Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
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, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (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 | 697.4 | ||
Character | \(\chi\) | \(=\) | 1110.697 |
Dual form | 1110.2.l.a.43.4 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.11117 | − | 1.94044i | 0.496931 | − | 0.867790i | ||||
\(6\) | −0.707107 | + | 0.707107i | −0.288675 | + | 0.288675i | ||||
\(7\) | 0.636201 | + | 0.636201i | 0.240461 | + | 0.240461i | 0.817041 | − | 0.576580i | \(-0.195613\pi\) |
−0.576580 | + | 0.817041i | \(0.695613\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 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 | ||||
\(13\) | − | 1.29147i | − | 0.358190i | −0.983832 | − | 0.179095i | \(-0.942683\pi\) | ||
0.983832 | − | 0.179095i | \(-0.0573169\pi\) | |||||||
\(14\) | 0.636201 | − | 0.636201i | 0.170032 | − | 0.170032i | ||||
\(15\) | −2.15781 | + | 0.586380i | −0.557145 | + | 0.151403i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.74699 | −1.39385 | −0.696925 | − | 0.717144i | \(-0.745449\pi\) | ||||
−0.696925 | + | 0.717144i | \(0.745449\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.10165 | − | 4.10165i | −0.940982 | − | 0.940982i | 0.0573705 | − | 0.998353i | \(-0.481728\pi\) |
−0.998353 | + | 0.0573705i | \(0.981728\pi\) | |||||||
\(20\) | −1.11117 | + | 1.94044i | −0.248465 | + | 0.433895i | ||||
\(21\) | − | 0.899724i | − | 0.196336i | ||||||
\(22\) | 2.26858 | 0.483663 | ||||||||
\(23\) | − | 8.53431i | − | 1.77953i | −0.456423 | − | 0.889763i | \(-0.650869\pi\) | ||
0.456423 | − | 0.889763i | \(-0.349131\pi\) | |||||||
\(24\) | 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 | −0.847217 | − | 0.531247i | \(-0.821723\pi\) |
0.531247 | + | 0.847217i | \(0.321723\pi\) | |||||||
\(30\) | 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 | \(-0.514261\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 1.60413 | − | 1.60413i | 0.279243 | − | 0.279243i | ||||
\(34\) | 5.74699i | 0.985601i | ||||||||
\(35\) | 1.94144 | − | 0.527580i | 0.328163 | − | 0.0891773i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 5.19618 | + | 3.16223i | 0.854247 | + | 0.519868i | ||||
\(38\) | −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 | \(0.751238\pi\) | |||||||
\(42\) | −0.899724 | −0.138830 | ||||||||
\(43\) | − | 0.853087i | − | 0.130094i | −0.997882 | − | 0.0650472i | \(-0.979280\pi\) | ||
0.997882 | − | 0.0650472i | \(-0.0207198\pi\) | |||||||
\(44\) | − | 2.26858i | − | 0.342002i | ||||||
\(45\) | 1.94044 | + | 1.11117i | 0.289263 | + | 0.165644i | ||||
\(46\) | −8.53431 | −1.25832 | ||||||||
\(47\) | −0.326713 | − | 0.326713i | −0.0476560 | − | 0.0476560i | 0.682877 | − | 0.730533i | \(-0.260728\pi\) |
−0.730533 | + | 0.682877i | \(0.760728\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 6.19050i | − | 0.884357i | ||||||
\(50\) | −4.31232 | + | 2.53060i | −0.609854 | + | 0.357880i | ||||
\(51\) | 4.06374 | + | 4.06374i | 0.569037 | + | 0.569037i | ||||
\(52\) | 1.29147i | 0.179095i | ||||||||
\(53\) | −6.79864 | + | 6.79864i | −0.933866 | + | 0.933866i | −0.997945 | − | 0.0640792i | \(-0.979589\pi\) |
0.0640792 | + | 0.997945i | \(0.479589\pi\) | |||||||
\(54\) | −0.707107 | − | 0.707107i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | 4.40204 | + | 2.52078i | 0.593571 | + | 0.339902i | ||||
\(56\) | −0.636201 | + | 0.636201i | −0.0850159 | + | 0.0850159i | ||||
\(57\) | 5.80061i | 0.768309i | ||||||||
\(58\) | 1.70155 | + | 1.70155i | 0.223424 | + | 0.223424i | ||||
\(59\) | 3.51171 | + | 3.51171i | 0.457186 | + | 0.457186i | 0.897731 | − | 0.440545i | \(-0.145215\pi\) |
−0.440545 | + | 0.897731i | \(0.645215\pi\) | |||||||
\(60\) | 2.15781 | − | 0.586380i | 0.278573 | − | 0.0757013i | ||||
\(61\) | −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 | \(-0.638177\pi\) |
0.907250 | + | 0.420591i | \(0.138177\pi\) | |||||||
\(68\) | 5.74699 | 0.696925 | ||||||||
\(69\) | −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 | \(0.861821\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −11.8322 | − | 11.8322i | −1.38486 | − | 1.38486i | −0.835751 | − | 0.549108i | \(-0.814968\pi\) |
−0.549108 | − | 0.835751i | \(-0.685032\pi\) | |||||||
\(74\) | 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 | \(0.00562329\pi\) |
0.0176652 | + | 0.999844i | \(0.494377\pi\) | |||||||
\(80\) | 1.11117 | − | 1.94044i | 0.124233 | − | 0.216948i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 9.02011 | 0.996104 | ||||||||
\(83\) | 9.12362 | − | 9.12362i | 1.00145 | − | 1.00145i | 0.00144791 | − | 0.999999i | \(-0.499539\pi\) |
0.999999 | − | 0.00144791i | \(-0.000460883\pi\) | |||||||
\(84\) | 0.899724i | 0.0981680i | ||||||||
\(85\) | −6.38589 | + | 11.1517i | −0.692647 | + | 1.20957i | ||||
\(86\) | −0.853087 | −0.0919907 | ||||||||
\(87\) | 2.40635 | 0.257988 | ||||||||
\(88\) | −2.26858 | −0.241832 | ||||||||
\(89\) | −6.32382 | + | 6.32382i | −0.670323 | + | 0.670323i | −0.957791 | − | 0.287467i | \(-0.907187\pi\) |
0.287467 | + | 0.957791i | \(0.407187\pi\) | |||||||
\(90\) | 1.11117 | − | 1.94044i | 0.117128 | − | 0.204540i | ||||
\(91\) | 0.821636 | − | 0.821636i | 0.0861308 | − | 0.0861308i | ||||
\(92\) | 8.53431i | 0.889763i | ||||||||
\(93\) | 8.21877i | 0.852247i | ||||||||
\(94\) | −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 | ||||
\(97\) | 9.28197 | 0.942441 | 0.471220 | − | 0.882015i | \(-0.343814\pi\) | ||||
0.471220 | + | 0.882015i | \(0.343814\pi\) | |||||||
\(98\) | −6.19050 | −0.625335 | ||||||||
\(99\) | −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 | ||||
\(103\) | 1.02968 | 0.101458 | 0.0507289 | − | 0.998712i | \(-0.483846\pi\) | ||||
0.0507289 | + | 0.998712i | \(0.483846\pi\) | |||||||
\(104\) | 1.29147 | 0.126639 | ||||||||
\(105\) | −1.74586 | − | 0.999748i | −0.170378 | − | 0.0975654i | ||||
\(106\) | 6.79864 | + | 6.79864i | 0.660343 | + | 0.660343i | ||||
\(107\) | −13.8598 | − | 13.8598i | −1.33988 | − | 1.33988i | −0.896171 | − | 0.443708i | \(-0.853663\pi\) |
−0.443708 | − | 0.896171i | \(-0.646337\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | 5.32683 | + | 5.32683i | 0.510218 | + | 0.510218i | 0.914593 | − | 0.404375i | \(-0.132511\pi\) |
−0.404375 | + | 0.914593i | \(0.632511\pi\) | |||||||
\(110\) | 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 | ||||
\(113\) | 17.2755 | 1.62515 | 0.812573 | − | 0.582859i | \(-0.198066\pi\) | ||||
0.812573 | + | 0.582859i | \(0.198066\pi\) | |||||||
\(114\) | 5.80061 | 0.543276 | ||||||||
\(115\) | −16.5603 | − | 9.48308i | −1.54426 | − | 0.884302i | ||||
\(116\) | 1.70155 | − | 1.70155i | 0.157985 | − | 0.157985i | ||||
\(117\) | 1.29147 | 0.119397 | ||||||||
\(118\) | 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 | ||||
