Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,2,Mod(1,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.a (trivial) |
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: | yes |
Analytic conductor: | \(10.2208514587\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 320) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 0.732051 | 0.422650 | 0.211325 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211325 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.26795 | −0.479240 | −0.239620 | − | 0.970867i | \(-0.577023\pi\) | ||||
−0.239620 | + | 0.970867i | \(0.577023\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.46410 | −1.04447 | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.46410 | −0.960769 | −0.480384 | − | 0.877058i | \(-0.659503\pi\) | ||||
−0.480384 | + | 0.877058i | \(0.659503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.732051 | 0.189015 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.928203 | −0.202551 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.19615 | −1.70902 | −0.854508 | − | 0.519438i | \(-0.826141\pi\) | ||||
−0.854508 | + | 0.519438i | \(0.826141\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.46410 | −1.69980 | −0.849901 | − | 0.526942i | \(-0.823339\pi\) | ||||
−0.849901 | + | 0.526942i | \(0.823339\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.53590 | −0.441443 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.26795 | −0.214323 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.53590 | −0.406069 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.53590 | −0.396041 | −0.198020 | − | 0.980198i | \(-0.563451\pi\) | ||||
−0.198020 | + | 0.980198i | \(0.563451\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1962 | 1.55490 | 0.777449 | − | 0.628946i | \(-0.216513\pi\) | ||||
0.777449 | + | 0.628946i | \(0.216513\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.46410 | −0.367327 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.19615 | −1.19553 | −0.597766 | − | 0.801671i | \(-0.703945\pi\) | ||||
−0.597766 | + | 0.801671i | \(0.703945\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.39230 | −0.770329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.53590 | 0.355097 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3923 | 1.42749 | 0.713746 | − | 0.700404i | \(-0.246997\pi\) | ||||
0.713746 | + | 0.700404i | \(0.246997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.46410 | −0.467099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.46410 | 0.193925 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9282 | 1.65529 | 0.827643 | − | 0.561254i | \(-0.189681\pi\) | ||||
0.827643 | + | 0.561254i | \(0.189681\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.12436 | 0.393632 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.1962 | −1.24566 | −0.622829 | − | 0.782358i | \(-0.714017\pi\) | ||||
−0.622829 | + | 0.782358i | \(0.714017\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.39230 | 0.521271 | 0.260635 | − | 0.965437i | \(-0.416068\pi\) | ||||
0.260635 | + | 0.965437i | \(0.416068\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.3923 | 1.68449 | 0.842246 | − | 0.539093i | \(-0.181233\pi\) | ||||
0.842246 | + | 0.539093i | \(0.181233\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.732051 | 0.0845299 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.39230 | 0.500550 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.73205 | −0.519410 | −0.259705 | − | 0.965688i | \(-0.583625\pi\) | ||||
−0.259705 | + | 0.965688i | \(0.583625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46410 | 0.375735 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.928203 | −0.0983893 | −0.0491947 | − | 0.998789i | \(-0.515665\pi\) | ||||
−0.0491947 | + | 0.998789i | \(0.515665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.39230 | 0.460439 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.92820 | −0.718421 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | 0.205196 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.39230 | −0.649040 | −0.324520 | − | 0.945879i | \(-0.605203\pi\) | ||||
−0.324520 | + | 0.945879i | \(0.605203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.53590 | 0.857890 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0000 | −1.19404 | −0.597022 | − | 0.802225i | \(-0.703650\pi\) | ||||
−0.597022 | + | 0.802225i | \(0.703650\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.19615 | −0.807591 | −0.403795 | − | 0.914849i | \(-0.632309\pi\) | ||||
−0.403795 | + | 0.914849i | \(0.632309\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.928203 | −0.0905834 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.7321 | −1.61755 | −0.808774 | − | 0.588119i | \(-0.799869\pi\) | ||||
−0.808774 | + | 0.588119i | \(0.799869\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.928203 | 0.0889057 | 0.0444529 | − | 0.999011i | \(-0.485846\pi\) | ||||
0.0444529 | + | 0.999011i | \(0.485846\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.39230 | −0.416899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.928203 | 0.0873180 | 0.0436590 | − | 0.999046i | \(-0.486098\pi\) | ||||
0.0436590 | + | 0.999046i | \(0.486098\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.19615 | −0.764295 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.53590 | 0.789144 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.39230 | −0.402642 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.85641 | −0.167387 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.80385 | −0.337537 | −0.168768 | − | 0.985656i | \(-0.553979\pi\) | ||||
−0.168768 | + | 0.985656i | \(0.553979\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.46410 | 0.657178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.3923 | 0.907980 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.53590 | −0.219890 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.9282 | −1.10453 | −0.552265 | − | 0.833668i | \(-0.686237\pi\) | ||||
