Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (of order \(4\), degree \(2\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 487.11 | ||
Character | \(\chi\) | \(=\) | 1110.487 |
Dual form | 1110.2.o.a.253.11 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.891783 | + | 2.05054i | −0.398817 | + | 0.917030i | ||||
\(6\) | −0.707107 | − | 0.707107i | −0.288675 | − | 0.288675i | ||||
\(7\) | −1.56460 | − | 1.56460i | −0.591365 | − | 0.591365i | 0.346635 | − | 0.938000i | \(-0.387324\pi\) |
−0.938000 | + | 0.346635i | \(0.887324\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.891783 | − | 2.05054i | 0.282007 | − | 0.648438i | ||||
\(11\) | 3.92190i | 1.18250i | 0.806489 | + | 0.591249i | \(0.201365\pi\) | ||||
−0.806489 | + | 0.591249i | \(0.798635\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | −0.319413 | −0.0885893 | −0.0442946 | − | 0.999019i | \(-0.514104\pi\) | ||||
−0.0442946 | + | 0.999019i | \(0.514104\pi\) | |||||||
\(14\) | 1.56460 | + | 1.56460i | 0.418158 | + | 0.418158i | ||||
\(15\) | −2.08054 | + | 0.819367i | −0.537193 | + | 0.211560i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.25497i | 0.304376i | 0.988352 | + | 0.152188i | \(0.0486319\pi\) | ||||
−0.988352 | + | 0.152188i | \(0.951368\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 2.17875 | − | 2.17875i | 0.499839 | − | 0.499839i | −0.411549 | − | 0.911388i | \(-0.635012\pi\) |
0.911388 | + | 0.411549i | \(0.135012\pi\) | |||||||
\(20\) | −0.891783 | + | 2.05054i | −0.199409 | + | 0.458515i | ||||
\(21\) | − | 2.21268i | − | 0.482847i | ||||||
\(22\) | − | 3.92190i | − | 0.836152i | ||||||
\(23\) | −1.15203 | −0.240215 | −0.120107 | − | 0.992761i | \(-0.538324\pi\) | ||||
−0.120107 | + | 0.992761i | \(0.538324\pi\) | |||||||
\(24\) | −0.707107 | − | 0.707107i | −0.144338 | − | 0.144338i | ||||
\(25\) | −3.40945 | − | 3.65728i | −0.681889 | − | 0.731455i | ||||
\(26\) | 0.319413 | 0.0626421 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | −1.56460 | − | 1.56460i | −0.295682 | − | 0.295682i | ||||
\(29\) | −1.22361 | − | 1.22361i | −0.227218 | − | 0.227218i | 0.584312 | − | 0.811529i | \(-0.301365\pi\) |
−0.811529 | + | 0.584312i | \(0.801365\pi\) | |||||||
\(30\) | 2.08054 | − | 0.819367i | 0.379853 | − | 0.149595i | ||||
\(31\) | −6.78274 | + | 6.78274i | −1.21822 | + | 1.21822i | −0.249959 | + | 0.968256i | \(0.580417\pi\) |
−0.968256 | + | 0.249959i | \(0.919583\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.77320 | + | 2.77320i | −0.482753 | + | 0.482753i | ||||
\(34\) | − | 1.25497i | − | 0.215226i | ||||||
\(35\) | 4.60357 | − | 1.81300i | 0.778146 | − | 0.306453i | ||||
\(36\) | 1.00000i | 0.166667i | ||||||||
\(37\) | −6.08275 | + | 0.0100817i | −0.999999 | + | 0.00165742i | ||||
\(38\) | −2.17875 | + | 2.17875i | −0.353440 | + | 0.353440i | ||||
\(39\) | −0.225859 | − | 0.225859i | −0.0361664 | − | 0.0361664i | ||||
\(40\) | 0.891783 | − | 2.05054i | 0.141003 | − | 0.324219i | ||||
\(41\) | 3.92813i | 0.613470i | 0.951795 | + | 0.306735i | \(0.0992366\pi\) | ||||
−0.951795 | + | 0.306735i | \(0.900763\pi\) | |||||||
\(42\) | 2.21268i | 0.341425i | ||||||||
\(43\) | −1.87330 | −0.285675 | −0.142838 | − | 0.989746i | \(-0.545623\pi\) | ||||
−0.142838 | + | 0.989746i | \(0.545623\pi\) | |||||||
\(44\) | 3.92190i | 0.591249i | ||||||||
\(45\) | −2.05054 | − | 0.891783i | −0.305677 | − | 0.132939i | ||||
\(46\) | 1.15203 | 0.169857 | ||||||||
\(47\) | −4.88442 | − | 4.88442i | −0.712466 | − | 0.712466i | 0.254585 | − | 0.967051i | \(-0.418061\pi\) |
−0.967051 | + | 0.254585i | \(0.918061\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 2.10403i | − | 0.300576i | ||||||
\(50\) | 3.40945 | + | 3.65728i | 0.482169 | + | 0.517217i | ||||
\(51\) | −0.887401 | + | 0.887401i | −0.124261 | + | 0.124261i | ||||
\(52\) | −0.319413 | −0.0442946 | ||||||||
\(53\) | −3.03226 | + | 3.03226i | −0.416513 | + | 0.416513i | −0.884000 | − | 0.467487i | \(-0.845160\pi\) |
0.467487 | + | 0.884000i | \(0.345160\pi\) | |||||||
\(54\) | 0.707107 | − | 0.707107i | 0.0962250 | − | 0.0962250i | ||||
\(55\) | −8.04202 | − | 3.49748i | −1.08439 | − | 0.471601i | ||||
\(56\) | 1.56460 | + | 1.56460i | 0.209079 | + | 0.209079i | ||||
\(57\) | 3.08122 | 0.408117 | ||||||||
\(58\) | 1.22361 | + | 1.22361i | 0.160667 | + | 0.160667i | ||||
\(59\) | 4.70399 | − | 4.70399i | 0.612407 | − | 0.612407i | −0.331165 | − | 0.943573i | \(-0.607442\pi\) |
0.943573 | + | 0.331165i | \(0.107442\pi\) | |||||||
\(60\) | −2.08054 | + | 0.819367i | −0.268596 | + | 0.105780i | ||||
\(61\) | −5.56135 | + | 5.56135i | −0.712058 | + | 0.712058i | −0.966965 | − | 0.254908i | \(-0.917955\pi\) |
0.254908 | + | 0.966965i | \(0.417955\pi\) | |||||||
\(62\) | 6.78274 | − | 6.78274i | 0.861408 | − | 0.861408i | ||||
\(63\) | 1.56460 | − | 1.56460i | 0.197122 | − | 0.197122i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.284847 | − | 0.654970i | 0.0353309 | − | 0.0812390i | ||||
\(66\) | 2.77320 | − | 2.77320i | 0.341358 | − | 0.341358i | ||||
\(67\) | 6.88391 | − | 6.88391i | 0.841003 | − | 0.841003i | −0.147986 | − | 0.988989i | \(-0.547279\pi\) |
0.988989 | + | 0.147986i | \(0.0472791\pi\) | |||||||
\(68\) | 1.25497i | 0.152188i | ||||||||
\(69\) | −0.814607 | − | 0.814607i | −0.0980672 | − | 0.0980672i | ||||
\(70\) | −4.60357 | + | 1.81300i | −0.550232 | + | 0.216695i | ||||
\(71\) | −3.29012 | −0.390466 | −0.195233 | − | 0.980757i | \(-0.562546\pi\) | ||||
−0.195233 | + | 0.980757i | \(0.562546\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | −8.53399 | − | 8.53399i | −0.998828 | − | 0.998828i | 0.00117124 | − | 0.999999i | \(-0.499627\pi\) |
−0.999999 | + | 0.00117124i | \(0.999627\pi\) | |||||||
\(74\) | 6.08275 | − | 0.0100817i | 0.707106 | − | 0.00117198i | ||||
\(75\) | 0.175243 | − | 4.99693i | 0.0202353 | − | 0.576996i | ||||
\(76\) | 2.17875 | − | 2.17875i | 0.249920 | − | 0.249920i | ||||
\(77\) | 6.13622 | − | 6.13622i | 0.699287 | − | 0.699287i | ||||
\(78\) | 0.225859 | + | 0.225859i | 0.0255735 | + | 0.0255735i | ||||
\(79\) | −3.59077 | + | 3.59077i | −0.403993 | + | 0.403993i | −0.879638 | − | 0.475645i | \(-0.842215\pi\) |
0.475645 | + | 0.879638i | \(0.342215\pi\) | |||||||
\(80\) | −0.891783 | + | 2.05054i | −0.0997044 | + | 0.229258i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | − | 3.92813i | − | 0.433789i | ||||||
\(83\) | −1.13008 | + | 1.13008i | −0.124042 | + | 0.124042i | −0.766403 | − | 0.642360i | \(-0.777955\pi\) |
0.642360 | + | 0.766403i | \(0.277955\pi\) | |||||||
\(84\) | − | 2.21268i | − | 0.241424i | ||||||
\(85\) | −2.57338 | − | 1.11916i | −0.279122 | − | 0.121390i | ||||
\(86\) | 1.87330 | 0.202003 | ||||||||
\(87\) | − | 1.73044i | − | 0.185523i | ||||||
\(88\) | − | 3.92190i | − | 0.418076i | ||||||
\(89\) | 1.33809 | + | 1.33809i | 0.141837 | + | 0.141837i | 0.774460 | − | 0.632623i | \(-0.218022\pi\) |
−0.632623 | + | 0.774460i | \(0.718022\pi\) | |||||||
\(90\) | 2.05054 | + | 0.891783i | 0.216146 | + | 0.0940022i | ||||
\(91\) | 0.499755 | + | 0.499755i | 0.0523886 | + | 0.0523886i | ||||
\(92\) | −1.15203 | −0.120107 | ||||||||
\(93\) | −9.59224 | −0.994669 | ||||||||
\(94\) | 4.88442 | + | 4.88442i | 0.503790 | + | 0.503790i | ||||
\(95\) | 2.52465 | + | 6.41059i | 0.259023 | + | 0.657712i | ||||
\(96\) | −0.707107 | − | 0.707107i | −0.0721688 | − | 0.0721688i | ||||
\(97\) | 4.01884i | 0.408051i | 0.978966 | + | 0.204025i | \(0.0654025\pi\) | ||||
−0.978966 | + | 0.204025i | \(0.934597\pi\) | |||||||
\(98\) | 2.10403i | 0.212539i | ||||||||
\(99\) | −3.92190 | −0.394166 | ||||||||
\(100\) | −3.40945 | − | 3.65728i | −0.340945 | − | 0.365728i | ||||
\(101\) | 11.0673i | 1.10124i | 0.834757 | + | 0.550618i | \(0.185608\pi\) | ||||
−0.834757 | + | 0.550618i | \(0.814392\pi\) | |||||||
\(102\) | 0.887401 | − | 0.887401i | 0.0878658 | − | 0.0878658i | ||||
\(103\) | − | 13.8134i | − | 1.36107i | −0.732715 | − | 0.680536i | \(-0.761747\pi\) | ||
0.732715 | − | 0.680536i | \(-0.238253\pi\) | |||||||
\(104\) | 0.319413 | 0.0313210 | ||||||||
\(105\) | 4.53720 | + | 1.97323i | 0.442785 | + | 0.192568i | ||||
\(106\) | 3.03226 | − | 3.03226i | 0.294520 | − | 0.294520i | ||||
\(107\) | 1.55870 | + | 1.55870i | 0.150685 | + | 0.150685i | 0.778424 | − | 0.627739i | \(-0.216019\pi\) |
−0.627739 | + | 0.778424i | \(0.716019\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | −4.24101 | + | 4.24101i | −0.406215 | + | 0.406215i | −0.880416 | − | 0.474201i | \(-0.842737\pi\) |
0.474201 | + | 0.880416i | \(0.342737\pi\) | |||||||
\(110\) | 8.04202 | + | 3.49748i | 0.766777 | + | 0.333472i | ||||
\(111\) | −4.30829 | − | 4.29403i | −0.408924 | − | 0.407571i | ||||
\(112\) | −1.56460 | − | 1.56460i | −0.147841 | − | 0.147841i | ||||
\(113\) | 16.5384i | 1.55580i | 0.628390 | + | 0.777899i | \(0.283714\pi\) | ||||
−0.628390 | + | 0.777899i | \(0.716286\pi\) | |||||||
\(114\) | −3.08122 | −0.288582 | ||||||||
\(115\) | 1.02736 | − | 2.36228i | 0.0958018 | − | 0.220284i | ||||
\(116\) | −1.22361 | − | 1.22361i | −0.113609 | − | 0.113609i | ||||
\(117\) | − | 0.319413i | − | 0.0295298i | ||||||
\(118\) | −4.70399 | + | 4.70399i | −0.433037 | + | 0.433037i | ||||
\(119\) | 1.96354 | − | 1.96354i | 0.179997 | − | 0.179997i | ||||
\(120\) | 2.08054 | − | 0.819367i | 0.189926 | − | 0.0747976i | ||||
