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 | 253.15 | ||
Character | \(\chi\) | \(=\) | 1110.253 |
Dual form | 1110.2.o.a.487.15 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(5\) | 1.94044 | − | 1.11117i | 0.867790 | − | 0.496931i | ||||
\(6\) | −0.707107 | + | 0.707107i | −0.288675 | + | 0.288675i | ||||
\(7\) | 0.636201 | − | 0.636201i | 0.240461 | − | 0.240461i | −0.576580 | − | 0.817041i | \(-0.695613\pi\) |
0.817041 | + | 0.576580i | \(0.195613\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.94044 | + | 1.11117i | −0.613620 | + | 0.351383i | ||||
\(11\) | 2.26858i | 0.684003i | 0.939699 | + | 0.342002i | \(0.111105\pi\) | ||||
−0.939699 | + | 0.342002i | \(0.888895\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | 1.29147 | 0.358190 | 0.179095 | − | 0.983832i | \(-0.442683\pi\) | ||||
0.179095 | + | 0.983832i | \(0.442683\pi\) | |||||||
\(14\) | −0.636201 | + | 0.636201i | −0.170032 | + | 0.170032i | ||||
\(15\) | 0.586380 | − | 2.15781i | 0.151403 | − | 0.557145i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.74699i | 1.39385i | 0.717144 | + | 0.696925i | \(0.245449\pi\) | ||||
−0.717144 | + | 0.696925i | \(0.754551\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 4.10165 | + | 4.10165i | 0.940982 | + | 0.940982i | 0.998353 | − | 0.0573705i | \(-0.0182716\pi\) |
−0.0573705 | + | 0.998353i | \(0.518272\pi\) | |||||||
\(20\) | 1.94044 | − | 1.11117i | 0.433895 | − | 0.248465i | ||||
\(21\) | − | 0.899724i | − | 0.196336i | ||||||
\(22\) | − | 2.26858i | − | 0.483663i | ||||||
\(23\) | 8.53431 | 1.77953 | 0.889763 | − | 0.456423i | \(-0.150869\pi\) | ||||
0.889763 | + | 0.456423i | \(0.150869\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | 2.53060 | − | 4.31232i | 0.506119 | − | 0.862464i | ||||
\(26\) | −1.29147 | −0.253278 | ||||||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0.636201 | − | 0.636201i | 0.120231 | − | 0.120231i | ||||
\(29\) | 1.70155 | − | 1.70155i | 0.315969 | − | 0.315969i | −0.531247 | − | 0.847217i | \(-0.678277\pi\) |
0.847217 | + | 0.531247i | \(0.178277\pi\) | |||||||
\(30\) | −0.586380 | + | 2.15781i | −0.107058 | + | 0.393961i | ||||
\(31\) | −5.81155 | − | 5.81155i | −1.04379 | − | 1.04379i | −0.998996 | − | 0.0447888i | \(-0.985739\pi\) |
−0.0447888 | − | 0.998996i | \(-0.514261\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.60413 | + | 1.60413i | 0.279243 | + | 0.279243i | ||||
\(34\) | − | 5.74699i | − | 0.985601i | ||||||
\(35\) | 0.527580 | − | 1.94144i | 0.0891773 | − | 0.328163i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 3.16223 | − | 5.19618i | 0.519868 | − | 0.854247i | ||||
\(38\) | −4.10165 | − | 4.10165i | −0.665375 | − | 0.665375i | ||||
\(39\) | 0.913209 | − | 0.913209i | 0.146230 | − | 0.146230i | ||||
\(40\) | −1.94044 | + | 1.11117i | −0.306810 | + | 0.175692i | ||||
\(41\) | 9.02011i | 1.40870i | 0.709851 | + | 0.704352i | \(0.248762\pi\) | ||||
−0.709851 | + | 0.704352i | \(0.751238\pi\) | |||||||
\(42\) | 0.899724i | 0.138830i | ||||||||
\(43\) | 0.853087 | 0.130094 | 0.0650472 | − | 0.997882i | \(-0.479280\pi\) | ||||
0.0650472 | + | 0.997882i | \(0.479280\pi\) | |||||||
\(44\) | 2.26858i | 0.342002i | ||||||||
\(45\) | −1.11117 | − | 1.94044i | −0.165644 | − | 0.289263i | ||||
\(46\) | −8.53431 | −1.25832 | ||||||||
\(47\) | −0.326713 | + | 0.326713i | −0.0476560 | + | 0.0476560i | −0.730533 | − | 0.682877i | \(-0.760728\pi\) |
0.682877 | + | 0.730533i | \(0.260728\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | 6.19050i | 0.884357i | ||||||||
\(50\) | −2.53060 | + | 4.31232i | −0.357880 | + | 0.609854i | ||||
\(51\) | 4.06374 | + | 4.06374i | 0.569037 | + | 0.569037i | ||||
\(52\) | 1.29147 | 0.179095 | ||||||||
\(53\) | −6.79864 | − | 6.79864i | −0.933866 | − | 0.933866i | 0.0640792 | − | 0.997945i | \(-0.479589\pi\) |
−0.997945 | + | 0.0640792i | \(0.979589\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | 2.52078 | + | 4.40204i | 0.339902 | + | 0.593571i | ||||
\(56\) | −0.636201 | + | 0.636201i | −0.0850159 | + | 0.0850159i | ||||
\(57\) | 5.80061 | 0.768309 | ||||||||
\(58\) | −1.70155 | + | 1.70155i | −0.223424 | + | 0.223424i | ||||
\(59\) | −3.51171 | − | 3.51171i | −0.457186 | − | 0.457186i | 0.440545 | − | 0.897731i | \(-0.354785\pi\) |
−0.897731 | + | 0.440545i | \(0.854785\pi\) | |||||||
\(60\) | 0.586380 | − | 2.15781i | 0.0757013 | − | 0.278573i | ||||
\(61\) | −2.06460 | − | 2.06460i | −0.264345 | − | 0.264345i | 0.562472 | − | 0.826817i | \(-0.309851\pi\) |
−0.826817 | + | 0.562472i | \(0.809851\pi\) | |||||||
\(62\) | 5.81155 | + | 5.81155i | 0.738068 | + | 0.738068i | ||||
\(63\) | −0.636201 | − | 0.636201i | −0.0801538 | − | 0.0801538i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.50602 | − | 1.43505i | 0.310834 | − | 0.177996i | ||||
\(66\) | −1.60413 | − | 1.60413i | −0.197455 | − | 0.197455i | ||||
\(67\) | −3.98347 | − | 3.98347i | −0.486659 | − | 0.486659i | 0.420591 | − | 0.907250i | \(-0.361823\pi\) |
−0.907250 | + | 0.420591i | \(0.861823\pi\) | |||||||
\(68\) | 5.74699i | 0.696925i | ||||||||
\(69\) | 6.03467 | − | 6.03467i | 0.726489 | − | 0.726489i | ||||
\(70\) | −0.527580 | + | 1.94144i | −0.0630579 | + | 0.232046i | ||||
\(71\) | −15.2892 | −1.81450 | −0.907248 | − | 0.420596i | \(-0.861821\pi\) | ||||
−0.907248 | + | 0.420596i | \(0.861821\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 11.8322 | − | 11.8322i | 1.38486 | − | 1.38486i | 0.549108 | − | 0.835751i | \(-0.314968\pi\) |
0.835751 | − | 0.549108i | \(-0.185032\pi\) | |||||||
\(74\) | −3.16223 | + | 5.19618i | −0.367602 | + | 0.604044i | ||||
\(75\) | −1.25987 | − | 4.83867i | −0.145477 | − | 0.558722i | ||||
\(76\) | 4.10165 | + | 4.10165i | 0.470491 | + | 0.470491i | ||||
\(77\) | 1.44327 | + | 1.44327i | 0.164476 | + | 0.164476i | ||||
\(78\) | −0.913209 | + | 0.913209i | −0.103401 | + | 0.103401i | ||||
\(79\) | −9.04382 | − | 9.04382i | −1.01751 | − | 1.01751i | −0.999844 | − | 0.0176652i | \(-0.994377\pi\) |
−0.0176652 | − | 0.999844i | \(-0.505623\pi\) | |||||||
\(80\) | 1.94044 | − | 1.11117i | 0.216948 | − | 0.124233i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | − | 9.02011i | − | 0.996104i | ||||||
\(83\) | 9.12362 | + | 9.12362i | 1.00145 | + | 1.00145i | 0.999999 | + | 0.00144791i | \(0.000460883\pi\) |
0.00144791 | + | 0.999999i | \(0.499539\pi\) | |||||||
\(84\) | − | 0.899724i | − | 0.0981680i | ||||||
\(85\) | 6.38589 | + | 11.1517i | 0.692647 | + | 1.20957i | ||||
\(86\) | −0.853087 | −0.0919907 | ||||||||
\(87\) | − | 2.40635i | − | 0.257988i | ||||||
\(88\) | − | 2.26858i | − | 0.241832i | ||||||
\(89\) | 6.32382 | − | 6.32382i | 0.670323 | − | 0.670323i | −0.287467 | − | 0.957791i | \(-0.592813\pi\) |
0.957791 | + | 0.287467i | \(0.0928132\pi\) | |||||||
\(90\) | 1.11117 | + | 1.94044i | 0.117128 | + | 0.204540i | ||||
\(91\) | 0.821636 | − | 0.821636i | 0.0861308 | − | 0.0861308i | ||||
\(92\) | 8.53431 | 0.889763 | ||||||||
\(93\) | −8.21877 | −0.852247 | ||||||||
\(94\) | 0.326713 | − | 0.326713i | 0.0336979 | − | 0.0336979i | ||||
\(95\) | 12.5166 | + | 3.40136i | 1.28418 | + | 0.348972i | ||||
\(96\) | −0.707107 | + | 0.707107i | −0.0721688 | + | 0.0721688i | ||||
\(97\) | − | 9.28197i | − | 0.942441i | −0.882015 | − | 0.471220i | \(-0.843814\pi\) | ||
0.882015 | − | 0.471220i | \(-0.156186\pi\) | |||||||
\(98\) | − | 6.19050i | − | 0.625335i | ||||||
\(99\) | 2.26858 | 0.228001 | ||||||||
\(100\) | 2.53060 | − | 4.31232i | 0.253060 | − | 0.431232i | ||||
\(101\) | 1.47408i | 0.146677i | 0.997307 | + | 0.0733383i | \(0.0233653\pi\) | ||||
−0.997307 | + | 0.0733383i | \(0.976635\pi\) | |||||||
\(102\) | −4.06374 | − | 4.06374i | −0.402370 | − | 0.402370i | ||||
\(103\) | 1.02968i | 0.101458i | 0.998712 | + | 0.0507289i | \(0.0161544\pi\) | ||||
−0.998712 | + | 0.0507289i | \(0.983846\pi\) | |||||||
\(104\) | −1.29147 | −0.126639 | ||||||||
\(105\) | −0.999748 | − | 1.74586i | −0.0975654 | − | 0.170378i | ||||
\(106\) | 6.79864 | + | 6.79864i | 0.660343 | + | 0.660343i | ||||
\(107\) | −13.8598 | + | 13.8598i | −1.33988 | + | 1.33988i | −0.443708 | + | 0.896171i | \(0.646337\pi\) |
−0.896171 | + | 0.443708i | \(0.853663\pi\) | |||||||
\(108\) | −0.707107 | − | 0.707107i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | −5.32683 | − | 5.32683i | −0.510218 | − | 0.510218i | 0.404375 | − | 0.914593i | \(-0.367489\pi\) |
−0.914593 | + | 0.404375i | \(0.867489\pi\) | |||||||
\(110\) | −2.52078 | − | 4.40204i | −0.240347 | − | 0.419718i | ||||
\(111\) | −1.43822 | − | 5.91029i | −0.136510 | − | 0.560980i | ||||
\(112\) | 0.636201 | − | 0.636201i | 0.0601153 | − | 0.0601153i | ||||
\(113\) | 17.2755i | 1.62515i | 0.582859 | + | 0.812573i | \(0.301934\pi\) | ||||
−0.582859 | + | 0.812573i | \(0.698066\pi\) | |||||||
\(114\) | −5.80061 | −0.543276 | ||||||||
\(115\) | 16.5603 | − | 9.48308i | 1.54426 | − | 0.884302i | ||||
\(116\) | 1.70155 | − | 1.70155i | 0.157985 | − | 0.157985i | ||||
\(117\) | − | 1.29147i | − | 0.119397i | ||||||
\(118\) | 3.51171 | + | 3.51171i | 0.323279 | + | 0.323279i | ||||
\(119\) | 3.65624 | + | 3.65624i | 0.335167 | + | 0.335167i | ||||
\(120\) | −0.586380 | + | 2.15781i | −0.0535289 | + | 0.196981i | ||||
\(121\) | 5.85354 | 0.532140 | ||||||||
\(122\) | 2.06460 | + | 2.06460i | 0.186920 | + | 0.186920i | ||||
