Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,2,Mod(161,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.55521286468\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.161 |
Dual form | 320.2.d.a.161.3 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 0.732051i | − 0.422650i | −0.977416 | − | 0.211325i | \(-0.932222\pi\) | ||||
0.977416 | − | 0.211325i | \(-0.0677778\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 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 | ||||||||
\(11\) | − 3.46410i | − 1.04447i | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||||
0.852803 | − | 0.522233i | \(-0.174901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 3.46410i | − 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | − 2.00000i | − 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.928203i | 0.202551i | ||||||||
\(22\) | 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 | ||||||||
\(27\) | − 4.00000i | − 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.46410 | 1.69980 | 0.849901 | − | 0.526942i | \(-0.176661\pi\) | ||||
0.849901 | + | 0.526942i | \(0.176661\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.53590 | −0.441443 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.26795i | 0.214323i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.00000i | 0.986394i | 0.869918 | + | 0.493197i | \(0.164172\pi\) | ||||
−0.869918 | + | 0.493197i | \(0.835828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.53590 | −0.406069 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.53590 | 0.396041 | 0.198020 | − | 0.980198i | \(-0.436549\pi\) | ||||
0.198020 | + | 0.980198i | \(0.436549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1962i | 1.55490i | 0.628946 | + | 0.777449i | \(0.283487\pi\) | ||||
−0.628946 | + | 0.777449i | \(0.716513\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 2.46410i | − 0.367327i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.19615 | 1.19553 | 0.597766 | − | 0.801671i | \(-0.296055\pi\) | ||||
0.597766 | + | 0.801671i | \(0.296055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.39230 | −0.770329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 2.53590i | − 0.355097i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 10.3923i | − 1.42749i | −0.700404 | − | 0.713746i | \(-0.746997\pi\) | ||||
0.700404 | − | 0.713746i | \(-0.253003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.46410 | −0.467099 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.46410 | −0.193925 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000i | 0.781133i | 0.920575 | + | 0.390567i | \(0.127721\pi\) | ||||
−0.920575 | + | 0.390567i | \(0.872279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9282i | 1.65529i | 0.561254 | + | 0.827643i | \(0.310319\pi\) | ||||
−0.561254 | + | 0.827643i | \(0.689681\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.12436 | −0.393632 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.1962i | 1.24566i | 0.782358 | + | 0.622829i | \(0.214017\pi\) | ||||
−0.782358 | + | 0.622829i | \(0.785983\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000i | 0.722315i | ||||||||
\(70\) | 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 | \(-0.818767\pi\) | ||||
−0.842246 | + | 0.539093i | \(0.818767\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.732051i | 0.0845299i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.39230i | 0.500550i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.0000 | 1.35011 | 0.675053 | − | 0.737769i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737769i | \(0.264121\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.73205i | 0.519410i | 0.965688 | + | 0.259705i | \(0.0836253\pi\) | ||||
−0.965688 | + | 0.259705i | \(0.916375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 3.46410i | − 0.375735i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.928203 | 0.0983893 | 0.0491947 | − | 0.998789i | \(-0.484335\pi\) | ||||
0.0491947 | + | 0.998789i | \(0.484335\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.39230i | 0.460439i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 6.92820i | − 0.718421i | ||||||||
\(94\) | 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 | ||||||||
\(99\) | − 8.53590i | − 0.857890i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000i | 1.19404i | 0.802225 | + | 0.597022i | \(0.203650\pi\) | ||||
−0.802225 | + | 0.597022i | \(0.796350\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | − 16.7321i | − 1.61755i | −0.588119 | − | 0.808774i | \(-0.700131\pi\) | ||||
0.588119 | − | 0.808774i | \(-0.299869\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.928203i | 0.0889057i | 0.999011 | + | 0.0444529i | \(0.0141545\pi\) | ||||
−0.999011 | + | 0.0444529i | \(0.985846\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 8.19615i | 0.764295i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 8.53590i | − 0.789144i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.39230 | −0.402642 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 1.85641i | − 0.167387i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.80385 | 0.337537 | 0.168768 | − | 0.985656i | \(-0.446021\pi\) | ||||
0.168768 | + | 0.985656i | \(0.446021\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.46410 | 0.657178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 10.3923i | − 0.907980i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.53590i | 0.219890i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9282 | 1.10453 | 0.552265 | − | 0.833668i | \(-0.313763\pi\) | ||||