−0.552265 | + | 0.833668i | \(0.686237\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | 1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.94744 | −0.325579 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0000 | 1.47462 | 0.737309 | − | 0.675556i | \(-0.236096\pi\) | ||||
0.737309 | + | 0.675556i | \(0.236096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.53590 | −0.206368 | −0.103184 | − | 0.994662i | \(-0.532903\pi\) | ||||
−0.103184 | + | 0.994662i | \(0.532903\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.53590 | −0.690086 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.46410 | −0.760175 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.928203 | −0.0740787 | −0.0370393 | − | 0.999314i | \(-0.511793\pi\) | ||||
−0.0370393 | + | 0.999314i | \(0.511793\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.60770 | 0.603329 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3923 | 0.819028 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.80385 | 0.454592 | 0.227296 | − | 0.973826i | \(-0.427011\pi\) | ||||
0.227296 | + | 0.973826i | \(0.427011\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.53590 | −0.197419 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.19615 | 0.634237 | 0.317119 | − | 0.948386i | \(-0.397285\pi\) | ||||
0.317119 | + | 0.948386i | \(0.397285\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.92820 | −0.376869 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.26795 | −0.0958479 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.39230 | 0.330146 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.8564 | 1.48414 | 0.742069 | − | 0.670324i | \(-0.233845\pi\) | ||||
0.742069 | + | 0.670324i | \(0.233845\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820 | 0.514969 | 0.257485 | − | 0.966282i | \(-0.417106\pi\) | ||||
0.257485 | + | 0.966282i | \(0.417106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.46410 | 0.699607 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | −0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | −0.877527 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.07180 | 0.368919 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.3923 | 1.18611 | 0.593053 | − | 0.805164i | \(-0.297923\pi\) | ||||
0.593053 | + | 0.805164i | \(0.297923\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.39230 | 0.460128 | 0.230064 | − | 0.973175i | \(-0.426106\pi\) | ||||
0.230064 | + | 0.973175i | \(0.426106\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.53590 | −0.181599 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.3923 | −0.740421 | −0.370211 | − | 0.928948i | \(-0.620714\pi\) | ||||
−0.370211 | + | 0.928948i | \(0.620714\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.92820 | 0.491127 | 0.245564 | − | 0.969380i | \(-0.421027\pi\) | ||||
0.245564 | + | 0.969380i | \(0.421027\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.46410 | −0.526477 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.53590 | −0.177115 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.1962 | 1.40373 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.92820 | −0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.39230 | −0.440064 | −0.220032 | − | 0.975493i | \(-0.570616\pi\) | ||||
−0.220032 | + | 0.975493i | \(0.570616\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.21539 | 0.220315 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.1962 | 0.695372 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.0000 | 0.814613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5359 | 0.711950 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.1244 | −1.01280 | −0.506401 | − | 0.862298i | \(-0.669024\pi\) | ||||
−0.506401 | + | 0.862298i | \(0.669024\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.5885 | −1.23376 | −0.616880 | − | 0.787058i | \(-0.711603\pi\) | ||||
−0.616880 | + | 0.787058i | \(0.711603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.9282 | −1.25081 | −0.625405 | − | 0.780300i | \(-0.715066\pi\) | ||||
−0.625405 | + | 0.780300i | \(0.715066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.21539 | 0.211557 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.60770 | 0.105324 | 0.0526618 | − | 0.998612i | \(-0.483229\pi\) | ||||
0.0526618 | + | 0.998612i | \(0.483229\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.19615 | −0.534658 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.78461 | −0.570622 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.7846 | 1.34444 | 0.672222 | − | 0.740349i | \(-0.265340\pi\) | ||||
0.672222 | + | 0.740349i | \(0.265340\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3923 | −1.31358 | −0.656792 | − | 0.754072i | \(-0.728087\pi\) | ||||
−0.656792 | + | 0.754072i | \(0.728087\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2679 | 0.979439 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.39230 | −0.344502 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.92820 | −0.440831 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.46410 | −0.219529 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4641 | 0.976085 | 0.488043 | − | 0.872820i | \(-0.337711\pi\) | ||||
0.488043 | + | 0.872820i | \(0.337711\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.3923 | 1.78501 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.53590 | 0.158804 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.60770 | 0.472719 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.1962 | 1.24535 | 0.622674 | − | 0.782481i | \(-0.286046\pi\) | ||||
0.622674 | + | 0.782481i | \(0.286046\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.3923 | 0.638394 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.679492 | −0.0415842 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.7846 | −0.901434 | −0.450717 | − | 0.892667i | \(-0.648832\pi\) | ||||
−0.450717 | + | 0.892667i | \(0.648832\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.39230 | 0.266814 | 0.133407 | − | 0.991061i | \(-0.457408\pi\) | ||||
