Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(145,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.145");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.bc (of order \(12\), degree \(4\), 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: | \(13.7981494693\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.145 |
Dual form | 1728.2.bc.a.1585.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | − | 3.73205i | −0.447214 | − | 1.66902i | −0.710025 | − | 0.704177i | \(-0.751316\pi\) |
0.262811 | − | 0.964847i | \(-0.415350\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.633975 | + | 0.366025i | −0.239620 | + | 0.138345i | −0.615002 | − | 0.788526i | \(-0.710845\pi\) |
0.375382 | + | 0.926870i | \(0.377511\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.86603 | + | 0.767949i | 0.864139 | + | 0.231545i | 0.663552 | − | 0.748130i | \(-0.269048\pi\) |
0.200587 | + | 0.979676i | \(0.435715\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.09808 | − | 1.63397i | 1.69130 | − | 0.453183i | 0.720577 | − | 0.693375i | \(-0.243877\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.26795 | 0.550058 | 0.275029 | − | 0.961436i | \(-0.411312\pi\) | ||||
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.633975 | + | 0.633975i | 0.145444 | + | 0.145444i | 0.776079 | − | 0.630635i | \(-0.217206\pi\) |
−0.630635 | + | 0.776079i | \(0.717206\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.09808 | + | 0.633975i | 0.228965 | + | 0.132193i | 0.610094 | − | 0.792329i | \(-0.291132\pi\) |
−0.381130 | + | 0.924522i | \(0.624465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.59808 | + | 4.96410i | −1.71962 | + | 0.992820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.633975 | + | 2.36603i | −0.117726 | + | 0.439360i | −0.999476 | − | 0.0323566i | \(-0.989699\pi\) |
0.881750 | + | 0.471717i | \(0.156365\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.73205 | − | 6.46410i | 0.670296 | − | 1.16099i | −0.307524 | − | 0.951540i | \(-0.599500\pi\) |
0.977820 | − | 0.209447i | \(-0.0671662\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | + | 2.00000i | 0.338062 | + | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.26795 | − | 1.26795i | 0.208450 | − | 0.208450i | −0.595159 | − | 0.803608i | \(-0.702911\pi\) |
0.803608 | + | 0.595159i | \(0.202911\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.59808 | − | 1.50000i | −0.405751 | − | 0.234261i | 0.283211 | − | 0.959058i | \(-0.408600\pi\) |
−0.688963 | + | 0.724797i | \(0.741934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.23205 | + | 0.330127i | 0.187886 | + | 0.0503439i | 0.351535 | − | 0.936175i | \(-0.385660\pi\) |
−0.163649 | + | 0.986519i | \(0.552326\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.83013 | − | 8.36603i | −0.704546 | − | 1.22031i | −0.966855 | − | 0.255326i | \(-0.917817\pi\) |
0.262309 | − | 0.964984i | \(-0.415516\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.23205 | + | 5.59808i | −0.461722 | + | 0.799725i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.535898 | − | 0.535898i | 0.0736113 | − | 0.0736113i | −0.669343 | − | 0.742954i | \(-0.733424\pi\) |
0.742954 | + | 0.669343i | \(0.233424\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 11.4641i | − | 1.54582i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.33013 | − | 4.96410i | −0.173168 | − | 0.646271i | −0.996856 | − | 0.0792287i | \(-0.974754\pi\) |
0.823689 | − | 0.567042i | \(-0.191912\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.803848 | − | 3.00000i | 0.102922 | − | 0.384111i | −0.895179 | − | 0.445707i | \(-0.852952\pi\) |
0.998101 | + | 0.0615961i | \(0.0196191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.1962 | − | 21.1244i | −1.51275 | − | 2.62015i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.23205 | − | 1.40192i | 0.639197 | − | 0.171272i | 0.0753572 | − | 0.997157i | \(-0.475990\pi\) |
0.563840 | + | 0.825884i | \(0.309324\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.9282i | − | 1.29694i | −0.761241 | − | 0.648470i | \(-0.775409\pi\) | ||
0.761241 | − | 0.648470i | \(-0.224591\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.73205i | − | 1.13905i | −0.821974 | − | 0.569525i | \(-0.807127\pi\) | ||
0.821974 | − | 0.569525i | \(-0.192873\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.09808 | + | 0.562178i | −0.239098 | + | 0.0640661i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | + | 10.3923i | 0.675053 | + | 1.16923i | 0.976453 | + | 0.215728i | \(0.0692125\pi\) |
−0.301401 | + | 0.953498i | \(0.597454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.366025 | − | 1.36603i | 0.0401765 | − | 0.149941i | −0.942924 | − | 0.333009i | \(-0.891936\pi\) |
0.983100 | + | 0.183068i | \(0.0586028\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.26795 | − | 8.46410i | −0.245994 | − | 0.918061i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000i | 0.212000i | 0.994366 | + | 0.106000i | \(0.0338043\pi\) | ||||
−0.994366 | + | 0.106000i | \(0.966196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.26795 | + | 3.26795i | −0.342574 | + | 0.342574i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.73205 | − | 3.00000i | 0.177705 | − | 0.307794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.13397 | − | 7.16025i | −0.419742 | − | 0.727014i | 0.576172 | − | 0.817329i | \(-0.304546\pi\) |
−0.995913 | + | 0.0903150i | \(0.971213\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.46410 | − | 2.00000i | −0.742706 | − | 0.199007i | −0.132426 | − | 0.991193i | \(-0.542277\pi\) |
−0.610280 | + | 0.792186i | \(0.708943\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.90192 | − | 4.56218i | −0.778600 | − | 0.449525i | 0.0573341 | − | 0.998355i | \(-0.481740\pi\) |
−0.835934 | + | 0.548830i | \(0.815073\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.4904 | + | 13.4904i | −1.30416 | + | 1.30416i | −0.378607 | + | 0.925558i | \(0.623597\pi\) |
−0.925558 | + | 0.378607i | \(0.876403\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.26795 | + | 7.26795i | 0.696143 | + | 0.696143i | 0.963576 | − | 0.267433i | \(-0.0861754\pi\) |