0.552265 | + | 0.833668i | \(0.313763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000i | 0.848189i | 0.905618 | + | 0.424094i | \(0.139408\pi\) | ||||
−0.905618 | + | 0.424094i | \(0.860592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 6.00000i | − 0.505291i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.0000 | −1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.94744i | 0.325579i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 18.0000i | − 1.47462i | −0.675556 | − | 0.737309i | \(-0.736096\pi\) | ||||
0.675556 | − | 0.737309i | \(-0.263904\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | − 9.46410i | − 0.760175i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 0.928203i | − 0.0740787i | −0.999314 | − | 0.0370393i | \(-0.988207\pi\) | ||||
0.999314 | − | 0.0370393i | \(-0.0117927\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.60770 | −0.603329 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.3923 | 0.819028 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 5.80385i | − 0.454592i | −0.973826 | − | 0.227296i | \(-0.927011\pi\) | ||||
0.973826 | − | 0.227296i | \(-0.0729886\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.53590i | 0.197419i | ||||||||
\(166\) | 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 | ||||||||
\(171\) | − 4.92820i | − 0.376869i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 6.00000i | − 0.456172i | −0.973641 | − | 0.228086i | \(-0.926753\pi\) | ||||
0.973641 | − | 0.228086i | \(-0.0732467\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.26795 | 0.0958479 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.39230 | 0.330146 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 19.8564i | − 1.48414i | −0.670324 | − | 0.742069i | \(-0.733845\pi\) | ||||
0.670324 | − | 0.742069i | \(-0.266155\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.92820i | − 0.514969i | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||||
0.966282 | − | 0.257485i | \(-0.0828937\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.46410 | 0.699607 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 12.0000i | − 0.877527i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.07180i | 0.368919i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.3923 | −1.18611 | −0.593053 | − | 0.805164i | \(-0.702077\pi\) | ||||
−0.593053 | + | 0.805164i | \(0.702077\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.39230 | 0.460128 | 0.230064 | − | 0.973175i | \(-0.426106\pi\) | ||||
0.230064 | + | 0.973175i | \(0.426106\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.53590i | 0.181599i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.3923i | 0.740421i | 0.928948 | + | 0.370211i | \(0.120714\pi\) | ||||
−0.928948 | + | 0.370211i | \(0.879286\pi\) | |||||||
\(198\) | 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 | ||||||||
\(205\) | − 2.53590i | − 0.177115i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.1962 | −1.40373 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.92820 | −0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.39230i | 0.440064i | 0.975493 | + | 0.220032i | \(0.0706162\pi\) | ||||
−0.975493 | + | 0.220032i | \(0.929384\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 3.21539i | − 0.220315i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.1962 | 0.695372 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.0000 | −0.814613 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5359i | 0.711950i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 12.0000i | − 0.807207i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.1244 | 1.01280 | 0.506401 | − | 0.862298i | \(-0.330976\pi\) | ||||
0.506401 | + | 0.862298i | \(0.330976\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.46410 | −0.164273 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.5885i | 1.23376i | 0.787058 | + | 0.616880i | \(0.211603\pi\) | ||||
−0.787058 | + | 0.616880i | \(0.788397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.9282i | 1.25081i | 0.780300 | + | 0.625405i | \(0.215066\pi\) | ||||
−0.780300 | + | 0.625405i | \(0.784934\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.21539 | 0.211557 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.60770 | −0.105324 | −0.0526618 | − | 0.998612i | \(-0.516771\pi\) | ||||
−0.0526618 | + | 0.998612i | \(0.516771\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 8.19615i | − 0.534658i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8.78461i | − 0.570622i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.7846 | −1.34444 | −0.672222 | − | 0.740349i | \(-0.734660\pi\) | ||||
−0.672222 | + | 0.740349i | \(0.734660\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3923 | −1.31358 | −0.656792 | − | 0.754072i | \(-0.728087\pi\) | ||||
−0.656792 | + | 0.754072i | \(0.728087\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.2679i | − 0.979439i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.39230i | 0.344502i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.92820 | −0.440831 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.46410 | 0.219529 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4641i | 0.976085i | 0.872820 | + | 0.488043i | \(0.162289\pi\) | ||||
