Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(573,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.573");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 573.5 | ||
Character | \(\chi\) | \(=\) | 770.573 |
Dual form | 770.2.l.c.727.5 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −0.0715208 | + | 0.0715208i | −0.0412925 | + | 0.0412925i | −0.727452 | − | 0.686159i | \(-0.759295\pi\) |
0.686159 | + | 0.727452i | \(0.259295\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.95282 | − | 1.08927i | 0.873327 | − | 0.487135i | ||||
\(6\) | − | 0.101146i | − | 0.0412925i | ||||||
\(7\) | 2.63480 | − | 0.240478i | 0.995861 | − | 0.0908922i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 2.98977i | 0.996590i | ||||||||
\(10\) | −0.610623 | + | 2.15108i | −0.193096 | + | 0.680231i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0.0715208 | + | 0.0715208i | 0.0206463 | + | 0.0206463i | ||||
\(13\) | −2.32898 | + | 2.32898i | −0.645944 | + | 0.645944i | −0.952010 | − | 0.306066i | \(-0.900987\pi\) |
0.306066 | + | 0.952010i | \(0.400987\pi\) | |||||||
\(14\) | −1.69304 | + | 2.03313i | −0.452484 | + | 0.543376i | ||||
\(15\) | −0.0617619 | + | 0.217572i | −0.0159468 | + | 0.0561769i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.41391 | + | 2.41391i | 0.585460 | + | 0.585460i | 0.936398 | − | 0.350939i | \(-0.114137\pi\) |
−0.350939 | + | 0.936398i | \(0.614137\pi\) | |||||||
\(18\) | −2.11409 | − | 2.11409i | −0.498295 | − | 0.498295i | ||||
\(19\) | 2.20465 | 0.505780 | 0.252890 | − | 0.967495i | \(-0.418619\pi\) | ||||
0.252890 | + | 0.967495i | \(0.418619\pi\) | |||||||
\(20\) | −1.08927 | − | 1.95282i | −0.243567 | − | 0.436663i | ||||
\(21\) | −0.171244 | + | 0.205642i | −0.0373684 | + | 0.0448748i | ||||
\(22\) | 0.707107 | − | 0.707107i | 0.150756 | − | 0.150756i | ||||
\(23\) | 1.77734 | + | 1.77734i | 0.370601 | + | 0.370601i | 0.867696 | − | 0.497095i | \(-0.165600\pi\) |
−0.497095 | + | 0.867696i | \(0.665600\pi\) | |||||||
\(24\) | −0.101146 | −0.0206463 | ||||||||
\(25\) | 2.62700 | − | 4.25428i | 0.525399 | − | 0.850856i | ||||
\(26\) | − | 3.29368i | − | 0.645944i | ||||||
\(27\) | −0.428393 | − | 0.428393i | −0.0824442 | − | 0.0824442i | ||||
\(28\) | −0.240478 | − | 2.63480i | −0.0454461 | − | 0.497930i | ||||
\(29\) | − | 5.97677i | − | 1.10986i | −0.831898 | − | 0.554929i | \(-0.812745\pi\) | ||
0.831898 | − | 0.554929i | \(-0.187255\pi\) | |||||||
\(30\) | −0.110175 | − | 0.197519i | −0.0201150 | − | 0.0360619i | ||||
\(31\) | 4.99705i | 0.897497i | 0.893658 | + | 0.448748i | \(0.148130\pi\) | ||||
−0.893658 | + | 0.448748i | \(0.851870\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0.0715208 | − | 0.0715208i | 0.0124502 | − | 0.0124502i | ||||
\(34\) | −3.41379 | −0.585460 | ||||||||
\(35\) | 4.88334 | − | 3.33961i | 0.825435 | − | 0.564497i | ||||
\(36\) | 2.98977 | 0.498295 | ||||||||
\(37\) | 6.33137 | − | 6.33137i | 1.04087 | − | 1.04087i | 0.0417425 | − | 0.999128i | \(-0.486709\pi\) |
0.999128 | − | 0.0417425i | \(-0.0132909\pi\) | |||||||
\(38\) | −1.55892 | + | 1.55892i | −0.252890 | + | 0.252890i | ||||
\(39\) | − | 0.333142i | − | 0.0533453i | ||||||
\(40\) | 2.15108 | + | 0.610623i | 0.340115 | + | 0.0965480i | ||||
\(41\) | 8.47999i | 1.32435i | 0.749348 | + | 0.662176i | \(0.230367\pi\) | ||||
−0.749348 | + | 0.662176i | \(0.769633\pi\) | |||||||
\(42\) | −0.0243233 | − | 0.266498i | −0.00375317 | − | 0.0411216i | ||||
\(43\) | −1.16231 | − | 1.16231i | −0.177250 | − | 0.177250i | 0.612906 | − | 0.790156i | \(-0.290000\pi\) |
−0.790156 | + | 0.612906i | \(0.790000\pi\) | |||||||
\(44\) | 1.00000i | 0.150756i | ||||||||
\(45\) | 3.25666 | + | 5.83848i | 0.485474 | + | 0.870349i | ||||
\(46\) | −2.51354 | −0.370601 | ||||||||
\(47\) | −4.80004 | − | 4.80004i | −0.700158 | − | 0.700158i | 0.264286 | − | 0.964444i | \(-0.414864\pi\) |
−0.964444 | + | 0.264286i | \(0.914864\pi\) | |||||||
\(48\) | 0.0715208 | − | 0.0715208i | 0.0103231 | − | 0.0103231i | ||||
\(49\) | 6.88434 | − | 1.26722i | 0.983477 | − | 0.181032i | ||||
\(50\) | 1.15066 | + | 4.86580i | 0.162728 | + | 0.688128i | ||||
\(51\) | −0.345290 | −0.0483502 | ||||||||
\(52\) | 2.32898 | + | 2.32898i | 0.322972 | + | 0.322972i | ||||
\(53\) | 3.59950 | + | 3.59950i | 0.494430 | + | 0.494430i | 0.909699 | − | 0.415269i | \(-0.136312\pi\) |
−0.415269 | + | 0.909699i | \(0.636312\pi\) | |||||||
\(54\) | 0.605839 | 0.0824442 | ||||||||
\(55\) | −1.95282 | + | 1.08927i | −0.263318 | + | 0.146877i | ||||
\(56\) | 2.03313 | + | 1.69304i | 0.271688 | + | 0.226242i | ||||
\(57\) | −0.157678 | + | 0.157678i | −0.0208850 | + | 0.0208850i | ||||
\(58\) | 4.22621 | + | 4.22621i | 0.554929 | + | 0.554929i | ||||
\(59\) | 3.32581 | 0.432984 | 0.216492 | − | 0.976284i | \(-0.430538\pi\) | ||||
0.216492 | + | 0.976284i | \(0.430538\pi\) | |||||||
\(60\) | 0.217572 | + | 0.0617619i | 0.0280885 | + | 0.00797342i | ||||
\(61\) | 11.2082i | 1.43507i | 0.696524 | + | 0.717534i | \(0.254729\pi\) | ||||
−0.696524 | + | 0.717534i | \(0.745271\pi\) | |||||||
\(62\) | −3.53345 | − | 3.53345i | −0.448748 | − | 0.448748i | ||||
\(63\) | 0.718974 | + | 7.87744i | 0.0905822 | + | 0.992465i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −2.01120 | + | 7.08497i | −0.249458 | + | 0.878782i | ||||
\(66\) | 0.101146i | 0.0124502i | ||||||||
\(67\) | 9.53332 | − | 9.53332i | 1.16468 | − | 1.16468i | 0.181242 | − | 0.983439i | \(-0.441988\pi\) |
0.983439 | − | 0.181242i | \(-0.0580116\pi\) | |||||||
\(68\) | 2.41391 | − | 2.41391i | 0.292730 | − | 0.292730i | ||||
\(69\) | −0.254233 | −0.0306061 | ||||||||
\(70\) | −1.09158 | + | 5.81450i | −0.130469 | + | 0.694966i | ||||
\(71\) | −8.78250 | −1.04229 | −0.521146 | − | 0.853468i | \(-0.674495\pi\) | ||||
−0.521146 | + | 0.853468i | \(0.674495\pi\) | |||||||
\(72\) | −2.11409 | + | 2.11409i | −0.249147 | + | 0.249147i | ||||
\(73\) | −2.07792 | + | 2.07792i | −0.243202 | + | 0.243202i | −0.818174 | − | 0.574971i | \(-0.805013\pi\) |
0.574971 | + | 0.818174i | \(0.305013\pi\) | |||||||
\(74\) | 8.95391i | 1.04087i | ||||||||
\(75\) | 0.116384 | + | 0.492154i | 0.0134389 | + | 0.0568291i | ||||
\(76\) | − | 2.20465i | − | 0.252890i | ||||||
\(77\) | −2.63480 | + | 0.240478i | −0.300263 | + | 0.0274050i | ||||
\(78\) | 0.235567 | + | 0.235567i | 0.0266727 | + | 0.0266727i | ||||
\(79\) | 2.87628i | 0.323607i | 0.986823 | + | 0.161803i | \(0.0517310\pi\) | ||||
−0.986823 | + | 0.161803i | \(0.948269\pi\) | |||||||
\(80\) | −1.95282 | + | 1.08927i | −0.218332 | + | 0.121784i | ||||
\(81\) | −8.90803 | −0.989781 | ||||||||
\(82\) | −5.99626 | − | 5.99626i | −0.662176 | − | 0.662176i | ||||
\(83\) | 3.19625 | − | 3.19625i | 0.350834 | − | 0.350834i | −0.509586 | − | 0.860420i | \(-0.670201\pi\) |
0.860420 | + | 0.509586i | \(0.170201\pi\) | |||||||
\(84\) | 0.205642 | + | 0.171244i | 0.0224374 | + | 0.0186842i | ||||
\(85\) | 7.34333 | + | 2.08454i | 0.796496 | + | 0.226100i | ||||
\(86\) | 1.64375 | 0.177250 | ||||||||
\(87\) | 0.427463 | + | 0.427463i | 0.0458289 | + | 0.0458289i | ||||
\(88\) | −0.707107 | − | 0.707107i | −0.0753778 | − | 0.0753778i | ||||
\(89\) | −10.6987 | −1.13406 | −0.567029 | − | 0.823698i | \(-0.691907\pi\) | ||||
−0.567029 | + | 0.823698i | \(0.691907\pi\) | |||||||
\(90\) | −6.43123 | − | 1.82562i | −0.677911 | − | 0.192438i | ||||
\(91\) | −5.57634 | + | 6.69648i | −0.584559 | + | 0.701982i | ||||
\(92\) | 1.77734 | − | 1.77734i | 0.185300 | − | 0.185300i | ||||
\(93\) | −0.357393 | − | 0.357393i | −0.0370599 | − | 0.0370599i | ||||
\(94\) | 6.78828 | 0.700158 | ||||||||
\(95\) | 4.30527 | − | 2.40145i | 0.441712 | − | 0.246383i | ||||
\(96\) | 0.101146i | 0.0103231i | ||||||||
\(97\) | −3.29793 | − | 3.29793i | −0.334854 | − | 0.334854i | 0.519572 | − | 0.854426i | \(-0.326091\pi\) |
−0.854426 | + | 0.519572i | \(0.826091\pi\) | |||||||
\(98\) | −3.97190 | + | 5.76403i | −0.401223 | + | 0.582255i | ||||
\(99\) | − | 2.98977i | − | 0.300483i | ||||||
\(100\) | −4.25428 | − | 2.62700i | −0.425428 | − | 0.262700i | ||||
\(101\) | 10.9777i | 1.09232i | 0.837680 | + | 0.546162i | \(0.183912\pi\) | ||||
−0.837680 | + | 0.546162i | \(0.816088\pi\) | |||||||
\(102\) | 0.244157 | − | 0.244157i | 0.0241751 | − | 0.0241751i | ||||
\(103\) | 11.1782 | − | 11.1782i | 1.10142 | − | 1.10142i | 0.107181 | − | 0.994240i | \(-0.465817\pi\) |
0.994240 | − | 0.107181i | \(-0.0341825\pi\) | |||||||
\(104\) | −3.29368 | −0.322972 | ||||||||
\(105\) | −0.110409 | + | 0.588112i | −0.0107748 | + | 0.0573938i | ||||
\(106\) | −5.09047 | −0.494430 | ||||||||
\(107\) | 6.05699 | − | 6.05699i | 0.585551 | − | 0.585551i | −0.350872 | − | 0.936423i | \(-0.614115\pi\) |
0.936423 | + | 0.350872i | \(0.114115\pi\) | |||||||
\(108\) | −0.428393 | + | 0.428393i | −0.0412221 | + | 0.0412221i | ||||
\(109\) | 8.73699i | 0.836852i | 0.908251 | + | 0.418426i | \(0.137418\pi\) | ||||
−0.908251 | + | 0.418426i | \(0.862582\pi\) | |||||||
\(110\) | 0.610623 | − | 2.15108i | 0.0582206 | − | 0.205097i | ||||
\(111\) | 0.905649i | 0.0859604i | ||||||||
\(112\) | −2.63480 | + | 0.240478i | −0.248965 | + | 0.0227230i | ||||
\(113\) | −7.26910 | − | 7.26910i | −0.683820 | − | 0.683820i | 0.277039 | − | 0.960859i | \(-0.410647\pi\) |
−0.960859 | + | 0.277039i | \(0.910647\pi\) | |||||||
\(114\) | − | 0.222990i | − | 0.0208850i | ||||||
\(115\) | 5.40682 | + | 1.53482i | 0.504188 | + | 0.143123i | ||||
\(116\) | −5.97677 | −0.554929 | ||||||||
\(117\) | −6.96313 | − | 6.96313i | −0.643741 | − | 0.643741i | ||||
\(118\) | −2.35170 | + | 2.35170i | −0.216492 | + | 0.216492i | ||||
