Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(1249,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7760643234\) |
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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 320) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.4 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.1249 |
Dual form | 1600.2.f.d.1249.3 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0.732051 | 0.422650 | 0.211325 | − | 0.977416i | \(-0.432222\pi\) | ||||
0.211325 | + | 0.977416i | \(0.432222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.26795i | 0.479240i | 0.970867 | + | 0.239620i | \(0.0770228\pi\) | ||||
−0.970867 | + | 0.239620i | \(0.922977\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 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 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.46410i | 0.840168i | 0.907485 | + | 0.420084i | \(0.137999\pi\) | ||||
−0.907485 | + | 0.420084i | \(0.862001\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | − 8.19615i | − 1.70902i | −0.519438 | − | 0.854508i | \(-0.673859\pi\) | ||||
0.519438 | − | 0.854508i | \(-0.326141\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.46410 | −1.69980 | −0.849901 | − | 0.526942i | \(-0.823339\pi\) | ||||
−0.849901 | + | 0.526942i | \(0.823339\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.53590i | 0.441443i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 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 | \(-0.436549\pi\) | ||||
0.198020 | + | 0.980198i | \(0.436549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.1962 | −1.55490 | −0.777449 | − | 0.628946i | \(-0.783487\pi\) | ||||
−0.777449 | + | 0.628946i | \(0.783487\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 8.19615i | − 1.19553i | −0.801671 | − | 0.597766i | \(-0.796055\pi\) | ||||
0.801671 | − | 0.597766i | \(-0.203945\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.39230 | 0.770329 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.53590i | 0.355097i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3923 | −1.42749 | −0.713746 | − | 0.700404i | \(-0.753003\pi\) | ||||
−0.713746 | + | 0.700404i | \(0.753003\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 1.46410i | − 0.193925i | ||||||||
\(58\) | 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 | ||||||||
\(63\) | − 3.12436i | − 0.393632i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.1962 | 1.24566 | 0.622829 | − | 0.782358i | \(-0.285983\pi\) | ||||
0.622829 | + | 0.782358i | \(0.285983\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 6.00000i | − 0.722315i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.39230 | −0.521271 | −0.260635 | − | 0.965437i | \(-0.583932\pi\) | ||||
−0.260635 | + | 0.965437i | \(0.583932\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.3923i | 1.68449i | 0.539093 | + | 0.842246i | \(0.318767\pi\) | ||||
−0.539093 | + | 0.842246i | \(0.681233\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.39230 | −0.500550 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | −4.73205 | −0.519410 | −0.259705 | − | 0.965688i | \(-0.583625\pi\) | ||||
−0.259705 | + | 0.965688i | \(0.583625\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 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 | ||||||||
\(91\) | − 4.39230i | − 0.460439i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.92820 | −0.718421 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 6.39230i | − 0.649040i | −0.945879 | − | 0.324520i | \(-0.894797\pi\) | ||||
0.945879 | − | 0.324520i | \(-0.105203\pi\) | |||||||
\(98\) | 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 | ||||||||
\(103\) | − 8.19615i | − 0.807591i | −0.914849 | − | 0.403795i | \(-0.867691\pi\) | ||||
0.914849 | − | 0.403795i | \(-0.132309\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.7321 | −1.61755 | −0.808774 | − | 0.588119i | \(-0.799869\pi\) | ||||
−0.808774 | + | 0.588119i | \(0.799869\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 0.928203i | − 0.0889057i | −0.999011 | − | 0.0444529i | \(-0.985846\pi\) | ||||
0.999011 | − | 0.0444529i | \(-0.0141545\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.39230 | −0.416899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 0.928203i | − 0.0873180i | −0.999046 | − | 0.0436590i | \(-0.986098\pi\) | ||||
