Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,2,Mod(13,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, 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("144.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.x (of order \(12\), degree \(4\), 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: | \(1.14984578911\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 133.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.133 |
Dual form | 144.2.x.c.13.1 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | + | 0.366025i | −0.965926 | + | 0.258819i | ||||
\(3\) | −0.866025 | + | 1.50000i | −0.500000 | + | 0.866025i | ||||
\(4\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(5\) | 1.00000 | − | 3.73205i | 0.447214 | − | 1.66902i | −0.262811 | − | 0.964847i | \(-0.584650\pi\) |
0.710025 | − | 0.704177i | \(-0.248684\pi\) | |||||||
\(6\) | 0.633975 | − | 2.36603i | 0.258819 | − | 0.965926i | ||||
\(7\) | 0.633975 | + | 0.366025i | 0.239620 | + | 0.138345i | 0.615002 | − | 0.788526i | \(-0.289155\pi\) |
−0.375382 | + | 0.926870i | \(0.622489\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | 5.46410i | 1.72790i | ||||||||
\(11\) | 2.86603 | − | 0.767949i | 0.864139 | − | 0.231545i | 0.200587 | − | 0.979676i | \(-0.435715\pi\) |
0.663552 | + | 0.748130i | \(0.269048\pi\) | |||||||
\(12\) | 3.46410i | 1.00000i | ||||||||
\(13\) | 6.09808 | + | 1.63397i | 1.69130 | + | 0.453183i | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) |
0.720577 | + | 0.693375i | \(0.243877\pi\) | |||||||
\(14\) | −1.00000 | − | 0.267949i | −0.267261 | − | 0.0716124i | ||||
\(15\) | 4.73205 | + | 4.73205i | 1.22181 | + | 1.22181i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −2.26795 | −0.550058 | −0.275029 | − | 0.961436i | \(-0.588688\pi\) | ||||
−0.275029 | + | 0.961436i | \(0.588688\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.707107 | + | 0.707107i | ||||
\(19\) | −0.633975 | + | 0.633975i | −0.145444 | + | 0.145444i | −0.776079 | − | 0.630635i | \(-0.782794\pi\) |
0.630635 | + | 0.776079i | \(0.282794\pi\) | |||||||
\(20\) | −2.00000 | − | 7.46410i | −0.447214 | − | 1.66902i | ||||
\(21\) | −1.09808 | + | 0.633975i | −0.239620 | + | 0.138345i | ||||
\(22\) | −3.63397 | + | 2.09808i | −0.774766 | + | 0.447311i | ||||
\(23\) | 1.09808 | − | 0.633975i | 0.228965 | − | 0.132193i | −0.381130 | − | 0.924522i | \(-0.624465\pi\) |
0.610094 | + | 0.792329i | \(0.291132\pi\) | |||||||
\(24\) | −1.26795 | − | 4.73205i | −0.258819 | − | 0.965926i | ||||
\(25\) | −8.59808 | − | 4.96410i | −1.71962 | − | 0.992820i | ||||
\(26\) | −8.92820 | −1.75096 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 1.46410 | 0.276689 | ||||||||
\(29\) | 0.633975 | + | 2.36603i | 0.117726 | + | 0.439360i | 0.999476 | − | 0.0323566i | \(-0.0103012\pi\) |
−0.881750 | + | 0.471717i | \(0.843635\pi\) | |||||||
\(30\) | −8.19615 | − | 4.73205i | −1.49641 | − | 0.863950i | ||||
\(31\) | −3.73205 | − | 6.46410i | −0.670296 | − | 1.16099i | −0.977820 | − | 0.209447i | \(-0.932834\pi\) |
0.307524 | − | 0.951540i | \(-0.400500\pi\) | |||||||
\(32\) | −1.46410 | + | 5.46410i | −0.258819 | + | 0.965926i | ||||
\(33\) | −1.33013 | + | 4.96410i | −0.231545 | + | 0.864139i | ||||
\(34\) | 3.09808 | − | 0.830127i | 0.531316 | − | 0.142366i | ||||
\(35\) | 2.00000 | − | 2.00000i | 0.338062 | − | 0.338062i | ||||
\(36\) | −5.19615 | − | 3.00000i | −0.866025 | − | 0.500000i | ||||
\(37\) | 1.26795 | + | 1.26795i | 0.208450 | + | 0.208450i | 0.803608 | − | 0.595159i | \(-0.202911\pi\) |
−0.595159 | + | 0.803608i | \(0.702911\pi\) | |||||||
\(38\) | 0.633975 | − | 1.09808i | 0.102844 | − | 0.178131i | ||||
\(39\) | −7.73205 | + | 7.73205i | −1.23812 | + | 1.23812i | ||||
\(40\) | 5.46410 | + | 9.46410i | 0.863950 | + | 1.49641i | ||||
\(41\) | 2.59808 | − | 1.50000i | 0.405751 | − | 0.234261i | −0.283211 | − | 0.959058i | \(-0.591400\pi\) |
0.688963 | + | 0.724797i | \(0.258066\pi\) | |||||||
\(42\) | 1.26795 | − | 1.26795i | 0.195649 | − | 0.195649i | ||||
\(43\) | −1.23205 | + | 0.330127i | −0.187886 | + | 0.0503439i | −0.351535 | − | 0.936175i | \(-0.614340\pi\) |
0.163649 | + | 0.986519i | \(0.447674\pi\) | |||||||
\(44\) | 4.19615 | − | 4.19615i | 0.632594 | − | 0.632594i | ||||
\(45\) | −11.1962 | + | 3.00000i | −1.66902 | + | 0.447214i | ||||
\(46\) | −1.26795 | + | 1.26795i | −0.186949 | + | 0.186949i | ||||
\(47\) | −4.83013 | + | 8.36603i | −0.704546 | + | 1.22031i | 0.262309 | + | 0.964984i | \(0.415516\pi\) |
−0.966855 | + | 0.255326i | \(0.917817\pi\) | |||||||
\(48\) | 3.46410 | + | 6.00000i | 0.500000 | + | 0.866025i | ||||
\(49\) | −3.23205 | − | 5.59808i | −0.461722 | − | 0.799725i | ||||
\(50\) | 13.5622 | + | 3.63397i | 1.91798 | + | 0.513922i | ||||
\(51\) | 1.96410 | − | 3.40192i | 0.275029 | − | 0.476365i | ||||
\(52\) | 12.1962 | − | 3.26795i | 1.69130 | − | 0.453183i | ||||
\(53\) | −0.535898 | − | 0.535898i | −0.0736113 | − | 0.0736113i | 0.669343 | − | 0.742954i | \(-0.266576\pi\) |
−0.742954 | + | 0.669343i | \(0.766576\pi\) | |||||||
\(54\) | −7.09808 | + | 1.90192i | −0.965926 | + | 0.258819i | ||||
\(55\) | − | 11.4641i | − | 1.54582i | ||||||
\(56\) | −2.00000 | + | 0.535898i | −0.267261 | + | 0.0716124i | ||||
\(57\) | −0.401924 | − | 1.50000i | −0.0532361 | − | 0.198680i | ||||
\(58\) | −1.73205 | − | 3.00000i | −0.227429 | − | 0.393919i | ||||
\(59\) | −1.33013 | + | 4.96410i | −0.173168 | + | 0.646271i | 0.823689 | + | 0.567042i | \(0.191912\pi\) |
−0.996856 | + | 0.0792287i | \(0.974754\pi\) | |||||||
\(60\) | 12.9282 | + | 3.46410i | 1.66902 | + | 0.447214i | ||||
\(61\) | 0.803848 | + | 3.00000i | 0.102922 | + | 0.384111i | 0.998101 | − | 0.0615961i | \(-0.0196191\pi\) |
−0.895179 | + | 0.445707i | \(0.852952\pi\) | |||||||
\(62\) | 7.46410 | + | 7.46410i | 0.947942 | + | 0.947942i | ||||
\(63\) | − | 2.19615i | − | 0.276689i | ||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 12.1962 | − | 21.1244i | 1.51275 | − | 2.62015i | ||||
\(66\) | − | 7.26795i | − | 0.894623i | ||||||
\(67\) | −5.23205 | − | 1.40192i | −0.639197 | − | 0.171272i | −0.0753572 | − | 0.997157i | \(-0.524010\pi\) |
−0.563840 | + | 0.825884i | \(0.690676\pi\) | |||||||
\(68\) | −3.92820 | + | 2.26795i | −0.476365 | + | 0.275029i | ||||
\(69\) | 2.19615i | 0.264386i | ||||||||
\(70\) | −2.00000 | + | 3.46410i | −0.239046 | + | 0.414039i | ||||
\(71\) | 10.9282i | 1.29694i | 0.761241 | + | 0.648470i | \(0.224591\pi\) | ||||
−0.761241 | + | 0.648470i | \(0.775409\pi\) | |||||||
\(72\) | 8.19615 | + | 2.19615i | 0.965926 | + | 0.258819i | ||||
\(73\) | 9.73205i | 1.13905i | 0.821974 | + | 0.569525i | \(0.192873\pi\) | ||||
−0.821974 | + | 0.569525i | \(0.807127\pi\) | |||||||
\(74\) | −2.19615 | − | 1.26795i | −0.255298 | − | 0.147396i | ||||
\(75\) | 14.8923 | − | 8.59808i | 1.71962 | − | 0.992820i | ||||
\(76\) | −0.464102 | + | 1.73205i | −0.0532361 | + | 0.198680i | ||||
\(77\) | 2.09808 | + | 0.562178i | 0.239098 | + | 0.0640661i | ||||
\(78\) | 7.73205 | − | 13.3923i | 0.875482 | − | 1.51638i | ||||
\(79\) | −6.00000 | + | 10.3923i | −0.675053 | + | 1.16923i | 0.301401 | + | 0.953498i | \(0.402546\pi\) |
−0.976453 | + | 0.215728i | \(0.930788\pi\) | |||||||
\(80\) | −10.9282 | − | 10.9282i | −1.22181 | − | 1.22181i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −3.00000 | + | 3.00000i | −0.331295 | + | 0.331295i | ||||
\(83\) | 0.366025 | + | 1.36603i | 0.0401765 | + | 0.149941i | 0.983100 | − | 0.183068i | \(-0.0586028\pi\) |
−0.942924 | + | 0.333009i | \(0.891936\pi\) | |||||||
\(84\) | −1.26795 | + | 2.19615i | −0.138345 | + | 0.239620i | ||||
\(85\) | −2.26795 | + | 8.46410i | −0.245994 | + | 0.918061i | ||||
\(86\) | 1.56218 | − | 0.901924i | 0.168454 | − | 0.0972569i | ||||
\(87\) | −4.09808 | − | 1.09808i | −0.439360 | − | 0.117726i | ||||
\(88\) | −4.19615 | + | 7.26795i | −0.447311 | + | 0.774766i | ||||
\(89\) | 2.00000i | 0.212000i | 0.994366 | + | 0.106000i | \(0.0338043\pi\) | ||||
−0.994366 | + | 0.106000i | \(0.966196\pi\) | |||||||
\(90\) | 14.1962 | − | 8.19615i | 1.49641 | − | 0.863950i | ||||
\(91\) | 3.26795 | + | 3.26795i | 0.342574 | + | 0.342574i | ||||
\(92\) | 1.26795 | − | 2.19615i | 0.132193 | − | 0.228965i | ||||
\(93\) | 12.9282 | 1.34059 | ||||||||
\(94\) | 3.53590 | − | 13.1962i | 0.364700 | − | 1.36108i | ||||
\(95\) | 1.73205 | + | 3.00000i | 0.177705 | + | 0.307794i | ||||
\(96\) | −6.92820 | − | 6.92820i | −0.707107 | − | 0.707107i | ||||
\(97\) | −4.13397 | + | 7.16025i | −0.419742 | + | 0.727014i | −0.995913 | − | 0.0903150i | \(-0.971213\pi\) |
0.576172 | + | 0.817329i | \(0.304546\pi\) | |||||||
\(98\) | 6.46410 | + | 6.46410i | 0.652973 | + | 0.652973i | ||||
\(99\) | −6.29423 | − | 6.29423i | −0.632594 | − | 0.632594i | ||||
\(100\) | −19.8564 | −1.98564 | ||||||||
\(101\) | 7.46410 | − | 2.00000i | 0.742706 | − | 0.199007i | 0.132426 | − | 0.991193i | \(-0.457723\pi\) |
0.610280 | + | 0.792186i | \(0.291057\pi\) | |||||||
\(102\) | −1.43782 | + | 5.36603i | −0.142366 | + | 0.531316i | ||||
\(103\) | 7.90192 | − | 4.56218i | 0.778600 | − | 0.449525i | −0.0573341 | − | 0.998355i | \(-0.518260\pi\) |
0.835934 | + | 0.548830i | \(0.184927\pi\) | |||||||
\(104\) | −15.4641 | + | 8.92820i | −1.51638 | + | 0.875482i | ||||
\(105\) | 1.26795 | + | 4.73205i | 0.123739 | + | 0.461801i | ||||
\(106\) | 0.928203 | + | 0.535898i | 0.0901551 | + | 0.0520511i | ||||
\(107\) | −13.4904 | − | 13.4904i | −1.30416 | − | 1.30416i | −0.925558 | − | 0.378607i | \(-0.876403\pi\) |
−0.378607 | − | 0.925558i | \(-0.623597\pi\) | |||||||
\(108\) | 9.00000 | − | 5.19615i | 0.866025 | − | 0.500000i | ||||
\(109\) | 7.26795 | − | 7.26795i | 0.696143 | − | 0.696143i | −0.267433 | − | 0.963576i | \(-0.586175\pi\) |
0.963576 | + | 0.267433i | \(0.0861754\pi\) | |||||||
\(110\) | 4.19615 | + | 15.6603i | 0.400087 | + | 1.49315i | ||||
\(111\) | −3.00000 | + | 0.803848i | −0.284747 | + | 0.0762978i | ||||
\(112\) | 2.53590 | − | 1.46410i | 0.239620 | − | 0.138345i | ||||
\(113\) | 6.92820 | + | 12.0000i | 0.651751 | + | 1.12887i | 0.982698 | + | 0.185216i | \(0.0592984\pi\) |
−0.330947 | + | 0.943649i | \(0.607368\pi\) | |||||||
