Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 323.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.323 |
Dual form | 847.2.f.m.729.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.80902 | + | 1.31433i | 1.27917 | + | 0.929370i | 0.999528 | − | 0.0307347i | \(-0.00978469\pi\) |
0.279641 | + | 0.960105i | \(0.409785\pi\) | |||||||
\(3\) | −0.381966 | + | 1.17557i | −0.220528 | + | 0.678716i | 0.778187 | + | 0.628033i | \(0.216140\pi\) |
−0.998715 | + | 0.0506828i | \(0.983860\pi\) | |||||||
\(4\) | 0.927051 | + | 2.85317i | 0.463525 | + | 1.42658i | ||||
\(5\) | 1.61803 | − | 1.17557i | 0.723607 | − | 0.525731i | −0.163928 | − | 0.986472i | \(-0.552416\pi\) |
0.887535 | + | 0.460741i | \(0.152416\pi\) | |||||||
\(6\) | −2.23607 | + | 1.62460i | −0.912871 | + | 0.663240i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | −0.690983 | + | 2.12663i | −0.244299 | + | 0.751876i | ||||
\(9\) | 1.19098 | + | 0.865300i | 0.396994 | + | 0.288433i | ||||
\(10\) | 4.47214 | 1.41421 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.70820 | −1.07047 | ||||||||
\(13\) | 2.61803 | + | 1.90211i | 0.726112 | + | 0.527551i | 0.888331 | − | 0.459204i | \(-0.151865\pi\) |
−0.162219 | + | 0.986755i | \(0.551865\pi\) | |||||||
\(14\) | 0.690983 | − | 2.12663i | 0.184673 | − | 0.568365i | ||||
\(15\) | 0.763932 | + | 2.35114i | 0.197246 | + | 0.607062i | ||||
\(16\) | 0.809017 | − | 0.587785i | 0.202254 | − | 0.146946i | ||||
\(17\) | −2.61803 | + | 1.90211i | −0.634967 | + | 0.461330i | −0.858117 | − | 0.513454i | \(-0.828366\pi\) |
0.223151 | + | 0.974784i | \(0.428366\pi\) | |||||||
\(18\) | 1.01722 | + | 3.13068i | 0.239761 | + | 0.737909i | ||||
\(19\) | −2.00000 | + | 6.15537i | −0.458831 | + | 1.41214i | 0.407746 | + | 0.913095i | \(0.366315\pi\) |
−0.866577 | + | 0.499043i | \(0.833685\pi\) | |||||||
\(20\) | 4.85410 | + | 3.52671i | 1.08541 | + | 0.788597i | ||||
\(21\) | 1.23607 | 0.269732 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.47214 | 0.515476 | 0.257738 | − | 0.966215i | \(-0.417023\pi\) | ||||
0.257738 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(24\) | −2.23607 | − | 1.62460i | −0.456435 | − | 0.331620i | ||||
\(25\) | −0.309017 | + | 0.951057i | −0.0618034 | + | 0.190211i | ||||
\(26\) | 2.23607 | + | 6.88191i | 0.438529 | + | 1.34965i | ||||
\(27\) | −4.47214 | + | 3.24920i | −0.860663 | + | 0.625308i | ||||
\(28\) | 2.42705 | − | 1.76336i | 0.458670 | − | 0.333243i | ||||
\(29\) | −2.61803 | − | 8.05748i | −0.486157 | − | 1.49624i | −0.830299 | − | 0.557319i | \(-0.811830\pi\) |
0.344142 | − | 0.938918i | \(-0.388170\pi\) | |||||||
\(30\) | −1.70820 | + | 5.25731i | −0.311874 | + | 0.959849i | ||||
\(31\) | 2.23607 | + | 1.62460i | 0.401610 | + | 0.291787i | 0.770196 | − | 0.637807i | \(-0.220158\pi\) |
−0.368587 | + | 0.929593i | \(0.620158\pi\) | |||||||
\(32\) | 6.70820 | 1.18585 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.23607 | −1.24098 | ||||||||