0.999046 | − | 0.0436590i | \(-0.0139015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 3.80385i | − 0.337537i | −0.985656 | − | 0.168768i | \(-0.946021\pi\) | ||||
0.985656 | − | 0.168768i | \(-0.0539790\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.46410 | −0.657178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.3923i | 0.907980i | 0.891007 | + | 0.453990i | \(0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.53590 | 0.219890 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9282i | 1.10453i | 0.833668 | + | 0.552265i | \(0.186237\pi\) | ||||
−0.833668 | + | 0.552265i | \(0.813763\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | − 12.0000i | − 1.00349i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.94744 | 0.325579 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.0000i | 1.47462i | 0.675556 | + | 0.737309i | \(0.263904\pi\) | ||||
−0.675556 | + | 0.737309i | \(0.736096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.53590 | 0.206368 | 0.103184 | − | 0.994662i | \(-0.467097\pi\) | ||||
0.103184 | + | 0.994662i | \(0.467097\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 8.53590i | − 0.690086i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.928203 | 0.0740787 | 0.0370393 | − | 0.999314i | \(-0.488207\pi\) | ||||
0.0370393 | + | 0.999314i | \(0.488207\pi\) | |||||||
\(158\) | 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 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 8.19615i | − 0.634237i | −0.948386 | − | 0.317119i | \(-0.897285\pi\) | ||||
0.948386 | − | 0.317119i | \(-0.102715\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.92820i | 0.376869i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.00000 | −0.456172 | −0.228086 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228086 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.39230i | 0.330146i | ||||||||
\(178\) | 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 | ||||||||
\(183\) | 9.46410i | 0.699607i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | −0.877527 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 5.07180i | − 0.368919i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.3923 | 1.18611 | 0.593053 | − | 0.805164i | \(-0.297923\pi\) | ||||
0.593053 | + | 0.805164i | \(0.297923\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 6.39230i | − 0.460128i | −0.973175 | − | 0.230064i | \(-0.926106\pi\) | ||||
0.973175 | − | 0.230064i | \(-0.0738936\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 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 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20.1962i | 1.40373i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.92820 | 0.479234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 6.39230i | − 0.440064i | −0.975493 | − | 0.220032i | \(-0.929384\pi\) | ||||
0.975493 | − | 0.220032i | \(-0.0706162\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.21539 | −0.220315 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 12.0000i | − 0.814613i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5359i | 0.711950i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 12.0000i | − 0.807207i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.1244i | 1.01280i | 0.862298 | + | 0.506401i | \(0.169024\pi\) | ||||
−0.862298 | + | 0.506401i | \(0.830976\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.5885 | 1.23376 | 0.616880 | − | 0.787058i | \(-0.288397\pi\) | ||||
0.616880 | + | 0.787058i | \(0.288397\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 18.9282i | − 1.25081i | −0.780300 | − | 0.625405i | \(-0.784934\pi\) | ||||
0.780300 | − | 0.625405i | \(-0.215066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.21539 | −0.211557 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.60770i | 0.105324i | 0.998612 | + | 0.0526618i | \(0.0167705\pi\) | ||||
−0.998612 | + | 0.0526618i | \(0.983229\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.78461 | 0.570622 | ||||||||
\(238\) | 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 | ||||||||
\(243\) | 15.2679 | 0.979439 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.92820i | 0.440831i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.46410 | −0.219529 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 15.4641i | − 0.976085i | −0.872820 | − | 0.488043i | \(-0.837711\pi\) | ||||