\(114\) | 1.09808 | + | 1.90192i | 0.102844 | + | 0.178131i | ||||
\(115\) | −1.26795 | − | 4.73205i | −0.118237 | − | 0.441266i | ||||
\(116\) | 3.46410 | + | 3.46410i | 0.321634 | + | 0.321634i | ||||
\(117\) | −4.90192 | − | 18.2942i | −0.453183 | − | 1.69130i | ||||
\(118\) | − | 7.26795i | − | 0.669069i | ||||||
\(119\) | −1.43782 | − | 0.830127i | −0.131805 | − | 0.0760976i | ||||
\(120\) | −18.9282 | −1.72790 | ||||||||
\(121\) | −1.90192 | + | 1.09808i | −0.172902 | + | 0.0998251i | ||||
\(122\) | −2.19615 | − | 3.80385i | −0.198830 | − | 0.344384i | ||||
\(123\) | 5.19615i | 0.468521i | ||||||||
\(124\) | −12.9282 | − | 7.46410i | −1.16099 | − | 0.670296i | ||||
\(125\) | −13.4641 | + | 13.4641i | −1.20427 | + | 1.20427i | ||||
\(126\) | 0.803848 | + | 3.00000i | 0.0716124 | + | 0.267261i | ||||
\(127\) | −6.19615 | −0.549820 | −0.274910 | − | 0.961470i | \(-0.588648\pi\) | ||||
−0.274910 | + | 0.961470i | \(0.588648\pi\) | |||||||
\(128\) | 2.92820 | + | 10.9282i | 0.258819 | + | 0.965926i | ||||
\(129\) | 0.571797 | − | 2.13397i | 0.0503439 | − | 0.187886i | ||||
\(130\) | −8.92820 | + | 33.3205i | −0.783055 | + | 2.92240i | ||||
\(131\) | −3.09808 | − | 0.830127i | −0.270680 | − | 0.0725285i | 0.120926 | − | 0.992662i | \(-0.461414\pi\) |
−0.391606 | + | 0.920133i | \(0.628080\pi\) | |||||||
\(132\) | 2.66025 | + | 9.92820i | 0.231545 | + | 0.864139i | ||||
\(133\) | −0.633975 | + | 0.169873i | −0.0549726 | + | 0.0147299i | ||||
\(134\) | 7.66025 | 0.661745 | ||||||||
\(135\) | 5.19615 | − | 19.3923i | 0.447214 | − | 1.66902i | ||||
\(136\) | 4.53590 | − | 4.53590i | 0.388950 | − | 0.388950i | ||||
\(137\) | −14.2583 | − | 8.23205i | −1.21817 | − | 0.703312i | −0.253645 | − | 0.967297i | \(-0.581629\pi\) |
−0.964527 | + | 0.263986i | \(0.914963\pi\) | |||||||
\(138\) | −0.803848 | − | 3.00000i | −0.0684280 | − | 0.255377i | ||||
\(139\) | 2.42820 | − | 9.06218i | 0.205958 | − | 0.768644i | −0.783198 | − | 0.621772i | \(-0.786413\pi\) |
0.989156 | − | 0.146872i | \(-0.0469204\pi\) | |||||||
\(140\) | 1.46410 | − | 5.46410i | 0.123739 | − | 0.461801i | ||||
\(141\) | −8.36603 | − | 14.4904i | −0.704546 | − | 1.22031i | ||||
\(142\) | −4.00000 | − | 14.9282i | −0.335673 | − | 1.25275i | ||||
\(143\) | 18.7321 | 1.56645 | ||||||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | 9.46410 | 0.785951 | ||||||||
\(146\) | −3.56218 | − | 13.2942i | −0.294808 | − | 1.10024i | ||||
\(147\) | 11.1962 | 0.923443 | ||||||||
\(148\) | 3.46410 | + | 0.928203i | 0.284747 | + | 0.0762978i | ||||
\(149\) | −0.830127 | + | 3.09808i | −0.0680067 | + | 0.253804i | −0.991557 | − | 0.129674i | \(-0.958607\pi\) |
0.923550 | + | 0.383478i | \(0.125274\pi\) | |||||||
\(150\) | −17.1962 | + | 17.1962i | −1.40406 | + | 1.40406i | ||||
\(151\) | 2.36603 | + | 1.36603i | 0.192544 | + | 0.111166i | 0.593173 | − | 0.805075i | \(-0.297875\pi\) |
−0.400629 | + | 0.916240i | \(0.631208\pi\) | |||||||
\(152\) | − | 2.53590i | − | 0.205689i | ||||||
\(153\) | 3.40192 | + | 5.89230i | 0.275029 | + | 0.476365i | ||||
\(154\) | −3.07180 | −0.247532 | ||||||||
\(155\) | −27.8564 | + | 7.46410i | −2.23748 | + | 0.599531i | ||||
\(156\) | −5.66025 | + | 21.1244i | −0.453183 | + | 1.69130i | ||||
\(157\) | 4.73205 | + | 1.26795i | 0.377659 | + | 0.101193i | 0.442655 | − | 0.896692i | \(-0.354037\pi\) |
−0.0649959 | + | 0.997886i | \(0.520703\pi\) | |||||||
\(158\) | 4.39230 | − | 16.3923i | 0.349433 | − | 1.30410i | ||||
\(159\) | 1.26795 | − | 0.339746i | 0.100555 | − | 0.0269436i | ||||
\(160\) | 18.9282 | + | 10.9282i | 1.49641 | + | 0.863950i | ||||
\(161\) | 0.928203 | 0.0731527 | ||||||||
\(162\) | 3.29423 | − | 12.2942i | 0.258819 | − | 0.965926i | ||||
\(163\) | −7.00000 | + | 7.00000i | −0.548282 | + | 0.548282i | −0.925944 | − | 0.377661i | \(-0.876728\pi\) |
0.377661 | + | 0.925944i | \(0.376728\pi\) | |||||||
\(164\) | 3.00000 | − | 5.19615i | 0.234261 | − | 0.405751i | ||||
\(165\) | 17.1962 | + | 9.92820i | 1.33872 | + | 0.772910i | ||||
\(166\) | −1.00000 | − | 1.73205i | −0.0776151 | − | 0.134433i | ||||
\(167\) | −0.464102 | + | 0.267949i | −0.0359133 | + | 0.0207345i | −0.517849 | − | 0.855472i | \(-0.673267\pi\) |
0.481936 | + | 0.876206i | \(0.339934\pi\) | |||||||
\(168\) | 0.928203 | − | 3.46410i | 0.0716124 | − | 0.267261i | ||||
\(169\) | 23.2583 | + | 13.4282i | 1.78910 | + | 1.03294i | ||||
\(170\) | − | 12.3923i | − | 0.950446i | ||||||
\(171\) | 2.59808 | + | 0.696152i | 0.198680 | + | 0.0532361i | ||||
\(172\) | −1.80385 | + | 1.80385i | −0.137542 | + | 0.137542i | ||||
\(173\) | 3.36603 | + | 12.5622i | 0.255914 | + | 0.955085i | 0.967580 | + | 0.252566i | \(0.0812745\pi\) |
−0.711665 | + | 0.702519i | \(0.752059\pi\) | |||||||
\(174\) | 6.00000 | 0.454859 | ||||||||
\(175\) | −3.63397 | − | 6.29423i | −0.274703 | − | 0.475799i | ||||
\(176\) | 3.07180 | − | 11.4641i | 0.231545 | − | 0.864139i | ||||
\(177\) | −6.29423 | − | 6.29423i | −0.473103 | − | 0.473103i | ||||
\(178\) | −0.732051 | − | 2.73205i | −0.0548695 | − | 0.204776i | ||||
\(179\) | 11.9282 | − | 11.9282i | 0.891556 | − | 0.891556i | −0.103114 | − | 0.994670i | \(-0.532881\pi\) |
0.994670 | + | 0.103114i | \(0.0328806\pi\) | |||||||
\(180\) | −16.3923 | + | 16.3923i | −1.22181 | + | 1.22181i | ||||
\(181\) | 13.3923 | + | 13.3923i | 0.995442 | + | 0.995442i | 0.999990 | − | 0.00454748i | \(-0.00144751\pi\) |
−0.00454748 | + | 0.999990i | \(0.501448\pi\) | |||||||
\(182\) | −5.66025 | − | 3.26795i | −0.419566 | − | 0.242237i | ||||
\(183\) | −5.19615 | − | 1.39230i | −0.384111 | − | 0.102922i | ||||
\(184\) | −0.928203 | + | 3.46410i | −0.0684280 | + | 0.255377i | ||||
\(185\) | 6.00000 | − | 3.46410i | 0.441129 | − | 0.254686i | ||||
\(186\) | −17.6603 | + | 4.73205i | −1.29491 | + | 0.346971i | ||||
\(187\) | −6.50000 | + | 1.74167i | −0.475327 | + | 0.127364i | ||||
\(188\) | 19.3205i | 1.40909i | ||||||||
\(189\) | 3.29423 | + | 1.90192i | 0.239620 | + | 0.138345i | ||||
\(190\) | −3.46410 | − | 3.46410i | −0.251312 | − | 0.251312i | ||||
\(191\) | 7.02628 | − | 12.1699i | 0.508404 | − | 0.880581i | −0.491549 | − | 0.870850i | \(-0.663569\pi\) |
0.999953 | − | 0.00973114i | \(-0.00309757\pi\) | |||||||
\(192\) | 12.0000 | + | 6.92820i | 0.866025 | + | 0.500000i | ||||
\(193\) | −9.13397 | − | 15.8205i | −0.657478 | − | 1.13879i | −0.981266 | − | 0.192656i | \(-0.938290\pi\) |
0.323789 | − | 0.946129i | \(-0.395043\pi\) | |||||||
\(194\) | 3.02628 | − | 11.2942i | 0.217274 | − | 0.810878i | ||||
\(195\) | 21.1244 | + | 36.5885i | 1.51275 | + | 2.62015i | ||||
\(196\) | −11.1962 | − | 6.46410i | −0.799725 | − | 0.461722i | ||||
\(197\) | −3.66025 | − | 3.66025i | −0.260782 | − | 0.260782i | 0.564590 | − | 0.825372i | \(-0.309034\pi\) |
−0.825372 | + | 0.564590i | \(0.809034\pi\) | |||||||
\(198\) | 10.9019 | + | 6.29423i | 0.774766 | + | 0.447311i | ||||
\(199\) | − | 0.875644i | − | 0.0620728i | −0.999518 | − | 0.0310364i | \(-0.990119\pi\) | ||
0.999518 | − | 0.0310364i | \(-0.00988078\pi\) | |||||||
\(200\) | 27.1244 | − | 7.26795i | 1.91798 | − | 0.513922i | ||||
\(201\) | 6.63397 | − | 6.63397i | 0.467924 | − | 0.467924i | ||||
\(202\) | −9.46410 | + | 5.46410i | −0.665892 | + | 0.384453i | ||||
\(203\) | −0.464102 | + | 1.73205i | −0.0325735 | + | 0.121566i | ||||
\(204\) | − | 7.85641i | − | 0.550058i | ||||||
\(205\) | −3.00000 | − | 11.1962i | −0.209529 | − | 0.781973i | ||||
\(206\) | −9.12436 | + | 9.12436i | −0.635724 | + | 0.635724i | ||||
\(207\) | −3.29423 | − | 1.90192i | −0.228965 | − | 0.132193i | ||||
\(208\) | 17.8564 | − | 17.8564i | 1.23812 | − | 1.23812i | ||||
\(209\) | −1.33013 | + | 2.30385i | −0.0920068 | + | 0.159360i | ||||
\(210\) | −3.46410 | − | 6.00000i | −0.239046 | − | 0.414039i | ||||
\(211\) | 4.09808 | + | 1.09808i | 0.282123 | + | 0.0755947i | 0.397106 | − | 0.917773i | \(-0.370015\pi\) |
−0.114983 | + | 0.993367i | \(0.536681\pi\) | |||||||
\(212\) | −1.46410 | − | 0.392305i | −0.100555 | − | 0.0269436i | ||||
\(213\) | −16.3923 | − | 9.46410i | −1.12318 | − | 0.648470i | ||||
\(214\) | 23.3660 | + | 13.4904i | 1.59727 | + | 0.922183i | ||||
\(215\) | 4.92820i | 0.336101i | ||||||||
\(216\) | −10.3923 | + | 10.3923i | −0.707107 | + | 0.707107i | ||||
\(217\) | − | 5.46410i | − | 0.370927i | ||||||
\(218\) | −7.26795 | + | 12.5885i | −0.492248 | + | 0.852598i | ||||
\(219\) | −14.5981 | − | 8.42820i | −0.986447 | − | 0.569525i | ||||
\(220\) | −11.4641 | − | 19.8564i | −0.772910 | − | 1.33872i | ||||
\(221\) | −13.8301 | − | 3.70577i | −0.930315 | − | 0.249277i | ||||
\(222\) | 3.80385 | − | 2.19615i | 0.255298 | − | 0.147396i | ||||
\(223\) | 11.0263 | − | 19.0981i | 0.738374 | − | 1.27890i | −0.214853 | − | 0.976646i | \(-0.568927\pi\) |
0.953227 | − | 0.302255i | \(-0.0977395\pi\) | |||||||
\(224\) | −2.92820 | + | 2.92820i | −0.195649 | + | 0.195649i | ||||
\(225\) | 29.7846i | 1.98564i | ||||||||
\(226\) | −13.8564 | − | 13.8564i | −0.921714 | − | 0.921714i | ||||
\(227\) | 3.86603 | + | 14.4282i | 0.256597 | + | 0.957633i | 0.967195 | + | 0.254035i | \(0.0817579\pi\) |
−0.710598 | + | 0.703598i | \(0.751575\pi\) | |||||||
\(228\) | −2.19615 | − | 2.19615i | −0.145444 | − | 0.145444i | ||||
\(229\) | −1.83013 | + | 6.83013i | −0.120938 | + | 0.451347i | −0.999662 | − | 0.0259823i | \(-0.991729\pi\) |
0.878724 | + | 0.477330i | \(0.158395\pi\) | |||||||
\(230\) | 3.46410 | + | 6.00000i | 0.228416 | + | 0.395628i | ||||
\(231\) | −2.66025 | + | 2.66025i | −0.175032 | + | 0.175032i | ||||
\(232\) | −6.00000 | − | 3.46410i | −0.393919 | − | 0.227429i | ||||
\(233\) | − | 7.19615i | − | 0.471436i | −0.971822 | − | 0.235718i | \(-0.924256\pi\) | ||
0.971822 | − | 0.235718i | \(-0.0757441\pi\) | |||||||
\(234\) | 13.3923 | + | 23.1962i | 0.875482 | + | 1.51638i | ||||
\(235\) | 26.3923 | + | 26.3923i | 1.72164 | + | 1.72164i | ||||
\(236\) | 2.66025 | + | 9.92820i | 0.173168 | + | 0.646271i | ||||
\(237\) | −10.3923 | − | 18.0000i | −0.675053 | − | 1.16923i | ||||
\(238\) | 2.26795 | + | 0.607695i | 0.147009 | + | 0.0393910i | ||||
\(239\) | −13.0981 | − | 22.6865i | −0.847244 | − | 1.46747i | −0.883658 | − | 0.468133i | \(-0.844927\pi\) |
0.0364139 | − | 0.999337i | \(-0.488407\pi\) | |||||||
