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 | 1009.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1009 |
Dual form | 1728.2.bc.d.721.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | 3.73205 | − | 1.00000i | 1.66902 | − | 0.447214i | 0.704177 | − | 0.710025i | \(-0.251316\pi\) |
0.964847 | + | 0.262811i | \(0.0846497\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.633975 | − | 0.366025i | 0.239620 | − | 0.138345i | −0.375382 | − | 0.926870i | \(-0.622489\pi\) |
0.615002 | + | 0.788526i | \(0.289155\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.767949 | + | 2.86603i | −0.231545 | + | 0.864139i | 0.748130 | + | 0.663552i | \(0.230952\pi\) |
−0.979676 | + | 0.200587i | \(0.935715\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.63397 | − | 6.09808i | −0.453183 | − | 1.69130i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.240192 | − | 0.970725i | \(-0.422790\pi\) | |||||||
\(14\) | 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 | −0.630635 | − | 0.776079i | \(-0.717206\pi\) |
0.776079 | + | 0.630635i | \(0.217206\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.09808 | − | 0.633975i | −0.228965 | − | 0.132193i | 0.381130 | − | 0.924522i | \(-0.375535\pi\) |
−0.610094 | + | 0.792329i | \(0.708868\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.59808 | − | 4.96410i | 1.71962 | − | 0.992820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.36603 | + | 0.633975i | 0.439360 | + | 0.117726i | 0.471717 | − | 0.881750i | \(-0.343635\pi\) |
−0.0323566 | + | 0.999476i | \(0.510301\pi\) | |||||||
\(30\) | 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 | 0.803608 | − | 0.595159i | \(-0.202911\pi\) |
−0.595159 | + | 0.803608i | \(0.702911\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.59808 | + | 1.50000i | 0.405751 | + | 0.234261i | 0.688963 | − | 0.724797i | \(-0.258066\pi\) |
−0.283211 | + | 0.959058i | \(0.591400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.330127 | + | 1.23205i | −0.0503439 | + | 0.187886i | −0.986519 | − | 0.163649i | \(-0.947674\pi\) |
0.936175 | + | 0.351535i | \(0.114340\pi\) | |||||||
\(44\) | 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 | 0.742954 | − | 0.669343i | \(-0.233424\pi\) |
−0.669343 | + | 0.742954i | \(0.733424\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.4641i | 1.54582i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.96410 | − | 1.33013i | 0.646271 | − | 0.173168i | 0.0792287 | − | 0.996856i | \(-0.474754\pi\) |
0.567042 | + | 0.823689i | \(0.308088\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 0.803848i | −0.384111 | − | 0.102922i | 0.0615961 | − | 0.998101i | \(-0.480381\pi\) |
−0.445707 | + | 0.895179i | \(0.647048\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.1962 | − | 21.1244i | −1.51275 | − | 2.62015i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.40192 | − | 5.23205i | −0.171272 | − | 0.639197i | −0.997157 | − | 0.0753572i | \(-0.975990\pi\) |
0.825884 | − | 0.563840i | \(-0.190676\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9282i | 1.29694i | 0.761241 | + | 0.648470i | \(0.224591\pi\) | ||||
−0.761241 | + | 0.648470i | \(0.775409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.73205i | 1.13905i | 0.821974 | + | 0.569525i | \(0.192873\pi\) | ||||
−0.821974 | + | 0.569525i | \(0.807127\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.562178 | + | 2.09808i | 0.0640661 | + | 0.239098i | ||||
\(78\) | 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 | ||||||||
\(83\) | −1.36603 | − | 0.366025i | −0.149941 | − | 0.0401765i | 0.183068 | − | 0.983100i | \(-0.441397\pi\) |
−0.333009 | + | 0.942924i | \(0.608064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.46410 | − | 2.26795i | 0.918061 | − | 0.245994i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.00000i | − | 0.212000i | −0.994366 | − | 0.106000i | \(-0.966196\pi\) | ||
0.994366 | − | 0.106000i | \(-0.0338043\pi\) | |||||||
\(90\) | 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 | ||||||||
\(101\) | 2.00000 | − | 7.46410i | 0.199007 | − | 0.742706i | −0.792186 | − | 0.610280i | \(-0.791057\pi\) |
0.991193 | − | 0.132426i | \(-0.0422765\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.90192 | + | 4.56218i | 0.778600 | + | 0.449525i | 0.835934 | − | 0.548830i | \(-0.184927\pi\) |