−0.267433 | + | 0.963576i | \(0.586175\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.92820 | + | 12.0000i | −0.651751 | + | 1.12887i | 0.330947 | + | 0.943649i | \(0.392632\pi\) |
−0.982698 | + | 0.185216i | \(0.940702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.26795 | − | 4.73205i | 0.118237 | − | 0.441266i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.43782 | + | 0.830127i | −0.131805 | + | 0.0760976i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.90192 | − | 1.09808i | −0.172902 | − | 0.0998251i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 13.4641 | + | 13.4641i | 1.20427 | + | 1.20427i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.19615 | 0.549820 | 0.274910 | − | 0.961470i | \(-0.411352\pi\) | ||||
0.274910 | + | 0.961470i | \(0.411352\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.09808 | + | 0.830127i | −0.270680 | + | 0.0725285i | −0.391606 | − | 0.920133i | \(-0.628080\pi\) |
0.120926 | + | 0.992662i | \(0.461414\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.633975 | − | 0.169873i | −0.0549726 | − | 0.0147299i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.2583 | − | 8.23205i | 1.21817 | − | 0.703312i | 0.253645 | − | 0.967297i | \(-0.418371\pi\) |
0.964527 | + | 0.263986i | \(0.0850372\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.42820 | − | 9.06218i | −0.205958 | − | 0.768644i | −0.989156 | − | 0.146872i | \(-0.953080\pi\) |
0.783198 | − | 0.621772i | \(-0.213587\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.7321 | 1.56645 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.46410 | 0.785951 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.830127 | + | 3.09808i | 0.0680067 | + | 0.253804i | 0.991557 | − | 0.129674i | \(-0.0413929\pi\) |
−0.923550 | + | 0.383478i | \(0.874726\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.36603 | + | 1.36603i | −0.192544 | + | 0.111166i | −0.593173 | − | 0.805075i | \(-0.702125\pi\) |
0.400629 | + | 0.916240i | \(0.368792\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −27.8564 | − | 7.46410i | −2.23748 | − | 0.599531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.73205 | − | 1.26795i | 0.377659 | − | 0.101193i | −0.0649959 | − | 0.997886i | \(-0.520703\pi\) |
0.442655 | + | 0.896692i | \(0.354037\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.928203 | −0.0731527 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.00000 | + | 7.00000i | 0.548282 | + | 0.548282i | 0.925944 | − | 0.377661i | \(-0.123272\pi\) |
−0.377661 | + | 0.925944i | \(0.623272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.464102 | − | 0.267949i | −0.0359133 | − | 0.0207345i | 0.481936 | − | 0.876206i | \(-0.339934\pi\) |
−0.517849 | + | 0.855472i | \(0.673267\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.2583 | − | 13.4282i | 1.78910 | − | 1.03294i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.36603 | + | 12.5622i | −0.255914 | + | 0.955085i | 0.711665 | + | 0.702519i | \(0.247941\pi\) |
−0.967580 | + | 0.252566i | \(0.918725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.63397 | − | 6.29423i | 0.274703 | − | 0.475799i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9282 | + | 11.9282i | 0.891556 | + | 0.891556i | 0.994670 | − | 0.103114i | \(-0.0328806\pi\) |
−0.103114 | + | 0.994670i | \(0.532881\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3923 | − | 13.3923i | 0.995442 | − | 0.995442i | −0.00454748 | − | 0.999990i | \(-0.501448\pi\) |
0.999990 | + | 0.00454748i | \(0.00144751\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | − | 3.46410i | −0.441129 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.50000 | + | 1.74167i | 0.475327 | + | 0.127364i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.02628 | + | 12.1699i | 0.508404 | + | 0.880581i | 0.999953 | + | 0.00973114i | \(0.00309757\pi\) |
−0.491549 | + | 0.870850i | \(0.663569\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.13397 | + | 15.8205i | −0.657478 | + | 1.13879i | 0.323789 | + | 0.946129i | \(0.395043\pi\) |
−0.981266 | + | 0.192656i | \(0.938290\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.66025 | − | 3.66025i | 0.260782 | − | 0.260782i | −0.564590 | − | 0.825372i | \(-0.690966\pi\) |
0.825372 | + | 0.564590i | \(0.190966\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 0.875644i | − | 0.0620728i | −0.999518 | − | 0.0310364i | \(-0.990119\pi\) | ||
0.999518 | − | 0.0310364i | \(-0.00988078\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.464102 | − | 1.73205i | −0.0325735 | − | 0.121566i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.00000 | + | 11.1962i | −0.209529 | + | 0.781973i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.33013 | + | 2.30385i | 0.0920068 | + | 0.159360i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.09808 | + | 1.09808i | −0.282123 | + | 0.0755947i | −0.397106 | − | 0.917773i | \(-0.629985\pi\) |
0.114983 | + | 0.993367i | \(0.463319\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 4.92820i | − | 0.336101i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.46410i | 0.370927i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8301 | − | 3.70577i | 0.930315 | − | 0.249277i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0263 | − | 19.0981i | −0.738374 | − | 1.27890i | −0.953227 | − | 0.302255i | \(-0.902260\pi\) |
0.214853 | − | 0.976646i | \(-0.431073\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.86603 | − | 14.4282i | 0.256597 | − | 0.957633i | −0.710598 | − | 0.703598i | \(-0.751575\pi\) |
0.967195 | − | 0.254035i | \(-0.0817579\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.83013 | − | 6.83013i | −0.120938 | − | 0.451347i | 0.878724 | − | 0.477330i | \(-0.158395\pi\) |
−0.999662 | + | 0.0259823i | \(0.991729\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 7.19615i | − | 0.471436i | −0.971822 | − | 0.235718i | \(-0.924256\pi\) | ||