\(121\) | −4.38131 | −0.398301 | ||||||||
\(122\) | 5.56135 | − | 5.56135i | 0.503501 | − | 0.503501i | ||||
\(123\) | −2.77761 | + | 2.77761i | −0.250448 | + | 0.250448i | ||||
\(124\) | −6.78274 | + | 6.78274i | −0.609108 | + | 0.609108i | ||||
\(125\) | 10.5399 | − | 3.72972i | 0.942716 | − | 0.333596i | ||||
\(126\) | −1.56460 | + | 1.56460i | −0.139386 | + | 0.139386i | ||||
\(127\) | 7.06209 | + | 7.06209i | 0.626659 | + | 0.626659i | 0.947226 | − | 0.320567i | \(-0.103873\pi\) |
−0.320567 | + | 0.947226i | \(0.603873\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −1.32462 | − | 1.32462i | −0.116626 | − | 0.116626i | ||||
\(130\) | −0.284847 | + | 0.654970i | −0.0249828 | + | 0.0574447i | ||||
\(131\) | −9.32171 | + | 9.32171i | −0.814442 | + | 0.814442i | −0.985296 | − | 0.170855i | \(-0.945347\pi\) |
0.170855 | + | 0.985296i | \(0.445347\pi\) | |||||||
\(132\) | −2.77320 | + | 2.77320i | −0.241376 | + | 0.241376i | ||||
\(133\) | −6.81776 | −0.591174 | ||||||||
\(134\) | −6.88391 | + | 6.88391i | −0.594679 | + | 0.594679i | ||||
\(135\) | −0.819367 | − | 2.08054i | −0.0705198 | − | 0.179064i | ||||
\(136\) | − | 1.25497i | − | 0.107613i | ||||||
\(137\) | −14.5752 | − | 14.5752i | −1.24525 | − | 1.24525i | −0.957796 | − | 0.287450i | \(-0.907193\pi\) |
−0.287450 | − | 0.957796i | \(-0.592807\pi\) | |||||||
\(138\) | 0.814607 | + | 0.814607i | 0.0693440 | + | 0.0693440i | ||||
\(139\) | −1.20629 | −0.102316 | −0.0511582 | − | 0.998691i | \(-0.516291\pi\) | ||||
−0.0511582 | + | 0.998691i | \(0.516291\pi\) | |||||||
\(140\) | 4.60357 | − | 1.81300i | 0.389073 | − | 0.153226i | ||||
\(141\) | − | 6.90761i | − | 0.581726i | ||||||
\(142\) | 3.29012 | 0.276101 | ||||||||
\(143\) | − | 1.25271i | − | 0.104757i | ||||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 3.60025 | − | 1.41786i | 0.298984 | − | 0.117747i | ||||
\(146\) | 8.53399 | + | 8.53399i | 0.706278 | + | 0.706278i | ||||
\(147\) | 1.48777 | − | 1.48777i | 0.122710 | − | 0.122710i | ||||
\(148\) | −6.08275 | + | 0.0100817i | −0.499999 | + | 0.000828712i | ||||
\(149\) | − | 0.425764i | − | 0.0348800i | −0.999848 | − | 0.0174400i | \(-0.994448\pi\) | ||
0.999848 | − | 0.0174400i | \(-0.00555160\pi\) | |||||||
\(150\) | −0.175243 | + | 4.99693i | −0.0143085 | + | 0.407997i | ||||
\(151\) | 18.6559i | 1.51820i | 0.650976 | + | 0.759098i | \(0.274360\pi\) | ||||
−0.650976 | + | 0.759098i | \(0.725640\pi\) | |||||||
\(152\) | −2.17875 | + | 2.17875i | −0.176720 | + | 0.176720i | ||||
\(153\) | −1.25497 | −0.101459 | ||||||||
\(154\) | −6.13622 | + | 6.13622i | −0.494471 | + | 0.494471i | ||||
\(155\) | −7.85956 | − | 19.9570i | −0.631295 | − | 1.60299i | ||||
\(156\) | −0.225859 | − | 0.225859i | −0.0180832 | − | 0.0180832i | ||||
\(157\) | 6.23375 | + | 6.23375i | 0.497507 | + | 0.497507i | 0.910661 | − | 0.413154i | \(-0.135573\pi\) |
−0.413154 | + | 0.910661i | \(0.635573\pi\) | |||||||
\(158\) | 3.59077 | − | 3.59077i | 0.285666 | − | 0.285666i | ||||
\(159\) | −4.28827 | −0.340082 | ||||||||
\(160\) | 0.891783 | − | 2.05054i | 0.0705016 | − | 0.162110i | ||||
\(161\) | 1.80247 | + | 1.80247i | 0.142054 | + | 0.142054i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | − | 15.4091i | − | 1.20693i | −0.797389 | − | 0.603466i | \(-0.793786\pi\) | ||
0.797389 | − | 0.603466i | \(-0.206214\pi\) | |||||||
\(164\) | 3.92813i | 0.306735i | ||||||||
\(165\) | −3.21347 | − | 8.15967i | −0.250169 | − | 0.635229i | ||||
\(166\) | 1.13008 | − | 1.13008i | 0.0877111 | − | 0.0877111i | ||||
\(167\) | 16.8371i | 1.30289i | 0.758694 | + | 0.651447i | \(0.225838\pi\) | ||||
−0.758694 | + | 0.651447i | \(0.774162\pi\) | |||||||
\(168\) | 2.21268i | 0.170712i | ||||||||
\(169\) | −12.8980 | −0.992152 | ||||||||
\(170\) | 2.57338 | + | 1.11916i | 0.197369 | + | 0.0858360i | ||||
\(171\) | 2.17875 | + | 2.17875i | 0.166613 | + | 0.166613i | ||||
\(172\) | −1.87330 | −0.142838 | ||||||||
\(173\) | −5.18404 | − | 5.18404i | −0.394136 | − | 0.394136i | 0.482023 | − | 0.876159i | \(-0.339902\pi\) |
−0.876159 | + | 0.482023i | \(0.839902\pi\) | |||||||
\(174\) | 1.73044i | 0.131184i | ||||||||
\(175\) | −0.387756 | + | 11.0566i | −0.0293116 | + | 0.835802i | ||||
\(176\) | 3.92190i | 0.295624i | ||||||||
\(177\) | 6.65245 | 0.500029 | ||||||||
\(178\) | −1.33809 | − | 1.33809i | −0.100294 | − | 0.100294i | ||||
\(179\) | 1.70251 | + | 1.70251i | 0.127252 | + | 0.127252i | 0.767864 | − | 0.640613i | \(-0.221320\pi\) |
−0.640613 | + | 0.767864i | \(0.721320\pi\) | |||||||
\(180\) | −2.05054 | − | 0.891783i | −0.152838 | − | 0.0664696i | ||||
\(181\) | 8.75170 | 0.650509 | 0.325254 | − | 0.945627i | \(-0.394550\pi\) | ||||
0.325254 | + | 0.945627i | \(0.394550\pi\) | |||||||
\(182\) | −0.499755 | − | 0.499755i | −0.0370443 | − | 0.0370443i | ||||
\(183\) | −7.86494 | −0.581393 | ||||||||
\(184\) | 1.15203 | 0.0849287 | ||||||||
\(185\) | 5.40382 | − | 12.4819i | 0.397297 | − | 0.917690i | ||||
\(186\) | 9.59224 | 0.703337 | ||||||||
\(187\) | −4.92188 | −0.359924 | ||||||||
\(188\) | −4.88442 | − | 4.88442i | −0.356233 | − | 0.356233i | ||||
\(189\) | 2.21268 | 0.160949 | ||||||||
\(190\) | −2.52465 | − | 6.41059i | −0.183157 | − | 0.465073i | ||||
\(191\) | 4.56780 | + | 4.56780i | 0.330514 | + | 0.330514i | 0.852782 | − | 0.522268i | \(-0.174914\pi\) |
−0.522268 | + | 0.852782i | \(0.674914\pi\) | |||||||
\(192\) | 0.707107 | + | 0.707107i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | −5.51547 | −0.397012 | −0.198506 | − | 0.980100i | \(-0.563609\pi\) | ||||
−0.198506 | + | 0.980100i | \(0.563609\pi\) | |||||||
\(194\) | − | 4.01884i | − | 0.288536i | ||||||
\(195\) | 0.664551 | − | 0.261716i | 0.0475895 | − | 0.0187419i | ||||
\(196\) | − | 2.10403i | − | 0.150288i | ||||||
\(197\) | −3.48510 | − | 3.48510i | −0.248303 | − | 0.248303i | 0.571971 | − | 0.820274i | \(-0.306179\pi\) |
−0.820274 | + | 0.571971i | \(0.806179\pi\) | |||||||
\(198\) | 3.92190 | 0.278717 | ||||||||
\(199\) | 11.0862 | + | 11.0862i | 0.785883 | + | 0.785883i | 0.980817 | − | 0.194933i | \(-0.0624490\pi\) |
−0.194933 | + | 0.980817i | \(0.562449\pi\) | |||||||
\(200\) | 3.40945 | + | 3.65728i | 0.241084 | + | 0.258609i | ||||
\(201\) | 9.73532 | 0.686676 | ||||||||
\(202\) | − | 11.0673i | − | 0.778692i | ||||||
\(203\) | 3.82892i | 0.268737i | ||||||||
\(204\) | −0.887401 | + | 0.887401i | −0.0621305 | + | 0.0621305i | ||||
\(205\) | −8.05479 | − | 3.50304i | −0.562571 | − | 0.244663i | ||||
\(206\) | 13.8134i | 0.962423i | ||||||||
\(207\) | − | 1.15203i | − | 0.0800715i | ||||||
\(208\) | −0.319413 | −0.0221473 | ||||||||
\(209\) | 8.54484 | + | 8.54484i | 0.591059 | + | 0.591059i | ||||
\(210\) | −4.53720 | − | 1.97323i | −0.313097 | − | 0.136166i | ||||
\(211\) | 27.2170 | 1.87370 | 0.936848 | − | 0.349737i | \(-0.113729\pi\) | ||||
0.936848 | + | 0.349737i | \(0.113729\pi\) | |||||||
\(212\) | −3.03226 | + | 3.03226i | −0.208257 | + | 0.208257i | ||||
\(213\) | −2.32647 | − | 2.32647i | −0.159407 | − | 0.159407i | ||||
\(214\) | −1.55870 | − | 1.55870i | −0.106551 | − | 0.106551i | ||||
\(215\) | 1.67057 | − | 3.84128i | 0.113932 | − | 0.261973i | ||||
\(216\) | 0.707107 | − | 0.707107i | 0.0481125 | − | 0.0481125i | ||||
\(217\) | 21.2246 | 1.44082 | ||||||||
\(218\) | 4.24101 | − | 4.24101i | 0.287237 | − | 0.287237i | ||||
\(219\) | − | 12.0689i | − | 0.815540i | ||||||
\(220\) | −8.04202 | − | 3.49748i | −0.542193 | − | 0.235800i | ||||
\(221\) | − | 0.400855i | − | 0.0269644i | ||||||
\(222\) | 4.30829 | + | 4.29403i | 0.289153 | + | 0.288196i | ||||
\(223\) | 11.1865 | − | 11.1865i | 0.749103 | − | 0.749103i | −0.225208 | − | 0.974311i | \(-0.572306\pi\) |
0.974311 | + | 0.225208i | \(0.0723061\pi\) | |||||||
\(224\) | 1.56460 | + | 1.56460i | 0.104539 | + | 0.104539i | ||||
\(225\) | 3.65728 | − | 3.40945i | 0.243818 | − | 0.227296i | ||||
\(226\) | − | 16.5384i | − | 1.10011i | ||||||
\(227\) | 1.74912i | 0.116093i | 0.998314 | + | 0.0580467i | \(0.0184872\pi\) | ||||
−0.998314 | + | 0.0580467i | \(0.981513\pi\) | |||||||
\(228\) | 3.08122 | 0.204058 | ||||||||
\(229\) | − | 8.51464i | − | 0.562663i | −0.959611 | − | 0.281332i | \(-0.909224\pi\) | ||
0.959611 | − | 0.281332i | \(-0.0907761\pi\) | |||||||
\(230\) | −1.02736 | + | 2.36228i | −0.0677421 | + | 0.155764i | ||||
\(231\) | 8.67793 | 0.570966 | ||||||||
\(232\) | 1.22361 | + | 1.22361i | 0.0803336 | + | 0.0803336i | ||||
\(233\) | 6.42533 | + | 6.42533i | 0.420938 | + | 0.420938i | 0.885526 | − | 0.464589i | \(-0.153798\pi\) |
−0.464589 | + | 0.885526i | \(0.653798\pi\) | |||||||
\(234\) | 0.319413i | 0.0208807i | ||||||||
\(235\) | 14.3716 | − | 5.65987i | 0.937497 | − | 0.369209i | ||||
\(236\) | 4.70399 | − | 4.70399i | 0.306204 | − | 0.306204i | ||||
\(237\) | −5.07811 | −0.329859 | ||||||||
\(238\) | −1.96354 | + | 1.96354i | −0.127277 | + | 0.127277i | ||||
\(239\) | −10.4976 | + | 10.4976i | −0.679036 | + | 0.679036i | −0.959782 | − | 0.280746i | \(-0.909418\pi\) |
0.280746 | + | 0.959782i | \(0.409418\pi\) | |||||||
\(240\) | −2.08054 | + | 0.819367i | −0.134298 | + | 0.0528899i | ||||
\(241\) | 6.66851 | + | 6.66851i | 0.429556 | + | 0.429556i | 0.888477 | − | 0.458921i | \(-0.151764\pi\) |
−0.458921 | + | 0.888477i | \(0.651764\pi\) | |||||||
\(242\) | 4.38131 | 0.281641 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −5.56135 | + | 5.56135i | −0.356029 | + | 0.356029i | ||||