\(35\) | −1.61803 | − | 1.17557i | −0.273498 | − | 0.198708i | ||||
\(36\) | −1.36475 | + | 4.20025i | −0.227458 | + | 0.700042i | ||||
\(37\) | −2.61803 | − | 8.05748i | −0.430402 | − | 1.32464i | −0.897726 | − | 0.440555i | \(-0.854782\pi\) |
0.467323 | − | 0.884086i | \(-0.345218\pi\) | |||||||
\(38\) | −11.7082 | + | 8.50651i | −1.89932 | + | 1.37994i | ||||
\(39\) | −3.23607 | + | 2.35114i | −0.518186 | + | 0.376484i | ||||
\(40\) | 1.38197 | + | 4.25325i | 0.218508 | + | 0.672499i | ||||
\(41\) | 3.47214 | − | 10.6861i | 0.542257 | − | 1.66889i | −0.185168 | − | 0.982707i | \(-0.559283\pi\) |
0.727425 | − | 0.686187i | \(-0.240717\pi\) | |||||||
\(42\) | 2.23607 | + | 1.62460i | 0.345033 | + | 0.250681i | ||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.94427 | 0.438906 | ||||||||
\(46\) | 4.47214 | + | 3.24920i | 0.659380 | + | 0.479068i | ||||
\(47\) | 0.854102 | − | 2.62866i | 0.124584 | − | 0.383429i | −0.869241 | − | 0.494388i | \(-0.835392\pi\) |
0.993825 | + | 0.110959i | \(0.0353922\pi\) | |||||||
\(48\) | 0.381966 | + | 1.17557i | 0.0551320 | + | 0.169679i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | −1.80902 | + | 1.31433i | −0.255834 | + | 0.185874i | ||||
\(51\) | −1.23607 | − | 3.80423i | −0.173084 | − | 0.532698i | ||||
\(52\) | −3.00000 | + | 9.23305i | −0.416025 | + | 1.28039i | ||||
\(53\) | 0.381966 | + | 0.277515i | 0.0524671 | + | 0.0381196i | 0.613710 | − | 0.789532i | \(-0.289677\pi\) |
−0.561243 | + | 0.827651i | \(0.689677\pi\) | |||||||
\(54\) | −12.3607 | −1.68208 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | −6.47214 | − | 4.70228i | −0.857255 | − | 0.622832i | ||||
\(58\) | 5.85410 | − | 18.0171i | 0.768681 | − | 2.36576i | ||||
\(59\) | −0.381966 | − | 1.17557i | −0.0497277 | − | 0.153046i | 0.923109 | − | 0.384538i | \(-0.125639\pi\) |
−0.972837 | + | 0.231492i | \(0.925639\pi\) | |||||||
\(60\) | −6.00000 | + | 4.35926i | −0.774597 | + | 0.562777i | ||||
\(61\) | −5.85410 | + | 4.25325i | −0.749541 | + | 0.544573i | −0.895685 | − | 0.444690i | \(-0.853314\pi\) |
0.146144 | + | 0.989263i | \(0.453314\pi\) | |||||||
\(62\) | 1.90983 | + | 5.87785i | 0.242549 | + | 0.746488i | ||||
\(63\) | 0.454915 | − | 1.40008i | 0.0573139 | − | 0.176394i | ||||
\(64\) | 10.5172 | + | 7.64121i | 1.31465 | + | 0.955151i | ||||
\(65\) | 6.47214 | 0.802770 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.4721 | 1.76805 | 0.884026 | − | 0.467437i | \(-0.154823\pi\) | ||||
0.884026 | + | 0.467437i | \(0.154823\pi\) | |||||||
\(68\) | −7.85410 | − | 5.70634i | −0.952450 | − | 0.691995i | ||||
\(69\) | −0.944272 | + | 2.90617i | −0.113677 | + | 0.349862i | ||||
\(70\) | −1.38197 | − | 4.25325i | −0.165177 | − | 0.508361i | ||||
\(71\) | 8.47214 | − | 6.15537i | 1.00546 | − | 0.730508i | 0.0422061 | − | 0.999109i | \(-0.486561\pi\) |
0.963251 | + | 0.268601i | \(0.0865614\pi\) | |||||||