0.971822 | − | 0.235718i | \(-0.0757441\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.3923 | + | 26.3923i | −1.72164 | + | 1.72164i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.0981 | + | 22.6865i | −0.847244 | + | 1.46747i | 0.0364139 | + | 0.999337i | \(0.488407\pi\) |
−0.883658 | + | 0.468133i | \(0.844927\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.40192 | − | 11.0885i | −0.412384 | − | 0.714270i | 0.582766 | − | 0.812640i | \(-0.301971\pi\) |
−0.995150 | + | 0.0983699i | \(0.968637\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24.1244 | + | 6.46410i | 1.54125 | + | 0.412976i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.90192 | + | 2.83013i | 0.311902 | + | 0.180077i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.83013 | − | 2.83013i | 0.178636 | − | 0.178636i | −0.612125 | − | 0.790761i | \(-0.709685\pi\) |
0.790761 | + | 0.612125i | \(0.209685\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.66025 | + | 2.66025i | 0.167249 | + | 0.167249i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.42820 | − | 7.66987i | 0.276224 | − | 0.478434i | −0.694219 | − | 0.719763i | \(-0.744250\pi\) |
0.970443 | + | 0.241330i | \(0.0775836\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.339746 | + | 1.26795i | −0.0211108 | + | 0.0787865i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.4904 | − | 13.5622i | 1.44848 | − | 0.836280i | 0.450088 | − | 0.892984i | \(-0.351393\pi\) |
0.998391 | + | 0.0567045i | \(0.0180593\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.53590 | − | 1.46410i | −0.155779 | − | 0.0899390i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.73205 | − | 4.73205i | −0.288518 | − | 0.288518i | 0.547976 | − | 0.836494i | \(-0.315399\pi\) |
−0.836494 | + | 0.547976i | \(0.815399\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.3923 | −1.23874 | −0.619372 | − | 0.785098i | \(-0.712613\pi\) | ||||
−0.619372 | + | 0.785098i | \(0.712613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −28.4545 | + | 7.62436i | −1.71587 | + | 0.459766i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.7583 | + | 4.22243i | 0.946826 | + | 0.253701i | 0.699015 | − | 0.715107i | \(-0.253622\pi\) |
0.247811 | + | 0.968808i | \(0.420289\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.66025 | + | 5.00000i | −0.516627 | + | 0.298275i | −0.735554 | − | 0.677466i | \(-0.763078\pi\) |
0.218926 | + | 0.975741i | \(0.429745\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.43782 | + | 27.7583i | 0.442133 | + | 1.65006i | 0.723398 | + | 0.690431i | \(0.242579\pi\) |
−0.281265 | + | 0.959630i | \(0.590754\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.19615 | 0.129635 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.8564 | −0.697436 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.63397 | + | 13.5622i | 0.212299 | + | 0.792311i | 0.987100 | + | 0.160106i | \(0.0511834\pi\) |
−0.774801 | + | 0.632205i | \(0.782150\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.1962 | + | 9.92820i | −1.00120 | + | 0.578042i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.73205 | + | 2.07180i | 0.447156 | + | 0.119815i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.901924 | + | 0.241670i | −0.0519860 | + | 0.0139296i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.0000 | −0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.0263 | + | 16.0263i | 0.914668 | + | 0.914668i | 0.996635 | − | 0.0819670i | \(-0.0261202\pi\) |
−0.0819670 | + | 0.996635i | \(0.526120\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.9019 | − | 8.02628i | −0.788306 | − | 0.455129i | 0.0510600 | − | 0.998696i | \(-0.483740\pi\) |
−0.839366 | + | 0.543567i | \(0.817073\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.6506 | + | 14.2321i | −1.39334 | + | 0.804443i | −0.993683 | − | 0.112223i | \(-0.964203\pi\) |
−0.399653 | + | 0.916666i | \(0.630869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.43782 | − | 31.4904i | 0.473915 | − | 1.76868i | −0.151577 | − | 0.988445i | \(-0.548435\pi\) |
0.625492 | − | 0.780231i | \(-0.284898\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.63397 | + | 6.29423i | −0.203464 | + | 0.352409i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.43782 | + | 1.43782i | 0.0800026 | + | 0.0800026i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −44.3205 | + | 44.3205i | −2.45846 | + | 2.45846i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.12436 | + | 3.53590i | 0.337647 | + | 0.194940i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.0263 | + | 5.09808i | 1.04578 | + | 0.280216i | 0.740506 | − | 0.672049i | \(-0.234586\pi\) |
0.305273 | + | 0.952265i | \(0.401252\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.4641 | − | 18.1244i | −0.571715 | − | 0.990239i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8923 | + | 20.5981i | −0.647815 | + | 1.12205i | 0.335829 | + | 0.941923i | \(0.390984\pi\) |
−0.983644 | + | 0.180126i | \(0.942350\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.6603 | − | 15.6603i | 0.848050 | − | 0.848050i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.85641i | − | 0.532196i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.62436 | + | 24.7224i | 0.355614 | + | 1.32717i | 0.879710 | + | 0.475510i | \(0.157737\pi\) |
−0.524096 | + | 0.851659i | \(0.675597\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.07180 | − | 7.73205i | 0.110901 | − | 0.413887i | −0.888047 | − | 0.459753i | \(-0.847938\pi\) |
0.998948 | + | 0.0458657i | \(0.0146046\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.1603 | + | 17.5981i | 0.540776 | + | 0.936651i | 0.998860 | + | 0.0477421i | \(0.0152026\pi\) |
−0.458084 | + | 0.888909i | \(0.651464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −40.7846 | + | 10.9282i | −2.16462 | + | 0.580009i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.7321i | 0.777528i | 0.921337 | + | 0.388764i | \(0.127098\pi\) | ||||
−0.921337 | + | 0.388764i | \(0.872902\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.1962i | − | 0.957692i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −36.3205 | + | 9.73205i | −1.90110 | + | 0.509399i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.1244 | + | 17.5359i | 0.528487 | + | 0.915366i | 0.999448 | + | 0.0332125i | \(0.0105738\pi\) |