\(240\) | 25.8564 | − | 6.92820i | 1.66902 | − | 0.447214i | ||||
\(241\) | −6.40192 | + | 11.0885i | −0.412384 | + | 0.714270i | −0.995150 | − | 0.0983699i | \(-0.968637\pi\) |
0.582766 | + | 0.812640i | \(0.301971\pi\) | |||||||
\(242\) | 2.19615 | − | 2.19615i | 0.141174 | − | 0.141174i | ||||
\(243\) | −7.79423 | − | 13.5000i | −0.500000 | − | 0.866025i | ||||
\(244\) | 4.39230 | + | 4.39230i | 0.281189 | + | 0.281189i | ||||
\(245\) | −24.1244 | + | 6.46410i | −1.54125 | + | 0.412976i | ||||
\(246\) | −1.90192 | − | 7.09808i | −0.121262 | − | 0.452557i | ||||
\(247\) | −4.90192 | + | 2.83013i | −0.311902 | + | 0.180077i | ||||
\(248\) | 20.3923 | + | 5.46410i | 1.29491 | + | 0.346971i | ||||
\(249\) | −2.36603 | − | 0.633975i | −0.149941 | − | 0.0401765i | ||||
\(250\) | 13.4641 | − | 23.3205i | 0.851545 | − | 1.47492i | ||||
\(251\) | 2.83013 | + | 2.83013i | 0.178636 | + | 0.178636i | 0.790761 | − | 0.612125i | \(-0.209685\pi\) |
−0.612125 | + | 0.790761i | \(0.709685\pi\) | |||||||
\(252\) | −2.19615 | − | 3.80385i | −0.138345 | − | 0.239620i | ||||
\(253\) | 2.66025 | − | 2.66025i | 0.167249 | − | 0.167249i | ||||
\(254\) | 8.46410 | − | 2.26795i | 0.531085 | − | 0.142304i | ||||
\(255\) | −10.7321 | − | 10.7321i | −0.672067 | − | 0.672067i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −4.42820 | − | 7.66987i | −0.276224 | − | 0.478434i | 0.694219 | − | 0.719763i | \(-0.255750\pi\) |
−0.970443 | + | 0.241330i | \(0.922416\pi\) | |||||||
\(258\) | 3.12436i | 0.194514i | ||||||||
\(259\) | 0.339746 | + | 1.26795i | 0.0211108 | + | 0.0787865i | ||||
\(260\) | − | 48.7846i | − | 3.02549i | ||||||
\(261\) | 5.19615 | − | 5.19615i | 0.321634 | − | 0.321634i | ||||
\(262\) | 4.53590 | 0.280229 | ||||||||
\(263\) | 23.4904 | + | 13.5622i | 1.44848 | + | 0.836280i | 0.998391 | − | 0.0567045i | \(-0.0180593\pi\) |
0.450088 | + | 0.892984i | \(0.351393\pi\) | |||||||
\(264\) | −7.26795 | − | 12.5885i | −0.447311 | − | 0.774766i | ||||
\(265\) | −2.53590 | + | 1.46410i | −0.155779 | + | 0.0899390i | ||||
\(266\) | 0.803848 | − | 0.464102i | 0.0492871 | − | 0.0284559i | ||||
\(267\) | −3.00000 | − | 1.73205i | −0.183597 | − | 0.106000i | ||||
\(268\) | −10.4641 | + | 2.80385i | −0.639197 | + | 0.171272i | ||||
\(269\) | 4.73205 | − | 4.73205i | 0.288518 | − | 0.288518i | −0.547976 | − | 0.836494i | \(-0.684601\pi\) |
0.836494 | + | 0.547976i | \(0.184601\pi\) | |||||||
\(270\) | 28.3923i | 1.72790i | ||||||||
\(271\) | 20.3923 | 1.23874 | 0.619372 | − | 0.785098i | \(-0.287387\pi\) | ||||
0.619372 | + | 0.785098i | \(0.287387\pi\) | |||||||
\(272\) | −4.53590 | + | 7.85641i | −0.275029 | + | 0.476365i | ||||
\(273\) | −7.73205 | + | 2.07180i | −0.467965 | + | 0.125391i | ||||
\(274\) | 22.4904 | + | 6.02628i | 1.35869 | + | 0.364061i | ||||
\(275\) | −28.4545 | − | 7.62436i | −1.71587 | − | 0.459766i | ||||
\(276\) | 2.19615 | + | 3.80385i | 0.132193 | + | 0.228965i | ||||
\(277\) | 15.7583 | − | 4.22243i | 0.946826 | − | 0.253701i | 0.247811 | − | 0.968808i | \(-0.420289\pi\) |
0.699015 | + | 0.715107i | \(0.253622\pi\) | |||||||
\(278\) | 13.2679i | 0.795759i | ||||||||
\(279\) | −11.1962 | + | 19.3923i | −0.670296 | + | 1.16099i | ||||
\(280\) | 8.00000i | 0.478091i | ||||||||
\(281\) | 8.66025 | + | 5.00000i | 0.516627 | + | 0.298275i | 0.735554 | − | 0.677466i | \(-0.236922\pi\) |
−0.218926 | + | 0.975741i | \(0.570255\pi\) | |||||||
\(282\) | 16.7321 | + | 16.7321i | 0.996379 | + | 0.996379i | ||||
\(283\) | −7.43782 | + | 27.7583i | −0.442133 | + | 1.65006i | 0.281265 | + | 0.959630i | \(0.409246\pi\) |
−0.723398 | + | 0.690431i | \(0.757421\pi\) | |||||||
\(284\) | 10.9282 | + | 18.9282i | 0.648470 | + | 1.12318i | ||||
\(285\) | −6.00000 | −0.355409 | ||||||||
\(286\) | −25.5885 | + | 6.85641i | −1.51308 | + | 0.405428i | ||||
\(287\) | 2.19615 | 0.129635 | ||||||||
\(288\) | 16.3923 | − | 4.39230i | 0.965926 | − | 0.258819i | ||||
\(289\) | −11.8564 | −0.697436 | ||||||||
\(290\) | −12.9282 | + | 3.46410i | −0.759170 | + | 0.203419i | ||||
\(291\) | −7.16025 | − | 12.4019i | −0.419742 | − | 0.727014i | ||||
\(292\) | 9.73205 | + | 16.8564i | 0.569525 | + | 0.986447i | ||||
\(293\) | −3.63397 | + | 13.5622i | −0.212299 | + | 0.792311i | 0.774801 | + | 0.632205i | \(0.217850\pi\) |
−0.987100 | + | 0.160106i | \(0.948817\pi\) | |||||||
\(294\) | −15.2942 | + | 4.09808i | −0.891978 | + | 0.239005i | ||||
\(295\) | 17.1962 | + | 9.92820i | 1.00120 | + | 0.578042i | ||||
\(296\) | −5.07180 | −0.294792 | ||||||||
\(297\) | 14.8923 | − | 3.99038i | 0.864139 | − | 0.231545i | ||||
\(298\) | − | 4.53590i | − | 0.262758i | ||||||
\(299\) | 7.73205 | − | 2.07180i | 0.447156 | − | 0.119815i | ||||
\(300\) | 17.1962 | − | 29.7846i | 0.992820 | − | 1.71962i | ||||
\(301\) | −0.901924 | − | 0.241670i | −0.0519860 | − | 0.0139296i | ||||
\(302\) | −3.73205 | − | 1.00000i | −0.214755 | − | 0.0575435i | ||||
\(303\) | −3.46410 | + | 12.9282i | −0.199007 | + | 0.742706i | ||||
\(304\) | 0.928203 | + | 3.46410i | 0.0532361 | + | 0.198680i | ||||
\(305\) | 12.0000 | 0.687118 | ||||||||
\(306\) | −6.80385 | − | 6.80385i | −0.388950 | − | 0.388950i | ||||
\(307\) | −16.0263 | + | 16.0263i | −0.914668 | + | 0.914668i | −0.996635 | − | 0.0819670i | \(-0.973880\pi\) |
0.0819670 | + | 0.996635i | \(0.473880\pi\) | |||||||
\(308\) | 4.19615 | − | 1.12436i | 0.239098 | − | 0.0640661i | ||||
\(309\) | 15.8038i | 0.899049i | ||||||||
\(310\) | 35.3205 | − | 20.3923i | 2.00607 | − | 1.15821i | ||||
\(311\) | −13.9019 | + | 8.02628i | −0.788306 | + | 0.455129i | −0.839366 | − | 0.543567i | \(-0.817073\pi\) |
0.0510600 | + | 0.998696i | \(0.483740\pi\) | |||||||
\(312\) | − | 30.9282i | − | 1.75096i | ||||||
\(313\) | −24.6506 | − | 14.2321i | −1.39334 | − | 0.804443i | −0.399653 | − | 0.916666i | \(-0.630869\pi\) |
−0.993683 | + | 0.112223i | \(0.964203\pi\) | |||||||
\(314\) | −6.92820 | −0.390981 | ||||||||
\(315\) | −8.19615 | − | 2.19615i | −0.461801 | − | 0.123739i | ||||
\(316\) | 24.0000i | 1.35011i | ||||||||
\(317\) | −8.43782 | − | 31.4904i | −0.473915 | − | 1.76868i | −0.625492 | − | 0.780231i | \(-0.715102\pi\) |
0.151577 | − | 0.988445i | \(-0.451565\pi\) | |||||||
\(318\) | −1.60770 | + | 0.928203i | −0.0901551 | + | 0.0520511i | ||||
\(319\) | 3.63397 | + | 6.29423i | 0.203464 | + | 0.352409i | ||||
\(320\) | −29.8564 | − | 8.00000i | −1.66902 | − | 0.447214i | ||||
\(321\) | 31.9186 | − | 8.55256i | 1.78152 | − | 0.477357i | ||||
\(322\) | −1.26795 | + | 0.339746i | −0.0706600 | + | 0.0189333i | ||||
\(323\) | 1.43782 | − | 1.43782i | 0.0800026 | − | 0.0800026i | ||||
\(324\) | 18.0000i | 1.00000i | ||||||||
\(325\) | −44.3205 | − | 44.3205i | −2.45846 | − | 2.45846i | ||||
\(326\) | 7.00000 | − | 12.1244i | 0.387694 | − | 0.671506i | ||||
\(327\) | 4.60770 | + | 17.1962i | 0.254806 | + | 0.950949i | ||||
\(328\) | −2.19615 | + | 8.19615i | −0.121262 | + | 0.452557i | ||||
\(329\) | −6.12436 | + | 3.53590i | −0.337647 | + | 0.194940i | ||||
\(330\) | −27.1244 | − | 7.26795i | −1.49315 | − | 0.400087i | ||||
\(331\) | −19.0263 | + | 5.09808i | −1.04578 | + | 0.280216i | −0.740506 | − | 0.672049i | \(-0.765414\pi\) |
−0.305273 | + | 0.952265i | \(0.598748\pi\) | |||||||
\(332\) | 2.00000 | + | 2.00000i | 0.109764 | + | 0.109764i | ||||
\(333\) | 1.39230 | − | 5.19615i | 0.0762978 | − | 0.284747i | ||||
\(334\) | 0.535898 | − | 0.535898i | 0.0293231 | − | 0.0293231i | ||||
\(335\) | −10.4641 | + | 18.1244i | −0.571715 | + | 0.990239i | ||||
\(336\) | 5.07180i | 0.276689i | ||||||||
\(337\) | −11.8923 | − | 20.5981i | −0.647815 | − | 1.12205i | −0.983644 | − | 0.180126i | \(-0.942350\pi\) |
0.335829 | − | 0.941923i | \(-0.390984\pi\) | |||||||
\(338\) | −36.6865 | − | 9.83013i | −1.99548 | − | 0.534688i | ||||
\(339\) | −24.0000 | −1.30350 | ||||||||
\(340\) | 4.53590 | + | 16.9282i | 0.245994 | + | 0.918061i | ||||
\(341\) | −15.6603 | − | 15.6603i | −0.848050 | − | 0.848050i | ||||
\(342\) | −3.80385 | −0.205689 | ||||||||
\(343\) | − | 9.85641i | − | 0.532196i | ||||||
\(344\) | 1.80385 | − | 3.12436i | 0.0972569 | − | 0.168454i | ||||
\(345\) | 8.19615 | + | 2.19615i | 0.441266 | + | 0.118237i | ||||
\(346\) | −9.19615 | − | 15.9282i | −0.494388 | − | 0.856306i | ||||
\(347\) | 6.62436 | − | 24.7224i | 0.355614 | − | 1.32717i | −0.524096 | − | 0.851659i | \(-0.675597\pi\) |
0.879710 | − | 0.475510i | \(-0.157737\pi\) | |||||||
\(348\) | −8.19615 | + | 2.19615i | −0.439360 | + | 0.117726i | ||||
\(349\) | 2.07180 | + | 7.73205i | 0.110901 | + | 0.413887i | 0.998948 | − | 0.0458657i | \(-0.0146046\pi\) |
−0.888047 | + | 0.459753i | \(0.847938\pi\) | |||||||
\(350\) | 7.26795 | + | 7.26795i | 0.388488 | + | 0.388488i | ||||
\(351\) | 31.6865 | + | 8.49038i | 1.69130 | + | 0.453183i | ||||
\(352\) | 16.7846i | 0.894623i | ||||||||
\(353\) | −10.1603 | + | 17.5981i | −0.540776 | + | 0.936651i | 0.458084 | + | 0.888909i | \(0.348536\pi\) |
−0.998860 | + | 0.0477421i | \(0.984797\pi\) | |||||||
\(354\) | 10.9019 | + | 6.29423i | 0.579431 | + | 0.334534i | ||||
\(355\) | 40.7846 | + | 10.9282i | 2.16462 | + | 0.580009i | ||||
\(356\) | 2.00000 | + | 3.46410i | 0.106000 | + | 0.183597i | ||||
\(357\) | 2.49038 | − | 1.43782i | 0.131805 | − | 0.0760976i | ||||
\(358\) | −11.9282 | + | 20.6603i | −0.630425 | + | 1.09193i | ||||
\(359\) | − | 14.7321i | − | 0.777528i | −0.921337 | − | 0.388764i | \(-0.872902\pi\) | ||
0.921337 | − | 0.388764i | \(-0.127098\pi\) | |||||||
\(360\) | 16.3923 | − | 28.3923i | 0.863950 | − | 1.49641i | ||||
\(361\) | 18.1962i | 0.957692i | ||||||||
\(362\) | −23.1962 | − | 13.3923i | −1.21916 | − | 0.703884i | ||||
\(363\) | − | 3.80385i | − | 0.199650i | ||||||
\(364\) | 8.92820 | + | 2.39230i | 0.467965 | + | 0.125391i | ||||
\(365\) | 36.3205 | + | 9.73205i | 1.90110 | + | 0.509399i | ||||
\(366\) | 7.60770 | 0.397661 | ||||||||
\(367\) | −10.1244 | + | 17.5359i | −0.528487 | + | 0.915366i | 0.470961 | + | 0.882154i | \(0.343907\pi\) |
−0.999448 | + | 0.0332125i | \(0.989426\pi\) | |||||||
\(368\) | − | 5.07180i | − | 0.264386i | ||||||
\(369\) | −7.79423 | − | 4.50000i | −0.405751 | − | 0.234261i | ||||
\(370\) | −6.92820 | + | 6.92820i | −0.360180 | + | 0.360180i | ||||