0.133407 | + | 0.991061i | \(0.457408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.21539 | 0.194604 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.46410 | −0.208893 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.8564 | 1.19306 | 0.596528 | − | 0.802592i | \(-0.296546\pi\) | ||||
0.596528 | + | 0.802592i | \(0.296546\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.3205 | 1.39616 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.3923 | 1.69374 | 0.846871 | − | 0.531798i | \(-0.178483\pi\) | ||||
0.846871 | + | 0.531798i | \(0.178483\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5885 | 0.629418 | 0.314709 | − | 0.949188i | \(-0.398093\pi\) | ||||
0.314709 | + | 0.949188i | \(0.398093\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.46410 | 0.0867259 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.21539 | 0.189798 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.67949 | −0.274317 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.0000 | −1.75262 | −0.876309 | − | 0.481749i | \(-0.840002\pi\) | ||||
−0.876309 | + | 0.481749i | \(0.840002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.8564 | 0.804030 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.3923 | 1.64197 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.9282 | −0.745169 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.78461 | −0.504663 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.9282 | 0.740267 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.1962 | −1.95168 | −0.975839 | − | 0.218492i | \(-0.929886\pi\) | ||||
−0.975839 | + | 0.218492i | \(0.929886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.00000 | −0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.60770 | 0.431393 | 0.215696 | − | 0.976460i | \(-0.430798\pi\) | ||||
0.215696 | + | 0.976460i | \(0.430798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.0000 | −1.24351 | −0.621757 | − | 0.783210i | \(-0.713581\pi\) | ||||
−0.621757 | + | 0.783210i | \(0.713581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.12436 | 0.176037 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.3923 | 1.25768 | 0.628839 | − | 0.777536i | \(-0.283531\pi\) | ||||
0.628839 | + | 0.777536i | \(0.283531\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.2487 | −0.683656 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.92820 | 0.385496 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.46410 | −0.192154 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.679492 | 0.0375760 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.3923 | 0.572946 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.60770 | 0.308227 | 0.154113 | − | 0.988053i | \(-0.450748\pi\) | ||||
0.154113 | + | 0.988053i | \(0.450748\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.7846 | 0.810192 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.1962 | −0.557075 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.679492 | 0.0369049 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.7846 | 1.77539 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7128 | 0.848412 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.00000 | −0.323029 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.0526 | −1.50594 | −0.752970 | − | 0.658055i | \(-0.771380\pi\) | ||||
−0.752970 | + | 0.658055i | \(0.771380\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.78461 | 0.470229 | 0.235115 | − | 0.971968i | \(-0.424453\pi\) | ||||
0.235115 | + | 0.971968i | \(0.424453\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.8564 | 0.739600 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.7846 | −0.786905 | −0.393453 | − | 0.919345i | \(-0.628719\pi\) | ||||
−0.393453 | + | 0.919345i | \(0.628719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.39230 | 0.233119 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.21539 | −0.170177 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.78461 | −0.463634 | −0.231817 | − | 0.972759i | \(-0.574467\pi\) | ||||
−0.231817 | + | 0.972759i | \(0.574467\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.732051 | 0.0384227 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.3923 | 0.753328 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0526 | 0.524739 | 0.262370 | − | 0.964967i | \(-0.415496\pi\) | ||||
0.262370 | + | 0.964967i | \(0.415496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.24871 | 0.325295 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.1769 | −0.684111 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.85641 | −0.406789 | −0.203395 | − | 0.979097i | \(-0.565197\pi\) | ||||
−0.203395 | + | 0.979097i | \(0.565197\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.732051 | 0.0378029 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000 | 0.102733 | 0.0513665 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513665 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.78461 | −0.142660 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.80385 | 0.194368 | 0.0971838 | − | 0.995266i | \(-0.469017\pi\) | ||||
0.0971838 | + | 0.995266i | \(0.469017\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.39230 | 0.223853 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.1244 | −1.27714 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.7846 | 1.35803 | 0.679017 | − | 0.734123i | \(-0.262406\pi\) | ||||
0.679017 | + | 0.734123i | \(0.262406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.3923 | −1.43586 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.60770 | 0.383757 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.4641 | −1.37838 | −0.689192 | − | 0.724579i | \(-0.742034\pi\) | ||||
−0.689192 | + | 0.724579i | \(0.742034\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.85641 | −0.0929366 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.14359 | −0.206921 | −0.103461 | − | 0.994634i | \(-0.532992\pi\) | ||||
