Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(23,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([9, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.r (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: | \(2.95446487479\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 347.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.347 |
Dual form | 370.2.r.a.193.1 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0.500000 | − | 1.86603i | 0.288675 | − | 1.07735i | −0.657437 | − | 0.753510i | \(-0.728359\pi\) |
0.946112 | − | 0.323840i | \(-0.104974\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.23205 | + | 1.86603i | −0.550990 | + | 0.834512i | ||||
\(6\) | −1.36603 | + | 1.36603i | −0.557678 | + | 0.557678i | ||||
\(7\) | −0.732051 | + | 2.73205i | −0.276689 | + | 1.03262i | 0.678012 | + | 0.735051i | \(0.262842\pi\) |
−0.954701 | + | 0.297567i | \(0.903825\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.633975 | − | 0.366025i | −0.211325 | − | 0.122008i | ||||
\(10\) | 2.00000 | − | 1.00000i | 0.632456 | − | 0.316228i | ||||
\(11\) | 2.00000i | 0.603023i | 0.953463 | + | 0.301511i | \(0.0974911\pi\) | ||||
−0.953463 | + | 0.301511i | \(0.902509\pi\) | |||||||
\(12\) | 1.86603 | − | 0.500000i | 0.538675 | − | 0.144338i | ||||
\(13\) | −2.13397 | + | 1.23205i | −0.591858 | + | 0.341709i | −0.765832 | − | 0.643041i | \(-0.777673\pi\) |
0.173974 | + | 0.984750i | \(0.444339\pi\) | |||||||
\(14\) | 2.00000 | − | 2.00000i | 0.534522 | − | 0.534522i | ||||
\(15\) | 2.86603 | + | 3.23205i | 0.740005 | + | 0.834512i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.09808 | + | 5.36603i | −0.751394 | + | 1.30145i | 0.195753 | + | 0.980653i | \(0.437285\pi\) |
−0.947147 | + | 0.320799i | \(0.896049\pi\) | |||||||
\(18\) | 0.366025 | + | 0.633975i | 0.0862730 | + | 0.149429i | ||||
\(19\) | −1.63397 | + | 6.09808i | −0.374859 | + | 1.39899i | 0.478691 | + | 0.877984i | \(0.341112\pi\) |
−0.853550 | + | 0.521011i | \(0.825555\pi\) | |||||||
\(20\) | −2.23205 | − | 0.133975i | −0.499102 | − | 0.0299576i | ||||
\(21\) | 4.73205 | + | 2.73205i | 1.03262 | + | 0.596182i | ||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | −1.86603 | − | 0.500000i | −0.380901 | − | 0.102062i | ||||
\(25\) | −1.96410 | − | 4.59808i | −0.392820 | − | 0.919615i | ||||
\(26\) | 2.46410 | 0.483250 | ||||||||
\(27\) | 3.09808 | − | 3.09808i | 0.596225 | − | 0.596225i | ||||
\(28\) | −2.73205 | + | 0.732051i | −0.516309 | + | 0.138345i | ||||
\(29\) | 4.73205 | − | 4.73205i | 0.878720 | − | 0.878720i | −0.114682 | − | 0.993402i | \(-0.536585\pi\) |
0.993402 | + | 0.114682i | \(0.0365850\pi\) | |||||||
\(30\) | −0.866025 | − | 4.23205i | −0.158114 | − | 0.772663i | ||||
\(31\) | 6.83013 | + | 6.83013i | 1.22673 | + | 1.22673i | 0.965195 | + | 0.261532i | \(0.0842278\pi\) |
0.261532 | + | 0.965195i | \(0.415772\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 3.73205 | + | 1.00000i | 0.649667 | + | 0.174078i | ||||
\(34\) | 5.36603 | − | 3.09808i | 0.920266 | − | 0.531316i | ||||
\(35\) | −4.19615 | − | 4.73205i | −0.709279 | − | 0.799863i | ||||
\(36\) | − | 0.732051i | − | 0.122008i | ||||||
\(37\) | 2.59808 | − | 5.50000i | 0.427121 | − | 0.904194i | ||||
\(38\) | 4.46410 | − | 4.46410i | 0.724173 | − | 0.724173i | ||||
\(39\) | 1.23205 | + | 4.59808i | 0.197286 | + | 0.736281i | ||||
\(40\) | 1.86603 | + | 1.23205i | 0.295045 | + | 0.194804i | ||||
\(41\) | −5.59808 | + | 3.23205i | −0.874273 | + | 0.504762i | −0.868766 | − | 0.495223i | \(-0.835086\pi\) |
−0.00550690 | + | 0.999985i | \(0.501753\pi\) | |||||||
\(42\) | −2.73205 | − | 4.73205i | −0.421565 | − | 0.730171i | ||||
\(43\) | 11.0000i | 1.67748i | 0.544529 | + | 0.838742i | \(0.316708\pi\) | ||||
−0.544529 | + | 0.838742i | \(0.683292\pi\) | |||||||
\(44\) | −1.73205 | + | 1.00000i | −0.261116 | + | 0.150756i | ||||
\(45\) | 1.46410 | − | 0.732051i | 0.218255 | − | 0.109128i | ||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | −6.19615 | − | 6.19615i | −0.903802 | − | 0.903802i | 0.0919609 | − | 0.995763i | \(-0.470687\pi\) |
−0.995763 | + | 0.0919609i | \(0.970687\pi\) | |||||||
\(48\) | 1.36603 | + | 1.36603i | 0.197169 | + | 0.197169i | ||||
\(49\) | −0.866025 | − | 0.500000i | −0.123718 | − | 0.0714286i | ||||
\(50\) | −0.598076 | + | 4.96410i | −0.0845807 | + | 0.702030i | ||||
\(51\) | 8.46410 | + | 8.46410i | 1.18521 | + | 1.18521i | ||||
\(52\) | −2.13397 | − | 1.23205i | −0.295929 | − | 0.170855i | ||||
\(53\) | −1.30385 | − | 4.86603i | −0.179097 | − | 0.668400i | −0.995817 | − | 0.0913660i | \(-0.970877\pi\) |
0.816720 | − | 0.577034i | \(-0.195790\pi\) | |||||||
\(54\) | −4.23205 | + | 1.13397i | −0.575909 | + | 0.154314i | ||||
\(55\) | −3.73205 | − | 2.46410i | −0.503230 | − | 0.332259i | ||||
\(56\) | 2.73205 | + | 0.732051i | 0.365086 | + | 0.0978244i | ||||
\(57\) | 10.5622 | + | 6.09808i | 1.39899 | + | 0.807710i | ||||
\(58\) | −6.46410 | + | 1.73205i | −0.848778 | + | 0.227429i | ||||
\(59\) | −3.09808 | + | 0.830127i | −0.403335 | + | 0.108073i | −0.454783 | − | 0.890602i | \(-0.650283\pi\) |
0.0514477 | + | 0.998676i | \(0.483616\pi\) | |||||||
\(60\) | −1.36603 | + | 4.09808i | −0.176353 | + | 0.529059i | ||||
\(61\) | 0.464102 | − | 1.73205i | 0.0594221 | − | 0.221766i | −0.929829 | − | 0.367991i | \(-0.880046\pi\) |
0.989251 | + | 0.146225i | \(0.0467123\pi\) | |||||||
\(62\) | −2.50000 | − | 9.33013i | −0.317500 | − | 1.18493i | ||||
\(63\) | 1.46410 | − | 1.46410i | 0.184459 | − | 0.184459i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.330127 | − | 5.50000i | 0.0409472 | − | 0.682191i | ||||
\(66\) | −2.73205 | − | 2.73205i | −0.336292 | − | 0.336292i | ||||
\(67\) | 5.36603 | + | 1.43782i | 0.655564 | + | 0.175658i | 0.571243 | − | 0.820781i | \(-0.306461\pi\) |
0.0843209 | + | 0.996439i | \(0.473128\pi\) | |||||||
\(68\) | −6.19615 | −0.751394 | ||||||||
\(69\) | −11.1962 | − | 3.00000i | −1.34786 | − | 0.361158i | ||||
\(70\) | 1.26795 | + | 6.19615i | 0.151549 | + | 0.740582i | ||||
\(71\) | 1.46410 | + | 2.53590i | 0.173757 | + | 0.300956i | 0.939730 | − | 0.341916i | \(-0.111076\pi\) |
−0.765973 | + | 0.642872i | \(0.777743\pi\) | |||||||
\(72\) | −0.366025 | + | 0.633975i | −0.0431365 | + | 0.0747146i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | −5.00000 | + | 3.46410i | −0.581238 | + | 0.402694i | ||||
\(75\) | −9.56218 | + | 1.36603i | −1.10415 | + | 0.157735i | ||||
\(76\) | −6.09808 | + | 1.63397i | −0.699497 | + | 0.187430i | ||||
\(77\) | −5.46410 | − | 1.46410i | −0.622692 | − | 0.166850i | ||||
\(78\) | 1.23205 | − | 4.59808i | 0.139502 | − | 0.520630i | ||||
\(79\) | −1.83013 | + | 6.83013i | −0.205905 | + | 0.768449i | 0.783266 | + | 0.621686i | \(0.213552\pi\) |
−0.989172 | + | 0.146763i | \(0.953115\pi\) | |||||||
\(80\) | −1.00000 | − | 2.00000i | −0.111803 | − | 0.223607i | ||||
\(81\) | −5.33013 | − | 9.23205i | −0.592236 | − | 1.02578i | ||||
\(82\) | 6.46410 | 0.713841 | ||||||||
\(83\) | 4.16987 | + | 15.5622i | 0.457703 | + | 1.70817i | 0.680017 | + | 0.733196i | \(0.261972\pi\) |
−0.222314 | + | 0.974975i | \(0.571361\pi\) | |||||||
\(84\) | 5.46410i | 0.596182i | ||||||||
\(85\) | −6.19615 | − | 12.3923i | −0.672067 | − | 1.34413i | ||||
\(86\) | 5.50000 | − | 9.52628i | 0.593080 | − | 1.02725i | ||||
\(87\) | −6.46410 | − | 11.1962i | −0.693024 | − | 1.20035i | ||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | −0.437822 | − | 1.63397i | −0.0464091 | − | 0.173201i | 0.938831 | − | 0.344377i | \(-0.111910\pi\) |
−0.985240 | + | 0.171176i | \(0.945243\pi\) | |||||||
\(90\) | −1.63397 | − | 0.0980762i | −0.172236 | − | 0.0103381i | ||||
\(91\) | −1.80385 | − | 6.73205i | −0.189095 | − | 0.705711i | ||||
\(92\) | 5.19615 | − | 3.00000i | 0.541736 | − | 0.312772i | ||||
\(93\) | 16.1603 | − | 9.33013i | 1.67574 | − | 0.967489i | ||||
\(94\) | 2.26795 | + | 8.46410i | 0.233921 | + | 0.873005i | ||||
\(95\) | −9.36603 | − | 10.5622i | −0.960934 | − | 1.08366i | ||||
\(96\) | −0.500000 | − | 1.86603i | −0.0510310 | − | 0.190450i | ||||
\(97\) | −1.46410 | −0.148657 | −0.0743285 | − | 0.997234i | \(-0.523681\pi\) | ||||
−0.0743285 | + | 0.997234i | \(0.523681\pi\) | |||||||
\(98\) | 0.500000 | + | 0.866025i | 0.0505076 | + | 0.0874818i | ||||
\(99\) | 0.732051 | − | 1.26795i | 0.0735739 | − | 0.127434i | ||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | 0.196152i | 0.0195179i | 0.999952 | + | 0.00975895i | \(0.00310642\pi\) | ||||
−0.999952 | + | 0.00975895i | \(0.996894\pi\) | |||||||
\(102\) | −3.09808 | − | 11.5622i | −0.306755 | − | 1.14483i | ||||
\(103\) | −6.19615 | −0.610525 | −0.305263 | − | 0.952268i | \(-0.598744\pi\) | ||||
−0.305263 | + | 0.952268i | \(0.598744\pi\) | |||||||
\(104\) | 1.23205 | + | 2.13397i | 0.120813 | + | 0.209253i | ||||
\(105\) | −10.9282 | + | 5.46410i | −1.06648 | + | 0.533242i | ||||
\(106\) | −1.30385 | + | 4.86603i | −0.126641 | + | 0.472630i | ||||
\(107\) | 3.59808 | − | 13.4282i | 0.347839 | − | 1.29815i | −0.541421 | − | 0.840752i | \(-0.682113\pi\) |
0.889260 | − | 0.457402i | \(-0.151220\pi\) | |||||||
\(108\) | 4.23205 | + | 1.13397i | 0.407229 | + | 0.109117i | ||||
\(109\) | 1.00000 | − | 0.267949i | 0.0957826 | − | 0.0256649i | −0.210609 | − | 0.977570i | \(-0.567545\pi\) |
0.306392 | + | 0.951905i | \(0.400878\pi\) | |||||||
\(110\) | 2.00000 | + | 4.00000i | 0.190693 | + | 0.381385i | ||||
\(111\) | −8.96410 | − | 7.59808i | −0.850835 | − | 0.721177i | ||||
\(112\) | −2.00000 | − | 2.00000i | −0.188982 | − | 0.188982i | ||||
\(113\) | −3.00000 | + | 5.19615i | −0.282216 | + | 0.488813i | −0.971930 | − | 0.235269i | \(-0.924403\pi\) |
0.689714 | + | 0.724082i | \(0.257736\pi\) | |||||||
\(114\) | −6.09808 | − | 10.5622i | −0.571137 | − | 0.989239i | ||||
\(115\) | 11.1962 | + | 7.39230i | 1.04405 | + | 0.689336i | ||||
\(116\) | 6.46410 | + | 1.73205i | 0.600177 | + | 0.160817i | ||||
\(117\) | 1.80385 | 0.166766 | ||||||||
\(118\) | 3.09808 | + | 0.830127i | 0.285201 | + | 0.0764194i | ||||
\(119\) | −12.3923 | − | 12.3923i | −1.13600 | − | 1.13600i | ||||