\(125\) | −11.1797 | + | 0.118740i | −0.999944 | + | 0.0106204i | ||||
\(126\) | 0.636201 | + | 0.636201i | 0.0566773 | + | 0.0566773i | ||||
\(127\) | 0.916380 | + | 0.916380i | 0.0813156 | + | 0.0813156i | 0.746595 | − | 0.665279i | \(-0.231687\pi\) |
−0.665279 | + | 0.746595i | \(0.731687\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −0.603223 | + | 0.603223i | −0.0531109 | + | 0.0531109i | ||||
\(130\) | −1.43505 | + | 2.50602i | −0.125862 | + | 0.219793i | ||||
\(131\) | −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 | ||||
\(133\) | − | 5.21895i | − | 0.452540i | ||||||
\(134\) | −3.98347 | − | 3.98347i | −0.344120 | − | 0.344120i | ||||
\(135\) | −0.586380 | − | 2.15781i | −0.0504675 | − | 0.185715i | ||||
\(136\) | − | 5.74699i | − | 0.492800i | ||||||
\(137\) | 10.4523 | + | 10.4523i | 0.893004 | + | 0.893004i | 0.994805 | − | 0.101801i | \(-0.0324605\pi\) |
−0.101801 | + | 0.994805i | \(0.532461\pi\) | |||||||
\(138\) | 6.03467 | + | 6.03467i | 0.513705 | + | 0.513705i | ||||
\(139\) | −14.4443 | −1.22515 | −0.612574 | − | 0.790414i | \(-0.709866\pi\) | ||||
−0.612574 | + | 0.790414i | \(0.709866\pi\) | |||||||
\(140\) | −1.94144 | + | 0.527580i | −0.164081 | + | 0.0445887i | ||||
\(141\) | 0.462042i | 0.0389110i | ||||||||
\(142\) | 15.2892i | 1.28304i | ||||||||
\(143\) | 2.92981 | 0.245003 | ||||||||
\(144\) | 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 | ||||
\(148\) | −5.19618 | − | 3.16223i | −0.427123 | − | 0.259934i | ||||
\(149\) | − | 19.0997i | − | 1.56471i | −0.622831 | − | 0.782356i | \(-0.714018\pi\) | ||
0.622831 | − | 0.782356i | \(-0.285982\pi\) | |||||||
\(150\) | 4.83867 | + | 1.25987i | 0.395076 | + | 0.102868i | ||||
\(151\) | − | 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 | ||||
\(153\) | − | 5.74699i | − | 0.464617i | ||||||
\(154\) | 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 | 0.999448 | − | 0.0332164i | \(-0.0105751\pi\) |
−0.0332164 | + | 0.999448i | \(0.510575\pi\) | |||||||
\(158\) | 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 | ||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 24.2268 | 1.89759 | 0.948795 | − | 0.315894i | \(-0.102304\pi\) | ||||
0.948795 | + | 0.315894i | \(0.102304\pi\) | |||||||
\(164\) | − | 9.02011i | − | 0.704352i | ||||||
\(165\) | −1.33025 | − | 4.89518i | −0.103560 | − | 0.381089i | ||||
\(166\) | −9.12362 | − | 9.12362i | −0.708130 | − | 0.708130i | ||||
\(167\) | 9.66372 | 0.747801 | 0.373900 | − | 0.927469i | \(-0.378020\pi\) | ||||
0.373900 | + | 0.927469i | \(0.378020\pi\) | |||||||
\(168\) | 0.899724 | 0.0694152 | ||||||||
\(169\) | 11.3321 | 0.871700 | ||||||||
\(170\) | 11.1517 | + | 6.38589i | 0.855295 | + | 0.489776i | ||||
\(171\) | 4.10165 | − | 4.10165i | 0.313661 | − | 0.313661i | ||||
\(172\) | 0.853087i | 0.0650472i | ||||||||
\(173\) | −6.77556 | − | 6.77556i | −0.515136 | − | 0.515136i | 0.400959 | − | 0.916096i | \(-0.368677\pi\) |
−0.916096 | + | 0.400959i | \(0.868677\pi\) | |||||||
\(174\) | − | 2.40635i | − | 0.182425i | ||||||
\(175\) | 1.13353 | − | 4.35347i | 0.0856870 | − | 0.329091i | ||||
\(176\) | 2.26858i | 0.171001i | ||||||||
\(177\) | − | 4.96631i | − | 0.373290i | ||||||
\(178\) | 6.32382 | + | 6.32382i | 0.473990 | + | 0.473990i | ||||
\(179\) | 7.36463 | − | 7.36463i | 0.550458 | − | 0.550458i | −0.376115 | − | 0.926573i | \(-0.622740\pi\) |
0.926573 | + | 0.376115i | \(0.122740\pi\) | |||||||
\(180\) | −1.94044 | − | 1.11117i | −0.144632 | − | 0.0828218i | ||||
\(181\) | −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 | ||||
\(183\) | 2.91979i | 0.215837i | ||||||||
\(184\) | 8.53431 | 0.629158 | ||||||||
\(185\) | 11.9100 | − | 6.56908i | 0.875638 | − | 0.482969i | ||||
\(186\) | 8.21877 | 0.602630 | ||||||||
\(187\) | − | 13.0375i | − | 0.953398i | ||||||
\(188\) | 0.326713 | + | 0.326713i | 0.0238280 | + | 0.0238280i | ||||
\(189\) | 0.899724 | 0.0654453 | ||||||||
\(190\) | 3.40136 | + | 12.5166i | 0.246760 | + | 0.908051i | ||||
\(191\) | −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 | ||||
\(193\) | 2.80664i | 0.202026i | 0.994885 | + | 0.101013i | \(0.0322084\pi\) | ||||
−0.994885 | + | 0.101013i | \(0.967792\pi\) | |||||||
\(194\) | − | 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 | 0.986200 | − | 0.165557i | \(-0.0529422\pi\) |
−0.165557 | + | 0.986200i | \(0.552942\pi\) | |||||||
\(198\) | 2.26858i | 0.161221i | ||||||||
\(199\) | 10.3470 | − | 10.3470i | 0.733481 | − | 0.733481i | −0.237827 | − | 0.971308i | \(-0.576435\pi\) |
0.971308 | + | 0.237827i | \(0.0764350\pi\) | |||||||
\(200\) | 4.31232 | − | 2.53060i | 0.304927 | − | 0.178940i | ||||
\(201\) | −5.63348 | −0.397355 | ||||||||
\(202\) | 1.47408 | 0.103716 | ||||||||
\(203\) | −2.16505 | −0.151957 | ||||||||
\(204\) | −4.06374 | − | 4.06374i | −0.284518 | − | 0.284518i | ||||
\(205\) | 17.5030 | + | 10.0229i | 1.22246 | + | 0.700029i | ||||
\(206\) | − | 1.02968i | − | 0.0717414i | ||||||
\(207\) | 8.53431 | 0.593175 | ||||||||
\(208\) | − | 1.29147i | − | 0.0895475i | ||||||
\(209\) | 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 | ||||
\(217\) | − | 7.39463i | − | 0.501980i | ||||||
\(218\) | 5.32683 | − | 5.32683i | 0.360779 | − | 0.360779i | ||||
\(219\) | 16.7333i | 1.13073i | ||||||||
\(220\) | −4.40204 | − | 2.52078i | −0.296786 | − | 0.169951i | ||||
\(221\) | 7.42208i | 0.499263i | ||||||||
\(222\) | −5.91029 | + | 1.43822i | −0.396673 | + | 0.0965269i | ||||
\(223\) | 16.8923 | − | 16.8923i | 1.13119 | − | 1.13119i | 0.141210 | − | 0.989980i | \(-0.454901\pi\) |
0.989980 | − | 0.141210i | \(-0.0450992\pi\) | |||||||
\(224\) | 0.636201 | − | 0.636201i | 0.0425080 | − | 0.0425080i | ||||
\(225\) | 4.31232 | − | 2.53060i | 0.287488 | − | 0.168706i | ||||
\(226\) | − | 17.2755i | − | 1.14915i | ||||||
\(227\) | −25.0030 | −1.65950 | −0.829752 | − | 0.558132i | \(-0.811518\pi\) | ||||
−0.829752 | + | 0.558132i | \(0.811518\pi\) | |||||||
\(228\) | − | 5.80061i | − | 0.384154i | ||||||
\(229\) | − | 11.3572i | − | 0.750503i | −0.926923 | − | 0.375252i | \(-0.877556\pi\) | ||
0.926923 | − | 0.375252i | \(-0.122444\pi\) | |||||||
\(230\) | −9.48308 | + | 16.5603i | −0.625296 | + | 1.09195i | ||||
\(231\) | 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 | \(-0.179038\pi\) |
−0.533271 | + | 0.845944i | \(0.679038\pi\) | |||||||
\(234\) | − | 1.29147i | − | 0.0844262i | ||||||
\(235\) | −0.997001 | + | 0.270932i | −0.0650371 | + | 0.0176737i | ||||
\(236\) | −3.51171 | − | 3.51171i | −0.228593 | − | 0.228593i | ||||
\(237\) | − | 12.7899i | − | 0.830793i | ||||||
\(238\) | −3.65624 | + | 3.65624i | −0.236999 | + | 0.236999i | ||||
\(239\) | −2.96858 | − | 2.96858i | −0.192022 | − | 0.192022i | 0.604547 | − | 0.796569i | \(-0.293354\pi\) |
−0.796569 | + | 0.604547i | \(0.793354\pi\) | |||||||