\(245\) | 4.31440 | + | 1.87634i | 0.275637 | + | 0.119875i | ||||
\(246\) | 2.77761 | − | 2.77761i | 0.177094 | − | 0.177094i | ||||
\(247\) | −0.695921 | + | 0.695921i | −0.0442804 | + | 0.0442804i | ||||
\(248\) | 6.78274 | − | 6.78274i | 0.430704 | − | 0.430704i | ||||
\(249\) | −1.59817 | −0.101280 | ||||||||
\(250\) | −10.5399 | + | 3.72972i | −0.666601 | + | 0.235888i | ||||
\(251\) | 19.9946 | − | 19.9946i | 1.26205 | − | 1.26205i | 0.311948 | − | 0.950099i | \(-0.399019\pi\) |
0.950099 | − | 0.311948i | \(-0.100981\pi\) | |||||||
\(252\) | 1.56460 | − | 1.56460i | 0.0985608 | − | 0.0985608i | ||||
\(253\) | − | 4.51814i | − | 0.284053i | ||||||
\(254\) | −7.06209 | − | 7.06209i | −0.443115 | − | 0.443115i | ||||
\(255\) | −1.02828 | − | 2.61102i | −0.0643936 | − | 0.163508i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 31.3639i | 1.95642i | 0.207609 | + | 0.978212i | \(0.433432\pi\) | ||||
−0.207609 | + | 0.978212i | \(0.566568\pi\) | |||||||
\(258\) | 1.32462 | + | 1.32462i | 0.0824673 | + | 0.0824673i | ||||
\(259\) | 9.53287 | + | 9.50133i | 0.592344 | + | 0.590384i | ||||
\(260\) | 0.284847 | − | 0.654970i | 0.0176655 | − | 0.0406195i | ||||
\(261\) | 1.22361 | − | 1.22361i | 0.0757393 | − | 0.0757393i | ||||
\(262\) | 9.32171 | − | 9.32171i | 0.575897 | − | 0.575897i | ||||
\(263\) | 7.40341 | + | 7.40341i | 0.456514 | + | 0.456514i | 0.897509 | − | 0.440995i | \(-0.145374\pi\) |
−0.440995 | + | 0.897509i | \(0.645374\pi\) | |||||||
\(264\) | 2.77320 | − | 2.77320i | 0.170679 | − | 0.170679i | ||||
\(265\) | −3.51366 | − | 8.92191i | −0.215843 | − | 0.548068i | ||||
\(266\) | 6.81776 | 0.418023 | ||||||||
\(267\) | 1.89234i | 0.115809i | ||||||||
\(268\) | 6.88391 | − | 6.88391i | 0.420502 | − | 0.420502i | ||||
\(269\) | 3.41947i | 0.208489i | 0.994552 | + | 0.104244i | \(0.0332424\pi\) | ||||
−0.994552 | + | 0.104244i | \(0.966758\pi\) | |||||||
\(270\) | 0.819367 | + | 2.08054i | 0.0498651 | + | 0.126618i | ||||
\(271\) | 17.8704 | 1.08555 | 0.542775 | − | 0.839878i | \(-0.317374\pi\) | ||||
0.542775 | + | 0.839878i | \(0.317374\pi\) | |||||||
\(272\) | 1.25497i | 0.0760940i | ||||||||
\(273\) | 0.706760i | 0.0427751i | ||||||||
\(274\) | 14.5752 | + | 14.5752i | 0.880522 | + | 0.880522i | ||||
\(275\) | 14.3435 | − | 13.3715i | 0.864944 | − | 0.806333i | ||||
\(276\) | −0.814607 | − | 0.814607i | −0.0490336 | − | 0.0490336i | ||||
\(277\) | −14.8527 | −0.892410 | −0.446205 | − | 0.894931i | \(-0.647225\pi\) | ||||
−0.446205 | + | 0.894931i | \(0.647225\pi\) | |||||||
\(278\) | 1.20629 | 0.0723486 | ||||||||
\(279\) | −6.78274 | − | 6.78274i | −0.406072 | − | 0.406072i | ||||
\(280\) | −4.60357 | + | 1.81300i | −0.275116 | + | 0.108347i | ||||
\(281\) | 4.56193 | + | 4.56193i | 0.272142 | + | 0.272142i | 0.829962 | − | 0.557820i | \(-0.188362\pi\) |
−0.557820 | + | 0.829962i | \(0.688362\pi\) | |||||||
\(282\) | 6.90761i | 0.411342i | ||||||||
\(283\) | 32.3891i | 1.92533i | 0.270692 | + | 0.962666i | \(0.412748\pi\) | ||||
−0.270692 | + | 0.962666i | \(0.587252\pi\) | |||||||
\(284\) | −3.29012 | −0.195233 | ||||||||
\(285\) | −2.74778 | + | 6.31816i | −0.162764 | + | 0.374256i | ||||
\(286\) | 1.25271i | 0.0740741i | ||||||||
\(287\) | 6.14596 | − | 6.14596i | 0.362785 | − | 0.362785i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 15.4250 | 0.907355 | ||||||||
\(290\) | −3.60025 | + | 1.41786i | −0.211414 | + | 0.0832599i | ||||
\(291\) | −2.84175 | + | 2.84175i | −0.166586 | + | 0.166586i | ||||
\(292\) | −8.53399 | − | 8.53399i | −0.499414 | − | 0.499414i | ||||
\(293\) | 2.93182 | − | 2.93182i | 0.171279 | − | 0.171279i | −0.616262 | − | 0.787541i | \(-0.711354\pi\) |
0.787541 | + | 0.616262i | \(0.211354\pi\) | |||||||
\(294\) | −1.48777 | + | 1.48777i | −0.0867688 | + | 0.0867688i | ||||
\(295\) | 5.45079 | + | 13.8407i | 0.317357 | + | 0.805835i | ||||
\(296\) | 6.08275 | − | 0.0100817i | 0.353553 | − | 0.000585988i | ||||
\(297\) | −2.77320 | − | 2.77320i | −0.160918 | − | 0.160918i | ||||
\(298\) | 0.425764i | 0.0246639i | ||||||||
\(299\) | 0.367973 | 0.0212804 | ||||||||
\(300\) | 0.175243 | − | 4.99693i | 0.0101176 | − | 0.288498i | ||||
\(301\) | 2.93097 | + | 2.93097i | 0.168938 | + | 0.168938i | ||||
\(302\) | − | 18.6559i | − | 1.07353i | ||||||
\(303\) | −7.82575 | + | 7.82575i | −0.449578 | + | 0.449578i | ||||
\(304\) | 2.17875 | − | 2.17875i | 0.124960 | − | 0.124960i | ||||
\(305\) | −6.44427 | − | 16.3633i | −0.368998 | − | 0.936960i | ||||
\(306\) | 1.25497 | 0.0717421 | ||||||||
\(307\) | 0.225281 | − | 0.225281i | 0.0128575 | − | 0.0128575i | −0.700649 | − | 0.713506i | \(-0.747106\pi\) |
0.713506 | + | 0.700649i | \(0.247106\pi\) | |||||||
\(308\) | 6.13622 | − | 6.13622i | 0.349644 | − | 0.349644i | ||||
\(309\) | 9.76753 | − | 9.76753i | 0.555655 | − | 0.555655i | ||||
\(310\) | 7.85956 | + | 19.9570i | 0.446393 | + | 1.13348i | ||||
\(311\) | 8.19803 | − | 8.19803i | 0.464868 | − | 0.464868i | −0.435379 | − | 0.900247i | \(-0.643386\pi\) |
0.900247 | + | 0.435379i | \(0.143386\pi\) | |||||||
\(312\) | 0.225859 | + | 0.225859i | 0.0127868 | + | 0.0127868i | ||||
\(313\) | −12.1187 | −0.684987 | −0.342494 | − | 0.939520i | \(-0.611271\pi\) | ||||
−0.342494 | + | 0.939520i | \(0.611271\pi\) | |||||||
\(314\) | −6.23375 | − | 6.23375i | −0.351791 | − | 0.351791i | ||||
\(315\) | 1.81300 | + | 4.60357i | 0.102151 | + | 0.259382i | ||||
\(316\) | −3.59077 | + | 3.59077i | −0.201996 | + | 0.201996i | ||||
\(317\) | −5.46058 | + | 5.46058i | −0.306697 | + | 0.306697i | −0.843627 | − | 0.536930i | \(-0.819584\pi\) |
0.536930 | + | 0.843627i | \(0.319584\pi\) | |||||||
\(318\) | 4.28827 | 0.240474 | ||||||||
\(319\) | 4.79886 | − | 4.79886i | 0.268685 | − | 0.268685i | ||||
\(320\) | −0.891783 | + | 2.05054i | −0.0498522 | + | 0.114629i | ||||
\(321\) | 2.20433i | 0.123034i | ||||||||
\(322\) | −1.80247 | − | 1.80247i | −0.100448 | − | 0.100448i | ||||
\(323\) | 2.73427 | + | 2.73427i | 0.152139 | + | 0.152139i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 1.08902 | + | 1.16818i | 0.0604081 | + | 0.0647991i | ||||
\(326\) | 15.4091i | 0.853430i | ||||||||
\(327\) | −5.99769 | −0.331673 | ||||||||
\(328\) | − | 3.92813i | − | 0.216895i | ||||||
\(329\) | 15.2844i | 0.842654i | ||||||||
\(330\) | 3.21347 | + | 8.15967i | 0.176896 | + | 0.449175i | ||||
\(331\) | 14.2462 | + | 14.2462i | 0.783041 | + | 0.783041i | 0.980343 | − | 0.197302i | \(-0.0632180\pi\) |
−0.197302 | + | 0.980343i | \(0.563218\pi\) | |||||||
\(332\) | −1.13008 | + | 1.13008i | −0.0620211 | + | 0.0620211i | ||||
\(333\) | −0.0100817 | − | 6.08275i | −0.000552474 | − | 0.333333i | ||||
\(334\) | − | 16.8371i | − | 0.921285i | ||||||
\(335\) | 7.97679 | + | 20.2547i | 0.435819 | + | 1.10663i | ||||
\(336\) | − | 2.21268i | − | 0.120712i | ||||||
\(337\) | 23.4318 | − | 23.4318i | 1.27641 | − | 1.27641i | 0.333746 | − | 0.942663i | \(-0.391687\pi\) |
0.942663 | − | 0.333746i | \(-0.108313\pi\) | |||||||
\(338\) | 12.8980 | 0.701557 | ||||||||
\(339\) | −11.6944 | + | 11.6944i | −0.635152 | + | 0.635152i | ||||
\(340\) | −2.57338 | − | 1.11916i | −0.139561 | − | 0.0606952i | ||||
\(341\) | −26.6012 | − | 26.6012i | −1.44054 | − | 1.44054i | ||||
\(342\) | −2.17875 | − | 2.17875i | −0.117813 | − | 0.117813i | ||||
\(343\) | −14.2442 | + | 14.2442i | −0.769115 | + | 0.769115i | ||||
\(344\) | 1.87330 | 0.101001 | ||||||||
\(345\) | 2.39684 | − | 0.943934i | 0.129041 | − | 0.0508197i | ||||
\(346\) | 5.18404 | + | 5.18404i | 0.278696 | + | 0.278696i | ||||
\(347\) | 4.74393 | 0.254667 | 0.127334 | − | 0.991860i | \(-0.459358\pi\) | ||||
0.127334 | + | 0.991860i | \(0.459358\pi\) | |||||||
\(348\) | − | 1.73044i | − | 0.0927613i | ||||||
\(349\) | − | 14.8248i | − | 0.793556i | −0.917915 | − | 0.396778i | \(-0.870128\pi\) | ||
0.917915 | − | 0.396778i | \(-0.129872\pi\) | |||||||
\(350\) | 0.387756 | − | 11.0566i | 0.0207264 | − | 0.591001i | ||||
\(351\) | 0.225859 | − | 0.225859i | 0.0120555 | − | 0.0120555i | ||||
\(352\) | − | 3.92190i | − | 0.209038i | ||||||
\(353\) | 23.4920i | 1.25035i | 0.780483 | + | 0.625177i | \(0.214973\pi\) | ||||
−0.780483 | + | 0.625177i | \(0.785027\pi\) | |||||||
\(354\) | −6.65245 | −0.353574 | ||||||||
\(355\) | 2.93407 | − | 6.74653i | 0.155725 | − | 0.358069i | ||||
\(356\) | 1.33809 | + | 1.33809i | 0.0709185 | + | 0.0709185i | ||||
\(357\) | 2.77686 | 0.146967 | ||||||||
\(358\) | −1.70251 | − | 1.70251i | −0.0899805 | − | 0.0899805i | ||||
\(359\) | 3.71905i | 0.196284i | 0.995172 | + | 0.0981419i | \(0.0312899\pi\) | ||||
−0.995172 | + | 0.0981419i | \(0.968710\pi\) | |||||||
\(360\) | 2.05054 | + | 0.891783i | 0.108073 | + | 0.0470011i | ||||
\(361\) | 9.50611i | 0.500322i | ||||||||
\(362\) | −8.75170 | −0.459979 | ||||||||
\(363\) | −3.09806 | − | 3.09806i | −0.162606 | − | 0.162606i | ||||
\(364\) | 0.499755 | + | 0.499755i | 0.0261943 | + | 0.0261943i | ||||
\(365\) | 25.1098 | − | 9.88884i | 1.31431 | − | 0.517606i | ||||
\(366\) | 7.86494 | 0.411107 | ||||||||
\(367\) | 20.2784 | + | 20.2784i | 1.05852 | + | 1.05852i | 0.998178 | + | 0.0603458i | \(0.0192203\pi\) |
0.0603458 | + | 0.998178i | \(0.480780\pi\) | |||||||
\(368\) | −1.15203 | −0.0600536 | ||||||||
\(369\) | −3.92813 | −0.204490 | ||||||||