−0.103461 | + | 0.994634i | \(0.532992\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.7846 | 1.63312 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.46410 | 0.221823 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.7846 | 1.03025 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.60770 | −0.178389 | −0.0891945 | − | 0.996014i | \(-0.528429\pi\) | ||||
−0.0891945 | + | 0.996014i | \(0.528429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.46410 | −0.466830 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.60770 | −0.374350 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.73205 | −0.232287 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.32051 | 0.358487 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.928203 | 0.0453457 | 0.0226728 | − | 0.999743i | \(-0.492782\pi\) | ||||
0.0226728 | + | 0.999743i | \(0.492782\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.1962 | 0.981971 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.46410 | 0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.3923 | −0.793279 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.78461 | 0.424125 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.3923 | 1.36761 | 0.683805 | − | 0.729665i | \(-0.260324\pi\) | ||||
0.683805 | + | 0.729665i | \(0.260324\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.3923 | 1.26833 | 0.634167 | − | 0.773196i | \(-0.281343\pi\) | ||||
0.634167 | + | 0.773196i | \(0.281343\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.3923 | −0.784150 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.9282 | −0.903394 | −0.451697 | − | 0.892171i | \(-0.649181\pi\) | ||||
−0.451697 | + | 0.892171i | \(0.649181\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.2872 | 0.632723 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.339746 | −0.0161418 | −0.00807091 | − | 0.999967i | \(-0.502569\pi\) | ||||
−0.00807091 | + | 0.999967i | \(0.502569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.928203 | −0.0440011 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.1769 | 0.623247 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.53590 | −0.119676 | −0.0598382 | − | 0.998208i | \(-0.519058\pi\) | ||||
−0.0598382 | + | 0.998208i | \(0.519058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.78461 | 0.413651 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.85641 | −0.0872216 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.39230 | 0.205914 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.7846 | −1.06582 | −0.532910 | − | 0.846172i | \(-0.678901\pi\) | ||||
−0.532910 | + | 0.846172i | \(0.678901\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.8564 | −0.646762 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.8038 | −0.734467 | −0.367234 | − | 0.930129i | \(-0.619695\pi\) | ||||
−0.367234 | + | 0.930129i | \(0.619695\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.92820 | −0.321288 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.9808 | 1.06342 | 0.531711 | − | 0.846926i | \(-0.321549\pi\) | ||||
0.531711 | + | 0.846926i | \(0.321549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9282 | 0.596969 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.679492 | −0.0313093 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35.3205 | −1.62404 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.6077 | −1.17250 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.7846 | 0.947697 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.60770 | 0.346162 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.39230 | −0.290260 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.1244 | −1.77289 | −0.886447 | − | 0.462830i | \(-0.846834\pi\) | ||||
−0.886447 | + | 0.462830i | \(0.846834\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.24871 | 0.192133 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.3923 | 1.01055 | 0.505275 | − | 0.862958i | \(-0.331391\pi\) | ||||
0.505275 | + | 0.862958i | \(0.331391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.53590 | 0.383660 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.56922 | −0.249814 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.5692 | 1.77136 | 0.885681 | − | 0.464295i | \(-0.153692\pi\) | ||||
0.885681 | + | 0.464295i | \(0.153692\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00000 | 0.268060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.19615 | −0.365448 | −0.182724 | − | 0.983164i | \(-0.558492\pi\) | ||||
−0.182724 | + | 0.983164i | \(0.558492\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.732051 | −0.0325115 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.78461 | −0.389371 | −0.194685 | − | 0.980866i | \(-0.562369\pi\) | ||||
−0.194685 | + | 0.980866i | \(0.562369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.2487 | −0.807275 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00000 | −0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.19615 | −0.361166 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28.3923 | 1.24869 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.39230 | −0.192801 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.8564 | −1.39565 | −0.697827 | − | 0.716266i | \(-0.745850\pi\) | ||||
−0.697827 | + | 0.716266i | \(0.745850\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.9808 | −0.655063 | −0.327531 | − | 0.944840i | \(-0.606217\pi\) | ||||
−0.327531 | + | 0.944840i | \(0.606217\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.928203 | −0.0405101 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.7846 | −1.42812 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.1769 | 1.92074 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.7846 | −0.641597 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.78461 | 0.380504 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.7321 | −0.723390 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.5359 | 0.627270 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.6795 | 0.804583 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.7128 | −0.675547 | −0.337773 | − | 0.941227i | \(-0.609674\pi\) | ||||