\(371\) | −0.143594 | − | 0.535898i | −0.00745501 | − | 0.0278225i | ||||
\(372\) | 22.3923 | − | 12.9282i | 1.16099 | − | 0.670296i | ||||
\(373\) | 1.50962 | − | 5.63397i | 0.0781651 | − | 0.291716i | −0.915767 | − | 0.401709i | \(-0.868416\pi\) |
0.993932 | + | 0.109993i | \(0.0350829\pi\) | |||||||
\(374\) | 8.24167 | − | 4.75833i | 0.426167 | − | 0.246047i | ||||
\(375\) | −8.53590 | − | 31.8564i | −0.440792 | − | 1.64506i | ||||
\(376\) | −7.07180 | − | 26.3923i | −0.364700 | − | 1.36108i | ||||
\(377\) | 15.4641i | 0.796442i | ||||||||
\(378\) | −5.19615 | − | 1.39230i | −0.267261 | − | 0.0716124i | ||||
\(379\) | −18.7583 | − | 18.7583i | −0.963551 | − | 0.963551i | 0.0358080 | − | 0.999359i | \(-0.488600\pi\) |
−0.999359 | + | 0.0358080i | \(0.988600\pi\) | |||||||
\(380\) | 6.00000 | + | 3.46410i | 0.307794 | + | 0.177705i | ||||
\(381\) | 5.36603 | − | 9.29423i | 0.274910 | − | 0.476158i | ||||
\(382\) | −5.14359 | + | 19.1962i | −0.263169 | + | 0.982161i | ||||
\(383\) | −3.26795 | − | 5.66025i | −0.166984 | − | 0.289225i | 0.770374 | − | 0.637593i | \(-0.220070\pi\) |
−0.937358 | + | 0.348367i | \(0.886736\pi\) | |||||||
\(384\) | −18.9282 | − | 5.07180i | −0.965926 | − | 0.258819i | ||||
\(385\) | 4.19615 | − | 7.26795i | 0.213856 | − | 0.370409i | ||||
\(386\) | 18.2679 | + | 18.2679i | 0.929814 | + | 0.929814i | ||||
\(387\) | 2.70577 | + | 2.70577i | 0.137542 | + | 0.137542i | ||||
\(388\) | 16.5359i | 0.839483i | ||||||||
\(389\) | 10.2942 | − | 2.75833i | 0.521938 | − | 0.139853i | 0.0117752 | − | 0.999931i | \(-0.496252\pi\) |
0.510163 | + | 0.860078i | \(0.329585\pi\) | |||||||
\(390\) | −42.2487 | − | 42.2487i | −2.13935 | − | 2.13935i | ||||
\(391\) | −2.49038 | + | 1.43782i | −0.125944 | + | 0.0727138i | ||||
\(392\) | 17.6603 | + | 4.73205i | 0.891978 | + | 0.239005i | ||||
\(393\) | 3.92820 | − | 3.92820i | 0.198152 | − | 0.198152i | ||||
\(394\) | 6.33975 | + | 3.66025i | 0.319392 | + | 0.184401i | ||||
\(395\) | 32.7846 | + | 32.7846i | 1.64957 | + | 1.64957i | ||||
\(396\) | −17.1962 | − | 4.60770i | −0.864139 | − | 0.231545i | ||||
\(397\) | −12.7321 | + | 12.7321i | −0.639003 | + | 0.639003i | −0.950310 | − | 0.311306i | \(-0.899233\pi\) |
0.311306 | + | 0.950310i | \(0.399233\pi\) | |||||||
\(398\) | 0.320508 | + | 1.19615i | 0.0160656 | + | 0.0599577i | ||||
\(399\) | 0.294229 | − | 1.09808i | 0.0147299 | − | 0.0549726i | ||||
\(400\) | −34.3923 | + | 19.8564i | −1.71962 | + | 0.992820i | ||||
\(401\) | 13.7942 | + | 23.8923i | 0.688851 | + | 1.19312i | 0.972210 | + | 0.234111i | \(0.0752179\pi\) |
−0.283359 | + | 0.959014i | \(0.591449\pi\) | |||||||
\(402\) | −6.63397 | + | 11.4904i | −0.330873 | + | 0.573088i | ||||
\(403\) | −12.1962 | − | 45.5167i | −0.607534 | − | 2.26735i | ||||
\(404\) | 10.9282 | − | 10.9282i | 0.543698 | − | 0.543698i | ||||
\(405\) | 24.5885 | + | 24.5885i | 1.22181 | + | 1.22181i | ||||
\(406\) | − | 2.53590i | − | 0.125855i | ||||||
\(407\) | 4.60770 | + | 2.66025i | 0.228395 | + | 0.131864i | ||||
\(408\) | 2.87564 | + | 10.7321i | 0.142366 | + | 0.531316i | ||||
\(409\) | 26.1340 | − | 15.0885i | 1.29224 | − | 0.746076i | 0.313191 | − | 0.949690i | \(-0.398602\pi\) |
0.979051 | + | 0.203614i | \(0.0652688\pi\) | |||||||
\(410\) | 8.19615 | + | 14.1962i | 0.404779 | + | 0.701098i | ||||
\(411\) | 24.6962 | − | 14.2583i | 1.21817 | − | 0.703312i | ||||
\(412\) | 9.12436 | − | 15.8038i | 0.449525 | − | 0.778600i | ||||
\(413\) | −2.66025 | + | 2.66025i | −0.130903 | + | 0.130903i | ||||
\(414\) | 5.19615 | + | 1.39230i | 0.255377 | + | 0.0684280i | ||||
\(415\) | 5.46410 | 0.268222 | ||||||||
\(416\) | −17.8564 | + | 30.9282i | −0.875482 | + | 1.51638i | ||||
\(417\) | 11.4904 | + | 11.4904i | 0.562686 | + | 0.562686i | ||||
\(418\) | 0.973721 | − | 3.63397i | 0.0476262 | − | 0.177744i | ||||
\(419\) | 31.2224 | + | 8.36603i | 1.52532 | + | 0.408707i | 0.921488 | − | 0.388408i | \(-0.126975\pi\) |
0.603828 | + | 0.797115i | \(0.293641\pi\) | |||||||
\(420\) | 6.92820 | + | 6.92820i | 0.338062 | + | 0.338062i | ||||
\(421\) | −2.19615 | + | 0.588457i | −0.107034 | + | 0.0286797i | −0.311938 | − | 0.950102i | \(-0.600978\pi\) |
0.204905 | + | 0.978782i | \(0.434312\pi\) | |||||||
\(422\) | −6.00000 | −0.292075 | ||||||||
\(423\) | 28.9808 | 1.40909 | ||||||||
\(424\) | 2.14359 | 0.104102 | ||||||||
\(425\) | 19.5000 | + | 11.2583i | 0.945889 | + | 0.546109i | ||||
\(426\) | 25.8564 | + | 6.92820i | 1.25275 | + | 0.335673i | ||||
\(427\) | −0.588457 | + | 2.19615i | −0.0284774 | + | 0.106279i | ||||
\(428\) | −36.8564 | − | 9.87564i | −1.78152 | − | 0.477357i | ||||
\(429\) | −16.2224 | + | 28.0981i | −0.783226 | + | 1.35659i | ||||
\(430\) | −1.80385 | − | 6.73205i | −0.0869893 | − | 0.324648i | ||||
\(431\) | −5.80385 | −0.279562 | −0.139781 | − | 0.990182i | \(-0.544640\pi\) | ||||
−0.139781 | + | 0.990182i | \(0.544640\pi\) | |||||||
\(432\) | 10.3923 | − | 18.0000i | 0.500000 | − | 0.866025i | ||||
\(433\) | −2.26795 | −0.108991 | −0.0544953 | − | 0.998514i | \(-0.517355\pi\) | ||||
−0.0544953 | + | 0.998514i | \(0.517355\pi\) | |||||||
\(434\) | 2.00000 | + | 7.46410i | 0.0960031 | + | 0.358288i | ||||
\(435\) | −8.19615 | + | 14.1962i | −0.392975 | + | 0.680653i | ||||
\(436\) | 5.32051 | − | 19.8564i | 0.254806 | − | 0.950949i | ||||
\(437\) | −0.294229 | + | 1.09808i | −0.0140749 | + | 0.0525281i | ||||
\(438\) | 23.0263 | + | 6.16987i | 1.10024 | + | 0.294808i | ||||
\(439\) | 4.85641 | + | 2.80385i | 0.231784 | + | 0.133820i | 0.611395 | − | 0.791326i | \(-0.290609\pi\) |
−0.379611 | + | 0.925146i | \(0.623942\pi\) | |||||||
\(440\) | 22.9282 | + | 22.9282i | 1.09306 | + | 1.09306i | ||||
\(441\) | −9.69615 | + | 16.7942i | −0.461722 | + | 0.799725i | ||||
\(442\) | 20.2487 | 0.963133 | ||||||||
\(443\) | 19.6244 | − | 5.25833i | 0.932381 | − | 0.249831i | 0.239511 | − | 0.970894i | \(-0.423013\pi\) |
0.692870 | + | 0.721063i | \(0.256346\pi\) | |||||||
\(444\) | −4.39230 | + | 4.39230i | −0.208450 | + | 0.208450i | ||||
\(445\) | 7.46410 | + | 2.00000i | 0.353832 | + | 0.0948091i | ||||
\(446\) | −8.07180 | + | 30.1244i | −0.382211 | + | 1.42643i | ||||
\(447\) | −3.92820 | − | 3.92820i | −0.185798 | − | 0.185798i | ||||
\(448\) | 2.92820 | − | 5.07180i | 0.138345 | − | 0.239620i | ||||
\(449\) | −20.6603 | −0.975018 | −0.487509 | − | 0.873118i | \(-0.662094\pi\) | ||||
−0.487509 | + | 0.873118i | \(0.662094\pi\) | |||||||
\(450\) | −10.9019 | − | 40.6865i | −0.513922 | − | 1.91798i | ||||
\(451\) | 6.29423 | − | 6.29423i | 0.296384 | − | 0.296384i | ||||
\(452\) | 24.0000 | + | 13.8564i | 1.12887 | + | 0.651751i | ||||
\(453\) | −4.09808 | + | 2.36603i | −0.192544 | + | 0.111166i | ||||
\(454\) | −10.5622 | − | 18.2942i | −0.495708 | − | 0.858591i | ||||
\(455\) | 15.4641 | − | 8.92820i | 0.724968 | − | 0.418561i | ||||
\(456\) | 3.80385 | + | 2.19615i | 0.178131 | + | 0.102844i | ||||
\(457\) | −20.2583 | − | 11.6962i | −0.947645 | − | 0.547123i | −0.0552962 | − | 0.998470i | \(-0.517610\pi\) |
−0.892348 | + | 0.451347i | \(0.850944\pi\) | |||||||
\(458\) | − | 10.0000i | − | 0.467269i | ||||||
\(459\) | −11.7846 | −0.550058 | ||||||||
\(460\) | −6.92820 | − | 6.92820i | −0.323029 | − | 0.323029i | ||||
\(461\) | −0.686533 | − | 2.56218i | −0.0319751 | − | 0.119333i | 0.948094 | − | 0.317991i | \(-0.103008\pi\) |
−0.980069 | + | 0.198659i | \(0.936342\pi\) | |||||||
\(462\) | 2.66025 | − | 4.60770i | 0.123766 | − | 0.214369i | ||||
\(463\) | −9.19615 | − | 15.9282i | −0.427381 | − | 0.740246i | 0.569258 | − | 0.822159i | \(-0.307231\pi\) |
−0.996640 | + | 0.0819125i | \(0.973897\pi\) | |||||||
\(464\) | 9.46410 | + | 2.53590i | 0.439360 | + | 0.117726i | ||||
\(465\) | 12.9282 | − | 48.2487i | 0.599531 | − | 2.23748i | ||||
\(466\) | 2.63397 | + | 9.83013i | 0.122017 | + | 0.455372i | ||||
\(467\) | 4.36603 | − | 4.36603i | 0.202036 | − | 0.202036i | −0.598836 | − | 0.800872i | \(-0.704370\pi\) |
0.800872 | + | 0.598836i | \(0.204370\pi\) | |||||||
\(468\) | −26.7846 | − | 26.7846i | −1.23812 | − | 1.23812i | ||||
\(469\) | −2.80385 | − | 2.80385i | −0.129470 | − | 0.129470i | ||||
\(470\) | −45.7128 | − | 26.3923i | −2.10857 | − | 1.21739i | ||||
\(471\) | −6.00000 | + | 6.00000i | −0.276465 | + | 0.276465i | ||||
\(472\) | −7.26795 | − | 12.5885i | −0.334534 | − | 0.579431i | ||||
\(473\) | −3.27757 | + | 1.89230i | −0.150703 | + | 0.0870083i | ||||
\(474\) | 20.7846 | + | 20.7846i | 0.954669 | + | 0.954669i | ||||
\(475\) | 8.59808 | − | 2.30385i | 0.394507 | − | 0.105708i | ||||
\(476\) | −3.32051 | −0.152195 | ||||||||
\(477\) | −0.588457 | + | 2.19615i | −0.0269436 | + | 0.100555i | ||||
\(478\) | 26.1962 | + | 26.1962i | 1.19818 | + | 1.19818i | ||||
\(479\) | 12.8301 | − | 22.2224i | 0.586223 | − | 1.01537i | −0.408498 | − | 0.912759i | \(-0.633947\pi\) |
0.994722 | − | 0.102610i | \(-0.0327193\pi\) | |||||||
\(480\) | −32.7846 | + | 18.9282i | −1.49641 | + | 0.863950i | ||||
\(481\) | 5.66025 | + | 9.80385i | 0.258085 | + | 0.447017i | ||||
\(482\) | 4.68653 | − | 17.4904i | 0.213466 | − | 0.796665i | ||||
\(483\) | −0.803848 | + | 1.39230i | −0.0365763 | + | 0.0633521i | ||||
\(484\) | −2.19615 | + | 3.80385i | −0.0998251 | + | 0.172902i | ||||
\(485\) | 22.5885 | + | 22.5885i | 1.02569 | + | 1.02569i | ||||
\(486\) | 15.5885 | + | 15.5885i | 0.707107 | + | 0.707107i | ||||
\(487\) | − | 16.1962i | − | 0.733918i | −0.930237 | − | 0.366959i | \(-0.880399\pi\) | ||
0.930237 | − | 0.366959i | \(-0.119601\pi\) | |||||||
\(488\) | −7.60770 | − | 4.39230i | −0.344384 | − | 0.198830i | ||||
\(489\) | −4.43782 | − | 16.5622i | −0.200685 | − | 0.748968i | ||||
\(490\) | 30.5885 | − | 17.6603i | 1.38185 | − | 0.797809i | ||||
\(491\) | 6.89230 | − | 25.7224i | 0.311045 | − | 1.16084i | −0.616570 | − | 0.787300i | \(-0.711478\pi\) |
0.927615 | − | 0.373537i | \(-0.121855\pi\) | |||||||
\(492\) | 5.19615 | + | 9.00000i | 0.234261 | + | 0.405751i | ||||
\(493\) | −1.43782 | − | 5.36603i | −0.0647563 | − | 0.241674i | ||||
\(494\) | 5.66025 | − | 5.66025i | 0.254667 | − | 0.254667i | ||||
\(495\) | −29.7846 | + | 17.1962i | −1.33872 | + | 0.772910i | ||||
\(496\) | −29.8564 | −1.34059 | ||||||||