−0.0573341 | + | 0.998355i | \(0.518260\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.4904 | − | 13.4904i | −1.30416 | − | 1.30416i | −0.925558 | − | 0.378607i | \(-0.876403\pi\) |
−0.378607 | − | 0.925558i | \(-0.623597\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.26795 | − | 7.26795i | 0.696143 | − | 0.696143i | −0.267433 | − | 0.963576i | \(-0.586175\pi\) |
0.963576 | + | 0.267433i | \(0.0861754\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | −4.73205 | − | 1.26795i | −0.441266 | − | 0.118237i | ||||
\(116\) | 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 | ||||||||
\(131\) | 0.830127 | + | 3.09808i | 0.0725285 | + | 0.270680i | 0.992662 | − | 0.120926i | \(-0.0385863\pi\) |
−0.920133 | + | 0.391606i | \(0.871920\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.169873 | − | 0.633975i | 0.0147299 | − | 0.0549726i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.2583 | + | 8.23205i | −1.21817 | + | 0.703312i | −0.964527 | − | 0.263986i | \(-0.914963\pi\) |
−0.253645 | + | 0.967297i | \(0.581629\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.06218 | − | 2.42820i | 0.768644 | − | 0.205958i | 0.146872 | − | 0.989156i | \(-0.453080\pi\) |
0.621772 | + | 0.783198i | \(0.286413\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | −3.09808 | + | 0.830127i | −0.253804 | + | 0.0680067i | −0.383478 | − | 0.923550i | \(-0.625274\pi\) |
0.129674 | + | 0.991557i | \(0.458607\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.36603 | − | 1.36603i | 0.192544 | − | 0.111166i | −0.400629 | − | 0.916240i | \(-0.631208\pi\) |
0.593173 | + | 0.805075i | \(0.297875\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.46410 | − | 27.8564i | 0.599531 | − | 2.23748i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.26795 | − | 4.73205i | −0.101193 | − | 0.377659i | 0.896692 | − | 0.442655i | \(-0.145963\pi\) |
−0.997886 | + | 0.0649959i | \(0.979297\pi\) | |||||||
\(158\) | 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 | −0.377661 | − | 0.925944i | \(-0.623272\pi\) |
0.925944 | + | 0.377661i | \(0.123272\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.464102 | + | 0.267949i | 0.0359133 | + | 0.0207345i | 0.517849 | − | 0.855472i | \(-0.326733\pi\) |
−0.481936 | + | 0.876206i | \(0.660066\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.2583 | + | 13.4282i | −1.78910 | + | 1.03294i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.5622 | + | 3.36603i | 0.955085 | + | 0.255914i | 0.702519 | − | 0.711665i | \(-0.252059\pi\) |
0.252566 | + | 0.967580i | \(0.418725\pi\) | |||||||
\(174\) | 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 | −0.103114 | − | 0.994670i | \(-0.532881\pi\) |
0.994670 | + | 0.103114i | \(0.0328806\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3923 | + | 13.3923i | 0.995442 | + | 0.995442i | 0.999990 | − | 0.00454748i | \(-0.00144751\pi\) |
−0.00454748 | + | 0.999990i | \(0.501448\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000 | + | 3.46410i | 0.441129 | + | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.74167 | + | 6.50000i | −0.127364 | + | 0.475327i | ||||
\(188\) | 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 | 0.825372 | − | 0.564590i | \(-0.190966\pi\) |
−0.564590 | + | 0.825372i | \(0.690966\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.875644i | 0.0620728i | 0.999518 | + | 0.0310364i | \(0.00988078\pi\) | ||||
−0.999518 | + | 0.0310364i | \(0.990119\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.73205 | − | 0.464102i | 0.121566 | − | 0.0325735i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1962 | + | 3.00000i | 0.781973 | + | 0.209529i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.33013 | + | 2.30385i | 0.0920068 | + | 0.159360i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.09808 | + | 4.09808i | 0.0755947 | + | 0.282123i | 0.993367 | − | 0.114983i | \(-0.0366812\pi\) |
−0.917773 | + | 0.397106i | \(0.870015\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | −3.70577 | − | 13.8301i | −0.249277 | − | 0.930315i | ||||
\(222\) | 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 | ||||||||
\(227\) | −14.4282 | − | 3.86603i | −0.957633 | − | 0.256597i | −0.254035 | − | 0.967195i | \(-0.581758\pi\) |