−0.337773 | + | 0.941227i | \(0.609674\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.07180 | 0.217652 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.928203 | 0.0397599 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.80385 | −0.0771270 | −0.0385635 | − | 0.999256i | \(-0.512278\pi\) | ||||
−0.0385635 | + | 0.999256i | \(0.512278\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −31.8564 | −1.35960 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.2154 | 0.647024 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.39230 | −0.186443 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.7846 | 0.626444 | 0.313222 | − | 0.949680i | \(-0.398592\pi\) | ||||
0.313222 | + | 0.949680i | \(0.398592\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −35.3205 | −1.49390 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.78461 | −0.370887 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −26.1962 | −1.10404 | −0.552018 | − | 0.833832i | \(-0.686142\pi\) | ||||
−0.552018 | + | 0.833832i | \(0.686142\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.928203 | 0.0390498 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.66025 | −0.237708 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.2487 | 1.77116 | 0.885579 | − | 0.464489i | \(-0.153762\pi\) | ||||
0.885579 | + | 0.464489i | \(0.153762\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.3923 | −1.27188 | −0.635939 | − | 0.771739i | \(-0.719387\pi\) | ||||
−0.635939 | + | 0.771739i | \(0.719387\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.19615 | −0.341803 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.00000 | −0.0832611 | −0.0416305 | − | 0.999133i | \(-0.513255\pi\) | ||||
−0.0416305 | + | 0.999133i | \(0.513255\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.67949 | 0.194473 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | 0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.0000 | −1.49097 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.53590 | 0.352916 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.5167 | 0.557892 | 0.278946 | − | 0.960307i | \(-0.410015\pi\) | ||||
0.278946 | + | 0.960307i | \(0.410015\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.9282 | −0.779923 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.60770 | −0.312939 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.928203 | −0.0381167 | −0.0190584 | − | 0.999818i | \(-0.506067\pi\) | ||||
−0.0190584 | + | 0.999818i | \(0.506067\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.39230 | −0.180067 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.07180 | 0.207575 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0000 | −0.490307 | −0.245153 | − | 0.969484i | \(-0.578838\pi\) | ||||
−0.245153 | + | 0.969484i | \(0.578838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.3923 | 0.831819 | 0.415910 | − | 0.909406i | \(-0.363463\pi\) | ||||
0.415910 | + | 0.909406i | \(0.363463\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.1244 | 1.02314 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.19615 | −0.332672 | −0.166336 | − | 0.986069i | \(-0.553194\pi\) | ||||
−0.166336 | + | 0.986069i | \(0.553194\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.3923 | 1.14863 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.6077 | 0.549610 | 0.274805 | − | 0.961500i | \(-0.411387\pi\) | ||||
0.274805 | + | 0.961500i | \(0.411387\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.85641 | −0.0748575 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.6077 | −0.547825 | −0.273913 | − | 0.961755i | \(-0.588318\pi\) | ||||
−0.273913 | + | 0.961755i | \(0.588318\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.78461 | 0.272696 | 0.136348 | − | 0.990661i | \(-0.456463\pi\) | ||||
0.136348 | + | 0.990661i | \(0.456463\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.7846 | 1.31560 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.17691 | 0.0471521 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.07180 | −0.202548 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.7846 | −0.828737 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.4641 | −0.854472 | −0.427236 | − | 0.904140i | \(-0.640513\pi\) | ||||
−0.427236 | + | 0.904140i | \(0.640513\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.67949 | −0.185993 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.80385 | −0.150951 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.6795 | 0.740108 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.8231 | −0.428155 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.39230 | −0.173486 | −0.0867428 | − | 0.996231i | \(-0.527646\pi\) | ||||
−0.0867428 | + | 0.996231i | \(0.527646\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.5885 | −0.417568 | −0.208784 | − | 0.977962i | \(-0.566951\pi\) | ||||
−0.208784 | + | 0.977962i | \(0.566951\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.46410 | 0.293899 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.5885 | 1.43844 | 0.719220 | − | 0.694782i | \(-0.244499\pi\) | ||||
0.719220 | + | 0.694782i | \(0.244499\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.7846 | −0.815867 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.78461 | 0.344296 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.1769 | −0.750451 | −0.375225 | − | 0.926934i | \(-0.622435\pi\) | ||||
−0.375225 | + | 0.926934i | \(0.622435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.3923 | 0.406061 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −35.4641 | −1.38359 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.6410 | −1.58315 | −0.791575 | − | 0.611073i | \(-0.790738\pi\) | ||||
−0.791575 | + | 0.611073i | \(0.790738\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.5692 | −1.38348 | −0.691741 | − | 0.722146i | \(-0.743156\pi\) | ||||