\(240\) | −2.15781 | + | 0.586380i | −0.139286 | + | 0.0378507i | ||||
\(241\) | −5.75647 | + | 5.75647i | −0.370807 | + | 0.370807i | −0.867771 | − | 0.496964i | \(-0.834448\pi\) |
0.496964 | + | 0.867771i | \(0.334448\pi\) | |||||||
\(242\) | − | 5.85354i | − | 0.376279i | ||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 2.06460 | + | 2.06460i | 0.132172 | + | 0.132172i | ||||
\(245\) | −12.0123 | − | 6.87870i | −0.767436 | − | 0.439464i | ||||
\(246\) | −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 | ||||
\(253\) | 19.3608 | 1.21720 | ||||||||
\(254\) | 0.916380 | − | 0.916380i | 0.0574988 | − | 0.0574988i | ||||
\(255\) | 12.4009 | − | 3.36992i | 0.776577 | − | 0.211033i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.80027 | 0.112298 | 0.0561488 | − | 0.998422i | \(-0.482118\pi\) | ||||
0.0561488 | + | 0.998422i | \(0.482118\pi\) | |||||||
\(258\) | 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 | \(-0.382280\pi\) |
−0.932389 | + | 0.361456i | \(0.882280\pi\) | |||||||
\(264\) | 1.60413 | + | 1.60413i | 0.0987274 | + | 0.0987274i | ||||
\(265\) | 5.63789 | + | 20.7468i | 0.346333 | + | 1.27447i | ||||
\(266\) | −5.21895 | −0.319994 | ||||||||
\(267\) | 8.94323 | 0.547317 | ||||||||
\(268\) | −3.98347 | + | 3.98347i | −0.243329 | + | 0.243329i | ||||
\(269\) | 0.689017i | 0.0420101i | 0.999779 | + | 0.0210051i | \(0.00668661\pi\) | ||||
−0.999779 | + | 0.0210051i | \(0.993313\pi\) | |||||||
\(270\) | −2.15781 | + | 0.586380i | −0.131320 | + | 0.0356859i | ||||
\(271\) | −14.7629 | −0.896783 | −0.448392 | − | 0.893837i | \(-0.648003\pi\) | ||||
−0.448392 | + | 0.893837i | \(0.648003\pi\) | |||||||
\(272\) | −5.74699 | −0.348462 | ||||||||
\(273\) | −1.16197 | −0.0703255 | ||||||||
\(274\) | 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 | ||||
\(277\) | − | 32.3771i | − | 1.94535i | −0.232172 | − | 0.972675i | \(-0.574583\pi\) | ||
0.232172 | − | 0.972675i | \(-0.425417\pi\) | |||||||
\(278\) | 14.4443i | 0.866310i | ||||||||
\(279\) | 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 | \(0.172054\pi\) | |||||||
\(282\) | 0.462042 | 0.0275142 | ||||||||
\(283\) | 6.56809 | 0.390433 | 0.195216 | − | 0.980760i | \(-0.437459\pi\) | ||||
0.195216 | + | 0.980760i | \(0.437459\pi\) | |||||||
\(284\) | 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 | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 16.0279 | 0.942818 | ||||||||
\(290\) | 5.19246 | − | 1.41104i | 0.304912 | − | 0.0828589i | ||||
\(291\) | −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 | −0.349353 | + | 0.936991i | \(0.613599\pi\) |
−0.936991 | + | 0.349353i | \(0.886401\pi\) | |||||||
\(294\) | 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 | ||||
\(298\) | −19.0997 | −1.10642 | ||||||||
\(299\) | −11.0218 | −0.637408 | ||||||||
\(300\) | 1.25987 | − | 4.83867i | 0.0727385 | − | 0.279361i | ||||
\(301\) | 0.542735 | − | 0.542735i | 0.0312827 | − | 0.0312827i | ||||
\(302\) | −3.42513 | −0.197094 | ||||||||
\(303\) | 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 | \(-0.684844\pi\) |
0.836077 | + | 0.548613i | \(0.184844\pi\) | |||||||
\(308\) | 1.44327 | − | 1.44327i | 0.0822382 | − | 0.0822382i | ||||
\(309\) | −0.728096 | − | 0.728096i | −0.0414199 | − | 0.0414199i | ||||
\(310\) | 4.81932 | + | 17.7346i | 0.273719 | + | 1.00726i | ||||
\(311\) | 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 | ||||
\(313\) | − | 19.5460i | − | 1.10481i | −0.833577 | − | 0.552404i | \(-0.813711\pi\) | ||
0.833577 | − | 0.552404i | \(-0.186289\pi\) | |||||||
\(314\) | 12.1068 | − | 12.1068i | 0.683229 | − | 0.683229i | ||||
\(315\) | 0.527580 | + | 1.94144i | 0.0297258 | + | 0.109388i | ||||
\(316\) | −9.04382 | − | 9.04382i | −0.508755 | − | 0.508755i | ||||
\(317\) | 5.03252 | − | 5.03252i | 0.282655 | − | 0.282655i | −0.551512 | − | 0.834167i | \(-0.685949\pi\) |
0.834167 | + | 0.551512i | \(0.185949\pi\) | |||||||
\(318\) | − | 9.61473i | − | 0.539168i | ||||||
\(319\) | −3.86010 | − | 3.86010i | −0.216124 | − | 0.216124i | ||||
\(320\) | −1.11117 | + | 1.94044i | −0.0621164 | + | 0.108474i | ||||
\(321\) | 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 | ||||||||
\(325\) | −5.56924 | + | 3.26819i | −0.308926 | + | 0.181287i | ||||
\(326\) | − | 24.2268i | − | 1.34180i | ||||||
\(327\) | − | 7.53328i | − | 0.416591i | ||||||
\(328\) | −9.02011 | −0.498052 | ||||||||
\(329\) | − | 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 | ||||
\(333\) | −3.16223 | + | 5.19618i | −0.173289 | + | 0.284749i | ||||
\(334\) | − | 9.66372i | − | 0.528775i | ||||||
\(335\) | −3.30336 | − | 12.1560i | −0.180482 | − | 0.664154i | ||||
\(336\) | − | 0.899724i | − | 0.0490840i | ||||||
\(337\) | 15.5648 | − | 15.5648i | 0.847866 | − | 0.847866i | −0.142000 | − | 0.989867i | \(-0.545353\pi\) |
0.989867 | + | 0.142000i | \(0.0453534\pi\) | |||||||
\(338\) | − | 11.3321i | − | 0.616385i | ||||||
\(339\) | −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 | ||||
\(347\) | − | 19.7799i | − | 1.06184i | −0.847422 | − | 0.530920i | \(-0.821846\pi\) | ||
0.847422 | − | 0.530920i | \(-0.178154\pi\) | |||||||
\(348\) | −2.40635 | −0.128994 | ||||||||
\(349\) | 5.47518i | 0.293080i | 0.989205 | + | 0.146540i | \(0.0468137\pi\) | ||||
−0.989205 | + | 0.146540i | \(0.953186\pi\) | |||||||
\(350\) | −4.35347 | − | 1.13353i | −0.232703 | − | 0.0605899i | ||||
\(351\) | −0.913209 | − | 0.913209i | −0.0487435 | − | 0.0487435i | ||||
\(352\) | 2.26858 | 0.120916 | ||||||||
\(353\) | 28.1816 | 1.49995 | 0.749976 | − | 0.661465i | \(-0.230065\pi\) | ||||
0.749976 | + | 0.661465i | \(0.230065\pi\) | |||||||
\(354\) | −4.96631 | −0.263956 | ||||||||
\(355\) | −16.9889 | + | 29.6678i | −0.901679 | + | 1.57460i | ||||
\(356\) | 6.32382 | − | 6.32382i | 0.335162 | − | 0.335162i | ||||
\(357\) | 5.17071i | 0.273663i | ||||||||
\(358\) | −7.36463 | − | 7.36463i | −0.389233 | − | 0.389233i | ||||
\(359\) | 2.05043i | 0.108218i | 0.998535 | + | 0.0541089i | \(0.0172318\pi\) | ||||
−0.998535 | + | 0.0541089i | \(0.982768\pi\) | |||||||
\(360\) | −1.11117 | + | 1.94044i | −0.0585639 | + | 0.102270i | ||||
\(361\) | 14.6470i | 0.770896i | ||||||||
\(362\) | 13.9651i | 0.733988i | ||||||||
\(363\) | −4.13907 | − | 4.13907i | −0.217245 | − | 0.217245i | ||||
\(364\) | −0.821636 | + | 0.821636i | −0.0430654 | + | 0.0430654i | ||||
\(365\) | −36.1074 | + | 9.81208i | −1.88995 | + | 0.513588i | ||||
\(366\) | 2.91979 | 0.152620 | ||||||||
\(367\) | −8.13886 | − | 8.13886i | −0.424845 | − | 0.424845i | 0.462023 | − | 0.886868i | \(-0.347124\pi\) |
−0.886868 | + | 0.462023i | \(0.847124\pi\) | |||||||
\(368\) | − | 8.53431i | − | 0.444882i | ||||||
\(369\) | −9.02011 | −0.469568 | ||||||||
\(370\) | −6.56908 | − | 11.9100i | −0.341510 | − | 0.619169i | ||||
\(371\) | −8.65061 | −0.449117 | ||||||||