−0.703598 | + | 0.710598i | \(0.748425\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.83013 | − | 1.83013i | 0.451347 | − | 0.120938i | −0.0259823 | − | 0.999662i | \(-0.508271\pi\) |
0.477330 | + | 0.878724i | \(0.341605\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.19615i | 0.471436i | 0.971822 | + | 0.235718i | \(0.0757441\pi\) | ||||
−0.971822 | + | 0.235718i | \(0.924256\pi\) | |||||||
\(234\) | 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 | ||||||||
\(245\) | −6.46410 | + | 24.1244i | −0.412976 | + | 1.54125i | ||||
\(246\) | 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 | 0.790761 | − | 0.612125i | \(-0.209685\pi\) |
−0.612125 | + | 0.790761i | \(0.709685\pi\) | |||||||
\(252\) | 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 | ||||||||
\(259\) | 1.26795 | + | 0.339746i | 0.0787865 | + | 0.0211108i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.4904 | + | 13.5622i | −1.44848 | + | 0.836280i | −0.998391 | − | 0.0567045i | \(-0.981941\pi\) |
−0.450088 | + | 0.892984i | \(0.648607\pi\) | |||||||
\(264\) | 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 | −0.836494 | − | 0.547976i | \(-0.815399\pi\) |
0.547976 | + | 0.836494i | \(0.315399\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | 7.62436 | + | 28.4545i | 0.459766 | + | 1.71587i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.22243 | + | 15.7583i | −0.253701 | + | 0.946826i | 0.715107 | + | 0.699015i | \(0.246378\pi\) |
−0.968808 | + | 0.247811i | \(0.920289\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.66025 | − | 5.00000i | 0.516627 | − | 0.298275i | −0.218926 | − | 0.975741i | \(-0.570255\pi\) |
0.735554 | + | 0.677466i | \(0.236922\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.7583 | + | 7.43782i | −1.65006 | + | 0.442133i | −0.959630 | − | 0.281265i | \(-0.909246\pi\) |
−0.690431 | + | 0.723398i | \(0.742579\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | −13.5622 | + | 3.63397i | −0.792311 | + | 0.212299i | −0.632205 | − | 0.774801i | \(-0.717850\pi\) |
−0.160106 | + | 0.987100i | \(0.551183\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.1962 | − | 9.92820i | 1.00120 | − | 0.578042i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.07180 | + | 7.73205i | −0.119815 | + | 0.447156i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.241670 | + | 0.901924i | 0.0139296 | + | 0.0519860i | ||||
\(302\) | 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 | −0.0819670 | − | 0.996635i | \(-0.526120\pi\) |
0.996635 | + | 0.0819670i | \(0.0261202\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.9019 | + | 8.02628i | 0.788306 | + | 0.455129i | 0.839366 | − | 0.543567i | \(-0.182927\pi\) |
−0.0510600 | + | 0.998696i | \(0.516260\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.6506 | − | 14.2321i | 1.39334 | − | 0.804443i | 0.399653 | − | 0.916666i | \(-0.369131\pi\) |
0.993683 | + | 0.112223i | \(0.0357972\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −31.4904 | − | 8.43782i | −1.76868 | − | 0.473915i | −0.780231 | − | 0.625492i | \(-0.784898\pi\) |
−0.988445 | + | 0.151577i | \(0.951565\pi\) | |||||||
\(318\) | 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 | ||||||||
\(331\) | −5.09808 | + | 19.0263i | −0.280216 | + | 1.04578i | 0.672049 | + | 0.740506i | \(0.265414\pi\) |
−0.952265 | + | 0.305273i | \(0.901252\pi\) | |||||||
\(332\) | 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 | ||||||||
\(347\) | −24.7224 | + | 6.62436i | −1.32717 | + | 0.355614i | −0.851659 | − | 0.524096i | \(-0.824403\pi\) |
−0.475510 | + | 0.879710i | \(0.657737\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.73205 | − | 2.07180i | −0.413887 | − | 0.110901i | 0.0458657 | − | 0.998948i | \(-0.485395\pi\) |
−0.459753 | + | 0.888047i | \(0.652062\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 10.9282 | + | 40.7846i | 0.580009 | + | 2.16462i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 14.7321i | − | 0.777528i | −0.921337 | − | 0.388764i | \(-0.872902\pi\) | ||
0.921337 | − | 0.388764i | \(-0.127098\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.1962i | 0.957692i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.73205 | + | 36.3205i | 0.509399 | + | 1.90110i | ||||