−0.872820 | + | 0.488043i | \(0.837711\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.3923i | 1.78501i | ||||||||
\(254\) | 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 | ||||||||
\(259\) | − 7.60770i | − 0.472719i | ||||||||
\(260\) | 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 | ||||||||
\(267\) | − 0.679492i | − 0.0415842i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 14.7846i | − 0.901434i | −0.892667 | − | 0.450717i | \(-0.851168\pi\) | ||||
0.892667 | − | 0.450717i | \(-0.148832\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.39230 | −0.266814 | −0.133407 | − | 0.991061i | \(-0.542592\pi\) | ||||
−0.133407 | + | 0.991061i | \(0.542592\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.21539 | 0.194604 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.46410i | 0.208893i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 19.8564i | − 1.19306i | −0.802592 | − | 0.596528i | \(-0.796546\pi\) | ||||
0.802592 | − | 0.596528i | \(-0.203454\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.3205 | 1.39616 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.3923 | −1.69374 | −0.846871 | − | 0.531798i | \(-0.821517\pi\) | ||||
−0.846871 | + | 0.531798i | \(0.821517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.5885i | 0.629418i | 0.949188 | + | 0.314709i | \(0.101907\pi\) | ||||
−0.949188 | + | 0.314709i | \(0.898093\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.46410i | 0.0867259i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.21539 | −0.189798 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.67949i | 0.274317i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.0000i | 1.75262i | 0.481749 | + | 0.876309i | \(0.340002\pi\) | ||||
−0.481749 | + | 0.876309i | \(0.659998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −13.8564 | −0.804030 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.3923i | 1.64197i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 12.9282i | − 0.745169i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.78461 | 0.504663 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.9282 | 0.740267 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.1962i | 1.95168i | 0.218492 | + | 0.975839i | \(0.429886\pi\) | ||||
−0.218492 | + | 0.975839i | \(0.570114\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000i | 0.341328i | ||||||||
\(310\) | 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 | \(-0.286419\pi\) | ||||
0.621757 | + | 0.783210i | \(0.286419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.12436i | 0.176037i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.3923i | 1.25768i | 0.777536 | + | 0.628839i | \(0.216469\pi\) | ||||
−0.777536 | + | 0.628839i | \(0.783531\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.2487 | −0.683656 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 6.92820i | − 0.385496i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.46410i | 0.192154i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.679492 | 0.0375760 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.3923 | −0.572946 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.60770i | 0.308227i | 0.988053 | + | 0.154113i | \(0.0492521\pi\) | ||||
−0.988053 | + | 0.154113i | \(0.950748\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.7846i | 0.810192i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | − 0.679492i | − 0.0369049i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 32.7846i | − 1.77539i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7128 | 0.848412 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.00000 | 0.323029 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 28.0526i | − 1.50594i | −0.658055 | − | 0.752970i | \(-0.728620\pi\) | ||||
0.658055 | − | 0.752970i | \(-0.271380\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.78461i | 0.470229i | 0.971968 | + | 0.235115i | \(0.0755466\pi\) | ||||
−0.971968 | + | 0.235115i | \(0.924453\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | − 4.39230i | − 0.233119i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.21539i | 0.170177i | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 0.732051i | 0.0384227i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.3923i | 0.753328i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0526 | −0.524739 | −0.262370 | − | 0.964967i | \(-0.584504\pi\) | ||||
−0.262370 | + | 0.964967i | \(0.584504\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.24871 | 0.325295 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.1769i | 0.684111i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.85641i | 0.406789i | 0.979097 | + | 0.203395i | \(0.0651974\pi\) | ||||
−0.979097 | + | 0.203395i | \(0.934803\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.732051 | 0.0378029 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000i | 0.102733i | 0.998680 | + | 0.0513665i | \(0.0163577\pi\) | ||||
−0.998680 | + | 0.0513665i | \(0.983642\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 2.78461i | − 0.142660i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.80385 | −0.194368 | −0.0971838 | − | 0.995266i | \(-0.530983\pi\) | ||||
−0.0971838 | + | 0.995266i | \(0.530983\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.39230 | 0.223853 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 25.1244i | 1.27714i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 26.7846i | − 1.35803i | −0.734123 | − | 0.679017i | \(-0.762406\pi\) | ||||