0.872820 | − | 0.488043i | \(-0.162289\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.3923 | 1.78501 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000i | 0.374270i | 0.982334 | + | 0.187135i | \(0.0599201\pi\) | ||||
−0.982334 | + | 0.187135i | \(0.940080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 7.60770i | − 0.472719i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.1962i | 1.24535i | 0.782481 | + | 0.622674i | \(0.213954\pi\) | ||||
−0.782481 | + | 0.622674i | \(0.786046\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.679492 | −0.0415842 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.7846i | 0.901434i | 0.892667 | + | 0.450717i | \(0.148832\pi\) | ||||
−0.892667 | + | 0.450717i | \(0.851168\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.39230 | 0.266814 | 0.133407 | − | 0.991061i | \(-0.457408\pi\) | ||||
0.133407 | + | 0.991061i | \(0.457408\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 3.21539i | − 0.194604i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 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 | \(-0.821517\pi\) | ||||
−0.846871 | + | 0.531798i | \(0.821517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5885 | −0.629418 | −0.314709 | − | 0.949188i | \(-0.601907\pi\) | ||||
−0.314709 | + | 0.949188i | \(0.601907\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.21539i | 0.189798i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 4.67949i | − 0.274317i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.0000 | 1.75262 | 0.876309 | − | 0.481749i | \(-0.159998\pi\) | ||||
0.876309 | + | 0.481749i | \(0.159998\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 13.8564i | − 0.804030i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.3923i | 1.64197i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 12.9282i | − 0.745169i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.78461i | 0.504663i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.1962 | 1.95168 | 0.975839 | − | 0.218492i | \(-0.0701137\pi\) | ||||
0.975839 | + | 0.218492i | \(0.0701137\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 6.00000i | − 0.341328i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.60770 | −0.431393 | −0.215696 | − | 0.976460i | \(-0.569202\pi\) | ||||
−0.215696 | + | 0.976460i | \(0.569202\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 22.0000i | − 1.24351i | −0.783210 | − | 0.621757i | \(-0.786419\pi\) | ||||
0.783210 | − | 0.621757i | \(-0.213581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.3923 | −1.25768 | −0.628839 | − | 0.777536i | \(-0.716469\pi\) | ||||
−0.628839 | + | 0.777536i | \(0.716469\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.2487 | −0.683656 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.92820 | 0.385496 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 0.679492i | − 0.0375760i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.3923 | 0.572946 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 5.60770i | − 0.308227i | −0.988053 | − | 0.154113i | \(-0.950748\pi\) | ||||
0.988053 | − | 0.154113i | \(-0.0492521\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.7846 | 0.810192 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 14.0000i | − 0.762629i | −0.924445 | − | 0.381314i | \(-0.875472\pi\) | ||||
0.924445 | − | 0.381314i | \(-0.124528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 0.679492i | − 0.0369049i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 32.7846i | − 1.77539i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7128i | 0.848412i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.0526 | −1.50594 | −0.752970 | − | 0.658055i | \(-0.771380\pi\) | ||||
−0.752970 | + | 0.658055i | \(0.771380\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 8.78461i | − 0.470229i | −0.971968 | − | 0.235115i | \(-0.924453\pi\) | ||||
0.971968 | − | 0.235115i | \(-0.0755466\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.8564 | 0.739600 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.7846i | 0.786905i | 0.919345 | + | 0.393453i | \(0.128719\pi\) | ||||
−0.919345 | + | 0.393453i | \(0.871281\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 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 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0526i | 0.524739i | 0.964967 | + | 0.262370i | \(0.0845040\pi\) | ||||