\(123\) | 6.37818 | + | 6.37818i | 0.575101 | + | 0.575101i | ||||
\(124\) | −5.81155 | − | 5.81155i | −0.521893 | − | 0.521893i | ||||
\(125\) | 0.118740 | − | 11.1797i | 0.0106204 | − | 0.999944i | ||||
\(126\) | 0.636201 | + | 0.636201i | 0.0566773 | + | 0.0566773i | ||||
\(127\) | 0.916380 | − | 0.916380i | 0.0813156 | − | 0.0813156i | −0.665279 | − | 0.746595i | \(-0.731687\pi\) |
0.746595 | + | 0.665279i | \(0.231687\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.603223 | − | 0.603223i | 0.0531109 | − | 0.0531109i | ||||
\(130\) | −2.50602 | + | 1.43505i | −0.219793 | + | 0.125862i | ||||
\(131\) | −6.28943 | − | 6.28943i | −0.549510 | − | 0.549510i | 0.376789 | − | 0.926299i | \(-0.377028\pi\) |
−0.926299 | + | 0.376789i | \(0.877028\pi\) | |||||||
\(132\) | 1.60413 | + | 1.60413i | 0.139622 | + | 0.139622i | ||||
\(133\) | 5.21895 | 0.452540 | ||||||||
\(134\) | 3.98347 | + | 3.98347i | 0.344120 | + | 0.344120i | ||||
\(135\) | −2.15781 | − | 0.586380i | −0.185715 | − | 0.0504675i | ||||
\(136\) | − | 5.74699i | − | 0.492800i | ||||||
\(137\) | 10.4523 | − | 10.4523i | 0.893004 | − | 0.893004i | −0.101801 | − | 0.994805i | \(-0.532461\pi\) |
0.994805 | + | 0.101801i | \(0.0324605\pi\) | |||||||
\(138\) | −6.03467 | + | 6.03467i | −0.513705 | + | 0.513705i | ||||
\(139\) | 14.4443 | 1.22515 | 0.612574 | − | 0.790414i | \(-0.290134\pi\) | ||||
0.612574 | + | 0.790414i | \(0.290134\pi\) | |||||||
\(140\) | 0.527580 | − | 1.94144i | 0.0445887 | − | 0.164081i | ||||
\(141\) | 0.462042i | 0.0389110i | ||||||||
\(142\) | 15.2892 | 1.28304 | ||||||||
\(143\) | 2.92981i | 0.245003i | ||||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 1.41104 | − | 5.19246i | 0.117180 | − | 0.431210i | ||||
\(146\) | −11.8322 | + | 11.8322i | −0.979243 | + | 0.979243i | ||||
\(147\) | 4.37734 | + | 4.37734i | 0.361037 | + | 0.361037i | ||||
\(148\) | 3.16223 | − | 5.19618i | 0.259934 | − | 0.427123i | ||||
\(149\) | 19.0997i | 1.56471i | 0.622831 | + | 0.782356i | \(0.285982\pi\) | ||||
−0.622831 | + | 0.782356i | \(0.714018\pi\) | |||||||
\(150\) | 1.25987 | + | 4.83867i | 0.102868 | + | 0.395076i | ||||
\(151\) | − | 3.42513i | − | 0.278733i | −0.990241 | − | 0.139367i | \(-0.955493\pi\) | ||
0.990241 | − | 0.139367i | \(-0.0445067\pi\) | |||||||
\(152\) | −4.10165 | − | 4.10165i | −0.332688 | − | 0.332688i | ||||
\(153\) | 5.74699 | 0.464617 | ||||||||
\(154\) | −1.44327 | − | 1.44327i | −0.116302 | − | 0.116302i | ||||
\(155\) | −17.7346 | − | 4.81932i | −1.42448 | − | 0.387097i | ||||
\(156\) | 0.913209 | − | 0.913209i | 0.0731152 | − | 0.0731152i | ||||
\(157\) | 12.1068 | − | 12.1068i | 0.966232 | − | 0.966232i | −0.0332164 | − | 0.999448i | \(-0.510575\pi\) |
0.999448 | + | 0.0332164i | \(0.0105751\pi\) | |||||||
\(158\) | 9.04382 | + | 9.04382i | 0.719488 | + | 0.719488i | ||||
\(159\) | −9.61473 | −0.762498 | ||||||||
\(160\) | −1.94044 | + | 1.11117i | −0.153405 | + | 0.0878458i | ||||
\(161\) | 5.42954 | − | 5.42954i | 0.427907 | − | 0.427907i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 24.2268i | 1.89759i | 0.315894 | + | 0.948795i | \(0.397696\pi\) | ||||
−0.315894 | + | 0.948795i | \(0.602304\pi\) | |||||||
\(164\) | 9.02011i | 0.704352i | ||||||||
\(165\) | 4.89518 | + | 1.33025i | 0.381089 | + | 0.103560i | ||||
\(166\) | −9.12362 | − | 9.12362i | −0.708130 | − | 0.708130i | ||||
\(167\) | − | 9.66372i | − | 0.747801i | −0.927469 | − | 0.373900i | \(-0.878020\pi\) | ||
0.927469 | − | 0.373900i | \(-0.121980\pi\) | |||||||
\(168\) | 0.899724i | 0.0694152i | ||||||||
\(169\) | −11.3321 | −0.871700 | ||||||||
\(170\) | −6.38589 | − | 11.1517i | −0.489776 | − | 0.855295i | ||||
\(171\) | 4.10165 | − | 4.10165i | 0.313661 | − | 0.313661i | ||||
\(172\) | 0.853087 | 0.0650472 | ||||||||
\(173\) | 6.77556 | − | 6.77556i | 0.515136 | − | 0.515136i | −0.400959 | − | 0.916096i | \(-0.631323\pi\) |
0.916096 | + | 0.400959i | \(0.131323\pi\) | |||||||
\(174\) | 2.40635i | 0.182425i | ||||||||
\(175\) | −1.13353 | − | 4.35347i | −0.0856870 | − | 0.329091i | ||||
\(176\) | 2.26858i | 0.171001i | ||||||||
\(177\) | −4.96631 | −0.373290 | ||||||||
\(178\) | −6.32382 | + | 6.32382i | −0.473990 | + | 0.473990i | ||||
\(179\) | −7.36463 | + | 7.36463i | −0.550458 | + | 0.550458i | −0.926573 | − | 0.376115i | \(-0.877260\pi\) |
0.376115 | + | 0.926573i | \(0.377260\pi\) | |||||||
\(180\) | −1.11117 | − | 1.94044i | −0.0828218 | − | 0.144632i | ||||
\(181\) | −13.9651 | −1.03802 | −0.519008 | − | 0.854769i | \(-0.673699\pi\) | ||||
−0.519008 | + | 0.854769i | \(0.673699\pi\) | |||||||
\(182\) | −0.821636 | + | 0.821636i | −0.0609037 | + | 0.0609037i | ||||
\(183\) | −2.91979 | −0.215837 | ||||||||
\(184\) | −8.53431 | −0.629158 | ||||||||
\(185\) | 0.362266 | − | 13.5966i | 0.0266343 | − | 0.999645i | ||||
\(186\) | 8.21877 | 0.602630 | ||||||||
\(187\) | −13.0375 | −0.953398 | ||||||||
\(188\) | −0.326713 | + | 0.326713i | −0.0238280 | + | 0.0238280i | ||||
\(189\) | −0.899724 | −0.0654453 | ||||||||
\(190\) | −12.5166 | − | 3.40136i | −0.908051 | − | 0.246760i | ||||
\(191\) | −11.6459 | + | 11.6459i | −0.842665 | + | 0.842665i | −0.989205 | − | 0.146540i | \(-0.953186\pi\) |
0.146540 | + | 0.989205i | \(0.453186\pi\) | |||||||
\(192\) | 0.707107 | − | 0.707107i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −2.80664 | −0.202026 | −0.101013 | − | 0.994885i | \(-0.532208\pi\) | ||||
−0.101013 | + | 0.994885i | \(0.532208\pi\) | |||||||
\(194\) | 9.28197i | 0.666406i | ||||||||
\(195\) | 0.757293 | − | 2.78676i | 0.0542309 | − | 0.199564i | ||||
\(196\) | 6.19050i | 0.442178i | ||||||||
\(197\) | 11.5183 | − | 11.5183i | 0.820643 | − | 0.820643i | −0.165557 | − | 0.986200i | \(-0.552942\pi\) |
0.986200 | + | 0.165557i | \(0.0529422\pi\) | |||||||
\(198\) | −2.26858 | −0.161221 | ||||||||
\(199\) | −10.3470 | + | 10.3470i | −0.733481 | + | 0.733481i | −0.971308 | − | 0.237827i | \(-0.923565\pi\) |
0.237827 | + | 0.971308i | \(0.423565\pi\) | |||||||
\(200\) | −2.53060 | + | 4.31232i | −0.178940 | + | 0.304927i | ||||
\(201\) | −5.63348 | −0.397355 | ||||||||
\(202\) | − | 1.47408i | − | 0.103716i | ||||||
\(203\) | − | 2.16505i | − | 0.151957i | ||||||
\(204\) | 4.06374 | + | 4.06374i | 0.284518 | + | 0.284518i | ||||
\(205\) | 10.0229 | + | 17.5030i | 0.700029 | + | 1.22246i | ||||
\(206\) | − | 1.02968i | − | 0.0717414i | ||||||
\(207\) | − | 8.53431i | − | 0.593175i | ||||||
\(208\) | 1.29147 | 0.0895475 | ||||||||
\(209\) | −9.30492 | + | 9.30492i | −0.643635 | + | 0.643635i | ||||
\(210\) | 0.999748 | + | 1.74586i | 0.0689892 | + | 0.120476i | ||||
\(211\) | −3.80993 | −0.262286 | −0.131143 | − | 0.991363i | \(-0.541865\pi\) | ||||
−0.131143 | + | 0.991363i | \(0.541865\pi\) | |||||||
\(212\) | −6.79864 | − | 6.79864i | −0.466933 | − | 0.466933i | ||||
\(213\) | −10.8111 | + | 10.8111i | −0.740765 | + | 0.740765i | ||||
\(214\) | 13.8598 | − | 13.8598i | 0.947438 | − | 0.947438i | ||||
\(215\) | 1.65536 | − | 0.947925i | 0.112895 | − | 0.0646480i | ||||
\(216\) | 0.707107 | + | 0.707107i | 0.0481125 | + | 0.0481125i | ||||
\(217\) | −7.39463 | −0.501980 | ||||||||
\(218\) | 5.32683 | + | 5.32683i | 0.360779 | + | 0.360779i | ||||
\(219\) | − | 16.7333i | − | 1.13073i | ||||||
\(220\) | 2.52078 | + | 4.40204i | 0.169951 | + | 0.296786i | ||||
\(221\) | 7.42208i | 0.499263i | ||||||||
\(222\) | 1.43822 | + | 5.91029i | 0.0965269 | + | 0.396673i | ||||
\(223\) | 16.8923 | + | 16.8923i | 1.13119 | + | 1.13119i | 0.989980 | + | 0.141210i | \(0.0450992\pi\) |
0.141210 | + | 0.989980i | \(0.454901\pi\) | |||||||
\(224\) | −0.636201 | + | 0.636201i | −0.0425080 | + | 0.0425080i | ||||
\(225\) | −4.31232 | − | 2.53060i | −0.287488 | − | 0.168706i | ||||
\(226\) | − | 17.2755i | − | 1.14915i | ||||||
\(227\) | 25.0030i | 1.65950i | 0.558132 | + | 0.829752i | \(0.311518\pi\) | ||||
−0.558132 | + | 0.829752i | \(0.688482\pi\) | |||||||
\(228\) | 5.80061 | 0.384154 | ||||||||
\(229\) | 11.3572i | 0.750503i | 0.926923 | + | 0.375252i | \(0.122444\pi\) | ||||
−0.926923 | + | 0.375252i | \(0.877556\pi\) | |||||||
\(230\) | −16.5603 | + | 9.48308i | −1.09195 | + | 0.625296i | ||||
\(231\) | 2.04110 | 0.134294 | ||||||||
\(232\) | −1.70155 | + | 1.70155i | −0.111712 | + | 0.111712i | ||||
\(233\) | −4.77274 | + | 4.77274i | −0.312673 | + | 0.312673i | −0.845944 | − | 0.533271i | \(-0.820962\pi\) |
0.533271 | + | 0.845944i | \(0.320962\pi\) | |||||||
\(234\) | 1.29147i | 0.0844262i | ||||||||
\(235\) | −0.270932 | + | 0.997001i | −0.0176737 | + | 0.0650371i | ||||
\(236\) | −3.51171 | − | 3.51171i | −0.228593 | − | 0.228593i | ||||
\(237\) | −12.7899 | −0.830793 | ||||||||
\(238\) | −3.65624 | − | 3.65624i | −0.236999 | − | 0.236999i | ||||
\(239\) | 2.96858 | + | 2.96858i | 0.192022 | + | 0.192022i | 0.796569 | − | 0.604547i | \(-0.206646\pi\) |
−0.604547 | + | 0.796569i | \(0.706646\pi\) | |||||||
\(240\) | 0.586380 | − | 2.15781i | 0.0378507 | − | 0.139286i | ||||
\(241\) | −5.75647 | + | 5.75647i | −0.370807 | + | 0.370807i | −0.867771 | − | 0.496964i | \(-0.834448\pi\) |
0.496964 | + | 0.867771i | \(0.334448\pi\) | |||||||
\(242\) | −5.85354 | −0.376279 | ||||||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | −2.06460 | − | 2.06460i | −0.132172 | − | 0.132172i | ||||