\(497\) | −4.00000 | + | 6.92820i | −0.179425 | + | 0.310772i | ||||
\(498\) | 3.46410 | 0.155230 | ||||||||
\(499\) | 6.33013 | + | 1.69615i | 0.283375 | + | 0.0759302i | 0.397707 | − | 0.917512i | \(-0.369806\pi\) |
−0.114332 | + | 0.993443i | \(0.536473\pi\) | |||||||
\(500\) | −9.85641 | + | 36.7846i | −0.440792 | + | 1.64506i | ||||
\(501\) | − | 0.928203i | − | 0.0414691i | ||||||
\(502\) | −4.90192 | − | 2.83013i | −0.218784 | − | 0.126315i | ||||
\(503\) | − | 27.7128i | − | 1.23565i | −0.786314 | − | 0.617827i | \(-0.788013\pi\) | ||
0.786314 | − | 0.617827i | \(-0.211987\pi\) | |||||||
\(504\) | 4.39230 | + | 4.39230i | 0.195649 | + | 0.195649i | ||||
\(505\) | − | 29.8564i | − | 1.32859i | ||||||
\(506\) | −2.66025 | + | 4.60770i | −0.118263 | + | 0.204837i | ||||
\(507\) | −40.2846 | + | 23.2583i | −1.78910 | + | 1.03294i | ||||
\(508\) | −10.7321 | + | 6.19615i | −0.476158 | + | 0.274910i | ||||
\(509\) | 16.9282 | + | 4.53590i | 0.750329 | + | 0.201050i | 0.613664 | − | 0.789567i | \(-0.289695\pi\) |
0.136665 | + | 0.990617i | \(0.456362\pi\) | |||||||
\(510\) | 18.5885 | + | 10.7321i | 0.823111 | + | 0.475223i | ||||
\(511\) | −3.56218 | + | 6.16987i | −0.157581 | + | 0.272939i | ||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | −3.29423 | + | 3.29423i | −0.145444 | + | 0.145444i | ||||
\(514\) | 8.85641 | + | 8.85641i | 0.390639 | + | 0.390639i | ||||
\(515\) | −9.12436 | − | 34.0526i | −0.402067 | − | 1.50054i | ||||
\(516\) | −1.14359 | − | 4.26795i | −0.0503439 | − | 0.187886i | ||||
\(517\) | −7.41858 | + | 27.6865i | −0.326269 | + | 1.21765i | ||||
\(518\) | −0.928203 | − | 1.60770i | −0.0407829 | − | 0.0706381i | ||||
\(519\) | −21.7583 | − | 5.83013i | −0.955085 | − | 0.255914i | ||||
\(520\) | 17.8564 | + | 66.6410i | 0.783055 | + | 2.92240i | ||||
\(521\) | − | 13.0000i | − | 0.569540i | −0.958596 | − | 0.284770i | \(-0.908083\pi\) | ||
0.958596 | − | 0.284770i | \(-0.0919173\pi\) | |||||||
\(522\) | −5.19615 | + | 9.00000i | −0.227429 | + | 0.393919i | ||||
\(523\) | −14.4641 | − | 14.4641i | −0.632471 | − | 0.632471i | 0.316216 | − | 0.948687i | \(-0.397588\pi\) |
−0.948687 | + | 0.316216i | \(0.897588\pi\) | |||||||
\(524\) | −6.19615 | + | 1.66025i | −0.270680 | + | 0.0725285i | ||||
\(525\) | 12.5885 | 0.549405 | ||||||||
\(526\) | −37.0526 | − | 9.92820i | −1.61557 | − | 0.432890i | ||||
\(527\) | 8.46410 | + | 14.6603i | 0.368702 | + | 0.638611i | ||||
\(528\) | 14.5359 | + | 14.5359i | 0.632594 | + | 0.632594i | ||||
\(529\) | −10.6962 | + | 18.5263i | −0.465050 | + | 0.805490i | ||||
\(530\) | 2.92820 | − | 2.92820i | 0.127193 | − | 0.127193i | ||||
\(531\) | 14.8923 | − | 3.99038i | 0.646271 | − | 0.173168i | ||||
\(532\) | −0.928203 | + | 0.928203i | −0.0402427 | + | 0.0402427i | ||||
\(533\) | 18.2942 | − | 4.90192i | 0.792411 | − | 0.212326i | ||||
\(534\) | 4.73205 | + | 1.26795i | 0.204776 | + | 0.0548695i | ||||
\(535\) | −63.8372 | + | 36.8564i | −2.75992 | + | 1.59344i | ||||
\(536\) | 13.2679 | − | 7.66025i | 0.573088 | − | 0.330873i | ||||
\(537\) | 7.56218 | + | 28.2224i | 0.326332 | + | 1.21789i | ||||
\(538\) | −4.73205 | + | 8.19615i | −0.204013 | + | 0.353361i | ||||
\(539\) | −13.5622 | − | 13.5622i | −0.584164 | − | 0.584164i | ||||
\(540\) | −10.3923 | − | 38.7846i | −0.447214 | − | 1.66902i | ||||
\(541\) | −8.19615 | + | 8.19615i | −0.352380 | + | 0.352380i | −0.860994 | − | 0.508614i | \(-0.830158\pi\) |
0.508614 | + | 0.860994i | \(0.330158\pi\) | |||||||
\(542\) | −27.8564 | + | 7.46410i | −1.19654 | + | 0.320611i | ||||
\(543\) | −31.6865 | + | 8.49038i | −1.35980 | + | 0.364357i | ||||
\(544\) | 3.32051 | − | 12.3923i | 0.142366 | − | 0.531316i | ||||
\(545\) | −19.8564 | − | 34.3923i | −0.850555 | − | 1.47320i | ||||
\(546\) | 9.80385 | − | 5.66025i | 0.419566 | − | 0.242237i | ||||
\(547\) | 8.37564 | + | 31.2583i | 0.358117 | + | 1.33651i | 0.876517 | + | 0.481371i | \(0.159861\pi\) |
−0.518400 | + | 0.855138i | \(0.673472\pi\) | |||||||
\(548\) | −32.9282 | −1.40662 | ||||||||
\(549\) | 6.58846 | − | 6.58846i | 0.281189 | − | 0.281189i | ||||
\(550\) | 41.6603 | 1.77640 | ||||||||
\(551\) | −1.90192 | − | 1.09808i | −0.0810247 | − | 0.0467796i | ||||
\(552\) | −4.39230 | − | 4.39230i | −0.186949 | − | 0.186949i | ||||
\(553\) | −7.60770 | + | 4.39230i | −0.323512 | + | 0.186780i | ||||
\(554\) | −19.9808 | + | 11.5359i | −0.848901 | + | 0.490113i | ||||
\(555\) | 12.0000i | 0.509372i | ||||||||
\(556\) | −4.85641 | − | 18.1244i | −0.205958 | − | 0.768644i | ||||
\(557\) | −25.1962 | + | 25.1962i | −1.06760 | + | 1.06760i | −0.0700519 | + | 0.997543i | \(0.522316\pi\) |
−0.997543 | + | 0.0700519i | \(0.977684\pi\) | |||||||
\(558\) | 8.19615 | − | 30.5885i | 0.346971 | − | 1.29491i | ||||
\(559\) | −8.05256 | −0.340587 | ||||||||
\(560\) | −2.92820 | − | 10.9282i | −0.123739 | − | 0.461801i | ||||
\(561\) | 3.01666 | − | 11.2583i | 0.127364 | − | 0.475327i | ||||
\(562\) | −13.6603 | − | 3.66025i | −0.576223 | − | 0.154398i | ||||
\(563\) | −3.76795 | − | 1.00962i | −0.158800 | − | 0.0425504i | 0.178543 | − | 0.983932i | \(-0.442862\pi\) |
−0.337343 | + | 0.941382i | \(0.609528\pi\) | |||||||
\(564\) | −28.9808 | − | 16.7321i | −1.22031 | − | 0.704546i | ||||
\(565\) | 51.7128 | − | 13.8564i | 2.17557 | − | 0.582943i | ||||
\(566\) | − | 40.6410i | − | 1.70827i | ||||||
\(567\) | −5.70577 | + | 3.29423i | −0.239620 | + | 0.138345i | ||||
\(568\) | −21.8564 | − | 21.8564i | −0.917074 | − | 0.917074i | ||||
\(569\) | −23.5981 | − | 13.6244i | −0.989283 | − | 0.571163i | −0.0842230 | − | 0.996447i | \(-0.526841\pi\) |
−0.905060 | + | 0.425284i | \(0.860174\pi\) | |||||||
\(570\) | 8.19615 | − | 2.19615i | 0.343299 | − | 0.0919867i | ||||
\(571\) | 5.33013 | − | 19.8923i | 0.223059 | − | 0.832467i | −0.760114 | − | 0.649790i | \(-0.774857\pi\) |
0.983173 | − | 0.182677i | \(-0.0584764\pi\) | |||||||
\(572\) | 32.4449 | − | 18.7321i | 1.35659 | − | 0.783226i | ||||
\(573\) | 12.1699 | + | 21.0788i | 0.508404 | + | 0.880581i | ||||
\(574\) | −3.00000 | + | 0.803848i | −0.125218 | + | 0.0335519i | ||||
\(575\) | −12.5885 | −0.524975 | ||||||||
\(576\) | −20.7846 | + | 12.0000i | −0.866025 | + | 0.500000i | ||||
\(577\) | 35.7846 | 1.48973 | 0.744866 | − | 0.667214i | \(-0.232513\pi\) | ||||
0.744866 | + | 0.667214i | \(0.232513\pi\) | |||||||
\(578\) | 16.1962 | − | 4.33975i | 0.673671 | − | 0.180510i | ||||
\(579\) | 31.6410 | 1.31496 | ||||||||
\(580\) | 16.3923 | − | 9.46410i | 0.680653 | − | 0.392975i | ||||
\(581\) | −0.267949 | + | 1.00000i | −0.0111164 | + | 0.0414870i | ||||
\(582\) | 14.3205 | + | 14.3205i | 0.593604 | + | 0.593604i | ||||
\(583\) | −1.94744 | − | 1.12436i | −0.0806548 | − | 0.0465661i | ||||
\(584\) | −19.4641 | − | 19.4641i | −0.805430 | − | 0.805430i | ||||
\(585\) | −73.1769 | −3.02549 | ||||||||
\(586\) | − | 19.8564i | − | 0.820261i | ||||||
\(587\) | 3.76795 | − | 1.00962i | 0.155520 | − | 0.0416714i | −0.180219 | − | 0.983626i | \(-0.557681\pi\) |
0.335739 | + | 0.941955i | \(0.391014\pi\) | |||||||
\(588\) | 19.3923 | − | 11.1962i | 0.799725 | − | 0.461722i | ||||
\(589\) | 6.46410 | + | 1.73205i | 0.266349 | + | 0.0713679i | ||||
\(590\) | −27.1244 | − | 7.26795i | −1.11669 | − | 0.299217i | ||||
\(591\) | 8.66025 | − | 2.32051i | 0.356235 | − | 0.0954529i | ||||
\(592\) | 6.92820 | − | 1.85641i | 0.284747 | − | 0.0762978i | ||||
\(593\) | 10.5359 | 0.432657 | 0.216329 | − | 0.976321i | \(-0.430592\pi\) | ||||
0.216329 | + | 0.976321i | \(0.430592\pi\) | |||||||
\(594\) | −18.8827 | + | 10.9019i | −0.774766 | + | 0.447311i | ||||
\(595\) | −4.53590 | + | 4.53590i | −0.185954 | + | 0.185954i | ||||
\(596\) | 1.66025 | + | 6.19615i | 0.0680067 | + | 0.253804i | ||||
\(597\) | 1.31347 | + | 0.758330i | 0.0537566 | + | 0.0310364i | ||||
\(598\) | −9.80385 | + | 5.66025i | −0.400909 | + | 0.231465i | ||||
\(599\) | −23.3205 | + | 13.4641i | −0.952850 | + | 0.550128i | −0.893965 | − | 0.448136i | \(-0.852088\pi\) |
−0.0588850 | + | 0.998265i | \(0.518755\pi\) | |||||||
\(600\) | −12.5885 | + | 46.9808i | −0.513922 | + | 1.91798i | ||||
\(601\) | 17.5526 | + | 10.1340i | 0.715984 | + | 0.413373i | 0.813273 | − | 0.581883i | \(-0.197684\pi\) |
−0.0972889 | + | 0.995256i | \(0.531017\pi\) | |||||||
\(602\) | 1.32051 | 0.0538199 | ||||||||
\(603\) | 4.20577 | + | 15.6962i | 0.171272 | + | 0.639197i | ||||
\(604\) | 5.46410 | 0.222331 | ||||||||
\(605\) | 2.19615 | + | 8.19615i | 0.0892863 | + | 0.333221i | ||||
\(606\) | − | 18.9282i | − | 0.768906i | ||||||
\(607\) | 22.5885 | + | 39.1244i | 0.916837 | + | 1.58801i | 0.804189 | + | 0.594374i | \(0.202600\pi\) |
0.112648 | + | 0.993635i | \(0.464067\pi\) | |||||||
\(608\) | −2.53590 | − | 4.39230i | −0.102844 | − | 0.178131i | ||||
\(609\) | −2.19615 | − | 2.19615i | −0.0889926 | − | 0.0889926i | ||||
\(610\) | −16.3923 | + | 4.39230i | −0.663705 | + | 0.177839i | ||||
\(611\) | −43.1244 | + | 43.1244i | −1.74462 | + | 1.74462i | ||||
\(612\) | 11.7846 | + | 6.80385i | 0.476365 | + | 0.275029i | ||||
\(613\) | 1.66025 | + | 1.66025i | 0.0670570 | + | 0.0670570i | 0.739840 | − | 0.672783i | \(-0.234901\pi\) |
−0.672783 | + | 0.739840i | \(0.734901\pi\) | |||||||
\(614\) | 16.0263 | − | 27.7583i | 0.646768 | − | 1.12024i | ||||
\(615\) | 19.3923 | + | 5.19615i | 0.781973 | + | 0.209529i | ||||
\(616\) | −5.32051 | + | 3.07180i | −0.214369 | + | 0.123766i | ||||
\(617\) | −3.91154 | + | 2.25833i | −0.157473 | + | 0.0909170i | −0.576666 | − | 0.816980i | \(-0.695646\pi\) |
0.419193 | + | 0.907897i | \(0.362313\pi\) | |||||||
\(618\) | −5.78461 | − | 21.5885i | −0.232691 | − | 0.868415i | ||||
\(619\) | 38.8205 | − | 10.4019i | 1.56033 | − | 0.418089i | 0.627561 | − | 0.778568i | \(-0.284053\pi\) |
0.932767 | + | 0.360479i | \(0.117387\pi\) | |||||||
\(620\) | −40.7846 | + | 40.7846i | −1.63795 | + | 1.63795i | ||||
\(621\) | 5.70577 | − | 3.29423i | 0.228965 | − | 0.132193i | ||||
\(622\) | 16.0526 | − | 16.0526i | 0.643649 | − | 0.643649i | ||||
\(623\) | −0.732051 | + | 1.26795i | −0.0293290 | + | 0.0507993i | ||||
\(624\) | 11.3205 | + | 42.2487i | 0.453183 | + | 1.69130i | ||||
\(625\) | 11.9641 | + | 20.7224i | 0.478564 | + | 0.828897i | ||||