\(372\) | − | 8.21877i | − | 0.426124i | ||||||
\(373\) | −9.78820 | − | 9.78820i | −0.506814 | − | 0.506814i | 0.406733 | − | 0.913547i | \(-0.366668\pi\) |
−0.913547 | + | 0.406733i | \(0.866668\pi\) | |||||||
\(374\) | −13.0375 | −0.674154 | ||||||||
\(375\) | 7.98921 | + | 7.82129i | 0.412561 | + | 0.403889i | ||||
\(376\) | 0.326713 | − | 0.326713i | 0.0168489 | − | 0.0168489i | ||||
\(377\) | 2.19750 | + | 2.19750i | 0.113177 | + | 0.113177i | ||||
\(378\) | − | 0.899724i | − | 0.0462768i | ||||||
\(379\) | − | 22.6146i | − | 1.16164i | −0.814034 | − | 0.580818i | \(-0.802733\pi\) | ||
0.814034 | − | 0.580818i | \(-0.197267\pi\) | |||||||
\(380\) | 12.5166 | − | 3.40136i | 0.642089 | − | 0.174486i | ||||
\(381\) | − | 1.29596i | − | 0.0663939i | ||||||
\(382\) | 11.6459 | + | 11.6459i | 0.595854 | + | 0.595854i | ||||
\(383\) | 9.52538i | 0.486724i | 0.969936 | + | 0.243362i | \(0.0782503\pi\) | ||||
−0.969936 | + | 0.243362i | \(0.921750\pi\) | |||||||
\(384\) | 0.707107 | − | 0.707107i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | 1.19686 | + | 4.40431i | 0.0609976 | + | 0.224464i | ||||
\(386\) | 2.80664 | 0.142854 | ||||||||
\(387\) | 0.853087 | 0.0433648 | ||||||||
\(388\) | −9.28197 | −0.471220 | ||||||||
\(389\) | 7.75553 | + | 7.75553i | 0.393221 | + | 0.393221i | 0.875834 | − | 0.482613i | \(-0.160312\pi\) |
−0.482613 | + | 0.875834i | \(0.660312\pi\) | |||||||
\(390\) | 2.78676 | − | 0.757293i | 0.141113 | − | 0.0383470i | ||||
\(391\) | 49.0466i | 2.48039i | ||||||||
\(392\) | 6.19050 | 0.312667 | ||||||||
\(393\) | 8.89460i | 0.448673i | ||||||||
\(394\) | 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 | \(-0.980521\pi\) |
0.0611581 | + | 0.998128i | \(0.480521\pi\) | |||||||
\(398\) | −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 | \(0.586548\pi\) | |||||||
\(402\) | 5.63348i | 0.280973i | ||||||||
\(403\) | −7.50545 | + | 7.50545i | −0.373873 | + | 0.373873i | ||||
\(404\) | − | 1.47408i | − | 0.0733383i | ||||||
\(405\) | −1.11117 | + | 1.94044i | −0.0552146 | + | 0.0964211i | ||||
\(406\) | 2.16505i | 0.107450i | ||||||||
\(407\) | −7.17378 | + | 11.7880i | −0.355591 | + | 0.584308i | ||||
\(408\) | −4.06374 | + | 4.06374i | −0.201185 | + | 0.201185i | ||||
\(409\) | −7.16339 | + | 7.16339i | −0.354207 | + | 0.354207i | −0.861672 | − | 0.507465i | \(-0.830582\pi\) |
0.507465 | + | 0.861672i | \(0.330582\pi\) | |||||||
\(410\) | 10.0229 | − | 17.5030i | 0.494995 | − | 0.864409i | ||||
\(411\) | − | 14.7818i | − | 0.729134i | ||||||
\(412\) | −1.02968 | −0.0507289 | ||||||||
\(413\) | 4.46831i | 0.219871i | ||||||||
\(414\) | − | 8.53431i | − | 0.419438i | ||||||
\(415\) | −7.56591 | − | 27.8417i | −0.371396 | − | 1.36670i | ||||
\(416\) | −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 | \(0.197998\pi\) | ||||
−0.812698 | + | 0.582686i | \(0.802002\pi\) | |||||||
\(420\) | 1.74586 | + | 0.999748i | 0.0851892 | + | 0.0487827i | ||||
\(421\) | −12.3787 | − | 12.3787i | −0.603301 | − | 0.603301i | 0.337886 | − | 0.941187i | \(-0.390288\pi\) |
−0.941187 | + | 0.337886i | \(0.890288\pi\) | |||||||
\(422\) | 3.80993i | 0.185464i | ||||||||
\(423\) | 0.326713 | − | 0.326713i | 0.0158853 | − | 0.0158853i | ||||
\(424\) | −6.79864 | − | 6.79864i | −0.330171 | − | 0.330171i | ||||
\(425\) | 14.5433 | + | 24.7828i | 0.705454 | + | 1.20214i | ||||
\(426\) | 10.8111 | − | 10.8111i | 0.523800 | − | 0.523800i | ||||
\(427\) | − | 2.62700i | − | 0.127130i | ||||||
\(428\) | 13.8598 | + | 13.8598i | 0.669940 | + | 0.669940i | ||||
\(429\) | −2.07169 | − | 2.07169i | −0.100022 | − | 0.100022i | ||||
\(430\) | −0.947925 | + | 1.65536i | −0.0457130 | + | 0.0798286i | ||||
\(431\) | 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 | −0.589781 | − | 0.807563i | \(-0.700786\pi\) |
0.807563 | + | 0.589781i | \(0.200786\pi\) | |||||||
\(434\) | −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 | ||||
\(438\) | 16.7333 | 0.799549 | ||||||||
\(439\) | 22.7618 | − | 22.7618i | 1.08636 | − | 1.08636i | 0.0904591 | − | 0.995900i | \(-0.471167\pi\) |
0.995900 | − | 0.0904591i | \(-0.0288334\pi\) | |||||||
\(440\) | −2.52078 | + | 4.40204i | −0.120174 | + | 0.209859i | ||||
\(441\) | 6.19050 | 0.294786 | ||||||||
\(442\) | 7.42208 | 0.353032 | ||||||||
\(443\) | −18.5368 | − | 18.5368i | −0.880708 | − | 0.880708i | 0.112899 | − | 0.993606i | \(-0.463986\pi\) |
−0.993606 | + | 0.112899i | \(0.963986\pi\) | |||||||
\(444\) | 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 | 0.901950 | − | 0.431841i | \(-0.142136\pi\) |
−0.431841 | + | 0.901950i | \(0.642136\pi\) | |||||||
\(450\) | −2.53060 | − | 4.31232i | −0.119293 | − | 0.203285i | ||||
\(451\) | −20.4629 | −0.963558 | ||||||||
\(452\) | −17.2755 | −0.812573 | ||||||||
\(453\) | −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 | ||||||||
\(457\) | −6.81678 | −0.318876 | −0.159438 | − | 0.987208i | \(-0.550968\pi\) | ||||
−0.159438 | + | 0.987208i | \(0.550968\pi\) | |||||||
\(458\) | −11.3572 | −0.530686 | ||||||||
\(459\) | −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 | \(-0.0526389\pi\) | |||||||
\(462\) | − | 2.04110i | − | 0.0949605i | ||||||
\(463\) | 32.0736i | 1.49059i | 0.666737 | + | 0.745293i | \(0.267690\pi\) | ||||
−0.666737 | + | 0.745293i | \(0.732310\pi\) | |||||||
\(464\) | −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 | ||||
\(467\) | 13.7531 | 0.636416 | 0.318208 | − | 0.948021i | \(-0.396919\pi\) | ||||
0.318208 | + | 0.948021i | \(0.396919\pi\) | |||||||
\(468\) | −1.29147 | −0.0596983 | ||||||||
\(469\) | 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 | ||||
\(473\) | 1.93530 | 0.0889851 | ||||||||
\(474\) | −12.7899 | −0.587459 | ||||||||
\(475\) | −7.30799 | + | 28.0672i | −0.335314 | + | 1.28781i | ||||
\(476\) | 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 | 0.970425 | − | 0.241404i | \(-0.0776079\pi\) |
−0.241404 | + | 0.970425i | \(0.577608\pi\) | |||||||
\(480\) | 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 | ||||
\(483\) | −7.67852 | −0.349385 | ||||||||
\(484\) | −5.85354 | −0.266070 | ||||||||
\(485\) | 10.3139 | − | 18.0111i | 0.468328 | − | 0.817841i | ||||
\(486\) | 0.707107 | − | 0.707107i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | 22.5078 | 1.01992 | 0.509962 | − | 0.860197i | \(-0.329659\pi\) | ||||
0.509962 | + | 0.860197i | \(0.329659\pi\) | |||||||
\(488\) | 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 | ||||
\(495\) | −2.52078 | + | 4.40204i | −0.113301 | + | 0.197857i | ||||
\(496\) | −5.81155 | − | 5.81155i | −0.260946 | − | 0.260946i | ||||
\(497\) | −9.72702 | − | 9.72702i | −0.436316 | − | 0.436316i | ||||
\(498\) | 12.9027i | 0.578186i | ||||||||
\(499\) | 5.68409 | − | 5.68409i | 0.254455 | − | 0.254455i | −0.568339 | − | 0.822794i | \(-0.692414\pi\) |