0.734123 | − | 0.679017i | \(-0.237594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.3923 | −1.43586 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.60770 | −0.383757 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 12.0000i | − 0.603786i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 27.4641i | − 1.37838i | −0.724579 | − | 0.689192i | \(-0.757966\pi\) | ||||
0.724579 | − | 0.689192i | \(-0.242034\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − 32.7846i | − 1.63312i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 4.46410i | − 0.221823i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.7846 | 1.03025 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.60770 | 0.178389 | 0.0891945 | − | 0.996014i | \(-0.471571\pi\) | ||||
0.0891945 | + | 0.996014i | \(0.471571\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 9.46410i | − 0.466830i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 7.60770i | − 0.374350i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.73205 | 0.232287 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.32051 | 0.358487 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 0.928203i | − 0.0453457i | −0.999743 | − | 0.0226728i | \(-0.992782\pi\) | ||||
0.999743 | − | 0.0226728i | \(-0.00721761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000i | 0.292422i | 0.989253 | + | 0.146211i | \(0.0467079\pi\) | ||||
−0.989253 | + | 0.146211i | \(0.953292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.1962 | 0.981971 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 16.3923i | − 0.793279i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.78461i | 0.424125i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.3923 | −1.36761 | −0.683805 | − | 0.729665i | \(-0.739676\pi\) | ||||
−0.683805 | + | 0.729665i | \(0.739676\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | 16.3923i | 0.784150i | ||||||||
\(438\) | 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 | ||||||||
\(443\) | − 0.339746i | − 0.0161418i | −0.999967 | − | 0.00807091i | \(-0.997431\pi\) | ||||
0.999967 | − | 0.00807091i | \(-0.00256908\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 0.928203i | − 0.0440011i | ||||||||
\(446\) | 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 | ||||||||
\(451\) | − 8.78461i | − 0.413651i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.85641i | 0.0872216i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.39230 | 0.205914 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.7846 | 1.06582 | 0.532910 | − | 0.846172i | \(-0.321099\pi\) | ||||
0.532910 | + | 0.846172i | \(0.321099\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 13.8564i | − 0.646762i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000i | 0.558896i | 0.960161 | + | 0.279448i | \(0.0901514\pi\) | ||||
−0.960161 | + | 0.279448i | \(0.909849\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.8038 | 0.734467 | 0.367234 | − | 0.930129i | \(-0.380305\pi\) | ||||
0.367234 | + | 0.930129i | \(0.380305\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.92820 | −0.321288 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 22.9808i | − 1.06342i | −0.846926 | − | 0.531711i | \(-0.821549\pi\) | ||||
0.846926 | − | 0.531711i | \(-0.178451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 12.9282i | − 0.596969i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.679492 | −0.0313093 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.3205 | 1.62404 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000i | 0.0917663i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 25.6077i | − 1.17250i | ||||||||
\(478\) | 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 | ||||||||
\(483\) | − 7.60770i | − 0.346162i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.39230i | 0.290260i | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 22.3923i | 1.01055i | 0.862958 | + | 0.505275i | \(0.168609\pi\) | ||||
−0.862958 | + | 0.505275i | \(0.831391\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.53590 | −0.383660 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.56922 | −0.249814 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 39.5692i | − 1.77136i | −0.464295 | − | 0.885681i | \(-0.653692\pi\) | ||||
0.464295 | − | 0.885681i | \(-0.346308\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 6.00000i | − 0.268060i | ||||||||
\(502\) | 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 | ||||||||
\(507\) | − 0.732051i | − 0.0325115i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 8.78461i | − 0.389371i | −0.980866 | − | 0.194685i | \(-0.937631\pi\) | ||||
0.980866 | − | 0.194685i | \(-0.0623686\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.2487 | 0.807275 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00000 | −0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.19615i | 0.361166i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 28.3923i | − 1.24869i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.39230 | −0.192801 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.8564 | 1.39565 | 0.697827 | − | 0.716266i | \(-0.254150\pi\) | ||||
0.697827 | + | 0.716266i | \(0.254150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 14.9808i | − 0.655063i | −0.944840 | − | 0.327531i | \(-0.893783\pi\) | ||||