−0.470961 | + | 0.882154i | \(0.656093\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.143594 | + | 0.535898i | −0.00745501 | + | 0.0278225i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.50962 | + | 5.63397i | 0.0781651 | + | 0.291716i | 0.993932 | − | 0.109993i | \(-0.0350829\pi\) |
−0.915767 | + | 0.401709i | \(0.868416\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.4641i | 0.796442i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7583 | − | 18.7583i | 0.963551 | − | 0.963551i | −0.0358080 | − | 0.999359i | \(-0.511400\pi\) |
0.999359 | + | 0.0358080i | \(0.0114005\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.26795 | + | 5.66025i | −0.166984 | + | 0.289225i | −0.937358 | − | 0.348367i | \(-0.886736\pi\) |
0.770374 | + | 0.637593i | \(0.220070\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.19615 | + | 7.26795i | 0.213856 | + | 0.370409i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.2942 | − | 2.75833i | −0.521938 | − | 0.139853i | −0.0117752 | − | 0.999931i | \(-0.503748\pi\) |
−0.510163 | + | 0.860078i | \(0.670415\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.49038 | + | 1.43782i | 0.125944 | + | 0.0727138i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 32.7846 | − | 32.7846i | 1.64957 | − | 1.64957i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.7321 | − | 12.7321i | −0.639003 | − | 0.639003i | 0.311306 | − | 0.950310i | \(-0.399233\pi\) |
−0.950310 | + | 0.311306i | \(0.899233\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.7942 | + | 23.8923i | −0.688851 | + | 1.19312i | 0.283359 | + | 0.959014i | \(0.408551\pi\) |
−0.972210 | + | 0.234111i | \(0.924782\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.1962 | − | 45.5167i | 0.607534 | − | 2.26735i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.60770 | − | 2.66025i | 0.228395 | − | 0.131864i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.1340 | + | 15.0885i | 1.29224 | + | 0.746076i | 0.979051 | − | 0.203614i | \(-0.0652688\pi\) |
0.313191 | + | 0.949690i | \(0.398602\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.66025 | + | 2.66025i | 0.130903 | + | 0.130903i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.46410 | −0.268222 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 31.2224 | − | 8.36603i | 1.52532 | − | 0.408707i | 0.603828 | − | 0.797115i | \(-0.293641\pi\) |
0.921488 | + | 0.388408i | \(0.126975\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.19615 | − | 0.588457i | −0.107034 | − | 0.0286797i | 0.204905 | − | 0.978782i | \(-0.434312\pi\) |
−0.311938 | + | 0.950102i | \(0.600978\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.5000 | + | 11.2583i | −0.945889 | + | 0.546109i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.588457 | + | 2.19615i | 0.0284774 | + | 0.106279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.80385 | −0.279562 | −0.139781 | − | 0.990182i | \(-0.544640\pi\) | ||||
−0.139781 | + | 0.990182i | \(0.544640\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.26795 | −0.108991 | −0.0544953 | − | 0.998514i | \(-0.517355\pi\) | ||||
−0.0544953 | + | 0.998514i | \(0.517355\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.294229 | + | 1.09808i | 0.0140749 | + | 0.0525281i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.85641 | + | 2.80385i | −0.231784 | + | 0.133820i | −0.611395 | − | 0.791326i | \(-0.709391\pi\) |
0.379611 | + | 0.925146i | \(0.376058\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.6244 | + | 5.25833i | 0.932381 | + | 0.249831i | 0.692870 | − | 0.721063i | \(-0.256346\pi\) |
0.239511 | + | 0.970894i | \(0.423013\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.46410 | − | 2.00000i | 0.353832 | − | 0.0948091i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.6603 | 0.975018 | 0.487509 | − | 0.873118i | \(-0.337906\pi\) | ||||
0.487509 | + | 0.873118i | \(0.337906\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.29423 | − | 6.29423i | −0.296384 | − | 0.296384i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.4641 | + | 8.92820i | 0.724968 | + | 0.418561i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.2583 | + | 11.6962i | −0.947645 | + | 0.547123i | −0.892348 | − | 0.451347i | \(-0.850944\pi\) |
−0.0552962 | + | 0.998470i | \(0.517610\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.686533 | − | 2.56218i | 0.0319751 | − | 0.119333i | −0.948094 | − | 0.317991i | \(-0.896992\pi\) |
0.980069 | + | 0.198659i | \(0.0636585\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.19615 | − | 15.9282i | 0.427381 | − | 0.740246i | −0.569258 | − | 0.822159i | \(-0.692769\pi\) |
0.996640 | + | 0.0819125i | \(0.0261028\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.36603 | + | 4.36603i | 0.202036 | + | 0.202036i | 0.800872 | − | 0.598836i | \(-0.204370\pi\) |
−0.598836 | + | 0.800872i | \(0.704370\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.80385 | + | 2.80385i | −0.129470 | + | 0.129470i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.27757 | + | 1.89230i | 0.150703 | + | 0.0870083i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.59808 | − | 2.30385i | −0.394507 | − | 0.105708i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.8301 | + | 22.2224i | 0.586223 | + | 1.01537i | 0.994722 | + | 0.102610i | \(0.0327193\pi\) |
−0.408498 | + | 0.912759i | \(0.633947\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.66025 | − | 9.80385i | 0.258085 | − | 0.447017i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.5885 | + | 22.5885i | −1.02569 | + | 1.02569i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16.1962i | − | 0.733918i | −0.930237 | − | 0.366959i | \(-0.880399\pi\) | ||
0.930237 | − | 0.366959i | \(-0.119601\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.89230 | + | 25.7224i | 0.311045 | + | 1.16084i | 0.927615 | + | 0.373537i | \(0.121855\pi\) |