\(626\) | 38.8827 | + | 10.4186i | 1.55406 | + | 0.416410i | ||||
\(627\) | −2.30385 | − | 3.99038i | −0.0920068 | − | 0.159360i | ||||
\(628\) | 9.46410 | − | 2.53590i | 0.377659 | − | 0.101193i | ||||
\(629\) | −2.87564 | − | 2.87564i | −0.114659 | − | 0.114659i | ||||
\(630\) | 12.0000 | 0.478091 | ||||||||
\(631\) | − | 38.3923i | − | 1.52837i | −0.644995 | − | 0.764187i | \(-0.723141\pi\) | ||
0.644995 | − | 0.764187i | \(-0.276859\pi\) | |||||||
\(632\) | −8.78461 | − | 32.7846i | −0.349433 | − | 1.30410i | ||||
\(633\) | −5.19615 | + | 5.19615i | −0.206529 | + | 0.206529i | ||||
\(634\) | 23.0526 | + | 39.9282i | 0.915534 | + | 1.58575i | ||||
\(635\) | −6.19615 | + | 23.1244i | −0.245887 | + | 0.917662i | ||||
\(636\) | 1.85641 | − | 1.85641i | 0.0736113 | − | 0.0736113i | ||||
\(637\) | −10.5622 | − | 39.4186i | −0.418489 | − | 1.56182i | ||||
\(638\) | −7.26795 | − | 7.26795i | −0.287741 | − | 0.287741i | ||||
\(639\) | 28.3923 | − | 16.3923i | 1.12318 | − | 0.648470i | ||||
\(640\) | 43.7128 | 1.72790 | ||||||||
\(641\) | −4.20577 | + | 7.28461i | −0.166118 | + | 0.287725i | −0.937052 | − | 0.349191i | \(-0.886457\pi\) |
0.770934 | + | 0.636915i | \(0.219790\pi\) | |||||||
\(642\) | −40.4711 | + | 23.3660i | −1.59727 | + | 0.922183i | ||||
\(643\) | −45.6506 | − | 12.2321i | −1.80029 | − | 0.482385i | −0.806263 | − | 0.591558i | \(-0.798513\pi\) |
−0.994023 | + | 0.109173i | \(0.965180\pi\) | |||||||
\(644\) | 1.60770 | − | 0.928203i | 0.0633521 | − | 0.0365763i | ||||
\(645\) | −7.39230 | − | 4.26795i | −0.291072 | − | 0.168050i | ||||
\(646\) | −1.43782 | + | 2.49038i | −0.0565704 | + | 0.0979827i | ||||
\(647\) | − | 13.2679i | − | 0.521617i | −0.965391 | − | 0.260808i | \(-0.916011\pi\) | ||
0.965391 | − | 0.260808i | \(-0.0839891\pi\) | |||||||
\(648\) | −6.58846 | − | 24.5885i | −0.258819 | − | 0.965926i | ||||
\(649\) | 15.2487i | 0.598564i | ||||||||
\(650\) | 76.7654 | + | 44.3205i | 3.01099 | + | 1.73839i | ||||
\(651\) | 8.19615 | + | 4.73205i | 0.321233 | + | 0.185464i | ||||
\(652\) | −5.12436 | + | 19.1244i | −0.200685 | + | 0.748968i | ||||
\(653\) | 5.63397 | + | 1.50962i | 0.220474 | + | 0.0590760i | 0.367365 | − | 0.930077i | \(-0.380260\pi\) |
−0.146891 | + | 0.989153i | \(0.546927\pi\) | |||||||
\(654\) | −12.5885 | − | 21.8038i | −0.492248 | − | 0.852598i | ||||
\(655\) | −6.19615 | + | 10.7321i | −0.242104 | + | 0.419336i | ||||
\(656\) | − | 12.0000i | − | 0.468521i | ||||||
\(657\) | 25.2846 | − | 14.5981i | 0.986447 | − | 0.569525i | ||||
\(658\) | 7.07180 | − | 7.07180i | 0.275687 | − | 0.275687i | ||||
\(659\) | 4.02628 | + | 15.0263i | 0.156842 | + | 0.585341i | 0.998941 | + | 0.0460178i | \(0.0146531\pi\) |
−0.842099 | + | 0.539323i | \(0.818680\pi\) | |||||||
\(660\) | 39.7128 | 1.54582 | ||||||||
\(661\) | 2.19615 | − | 8.19615i | 0.0854204 | − | 0.318793i | −0.909973 | − | 0.414667i | \(-0.863898\pi\) |
0.995393 | + | 0.0958740i | \(0.0305646\pi\) | |||||||
\(662\) | 24.1244 | − | 13.9282i | 0.937620 | − | 0.541335i | ||||
\(663\) | 17.5359 | − | 17.5359i | 0.681038 | − | 0.681038i | ||||
\(664\) | −3.46410 | − | 2.00000i | −0.134433 | − | 0.0776151i | ||||
\(665\) | 2.53590i | 0.0983379i | ||||||||
\(666\) | 7.60770i | 0.294792i | ||||||||
\(667\) | 2.19615 | + | 2.19615i | 0.0850354 | + | 0.0850354i | ||||
\(668\) | −0.535898 | + | 0.928203i | −0.0207345 | + | 0.0359133i | ||||
\(669\) | 19.0981 | + | 33.0788i | 0.738374 | + | 1.27890i | ||||
\(670\) | 7.66025 | − | 28.5885i | 0.295941 | − | 1.10447i | ||||
\(671\) | 4.60770 | + | 7.98076i | 0.177878 | + | 0.308094i | ||||
\(672\) | −1.85641 | − | 6.92820i | −0.0716124 | − | 0.267261i | ||||
\(673\) | 8.80385 | − | 15.2487i | 0.339363 | − | 0.587795i | −0.644950 | − | 0.764225i | \(-0.723122\pi\) |
0.984313 | + | 0.176430i | \(0.0564550\pi\) | |||||||
\(674\) | 23.7846 | + | 23.7846i | 0.916149 | + | 0.916149i | ||||
\(675\) | −44.6769 | − | 25.7942i | −1.71962 | − | 0.992820i | ||||
\(676\) | 53.7128 | 2.06588 | ||||||||
\(677\) | 4.73205 | − | 1.26795i | 0.181867 | − | 0.0487312i | −0.166736 | − | 0.986002i | \(-0.553323\pi\) |
0.348603 | + | 0.937270i | \(0.386656\pi\) | |||||||
\(678\) | 32.7846 | − | 8.78461i | 1.25909 | − | 0.337371i | ||||
\(679\) | −5.24167 | + | 3.02628i | −0.201157 | + | 0.116138i | ||||
\(680\) | −12.3923 | − | 21.4641i | −0.475223 | − | 0.823111i | ||||
\(681\) | −24.9904 | − | 6.69615i | −0.957633 | − | 0.256597i | ||||
\(682\) | 27.1244 | + | 15.6603i | 1.03865 | + | 0.599662i | ||||
\(683\) | −4.70577 | − | 4.70577i | −0.180061 | − | 0.180061i | 0.611321 | − | 0.791383i | \(-0.290638\pi\) |
−0.791383 | + | 0.611321i | \(0.790638\pi\) | |||||||
\(684\) | 5.19615 | − | 1.39230i | 0.198680 | − | 0.0532361i | ||||
\(685\) | −44.9808 | + | 44.9808i | −1.71863 | + | 1.71863i | ||||
\(686\) | 3.60770 | + | 13.4641i | 0.137742 | + | 0.514062i | ||||
\(687\) | −8.66025 | − | 8.66025i | −0.330409 | − | 0.330409i | ||||
\(688\) | −1.32051 | + | 4.92820i | −0.0503439 | + | 0.187886i | ||||
\(689\) | −2.39230 | − | 4.14359i | −0.0911396 | − | 0.157858i | ||||
\(690\) | −12.0000 | −0.456832 | ||||||||
\(691\) | −6.29423 | − | 23.4904i | −0.239444 | − | 0.893616i | −0.976095 | − | 0.217344i | \(-0.930261\pi\) |
0.736651 | − | 0.676273i | \(-0.236406\pi\) | |||||||
\(692\) | 18.3923 | + | 18.3923i | 0.699171 | + | 0.699171i | ||||
\(693\) | −1.68653 | − | 6.29423i | −0.0640661 | − | 0.239098i | ||||
\(694\) | 36.1962i | 1.37399i | ||||||||
\(695\) | −31.3923 | − | 18.1244i | −1.19078 | − | 0.687496i | ||||
\(696\) | 10.3923 | − | 6.00000i | 0.393919 | − | 0.227429i | ||||
\(697\) | −5.89230 | + | 3.40192i | −0.223187 | + | 0.128857i | ||||
\(698\) | −5.66025 | − | 9.80385i | −0.214244 | − | 0.371081i | ||||
\(699\) | 10.7942 | + | 6.23205i | 0.408275 | + | 0.235718i | ||||
\(700\) | −12.5885 | − | 7.26795i | −0.475799 | − | 0.274703i | ||||
\(701\) | 10.6603 | − | 10.6603i | 0.402632 | − | 0.402632i | −0.476527 | − | 0.879160i | \(-0.658105\pi\) |
0.879160 | + | 0.476527i | \(0.158105\pi\) | |||||||
\(702\) | −46.3923 | −1.75096 | ||||||||
\(703\) | −1.60770 | −0.0606354 | ||||||||
\(704\) | −6.14359 | − | 22.9282i | −0.231545 | − | 0.864139i | ||||
\(705\) | −62.4449 | + | 16.7321i | −2.35181 | + | 0.630165i | ||||
\(706\) | 7.43782 | − | 27.7583i | 0.279926 | − | 1.04470i | ||||
\(707\) | 5.46410 | + | 1.46410i | 0.205499 | + | 0.0550632i | ||||
\(708\) | −17.1962 | − | 4.60770i | −0.646271 | − | 0.173168i | ||||
\(709\) | −20.1962 | + | 5.41154i | −0.758482 | + | 0.203235i | −0.617277 | − | 0.786746i | \(-0.711764\pi\) |
−0.141205 | + | 0.989980i | \(0.545098\pi\) | |||||||
\(710\) | −59.7128 | −2.24098 | ||||||||
\(711\) | 36.0000 | 1.35011 | ||||||||
\(712\) | −4.00000 | − | 4.00000i | −0.149906 | − | 0.149906i | ||||
\(713\) | −8.19615 | − | 4.73205i | −0.306948 | − | 0.177217i | ||||
\(714\) | −2.87564 | + | 2.87564i | −0.107618 | + | 0.107618i | ||||
\(715\) | 18.7321 | − | 69.9090i | 0.700539 | − | 2.61445i | ||||
\(716\) | 8.73205 | − | 32.5885i | 0.326332 | − | 1.21789i | ||||
\(717\) | 45.3731 | 1.69449 | ||||||||
\(718\) | 5.39230 | + | 20.1244i | 0.201239 | + | 0.751034i | ||||
\(719\) | −16.3923 | −0.611330 | −0.305665 | − | 0.952139i | \(-0.598879\pi\) | ||||
−0.305665 | + | 0.952139i | \(0.598879\pi\) | |||||||
\(720\) | −12.0000 | + | 44.7846i | −0.447214 | + | 1.66902i | ||||
\(721\) | 6.67949 | 0.248757 | ||||||||
\(722\) | −6.66025 | − | 24.8564i | −0.247869 | − | 0.925060i | ||||
\(723\) | −11.0885 | − | 19.2058i | −0.412384 | − | 0.714270i | ||||
\(724\) | 36.5885 | + | 9.80385i | 1.35980 | + | 0.364357i | ||||
\(725\) | 6.29423 | − | 23.4904i | 0.233762 | − | 0.872411i | ||||
\(726\) | 1.39230 | + | 5.19615i | 0.0516733 | + | 0.192847i | ||||
\(727\) | 31.8109 | + | 18.3660i | 1.17980 | + | 0.681158i | 0.955968 | − | 0.293470i | \(-0.0948099\pi\) |
0.223832 | + | 0.974628i | \(0.428143\pi\) | |||||||
\(728\) | −13.0718 | −0.484473 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | −53.1769 | −1.96817 | ||||||||
\(731\) | 2.79423 | − | 0.748711i | 0.103348 | − | 0.0276921i | ||||
\(732\) | −10.3923 | + | 2.78461i | −0.384111 | + | 0.102922i | ||||
\(733\) | −29.9545 | − | 8.02628i | −1.10639 | − | 0.296457i | −0.341028 | − | 0.940053i | \(-0.610775\pi\) |
−0.765366 | + | 0.643596i | \(0.777442\pi\) | |||||||
\(734\) | 7.41154 | − | 27.6603i | 0.273565 | − | 1.02096i | ||||
\(735\) | 11.1962 | − | 41.7846i | 0.412976 | − | 1.54125i | ||||
\(736\) | 1.85641 | + | 6.92820i | 0.0684280 | + | 0.255377i | ||||
\(737\) | −16.0718 | −0.592012 | ||||||||
\(738\) | 12.2942 | + | 3.29423i | 0.452557 | + | 0.121262i | ||||
\(739\) | 21.2224 | − | 21.2224i | 0.780680 | − | 0.780680i | −0.199266 | − | 0.979945i | \(-0.563856\pi\) |
0.979945 | + | 0.199266i | \(0.0638557\pi\) | |||||||
\(740\) | 6.92820 | − | 12.0000i | 0.254686 | − | 0.441129i | ||||
\(741\) | − | 9.80385i | − | 0.360153i | ||||||
\(742\) | 0.392305 | + | 0.679492i | 0.0144020 | + | 0.0249449i | ||||
\(743\) | 2.24167 | − | 1.29423i | 0.0822389 | − | 0.0474806i | −0.458317 | − | 0.888789i | \(-0.651547\pi\) |
0.540556 | + | 0.841308i | \(0.318214\pi\) | |||||||
\(744\) | −25.8564 | + | 25.8564i | −0.947942 | + | 0.947942i | ||||
\(745\) | 10.7321 | + | 6.19615i | 0.393192 | + | 0.227009i | ||||
\(746\) | 8.24871i | 0.302007i | ||||||||
\(747\) | 3.00000 | − | 3.00000i | 0.109764 | − | 0.109764i | ||||
\(748\) | −9.51666 | + | 9.51666i | −0.347964 | + | 0.347964i | ||||
\(749\) | −3.61474 | − | 13.4904i | −0.132080 | − | 0.492928i | ||||
\(750\) | 23.3205 | + | 40.3923i | 0.851545 | + | 1.47492i | ||||
\(751\) | 18.8564 | + | 32.6603i | 0.688080 | + | 1.19179i | 0.972458 | + | 0.233077i | \(0.0748796\pi\) |
−0.284378 | + | 0.958712i | \(0.591787\pi\) | |||||||
\(752\) | 19.3205 | + | 33.4641i | 0.704546 | + | 1.22031i | ||||
\(753\) | −6.69615 | + | 1.79423i | −0.244021 | + | 0.0653853i | ||||
\(754\) | −5.66025 | − | 21.1244i | −0.206134 | − | 0.769304i | ||||
\(755\) | 7.46410 | − | 7.46410i | 0.271646 | − | 0.271646i | ||||
\(756\) | 7.60770 | 0.276689 | ||||||||
\(757\) | −6.07180 | − | 6.07180i | −0.220683 | − | 0.220683i | 0.588103 | − | 0.808786i | \(-0.299875\pi\) |