\(119\) | 6.94067 | + | 5.77968i | 0.636250 | + | 0.529823i | ||||
\(120\) | −0.197519 | + | 0.110175i | −0.0180309 | + | 0.0100575i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −7.92542 | − | 7.92542i | −0.717534 | − | 0.717534i | ||||
\(123\) | −0.606496 | − | 0.606496i | −0.0546859 | − | 0.0546859i | ||||
\(124\) | 4.99705 | 0.448748 | ||||||||
\(125\) | 0.496003 | − | 11.1693i | 0.0443639 | − | 0.999015i | ||||
\(126\) | −6.07859 | − | 5.06180i | −0.541523 | − | 0.450941i | ||||
\(127\) | 5.92401 | − | 5.92401i | 0.525671 | − | 0.525671i | −0.393608 | − | 0.919279i | \(-0.628773\pi\) |
0.919279 | + | 0.393608i | \(0.128773\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0.166258 | 0.0146382 | ||||||||
\(130\) | −3.58770 | − | 6.43196i | −0.314662 | − | 0.564120i | ||||
\(131\) | − | 10.4059i | − | 0.909169i | −0.890704 | − | 0.454585i | \(-0.849788\pi\) | ||
0.890704 | − | 0.454585i | \(-0.150212\pi\) | |||||||
\(132\) | −0.0715208 | − | 0.0715208i | −0.00622508 | − | 0.00622508i | ||||
\(133\) | 5.80880 | − | 0.530169i | 0.503687 | − | 0.0459715i | ||||
\(134\) | 13.4821i | 1.16468i | ||||||||
\(135\) | −1.30321 | − | 0.369939i | −0.112162 | − | 0.0318393i | ||||
\(136\) | 3.41379i | 0.292730i | ||||||||
\(137\) | −5.98561 | + | 5.98561i | −0.511386 | + | 0.511386i | −0.914951 | − | 0.403565i | \(-0.867771\pi\) |
0.403565 | + | 0.914951i | \(0.367771\pi\) | |||||||
\(138\) | 0.179770 | − | 0.179770i | 0.0153030 | − | 0.0153030i | ||||
\(139\) | 5.22788 | 0.443423 | 0.221711 | − | 0.975112i | \(-0.428836\pi\) | ||||
0.221711 | + | 0.975112i | \(0.428836\pi\) | |||||||
\(140\) | −3.33961 | − | 4.88334i | −0.282249 | − | 0.412718i | ||||
\(141\) | 0.686605 | 0.0578226 | ||||||||
\(142\) | 6.21017 | − | 6.21017i | 0.521146 | − | 0.521146i | ||||
\(143\) | 2.32898 | − | 2.32898i | 0.194760 | − | 0.194760i | ||||
\(144\) | − | 2.98977i | − | 0.249147i | ||||||
\(145\) | −6.51029 | − | 11.6715i | −0.540651 | − | 0.969269i | ||||
\(146\) | − | 2.93862i | − | 0.243202i | ||||||
\(147\) | −0.401741 | + | 0.583006i | −0.0331350 | + | 0.0480855i | ||||
\(148\) | −6.33137 | − | 6.33137i | −0.520435 | − | 0.520435i | ||||
\(149\) | − | 2.62196i | − | 0.214799i | −0.994216 | − | 0.107400i | \(-0.965748\pi\) | ||
0.994216 | − | 0.107400i | \(-0.0342524\pi\) | |||||||
\(150\) | −0.430302 | − | 0.265709i | −0.0351340 | − | 0.0216951i | ||||
\(151\) | 1.43640 | 0.116893 | 0.0584463 | − | 0.998291i | \(-0.481385\pi\) | ||||
0.0584463 | + | 0.998291i | \(0.481385\pi\) | |||||||
\(152\) | 1.55892 | + | 1.55892i | 0.126445 | + | 0.126445i | ||||
\(153\) | −7.21704 | + | 7.21704i | −0.583463 | + | 0.583463i | ||||
\(154\) | 1.69304 | − | 2.03313i | 0.136429 | − | 0.163834i | ||||
\(155\) | 5.44312 | + | 9.75833i | 0.437202 | + | 0.783808i | ||||
\(156\) | −0.333142 | −0.0266727 | ||||||||
\(157\) | 12.9197 | + | 12.9197i | 1.03110 | + | 1.03110i | 0.999500 | + | 0.0316032i | \(0.0100613\pi\) |
0.0316032 | + | 0.999500i | \(0.489939\pi\) | |||||||
\(158\) | −2.03384 | − | 2.03384i | −0.161803 | − | 0.161803i | ||||
\(159\) | −0.514879 | −0.0408325 | ||||||||
\(160\) | 0.610623 | − | 2.15108i | 0.0482740 | − | 0.170058i | ||||
\(161\) | 5.11035 | + | 4.25552i | 0.402752 | + | 0.335382i | ||||
\(162\) | 6.29893 | − | 6.29893i | 0.494891 | − | 0.494891i | ||||
\(163\) | −17.2431 | − | 17.2431i | −1.35058 | − | 1.35058i | −0.885008 | − | 0.465576i | \(-0.845847\pi\) |
−0.465576 | − | 0.885008i | \(-0.654153\pi\) | |||||||
\(164\) | 8.47999 | 0.662176 | ||||||||
\(165\) | 0.0617619 | − | 0.217572i | 0.00480815 | − | 0.0169380i | ||||
\(166\) | 4.52017i | 0.350834i | ||||||||
\(167\) | −14.8739 | − | 14.8739i | −1.15098 | − | 1.15098i | −0.986357 | − | 0.164620i | \(-0.947360\pi\) |
−0.164620 | − | 0.986357i | \(-0.552640\pi\) | |||||||
\(168\) | −0.266498 | + | 0.0243233i | −0.0205608 | + | 0.00187658i | ||||
\(169\) | 2.15166i | 0.165512i | ||||||||
\(170\) | −6.66651 | + | 3.71853i | −0.511298 | + | 0.285198i | ||||
\(171\) | 6.59138i | 0.504056i | ||||||||
\(172\) | −1.16231 | + | 1.16231i | −0.0886250 | + | 0.0886250i | ||||
\(173\) | −10.7916 | + | 10.7916i | −0.820470 | + | 0.820470i | −0.986175 | − | 0.165706i | \(-0.947010\pi\) |
0.165706 | + | 0.986175i | \(0.447010\pi\) | |||||||
\(174\) | −0.604524 | −0.0458289 | ||||||||
\(175\) | 5.89855 | − | 11.8409i | 0.445888 | − | 0.895089i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −0.237865 | + | 0.237865i | −0.0178790 | + | 0.0178790i | ||||
\(178\) | 7.56512 | − | 7.56512i | 0.567029 | − | 0.567029i | ||||
\(179\) | − | 7.88097i | − | 0.589051i | −0.955644 | − | 0.294526i | \(-0.904838\pi\) | ||
0.955644 | − | 0.294526i | \(-0.0951616\pi\) | |||||||
\(180\) | 5.83848 | − | 3.25666i | 0.435174 | − | 0.242737i | ||||
\(181\) | − | 25.8379i | − | 1.92052i | −0.279112 | − | 0.960259i | \(-0.590040\pi\) | ||
0.279112 | − | 0.960259i | \(-0.409960\pi\) | |||||||
\(182\) | −0.792058 | − | 8.67819i | −0.0587113 | − | 0.643270i | ||||
\(183\) | −0.801622 | − | 0.801622i | −0.0592576 | − | 0.0592576i | ||||
\(184\) | 2.51354i | 0.185300i | ||||||||
\(185\) | 5.46746 | − | 19.2606i | 0.401976 | − | 1.41606i | ||||
\(186\) | 0.505430 | 0.0370599 | ||||||||
\(187\) | −2.41391 | − | 2.41391i | −0.176523 | − | 0.176523i | ||||
\(188\) | −4.80004 | + | 4.80004i | −0.350079 | + | 0.350079i | ||||
\(189\) | −1.23175 | − | 1.02571i | −0.0895965 | − | 0.0746095i | ||||
\(190\) | −1.34621 | + | 4.74237i | −0.0976642 | + | 0.344047i | ||||
\(191\) | −23.4159 | −1.69432 | −0.847159 | − | 0.531339i | \(-0.821689\pi\) | ||||
−0.847159 | + | 0.531339i | \(0.821689\pi\) | |||||||
\(192\) | −0.0715208 | − | 0.0715208i | −0.00516157 | − | 0.00516157i | ||||
\(193\) | 12.0396 | + | 12.0396i | 0.866632 | + | 0.866632i | 0.992098 | − | 0.125465i | \(-0.0400424\pi\) |
−0.125465 | + | 0.992098i | \(0.540042\pi\) | |||||||
\(194\) | 4.66398 | 0.334854 | ||||||||
\(195\) | −0.362880 | − | 0.650565i | −0.0259864 | − | 0.0465879i | ||||
\(196\) | −1.26722 | − | 6.88434i | −0.0905160 | − | 0.491739i | ||||
\(197\) | −12.7592 | + | 12.7592i | −0.909057 | + | 0.909057i | −0.996196 | − | 0.0871394i | \(-0.972227\pi\) |
0.0871394 | + | 0.996196i | \(0.472227\pi\) | |||||||
\(198\) | 2.11409 | + | 2.11409i | 0.150242 | + | 0.150242i | ||||
\(199\) | −1.49431 | −0.105929 | −0.0529643 | − | 0.998596i | \(-0.516867\pi\) | ||||
−0.0529643 | + | 0.998596i | \(0.516867\pi\) | |||||||
\(200\) | 4.86580 | − | 1.15066i | 0.344064 | − | 0.0813641i | ||||
\(201\) | 1.36366i | 0.0961852i | ||||||||
\(202\) | −7.76242 | − | 7.76242i | −0.546162 | − | 0.546162i | ||||
\(203\) | −1.43728 | − | 15.7476i | −0.100877 | − | 1.10526i | ||||
\(204\) | 0.345290i | 0.0241751i | ||||||||
\(205\) | 9.23697 | + | 16.5599i | 0.645138 | + | 1.15659i | ||||
\(206\) | 15.8084i | 1.10142i | ||||||||
\(207\) | −5.31384 | + | 5.31384i | −0.369337 | + | 0.369337i | ||||
\(208\) | 2.32898 | − | 2.32898i | 0.161486 | − | 0.161486i | ||||
\(209\) | −2.20465 | −0.152499 | ||||||||
\(210\) | −0.337787 | − | 0.493929i | −0.0233095 | − | 0.0340843i | ||||
\(211\) | −24.1976 | −1.66583 | −0.832916 | − | 0.553399i | \(-0.813330\pi\) | ||||
−0.832916 | + | 0.553399i | \(0.813330\pi\) | |||||||
\(212\) | 3.59950 | − | 3.59950i | 0.247215 | − | 0.247215i | ||||
\(213\) | 0.628131 | − | 0.628131i | 0.0430389 | − | 0.0430389i | ||||
\(214\) | 8.56588i | 0.585551i | ||||||||
\(215\) | −3.53583 | − | 1.00371i | −0.241142 | − | 0.0684525i | ||||
\(216\) | − | 0.605839i | − | 0.0412221i | ||||||
\(217\) | 1.20168 | + | 13.1662i | 0.0815754 | + | 0.893782i | ||||
\(218\) | −6.17799 | − | 6.17799i | −0.418426 | − | 0.418426i | ||||
\(219\) | − | 0.297229i | − | 0.0200849i | ||||||
\(220\) | 1.08927 | + | 1.95282i | 0.0734383 | + | 0.131659i | ||||
\(221\) | −11.2439 | −0.756349 | ||||||||
\(222\) | −0.640391 | − | 0.640391i | −0.0429802 | − | 0.0429802i | ||||
\(223\) | 14.3774 | − | 14.3774i | 0.962785 | − | 0.962785i | −0.0365471 | − | 0.999332i | \(-0.511636\pi\) |
0.999332 | + | 0.0365471i | \(0.0116359\pi\) | |||||||
\(224\) | 1.69304 | − | 2.03313i | 0.113121 | − | 0.135844i | ||||
\(225\) | 12.7193 | + | 7.85411i | 0.847954 | + | 0.523608i | ||||
\(226\) | 10.2801 | 0.683820 | ||||||||
\(227\) | 6.98271 | + | 6.98271i | 0.463459 | + | 0.463459i | 0.899787 | − | 0.436329i | \(-0.143721\pi\) |
−0.436329 | + | 0.899787i | \(0.643721\pi\) | |||||||
\(228\) | 0.157678 | + | 0.157678i | 0.0104425 | + | 0.0104425i | ||||
\(229\) | −0.136302 | −0.00900707 | −0.00450354 | − | 0.999990i | \(-0.501434\pi\) | ||||
−0.00450354 | + | 0.999990i | \(0.501434\pi\) | |||||||
\(230\) | −4.90848 | + | 2.73791i | −0.323656 | + | 0.180533i | ||||
\(231\) | 0.171244 | − | 0.205642i | 0.0112670 | − | 0.0135303i | ||||
\(232\) | 4.22621 | − | 4.22621i | 0.277465 | − | 0.277465i | ||||
\(233\) | −16.2560 | − | 16.2560i | −1.06496 | − | 1.06496i | −0.997738 | − | 0.0672252i | \(-0.978585\pi\) |
−0.0672252 | − | 0.997738i | \(-0.521415\pi\) | |||||||
\(234\) | 9.84735 | 0.643741 | ||||||||
\(235\) | −14.6021 | − | 4.14508i | −0.952538 | − | 0.270395i | ||||
\(236\) | − | 3.32581i | − | 0.216492i | ||||||
\(237\) | −0.205714 | − | 0.205714i | −0.0133625 | − | 0.0133625i | ||||
\(238\) | −8.99465 | + | 0.820941i | −0.583037 | + | 0.0532137i | ||||
\(239\) | 5.90173i | 0.381751i | 0.981614 | + | 0.190876i | \(0.0611327\pi\) | ||||
−0.981614 | + | 0.190876i | \(0.938867\pi\) | |||||||
\(240\) | 0.0617619 | − | 0.217572i | 0.00398671 | − | 0.0140442i | ||||
\(241\) | − | 6.08298i | − | 0.391839i | −0.980620 | − | 0.195920i | \(-0.937231\pi\) | ||