\(366\) | 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 | ||||||||
\(371\) | 0.535898 | + | 0.143594i | 0.0278225 | + | 0.00745501i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.63397 | + | 1.50962i | −0.291716 | + | 0.0781651i | −0.401709 | − | 0.915767i | \(-0.631584\pi\) |
0.109993 | + | 0.993932i | \(0.464917\pi\) | |||||||
\(374\) | 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 | 0.999359 | − | 0.0358080i | \(-0.0114005\pi\) |
−0.0358080 | + | 0.999359i | \(0.511400\pi\) | |||||||
\(380\) | 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 | ||||||||
\(389\) | 2.75833 | − | 10.2942i | 0.139853 | − | 0.521938i | −0.860078 | − | 0.510163i | \(-0.829585\pi\) |
0.999931 | − | 0.0117752i | \(-0.00374824\pi\) | |||||||
\(390\) | 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 | −0.950310 | − | 0.311306i | \(-0.899233\pi\) |
0.311306 | + | 0.950310i | \(0.399233\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | −45.5167 | − | 12.1962i | −2.26735 | − | 0.607534i | ||||
\(404\) | 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 | −0.313191 | − | 0.949690i | \(-0.601398\pi\) |
−0.979051 | + | 0.203614i | \(0.934731\pi\) | |||||||
\(410\) | 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 | ||||||||
\(419\) | −8.36603 | − | 31.2224i | −0.408707 | − | 1.52532i | −0.797115 | − | 0.603828i | \(-0.793641\pi\) |
0.388408 | − | 0.921488i | \(-0.373025\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.588457 | − | 2.19615i | 0.0286797 | − | 0.107034i | −0.950102 | − | 0.311938i | \(-0.899022\pi\) |
0.978782 | + | 0.204905i | \(0.0656884\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 19.5000 | − | 11.2583i | 0.945889 | − | 0.546109i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.19615 | + | 0.588457i | −0.106279 | + | 0.0284774i | ||||
\(428\) | 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 | ||||||||
\(437\) | −1.09808 | + | 0.294229i | −0.0525281 | + | 0.0140749i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.85641 | − | 2.80385i | 0.231784 | − | 0.133820i | −0.379611 | − | 0.925146i | \(-0.623942\pi\) |
0.611395 | + | 0.791326i | \(0.290609\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.25833 | + | 19.6244i | −0.249831 | + | 0.932381i | 0.721063 | + | 0.692870i | \(0.243654\pi\) |
−0.970894 | + | 0.239511i | \(0.923013\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.00000 | − | 7.46410i | −0.0948091 | − | 0.353832i | ||||
\(446\) | 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 | 0.0552962 | − | 0.998470i | \(-0.482390\pi\) |
0.892348 | + | 0.451347i | \(0.149056\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.56218 | − | 0.686533i | −0.119333 | − | 0.0319751i | 0.198659 | − | 0.980069i | \(-0.436342\pi\) |
−0.317991 | + | 0.948094i | \(0.603008\pi\) | |||||||
\(462\) | 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 | −0.598836 | − | 0.800872i | \(-0.704370\pi\) |
0.800872 | + | 0.598836i | \(0.204370\pi\) | |||||||
\(468\) | 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 | ||||||||
\(475\) | 2.30385 | − | 8.59808i | 0.105708 | − | 0.394507i | ||||
\(476\) | 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 | \(0.119601\pi\) | ||||
−0.930237 | + | 0.366959i | \(0.880399\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.7224 | + | 6.89230i | −1.16084 | + | 0.311045i | −0.787300 | − | 0.616570i | \(-0.788522\pi\) |
−0.373537 | + | 0.927615i | \(0.621855\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.36603 | + | 1.43782i | 0.241674 | + | 0.0647563i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.00000 | + | 6.92820i | 0.179425 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.69615 | + | 6.33013i | 0.0759302 | + | 0.283375i | 0.993443 | − | 0.114332i | \(-0.0364727\pi\) |
−0.917512 | + | 0.397707i | \(0.869806\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 27.7128i | − | 1.23565i | −0.786314 | − | 0.617827i | \(-0.788013\pi\) | ||
0.786314 | − | 0.617827i | \(-0.211987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 29.8564i | − | 1.32859i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.53590 | + | 16.9282i | 0.201050 | + | 0.750329i | 0.990617 | + | 0.136665i | \(0.0436385\pi\) |