\(370\) | −5.40382 | + | 12.4819i | −0.280931 | + | 0.648905i | ||||
\(371\) | 9.48858 | 0.492623 | ||||||||
\(372\) | −9.59224 | −0.497334 | ||||||||
\(373\) | −17.0249 | − | 17.0249i | −0.881515 | − | 0.881515i | 0.112174 | − | 0.993689i | \(-0.464219\pi\) |
−0.993689 | + | 0.112174i | \(0.964219\pi\) | |||||||
\(374\) | 4.92188 | 0.254505 | ||||||||
\(375\) | 10.0901 | + | 4.81552i | 0.521052 | + | 0.248672i | ||||
\(376\) | 4.88442 | + | 4.88442i | 0.251895 | + | 0.251895i | ||||
\(377\) | 0.390836 | + | 0.390836i | 0.0201291 | + | 0.0201291i | ||||
\(378\) | −2.21268 | −0.113808 | ||||||||
\(379\) | 3.59500i | 0.184663i | 0.995728 | + | 0.0923313i | \(0.0294319\pi\) | ||||
−0.995728 | + | 0.0923313i | \(0.970568\pi\) | |||||||
\(380\) | 2.52465 | + | 6.41059i | 0.129512 | + | 0.328856i | ||||
\(381\) | 9.98731i | 0.511665i | ||||||||
\(382\) | −4.56780 | − | 4.56780i | −0.233709 | − | 0.233709i | ||||
\(383\) | −18.9973 | −0.970715 | −0.485358 | − | 0.874316i | \(-0.661311\pi\) | ||||
−0.485358 | + | 0.874316i | \(0.661311\pi\) | |||||||
\(384\) | −0.707107 | − | 0.707107i | −0.0360844 | − | 0.0360844i | ||||
\(385\) | 7.11040 | + | 18.0548i | 0.362380 | + | 0.920156i | ||||
\(386\) | 5.51547 | 0.280730 | ||||||||
\(387\) | − | 1.87330i | − | 0.0952251i | ||||||
\(388\) | 4.01884i | 0.204025i | ||||||||
\(389\) | −9.52518 | + | 9.52518i | −0.482946 | + | 0.482946i | −0.906071 | − | 0.423125i | \(-0.860933\pi\) |
0.423125 | + | 0.906071i | \(0.360933\pi\) | |||||||
\(390\) | −0.664551 | + | 0.261716i | −0.0336509 | + | 0.0132525i | ||||
\(391\) | − | 1.44577i | − | 0.0731155i | ||||||
\(392\) | 2.10403i | 0.106270i | ||||||||
\(393\) | −13.1829 | −0.664989 | ||||||||
\(394\) | 3.48510 | + | 3.48510i | 0.175577 | + | 0.175577i | ||||
\(395\) | −4.16084 | − | 10.5652i | −0.209354 | − | 0.531593i | ||||
\(396\) | −3.92190 | −0.197083 | ||||||||
\(397\) | −6.55806 | + | 6.55806i | −0.329139 | + | 0.329139i | −0.852259 | − | 0.523120i | \(-0.824768\pi\) |
0.523120 | + | 0.852259i | \(0.324768\pi\) | |||||||
\(398\) | −11.0862 | − | 11.0862i | −0.555703 | − | 0.555703i | ||||
\(399\) | −4.82088 | − | 4.82088i | −0.241346 | − | 0.241346i | ||||
\(400\) | −3.40945 | − | 3.65728i | −0.170472 | − | 0.182864i | ||||
\(401\) | −3.25081 | + | 3.25081i | −0.162337 | + | 0.162337i | −0.783601 | − | 0.621264i | \(-0.786619\pi\) |
0.621264 | + | 0.783601i | \(0.286619\pi\) | |||||||
\(402\) | −9.73532 | −0.485554 | ||||||||
\(403\) | 2.16650 | − | 2.16650i | 0.107921 | − | 0.107921i | ||||
\(404\) | 11.0673i | 0.550618i | ||||||||
\(405\) | 0.891783 | − | 2.05054i | 0.0443130 | − | 0.101892i | ||||
\(406\) | − | 3.82892i | − | 0.190026i | ||||||
\(407\) | −0.0395395 | − | 23.8560i | −0.00195990 | − | 1.18250i | ||||
\(408\) | 0.887401 | − | 0.887401i | 0.0439329 | − | 0.0439329i | ||||
\(409\) | −13.3605 | − | 13.3605i | −0.660637 | − | 0.660637i | 0.294893 | − | 0.955530i | \(-0.404716\pi\) |
−0.955530 | + | 0.294893i | \(0.904716\pi\) | |||||||
\(410\) | 8.05479 | + | 3.50304i | 0.397798 | + | 0.173003i | ||||
\(411\) | − | 20.6125i | − | 1.01674i | ||||||
\(412\) | − | 13.8134i | − | 0.680536i | ||||||
\(413\) | −14.7198 | −0.724312 | ||||||||
\(414\) | 1.15203i | 0.0566191i | ||||||||
\(415\) | −1.30949 | − | 3.32506i | −0.0642803 | − | 0.163221i | ||||
\(416\) | 0.319413 | 0.0156605 | ||||||||
\(417\) | −0.852977 | − | 0.852977i | −0.0417705 | − | 0.0417705i | ||||
\(418\) | −8.54484 | − | 8.54484i | −0.417942 | − | 0.417942i | ||||
\(419\) | − | 18.6060i | − | 0.908963i | −0.890756 | − | 0.454481i | \(-0.849825\pi\) | ||
0.890756 | − | 0.454481i | \(-0.150175\pi\) | |||||||
\(420\) | 4.53720 | + | 1.97323i | 0.221393 | + | 0.0962839i | ||||
\(421\) | 4.15626 | − | 4.15626i | 0.202564 | − | 0.202564i | −0.598534 | − | 0.801098i | \(-0.704250\pi\) |
0.801098 | + | 0.598534i | \(0.204250\pi\) | |||||||
\(422\) | −27.2170 | −1.32490 | ||||||||
\(423\) | 4.88442 | − | 4.88442i | 0.237489 | − | 0.237489i | ||||
\(424\) | 3.03226 | − | 3.03226i | 0.147260 | − | 0.147260i | ||||
\(425\) | 4.58979 | − | 4.27877i | 0.222637 | − | 0.207551i | ||||
\(426\) | 2.32647 | + | 2.32647i | 0.112718 | + | 0.112718i | ||||
\(427\) | 17.4026 | 0.842172 | ||||||||
\(428\) | 1.55870 | + | 1.55870i | 0.0753426 | + | 0.0753426i | ||||
\(429\) | 0.885798 | − | 0.885798i | 0.0427667 | − | 0.0427667i | ||||
\(430\) | −1.67057 | + | 3.84128i | −0.0805623 | + | 0.185243i | ||||
\(431\) | −7.99513 | + | 7.99513i | −0.385112 | + | 0.385112i | −0.872940 | − | 0.487828i | \(-0.837789\pi\) |
0.487828 | + | 0.872940i | \(0.337789\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | 21.8861 | − | 21.8861i | 1.05178 | − | 1.05178i | 0.0531948 | − | 0.998584i | \(-0.483060\pi\) |
0.998584 | − | 0.0531948i | \(-0.0169404\pi\) | |||||||
\(434\) | −21.2246 | −1.01881 | ||||||||
\(435\) | 3.54834 | + | 1.54318i | 0.170130 | + | 0.0739897i | ||||
\(436\) | −4.24101 | + | 4.24101i | −0.203107 | + | 0.203107i | ||||
\(437\) | −2.50998 | + | 2.50998i | −0.120069 | + | 0.120069i | ||||
\(438\) | 12.0689i | 0.576674i | ||||||||
\(439\) | 19.4929 | + | 19.4929i | 0.930345 | + | 0.930345i | 0.997727 | − | 0.0673822i | \(-0.0214647\pi\) |
−0.0673822 | + | 0.997727i | \(0.521465\pi\) | |||||||
\(440\) | 8.04202 | + | 3.49748i | 0.383388 | + | 0.166736i | ||||
\(441\) | 2.10403 | 0.100192 | ||||||||
\(442\) | 0.400855i | 0.0190667i | ||||||||
\(443\) | −1.25482 | − | 1.25482i | −0.0596181 | − | 0.0596181i | 0.676669 | − | 0.736287i | \(-0.263423\pi\) |
−0.736287 | + | 0.676669i | \(0.763423\pi\) | |||||||
\(444\) | −4.30829 | − | 4.29403i | −0.204462 | − | 0.203786i | ||||
\(445\) | −3.93709 | + | 1.55052i | −0.186636 | + | 0.0735018i | ||||
\(446\) | −11.1865 | + | 11.1865i | −0.529696 | + | 0.529696i | ||||
\(447\) | 0.301061 | − | 0.301061i | 0.0142397 | − | 0.0142397i | ||||
\(448\) | −1.56460 | − | 1.56460i | −0.0739206 | − | 0.0739206i | ||||
\(449\) | −5.51963 | + | 5.51963i | −0.260487 | + | 0.260487i | −0.825252 | − | 0.564765i | \(-0.808967\pi\) |
0.564765 | + | 0.825252i | \(0.308967\pi\) | |||||||
\(450\) | −3.65728 | + | 3.40945i | −0.172406 | + | 0.160723i | ||||
\(451\) | −15.4057 | −0.725427 | ||||||||
\(452\) | 16.5384i | 0.777899i | ||||||||
\(453\) | −13.1917 | + | 13.1917i | −0.619801 | + | 0.619801i | ||||
\(454\) | − | 1.74912i | − | 0.0820905i | ||||||
\(455\) | −1.47044 | + | 0.579096i | −0.0689354 | + | 0.0271484i | ||||
\(456\) | −3.08122 | −0.144291 | ||||||||
\(457\) | − | 6.65948i | − | 0.311517i | −0.987795 | − | 0.155759i | \(-0.950218\pi\) | ||
0.987795 | − | 0.155759i | \(-0.0497822\pi\) | |||||||
\(458\) | 8.51464i | 0.397863i | ||||||||
\(459\) | −0.887401 | − | 0.887401i | −0.0414203 | − | 0.0414203i | ||||
\(460\) | 1.02736 | − | 2.36228i | 0.0479009 | − | 0.110142i | ||||
\(461\) | −24.8127 | − | 24.8127i | −1.15564 | − | 1.15564i | −0.985403 | − | 0.170240i | \(-0.945546\pi\) |
−0.170240 | − | 0.985403i | \(-0.554454\pi\) | |||||||
\(462\) | −8.67793 | −0.403734 | ||||||||
\(463\) | 0.607120 | 0.0282153 | 0.0141076 | − | 0.999900i | \(-0.495509\pi\) | ||||
0.0141076 | + | 0.999900i | \(0.495509\pi\) | |||||||
\(464\) | −1.22361 | − | 1.22361i | −0.0568045 | − | 0.0568045i | ||||
\(465\) | 8.55419 | − | 19.6693i | 0.396691 | − | 0.912141i | ||||
\(466\) | −6.42533 | − | 6.42533i | −0.297648 | − | 0.297648i | ||||
\(467\) | − | 14.2821i | − | 0.660896i | −0.943824 | − | 0.330448i | \(-0.892800\pi\) | ||
0.943824 | − | 0.330448i | \(-0.107200\pi\) | |||||||
\(468\) | − | 0.319413i | − | 0.0147649i | ||||||
\(469\) | −21.5412 | −0.994679 | ||||||||
\(470\) | −14.3716 | + | 5.65987i | −0.662910 | + | 0.261070i | ||||
\(471\) | 8.81585i | 0.406213i | ||||||||
\(472\) | −4.70399 | + | 4.70399i | −0.216519 | + | 0.216519i | ||||
\(473\) | − | 7.34689i | − | 0.337810i | ||||||
\(474\) | 5.07811 | 0.233245 | ||||||||
\(475\) | −15.3966 | − | 0.539960i | −0.706445 | − | 0.0247751i | ||||
\(476\) | 1.96354 | − | 1.96354i | 0.0899986 | − | 0.0899986i | ||||
\(477\) | −3.03226 | − | 3.03226i | −0.138838 | − | 0.138838i | ||||
\(478\) | 10.4976 | − | 10.4976i | 0.480151 | − | 0.480151i | ||||
\(479\) | −12.8987 | + | 12.8987i | −0.589358 | + | 0.589358i | −0.937458 | − | 0.348100i | \(-0.886827\pi\) |
0.348100 | + | 0.937458i | \(0.386827\pi\) | |||||||
\(480\) | 2.08054 | − | 0.819367i | 0.0949631 | − | 0.0373988i | ||||
\(481\) | 1.94291 | − | 0.00322023i | 0.0885891 | − | 0.000146830i | ||||
\(482\) | −6.66851 | − | 6.66851i | −0.303742 | − | 0.303742i | ||||
\(483\) | 2.54907i | 0.115987i | ||||||||
\(484\) | −4.38131 | −0.199151 | ||||||||
\(485\) | −8.24079 | − | 3.58393i | −0.374195 | − | 0.162738i | ||||
\(486\) | 0.707107 | + | 0.707107i | 0.0320750 | + | 0.0320750i | ||||
\(487\) | 0.169467i | 0.00767930i | 0.999993 | + | 0.00383965i | \(0.00122220\pi\) | ||||
−0.999993 | + | 0.00383965i | \(0.998778\pi\) | |||||||
\(488\) | 5.56135 | − | 5.56135i | 0.251750 | − | 0.251750i | ||||
\(489\) | 10.8959 | − | 10.8959i | 0.492728 | − | 0.492728i | ||||
\(490\) | −4.31440 | − | 1.87634i | −0.194905 | − | 0.0847644i | ||||
\(491\) | 11.6118 | 0.524033 | 0.262016 | − | 0.965063i | \(-0.415613\pi\) | ||||
0.262016 | + | 0.965063i | \(0.415613\pi\) | |||||||
\(492\) | −2.77761 | + | 2.77761i | −0.125224 | + | 0.125224i | ||||
\(493\) | 1.53559 | − | 1.53559i | 0.0691596 | − | 0.0691596i | ||||