0.980620 | − | 0.195920i | \(-0.0627692\pi\) | |||||||
\(242\) | −0.707107 | + | 0.707107i | −0.0454545 | + | 0.0454545i | ||||
\(243\) | 1.92229 | − | 1.92229i | 0.123315 | − | 0.123315i | ||||
\(244\) | 11.2082 | 0.717534 | ||||||||
\(245\) | 12.0635 | − | 9.97354i | 0.770710 | − | 0.637186i | ||||
\(246\) | 0.857714 | 0.0546859 | ||||||||
\(247\) | −5.13459 | + | 5.13459i | −0.326706 | + | 0.326706i | ||||
\(248\) | −3.53345 | + | 3.53345i | −0.224374 | + | 0.224374i | ||||
\(249\) | 0.457196i | 0.0289736i | ||||||||
\(250\) | 7.54718 | + | 8.24864i | 0.477326 | + | 0.521690i | ||||
\(251\) | − | 13.3303i | − | 0.841401i | −0.907200 | − | 0.420700i | \(-0.861784\pi\) | ||
0.907200 | − | 0.420700i | \(-0.138216\pi\) | |||||||
\(252\) | 7.87744 | − | 0.718974i | 0.496232 | − | 0.0452911i | ||||
\(253\) | −1.77734 | − | 1.77734i | −0.111740 | − | 0.111740i | ||||
\(254\) | 8.37782i | 0.525671i | ||||||||
\(255\) | −0.674288 | + | 0.376113i | −0.0422256 | + | 0.0235531i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.1951 | − | 12.1951i | −0.760708 | − | 0.760708i | 0.215743 | − | 0.976450i | \(-0.430783\pi\) |
−0.976450 | + | 0.215743i | \(0.930783\pi\) | |||||||
\(258\) | −0.117562 | + | 0.117562i | −0.00731910 | + | 0.00731910i | ||||
\(259\) | 15.1593 | − | 18.2045i | 0.941955 | − | 1.13117i | ||||
\(260\) | 7.08497 | + | 2.01120i | 0.439391 | + | 0.124729i | ||||
\(261\) | 17.8692 | 1.10607 | ||||||||
\(262\) | 7.35809 | + | 7.35809i | 0.454585 | + | 0.454585i | ||||
\(263\) | 1.13084 | + | 1.13084i | 0.0697304 | + | 0.0697304i | 0.741112 | − | 0.671382i | \(-0.234299\pi\) |
−0.671382 | + | 0.741112i | \(0.734299\pi\) | |||||||
\(264\) | 0.101146 | 0.00622508 | ||||||||
\(265\) | 10.9500 | + | 3.10836i | 0.672653 | + | 0.190945i | ||||
\(266\) | −3.73256 | + | 4.48233i | −0.228858 | + | 0.274829i | ||||
\(267\) | 0.765178 | − | 0.765178i | 0.0468282 | − | 0.0468282i | ||||
\(268\) | −9.53332 | − | 9.53332i | −0.582340 | − | 0.582340i | ||||
\(269\) | −16.1191 | −0.982799 | −0.491400 | − | 0.870934i | \(-0.663515\pi\) | ||||
−0.491400 | + | 0.870934i | \(0.663515\pi\) | |||||||
\(270\) | 1.18309 | − | 0.659920i | 0.0720008 | − | 0.0401615i | ||||
\(271\) | − | 5.27398i | − | 0.320372i | −0.987087 | − | 0.160186i | \(-0.948791\pi\) | ||
0.987087 | − | 0.160186i | \(-0.0512094\pi\) | |||||||
\(272\) | −2.41391 | − | 2.41391i | −0.146365 | − | 0.146365i | ||||
\(273\) | −0.0801133 | − | 0.877761i | −0.00484867 | − | 0.0531245i | ||||
\(274\) | − | 8.46494i | − | 0.511386i | ||||||
\(275\) | −2.62700 | + | 4.25428i | −0.158414 | + | 0.256543i | ||||
\(276\) | 0.254233i | 0.0153030i | ||||||||
\(277\) | 6.53318 | − | 6.53318i | 0.392541 | − | 0.392541i | −0.483051 | − | 0.875592i | \(-0.660471\pi\) |
0.875592 | + | 0.483051i | \(0.160471\pi\) | |||||||
\(278\) | −3.69667 | + | 3.69667i | −0.221711 | + | 0.221711i | ||||
\(279\) | −14.9400 | −0.894436 | ||||||||
\(280\) | 5.81450 | + | 1.09158i | 0.347483 | + | 0.0652345i | ||||
\(281\) | 2.68515 | 0.160183 | 0.0800913 | − | 0.996788i | \(-0.474479\pi\) | ||||
0.0800913 | + | 0.996788i | \(0.474479\pi\) | |||||||
\(282\) | −0.485503 | + | 0.485503i | −0.0289113 | + | 0.0289113i | ||||
\(283\) | −19.3234 | + | 19.3234i | −1.14866 | + | 1.14866i | −0.161842 | + | 0.986817i | \(0.551744\pi\) |
−0.986817 | + | 0.161842i | \(0.948256\pi\) | |||||||
\(284\) | 8.78250i | 0.521146i | ||||||||
\(285\) | −0.136163 | + | 0.479670i | −0.00806560 | + | 0.0284132i | ||||
\(286\) | 3.29368i | 0.194760i | ||||||||
\(287\) | 2.03925 | + | 22.3431i | 0.120373 | + | 1.31887i | ||||
\(288\) | 2.11409 | + | 2.11409i | 0.124574 | + | 0.124574i | ||||
\(289\) | − | 5.34605i | − | 0.314473i | ||||||
\(290\) | 12.8565 | + | 3.64955i | 0.754960 | + | 0.214309i | ||||
\(291\) | 0.471741 | 0.0276539 | ||||||||
\(292\) | 2.07792 | + | 2.07792i | 0.121601 | + | 0.121601i | ||||
\(293\) | −16.0098 | + | 16.0098i | −0.935304 | + | 0.935304i | −0.998031 | − | 0.0627265i | \(-0.980020\pi\) |
0.0627265 | + | 0.998031i | \(0.480020\pi\) | |||||||
\(294\) | −0.128174 | − | 0.696321i | −0.00747527 | − | 0.0406103i | ||||
\(295\) | 6.49471 | − | 3.62270i | 0.378136 | − | 0.210922i | ||||
\(296\) | 8.95391 | 0.520435 | ||||||||
\(297\) | 0.428393 | + | 0.428393i | 0.0248579 | + | 0.0248579i | ||||
\(298\) | 1.85400 | + | 1.85400i | 0.107400 | + | 0.107400i | ||||
\(299\) | −8.27879 | −0.478775 | ||||||||
\(300\) | 0.492154 | − | 0.116384i | 0.0284145 | − | 0.00671946i | ||||
\(301\) | −3.34195 | − | 2.78294i | −0.192627 | − | 0.160406i | ||||
\(302\) | −1.01569 | + | 1.01569i | −0.0584463 | + | 0.0584463i | ||||
\(303\) | −0.785135 | − | 0.785135i | −0.0451048 | − | 0.0451048i | ||||
\(304\) | −2.20465 | −0.126445 | ||||||||
\(305\) | 12.2088 | + | 21.8876i | 0.699071 | + | 1.25328i | ||||
\(306\) | − | 10.2064i | − | 0.583463i | ||||||
\(307\) | −13.9838 | − | 13.9838i | −0.798099 | − | 0.798099i | 0.184697 | − | 0.982796i | \(-0.440870\pi\) |
−0.982796 | + | 0.184697i | \(0.940870\pi\) | |||||||
\(308\) | 0.240478 | + | 2.63480i | 0.0137025 | + | 0.150132i | ||||
\(309\) | 1.59895i | 0.0909609i | ||||||||
\(310\) | −10.7490 | − | 3.05131i | −0.610505 | − | 0.173303i | ||||
\(311\) | 25.3533i | 1.43765i | 0.695188 | + | 0.718827i | \(0.255321\pi\) | ||||
−0.695188 | + | 0.718827i | \(0.744679\pi\) | |||||||
\(312\) | 0.235567 | − | 0.235567i | 0.0133363 | − | 0.0133363i | ||||
\(313\) | −19.7694 | + | 19.7694i | −1.11744 | + | 1.11744i | −0.125319 | + | 0.992117i | \(0.539995\pi\) |
−0.992117 | + | 0.125319i | \(0.960005\pi\) | |||||||
\(314\) | −18.2712 | −1.03110 | ||||||||
\(315\) | 9.98466 | + | 14.6001i | 0.562572 | + | 0.822620i | ||||
\(316\) | 2.87628 | 0.161803 | ||||||||
\(317\) | 8.97452 | − | 8.97452i | 0.504059 | − | 0.504059i | −0.408638 | − | 0.912697i | \(-0.633996\pi\) |
0.912697 | + | 0.408638i | \(0.133996\pi\) | |||||||
\(318\) | 0.364074 | − | 0.364074i | 0.0204163 | − | 0.0204163i | ||||
\(319\) | 5.97677i | 0.334635i | ||||||||
\(320\) | 1.08927 | + | 1.95282i | 0.0608919 | + | 0.109166i | ||||
\(321\) | 0.866401i | 0.0483578i | ||||||||
\(322\) | −6.62267 | + | 0.604451i | −0.369067 | + | 0.0336847i | ||||
\(323\) | 5.32182 | + | 5.32182i | 0.296114 | + | 0.296114i | ||||
\(324\) | 8.90803i | 0.494891i | ||||||||
\(325\) | 3.78992 | + | 16.0264i | 0.210227 | + | 0.888984i | ||||
\(326\) | 24.3854 | 1.35058 | ||||||||
\(327\) | −0.624876 | − | 0.624876i | −0.0345557 | − | 0.0345557i | ||||
\(328\) | −5.99626 | + | 5.99626i | −0.331088 | + | 0.331088i | ||||
\(329\) | −13.8015 | − | 11.4928i | −0.760899 | − | 0.633621i | ||||
\(330\) | 0.110175 | + | 0.197519i | 0.00606491 | + | 0.0108731i | ||||
\(331\) | 16.0212 | 0.880607 | 0.440303 | − | 0.897849i | \(-0.354871\pi\) | ||||
0.440303 | + | 0.897849i | \(0.354871\pi\) | |||||||
\(332\) | −3.19625 | − | 3.19625i | −0.175417 | − | 0.175417i | ||||
\(333\) | 18.9293 | + | 18.9293i | 1.03732 | + | 1.03732i | ||||
\(334\) | 21.0349 | 1.15098 | ||||||||
\(335\) | 8.23251 | − | 29.0012i | 0.449790 | − | 1.58450i | ||||
\(336\) | 0.171244 | − | 0.205642i | 0.00934211 | − | 0.0112187i | ||||
\(337\) | 12.2483 | − | 12.2483i | 0.667206 | − | 0.667206i | −0.289862 | − | 0.957068i | \(-0.593610\pi\) |
0.957068 | + | 0.289862i | \(0.0936096\pi\) | |||||||
\(338\) | −1.52145 | − | 1.52145i | −0.0827561 | − | 0.0827561i | ||||
\(339\) | 1.03978 | 0.0564733 | ||||||||
\(340\) | 2.08454 | − | 7.34333i | 0.113050 | − | 0.398248i | ||||
\(341\) | − | 4.99705i | − | 0.270605i | ||||||
\(342\) | −4.66081 | − | 4.66081i | −0.252028 | − | 0.252028i | ||||
\(343\) | 17.8341 | − | 4.99441i | 0.962952 | − | 0.269673i | ||||
\(344\) | − | 1.64375i | − | 0.0886250i | ||||||
\(345\) | −0.496471 | + | 0.276928i | −0.0267291 | + | 0.0149093i | ||||
\(346\) | − | 15.2616i | − | 0.820470i | ||||||
\(347\) | 8.93061 | − | 8.93061i | 0.479420 | − | 0.479420i | −0.425526 | − | 0.904946i | \(-0.639911\pi\) |
0.904946 | + | 0.425526i | \(0.139911\pi\) | |||||||
\(348\) | 0.427463 | − | 0.427463i | 0.0229144 | − | 0.0229144i | ||||
\(349\) | −14.1309 | −0.756409 | −0.378204 | − | 0.925722i | \(-0.623458\pi\) | ||||
−0.378204 | + | 0.925722i | \(0.623458\pi\) | |||||||
\(350\) | 4.20188 | + | 12.5437i | 0.224600 | + | 0.670488i | ||||
\(351\) | 1.99544 | 0.106509 | ||||||||
\(352\) | −0.707107 | + | 0.707107i | −0.0376889 | + | 0.0376889i | ||||
\(353\) | −11.7222 | + | 11.7222i | −0.623912 | + | 0.623912i | −0.946529 | − | 0.322617i | \(-0.895437\pi\) |
0.322617 | + | 0.946529i | \(0.395437\pi\) | |||||||
\(354\) | − | 0.336391i | − | 0.0178790i | ||||||
\(355\) | −17.1506 | + | 9.56649i | −0.910261 | + | 0.507737i | ||||
\(356\) | 10.6987i | 0.567029i | ||||||||
\(357\) | −0.909770 | + | 0.0830346i | −0.0481501 | + | 0.00439466i | ||||
\(358\) | 5.57268 | + | 5.57268i | 0.294526 | + | 0.294526i | ||||
\(359\) | 33.7189i | 1.77962i | 0.456334 | + | 0.889809i | \(0.349162\pi\) | ||||
−0.456334 | + | 0.889809i | \(0.650838\pi\) | |||||||
\(360\) | −1.82562 | + | 6.43123i | −0.0962188 | + | 0.338956i | ||||
\(361\) | −14.1395 | −0.744186 | ||||||||
\(362\) | 18.2702 | + | 18.2702i | 0.960259 | + | 0.960259i | ||||
\(363\) | −0.0715208 | + | 0.0715208i | −0.00375387 | + | 0.00375387i | ||||
\(364\) | 6.69648 | + | 5.57634i | 0.350991 | + | 0.292280i | ||||
\(365\) | −1.79439 | + | 6.32121i | −0.0939227 | + | 0.330867i | ||||
\(366\) | 1.13366 | 0.0592576 | ||||||||
\(367\) | −14.3586 | − | 14.3586i | −0.749510 | − | 0.749510i | 0.224877 | − | 0.974387i | \(-0.427802\pi\) |