−0.808786 | + | 0.588103i | \(0.799875\pi\) | |||||||
\(758\) | 32.4904 | + | 18.7583i | 1.18010 | + | 0.681333i | ||||
\(759\) | 1.68653 | + | 6.29423i | 0.0612173 | + | 0.228466i | ||||
\(760\) | −9.46410 | − | 2.53590i | −0.343299 | − | 0.0919867i | ||||
\(761\) | −27.3731 | + | 15.8038i | −0.992273 | + | 0.572889i | −0.905953 | − | 0.423378i | \(-0.860844\pi\) |
−0.0863200 | + | 0.996267i | \(0.527511\pi\) | |||||||
\(762\) | −3.92820 | + | 14.6603i | −0.142304 | + | 0.531085i | ||||
\(763\) | 7.26795 | − | 1.94744i | 0.263117 | − | 0.0705021i | ||||
\(764\) | − | 28.1051i | − | 1.01681i | ||||||
\(765\) | 25.3923 | − | 6.80385i | 0.918061 | − | 0.245994i | ||||
\(766\) | 6.53590 | + | 6.53590i | 0.236152 | + | 0.236152i | ||||
\(767\) | −16.2224 | + | 28.0981i | −0.585758 | + | 1.01456i | ||||
\(768\) | 27.7128 | 1.00000 | ||||||||
\(769\) | 10.1244 | + | 17.5359i | 0.365094 | + | 0.632361i | 0.988791 | − | 0.149305i | \(-0.0477036\pi\) |
−0.623698 | + | 0.781666i | \(0.714370\pi\) | |||||||
\(770\) | −3.07180 | + | 11.4641i | −0.110700 | + | 0.413138i | ||||
\(771\) | 15.3397 | 0.552447 | ||||||||
\(772\) | −31.6410 | − | 18.2679i | −1.13879 | − | 0.657478i | ||||
\(773\) | 4.41154 | + | 4.41154i | 0.158672 | + | 0.158672i | 0.781978 | − | 0.623306i | \(-0.214211\pi\) |
−0.623306 | + | 0.781978i | \(0.714211\pi\) | |||||||
\(774\) | −4.68653 | − | 2.70577i | −0.168454 | − | 0.0972569i | ||||
\(775\) | 74.1051i | 2.66193i | ||||||||
\(776\) | −6.05256 | − | 22.5885i | −0.217274 | − | 0.810878i | ||||
\(777\) | −2.19615 | − | 0.588457i | −0.0787865 | − | 0.0211108i | ||||
\(778\) | −13.0526 | + | 7.53590i | −0.467957 | + | 0.270175i | ||||
\(779\) | −0.696152 | + | 2.59808i | −0.0249422 | + | 0.0930857i | ||||
\(780\) | 73.1769 | + | 42.2487i | 2.62015 | + | 1.51275i | ||||
\(781\) | 8.39230 | + | 31.3205i | 0.300300 | + | 1.12074i | ||||
\(782\) | 2.87564 | − | 2.87564i | 0.102833 | − | 0.102833i | ||||
\(783\) | 3.29423 | + | 12.2942i | 0.117726 | + | 0.439360i | ||||
\(784\) | −25.8564 | −0.923443 | ||||||||
\(785\) | 9.46410 | − | 16.3923i | 0.337788 | − | 0.585066i | ||||
\(786\) | −3.92820 | + | 6.80385i | −0.140114 | + | 0.242685i | ||||
\(787\) | 49.8109 | + | 13.3468i | 1.77557 | + | 0.475762i | 0.989764 | − | 0.142716i | \(-0.0455834\pi\) |
0.785803 | + | 0.618477i | \(0.212250\pi\) | |||||||
\(788\) | −10.0000 | − | 2.67949i | −0.356235 | − | 0.0954529i | ||||
\(789\) | −40.6865 | + | 23.4904i | −1.44848 | + | 0.836280i | ||||
\(790\) | −56.7846 | − | 32.7846i | −2.02031 | − | 1.16642i | ||||
\(791\) | 10.1436i | 0.360665i | ||||||||
\(792\) | 25.1769 | 0.894623 | ||||||||
\(793\) | 19.6077i | 0.696290i | ||||||||
\(794\) | 12.7321 | − | 22.0526i | 0.451844 | − | 0.782616i | ||||
\(795\) | − | 5.07180i | − | 0.179878i | ||||||
\(796\) | −0.875644 | − | 1.51666i | −0.0310364 | − | 0.0537566i | ||||
\(797\) | −54.1769 | − | 14.5167i | −1.91904 | − | 0.514206i | −0.989275 | − | 0.146065i | \(-0.953339\pi\) |
−0.929770 | − | 0.368142i | \(-0.879994\pi\) | |||||||
\(798\) | 1.60770i | 0.0569118i | ||||||||
\(799\) | 10.9545 | − | 18.9737i | 0.387542 | − | 0.671242i | ||||
\(800\) | 39.7128 | − | 39.7128i | 1.40406 | − | 1.40406i | ||||
\(801\) | 5.19615 | − | 3.00000i | 0.183597 | − | 0.106000i | ||||
\(802\) | −27.5885 | − | 27.5885i | −0.974182 | − | 0.974182i | ||||
\(803\) | 7.47372 | + | 27.8923i | 0.263742 | + | 0.984298i | ||||
\(804\) | 4.85641 | − | 18.1244i | 0.171272 | − | 0.639197i | ||||
\(805\) | 0.928203 | − | 3.46410i | 0.0327149 | − | 0.122094i | ||||
\(806\) | 33.3205 | + | 57.7128i | 1.17366 | + | 2.03285i | ||||
\(807\) | 3.00000 | + | 11.1962i | 0.105605 | + | 0.394123i | ||||
\(808\) | −10.9282 | + | 18.9282i | −0.384453 | + | 0.665892i | ||||
\(809\) | − | 28.3205i | − | 0.995696i | −0.867264 | − | 0.497848i | \(-0.834124\pi\) | ||
0.867264 | − | 0.497848i | \(-0.165876\pi\) | |||||||
\(810\) | −42.5885 | − | 24.5885i | −1.49641 | − | 0.863950i | ||||
\(811\) | 5.02628 | + | 5.02628i | 0.176497 | + | 0.176497i | 0.789827 | − | 0.613330i | \(-0.210170\pi\) |
−0.613330 | + | 0.789827i | \(0.710170\pi\) | |||||||
\(812\) | 0.928203 | + | 3.46410i | 0.0325735 | + | 0.121566i | ||||
\(813\) | −17.6603 | + | 30.5885i | −0.619372 | + | 1.07278i | ||||
\(814\) | −7.26795 | − | 1.94744i | −0.254741 | − | 0.0682578i | ||||
\(815\) | 19.1244 | + | 33.1244i | 0.669897 | + | 1.16030i | ||||
\(816\) | −7.85641 | − | 13.6077i | −0.275029 | − | 0.476365i | ||||
\(817\) | 0.571797 | − | 0.990381i | 0.0200046 | − | 0.0346490i | ||||
\(818\) | −30.1769 | + | 30.1769i | −1.05511 | + | 1.05511i | ||||
\(819\) | 3.58846 | − | 13.3923i | 0.125391 | − | 0.467965i | ||||
\(820\) | −16.3923 | − | 16.3923i | −0.572444 | − | 0.572444i | ||||
\(821\) | 32.2224 | − | 8.63397i | 1.12457 | − | 0.301328i | 0.351839 | − | 0.936061i | \(-0.385556\pi\) |
0.772732 | + | 0.634733i | \(0.218890\pi\) | |||||||
\(822\) | −28.5167 | + | 28.5167i | −0.994633 | + | 0.994633i | ||||
\(823\) | 10.7321 | − | 6.19615i | 0.374096 | − | 0.215984i | −0.301151 | − | 0.953577i | \(-0.597371\pi\) |
0.675246 | + | 0.737592i | \(0.264037\pi\) | |||||||
\(824\) | −6.67949 | + | 24.9282i | −0.232691 | + | 0.868415i | ||||
\(825\) | 36.0788 | − | 36.0788i | 1.25610 | − | 1.25610i | ||||
\(826\) | 2.66025 | − | 4.60770i | 0.0925621 | − | 0.160322i | ||||
\(827\) | 24.4641 | + | 24.4641i | 0.850700 | + | 0.850700i | 0.990219 | − | 0.139519i | \(-0.0445557\pi\) |
−0.139519 | + | 0.990219i | \(0.544556\pi\) | |||||||
\(828\) | −7.60770 | −0.264386 | ||||||||
\(829\) | 24.5167 | − | 24.5167i | 0.851499 | − | 0.851499i | −0.138819 | − | 0.990318i | \(-0.544331\pi\) |
0.990318 | + | 0.138819i | \(0.0443306\pi\) | |||||||
\(830\) | −7.46410 | + | 2.00000i | −0.259083 | + | 0.0694210i | ||||
\(831\) | −7.31347 | + | 27.2942i | −0.253701 | + | 0.946826i | ||||
\(832\) | 13.0718 | − | 48.7846i | 0.453183 | − | 1.69130i | ||||
\(833\) | 7.33013 | + | 12.6962i | 0.253974 | + | 0.439896i | ||||
\(834\) | −19.9019 | − | 11.4904i | −0.689147 | − | 0.397879i | ||||
\(835\) | 0.535898 | + | 2.00000i | 0.0185455 | + | 0.0692129i | ||||
\(836\) | 5.32051i | 0.184014i | ||||||||
\(837\) | −19.3923 | − | 33.5885i | −0.670296 | − | 1.16099i | ||||
\(838\) | −45.7128 | −1.57912 | ||||||||
\(839\) | −35.4449 | − | 20.4641i | −1.22369 | − | 0.706499i | −0.257989 | − | 0.966148i | \(-0.583060\pi\) |
−0.965703 | + | 0.259649i | \(0.916393\pi\) | |||||||
\(840\) | −12.0000 | − | 6.92820i | −0.414039 | − | 0.239046i | ||||
\(841\) | 19.9186 | − | 11.5000i | 0.686848 | − | 0.396552i | ||||
\(842\) | 2.78461 | − | 1.60770i | 0.0959640 | − | 0.0554048i | ||||
\(843\) | −15.0000 | + | 8.66025i | −0.516627 | + | 0.298275i | ||||
\(844\) | 8.19615 | − | 2.19615i | 0.282123 | − | 0.0755947i | ||||
\(845\) | 73.3731 | − | 73.3731i | 2.52411 | − | 2.52411i | ||||
\(846\) | −39.5885 | + | 10.6077i | −1.36108 | + | 0.364700i | ||||
\(847\) | −1.60770 | −0.0552411 | ||||||||
\(848\) | −2.92820 | + | 0.784610i | −0.100555 | + | 0.0269436i | ||||
\(849\) | −35.1962 | − | 35.1962i | −1.20793 | − | 1.20793i | ||||
\(850\) | −30.7583 | − | 8.24167i | −1.05500 | − | 0.282687i | ||||
\(851\) | 2.19615 | + | 0.588457i | 0.0752831 | + | 0.0201721i | ||||
\(852\) | −37.8564 | −1.29694 | ||||||||
\(853\) | −12.5622 | + | 3.36603i | −0.430121 | + | 0.115251i | −0.467383 | − | 0.884055i | \(-0.654803\pi\) |
0.0372621 | + | 0.999306i | \(0.488136\pi\) | |||||||
\(854\) | − | 3.21539i | − | 0.110028i | ||||||
\(855\) | 5.19615 | − | 9.00000i | 0.177705 | − | 0.307794i | ||||
\(856\) | 53.9615 | 1.84437 | ||||||||
\(857\) | 20.9090 | + | 12.0718i | 0.714237 | + | 0.412365i | 0.812628 | − | 0.582783i | \(-0.198036\pi\) |
−0.0983911 | + | 0.995148i | \(0.531370\pi\) | |||||||
\(858\) | 11.8756 | − | 44.3205i | 0.405428 | − | 1.51308i | ||||
\(859\) | −8.25833 | + | 30.8205i | −0.281771 | + | 1.05158i | 0.669396 | + | 0.742905i | \(0.266553\pi\) |
−0.951167 | + | 0.308677i | \(0.900114\pi\) | |||||||
\(860\) | 4.92820 | + | 8.53590i | 0.168050 | + | 0.291072i | ||||
\(861\) | −1.90192 | + | 3.29423i | −0.0648174 | + | 0.112267i | ||||
\(862\) | 7.92820 | − | 2.12436i | 0.270036 | − | 0.0723558i | ||||
\(863\) | −8.53590 | −0.290565 | −0.145283 | − | 0.989390i | \(-0.546409\pi\) | ||||
−0.145283 | + | 0.989390i | \(0.546409\pi\) | |||||||
\(864\) | −7.60770 | + | 28.3923i | −0.258819 | + | 0.965926i | ||||
\(865\) | 50.2487 | 1.70851 | ||||||||
\(866\) | 3.09808 | − | 0.830127i | 0.105277 | − | 0.0282089i | ||||
\(867\) | 10.2679 | − | 17.7846i | 0.348718 | − | 0.603997i | ||||
\(868\) | −5.46410 | − | 9.46410i | −0.185464 | − | 0.321233i | ||||
\(869\) | −9.21539 | + | 34.3923i | −0.312611 | + | 1.16668i | ||||
\(870\) | 6.00000 | − | 22.3923i | 0.203419 | − | 0.759170i | ||||
\(871\) | −29.6147 | − | 17.0981i | −1.00346 | − | 0.579346i | ||||
\(872\) | 29.0718i | 0.984495i | ||||||||
\(873\) | 24.8038 | 0.839483 | ||||||||
\(874\) | − | 1.60770i | − | 0.0543811i | ||||||
\(875\) | −13.4641 | + | 3.60770i | −0.455170 | + | 0.121962i | ||||
\(876\) | −33.7128 | −1.13905 | ||||||||
\(877\) | −1.53590 | − | 0.411543i | −0.0518636 | − | 0.0138968i | 0.232794 | − | 0.972526i | \(-0.425213\pi\) |
−0.284658 | + | 0.958629i | \(0.591880\pi\) | |||||||
\(878\) | −7.66025 | − | 2.05256i | −0.258521 | − | 0.0692705i | ||||
\(879\) | −17.1962 | − | 17.1962i | −0.580012 | − | 0.580012i | ||||
\(880\) | −39.7128 | − | 22.9282i | −1.33872 | − | 0.772910i | ||||
\(881\) | −7.32051 | −0.246634 | −0.123317 | − | 0.992367i | \(-0.539353\pi\) | ||||
−0.123317 | + | 0.992367i | \(0.539353\pi\) | |||||||
\(882\) | 7.09808 | − | 26.4904i | 0.239005 | − | 0.891978i | ||||
\(883\) | −14.3660 | + | 14.3660i | −0.483455 | + | 0.483455i | −0.906233 | − | 0.422778i | \(-0.861055\pi\) |
0.422778 | + | 0.906233i | \(0.361055\pi\) | |||||||
\(884\) | −27.6603 | + | 7.41154i | −0.930315 | + | 0.249277i | ||||
\(885\) | −29.7846 | + | 17.1962i | −1.00120 | + | 0.578042i | ||||
\(886\) | −24.8827 | + | 14.3660i | −0.835950 | + | 0.482636i | ||||
\(887\) | 33.1244 | − | 19.1244i | 1.11221 | − | 0.642133i | 0.172807 | − | 0.984956i | \(-0.444716\pi\) |
