924i | − 0.897391i | −0.893685 | − | 0.448695i | \(-0.851889\pi\) | ||||
0.893685 | − | 0.448695i | \(-0.148111\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47.9352i | 1.74454i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.5168i | 1.18184i | 0.806728 | + | 0.590922i | \(0.201236\pi\) | ||||
−0.806728 | + | 0.590922i | \(0.798764\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 21.5639i | − 0.781689i | −0.920457 | − | 0.390845i | \(-0.872183\pi\) | ||||
0.920457 | − | 0.390845i | \(-0.127817\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.8362 | −0.428499 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.5164 | −0.740806 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.56057 | −0.0562756 | −0.0281378 | − | 0.999604i | \(-0.508958\pi\) | ||||
−0.0281378 | + | 0.999604i | \(0.508958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0539 | 0.865160 | 0.432580 | − | 0.901596i | \(-0.357603\pi\) | ||||
0.432580 | + | 0.901596i | \(0.357603\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.41855i | 0.230561i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 17.8138i | − 0.638244i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 12.5336i | − 0.448486i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46.5854i | 1.66270i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.99996 | −0.142583 | −0.0712916 | − | 0.997456i | \(-0.522712\pi\) | ||||
−0.0712916 | + | 0.997456i | \(0.522712\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.3287 | −0.545025 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.80635 | −0.312723 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.18205 | −0.254401 | −0.127201 | − | 0.991877i | \(-0.540599\pi\) | ||||
−0.127201 | + | 0.991877i | \(0.540599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 43.1896i | 1.52794i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 12.1196i | − 0.427691i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.71853i | − 0.0958155i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.2698i | 1.69707i | 0.529136 | + | 0.848537i | \(0.322516\pi\) | ||||
−0.529136 | + | 0.848537i | \(0.677484\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.3182 | −0.713469 | −0.356735 | − | 0.934206i | \(-0.616110\pi\) | ||||
−0.356735 | + | 0.934206i | \(0.616110\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17.9823 | −0.629891 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.43682 | 0.0852537 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.0745 | −1.22411 | −0.612055 | − | 0.790815i | \(-0.709657\pi\) | ||||
−0.612055 | + | 0.790815i | \(0.709657\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 15.4211i | − 0.537544i | −0.963204 | − | 0.268772i | \(-0.913382\pi\) | ||||
0.963204 | − | 0.268772i | \(-0.0866179\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.5561i | 0.958218i | 0.877755 | + | 0.479109i | \(0.159040\pi\) | ||||
−0.877755 | + | 0.479109i | \(0.840960\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 56.9495i | 1.97794i | 0.148124 | + | 0.988969i | \(0.452677\pi\) | ||||
−0.148124 | + | 0.988969i | \(0.547323\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 3.87222i | − 0.134164i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 36.9992 | 1.28041 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.54853 | −0.0879849 | −0.0439925 | − | 0.999032i | \(-0.514008\pi\) | ||||
−0.0439925 | + | 0.999032i | \(0.514008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.1020 | −0.693173 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.6353 | 0.950683 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 9.34033i | − 0.320937i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 3.60704i | − 0.123648i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 23.1990i | − 0.794319i | −0.917750 | − | 0.397159i | \(-0.869996\pi\) | ||||
0.917750 | − | 0.397159i | \(-0.130004\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 19.5713i | − 0.668544i | −0.942477 | − | 0.334272i | \(-0.891510\pi\) | ||||
0.942477 | − | 0.334272i | \(-0.108490\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.8322 | 1.73437 | 0.867186 | − | 0.497985i | \(-0.165927\pi\) | ||||
0.867186 | + | 0.497985i | \(0.165927\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.1106 | −1.33134 | −0.665671 | − | 0.746246i | \(-0.731854\pi\) | ||||
−0.665671 | + | 0.746246i | \(0.731854\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.7383 | −1.11314 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.2129 | 0.719598 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 8.26162i | − 0.279934i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.48831i | 0.151733i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.1514i | 0.883070i | 0.897244 | + | 0.441535i | \(0.145566\pi\) | ||||
−0.897244 | + | 0.441535i | \(0.854434\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 49.2277i | − 1.65852i | −0.558860 | − | 0.829262i | \(-0.688761\pi\) | ||||
0.558860 | − | 0.829262i | \(-0.311239\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.3014 | −1.49086 | −0.745430 | − | 0.666584i | \(-0.767756\pi\) | ||||