0.822794 | + | 0.568339i | \(0.192414\pi\) | |||||||
\(500\) | 11.1797 | − | 0.118740i | 0.499972 | − | 0.00531022i | ||||
\(501\) | −6.83328 | − | 6.83328i | −0.305288 | − | 0.305288i | ||||
\(502\) | −14.7749 | + | 14.7749i | −0.659437 | + | 0.659437i | ||||
\(503\) | − | 3.69027i | − | 0.164541i | −0.996610 | − | 0.0822705i | \(-0.973783\pi\) | ||
0.996610 | − | 0.0822705i | \(-0.0262171\pi\) | |||||||
\(504\) | −0.636201 | − | 0.636201i | −0.0283386 | − | 0.0283386i | ||||
\(505\) | 2.86036 | + | 1.63796i | 0.127285 | + | 0.0728882i | ||||
\(506\) | − | 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 | \(-0.458126\pi\) | ||||
0.131172 | + | 0.991360i | \(0.458126\pi\) | |||||||
\(510\) | −3.36992 | − | 12.4009i | −0.149223 | − | 0.549123i | ||||
\(511\) | − | 15.0554i | − | 0.666010i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −5.80061 | −0.256103 | ||||||||
\(514\) | − | 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 | ||||
\(518\) | 5.31763 | − | 1.29400i | 0.233643 | − | 0.0568551i | ||||
\(519\) | 9.58209i | 0.420607i | ||||||||
\(520\) | 1.43505 | − | 2.50602i | 0.0629310 | − | 0.109896i | ||||
\(521\) | 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 | ||||
\(523\) | 17.1466i | 0.749767i | 0.927072 | + | 0.374883i | \(0.122317\pi\) | ||||
−0.927072 | + | 0.374883i | \(0.877683\pi\) | |||||||
\(524\) | 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 | ||||
\(532\) | 5.21895i | 0.226270i | ||||||||
\(533\) | 11.6492 | 0.504583 | ||||||||
\(534\) | − | 8.94323i | − | 0.387011i | ||||||
\(535\) | −42.2948 | + | 11.4935i | −1.82856 | + | 0.496907i | ||||
\(536\) | 3.98347 | + | 3.98347i | 0.172060 | + | 0.172060i | ||||
\(537\) | −10.4152 | −0.449447 | ||||||||
\(538\) | 0.689017 | 0.0297056 | ||||||||
\(539\) | 14.0436 | 0.604903 | ||||||||
\(540\) | 0.586380 | + | 2.15781i | 0.0252338 | + | 0.0928575i | ||||
\(541\) | −11.6362 | + | 11.6362i | −0.500279 | + | 0.500279i | −0.911525 | − | 0.411245i | \(-0.865094\pi\) |
0.411245 | + | 0.911525i | \(0.365094\pi\) | |||||||
\(542\) | 14.7629i | 0.634122i | ||||||||
\(543\) | 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 | ||||||||
\(547\) | 37.0105i | 1.58245i | 0.611523 | + | 0.791226i | \(0.290557\pi\) | ||||
−0.611523 | + | 0.791226i | \(0.709443\pi\) | |||||||
\(548\) | −10.4523 | − | 10.4523i | −0.446502 | − | 0.446502i | ||||
\(549\) | 2.06460 | − | 2.06460i | 0.0881150 | − | 0.0881150i | ||||
\(550\) | −5.74087 | − | 9.78285i | −0.244791 | − | 0.417142i | ||||
\(551\) | 13.9583 | 0.594643 | ||||||||
\(552\) | −6.03467 | − | 6.03467i | −0.256853 | − | 0.256853i | ||||
\(553\) | 11.5074i | 0.489343i | ||||||||
\(554\) | −32.3771 | −1.37557 | ||||||||
\(555\) | −13.0667 | − | 3.77657i | −0.554649 | − | 0.160307i | ||||
\(556\) | 14.4443 | 0.612574 | ||||||||
\(557\) | − | 5.02764i | − | 0.213028i | −0.994311 | − | 0.106514i | \(-0.966031\pi\) | ||
0.994311 | − | 0.106514i | \(-0.0339689\pi\) | |||||||
\(558\) | −5.81155 | − | 5.81155i | −0.246023 | − | 0.246023i | ||||
\(559\) | −1.10174 | −0.0465985 | ||||||||
\(560\) | 1.94144 | − | 0.527580i | 0.0820407 | − | 0.0222943i | ||||
\(561\) | −9.21892 | + | 9.21892i | −0.389223 | + | 0.389223i | ||||
\(562\) | −5.74725 | − | 5.74725i | −0.242433 | − | 0.242433i | ||||
\(563\) | 14.7235i | 0.620522i | 0.950651 | + | 0.310261i | \(0.100416\pi\) | ||||
−0.950651 | + | 0.310261i | \(0.899584\pi\) | |||||||
\(564\) | − | 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 | ||||
\(568\) | − | 15.2892i | − | 0.641521i | ||||||
\(569\) | −15.1302 | + | 15.1302i | −0.634291 | + | 0.634291i | −0.949141 | − | 0.314850i | \(-0.898046\pi\) |
0.314850 | + | 0.949141i | \(0.398046\pi\) | |||||||
\(570\) | 6.44547 | − | 11.2557i | 0.269971 | − | 0.471450i | ||||
\(571\) | −0.732604 | −0.0306585 | −0.0153293 | − | 0.999882i | \(-0.504880\pi\) | ||||
−0.0153293 | + | 0.999882i | \(0.504880\pi\) | |||||||
\(572\) | −2.92981 | −0.122502 | ||||||||
\(573\) | 16.4697 | 0.688033 | ||||||||
\(574\) | 5.73860 | + | 5.73860i | 0.239525 | + | 0.239525i | ||||
\(575\) | −36.8026 | + | 21.5969i | −1.53478 | + | 0.900653i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 13.0938 | 0.545102 | 0.272551 | − | 0.962141i | \(-0.412133\pi\) | ||||
0.272551 | + | 0.962141i | \(0.412133\pi\) | |||||||
\(578\) | − | 16.0279i | − | 0.666673i | ||||||
\(579\) | 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 | ||||
\(587\) | − | 25.6946i | − | 1.06053i | −0.847832 | − | 0.530265i | \(-0.822092\pi\) | ||
0.847832 | − | 0.530265i | \(-0.177908\pi\) | |||||||
\(588\) | 4.37734 | − | 4.37734i | 0.180519 | − | 0.180519i | ||||
\(589\) | 47.6739i | 1.96437i | ||||||||
\(590\) | −2.91214 | − | 10.7164i | −0.119891 | − | 0.441186i | ||||
\(591\) | − | 16.2893i | − | 0.670052i | ||||||
\(592\) | 5.19618 | + | 3.16223i | 0.213562 | + | 0.129967i | ||||
\(593\) | −32.7884 | + | 32.7884i | −1.34646 | + | 1.34646i | −0.456986 | + | 0.889474i | \(0.651071\pi\) |
−0.889474 | + | 0.456986i | \(0.848929\pi\) | |||||||
\(594\) | 1.60413 | − | 1.60413i | 0.0658182 | − | 0.0658182i | ||||
\(595\) | −11.1574 | + | 3.03200i | −0.457410 | + | 0.124300i | ||||
\(596\) | 19.0997i | 0.782356i | ||||||||
\(597\) | −14.6329 | −0.598885 | ||||||||
\(598\) | 11.0218i | 0.450716i | ||||||||
\(599\) | − | 32.7946i | − | 1.33995i | −0.742383 | − | 0.669975i | \(-0.766305\pi\) | ||
0.742383 | − | 0.669975i | \(-0.233695\pi\) | |||||||
\(600\) | −4.83867 | − | 1.25987i | −0.197538 | − | 0.0514339i | ||||
\(601\) | 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 | ||||||||
\(605\) | 6.50428 | − | 11.3584i | 0.264437 | − | 0.461785i | ||||
\(606\) | −1.04233 | − | 1.04233i | −0.0423419 | − | 0.0423419i | ||||
\(607\) | − | 26.7432i | − | 1.08547i | −0.839903 | − | 0.542737i | \(-0.817388\pi\) | ||
0.839903 | − | 0.542737i | \(-0.182612\pi\) | |||||||
\(608\) | −4.10165 | + | 4.10165i | −0.166344 | + | 0.166344i | ||||
\(609\) | 1.53092 | + | 1.53092i | 0.0620362 | + | 0.0620362i | ||||
\(610\) | 1.71210 | + | 6.30035i | 0.0693210 | + | 0.255094i | ||||
\(611\) | −0.421941 | + | 0.421941i | −0.0170699 | + | 0.0170699i | ||||
\(612\) | 5.74699i | 0.232308i | ||||||||
\(613\) | −23.6704 | − | 23.6704i | −0.956040 | − | 0.956040i | 0.0430339 | − | 0.999074i | \(-0.486298\pi\) |
−0.999074 | + | 0.0430339i | \(0.986298\pi\) | |||||||
\(614\) | −5.03677 | − | 5.03677i | −0.203268 | − | 0.203268i | ||||
\(615\) | −5.28921 | − | 19.4637i | −0.213281 | − | 0.784852i | ||||
\(616\) | −1.44327 | − | 1.44327i | −0.0581512 | − | 0.0581512i | ||||
\(617\) | 3.77510 | − | 3.77510i | 0.151980 | − | 0.151980i | −0.627022 | − | 0.779002i | \(-0.715726\pi\) |
0.779002 | + | 0.627022i | \(0.215726\pi\) | |||||||
\(618\) | −0.728096 | + | 0.728096i | −0.0292883 | + | 0.0292883i | ||||