−0.691741 | + | 0.722146i | \(0.743156\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.78461 | −0.341166 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.53590 | −0.0983379 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.0718 | −0.428060 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −44.7846 | −1.72889 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.1769 | −1.51016 | −0.755080 | − | 0.655633i | \(-0.772402\pi\) | ||||
−0.755080 | + | 0.655633i | \(0.772402\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.1769 | −1.65942 | −0.829712 | − | 0.558192i | \(-0.811495\pi\) | ||||
−0.829712 | + | 0.558192i | \(0.811495\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.10512 | 0.311046 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.6077 | −0.521448 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.6603 | −0.446167 | −0.223084 | − | 0.974799i | \(-0.571612\pi\) | ||||
−0.223084 | + | 0.974799i | \(0.571612\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.9282 | −0.493961 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.8564 | −0.528655 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.60770 | −0.213327 | −0.106663 | − | 0.994295i | \(-0.534017\pi\) | ||||
−0.106663 | + | 0.994295i | \(0.534017\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.8231 | −0.411135 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.0000 | 0.379322 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.78461 | −0.332741 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.17691 | 0.0445150 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.7846 | 0.558407 | 0.279204 | − | 0.960232i | \(-0.409930\pi\) | ||||
0.279204 | + | 0.960232i | \(0.409930\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | −0.452589 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | −0.225973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.2154 | 0.572234 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.1436 | 0.380951 | 0.190475 | − | 0.981692i | \(-0.438997\pi\) | ||||
0.190475 | + | 0.981692i | \(0.438997\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.5692 | 1.10893 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 77.5692 | 2.90499 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.2154 | 0.568229 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.7846 | 1.67018 | 0.835092 | − | 0.550110i | \(-0.185414\pi\) | ||||
0.835092 | + | 0.550110i | \(0.185414\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.3923 | 0.387030 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.9282 | −0.555186 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.0526 | −1.26294 | −0.631470 | − | 0.775401i | \(-0.717548\pi\) | ||||
−0.631470 | + | 0.775401i | \(0.717548\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 35.3205 | 1.30638 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.7846 | −1.43254 | −0.716271 | − | 0.697822i | \(-0.754153\pi\) | ||||
−0.716271 | + | 0.697822i | \(0.754153\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.94744 | −0.145604 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.3205 | 1.30105 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.00000 | −0.0735712 | −0.0367856 | − | 0.999323i | \(-0.511712\pi\) | ||||
−0.0367856 | + | 0.999323i | \(0.511712\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.07180 | −0.186317 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.5885 | −1.34230 | −0.671150 | − | 0.741321i | \(-0.734199\pi\) | ||||
−0.671150 | + | 0.741321i | \(0.734199\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0000 | 0.659469 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.6603 | 0.426626 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.2154 | 0.775193 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.3923 | −1.47394 | −0.736968 | − | 0.675928i | \(-0.763743\pi\) | ||||
−0.736968 | + | 0.675928i | \(0.763743\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.3205 | 0.412542 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.53590 | −0.0922908 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.0718 | −0.838559 | −0.419279 | − | 0.907857i | \(-0.637717\pi\) | ||||
−0.419279 | + | 0.907857i | \(0.637717\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.7846 | 0.754434 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.7128 | 0.787089 | 0.393544 | − | 0.919306i | \(-0.371249\pi\) | ||||
0.393544 | + | 0.919306i | \(0.371249\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.17691 | −0.0426072 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.53590 | −0.308616 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.7846 | −0.750489 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.78461 | −0.244659 | −0.122330 | − | 0.992490i | \(-0.539037\pi\) | ||||
−0.122330 | + | 0.992490i | \(0.539037\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.39230 | 0.158185 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 46.3923 | 1.66862 | 0.834308 | − | 0.551299i | \(-0.185868\pi\) | ||||
0.834308 | + | 0.551299i | \(0.185868\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.46410 | −0.339961 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.56922 | 0.199795 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.07180 | −0.181716 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.2154 | −0.544449 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.928203 | −0.0331290 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.80385 | 0.206885 | 0.103442 | − | 0.994635i | \(-0.467014\pi\) | ||||
0.103442 | + | 0.994635i | \(0.467014\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.7846 | 0.526346 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.17691 | −0.0418463 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −44.7846 | −1.59035 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.60770 | 0.269817 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.60770 | −0.0569475 | −0.0284737 | − | 0.999595i | \(-0.509065\pi\) | ||||