\(120\) | 3.23205 | − | 2.86603i | 0.295045 | − | 0.261631i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −1.26795 | + | 1.26795i | −0.114795 | + | 0.114795i | ||||
\(123\) | 3.23205 | + | 12.0622i | 0.291424 | + | 1.08761i | ||||
\(124\) | −2.50000 | + | 9.33013i | −0.224507 | + | 0.837870i | ||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | −2.00000 | + | 0.535898i | −0.178174 | + | 0.0477416i | ||||
\(127\) | −8.83013 | + | 2.36603i | −0.783547 | + | 0.209951i | −0.628348 | − | 0.777932i | \(-0.716269\pi\) |
−0.155199 | + | 0.987883i | \(0.549602\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 20.5263 | + | 5.50000i | 1.80724 | + | 0.484248i | ||||
\(130\) | −3.03590 | + | 4.59808i | −0.266266 | + | 0.403278i | ||||
\(131\) | 0.732051 | − | 0.196152i | 0.0639596 | − | 0.0171379i | −0.226697 | − | 0.973965i | \(-0.572793\pi\) |
0.290657 | + | 0.956827i | \(0.406126\pi\) | |||||||
\(132\) | 1.00000 | + | 3.73205i | 0.0870388 | + | 0.324833i | ||||
\(133\) | −15.4641 | − | 8.92820i | −1.34091 | − | 0.774173i | ||||
\(134\) | −3.92820 | − | 3.92820i | −0.339345 | − | 0.339345i | ||||
\(135\) | 1.96410 | + | 9.59808i | 0.169043 | + | 0.826071i | ||||
\(136\) | 5.36603 | + | 3.09808i | 0.460133 | + | 0.265658i | ||||
\(137\) | 2.00000 | + | 2.00000i | 0.170872 | + | 0.170872i | 0.787362 | − | 0.616491i | \(-0.211446\pi\) |
−0.616491 | + | 0.787362i | \(0.711446\pi\) | |||||||
\(138\) | 8.19615 | + | 8.19615i | 0.697703 | + | 0.697703i | ||||
\(139\) | 5.46410 | − | 9.46410i | 0.463459 | − | 0.802735i | −0.535671 | − | 0.844426i | \(-0.679941\pi\) |
0.999131 | + | 0.0416919i | \(0.0132748\pi\) | |||||||
\(140\) | 2.00000 | − | 6.00000i | 0.169031 | − | 0.507093i | ||||
\(141\) | −14.6603 | + | 8.46410i | −1.23462 | + | 0.712806i | ||||
\(142\) | − | 2.92820i | − | 0.245729i | ||||||
\(143\) | −2.46410 | − | 4.26795i | −0.206059 | − | 0.356904i | ||||
\(144\) | 0.633975 | − | 0.366025i | 0.0528312 | − | 0.0305021i | ||||
\(145\) | 3.00000 | + | 14.6603i | 0.249136 | + | 1.21747i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.36603 | + | 1.36603i | −0.112668 | + | 0.112668i | ||||
\(148\) | 6.06218 | − | 0.500000i | 0.498308 | − | 0.0410997i | ||||
\(149\) | − | 22.7321i | − | 1.86228i | −0.364659 | − | 0.931141i | \(-0.618814\pi\) | ||
0.364659 | − | 0.931141i | \(-0.381186\pi\) | |||||||
\(150\) | 8.96410 | + | 3.59808i | 0.731916 | + | 0.293782i | ||||
\(151\) | −2.76795 | + | 1.59808i | −0.225253 | + | 0.130050i | −0.608380 | − | 0.793646i | \(-0.708180\pi\) |
0.383127 | + | 0.923695i | \(0.374847\pi\) | |||||||
\(152\) | 6.09808 | + | 1.63397i | 0.494619 | + | 0.132533i | ||||
\(153\) | 3.92820 | − | 2.26795i | 0.317576 | − | 0.183353i | ||||
\(154\) | 4.00000 | + | 4.00000i | 0.322329 | + | 0.322329i | ||||
\(155\) | −21.1603 | + | 4.33013i | −1.69963 | + | 0.347804i | ||||
\(156\) | −3.36603 | + | 3.36603i | −0.269498 | + | 0.269498i | ||||
\(157\) | 19.6244 | − | 5.25833i | 1.56619 | − | 0.419660i | 0.631576 | − | 0.775314i | \(-0.282408\pi\) |
0.934618 | + | 0.355653i | \(0.115742\pi\) | |||||||
\(158\) | 5.00000 | − | 5.00000i | 0.397779 | − | 0.397779i | ||||
\(159\) | −9.73205 | −0.771802 | ||||||||
\(160\) | −0.133975 | + | 2.23205i | −0.0105916 | + | 0.176459i | ||||
\(161\) | 16.3923 | + | 4.39230i | 1.29189 | + | 0.346162i | ||||
\(162\) | 10.6603i | 0.837549i | ||||||||
\(163\) | 1.76795 | − | 3.06218i | 0.138476 | − | 0.239848i | −0.788444 | − | 0.615107i | \(-0.789113\pi\) |
0.926920 | + | 0.375259i | \(0.122446\pi\) | |||||||
\(164\) | −5.59808 | − | 3.23205i | −0.437136 | − | 0.252381i | ||||
\(165\) | −6.46410 | + | 5.73205i | −0.503230 | + | 0.446240i | ||||
\(166\) | 4.16987 | − | 15.5622i | 0.323645 | − | 1.20786i | ||||
\(167\) | 10.3660 | + | 17.9545i | 0.802147 | + | 1.38936i | 0.918200 | + | 0.396117i | \(0.129642\pi\) |
−0.116053 | + | 0.993243i | \(0.537024\pi\) | |||||||
\(168\) | 2.73205 | − | 4.73205i | 0.210782 | − | 0.365086i | ||||
\(169\) | −3.46410 | + | 6.00000i | −0.266469 | + | 0.461538i | ||||
\(170\) | −0.830127 | + | 13.8301i | −0.0636678 | + | 1.06072i | ||||
\(171\) | 3.26795 | − | 3.26795i | 0.249906 | − | 0.249906i | ||||
\(172\) | −9.52628 | + | 5.50000i | −0.726372 | + | 0.419371i | ||||
\(173\) | 23.4904 | − | 6.29423i | 1.78594 | − | 0.478541i | 0.794295 | − | 0.607532i | \(-0.207841\pi\) |
0.991646 | + | 0.128991i | \(0.0411739\pi\) | |||||||
\(174\) | 12.9282i | 0.980085i | ||||||||
\(175\) | 14.0000 | − | 2.00000i | 1.05830 | − | 0.151186i | ||||
\(176\) | −1.73205 | − | 1.00000i | −0.130558 | − | 0.0753778i | ||||
\(177\) | 6.19615i | 0.465731i | ||||||||
\(178\) | −0.437822 | + | 1.63397i | −0.0328162 | + | 0.122472i | ||||
\(179\) | −10.3923 | + | 10.3923i | −0.776757 | + | 0.776757i | −0.979278 | − | 0.202521i | \(-0.935087\pi\) |
0.202521 | + | 0.979278i | \(0.435087\pi\) | |||||||
\(180\) | 1.36603 | + | 0.901924i | 0.101818 | + | 0.0672254i | ||||
\(181\) | 6.90192 | + | 11.9545i | 0.513016 | + | 0.888570i | 0.999886 | + | 0.0150953i | \(0.00480517\pi\) |
−0.486870 | + | 0.873474i | \(0.661861\pi\) | |||||||
\(182\) | −1.80385 | + | 6.73205i | −0.133710 | + | 0.499013i | ||||
\(183\) | −3.00000 | − | 1.73205i | −0.221766 | − | 0.128037i | ||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | 7.06218 | + | 11.6244i | 0.519222 | + | 0.854640i | ||||
\(186\) | −18.6603 | −1.36824 | ||||||||
\(187\) | −10.7321 | − | 6.19615i | −0.784805 | − | 0.453108i | ||||
\(188\) | 2.26795 | − | 8.46410i | 0.165407 | − | 0.617308i | ||||
\(189\) | 6.19615 | + | 10.7321i | 0.450704 | + | 0.780642i | ||||
\(190\) | 2.83013 | + | 13.8301i | 0.205319 | + | 1.00334i | ||||
\(191\) | −1.83013 | + | 1.83013i | −0.132423 | + | 0.132423i | −0.770212 | − | 0.637788i | \(-0.779849\pi\) |
0.637788 | + | 0.770212i | \(0.279849\pi\) | |||||||
\(192\) | −0.500000 | + | 1.86603i | −0.0360844 | + | 0.134669i | ||||
\(193\) | 0.339746i | 0.0244554i | 0.999925 | + | 0.0122277i | \(0.00389230\pi\) | ||||
−0.999925 | + | 0.0122277i | \(0.996108\pi\) | |||||||
\(194\) | 1.26795 | + | 0.732051i | 0.0910334 | + | 0.0525582i | ||||
\(195\) | −10.0981 | − | 3.36603i | −0.723138 | − | 0.241046i | ||||
\(196\) | − | 1.00000i | − | 0.0714286i | ||||||
\(197\) | 7.86603 | − | 2.10770i | 0.560431 | − | 0.150167i | 0.0325267 | − | 0.999471i | \(-0.489645\pi\) |
0.527904 | + | 0.849304i | \(0.322978\pi\) | |||||||
\(198\) | −1.26795 | + | 0.732051i | −0.0901092 | + | 0.0520246i | ||||
\(199\) | 14.7583 | − | 14.7583i | 1.04619 | − | 1.04619i | 0.0473100 | − | 0.998880i | \(-0.484935\pi\) |
0.998880 | − | 0.0473100i | \(-0.0150649\pi\) | |||||||
\(200\) | −4.59808 | + | 1.96410i | −0.325133 | + | 0.138883i | ||||
\(201\) | 5.36603 | − | 9.29423i | 0.378490 | − | 0.655564i | ||||
\(202\) | 0.0980762 | − | 0.169873i | 0.00690062 | − | 0.0119522i | ||||
\(203\) | 9.46410 | + | 16.3923i | 0.664250 | + | 1.15051i | ||||
\(204\) | −3.09808 | + | 11.5622i | −0.216909 | + | 0.809514i | ||||
\(205\) | 0.866025 | − | 14.4282i | 0.0604858 | − | 1.00771i | ||||
\(206\) | 5.36603 | + | 3.09808i | 0.373869 | + | 0.215853i | ||||
\(207\) | −2.19615 | + | 3.80385i | −0.152643 | + | 0.264386i | ||||
\(208\) | − | 2.46410i | − | 0.170855i | ||||||
\(209\) | −12.1962 | − | 3.26795i | −0.843626 | − | 0.226049i | ||||
\(210\) | 12.1962 | + | 0.732051i | 0.841614 | + | 0.0505163i | ||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 3.56218 | − | 3.56218i | 0.244651 | − | 0.244651i | ||||
\(213\) | 5.46410 | − | 1.46410i | 0.374394 | − | 0.100319i | ||||
\(214\) | −9.83013 | + | 9.83013i | −0.671974 | + | 0.671974i | ||||
\(215\) | −20.5263 | − | 13.5526i | −1.39988 | − | 0.924277i | ||||
\(216\) | −3.09808 | − | 3.09808i | −0.210797 | − | 0.210797i | ||||
\(217\) | −23.6603 | + | 13.6603i | −1.60616 | + | 0.927318i | ||||
\(218\) | −1.00000 | − | 0.267949i | −0.0677285 | − | 0.0181478i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.267949 | − | 4.46410i | 0.0180651 | − | 0.300970i | ||||
\(221\) | − | 15.2679i | − | 1.02703i | ||||||
\(222\) | 3.96410 | + | 11.0622i | 0.266053 | + | 0.742445i | ||||
\(223\) | −12.9282 | + | 12.9282i | −0.865737 | + | 0.865737i | −0.991997 | − | 0.126261i | \(-0.959702\pi\) |
0.126261 | + | 0.991997i | \(0.459702\pi\) | |||||||
\(224\) | 0.732051 | + | 2.73205i | 0.0489122 | + | 0.182543i | ||||
\(225\) | −0.437822 | + | 3.63397i | −0.0291881 | + | 0.242265i | ||||
\(226\) | 5.19615 | − | 3.00000i | 0.345643 | − | 0.199557i | ||||
\(227\) | −1.33013 | − | 2.30385i | −0.0882836 | − | 0.152912i | 0.818502 | − | 0.574504i | \(-0.194805\pi\) |
−0.906786 | + | 0.421592i | \(0.861472\pi\) | |||||||
\(228\) | 12.1962i | 0.807710i | ||||||||
\(229\) | 15.2942 | − | 8.83013i | 1.01067 | − | 0.583511i | 0.0992830 | − | 0.995059i | \(-0.468345\pi\) |
0.911388 | + | 0.411548i | \(0.135012\pi\) | |||||||
\(230\) | −6.00000 | − | 12.0000i | −0.395628 | − | 0.791257i | ||||
\(231\) | −5.46410 | + | 9.46410i | −0.359511 | + | 0.622692i | ||||
\(232\) | −4.73205 | − | 4.73205i | −0.310674 | − | 0.310674i | ||||
\(233\) | −15.8564 | − | 15.8564i | −1.03879 | − | 1.03879i | −0.999217 | − | 0.0395710i | \(-0.987401\pi\) |
−0.0395710 | − | 0.999217i | \(-0.512599\pi\) | |||||||
\(234\) | −1.56218 | − | 0.901924i | −0.102123 | − | 0.0589606i | ||||
\(235\) | 19.1962 | − | 3.92820i | 1.25222 | − | 0.256248i | ||||
\(236\) | −2.26795 | − | 2.26795i | −0.147631 | − | 0.147631i | ||||
\(237\) | 11.8301 | + | 6.83013i | 0.768449 | + | 0.443664i | ||||
\(238\) | 4.53590 | + | 16.9282i | 0.294019 | + | 1.09729i | ||||
\(239\) | 14.8301 | − | 3.97372i | 0.959281 | − | 0.257039i | 0.254985 | − | 0.966945i | \(-0.417929\pi\) |
0.704296 | + | 0.709906i | \(0.251263\pi\) | |||||||
\(240\) | −4.23205 | + | 0.866025i | −0.273178 | + | 0.0559017i | ||||
\(241\) | 18.0263 | + | 4.83013i | 1.16117 | + | 0.311136i | 0.787435 | − | 0.616398i | \(-0.211409\pi\) |
0.373740 | + | 0.927534i | \(0.378075\pi\) | |||||||
\(242\) | −6.06218 | − | 3.50000i | −0.389692 | − | 0.224989i | ||||
\(243\) | −7.19615 | + | 1.92820i | −0.461633 | + | 0.123694i | ||||