\(619\) | 9.65130 | 0.387918 | 0.193959 | − | 0.981010i | \(-0.437867\pi\) | ||||
0.193959 | + | 0.981010i | \(0.437867\pi\) | |||||||
\(620\) | 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 | ||||
\(623\) | −8.04644 | −0.322374 | ||||||||
\(624\) | −0.913209 | + | 0.913209i | −0.0365576 | + | 0.0365576i | ||||
\(625\) | −12.1922 | + | 21.8255i | −0.487687 | + | 0.873019i | ||||
\(626\) | −19.5460 | −0.781217 | ||||||||
\(627\) | −13.1592 | −0.525526 | ||||||||
\(628\) | −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 | ||||
\(635\) | 2.79643 | − | 0.759923i | 0.110973 | − | 0.0301566i | ||||
\(636\) | −9.61473 | −0.381249 | ||||||||
\(637\) | −7.99485 | −0.316768 | ||||||||
\(638\) | −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 | \(0.549293\pi\) | |||||||
\(642\) | 19.6007 | 0.773580 | ||||||||
\(643\) | −39.3070 | −1.55012 | −0.775058 | − | 0.631890i | \(-0.782279\pi\) | ||||
−0.775058 | + | 0.631890i | \(0.782279\pi\) | |||||||
\(644\) | −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 | ||||
\(647\) | − | 31.8619i | − | 1.25262i | −0.779573 | − | 0.626311i | \(-0.784564\pi\) | ||
0.779573 | − | 0.626311i | \(-0.215436\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −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 | ||||
\(652\) | −24.2268 | −0.948795 | ||||||||
\(653\) | 40.2027 | 1.57325 | 0.786626 | − | 0.617430i | \(-0.211826\pi\) | ||||
0.786626 | + | 0.617430i | \(0.211826\pi\) | |||||||
\(654\) | −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 | ||||
\(658\) | −0.415710 | −0.0162061 | ||||||||
\(659\) | −22.6033 | −0.880499 | −0.440250 | − | 0.897875i | \(-0.645110\pi\) | ||||
−0.440250 | + | 0.897875i | \(0.645110\pi\) | |||||||
\(660\) | 1.33025 | + | 4.89518i | 0.0517799 | + | 0.190545i | ||||
\(661\) | 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 | ||||
\(668\) | −9.66372 | −0.373900 | ||||||||
\(669\) | −23.8893 | −0.923612 | ||||||||
\(670\) | −12.1560 | + | 3.30336i | −0.469628 | + | 0.127620i | ||||
\(671\) | 4.68371 | − | 4.68371i | 0.180813 | − | 0.180813i | ||||
\(672\) | −0.899724 | −0.0347076 | ||||||||
\(673\) | 23.9631 | − | 23.9631i | 0.923709 | − | 0.923709i | −0.0735806 | − | 0.997289i | \(-0.523443\pi\) |
0.997289 | + | 0.0735806i | \(0.0234426\pi\) | |||||||
\(674\) | −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 | \(-0.916122\pi\) |
0.260470 | + | 0.965482i | \(0.416122\pi\) | |||||||
\(678\) | −12.2157 | + | 12.2157i | −0.469139 | + | 0.469139i | ||||
\(679\) | 5.90520 | + | 5.90520i | 0.226621 | + | 0.226621i | ||||
\(680\) | −11.1517 | − | 6.38589i | −0.427647 | − | 0.244888i | ||||
\(681\) | 17.6798 | + | 17.6798i | 0.677490 | + | 0.677490i | ||||
\(682\) | −13.1840 | − | 13.1840i | −0.504841 | − | 0.504841i | ||||
\(683\) | − | 2.79715i | − | 0.107030i | −0.998567 | − | 0.0535149i | \(-0.982958\pi\) | ||
0.998567 | − | 0.0535149i | \(-0.0170425\pi\) | |||||||
\(684\) | −4.10165 | + | 4.10165i | −0.156830 | + | 0.156830i | ||||
\(685\) | 31.8965 | − | 8.66777i | 1.21870 | − | 0.331179i | ||||
\(686\) | −8.39181 | − | 8.39181i | −0.320401 | − | 0.320401i | ||||
\(687\) | −8.03073 | + | 8.03073i | −0.306392 | + | 0.306392i | ||||
\(688\) | − | 0.853087i | − | 0.0325236i | ||||||
\(689\) | 8.78026 | + | 8.78026i | 0.334501 | + | 0.334501i | ||||
\(690\) | 18.4154 | − | 5.00435i | 0.701064 | − | 0.190512i | ||||
\(691\) | 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 | ||||||||
\(695\) | −16.0501 | + | 28.0282i | −0.608813 | + | 1.06317i | ||||
\(696\) | 2.40635i | 0.0912125i | ||||||||
\(697\) | − | 51.8385i | − | 1.96352i | ||||||
\(698\) | 5.47518 | 0.207239 | ||||||||
\(699\) | − | 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 | ||||
\(703\) | −8.34254 | − | 34.2833i | −0.314645 | − | 1.29302i | ||||
\(704\) | − | 2.26858i | − | 0.0855004i | ||||||
\(705\) | 0.896564 | + | 0.513408i | 0.0337665 | + | 0.0193361i | ||||
\(706\) | − | 28.1816i | − | 1.06063i | ||||||
\(707\) | −0.937812 | + | 0.937812i | −0.0352701 | + | 0.0352701i | ||||
\(708\) | 4.96631i | 0.186645i | ||||||||
\(709\) | −6.08101 | − | 6.08101i | −0.228377 | − | 0.228377i | 0.583637 | − | 0.812014i | \(-0.301629\pi\) |
−0.812014 | + | 0.583637i | \(0.801629\pi\) | |||||||
\(710\) | 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 | ||||
\(717\) | 4.19821i | 0.156785i | ||||||||
\(718\) | 2.05043 | 0.0765215 | ||||||||
\(719\) | 37.1763i | 1.38644i | 0.720724 | + | 0.693222i | \(0.243809\pi\) | ||||
−0.720724 | + | 0.693222i | \(0.756191\pi\) | |||||||
\(720\) | 1.94044 | + | 1.11117i | 0.0723158 | + | 0.0414109i | ||||
\(721\) | 0.655086 | + | 0.655086i | 0.0243967 | + | 0.0243967i | ||||
\(722\) | 14.6470 | 0.545106 | ||||||||
\(723\) | 8.14088 | 0.302762 | ||||||||
\(724\) | 13.9651 | 0.519008 | ||||||||
\(725\) | 11.6435 | + | 3.03168i | 0.432430 | + | 0.112594i | ||||
\(726\) | −4.13907 | + | 4.13907i | −0.153615 | + | 0.153615i | ||||
\(727\) | − | 10.8041i | − | 0.400701i | −0.979724 | − | 0.200350i | \(-0.935792\pi\) | ||
0.979724 | − | 0.200350i | \(-0.0642081\pi\) | |||||||
\(728\) | 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 | ||||||||
\(732\) | − | 2.91979i | − | 0.107918i | ||||||
\(733\) | −2.31409 | − | 2.31409i | −0.0854728 | − | 0.0854728i | 0.663078 | − | 0.748551i | \(-0.269250\pi\) |
−0.748551 | + | 0.663078i | \(0.769250\pi\) | |||||||
\(734\) | −8.13886 | + | 8.13886i | −0.300411 | + | 0.300411i | ||||
\(735\) | 3.62998 | + | 13.3579i | 0.133894 | + | 0.492715i | ||||
\(736\) | −8.53431 | −0.314579 | ||||||||
\(737\) | 9.03684 | + | 9.03684i | 0.332876 | + | 0.332876i | ||||
\(738\) | 9.02011i | 0.332035i | ||||||||
\(739\) | −3.59606 | −0.132283 | −0.0661416 | − | 0.997810i | \(-0.521069\pi\) | ||||
−0.0661416 | + | 0.997810i | \(0.521069\pi\) | |||||||
\(740\) | −11.9100 | + | 6.56908i | −0.437819 | + | 0.241484i | ||||
\(741\) | 7.49132 | 0.275201 | ||||||||
\(742\) | 8.65061i | 0.317574i | ||||||||
\(743\) | 7.78930 | + | 7.78930i | 0.285762 | + | 0.285762i | 0.835402 | − | 0.549640i | \(-0.185235\pi\) |
−0.549640 | + | 0.835402i | \(0.685235\pi\) | |||||||
\(744\) | −8.21877 | −0.301315 | ||||||||
\(745\) | −37.0619 | − | 21.2231i | −1.35784 | − | 0.777554i | ||||
\(746\) | −9.78820 | + | 9.78820i | −0.358371 | + | 0.358371i | ||||
\(747\) | 9.12362 | + | 9.12362i | 0.333816 | + | 0.333816i | ||||
\(748\) | 13.0375i | 0.476699i | ||||||||
\(749\) | − | 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 | ||||
\(753\) | 20.8949i | 0.761452i | ||||||||
\(754\) | 2.19750 | − | 2.19750i | 0.0800283 | − | 0.0800283i | ||||
\(755\) | −6.64625 | − | 3.80591i | −0.241882 | − | 0.138511i | ||||
\(756\) | −0.899724 | −0.0327227 | ||||||||
\(757\) | 2.85691 | 0.103836 | 0.0519182 | − | 0.998651i | \(-0.483467\pi\) | ||||
0.0519182 | + | 0.998651i | \(0.483467\pi\) | |||||||