−0.0284737 | + | 0.999595i | \(0.509065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.3923 | −1.00445 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.28719 | 0.0808138 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −49.8564 | −1.75939 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.3923 | 0.366281 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.8231 | −0.380991 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.5692 | −1.25055 | −0.625274 | − | 0.780406i | \(-0.715013\pi\) | ||||
−0.625274 | + | 0.780406i | \(0.715013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38.3923 | −1.34814 | −0.674068 | − | 0.738669i | \(-0.735455\pi\) | ||||
−0.674068 | + | 0.738669i | \(0.735455\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.21539 | 0.112769 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.80385 | 0.203300 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.3923 | 0.713436 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.8231 | −0.378189 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.7846 | −1.77240 | −0.886198 | − | 0.463308i | \(-0.846663\pi\) | ||||
−0.886198 | + | 0.463308i | \(0.846663\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.8372 | −1.07492 | −0.537458 | − | 0.843290i | \(-0.680615\pi\) | ||||
−0.537458 | + | 0.843290i | \(0.680615\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.53590 | −0.0882886 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.73205 | 0.164550 | 0.0822748 | − | 0.996610i | \(-0.473781\pi\) | ||||
0.0822748 | + | 0.996610i | \(0.473781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.7846 | 1.76382 | 0.881911 | − | 0.471416i | \(-0.156257\pi\) | ||||
0.881911 | + | 0.471416i | \(0.156257\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.5359 | 0.504245 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.6795 | −0.647206 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.19615 | 0.283640 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37.8564 | 1.30851 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.78461 | −0.303278 | −0.151639 | − | 0.988436i | \(-0.548455\pi\) | ||||
−0.151639 | + | 0.988436i | \(0.548455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.7846 | 0.715860 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.26795 | −0.0435672 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.75129 | 0.266024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 49.1769 | 1.68576 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.46410 | 0.118609 | 0.0593043 | − | 0.998240i | \(-0.481112\pi\) | ||||
0.0593043 | + | 0.998240i | \(0.481112\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.92820 | −0.168541 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.1436 | 0.551455 | 0.275727 | − | 0.961236i | \(-0.411081\pi\) | ||||
0.275727 | + | 0.961236i | \(0.411081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −51.5692 | −1.75952 | −0.879760 | − | 0.475419i | \(-0.842296\pi\) | ||||
−0.879760 | + | 0.475419i | \(0.842296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.35383 | 0.0802183 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.9808 | 1.39500 | 0.697501 | − | 0.716584i | \(-0.254295\pi\) | ||||
0.697501 | + | 0.716584i | \(0.254295\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.66025 | −0.124309 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.5692 | 1.41014 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.3205 | 1.19679 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.7513 | 0.533100 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.26795 | −0.0428645 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.85641 | 0.265292 | 0.132646 | − | 0.991163i | \(-0.457653\pi\) | ||||
0.132646 | + | 0.991163i | \(0.457653\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −21.9615 | −0.740744 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.60770 | −0.256310 | −0.128155 | − | 0.991754i | \(-0.540905\pi\) | ||||
−0.128155 | + | 0.991754i | \(0.540905\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.80385 | 0.195315 | 0.0976575 | − | 0.995220i | \(-0.468865\pi\) | ||||
0.0976575 | + | 0.995220i | \(0.468865\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.39230 | 0.147646 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.3731 | 0.717637 | 0.358819 | − | 0.933407i | \(-0.383180\pi\) | ||||
0.358819 | + | 0.933407i | \(0.383180\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.82309 | 0.161761 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.4641 | −0.518067 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.3923 | −0.548548 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.8564 | 0.663726 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.7846 | 0.693978 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.46410 | −0.314946 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.92820 | 0.230301 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.41154 | 0.0468695 | 0.0234348 | − | 0.999725i | \(-0.492540\pi\) | ||||
0.0234348 | + | 0.999725i | \(0.492540\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.5692 | 0.980749 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.1769 | −1.23173 | −0.615863 | − | 0.787853i | \(-0.711193\pi\) | ||||
−0.615863 | + | 0.787853i | \(0.711193\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.3923 | 0.542506 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.46410 | 0.312874 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.1769 | −0.435140 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.7128 | −1.31000 | −0.655002 | − | 0.755627i | \(-0.727332\pi\) | ||||
−0.655002 | + | 0.755627i | \(0.727332\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.0333 | −0.824876 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15.2154 | −0.500821 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.1962 | 0.663329 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.60770 | 0.249600 | 0.124800 | − | 0.992182i | \(-0.460171\pi\) | ||||