\(244\) | 1.73205 | − | 0.464102i | 0.110883 | − | 0.0297111i | ||||
\(245\) | 2.00000 | − | 1.00000i | 0.127775 | − | 0.0638877i | ||||
\(246\) | 3.23205 | − | 12.0622i | 0.206068 | − | 0.769056i | ||||
\(247\) | −4.02628 | − | 15.0263i | −0.256186 | − | 0.956099i | ||||
\(248\) | 6.83013 | − | 6.83013i | 0.433713 | − | 0.433713i | ||||
\(249\) | 31.1244 | 1.97243 | ||||||||
\(250\) | −8.52628 | − | 7.23205i | −0.539249 | − | 0.457395i | ||||
\(251\) | 5.73205 | + | 5.73205i | 0.361804 | + | 0.361804i | 0.864477 | − | 0.502673i | \(-0.167650\pi\) |
−0.502673 | + | 0.864477i | \(0.667650\pi\) | |||||||
\(252\) | 2.00000 | + | 0.535898i | 0.125988 | + | 0.0337584i | ||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 8.83013 | + | 2.36603i | 0.554051 | + | 0.148458i | ||||
\(255\) | −26.2224 | + | 5.36603i | −1.64211 | + | 0.336034i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −0.169873 | + | 0.294229i | −0.0105964 | + | 0.0183535i | −0.871275 | − | 0.490795i | \(-0.836706\pi\) |
0.860679 | + | 0.509149i | \(0.170040\pi\) | |||||||
\(258\) | −15.0263 | − | 15.0263i | −0.935495 | − | 0.935495i | ||||
\(259\) | 13.1244 | + | 11.1244i | 0.815508 | + | 0.691234i | ||||
\(260\) | 4.92820 | − | 2.46410i | 0.305634 | − | 0.152817i | ||||
\(261\) | −4.73205 | + | 1.26795i | −0.292907 | + | 0.0784841i | ||||
\(262\) | −0.732051 | − | 0.196152i | −0.0452262 | − | 0.0121183i | ||||
\(263\) | −0.0262794 | + | 0.0980762i | −0.00162046 | + | 0.00604764i | −0.966731 | − | 0.255794i | \(-0.917663\pi\) |
0.965111 | + | 0.261842i | \(0.0843298\pi\) | |||||||
\(264\) | 1.00000 | − | 3.73205i | 0.0615457 | − | 0.229692i | ||||
\(265\) | 10.6865 | + | 3.56218i | 0.656469 | + | 0.218823i | ||||
\(266\) | 8.92820 | + | 15.4641i | 0.547423 | + | 0.948165i | ||||
\(267\) | −3.26795 | −0.199995 | ||||||||
\(268\) | 1.43782 | + | 5.36603i | 0.0878290 | + | 0.327782i | ||||
\(269\) | − | 6.58846i | − | 0.401705i | −0.979621 | − | 0.200853i | \(-0.935629\pi\) | ||
0.979621 | − | 0.200853i | \(-0.0643712\pi\) | |||||||
\(270\) | 3.09808 | − | 9.29423i | 0.188543 | − | 0.565629i | ||||
\(271\) | 5.23205 | − | 9.06218i | 0.317824 | − | 0.550488i | −0.662209 | − | 0.749319i | \(-0.730381\pi\) |
0.980034 | + | 0.198831i | \(0.0637144\pi\) | |||||||
\(272\) | −3.09808 | − | 5.36603i | −0.187848 | − | 0.325363i | ||||
\(273\) | −13.4641 | −0.814885 | ||||||||
\(274\) | −0.732051 | − | 2.73205i | −0.0442248 | − | 0.165049i | ||||
\(275\) | 9.19615 | − | 3.92820i | 0.554549 | − | 0.236880i | ||||
\(276\) | −3.00000 | − | 11.1962i | −0.180579 | − | 0.673929i | ||||
\(277\) | −14.4282 | + | 8.33013i | −0.866907 | + | 0.500509i | −0.866319 | − | 0.499491i | \(-0.833520\pi\) |
−0.000587640 | 1.00000i | \(0.500187\pi\) | ||||||||
\(278\) | −9.46410 | + | 5.46410i | −0.567619 | + | 0.327715i | ||||
\(279\) | −1.83013 | − | 6.83013i | −0.109567 | − | 0.408909i | ||||
\(280\) | −4.73205 | + | 4.19615i | −0.282794 | + | 0.250768i | ||||
\(281\) | −0.624356 | − | 2.33013i | −0.0372459 | − | 0.139004i | 0.944799 | − | 0.327650i | \(-0.106257\pi\) |
−0.982045 | + | 0.188646i | \(0.939590\pi\) | |||||||
\(282\) | 16.9282 | 1.00806 | ||||||||
\(283\) | −6.50000 | − | 11.2583i | −0.386385 | − | 0.669238i | 0.605575 | − | 0.795788i | \(-0.292943\pi\) |
−0.991960 | + | 0.126550i | \(0.959610\pi\) | |||||||
\(284\) | −1.46410 | + | 2.53590i | −0.0868784 | + | 0.150478i | ||||
\(285\) | −24.3923 | + | 12.1962i | −1.44488 | + | 0.722438i | ||||
\(286\) | 4.92820i | 0.291411i | ||||||||
\(287\) | −4.73205 | − | 17.6603i | −0.279324 | − | 1.04245i | ||||
\(288\) | −0.732051 | −0.0431365 | ||||||||
\(289\) | −10.6962 | − | 18.5263i | −0.629185 | − | 1.08978i | ||||
\(290\) | 4.73205 | − | 14.1962i | 0.277876 | − | 0.833627i | ||||
\(291\) | −0.732051 | + | 2.73205i | −0.0429136 | + | 0.160156i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.13397 | − | 0.839746i | −0.183089 | − | 0.0490585i | 0.166110 | − | 0.986107i | \(-0.446879\pi\) |
−0.349198 | + | 0.937049i | \(0.613546\pi\) | |||||||
\(294\) | 1.86603 | − | 0.500000i | 0.108829 | − | 0.0291606i | ||||
\(295\) | 2.26795 | − | 6.80385i | 0.132045 | − | 0.396135i | ||||
\(296\) | −5.50000 | − | 2.59808i | −0.319681 | − | 0.151010i | ||||
\(297\) | 6.19615 | + | 6.19615i | 0.359537 | + | 0.359537i | ||||
\(298\) | −11.3660 | + | 19.6865i | −0.658416 | + | 1.14041i | ||||
\(299\) | 7.39230 | + | 12.8038i | 0.427508 | + | 0.740466i | ||||
\(300\) | −5.96410 | − | 7.59808i | −0.344338 | − | 0.438675i | ||||
\(301\) | −30.0526 | − | 8.05256i | −1.73220 | − | 0.464142i | ||||
\(302\) | 3.19615 | 0.183918 | ||||||||
\(303\) | 0.366025 | + | 0.0980762i | 0.0210276 | + | 0.00563433i | ||||
\(304\) | −4.46410 | − | 4.46410i | −0.256034 | − | 0.256034i | ||||
\(305\) | 2.66025 | + | 3.00000i | 0.152326 | + | 0.171780i | ||||
\(306\) | −4.53590 | −0.259300 | ||||||||
\(307\) | 15.4186 | − | 15.4186i | 0.879985 | − | 0.879985i | −0.113547 | − | 0.993533i | \(-0.536221\pi\) |
0.993533 | + | 0.113547i | \(0.0362214\pi\) | |||||||
\(308\) | −1.46410 | − | 5.46410i | −0.0834249 | − | 0.311346i | ||||
\(309\) | −3.09808 | + | 11.5622i | −0.176243 | + | 0.657749i | ||||
\(310\) | 20.4904 | + | 6.83013i | 1.16378 | + | 0.387925i | ||||
\(311\) | 15.2583 | − | 4.08846i | 0.865221 | − | 0.231835i | 0.201201 | − | 0.979550i | \(-0.435516\pi\) |
0.664020 | + | 0.747715i | \(0.268849\pi\) | |||||||
\(312\) | 4.59808 | − | 1.23205i | 0.260315 | − | 0.0697511i | ||||
\(313\) | −15.1244 | − | 8.73205i | −0.854879 | − | 0.493565i | 0.00741498 | − | 0.999973i | \(-0.497640\pi\) |
−0.862294 | + | 0.506408i | \(0.830973\pi\) | |||||||
\(314\) | −19.6244 | − | 5.25833i | −1.10747 | − | 0.296745i | ||||
\(315\) | 0.928203 | + | 4.53590i | 0.0522983 | + | 0.255569i | ||||
\(316\) | −6.83013 | + | 1.83013i | −0.384225 | + | 0.102953i | ||||
\(317\) | 7.18653 | + | 26.8205i | 0.403636 | + | 1.50639i | 0.806558 | + | 0.591155i | \(0.201328\pi\) |
−0.402922 | + | 0.915234i | \(0.632005\pi\) | |||||||
\(318\) | 8.42820 | + | 4.86603i | 0.472630 | + | 0.272873i | ||||
\(319\) | 9.46410 | + | 9.46410i | 0.529888 | + | 0.529888i | ||||
\(320\) | 1.23205 | − | 1.86603i | 0.0688737 | − | 0.104314i | ||||
\(321\) | −23.2583 | − | 13.4282i | −1.29815 | − | 0.749489i | ||||
\(322\) | −12.0000 | − | 12.0000i | −0.668734 | − | 0.668734i | ||||
\(323\) | −27.6603 | − | 27.6603i | −1.53906 | − | 1.53906i | ||||
\(324\) | 5.33013 | − | 9.23205i | 0.296118 | − | 0.512892i | ||||
\(325\) | 9.85641 | + | 7.39230i | 0.546735 | + | 0.410051i | ||||
\(326\) | −3.06218 | + | 1.76795i | −0.169598 | + | 0.0979176i | ||||
\(327\) | − | 2.00000i | − | 0.110600i | ||||||
\(328\) | 3.23205 | + | 5.59808i | 0.178460 | + | 0.309102i | ||||
\(329\) | 21.4641 | − | 12.3923i | 1.18335 | − | 0.683210i | ||||
\(330\) | 8.46410 | − | 1.73205i | 0.465933 | − | 0.0953463i | ||||
\(331\) | 0.830127 | + | 3.09808i | 0.0456279 | + | 0.170286i | 0.984980 | − | 0.172669i | \(-0.0552390\pi\) |
−0.939352 | + | 0.342954i | \(0.888572\pi\) | |||||||
\(332\) | −11.3923 | + | 11.3923i | −0.625234 | + | 0.625234i | ||||
\(333\) | −3.66025 | + | 2.53590i | −0.200581 | + | 0.138966i | ||||
\(334\) | − | 20.7321i | − | 1.13441i | ||||||
\(335\) | −9.29423 | + | 8.24167i | −0.507798 | + | 0.450291i | ||||
\(336\) | −4.73205 | + | 2.73205i | −0.258155 | + | 0.149046i | ||||
\(337\) | 7.56218 | + | 2.02628i | 0.411938 | + | 0.110378i | 0.458835 | − | 0.888521i | \(-0.348267\pi\) |
−0.0468974 | + | 0.998900i | \(0.514933\pi\) | |||||||
\(338\) | 6.00000 | − | 3.46410i | 0.326357 | − | 0.188422i | ||||
\(339\) | 8.19615 | + | 8.19615i | 0.445154 | + | 0.445154i | ||||
\(340\) | 7.63397 | − | 11.5622i | 0.414010 | − | 0.627047i | ||||
\(341\) | −13.6603 | + | 13.6603i | −0.739744 | + | 0.739744i | ||||
\(342\) | −4.46410 | + | 1.19615i | −0.241391 | + | 0.0646805i | ||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | 11.0000 | 0.593080 | ||||||||
\(345\) | 19.3923 | − | 17.1962i | 1.04405 | − | 0.925810i | ||||
\(346\) | −23.4904 | − | 6.29423i | −1.26285 | − | 0.338380i | ||||
\(347\) | 19.8564i | 1.06595i | 0.846132 | + | 0.532974i | \(0.178926\pi\) | ||||
−0.846132 | + | 0.532974i | \(0.821074\pi\) | |||||||
\(348\) | 6.46410 | − | 11.1962i | 0.346512 | − | 0.600177i | ||||
\(349\) | −31.0981 | − | 17.9545i | −1.66464 | − | 0.961081i | −0.970454 | − | 0.241288i | \(-0.922430\pi\) |
−0.694188 | − | 0.719793i | \(-0.744236\pi\) | |||||||
\(350\) | −13.1244 | − | 5.26795i | −0.701526 | − | 0.281584i | ||||
\(351\) | −2.79423 | + | 10.4282i | −0.149145 | + | 0.556616i | ||||
\(352\) | 1.00000 | + | 1.73205i | 0.0533002 | + | 0.0923186i | ||||
\(353\) | −16.3923 | + | 28.3923i | −0.872474 | + | 1.51117i | −0.0130453 | + | 0.999915i | \(0.504153\pi\) |
−0.859429 | + | 0.511255i | \(0.829181\pi\) | |||||||
\(354\) | 3.09808 | − | 5.36603i | 0.164661 | − | 0.285201i | ||||
\(355\) | −6.53590 | − | 0.392305i | −0.346889 | − | 0.0208214i | ||||
\(356\) | 1.19615 | − | 1.19615i | 0.0633960 | − | 0.0633960i | ||||
\(357\) | −29.3205 | + | 16.9282i | −1.55181 | + | 0.895936i | ||||
\(358\) | 14.1962 | − | 3.80385i | 0.750290 | − | 0.201040i | ||||
\(359\) | 3.39230i | 0.179039i | 0.995985 | + | 0.0895195i | \(0.0285331\pi\) | ||||
−0.995985 | + | 0.0895195i | \(0.971467\pi\) | |||||||
\(360\) | −0.732051 | − | 1.46410i | −0.0385825 | − | 0.0771649i | ||||
\(361\) | −18.0622 | − | 10.4282i | −0.950641 | − | 0.548853i | ||||
\(362\) | − | 13.8038i | − | 0.725514i | ||||||
\(363\) | 3.50000 | − | 13.0622i | 0.183702 | − | 0.685587i | ||||
\(364\) | 4.92820 | − | 4.92820i | 0.258308 | − | 0.258308i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.73205 | + | 3.00000i | 0.0905357 | + | 0.156813i | ||||
\(367\) | −9.32051 | + | 34.7846i | −0.486527 | + | 1.81574i | 0.0865595 | + | 0.996247i | \(0.472413\pi\) |
−0.573086 | + | 0.819495i | \(0.694254\pi\) | |||||||
\(368\) | 5.19615 | + | 3.00000i | 0.270868 | + | 0.156386i | ||||
\(369\) | 4.73205 | 0.246341 | ||||||||
\(370\) | −0.303848 | − | 13.5981i | −0.0157963 | − | 0.706930i | ||||