−0.789567 | + | 0.613664i | \(0.789695\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.56218 | + | 6.16987i | 0.157581 | + | 0.272939i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 34.0526 | + | 9.12436i | 1.50054 | + | 0.402067i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.6865 | − | 7.41858i | 1.21765 | − | 0.326269i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0000i | 0.569540i | 0.958596 | + | 0.284770i | \(0.0919173\pi\) | ||||
−0.958596 | + | 0.284770i | \(0.908083\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.4641 | + | 14.4641i | 0.632471 | + | 0.632471i | 0.948687 | − | 0.316216i | \(-0.102412\pi\) |
−0.316216 | + | 0.948687i | \(0.602412\pi\) | |||||||
\(524\) | 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 | ||||||||
\(533\) | 4.90192 | − | 18.2942i | 0.212326 | − | 0.792411i | ||||
\(534\) | 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 | −0.860994 | − | 0.508614i | \(-0.830158\pi\) |
0.508614 | + | 0.860994i | \(0.330158\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.8564 | − | 34.3923i | 0.850555 | − | 1.47320i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.2583 | + | 8.37564i | 1.33651 | + | 0.358117i | 0.855138 | − | 0.518400i | \(-0.173472\pi\) |
0.481371 | + | 0.876517i | \(0.340139\pi\) | |||||||
\(548\) | 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 | 0.0700519 | − | 0.997543i | \(-0.477684\pi\) |
0.997543 | − | 0.0700519i | \(-0.0223165\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.05256 | 0.340587 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.00962 | + | 3.76795i | 0.0425504 | + | 0.158800i | 0.983932 | − | 0.178543i | \(-0.0571384\pi\) |
−0.941382 | + | 0.337343i | \(0.890472\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.8564 | + | 51.7128i | −0.582943 | + | 2.17557i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.5981 | + | 13.6244i | −0.989283 | + | 0.571163i | −0.905060 | − | 0.425284i | \(-0.860174\pi\) |
−0.0842230 | + | 0.996447i | \(0.526841\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.8923 | − | 5.33013i | 0.832467 | − | 0.223059i | 0.182677 | − | 0.983173i | \(-0.441524\pi\) |
0.649790 | + | 0.760114i | \(0.274857\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | −1.00000 | + | 0.267949i | −0.0414870 | + | 0.0111164i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.94744 | + | 1.12436i | −0.0806548 | + | 0.0465661i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.00962 | + | 3.76795i | −0.0416714 | + | 0.155520i | −0.983626 | − | 0.180219i | \(-0.942319\pi\) |
0.941955 | + | 0.335739i | \(0.108986\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.73205 | − | 6.46410i | −0.0713679 | − | 0.266349i | ||||
\(590\) | 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 | 0.893965 | − | 0.448136i | \(-0.147912\pi\) |
0.0588850 | + | 0.998265i | \(0.481245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.5526 | + | 10.1340i | −0.715984 | + | 0.413373i | −0.813273 | − | 0.581883i | \(-0.802316\pi\) |
0.0972889 | + | 0.995256i | \(0.468983\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.19615 | + | 2.19615i | 0.333221 | + | 0.0892863i | ||||
\(606\) | 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 | 0.739840 | − | 0.672783i | \(-0.234901\pi\) |
−0.672783 | + | 0.739840i | \(0.734901\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.91154 | − | 2.25833i | −0.157473 | − | 0.0909170i | 0.419193 | − | 0.907897i | \(-0.362313\pi\) |
−0.576666 | + | 0.816980i | \(0.695646\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.4019 | − | 38.8205i | 0.418089 | − | 1.56033i | −0.360479 | − | 0.932767i | \(-0.617387\pi\) |
0.778568 | − | 0.627561i | \(-0.215947\pi\) | |||||||
\(620\) | 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 | \(0.276859\pi\) | ||||
−0.644995 | + | 0.764187i | \(0.723141\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23.1244 | − | 6.19615i | 0.917662 | − | 0.245887i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.4186 | + | 10.5622i | 1.56182 | + | 0.418489i | ||||
\(638\) | 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 | ||||||||
\(643\) | −12.2321 | − | 45.6506i | −0.482385 | − | 1.80029i | −0.591558 | − | 0.806263i | \(-0.701487\pi\) |
0.109173 | − | 0.994023i | \(-0.465180\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 13.2679i | − | 0.521617i | −0.965391 | − | 0.260808i | \(-0.916011\pi\) | ||