\(245\) | 6.87870 | + | 12.0123i | 0.439464 | + | 0.767436i | ||||
\(246\) | −6.37818 | − | 6.37818i | −0.406658 | − | 0.406658i | ||||
\(247\) | 5.29716 | + | 5.29716i | 0.337050 | + | 0.337050i | ||||
\(248\) | 5.81155 | + | 5.81155i | 0.369034 | + | 0.369034i | ||||
\(249\) | 12.9027 | 0.817678 | ||||||||
\(250\) | −0.118740 | + | 11.1797i | −0.00750979 | + | 0.707067i | ||||
\(251\) | −14.7749 | − | 14.7749i | −0.932584 | − | 0.932584i | 0.0652824 | − | 0.997867i | \(-0.479205\pi\) |
−0.997867 | + | 0.0652824i | \(0.979205\pi\) | |||||||
\(252\) | −0.636201 | − | 0.636201i | −0.0400769 | − | 0.0400769i | ||||
\(253\) | 19.3608i | 1.21720i | ||||||||
\(254\) | −0.916380 | + | 0.916380i | −0.0574988 | + | 0.0574988i | ||||
\(255\) | 12.4009 | + | 3.36992i | 0.776577 | + | 0.211033i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 1.80027i | − | 0.112298i | −0.998422 | − | 0.0561488i | \(-0.982118\pi\) | ||
0.998422 | − | 0.0561488i | \(-0.0178821\pi\) | |||||||
\(258\) | −0.603223 | + | 0.603223i | −0.0375550 | + | 0.0375550i | ||||
\(259\) | −1.29400 | − | 5.31763i | −0.0804053 | − | 0.330421i | ||||
\(260\) | 2.50602 | − | 1.43505i | 0.155417 | − | 0.0889978i | ||||
\(261\) | −1.70155 | − | 1.70155i | −0.105323 | − | 0.105323i | ||||
\(262\) | 6.28943 | + | 6.28943i | 0.388563 | + | 0.388563i | ||||
\(263\) | 9.25899 | − | 9.25899i | 0.570934 | − | 0.570934i | −0.361456 | − | 0.932389i | \(-0.617720\pi\) |
0.932389 | + | 0.361456i | \(0.117720\pi\) | |||||||
\(264\) | −1.60413 | − | 1.60413i | −0.0987274 | − | 0.0987274i | ||||
\(265\) | −20.7468 | − | 5.63789i | −1.27447 | − | 0.346333i | ||||
\(266\) | −5.21895 | −0.319994 | ||||||||
\(267\) | − | 8.94323i | − | 0.547317i | ||||||
\(268\) | −3.98347 | − | 3.98347i | −0.243329 | − | 0.243329i | ||||
\(269\) | − | 0.689017i | − | 0.0420101i | −0.999779 | − | 0.0210051i | \(-0.993313\pi\) | ||
0.999779 | − | 0.0210051i | \(-0.00668661\pi\) | |||||||
\(270\) | 2.15781 | + | 0.586380i | 0.131320 | + | 0.0356859i | ||||
\(271\) | −14.7629 | −0.896783 | −0.448392 | − | 0.893837i | \(-0.648003\pi\) | ||||
−0.448392 | + | 0.893837i | \(0.648003\pi\) | |||||||
\(272\) | 5.74699i | 0.348462i | ||||||||
\(273\) | − | 1.16197i | − | 0.0703255i | ||||||
\(274\) | −10.4523 | + | 10.4523i | −0.631449 | + | 0.631449i | ||||
\(275\) | 9.78285 | + | 5.74087i | 0.589928 | + | 0.346187i | ||||
\(276\) | 6.03467 | − | 6.03467i | 0.363244 | − | 0.363244i | ||||
\(277\) | −32.3771 | −1.94535 | −0.972675 | − | 0.232172i | \(-0.925417\pi\) | ||||
−0.972675 | + | 0.232172i | \(0.925417\pi\) | |||||||
\(278\) | −14.4443 | −0.866310 | ||||||||
\(279\) | −5.81155 | + | 5.81155i | −0.347928 | + | 0.347928i | ||||
\(280\) | −0.527580 | + | 1.94144i | −0.0315289 | + | 0.116023i | ||||
\(281\) | 5.74725 | − | 5.74725i | 0.342852 | − | 0.342852i | −0.514586 | − | 0.857439i | \(-0.672054\pi\) |
0.857439 | + | 0.514586i | \(0.172054\pi\) | |||||||
\(282\) | − | 0.462042i | − | 0.0275142i | ||||||
\(283\) | 6.56809i | 0.390433i | 0.980760 | + | 0.195216i | \(0.0625409\pi\) | ||||
−0.980760 | + | 0.195216i | \(0.937459\pi\) | |||||||
\(284\) | −15.2892 | −0.907248 | ||||||||
\(285\) | 11.2557 | − | 6.44547i | 0.666731 | − | 0.381797i | ||||
\(286\) | − | 2.92981i | − | 0.173243i | ||||||
\(287\) | 5.73860 | + | 5.73860i | 0.338739 | + | 0.338739i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −16.0279 | −0.942818 | ||||||||
\(290\) | −1.41104 | + | 5.19246i | −0.0828589 | + | 0.304912i | ||||
\(291\) | −6.56334 | − | 6.56334i | −0.384750 | − | 0.384750i | ||||
\(292\) | 11.8322 | − | 11.8322i | 0.692430 | − | 0.692430i | ||||
\(293\) | −22.0187 | − | 22.0187i | −1.28634 | − | 1.28634i | −0.936991 | − | 0.349353i | \(-0.886401\pi\) |
−0.349353 | − | 0.936991i | \(-0.613599\pi\) | |||||||
\(294\) | −4.37734 | − | 4.37734i | −0.255292 | − | 0.255292i | ||||
\(295\) | −10.7164 | − | 2.91214i | −0.623931 | − | 0.169551i | ||||
\(296\) | −3.16223 | + | 5.19618i | −0.183801 | + | 0.302022i | ||||
\(297\) | 1.60413 | − | 1.60413i | 0.0930811 | − | 0.0930811i | ||||
\(298\) | − | 19.0997i | − | 1.10642i | ||||||
\(299\) | 11.0218 | 0.637408 | ||||||||
\(300\) | −1.25987 | − | 4.83867i | −0.0727385 | − | 0.279361i | ||||
\(301\) | 0.542735 | − | 0.542735i | 0.0312827 | − | 0.0312827i | ||||
\(302\) | 3.42513i | 0.197094i | ||||||||
\(303\) | 1.04233 | + | 1.04233i | 0.0598805 | + | 0.0598805i | ||||
\(304\) | 4.10165 | + | 4.10165i | 0.235246 | + | 0.235246i | ||||
\(305\) | −6.30035 | − | 1.71210i | −0.360757 | − | 0.0980347i | ||||
\(306\) | −5.74699 | −0.328534 | ||||||||
\(307\) | −5.03677 | − | 5.03677i | −0.287464 | − | 0.287464i | 0.548613 | − | 0.836077i | \(-0.315156\pi\) |
−0.836077 | + | 0.548613i | \(0.815156\pi\) | |||||||
\(308\) | 1.44327 | + | 1.44327i | 0.0822382 | + | 0.0822382i | ||||
\(309\) | 0.728096 | + | 0.728096i | 0.0414199 | + | 0.0414199i | ||||
\(310\) | 17.7346 | + | 4.81932i | 1.00726 | + | 0.273719i | ||||
\(311\) | 3.85553 | + | 3.85553i | 0.218627 | + | 0.218627i | 0.807920 | − | 0.589293i | \(-0.200594\pi\) |
−0.589293 | + | 0.807920i | \(0.700594\pi\) | |||||||
\(312\) | −0.913209 | + | 0.913209i | −0.0517003 | + | 0.0517003i | ||||
\(313\) | 19.5460 | 1.10481 | 0.552404 | − | 0.833577i | \(-0.313711\pi\) | ||||
0.552404 | + | 0.833577i | \(0.313711\pi\) | |||||||
\(314\) | −12.1068 | + | 12.1068i | −0.683229 | + | 0.683229i | ||||
\(315\) | −1.94144 | − | 0.527580i | −0.109388 | − | 0.0297258i | ||||
\(316\) | −9.04382 | − | 9.04382i | −0.508755 | − | 0.508755i | ||||
\(317\) | −5.03252 | − | 5.03252i | −0.282655 | − | 0.282655i | 0.551512 | − | 0.834167i | \(-0.314051\pi\) |
−0.834167 | + | 0.551512i | \(0.814051\pi\) | |||||||
\(318\) | 9.61473 | 0.539168 | ||||||||
\(319\) | 3.86010 | + | 3.86010i | 0.216124 | + | 0.216124i | ||||
\(320\) | 1.94044 | − | 1.11117i | 0.108474 | − | 0.0621164i | ||||
\(321\) | 19.6007i | 1.09401i | ||||||||
\(322\) | −5.42954 | + | 5.42954i | −0.302576 | + | 0.302576i | ||||
\(323\) | −23.5721 | + | 23.5721i | −1.31159 | + | 1.31159i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 3.26819 | − | 5.56924i | 0.181287 | − | 0.308926i | ||||
\(326\) | − | 24.2268i | − | 1.34180i | ||||||
\(327\) | −7.53328 | −0.416591 | ||||||||
\(328\) | − | 9.02011i | − | 0.498052i | ||||||
\(329\) | 0.415710i | 0.0229189i | ||||||||
\(330\) | −4.89518 | − | 1.33025i | −0.269471 | − | 0.0732279i | ||||
\(331\) | −3.25748 | + | 3.25748i | −0.179048 | + | 0.179048i | −0.790941 | − | 0.611893i | \(-0.790408\pi\) |
0.611893 | + | 0.790941i | \(0.290408\pi\) | |||||||
\(332\) | 9.12362 | + | 9.12362i | 0.500723 | + | 0.500723i | ||||
\(333\) | −5.19618 | − | 3.16223i | −0.284749 | − | 0.173289i | ||||
\(334\) | 9.66372i | 0.528775i | ||||||||
\(335\) | −12.1560 | − | 3.30336i | −0.664154 | − | 0.180482i | ||||
\(336\) | − | 0.899724i | − | 0.0490840i | ||||||
\(337\) | −15.5648 | − | 15.5648i | −0.847866 | − | 0.847866i | 0.142000 | − | 0.989867i | \(-0.454647\pi\) |
−0.989867 | + | 0.142000i | \(0.954647\pi\) | |||||||
\(338\) | 11.3321 | 0.616385 | ||||||||
\(339\) | 12.2157 | + | 12.2157i | 0.663463 | + | 0.663463i | ||||
\(340\) | 6.38589 | + | 11.1517i | 0.346324 | + | 0.604785i | ||||
\(341\) | 13.1840 | − | 13.1840i | 0.713953 | − | 0.713953i | ||||
\(342\) | −4.10165 | + | 4.10165i | −0.221792 | + | 0.221792i | ||||
\(343\) | 8.39181 | + | 8.39181i | 0.453115 | + | 0.453115i | ||||
\(344\) | −0.853087 | −0.0459953 | ||||||||
\(345\) | 5.00435 | − | 18.4154i | 0.269425 | − | 0.991454i | ||||
\(346\) | −6.77556 | + | 6.77556i | −0.364256 | + | 0.364256i | ||||
\(347\) | −19.7799 | −1.06184 | −0.530920 | − | 0.847422i | \(-0.678154\pi\) | ||||
−0.530920 | + | 0.847422i | \(0.678154\pi\) | |||||||
\(348\) | − | 2.40635i | − | 0.128994i | ||||||
\(349\) | − | 5.47518i | − | 0.293080i | −0.989205 | − | 0.146540i | \(-0.953186\pi\) | ||
0.989205 | − | 0.146540i | \(-0.0468137\pi\) | |||||||
\(350\) | 1.13353 | + | 4.35347i | 0.0605899 | + | 0.232703i | ||||
\(351\) | −0.913209 | − | 0.913209i | −0.0487435 | − | 0.0487435i | ||||
\(352\) | − | 2.26858i | − | 0.120916i | ||||||
\(353\) | 28.1816i | 1.49995i | 0.661465 | + | 0.749976i | \(0.269935\pi\) | ||||
−0.661465 | + | 0.749976i | \(0.730065\pi\) | |||||||
\(354\) | 4.96631 | 0.263956 | ||||||||
\(355\) | −29.6678 | + | 16.9889i | −1.57460 | + | 0.901679i | ||||
\(356\) | 6.32382 | − | 6.32382i | 0.335162 | − | 0.335162i | ||||
\(357\) | 5.17071 | 0.273663 | ||||||||
\(358\) | 7.36463 | − | 7.36463i | 0.389233 | − | 0.389233i | ||||
\(359\) | − | 2.05043i | − | 0.108218i | −0.998535 | − | 0.0541089i | \(-0.982768\pi\) | ||
0.998535 | − | 0.0541089i | \(-0.0172318\pi\) | |||||||
\(360\) | 1.11117 | + | 1.94044i | 0.0585639 | + | 0.102270i | ||||
\(361\) | 14.6470i | 0.770896i | ||||||||
\(362\) | 13.9651 | 0.733988 | ||||||||
\(363\) | 4.13907 | − | 4.13907i | 0.217245 | − | 0.217245i | ||||
\(364\) | 0.821636 | − | 0.821636i | 0.0430654 | − | 0.0430654i | ||||
\(365\) | 9.81208 | − | 36.1074i | 0.513588 | − | 1.88995i | ||||
\(366\) | 2.91979 | 0.152620 | ||||||||
\(367\) | −8.13886 | + | 8.13886i | −0.424845 | + | 0.424845i | −0.886868 | − | 0.462023i | \(-0.847124\pi\) |
0.462023 | + | 0.886868i | \(0.347124\pi\) | |||||||
\(368\) | 8.53431 | 0.444882 | ||||||||
\(369\) | 9.02011 | 0.469568 | ||||||||