\(371\) | 14.2487 | 0.739756 | ||||||||
\(372\) | 16.1603 | + | 9.33013i | 0.837870 | + | 0.483745i | ||||
\(373\) | 1.37564 | − | 5.13397i | 0.0712282 | − | 0.265827i | −0.921123 | − | 0.389271i | \(-0.872727\pi\) |
0.992352 | + | 0.123443i | \(0.0393938\pi\) | |||||||
\(374\) | 6.19615 | + | 10.7321i | 0.320395 | + | 0.554941i | ||||
\(375\) | 9.23205 | − | 19.5263i | 0.476741 | − | 1.00833i | ||||
\(376\) | −6.19615 | + | 6.19615i | −0.319542 | + | 0.319542i | ||||
\(377\) | −4.26795 | + | 15.9282i | −0.219811 | + | 0.820344i | ||||
\(378\) | − | 12.3923i | − | 0.637391i | ||||||
\(379\) | 12.5885 | + | 7.26795i | 0.646626 | + | 0.373329i | 0.787162 | − | 0.616746i | \(-0.211549\pi\) |
−0.140537 | + | 0.990075i | \(0.544883\pi\) | |||||||
\(380\) | 4.46410 | − | 13.3923i | 0.229004 | − | 0.687011i | ||||
\(381\) | 17.6603i | 0.904762i | ||||||||
\(382\) | 2.50000 | − | 0.669873i | 0.127911 | − | 0.0342737i | ||||
\(383\) | 13.3923 | − | 7.73205i | 0.684315 | − | 0.395089i | −0.117164 | − | 0.993113i | \(-0.537380\pi\) |
0.801479 | + | 0.598023i | \(0.204047\pi\) | |||||||
\(384\) | 1.36603 | − | 1.36603i | 0.0697097 | − | 0.0697097i | ||||
\(385\) | 9.46410 | − | 8.39230i | 0.482335 | − | 0.427711i | ||||
\(386\) | 0.169873 | − | 0.294229i | 0.00864631 | − | 0.0149758i | ||||
\(387\) | 4.02628 | − | 6.97372i | 0.204667 | − | 0.354494i | ||||
\(388\) | −0.732051 | − | 1.26795i | −0.0371642 | − | 0.0643704i | ||||
\(389\) | 0.901924 | − | 3.36603i | 0.0457294 | − | 0.170664i | −0.939285 | − | 0.343139i | \(-0.888510\pi\) |
0.985014 | + | 0.172475i | \(0.0551764\pi\) | |||||||
\(390\) | 7.06218 | + | 7.96410i | 0.357607 | + | 0.403278i | ||||
\(391\) | 32.1962 | + | 18.5885i | 1.62823 | + | 0.940059i | ||||
\(392\) | −0.500000 | + | 0.866025i | −0.0252538 | + | 0.0437409i | ||||
\(393\) | − | 1.46410i | − | 0.0738542i | ||||||
\(394\) | −7.86603 | − | 2.10770i | −0.396285 | − | 0.106184i | ||||
\(395\) | −10.4904 | − | 11.8301i | −0.527828 | − | 0.595238i | ||||
\(396\) | 1.46410 | 0.0735739 | ||||||||
\(397\) | −2.24167 | + | 2.24167i | −0.112506 | + | 0.112506i | −0.761119 | − | 0.648613i | \(-0.775350\pi\) |
0.648613 | + | 0.761119i | \(0.275350\pi\) | |||||||
\(398\) | −20.1603 | + | 5.40192i | −1.01054 | + | 0.270774i | ||||
\(399\) | −24.3923 | + | 24.3923i | −1.22114 | + | 1.22114i | ||||
\(400\) | 4.96410 | + | 0.598076i | 0.248205 | + | 0.0299038i | ||||
\(401\) | −16.1244 | − | 16.1244i | −0.805212 | − | 0.805212i | 0.178693 | − | 0.983905i | \(-0.442813\pi\) |
−0.983905 | + | 0.178693i | \(0.942813\pi\) | |||||||
\(402\) | −9.29423 | + | 5.36603i | −0.463554 | + | 0.267633i | ||||
\(403\) | −22.9904 | − | 6.16025i | −1.14523 | − | 0.306864i | ||||
\(404\) | −0.169873 | + | 0.0980762i | −0.00845150 | + | 0.00487947i | ||||
\(405\) | 23.7942 | + | 1.42820i | 1.18234 | + | 0.0709680i | ||||
\(406\) | − | 18.9282i | − | 0.939391i | ||||||
\(407\) | 11.0000 | + | 5.19615i | 0.545250 | + | 0.257564i | ||||
\(408\) | 8.46410 | − | 8.46410i | 0.419035 | − | 0.419035i | ||||
\(409\) | −7.10770 | − | 26.5263i | −0.351453 | − | 1.31164i | −0.884890 | − | 0.465800i | \(-0.845767\pi\) |
0.533437 | − | 0.845840i | \(-0.320900\pi\) | |||||||
\(410\) | −7.96410 | + | 12.0622i | −0.393319 | + | 0.595709i | ||||
\(411\) | 4.73205 | − | 2.73205i | 0.233415 | − | 0.134762i | ||||
\(412\) | −3.09808 | − | 5.36603i | −0.152631 | − | 0.264365i | ||||
\(413\) | − | 9.07180i | − | 0.446394i | ||||||
\(414\) | 3.80385 | − | 2.19615i | 0.186949 | − | 0.107935i | ||||
\(415\) | −34.1769 | − | 11.3923i | −1.67768 | − | 0.559226i | ||||
\(416\) | −1.23205 | + | 2.13397i | −0.0604063 | + | 0.104627i | ||||
\(417\) | −14.9282 | − | 14.9282i | −0.731037 | − | 0.731037i | ||||
\(418\) | 8.92820 | + | 8.92820i | 0.436693 | + | 0.436693i | ||||
\(419\) | 12.4186 | + | 7.16987i | 0.606688 | + | 0.350271i | 0.771668 | − | 0.636026i | \(-0.219423\pi\) |
−0.164980 | + | 0.986297i | \(0.552756\pi\) | |||||||
\(420\) | −10.1962 | − | 6.73205i | −0.497521 | − | 0.328490i | ||||
\(421\) | −8.66025 | − | 8.66025i | −0.422075 | − | 0.422075i | 0.463843 | − | 0.885918i | \(-0.346470\pi\) |
−0.885918 | + | 0.463843i | \(0.846470\pi\) | |||||||
\(422\) | −3.46410 | − | 2.00000i | −0.168630 | − | 0.0973585i | ||||
\(423\) | 1.66025 | + | 6.19615i | 0.0807243 | + | 0.301267i | ||||
\(424\) | −4.86603 | + | 1.30385i | −0.236315 | + | 0.0633204i | ||||
\(425\) | 30.7583 | + | 3.70577i | 1.49200 | + | 0.179756i | ||||
\(426\) | −5.46410 | − | 1.46410i | −0.264737 | − | 0.0709360i | ||||
\(427\) | 4.39230 | + | 2.53590i | 0.212559 | + | 0.122721i | ||||
\(428\) | 13.4282 | − | 3.59808i | 0.649077 | − | 0.173920i | ||||
\(429\) | −9.19615 | + | 2.46410i | −0.443994 | + | 0.118968i | ||||
\(430\) | 11.0000 | + | 22.0000i | 0.530467 | + | 1.06093i | ||||
\(431\) | −4.10770 | + | 15.3301i | −0.197861 | + | 0.738426i | 0.793647 | + | 0.608379i | \(0.208180\pi\) |
−0.991508 | + | 0.130048i | \(0.958487\pi\) | |||||||
\(432\) | 1.13397 | + | 4.23205i | 0.0545584 | + | 0.203615i | ||||
\(433\) | 3.19615 | − | 3.19615i | 0.153597 | − | 0.153597i | −0.626125 | − | 0.779723i | \(-0.715360\pi\) |
0.779723 | + | 0.626125i | \(0.215360\pi\) | |||||||
\(434\) | 27.3205 | 1.31143 | ||||||||
\(435\) | 28.8564 | + | 1.73205i | 1.38356 | + | 0.0830455i | ||||
\(436\) | 0.732051 | + | 0.732051i | 0.0350589 | + | 0.0350589i | ||||
\(437\) | 36.5885 | + | 9.80385i | 1.75026 | + | 0.468982i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.866025 | + | 0.232051i | 0.0413331 | + | 0.0110752i | 0.279426 | − | 0.960167i | \(-0.409856\pi\) |
−0.238093 | + | 0.971242i | \(0.576522\pi\) | |||||||
\(440\) | −2.46410 | + | 3.73205i | −0.117471 | + | 0.177919i | ||||
\(441\) | 0.366025 | + | 0.633975i | 0.0174298 | + | 0.0301893i | ||||
\(442\) | −7.63397 | + | 13.2224i | −0.363111 | + | 0.628927i | ||||
\(443\) | 18.7583 | + | 18.7583i | 0.891235 | + | 0.891235i | 0.994639 | − | 0.103404i | \(-0.0329735\pi\) |
−0.103404 | + | 0.994639i | \(0.532974\pi\) | |||||||
\(444\) | 2.09808 | − | 11.5622i | 0.0995703 | − | 0.548717i | ||||
\(445\) | 3.58846 | + | 1.19615i | 0.170109 | + | 0.0567031i | ||||
\(446\) | 17.6603 | − | 4.73205i | 0.836237 | − | 0.224069i | ||||
\(447\) | −42.4186 | − | 11.3660i | −2.00633 | − | 0.537595i | ||||
\(448\) | 0.732051 | − | 2.73205i | 0.0345861 | − | 0.129077i | ||||
\(449\) | −0.428203 | + | 1.59808i | −0.0202082 | + | 0.0754179i | −0.975294 | − | 0.220913i | \(-0.929096\pi\) |
0.955085 | + | 0.296331i | \(0.0957630\pi\) | |||||||
\(450\) | 2.19615 | − | 2.92820i | 0.103528 | − | 0.138037i | ||||
\(451\) | −6.46410 | − | 11.1962i | −0.304383 | − | 0.527206i | ||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | 1.59808 | + | 5.96410i | 0.0750842 | + | 0.280218i | ||||
\(454\) | 2.66025i | 0.124852i | ||||||||
\(455\) | 14.7846 | + | 4.92820i | 0.693113 | + | 0.231038i | ||||
\(456\) | 6.09808 | − | 10.5622i | 0.285569 | − | 0.494619i | ||||
\(457\) | −13.3923 | − | 23.1962i | −0.626466 | − | 1.08507i | −0.988255 | − | 0.152811i | \(-0.951168\pi\) |
0.361790 | − | 0.932260i | \(-0.382166\pi\) | |||||||
\(458\) | −17.6603 | −0.825209 | ||||||||
\(459\) | 7.02628 | + | 26.2224i | 0.327959 | + | 1.22396i | ||||
\(460\) | −0.803848 | + | 13.3923i | −0.0374796 | + | 0.624419i | ||||
\(461\) | −4.53590 | − | 16.9282i | −0.211258 | − | 0.788425i | −0.987450 | − | 0.157929i | \(-0.949518\pi\) |
0.776193 | − | 0.630496i | \(-0.217148\pi\) | |||||||
\(462\) | 9.46410 | − | 5.46410i | 0.440310 | − | 0.254213i | ||||
\(463\) | −7.22243 | + | 4.16987i | −0.335655 | + | 0.193790i | −0.658349 | − | 0.752713i | \(-0.728745\pi\) |
0.322694 | + | 0.946503i | \(0.395412\pi\) | |||||||
\(464\) | 1.73205 | + | 6.46410i | 0.0804084 | + | 0.300088i | ||||
\(465\) | −2.50000 | + | 41.6506i | −0.115935 | + | 1.93150i | ||||
\(466\) | 5.80385 | + | 21.6603i | 0.268858 | + | 1.00339i | ||||
\(467\) | 29.9282 | 1.38491 | 0.692456 | − | 0.721460i | \(-0.256529\pi\) | ||||
0.692456 | + | 0.721460i | \(0.256529\pi\) | |||||||
\(468\) | 0.901924 | + | 1.56218i | 0.0416914 | + | 0.0722117i | ||||
\(469\) | −7.85641 | + | 13.6077i | −0.362775 | + | 0.628345i | ||||
\(470\) | −18.5885 | − | 6.19615i | −0.857422 | − | 0.285807i | ||||
\(471\) | − | 39.2487i | − | 1.80849i | ||||||
\(472\) | 0.830127 | + | 3.09808i | 0.0382097 | + | 0.142601i | ||||
\(473\) | −22.0000 | −1.01156 | ||||||||
\(474\) | −6.83013 | − | 11.8301i | −0.313718 | − | 0.543376i | ||||
\(475\) | 31.2487 | − | 4.46410i | 1.43379 | − | 0.204827i | ||||
\(476\) | 4.53590 | − | 16.9282i | 0.207903 | − | 0.775903i | ||||
\(477\) | −0.954483 | + | 3.56218i | −0.0437028 | + | 0.163101i | ||||
\(478\) | −14.8301 | − | 3.97372i | −0.678314 | − | 0.181754i | ||||
\(479\) | −3.96410 | + | 1.06218i | −0.181124 | + | 0.0485321i | −0.348241 | − | 0.937405i | \(-0.613221\pi\) |
0.167117 | + | 0.985937i | \(0.446554\pi\) | |||||||
\(480\) | 4.09808 | + | 1.36603i | 0.187051 | + | 0.0623502i | ||||
\(481\) | 1.23205 | + | 14.9378i | 0.0561767 | + | 0.681106i | ||||
\(482\) | −13.1962 | − | 13.1962i | −0.601068 | − | 0.601068i | ||||
\(483\) | 16.3923 | − | 28.3923i | 0.745876 | − | 1.29189i | ||||
\(484\) | 3.50000 | + | 6.06218i | 0.159091 | + | 0.275554i | ||||
\(485\) | 1.80385 | − | 2.73205i | 0.0819085 | − | 0.124056i | ||||
\(486\) | 7.19615 | + | 1.92820i | 0.326424 | + | 0.0874651i | ||||
\(487\) | 41.4641 | 1.87892 | 0.939459 | − | 0.342662i | \(-0.111328\pi\) | ||||
0.939459 | + | 0.342662i | \(0.111328\pi\) | |||||||
\(488\) | −1.73205 | − | 0.464102i | −0.0784063 | − | 0.0210089i | ||||
\(489\) | −4.83013 | − | 4.83013i | −0.218426 | − | 0.218426i | ||||
\(490\) | −2.23205 | − | 0.133975i | −0.100834 | − | 0.00605236i | ||||
\(491\) | −8.19615 | −0.369887 | −0.184944 | − | 0.982749i | \(-0.559210\pi\) | ||||
−0.184944 | + | 0.982749i | \(0.559210\pi\) | |||||||
\(492\) | −8.83013 | + | 8.83013i | −0.398093 | + | 0.398093i | ||||
\(493\) | 10.7321 | + | 40.0526i | 0.483347 | + | 1.80388i | ||||
\(494\) | −4.02628 | + | 15.0263i | −0.181151 | + | 0.676064i | ||||