−0.616570 | + | 0.787300i | \(0.711478\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.43782 | + | 5.36603i | −0.0647563 | + | 0.241674i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.00000 | + | 6.92820i | 0.179425 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.33013 | + | 1.69615i | −0.283375 | + | 0.0759302i | −0.397707 | − | 0.917512i | \(-0.630194\pi\) |
0.114332 | + | 0.993443i | \(0.463527\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.7128i | 1.23565i | 0.786314 | + | 0.617827i | \(0.211987\pi\) | ||||
−0.786314 | + | 0.617827i | \(0.788013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.8564i | 1.32859i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.9282 | + | 4.53590i | −0.750329 | + | 0.201050i | −0.613664 | − | 0.789567i | \(-0.710305\pi\) |
−0.136665 | + | 0.990617i | \(0.543638\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.56218 | + | 6.16987i | 0.157581 | + | 0.272939i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.12436 | + | 34.0526i | −0.402067 | + | 1.50054i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.41858 | − | 27.6865i | −0.326269 | − | 1.21765i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13.0000i | − | 0.569540i | −0.958596 | − | 0.284770i | \(-0.908083\pi\) | ||
0.958596 | − | 0.284770i | \(-0.0919173\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.4641 | − | 14.4641i | 0.632471 | − | 0.632471i | −0.316216 | − | 0.948687i | \(-0.602412\pi\) |
0.948687 | + | 0.316216i | \(0.102412\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.46410 | − | 14.6603i | 0.368702 | − | 0.638611i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.6962 | − | 18.5263i | −0.465050 | − | 0.805490i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.2942 | − | 4.90192i | −0.792411 | − | 0.212326i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 63.8372 | + | 36.8564i | 2.75992 | + | 1.59344i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.5622 | + | 13.5622i | −0.584164 | + | 0.584164i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.19615 | − | 8.19615i | −0.352380 | − | 0.352380i | 0.508614 | − | 0.860994i | \(-0.330158\pi\) |
−0.860994 | + | 0.508614i | \(0.830158\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.8564 | − | 34.3923i | 0.850555 | − | 1.47320i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.37564 | + | 31.2583i | −0.358117 | + | 1.33651i | 0.518400 | + | 0.855138i | \(0.326528\pi\) |
−0.876517 | + | 0.481371i | \(0.840139\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.90192 | + | 1.09808i | −0.0810247 | + | 0.0467796i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.60770 | − | 4.39230i | −0.323512 | − | 0.186780i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.1962 | + | 25.1962i | 1.06760 | + | 1.06760i | 0.997543 | + | 0.0700519i | \(0.0223165\pi\) |
0.0700519 | + | 0.997543i | \(0.477684\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.05256 | 0.340587 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.76795 | + | 1.00962i | −0.158800 | + | 0.0425504i | −0.337343 | − | 0.941382i | \(-0.609528\pi\) |
0.178543 | + | 0.983932i | \(0.442862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 51.7128 | + | 13.8564i | 2.17557 | + | 0.582943i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.5981 | − | 13.6244i | 0.989283 | − | 0.571163i | 0.0842230 | − | 0.996447i | \(-0.473159\pi\) |
0.905060 | + | 0.425284i | \(0.139826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.33013 | − | 19.8923i | −0.223059 | − | 0.832467i | −0.983173 | − | 0.182677i | \(-0.941524\pi\) |
0.760114 | − | 0.649790i | \(-0.225143\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.5885 | −0.524975 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.7846 | 1.48973 | 0.744866 | − | 0.667214i | \(-0.232513\pi\) | ||||
0.744866 | + | 0.667214i | \(0.232513\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.267949 | + | 1.00000i | 0.0111164 | + | 0.0414870i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.94744 | − | 1.12436i | 0.0806548 | − | 0.0465661i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.76795 | + | 1.00962i | 0.155520 | + | 0.0416714i | 0.335739 | − | 0.941955i | \(-0.391014\pi\) |
−0.180219 | + | 0.983626i | \(0.557681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.46410 | − | 1.73205i | 0.266349 | − | 0.0713679i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.5359 | −0.432657 | −0.216329 | − | 0.976321i | \(-0.569408\pi\) | ||||
−0.216329 | + | 0.976321i | \(0.569408\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.53590 | + | 4.53590i | 0.185954 | + | 0.185954i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23.3205 | − | 13.4641i | −0.952850 | − | 0.550128i | −0.0588850 | − | 0.998265i | \(-0.518755\pi\) |
−0.893965 | + | 0.448136i | \(0.852088\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.5526 | − | 10.1340i | 0.715984 | − | 0.413373i | −0.0972889 | − | 0.995256i | \(-0.531017\pi\) |
0.813273 | + | 0.581883i | \(0.197684\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.19615 | + | 8.19615i | −0.0892863 | + | 0.333221i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.5885 | + | 39.1244i | −0.916837 | + | 1.58801i | −0.112648 | + | 0.993635i | \(0.535933\pi\) |
−0.804189 | + | 0.594374i | \(0.797400\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.1244 | − | 43.1244i | −1.74462 | − | 1.74462i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.66025 | − | 1.66025i | 0.0670570 | − | 0.0670570i | −0.672783 | − | 0.739840i | \(-0.734901\pi\) |
0.739840 | + | 0.672783i | \(0.234901\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.91154 | + | 2.25833i | 0.157473 | + | 0.0909170i | 0.576666 | − | 0.816980i | \(-0.304354\pi\) |
−0.419193 | + | 0.907897i | \(0.637687\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.8205 | − | 10.4019i | −1.56033 | − | 0.418089i | −0.627561 | − | 0.778568i | \(-0.715947\pi\) |
−0.932767 | + | 0.360479i | \(0.882613\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.732051 | − | 1.26795i | −0.0293290 | − | 0.0507993i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.9641 | − | 20.7224i | 0.478564 | − | 0.828897i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.87564 | − | 2.87564i | 0.114659 | − | 0.114659i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 38.3923i | − | 1.52837i | −0.644995 | − | 0.764187i | \(-0.723141\pi\) | ||