\(370\) | −0.362266 | + | 13.5966i | −0.0188333 | + | 0.706856i | ||||
\(371\) | −8.65061 | −0.449117 | ||||||||
\(372\) | −8.21877 | −0.426124 | ||||||||
\(373\) | 9.78820 | − | 9.78820i | 0.506814 | − | 0.506814i | −0.406733 | − | 0.913547i | \(-0.633332\pi\) |
0.913547 | + | 0.406733i | \(0.133332\pi\) | |||||||
\(374\) | 13.0375 | 0.674154 | ||||||||
\(375\) | −7.82129 | − | 7.98921i | −0.403889 | − | 0.412561i | ||||
\(376\) | 0.326713 | − | 0.326713i | 0.0168489 | − | 0.0168489i | ||||
\(377\) | 2.19750 | − | 2.19750i | 0.113177 | − | 0.113177i | ||||
\(378\) | 0.899724 | 0.0462768 | ||||||||
\(379\) | 22.6146i | 1.16164i | 0.814034 | + | 0.580818i | \(0.197267\pi\) | ||||
−0.814034 | + | 0.580818i | \(0.802733\pi\) | |||||||
\(380\) | 12.5166 | + | 3.40136i | 0.642089 | + | 0.174486i | ||||
\(381\) | − | 1.29596i | − | 0.0663939i | ||||||
\(382\) | 11.6459 | − | 11.6459i | 0.595854 | − | 0.595854i | ||||
\(383\) | −9.52538 | −0.486724 | −0.243362 | − | 0.969936i | \(-0.578250\pi\) | ||||
−0.243362 | + | 0.969936i | \(0.578250\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | 4.40431 | + | 1.19686i | 0.224464 | + | 0.0609976i | ||||
\(386\) | 2.80664 | 0.142854 | ||||||||
\(387\) | − | 0.853087i | − | 0.0433648i | ||||||
\(388\) | − | 9.28197i | − | 0.471220i | ||||||
\(389\) | −7.75553 | − | 7.75553i | −0.393221 | − | 0.393221i | 0.482613 | − | 0.875834i | \(-0.339688\pi\) |
−0.875834 | + | 0.482613i | \(0.839688\pi\) | |||||||
\(390\) | −0.757293 | + | 2.78676i | −0.0383470 | + | 0.141113i | ||||
\(391\) | 49.0466i | 2.48039i | ||||||||
\(392\) | − | 6.19050i | − | 0.312667i | ||||||
\(393\) | −8.89460 | −0.448673 | ||||||||
\(394\) | −11.5183 | + | 11.5183i | −0.580282 | + | 0.580282i | ||||
\(395\) | −27.5982 | − | 7.49973i | −1.38862 | − | 0.377353i | ||||
\(396\) | 2.26858 | 0.114001 | ||||||||
\(397\) | 18.6690 | + | 18.6690i | 0.936970 | + | 0.936970i | 0.998128 | − | 0.0611581i | \(-0.0194794\pi\) |
−0.0611581 | + | 0.998128i | \(0.519479\pi\) | |||||||
\(398\) | 10.3470 | − | 10.3470i | 0.518649 | − | 0.518649i | ||||
\(399\) | 3.69035 | − | 3.69035i | 0.184749 | − | 0.184749i | ||||
\(400\) | 2.53060 | − | 4.31232i | 0.126530 | − | 0.215616i | ||||
\(401\) | 13.9114 | + | 13.9114i | 0.694702 | + | 0.694702i | 0.963263 | − | 0.268561i | \(-0.0865481\pi\) |
−0.268561 | + | 0.963263i | \(0.586548\pi\) | |||||||
\(402\) | 5.63348 | 0.280973 | ||||||||
\(403\) | −7.50545 | − | 7.50545i | −0.373873 | − | 0.373873i | ||||
\(404\) | 1.47408i | 0.0733383i | ||||||||
\(405\) | −1.94044 | + | 1.11117i | −0.0964211 | + | 0.0552146i | ||||
\(406\) | 2.16505i | 0.107450i | ||||||||
\(407\) | 11.7880 | + | 7.17378i | 0.584308 | + | 0.355591i | ||||
\(408\) | −4.06374 | − | 4.06374i | −0.201185 | − | 0.201185i | ||||
\(409\) | 7.16339 | − | 7.16339i | 0.354207 | − | 0.354207i | −0.507465 | − | 0.861672i | \(-0.669418\pi\) |
0.861672 | + | 0.507465i | \(0.169418\pi\) | |||||||
\(410\) | −10.0229 | − | 17.5030i | −0.494995 | − | 0.864409i | ||||
\(411\) | − | 14.7818i | − | 0.729134i | ||||||
\(412\) | 1.02968i | 0.0507289i | ||||||||
\(413\) | −4.46831 | −0.219871 | ||||||||
\(414\) | 8.53431i | 0.419438i | ||||||||
\(415\) | 27.8417 | + | 7.56591i | 1.36670 | + | 0.371396i | ||||
\(416\) | −1.29147 | −0.0633196 | ||||||||
\(417\) | 10.2136 | − | 10.2136i | 0.500164 | − | 0.500164i | ||||
\(418\) | 9.30492 | − | 9.30492i | 0.455119 | − | 0.455119i | ||||
\(419\) | − | 23.8546i | − | 1.16537i | −0.812698 | − | 0.582686i | \(-0.802002\pi\) | ||
0.812698 | − | 0.582686i | \(-0.197998\pi\) | |||||||
\(420\) | −0.999748 | − | 1.74586i | −0.0487827 | − | 0.0851892i | ||||
\(421\) | −12.3787 | − | 12.3787i | −0.603301 | − | 0.603301i | 0.337886 | − | 0.941187i | \(-0.390288\pi\) |
−0.941187 | + | 0.337886i | \(0.890288\pi\) | |||||||
\(422\) | 3.80993 | 0.185464 | ||||||||
\(423\) | 0.326713 | + | 0.326713i | 0.0158853 | + | 0.0158853i | ||||
\(424\) | 6.79864 | + | 6.79864i | 0.330171 | + | 0.330171i | ||||
\(425\) | 24.7828 | + | 14.5433i | 1.20214 | + | 0.705454i | ||||
\(426\) | 10.8111 | − | 10.8111i | 0.523800 | − | 0.523800i | ||||
\(427\) | −2.62700 | −0.127130 | ||||||||
\(428\) | −13.8598 | + | 13.8598i | −0.669940 | + | 0.669940i | ||||
\(429\) | 2.07169 | + | 2.07169i | 0.100022 | + | 0.100022i | ||||
\(430\) | −1.65536 | + | 0.947925i | −0.0798286 | + | 0.0457130i | ||||
\(431\) | 5.50143 | + | 5.50143i | 0.264995 | + | 0.264995i | 0.827080 | − | 0.562085i | \(-0.190001\pi\) |
−0.562085 | + | 0.827080i | \(0.690001\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 4.53175 | + | 4.53175i | 0.217782 | + | 0.217782i | 0.807563 | − | 0.589781i | \(-0.200786\pi\) |
−0.589781 | + | 0.807563i | \(0.700786\pi\) | |||||||
\(434\) | 7.39463 | 0.354954 | ||||||||
\(435\) | −2.67387 | − | 4.66938i | −0.128202 | − | 0.223879i | ||||
\(436\) | −5.32683 | − | 5.32683i | −0.255109 | − | 0.255109i | ||||
\(437\) | 35.0047 | + | 35.0047i | 1.67450 | + | 1.67450i | ||||
\(438\) | 16.7333i | 0.799549i | ||||||||
\(439\) | −22.7618 | + | 22.7618i | −1.08636 | + | 1.08636i | −0.0904591 | + | 0.995900i | \(0.528833\pi\) |
−0.995900 | + | 0.0904591i | \(0.971167\pi\) | |||||||
\(440\) | −2.52078 | − | 4.40204i | −0.120174 | − | 0.209859i | ||||
\(441\) | 6.19050 | 0.294786 | ||||||||
\(442\) | − | 7.42208i | − | 0.353032i | ||||||
\(443\) | 18.5368 | − | 18.5368i | 0.880708 | − | 0.880708i | −0.112899 | − | 0.993606i | \(-0.536014\pi\) |
0.993606 | + | 0.112899i | \(0.0360136\pi\) | |||||||
\(444\) | −1.43822 | − | 5.91029i | −0.0682549 | − | 0.280490i | ||||
\(445\) | 5.24413 | − | 19.2978i | 0.248596 | − | 0.914804i | ||||
\(446\) | −16.8923 | − | 16.8923i | −0.799872 | − | 0.799872i | ||||
\(447\) | 13.5056 | + | 13.5056i | 0.638791 | + | 0.638791i | ||||
\(448\) | 0.636201 | − | 0.636201i | 0.0300577 | − | 0.0300577i | ||||
\(449\) | −9.96142 | − | 9.96142i | −0.470109 | − | 0.470109i | 0.431841 | − | 0.901950i | \(-0.357864\pi\) |
−0.901950 | + | 0.431841i | \(0.857864\pi\) | |||||||
\(450\) | 4.31232 | + | 2.53060i | 0.203285 | + | 0.119293i | ||||
\(451\) | −20.4629 | −0.963558 | ||||||||
\(452\) | 17.2755i | 0.812573i | ||||||||
\(453\) | −2.42193 | − | 2.42193i | −0.113792 | − | 0.113792i | ||||
\(454\) | − | 25.0030i | − | 1.17345i | ||||||
\(455\) | 0.681355 | − | 2.50731i | 0.0319424 | − | 0.117545i | ||||
\(456\) | −5.80061 | −0.271638 | ||||||||
\(457\) | 6.81678i | 0.318876i | 0.987208 | + | 0.159438i | \(0.0509681\pi\) | ||||
−0.987208 | + | 0.159438i | \(0.949032\pi\) | |||||||
\(458\) | − | 11.3572i | − | 0.530686i | ||||||
\(459\) | 4.06374 | − | 4.06374i | 0.189679 | − | 0.189679i | ||||
\(460\) | 16.5603 | − | 9.48308i | 0.772128 | − | 0.442151i | ||||
\(461\) | 24.7125 | − | 24.7125i | 1.15097 | − | 1.15097i | 0.164617 | − | 0.986358i | \(-0.447361\pi\) |
0.986358 | − | 0.164617i | \(-0.0526389\pi\) | |||||||
\(462\) | −2.04110 | −0.0949605 | ||||||||
\(463\) | −32.0736 | −1.49059 | −0.745293 | − | 0.666737i | \(-0.767690\pi\) | ||||
−0.745293 | + | 0.666737i | \(0.767690\pi\) | |||||||
\(464\) | 1.70155 | − | 1.70155i | 0.0789924 | − | 0.0789924i | ||||
\(465\) | −15.9480 | + | 9.13247i | −0.739572 | + | 0.423508i | ||||
\(466\) | 4.77274 | − | 4.77274i | 0.221093 | − | 0.221093i | ||||
\(467\) | − | 13.7531i | − | 0.636416i | −0.948021 | − | 0.318208i | \(-0.896919\pi\) | ||
0.948021 | − | 0.318208i | \(-0.103081\pi\) | |||||||
\(468\) | − | 1.29147i | − | 0.0596983i | ||||||
\(469\) | −5.06858 | −0.234045 | ||||||||
\(470\) | 0.270932 | − | 0.997001i | 0.0124972 | − | 0.0459882i | ||||
\(471\) | − | 17.1217i | − | 0.788925i | ||||||
\(472\) | 3.51171 | + | 3.51171i | 0.161640 | + | 0.161640i | ||||
\(473\) | 1.93530i | 0.0889851i | ||||||||
\(474\) | 12.7899 | 0.587459 | ||||||||
\(475\) | 28.0672 | − | 7.30799i | 1.28781 | − | 0.335314i | ||||
\(476\) | 3.65624 | + | 3.65624i | 0.167584 | + | 0.167584i | ||||
\(477\) | −6.79864 | + | 6.79864i | −0.311289 | + | 0.311289i | ||||
\(478\) | −2.96858 | − | 2.96858i | −0.135780 | − | 0.135780i | ||||
\(479\) | −15.9554 | − | 15.9554i | −0.729021 | − | 0.729021i | 0.241404 | − | 0.970425i | \(-0.422392\pi\) |
−0.970425 | + | 0.241404i | \(0.922392\pi\) | |||||||
\(480\) | −0.586380 | + | 2.15781i | −0.0267645 | + | 0.0984903i | ||||
\(481\) | 4.08393 | − | 6.71072i | 0.186211 | − | 0.305983i | ||||
\(482\) | 5.75647 | − | 5.75647i | 0.262200 | − | 0.262200i | ||||
\(483\) | − | 7.67852i | − | 0.349385i | ||||||
\(484\) | 5.85354 | 0.266070 | ||||||||
\(485\) | −10.3139 | − | 18.0111i | −0.468328 | − | 0.817841i | ||||
\(486\) | 0.707107 | − | 0.707107i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | − | 22.5078i | − | 1.01992i | −0.860197 | − | 0.509962i | \(-0.829659\pi\) | ||
0.860197 | − | 0.509962i | \(-0.170341\pi\) | |||||||
\(488\) | 2.06460 | + | 2.06460i | 0.0934600 | + | 0.0934600i | ||||
\(489\) | 17.1309 | + | 17.1309i | 0.774688 | + | 0.774688i | ||||
\(490\) | −6.87870 | − | 12.0123i | −0.310748 | − | 0.542659i | ||||
\(491\) | 31.0223 | 1.40002 | 0.700008 | − | 0.714135i | \(-0.253180\pi\) | ||||
0.700008 | + | 0.714135i | \(0.253180\pi\) | |||||||
\(492\) | 6.37818 | + | 6.37818i | 0.287550 | + | 0.287550i | ||||
\(493\) | 9.77878 | + | 9.77878i | 0.440414 | + | 0.440414i | ||||
\(494\) | −5.29716 | − | 5.29716i | −0.238331 | − | 0.238331i | ||||