0.965391 | − | 0.260808i | \(-0.0839891\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.2487i | 0.598564i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.50962 | + | 5.63397i | 0.0590760 | + | 0.220474i | 0.989153 | − | 0.146891i | \(-0.0469266\pi\) |
−0.930077 | + | 0.367365i | \(0.880260\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.19615 | + | 10.7321i | 0.242104 | + | 0.419336i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.0263 | − | 4.02628i | −0.585341 | − | 0.156842i | −0.0460178 | − | 0.998941i | \(-0.514653\pi\) |
−0.539323 | + | 0.842099i | \(0.681320\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.19615 | + | 2.19615i | −0.318793 | + | 0.0854204i | −0.414667 | − | 0.909973i | \(-0.636102\pi\) |
0.0958740 | + | 0.995393i | \(0.469435\pi\) | |||||||
\(662\) | 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 | ||||||||
\(677\) | 1.26795 | − | 4.73205i | 0.0487312 | − | 0.181867i | −0.937270 | − | 0.348603i | \(-0.886656\pi\) |
0.986002 | + | 0.166736i | \(0.0533227\pi\) | |||||||
\(678\) | 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 | 0.611321 | − | 0.791383i | \(-0.290638\pi\) |
−0.791383 | + | 0.611321i | \(0.790638\pi\) | |||||||
\(684\) | 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 | ||||||||
\(691\) | −23.4904 | − | 6.29423i | −0.893616 | − | 0.239444i | −0.217344 | − | 0.976095i | \(-0.569739\pi\) |
−0.676273 | + | 0.736651i | \(0.736406\pi\) | |||||||
\(692\) | 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 | −0.879160 | − | 0.476527i | \(-0.841895\pi\) |
0.476527 | + | 0.879160i | \(0.341895\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.60770 | 0.0606354 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.46410 | − | 5.46410i | −0.0550632 | − | 0.205499i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.41154 | − | 20.1962i | 0.203235 | − | 0.758482i | −0.786746 | − | 0.617277i | \(-0.788236\pi\) |
0.989980 | − | 0.141205i | \(-0.0450977\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.19615 | + | 4.73205i | −0.306948 | + | 0.177217i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 69.9090 | − | 18.7321i | 2.61445 | − | 0.700539i | ||||
\(716\) | 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 | ||||||||
\(725\) | 23.4904 | − | 6.29423i | 0.872411 | − | 0.233762i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.8109 | − | 18.3660i | 1.17980 | − | 0.681158i | 0.223832 | − | 0.974628i | \(-0.428143\pi\) |
0.955968 | + | 0.293470i | \(0.0948099\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.748711 | + | 2.79423i | −0.0276921 | + | 0.103348i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.02628 | + | 29.9545i | 0.296457 | + | 1.10639i | 0.940053 | + | 0.341028i | \(0.110775\pi\) |
−0.643596 | + | 0.765366i | \(0.722558\pi\) | |||||||
\(734\) | 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 | −0.979945 | − | 0.199266i | \(-0.936144\pi\) |
0.199266 | + | 0.979945i | \(0.436144\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.24167 | − | 1.29423i | −0.0822389 | − | 0.0474806i | 0.458317 | − | 0.888789i | \(-0.348453\pi\) |
−0.540556 | + | 0.841308i | \(0.681786\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.7321 | + | 6.19615i | −0.393192 | + | 0.227009i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.4904 | − | 3.61474i | −0.492928 | − | 0.132080i | ||||
\(750\) | 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 | 0.588103 | − | 0.808786i | \(-0.299875\pi\) |
−0.808786 | + | 0.588103i | \(0.799875\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.3731 | − | 15.8038i | −0.992273 | − | 0.572889i | −0.0863200 | − | 0.996267i | \(-0.527511\pi\) |
−0.905953 | + | 0.423378i | \(0.860844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.94744 | − | 7.26795i | 0.0705021 | − | 0.263117i | ||||
\(764\) | 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 | 0.623306 | − | 0.781978i | \(-0.285789\pi\) |
−0.781978 | + | 0.623306i | \(0.785789\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 74.1051i | − | 2.66193i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.59808 | − | 0.696152i | 0.0930857 | − | 0.0249422i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.3205 | − | 8.39230i | −1.12074 | − | 0.300300i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.46410 | − | 16.3923i | −0.337788 | − | 0.585066i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.3468 | + | 49.8109i | 0.475762 | + | 1.77557i | 0.618477 | + | 0.785803i | \(0.287750\pi\) |