−0.974387 | + | 0.224877i | \(0.927802\pi\) | |||||||
\(368\) | −1.77734 | − | 1.77734i | −0.0926502 | − | 0.0926502i | ||||
\(369\) | −25.3532 | −1.31984 | ||||||||
\(370\) | 9.75320 | + | 17.4854i | 0.507044 | + | 0.909020i | ||||
\(371\) | 10.3496 | + | 8.61837i | 0.537323 | + | 0.447444i | ||||
\(372\) | −0.357393 | + | 0.357393i | −0.0185300 | + | 0.0185300i | ||||
\(373\) | 5.92772 | + | 5.92772i | 0.306926 | + | 0.306926i | 0.843716 | − | 0.536790i | \(-0.180363\pi\) |
−0.536790 | + | 0.843716i | \(0.680363\pi\) | |||||||
\(374\) | 3.41379 | 0.176523 | ||||||||
\(375\) | 0.763365 | + | 0.834314i | 0.0394200 | + | 0.0430838i | ||||
\(376\) | − | 6.78828i | − | 0.350079i | ||||||
\(377\) | 13.9198 | + | 13.9198i | 0.716906 | + | 0.716906i | ||||
\(378\) | 1.59626 | − | 0.145691i | 0.0821030 | − | 0.00749354i | ||||
\(379\) | − | 29.1754i | − | 1.49864i | −0.662207 | − | 0.749321i | \(-0.730380\pi\) | ||
0.662207 | − | 0.749321i | \(-0.269620\pi\) | |||||||
\(380\) | −2.40145 | − | 4.30527i | −0.123192 | − | 0.220856i | ||||
\(381\) | 0.847380i | 0.0434126i | ||||||||
\(382\) | 16.5576 | − | 16.5576i | 0.847159 | − | 0.847159i | ||||
\(383\) | −6.25262 | + | 6.25262i | −0.319494 | + | 0.319494i | −0.848573 | − | 0.529079i | \(-0.822538\pi\) |
0.529079 | + | 0.848573i | \(0.322538\pi\) | |||||||
\(384\) | 0.101146 | 0.00516157 | ||||||||
\(385\) | −4.88334 | + | 3.33961i | −0.248878 | + | 0.170202i | ||||
\(386\) | −17.0266 | −0.866632 | ||||||||
\(387\) | 3.47503 | − | 3.47503i | 0.176646 | − | 0.176646i | ||||
\(388\) | −3.29793 | + | 3.29793i | −0.167427 | + | 0.167427i | ||||
\(389\) | − | 8.63838i | − | 0.437983i | −0.975727 | − | 0.218992i | \(-0.929723\pi\) | ||
0.975727 | − | 0.218992i | \(-0.0702767\pi\) | |||||||
\(390\) | 0.716614 | + | 0.203424i | 0.0362871 | + | 0.0103008i | ||||
\(391\) | 8.58069i | 0.433944i | ||||||||
\(392\) | 5.76403 | + | 3.97190i | 0.291127 | + | 0.200611i | ||||
\(393\) | 0.744239 | + | 0.744239i | 0.0375419 | + | 0.0375419i | ||||
\(394\) | − | 18.0443i | − | 0.909057i | ||||||
\(395\) | 3.13304 | + | 5.61685i | 0.157640 | + | 0.282614i | ||||
\(396\) | −2.98977 | −0.150242 | ||||||||
\(397\) | 10.3438 | + | 10.3438i | 0.519138 | + | 0.519138i | 0.917311 | − | 0.398172i | \(-0.130355\pi\) |
−0.398172 | + | 0.917311i | \(0.630355\pi\) | |||||||
\(398\) | 1.05663 | − | 1.05663i | 0.0529643 | − | 0.0529643i | ||||
\(399\) | −0.377532 | + | 0.453368i | −0.0189002 | + | 0.0226968i | ||||
\(400\) | −2.62700 | + | 4.25428i | −0.131350 | + | 0.212714i | ||||
\(401\) | 7.92538 | 0.395775 | 0.197887 | − | 0.980225i | \(-0.436592\pi\) | ||||
0.197887 | + | 0.980225i | \(0.436592\pi\) | |||||||
\(402\) | −0.964254 | − | 0.964254i | −0.0480926 | − | 0.0480926i | ||||
\(403\) | −11.6381 | − | 11.6381i | −0.579733 | − | 0.579733i | ||||
\(404\) | 10.9777 | 0.546162 | ||||||||
\(405\) | −17.3958 | + | 9.70322i | −0.864402 | + | 0.482157i | ||||
\(406\) | 12.1515 | + | 10.1189i | 0.603071 | + | 0.502193i | ||||
\(407\) | −6.33137 | + | 6.33137i | −0.313834 | + | 0.313834i | ||||
\(408\) | −0.244157 | − | 0.244157i | −0.0120876 | − | 0.0120876i | ||||
\(409\) | 29.7189 | 1.46950 | 0.734752 | − | 0.678336i | \(-0.237299\pi\) | ||||
0.734752 | + | 0.678336i | \(0.237299\pi\) | |||||||
\(410\) | −18.2411 | − | 5.17808i | −0.900865 | − | 0.255727i | ||||
\(411\) | − | 0.856191i | − | 0.0422328i | ||||||
\(412\) | −11.1782 | − | 11.1782i | −0.550710 | − | 0.550710i | ||||
\(413\) | 8.76285 | − | 0.799785i | 0.431192 | − | 0.0393548i | ||||
\(414\) | − | 7.51490i | − | 0.369337i | ||||||
\(415\) | 2.76012 | − | 9.72325i | 0.135489 | − | 0.477296i | ||||
\(416\) | 3.29368i | 0.161486i | ||||||||
\(417\) | −0.373902 | + | 0.373902i | −0.0183100 | + | 0.0183100i | ||||
\(418\) | 1.55892 | − | 1.55892i | 0.0762493 | − | 0.0762493i | ||||
\(419\) | −6.93525 | −0.338809 | −0.169405 | − | 0.985547i | \(-0.554184\pi\) | ||||
−0.169405 | + | 0.985547i | \(0.554184\pi\) | |||||||
\(420\) | 0.588112 | + | 0.110409i | 0.0286969 | + | 0.00538740i | ||||
\(421\) | 24.4211 | 1.19021 | 0.595106 | − | 0.803647i | \(-0.297110\pi\) | ||||
0.595106 | + | 0.803647i | \(0.297110\pi\) | |||||||
\(422\) | 17.1103 | − | 17.1103i | 0.832916 | − | 0.832916i | ||||
\(423\) | 14.3510 | − | 14.3510i | 0.697770 | − | 0.697770i | ||||
\(424\) | 5.09047i | 0.247215i | ||||||||
\(425\) | 16.6108 | − | 3.92812i | 0.805742 | − | 0.190542i | ||||
\(426\) | 0.888312i | 0.0430389i | ||||||||
\(427\) | 2.69534 | + | 29.5315i | 0.130436 | + | 1.42913i | ||||
\(428\) | −6.05699 | − | 6.05699i | −0.292776 | − | 0.292776i | ||||
\(429\) | 0.333142i | 0.0160842i | ||||||||
\(430\) | 3.20994 | − | 1.79048i | 0.154797 | − | 0.0863447i | ||||
\(431\) | −10.7599 | −0.518288 | −0.259144 | − | 0.965839i | \(-0.583441\pi\) | ||||
−0.259144 | + | 0.965839i | \(0.583441\pi\) | |||||||
\(432\) | 0.428393 | + | 0.428393i | 0.0206111 | + | 0.0206111i | ||||
\(433\) | 11.5614 | − | 11.5614i | 0.555604 | − | 0.555604i | −0.372449 | − | 0.928053i | \(-0.621482\pi\) |
0.928053 | + | 0.372449i | \(0.121482\pi\) | |||||||
\(434\) | −10.1596 | − | 8.46021i | −0.487679 | − | 0.406103i | ||||
\(435\) | 1.30038 | + | 0.369136i | 0.0623484 | + | 0.0176987i | ||||
\(436\) | 8.73699 | 0.418426 | ||||||||
\(437\) | 3.91840 | + | 3.91840i | 0.187443 | + | 0.187443i | ||||
\(438\) | 0.210173 | + | 0.210173i | 0.0100424 | + | 0.0100424i | ||||
\(439\) | −12.4834 | −0.595800 | −0.297900 | − | 0.954597i | \(-0.596286\pi\) | ||||
−0.297900 | + | 0.954597i | \(0.596286\pi\) | |||||||
\(440\) | −2.15108 | − | 0.610623i | −0.102549 | − | 0.0291103i | ||||
\(441\) | 3.78871 | + | 20.5826i | 0.180415 | + | 0.980123i | ||||
\(442\) | 7.95066 | − | 7.95066i | 0.378174 | − | 0.378174i | ||||
\(443\) | 7.25752 | + | 7.25752i | 0.344815 | + | 0.344815i | 0.858174 | − | 0.513359i | \(-0.171599\pi\) |
−0.513359 | + | 0.858174i | \(0.671599\pi\) | |||||||
\(444\) | 0.905649 | 0.0429802 | ||||||||
\(445\) | −20.8926 | + | 11.6537i | −0.990404 | + | 0.552439i | ||||
\(446\) | 20.3328i | 0.962785i | ||||||||
\(447\) | 0.187524 | + | 0.187524i | 0.00886960 | + | 0.00886960i | ||||
\(448\) | 0.240478 | + | 2.63480i | 0.0113615 | + | 0.124483i | ||||
\(449\) | 6.97090i | 0.328977i | 0.986379 | + | 0.164489i | \(0.0525974\pi\) | ||||
−0.986379 | + | 0.164489i | \(0.947403\pi\) | |||||||
\(450\) | −14.5476 | + | 3.44021i | −0.685781 | + | 0.162173i | ||||
\(451\) | − | 8.47999i | − | 0.399307i | ||||||
\(452\) | −7.26910 | + | 7.26910i | −0.341910 | + | 0.341910i | ||||
\(453\) | −0.102732 | + | 0.102732i | −0.00482679 | + | 0.00482679i | ||||
\(454\) | −9.87504 | −0.463459 | ||||||||
\(455\) | −3.59533 | + | 19.1511i | −0.168551 | + | 0.897819i | ||||
\(456\) | −0.222990 | −0.0104425 | ||||||||
\(457\) | 12.4271 | − | 12.4271i | 0.581314 | − | 0.581314i | −0.353950 | − | 0.935264i | \(-0.615162\pi\) |
0.935264 | + | 0.353950i | \(0.115162\pi\) | |||||||
\(458\) | 0.0963799 | − | 0.0963799i | 0.00450354 | − | 0.00450354i | ||||
\(459\) | − | 2.06821i | − | 0.0965356i | ||||||
\(460\) | 1.53482 | − | 5.40682i | 0.0715615 | − | 0.252094i | ||||
\(461\) | − | 11.4215i | − | 0.531951i | −0.963980 | − | 0.265976i | \(-0.914306\pi\) | ||
0.963980 | − | 0.265976i | \(-0.0856941\pi\) | |||||||
\(462\) | 0.0243233 | + | 0.266498i | 0.00113162 | + | 0.0123986i | ||||
\(463\) | 14.6778 | + | 14.6778i | 0.682134 | + | 0.682134i | 0.960481 | − | 0.278347i | \(-0.0897865\pi\) |
−0.278347 | + | 0.960481i | \(0.589786\pi\) | |||||||
\(464\) | 5.97677i | 0.277465i | ||||||||
\(465\) | −1.08722 | − | 0.308627i | −0.0504186 | − | 0.0143122i | ||||
\(466\) | 22.9894 | 1.06496 | ||||||||
\(467\) | 10.4596 | + | 10.4596i | 0.484011 | + | 0.484011i | 0.906410 | − | 0.422399i | \(-0.138812\pi\) |
−0.422399 | + | 0.906410i | \(0.638812\pi\) | |||||||
\(468\) | −6.96313 | + | 6.96313i | −0.321871 | + | 0.321871i | ||||
\(469\) | 22.8258 | − | 27.4109i | 1.05400 | − | 1.26572i | ||||
\(470\) | 13.2563 | − | 7.39425i | 0.611467 | − | 0.341071i | ||||
\(471\) | −1.84805 | −0.0851538 | ||||||||
\(472\) | 2.35170 | + | 2.35170i | 0.108246 | + | 0.108246i | ||||
\(473\) | 1.16231 | + | 1.16231i | 0.0534429 | + | 0.0534429i | ||||
\(474\) | 0.290923 | 0.0133625 | ||||||||
\(475\) | 5.79160 | − | 9.37918i | 0.265737 | − | 0.430346i | ||||
\(476\) | 5.77968 | − | 6.94067i | 0.264911 | − | 0.318125i | ||||
\(477\) | −10.7617 | + | 10.7617i | −0.492744 | + | 0.492744i | ||||
\(478\) | −4.17315 | − | 4.17315i | −0.190876 | − | 0.190876i | ||||
\(479\) | 7.45211 | 0.340496 | 0.170248 | − | 0.985401i | \(-0.445543\pi\) | ||||
0.170248 | + | 0.985401i | \(0.445543\pi\) | |||||||
\(480\) | 0.110175 | + | 0.197519i | 0.00502876 | + | 0.00901547i | ||||
\(481\) | 29.4913i | 1.34469i | ||||||||
\(482\) | 4.30132 | + | 4.30132i | 0.195920 | + | 0.195920i | ||||
\(483\) | −0.669854 | + | 0.0611376i | −0.0304794 | + | 0.00278186i | ||||
\(484\) | − | 1.00000i | − | 0.0454545i | ||||||
\(485\) | −10.0326 | − | 2.84793i | −0.455556 | − | 0.129318i | ||||
\(486\) | 2.71853i | 0.123315i | ||||||||
\(487\) | −9.32786 | + | 9.32786i | −0.422686 | + | 0.422686i | −0.886127 | − | 0.463442i | \(-0.846614\pi\) |
0.463442 | + | 0.886127i | \(0.346614\pi\) | |||||||
\(488\) | −7.92542 | + | 7.92542i | −0.358767 | + | 0.358767i | ||||
\(489\) | 2.46648 | 0.111538 | ||||||||
\(490\) | −1.47784 | + | 15.5826i | −0.0667620 | + | 0.703948i | ||||
\(491\) | −22.9262 | −1.03465 | −0.517324 | − | 0.855790i | \(-0.673072\pi\) | ||||
−0.517324 | + | 0.855790i | \(0.673072\pi\) | |||||||
\(492\) | −0.606496 | + | 0.606496i | −0.0273429 | + | 0.0273429i | ||||