0.644995 | − | 0.764187i | \(-0.276859\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.19615 | − | 23.1244i | −0.245887 | − | 0.917662i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.5622 | + | 39.4186i | −0.418489 | + | 1.56182i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.20577 | + | 7.28461i | 0.166118 | + | 0.287725i | 0.937052 | − | 0.349191i | \(-0.113543\pi\) |
−0.770934 | + | 0.636915i | \(0.780210\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.6506 | − | 12.2321i | 1.80029 | − | 0.482385i | 0.806263 | − | 0.591558i | \(-0.201487\pi\) |
0.994023 | + | 0.109173i | \(0.0348202\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.2679i | 0.521617i | 0.965391 | + | 0.260808i | \(0.0839891\pi\) | ||||
−0.965391 | + | 0.260808i | \(0.916011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 15.2487i | − | 0.598564i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.63397 | + | 1.50962i | −0.220474 | + | 0.0590760i | −0.367365 | − | 0.930077i | \(-0.619740\pi\) |
0.146891 | + | 0.989153i | \(0.453073\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.19615 | + | 10.7321i | 0.242104 | + | 0.419336i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.02628 | − | 15.0263i | 0.156842 | − | 0.585341i | −0.842099 | − | 0.539323i | \(-0.818680\pi\) |
0.998941 | − | 0.0460178i | \(-0.0146531\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.19615 | + | 8.19615i | 0.0854204 | + | 0.318793i | 0.995393 | − | 0.0958740i | \(-0.0305646\pi\) |
−0.909973 | + | 0.414667i | \(0.863898\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.53590i | 0.0983379i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.19615 | + | 2.19615i | −0.0850354 | + | 0.0850354i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.60770 | − | 7.98076i | 0.177878 | − | 0.308094i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.80385 | + | 15.2487i | 0.339363 | + | 0.587795i | 0.984313 | − | 0.176430i | \(-0.0564550\pi\) |
−0.644950 | + | 0.764225i | \(0.723122\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.73205 | − | 1.26795i | −0.181867 | − | 0.0487312i | 0.166736 | − | 0.986002i | \(-0.446677\pi\) |
−0.348603 | + | 0.937270i | \(0.613344\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.24167 | + | 3.02628i | 0.201157 | + | 0.116138i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.70577 | + | 4.70577i | −0.180061 | + | 0.180061i | −0.791383 | − | 0.611321i | \(-0.790638\pi\) |
0.611321 | + | 0.791383i | \(0.290638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −44.9808 | − | 44.9808i | −1.71863 | − | 1.71863i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.39230 | − | 4.14359i | 0.0911396 | − | 0.157858i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.29423 | − | 23.4904i | 0.239444 | − | 0.893616i | −0.736651 | − | 0.676273i | \(-0.763594\pi\) |
0.976095 | − | 0.217344i | \(-0.0697392\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −31.3923 | + | 18.1244i | −1.19078 | + | 0.687496i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.89230 | − | 3.40192i | −0.223187 | − | 0.128857i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.6603 | − | 10.6603i | −0.402632 | − | 0.402632i | 0.476527 | − | 0.879160i | \(-0.341895\pi\) |
−0.879160 | + | 0.476527i | \(0.841895\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.60770 | 0.0606354 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.46410 | − | 1.46410i | 0.205499 | − | 0.0550632i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.1962 | − | 5.41154i | −0.758482 | − | 0.203235i | −0.141205 | − | 0.989980i | \(-0.545098\pi\) |
−0.617277 | + | 0.786746i | \(0.711764\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.19615 | − | 4.73205i | 0.306948 | − | 0.177217i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.7321 | − | 69.9090i | −0.700539 | − | 2.61445i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.3923 | −0.611330 | −0.305665 | − | 0.952139i | \(-0.598879\pi\) | ||||
−0.305665 | + | 0.952139i | \(0.598879\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.67949 | 0.248757 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.29423 | − | 23.4904i | −0.233762 | − | 0.872411i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.8109 | + | 18.3660i | −1.17980 | + | 0.681158i | −0.955968 | − | 0.293470i | \(-0.905190\pi\) |
−0.223832 | + | 0.974628i | \(0.571857\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.79423 | + | 0.748711i | 0.103348 | + | 0.0276921i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.9545 | + | 8.02628i | −1.10639 | + | 0.296457i | −0.765366 | − | 0.643596i | \(-0.777442\pi\) |
−0.341028 | + | 0.940053i | \(0.610775\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.0718 | 0.592012 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.2224 | − | 21.2224i | −0.780680 | − | 0.780680i | 0.199266 | − | 0.979945i | \(-0.436144\pi\) |
−0.979945 | + | 0.199266i | \(0.936144\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.24167 | + | 1.29423i | 0.0822389 | + | 0.0474806i | 0.540556 | − | 0.841308i | \(-0.318214\pi\) |
−0.458317 | + | 0.888789i | \(0.651547\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.7321 | − | 6.19615i | 0.393192 | − | 0.227009i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.61474 | − | 13.4904i | 0.132080 | − | 0.492928i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.8564 | + | 32.6603i | −0.688080 | + | 1.19179i | 0.284378 | + | 0.958712i | \(0.408213\pi\) |
−0.972458 | + | 0.233077i | \(0.925120\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.46410 | + | 7.46410i | 0.271646 | + | 0.271646i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.07180 | + | 6.07180i | −0.220683 | + | 0.220683i | −0.808786 | − | 0.588103i | \(-0.799875\pi\) |
0.588103 | + | 0.808786i | \(0.299875\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.3731 | + | 15.8038i | 0.992273 | + | 0.572889i | 0.905953 | − | 0.423378i | \(-0.139156\pi\) |