−0.142716 | + | 0.989764i | \(0.545583\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | −14.5167 | − | 54.1769i | −0.514206 | − | 1.91904i | −0.368142 | − | 0.929770i | \(-0.620006\pi\) |
−0.146065 | − | 0.989275i | \(-0.546661\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.9545 | − | 18.9737i | −0.387542 | − | 0.671242i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.8923 | − | 7.47372i | −0.984298 | − | 0.263742i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.46410 | + | 0.928203i | −0.122094 | + | 0.0327149i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.3205i | 0.995696i | 0.867264 | + | 0.497848i | \(0.165876\pi\) | ||||
−0.867264 | + | 0.497848i | \(0.834124\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.02628 | − | 5.02628i | −0.176497 | − | 0.176497i | 0.613330 | − | 0.789827i | \(-0.289830\pi\) |
−0.789827 | + | 0.613330i | \(0.789830\pi\) | |||||||
\(812\) | 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 | ||||||||
\(821\) | 8.63397 | − | 32.2224i | 0.301328 | − | 1.12457i | −0.634733 | − | 0.772732i | \(-0.718890\pi\) |
0.936061 | − | 0.351839i | \(-0.114444\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.7321 | + | 6.19615i | 0.374096 | + | 0.215984i | 0.675246 | − | 0.737592i | \(-0.264037\pi\) |
−0.301151 | + | 0.953577i | \(0.597371\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.4641 | + | 24.4641i | 0.850700 | + | 0.850700i | 0.990219 | − | 0.139519i | \(-0.0445557\pi\) |
−0.139519 | + | 0.990219i | \(0.544556\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.5167 | − | 24.5167i | 0.851499 | − | 0.851499i | −0.138819 | − | 0.990318i | \(-0.544331\pi\) |
0.990318 | + | 0.138819i | \(0.0443306\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.33013 | + | 12.6962i | −0.253974 | + | 0.439896i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.00000 | + | 0.535898i | 0.0692129 | + | 0.0185455i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.4449 | − | 20.4641i | 1.22369 | − | 0.706499i | 0.257989 | − | 0.966148i | \(-0.416940\pi\) |
0.965703 | + | 0.259649i | \(0.0836067\pi\) | |||||||
\(840\) | 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 | ||||||||
\(851\) | −0.588457 | − | 2.19615i | −0.0201721 | − | 0.0752831i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.36603 | − | 12.5622i | 0.115251 | − | 0.430121i | −0.884055 | − | 0.467383i | \(-0.845197\pi\) |
0.999306 | + | 0.0372621i | \(0.0118636\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.9090 | − | 12.0718i | 0.714237 | − | 0.412365i | −0.0983911 | − | 0.995148i | \(-0.531370\pi\) |
0.812628 | + | 0.582783i | \(0.198036\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.8205 | + | 8.25833i | −1.05158 | + | 0.281771i | −0.742905 | − | 0.669396i | \(-0.766553\pi\) |
−0.308677 | + | 0.951167i | \(0.599886\pi\) | |||||||
\(860\) | 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 | ||||||||
\(869\) | −34.3923 | + | 9.21539i | −1.16668 | + | 0.312611i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.6147 | + | 17.0981i | −1.00346 | + | 0.579346i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.60770 | − | 13.4641i | 0.121962 | − | 0.455170i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.411543 | + | 1.53590i | 0.0138968 | + | 0.0518636i | 0.972526 | − | 0.232794i | \(-0.0747868\pi\) |
−0.958629 | + | 0.284658i | \(0.908120\pi\) | |||||||
\(878\) | 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 | −0.422778 | − | 0.906233i | \(-0.638945\pi\) |
0.906233 | + | 0.422778i | \(0.138945\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.1244 | − | 19.1244i | −1.11221 | − | 0.642133i | −0.172807 | − | 0.984956i | \(-0.555284\pi\) |
−0.939400 | + | 0.342823i | \(0.888617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.92820 | − | 2.26795i | 0.131748 | − | 0.0760646i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.36603 | − | 2.24167i | −0.279958 | − | 0.0750146i | ||||
\(894\) | 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 | ||||||||