\(495\) | 1.46410 | + | 2.92820i | 0.0658065 | + | 0.131613i | ||||
\(496\) | −9.33013 | + | 2.50000i | −0.418935 | + | 0.112253i | ||||
\(497\) | −8.00000 | + | 2.14359i | −0.358849 | + | 0.0961533i | ||||
\(498\) | −26.9545 | − | 15.5622i | −1.20786 | − | 0.697358i | ||||
\(499\) | −15.1962 | − | 4.07180i | −0.680273 | − | 0.182279i | −0.0978952 | − | 0.995197i | \(-0.531211\pi\) |
−0.582378 | + | 0.812918i | \(0.697878\pi\) | |||||||
\(500\) | 3.76795 | + | 10.5263i | 0.168508 | + | 0.470750i | ||||
\(501\) | 38.6865 | − | 10.3660i | 1.72839 | − | 0.463120i | ||||
\(502\) | −2.09808 | − | 7.83013i | −0.0936417 | − | 0.349476i | ||||
\(503\) | −2.49038 | − | 1.43782i | −0.111041 | − | 0.0641093i | 0.443451 | − | 0.896299i | \(-0.353754\pi\) |
−0.554492 | + | 0.832189i | \(0.687087\pi\) | |||||||
\(504\) | −1.46410 | − | 1.46410i | −0.0652163 | − | 0.0652163i | ||||
\(505\) | −0.366025 | − | 0.241670i | −0.0162879 | − | 0.0107542i | ||||
\(506\) | −10.3923 | − | 6.00000i | −0.461994 | − | 0.266733i | ||||
\(507\) | 9.46410 | + | 9.46410i | 0.420316 | + | 0.420316i | ||||
\(508\) | −6.46410 | − | 6.46410i | −0.286798 | − | 0.286798i | ||||
\(509\) | 5.07180 | − | 8.78461i | 0.224803 | − | 0.389371i | −0.731457 | − | 0.681888i | \(-0.761159\pi\) |
0.956260 | + | 0.292517i | \(0.0944927\pi\) | |||||||
\(510\) | 25.3923 | + | 8.46410i | 1.12439 | + | 0.374797i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 13.8301 | + | 23.9545i | 0.610615 | + | 1.05762i | ||||
\(514\) | 0.294229 | − | 0.169873i | 0.0129779 | − | 0.00749278i | ||||
\(515\) | 7.63397 | − | 11.5622i | 0.336393 | − | 0.509490i | ||||
\(516\) | 5.50000 | + | 20.5263i | 0.242124 | + | 0.903619i | ||||
\(517\) | 12.3923 | − | 12.3923i | 0.545013 | − | 0.545013i | ||||
\(518\) | −5.80385 | − | 16.1962i | −0.255006 | − | 0.711618i | ||||
\(519\) | − | 46.9808i | − | 2.06223i | ||||||
\(520\) | −5.50000 | − | 0.330127i | −0.241191 | − | 0.0144770i | ||||
\(521\) | −17.0885 | + | 9.86603i | −0.748659 | + | 0.432238i | −0.825209 | − | 0.564827i | \(-0.808943\pi\) |
0.0765502 | + | 0.997066i | \(0.475609\pi\) | |||||||
\(522\) | 4.73205 | + | 1.26795i | 0.207116 | + | 0.0554966i | ||||
\(523\) | −16.6244 | + | 9.59808i | −0.726932 | + | 0.419695i | −0.817299 | − | 0.576214i | \(-0.804529\pi\) |
0.0903665 | + | 0.995909i | \(0.471196\pi\) | |||||||
\(524\) | 0.535898 | + | 0.535898i | 0.0234108 | + | 0.0234108i | ||||
\(525\) | 3.26795 | − | 27.1244i | 0.142625 | − | 1.18380i | ||||
\(526\) | 0.0717968 | − | 0.0717968i | 0.00313049 | − | 0.00313049i | ||||
\(527\) | −57.8109 | + | 15.4904i | −2.51828 | + | 0.674772i | ||||
\(528\) | −2.73205 | + | 2.73205i | −0.118897 | + | 0.118897i | ||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −7.47372 | − | 8.42820i | −0.324638 | − | 0.366098i | ||||
\(531\) | 2.26795 | + | 0.607695i | 0.0984206 | + | 0.0263717i | ||||
\(532\) | − | 17.8564i | − | 0.774173i | ||||||
\(533\) | 7.96410 | − | 13.7942i | 0.344964 | − | 0.597494i | ||||
\(534\) | 2.83013 | + | 1.63397i | 0.122472 | + | 0.0707090i | ||||
\(535\) | 20.6244 | + | 23.2583i | 0.891669 | + | 1.00555i | ||||
\(536\) | 1.43782 | − | 5.36603i | 0.0621045 | − | 0.231777i | ||||
\(537\) | 14.1962 | + | 24.5885i | 0.612609 | + | 1.06107i | ||||
\(538\) | −3.29423 | + | 5.70577i | −0.142024 | + | 0.245993i | ||||
\(539\) | 1.00000 | − | 1.73205i | 0.0430730 | − | 0.0746047i | ||||
\(540\) | −7.33013 | + | 6.50000i | −0.315438 | + | 0.279715i | ||||
\(541\) | 5.07180 | − | 5.07180i | 0.218054 | − | 0.218054i | −0.589624 | − | 0.807678i | \(-0.700724\pi\) |
0.807678 | + | 0.589624i | \(0.200724\pi\) | |||||||
\(542\) | −9.06218 | + | 5.23205i | −0.389254 | + | 0.224736i | ||||
\(543\) | 25.7583 | − | 6.90192i | 1.10540 | − | 0.296190i | ||||
\(544\) | 6.19615i | 0.265658i | ||||||||
\(545\) | −0.732051 | + | 2.19615i | −0.0313576 | + | 0.0940728i | ||||
\(546\) | 11.6603 | + | 6.73205i | 0.499013 | + | 0.288105i | ||||
\(547\) | 17.9808i | 0.768802i | 0.923166 | + | 0.384401i | \(0.125592\pi\) | ||||
−0.923166 | + | 0.384401i | \(0.874408\pi\) | |||||||
\(548\) | −0.732051 | + | 2.73205i | −0.0312717 | + | 0.116707i | ||||
\(549\) | −0.928203 | + | 0.928203i | −0.0396147 | + | 0.0396147i | ||||
\(550\) | −9.92820 | − | 1.19615i | −0.423340 | − | 0.0510041i | ||||
\(551\) | 21.1244 | + | 36.5885i | 0.899928 | + | 1.55872i | ||||
\(552\) | −3.00000 | + | 11.1962i | −0.127688 | + | 0.476540i | ||||
\(553\) | −17.3205 | − | 10.0000i | −0.736543 | − | 0.425243i | ||||
\(554\) | 16.6603 | 0.707826 | ||||||||
\(555\) | 25.2224 | − | 7.36603i | 1.07063 | − | 0.312670i | ||||
\(556\) | 10.9282 | 0.463459 | ||||||||
\(557\) | 32.3827 | + | 18.6962i | 1.37210 | + | 0.792181i | 0.991192 | − | 0.132432i | \(-0.0422787\pi\) |
0.380906 | + | 0.924614i | \(0.375612\pi\) | |||||||
\(558\) | −1.83013 | + | 6.83013i | −0.0774755 | + | 0.289142i | ||||
\(559\) | −13.5526 | − | 23.4737i | −0.573212 | − | 0.992833i | ||||
\(560\) | 6.19615 | − | 1.26795i | 0.261835 | − | 0.0535806i | ||||
\(561\) | −16.9282 | + | 16.9282i | −0.714709 | + | 0.714709i | ||||
\(562\) | −0.624356 | + | 2.33013i | −0.0263369 | + | 0.0982905i | ||||
\(563\) | − | 15.6077i | − | 0.657786i | −0.944367 | − | 0.328893i | \(-0.893324\pi\) | ||
0.944367 | − | 0.328893i | \(-0.106676\pi\) | |||||||
\(564\) | −14.6603 | − | 8.46410i | −0.617308 | − | 0.356403i | ||||
\(565\) | −6.00000 | − | 12.0000i | −0.252422 | − | 0.504844i | ||||
\(566\) | 13.0000i | 0.546431i | ||||||||
\(567\) | 29.1244 | − | 7.80385i | 1.22311 | − | 0.327731i | ||||
\(568\) | 2.53590 | − | 1.46410i | 0.106404 | − | 0.0614323i | ||||
\(569\) | −16.3660 | + | 16.3660i | −0.686099 | + | 0.686099i | −0.961368 | − | 0.275268i | \(-0.911233\pi\) |
0.275268 | + | 0.961368i | \(0.411233\pi\) | |||||||
\(570\) | 27.2224 | + | 1.63397i | 1.14022 | + | 0.0684397i | ||||
\(571\) | 20.7583 | − | 35.9545i | 0.868709 | − | 1.50465i | 0.00539254 | − | 0.999985i | \(-0.498283\pi\) |
0.863317 | − | 0.504663i | \(-0.168383\pi\) | |||||||
\(572\) | 2.46410 | − | 4.26795i | 0.103029 | − | 0.178452i | ||||
\(573\) | 2.50000 | + | 4.33013i | 0.104439 | + | 0.180894i | ||||
\(574\) | −4.73205 | + | 17.6603i | −0.197512 | + | 0.737125i | ||||
\(575\) | −27.5885 | + | 11.7846i | −1.15052 | + | 0.491452i | ||||
\(576\) | 0.633975 | + | 0.366025i | 0.0264156 | + | 0.0152511i | ||||
\(577\) | −2.53590 | + | 4.39230i | −0.105571 | + | 0.182854i | −0.913971 | − | 0.405779i | \(-0.867000\pi\) |
0.808400 | + | 0.588633i | \(0.200334\pi\) | |||||||
\(578\) | 21.3923i | 0.889803i | ||||||||
\(579\) | 0.633975 | + | 0.169873i | 0.0263471 | + | 0.00705968i | ||||
\(580\) | −11.1962 | + | 9.92820i | −0.464895 | + | 0.412246i | ||||
\(581\) | −45.5692 | −1.89053 | ||||||||
\(582\) | 2.00000 | − | 2.00000i | 0.0829027 | − | 0.0829027i | ||||
\(583\) | 9.73205 | − | 2.60770i | 0.403060 | − | 0.108000i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.22243 | + | 3.36603i | −0.0918862 | + | 0.139168i | ||||
\(586\) | 2.29423 | + | 2.29423i | 0.0947737 | + | 0.0947737i | ||||
\(587\) | −12.4019 | + | 7.16025i | −0.511882 | + | 0.295535i | −0.733607 | − | 0.679574i | \(-0.762165\pi\) |
0.221725 | + | 0.975109i | \(0.428831\pi\) | |||||||
\(588\) | −1.86603 | − | 0.500000i | −0.0769536 | − | 0.0206197i | ||||
\(589\) | −52.8109 | + | 30.4904i | −2.17603 | + | 1.25633i | ||||
\(590\) | −5.36603 | + | 4.75833i | −0.220916 | + | 0.195897i | ||||
\(591\) | − | 15.7321i | − | 0.647130i | ||||||
\(592\) | 3.46410 | + | 5.00000i | 0.142374 | + | 0.205499i | ||||
\(593\) | −18.6603 | + | 18.6603i | −0.766285 | + | 0.766285i | −0.977450 | − | 0.211166i | \(-0.932274\pi\) |
0.211166 | + | 0.977450i | \(0.432274\pi\) | |||||||
\(594\) | −2.26795 | − | 8.46410i | −0.0930551 | − | 0.347286i | ||||
\(595\) | 38.3923 | − | 7.85641i | 1.57393 | − | 0.322081i | ||||
\(596\) | 19.6865 | − | 11.3660i | 0.806392 | − | 0.465571i | ||||
\(597\) | −20.1603 | − | 34.9186i | −0.825104 | − | 1.42912i | ||||
\(598\) | − | 14.7846i | − | 0.604588i | ||||||
\(599\) | −39.6051 | + | 22.8660i | −1.61822 | + | 0.934280i | −0.630841 | + | 0.775912i | \(0.717290\pi\) |
−0.987380 | + | 0.158368i | \(0.949377\pi\) | |||||||
\(600\) | 1.36603 | + | 9.56218i | 0.0557678 | + | 0.390374i | ||||
\(601\) | 13.7942 | − | 23.8923i | 0.562678 | − | 0.974587i | −0.434583 | − | 0.900632i | \(-0.643104\pi\) |
0.997262 | − | 0.0739558i | \(-0.0235624\pi\) | |||||||
\(602\) | 22.0000 | + | 22.0000i | 0.896653 | + | 0.896653i | ||||
\(603\) | −2.87564 | − | 2.87564i | −0.117105 | − | 0.117105i | ||||
\(604\) | −2.76795 | − | 1.59808i | −0.112626 | − | 0.0650248i | ||||
\(605\) | −8.62436 | + | 13.0622i | −0.350630 | + | 0.531053i | ||||
\(606\) | −0.267949 | − | 0.267949i | −0.0108847 | − | 0.0108847i | ||||
\(607\) | −12.1699 | − | 7.02628i | −0.493960 | − | 0.285188i | 0.232256 | − | 0.972655i | \(-0.425389\pi\) |
−0.726216 | + | 0.687467i | \(0.758723\pi\) | |||||||
\(608\) | 1.63397 | + | 6.09808i | 0.0662664 | + | 0.247310i | ||||
\(609\) | 35.3205 | − | 9.46410i | 1.43126 | − | 0.383505i | ||||
\(610\) | −0.803848 | − | 3.92820i | −0.0325468 | − | 0.159048i | ||||
\(611\) | 20.8564 | + | 5.58846i | 0.843760 | + | 0.226085i | ||||
\(612\) | 3.92820 | + | 2.26795i | 0.158788 | + | 0.0916764i | ||||
\(613\) | 28.4186 | − | 7.61474i | 1.14782 | − | 0.307556i | 0.365726 | − | 0.930722i | \(-0.380821\pi\) |
0.782089 | + | 0.623166i | \(0.214154\pi\) | |||||||
\(614\) | −21.0622 | + | 5.64359i | −0.850000 | + | 0.227757i | ||||
\(615\) | −26.4904 | − | 8.83013i | −1.06820 | − | 0.356065i | ||||
\(616\) | −1.46410 | + | 5.46410i | −0.0589903 | + | 0.220155i | ||||
\(617\) | −6.41858 | − | 23.9545i | −0.258402 | − | 0.964371i | −0.966166 | − | 0.257922i | \(-0.916962\pi\) |
0.707763 | − | 0.706450i | \(-0.249704\pi\) | |||||||
\(618\) | 8.46410 | − | 8.46410i | 0.340476 | − | 0.340476i | ||||
\(619\) | −13.0718 | −0.525400 | −0.262700 | − | 0.964878i | \(-0.584613\pi\) | ||||
−0.262700 | + | 0.964878i | \(0.584613\pi\) | |||||||
\(620\) | −14.3301 | − | 16.1603i | −0.575512 | − | 0.649011i | ||||