0.944840 | − | 0.327531i | \(-0.106217\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 0.928203i | − 0.0405101i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.7846 | 1.42812 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.1769 | 1.92074 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.7846i | 0.641597i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 8.78461i | − 0.380504i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.7321 | −0.723390 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.5359 | −0.627270 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.6795i | 0.804583i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 15.7128i | − 0.675547i | −0.941227 | − | 0.337773i | \(-0.890326\pi\) | ||||
0.941227 | − | 0.337773i | \(-0.109674\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.07180 | −0.217652 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.928203 | 0.0397599 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.80385i | 0.0771270i | 0.999256 | + | 0.0385635i | \(0.0122782\pi\) | ||||
−0.999256 | + | 0.0385635i | \(0.987722\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.8564i | 1.35960i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.2154 | −0.647024 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 4.39230i | − 0.186443i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.7846i | 0.626444i | 0.949680 | + | 0.313222i | \(0.101408\pi\) | ||||
−0.949680 | + | 0.313222i | \(0.898592\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35.3205 | 1.49390 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.78461 | −0.370887 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.1962i | 1.10404i | 0.833832 | + | 0.552018i | \(0.186142\pi\) | ||||
−0.833832 | + | 0.552018i | \(0.813858\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 0.928203i | − 0.0390498i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.66025 | −0.237708 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −42.2487 | −1.77116 | −0.885579 | − | 0.464489i | \(-0.846238\pi\) | ||||
−0.885579 | + | 0.464489i | \(0.846238\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 30.3923i | − 1.27188i | −0.771739 | − | 0.635939i | \(-0.780613\pi\) | ||||
0.771739 | − | 0.635939i | \(-0.219387\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000i | 0.501307i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | − 4.67949i | − 0.194473i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.00000i | − 0.248922i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −36.0000 | −1.49097 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.53590 | −0.352916 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.5167i | 0.557892i | 0.960307 | + | 0.278946i | \(0.0899851\pi\) | ||||
−0.960307 | + | 0.278946i | \(0.910015\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 18.9282i | − 0.779923i | ||||||||
\(590\) | 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 | ||||||||
\(595\) | 4.39230i | 0.180067i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 5.07180i | − 0.207575i | ||||||||
\(598\) | 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 | \(-0.636537\pi\) | ||||
−0.415910 | + | 0.909406i | \(0.636537\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.1244i | 1.02314i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000i | 0.0406558i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.19615 | 0.332672 | 0.166336 | − | 0.986069i | \(-0.446806\pi\) | ||||
0.166336 | + | 0.986069i | \(0.446806\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 28.3923i | − 1.14863i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 13.6077i | − 0.549610i | −0.961500 | − | 0.274805i | \(-0.911387\pi\) | ||||
0.961500 | − | 0.274805i | \(-0.0886132\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.85641 | −0.0748575 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.6077 | 0.547825 | 0.273913 | − | 0.961755i | \(-0.411682\pi\) | ||||
0.273913 | + | 0.961755i | \(0.411682\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.78461i | 0.272696i | 0.990661 | + | 0.136348i | \(0.0435366\pi\) | ||||
−0.990661 | + | 0.136348i | \(0.956463\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.7846i | 1.31560i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.17691 | −0.0471521 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.07180i | 0.202548i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.7846i | 0.828737i | ||||||||
\(630\) | 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 | ||||||||
\(635\) | − 3.80385i | − 0.150951i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.6795i | 0.740108i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | 10.5885i | 0.417568i | 0.977962 | + | 0.208784i | \(0.0669506\pi\) | ||||
−0.977962 | + | 0.208784i | \(0.933049\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 7.46410i | − 0.293899i | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 8.78461i | 0.344296i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 19.1769i | − 0.750451i | −0.926934 | − | 0.375225i | \(-0.877565\pi\) | ||||
0.926934 | − | 0.375225i | \(-0.122435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.3923 | −0.406061 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −35.4641 | −1.38359 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.6410i | 1.58315i | 0.611073 | + | 0.791575i | \(0.290738\pi\) | ||||