\(493\) | 14.4274 | − | 14.4274i | 0.649777 | − | 0.649777i | ||||
\(494\) | − | 7.26140i | − | 0.326706i | ||||||
\(495\) | −3.25666 | − | 5.83848i | −0.146376 | − | 0.262420i | ||||
\(496\) | − | 4.99705i | − | 0.224374i | ||||||
\(497\) | −23.1401 | + | 2.11200i | −1.03798 | + | 0.0947362i | ||||
\(498\) | −0.323286 | − | 0.323286i | −0.0144868 | − | 0.0144868i | ||||
\(499\) | 25.5090i | 1.14194i | 0.820971 | + | 0.570970i | \(0.193433\pi\) | ||||
−0.820971 | + | 0.570970i | \(0.806567\pi\) | |||||||
\(500\) | −11.1693 | − | 0.496003i | −0.499508 | − | 0.0221819i | ||||
\(501\) | 2.12759 | 0.0950535 | ||||||||
\(502\) | 9.42594 | + | 9.42594i | 0.420700 | + | 0.420700i | ||||
\(503\) | 16.9751 | − | 16.9751i | 0.756884 | − | 0.756884i | −0.218870 | − | 0.975754i | \(-0.570237\pi\) |
0.975754 | + | 0.218870i | \(0.0702371\pi\) | |||||||
\(504\) | −5.06180 | + | 6.07859i | −0.225471 | + | 0.270762i | ||||
\(505\) | 11.9577 | + | 21.4375i | 0.532109 | + | 0.953955i | ||||
\(506\) | 2.51354 | 0.111740 | ||||||||
\(507\) | −0.153888 | − | 0.153888i | −0.00683442 | − | 0.00683442i | ||||
\(508\) | −5.92401 | − | 5.92401i | −0.262836 | − | 0.262836i | ||||
\(509\) | −12.2625 | −0.543524 | −0.271762 | − | 0.962364i | \(-0.587606\pi\) | ||||
−0.271762 | + | 0.962364i | \(0.587606\pi\) | |||||||
\(510\) | 0.210842 | − | 0.742746i | 0.00933624 | − | 0.0328893i | ||||
\(511\) | −4.97521 | + | 5.97460i | −0.220090 | + | 0.264301i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −0.944454 | − | 0.944454i | −0.0416987 | − | 0.0416987i | ||||
\(514\) | 17.2464 | 0.760708 | ||||||||
\(515\) | 9.65295 | − | 34.0050i | 0.425360 | − | 1.49844i | ||||
\(516\) | − | 0.166258i | − | 0.00731910i | ||||||
\(517\) | 4.80004 | + | 4.80004i | 0.211106 | + | 0.211106i | ||||
\(518\) | 2.15322 | + | 23.5918i | 0.0946070 | + | 1.03656i | ||||
\(519\) | − | 1.54365i | − | 0.0677585i | ||||||
\(520\) | −6.43196 | + | 3.58770i | −0.282060 | + | 0.157331i | ||||
\(521\) | − | 14.7148i | − | 0.644669i | −0.946626 | − | 0.322335i | \(-0.895532\pi\) | ||
0.946626 | − | 0.322335i | \(-0.104468\pi\) | |||||||
\(522\) | −12.6354 | + | 12.6354i | −0.553037 | + | 0.553037i | ||||
\(523\) | −13.1748 | + | 13.1748i | −0.576092 | + | 0.576092i | −0.933824 | − | 0.357732i | \(-0.883550\pi\) |
0.357732 | + | 0.933824i | \(0.383550\pi\) | |||||||
\(524\) | −10.4059 | −0.454585 | ||||||||
\(525\) | 0.425002 | + | 1.26874i | 0.0185486 | + | 0.0553723i | ||||
\(526\) | −1.59924 | −0.0697304 | ||||||||
\(527\) | −12.0624 | + | 12.0624i | −0.525448 | + | 0.525448i | ||||
\(528\) | −0.0715208 | + | 0.0715208i | −0.00311254 | + | 0.00311254i | ||||
\(529\) | − | 16.6821i | − | 0.725310i | ||||||
\(530\) | −9.94076 | + | 5.54488i | −0.431799 | + | 0.240854i | ||||
\(531\) | 9.94341i | 0.431507i | ||||||||
\(532\) | −0.530169 | − | 5.80880i | −0.0229857 | − | 0.251843i | ||||
\(533\) | −19.7498 | − | 19.7498i | −0.855458 | − | 0.855458i | ||||
\(534\) | 1.08213i | 0.0468282i | ||||||||
\(535\) | 5.23052 | − | 18.4259i | 0.226135 | − | 0.796620i | ||||
\(536\) | 13.4821 | 0.582340 | ||||||||
\(537\) | 0.563653 | + | 0.563653i | 0.0243234 | + | 0.0243234i | ||||
\(538\) | 11.3979 | − | 11.3979i | 0.491400 | − | 0.491400i | ||||
\(539\) | −6.88434 | + | 1.26722i | −0.296530 | + | 0.0545832i | ||||
\(540\) | −0.369939 | + | 1.30321i | −0.0159197 | + | 0.0560811i | ||||
\(541\) | −9.59555 | −0.412545 | −0.206272 | − | 0.978495i | \(-0.566133\pi\) | ||||
−0.206272 | + | 0.978495i | \(0.566133\pi\) | |||||||
\(542\) | 3.72927 | + | 3.72927i | 0.160186 | + | 0.160186i | ||||
\(543\) | 1.84795 | + | 1.84795i | 0.0793030 | + | 0.0793030i | ||||
\(544\) | 3.41379 | 0.146365 | ||||||||
\(545\) | 9.51692 | + | 17.0618i | 0.407660 | + | 0.730846i | ||||
\(546\) | 0.677320 | + | 0.564022i | 0.0289866 | + | 0.0241379i | ||||
\(547\) | 21.9557 | − | 21.9557i | 0.938759 | − | 0.938759i | −0.0594707 | − | 0.998230i | \(-0.518941\pi\) |
0.998230 | + | 0.0594707i | \(0.0189413\pi\) | |||||||
\(548\) | 5.98561 | + | 5.98561i | 0.255693 | + | 0.255693i | ||||
\(549\) | −33.5100 | −1.43017 | ||||||||
\(550\) | −1.15066 | − | 4.86580i | −0.0490644 | − | 0.207478i | ||||
\(551\) | − | 13.1767i | − | 0.561344i | ||||||
\(552\) | −0.179770 | − | 0.179770i | −0.00765152 | − | 0.00765152i | ||||
\(553\) | 0.691682 | + | 7.57842i | 0.0294133 | + | 0.322267i | ||||
\(554\) | 9.23932i | 0.392541i | ||||||||
\(555\) | 0.986493 | + | 1.76857i | 0.0418743 | + | 0.0750715i | ||||
\(556\) | − | 5.22788i | − | 0.221711i | ||||||
\(557\) | 1.77779 | − | 1.77779i | 0.0753274 | − | 0.0753274i | −0.668439 | − | 0.743767i | \(-0.733037\pi\) |
0.743767 | + | 0.668439i | \(0.233037\pi\) | |||||||
\(558\) | 10.5642 | − | 10.5642i | 0.447218 | − | 0.447218i | ||||
\(559\) | 5.41399 | 0.228987 | ||||||||
\(560\) | −4.88334 | + | 3.33961i | −0.206359 | + | 0.141124i | ||||
\(561\) | 0.345290 | 0.0145781 | ||||||||
\(562\) | −1.89869 | + | 1.89869i | −0.0800913 | + | 0.0800913i | ||||
\(563\) | 10.4762 | − | 10.4762i | 0.441521 | − | 0.441521i | −0.451002 | − | 0.892523i | \(-0.648933\pi\) |
0.892523 | + | 0.451002i | \(0.148933\pi\) | |||||||
\(564\) | − | 0.686605i | − | 0.0289113i | ||||||
\(565\) | −22.1132 | − | 6.27725i | −0.930311 | − | 0.264086i | ||||
\(566\) | − | 27.3275i | − | 1.14866i | ||||||
\(567\) | −23.4709 | + | 2.14219i | −0.985684 | + | 0.0899634i | ||||
\(568\) | −6.21017 | − | 6.21017i | −0.260573 | − | 0.260573i | ||||
\(569\) | 8.40769i | 0.352469i | 0.984348 | + | 0.176234i | \(0.0563917\pi\) | ||||
−0.984348 | + | 0.176234i | \(0.943608\pi\) | |||||||
\(570\) | −0.242896 | − | 0.435459i | −0.0101738 | − | 0.0182394i | ||||
\(571\) | 24.7017 | 1.03373 | 0.516867 | − | 0.856065i | \(-0.327098\pi\) | ||||
0.516867 | + | 0.856065i | \(0.327098\pi\) | |||||||
\(572\) | −2.32898 | − | 2.32898i | −0.0973798 | − | 0.0973798i | ||||
\(573\) | 1.67473 | − | 1.67473i | 0.0699627 | − | 0.0699627i | ||||
\(574\) | −17.2409 | − | 14.3570i | −0.719622 | − | 0.599249i | ||||
\(575\) | 12.2304 | − | 2.89223i | 0.510041 | − | 0.120614i | ||||
\(576\) | −2.98977 | −0.124574 | ||||||||
\(577\) | −14.9572 | − | 14.9572i | −0.622678 | − | 0.622678i | 0.323537 | − | 0.946215i | \(-0.395128\pi\) |
−0.946215 | + | 0.323537i | \(0.895128\pi\) | |||||||
\(578\) | 3.78023 | + | 3.78023i | 0.157237 | + | 0.157237i | ||||
\(579\) | −1.72217 | −0.0715709 | ||||||||
\(580\) | −11.6715 | + | 6.51029i | −0.484634 | + | 0.270325i | ||||
\(581\) | 7.65284 | − | 9.19010i | 0.317493 | − | 0.381269i | ||||
\(582\) | −0.333571 | + | 0.333571i | −0.0138270 | + | 0.0138270i | ||||
\(583\) | −3.59950 | − | 3.59950i | −0.149076 | − | 0.149076i | ||||
\(584\) | −2.93862 | −0.121601 | ||||||||
\(585\) | −21.1824 | − | 6.01302i | −0.875786 | − | 0.248608i | ||||
\(586\) | − | 22.6413i | − | 0.935304i | ||||||
\(587\) | 13.4550 | + | 13.4550i | 0.555346 | + | 0.555346i | 0.927979 | − | 0.372633i | \(-0.121545\pi\) |
−0.372633 | + | 0.927979i | \(0.621545\pi\) | |||||||
\(588\) | 0.583006 | + | 0.401741i | 0.0240428 | + | 0.0165675i | ||||
\(589\) | 11.0167i | 0.453936i | ||||||||
\(590\) | −2.03082 | + | 7.15408i | −0.0836074 | + | 0.294529i | ||||
\(591\) | − | 1.82510i | − | 0.0750745i | ||||||
\(592\) | −6.33137 | + | 6.33137i | −0.260218 | + | 0.260218i | ||||
\(593\) | 12.6950 | − | 12.6950i | 0.521322 | − | 0.521322i | −0.396649 | − | 0.917970i | \(-0.629827\pi\) |
0.917970 | + | 0.396649i | \(0.129827\pi\) | |||||||
\(594\) | −0.605839 | −0.0248579 | ||||||||
\(595\) | 19.8495 | + | 3.72643i | 0.813750 | + | 0.152769i | ||||
\(596\) | −2.62196 | −0.107400 | ||||||||
\(597\) | 0.106874 | − | 0.106874i | 0.00437406 | − | 0.00437406i | ||||
\(598\) | 5.85399 | − | 5.85399i | 0.239388 | − | 0.239388i | ||||
\(599\) | − | 35.9067i | − | 1.46711i | −0.679631 | − | 0.733554i | \(-0.737860\pi\) | ||
0.679631 | − | 0.733554i | \(-0.262140\pi\) | |||||||
\(600\) | −0.265709 | + | 0.430302i | −0.0108475 | + | 0.0175670i | ||||
\(601\) | 23.5376i | 0.960118i | 0.877236 | + | 0.480059i | \(0.159385\pi\) | ||||
−0.877236 | + | 0.480059i | \(0.840615\pi\) | |||||||
\(602\) | 4.33095 | − | 0.395286i | 0.176516 | − | 0.0161106i | ||||
\(603\) | 28.5024 | + | 28.5024i | 1.16071 | + | 1.16071i | ||||
\(604\) | − | 1.43640i | − | 0.0584463i | ||||||
\(605\) | 1.95282 | − | 1.08927i | 0.0793933 | − | 0.0442850i | ||||
\(606\) | 1.11035 | 0.0451048 | ||||||||
\(607\) | −19.9351 | − | 19.9351i | −0.809143 | − | 0.809143i | 0.175361 | − | 0.984504i | \(-0.443891\pi\) |
−0.984504 | + | 0.175361i | \(0.943891\pi\) | |||||||
\(608\) | 1.55892 | − | 1.55892i | 0.0632225 | − | 0.0632225i | ||||
\(609\) | 1.22908 | + | 1.02348i | 0.0498046 | + | 0.0414737i | ||||
\(610\) | −24.1098 | − | 6.84401i | −0.976177 | − | 0.277106i | ||||
\(611\) | 22.3585 | 0.904526 | ||||||||
\(612\) | 7.21704 | + | 7.21704i | 0.291732 | + | 0.291732i | ||||
\(613\) | −24.4323 | − | 24.4323i | −0.986809 | − | 0.986809i | 0.0131047 | − | 0.999914i | \(-0.495829\pi\) |
−0.999914 | + | 0.0131047i | \(0.995829\pi\) | |||||||
\(614\) | 19.7761 | 0.798099 | ||||||||
\(615\) | −1.84501 | − | 0.523740i | −0.0743980 | − | 0.0211192i | ||||
\(616\) | −2.03313 | − | 1.69304i | −0.0819171 | − | 0.0682146i | ||||
\(617\) | −1.92851 | + | 1.92851i | −0.0776389 | + | 0.0776389i | −0.744860 | − | 0.667221i | \(-0.767484\pi\) |
0.667221 | + | 0.744860i | \(0.267484\pi\) | |||||||
\(618\) | −1.13063 | − | 1.13063i | −0.0454805 | − | 0.0454805i | ||||
\(619\) | 11.8647 | 0.476884 | 0.238442 | − | 0.971157i | \(-0.423363\pi\) | ||||