0.0863200 | + | 0.996267i | \(0.472489\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.26795 | − | 1.94744i | −0.263117 | − | 0.0705021i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.2224 | − | 28.0981i | −0.585758 | − | 1.01456i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.1244 | − | 17.5359i | 0.365094 | − | 0.632361i | −0.623698 | − | 0.781666i | \(-0.714370\pi\) |
0.988791 | + | 0.149305i | \(0.0477036\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.41154 | + | 4.41154i | −0.158672 | + | 0.158672i | −0.781978 | − | 0.623306i | \(-0.785789\pi\) |
0.623306 | + | 0.781978i | \(0.285789\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 74.1051i | 2.66193i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.696152 | − | 2.59808i | −0.0249422 | − | 0.0930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.39230 | − | 31.3205i | 0.300300 | − | 1.12074i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.46410 | − | 16.3923i | −0.337788 | − | 0.585066i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.8109 | + | 13.3468i | −1.77557 | + | 0.475762i | −0.989764 | − | 0.142716i | \(-0.954417\pi\) |
−0.785803 | + | 0.618477i | \(0.787750\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 10.1436i | − | 0.360665i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 19.6077i | − | 0.696290i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 54.1769 | − | 14.5167i | 1.91904 | − | 0.514206i | 0.929770 | − | 0.368142i | \(-0.120006\pi\) |
0.989275 | − | 0.146065i | \(-0.0466609\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.9545 | − | 18.9737i | −0.387542 | − | 0.671242i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.47372 | − | 27.8923i | 0.263742 | − | 0.984298i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.928203 | + | 3.46410i | 0.0327149 | + | 0.122094i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 28.3205i | − | 0.995696i | −0.867264 | − | 0.497848i | \(-0.834124\pi\) | ||
0.867264 | − | 0.497848i | \(-0.165876\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.02628 | + | 5.02628i | −0.176497 | + | 0.176497i | −0.789827 | − | 0.613330i | \(-0.789830\pi\) |
0.613330 | + | 0.789827i | \(0.289830\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.1244 | − | 33.1244i | 0.669897 | − | 1.16030i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.571797 | + | 0.990381i | 0.0200046 | + | 0.0346490i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.2224 | − | 8.63397i | −1.12457 | − | 0.301328i | −0.351839 | − | 0.936061i | \(-0.614444\pi\) |
−0.772732 | + | 0.634733i | \(0.781110\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.7321 | − | 6.19615i | −0.374096 | − | 0.215984i | 0.301151 | − | 0.953577i | \(-0.402629\pi\) |
−0.675246 | + | 0.737592i | \(0.735963\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.4641 | − | 24.4641i | 0.850700 | − | 0.850700i | −0.139519 | − | 0.990219i | \(-0.544556\pi\) |
0.990219 | + | 0.139519i | \(0.0445557\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.5167 | + | 24.5167i | 0.851499 | + | 0.851499i | 0.990318 | − | 0.138819i | \(-0.0443306\pi\) |
−0.138819 | + | 0.990318i | \(0.544331\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.33013 | + | 12.6962i | −0.253974 | + | 0.439896i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.535898 | + | 2.00000i | −0.0185455 | + | 0.0692129i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.4449 | + | 20.4641i | −1.22369 | + | 0.706499i | −0.965703 | − | 0.259649i | \(-0.916393\pi\) |
−0.257989 | + | 0.966148i | \(0.583060\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.9186 | + | 11.5000i | 0.686848 | + | 0.396552i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −73.3731 | − | 73.3731i | −2.52411 | − | 2.52411i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.60770 | 0.0552411 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.19615 | − | 0.588457i | 0.0752831 | − | 0.0201721i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.5622 | − | 3.36603i | −0.430121 | − | 0.115251i | 0.0372621 | − | 0.999306i | \(-0.488136\pi\) |
−0.467383 | + | 0.884055i | \(0.654803\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.9090 | + | 12.0718i | −0.714237 | + | 0.412365i | −0.812628 | − | 0.582783i | \(-0.801964\pi\) |
0.0983911 | + | 0.995148i | \(0.468630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.25833 | + | 30.8205i | 0.281771 | + | 1.05158i | 0.951167 | + | 0.308677i | \(0.0998861\pi\) |
−0.669396 | + | 0.742905i | \(0.733447\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.53590 | −0.290565 | −0.145283 | − | 0.989390i | \(-0.546409\pi\) | ||||
−0.145283 | + | 0.989390i | \(0.546409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 50.2487 | 1.70851 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.21539 | + | 34.3923i | 0.312611 | + | 1.16668i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.6147 | − | 17.0981i | 1.00346 | − | 0.579346i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.4641 | − | 3.60770i | −0.455170 | − | 0.121962i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.53590 | + | 0.411543i | −0.0518636 | + | 0.0138968i | −0.284658 | − | 0.958629i | \(-0.591880\pi\) |
0.232794 | + | 0.972526i | \(0.425213\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.32051 | 0.246634 | 0.123317 | − | 0.992367i | \(-0.460647\pi\) | ||||
0.123317 | + | 0.992367i | \(0.460647\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.3660 | + | 14.3660i | 0.483455 | + | 0.483455i | 0.906233 | − | 0.422778i | \(-0.138945\pi\) |
−0.422778 | + | 0.906233i | \(0.638945\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.1244 | + | 19.1244i | 1.11221 | + | 0.642133i | 0.939400 | − | 0.342823i | \(-0.111383\pi\) |