\(494\) | 0.695921 | − | 0.695921i | 0.0313110 | − | 0.0313110i | ||||
\(495\) | 3.49748 | − | 8.04202i | 0.157200 | − | 0.361462i | ||||
\(496\) | −6.78274 | + | 6.78274i | −0.304554 | + | 0.304554i | ||||
\(497\) | 5.14774 | + | 5.14774i | 0.230908 | + | 0.230908i | ||||
\(498\) | 1.59817 | 0.0716158 | ||||||||
\(499\) | 15.8556 | + | 15.8556i | 0.709793 | + | 0.709793i | 0.966492 | − | 0.256698i | \(-0.0826347\pi\) |
−0.256698 | + | 0.966492i | \(0.582635\pi\) | |||||||
\(500\) | 10.5399 | − | 3.72972i | 0.471358 | − | 0.166798i | ||||
\(501\) | −11.9056 | + | 11.9056i | −0.531904 | + | 0.531904i | ||||
\(502\) | −19.9946 | + | 19.9946i | −0.892402 | + | 0.892402i | ||||
\(503\) | 22.2525 | 0.992190 | 0.496095 | − | 0.868268i | \(-0.334767\pi\) | ||||
0.496095 | + | 0.868268i | \(0.334767\pi\) | |||||||
\(504\) | −1.56460 | + | 1.56460i | −0.0696930 | + | 0.0696930i | ||||
\(505\) | −22.6939 | − | 9.86962i | −1.00987 | − | 0.439192i | ||||
\(506\) | 4.51814i | 0.200856i | ||||||||
\(507\) | −9.12025 | − | 9.12025i | −0.405044 | − | 0.405044i | ||||
\(508\) | 7.06209 | + | 7.06209i | 0.313330 | + | 0.313330i | ||||
\(509\) | −23.6164 | −1.04678 | −0.523390 | − | 0.852093i | \(-0.675333\pi\) | ||||
−0.523390 | + | 0.852093i | \(0.675333\pi\) | |||||||
\(510\) | 1.02828 | + | 2.61102i | 0.0455332 | + | 0.115618i | ||||
\(511\) | 26.7046i | 1.18134i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.08122i | 0.136039i | ||||||||
\(514\) | − | 31.3639i | − | 1.38340i | ||||||
\(515\) | 28.3249 | + | 12.3185i | 1.24814 | + | 0.542819i | ||||
\(516\) | −1.32462 | − | 1.32462i | −0.0583132 | − | 0.0583132i | ||||
\(517\) | 19.1562 | − | 19.1562i | 0.842489 | − | 0.842489i | ||||
\(518\) | −9.53287 | − | 9.50133i | −0.418850 | − | 0.417464i | ||||
\(519\) | − | 7.33134i | − | 0.321810i | ||||||
\(520\) | −0.284847 | + | 0.654970i | −0.0124914 | + | 0.0287223i | ||||
\(521\) | − | 17.0507i | − | 0.747006i | −0.927629 | − | 0.373503i | \(-0.878157\pi\) | ||
0.927629 | − | 0.373503i | \(-0.121843\pi\) | |||||||
\(522\) | −1.22361 | + | 1.22361i | −0.0535558 | + | 0.0535558i | ||||
\(523\) | −23.5794 | −1.03105 | −0.515527 | − | 0.856873i | \(-0.672404\pi\) | ||||
−0.515527 | + | 0.856873i | \(0.672404\pi\) | |||||||
\(524\) | −9.32171 | + | 9.32171i | −0.407221 | + | 0.407221i | ||||
\(525\) | −8.09240 | + | 7.54403i | −0.353181 | + | 0.329248i | ||||
\(526\) | −7.40341 | − | 7.40341i | −0.322804 | − | 0.322804i | ||||
\(527\) | −8.51216 | − | 8.51216i | −0.370795 | − | 0.370795i | ||||
\(528\) | −2.77320 | + | 2.77320i | −0.120688 | + | 0.120688i | ||||
\(529\) | −21.6728 | −0.942297 | ||||||||
\(530\) | 3.51366 | + | 8.92191i | 0.152624 | + | 0.387543i | ||||
\(531\) | 4.70399 | + | 4.70399i | 0.204136 | + | 0.204136i | ||||
\(532\) | −6.81776 | −0.295587 | ||||||||
\(533\) | − | 1.25470i | − | 0.0543469i | ||||||
\(534\) | − | 1.89234i | − | 0.0818896i | ||||||
\(535\) | −4.58620 | + | 1.80616i | −0.198279 | + | 0.0780870i | ||||
\(536\) | −6.88391 | + | 6.88391i | −0.297340 | + | 0.297340i | ||||
\(537\) | 2.40771i | 0.103901i | ||||||||
\(538\) | − | 3.41947i | − | 0.147424i | ||||||
\(539\) | 8.25180 | 0.355430 | ||||||||
\(540\) | −0.819367 | − | 2.08054i | −0.0352599 | − | 0.0895321i | ||||
\(541\) | −10.2113 | − | 10.2113i | −0.439020 | − | 0.439020i | 0.452662 | − | 0.891682i | \(-0.350474\pi\) |
−0.891682 | + | 0.452662i | \(0.850474\pi\) | |||||||
\(542\) | −17.8704 | −0.767600 | ||||||||
\(543\) | 6.18839 | + | 6.18839i | 0.265569 | + | 0.265569i | ||||
\(544\) | − | 1.25497i | − | 0.0538066i | ||||||
\(545\) | −4.91431 | − | 12.4784i | −0.210506 | − | 0.534517i | ||||
\(546\) | − | 0.706760i | − | 0.0302465i | ||||||
\(547\) | 26.3899 | 1.12835 | 0.564176 | − | 0.825655i | \(-0.309194\pi\) | ||||
0.564176 | + | 0.825655i | \(0.309194\pi\) | |||||||
\(548\) | −14.5752 | − | 14.5752i | −0.622623 | − | 0.622623i | ||||
\(549\) | −5.56135 | − | 5.56135i | −0.237353 | − | 0.237353i | ||||
\(550\) | −14.3435 | + | 13.3715i | −0.611608 | + | 0.570163i | ||||
\(551\) | −5.33186 | −0.227145 | ||||||||
\(552\) | 0.814607 | + | 0.814607i | 0.0346720 | + | 0.0346720i | ||||
\(553\) | 11.2363 | 0.477814 | ||||||||
\(554\) | 14.8527 | 0.631029 | ||||||||
\(555\) | 12.6471 | − | 5.00498i | 0.536841 | − | 0.212450i | ||||
\(556\) | −1.20629 | −0.0511582 | ||||||||
\(557\) | −33.0054 | −1.39849 | −0.699243 | − | 0.714885i | \(-0.746479\pi\) | ||||
−0.699243 | + | 0.714885i | \(0.746479\pi\) | |||||||
\(558\) | 6.78274 | + | 6.78274i | 0.287136 | + | 0.287136i | ||||
\(559\) | 0.598356 | 0.0253078 | ||||||||
\(560\) | 4.60357 | − | 1.81300i | 0.194536 | − | 0.0766132i | ||||
\(561\) | −3.48030 | − | 3.48030i | −0.146938 | − | 0.146938i | ||||
\(562\) | −4.56193 | − | 4.56193i | −0.192434 | − | 0.192434i | ||||
\(563\) | 2.41113 | 0.101617 | 0.0508086 | − | 0.998708i | \(-0.483820\pi\) | ||||
0.0508086 | + | 0.998708i | \(0.483820\pi\) | |||||||
\(564\) | − | 6.90761i | − | 0.290863i | ||||||
\(565\) | −33.9126 | − | 14.7486i | −1.42671 | − | 0.620479i | ||||
\(566\) | − | 32.3891i | − | 1.36142i | ||||||
\(567\) | 1.56460 | + | 1.56460i | 0.0657072 | + | 0.0657072i | ||||
\(568\) | 3.29012 | 0.138050 | ||||||||
\(569\) | 16.6810 | + | 16.6810i | 0.699306 | + | 0.699306i | 0.964261 | − | 0.264955i | \(-0.0853571\pi\) |
−0.264955 | + | 0.964261i | \(0.585357\pi\) | |||||||
\(570\) | 2.74778 | − | 6.31816i | 0.115092 | − | 0.264639i | ||||
\(571\) | −34.7939 | −1.45608 | −0.728041 | − | 0.685534i | \(-0.759569\pi\) | ||||
−0.728041 | + | 0.685534i | \(0.759569\pi\) | |||||||
\(572\) | − | 1.25271i | − | 0.0523783i | ||||||
\(573\) | 6.45984i | 0.269864i | ||||||||
\(574\) | −6.14596 | + | 6.14596i | −0.256528 | + | 0.256528i | ||||
\(575\) | 3.92778 | + | 4.21329i | 0.163800 | + | 0.175706i | ||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | 42.4452i | 1.76702i | 0.468414 | + | 0.883509i | \(0.344826\pi\) | ||||
−0.468414 | + | 0.883509i | \(0.655174\pi\) | |||||||
\(578\) | −15.4250 | −0.641597 | ||||||||
\(579\) | −3.90003 | − | 3.90003i | −0.162080 | − | 0.162080i | ||||
\(580\) | 3.60025 | − | 1.41786i | 0.149492 | − | 0.0588736i | ||||
\(581\) | 3.53625 | 0.146708 | ||||||||
\(582\) | 2.84175 | − | 2.84175i | 0.117794 | − | 0.117794i | ||||
\(583\) | −11.8922 | − | 11.8922i | −0.492526 | − | 0.492526i | ||||
\(584\) | 8.53399 | + | 8.53399i | 0.353139 | + | 0.353139i | ||||
\(585\) | 0.654970 | + | 0.284847i | 0.0270797 | + | 0.0117770i | ||||
\(586\) | −2.93182 | + | 2.93182i | −0.121112 | + | 0.121112i | ||||
\(587\) | −25.7512 | −1.06287 | −0.531433 | − | 0.847100i | \(-0.678346\pi\) | ||||
−0.531433 | + | 0.847100i | \(0.678346\pi\) | |||||||
\(588\) | 1.48777 | − | 1.48777i | 0.0613548 | − | 0.0613548i | ||||
\(589\) | 29.5558i | 1.21782i | ||||||||
\(590\) | −5.45079 | − | 13.8407i | −0.224406 | − | 0.569811i | ||||
\(591\) | − | 4.92868i | − | 0.202739i | ||||||
\(592\) | −6.08275 | + | 0.0100817i | −0.250000 | + | 0.000414356i | ||||
\(593\) | −17.7350 | + | 17.7350i | −0.728289 | + | 0.728289i | −0.970279 | − | 0.241990i | \(-0.922200\pi\) |
0.241990 | + | 0.970279i | \(0.422200\pi\) | |||||||
\(594\) | 2.77320 | + | 2.77320i | 0.113786 | + | 0.113786i | ||||
\(595\) | 2.27527 | + | 5.77736i | 0.0932768 | + | 0.236849i | ||||
\(596\) | − | 0.425764i | − | 0.0174400i | ||||||
\(597\) | 15.6783i | 0.641671i | ||||||||
\(598\) | −0.367973 | −0.0150475 | ||||||||
\(599\) | − | 33.5799i | − | 1.37204i | −0.727583 | − | 0.686020i | \(-0.759356\pi\) | ||
0.727583 | − | 0.686020i | \(-0.240644\pi\) | |||||||
\(600\) | −0.175243 | + | 4.99693i | −0.00715425 | + | 0.203999i | ||||
\(601\) | −28.5324 | −1.16386 | −0.581930 | − | 0.813239i | \(-0.697702\pi\) | ||||
−0.581930 | + | 0.813239i | \(0.697702\pi\) | |||||||
\(602\) | −2.93097 | − | 2.93097i | −0.119457 | − | 0.119457i | ||||
\(603\) | 6.88391 | + | 6.88391i | 0.280334 | + | 0.280334i | ||||
\(604\) | 18.6559i | 0.759098i | ||||||||
\(605\) | 3.90718 | − | 8.98406i | 0.158849 | − | 0.365254i | ||||
\(606\) | 7.82575 | − | 7.82575i | 0.317900 | − | 0.317900i | ||||
\(607\) | 26.3325 | 1.06880 | 0.534401 | − | 0.845231i | \(-0.320537\pi\) | ||||
0.534401 | + | 0.845231i | \(0.320537\pi\) | |||||||
\(608\) | −2.17875 | + | 2.17875i | −0.0883599 | + | 0.0883599i | ||||
\(609\) | −2.70745 | + | 2.70745i | −0.109712 | + | 0.109712i | ||||
\(610\) | 6.44427 | + | 16.3633i | 0.260921 | + | 0.662531i | ||||
\(611\) | 1.56015 | + | 1.56015i | 0.0631168 | + | 0.0631168i | ||||
\(612\) | −1.25497 | −0.0507293 | ||||||||
\(613\) | 18.6885 | + | 18.6885i | 0.754820 | + | 0.754820i | 0.975375 | − | 0.220555i | \(-0.0707868\pi\) |
−0.220555 | + | 0.975375i | \(0.570787\pi\) | |||||||
\(614\) | −0.225281 | + | 0.225281i | −0.00909162 | + | 0.00909162i | ||||
\(615\) | −3.21858 | − | 8.17262i | −0.129786 | − | 0.329552i | ||||
\(616\) | −6.13622 | + | 6.13622i | −0.247235 | + | 0.247235i | ||||
\(617\) | 3.48887 | − | 3.48887i | 0.140457 | − | 0.140457i | −0.633382 | − | 0.773839i | \(-0.718334\pi\) |
0.773839 | + | 0.633382i | \(0.218334\pi\) | |||||||
\(618\) | −9.76753 | + | 9.76753i | −0.392907 | + | 0.392907i | ||||
\(619\) | −3.83734 | −0.154236 | −0.0771178 | − | 0.997022i | \(-0.524572\pi\) | ||||
−0.0771178 | + | 0.997022i | \(0.524572\pi\) | |||||||