\(621\) | −18.5885 | − | 18.5885i | −0.745929 | − | 0.745929i | ||||
\(622\) | −15.2583 | − | 4.08846i | −0.611803 | − | 0.163932i | ||||
\(623\) | 4.78461 | 0.191691 | ||||||||
\(624\) | −4.59808 | − | 1.23205i | −0.184070 | − | 0.0493215i | ||||
\(625\) | −17.2846 | + | 18.0622i | −0.691384 | + | 0.722487i | ||||
\(626\) | 8.73205 | + | 15.1244i | 0.349003 | + | 0.604491i | ||||
\(627\) | −12.1962 | + | 21.1244i | −0.487067 | + | 0.843626i | ||||
\(628\) | 14.3660 | + | 14.3660i | 0.573267 | + | 0.573267i | ||||
\(629\) | 21.4641 | + | 30.9808i | 0.855830 | + | 1.23528i | ||||
\(630\) | 1.46410 | − | 4.39230i | 0.0583312 | − | 0.174994i | ||||
\(631\) | −5.06218 | + | 1.35641i | −0.201522 | + | 0.0539977i | −0.358168 | − | 0.933657i | \(-0.616599\pi\) |
0.156646 | + | 0.987655i | \(0.449932\pi\) | |||||||
\(632\) | 6.83013 | + | 1.83013i | 0.271688 | + | 0.0727985i | ||||
\(633\) | 2.00000 | − | 7.46410i | 0.0794929 | − | 0.296671i | ||||
\(634\) | 7.18653 | − | 26.8205i | 0.285414 | − | 1.06518i | ||||
\(635\) | 6.46410 | − | 19.3923i | 0.256520 | − | 0.769560i | ||||
\(636\) | −4.86603 | − | 8.42820i | −0.192950 | − | 0.334200i | ||||
\(637\) | 2.46410 | 0.0976313 | ||||||||
\(638\) | −3.46410 | − | 12.9282i | −0.137145 | − | 0.511832i | ||||
\(639\) | − | 2.14359i | − | 0.0847992i | ||||||
\(640\) | −2.00000 | + | 1.00000i | −0.0790569 | + | 0.0395285i | ||||
\(641\) | −21.9904 | + | 38.0885i | −0.868568 | + | 1.50440i | −0.00510745 | + | 0.999987i | \(0.501626\pi\) |
−0.863460 | + | 0.504417i | \(0.831708\pi\) | |||||||
\(642\) | 13.4282 | + | 23.2583i | 0.529969 | + | 0.917933i | ||||
\(643\) | −3.73205 | −0.147178 | −0.0735889 | − | 0.997289i | \(-0.523445\pi\) | ||||
−0.0735889 | + | 0.997289i | \(0.523445\pi\) | |||||||
\(644\) | 4.39230 | + | 16.3923i | 0.173081 | + | 0.645947i | ||||
\(645\) | −35.5526 | + | 31.5263i | −1.39988 | + | 1.24135i | ||||
\(646\) | 10.1244 | + | 37.7846i | 0.398337 | + | 1.48662i | ||||
\(647\) | 33.2942 | − | 19.2224i | 1.30893 | − | 0.755712i | 0.327013 | − | 0.945020i | \(-0.393958\pi\) |
0.981918 | + | 0.189308i | \(0.0606244\pi\) | |||||||
\(648\) | −9.23205 | + | 5.33013i | −0.362669 | + | 0.209387i | ||||
\(649\) | −1.66025 | − | 6.19615i | −0.0651707 | − | 0.243220i | ||||
\(650\) | −4.83975 | − | 11.3301i | −0.189830 | − | 0.444404i | ||||
\(651\) | 13.6603 | + | 50.9808i | 0.535388 | + | 1.99809i | ||||
\(652\) | 3.53590 | 0.138476 | ||||||||
\(653\) | 7.62436 | + | 13.2058i | 0.298364 | + | 0.516782i | 0.975762 | − | 0.218835i | \(-0.0702257\pi\) |
−0.677398 | + | 0.735617i | \(0.736892\pi\) | |||||||
\(654\) | −1.00000 | + | 1.73205i | −0.0391031 | + | 0.0677285i | ||||
\(655\) | −0.535898 | + | 1.60770i | −0.0209393 | + | 0.0628178i | ||||
\(656\) | − | 6.46410i | − | 0.252381i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.7846 | −0.966205 | ||||||||
\(659\) | 20.3923 | + | 35.3205i | 0.794371 | + | 1.37589i | 0.923238 | + | 0.384230i | \(0.125533\pi\) |
−0.128866 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(660\) | −8.19615 | − | 2.73205i | −0.319035 | − | 0.106345i | ||||
\(661\) | 6.41858 | − | 23.9545i | 0.249654 | − | 0.931721i | −0.721333 | − | 0.692589i | \(-0.756470\pi\) |
0.970987 | − | 0.239133i | \(-0.0768631\pi\) | |||||||
\(662\) | 0.830127 | − | 3.09808i | 0.0322638 | − | 0.120410i | ||||
\(663\) | −28.4904 | − | 7.63397i | −1.10647 | − | 0.296479i | ||||
\(664\) | 15.5622 | − | 4.16987i | 0.603930 | − | 0.161822i | ||||
\(665\) | 35.7128 | − | 17.8564i | 1.38488 | − | 0.692442i | ||||
\(666\) | 4.43782 | − | 0.366025i | 0.171962 | − | 0.0141832i | ||||
\(667\) | −28.3923 | − | 28.3923i | −1.09935 | − | 1.09935i | ||||
\(668\) | −10.3660 | + | 17.9545i | −0.401074 | + | 0.694680i | ||||
\(669\) | 17.6603 | + | 30.5885i | 0.682785 | + | 1.18262i | ||||
\(670\) | 12.1699 | − | 2.49038i | 0.470163 | − | 0.0962118i | ||||
\(671\) | 3.46410 | + | 0.928203i | 0.133730 | + | 0.0358329i | ||||
\(672\) | 5.46410 | 0.210782 | ||||||||
\(673\) | 30.4904 | + | 8.16987i | 1.17532 | + | 0.314925i | 0.793068 | − | 0.609133i | \(-0.208483\pi\) |
0.382250 | + | 0.924059i | \(0.375149\pi\) | |||||||
\(674\) | −5.53590 | − | 5.53590i | −0.213235 | − | 0.213235i | ||||
\(675\) | −20.3301 | − | 8.16025i | −0.782507 | − | 0.314088i | ||||
\(676\) | −6.92820 | −0.266469 | ||||||||
\(677\) | −11.3923 | + | 11.3923i | −0.437842 | + | 0.437842i | −0.891285 | − | 0.453443i | \(-0.850195\pi\) |
0.453443 | + | 0.891285i | \(0.350195\pi\) | |||||||
\(678\) | −3.00000 | − | 11.1962i | −0.115214 | − | 0.429986i | ||||
\(679\) | 1.07180 | − | 4.00000i | 0.0411318 | − | 0.153506i | ||||
\(680\) | −12.3923 | + | 6.19615i | −0.475223 | + | 0.237612i | ||||
\(681\) | −4.96410 | + | 1.33013i | −0.190225 | + | 0.0509706i | ||||
\(682\) | 18.6603 | − | 5.00000i | 0.714538 | − | 0.191460i | ||||
\(683\) | 11.5981 | + | 6.69615i | 0.443788 | + | 0.256221i | 0.705203 | − | 0.709005i | \(-0.250856\pi\) |
−0.261415 | + | 0.965226i | \(0.584189\pi\) | |||||||
\(684\) | 4.46410 | + | 1.19615i | 0.170689 | + | 0.0457360i | ||||
\(685\) | −6.19615 | + | 1.26795i | −0.236743 | + | 0.0484458i | ||||
\(686\) | 16.3923 | − | 4.39230i | 0.625861 | − | 0.167699i | ||||
\(687\) | −8.83013 | − | 32.9545i | −0.336890 | − | 1.25729i | ||||
\(688\) | −9.52628 | − | 5.50000i | −0.363186 | − | 0.209686i | ||||
\(689\) | 8.77757 | + | 8.77757i | 0.334399 | + | 0.334399i | ||||
\(690\) | −25.3923 | + | 5.19615i | −0.966669 | + | 0.197814i | ||||
\(691\) | 24.7583 | + | 14.2942i | 0.941851 | + | 0.543778i | 0.890540 | − | 0.454905i | \(-0.150327\pi\) |
0.0513111 | + | 0.998683i | \(0.483660\pi\) | |||||||
\(692\) | 17.1962 | + | 17.1962i | 0.653700 | + | 0.653700i | ||||
\(693\) | 2.92820 | + | 2.92820i | 0.111233 | + | 0.111233i | ||||
\(694\) | 9.92820 | − | 17.1962i | 0.376869 | − | 0.652757i | ||||
\(695\) | 10.9282 | + | 21.8564i | 0.414530 | + | 0.829061i | ||||
\(696\) | −11.1962 | + | 6.46410i | −0.424389 | + | 0.245021i | ||||
\(697\) | − | 40.0526i | − | 1.51710i | ||||||
\(698\) | 17.9545 | + | 31.0981i | 0.679587 | + | 1.17708i | ||||
\(699\) | −37.5167 | + | 21.6603i | −1.41901 | + | 0.819266i | ||||
\(700\) | 8.73205 | + | 11.1244i | 0.330040 | + | 0.420461i | ||||
\(701\) | −1.50962 | − | 5.63397i | −0.0570175 | − | 0.212792i | 0.931539 | − | 0.363640i | \(-0.118466\pi\) |
−0.988557 | + | 0.150848i | \(0.951800\pi\) | |||||||
\(702\) | 7.63397 | − | 7.63397i | 0.288126 | − | 0.288126i | ||||
\(703\) | 29.2942 | + | 24.8301i | 1.10485 | + | 0.936486i | ||||
\(704\) | − | 2.00000i | − | 0.0753778i | ||||||
\(705\) | 2.26795 | − | 37.7846i | 0.0854159 | − | 1.42305i | ||||
\(706\) | 28.3923 | − | 16.3923i | 1.06856 | − | 0.616933i | ||||
\(707\) | −0.535898 | − | 0.143594i | −0.0201545 | − | 0.00540039i | ||||
\(708\) | −5.36603 | + | 3.09808i | −0.201668 | + | 0.116433i | ||||
\(709\) | −20.0718 | − | 20.0718i | −0.753812 | − | 0.753812i | 0.221376 | − | 0.975188i | \(-0.428945\pi\) |
−0.975188 | + | 0.221376i | \(0.928945\pi\) | |||||||
\(710\) | 5.46410 | + | 3.60770i | 0.205064 | + | 0.135394i | ||||
\(711\) | 3.66025 | − | 3.66025i | 0.137270 | − | 0.137270i | ||||
\(712\) | −1.63397 | + | 0.437822i | −0.0612358 | + | 0.0164081i | ||||
\(713\) | 40.9808 | − | 40.9808i | 1.53474 | − | 1.53474i | ||||
\(714\) | 33.8564 | 1.26704 | ||||||||
\(715\) | 11.0000 | + | 0.660254i | 0.411377 | + | 0.0246921i | ||||
\(716\) | −14.1962 | − | 3.80385i | −0.530535 | − | 0.142156i | ||||
\(717\) | − | 29.6603i | − | 1.10768i | ||||||
\(718\) | 1.69615 | − | 2.93782i | 0.0632998 | − | 0.109639i | ||||
\(719\) | −44.4282 | − | 25.6506i | −1.65689 | − | 0.956607i | −0.974136 | − | 0.225961i | \(-0.927448\pi\) |
−0.682756 | − | 0.730646i | \(-0.739219\pi\) | |||||||
\(720\) | −0.0980762 | + | 1.63397i | −0.00365508 | + | 0.0608946i | ||||
\(721\) | 4.53590 | − | 16.9282i | 0.168926 | − | 0.630439i | ||||
\(722\) | 10.4282 | + | 18.0622i | 0.388098 | + | 0.672205i | ||||
\(723\) | 18.0263 | − | 31.2224i | 0.670405 | − | 1.16117i | ||||
\(724\) | −6.90192 | + | 11.9545i | −0.256508 | + | 0.444285i | ||||
\(725\) | −31.0526 | − | 12.4641i | −1.15326 | − | 0.462905i | ||||
\(726\) | −9.56218 | + | 9.56218i | −0.354886 | + | 0.354886i | ||||
\(727\) | 35.1962 | − | 20.3205i | 1.30535 | − | 0.753646i | 0.324036 | − | 0.946045i | \(-0.394960\pi\) |
0.981317 | + | 0.192399i | \(0.0616267\pi\) | |||||||
\(728\) | −6.73205 | + | 1.80385i | −0.249506 | + | 0.0668550i | ||||
\(729\) | − | 17.5885i | − | 0.651424i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −59.0263 | − | 34.0788i | −2.18317 | − | 1.26045i | ||||
\(732\) | − | 3.46410i | − | 0.128037i | ||||||
\(733\) | −11.2224 | + | 41.8827i | −0.414510 | + | 1.54697i | 0.371305 | + | 0.928511i | \(0.378910\pi\) |
−0.785815 | + | 0.618461i | \(0.787756\pi\) | |||||||
\(734\) | 25.4641 | − | 25.4641i | 0.939897 | − | 0.939897i | ||||
\(735\) | −0.866025 | − | 4.23205i | −0.0319438 | − | 0.156102i | ||||
\(736\) | −3.00000 | − | 5.19615i | −0.110581 | − | 0.191533i | ||||
\(737\) | −2.87564 | + | 10.7321i | −0.105926 | + | 0.395320i | ||||
\(738\) | −4.09808 | − | 2.36603i | −0.150852 | − | 0.0870946i | ||||
\(739\) | 18.1962 | 0.669356 | 0.334678 | − | 0.942332i | \(-0.391372\pi\) | ||||
0.334678 | + | 0.942332i | \(0.391372\pi\) | |||||||
\(740\) | −6.53590 | + | 11.9282i | −0.240264 | + | 0.438489i | ||||
\(741\) | −30.0526 | −1.10401 | ||||||||
\(742\) | −12.3397 | − | 7.12436i | −0.453006 | − | 0.261543i | ||||
\(743\) | −7.50962 | + | 28.0263i | −0.275501 | + | 1.02818i | 0.680004 | + | 0.733209i | \(0.261978\pi\) |
−0.955505 | + | 0.294976i | \(0.904688\pi\) | |||||||
\(744\) | −9.33013 | − | 16.1603i | −0.342059 | − | 0.592464i | ||||
\(745\) | 42.4186 | + | 28.0070i | 1.55410 | + | 1.02610i | ||||
\(746\) | −3.75833 | + | 3.75833i | −0.137602 | + | 0.137602i | ||||
\(747\) | 3.05256 | − | 11.3923i | 0.111687 | − | 0.416823i | ||||
\(748\) | − | 12.3923i | − | 0.453108i | ||||||
\(749\) | 34.0526 | + | 19.6603i | 1.24425 | + | 0.718370i | ||||