\(495\) | 4.40204 | − | 2.52078i | 0.197857 | − | 0.113301i | ||||
\(496\) | −5.81155 | − | 5.81155i | −0.260946 | − | 0.260946i | ||||
\(497\) | −9.72702 | + | 9.72702i | −0.436316 | + | 0.436316i | ||||
\(498\) | −12.9027 | −0.578186 | ||||||||
\(499\) | −5.68409 | + | 5.68409i | −0.254455 | + | 0.254455i | −0.822794 | − | 0.568339i | \(-0.807586\pi\) |
0.568339 | + | 0.822794i | \(0.307586\pi\) | |||||||
\(500\) | 0.118740 | − | 11.1797i | 0.00531022 | − | 0.499972i | ||||
\(501\) | −6.83328 | − | 6.83328i | −0.305288 | − | 0.305288i | ||||
\(502\) | 14.7749 | + | 14.7749i | 0.659437 | + | 0.659437i | ||||
\(503\) | 3.69027 | 0.164541 | 0.0822705 | − | 0.996610i | \(-0.473783\pi\) | ||||
0.0822705 | + | 0.996610i | \(0.473783\pi\) | |||||||
\(504\) | 0.636201 | + | 0.636201i | 0.0283386 | + | 0.0283386i | ||||
\(505\) | 1.63796 | + | 2.86036i | 0.0728882 | + | 0.127285i | ||||
\(506\) | − | 19.3608i | − | 0.860692i | ||||||
\(507\) | −8.01300 | + | 8.01300i | −0.355870 | + | 0.355870i | ||||
\(508\) | 0.916380 | − | 0.916380i | 0.0406578 | − | 0.0406578i | ||||
\(509\) | −5.91876 | −0.262345 | −0.131172 | − | 0.991360i | \(-0.541874\pi\) | ||||
−0.131172 | + | 0.991360i | \(0.541874\pi\) | |||||||
\(510\) | −12.4009 | − | 3.36992i | −0.549123 | − | 0.149223i | ||||
\(511\) | − | 15.0554i | − | 0.666010i | ||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | − | 5.80061i | − | 0.256103i | ||||||
\(514\) | 1.80027i | 0.0794064i | ||||||||
\(515\) | 1.14415 | + | 1.99804i | 0.0504175 | + | 0.0880440i | ||||
\(516\) | 0.603223 | − | 0.603223i | 0.0265554 | − | 0.0265554i | ||||
\(517\) | −0.741175 | − | 0.741175i | −0.0325969 | − | 0.0325969i | ||||
\(518\) | 1.29400 | + | 5.31763i | 0.0568551 | + | 0.233643i | ||||
\(519\) | − | 9.58209i | − | 0.420607i | ||||||
\(520\) | −2.50602 | + | 1.43505i | −0.109896 | + | 0.0629310i | ||||
\(521\) | 21.8007i | 0.955107i | 0.878603 | + | 0.477554i | \(0.158476\pi\) | ||||
−0.878603 | + | 0.477554i | \(0.841524\pi\) | |||||||
\(522\) | 1.70155 | + | 1.70155i | 0.0744747 | + | 0.0744747i | ||||
\(523\) | −17.1466 | −0.749767 | −0.374883 | − | 0.927072i | \(-0.622317\pi\) | ||||
−0.374883 | + | 0.927072i | \(0.622317\pi\) | |||||||
\(524\) | −6.28943 | − | 6.28943i | −0.274755 | − | 0.274755i | ||||
\(525\) | −3.87990 | − | 2.27684i | −0.169333 | − | 0.0993694i | ||||
\(526\) | −9.25899 | + | 9.25899i | −0.403711 | + | 0.403711i | ||||
\(527\) | 33.3989 | − | 33.3989i | 1.45488 | − | 1.45488i | ||||
\(528\) | 1.60413 | + | 1.60413i | 0.0698108 | + | 0.0698108i | ||||
\(529\) | 49.8344 | 2.16671 | ||||||||
\(530\) | 20.7468 | + | 5.63789i | 0.901184 | + | 0.244894i | ||||
\(531\) | −3.51171 | + | 3.51171i | −0.152395 | + | 0.152395i | ||||
\(532\) | 5.21895 | 0.226270 | ||||||||
\(533\) | 11.6492i | 0.504583i | ||||||||
\(534\) | 8.94323i | 0.387011i | ||||||||
\(535\) | −11.4935 | + | 42.2948i | −0.496907 | + | 1.82856i | ||||
\(536\) | 3.98347 | + | 3.98347i | 0.172060 | + | 0.172060i | ||||
\(537\) | 10.4152i | 0.449447i | ||||||||
\(538\) | 0.689017i | 0.0297056i | ||||||||
\(539\) | −14.0436 | −0.604903 | ||||||||
\(540\) | −2.15781 | − | 0.586380i | −0.0928575 | − | 0.0252338i | ||||
\(541\) | −11.6362 | + | 11.6362i | −0.500279 | + | 0.500279i | −0.911525 | − | 0.411245i | \(-0.865094\pi\) |
0.411245 | + | 0.911525i | \(0.365094\pi\) | |||||||
\(542\) | 14.7629 | 0.634122 | ||||||||
\(543\) | −9.87480 | + | 9.87480i | −0.423768 | + | 0.423768i | ||||
\(544\) | − | 5.74699i | − | 0.246400i | ||||||
\(545\) | −16.2554 | − | 4.41736i | −0.696305 | − | 0.189219i | ||||
\(546\) | 1.16197i | 0.0497277i | ||||||||
\(547\) | 37.0105 | 1.58245 | 0.791226 | − | 0.611523i | \(-0.209443\pi\) | ||||
0.791226 | + | 0.611523i | \(0.209443\pi\) | |||||||
\(548\) | 10.4523 | − | 10.4523i | 0.446502 | − | 0.446502i | ||||
\(549\) | −2.06460 | + | 2.06460i | −0.0881150 | + | 0.0881150i | ||||
\(550\) | −9.78285 | − | 5.74087i | −0.417142 | − | 0.244791i | ||||
\(551\) | 13.9583 | 0.594643 | ||||||||
\(552\) | −6.03467 | + | 6.03467i | −0.256853 | + | 0.256853i | ||||
\(553\) | −11.5074 | −0.489343 | ||||||||
\(554\) | 32.3771 | 1.37557 | ||||||||
\(555\) | −9.35812 | − | 9.87044i | −0.397230 | − | 0.418977i | ||||
\(556\) | 14.4443 | 0.612574 | ||||||||
\(557\) | −5.02764 | −0.213028 | −0.106514 | − | 0.994311i | \(-0.533969\pi\) | ||||
−0.106514 | + | 0.994311i | \(0.533969\pi\) | |||||||
\(558\) | 5.81155 | − | 5.81155i | 0.246023 | − | 0.246023i | ||||
\(559\) | 1.10174 | 0.0465985 | ||||||||
\(560\) | 0.527580 | − | 1.94144i | 0.0222943 | − | 0.0820407i | ||||
\(561\) | −9.21892 | + | 9.21892i | −0.389223 | + | 0.389223i | ||||
\(562\) | −5.74725 | + | 5.74725i | −0.242433 | + | 0.242433i | ||||
\(563\) | −14.7235 | −0.620522 | −0.310261 | − | 0.950651i | \(-0.600416\pi\) | ||||
−0.310261 | + | 0.950651i | \(0.600416\pi\) | |||||||
\(564\) | 0.462042i | 0.0194555i | ||||||||
\(565\) | 19.1961 | + | 33.5221i | 0.807586 | + | 1.41029i | ||||
\(566\) | − | 6.56809i | − | 0.276078i | ||||||
\(567\) | −0.636201 | + | 0.636201i | −0.0267179 | + | 0.0267179i | ||||
\(568\) | 15.2892 | 0.641521 | ||||||||
\(569\) | 15.1302 | − | 15.1302i | 0.634291 | − | 0.634291i | −0.314850 | − | 0.949141i | \(-0.601954\pi\) |
0.949141 | + | 0.314850i | \(0.101954\pi\) | |||||||
\(570\) | −11.2557 | + | 6.44547i | −0.471450 | + | 0.269971i | ||||
\(571\) | −0.732604 | −0.0306585 | −0.0153293 | − | 0.999882i | \(-0.504880\pi\) | ||||
−0.0153293 | + | 0.999882i | \(0.504880\pi\) | |||||||
\(572\) | 2.92981i | 0.122502i | ||||||||
\(573\) | 16.4697i | 0.688033i | ||||||||
\(574\) | −5.73860 | − | 5.73860i | −0.239525 | − | 0.239525i | ||||
\(575\) | 21.5969 | − | 36.8026i | 0.900653 | − | 1.53478i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 13.0938i | − | 0.545102i | −0.962141 | − | 0.272551i | \(-0.912133\pi\) | ||
0.962141 | − | 0.272551i | \(-0.0878673\pi\) | |||||||
\(578\) | 16.0279 | 0.666673 | ||||||||
\(579\) | −1.98459 | + | 1.98459i | −0.0824768 | + | 0.0824768i | ||||
\(580\) | 1.41104 | − | 5.19246i | 0.0585901 | − | 0.215605i | ||||
\(581\) | 11.6089 | 0.481619 | ||||||||
\(582\) | 6.56334 | + | 6.56334i | 0.272059 | + | 0.272059i | ||||
\(583\) | 15.4233 | − | 15.4233i | 0.638767 | − | 0.638767i | ||||
\(584\) | −11.8322 | + | 11.8322i | −0.489622 | + | 0.489622i | ||||
\(585\) | −1.43505 | − | 2.50602i | −0.0593319 | − | 0.103611i | ||||
\(586\) | 22.0187 | + | 22.0187i | 0.909583 | + | 0.909583i | ||||
\(587\) | −25.6946 | −1.06053 | −0.530265 | − | 0.847832i | \(-0.677908\pi\) | ||||
−0.530265 | + | 0.847832i | \(0.677908\pi\) | |||||||
\(588\) | 4.37734 | + | 4.37734i | 0.180519 | + | 0.180519i | ||||
\(589\) | − | 47.6739i | − | 1.96437i | ||||||
\(590\) | 10.7164 | + | 2.91214i | 0.441186 | + | 0.119891i | ||||
\(591\) | − | 16.2893i | − | 0.670052i | ||||||
\(592\) | 3.16223 | − | 5.19618i | 0.129967 | − | 0.213562i | ||||
\(593\) | −32.7884 | − | 32.7884i | −1.34646 | − | 1.34646i | −0.889474 | − | 0.456986i | \(-0.848929\pi\) |
−0.456986 | − | 0.889474i | \(-0.651071\pi\) | |||||||
\(594\) | −1.60413 | + | 1.60413i | −0.0658182 | + | 0.0658182i | ||||
\(595\) | 11.1574 | + | 3.03200i | 0.457410 | + | 0.124300i | ||||
\(596\) | 19.0997i | 0.782356i | ||||||||
\(597\) | 14.6329i | 0.598885i | ||||||||
\(598\) | −11.0218 | −0.450716 | ||||||||
\(599\) | 32.7946i | 1.33995i | 0.742383 | + | 0.669975i | \(0.233695\pi\) | ||||
−0.742383 | + | 0.669975i | \(0.766305\pi\) | |||||||
\(600\) | 1.25987 | + | 4.83867i | 0.0514339 | + | 0.197538i | ||||
\(601\) | 27.3053 | 1.11381 | 0.556904 | − | 0.830577i | \(-0.311989\pi\) | ||||
0.556904 | + | 0.830577i | \(0.311989\pi\) | |||||||
\(602\) | −0.542735 | + | 0.542735i | −0.0221202 | + | 0.0221202i | ||||
\(603\) | −3.98347 | + | 3.98347i | −0.162220 | + | 0.162220i | ||||
\(604\) | − | 3.42513i | − | 0.139367i | ||||||
\(605\) | 11.3584 | − | 6.50428i | 0.461785 | − | 0.264437i | ||||
\(606\) | −1.04233 | − | 1.04233i | −0.0423419 | − | 0.0423419i | ||||
\(607\) | −26.7432 | −1.08547 | −0.542737 | − | 0.839903i | \(-0.682612\pi\) | ||||
−0.542737 | + | 0.839903i | \(0.682612\pi\) | |||||||
\(608\) | −4.10165 | − | 4.10165i | −0.166344 | − | 0.166344i | ||||
\(609\) | −1.53092 | − | 1.53092i | −0.0620362 | − | 0.0620362i | ||||
\(610\) | 6.30035 | + | 1.71210i | 0.255094 | + | 0.0693210i | ||||
\(611\) | −0.421941 | + | 0.421941i | −0.0170699 | + | 0.0170699i | ||||
\(612\) | 5.74699 | 0.232308 | ||||||||
\(613\) | 23.6704 | − | 23.6704i | 0.956040 | − | 0.956040i | −0.0430339 | − | 0.999074i | \(-0.513702\pi\) |
0.999074 | + | 0.0430339i | \(0.0137024\pi\) | |||||||
\(614\) | 5.03677 | + | 5.03677i | 0.203268 | + | 0.203268i | ||||
\(615\) | 19.4637 | + | 5.28921i | 0.784852 | + | 0.213281i | ||||
\(616\) | −1.44327 | − | 1.44327i | −0.0581512 | − | 0.0581512i | ||||
\(617\) | −3.77510 | − | 3.77510i | −0.151980 | − | 0.151980i | 0.627022 | − | 0.779002i | \(-0.284274\pi\) |
−0.779002 | + | 0.627022i | \(0.784274\pi\) | |||||||
\(618\) | −0.728096 | − | 0.728096i | −0.0292883 | − | 0.0292883i | ||||
\(619\) | −9.65130 | −0.387918 | −0.193959 | − | 0.981010i | \(-0.562133\pi\) | ||||
−0.193959 | + | 0.981010i | \(0.562133\pi\) | |||||||
\(620\) | −17.7346 | − | 4.81932i | −0.712238 | − | 0.193549i | ||||