0.939400 | + | 0.342823i | \(0.111383\pi\) | |||||||
\(888\) | 4.39230 | − | 7.60770i | 0.147396 | − | 0.255298i | ||||
\(889\) | −3.92820 | − | 2.26795i | −0.131748 | − | 0.0760646i | ||||
\(890\) | −10.9282 | −0.366314 | ||||||||
\(891\) | −6.91154 | + | 25.7942i | −0.231545 | + | 0.864139i | ||||
\(892\) | − | 44.1051i | − | 1.47675i | ||||||
\(893\) | −2.24167 | − | 8.36603i | −0.0750146 | − | 0.279958i | ||||
\(894\) | 6.80385 | + | 3.92820i | 0.227555 | + | 0.131379i | ||||
\(895\) | −32.5885 | − | 56.4449i | −1.08931 | − | 1.88674i | ||||
\(896\) | −2.14359 | + | 8.00000i | −0.0716124 | + | 0.267261i | ||||
\(897\) | −3.58846 | + | 13.3923i | −0.119815 | + | 0.447156i | ||||
\(898\) | 28.2224 | − | 7.56218i | 0.941795 | − | 0.252353i | ||||
\(899\) | 12.9282 | − | 12.9282i | 0.431180 | − | 0.431180i | ||||
\(900\) | 29.7846 | + | 51.5885i | 0.992820 | + | 1.71962i | ||||
\(901\) | 1.21539 | + | 1.21539i | 0.0404905 | + | 0.0404905i | ||||
\(902\) | −6.29423 | + | 10.9019i | −0.209575 | + | 0.362994i | ||||
\(903\) | 1.14359 | − | 1.14359i | 0.0380564 | − | 0.0380564i | ||||
\(904\) | −37.8564 | − | 10.1436i | −1.25909 | − | 0.337371i | ||||
\(905\) | 63.3731 | − | 36.5885i | 2.10659 | − | 1.21624i | ||||
\(906\) | 4.73205 | − | 4.73205i | 0.157212 | − | 0.157212i | ||||
\(907\) | −16.7942 | + | 4.50000i | −0.557643 | + | 0.149420i | −0.526623 | − | 0.850099i | \(-0.676542\pi\) |
−0.0310198 | + | 0.999519i | \(0.509876\pi\) | |||||||
\(908\) | 21.1244 | + | 21.1244i | 0.701036 | + | 0.701036i | ||||
\(909\) | −16.3923 | − | 16.3923i | −0.543698 | − | 0.543698i | ||||
\(910\) | −17.8564 | + | 17.8564i | −0.591934 | + | 0.591934i | ||||
\(911\) | −4.46410 | + | 7.73205i | −0.147902 | + | 0.256174i | −0.930452 | − | 0.366414i | \(-0.880585\pi\) |
0.782550 | + | 0.622588i | \(0.213919\pi\) | |||||||
\(912\) | −6.00000 | − | 1.60770i | −0.198680 | − | 0.0532361i | ||||
\(913\) | 2.09808 | + | 3.63397i | 0.0694362 | + | 0.120267i | ||||
\(914\) | 31.9545 | + | 8.56218i | 1.05696 | + | 0.283212i | ||||
\(915\) | −10.3923 | + | 18.0000i | −0.343559 | + | 0.595062i | ||||
\(916\) | 3.66025 | + | 13.6603i | 0.120938 | + | 0.451347i | ||||
\(917\) | −1.66025 | − | 1.66025i | −0.0548264 | − | 0.0548264i | ||||
\(918\) | 16.0981 | − | 4.31347i | 0.531316 | − | 0.142366i | ||||
\(919\) | 32.9808i | 1.08793i | 0.839106 | + | 0.543967i | \(0.183079\pi\) | ||||
−0.839106 | + | 0.543967i | \(0.816921\pi\) | |||||||
\(920\) | 12.0000 | + | 6.92820i | 0.395628 | + | 0.228416i | ||||
\(921\) | −10.1603 | − | 37.9186i | −0.334792 | − | 1.24946i | ||||
\(922\) | 1.87564 | + | 3.24871i | 0.0617711 | + | 0.106991i | ||||
\(923\) | −17.8564 | + | 66.6410i | −0.587751 | + | 2.19352i | ||||
\(924\) | −1.94744 | + | 7.26795i | −0.0640661 | + | 0.239098i | ||||
\(925\) | −4.60770 | − | 17.1962i | −0.151500 | − | 0.565406i | ||||
\(926\) | 18.3923 | + | 18.3923i | 0.604409 | + | 0.604409i | ||||
\(927\) | −23.7058 | − | 13.6865i | −0.778600 | − | 0.449525i | ||||
\(928\) | −13.8564 | −0.454859 | ||||||||
\(929\) | −18.4641 | + | 31.9808i | −0.605788 | + | 1.04925i | 0.386139 | + | 0.922441i | \(0.373809\pi\) |
−0.991926 | + | 0.126814i | \(0.959525\pi\) | |||||||
\(930\) | 70.6410i | 2.31641i | ||||||||
\(931\) | 5.59808 | + | 1.50000i | 0.183470 | + | 0.0491605i | ||||
\(932\) | −7.19615 | − | 12.4641i | −0.235718 | − | 0.408275i | ||||
\(933\) | − | 27.8038i | − | 0.910257i | ||||||
\(934\) | −4.36603 | + | 7.56218i | −0.142861 | + | 0.247442i | ||||
\(935\) | 26.0000i | 0.850291i | ||||||||
\(936\) | 46.3923 | + | 26.7846i | 1.51638 | + | 0.875482i | ||||
\(937\) | − | 51.1769i | − | 1.67188i | −0.548823 | − | 0.835938i | \(-0.684924\pi\) | ||
0.548823 | − | 0.835938i | \(-0.315076\pi\) | |||||||
\(938\) | 4.85641 | + | 2.80385i | 0.158567 | + | 0.0915489i | ||||
\(939\) | 42.6962 | − | 24.6506i | 1.39334 | − | 0.804443i | ||||
\(940\) | 72.1051 | + | 19.3205i | 2.35181 | + | 0.630165i | ||||
\(941\) | −12.1962 | − | 3.26795i | −0.397583 | − | 0.106532i | 0.0544870 | − | 0.998514i | \(-0.482648\pi\) |
−0.452070 | + | 0.891982i | \(0.649314\pi\) | |||||||
\(942\) | 6.00000 | − | 10.3923i | 0.195491 | − | 0.338600i | ||||
\(943\) | 1.90192 | − | 3.29423i | 0.0619352 | − | 0.107275i | ||||
\(944\) | 14.5359 | + | 14.5359i | 0.473103 | + | 0.473103i | ||||
\(945\) | 10.3923 | − | 10.3923i | 0.338062 | − | 0.338062i | ||||
\(946\) | 3.78461 | − | 3.78461i | 0.123048 | − | 0.123048i | ||||
\(947\) | −4.01666 | − | 14.9904i | −0.130524 | − | 0.487122i | 0.869452 | − | 0.494017i | \(-0.164472\pi\) |
−0.999976 | + | 0.00689497i | \(0.997805\pi\) | |||||||
\(948\) | −36.0000 | − | 20.7846i | −1.16923 | − | 0.675053i | ||||
\(949\) | −15.9019 | + | 59.3468i | −0.516198 | + | 1.92648i | ||||
\(950\) | −10.9019 | + | 6.29423i | −0.353705 | + | 0.204212i | ||||
\(951\) | 54.5429 | + | 14.6147i | 1.76868 | + | 0.473915i | ||||
\(952\) | 4.53590 | − | 1.21539i | 0.147009 | − | 0.0393910i | ||||
\(953\) | 59.1051i | 1.91460i | 0.289092 | + | 0.957301i | \(0.406647\pi\) | ||||
−0.289092 | + | 0.957301i | \(0.593353\pi\) | |||||||
\(954\) | − | 3.21539i | − | 0.104102i | ||||||
\(955\) | −38.3923 | − | 38.3923i | −1.24235 | − | 1.24235i | ||||
\(956\) | −45.3731 | − | 26.1962i | −1.46747 | − | 0.847244i | ||||
\(957\) | −12.5885 | −0.406927 | ||||||||
\(958\) | −9.39230 | + | 35.0526i | −0.303452 | + | 1.13250i | ||||
\(959\) | −6.02628 | − | 10.4378i | −0.194599 | − | 0.337055i | ||||
\(960\) | 37.8564 | − | 37.8564i | 1.22181 | − | 1.22181i | ||||
\(961\) | −12.3564 | + | 21.4019i | −0.398594 | + | 0.690385i | ||||
\(962\) | −11.3205 | − | 11.3205i | −0.364988 | − | 0.364988i | ||||
\(963\) | −14.8135 | + | 55.2846i | −0.477357 | + | 1.78152i | ||||
\(964\) | 25.6077i | 0.824768i | ||||||||
\(965\) | −68.1769 | + | 18.2679i | −2.19469 | + | 0.588066i | ||||
\(966\) | 0.588457 | − | 2.19615i | 0.0189333 | − | 0.0706600i | ||||
\(967\) | 9.16987 | − | 5.29423i | 0.294883 | − | 0.170251i | −0.345259 | − | 0.938508i | \(-0.612209\pi\) |
0.640142 | + | 0.768257i | \(0.278876\pi\) | |||||||
\(968\) | 1.60770 | − | 6.00000i | 0.0516733 | − | 0.192847i | ||||
\(969\) | 0.911543 | + | 3.40192i | 0.0292830 | + | 0.109286i | ||||
\(970\) | −39.1244 | − | 22.5885i | −1.25621 | − | 0.725272i | ||||
\(971\) | 22.4641 | + | 22.4641i | 0.720907 | + | 0.720907i | 0.968790 | − | 0.247883i | \(-0.0797348\pi\) |
−0.247883 | + | 0.968790i | \(0.579735\pi\) | |||||||
\(972\) | −27.0000 | − | 15.5885i | −0.866025 | − | 0.500000i | ||||
\(973\) | 4.85641 | − | 4.85641i | 0.155689 | − | 0.155689i | ||||
\(974\) | 5.92820 | + | 22.1244i | 0.189952 | + | 0.708910i | ||||
\(975\) | 104.863 | − | 28.0981i | 3.35832 | − | 0.899859i | ||||
\(976\) | 12.0000 | + | 3.21539i | 0.384111 | + | 0.102922i | ||||
\(977\) | −9.93782 | − | 17.2128i | −0.317939 | − | 0.550687i | 0.662119 | − | 0.749399i | \(-0.269657\pi\) |
−0.980058 | + | 0.198712i | \(0.936324\pi\) | |||||||
\(978\) | 12.1244 | + | 21.0000i | 0.387694 | + | 0.671506i | ||||
\(979\) | 1.53590 | + | 5.73205i | 0.0490875 | + | 0.183197i | ||||
\(980\) | −35.3205 | + | 35.3205i | −1.12827 | + | 1.12827i | ||||
\(981\) | −29.7846 | − | 7.98076i | −0.950949 | − | 0.254806i | ||||
\(982\) | 37.6603i | 1.20179i | ||||||||
\(983\) | −13.8564 | − | 8.00000i | −0.441951 | − | 0.255160i | 0.262474 | − | 0.964939i | \(-0.415462\pi\) |
−0.704425 | + | 0.709779i | \(0.748795\pi\) | |||||||
\(984\) | −10.3923 | − | 10.3923i | −0.331295 | − | 0.331295i | ||||
\(985\) | −17.3205 | + | 10.0000i | −0.551877 | + | 0.318626i | ||||
\(986\) | 3.92820 | + | 6.80385i | 0.125099 | + | 0.216679i | ||||
\(987\) | − | 12.2487i | − | 0.389881i | ||||||
\(988\) | −5.66025 | + | 9.80385i | −0.180077 | + | 0.311902i | ||||
\(989\) | −1.14359 | + | 1.14359i | −0.0363642 | + | 0.0363642i | ||||
\(990\) | 34.3923 | − | 34.3923i | 1.09306 | − | 1.09306i | ||||
\(991\) | −32.6410 | −1.03688 | −0.518438 | − | 0.855115i | \(-0.673486\pi\) | ||||
−0.518438 | + | 0.855115i | \(0.673486\pi\) | |||||||
\(992\) | 40.7846 | − | 10.9282i | 1.29491 | − | 0.346971i | ||||
\(993\) | 8.83013 | − | 32.9545i | 0.280216 | − | 1.04578i | ||||
\(994\) | 2.92820 | − | 10.9282i | 0.0928770 | − | 0.346622i | ||||
\(995\) | −3.26795 | − | 0.875644i | −0.103601 | − | 0.0277598i | ||||
\(996\) | −4.73205 | + | 1.26795i | −0.149941 | + | 0.0401765i | ||||
\(997\) | 32.1244 | − | 8.60770i | 1.01739 | − | 0.272608i | 0.288675 | − | 0.957427i | \(-0.406785\pi\) |
0.728713 | + | 0.684819i | \(0.240119\pi\) | |||||||
\(998\) | −9.26795 | −0.293372 | ||||||||
\(999\) | 6.58846 | + | 6.58846i | 0.208450 | + | 0.208450i |
(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 | 144.2.x.c.133.1 | yes | 4 | |
3.2 | odd | 2 | 432.2.y.b.181.1 | 4 | |||
4.3 | odd | 2 | 576.2.bb.c.241.1 | 4 | |||
9.4 | even | 3 | 144.2.x.b.85.1 | yes | 4 | ||
9.5 | odd | 6 | 432.2.y.c.37.1 | 4 | |||
12.11 | even | 2 | 1728.2.bc.a.1585.1 | 4 | |||
16.3 | odd | 4 | 576.2.bb.d.529.1 | 4 | |||
16.13 | even | 4 | 144.2.x.b.61.1 | ✓ | 4 | ||
36.23 | even | 6 | 1728.2.bc.d.1009.1 | 4 | |||
36.31 | odd | 6 | 576.2.bb.d.49.1 | 4 | |||
48.29 | odd | 4 | 432.2.y.c.397.1 | 4 | |||
48.35 | even | 4 | 1728.2.bc.d.721.1 | 4 | |||
144.13 | even | 12 | inner | 144.2.x.c.13.1 | yes | 4 | |
144.67 | odd | 12 | 576.2.bb.c.337.1 | 4 | |||
144.77 | odd | 12 | 432.2.y.b.253.1 | 4 | |||
144.131 | even | 12 | 1728.2.bc.a.145.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.b.61.1 | ✓ | 4 | 16.13 | even | 4 | ||
144.2.x.b.85.1 | yes | 4 | 9.4 | even | 3 | ||
144.2.x.c.13.1 | yes | 4 | 144.13 | even | 12 | inner | |
144.2.x.c.133.1 | yes | 4 | 1.1 | even | 1 | trivial | |
432.2.y.b.181.1 | 4 | 3.2 | odd | 2 | |||
432.2.y.b.253.1 | 4 | 144.77 | odd | 12 | |||
432.2.y.c.37.1 | 4 | 9.5 | odd | 6 | |||
432.2.y.c.397.1 | 4 | 48.29 | odd | 4 | |||
576.2.bb.c.241.1 | 4 | 4.3 | odd | 2 | |||
576.2.bb.c.337.1 | 4 | 144.67 | odd | 12 | |||
576.2.bb.d.49.1 | 4 | 36.31 | odd | 6 | |||
576.2.bb.d.529.1 | 4 | 16.3 | odd | 4 | |||
1728.2.bc.a.145.1 | 4 | 144.131 | even | 12 | |||
1728.2.bc.a.1585.1 | 4 | 12.11 | even | 2 | |||
1728.2.bc.d.721.1 | 4 | 48.35 | even | 4 | |||
1728.2.bc.d.1009.1 | 4 | 36.23 | even | 6 |