\(750\) | −17.7583 | + | 12.2942i | −0.648443 | + | 0.448922i | ||||
\(751\) | − | 30.1769i | − | 1.10117i | −0.834779 | − | 0.550586i | \(-0.814404\pi\) | ||
0.834779 | − | 0.550586i | \(-0.185596\pi\) | |||||||
\(752\) | 8.46410 | − | 2.26795i | 0.308654 | − | 0.0827036i | ||||
\(753\) | 13.5622 | − | 7.83013i | 0.494233 | − | 0.285346i | ||||
\(754\) | 11.6603 | − | 11.6603i | 0.424641 | − | 0.424641i | ||||
\(755\) | 0.428203 | − | 7.13397i | 0.0155839 | − | 0.259632i | ||||
\(756\) | −6.19615 | + | 10.7321i | −0.225352 | + | 0.390321i | ||||
\(757\) | −8.50000 | + | 14.7224i | −0.308938 | + | 0.535096i | −0.978130 | − | 0.207993i | \(-0.933307\pi\) |
0.669193 | + | 0.743089i | \(0.266640\pi\) | |||||||
\(758\) | −7.26795 | − | 12.5885i | −0.263984 | − | 0.457233i | ||||
\(759\) | 6.00000 | − | 22.3923i | 0.217786 | − | 0.812789i | ||||
\(760\) | −10.5622 | + | 9.36603i | −0.383130 | + | 0.339741i | ||||
\(761\) | −2.53590 | − | 1.46410i | −0.0919262 | − | 0.0530736i | 0.453332 | − | 0.891342i | \(-0.350235\pi\) |
−0.545258 | + | 0.838268i | \(0.683568\pi\) | |||||||
\(762\) | 8.83013 | − | 15.2942i | 0.319882 | − | 0.554051i | ||||
\(763\) | 2.92820i | 0.106008i | ||||||||
\(764\) | −2.50000 | − | 0.669873i | −0.0904468 | − | 0.0242352i | ||||
\(765\) | −0.607695 | + | 10.1244i | −0.0219713 | + | 0.366047i | ||||
\(766\) | −15.4641 | −0.558741 | ||||||||
\(767\) | 5.58846 | − | 5.58846i | 0.201787 | − | 0.201787i | ||||
\(768\) | −1.86603 | + | 0.500000i | −0.0673344 | + | 0.0180422i | ||||
\(769\) | 33.9282 | − | 33.9282i | 1.22348 | − | 1.22348i | 0.257097 | − | 0.966386i | \(-0.417234\pi\) |
0.966386 | − | 0.257097i | \(-0.0827659\pi\) | |||||||
\(770\) | −12.3923 | + | 2.53590i | −0.446588 | + | 0.0913874i | ||||
\(771\) | 0.464102 | + | 0.464102i | 0.0167142 | + | 0.0167142i | ||||
\(772\) | −0.294229 | + | 0.169873i | −0.0105895 | + | 0.00611386i | ||||
\(773\) | −15.6244 | − | 4.18653i | −0.561969 | − | 0.150579i | −0.0333582 | − | 0.999443i | \(-0.510620\pi\) |
−0.528611 | + | 0.848864i | \(0.677287\pi\) | |||||||
\(774\) | −6.97372 | + | 4.02628i | −0.250665 | + | 0.144722i | ||||
\(775\) | 17.9904 | − | 44.8205i | 0.646234 | − | 1.61000i | ||||
\(776\) | 1.46410i | 0.0525582i | ||||||||
\(777\) | 27.3205 | − | 18.9282i | 0.980118 | − | 0.679046i | ||||
\(778\) | −2.46410 | + | 2.46410i | −0.0883423 | + | 0.0883423i | ||||
\(779\) | −10.5622 | − | 39.4186i | −0.378429 | − | 1.41232i | ||||
\(780\) | −2.13397 | − | 10.4282i | −0.0764085 | − | 0.373390i | ||||
\(781\) | −5.07180 | + | 2.92820i | −0.181483 | + | 0.104779i | ||||
\(782\) | −18.5885 | − | 32.1962i | −0.664722 | − | 1.15133i | ||||
\(783\) | − | 29.3205i | − | 1.04783i | ||||||
\(784\) | 0.866025 | − | 0.500000i | 0.0309295 | − | 0.0178571i | ||||
\(785\) | −14.3660 | + | 43.0981i | −0.512745 | + | 1.53824i | ||||
\(786\) | −0.732051 | + | 1.26795i | −0.0261114 | + | 0.0452262i | ||||
\(787\) | −6.68653 | − | 6.68653i | −0.238349 | − | 0.238349i | 0.577817 | − | 0.816166i | \(-0.303905\pi\) |
−0.816166 | + | 0.577817i | \(0.803905\pi\) | |||||||
\(788\) | 5.75833 | + | 5.75833i | 0.205132 | + | 0.205132i | ||||
\(789\) | 0.169873 | + | 0.0980762i | 0.00604764 | + | 0.00349161i | ||||
\(790\) | 3.16987 | + | 15.4904i | 0.112779 | + | 0.551123i | ||||
\(791\) | −12.0000 | − | 12.0000i | −0.426671 | − | 0.426671i | ||||
\(792\) | −1.26795 | − | 0.732051i | −0.0450546 | − | 0.0260123i | ||||
\(793\) | 1.14359 | + | 4.26795i | 0.0406102 | + | 0.151559i | ||||
\(794\) | 3.06218 | − | 0.820508i | 0.108673 | − | 0.0291187i | ||||
\(795\) | 11.9904 | − | 18.1603i | 0.425255 | − | 0.644078i | ||||
\(796\) | 20.1603 | + | 5.40192i | 0.714561 | + | 0.191466i | ||||
\(797\) | −19.0359 | − | 10.9904i | −0.674286 | − | 0.389299i | 0.123413 | − | 0.992355i | \(-0.460616\pi\) |
−0.797699 | + | 0.603056i | \(0.793949\pi\) | |||||||
\(798\) | 33.3205 | − | 8.92820i | 1.17953 | − | 0.316055i | ||||
\(799\) | 52.4449 | − | 14.0526i | 1.85537 | − | 0.497144i | ||||
\(800\) | −4.00000 | − | 3.00000i | −0.141421 | − | 0.106066i | ||||
\(801\) | −0.320508 | + | 1.19615i | −0.0113246 | + | 0.0422640i | ||||
\(802\) | 5.90192 | + | 22.0263i | 0.208404 | + | 0.777775i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 10.7321 | 0.378490 | ||||||||
\(805\) | −28.3923 | + | 25.1769i | −1.00070 | + | 0.887370i | ||||
\(806\) | 16.8301 | + | 16.8301i | 0.592816 | + | 0.592816i | ||||
\(807\) | −12.2942 | − | 3.29423i | −0.432777 | − | 0.115962i | ||||
\(808\) | 0.196152 | 0.00690062 | ||||||||
\(809\) | −35.7224 | − | 9.57180i | −1.25593 | − | 0.336526i | −0.431308 | − | 0.902205i | \(-0.641948\pi\) |
−0.824626 | + | 0.565678i | \(0.808614\pi\) | |||||||
\(810\) | −19.8923 | − | 13.1340i | −0.698944 | − | 0.461481i | ||||
\(811\) | 3.49038 | + | 6.04552i | 0.122564 | + | 0.212287i | 0.920778 | − | 0.390087i | \(-0.127555\pi\) |
−0.798214 | + | 0.602374i | \(0.794222\pi\) | |||||||
\(812\) | −9.46410 | + | 16.3923i | −0.332125 | + | 0.575257i | ||||
\(813\) | −14.2942 | − | 14.2942i | −0.501320 | − | 0.501320i | ||||
\(814\) | −6.92820 | − | 10.0000i | −0.242833 | − | 0.350500i | ||||
\(815\) | 3.53590 | + | 7.07180i | 0.123857 | + | 0.247714i | ||||
\(816\) | −11.5622 | + | 3.09808i | −0.404757 | + | 0.108454i | ||||
\(817\) | −67.0788 | − | 17.9737i | −2.34679 | − | 0.628821i | ||||
\(818\) | −7.10770 | + | 26.5263i | −0.248515 | + | 0.927470i | ||||
\(819\) | −1.32051 | + | 4.92820i | −0.0461423 | + | 0.172205i | ||||
\(820\) | 12.9282 | − | 6.46410i | 0.451472 | − | 0.225736i | ||||
\(821\) | 10.5622 | + | 18.2942i | 0.368623 | + | 0.638473i | 0.989350 | − | 0.145553i | \(-0.0464962\pi\) |
−0.620728 | + | 0.784026i | \(0.713163\pi\) | |||||||
\(822\) | −5.46410 | −0.190582 | ||||||||
\(823\) | −8.97372 | − | 33.4904i | −0.312804 | − | 1.16740i | −0.926016 | − | 0.377483i | \(-0.876790\pi\) |
0.613212 | − | 0.789918i | \(-0.289877\pi\) | |||||||
\(824\) | 6.19615i | 0.215853i | ||||||||
\(825\) | −2.73205 | − | 19.1244i | −0.0951178 | − | 0.665825i | ||||
\(826\) | −4.53590 | + | 7.85641i | −0.157824 | + | 0.273359i | ||||
\(827\) | 6.92820 | + | 12.0000i | 0.240917 | + | 0.417281i | 0.960976 | − | 0.276632i | \(-0.0892184\pi\) |
−0.720059 | + | 0.693913i | \(0.755885\pi\) | |||||||
\(828\) | −4.39230 | −0.152643 | ||||||||
\(829\) | 12.4186 | + | 46.3468i | 0.431315 | + | 1.60969i | 0.749733 | + | 0.661740i | \(0.230182\pi\) |
−0.318418 | + | 0.947950i | \(0.603152\pi\) | |||||||
\(830\) | 23.9019 | + | 26.9545i | 0.829648 | + | 0.935604i | ||||
\(831\) | 8.33013 | + | 31.0885i | 0.288969 | + | 1.07845i | ||||
\(832\) | 2.13397 | − | 1.23205i | 0.0739823 | − | 0.0427137i | ||||
\(833\) | 5.36603 | − | 3.09808i | 0.185922 | − | 0.107342i | ||||
\(834\) | 5.46410 | + | 20.3923i | 0.189206 | + | 0.706128i | ||||
\(835\) | −46.2750 | − | 2.77757i | −1.60141 | − | 0.0961217i | ||||
\(836\) | −3.26795 | − | 12.1962i | −0.113024 | − | 0.421813i | ||||
\(837\) | 42.3205 | 1.46281 | ||||||||
\(838\) | −7.16987 | − | 12.4186i | −0.247679 | − | 0.428993i | ||||
\(839\) | −12.0622 | + | 20.8923i | −0.416433 | + | 0.721282i | −0.995578 | − | 0.0939421i | \(-0.970053\pi\) |
0.579145 | + | 0.815225i | \(0.303386\pi\) | |||||||
\(840\) | 5.46410 | + | 10.9282i | 0.188529 | + | 0.377059i | ||||
\(841\) | − | 15.7846i | − | 0.544297i | ||||||
\(842\) | 3.16987 | + | 11.8301i | 0.109241 | + | 0.407693i | ||||
\(843\) | −4.66025 | −0.160508 | ||||||||
\(844\) | 2.00000 | + | 3.46410i | 0.0688428 | + | 0.119239i | ||||
\(845\) | −6.92820 | − | 13.8564i | −0.238337 | − | 0.476675i | ||||
\(846\) | 1.66025 | − | 6.19615i | 0.0570807 | − | 0.213028i | ||||
\(847\) | −5.12436 | + | 19.1244i | −0.176075 | + | 0.657121i | ||||
\(848\) | 4.86603 | + | 1.30385i | 0.167100 | + | 0.0447743i | ||||
\(849\) | −24.2583 | + | 6.50000i | −0.832544 | + | 0.223079i | ||||
\(850\) | −24.7846 | − | 18.5885i | −0.850105 | − | 0.637579i | ||||
\(851\) | −33.0000 | − | 15.5885i | −1.13123 | − | 0.534365i | ||||
\(852\) | 4.00000 | + | 4.00000i | 0.137038 | + | 0.137038i | ||||
\(853\) | −3.03590 | + | 5.25833i | −0.103947 | + | 0.180042i | −0.913308 | − | 0.407271i | \(-0.866481\pi\) |
0.809360 | + | 0.587312i | \(0.199814\pi\) | |||||||
\(854\) | −2.53590 | − | 4.39230i | −0.0867767 | − | 0.150302i | ||||
\(855\) | 2.07180 | + | 10.1244i | 0.0708540 | + | 0.346246i | ||||
\(856\) | −13.4282 | − | 3.59808i | −0.458967 | − | 0.122980i | ||||
\(857\) | −10.7321 | −0.366600 | −0.183300 | − | 0.983057i | \(-0.558678\pi\) | ||||
−0.183300 | + | 0.983057i | \(0.558678\pi\) | |||||||
\(858\) | 9.19615 | + | 2.46410i | 0.313951 | + | 0.0841230i | ||||
\(859\) | 27.0000 | + | 27.0000i | 0.921228 | + | 0.921228i | 0.997116 | − | 0.0758882i | \(-0.0241792\pi\) |
−0.0758882 | + | 0.997116i | \(0.524179\pi\) | |||||||
\(860\) | 1.47372 | − | 24.5526i | 0.0502535 | − | 0.837235i | ||||
\(861\) | −35.3205 | −1.20372 | ||||||||
\(862\) | 11.2224 | − | 11.2224i | 0.382238 | − | 0.382238i | ||||
\(863\) | 0.241670 | + | 0.901924i | 0.00822653 | + | 0.0307018i | 0.969917 | − | 0.243435i | \(-0.0782744\pi\) |
−0.961691 | + | 0.274137i | \(0.911608\pi\) | |||||||
\(864\) | 1.13397 | − | 4.23205i | 0.0385786 | − | 0.143977i | ||||
\(865\) | −17.1962 | + | 51.5885i | −0.584687 | + | 1.75406i | ||||
\(866\) | −4.36603 | + | 1.16987i | −0.148364 | + | 0.0397539i | ||||
\(867\) | −39.9186 | + | 10.6962i | −1.35571 | + | 0.363260i | ||||
\(868\) | −23.6603 | − | 13.6603i | −0.803081 | − | 0.463659i | ||||
\(869\) | −13.6603 | − | 3.66025i | −0.463392 | − | 0.124166i | ||||
\(870\) | −24.1244 | − | 15.9282i | −0.817892 | − | 0.540017i | ||||
\(871\) | −13.2224 | + | 3.54294i | −0.448025 | + | 0.120048i | ||||
\(872\) | −0.267949 | − | 1.00000i | −0.00907390 | − | 0.0338643i | ||||
\(873\) | 0.928203 | + | 0.535898i | 0.0314149 | + | 0.0181374i | ||||
\(874\) | −26.7846 | − | 26.7846i | −0.906003 | − | 0.906003i | ||||
\(875\) | −13.5167 | + | 28.5885i | −0.456947 | + | 0.966466i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.1699 | − | 21.1699i | −0.714856 | − | 0.714856i | 0.252691 | − | 0.967547i | \(-0.418684\pi\) |