\(72\) | −2.66312 | + | 1.93487i | −0.313852 | + | 0.228027i | ||||
\(73\) | 0.236068 | + | 0.726543i | 0.0276297 | + | 0.0850354i | 0.963920 | − | 0.266190i | \(-0.0857650\pi\) |
−0.936291 | + | 0.351226i | \(0.885765\pi\) | |||||||
\(74\) | 5.85410 | − | 18.0171i | 0.680526 | − | 2.09444i | ||||
\(75\) | −1.00000 | − | 0.726543i | −0.115470 | − | 0.0838939i | ||||
\(76\) | −19.4164 | −2.22721 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −8.94427 | −1.01274 | ||||||||
\(79\) | −7.23607 | − | 5.25731i | −0.814121 | − | 0.591494i | 0.100901 | − | 0.994896i | \(-0.467827\pi\) |
−0.915023 | + | 0.403403i | \(0.867827\pi\) | |||||||
\(80\) | 0.618034 | − | 1.90211i | 0.0690983 | − | 0.212663i | ||||
\(81\) | −0.746711 | − | 2.29814i | −0.0829679 | − | 0.255349i | ||||
\(82\) | 20.3262 | − | 14.7679i | 2.24466 | − | 1.63084i | ||||
\(83\) | −9.23607 | + | 6.71040i | −1.01379 | + | 0.736562i | −0.965001 | − | 0.262247i | \(-0.915536\pi\) |
−0.0487895 | + | 0.998809i | \(0.515536\pi\) | |||||||
\(84\) | 1.14590 | + | 3.52671i | 0.125028 | + | 0.384796i | ||||
\(85\) | −2.00000 | + | 6.15537i | −0.216930 | + | 0.667643i | ||||
\(86\) | −14.4721 | − | 10.5146i | −1.56057 | − | 1.13382i | ||||
\(87\) | 10.4721 | 1.12273 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 5.32624 | + | 3.86974i | 0.561435 | + | 0.407906i | ||||
\(91\) | 1.00000 | − | 3.07768i | 0.104828 | − | 0.322629i | ||||
\(92\) | 2.29180 | + | 7.05342i | 0.238936 | + | 0.735370i | ||||
\(93\) | −2.76393 | + | 2.00811i | −0.286606 | + | 0.208232i | ||||
\(94\) | 5.00000 | − | 3.63271i | 0.515711 | − | 0.374686i | ||||
\(95\) | 4.00000 | + | 12.3107i | 0.410391 | + | 1.26305i | ||||
\(96\) | −2.56231 | + | 7.88597i | −0.261514 | + | 0.804858i | ||||
\(97\) | −14.0902 | − | 10.2371i | −1.43064 | − | 1.03942i | −0.989897 | − | 0.141787i | \(-0.954715\pi\) |
−0.440743 | − | 0.897633i | \(-0.645285\pi\) | |||||||
\(98\) | −2.23607 | −0.225877 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | −3.85410 | − | 2.80017i | −0.383497 | − | 0.278627i | 0.379288 | − | 0.925279i | \(-0.376169\pi\) |
−0.762786 | + | 0.646651i | \(0.776169\pi\) | |||||||
\(102\) | 2.76393 | − | 8.50651i | 0.273670 | − | 0.842270i | ||||
\(103\) | 2.38197 | + | 7.33094i | 0.234702 | + | 0.722339i | 0.997161 | + | 0.0753019i | \(0.0239920\pi\) |
−0.762459 | + | 0.647037i | \(0.776008\pi\) | |||||||
\(104\) | −5.85410 | + | 4.25325i | −0.574042 | + | 0.417066i | ||||
\(105\) | 2.00000 | − | 1.45309i | 0.195180 | − | 0.141807i | ||||
\(106\) | 0.326238 | + | 1.00406i | 0.0316870 | + | 0.0975226i | ||||
\(107\) | 1.23607 | − | 3.80423i | 0.119495 | − | 0.367768i | −0.873363 | − | 0.487070i | \(-0.838066\pi\) |
0.992858 | + | 0.119302i | \(0.0380656\pi\) | |||||||
\(108\) | −13.4164 | − | 9.74759i | −1.29099 | − | 0.937962i | ||||
\(109\) | 4.47214 | 0.428353 | 0.214176 | − | 0.976795i | \(-0.431293\pi\) | ||||