−0.964967 | + | 0.262370i | \(0.915496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.24871 | −0.325295 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 13.1769i | − 0.684111i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.85641 | 0.406789 | 0.203395 | − | 0.979097i | \(-0.434803\pi\) | ||||
0.203395 | + | 0.979097i | \(0.434803\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(383\) | − 3.80385i | − 0.194368i | −0.995266 | − | 0.0971838i | \(-0.969017\pi\) | ||||
0.995266 | − | 0.0971838i | \(-0.0309835\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 25.1244 | 1.27714 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.7846i | 1.35803i | 0.734123 | + | 0.679017i | \(0.237594\pi\) | ||||
−0.734123 | + | 0.679017i | \(0.762406\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.3923 | 1.43586 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.60770i | 0.383757i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.4641 | 1.37838 | 0.689192 | − | 0.724579i | \(-0.257966\pi\) | ||||
0.689192 | + | 0.724579i | \(0.257966\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 20.7846i | − 1.03025i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.60770 | −0.178389 | −0.0891945 | − | 0.996014i | \(-0.528429\pi\) | ||||
−0.0891945 | + | 0.996014i | \(0.528429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.46410i | 0.466830i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.60770 | −0.374350 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.32051i | 0.358487i | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 20.1962i | 0.981971i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.3923 | −0.793279 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 8.78461i | − 0.424125i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.3923 | 1.36761 | 0.683805 | − | 0.729665i | \(-0.260324\pi\) | ||||
0.683805 | + | 0.729665i | \(0.260324\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 26.3923i | − 1.26833i | −0.773196 | − | 0.634167i | \(-0.781343\pi\) | ||||
0.773196 | − | 0.634167i | \(-0.218657\pi\) | |||||||
\(434\) | 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 | \(-0.497431\pi\) | ||||
0.00807091 | + | 0.999967i | \(0.497431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.1769i | 0.623247i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.53590 | 0.119676 | 0.0598382 | − | 0.998208i | \(-0.480942\pi\) | ||||
0.0598382 | + | 0.998208i | \(0.480942\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.78461i | 0.413651i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.85641 | 0.0872216 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.7846i | 1.06582i | 0.846172 | + | 0.532910i | \(0.178901\pi\) | ||||
−0.846172 | + | 0.532910i | \(0.821099\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 15.8038i | 0.734467i | 0.930129 | + | 0.367234i | \(0.119695\pi\) | ||||
−0.930129 | + | 0.367234i | \(0.880305\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.9808 | −1.06342 | −0.531711 | − | 0.846926i | \(-0.678451\pi\) | ||||
−0.531711 | + | 0.846926i | \(0.678451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9282i | 0.596969i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.679492 | 0.0313093 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 35.3205i | − 1.62404i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 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 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.1244i | 1.77289i | 0.462830 | + | 0.886447i | \(0.346834\pi\) | ||||
−0.462830 | + | 0.886447i | \(0.653166\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.24871 | 0.192133 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 22.3923i | − 1.01055i | −0.862958 | − | 0.505275i | \(-0.831391\pi\) | ||||
0.862958 | − | 0.505275i | \(-0.168609\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 5.56922i | − 0.249814i | ||||||||
\(498\) | 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 | ||||||||
\(503\) | − 8.19615i | − 0.365448i | −0.983164 | − | 0.182724i | \(-0.941508\pi\) | ||||
0.983164 | − | 0.182724i | \(-0.0584915\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.732051 | −0.0325115 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.78461i | 0.389371i | 0.980866 | + | 0.194685i | \(0.0623686\pi\) | ||||
−0.980866 | + | 0.194685i | \(0.937631\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.2487 | −0.807275 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.00000i | 0.353209i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 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 | \(-0.254150\pi\) | ||||