0.124800 | + | 0.992182i | \(0.460171\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.7846 | −0.353451 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.56922 | 0.182328 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0000 | −0.392442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.60770 | 0.313870 | 0.156935 | − | 0.987609i | \(-0.449839\pi\) | ||||
0.156935 | + | 0.987609i | \(0.449839\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.1051 | −0.525571 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.7846 | −0.677559 | −0.338779 | − | 0.940866i | \(-0.610014\pi\) | ||||
−0.338779 | + | 0.940866i | \(0.610014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.7846 | 0.676840 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.07180 | 0.164986 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.8038 | 1.48843 | 0.744213 | − | 0.667943i | \(-0.232825\pi\) | ||||
0.744213 | + | 0.667943i | \(0.232825\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.8564 | −1.61841 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.3923 | 0.531557 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24.9282 | −0.807504 | −0.403752 | − | 0.914869i | \(-0.632294\pi\) | ||||
−0.403752 | + | 0.914869i | \(0.632294\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.3923 | 0.530443 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.3923 | 0.529335 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58.5692 | 1.88933 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 41.2295 | 1.32860 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.39230 | 0.205776 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.19615 | 0.263570 | 0.131785 | − | 0.991278i | \(-0.457929\pi\) | ||||
0.131785 | + | 0.991278i | \(0.457929\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.07180 | 0.162930 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.0333 | −1.06009 | −0.530045 | − | 0.847970i | \(-0.677825\pi\) | ||||
−0.530045 | + | 0.847970i | \(0.677825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.6795 | −0.406486 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.53590 | −0.0812137 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.32051 | 0.170218 | 0.0851091 | − | 0.996372i | \(-0.472876\pi\) | ||||
0.0851091 | + | 0.996372i | \(0.472876\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.21539 | 0.102764 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.28719 | −0.0730243 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.4115 | 0.363972 | 0.181986 | − | 0.983301i | \(-0.441747\pi\) | ||||
0.181986 | + | 0.983301i | \(0.441747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.3923 | −0.331126 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.60770 | 0.242156 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −83.5692 | −2.65735 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.1051 | 1.40105 | 0.700523 | − | 0.713630i | \(-0.252950\pi\) | ||||
0.700523 | + | 0.713630i | \(0.252950\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.10512 | 0.130272 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.92820 | 0.219639 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.6077 | 0.811004 | 0.405502 | − | 0.914094i | \(-0.367097\pi\) | ||||
0.405502 | + | 0.914094i | \(0.367097\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.0000 | 0.759326 |
(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 | 1280.2.a.c.1.2 | 2 | ||
4.3 | odd | 2 | 1280.2.a.p.1.1 | 2 | |||
5.4 | even | 2 | 6400.2.a.ck.1.1 | 2 | |||
8.3 | odd | 2 | 1280.2.a.b.1.2 | 2 | |||
8.5 | even | 2 | 1280.2.a.m.1.1 | 2 | |||
16.3 | odd | 4 | 320.2.d.a.161.2 | ✓ | 4 | ||
16.5 | even | 4 | 320.2.d.b.161.2 | yes | 4 | ||
16.11 | odd | 4 | 320.2.d.a.161.3 | yes | 4 | ||
16.13 | even | 4 | 320.2.d.b.161.3 | yes | 4 | ||
20.19 | odd | 2 | 6400.2.a.y.1.2 | 2 | |||
40.19 | odd | 2 | 6400.2.a.cd.1.1 | 2 | |||
40.29 | even | 2 | 6400.2.a.bf.1.2 | 2 | |||
48.5 | odd | 4 | 2880.2.k.l.1441.1 | 4 | |||
48.11 | even | 4 | 2880.2.k.e.1441.2 | 4 | |||
48.29 | odd | 4 | 2880.2.k.l.1441.3 | 4 | |||
48.35 | even | 4 | 2880.2.k.e.1441.4 | 4 | |||
80.3 | even | 4 | 1600.2.f.e.1249.4 | 4 | |||
80.13 | odd | 4 | 1600.2.f.h.1249.1 | 4 | |||
80.19 | odd | 4 | 1600.2.d.h.801.3 | 4 | |||
80.27 | even | 4 | 1600.2.f.e.1249.3 | 4 | |||
80.29 | even | 4 | 1600.2.d.b.801.2 | 4 | |||
80.37 | odd | 4 | 1600.2.f.h.1249.2 | 4 | |||
80.43 | even | 4 | 1600.2.f.i.1249.2 | 4 | |||
80.53 | odd | 4 | 1600.2.f.d.1249.3 | 4 | |||
80.59 | odd | 4 | 1600.2.d.h.801.2 | 4 | |||
80.67 | even | 4 | 1600.2.f.i.1249.1 | 4 | |||
80.69 | even | 4 | 1600.2.d.b.801.3 | 4 | |||
80.77 | odd | 4 | 1600.2.f.d.1249.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.2.d.a.161.2 | ✓ | 4 | 16.3 | odd | 4 | ||
320.2.d.a.161.3 | yes | 4 | 16.11 | odd | 4 | ||
320.2.d.b.161.2 | yes | 4 | 16.5 | even | 4 | ||
320.2.d.b.161.3 | yes | 4 | 16.13 | even | 4 | ||
1280.2.a.b.1.2 | 2 | 8.3 | odd | 2 | |||
1280.2.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1280.2.a.m.1.1 | 2 | 8.5 | even | 2 | |||
1280.2.a.p.1.1 | 2 | 4.3 | odd | 2 | |||
1600.2.d.b.801.2 | 4 | 80.29 | even | 4 | |||
1600.2.d.b.801.3 | 4 | 80.69 | even | 4 | |||
1600.2.d.h.801.2 | 4 | 80.59 | odd | 4 | |||
1600.2.d.h.801.3 | 4 | 80.19 | odd | 4 | |||
1600.2.f.d.1249.3 | 4 | 80.53 | odd | 4 | |||
1600.2.f.d.1249.4 | 4 | 80.77 | odd | 4 | |||
1600.2.f.e.1249.3 | 4 | 80.27 | even | 4 | |||
1600.2.f.e.1249.4 | 4 | 80.3 | even | 4 | |||
1600.2.f.h.1249.1 | 4 | 80.13 | odd | 4 | |||
1600.2.f.h.1249.2 | 4 | 80.37 | odd | 4 | |||
1600.2.f.i.1249.1 | 4 | 80.67 | even | 4 | |||
1600.2.f.i.1249.2 | 4 | 80.43 | even | 4 | |||
2880.2.k.e.1441.2 | 4 | 48.11 | even | 4 | |||
2880.2.k.e.1441.4 | 4 | 48.35 | even | 4 | |||
2880.2.k.l.1441.1 | 4 | 48.5 | odd | 4 | |||
2880.2.k.l.1441.3 | 4 | 48.29 | odd | 4 | |||
6400.2.a.y.1.2 | 2 | 20.19 | odd | 2 | |||
6400.2.a.bf.1.2 | 2 | 40.29 | even | 2 | |||
6400.2.a.cd.1.1 | 2 | 40.19 | odd | 2 | |||
6400.2.a.ck.1.1 | 2 | 5.4 | even | 2 |