\(621\) | −6.03467 | − | 6.03467i | −0.242163 | − | 0.242163i | ||||
\(622\) | −3.85553 | − | 3.85553i | −0.154593 | − | 0.154593i | ||||
\(623\) | − | 8.04644i | − | 0.322374i | ||||||
\(624\) | 0.913209 | − | 0.913209i | 0.0365576 | − | 0.0365576i | ||||
\(625\) | −12.1922 | − | 21.8255i | −0.487687 | − | 0.873019i | ||||
\(626\) | −19.5460 | −0.781217 | ||||||||
\(627\) | 13.1592i | 0.525526i | ||||||||
\(628\) | 12.1068 | − | 12.1068i | 0.483116 | − | 0.483116i | ||||
\(629\) | 29.8624 | + | 18.1733i | 1.19069 | + | 0.724618i | ||||
\(630\) | 1.94144 | + | 0.527580i | 0.0773487 | + | 0.0210193i | ||||
\(631\) | 9.32454 | + | 9.32454i | 0.371204 | + | 0.371204i | 0.867916 | − | 0.496712i | \(-0.165459\pi\) |
−0.496712 | + | 0.867916i | \(0.665459\pi\) | |||||||
\(632\) | 9.04382 | + | 9.04382i | 0.359744 | + | 0.359744i | ||||
\(633\) | −2.69402 | + | 2.69402i | −0.107078 | + | 0.107078i | ||||
\(634\) | 5.03252 | + | 5.03252i | 0.199867 | + | 0.199867i | ||||
\(635\) | 0.759923 | − | 2.79643i | 0.0301566 | − | 0.110973i | ||||
\(636\) | −9.61473 | −0.381249 | ||||||||
\(637\) | 7.99485i | 0.316768i | ||||||||
\(638\) | −3.86010 | − | 3.86010i | −0.152823 | − | 0.152823i | ||||
\(639\) | 15.2892i | 0.604832i | ||||||||
\(640\) | −1.94044 | + | 1.11117i | −0.0767025 | + | 0.0439229i | ||||
\(641\) | −7.81012 | −0.308481 | −0.154241 | − | 0.988033i | \(-0.549293\pi\) | ||||
−0.154241 | + | 0.988033i | \(0.549293\pi\) | |||||||
\(642\) | − | 19.6007i | − | 0.773580i | ||||||
\(643\) | − | 39.3070i | − | 1.55012i | −0.631890 | − | 0.775058i | \(-0.717721\pi\) | ||
0.631890 | − | 0.775058i | \(-0.282279\pi\) | |||||||
\(644\) | 5.42954 | − | 5.42954i | 0.213954 | − | 0.213954i | ||||
\(645\) | 0.500233 | − | 1.84080i | 0.0196966 | − | 0.0724815i | ||||
\(646\) | 23.5721 | − | 23.5721i | 0.927433 | − | 0.927433i | ||||
\(647\) | −31.8619 | −1.25262 | −0.626311 | − | 0.779573i | \(-0.715436\pi\) | ||||
−0.626311 | + | 0.779573i | \(0.715436\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 7.96660 | − | 7.96660i | 0.312716 | − | 0.312716i | ||||
\(650\) | −3.26819 | + | 5.56924i | −0.128189 | + | 0.218443i | ||||
\(651\) | −5.22879 | + | 5.22879i | −0.204933 | + | 0.204933i | ||||
\(652\) | 24.2268i | 0.948795i | ||||||||
\(653\) | 40.2027i | 1.57325i | 0.617430 | + | 0.786626i | \(0.288174\pi\) | ||||
−0.617430 | + | 0.786626i | \(0.711826\pi\) | |||||||
\(654\) | 7.53328 | 0.294575 | ||||||||
\(655\) | −19.1929 | − | 5.21562i | −0.749929 | − | 0.203791i | ||||
\(656\) | 9.02011i | 0.352176i | ||||||||
\(657\) | −11.8322 | − | 11.8322i | −0.461620 | − | 0.461620i | ||||
\(658\) | − | 0.415710i | − | 0.0162061i | ||||||
\(659\) | 22.6033 | 0.880499 | 0.440250 | − | 0.897875i | \(-0.354890\pi\) | ||||
0.440250 | + | 0.897875i | \(0.354890\pi\) | |||||||
\(660\) | 4.89518 | + | 1.33025i | 0.190545 | + | 0.0517799i | ||||
\(661\) | 20.1421 | + | 20.1421i | 0.783436 | + | 0.783436i | 0.980409 | − | 0.196973i | \(-0.0631111\pi\) |
−0.196973 | + | 0.980409i | \(0.563111\pi\) | |||||||
\(662\) | 3.25748 | − | 3.25748i | 0.126606 | − | 0.126606i | ||||
\(663\) | 5.24820 | + | 5.24820i | 0.203823 | + | 0.203823i | ||||
\(664\) | −9.12362 | − | 9.12362i | −0.354065 | − | 0.354065i | ||||
\(665\) | 10.1270 | − | 5.79914i | 0.392710 | − | 0.224881i | ||||
\(666\) | 5.19618 | + | 3.16223i | 0.201348 | + | 0.122534i | ||||
\(667\) | 14.5215 | − | 14.5215i | 0.562276 | − | 0.562276i | ||||
\(668\) | − | 9.66372i | − | 0.373900i | ||||||
\(669\) | 23.8893 | 0.923612 | ||||||||
\(670\) | 12.1560 | + | 3.30336i | 0.469628 | + | 0.127620i | ||||
\(671\) | 4.68371 | − | 4.68371i | 0.180813 | − | 0.180813i | ||||
\(672\) | 0.899724i | 0.0347076i | ||||||||
\(673\) | 23.9631 | + | 23.9631i | 0.923709 | + | 0.923709i | 0.997289 | − | 0.0735806i | \(-0.0234426\pi\) |
−0.0735806 | + | 0.997289i | \(0.523443\pi\) | |||||||
\(674\) | 15.5648 | + | 15.5648i | 0.599532 | + | 0.599532i | ||||
\(675\) | −4.83867 | + | 1.25987i | −0.186241 | + | 0.0484923i | ||||
\(676\) | −11.3321 | −0.435850 | ||||||||
\(677\) | 18.3439 | + | 18.3439i | 0.705012 | + | 0.705012i | 0.965482 | − | 0.260470i | \(-0.0838776\pi\) |
−0.260470 | + | 0.965482i | \(0.583878\pi\) | |||||||
\(678\) | −12.2157 | − | 12.2157i | −0.469139 | − | 0.469139i | ||||
\(679\) | −5.90520 | − | 5.90520i | −0.226621 | − | 0.226621i | ||||
\(680\) | −6.38589 | − | 11.1517i | −0.244888 | − | 0.427647i | ||||
\(681\) | 17.6798 | + | 17.6798i | 0.677490 | + | 0.677490i | ||||
\(682\) | −13.1840 | + | 13.1840i | −0.504841 | + | 0.504841i | ||||
\(683\) | 2.79715 | 0.107030 | 0.0535149 | − | 0.998567i | \(-0.482958\pi\) | ||||
0.0535149 | + | 0.998567i | \(0.482958\pi\) | |||||||
\(684\) | 4.10165 | − | 4.10165i | 0.156830 | − | 0.156830i | ||||
\(685\) | 8.66777 | − | 31.8965i | 0.331179 | − | 1.21870i | ||||
\(686\) | −8.39181 | − | 8.39181i | −0.320401 | − | 0.320401i | ||||
\(687\) | 8.03073 | + | 8.03073i | 0.306392 | + | 0.306392i | ||||
\(688\) | 0.853087 | 0.0325236 | ||||||||
\(689\) | −8.78026 | − | 8.78026i | −0.334501 | − | 0.334501i | ||||
\(690\) | −5.00435 | + | 18.4154i | −0.190512 | + | 0.701064i | ||||
\(691\) | 7.07761i | 0.269245i | 0.990897 | + | 0.134623i | \(0.0429822\pi\) | ||||
−0.990897 | + | 0.134623i | \(0.957018\pi\) | |||||||
\(692\) | 6.77556 | − | 6.77556i | 0.257568 | − | 0.257568i | ||||
\(693\) | 1.44327 | − | 1.44327i | 0.0548255 | − | 0.0548255i | ||||
\(694\) | 19.7799 | 0.750835 | ||||||||
\(695\) | 28.0282 | − | 16.0501i | 1.06317 | − | 0.608813i | ||||
\(696\) | 2.40635i | 0.0912125i | ||||||||
\(697\) | −51.8385 | −1.96352 | ||||||||
\(698\) | 5.47518i | 0.207239i | ||||||||
\(699\) | 6.74968i | 0.255296i | ||||||||
\(700\) | −1.13353 | − | 4.35347i | −0.0428435 | − | 0.164546i | ||||
\(701\) | −25.0871 | + | 25.0871i | −0.947527 | + | 0.947527i | −0.998690 | − | 0.0511635i | \(-0.983707\pi\) |
0.0511635 | + | 0.998690i | \(0.483707\pi\) | |||||||
\(702\) | 0.913209 | + | 0.913209i | 0.0344668 | + | 0.0344668i | ||||
\(703\) | 34.2833 | − | 8.34254i | 1.29302 | − | 0.314645i | ||||
\(704\) | 2.26858i | 0.0855004i | ||||||||
\(705\) | 0.513408 | + | 0.896564i | 0.0193361 | + | 0.0337665i | ||||
\(706\) | − | 28.1816i | − | 1.06063i | ||||||
\(707\) | 0.937812 | + | 0.937812i | 0.0352701 | + | 0.0352701i | ||||
\(708\) | −4.96631 | −0.186645 | ||||||||
\(709\) | 6.08101 | + | 6.08101i | 0.228377 | + | 0.228377i | 0.812014 | − | 0.583637i | \(-0.198371\pi\) |
−0.583637 | + | 0.812014i | \(0.698371\pi\) | |||||||
\(710\) | 29.6678 | − | 16.9889i | 1.11341 | − | 0.637584i | ||||
\(711\) | −9.04382 | + | 9.04382i | −0.339170 | + | 0.339170i | ||||
\(712\) | −6.32382 | + | 6.32382i | −0.236995 | + | 0.236995i | ||||
\(713\) | −49.5976 | − | 49.5976i | −1.85744 | − | 1.85744i | ||||
\(714\) | −5.17071 | −0.193509 | ||||||||
\(715\) | 3.25552 | + | 5.68511i | 0.121750 | + | 0.212611i | ||||
\(716\) | −7.36463 | + | 7.36463i | −0.275229 | + | 0.275229i | ||||
\(717\) | 4.19821 | 0.156785 | ||||||||
\(718\) | 2.05043i | 0.0765215i | ||||||||
\(719\) | − | 37.1763i | − | 1.38644i | −0.720724 | − | 0.693222i | \(-0.756191\pi\) | ||
0.720724 | − | 0.693222i | \(-0.243809\pi\) | |||||||
\(720\) | −1.11117 | − | 1.94044i | −0.0414109 | − | 0.0723158i | ||||
\(721\) | 0.655086 | + | 0.655086i | 0.0243967 | + | 0.0243967i | ||||
\(722\) | − | 14.6470i | − | 0.545106i | ||||||
\(723\) | 8.14088i | 0.302762i | ||||||||
\(724\) | −13.9651 | −0.519008 | ||||||||
\(725\) | −3.03168 | − | 11.6435i | −0.112594 | − | 0.432430i | ||||
\(726\) | −4.13907 | + | 4.13907i | −0.153615 | + | 0.153615i | ||||
\(727\) | −10.8041 | −0.400701 | −0.200350 | − | 0.979724i | \(-0.564208\pi\) | ||||
−0.200350 | + | 0.979724i | \(0.564208\pi\) | |||||||
\(728\) | −0.821636 | + | 0.821636i | −0.0304519 | + | 0.0304519i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −9.81208 | + | 36.1074i | −0.363161 | + | 1.33639i | ||||
\(731\) | 4.90268i | 0.181332i | ||||||||
\(732\) | −2.91979 | −0.107918 | ||||||||
\(733\) | 2.31409 | − | 2.31409i | 0.0854728 | − | 0.0854728i | −0.663078 | − | 0.748551i | \(-0.730750\pi\) |
0.748551 | + | 0.663078i | \(0.230750\pi\) | |||||||
\(734\) | 8.13886 | − | 8.13886i | 0.300411 | − | 0.300411i | ||||
\(735\) | 13.3579 | + | 3.62998i | 0.492715 | + | 0.133894i | ||||
\(736\) | −8.53431 | −0.314579 | ||||||||
\(737\) | 9.03684 | − | 9.03684i | 0.332876 | − | 0.332876i | ||||
\(738\) | −9.02011 | −0.332035 | ||||||||
\(739\) | 3.59606 | 0.132283 | 0.0661416 | − | 0.997810i | \(-0.478931\pi\) | ||||
0.0661416 | + | 0.997810i | \(0.478931\pi\) | |||||||
\(740\) | 0.362266 | − | 13.5966i | 0.0133172 | − | 0.499823i | ||||
\(741\) | 7.49132 | 0.275201 | ||||||||
\(742\) | 8.65061 | 0.317574 | ||||||||
\(743\) | −7.78930 | + | 7.78930i | −0.285762 | + | 0.285762i | −0.835402 | − | 0.549640i | \(-0.814765\pi\) |
0.549640 | + | 0.835402i | \(0.314765\pi\) | |||||||
\(744\) | 8.21877 | 0.301315 | ||||||||
\(745\) | 21.2231 | + | 37.0619i | 0.777554 | + | 1.35784i | ||||
\(746\) | −9.78820 | + | 9.78820i | −0.358371 | + | 0.358371i | ||||
\(747\) | 9.12362 | − | 9.12362i | 0.333816 | − | 0.333816i | ||||
\(748\) | −13.0375 | −0.476699 | ||||||||
\(749\) | 17.6353i | 0.644379i | ||||||||
\(750\) | 7.82129 | + | 7.98921i | 0.285593 | + | 0.291725i | ||||