0.697827 | + | 0.716266i | \(0.254150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.9808 | 0.655063 | 0.327531 | − | 0.944840i | \(-0.393783\pi\) | ||||
0.327531 | + | 0.944840i | \(0.393783\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 32.7846i | − 1.42812i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −44.1769 | −1.92074 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 14.7846i | − 0.641597i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.78461 | −0.380504 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 14.5359i | − 0.627270i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | − 5.07180i | − 0.217652i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.80385 | 0.0771270 | 0.0385635 | − | 0.999256i | \(-0.487722\pi\) | ||||
0.0385635 | + | 0.999256i | \(0.487722\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 31.8564i | − 1.35960i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.2154i | 0.647024i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.7846 | −0.626444 | −0.313222 | − | 0.949680i | \(-0.601408\pi\) | ||||
−0.313222 | + | 0.949680i | \(0.601408\pi\) | |||||||
\(558\) | 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 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.66025i | 0.237708i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.2487 | 1.77116 | 0.885579 | − | 0.464489i | \(-0.153762\pi\) | ||||
0.885579 | + | 0.464489i | \(0.153762\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.3923i | 1.27188i | 0.771739 | + | 0.635939i | \(0.219387\pi\) | ||||
−0.771739 | + | 0.635939i | \(0.780613\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 2.00000i | − 0.0832611i | −0.999133 | − | 0.0416305i | \(-0.986745\pi\) | ||||
0.999133 | − | 0.0416305i | \(-0.0132552\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 4.67949i | − 0.194473i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.00000i | − 0.248922i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 36.0000i | − 1.49097i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.5167 | 0.557892 | 0.278946 | − | 0.960307i | \(-0.410015\pi\) | ||||
0.278946 | + | 0.960307i | \(0.410015\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.9282i | 0.779923i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.60770 | −0.312939 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.928203i | 0.0381167i | 0.999818 | + | 0.0190584i | \(0.00606683\pi\) | ||||
−0.999818 | + | 0.0190584i | \(0.993933\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 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 | \(-0.636537\pi\) | ||||
−0.415910 | + | 0.909406i | \(0.636537\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.1244 | −1.02314 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 8.19615i | − 0.332672i | −0.986069 | − | 0.166336i | \(-0.946806\pi\) | ||||
0.986069 | − | 0.166336i | \(-0.0531936\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.3923i | 1.14863i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.6077 | −0.549610 | −0.274805 | − | 0.961500i | \(-0.588613\pi\) | ||||
−0.274805 | + | 0.961500i | \(0.588613\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.6077i | 0.547825i | 0.961755 | + | 0.273913i | \(0.0883179\pi\) | ||||
−0.961755 | + | 0.273913i | \(0.911682\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | − 1.17691i | − 0.0471521i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.07180 | 0.202548 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 20.7846i | − 0.828737i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.4641 | 0.854472 | 0.427236 | − | 0.904140i | \(-0.359487\pi\) | ||||
0.427236 | + | 0.904140i | \(0.359487\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 4.67949i | − 0.185993i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 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 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 36.5885i | − 1.43844i | −0.694782 | − | 0.719220i | \(-0.744499\pi\) | ||||
0.694782 | − | 0.719220i | \(-0.255501\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.7846 | −0.815867 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 8.78461i | − 0.344296i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.1769 | −0.750451 | −0.375225 | − | 0.926934i | \(-0.622435\pi\) | ||||