−0.967547 | + | 0.252691i | \(0.918684\pi\) | |||||||
\(878\) | −0.633975 | − | 0.633975i | −0.0213956 | − | 0.0213956i | ||||
\(879\) | −3.13397 | + | 5.42820i | −0.105706 | + | 0.183089i | ||||
\(880\) | 4.00000 | − | 2.00000i | 0.134840 | − | 0.0674200i | ||||
\(881\) | 25.0526 | − | 14.4641i | 0.844042 | − | 0.487308i | −0.0145940 | − | 0.999894i | \(-0.504646\pi\) |
0.858636 | + | 0.512586i | \(0.171312\pi\) | |||||||
\(882\) | − | 0.732051i | − | 0.0246494i | ||||||
\(883\) | 6.59808 | + | 11.4282i | 0.222043 | + | 0.384590i | 0.955428 | − | 0.295224i | \(-0.0953941\pi\) |
−0.733385 | + | 0.679813i | \(0.762061\pi\) | |||||||
\(884\) | 13.2224 | − | 7.63397i | 0.444719 | − | 0.256758i | ||||
\(885\) | −11.5622 | − | 7.63397i | −0.388658 | − | 0.256613i | ||||
\(886\) | −6.86603 | − | 25.6244i | −0.230669 | − | 0.860867i | ||||
\(887\) | −6.60770 | + | 6.60770i | −0.221865 | + | 0.221865i | −0.809283 | − | 0.587419i | \(-0.800144\pi\) |
0.587419 | + | 0.809283i | \(0.300144\pi\) | |||||||
\(888\) | −7.59808 | + | 8.96410i | −0.254975 | + | 0.300816i | ||||
\(889\) | − | 25.8564i | − | 0.867196i | ||||||
\(890\) | −2.50962 | − | 2.83013i | −0.0841226 | − | 0.0948661i | ||||
\(891\) | 18.4641 | − | 10.6603i | 0.618571 | − | 0.357132i | ||||
\(892\) | −17.6603 | − | 4.73205i | −0.591309 | − | 0.158441i | ||||
\(893\) | 47.9090 | − | 27.6603i | 1.60321 | − | 0.925615i | ||||
\(894\) | 31.0526 | + | 31.0526i | 1.03855 | + | 1.03855i | ||||
\(895\) | −6.58846 | − | 32.1962i | −0.220228 | − | 1.07620i | ||||
\(896\) | −2.00000 | + | 2.00000i | −0.0668153 | + | 0.0668153i | ||||
\(897\) | 27.5885 | − | 7.39230i | 0.921152 | − | 0.246822i | ||||
\(898\) | 1.16987 | − | 1.16987i | 0.0390392 | − | 0.0390392i | ||||
\(899\) | 64.6410 | 2.15590 | ||||||||
\(900\) | −3.36603 | + | 1.43782i | −0.112201 | + | 0.0479274i | ||||
\(901\) | 30.1506 | + | 8.07884i | 1.00446 | + | 0.269145i | ||||
\(902\) | 12.9282i | 0.430462i | ||||||||
\(903\) | −30.0526 | + | 52.0526i | −1.00009 | + | 1.73220i | ||||
\(904\) | 5.19615 | + | 3.00000i | 0.172821 | + | 0.0997785i | ||||
\(905\) | −30.8109 | − | 1.84936i | −1.02419 | − | 0.0614750i | ||||
\(906\) | 1.59808 | − | 5.96410i | 0.0530925 | − | 0.198144i | ||||
\(907\) | 18.5885 | + | 32.1962i | 0.617220 | + | 1.06906i | 0.989991 | + | 0.141132i | \(0.0450743\pi\) |
−0.372771 | + | 0.927923i | \(0.621592\pi\) | |||||||
\(908\) | 1.33013 | − | 2.30385i | 0.0441418 | − | 0.0764559i | ||||
\(909\) | 0.0717968 | − | 0.124356i | 0.00238135 | − | 0.00412462i | ||||
\(910\) | −10.3397 | − | 11.6603i | −0.342759 | − | 0.386534i | ||||
\(911\) | 8.63397 | − | 8.63397i | 0.286056 | − | 0.286056i | −0.549462 | − | 0.835519i | \(-0.685167\pi\) |
0.835519 | + | 0.549462i | \(0.185167\pi\) | |||||||
\(912\) | −10.5622 | + | 6.09808i | −0.349749 | + | 0.201927i | ||||
\(913\) | −31.1244 | + | 8.33975i | −1.03007 | + | 0.276005i | ||||
\(914\) | 26.7846i | 0.885956i | ||||||||
\(915\) | 6.92820 | − | 3.46410i | 0.229039 | − | 0.114520i | ||||
\(916\) | 15.2942 | + | 8.83013i | 0.505336 | + | 0.291756i | ||||
\(917\) | 2.14359i | 0.0707877i | ||||||||
\(918\) | 7.02628 | − | 26.2224i | 0.231902 | − | 0.865469i | ||||
\(919\) | −25.7846 | + | 25.7846i | −0.850556 | + | 0.850556i | −0.990202 | − | 0.139646i | \(-0.955404\pi\) |
0.139646 | + | 0.990202i | \(0.455404\pi\) | |||||||
\(920\) | 7.39230 | − | 11.1962i | 0.243717 | − | 0.369126i | ||||
\(921\) | −21.0622 | − | 36.4808i | −0.694022 | − | 1.20208i | ||||
\(922\) | −4.53590 | + | 16.9282i | −0.149382 | + | 0.557501i | ||||
\(923\) | −6.24871 | − | 3.60770i | −0.205679 | − | 0.118749i | ||||
\(924\) | −10.9282 | −0.359511 | ||||||||
\(925\) | −30.3923 | − | 1.14359i | −0.999293 | − | 0.0376011i | ||||
\(926\) | 8.33975 | 0.274061 | ||||||||
\(927\) | 3.92820 | + | 2.26795i | 0.129019 | + | 0.0744892i | ||||
\(928\) | 1.73205 | − | 6.46410i | 0.0568574 | − | 0.212195i | ||||
\(929\) | 0.330127 | + | 0.571797i | 0.0108311 | + | 0.0187600i | 0.871390 | − | 0.490591i | \(-0.163219\pi\) |
−0.860559 | + | 0.509351i | \(0.829886\pi\) | |||||||
\(930\) | 22.9904 | − | 34.8205i | 0.753884 | − | 1.14181i | ||||
\(931\) | 4.46410 | − | 4.46410i | 0.146305 | − | 0.146305i | ||||
\(932\) | 5.80385 | − | 21.6603i | 0.190111 | − | 0.709505i | ||||
\(933\) | − | 30.5167i | − | 0.999071i | ||||||
\(934\) | −25.9186 | − | 14.9641i | −0.848082 | − | 0.489640i | ||||
\(935\) | 24.7846 | − | 12.3923i | 0.810543 | − | 0.405272i | ||||
\(936\) | − | 1.80385i | − | 0.0589606i | ||||||
\(937\) | −36.2224 | + | 9.70577i | −1.18334 | + | 0.317074i | −0.796249 | − | 0.604970i | \(-0.793185\pi\) |
−0.387087 | + | 0.922043i | \(0.626519\pi\) | |||||||
\(938\) | 13.6077 | − | 7.85641i | 0.444307 | − | 0.256521i | ||||
\(939\) | −23.8564 | + | 23.8564i | −0.778524 | + | 0.778524i | ||||
\(940\) | 13.0000 | + | 14.6603i | 0.424013 | + | 0.478165i | ||||
\(941\) | −16.5885 | + | 28.7321i | −0.540768 | + | 0.936638i | 0.458092 | + | 0.888905i | \(0.348533\pi\) |
−0.998860 | + | 0.0477332i | \(0.984800\pi\) | |||||||
\(942\) | −19.6244 | + | 33.9904i | −0.639396 | + | 1.10747i | ||||
\(943\) | 19.3923 | + | 33.5885i | 0.631500 | + | 1.09379i | ||||
\(944\) | 0.830127 | − | 3.09808i | 0.0270183 | − | 0.100834i | ||||
\(945\) | −27.6603 | − | 1.66025i | −0.899788 | − | 0.0540081i | ||||
\(946\) | 19.0526 | + | 11.0000i | 0.619452 | + | 0.357641i | ||||
\(947\) | 22.7679 | − | 39.4352i | 0.739859 | − | 1.28147i | −0.212700 | − | 0.977118i | \(-0.568226\pi\) |
0.952558 | − | 0.304356i | \(-0.0984411\pi\) | |||||||
\(948\) | 13.6603i | 0.443664i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −29.2942 | − | 11.7583i | −0.950430 | − | 0.381491i | ||||
\(951\) | 53.6410 | 1.73943 | ||||||||
\(952\) | −12.3923 | + | 12.3923i | −0.401637 | + | 0.401637i | ||||
\(953\) | 48.0526 | − | 12.8756i | 1.55658 | − | 0.417083i | 0.624998 | − | 0.780626i | \(-0.285100\pi\) |
0.931577 | + | 0.363543i | \(0.118433\pi\) | |||||||
\(954\) | 2.60770 | − | 2.60770i | 0.0844272 | − | 0.0844272i | ||||
\(955\) | −1.16025 | − | 5.66987i | −0.0375449 | − | 0.183473i | ||||
\(956\) | 10.8564 | + | 10.8564i | 0.351121 | + | 0.351121i | ||||
\(957\) | 22.3923 | − | 12.9282i | 0.723840 | − | 0.417909i | ||||
\(958\) | 3.96410 | + | 1.06218i | 0.128074 | + | 0.0343174i | ||||
\(959\) | −6.92820 | + | 4.00000i | −0.223723 | + | 0.129167i | ||||
\(960\) | −2.86603 | − | 3.23205i | −0.0925006 | − | 0.104314i | ||||
\(961\) | 62.3013i | 2.00972i | ||||||||
\(962\) | 6.40192 | − | 13.5526i | 0.206406 | − | 0.436952i | ||||
\(963\) | −7.19615 | + | 7.19615i | −0.231893 | + | 0.231893i | ||||
\(964\) | 4.83013 | + | 18.0263i | 0.155568 | + | 0.580587i | ||||
\(965\) | −0.633975 | − | 0.418584i | −0.0204084 | − | 0.0134747i | ||||
\(966\) | −28.3923 | + | 16.3923i | −0.913507 | + | 0.527414i | ||||
\(967\) | −19.0263 | − | 32.9545i | −0.611844 | − | 1.05974i | −0.990929 | − | 0.134383i | \(-0.957095\pi\) |
0.379086 | − | 0.925362i | \(-0.376239\pi\) | |||||||
\(968\) | − | 7.00000i | − | 0.224989i | ||||||
\(969\) | −65.4449 | + | 37.7846i | −2.10239 | + | 1.21382i | ||||
\(970\) | −2.92820 | + | 1.46410i | −0.0940189 | + | 0.0470095i | ||||
\(971\) | 12.4904 | − | 21.6340i | 0.400835 | − | 0.694267i | −0.592992 | − | 0.805209i | \(-0.702053\pi\) |
0.993827 | + | 0.110941i | \(0.0353866\pi\) | |||||||
\(972\) | −5.26795 | − | 5.26795i | −0.168970 | − | 0.168970i | ||||
\(973\) | 21.8564 | + | 21.8564i | 0.700684 | + | 0.700684i | ||||
\(974\) | −35.9090 | − | 20.7321i | −1.15060 | − | 0.664298i | ||||
\(975\) | 18.7224 | − | 14.6962i | 0.599598 | − | 0.470654i | ||||
\(976\) | 1.26795 | + | 1.26795i | 0.0405861 | + | 0.0405861i | ||||
\(977\) | 38.3660 | + | 22.1506i | 1.22744 | + | 0.708662i | 0.966493 | − | 0.256692i | \(-0.0826326\pi\) |
0.260945 | + | 0.965354i | \(0.415966\pi\) | |||||||
\(978\) | 1.76795 | + | 6.59808i | 0.0565328 | + | 0.210983i | ||||
\(979\) | 3.26795 | − | 0.875644i | 0.104444 | − | 0.0279857i | ||||
\(980\) | 1.86603 | + | 1.23205i | 0.0596080 | + | 0.0393564i | ||||
\(981\) | −0.732051 | − | 0.196152i | −0.0233726 | − | 0.00626266i | ||||
\(982\) | 7.09808 | + | 4.09808i | 0.226509 | + | 0.130775i | ||||
\(983\) | −30.1244 | + | 8.07180i | −0.960818 | + | 0.257450i | −0.704946 | − | 0.709261i | \(-0.749029\pi\) |
−0.255871 | + | 0.966711i | \(0.582362\pi\) | |||||||
\(984\) | 12.0622 | − | 3.23205i | 0.384528 | − | 0.103034i | ||||
\(985\) | −5.75833 | + | 17.2750i | −0.183476 | + | 0.550427i | ||||
\(986\) | 10.7321 | − | 40.0526i | 0.341778 | − | 1.27553i | ||||
\(987\) | −12.3923 | − | 46.2487i | −0.394451 | − | 1.47211i | ||||
\(988\) | 11.0000 | − | 11.0000i | 0.349957 | − | 0.349957i | ||||
\(989\) | 66.0000 | 2.09868 | ||||||||
\(990\) | 0.196152 | − | 3.26795i | 0.00623413 | − | 0.103862i | ||||
\(991\) | 13.0981 | + | 13.0981i | 0.416074 | + | 0.416074i | 0.883848 | − | 0.467774i | \(-0.154944\pi\) |
−0.467774 | + | 0.883848i | \(0.654944\pi\) | |||||||
\(992\) | 9.33013 | + | 2.50000i | 0.296232 | + | 0.0793751i | ||||
\(993\) | 6.19615 | 0.196629 | ||||||||
\(994\) | 8.00000 | + | 2.14359i | 0.253745 | + | 0.0679907i | ||||
\(995\) | 9.35641 | + | 45.7224i | 0.296618 | + | 1.44950i | ||||
\(996\) | 15.5622 | + | 26.9545i | 0.493106 | + | 0.854085i | ||||
\(997\) | −15.0885 | + | 26.1340i | −0.477856 | + | 0.827671i | −0.999678 | − | 0.0253834i | \(-0.991919\pi\) |
0.521822 | + | 0.853055i | \(0.325253\pi\) | |||||||
\(998\) | 11.1244 | + | 11.1244i | 0.352135 | + | 0.352135i | ||||
\(999\) | −8.99038 | − | 25.0885i | −0.284443 | − | 0.793764i |
(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 | 370.2.r.a.347.1 | yes | 4 | |
5.3 | odd | 4 | 370.2.q.a.273.1 | yes | 4 | ||
37.8 | odd | 12 | 370.2.q.a.267.1 | ✓ | 4 | ||
185.8 | even | 12 | inner | 370.2.r.a.193.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.q.a.267.1 | ✓ | 4 | 37.8 | odd | 12 | ||
370.2.q.a.273.1 | yes | 4 | 5.3 | odd | 4 | ||
370.2.r.a.193.1 | yes | 4 | 185.8 | even | 12 | inner | |
370.2.r.a.347.1 | yes | 4 | 1.1 | even | 1 | trivial |