0.238442 | + | 0.971157i | \(0.423363\pi\) | |||||||
\(620\) | 9.75833 | − | 5.44312i | 0.391904 | − | 0.218601i | ||||
\(621\) | − | 1.52280i | − | 0.0611078i | ||||||
\(622\) | −17.9275 | − | 17.9275i | −0.718827 | − | 0.718827i | ||||
\(623\) | −28.1889 | + | 2.57280i | −1.12936 | + | 0.103077i | ||||
\(624\) | 0.333142i | 0.0133363i | ||||||||
\(625\) | −11.1978 | − | 22.3520i | −0.447911 | − | 0.894078i | ||||
\(626\) | − | 27.9582i | − | 1.11744i | ||||||
\(627\) | 0.157678 | − | 0.157678i | 0.00629705 | − | 0.00629705i | ||||
\(628\) | 12.9197 | − | 12.9197i | 0.515552 | − | 0.515552i | ||||
\(629\) | 30.5668 | 1.21878 | ||||||||
\(630\) | −17.3840 | − | 3.26358i | −0.692596 | − | 0.130024i | ||||
\(631\) | −47.5513 | −1.89299 | −0.946494 | − | 0.322721i | \(-0.895402\pi\) | ||||
−0.946494 | + | 0.322721i | \(0.895402\pi\) | |||||||
\(632\) | −2.03384 | + | 2.03384i | −0.0809017 | + | 0.0809017i | ||||
\(633\) | 1.73063 | − | 1.73063i | 0.0687864 | − | 0.0687864i | ||||
\(634\) | 12.6919i | 0.504059i | ||||||||
\(635\) | 5.11569 | − | 18.0213i | 0.203010 | − | 0.715155i | ||||
\(636\) | 0.514879i | 0.0204163i | ||||||||
\(637\) | −13.0822 | + | 18.9849i | −0.518335 | + | 0.752208i | ||||
\(638\) | −4.22621 | − | 4.22621i | −0.167317 | − | 0.167317i | ||||
\(639\) | − | 26.2577i | − | 1.03874i | ||||||
\(640\) | −2.15108 | − | 0.610623i | −0.0850288 | − | 0.0241370i | ||||
\(641\) | 38.1531 | 1.50696 | 0.753478 | − | 0.657473i | \(-0.228374\pi\) | ||||
0.753478 | + | 0.657473i | \(0.228374\pi\) | |||||||
\(642\) | −0.612638 | − | 0.612638i | −0.0241789 | − | 0.0241789i | ||||
\(643\) | 12.3659 | − | 12.3659i | 0.487664 | − | 0.487664i | −0.419904 | − | 0.907568i | \(-0.637936\pi\) |
0.907568 | + | 0.419904i | \(0.137936\pi\) | |||||||
\(644\) | 4.25552 | − | 5.11035i | 0.167691 | − | 0.201376i | ||||
\(645\) | 0.324672 | − | 0.181099i | 0.0127839 | − | 0.00713078i | ||||
\(646\) | −7.52619 | −0.296114 | ||||||||
\(647\) | −26.3540 | − | 26.3540i | −1.03608 | − | 1.03608i | −0.999324 | − | 0.0367565i | \(-0.988297\pi\) |
−0.0367565 | − | 0.999324i | \(-0.511703\pi\) | |||||||
\(648\) | −6.29893 | − | 6.29893i | −0.247445 | − | 0.247445i | ||||
\(649\) | −3.32581 | −0.130550 | ||||||||
\(650\) | −14.0122 | − | 8.65249i | −0.549605 | − | 0.339379i | ||||
\(651\) | −1.02760 | − | 0.855713i | −0.0402750 | − | 0.0335381i | ||||
\(652\) | −17.2431 | + | 17.2431i | −0.675292 | + | 0.675292i | ||||
\(653\) | −7.24581 | − | 7.24581i | −0.283550 | − | 0.283550i | 0.550973 | − | 0.834523i | \(-0.314257\pi\) |
−0.834523 | + | 0.550973i | \(0.814257\pi\) | |||||||
\(654\) | 0.883709 | 0.0345557 | ||||||||
\(655\) | −11.3348 | − | 20.3209i | −0.442888 | − | 0.794002i | ||||
\(656\) | − | 8.47999i | − | 0.331088i | ||||||
\(657\) | −6.21250 | − | 6.21250i | −0.242373 | − | 0.242373i | ||||
\(658\) | 17.8858 | − | 1.63243i | 0.697260 | − | 0.0636389i | ||||
\(659\) | − | 27.4624i | − | 1.06978i | −0.844921 | − | 0.534891i | \(-0.820353\pi\) | ||
0.844921 | − | 0.534891i | \(-0.179647\pi\) | |||||||
\(660\) | −0.217572 | − | 0.0617619i | −0.00846899 | − | 0.00240408i | ||||
\(661\) | − | 43.3288i | − | 1.68530i | −0.538464 | − | 0.842648i | \(-0.680995\pi\) | ||
0.538464 | − | 0.842648i | \(-0.319005\pi\) | |||||||
\(662\) | −11.3287 | + | 11.3287i | −0.440303 | + | 0.440303i | ||||
\(663\) | 0.804175 | − | 0.804175i | 0.0312316 | − | 0.0312316i | ||||
\(664\) | 4.52017 | 0.175417 | ||||||||
\(665\) | 10.7660 | − | 7.36265i | 0.417489 | − | 0.285512i | ||||
\(666\) | −26.7701 | −1.03732 | ||||||||
\(667\) | 10.6227 | − | 10.6227i | 0.411314 | − | 0.411314i | ||||
\(668\) | −14.8739 | + | 14.8739i | −0.575489 | + | 0.575489i | ||||
\(669\) | 2.05657i | 0.0795116i | ||||||||
\(670\) | 14.6857 | + | 26.3282i | 0.567356 | + | 1.01715i | ||||
\(671\) | − | 11.2082i | − | 0.432689i | ||||||
\(672\) | 0.0243233 | + | 0.266498i | 0.000938292 | + | 0.0102804i | ||||
\(673\) | 18.0721 | + | 18.0721i | 0.696628 | + | 0.696628i | 0.963682 | − | 0.267054i | \(-0.0860501\pi\) |
−0.267054 | + | 0.963682i | \(0.586050\pi\) | |||||||
\(674\) | 17.3217i | 0.667206i | ||||||||
\(675\) | −2.94789 | + | 0.697116i | −0.113464 | + | 0.0268320i | ||||
\(676\) | 2.15166 | 0.0827561 | ||||||||
\(677\) | 29.8145 | + | 29.8145i | 1.14586 | + | 1.14586i | 0.987358 | + | 0.158505i | \(0.0506675\pi\) |
0.158505 | + | 0.987358i | \(0.449333\pi\) | |||||||
\(678\) | −0.735238 | + | 0.735238i | −0.0282366 | + | 0.0282366i | ||||
\(679\) | −9.48246 | − | 7.89630i | −0.363904 | − | 0.303032i | ||||
\(680\) | 3.71853 | + | 6.66651i | 0.142599 | + | 0.255649i | ||||
\(681\) | −0.998817 | −0.0382748 | ||||||||
\(682\) | 3.53345 | + | 3.53345i | 0.135303 | + | 0.135303i | ||||
\(683\) | 10.0456 | + | 10.0456i | 0.384383 | + | 0.384383i | 0.872679 | − | 0.488295i | \(-0.162381\pi\) |
−0.488295 | + | 0.872679i | \(0.662381\pi\) | |||||||
\(684\) | 6.59138 | 0.252028 | ||||||||
\(685\) | −5.16889 | + | 18.2087i | −0.197493 | + | 0.695720i | ||||
\(686\) | −9.07904 | + | 16.1422i | −0.346640 | + | 0.616312i | ||||
\(687\) | 0.00974840 | − | 0.00974840i | 0.000371925 | − | 0.000371925i | ||||
\(688\) | 1.16231 | + | 1.16231i | 0.0443125 | + | 0.0443125i | ||||
\(689\) | −16.7664 | −0.638748 | ||||||||
\(690\) | 0.155241 | − | 0.546876i | 0.00590992 | − | 0.0208192i | ||||
\(691\) | 48.2925i | 1.83713i | 0.395268 | + | 0.918566i | \(0.370652\pi\) | ||||
−0.395268 | + | 0.918566i | \(0.629348\pi\) | |||||||
\(692\) | 10.7916 | + | 10.7916i | 0.410235 | + | 0.410235i | ||||
\(693\) | −0.718974 | − | 7.87744i | −0.0273116 | − | 0.299239i | ||||
\(694\) | 12.6298i | 0.479420i | ||||||||
\(695\) | 10.2091 | − | 5.69455i | 0.387253 | − | 0.216007i | ||||
\(696\) | 0.604524i | 0.0229144i | ||||||||
\(697\) | −20.4700 | + | 20.4700i | −0.775355 | + | 0.775355i | ||||
\(698\) | 9.99204 | − | 9.99204i | 0.378204 | − | 0.378204i | ||||
\(699\) | 2.32528 | 0.0879500 | ||||||||
\(700\) | −11.8409 | − | 5.89855i | −0.447544 | − | 0.222944i | ||||
\(701\) | −40.4290 | −1.52698 | −0.763491 | − | 0.645818i | \(-0.776516\pi\) | ||||
−0.763491 | + | 0.645818i | \(0.776516\pi\) | |||||||
\(702\) | −1.41099 | + | 1.41099i | −0.0532544 | + | 0.0532544i | ||||
\(703\) | 13.9584 | − | 13.9584i | 0.526452 | − | 0.526452i | ||||
\(704\) | − | 1.00000i | − | 0.0376889i | ||||||
\(705\) | 1.34082 | − | 0.747896i | 0.0504980 | − | 0.0281674i | ||||
\(706\) | − | 16.5778i | − | 0.623912i | ||||||
\(707\) | 2.63990 | + | 28.9241i | 0.0992837 | + | 1.08780i | ||||
\(708\) | 0.237865 | + | 0.237865i | 0.00893950 | + | 0.00893950i | ||||
\(709\) | 47.7680i | 1.79396i | 0.442066 | + | 0.896982i | \(0.354246\pi\) | ||||
−0.442066 | + | 0.896982i | \(0.645754\pi\) | |||||||
\(710\) | 5.36280 | − | 18.8919i | 0.201262 | − | 0.708999i | ||||
\(711\) | −8.59941 | −0.322503 | ||||||||
\(712\) | −7.56512 | − | 7.56512i | −0.283515 | − | 0.283515i | ||||
\(713\) | −8.88145 | + | 8.88145i | −0.332613 | + | 0.332613i | ||||
\(714\) | 0.584590 | − | 0.702019i | 0.0218777 | − | 0.0262724i | ||||
\(715\) | 2.01120 | − | 7.08497i | 0.0752146 | − | 0.264963i | ||||
\(716\) | −7.88097 | −0.294526 | ||||||||
\(717\) | −0.422096 | − | 0.422096i | −0.0157635 | − | 0.0157635i | ||||
\(718\) | −23.8429 | − | 23.8429i | −0.889809 | − | 0.889809i | ||||
\(719\) | 8.73237 | 0.325662 | 0.162831 | − | 0.986654i | \(-0.447937\pi\) | ||||
0.162831 | + | 0.986654i | \(0.447937\pi\) | |||||||
\(720\) | −3.25666 | − | 5.83848i | −0.121368 | − | 0.217587i | ||||
\(721\) | 26.7642 | − | 32.1404i | 0.996751 | − | 1.19697i | ||||
\(722\) | 9.99816 | − | 9.99816i | 0.372093 | − | 0.372093i | ||||
\(723\) | 0.435059 | + | 0.435059i | 0.0161800 | + | 0.0161800i | ||||
\(724\) | −25.8379 | −0.960259 | ||||||||
\(725\) | −25.4268 | − | 15.7010i | −0.944329 | − | 0.583119i | ||||
\(726\) | − | 0.101146i | − | 0.00375387i | ||||||
\(727\) | 7.82764 | + | 7.82764i | 0.290311 | + | 0.290311i | 0.837203 | − | 0.546892i | \(-0.184189\pi\) |
−0.546892 | + | 0.837203i | \(0.684189\pi\) | |||||||
\(728\) | −8.67819 | + | 0.792058i | −0.321635 | + | 0.0293556i | ||||
\(729\) | − | 26.4491i | − | 0.979597i | ||||||
\(730\) | −3.20094 | − | 5.73860i | −0.118472 | − | 0.212395i | ||||
\(731\) | − | 5.61141i | − | 0.207546i | ||||||
\(732\) | −0.801622 | + | 0.801622i | −0.0296288 | + | 0.0296288i | ||||
\(733\) | −16.9468 | + | 16.9468i | −0.625944 | + | 0.625944i | −0.947045 | − | 0.321101i | \(-0.895947\pi\) |
0.321101 | + | 0.947045i | \(0.395947\pi\) | |||||||
\(734\) | 20.3061 | 0.749510 | ||||||||
\(735\) | −0.149477 | + | 1.57611i | −0.00551355 | + | 0.0581356i | ||||
\(736\) | 2.51354 | 0.0926502 | ||||||||
\(737\) | −9.53332 | + | 9.53332i | −0.351164 | + | 0.351164i | ||||
\(738\) | 17.9274 | − | 17.9274i | 0.659918 | − | 0.659918i | ||||
\(739\) | 14.9605i | 0.550331i | 0.961397 | + | 0.275166i | \(0.0887327\pi\) | ||||
−0.961397 | + | 0.275166i | \(0.911267\pi\) | |||||||
\(740\) | −19.2606 | − | 5.46746i | −0.708032 | − | 0.200988i | ||||
\(741\) | − | 0.734459i | − | 0.0269810i | ||||||
\(742\) | −13.4124 | + | 1.22415i | −0.492383 | + | 0.0449398i | ||||
\(743\) | −10.5859 | − | 10.5859i | −0.388359 | − | 0.388359i | 0.485743 | − | 0.874102i | \(-0.338549\pi\) |
−0.874102 | + | 0.485743i | \(0.838549\pi\) | |||||||
\(744\) | − | 0.505430i | − | 0.0185300i | ||||||
\(745\) | −2.85601 | − | 5.12021i | −0.104636 | − | 0.187590i | ||||
\(746\) | −8.38306 | −0.306926 | ||||||||
\(747\) | 9.55604 | + | 9.55604i | 0.349637 | + | 0.349637i | ||||
\(748\) | −2.41391 | + | 2.41391i | −0.0882614 | + | 0.0882614i | ||||