\(620\) | −7.85956 | − | 19.9570i | −0.315647 | − | 0.801493i | ||||
\(621\) | 0.814607 | − | 0.814607i | 0.0326891 | − | 0.0326891i | ||||
\(622\) | −8.19803 | + | 8.19803i | −0.328711 | + | 0.328711i | ||||
\(623\) | − | 4.18715i | − | 0.167755i | ||||||
\(624\) | −0.225859 | − | 0.225859i | −0.00904160 | − | 0.00904160i | ||||
\(625\) | −1.75135 | + | 24.9386i | −0.0700540 | + | 0.997543i | ||||
\(626\) | 12.1187 | 0.484359 | ||||||||
\(627\) | 12.0842i | 0.482597i | ||||||||
\(628\) | 6.23375 | + | 6.23375i | 0.248754 | + | 0.248754i | ||||
\(629\) | −0.0126523 | − | 7.63370i | −0.000504480 | − | 0.304376i | ||||
\(630\) | −1.81300 | − | 4.60357i | −0.0722316 | − | 0.183411i | ||||
\(631\) | 15.4358 | − | 15.4358i | 0.614490 | − | 0.614490i | −0.329623 | − | 0.944113i | \(-0.606922\pi\) |
0.944113 | + | 0.329623i | \(0.106922\pi\) | |||||||
\(632\) | 3.59077 | − | 3.59077i | 0.142833 | − | 0.142833i | ||||
\(633\) | 19.2453 | + | 19.2453i | 0.764933 | + | 0.764933i | ||||
\(634\) | 5.46058 | − | 5.46058i | 0.216868 | − | 0.216868i | ||||
\(635\) | −20.7790 | + | 8.18326i | −0.824588 | + | 0.324743i | ||||
\(636\) | −4.28827 | −0.170041 | ||||||||
\(637\) | 0.672055i | 0.0266278i | ||||||||
\(638\) | −4.79886 | + | 4.79886i | −0.189989 | + | 0.189989i | ||||
\(639\) | − | 3.29012i | − | 0.130155i | ||||||
\(640\) | 0.891783 | − | 2.05054i | 0.0352508 | − | 0.0810548i | ||||
\(641\) | −41.6890 | −1.64662 | −0.823309 | − | 0.567594i | \(-0.807874\pi\) | ||||
−0.823309 | + | 0.567594i | \(0.807874\pi\) | |||||||
\(642\) | − | 2.20433i | − | 0.0869982i | ||||||
\(643\) | 3.74780i | 0.147799i | 0.997266 | + | 0.0738993i | \(0.0235443\pi\) | ||||
−0.997266 | + | 0.0738993i | \(0.976456\pi\) | |||||||
\(644\) | 1.80247 | + | 1.80247i | 0.0710272 | + | 0.0710272i | ||||
\(645\) | 3.89747 | − | 1.53492i | 0.153463 | − | 0.0604373i | ||||
\(646\) | −2.73427 | − | 2.73427i | −0.107579 | − | 0.107579i | ||||
\(647\) | −3.49319 | −0.137331 | −0.0686657 | − | 0.997640i | \(-0.521874\pi\) | ||||
−0.0686657 | + | 0.997640i | \(0.521874\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 18.4486 | + | 18.4486i | 0.724170 | + | 0.724170i | ||||
\(650\) | −1.08902 | − | 1.16818i | −0.0427150 | − | 0.0458199i | ||||
\(651\) | 15.0080 | + | 15.0080i | 0.588212 | + | 0.588212i | ||||
\(652\) | − | 15.4091i | − | 0.603466i | ||||||
\(653\) | 32.5364i | 1.27325i | 0.771175 | + | 0.636624i | \(0.219670\pi\) | ||||
−0.771175 | + | 0.636624i | \(0.780330\pi\) | |||||||
\(654\) | 5.99769 | 0.234528 | ||||||||
\(655\) | −10.8016 | − | 27.4275i | −0.422054 | − | 1.07168i | ||||
\(656\) | 3.92813i | 0.153368i | ||||||||
\(657\) | 8.53399 | − | 8.53399i | 0.332943 | − | 0.332943i | ||||
\(658\) | − | 15.2844i | − | 0.595847i | ||||||
\(659\) | −2.62449 | −0.102236 | −0.0511178 | − | 0.998693i | \(-0.516278\pi\) | ||||
−0.0511178 | + | 0.998693i | \(0.516278\pi\) | |||||||
\(660\) | −3.21347 | − | 8.15967i | −0.125084 | − | 0.317615i | ||||
\(661\) | 0.358911 | − | 0.358911i | 0.0139600 | − | 0.0139600i | −0.700092 | − | 0.714052i | \(-0.746858\pi\) |
0.714052 | + | 0.700092i | \(0.246858\pi\) | |||||||
\(662\) | −14.2462 | − | 14.2462i | −0.553693 | − | 0.553693i | ||||
\(663\) | 0.283447 | − | 0.283447i | 0.0110082 | − | 0.0110082i | ||||
\(664\) | 1.13008 | − | 1.13008i | 0.0438556 | − | 0.0438556i | ||||
\(665\) | 6.07996 | − | 13.9801i | 0.235771 | − | 0.542125i | ||||
\(666\) | 0.0100817 | + | 6.08275i | 0.000390658 | + | 0.235702i | ||||
\(667\) | 1.40963 | + | 1.40963i | 0.0545810 | + | 0.0545810i | ||||
\(668\) | 16.8371i | 0.651447i | ||||||||
\(669\) | 15.8201 | 0.611640 | ||||||||
\(670\) | −7.97679 | − | 20.2547i | −0.308170 | − | 0.782507i | ||||
\(671\) | −21.8111 | − | 21.8111i | −0.842007 | − | 0.842007i | ||||
\(672\) | 2.21268i | 0.0853561i | ||||||||
\(673\) | −14.4928 | + | 14.4928i | −0.558658 | + | 0.558658i | −0.928925 | − | 0.370267i | \(-0.879266\pi\) |
0.370267 | + | 0.928925i | \(0.379266\pi\) | |||||||
\(674\) | −23.4318 | + | 23.4318i | −0.902557 | + | 0.902557i | ||||
\(675\) | 4.99693 | + | 0.175243i | 0.192332 | + | 0.00674509i | ||||
\(676\) | −12.8980 | −0.496076 | ||||||||
\(677\) | −9.12580 | + | 9.12580i | −0.350733 | + | 0.350733i | −0.860382 | − | 0.509649i | \(-0.829775\pi\) |
0.509649 | + | 0.860382i | \(0.329775\pi\) | |||||||
\(678\) | 11.6944 | − | 11.6944i | 0.449120 | − | 0.449120i | ||||
\(679\) | 6.28788 | − | 6.28788i | 0.241307 | − | 0.241307i | ||||
\(680\) | 2.57338 | + | 1.11916i | 0.0986845 | + | 0.0429180i | ||||
\(681\) | −1.23682 | + | 1.23682i | −0.0473949 | + | 0.0473949i | ||||
\(682\) | 26.6012 | + | 26.6012i | 1.01861 | + | 1.01861i | ||||
\(683\) | 24.7098 | 0.945493 | 0.472746 | − | 0.881199i | \(-0.343263\pi\) | ||||
0.472746 | + | 0.881199i | \(0.343263\pi\) | |||||||
\(684\) | 2.17875 | + | 2.17875i | 0.0833065 | + | 0.0833065i | ||||
\(685\) | 42.8850 | − | 16.8892i | 1.63855 | − | 0.645302i | ||||
\(686\) | 14.2442 | − | 14.2442i | 0.543846 | − | 0.543846i | ||||
\(687\) | 6.02076 | − | 6.02076i | 0.229706 | − | 0.229706i | ||||
\(688\) | −1.87330 | −0.0714188 | ||||||||
\(689\) | 0.968545 | − | 0.968545i | 0.0368986 | − | 0.0368986i | ||||
\(690\) | −2.39684 | + | 0.943934i | −0.0912461 | + | 0.0359349i | ||||
\(691\) | 47.7183i | 1.81529i | 0.419739 | + | 0.907645i | \(0.362121\pi\) | ||||
−0.419739 | + | 0.907645i | \(0.637879\pi\) | |||||||
\(692\) | −5.18404 | − | 5.18404i | −0.197068 | − | 0.197068i | ||||
\(693\) | 6.13622 | + | 6.13622i | 0.233096 | + | 0.233096i | ||||
\(694\) | −4.74393 | −0.180077 | ||||||||
\(695\) | 1.07575 | − | 2.47355i | 0.0408055 | − | 0.0938272i | ||||
\(696\) | 1.73044i | 0.0655921i | ||||||||
\(697\) | −4.92970 | −0.186726 | ||||||||
\(698\) | 14.8248i | 0.561128i | ||||||||
\(699\) | 9.08679i | 0.343694i | ||||||||
\(700\) | −0.387756 | + | 11.0566i | −0.0146558 | + | 0.417901i | ||||
\(701\) | −2.69605 | − | 2.69605i | −0.101828 | − | 0.101828i | 0.654357 | − | 0.756186i | \(-0.272939\pi\) |
−0.756186 | + | 0.654357i | \(0.772939\pi\) | |||||||
\(702\) | −0.225859 | + | 0.225859i | −0.00852451 | + | 0.00852451i | ||||
\(703\) | −13.2308 | + | 13.2748i | −0.499010 | + | 0.500667i | ||||
\(704\) | 3.92190i | 0.147812i | ||||||||
\(705\) | 14.1644 | + | 6.16009i | 0.533460 | + | 0.232002i | ||||
\(706\) | − | 23.4920i | − | 0.884134i | ||||||
\(707\) | 17.3159 | − | 17.3159i | 0.651232 | − | 0.651232i | ||||
\(708\) | 6.65245 | 0.250014 | ||||||||
\(709\) | −20.0239 | + | 20.0239i | −0.752014 | + | 0.752014i | −0.974855 | − | 0.222841i | \(-0.928467\pi\) |
0.222841 | + | 0.974855i | \(0.428467\pi\) | |||||||
\(710\) | −2.93407 | + | 6.74653i | −0.110114 | + | 0.253193i | ||||
\(711\) | −3.59077 | − | 3.59077i | −0.134664 | − | 0.134664i | ||||
\(712\) | −1.33809 | − | 1.33809i | −0.0501470 | − | 0.0501470i | ||||
\(713\) | 7.81391 | − | 7.81391i | 0.292633 | − | 0.292633i | ||||
\(714\) | −2.77686 | −0.103921 | ||||||||
\(715\) | 2.56873 | + | 1.11714i | 0.0960650 | + | 0.0417788i | ||||
\(716\) | 1.70251 | + | 1.70251i | 0.0636258 | + | 0.0636258i | ||||
\(717\) | −14.8459 | −0.554431 | ||||||||
\(718\) | − | 3.71905i | − | 0.138794i | ||||||
\(719\) | − | 32.6337i | − | 1.21703i | −0.793541 | − | 0.608517i | \(-0.791765\pi\) | ||
0.793541 | − | 0.608517i | \(-0.208235\pi\) | |||||||
\(720\) | −2.05054 | − | 0.891783i | −0.0764192 | − | 0.0332348i | ||||
\(721\) | −21.6124 | + | 21.6124i | −0.804889 | + | 0.804889i | ||||
\(722\) | − | 9.50611i | − | 0.353781i | ||||||
\(723\) | 9.43070i | 0.350731i | ||||||||
\(724\) | 8.75170 | 0.325254 | ||||||||
\(725\) | −0.303247 | + | 8.64688i | −0.0112623 | + | 0.321137i | ||||
\(726\) | 3.09806 | + | 3.09806i | 0.114980 | + | 0.114980i | ||||
\(727\) | −21.1503 | −0.784422 | −0.392211 | − | 0.919875i | \(-0.628290\pi\) | ||||
−0.392211 | + | 0.919875i | \(0.628290\pi\) | |||||||
\(728\) | −0.499755 | − | 0.499755i | −0.0185222 | − | 0.0185222i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −25.1098 | + | 9.88884i | −0.929354 | + | 0.366002i | ||||
\(731\) | − | 2.35094i | − | 0.0869527i | ||||||
\(732\) | −7.86494 | −0.290696 | ||||||||
\(733\) | 26.3403 | + | 26.3403i | 0.972902 | + | 0.972902i | 0.999642 | − | 0.0267403i | \(-0.00851273\pi\) |
−0.0267403 | + | 0.999642i | \(0.508513\pi\) | |||||||
\(734\) | −20.2784 | − | 20.2784i | −0.748489 | − | 0.748489i | ||||
\(735\) | 1.72397 | + | 4.37752i | 0.0635897 | + | 0.161467i | ||||
\(736\) | 1.15203 | 0.0424643 | ||||||||
\(737\) | 26.9980 | + | 26.9980i | 0.994485 | + | 0.994485i | ||||
\(738\) | 3.92813 | 0.144596 | ||||||||
\(739\) | 27.2865 | 1.00375 | 0.501876 | − | 0.864940i | \(-0.332643\pi\) | ||||
0.501876 | + | 0.864940i | \(0.332643\pi\) | |||||||
\(740\) | 5.40382 | − | 12.4819i | 0.198648 | − | 0.458845i | ||||
\(741\) | −0.984181 | −0.0361548 | ||||||||
\(742\) | −9.48858 | −0.348337 | ||||||||
\(743\) | −18.6520 | − | 18.6520i | −0.684276 | − | 0.684276i | 0.276684 | − | 0.960961i | \(-0.410764\pi\) |
−0.960961 | + | 0.276684i | \(0.910764\pi\) | |||||||
\(744\) | 9.59224 | 0.351668 | ||||||||
\(745\) | 0.873048 | + | 0.379689i | 0.0319860 | + | 0.0139107i | ||||
\(746\) | 17.0249 | + | 17.0249i | 0.623325 | + | 0.623325i | ||||
\(747\) | −1.13008 | − | 1.13008i | −0.0413474 | − | 0.0413474i | ||||
\(748\) | −4.92188 | −0.179962 | ||||||||
\(749\) | − | 4.87750i | − | 0.178220i | ||||||