\(751\) | 31.8319i | 1.16156i | 0.814059 | + | 0.580782i | \(0.197253\pi\) | ||||
−0.814059 | + | 0.580782i | \(0.802747\pi\) | |||||||
\(752\) | −0.326713 | + | 0.326713i | −0.0119140 | + | 0.0119140i | ||||
\(753\) | −20.8949 | −0.761452 | ||||||||
\(754\) | −2.19750 | + | 2.19750i | −0.0800283 | + | 0.0800283i | ||||
\(755\) | −3.80591 | − | 6.64625i | −0.138511 | − | 0.241882i | ||||
\(756\) | −0.899724 | −0.0327227 | ||||||||
\(757\) | − | 2.85691i | − | 0.103836i | −0.998651 | − | 0.0519182i | \(-0.983467\pi\) | ||
0.998651 | − | 0.0519182i | \(-0.0165335\pi\) | |||||||
\(758\) | − | 22.6146i | − | 0.821400i | ||||||
\(759\) | 13.6901 | + | 13.6901i | 0.496921 | + | 0.496921i | ||||
\(760\) | −12.5166 | − | 3.40136i | −0.454026 | − | 0.123380i | ||||
\(761\) | − | 3.11943i | − | 0.113079i | −0.998400 | − | 0.0565396i | \(-0.981993\pi\) | ||
0.998400 | − | 0.0565396i | \(-0.0180067\pi\) | |||||||
\(762\) | 1.29596i | 0.0469476i | ||||||||
\(763\) | −6.77787 | −0.245376 | ||||||||
\(764\) | −11.6459 | + | 11.6459i | −0.421332 | + | 0.421332i | ||||
\(765\) | 11.1517 | − | 6.38589i | 0.403190 | − | 0.230882i | ||||
\(766\) | 9.52538 | 0.344166 | ||||||||
\(767\) | −4.53527 | − | 4.53527i | −0.163759 | − | 0.163759i | ||||
\(768\) | 0.707107 | − | 0.707107i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | −22.4056 | + | 22.4056i | −0.807966 | + | 0.807966i | −0.984326 | − | 0.176360i | \(-0.943568\pi\) |
0.176360 | + | 0.984326i | \(0.443568\pi\) | |||||||
\(770\) | −4.40431 | − | 1.19686i | −0.158720 | − | 0.0431318i | ||||
\(771\) | −1.27298 | − | 1.27298i | −0.0458453 | − | 0.0458453i | ||||
\(772\) | −2.80664 | −0.101013 | ||||||||
\(773\) | −1.90608 | − | 1.90608i | −0.0685571 | − | 0.0685571i | 0.671997 | − | 0.740554i | \(-0.265437\pi\) |
−0.740554 | + | 0.671997i | \(0.765437\pi\) | |||||||
\(774\) | 0.853087i | 0.0306636i | ||||||||
\(775\) | −39.7679 | + | 10.3546i | −1.42851 | + | 0.371947i | ||||
\(776\) | 9.28197i | 0.333203i | ||||||||
\(777\) | −4.67513 | − | 2.84514i | −0.167719 | − | 0.102069i | ||||
\(778\) | 7.75553 | + | 7.75553i | 0.278049 | + | 0.278049i | ||||
\(779\) | −36.9973 | + | 36.9973i | −1.32557 | + | 1.32557i | ||||
\(780\) | 0.757293 | − | 2.78676i | 0.0271154 | − | 0.0997819i | ||||
\(781\) | − | 34.6848i | − | 1.24112i | ||||||
\(782\) | − | 49.0466i | − | 1.75390i | ||||||
\(783\) | −2.40635 | −0.0859960 | ||||||||
\(784\) | 6.19050i | 0.221089i | ||||||||
\(785\) | 10.0398 | − | 36.9454i | 0.358336 | − | 1.31864i | ||||
\(786\) | 8.89460 | 0.317260 | ||||||||
\(787\) | −24.9409 | + | 24.9409i | −0.889045 | + | 0.889045i | −0.994431 | − | 0.105386i | \(-0.966392\pi\) |
0.105386 | + | 0.994431i | \(0.466392\pi\) | |||||||
\(788\) | 11.5183 | − | 11.5183i | 0.410322 | − | 0.410322i | ||||
\(789\) | − | 13.0942i | − | 0.466165i | ||||||
\(790\) | 27.5982 | + | 7.49973i | 0.981900 | + | 0.266829i | ||||
\(791\) | 10.9907 | + | 10.9907i | 0.390785 | + | 0.390785i | ||||
\(792\) | −2.26858 | −0.0806106 | ||||||||
\(793\) | −2.66637 | − | 2.66637i | −0.0946857 | − | 0.0946857i | ||||
\(794\) | −18.6690 | − | 18.6690i | −0.662538 | − | 0.662538i | ||||
\(795\) | −18.6568 | + | 10.6836i | −0.661688 | + | 0.378909i | ||||
\(796\) | −10.3470 | + | 10.3470i | −0.366740 | + | 0.366740i | ||||
\(797\) | −33.5854 | −1.18966 | −0.594828 | − | 0.803853i | \(-0.702780\pi\) | ||||
−0.594828 | + | 0.803853i | \(0.702780\pi\) | |||||||
\(798\) | −3.69035 | + | 3.69035i | −0.130637 | + | 0.130637i | ||||
\(799\) | −1.87762 | − | 1.87762i | −0.0664253 | − | 0.0664253i | ||||
\(800\) | −2.53060 | + | 4.31232i | −0.0894701 | + | 0.152463i | ||||
\(801\) | −6.32382 | − | 6.32382i | −0.223441 | − | 0.223441i | ||||
\(802\) | −13.9114 | − | 13.9114i | −0.491228 | − | 0.491228i | ||||
\(803\) | 26.8424 | + | 26.8424i | 0.947248 | + | 0.947248i | ||||
\(804\) | −5.63348 | −0.198678 | ||||||||
\(805\) | 4.50253 | − | 16.5688i | 0.158693 | − | 0.583974i | ||||
\(806\) | 7.50545 | + | 7.50545i | 0.264368 | + | 0.264368i | ||||
\(807\) | −0.487209 | − | 0.487209i | −0.0171506 | − | 0.0171506i | ||||
\(808\) | − | 1.47408i | − | 0.0518580i | ||||||
\(809\) | 4.59489 | − | 4.59489i | 0.161548 | − | 0.161548i | −0.621704 | − | 0.783252i | \(-0.713559\pi\) |
0.783252 | + | 0.621704i | \(0.213559\pi\) | |||||||
\(810\) | 1.94044 | − | 1.11117i | 0.0681800 | − | 0.0390426i | ||||
\(811\) | −26.4363 | −0.928304 | −0.464152 | − | 0.885756i | \(-0.653641\pi\) | ||||
−0.464152 | + | 0.885756i | \(0.653641\pi\) | |||||||
\(812\) | − | 2.16505i | − | 0.0759785i | ||||||
\(813\) | −10.4390 | + | 10.4390i | −0.366110 | + | 0.366110i | ||||
\(814\) | −11.7880 | − | 7.17378i | −0.413168 | − | 0.251441i | ||||
\(815\) | 26.9201 | + | 47.0106i | 0.942971 | + | 1.64671i | ||||
\(816\) | 4.06374 | + | 4.06374i | 0.142259 | + | 0.142259i | ||||
\(817\) | 3.49906 | + | 3.49906i | 0.122417 | + | 0.122417i | ||||
\(818\) | −7.16339 | + | 7.16339i | −0.250462 | + | 0.250462i | ||||
\(819\) | −0.821636 | − | 0.821636i | −0.0287103 | − | 0.0287103i | ||||
\(820\) | 10.0229 | + | 17.5030i | 0.350014 | + | 0.611230i | ||||
\(821\) | 38.5813 | 1.34650 | 0.673248 | − | 0.739417i | \(-0.264899\pi\) | ||||
0.673248 | + | 0.739417i | \(0.264899\pi\) | |||||||
\(822\) | 14.7818i | 0.515576i | ||||||||
\(823\) | 9.95130 | + | 9.95130i | 0.346881 | + | 0.346881i | 0.858946 | − | 0.512066i | \(-0.171120\pi\) |
−0.512066 | + | 0.858946i | \(0.671120\pi\) | |||||||
\(824\) | − | 1.02968i | − | 0.0358707i | ||||||
\(825\) | 10.9769 | − | 2.85811i | 0.382167 | − | 0.0995067i | ||||
\(826\) | 4.46831 | 0.155472 | ||||||||
\(827\) | − | 3.10451i | − | 0.107954i | −0.998542 | − | 0.0539772i | \(-0.982810\pi\) | ||
0.998542 | − | 0.0539772i | \(-0.0171898\pi\) | |||||||
\(828\) | − | 8.53431i | − | 0.296588i | ||||||
\(829\) | 8.47013 | − | 8.47013i | 0.294180 | − | 0.294180i | −0.544549 | − | 0.838729i | \(-0.683299\pi\) |
0.838729 | + | 0.544549i | \(0.183299\pi\) | |||||||
\(830\) | −27.8417 | − | 7.56591i | −0.966400 | − | 0.262616i | ||||
\(831\) | −22.8940 | + | 22.8940i | −0.794186 | + | 0.794186i | ||||
\(832\) | 1.29147 | 0.0447737 | ||||||||
\(833\) | −35.5767 | −1.23266 | ||||||||
\(834\) | −10.2136 | + | 10.2136i | −0.353669 | + | 0.353669i | ||||
\(835\) | −10.7380 | − | 18.7518i | −0.371605 | − | 0.648934i | ||||
\(836\) | −9.30492 | + | 9.30492i | −0.321818 | + | 0.321818i | ||||
\(837\) | 8.21877i | 0.284082i | ||||||||
\(838\) | 23.8546i | 0.824042i | ||||||||
\(839\) | −6.41357 | −0.221421 | −0.110711 | − | 0.993853i | \(-0.535313\pi\) | ||||
−0.110711 | + | 0.993853i | \(0.535313\pi\) | |||||||
\(840\) | 0.999748 | + | 1.74586i | 0.0344946 | + | 0.0602378i | ||||
\(841\) | 23.2095i | 0.800327i | ||||||||
\(842\) | 12.3787 | + | 12.3787i | 0.426598 | + | 0.426598i | ||||
\(843\) | − | 8.12784i | − | 0.279938i | ||||||
\(844\) | −3.80993 | −0.131143 | ||||||||
\(845\) | −21.9892 | + | 12.5919i | −0.756453 | + | 0.433175i | ||||
\(846\) | −0.326713 | − | 0.326713i | −0.0112326 | − | 0.0112326i | ||||
\(847\) | 3.72403 | − | 3.72403i | 0.127959 | − | 0.127959i | ||||
\(848\) | −6.79864 | − | 6.79864i | −0.233466 | − | 0.233466i | ||||
\(849\) | 4.64434 | + | 4.64434i | 0.159393 | + | 0.159393i | ||||
\(850\) | −24.7828 | − | 14.5433i | −0.850045 | − | 0.498832i | ||||
\(851\) | 26.9875 | − | 44.3458i | 0.925118 | − | 1.52015i | ||||
\(852\) | −10.8111 | + | 10.8111i | −0.370382 | + | 0.370382i | ||||
\(853\) | − | 46.7208i | − | 1.59969i | −0.600207 | − | 0.799845i | \(-0.704915\pi\) | ||
0.600207 | − | 0.799845i | \(-0.295085\pi\) | |||||||
\(854\) | 2.62700 | 0.0898941 | ||||||||
\(855\) | 3.40136 | − | 12.5166i | 0.116324 | − | 0.428060i | ||||
\(856\) | 13.8598 | − | 13.8598i | 0.473719 | − | 0.473719i | ||||
\(857\) | 36.8302i | 1.25810i | 0.777367 | + | 0.629048i | \(0.216555\pi\) | ||||
−0.777367 | + | 0.629048i | \(0.783445\pi\) | |||||||
\(858\) | −2.07169 | − | 2.07169i | −0.0707263 | − | 0.0707263i | ||||
\(859\) | −33.3859 | − | 33.3859i | −1.13911 | − | 1.13911i | −0.988610 | − | 0.150502i | \(-0.951911\pi\) |
−0.150502 | − | 0.988610i | \(-0.548089\pi\) | |||||||
\(860\) | 1.65536 | − | 0.947925i | 0.0564474 | − | 0.0323240i | ||||
\(861\) | 8.11561 | 0.276579 | ||||||||
\(862\) | −5.50143 | − | 5.50143i | −0.187379 | − | 0.187379i | ||||
\(863\) | −1.49779 | − | 1.49779i | −0.0509855 | − | 0.0509855i | 0.681154 | − | 0.732140i | \(-0.261478\pi\) |
−0.732140 | + | 0.681154i | \(0.761478\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | 5.61875 | − | 20.6764i | 0.191043 | − | 0.703018i | ||||
\(866\) | −4.53175 | − | 4.53175i | −0.153995 | − | 0.153995i | ||||
\(867\) | −11.3334 | + | 11.3334i | −0.384904 | + | 0.384904i | ||||
\(868\) | −7.39463 | −0.250990 | ||||||||
\(869\) | 20.5166 | − | 20.5166i | 0.695980 | − | 0.695980i | ||||
\(870\) | 2.67387 | + | 4.66938i | 0.0906527 | + | 0.158307i | ||||
\(871\) | −5.14455 | − | 5.14455i | −0.174316 | − | 0.174316i | ||||
\(872\) | 5.32683 | + | 5.32683i | 0.180389 | + | 0.180389i | ||||
\(873\) | −9.28197 | −0.314147 | ||||||||
\(874\) | −35.0047 | − | 35.0047i | −1.18405 | − | 1.18405i | ||||
\(875\) | −7.03700 | − | 7.18809i | −0.237894 | − | 0.243002i | ||||
\(876\) | − | 16.7333i | − | 0.565366i | ||||||