0.172807 | + | 0.984956i | \(0.444716\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.92820 | + | 2.26795i | −0.131748 | + | 0.0760646i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.24167 | − | 8.36603i | 0.0750146 | − | 0.279958i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.5885 | − | 56.4449i | 1.08931 | − | 1.88674i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.9282 | + | 12.9282i | 0.431180 | + | 0.431180i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.21539 | − | 1.21539i | 0.0404905 | − | 0.0404905i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −63.3731 | − | 36.5885i | −2.10659 | − | 1.21624i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.7942 | + | 4.50000i | 0.557643 | + | 0.149420i | 0.526623 | − | 0.850099i | \(-0.323458\pi\) |
0.0310198 | + | 0.999519i | \(0.490124\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.46410 | − | 7.73205i | −0.147902 | − | 0.256174i | 0.782550 | − | 0.622588i | \(-0.213919\pi\) |
−0.930452 | + | 0.366414i | \(0.880585\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.09808 | − | 3.63397i | 0.0694362 | − | 0.120267i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.66025 | − | 1.66025i | 0.0548264 | − | 0.0548264i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.9808i | 1.08793i | 0.839106 | + | 0.543967i | \(0.183079\pi\) | ||||
−0.839106 | + | 0.543967i | \(0.816921\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.8564 | − | 66.6410i | −0.587751 | − | 2.19352i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.60770 | + | 17.1962i | −0.151500 | + | 0.565406i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18.4641 | + | 31.9808i | 0.605788 | + | 1.04925i | 0.991926 | + | 0.126814i | \(0.0404752\pi\) |
−0.386139 | + | 0.922441i | \(0.626191\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.59808 | + | 1.50000i | −0.183470 | + | 0.0491605i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 26.0000i | − | 0.850291i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 51.1769i | 1.67188i | 0.548823 | + | 0.835938i | \(0.315076\pi\) | ||||
−0.548823 | + | 0.835938i | \(0.684924\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.1962 | − | 3.26795i | 0.397583 | − | 0.106532i | −0.0544870 | − | 0.998514i | \(-0.517352\pi\) |
0.452070 | + | 0.891982i | \(0.350686\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.90192 | − | 3.29423i | −0.0619352 | − | 0.107275i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.01666 | + | 14.9904i | −0.130524 | + | 0.487122i | −0.999976 | − | 0.00689497i | \(-0.997805\pi\) |
0.869452 | + | 0.494017i | \(0.164472\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.9019 | − | 59.3468i | −0.516198 | − | 1.92648i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 59.1051i | 1.91460i | 0.289092 | + | 0.957301i | \(0.406647\pi\) | ||||
−0.289092 | + | 0.957301i | \(0.593353\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 38.3923 | − | 38.3923i | 1.24235 | − | 1.24235i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.02628 | + | 10.4378i | −0.194599 | + | 0.337055i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.3564 | − | 21.4019i | −0.398594 | − | 0.690385i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 68.1769 | + | 18.2679i | 2.19469 | + | 0.588066i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.16987 | − | 5.29423i | −0.294883 | − | 0.170251i | 0.345259 | − | 0.938508i | \(-0.387791\pi\) |
−0.640142 | + | 0.768257i | \(0.721124\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.4641 | − | 22.4641i | 0.720907 | − | 0.720907i | −0.247883 | − | 0.968790i | \(-0.579735\pi\) |
0.968790 | + | 0.247883i | \(0.0797348\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.85641 | + | 4.85641i | 0.155689 | + | 0.155689i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.93782 | − | 17.2128i | 0.317939 | − | 0.550687i | −0.662119 | − | 0.749399i | \(-0.730343\pi\) |
0.980058 | + | 0.198712i | \(0.0636759\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.53590 | + | 5.73205i | −0.0490875 | + | 0.183197i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.8564 | + | 8.00000i | −0.441951 | + | 0.255160i | −0.704425 | − | 0.709779i | \(-0.748795\pi\) |
0.262474 | + | 0.964939i | \(0.415462\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.3205 | − | 10.0000i | −0.551877 | − | 0.318626i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.14359 | + | 1.14359i | 0.0363642 | + | 0.0363642i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.6410 | 1.03688 | 0.518438 | − | 0.855115i | \(-0.326514\pi\) | ||||
0.518438 | + | 0.855115i | \(0.326514\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.26795 | + | 0.875644i | −0.103601 | + | 0.0277598i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.1244 | + | 8.60770i | 1.01739 | + | 0.272608i | 0.728713 | − | 0.684819i | \(-0.240119\pi\) |
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.2.bc.a.145.1 | 4 | ||
3.2 | odd | 2 | 576.2.bb.c.337.1 | 4 | |||
4.3 | odd | 2 | 432.2.y.b.253.1 | 4 | |||
9.2 | odd | 6 | 576.2.bb.d.529.1 | 4 | |||
9.7 | even | 3 | 1728.2.bc.d.721.1 | 4 | |||
12.11 | even | 2 | 144.2.x.c.13.1 | yes | 4 | ||
16.5 | even | 4 | 1728.2.bc.d.1009.1 | 4 | |||
16.11 | odd | 4 | 432.2.y.c.37.1 | 4 | |||
36.7 | odd | 6 | 432.2.y.c.397.1 | 4 | |||
36.11 | even | 6 | 144.2.x.b.61.1 | ✓ | 4 | ||
48.5 | odd | 4 | 576.2.bb.d.49.1 | 4 | |||
48.11 | even | 4 | 144.2.x.b.85.1 | yes | 4 | ||
144.11 | even | 12 | 144.2.x.c.133.1 | yes | 4 | ||
144.43 | odd | 12 | 432.2.y.b.181.1 | 4 | |||
144.101 | odd | 12 | 576.2.bb.c.241.1 | 4 | |||
144.133 | even | 12 | inner | 1728.2.bc.a.1585.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.b.61.1 | ✓ | 4 | 36.11 | even | 6 | ||
144.2.x.b.85.1 | yes | 4 | 48.11 | even | 4 | ||
144.2.x.c.13.1 | yes | 4 | 12.11 | even | 2 | ||
144.2.x.c.133.1 | yes | 4 | 144.11 | even | 12 | ||
432.2.y.b.181.1 | 4 | 144.43 | odd | 12 | |||
432.2.y.b.253.1 | 4 | 4.3 | odd | 2 | |||
432.2.y.c.37.1 | 4 | 16.11 | odd | 4 | |||
432.2.y.c.397.1 | 4 | 36.7 | odd | 6 | |||
576.2.bb.c.241.1 | 4 | 144.101 | odd | 12 | |||
576.2.bb.c.337.1 | 4 | 3.2 | odd | 2 | |||
576.2.bb.d.49.1 | 4 | 48.5 | odd | 4 | |||
576.2.bb.d.529.1 | 4 | 9.2 | odd | 6 | |||
1728.2.bc.a.145.1 | 4 | 1.1 | even | 1 | trivial | ||
1728.2.bc.a.1585.1 | 4 | 144.133 | even | 12 | inner | ||
1728.2.bc.d.721.1 | 4 | 9.7 | even | 3 | |||
1728.2.bc.d.1009.1 | 4 | 16.5 | even | 4 |