\(749\) | 14.5024 | − | 17.4155i | 0.529906 | − | 0.636350i | ||||
\(750\) | −1.12973 | − | 0.0501686i | −0.0412519 | − | 0.00183190i | ||||
\(751\) | 5.62163 | 0.205136 | 0.102568 | − | 0.994726i | \(-0.467294\pi\) | ||||
0.102568 | + | 0.994726i | \(0.467294\pi\) | |||||||
\(752\) | 4.80004 | + | 4.80004i | 0.175040 | + | 0.175040i | ||||
\(753\) | 0.953393 | + | 0.953393i | 0.0347436 | + | 0.0347436i | ||||
\(754\) | −19.6856 | −0.716906 | ||||||||
\(755\) | 2.80503 | − | 1.56462i | 0.102085 | − | 0.0569425i | ||||
\(756\) | −1.02571 | + | 1.23175i | −0.0373047 | + | 0.0447983i | ||||
\(757\) | −7.51547 | + | 7.51547i | −0.273155 | + | 0.273155i | −0.830369 | − | 0.557214i | \(-0.811870\pi\) |
0.557214 | + | 0.830369i | \(0.311870\pi\) | |||||||
\(758\) | 20.6301 | + | 20.6301i | 0.749321 | + | 0.749321i | ||||
\(759\) | 0.254233 | 0.00922809 | ||||||||
\(760\) | 4.74237 | + | 1.34621i | 0.172024 | + | 0.0488321i | ||||
\(761\) | − | 41.6701i | − | 1.51054i | −0.655414 | − | 0.755270i | \(-0.727506\pi\) | ||
0.655414 | − | 0.755270i | \(-0.272494\pi\) | |||||||
\(762\) | −0.599188 | − | 0.599188i | −0.0217063 | − | 0.0217063i | ||||
\(763\) | 2.10106 | + | 23.0202i | 0.0760633 | + | 0.833388i | ||||
\(764\) | 23.4159i | 0.847159i | ||||||||
\(765\) | −6.23229 | + | 21.9549i | −0.225329 | + | 0.793780i | ||||
\(766\) | − | 8.84254i | − | 0.319494i | ||||||
\(767\) | −7.74577 | + | 7.74577i | −0.279683 | + | 0.279683i | ||||
\(768\) | −0.0715208 | + | 0.0715208i | −0.00258078 | + | 0.00258078i | ||||
\(769\) | −20.9854 | −0.756755 | −0.378377 | − | 0.925651i | \(-0.623518\pi\) | ||||
−0.378377 | + | 0.925651i | \(0.623518\pi\) | |||||||
\(770\) | 1.09158 | − | 5.81450i | 0.0393379 | − | 0.209540i | ||||
\(771\) | 1.74440 | 0.0628231 | ||||||||
\(772\) | 12.0396 | − | 12.0396i | 0.433316 | − | 0.433316i | ||||
\(773\) | 7.21149 | − | 7.21149i | 0.259379 | − | 0.259379i | −0.565422 | − | 0.824802i | \(-0.691287\pi\) |
0.824802 | + | 0.565422i | \(0.191287\pi\) | |||||||
\(774\) | 4.91443i | 0.176646i | ||||||||
\(775\) | 21.2588 | + | 13.1272i | 0.763640 | + | 0.471544i | ||||
\(776\) | − | 4.66398i | − | 0.167427i | ||||||
\(777\) | 0.217789 | + | 2.38620i | 0.00781313 | + | 0.0856046i | ||||
\(778\) | 6.10826 | + | 6.10826i | 0.218992 | + | 0.218992i | ||||
\(779\) | 18.6954i | 0.669832i | ||||||||
\(780\) | −0.650565 | + | 0.362880i | −0.0232940 | + | 0.0129932i | ||||
\(781\) | 8.78250 | 0.314263 | ||||||||
\(782\) | −6.06746 | − | 6.06746i | −0.216972 | − | 0.216972i | ||||
\(783\) | −2.56041 | + | 2.56041i | −0.0915014 | + | 0.0915014i | ||||
\(784\) | −6.88434 | + | 1.26722i | −0.245869 | + | 0.0452580i | ||||
\(785\) | 39.3028 | + | 11.1568i | 1.40278 | + | 0.398204i | ||||
\(786\) | −1.05251 | −0.0375419 | ||||||||
\(787\) | 34.6798 | + | 34.6798i | 1.23620 | + | 1.23620i | 0.961541 | + | 0.274661i | \(0.0885656\pi\) |
0.274661 | + | 0.961541i | \(0.411434\pi\) | |||||||
\(788\) | 12.7592 | + | 12.7592i | 0.454528 | + | 0.454528i | ||||
\(789\) | −0.161757 | −0.00575869 | ||||||||
\(790\) | −6.18710 | − | 1.75632i | −0.220127 | − | 0.0624872i | ||||
\(791\) | −20.9007 | − | 17.4046i | −0.743143 | − | 0.618835i | ||||
\(792\) | 2.11409 | − | 2.11409i | 0.0751208 | − | 0.0751208i | ||||
\(793\) | −26.1038 | − | 26.1038i | −0.926974 | − | 0.926974i | ||||
\(794\) | −14.6283 | −0.519138 | ||||||||
\(795\) | −1.00546 | + | 0.560840i | −0.0356601 | + | 0.0198909i | ||||
\(796\) | 1.49431i | 0.0529643i | ||||||||
\(797\) | 37.7255 | + | 37.7255i | 1.33631 | + | 1.33631i | 0.899607 | + | 0.436700i | \(0.143853\pi\) |
0.436700 | + | 0.899607i | \(0.356147\pi\) | |||||||
\(798\) | −0.0536243 | − | 0.587535i | −0.00189828 | − | 0.0207985i | ||||
\(799\) | − | 23.1738i | − | 0.819829i | ||||||
\(800\) | −1.15066 | − | 4.86580i | −0.0406821 | − | 0.172032i | ||||
\(801\) | − | 31.9866i | − | 1.13019i | ||||||
\(802\) | −5.60409 | + | 5.60409i | −0.197887 | + | 0.197887i | ||||
\(803\) | 2.07792 | − | 2.07792i | 0.0733282 | − | 0.0733282i | ||||
\(804\) | 1.36366 | 0.0480926 | ||||||||
\(805\) | 14.6150 | + | 2.74373i | 0.515110 | + | 0.0967039i | ||||
\(806\) | 16.4587 | 0.579733 | ||||||||
\(807\) | 1.15285 | − | 1.15285i | 0.0405823 | − | 0.0405823i | ||||
\(808\) | −7.76242 | + | 7.76242i | −0.273081 | + | 0.273081i | ||||
\(809\) | 3.18549i | 0.111996i | 0.998431 | + | 0.0559979i | \(0.0178340\pi\) | ||||
−0.998431 | + | 0.0559979i | \(0.982166\pi\) | |||||||
\(810\) | 5.43945 | − | 19.1619i | 0.191123 | − | 0.673280i | ||||
\(811\) | − | 21.8060i | − | 0.765711i | −0.923808 | − | 0.382856i | \(-0.874941\pi\) | ||
0.923808 | − | 0.382856i | \(-0.125059\pi\) | |||||||
\(812\) | −15.7476 | + | 1.43728i | −0.552632 | + | 0.0504387i | ||||
\(813\) | 0.377199 | + | 0.377199i | 0.0132290 | + | 0.0132290i | ||||
\(814\) | − | 8.95391i | − | 0.313834i | ||||||
\(815\) | −52.4550 | − | 14.8903i | −1.83742 | − | 0.521585i | ||||
\(816\) | 0.345290 | 0.0120876 | ||||||||
\(817\) | −2.56247 | − | 2.56247i | −0.0896496 | − | 0.0896496i | ||||
\(818\) | −21.0144 | + | 21.0144i | −0.734752 | + | 0.734752i | ||||
\(819\) | −20.0209 | − | 16.6720i | −0.699588 | − | 0.582566i | ||||
\(820\) | 16.5599 | − | 9.23697i | 0.578296 | − | 0.322569i | ||||
\(821\) | 52.2377 | 1.82311 | 0.911554 | − | 0.411180i | \(-0.134883\pi\) | ||||
0.911554 | + | 0.411180i | \(0.134883\pi\) | |||||||
\(822\) | 0.605419 | + | 0.605419i | 0.0211164 | + | 0.0211164i | ||||
\(823\) | 23.7810 | + | 23.7810i | 0.828954 | + | 0.828954i | 0.987372 | − | 0.158418i | \(-0.0506394\pi\) |
−0.158418 | + | 0.987372i | \(0.550639\pi\) | |||||||
\(824\) | 15.8084 | 0.550710 | ||||||||
\(825\) | −0.116384 | − | 0.492154i | −0.00405199 | − | 0.0171346i | ||||
\(826\) | −5.63074 | + | 6.76180i | −0.195918 | + | 0.235273i | ||||
\(827\) | 7.97578 | − | 7.97578i | 0.277345 | − | 0.277345i | −0.554703 | − | 0.832048i | \(-0.687168\pi\) |
0.832048 | + | 0.554703i | \(0.187168\pi\) | |||||||
\(828\) | 5.31384 | + | 5.31384i | 0.184669 | + | 0.184669i | ||||
\(829\) | −44.2643 | −1.53736 | −0.768681 | − | 0.639633i | \(-0.779086\pi\) | ||||
−0.768681 | + | 0.639633i | \(0.779086\pi\) | |||||||
\(830\) | 4.92367 | + | 8.82708i | 0.170903 | + | 0.306392i | ||||
\(831\) | 0.934516i | 0.0324180i | ||||||||
\(832\) | −2.32898 | − | 2.32898i | −0.0807430 | − | 0.0807430i | ||||
\(833\) | 19.6772 | + | 13.5592i | 0.681773 | + | 0.469800i | ||||
\(834\) | − | 0.528777i | − | 0.0183100i | ||||||
\(835\) | −45.2477 | − | 12.8444i | −1.56586 | − | 0.444498i | ||||
\(836\) | 2.20465i | 0.0762493i | ||||||||
\(837\) | 2.14070 | − | 2.14070i | 0.0739934 | − | 0.0739934i | ||||
\(838\) | 4.90397 | − | 4.90397i | 0.169405 | − | 0.169405i | ||||
\(839\) | 14.2746 | 0.492814 | 0.246407 | − | 0.969166i | \(-0.420750\pi\) | ||||
0.246407 | + | 0.969166i | \(0.420750\pi\) | |||||||
\(840\) | −0.493929 | + | 0.337787i | −0.0170422 | + | 0.0116548i | ||||
\(841\) | −6.72177 | −0.231785 | ||||||||
\(842\) | −17.2683 | + | 17.2683i | −0.595106 | + | 0.595106i | ||||
\(843\) | −0.192044 | + | 0.192044i | −0.00661434 | + | 0.00661434i | ||||
\(844\) | 24.1976i | 0.832916i | ||||||||
\(845\) | 2.34373 | + | 4.20180i | 0.0806267 | + | 0.144546i | ||||
\(846\) | 20.2954i | 0.697770i | ||||||||
\(847\) | 2.63480 | − | 0.240478i | 0.0905328 | − | 0.00826293i | ||||
\(848\) | −3.59950 | − | 3.59950i | −0.123608 | − | 0.123608i | ||||
\(849\) | − | 2.76405i | − | 0.0948621i | ||||||
\(850\) | −8.96801 | + | 14.5232i | −0.307600 | + | 0.498142i | ||||
\(851\) | 22.5060 | 0.771495 | ||||||||
\(852\) | −0.628131 | − | 0.628131i | −0.0215194 | − | 0.0215194i | ||||
\(853\) | 10.2914 | − | 10.2914i | 0.352370 | − | 0.352370i | −0.508621 | − | 0.860991i | \(-0.669845\pi\) |
0.860991 | + | 0.508621i | \(0.169845\pi\) | |||||||
\(854\) | −22.7878 | − | 18.9760i | −0.779782 | − | 0.649346i | ||||
\(855\) | 7.17977 | + | 12.8718i | 0.245543 | + | 0.440205i | ||||
\(856\) | 8.56588 | 0.292776 | ||||||||
\(857\) | 4.63187 | + | 4.63187i | 0.158222 | + | 0.158222i | 0.781778 | − | 0.623557i | \(-0.214313\pi\) |
−0.623557 | + | 0.781778i | \(0.714313\pi\) | |||||||
\(858\) | −0.235567 | − | 0.235567i | −0.00804211 | − | 0.00804211i | ||||
\(859\) | 17.4622 | 0.595802 | 0.297901 | − | 0.954597i | \(-0.403713\pi\) | ||||
0.297901 | + | 0.954597i | \(0.403713\pi\) | |||||||
\(860\) | −1.00371 | + | 3.53583i | −0.0342263 | + | 0.120571i | ||||
\(861\) | −1.74384 | − | 1.45215i | −0.0594300 | − | 0.0494890i | ||||
\(862\) | 7.60843 | − | 7.60843i | 0.259144 | − | 0.259144i | ||||
\(863\) | −12.3634 | − | 12.3634i | −0.420854 | − | 0.420854i | 0.464644 | − | 0.885498i | \(-0.346182\pi\) |
−0.885498 | + | 0.464644i | \(0.846182\pi\) | |||||||
\(864\) | −0.605839 | −0.0206111 | ||||||||
\(865\) | −9.31910 | + | 32.8289i | −0.316859 | + | 1.11622i | ||||
\(866\) | 16.3502i | 0.555604i | ||||||||
\(867\) | 0.382353 | + | 0.382353i | 0.0129854 | + | 0.0129854i | ||||
\(868\) | 13.1662 | − | 1.20168i | 0.446891 | − | 0.0407877i | ||||
\(869\) | − | 2.87628i | − | 0.0975711i | ||||||
\(870\) | −1.18053 | + | 0.658488i | −0.0400236 | + | 0.0223248i | ||||
\(871\) | 44.4059i | 1.50464i | ||||||||
\(872\) | −6.17799 | + | 6.17799i | −0.209213 | + | 0.209213i | ||||
\(873\) | 9.86005 | − | 9.86005i | 0.333712 | − | 0.333712i | ||||
\(874\) | −5.54146 | −0.187443 | ||||||||
\(875\) | −1.37911 | − | 29.5482i | −0.0466225 | − | 0.998913i | ||||
\(876\) | −0.297229 | −0.0100424 | ||||||||
\(877\) | −21.8767 | + | 21.8767i | −0.738722 | + | 0.738722i | −0.972331 | − | 0.233609i | \(-0.924947\pi\) |