\(750\) | −10.0901 | − | 4.81552i | −0.368440 | − | 0.175838i | ||||
\(751\) | − | 29.3632i | − | 1.07148i | −0.844384 | − | 0.535738i | \(-0.820033\pi\) | ||
0.844384 | − | 0.535738i | \(-0.179967\pi\) | |||||||
\(752\) | −4.88442 | − | 4.88442i | −0.178116 | − | 0.178116i | ||||
\(753\) | 28.2766 | 1.03046 | ||||||||
\(754\) | −0.390836 | − | 0.390836i | −0.0142334 | − | 0.0142334i | ||||
\(755\) | −38.2547 | − | 16.6370i | −1.39223 | − | 0.605483i | ||||
\(756\) | 2.21268 | 0.0804745 | ||||||||
\(757\) | 36.6279i | 1.33126i | 0.746281 | + | 0.665631i | \(0.231838\pi\) | ||||
−0.746281 | + | 0.665631i | \(0.768162\pi\) | |||||||
\(758\) | − | 3.59500i | − | 0.130576i | ||||||
\(759\) | 3.19481 | − | 3.19481i | 0.115964 | − | 0.115964i | ||||
\(760\) | −2.52465 | − | 6.41059i | −0.0915785 | − | 0.232536i | ||||
\(761\) | − | 13.4727i | − | 0.488386i | −0.969727 | − | 0.244193i | \(-0.921477\pi\) | ||
0.969727 | − | 0.244193i | \(-0.0785230\pi\) | |||||||
\(762\) | − | 9.98731i | − | 0.361802i | ||||||
\(763\) | 13.2710 | 0.480442 | ||||||||
\(764\) | 4.56780 | + | 4.56780i | 0.165257 | + | 0.165257i | ||||
\(765\) | 1.11916 | − | 2.57338i | 0.0404635 | − | 0.0930407i | ||||
\(766\) | 18.9973 | 0.686399 | ||||||||
\(767\) | −1.50252 | + | 1.50252i | −0.0542527 | + | 0.0542527i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −11.9916 | − | 11.9916i | −0.432427 | − | 0.432427i | 0.457026 | − | 0.889453i | \(-0.348915\pi\) |
−0.889453 | + | 0.457026i | \(0.848915\pi\) | |||||||
\(770\) | −7.11040 | − | 18.0548i | −0.256241 | − | 0.650648i | ||||
\(771\) | −22.1776 | + | 22.1776i | −0.798707 | + | 0.798707i | ||||
\(772\) | −5.51547 | −0.198506 | ||||||||
\(773\) | 14.0271 | − | 14.0271i | 0.504520 | − | 0.504520i | −0.408319 | − | 0.912839i | \(-0.633885\pi\) |
0.912839 | + | 0.408319i | \(0.133885\pi\) | |||||||
\(774\) | 1.87330i | 0.0673343i | ||||||||
\(775\) | 47.9317 | + | 1.68097i | 1.72176 | + | 0.0603822i | ||||
\(776\) | − | 4.01884i | − | 0.144268i | ||||||
\(777\) | 0.0223076 | + | 13.4592i | 0.000800282 | + | 0.482846i | ||||
\(778\) | 9.52518 | − | 9.52518i | 0.341494 | − | 0.341494i | ||||
\(779\) | 8.55840 | + | 8.55840i | 0.306637 | + | 0.306637i | ||||
\(780\) | 0.664551 | − | 0.261716i | 0.0237948 | − | 0.00937095i | ||||
\(781\) | − | 12.9035i | − | 0.461725i | ||||||
\(782\) | 1.44577i | 0.0517005i | ||||||||
\(783\) | 1.73044 | 0.0618409 | ||||||||
\(784\) | − | 2.10403i | − | 0.0751440i | ||||||
\(785\) | −18.3417 | + | 7.22341i | −0.654644 | + | 0.257815i | ||||
\(786\) | 13.1829 | 0.470218 | ||||||||
\(787\) | −7.13187 | − | 7.13187i | −0.254224 | − | 0.254224i | 0.568476 | − | 0.822700i | \(-0.307533\pi\) |
−0.822700 | + | 0.568476i | \(0.807533\pi\) | |||||||
\(788\) | −3.48510 | − | 3.48510i | −0.124152 | − | 0.124152i | ||||
\(789\) | 10.4700i | 0.372742i | ||||||||
\(790\) | 4.16084 | + | 10.5652i | 0.148036 | + | 0.375893i | ||||
\(791\) | 25.8760 | − | 25.8760i | 0.920043 | − | 0.920043i | ||||
\(792\) | 3.92190 | 0.139359 | ||||||||
\(793\) | 1.77637 | − | 1.77637i | 0.0630807 | − | 0.0630807i | ||||
\(794\) | 6.55806 | − | 6.55806i | 0.232737 | − | 0.232737i | ||||
\(795\) | 3.82420 | − | 8.79328i | 0.135631 | − | 0.311865i | ||||
\(796\) | 11.0862 | + | 11.0862i | 0.392942 | + | 0.392942i | ||||
\(797\) | 5.26825 | 0.186611 | 0.0933054 | − | 0.995638i | \(-0.470257\pi\) | ||||
0.0933054 | + | 0.995638i | \(0.470257\pi\) | |||||||
\(798\) | 4.82088 | + | 4.82088i | 0.170657 | + | 0.170657i | ||||
\(799\) | 6.12982 | − | 6.12982i | 0.216857 | − | 0.216857i | ||||
\(800\) | 3.40945 | + | 3.65728i | 0.120542 | + | 0.129304i | ||||
\(801\) | −1.33809 | + | 1.33809i | −0.0472790 | + | 0.0472790i | ||||
\(802\) | 3.25081 | − | 3.25081i | 0.114790 | − | 0.114790i | ||||
\(803\) | 33.4695 | − | 33.4695i | 1.18111 | − | 1.18111i | ||||
\(804\) | 9.73532 | 0.343338 | ||||||||
\(805\) | −5.30345 | + | 2.08863i | −0.186922 | + | 0.0736144i | ||||
\(806\) | −2.16650 | + | 2.16650i | −0.0763115 | + | 0.0763115i | ||||
\(807\) | −2.41793 | + | 2.41793i | −0.0851151 | + | 0.0851151i | ||||
\(808\) | − | 11.0673i | − | 0.389346i | ||||||
\(809\) | −7.49771 | − | 7.49771i | −0.263605 | − | 0.263605i | 0.562912 | − | 0.826517i | \(-0.309681\pi\) |
−0.826517 | + | 0.562912i | \(0.809681\pi\) | |||||||
\(810\) | −0.891783 | + | 2.05054i | −0.0313341 | + | 0.0720487i | ||||
\(811\) | 17.4655 | 0.613296 | 0.306648 | − | 0.951823i | \(-0.400793\pi\) | ||||
0.306648 | + | 0.951823i | \(0.400793\pi\) | |||||||
\(812\) | 3.82892i | 0.134369i | ||||||||
\(813\) | 12.6363 | + | 12.6363i | 0.443174 | + | 0.443174i | ||||
\(814\) | 0.0395395 | + | 23.8560i | 0.00138586 | + | 0.836151i | ||||
\(815\) | 31.5970 | + | 13.7416i | 1.10679 | + | 0.481346i | ||||
\(816\) | −0.887401 | + | 0.887401i | −0.0310652 | + | 0.0310652i | ||||
\(817\) | −4.08144 | + | 4.08144i | −0.142792 | + | 0.142792i | ||||
\(818\) | 13.3605 | + | 13.3605i | 0.467141 | + | 0.467141i | ||||
\(819\) | −0.499755 | + | 0.499755i | −0.0174629 | + | 0.0174629i | ||||
\(820\) | −8.05479 | − | 3.50304i | −0.281286 | − | 0.122331i | ||||
\(821\) | −30.4173 | −1.06157 | −0.530786 | − | 0.847506i | \(-0.678103\pi\) | ||||
−0.530786 | + | 0.847506i | \(0.678103\pi\) | |||||||
\(822\) | 20.6125i | 0.718943i | ||||||||
\(823\) | 34.7921 | − | 34.7921i | 1.21278 | − | 1.21278i | 0.242667 | − | 0.970110i | \(-0.421978\pi\) |
0.970110 | − | 0.242667i | \(-0.0780221\pi\) | |||||||
\(824\) | 13.8134i | 0.481211i | ||||||||
\(825\) | 19.5975 | + | 0.687284i | 0.682296 | + | 0.0239282i | ||||
\(826\) | 14.7198 | 0.512166 | ||||||||
\(827\) | − | 37.5059i | − | 1.30421i | −0.758129 | − | 0.652104i | \(-0.773886\pi\) | ||
0.758129 | − | 0.652104i | \(-0.226114\pi\) | |||||||
\(828\) | − | 1.15203i | − | 0.0400358i | ||||||
\(829\) | −38.6319 | − | 38.6319i | −1.34174 | − | 1.34174i | −0.894327 | − | 0.447414i | \(-0.852345\pi\) |
−0.447414 | − | 0.894327i | \(-0.647655\pi\) | |||||||
\(830\) | 1.30949 | + | 3.32506i | 0.0454530 | + | 0.115414i | ||||
\(831\) | −10.5024 | − | 10.5024i | −0.364325 | − | 0.364325i | ||||
\(832\) | −0.319413 | −0.0110737 | ||||||||
\(833\) | 2.64050 | 0.0914881 | ||||||||
\(834\) | 0.852977 | + | 0.852977i | 0.0295362 | + | 0.0295362i | ||||
\(835\) | −34.5252 | − | 15.0150i | −1.19479 | − | 0.519617i | ||||
\(836\) | 8.54484 | + | 8.54484i | 0.295529 | + | 0.295529i | ||||
\(837\) | − | 9.59224i | − | 0.331556i | ||||||
\(838\) | 18.6060i | 0.642734i | ||||||||
\(839\) | −14.2744 | −0.492807 | −0.246404 | − | 0.969167i | \(-0.579249\pi\) | ||||
−0.246404 | + | 0.969167i | \(0.579249\pi\) | |||||||
\(840\) | −4.53720 | − | 1.97323i | −0.156548 | − | 0.0680830i | ||||
\(841\) | − | 26.0056i | − | 0.896744i | ||||||
\(842\) | −4.15626 | + | 4.15626i | −0.143234 | + | 0.143234i | ||||
\(843\) | 6.45155i | 0.222203i | ||||||||
\(844\) | 27.2170 | 0.936848 | ||||||||
\(845\) | 11.5022 | − | 26.4478i | 0.395687 | − | 0.909833i | ||||
\(846\) | −4.88442 | + | 4.88442i | −0.167930 | + | 0.167930i | ||||
\(847\) | 6.85502 | + | 6.85502i | 0.235541 | + | 0.235541i | ||||
\(848\) | −3.03226 | + | 3.03226i | −0.104128 | + | 0.104128i | ||||
\(849\) | −22.9026 | + | 22.9026i | −0.786014 | + | 0.786014i | ||||
\(850\) | −4.58979 | + | 4.27877i | −0.157428 | + | 0.146760i | ||||
\(851\) | 7.00751 | − | 0.0116144i | 0.240214 | − | 0.000398137i | ||||
\(852\) | −2.32647 | − | 2.32647i | −0.0797035 | − | 0.0797035i | ||||
\(853\) | − | 37.6236i | − | 1.28821i | −0.764938 | − | 0.644104i | \(-0.777231\pi\) | ||
0.764938 | − | 0.644104i | \(-0.222769\pi\) | |||||||
\(854\) | −17.4026 | −0.595505 | ||||||||
\(855\) | −6.41059 | + | 2.52465i | −0.219237 | + | 0.0863410i | ||||
\(856\) | −1.55870 | − | 1.55870i | −0.0532753 | − | 0.0532753i | ||||
\(857\) | 25.5393i | 0.872405i | 0.899849 | + | 0.436202i | \(0.143677\pi\) | ||||
−0.899849 | + | 0.436202i | \(0.856323\pi\) | |||||||
\(858\) | −0.885798 | + | 0.885798i | −0.0302406 | + | 0.0302406i | ||||
\(859\) | 35.0362 | − | 35.0362i | 1.19542 | − | 1.19542i | 0.219897 | − | 0.975523i | \(-0.429428\pi\) |
0.975523 | − | 0.219897i | \(-0.0705722\pi\) | |||||||
\(860\) | 1.67057 | − | 3.84128i | 0.0569661 | − | 0.130986i | ||||
\(861\) | 8.69170 | 0.296212 | ||||||||
\(862\) | 7.99513 | − | 7.99513i | 0.272315 | − | 0.272315i | ||||
\(863\) | −34.9362 | + | 34.9362i | −1.18924 | + | 1.18924i | −0.211964 | + | 0.977277i | \(0.567986\pi\) |
−0.977277 | + | 0.211964i | \(0.932014\pi\) | |||||||
\(864\) | 0.707107 | − | 0.707107i | 0.0240563 | − | 0.0240563i | ||||
\(865\) | 15.2531 | − | 6.00706i | 0.518622 | − | 0.204246i | ||||
\(866\) | −21.8861 | + | 21.8861i | −0.743720 | + | 0.743720i | ||||
\(867\) | 10.9072 | + | 10.9072i | 0.370426 | + | 0.370426i | ||||
\(868\) | 21.2246 | 0.720409 | ||||||||
\(869\) | −14.0826 | − | 14.0826i | −0.477721 | − | 0.477721i | ||||
\(870\) | −3.54834 | − | 1.54318i | −0.120300 | − | 0.0523186i | ||||
\(871\) | −2.19881 | + | 2.19881i | −0.0745039 | + | 0.0745039i | ||||
\(872\) | 4.24101 | − | 4.24101i | 0.143619 | − | 0.143619i | ||||
\(873\) | −4.01884 | −0.136017 | ||||||||
\(874\) | 2.50998 | − | 2.50998i | 0.0849014 | − | 0.0849014i | ||||
\(875\) | −22.3263 | − | 10.6552i | −0.754766 | − | 0.360212i | ||||
\(876\) | − | 12.0689i | − | 0.407770i | ||||||