−0.611073 | + | 0.791575i | \(0.709262\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.5692i | 1.38348i | 0.722146 | + | 0.691741i | \(0.243156\pi\) | ||||
−0.722146 | + | 0.691741i | \(0.756844\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.78461 | −0.341166 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.53590 | 0.0983379 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 11.0718i | − 0.428060i | ||||||||
\(670\) | 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 | ||||||||
\(675\) | 4.00000i | 0.153960i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 43.1769i | 1.65942i | 0.558192 | + | 0.829712i | \(0.311495\pi\) | ||||
−0.558192 | + | 0.829712i | \(0.688505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.10512 | 0.311046 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.6077 | 0.521448 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 11.6603i | − 0.446167i | −0.974799 | − | 0.223084i | \(-0.928388\pi\) | ||||
0.974799 | − | 0.223084i | \(-0.0716123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 12.9282i | − 0.493961i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.8564 | 0.528655 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.0000 | −1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.60770i | 0.213327i | 0.994295 | + | 0.106663i | \(0.0340167\pi\) | ||||
−0.994295 | + | 0.106663i | \(0.965983\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.8231i | 0.411135i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.0000 | 0.379322 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.78461 | 0.332741 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.17691i | 0.0445150i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.7846i | 0.558407i | 0.960232 | + | 0.279204i | \(0.0900704\pi\) | ||||
−0.960232 | + | 0.279204i | \(0.909930\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | 0.452589 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.00000 | −0.225973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 15.2154i | − 0.572234i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 10.1436i | − 0.380951i | −0.981692 | − | 0.190475i | \(-0.938997\pi\) | ||||
0.981692 | − | 0.190475i | \(-0.0610029\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.5692 | 1.10893 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −77.5692 | −2.90499 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.0000i | 0.448775i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.2154i | 0.568229i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −44.7846 | −1.67018 | −0.835092 | − | 0.550110i | \(-0.814586\pi\) | ||||
−0.835092 | + | 0.550110i | \(0.814586\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.3923 | 0.387030 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.9282i | 0.555186i | ||||||||
\(724\) | 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 | ||||||||
\(731\) | 35.3205i | 1.30638i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 38.7846i | − 1.43254i | −0.697822 | − | 0.716271i | \(-0.745847\pi\) | ||||
0.697822 | − | 0.716271i | \(-0.254153\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.94744 | 0.145604 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.3205 | 1.30105 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.00000i | 0.0735712i | 0.999323 | + | 0.0367856i | \(0.0117119\pi\) | ||||
−0.999323 | + | 0.0367856i | \(0.988288\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.07180i | 0.186317i | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 11.6603i | 0.426626i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.2154i | 0.775193i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.3923 | 1.47394 | 0.736968 | − | 0.675928i | \(-0.236257\pi\) | ||||
0.736968 | + | 0.675928i | \(0.236257\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.3205 | 0.412542 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.53590i | 0.0922908i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.0718i | 0.838559i | 0.907857 | + | 0.419279i | \(0.137717\pi\) | ||||
−0.907857 | + | 0.419279i | \(0.862283\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.7846 | 0.754434 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.7128 | −0.787089 | −0.393544 | − | 0.919306i | \(-0.628751\pi\) | ||||
−0.393544 | + | 0.919306i | \(0.628751\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.17691i | − 0.0426072i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 8.53590i | − 0.308616i | ||||||||
\(766\) | 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 | ||||||||
\(771\) | − 4.39230i | − 0.158185i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 46.3923i | − 1.66862i | −0.551299 | − | 0.834308i | \(-0.685868\pi\) | ||||
0.551299 | − | 0.834308i | \(-0.314132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.46410 | −0.339961 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.56922 | −0.199795 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 5.07180i | − 0.181716i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 15.2154i | − 0.544449i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.928203 | −0.0331290 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 5.80385i | − 0.206885i | −0.994635 | − | 0.103442i | \(-0.967014\pi\) | ||||