\(758\) | −22.6146 | −0.821400 | ||||||||
\(759\) | −13.6901 | − | 13.6901i | −0.496921 | − | 0.496921i | ||||
\(760\) | −3.40136 | − | 12.5166i | −0.123380 | − | 0.454026i | ||||
\(761\) | − | 3.11943i | − | 0.113079i | −0.998400 | − | 0.0565396i | \(-0.981993\pi\) | ||
0.998400 | − | 0.0565396i | \(-0.0180067\pi\) | |||||||
\(762\) | −1.29596 | −0.0469476 | ||||||||
\(763\) | 6.77787i | 0.245376i | ||||||||
\(764\) | 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 | −0.176360 | − | 0.984326i | \(-0.556432\pi\) |
0.984326 | + | 0.176360i | \(0.0564322\pi\) | |||||||
\(770\) | 4.40431 | − | 1.19686i | 0.158720 | − | 0.0431318i | ||||
\(771\) | −1.27298 | − | 1.27298i | −0.0458453 | − | 0.0458453i | ||||
\(772\) | − | 2.80664i | − | 0.101013i | ||||||
\(773\) | −1.90608 | + | 1.90608i | −0.0685571 | + | 0.0685571i | −0.740554 | − | 0.671997i | \(-0.765437\pi\) |
0.671997 | + | 0.740554i | \(0.265437\pi\) | |||||||
\(774\) | − | 0.853087i | − | 0.0306636i | ||||||
\(775\) | −10.3546 | + | 39.7679i | −0.371947 | + | 1.42851i | ||||
\(776\) | 9.28197i | 0.333203i | ||||||||
\(777\) | 2.84514 | − | 4.67513i | 0.102069 | − | 0.167719i | ||||
\(778\) | 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 | ||||||
\(782\) | 49.0466 | 1.75390 | ||||||||
\(783\) | 2.40635i | 0.0859960i | ||||||||
\(784\) | − | 6.19050i | − | 0.221089i | ||||||
\(785\) | 36.9454 | − | 10.0398i | 1.31864 | − | 0.358336i | ||||
\(786\) | 8.89460 | 0.317260 | ||||||||
\(787\) | −24.9409 | − | 24.9409i | −0.889045 | − | 0.889045i | 0.105386 | − | 0.994431i | \(-0.466392\pi\) |
−0.994431 | + | 0.105386i | \(0.966392\pi\) | |||||||
\(788\) | −11.5183 | − | 11.5183i | −0.410322 | − | 0.410322i | ||||
\(789\) | 13.0942i | 0.466165i | ||||||||
\(790\) | −7.49973 | − | 27.5982i | −0.266829 | − | 0.981900i | ||||
\(791\) | 10.9907 | + | 10.9907i | 0.390785 | + | 0.390785i | ||||
\(792\) | − | 2.26858i | − | 0.0806106i | ||||||
\(793\) | −2.66637 | + | 2.66637i | −0.0946857 | + | 0.0946857i | ||||
\(794\) | 18.6690 | + | 18.6690i | 0.662538 | + | 0.662538i | ||||
\(795\) | 10.6836 | − | 18.6568i | 0.378909 | − | 0.661688i | ||||
\(796\) | −10.3470 | + | 10.3470i | −0.366740 | + | 0.366740i | ||||
\(797\) | − | 33.5854i | − | 1.18966i | −0.803853 | − | 0.594828i | \(-0.797220\pi\) | ||
0.803853 | − | 0.594828i | \(-0.202780\pi\) | |||||||
\(798\) | 3.69035 | + | 3.69035i | 0.130637 | + | 0.130637i | ||||
\(799\) | 1.87762 | + | 1.87762i | 0.0664253 | + | 0.0664253i | ||||
\(800\) | −4.31232 | + | 2.53060i | −0.152463 | + | 0.0894701i | ||||
\(801\) | −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 | ||||
\(808\) | −1.47408 | −0.0518580 | ||||||||
\(809\) | −4.59489 | + | 4.59489i | −0.161548 | + | 0.161548i | −0.783252 | − | 0.621704i | \(-0.786441\pi\) |
0.621704 | + | 0.783252i | \(0.286441\pi\) | |||||||
\(810\) | 1.94044 | + | 1.11117i | 0.0681800 | + | 0.0390426i | ||||
\(811\) | −26.4363 | −0.928304 | −0.464152 | − | 0.885756i | \(-0.653641\pi\) | ||||
−0.464152 | + | 0.885756i | \(0.653641\pi\) | |||||||
\(812\) | 2.16505 | 0.0759785 | ||||||||
\(813\) | 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 | ||||
\(820\) | −17.5030 | − | 10.0229i | −0.611230 | − | 0.350014i | ||||
\(821\) | 38.5813 | 1.34650 | 0.673248 | − | 0.739417i | \(-0.264899\pi\) | ||||
0.673248 | + | 0.739417i | \(0.264899\pi\) | |||||||
\(822\) | −14.7818 | −0.515576 | ||||||||
\(823\) | 9.95130 | − | 9.95130i | 0.346881 | − | 0.346881i | −0.512066 | − | 0.858946i | \(-0.671120\pi\) |
0.858946 | + | 0.512066i | \(0.171120\pi\) | |||||||
\(824\) | 1.02968i | 0.0358707i | ||||||||
\(825\) | −10.9769 | − | 2.85811i | −0.382167 | − | 0.0995067i | ||||
\(826\) | 4.46831 | 0.155472 | ||||||||
\(827\) | 3.10451 | 0.107954 | 0.0539772 | − | 0.998542i | \(-0.482810\pi\) | ||||
0.0539772 | + | 0.998542i | \(0.482810\pi\) | |||||||
\(828\) | −8.53431 | −0.296588 | ||||||||
\(829\) | −8.47013 | + | 8.47013i | −0.294180 | + | 0.294180i | −0.838729 | − | 0.544549i | \(-0.816701\pi\) |
0.544549 | + | 0.838729i | \(0.316701\pi\) | |||||||
\(830\) | −27.8417 | + | 7.56591i | −0.966400 | + | 0.262616i | ||||
\(831\) | −22.8940 | + | 22.8940i | −0.794186 | + | 0.794186i | ||||
\(832\) | 1.29147i | 0.0447737i | ||||||||
\(833\) | 35.5767i | 1.23266i | ||||||||
\(834\) | 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 | ||||
\(837\) | −8.21877 | −0.284082 | ||||||||
\(838\) | 23.8546 | 0.824042 | ||||||||
\(839\) | 6.41357 | 0.221421 | 0.110711 | − | 0.993853i | \(-0.464687\pi\) | ||||
0.110711 | + | 0.993853i | \(0.464687\pi\) | |||||||
\(840\) | 0.999748 | − | 1.74586i | 0.0344946 | − | 0.0602378i | ||||
\(841\) | 23.2095i | 0.800327i | ||||||||
\(842\) | −12.3787 | + | 12.3787i | −0.426598 | + | 0.426598i | ||||
\(843\) | −8.12784 | −0.279938 | ||||||||
\(844\) | 3.80993 | 0.131143 | ||||||||
\(845\) | 12.5919 | − | 21.9892i | 0.433175 | − | 0.756453i | ||||
\(846\) | −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 | ||||
\(853\) | −46.7208 | −1.59969 | −0.799845 | − | 0.600207i | \(-0.795085\pi\) | ||||
−0.799845 | + | 0.600207i | \(0.795085\pi\) | |||||||
\(854\) | −2.62700 | −0.0898941 | ||||||||
\(855\) | −3.40136 | − | 12.5166i | −0.116324 | − | 0.428060i | ||||
\(856\) | 13.8598 | − | 13.8598i | 0.473719 | − | 0.473719i | ||||
\(857\) | −36.8302 | −1.25810 | −0.629048 | − | 0.777367i | \(-0.716555\pi\) | ||||
−0.629048 | + | 0.777367i | \(0.716555\pi\) | |||||||
\(858\) | −2.07169 | + | 2.07169i | −0.0707263 | + | 0.0707263i | ||||
\(859\) | 33.3859 | + | 33.3859i | 1.13911 | + | 1.13911i | 0.988610 | + | 0.150502i | \(0.0480891\pi\) |
0.150502 | + | 0.988610i | \(0.451911\pi\) | |||||||
\(860\) | 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 | −0.732140 | − | 0.681154i | \(-0.761478\pi\) |
0.681154 | + | 0.732140i | \(0.261478\pi\) | |||||||
\(864\) | −0.707107 | − | 0.707107i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | −20.6764 | + | 5.61875i | −0.703018 | + | 0.191043i | ||||
\(866\) | −4.53175 | − | 4.53175i | −0.153995 | − | 0.153995i | ||||
\(867\) | −11.3334 | − | 11.3334i | −0.384904 | − | 0.384904i | ||||
\(868\) | 7.39463i | 0.250990i | ||||||||
\(869\) | −20.5166 | + | 20.5166i | −0.695980 | + | 0.695980i | ||||
\(870\) | −4.66938 | − | 2.67387i | −0.158307 | − | 0.0906527i | ||||
\(871\) | −5.14455 | − | 5.14455i | −0.174316 | − | 0.174316i | ||||
\(872\) | −5.32683 | + | 5.32683i | −0.180389 | + | 0.180389i | ||||
\(873\) | 9.28197i | 0.314147i | ||||||||
\(874\) | 35.0047 | + | 35.0047i | 1.18405 | + | 1.18405i | ||||
\(875\) | −7.18809 | − | 7.03700i | −0.243002 | − | 0.237894i | ||||
\(876\) | − | 16.7333i | − | 0.565366i | ||||||
\(877\) | 8.78482 | + | 8.78482i | 0.296642 | + | 0.296642i | 0.839697 | − | 0.543055i | \(-0.182732\pi\) |
−0.543055 | + | 0.839697i | \(0.682732\pi\) | |||||||