\(907\) | −4.50000 | + | 16.7942i | −0.149420 | + | 0.557643i | 0.850099 | + | 0.526623i | \(0.176542\pi\) |
−0.999519 | + | 0.0310198i | \(0.990124\pi\) | |||||||
\(908\) | 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 | \(-0.816921\pi\) | ||
0.839106 | − | 0.543967i | \(-0.183079\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 66.6410 | − | 17.8564i | 2.19352 | − | 0.587751i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.1962 | + | 4.60770i | 0.565406 | + | 0.151500i | ||||
\(926\) | 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 | ||||||||
\(931\) | 1.50000 | + | 5.59808i | 0.0491605 | + | 0.183470i | ||||
\(932\) | 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 | \(-0.684924\pi\) | ||
0.548823 | − | 0.835938i | \(-0.315076\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.26795 | − | 12.1962i | −0.106532 | − | 0.397583i | 0.891982 | − | 0.452070i | \(-0.149314\pi\) |
−0.998514 | + | 0.0544870i | \(0.982648\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.90192 | − | 3.29423i | −0.0619352 | − | 0.107275i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.9904 | + | 4.01666i | 0.487122 | + | 0.130524i | 0.494017 | − | 0.869452i | \(-0.335528\pi\) |
−0.00689497 | + | 0.999976i | \(0.502195\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.3468 | − | 15.9019i | 1.92648 | − | 0.516198i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 59.1051i | − | 1.91460i | −0.289092 | − | 0.957301i | \(-0.593353\pi\) | ||
0.289092 | − | 0.957301i | \(-0.406647\pi\) | |||||||
\(954\) | 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 | ||||||||
\(965\) | −18.2679 | + | 68.1769i | −0.588066 | + | 2.19469i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.16987 | + | 5.29423i | 0.294883 | + | 0.170251i | 0.640142 | − | 0.768257i | \(-0.278876\pi\) |
−0.345259 | + | 0.938508i | \(0.612209\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.4641 | + | 22.4641i | 0.720907 | + | 0.720907i | 0.968790 | − | 0.247883i | \(-0.0797348\pi\) |
−0.247883 | + | 0.968790i | \(0.579735\pi\) | |||||||
\(972\) | 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 | ||||||||
\(979\) | 5.73205 | + | 1.53590i | 0.183197 | + | 0.0490875i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.8564 | − | 8.00000i | 0.441951 | − | 0.255160i | −0.262474 | − | 0.964939i | \(-0.584538\pi\) |
0.704425 | + | 0.709779i | \(0.251205\pi\) | |||||||
\(984\) | 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 | ||||||||
\(995\) | 0.875644 | + | 3.26795i | 0.0277598 | + | 0.103601i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.60770 | + | 32.1244i | −0.272608 | + | 1.01739i | 0.684819 | + | 0.728713i | \(0.259881\pi\) |
−0.957427 | + | 0.288675i | \(0.906785\pi\) | |||||||
\(998\) | 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.d.1009.1 | 4 | ||
3.2 | odd | 2 | 576.2.bb.d.49.1 | 4 | |||
4.3 | odd | 2 | 432.2.y.c.37.1 | 4 | |||
9.2 | odd | 6 | 576.2.bb.c.241.1 | 4 | |||
9.7 | even | 3 | 1728.2.bc.a.1585.1 | 4 | |||
12.11 | even | 2 | 144.2.x.b.85.1 | yes | 4 | ||
16.3 | odd | 4 | 432.2.y.b.253.1 | 4 | |||
16.13 | even | 4 | 1728.2.bc.a.145.1 | 4 | |||
36.7 | odd | 6 | 432.2.y.b.181.1 | 4 | |||
36.11 | even | 6 | 144.2.x.c.133.1 | yes | 4 | ||
48.29 | odd | 4 | 576.2.bb.c.337.1 | 4 | |||
48.35 | even | 4 | 144.2.x.c.13.1 | yes | 4 | ||
144.29 | odd | 12 | 576.2.bb.d.529.1 | 4 | |||
144.61 | even | 12 | inner | 1728.2.bc.d.721.1 | 4 | ||
144.83 | even | 12 | 144.2.x.b.61.1 | ✓ | 4 | ||
144.115 | odd | 12 | 432.2.y.c.397.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.b.61.1 | ✓ | 4 | 144.83 | even | 12 | ||
144.2.x.b.85.1 | yes | 4 | 12.11 | even | 2 | ||
144.2.x.c.13.1 | yes | 4 | 48.35 | even | 4 | ||
144.2.x.c.133.1 | yes | 4 | 36.11 | even | 6 | ||
432.2.y.b.181.1 | 4 | 36.7 | odd | 6 | |||
432.2.y.b.253.1 | 4 | 16.3 | odd | 4 | |||
432.2.y.c.37.1 | 4 | 4.3 | odd | 2 | |||
432.2.y.c.397.1 | 4 | 144.115 | odd | 12 | |||
576.2.bb.c.241.1 | 4 | 9.2 | odd | 6 | |||
576.2.bb.c.337.1 | 4 | 48.29 | odd | 4 | |||
576.2.bb.d.49.1 | 4 | 3.2 | odd | 2 | |||
576.2.bb.d.529.1 | 4 | 144.29 | odd | 12 | |||
1728.2.bc.a.145.1 | 4 | 16.13 | even | 4 | |||
1728.2.bc.a.1585.1 | 4 | 9.7 | even | 3 | |||
1728.2.bc.d.721.1 | 4 | 144.61 | even | 12 | inner | ||
1728.2.bc.d.1009.1 | 4 | 1.1 | even | 1 | trivial |