0.994635 | − | 0.103442i | \(-0.0329857\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 14.7846i | − 0.526346i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.17691 | −0.0418463 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44.7846 | 1.59035 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.60770i | 0.269817i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.60770i | − 0.0569475i | −0.999595 | − | 0.0284737i | \(-0.990935\pi\) | ||||
0.999595 | − | 0.0284737i | \(-0.00906470\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.3923 | 1.00445 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.28719 | 0.0808138 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 49.8564i | 1.75939i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 10.3923i | − 0.366281i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.8231 | −0.380991 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 35.5692 | 1.25055 | 0.625274 | − | 0.780406i | \(-0.284987\pi\) | ||||
0.625274 | + | 0.780406i | \(0.284987\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 38.3923i | − 1.34814i | −0.738669 | − | 0.674068i | \(-0.764545\pi\) | ||||
0.738669 | − | 0.674068i | \(-0.235455\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.21539i | 0.112769i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.80385 | −0.203300 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.3923 | 0.713436 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.8231i | 0.378189i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.7846i | 1.77240i | 0.463308 | + | 0.886198i | \(0.346663\pi\) | ||||
−0.463308 | + | 0.886198i | \(0.653337\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | 4.73205i | 0.164550i | 0.996610 | + | 0.0822748i | \(0.0262185\pi\) | ||||
−0.996610 | + | 0.0822748i | \(0.973781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.7846i | 1.76382i | 0.471416 | + | 0.881911i | \(0.343743\pi\) | ||||
−0.471416 | + | 0.881911i | \(0.656257\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.5359 | −0.504245 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.6795 | −0.647206 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 8.19615i | − 0.283640i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 37.8564i | − 1.30851i | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 20.7846i | 0.715860i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.00000i | − 0.0344010i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.26795 | 0.0435672 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.75129 | 0.266024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 49.1769i | − 1.68576i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 3.46410i | − 0.118609i | −0.998240 | − | 0.0593043i | \(-0.981112\pi\) | ||||
0.998240 | − | 0.0593043i | \(-0.0188882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.92820 | −0.168541 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.1436 | −0.551455 | −0.275727 | − | 0.961236i | \(-0.588919\pi\) | ||||
−0.275727 | + | 0.961236i | \(0.588919\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 51.5692i | − 1.75952i | −0.475419 | − | 0.879760i | \(-0.657704\pi\) | ||||
0.475419 | − | 0.879760i | \(-0.342296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.35383i | 0.0802183i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.9808 | −1.39500 | −0.697501 | − | 0.716584i | \(-0.745705\pi\) | ||||
−0.697501 | + | 0.716584i | \(0.745705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.66025i | 0.124309i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 41.5692i | − 1.41014i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.3205 | 1.19679 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.7513 | −0.533100 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.26795i | − 0.0428645i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.85641i | 0.265292i | 0.991163 | + | 0.132646i | \(0.0423473\pi\) | ||||
−0.991163 | + | 0.132646i | \(0.957653\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − 5.80385i | − 0.195315i | −0.995220 | − | 0.0976575i | \(-0.968865\pi\) | ||||
0.995220 | − | 0.0976575i | \(-0.0311350\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 4.39230i | − 0.147646i | ||||||||
\(886\) | 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 | ||||||||
\(891\) | − 15.4641i | − 0.518067i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 16.3923i | − 0.548548i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.8564 | −0.663726 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.7846 | 0.693978 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 36.0000i | − 1.19933i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.46410 | −0.314946 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.92820 | −0.230301 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.41154i | 0.0468695i | 0.999725 | + | 0.0234348i | \(0.00746020\pi\) | ||||
−0.999725 | + | 0.0234348i | \(0.992540\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.5692i | 0.980749i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.1769 | 1.23173 | 0.615863 | − | 0.787853i | \(-0.288807\pi\) | ||||
0.615863 | + | 0.787853i | \(0.288807\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.3923 | 0.542506 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 9.46410i | − 0.312874i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.1769i | 0.435140i | ||||||||
\(918\) | 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 | ||||||||