−0.745430 | + | 0.666584i | \(0.767756\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.83633 | 0.229542 | 0.114771 | − | 0.993392i | \(-0.463387\pi\) | ||||
0.114771 | + | 0.993392i | \(0.463387\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.55275 | −0.219772 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.7791 | 0.762272 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 25.2430i | − 0.843780i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.53908i | 0.184739i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 17.1882i | − 0.572622i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 7.22895i | − 0.240298i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.2295 | −0.804528 | −0.402264 | − | 0.915524i | \(-0.631777\pi\) | ||||
−0.402264 | + | 0.915524i | \(0.631777\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.75748 | 0.223885 | 0.111943 | − | 0.993715i | \(-0.464293\pi\) | ||||
0.111943 | + | 0.993715i | \(0.464293\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.79435 | 0.158670 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.6893 | −0.386014 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.77205i | 0.0584546i | 0.999573 | + | 0.0292273i | \(0.00930466\pi\) | ||||
−0.999573 | + | 0.0292273i | \(0.990695\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.1929i | 0.598827i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 13.3370i | − 0.438519i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.3376i | 0.503212i | 0.967830 | + | 0.251606i | \(0.0809587\pi\) | ||||
−0.967830 | + | 0.251606i | \(0.919041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.04228 | −0.0669332 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.5067 | 0.474420 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.6373 | −1.58891 | −0.794456 | − | 0.607322i | \(-0.792244\pi\) | ||||
−0.794456 | + | 0.607322i | \(0.792244\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.4202 | −1.12207 | −0.561034 | − | 0.827793i | \(-0.689596\pi\) | ||||
−0.561034 | + | 0.827793i | \(0.689596\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 8.15410i | − 0.265534i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 27.8402i | − 0.904684i | −0.891844 | − | 0.452342i | \(-0.850589\pi\) | ||||
0.891844 | − | 0.452342i | \(-0.149411\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.5921i | 0.571062i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.7401i | 0.736624i | 0.929702 | + | 0.368312i | \(0.120064\pi\) | ||||
−0.929702 | + | 0.368312i | \(0.879936\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.89491 | −0.320192 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.35868 | −0.237624 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.5519 | 0.888770 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 60.2050 | 1.93807 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.0470i | 0.901931i | 0.892541 | + | 0.450965i | \(0.148920\pi\) | ||||
−0.892541 | + | 0.450965i | \(0.851080\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 10.0931i | − 0.323904i | −0.986799 | − | 0.161952i | \(-0.948221\pi\) | ||||
0.986799 | − | 0.161952i | \(-0.0517790\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 15.2683i | − 0.489479i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1.93536i | − 0.0619176i | −0.999521 | − | 0.0309588i | \(-0.990144\pi\) | ||||
0.999521 | − | 0.0309588i | \(-0.00985607\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.7553 | 0.503543 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.8652 | −1.46287 | −0.731436 | − | 0.681910i | \(-0.761150\pi\) | ||||
−0.731436 | + | 0.681910i | \(0.761150\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −47.5594 | −1.51537 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.11544 | 0.0354688 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.5946i | 0.654209i | 0.944988 | + | 0.327105i | \(0.106073\pi\) | ||||
−0.944988 | + | 0.327105i | \(0.893927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 33.0692i | − 1.04837i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 11.0478i | − 0.349889i | −0.984578 | − | 0.174944i | \(-0.944025\pi\) | ||||
0.984578 | − | 0.174944i | \(-0.0559745\pi\) | |||||||
\(998\) | 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.5615.41 | 48 | ||
3.2 | odd | 2 | inner | 6048.2.j.d.5615.8 | 48 | ||
4.3 | odd | 2 | 1512.2.j.d.323.47 | yes | 48 | ||
8.3 | odd | 2 | inner | 6048.2.j.d.5615.7 | 48 | ||
8.5 | even | 2 | 1512.2.j.d.323.1 | ✓ | 48 | ||
12.11 | even | 2 | 1512.2.j.d.323.2 | yes | 48 | ||
24.5 | odd | 2 | 1512.2.j.d.323.48 | yes | 48 | ||
24.11 | even | 2 | inner | 6048.2.j.d.5615.42 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.d.323.1 | ✓ | 48 | 8.5 | even | 2 | ||
1512.2.j.d.323.2 | yes | 48 | 12.11 | even | 2 | ||
1512.2.j.d.323.47 | yes | 48 | 4.3 | odd | 2 | ||
1512.2.j.d.323.48 | yes | 48 | 24.5 | odd | 2 | ||
6048.2.j.d.5615.7 | 48 | 8.3 | odd | 2 | inner | ||
6048.2.j.d.5615.8 | 48 | 3.2 | odd | 2 | inner | ||
6048.2.j.d.5615.41 | 48 | 1.1 | even | 1 | trivial | ||
6048.2.j.d.5615.42 | 48 | 24.11 | even | 2 | inner |