\(877\) | −36.4441 | − | 36.4441i | −1.23063 | − | 1.23063i | −0.963722 | − | 0.266909i | \(-0.913998\pi\) |
−0.266909 | − | 0.963722i | \(-0.586002\pi\) | |||||||
\(878\) | −19.4929 | − | 19.4929i | −0.657853 | − | 0.657853i | ||||
\(879\) | 4.14622 | 0.139848 | ||||||||
\(880\) | −8.04202 | − | 3.49748i | −0.271097 | − | 0.117900i | ||||
\(881\) | − | 41.8468i | − | 1.40986i | −0.709279 | − | 0.704928i | \(-0.750979\pi\) | ||
0.709279 | − | 0.704928i | \(-0.249021\pi\) | |||||||
\(882\) | −2.10403 | −0.0708464 | ||||||||
\(883\) | − | 6.73598i | − | 0.226684i | −0.993556 | − | 0.113342i | \(-0.963844\pi\) | ||
0.993556 | − | 0.113342i | \(-0.0361555\pi\) | |||||||
\(884\) | − | 0.400855i | − | 0.0134822i | ||||||
\(885\) | −5.93254 | + | 13.6411i | −0.199420 | + | 0.458541i | ||||
\(886\) | 1.25482 | + | 1.25482i | 0.0421564 | + | 0.0421564i | ||||
\(887\) | 5.08587 | − | 5.08587i | 0.170767 | − | 0.170767i | −0.616549 | − | 0.787316i | \(-0.711470\pi\) |
0.787316 | + | 0.616549i | \(0.211470\pi\) | |||||||
\(888\) | 4.30829 | + | 4.29403i | 0.144577 | + | 0.144098i | ||||
\(889\) | − | 22.0987i | − | 0.741168i | ||||||
\(890\) | 3.93709 | − | 1.55052i | 0.131972 | − | 0.0519736i | ||||
\(891\) | − | 3.92190i | − | 0.131389i | ||||||
\(892\) | 11.1865 | − | 11.1865i | 0.374551 | − | 0.374551i | ||||
\(893\) | −21.2838 | −0.712237 | ||||||||
\(894\) | −0.301061 | + | 0.301061i | −0.0100690 | + | 0.0100690i | ||||
\(895\) | −5.00934 | + | 1.97280i | −0.167444 | + | 0.0659435i | ||||
\(896\) | 1.56460 | + | 1.56460i | 0.0522697 | + | 0.0522697i | ||||
\(897\) | 0.260196 | + | 0.260196i | 0.00868770 | + | 0.00868770i | ||||
\(898\) | 5.51963 | − | 5.51963i | 0.184192 | − | 0.184192i | ||||
\(899\) | 16.5988 | 0.553601 | ||||||||
\(900\) | 3.65728 | − | 3.40945i | 0.121909 | − | 0.113648i | ||||
\(901\) | −3.80541 | − | 3.80541i | −0.126777 | − | 0.126777i | ||||
\(902\) | 15.4057 | 0.512955 | ||||||||
\(903\) | 4.14502i | 0.137937i | ||||||||
\(904\) | − | 16.5384i | − | 0.550057i | ||||||
\(905\) | −7.80462 | + | 17.9457i | −0.259434 | + | 0.596536i | ||||
\(906\) | 13.1917 | − | 13.1917i | 0.438265 | − | 0.438265i | ||||
\(907\) | − | 5.02600i | − | 0.166886i | −0.996513 | − | 0.0834428i | \(-0.973408\pi\) | ||
0.996513 | − | 0.0834428i | \(-0.0265916\pi\) | |||||||
\(908\) | 1.74912i | 0.0580467i | ||||||||
\(909\) | −11.0673 | −0.367079 | ||||||||
\(910\) | 1.47044 | − | 0.579096i | 0.0487447 | − | 0.0191968i | ||||
\(911\) | −6.78195 | − | 6.78195i | −0.224696 | − | 0.224696i | 0.585777 | − | 0.810473i | \(-0.300790\pi\) |
−0.810473 | + | 0.585777i | \(0.800790\pi\) | |||||||
\(912\) | 3.08122 | 0.102029 | ||||||||
\(913\) | −4.43206 | − | 4.43206i | −0.146680 | − | 0.146680i | ||||
\(914\) | 6.65948i | 0.220276i | ||||||||
\(915\) | 7.01382 | − | 16.1274i | 0.231870 | − | 0.533155i | ||||
\(916\) | − | 8.51464i | − | 0.281332i | ||||||
\(917\) | 29.1696 | 0.963264 | ||||||||
\(918\) | 0.887401 | + | 0.887401i | 0.0292886 | + | 0.0292886i | ||||
\(919\) | −5.23943 | − | 5.23943i | −0.172833 | − | 0.172833i | 0.615390 | − | 0.788223i | \(-0.288999\pi\) |
−0.788223 | + | 0.615390i | \(0.788999\pi\) | |||||||
\(920\) | −1.02736 | + | 2.36228i | −0.0338710 | + | 0.0778822i | ||||
\(921\) | 0.318596 | 0.0104981 | ||||||||
\(922\) | 24.8127 | + | 24.8127i | 0.817163 | + | 0.817163i | ||||
\(923\) | 1.05091 | 0.0345911 | ||||||||
\(924\) | 8.67793 | 0.285483 | ||||||||
\(925\) | 20.7757 | + | 22.2119i | 0.683101 | + | 0.730324i | ||||
\(926\) | −0.607120 | −0.0199512 | ||||||||
\(927\) | 13.8134 | 0.453690 | ||||||||
\(928\) | 1.22361 | + | 1.22361i | 0.0401668 | + | 0.0401668i | ||||
\(929\) | 41.3020 | 1.35507 | 0.677537 | − | 0.735488i | \(-0.263047\pi\) | ||||
0.677537 | + | 0.735488i | \(0.263047\pi\) | |||||||
\(930\) | −8.55419 | + | 19.6693i | −0.280503 | + | 0.644981i | ||||
\(931\) | −4.58415 | − | 4.58415i | −0.150240 | − | 0.150240i | ||||
\(932\) | 6.42533 | + | 6.42533i | 0.210469 | + | 0.210469i | ||||
\(933\) | 11.5938 | 0.379563 | ||||||||
\(934\) | 14.2821i | 0.467324i | ||||||||
\(935\) | 4.38925 | − | 10.0925i | 0.143544 | − | 0.330061i | ||||
\(936\) | 0.319413i | 0.0104403i | ||||||||
\(937\) | 30.8614 | + | 30.8614i | 1.00820 | + | 1.00820i | 0.999966 | + | 0.00823050i | \(0.00261988\pi\) |
0.00823050 | + | 0.999966i | \(0.497380\pi\) | |||||||
\(938\) | 21.5412 | 0.703344 | ||||||||
\(939\) | −8.56918 | − | 8.56918i | −0.279645 | − | 0.279645i | ||||
\(940\) | 14.3716 | − | 5.65987i | 0.468748 | − | 0.184605i | ||||
\(941\) | −5.06512 | −0.165118 | −0.0825590 | − | 0.996586i | \(-0.526309\pi\) | ||||
−0.0825590 | + | 0.996586i | \(0.526309\pi\) | |||||||
\(942\) | − | 8.81585i | − | 0.287236i | ||||||
\(943\) | − | 4.52532i | − | 0.147365i | ||||||
\(944\) | 4.70399 | − | 4.70399i | 0.153102 | − | 0.153102i | ||||
\(945\) | −1.97323 | + | 4.53720i | −0.0641893 | + | 0.147595i | ||||
\(946\) | 7.34689i | 0.238868i | ||||||||
\(947\) | 59.8123i | 1.94364i | 0.235726 | + | 0.971819i | \(0.424253\pi\) | ||||
−0.235726 | + | 0.971819i | \(0.575747\pi\) | |||||||
\(948\) | −5.07811 | −0.164929 | ||||||||
\(949\) | 2.72587 | + | 2.72587i | 0.0884855 | + | 0.0884855i | ||||
\(950\) | 15.3966 | + | 0.539960i | 0.499532 | + | 0.0175186i | ||||
\(951\) | −7.72243 | −0.250417 | ||||||||
\(952\) | −1.96354 | + | 1.96354i | −0.0636386 | + | 0.0636386i | ||||
\(953\) | 17.6361 | + | 17.6361i | 0.571291 | + | 0.571291i | 0.932489 | − | 0.361198i | \(-0.117632\pi\) |
−0.361198 | + | 0.932489i | \(0.617632\pi\) | |||||||
\(954\) | 3.03226 | + | 3.03226i | 0.0981732 | + | 0.0981732i | ||||
\(955\) | −13.4399 | + | 5.29298i | −0.434906 | + | 0.171277i | ||||
\(956\) | −10.4976 | + | 10.4976i | −0.339518 | + | 0.339518i | ||||
\(957\) | 6.78661 | 0.219380 | ||||||||
\(958\) | 12.8987 | − | 12.8987i | 0.416739 | − | 0.416739i | ||||
\(959\) | 45.6089i | 1.47279i | ||||||||
\(960\) | −2.08054 | + | 0.819367i | −0.0671491 | + | 0.0264449i | ||||
\(961\) | − | 61.0110i | − | 1.96810i | ||||||
\(962\) | −1.94291 | + | 0.00322023i | −0.0626420 | + | 0.000103824i | ||||
\(963\) | −1.55870 | + | 1.55870i | −0.0502284 | + | 0.0502284i | ||||
\(964\) | 6.66851 | + | 6.66851i | 0.214778 | + | 0.214778i | ||||
\(965\) | 4.91860 | − | 11.3097i | 0.158335 | − | 0.364072i | ||||
\(966\) | − | 2.54907i | − | 0.0820151i | ||||||
\(967\) | 39.1113i | 1.25773i | 0.777513 | + | 0.628867i | \(0.216481\pi\) | ||||
−0.777513 | + | 0.628867i | \(0.783519\pi\) | |||||||
\(968\) | 4.38131 | 0.140821 | ||||||||
\(969\) | 3.86685i | 0.124221i | ||||||||
\(970\) | 8.24079 | + | 3.58393i | 0.264596 | + | 0.115073i | ||||
\(971\) | 49.6084 | 1.59201 | 0.796004 | − | 0.605291i | \(-0.206943\pi\) | ||||
0.796004 | + | 0.605291i | \(0.206943\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 1.88737 | + | 1.88737i | 0.0605063 | + | 0.0605063i | ||||
\(974\) | − | 0.169467i | − | 0.00543009i | ||||||
\(975\) | −0.0559748 | + | 1.59608i | −0.00179263 | + | 0.0511156i | ||||
\(976\) | −5.56135 | + | 5.56135i | −0.178014 | + | 0.178014i | ||||
\(977\) | −17.0944 | −0.546899 | −0.273450 | − | 0.961886i | \(-0.588165\pi\) | ||||
−0.273450 | + | 0.961886i | \(0.588165\pi\) | |||||||
\(978\) | −10.8959 | + | 10.8959i | −0.348411 | + | 0.348411i | ||||
\(979\) | −5.24785 | + | 5.24785i | −0.167722 | + | 0.167722i | ||||
\(980\) | 4.31440 | + | 1.87634i | 0.137819 | + | 0.0599374i | ||||
\(981\) | −4.24101 | − | 4.24101i | −0.135405 | − | 0.135405i | ||||
\(982\) | −11.6118 | −0.370547 | ||||||||
\(983\) | 14.4506 | + | 14.4506i | 0.460901 | + | 0.460901i | 0.898951 | − | 0.438050i | \(-0.144331\pi\) |
−0.438050 | + | 0.898951i | \(0.644331\pi\) | |||||||
\(984\) | 2.77761 | − | 2.77761i | 0.0885468 | − | 0.0885468i | ||||
\(985\) | 10.2543 | − | 4.03839i | 0.326729 | − | 0.128674i | ||||
\(986\) | −1.53559 | + | 1.53559i | −0.0489033 | + | 0.0489033i | ||||
\(987\) | −10.8077 | + | 10.8077i | −0.344012 | + | 0.344012i | ||||
\(988\) | −0.695921 | + | 0.695921i | −0.0221402 | + | 0.0221402i | ||||
\(989\) | 2.15809 | 0.0686233 | ||||||||
\(990\) | −3.49748 | + | 8.04202i | −0.111157 | + | 0.255592i | ||||
\(991\) | −10.9464 | + | 10.9464i | −0.347723 | + | 0.347723i | −0.859261 | − | 0.511538i | \(-0.829076\pi\) |
0.511538 | + | 0.859261i | \(0.329076\pi\) | |||||||
\(992\) | 6.78274 | − | 6.78274i | 0.215352 | − | 0.215352i | ||||
\(993\) | 20.1471i | 0.639350i | ||||||||
\(994\) | −5.14774 | − | 5.14774i | −0.163276 | − | 0.163276i | ||||
\(995\) | −32.6193 | + | 12.8463i | −1.03410 | + | 0.407255i | ||||
\(996\) | −1.59817 | −0.0506400 | ||||||||
\(997\) | 32.8775i | 1.04124i | 0.853788 | + | 0.520621i | \(0.174299\pi\) | ||||
−0.853788 | + | 0.520621i | \(0.825701\pi\) | |||||||
\(998\) | −15.8556 | − | 15.8556i | −0.501899 | − | 0.501899i | ||||
\(999\) | 4.29403 | − | 4.30829i | 0.135857 | − | 0.136308i |
(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 | 1110.2.o.a.487.11 | yes | 36 | |
5.3 | odd | 4 | 1110.2.l.a.43.8 | ✓ | 36 | ||
37.31 | odd | 4 | 1110.2.l.a.697.8 | yes | 36 | ||
185.68 | even | 4 | inner | 1110.2.o.a.253.11 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.8 | ✓ | 36 | 5.3 | odd | 4 | ||
1110.2.l.a.697.8 | yes | 36 | 37.31 | odd | 4 | ||
1110.2.o.a.253.11 | yes | 36 | 185.68 | even | 4 | inner | |
1110.2.o.a.487.11 | yes | 36 | 1.1 | even | 1 | trivial |