\(923\) | − 15.2154i | − 0.500821i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 6.00000i | − 0.197279i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 10.7846i | 0.353451i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 5.56922i | − 0.182328i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0000 | −0.392442 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.60770 | −0.313870 | −0.156935 | − | 0.987609i | \(-0.550161\pi\) | ||||
−0.156935 | + | 0.987609i | \(0.550161\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 16.1051i | − 0.525571i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 20.7846i | − 0.677559i | −0.940866 | − | 0.338779i | \(-0.889986\pi\) | ||||
0.940866 | − | 0.338779i | \(-0.110014\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.7846 | −0.676840 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.07180 | 0.164986 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 45.8038i | − 1.48843i | −0.667943 | − | 0.744213i | \(-0.732825\pi\) | ||||
0.667943 | − | 0.744213i | \(-0.267175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 49.8564i | 1.61841i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.3923 | 0.531557 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.9282 | 0.807504 | 0.403752 | − | 0.914869i | \(-0.367706\pi\) | ||||
0.403752 | + | 0.914869i | \(0.367706\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.3923i | 0.530443i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.3923 | −0.529335 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58.5692 | 1.88933 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 41.2295i | − 1.32860i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 6.39230i | − 0.205776i | ||||||||
\(966\) | 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 | ||||||||
\(971\) | − 33.0333i | − 1.06009i | −0.847970 | − | 0.530045i | \(-0.822175\pi\) | ||||
0.847970 | − | 0.530045i | \(-0.177825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 12.6795i | − 0.406486i | ||||||||
\(974\) | 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 | ||||||||
\(979\) | − 3.21539i | − 0.102764i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.28719i | 0.0730243i | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 7.60770i | 0.242156i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 83.5692i | − 2.65735i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.1051 | −1.40105 | −0.700523 | − | 0.713630i | \(-0.747050\pi\) | ||||
−0.700523 | + | 0.713630i | \(0.747050\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.10512 | 0.130272 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 6.92820i | − 0.219639i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 25.6077i | − 0.811004i | −0.914094 | − | 0.405502i | \(-0.867097\pi\) | ||||
0.914094 | − | 0.405502i | \(-0.132903\pi\) | |||||||
\(998\) | 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 | 320.2.d.a.161.2 | ✓ | 4 | |
3.2 | odd | 2 | 2880.2.k.e.1441.4 | 4 | |||
4.3 | odd | 2 | 320.2.d.b.161.3 | yes | 4 | ||
5.2 | odd | 4 | 1600.2.f.i.1249.1 | 4 | |||
5.3 | odd | 4 | 1600.2.f.e.1249.4 | 4 | |||
5.4 | even | 2 | 1600.2.d.h.801.3 | 4 | |||
8.3 | odd | 2 | 320.2.d.b.161.2 | yes | 4 | ||
8.5 | even | 2 | inner | 320.2.d.a.161.3 | yes | 4 | |
12.11 | even | 2 | 2880.2.k.l.1441.3 | 4 | |||
16.3 | odd | 4 | 1280.2.a.m.1.1 | 2 | |||
16.5 | even | 4 | 1280.2.a.p.1.1 | 2 | |||
16.11 | odd | 4 | 1280.2.a.c.1.2 | 2 | |||
16.13 | even | 4 | 1280.2.a.b.1.2 | 2 | |||
20.3 | even | 4 | 1600.2.f.h.1249.1 | 4 | |||
20.7 | even | 4 | 1600.2.f.d.1249.4 | 4 | |||
20.19 | odd | 2 | 1600.2.d.b.801.2 | 4 | |||
24.5 | odd | 2 | 2880.2.k.e.1441.2 | 4 | |||
24.11 | even | 2 | 2880.2.k.l.1441.1 | 4 | |||
40.3 | even | 4 | 1600.2.f.d.1249.3 | 4 | |||
40.13 | odd | 4 | 1600.2.f.i.1249.2 | 4 | |||
40.19 | odd | 2 | 1600.2.d.b.801.3 | 4 | |||
40.27 | even | 4 | 1600.2.f.h.1249.2 | 4 | |||
40.29 | even | 2 | 1600.2.d.h.801.2 | 4 | |||
40.37 | odd | 4 | 1600.2.f.e.1249.3 | 4 | |||
80.19 | odd | 4 | 6400.2.a.bf.1.2 | 2 | |||
80.29 | even | 4 | 6400.2.a.cd.1.1 | 2 | |||
80.59 | odd | 4 | 6400.2.a.ck.1.1 | 2 | |||
80.69 | even | 4 | 6400.2.a.y.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.2.d.a.161.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
320.2.d.a.161.3 | yes | 4 | 8.5 | even | 2 | inner | |
320.2.d.b.161.2 | yes | 4 | 8.3 | odd | 2 | ||
320.2.d.b.161.3 | yes | 4 | 4.3 | odd | 2 | ||
1280.2.a.b.1.2 | 2 | 16.13 | even | 4 | |||
1280.2.a.c.1.2 | 2 | 16.11 | odd | 4 | |||
1280.2.a.m.1.1 | 2 | 16.3 | odd | 4 | |||
1280.2.a.p.1.1 | 2 | 16.5 | even | 4 | |||
1600.2.d.b.801.2 | 4 | 20.19 | odd | 2 | |||
1600.2.d.b.801.3 | 4 | 40.19 | odd | 2 | |||
1600.2.d.h.801.2 | 4 | 40.29 | even | 2 | |||
1600.2.d.h.801.3 | 4 | 5.4 | even | 2 | |||
1600.2.f.d.1249.3 | 4 | 40.3 | even | 4 | |||
1600.2.f.d.1249.4 | 4 | 20.7 | even | 4 | |||
1600.2.f.e.1249.3 | 4 | 40.37 | odd | 4 | |||
1600.2.f.e.1249.4 | 4 | 5.3 | odd | 4 | |||
1600.2.f.h.1249.1 | 4 | 20.3 | even | 4 | |||
1600.2.f.h.1249.2 | 4 | 40.27 | even | 4 | |||
1600.2.f.i.1249.1 | 4 | 5.2 | odd | 4 | |||
1600.2.f.i.1249.2 | 4 | 40.13 | odd | 4 | |||
2880.2.k.e.1441.2 | 4 | 24.5 | odd | 2 | |||
2880.2.k.e.1441.4 | 4 | 3.2 | odd | 2 | |||
2880.2.k.l.1441.1 | 4 | 24.11 | even | 2 | |||
2880.2.k.l.1441.3 | 4 | 12.11 | even | 2 | |||
6400.2.a.y.1.2 | 2 | 80.69 | even | 4 | |||
6400.2.a.bf.1.2 | 2 | 80.19 | odd | 4 | |||
6400.2.a.cd.1.1 | 2 | 80.29 | even | 4 | |||
6400.2.a.ck.1.1 | 2 | 80.59 | odd | 4 |