\(877\) | 8.78482 | − | 8.78482i | 0.296642 | − | 0.296642i | −0.543055 | − | 0.839697i | \(-0.682732\pi\) |
0.839697 | + | 0.543055i | \(0.182732\pi\) | |||||||
\(878\) | 22.7618 | − | 22.7618i | 0.768172 | − | 0.768172i | ||||
\(879\) | −31.1391 | −1.05030 | ||||||||
\(880\) | 2.52078 | + | 4.40204i | 0.0849756 | + | 0.148393i | ||||
\(881\) | − | 19.0001i | − | 0.640128i | −0.947396 | − | 0.320064i | \(-0.896296\pi\) | ||
0.947396 | − | 0.320064i | \(-0.103704\pi\) | |||||||
\(882\) | −6.19050 | −0.208445 | ||||||||
\(883\) | − | 10.1981i | − | 0.343193i | −0.985167 | − | 0.171596i | \(-0.945108\pi\) | ||
0.985167 | − | 0.171596i | \(-0.0548925\pi\) | |||||||
\(884\) | 7.42208i | 0.249631i | ||||||||
\(885\) | −9.63681 | + | 5.51842i | −0.323938 | + | 0.185500i | ||||
\(886\) | −18.5368 | + | 18.5368i | −0.622754 | + | 0.622754i | ||||
\(887\) | −12.1095 | − | 12.1095i | −0.406597 | − | 0.406597i | 0.473953 | − | 0.880550i | \(-0.342827\pi\) |
−0.880550 | + | 0.473953i | \(0.842827\pi\) | |||||||
\(888\) | 1.43822 | + | 5.91029i | 0.0482635 | + | 0.198336i | ||||
\(889\) | − | 1.16600i | − | 0.0391065i | ||||||
\(890\) | −5.24413 | + | 19.2978i | −0.175784 | + | 0.646864i | ||||
\(891\) | − | 2.26858i | − | 0.0760004i | ||||||
\(892\) | 16.8923 | + | 16.8923i | 0.565595 | + | 0.565595i | ||||
\(893\) | −2.68012 | −0.0896869 | ||||||||
\(894\) | −13.5056 | − | 13.5056i | −0.451694 | − | 0.451694i | ||||
\(895\) | −6.10724 | + | 22.4740i | −0.204143 | + | 0.751222i | ||||
\(896\) | −0.636201 | + | 0.636201i | −0.0212540 | + | 0.0212540i | ||||
\(897\) | 7.79360 | − | 7.79360i | 0.260221 | − | 0.260221i | ||||
\(898\) | 9.96142 | + | 9.96142i | 0.332417 | + | 0.332417i | ||||
\(899\) | −19.7773 | −0.659609 | ||||||||
\(900\) | −4.31232 | − | 2.53060i | −0.143744 | − | 0.0843532i | ||||
\(901\) | 39.0717 | − | 39.0717i | 1.30167 | − | 1.30167i | ||||
\(902\) | 20.4629 | 0.681338 | ||||||||
\(903\) | − | 0.767543i | − | 0.0255422i | ||||||
\(904\) | − | 17.2755i | − | 0.574576i | ||||||
\(905\) | −27.0984 | + | 15.5176i | −0.900780 | + | 0.515822i | ||||
\(906\) | 2.42193 | + | 2.42193i | 0.0804634 | + | 0.0804634i | ||||
\(907\) | − | 0.471868i | − | 0.0156681i | −0.999969 | − | 0.00783407i | \(-0.997506\pi\) | ||
0.999969 | − | 0.00783407i | \(-0.00249369\pi\) | |||||||
\(908\) | 25.0030i | 0.829752i | ||||||||
\(909\) | 1.47408 | 0.0488922 | ||||||||
\(910\) | −0.681355 | + | 2.50731i | −0.0225867 | + | 0.0831166i | ||||
\(911\) | 18.6659 | − | 18.6659i | 0.618430 | − | 0.618430i | −0.326698 | − | 0.945129i | \(-0.605936\pi\) |
0.945129 | + | 0.326698i | \(0.105936\pi\) | |||||||
\(912\) | 5.80061 | 0.192077 | ||||||||
\(913\) | −20.6977 | + | 20.6977i | −0.684993 | + | 0.684993i | ||||
\(914\) | − | 6.81678i | − | 0.225479i | ||||||
\(915\) | −5.66566 | + | 3.24438i | −0.187301 | + | 0.107256i | ||||
\(916\) | 11.3572i | 0.375252i | ||||||||
\(917\) | −8.00269 | −0.264272 | ||||||||
\(918\) | −4.06374 | + | 4.06374i | −0.134123 | + | 0.134123i | ||||
\(919\) | −24.0718 | + | 24.0718i | −0.794054 | + | 0.794054i | −0.982151 | − | 0.188096i | \(-0.939768\pi\) |
0.188096 | + | 0.982151i | \(0.439768\pi\) | |||||||
\(920\) | −16.5603 | + | 9.48308i | −0.545977 | + | 0.312648i | ||||
\(921\) | −7.12307 | −0.234713 | ||||||||
\(922\) | −24.7125 | + | 24.7125i | −0.813862 | + | 0.813862i | ||||
\(923\) | −19.7456 | −0.649934 | ||||||||
\(924\) | 2.04110 | 0.0671472 | ||||||||
\(925\) | −14.4052 | − | 26.7860i | −0.473642 | − | 0.880718i | ||||
\(926\) | 32.0736 | 1.05400 | ||||||||
\(927\) | 1.02968 | 0.0338192 | ||||||||
\(928\) | −1.70155 | + | 1.70155i | −0.0558560 | + | 0.0558560i | ||||
\(929\) | 8.12677 | 0.266631 | 0.133315 | − | 0.991074i | \(-0.457438\pi\) | ||||
0.133315 | + | 0.991074i | \(0.457438\pi\) | |||||||
\(930\) | 15.9480 | − | 9.13247i | 0.522956 | − | 0.299465i | ||||
\(931\) | −25.3912 | + | 25.3912i | −0.832164 | + | 0.832164i | ||||
\(932\) | −4.77274 | + | 4.77274i | −0.156336 | + | 0.156336i | ||||
\(933\) | 5.45254 | 0.178508 | ||||||||
\(934\) | 13.7531i | 0.450014i | ||||||||
\(935\) | −25.2985 | + | 14.4869i | −0.827349 | + | 0.473773i | ||||
\(936\) | 1.29147i | 0.0422131i | ||||||||
\(937\) | −21.4124 | + | 21.4124i | −0.699513 | + | 0.699513i | −0.964305 | − | 0.264793i | \(-0.914696\pi\) |
0.264793 | + | 0.964305i | \(0.414696\pi\) | |||||||
\(938\) | 5.06858 | 0.165495 | ||||||||
\(939\) | 13.8211 | − | 13.8211i | 0.451036 | − | 0.451036i | ||||
\(940\) | −0.270932 | + | 0.997001i | −0.00883683 | + | 0.0325186i | ||||
\(941\) | −6.32110 | −0.206062 | −0.103031 | − | 0.994678i | \(-0.532854\pi\) | ||||
−0.103031 | + | 0.994678i | \(0.532854\pi\) | |||||||
\(942\) | 17.1217i | 0.557854i | ||||||||
\(943\) | 76.9804i | 2.50683i | ||||||||
\(944\) | −3.51171 | − | 3.51171i | −0.114296 | − | 0.114296i | ||||
\(945\) | −1.74586 | + | 0.999748i | −0.0567928 | + | 0.0325218i | ||||
\(946\) | − | 1.93530i | − | 0.0629219i | ||||||
\(947\) | − | 29.6137i | − | 0.962316i | −0.876634 | − | 0.481158i | \(-0.840216\pi\) | ||
0.876634 | − | 0.481158i | \(-0.159784\pi\) | |||||||
\(948\) | −12.7899 | −0.415396 | ||||||||
\(949\) | 15.2810 | − | 15.2810i | 0.496043 | − | 0.496043i | ||||
\(950\) | −28.0672 | + | 7.30799i | −0.910621 | + | 0.237103i | ||||
\(951\) | −7.11706 | −0.230787 | ||||||||
\(952\) | −3.65624 | − | 3.65624i | −0.118499 | − | 0.118499i | ||||
\(953\) | −25.1832 | + | 25.1832i | −0.815765 | + | 0.815765i | −0.985491 | − | 0.169727i | \(-0.945712\pi\) |
0.169727 | + | 0.985491i | \(0.445712\pi\) | |||||||
\(954\) | 6.79864 | − | 6.79864i | 0.220114 | − | 0.220114i | ||||
\(955\) | −9.65751 | + | 35.5386i | −0.312510 | + | 1.15000i | ||||
\(956\) | 2.96858 | + | 2.96858i | 0.0960109 | + | 0.0960109i | ||||
\(957\) | 5.45901 | 0.176465 | ||||||||
\(958\) | 15.9554 | + | 15.9554i | 0.515496 | + | 0.515496i | ||||
\(959\) | − | 13.2996i | − | 0.429466i | ||||||
\(960\) | 0.586380 | − | 2.15781i | 0.0189253 | − | 0.0696431i | ||||
\(961\) | 36.5482i | 1.17898i | ||||||||
\(962\) | −4.08393 | + | 6.71072i | −0.131671 | + | 0.216362i | ||||
\(963\) | 13.8598 | + | 13.8598i | 0.446627 | + | 0.446627i | ||||
\(964\) | −5.75647 | + | 5.75647i | −0.185403 | + | 0.185403i | ||||
\(965\) | −5.44611 | + | 3.11866i | −0.175316 | + | 0.100393i | ||||
\(966\) | 7.67852i | 0.247052i | ||||||||
\(967\) | − | 12.3262i | − | 0.396385i | −0.980163 | − | 0.198192i | \(-0.936493\pi\) | ||
0.980163 | − | 0.198192i | \(-0.0635071\pi\) | |||||||
\(968\) | −5.85354 | −0.188140 | ||||||||
\(969\) | 33.3360i | 1.07091i | ||||||||
\(970\) | 10.3139 | + | 18.0111i | 0.331158 | + | 0.578301i | ||||
\(971\) | 4.53299 | 0.145471 | 0.0727353 | − | 0.997351i | \(-0.476827\pi\) | ||||
0.0727353 | + | 0.997351i | \(0.476827\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 9.18946 | − | 9.18946i | 0.294601 | − | 0.294601i | ||||
\(974\) | 22.5078i | 0.721195i | ||||||||
\(975\) | −1.62708 | − | 6.24901i | −0.0521084 | − | 0.200128i | ||||
\(976\) | −2.06460 | − | 2.06460i | −0.0660862 | − | 0.0660862i | ||||
\(977\) | 42.8715 | 1.37158 | 0.685790 | − | 0.727799i | \(-0.259457\pi\) | ||||
0.685790 | + | 0.727799i | \(0.259457\pi\) | |||||||
\(978\) | −17.1309 | − | 17.1309i | −0.547787 | − | 0.547787i | ||||
\(979\) | 14.3461 | + | 14.3461i | 0.458503 | + | 0.458503i | ||||
\(980\) | 6.87870 | + | 12.0123i | 0.219732 | + | 0.383718i | ||||
\(981\) | −5.32683 | + | 5.32683i | −0.170073 | + | 0.170073i | ||||
\(982\) | −31.0223 | −0.989961 | ||||||||
\(983\) | −23.7970 | + | 23.7970i | −0.759006 | + | 0.759006i | −0.976141 | − | 0.217136i | \(-0.930329\pi\) |
0.217136 | + | 0.976141i | \(0.430329\pi\) | |||||||
\(984\) | −6.37818 | − | 6.37818i | −0.203329 | − | 0.203329i | ||||
\(985\) | 9.55172 | − | 35.1493i | 0.304343 | − | 1.11995i | ||||
\(986\) | −9.77878 | − | 9.77878i | −0.311420 | − | 0.311420i | ||||
\(987\) | 0.293952 | + | 0.293952i | 0.00935658 | + | 0.00935658i | ||||
\(988\) | 5.29716 | + | 5.29716i | 0.168525 | + | 0.168525i | ||||
\(989\) | 7.28050 | 0.231507 | ||||||||
\(990\) | −4.40204 | + | 2.52078i | −0.139906 | + | 0.0801158i | ||||
\(991\) | −3.21857 | − | 3.21857i | −0.102241 | − | 0.102241i | 0.654136 | − | 0.756377i | \(-0.273032\pi\) |
−0.756377 | + | 0.654136i | \(0.773032\pi\) | |||||||
\(992\) | 5.81155 | + | 5.81155i | 0.184517 | + | 0.184517i | ||||
\(993\) | 4.60678i | 0.146192i | ||||||||
\(994\) | 9.72702 | − | 9.72702i | 0.308522 | − | 0.308522i | ||||
\(995\) | −8.58044 | + | 31.5751i | −0.272018 | + | 1.00100i | ||||
\(996\) | 12.9027 | 0.408839 | ||||||||
\(997\) | − | 27.5415i | − | 0.872248i | −0.899887 | − | 0.436124i | \(-0.856351\pi\) | ||
0.899887 | − | 0.436124i | \(-0.143649\pi\) | |||||||
\(998\) | 5.68409 | − | 5.68409i | 0.179927 | − | 0.179927i | ||||
\(999\) | −5.91029 | + | 1.43822i | −0.186993 | + | 0.0455032i |
(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.253.15 | yes | 36 | |
5.2 | odd | 4 | 1110.2.l.a.697.4 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.l.a.43.4 | ✓ | 36 | ||
185.117 | even | 4 | inner | 1110.2.o.a.487.15 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.4 | ✓ | 36 | 37.6 | odd | 4 | ||
1110.2.l.a.697.4 | yes | 36 | 5.2 | odd | 4 | ||
1110.2.o.a.253.15 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.487.15 | yes | 36 | 185.117 | even | 4 | inner |