0.214176 | + | 0.976795i | \(0.431293\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4721 | 0.993971 | ||||||||
\(112\) | −0.809017 | − | 0.587785i | −0.0764449 | − | 0.0555405i | ||||
\(113\) | 0.618034 | − | 1.90211i | 0.0581397 | − | 0.178936i | −0.917769 | − | 0.397114i | \(-0.870012\pi\) |
0.975909 | + | 0.218179i | \(0.0700116\pi\) | |||||||
\(114\) | −5.52786 | − | 17.0130i | −0.517732 | − | 1.59341i | ||||
\(115\) | 4.00000 | − | 2.90617i | 0.373002 | − | 0.271002i | ||||
\(116\) | 20.5623 | − | 14.9394i | 1.90916 | − | 1.38709i | ||||
\(117\) | 1.47214 | + | 4.53077i | 0.136099 | + | 0.418870i | ||||
\(118\) | 0.854102 | − | 2.62866i | 0.0786265 | − | 0.241987i | ||||
\(119\) | 2.61803 | + | 1.90211i | 0.239995 | + | 0.174366i | ||||
\(120\) | −5.52786 | −0.504623 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −16.1803 | −1.46490 | ||||||||
\(123\) | 11.2361 | + | 8.16348i | 1.01312 | + | 0.736076i | ||||
\(124\) | −2.56231 | + | 7.88597i | −0.230102 | + | 0.708181i | ||||
\(125\) | 3.70820 | + | 11.4127i | 0.331672 | + | 1.02078i | ||||
\(126\) | 2.66312 | − | 1.93487i | 0.237249 | − | 0.172372i | ||||
\(127\) | 2.47214 | − | 1.79611i | 0.219367 | − | 0.159379i | −0.472675 | − | 0.881237i | \(-0.656712\pi\) |
0.692041 | + | 0.721858i | \(0.256712\pi\) | |||||||
\(128\) | 4.83688 | + | 14.8864i | 0.427524 | + | 1.31578i | ||||
\(129\) | 3.05573 | − | 9.40456i | 0.269042 | − | 0.828026i | ||||
\(130\) | 11.7082 | + | 8.50651i | 1.02688 | + | 0.746070i | ||||
\(131\) | −21.8885 | −1.91241 | −0.956205 | − | 0.292696i | \(-0.905448\pi\) | ||||
−0.956205 | + | 0.292696i | \(0.905448\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.47214 | 0.561205 | ||||||||
\(134\) | 26.1803 | + | 19.0211i | 2.26164 | + | 1.64318i | ||||
\(135\) | −3.41641 | + | 10.5146i | −0.294038 | + | 0.904955i | ||||
\(136\) | −2.23607 | − | 6.88191i | −0.191741 | − | 0.590119i | ||||
\(137\) | −13.3262 | + | 9.68208i | −1.13854 | + | 0.827196i | −0.986915 | − | 0.161243i | \(-0.948450\pi\) |
−0.151623 | + | 0.988438i | \(0.548450\pi\) | |||||||
\(138\) | −5.52786 | + | 4.01623i | −0.470563 | + | 0.341884i | ||||
\(139\) | 0.472136 | + | 1.45309i | 0.0400460 | + | 0.123249i | 0.969081 | − | 0.246743i | \(-0.0793604\pi\) |
−0.929035 | + | 0.369992i | \(0.879360\pi\) | |||||||
\(140\) | 1.85410 | − | 5.70634i | 0.156700 | − | 0.482274i | ||||
\(141\) | 2.76393 | + | 2.00811i | 0.232765 | + | 0.169114i | ||||
\(142\) | 23.4164 | 1.96506 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.47214 | 0.122678 | ||||||||
\(145\) | −13.7082 | − | 9.95959i | −1.13840 | − | 0.827099i | ||||
\(146\) | −0.527864 | + | 1.62460i | −0.0436863 | + | 0.134453i | ||||
\(147\) | −0.381966 | − | 1.17557i | −0.0315040 | − | 0.0969594i | ||||
\(148\) | 20.5623 | − | 14.9394i | 1.69021 | − | 1.22801i | ||||
\(149\) | 11.3262 | − | 8.22899i | 0.927882 | − | 0.674145i | −0.0175917 | − | 0.999845i | \(-0.505600\pi\) |