\(878\) | −22.7618 | − | 22.7618i | −0.768172 | − | 0.768172i | ||||
\(879\) | 31.1391 | 1.05030 | ||||||||
\(880\) | 4.40204 | + | 2.52078i | 0.148393 | + | 0.0849756i | ||||
\(881\) | − | 19.0001i | − | 0.640128i | −0.947396 | − | 0.320064i | \(-0.896296\pi\) | ||
0.947396 | − | 0.320064i | \(-0.103704\pi\) | |||||||
\(882\) | − | 6.19050i | − | 0.208445i | ||||||
\(883\) | −10.1981 | −0.343193 | −0.171596 | − | 0.985167i | \(-0.554892\pi\) | ||||
−0.171596 | + | 0.985167i | \(0.554892\pi\) | |||||||
\(884\) | − | 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 | \(-0.657173\pi\) |
0.880550 | + | 0.473953i | \(0.157173\pi\) | |||||||
\(888\) | 5.91029 | − | 1.43822i | 0.198336 | − | 0.0482635i | ||||
\(889\) | 1.16600i | 0.0391065i | ||||||||
\(890\) | 19.2978 | − | 5.24413i | 0.646864 | − | 0.175784i | ||||
\(891\) | − | 2.26858i | − | 0.0760004i | ||||||
\(892\) | −16.8923 | + | 16.8923i | −0.565595 | + | 0.565595i | ||||
\(893\) | 2.68012i | 0.0896869i | ||||||||
\(894\) | 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 | ||||
\(902\) | 20.4629i | 0.681338i | ||||||||
\(903\) | −0.767543 | −0.0255422 | ||||||||
\(904\) | 17.2755i | 0.574576i | ||||||||
\(905\) | −15.5176 | + | 27.0984i | −0.515822 | + | 0.900780i | ||||
\(906\) | 2.42193 | + | 2.42193i | 0.0804634 | + | 0.0804634i | ||||
\(907\) | 0.471868 | 0.0156681 | 0.00783407 | − | 0.999969i | \(-0.497506\pi\) | ||||
0.00783407 | + | 0.999969i | \(0.497506\pi\) | |||||||
\(908\) | 25.0030 | 0.829752 | ||||||||
\(909\) | −1.47408 | −0.0488922 | ||||||||
\(910\) | −2.50731 | + | 0.681355i | −0.0831166 | + | 0.0225867i | ||||
\(911\) | 18.6659 | − | 18.6659i | 0.618430 | − | 0.618430i | −0.326698 | − | 0.945129i | \(-0.605936\pi\) |
0.945129 | + | 0.326698i | \(0.105936\pi\) | |||||||
\(912\) | 5.80061i | 0.192077i | ||||||||
\(913\) | 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 | ||||||||
\(917\) | − | 8.00269i | − | 0.264272i | ||||||
\(918\) | 4.06374 | + | 4.06374i | 0.134123 | + | 0.134123i | ||||
\(919\) | 24.0718 | − | 24.0718i | 0.794054 | − | 0.794054i | −0.188096 | − | 0.982151i | \(-0.560232\pi\) |
0.982151 | + | 0.188096i | \(0.0602317\pi\) | |||||||
\(920\) | 9.48308 | − | 16.5603i | 0.312648 | − | 0.545977i | ||||
\(921\) | −7.12307 | −0.234713 | ||||||||
\(922\) | −24.7125 | − | 24.7125i | −0.813862 | − | 0.813862i | ||||
\(923\) | 19.7456i | 0.649934i | ||||||||
\(924\) | −2.04110 | −0.0671472 | ||||||||
\(925\) | 0.487112 | − | 30.4099i | 0.0160161 | − | 0.999872i | ||||
\(926\) | 32.0736 | 1.05400 | ||||||||
\(927\) | 1.02968i | 0.0338192i | ||||||||
\(928\) | 1.70155 | + | 1.70155i | 0.0558560 | + | 0.0558560i | ||||
\(929\) | −8.12677 | −0.266631 | −0.133315 | − | 0.991074i | \(-0.542562\pi\) | ||||
−0.133315 | + | 0.991074i | \(0.542562\pi\) | |||||||
\(930\) | 9.13247 | − | 15.9480i | 0.299465 | − | 0.522956i | ||||
\(931\) | −25.3912 | + | 25.3912i | −0.832164 | + | 0.832164i | ||||
\(932\) | −4.77274 | − | 4.77274i | −0.156336 | − | 0.156336i | ||||
\(933\) | − | 5.45254i | − | 0.178508i | ||||||
\(934\) | − | 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 | 0.264793 | − | 0.964305i | \(-0.414696\pi\) |
−0.964305 | + | 0.264793i | \(0.914696\pi\) | |||||||
\(938\) | − | 5.06858i | − | 0.165495i | ||||||
\(939\) | −13.8211 | + | 13.8211i | −0.451036 | + | 0.451036i | ||||
\(940\) | 0.997001 | − | 0.270932i | 0.0325186 | − | 0.00883683i | ||||
\(941\) | −6.32110 | −0.206062 | −0.103031 | − | 0.994678i | \(-0.532854\pi\) | ||||
−0.103031 | + | 0.994678i | \(0.532854\pi\) | |||||||
\(942\) | −17.1217 | −0.557854 | ||||||||
\(943\) | 76.9804 | 2.50683 | ||||||||
\(944\) | 3.51171 | + | 3.51171i | 0.114296 | + | 0.114296i | ||||
\(945\) | 0.999748 | − | 1.74586i | 0.0325218 | − | 0.0567928i | ||||
\(946\) | − | 1.93530i | − | 0.0629219i | ||||||
\(947\) | 29.6137 | 0.962316 | 0.481158 | − | 0.876634i | \(-0.340216\pi\) | ||||
0.481158 | + | 0.876634i | \(0.340216\pi\) | |||||||
\(948\) | 12.7899i | 0.415396i | ||||||||
\(949\) | −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 | \(-0.0542884\pi\) |
−0.169727 | + | 0.985491i | \(0.554288\pi\) | |||||||
\(954\) | −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 | ||||
\(957\) | 5.45901i | 0.176465i | ||||||||
\(958\) | 15.9554 | − | 15.9554i | 0.515496 | − | 0.515496i | ||||
\(959\) | 13.2996i | 0.429466i | ||||||||
\(960\) | 2.15781 | − | 0.586380i | 0.0696431 | − | 0.0189253i | ||||
\(961\) | 36.5482i | 1.17898i | ||||||||
\(962\) | −6.71072 | − | 4.08393i | −0.216362 | − | 0.131671i | ||||
\(963\) | 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 | ||||||||
\(967\) | 12.3262 | 0.396385 | 0.198192 | − | 0.980163i | \(-0.436493\pi\) | ||||
0.198192 | + | 0.980163i | \(0.436493\pi\) | |||||||
\(968\) | 5.85354i | 0.188140i | ||||||||
\(969\) | − | 33.3360i | − | 1.07091i | ||||||
\(970\) | −18.0111 | − | 10.3139i | −0.578301 | − | 0.331158i | ||||
\(971\) | 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 | ||||||
\(975\) | 6.24901 | + | 1.62708i | 0.200128 | + | 0.0521084i | ||||
\(976\) | −2.06460 | − | 2.06460i | −0.0660862 | − | 0.0660862i | ||||
\(977\) | 42.8715i | 1.37158i | 0.727799 | + | 0.685790i | \(0.240543\pi\) | ||||
−0.727799 | + | 0.685790i | \(0.759457\pi\) | |||||||
\(978\) | −17.1309 | + | 17.1309i | −0.547787 | + | 0.547787i | ||||
\(979\) | −14.3461 | − | 14.3461i | −0.458503 | − | 0.458503i | ||||
\(980\) | 12.0123 | + | 6.87870i | 0.383718 | + | 0.219732i | ||||
\(981\) | −5.32683 | + | 5.32683i | −0.170073 | + | 0.170073i | ||||
\(982\) | − | 31.0223i | − | 0.989961i | ||||||
\(983\) | 23.7970 | + | 23.7970i | 0.759006 | + | 0.759006i | 0.976141 | − | 0.217136i | \(-0.0696714\pi\) |
−0.217136 | + | 0.976141i | \(0.569671\pi\) | |||||||
\(984\) | 6.37818 | + | 6.37818i | 0.203329 | + | 0.203329i | ||||
\(985\) | 35.1493 | − | 9.55172i | 1.11995 | − | 0.304343i | ||||
\(986\) | −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 | ||||
\(993\) | 4.60678 | 0.146192 | ||||||||
\(994\) | −9.72702 | + | 9.72702i | −0.308522 | + | 0.308522i | ||||
\(995\) | −8.58044 | − | 31.5751i | −0.272018 | − | 1.00100i | ||||
\(996\) | 12.9027 | 0.408839 | ||||||||
\(997\) | 27.5415 | 0.872248 | 0.436124 | − | 0.899887i | \(-0.356351\pi\) | ||||
0.436124 | + | 0.899887i | \(0.356351\pi\) | |||||||
\(998\) | −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.l.a.697.4 | yes | 36 | |
5.3 | odd | 4 | 1110.2.o.a.253.15 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.o.a.487.15 | yes | 36 | ||
185.43 | even | 4 | inner | 1110.2.l.a.43.4 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.4 | ✓ | 36 | 185.43 | even | 4 | inner | |
1110.2.l.a.697.4 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.253.15 | yes | 36 | 5.3 | odd | 4 | ||
1110.2.o.a.487.15 | yes | 36 | 37.6 | odd | 4 |