−0.375225 | + | 0.926934i | \(0.622435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 35.4641i | − 1.38359i | ||||||||
\(658\) | 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 | ||||||||
\(663\) | − 8.78461i | − 0.341166i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.0718i | 0.428060i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −44.7846 | −1.72889 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.1769i | 1.51016i | 0.655633 | + | 0.755080i | \(0.272402\pi\) | ||||
−0.655633 | + | 0.755080i | \(0.727598\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 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 | \(-0.428388\pi\) | ||||
0.223084 | + | 0.974799i | \(0.428388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 13.8564i | − 0.528655i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.0000 | 1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 5.60770i | − 0.213327i | −0.994295 | − | 0.106663i | \(-0.965983\pi\) | ||||
0.994295 | − | 0.106663i | \(-0.0340167\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.8231 | 0.411135 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.78461i | 0.332741i | ||||||||
\(698\) | 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 | ||||||||
\(703\) | 12.0000i | 0.452589i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.2154 | −0.572234 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.1436i | 0.380951i | 0.981692 | + | 0.190475i | \(0.0610029\pi\) | ||||
−0.981692 | + | 0.190475i | \(0.938997\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.5692 | −1.10893 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 77.5692i | 2.90499i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.2154 | −0.568229 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | −14.9282 | −0.555186 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.0526i | 1.26294i | 0.775401 | + | 0.631470i | \(0.217548\pi\) | ||||
−0.775401 | + | 0.631470i | \(0.782452\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 35.3205i | − 1.30638i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.7846 | −1.43254 | −0.716271 | − | 0.697822i | \(-0.754153\pi\) | ||||
−0.716271 | + | 0.697822i | \(0.754153\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.3205i | 1.30105i | ||||||||
\(738\) | 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 | ||||||||
\(743\) | − 36.5885i | − 1.34230i | −0.741321 | − | 0.671150i | \(-0.765801\pi\) | ||||
0.741321 | − | 0.671150i | \(-0.234199\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.6603 | 0.426626 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 21.2154i | − 0.775193i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.3923 | −1.47394 | −0.736968 | − | 0.675928i | \(-0.763743\pi\) | ||||
−0.736968 | + | 0.675928i | \(0.763743\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 11.3205i | − 0.412542i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 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 | \(-0.628751\pi\) | ||||
−0.393544 | + | 0.919306i | \(0.628751\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.17691 | 0.0426072 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 20.7846i | − 0.750489i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.78461 | 0.244659 | 0.122330 | − | 0.992490i | \(-0.460963\pi\) | ||||
0.122330 | + | 0.992490i | \(0.460963\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.39230i | 0.158185i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −46.3923 | −1.66862 | −0.834308 | − | 0.551299i | \(-0.814132\pi\) | ||||
−0.834308 | + | 0.551299i | \(0.814132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 5.56922i | − 0.199795i | ||||||||
\(778\) | 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 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.80385 | −0.206885 | −0.103442 | − | 0.994635i | \(-0.532986\pi\) | ||||
−0.103442 | + | 0.994635i | \(0.532986\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.7846i | 0.526346i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.17691 | 0.0418463 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 44.7846i | − 1.59035i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.60770 | 0.0569475 | 0.0284737 | − | 0.999595i | \(-0.490935\pi\) | ||||
0.0284737 | + | 0.999595i | \(0.490935\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.8231i | 0.380991i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.5692 | −1.25055 | −0.625274 | − | 0.780406i | \(-0.715013\pi\) | ||||