0.945473 | + | 0.325700i | \(0.105600\pi\) | |||||||
\(150\) | −0.854102 | − | 2.62866i | −0.0697371 | − | 0.214629i | ||||
\(151\) | −2.76393 | + | 8.50651i | −0.224926 | + | 0.692250i | 0.773374 | + | 0.633951i | \(0.218568\pi\) |
−0.998299 | + | 0.0582992i | \(0.981432\pi\) | |||||||
\(152\) | −11.7082 | − | 8.50651i | −0.949661 | − | 0.689969i | ||||
\(153\) | −4.76393 | −0.385141 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.52786 | 0.444009 | ||||||||
\(156\) | −9.70820 | − | 7.05342i | −0.777278 | − | 0.564726i | ||||
\(157\) | 3.38197 | − | 10.4086i | 0.269910 | − | 0.830698i | −0.720611 | − | 0.693340i | \(-0.756139\pi\) |
0.990521 | − | 0.137359i | \(-0.0438614\pi\) | |||||||
\(158\) | −6.18034 | − | 19.0211i | −0.491681 | − | 1.51324i | ||||
\(159\) | −0.472136 | + | 0.343027i | −0.0374428 | + | 0.0272038i | ||||
\(160\) | 10.8541 | − | 7.88597i | 0.858092 | − | 0.623440i | ||||
\(161\) | −0.763932 | − | 2.35114i | −0.0602063 | − | 0.185296i | ||||
\(162\) | 1.66970 | − | 5.13880i | 0.131184 | − | 0.403742i | ||||
\(163\) | 2.76393 | + | 2.00811i | 0.216488 | + | 0.157288i | 0.690744 | − | 0.723099i | \(-0.257283\pi\) |
−0.474256 | + | 0.880387i | \(0.657283\pi\) | |||||||
\(164\) | 33.7082 | 2.63217 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.5279 | −1.98135 | ||||||||
\(167\) | 4.00000 | + | 2.90617i | 0.309529 | + | 0.224886i | 0.731694 | − | 0.681633i | \(-0.238730\pi\) |
−0.422165 | + | 0.906519i | \(0.638730\pi\) | |||||||
\(168\) | −0.854102 | + | 2.62866i | −0.0658954 | + | 0.202805i | ||||
\(169\) | −0.781153 | − | 2.40414i | −0.0600887 | − | 0.184934i | ||||
\(170\) | −11.7082 | + | 8.50651i | −0.897978 | + | 0.652419i | ||||
\(171\) | −7.70820 | + | 5.60034i | −0.589461 | + | 0.428269i | ||||
\(172\) | −7.41641 | − | 22.8254i | −0.565496 | − | 1.74042i | ||||
\(173\) | 3.94427 | − | 12.1392i | 0.299877 | − | 0.922928i | −0.681662 | − | 0.731667i | \(-0.738742\pi\) |
0.981539 | − | 0.191261i | \(-0.0612575\pi\) | |||||||
\(174\) | 18.9443 | + | 13.7638i | 1.43616 | + | 1.04343i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.52786 | 0.114841 | ||||||||
\(178\) | 3.61803 | + | 2.62866i | 0.271183 | + | 0.197026i | ||||
\(179\) | −2.76393 | + | 8.50651i | −0.206586 | + | 0.635806i | 0.793059 | + | 0.609145i | \(0.208487\pi\) |
−0.999645 | + | 0.0266609i | \(0.991513\pi\) | |||||||
\(180\) | 2.72949 | + | 8.40051i | 0.203444 | + | 0.626137i | ||||
\(181\) | 20.5623 | − | 14.9394i | 1.52838 | − | 1.11044i | 0.571256 | − | 0.820772i | \(-0.306456\pi\) |
0.957128 | − | 0.289664i | \(-0.0935436\pi\) | |||||||
\(182\) | 5.85410 | − | 4.25325i | 0.433935 | − | 0.315272i | ||||
\(183\) | −2.76393 | − | 8.50651i | −0.204316 | − | 0.628819i | ||||
\(184\) | −1.70820 | + | 5.25731i | −0.125930 | + | 0.387574i | ||||
\(185\) | −13.7082 | − | 9.95959i | −1.00785 | − | 0.732244i | ||||