0.233609 | + | 0.972331i | \(0.424947\pi\) | |||||||
\(878\) | 8.82709 | − | 8.82709i | 0.297900 | − | 0.297900i | ||||
\(879\) | − | 2.29007i | − | 0.0772422i | ||||||
\(880\) | 1.95282 | − | 1.08927i | 0.0658295 | − | 0.0367192i | ||||
\(881\) | 42.6802i | 1.43793i | 0.695045 | + | 0.718966i | \(0.255384\pi\) | ||||
−0.695045 | + | 0.718966i | \(0.744616\pi\) | |||||||
\(882\) | −17.2331 | − | 11.8751i | −0.580269 | − | 0.399854i | ||||
\(883\) | 16.6870 | + | 16.6870i | 0.561563 | + | 0.561563i | 0.929751 | − | 0.368188i | \(-0.120022\pi\) |
−0.368188 | + | 0.929751i | \(0.620022\pi\) | |||||||
\(884\) | 11.2439i | 0.378174i | ||||||||
\(885\) | −0.205408 | + | 0.723604i | −0.00690473 | + | 0.0243237i | ||||
\(886\) | −10.2637 | −0.344815 | ||||||||
\(887\) | −16.6285 | − | 16.6285i | −0.558331 | − | 0.558331i | 0.370501 | − | 0.928832i | \(-0.379186\pi\) |
−0.928832 | + | 0.370501i | \(0.879186\pi\) | |||||||
\(888\) | −0.640391 | + | 0.640391i | −0.0214901 | + | 0.0214901i | ||||
\(889\) | 14.1840 | − | 17.0332i | 0.475716 | − | 0.571275i | ||||
\(890\) | 6.53287 | − | 23.0137i | 0.218982 | − | 0.771422i | ||||
\(891\) | 8.90803 | 0.298430 | ||||||||
\(892\) | −14.3774 | − | 14.3774i | −0.481392 | − | 0.481392i | ||||
\(893\) | −10.5824 | − | 10.5824i | −0.354126 | − | 0.354126i | ||||
\(894\) | −0.265200 | −0.00886960 | ||||||||
\(895\) | −8.58447 | − | 15.3901i | −0.286947 | − | 0.514434i | ||||
\(896\) | −2.03313 | − | 1.69304i | −0.0679221 | − | 0.0565605i | ||||
\(897\) | 0.592106 | − | 0.592106i | 0.0197698 | − | 0.0197698i | ||||
\(898\) | −4.92917 | − | 4.92917i | −0.164489 | − | 0.164489i | ||||
\(899\) | 29.8662 | 0.996094 | ||||||||
\(900\) | 7.85411 | − | 12.7193i | 0.261804 | − | 0.423977i | ||||
\(901\) | 17.3778i | 0.578938i | ||||||||
\(902\) | 5.99626 | + | 5.99626i | 0.199654 | + | 0.199654i | ||||
\(903\) | 0.438057 | − | 0.0399814i | 0.0145776 | − | 0.00133050i | ||||
\(904\) | − | 10.2801i | − | 0.341910i | ||||||
\(905\) | −28.1444 | − | 50.4568i | −0.935551 | − | 1.67724i | ||||
\(906\) | − | 0.145286i | − | 0.00482679i | ||||||
\(907\) | −12.2498 | + | 12.2498i | −0.406748 | + | 0.406748i | −0.880603 | − | 0.473855i | \(-0.842862\pi\) |
0.473855 | + | 0.880603i | \(0.342862\pi\) | |||||||
\(908\) | 6.98271 | − | 6.98271i | 0.231729 | − | 0.231729i | ||||
\(909\) | −32.8208 | −1.08860 | ||||||||
\(910\) | −10.9996 | − | 16.0842i | −0.364634 | − | 0.533185i | ||||
\(911\) | −5.64056 | −0.186880 | −0.0934401 | − | 0.995625i | \(-0.529786\pi\) | ||||
−0.0934401 | + | 0.995625i | \(0.529786\pi\) | |||||||
\(912\) | 0.157678 | − | 0.157678i | 0.00522124 | − | 0.00522124i | ||||
\(913\) | −3.19625 | + | 3.19625i | −0.105780 | + | 0.105780i | ||||
\(914\) | 17.5745i | 0.581314i | ||||||||
\(915\) | −2.43860 | − | 0.692242i | −0.0806177 | − | 0.0228848i | ||||
\(916\) | 0.136302i | 0.00450354i | ||||||||
\(917\) | −2.50239 | − | 27.4175i | −0.0826364 | − | 0.905406i | ||||
\(918\) | 1.46244 | + | 1.46244i | 0.0482678 | + | 0.0482678i | ||||
\(919\) | 36.5538i | 1.20580i | 0.797817 | + | 0.602900i | \(0.205988\pi\) | ||||
−0.797817 | + | 0.602900i | \(0.794012\pi\) | |||||||
\(920\) | 2.73791 | + | 4.90848i | 0.0902663 | + | 0.161828i | ||||
\(921\) | 2.00027 | 0.0659111 | ||||||||
\(922\) | 8.07620 | + | 8.07620i | 0.265976 | + | 0.265976i | ||||
\(923\) | 20.4543 | − | 20.4543i | 0.673262 | − | 0.673262i | ||||
\(924\) | −0.205642 | − | 0.171244i | −0.00676513 | − | 0.00563350i | ||||
\(925\) | −10.3029 | − | 43.5679i | −0.338758 | − | 1.43250i | ||||
\(926\) | −20.7575 | −0.682134 | ||||||||
\(927\) | 33.4202 | + | 33.4202i | 1.09766 | + | 1.09766i | ||||
\(928\) | −4.22621 | − | 4.22621i | −0.138732 | − | 0.138732i | ||||
\(929\) | 27.8619 | 0.914121 | 0.457060 | − | 0.889436i | \(-0.348902\pi\) | ||||
0.457060 | + | 0.889436i | \(0.348902\pi\) | |||||||
\(930\) | 0.987012 | − | 0.550548i | 0.0323654 | − | 0.0180532i | ||||
\(931\) | 15.1775 | − | 2.79378i | 0.497423 | − | 0.0915624i | ||||
\(932\) | −16.2560 | + | 16.2560i | −0.532481 | + | 0.532481i | ||||
\(933\) | −1.81329 | − | 1.81329i | −0.0593644 | − | 0.0593644i | ||||
\(934\) | −14.7921 | −0.484011 | ||||||||
\(935\) | −7.34333 | − | 2.08454i | −0.240153 | − | 0.0681717i | ||||
\(936\) | − | 9.84735i | − | 0.321871i | ||||||
\(937\) | 18.9935 | + | 18.9935i | 0.620491 | + | 0.620491i | 0.945657 | − | 0.325166i | \(-0.105420\pi\) |
−0.325166 | + | 0.945657i | \(0.605420\pi\) | |||||||
\(938\) | 3.24216 | + | 35.5228i | 0.105860 | + | 1.15986i | ||||
\(939\) | − | 2.82785i | − | 0.0922835i | ||||||
\(940\) | −4.14508 | + | 14.6021i | −0.135198 | + | 0.476269i | ||||
\(941\) | 4.42718i | 0.144322i | 0.997393 | + | 0.0721609i | \(0.0229895\pi\) | ||||
−0.997393 | + | 0.0721609i | \(0.977010\pi\) | |||||||
\(942\) | 1.30677 | − | 1.30677i | 0.0425769 | − | 0.0425769i | ||||
\(943\) | −15.0718 | + | 15.0718i | −0.490806 | + | 0.490806i | ||||
\(944\) | −3.32581 | −0.108246 | ||||||||
\(945\) | −3.52265 | − | 0.661323i | −0.114592 | − | 0.0215128i | ||||
\(946\) | −1.64375 | −0.0534429 | ||||||||
\(947\) | 22.9444 | − | 22.9444i | 0.745591 | − | 0.745591i | −0.228057 | − | 0.973648i | \(-0.573237\pi\) |
0.973648 | + | 0.228057i | \(0.0732371\pi\) | |||||||
\(948\) | −0.205714 | + | 0.205714i | −0.00668127 | + | 0.00668127i | ||||
\(949\) | − | 9.67889i | − | 0.314190i | ||||||
\(950\) | 2.53680 | + | 10.7274i | 0.0823047 | + | 0.348041i | ||||
\(951\) | 1.28373i | 0.0416277i | ||||||||
\(952\) | 0.820941 | + | 8.99465i | 0.0266069 | + | 0.291518i | ||||
\(953\) | 9.18554 | + | 9.18554i | 0.297549 | + | 0.297549i | 0.840053 | − | 0.542504i | \(-0.182524\pi\) |
−0.542504 | + | 0.840053i | \(0.682524\pi\) | |||||||
\(954\) | − | 15.2193i | − | 0.492744i | ||||||
\(955\) | −45.7271 | + | 25.5062i | −1.47969 | + | 0.825361i | ||||
\(956\) | 5.90173 | 0.190876 | ||||||||
\(957\) | −0.427463 | − | 0.427463i | −0.0138179 | − | 0.0138179i | ||||
\(958\) | −5.26944 | + | 5.26944i | −0.170248 | + | 0.170248i | ||||
\(959\) | −14.3315 | + | 17.2103i | −0.462788 | + | 0.555750i | ||||
\(960\) | −0.217572 | − | 0.0617619i | −0.00702211 | − | 0.00199336i | ||||
\(961\) | 6.02949 | 0.194500 | ||||||||
\(962\) | −20.8535 | − | 20.8535i | −0.672345 | − | 0.672345i | ||||
\(963\) | 18.1090 | + | 18.1090i | 0.583555 | + | 0.583555i | ||||
\(964\) | −6.08298 | −0.195920 | ||||||||
\(965\) | 36.6256 | + | 10.3969i | 1.17902 | + | 0.334687i | ||||
\(966\) | 0.430428 | − | 0.516889i | 0.0138488 | − | 0.0166306i | ||||
\(967\) | −3.13051 | + | 3.13051i | −0.100670 | + | 0.100670i | −0.755648 | − | 0.654978i | \(-0.772678\pi\) |
0.654978 | + | 0.755648i | \(0.272678\pi\) | |||||||
\(968\) | 0.707107 | + | 0.707107i | 0.0227273 | + | 0.0227273i | ||||
\(969\) | −0.761242 | −0.0244546 | ||||||||
\(970\) | 9.10790 | − | 5.08031i | 0.292437 | − | 0.163119i | ||||
\(971\) | − | 51.0803i | − | 1.63924i | −0.572905 | − | 0.819622i | \(-0.694183\pi\) | ||
0.572905 | − | 0.819622i | \(-0.305817\pi\) | |||||||
\(972\) | −1.92229 | − | 1.92229i | −0.0616574 | − | 0.0616574i | ||||
\(973\) | 13.7744 | − | 1.25719i | 0.441587 | − | 0.0403037i | ||||
\(974\) | − | 13.1916i | − | 0.422686i | ||||||
\(975\) | −1.41728 | − | 0.875162i | −0.0453892 | − | 0.0280276i | ||||
\(976\) | − | 11.2082i | − | 0.358767i | ||||||
\(977\) | 9.99224 | − | 9.99224i | 0.319680 | − | 0.319680i | −0.528964 | − | 0.848644i | \(-0.677419\pi\) |
0.848644 | + | 0.528964i | \(0.177419\pi\) | |||||||
\(978\) | −1.74406 | + | 1.74406i | −0.0557690 | + | 0.0557690i | ||||
\(979\) | 10.6987 | 0.341932 | ||||||||
\(980\) | −9.97354 | − | 12.0635i | −0.318593 | − | 0.385355i | ||||
\(981\) | −26.1216 | −0.833998 | ||||||||
\(982\) | 16.2113 | − | 16.2113i | 0.517324 | − | 0.517324i | ||||
\(983\) | −27.4320 | + | 27.4320i | −0.874943 | + | 0.874943i | −0.993006 | − | 0.118063i | \(-0.962332\pi\) |
0.118063 | + | 0.993006i | \(0.462332\pi\) | |||||||
\(984\) | − | 0.857714i | − | 0.0273429i | ||||||
\(985\) | −11.0182 | + | 38.8146i | −0.351070 | + | 1.23674i | ||||
\(986\) | 20.4034i | 0.649777i | ||||||||
\(987\) | 1.80907 | − | 0.165114i | 0.0575833 | − | 0.00525562i | ||||
\(988\) | 5.13459 | + | 5.13459i | 0.163353 | + | 0.163353i | ||||
\(989\) | − | 4.13163i | − | 0.131378i | ||||||
\(990\) | 6.43123 | + | 1.82562i | 0.204398 | + | 0.0580221i | ||||
\(991\) | −7.82123 | −0.248449 | −0.124225 | − | 0.992254i | \(-0.539644\pi\) | ||||
−0.124225 | + | 0.992254i | \(0.539644\pi\) | |||||||
\(992\) | 3.53345 | + | 3.53345i | 0.112187 | + | 0.112187i | ||||
\(993\) | −1.14585 | + | 1.14585i | −0.0363625 | + | 0.0363625i | ||||
\(994\) | 14.8691 | − | 17.8560i | 0.471621 | − | 0.566357i | ||||
\(995\) | −2.91811 | + | 1.62770i | −0.0925102 | + | 0.0516015i | ||||
\(996\) | 0.457196 | 0.0144868 | ||||||||
\(997\) | −35.2372 | − | 35.2372i | −1.11597 | − | 1.11597i | −0.992326 | − | 0.123649i | \(-0.960540\pi\) |
−0.123649 | − | 0.992326i | \(-0.539460\pi\) | |||||||
\(998\) | −18.0376 | − | 18.0376i | −0.570970 | − | 0.570970i | ||||
\(999\) | −5.42463 | −0.171628 |
(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 | 770.2.l.c.573.5 | ✓ | 40 | |
5.2 | odd | 4 | inner | 770.2.l.c.727.6 | yes | 40 | |
7.6 | odd | 2 | inner | 770.2.l.c.573.6 | yes | 40 | |
35.27 | even | 4 | inner | 770.2.l.c.727.5 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.l.c.573.5 | ✓ | 40 | 1.1 | even | 1 | trivial | |
770.2.l.c.573.6 | yes | 40 | 7.6 | odd | 2 | inner | |
770.2.l.c.727.5 | yes | 40 | 35.27 | even | 4 | inner | |
770.2.l.c.727.6 | yes | 40 | 5.2 | odd | 4 | inner |