−0.625274 | + | 0.780406i | \(0.715013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.3923i | 1.34814i | 0.738669 | + | 0.674068i | \(0.235455\pi\) | ||||
−0.738669 | + | 0.674068i | \(0.764545\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.21539 | 0.112769 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.3923i | 0.713436i | ||||||||
\(818\) | 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 | ||||||||
\(823\) | − 30.8372i | − 1.07492i | −0.843290 | − | 0.537458i | \(-0.819385\pi\) | ||||
0.843290 | − | 0.537458i | \(-0.180615\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.73205 | 0.164550 | 0.0822748 | − | 0.996610i | \(-0.473781\pi\) | ||||
0.0822748 | + | 0.996610i | \(0.473781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 50.7846i | − 1.76382i | −0.471416 | − | 0.881911i | \(-0.656257\pi\) | ||||
0.471416 | − | 0.881911i | \(-0.343743\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.5359 | 0.504245 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.6795i | 0.647206i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 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 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.26795i | − 0.0435672i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.75129 | −0.266024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 49.1769i | 1.68576i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.46410 | −0.118609 | −0.0593043 | − | 0.998240i | \(-0.518888\pi\) | ||||
−0.0593043 | + | 0.998240i | \(0.518888\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 16.1436i | − 0.551455i | −0.961236 | − | 0.275727i | \(-0.911081\pi\) | ||||
0.961236 | − | 0.275727i | \(-0.0889187\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | − 40.9808i | − 1.39500i | −0.716584 | − | 0.697501i | \(-0.754295\pi\) | ||||
0.716584 | − | 0.697501i | \(-0.245705\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.66025 | 0.124309 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.5692i | 1.41014i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.3205 | −1.19679 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.7513i | 0.533100i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.85641 | −0.265292 | −0.132646 | − | 0.991163i | \(-0.542347\pi\) | ||||
−0.132646 | + | 0.991163i | \(0.542347\pi\) | |||||||
\(878\) | 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 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 21.3731i | − 0.717637i | −0.933407 | − | 0.358819i | \(-0.883180\pi\) | ||||
0.933407 | − | 0.358819i | \(-0.116820\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.82309 | 0.161761 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.4641i | 0.518067i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.3923 | −0.548548 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.7846i | 0.693978i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 36.0000i | − 1.19933i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 9.46410i | − 0.314946i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.41154 | 0.0468695 | 0.0234348 | − | 0.999725i | \(-0.492540\pi\) | ||||
0.0234348 | + | 0.999725i | \(0.492540\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 29.5692i | − 0.980749i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.1769 | −1.23173 | −0.615863 | − | 0.787853i | \(-0.711193\pi\) | ||||
−0.615863 | + | 0.787853i | \(0.711193\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 16.3923i | − 0.542506i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 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 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.1962i | 0.663329i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.60770 | −0.249600 | −0.124800 | − | 0.992182i | \(-0.539829\pi\) | ||||
−0.124800 | + | 0.992182i | \(0.539829\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 10.7846i | − 0.353451i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.56922 | −0.182328 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 9.60770i | − 0.313870i | −0.987609 | − | 0.156935i | \(-0.949839\pi\) | ||||
0.987609 | − | 0.156935i | \(-0.0501613\pi\) | |||||||
\(938\) | 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 | ||||||||
\(943\) | − 20.7846i | − 0.676840i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −45.8038 | −1.48843 | −0.744213 | − | 0.667943i | \(-0.767175\pi\) | ||||
−0.744213 | + | 0.667943i | \(0.767175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 49.8564i | − 1.61841i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.3923 | −0.531557 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 24.9282i | − 0.807504i | −0.914869 | − | 0.403752i | \(-0.867706\pi\) | ||||
0.914869 | − | 0.403752i | \(-0.132294\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 8.19615i | − 0.263570i | −0.991278 | − | 0.131785i | \(-0.957929\pi\) | ||||
0.991278 | − | 0.131785i | \(-0.0420709\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.07180 | 0.162930 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.0333i | 1.06009i | 0.847970 | + | 0.530045i | \(0.177825\pi\) | ||||
−0.847970 | + | 0.530045i | \(0.822175\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.6795 | −0.406486 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.32051i | 0.170218i | 0.996372 | + | 0.0851091i | \(0.0271239\pi\) | ||||
−0.996372 | + | 0.0851091i | \(0.972876\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 3.21539i | − 0.102764i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.28719i | 0.0730243i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.4115i | 0.363972i | 0.983301 | + | 0.181986i | \(0.0582525\pi\) | ||||
−0.983301 | + | 0.181986i | \(0.941747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.60770 | 0.242156 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 83.5692i | 2.65735i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.1051 | 1.40105 | 0.700523 | − | 0.713630i | \(-0.252950\pi\) | ||||
0.700523 | + | 0.713630i | \(0.252950\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 4.10512i | − 0.130272i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 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 | 1600.2.f.d.1249.4 | 4 | ||
4.3 | odd | 2 | 1600.2.f.i.1249.1 | 4 | |||
5.2 | odd | 4 | 1600.2.d.b.801.2 | 4 | |||
5.3 | odd | 4 | 320.2.d.b.161.3 | yes | 4 | ||
5.4 | even | 2 | 1600.2.f.h.1249.1 | 4 | |||
8.3 | odd | 2 | 1600.2.f.e.1249.3 | 4 | |||
8.5 | even | 2 | 1600.2.f.h.1249.2 | 4 | |||
15.8 | even | 4 | 2880.2.k.l.1441.3 | 4 | |||
20.3 | even | 4 | 320.2.d.a.161.2 | ✓ | 4 | ||
20.7 | even | 4 | 1600.2.d.h.801.3 | 4 | |||
20.19 | odd | 2 | 1600.2.f.e.1249.4 | 4 | |||
40.3 | even | 4 | 320.2.d.a.161.3 | yes | 4 | ||
40.13 | odd | 4 | 320.2.d.b.161.2 | yes | 4 | ||
40.19 | odd | 2 | 1600.2.f.i.1249.2 | 4 | |||
40.27 | even | 4 | 1600.2.d.h.801.2 | 4 | |||
40.29 | even | 2 | inner | 1600.2.f.d.1249.3 | 4 | ||
40.37 | odd | 4 | 1600.2.d.b.801.3 | 4 | |||
60.23 | odd | 4 | 2880.2.k.e.1441.4 | 4 | |||
80.3 | even | 4 | 1280.2.a.b.1.2 | 2 | |||
80.13 | odd | 4 | 1280.2.a.m.1.1 | 2 | |||
80.27 | even | 4 | 6400.2.a.y.1.2 | 2 | |||
80.37 | odd | 4 | 6400.2.a.ck.1.1 | 2 | |||
80.43 | even | 4 | 1280.2.a.p.1.1 | 2 | |||
80.53 | odd | 4 | 1280.2.a.c.1.2 | 2 | |||
80.67 | even | 4 | 6400.2.a.cd.1.1 | 2 | |||
80.77 | odd | 4 | 6400.2.a.bf.1.2 | 2 | |||
120.53 | even | 4 | 2880.2.k.l.1441.1 | 4 | |||
120.83 | odd | 4 | 2880.2.k.e.1441.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.2.d.a.161.2 | ✓ | 4 | 20.3 | even | 4 | ||
320.2.d.a.161.3 | yes | 4 | 40.3 | even | 4 | ||
320.2.d.b.161.2 | yes | 4 | 40.13 | odd | 4 | ||
320.2.d.b.161.3 | yes | 4 | 5.3 | odd | 4 | ||
1280.2.a.b.1.2 | 2 | 80.3 | even | 4 | |||
1280.2.a.c.1.2 | 2 | 80.53 | odd | 4 | |||
1280.2.a.m.1.1 | 2 | 80.13 | odd | 4 | |||
1280.2.a.p.1.1 | 2 | 80.43 | even | 4 | |||
1600.2.d.b.801.2 | 4 | 5.2 | odd | 4 | |||
1600.2.d.b.801.3 | 4 | 40.37 | odd | 4 | |||
1600.2.d.h.801.2 | 4 | 40.27 | even | 4 | |||
1600.2.d.h.801.3 | 4 | 20.7 | even | 4 | |||
1600.2.f.d.1249.3 | 4 | 40.29 | even | 2 | inner | ||
1600.2.f.d.1249.4 | 4 | 1.1 | even | 1 | trivial | ||
1600.2.f.e.1249.3 | 4 | 8.3 | odd | 2 | |||
1600.2.f.e.1249.4 | 4 | 20.19 | odd | 2 | |||
1600.2.f.h.1249.1 | 4 | 5.4 | even | 2 | |||
1600.2.f.h.1249.2 | 4 | 8.5 | even | 2 | |||
1600.2.f.i.1249.1 | 4 | 4.3 | odd | 2 | |||
1600.2.f.i.1249.2 | 4 | 40.19 | odd | 2 | |||
2880.2.k.e.1441.2 | 4 | 120.83 | odd | 4 | |||
2880.2.k.e.1441.4 | 4 | 60.23 | odd | 4 | |||
2880.2.k.l.1441.1 | 4 | 120.53 | even | 4 | |||
2880.2.k.l.1441.3 | 4 | 15.8 | even | 4 | |||
6400.2.a.y.1.2 | 2 | 80.27 | even | 4 | |||
6400.2.a.bf.1.2 | 2 | 80.77 | odd | 4 | |||
6400.2.a.cd.1.1 | 2 | 80.67 | even | 4 | |||
6400.2.a.ck.1.1 | 2 | 80.37 | odd | 4 |