\(186\) | −7.63932 | −0.560142 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.29180 | 0.604741 | ||||||||
\(189\) | 4.47214 | + | 3.24920i | 0.325300 | + | 0.236344i | ||||
\(190\) | −8.94427 | + | 27.5276i | −0.648886 | + | 1.99706i | ||||
\(191\) | −0.944272 | − | 2.90617i | −0.0683251 | − | 0.210283i | 0.911064 | − | 0.412264i | \(-0.135262\pi\) |
−0.979389 | + | 0.201981i | \(0.935262\pi\) | |||||||
\(192\) | −13.0000 | + | 9.44505i | −0.938194 | + | 0.681638i | ||||
\(193\) | 9.61803 | − | 6.98791i | 0.692321 | − | 0.503001i | −0.185101 | − | 0.982719i | \(-0.559261\pi\) |
0.877422 | + | 0.479719i | \(0.159261\pi\) | |||||||
\(194\) | −12.0344 | − | 37.0382i | −0.864023 | − | 2.65919i | ||||
\(195\) | −2.47214 | + | 7.60845i | −0.177033 | + | 0.544853i | ||||
\(196\) | −2.42705 | − | 1.76336i | −0.173361 | − | 0.125954i | ||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.18034 | −0.154560 | −0.0772801 | − | 0.997009i | \(-0.524624\pi\) | ||||
−0.0772801 | + | 0.997009i | \(0.524624\pi\) | |||||||
\(200\) | −1.80902 | − | 1.31433i | −0.127917 | − | 0.0929370i | ||||
\(201\) | −5.52786 | + | 17.0130i | −0.389905 | + | 1.20001i | ||||
\(202\) | −3.29180 | − | 10.1311i | −0.231610 | − | 0.712822i | ||||
\(203\) | −6.85410 | + | 4.97980i | −0.481064 | + | 0.349513i | ||||
\(204\) | 9.70820 | − | 7.05342i | 0.679710 | − | 0.493838i | ||||
\(205\) | −6.94427 | − | 21.3723i | −0.485009 | − | 1.49270i | ||||
\(206\) | −5.32624 | + | 16.3925i | −0.371097 | + | 1.14212i | ||||
\(207\) | 2.94427 | + | 2.13914i | 0.204641 | + | 0.148680i | ||||
\(208\) | 3.23607 | 0.224381 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 5.52786 | 0.381459 | ||||||||
\(211\) | −11.2361 | − | 8.16348i | −0.773523 | − | 0.561997i | 0.129505 | − | 0.991579i | \(-0.458661\pi\) |
−0.903028 | + | 0.429582i | \(0.858661\pi\) | |||||||
\(212\) | −0.437694 | + | 1.34708i | −0.0300610 | + | 0.0925181i | ||||
\(213\) | 4.00000 | + | 12.3107i | 0.274075 | + | 0.843518i | ||||
\(214\) | 7.23607 | − | 5.25731i | 0.494647 | − | 0.359382i | ||||
\(215\) | −12.9443 | + | 9.40456i | −0.882792 | + | 0.641386i | ||||
\(216\) | −3.81966 | − | 11.7557i | −0.259895 | − | 0.799874i | ||||
\(217\) | 0.854102 | − | 2.62866i | 0.0579802 | − | 0.178445i | ||||
\(218\) | 8.09017 | + | 5.87785i | 0.547935 | + | 0.398098i | ||||
\(219\) | −0.944272 | −0.0638080 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4721 | −0.704432 | ||||||||
\(222\) | 18.9443 | + | 13.7638i | 1.27146 | + | 0.923767i | ||||
\(223\) | −3.14590 | + | 9.68208i | −0.210665 | + | 0.648360i | 0.788768 | + | 0.614691i | \(0.210719\pi\) |
−0.999433 | + | 0.0336691i | \(0.989281\pi\) | |||||||
\(224\) | −2.07295 | − | 6.37988i | −0.138505 | − | 0.426274i | ||||
\(225\) | −1.19098 | + | 0.865300i | −0.0793989 | + | 0.0576867i | ||||
\(226\) | 3.61803 | − | 2.62866i | 0.240668 | − | 0.174856i | ||||
\(227\) | −1.81966 | − | 5.60034i | −0.120775 | − | 0.371707i | 0.872333 | − | 0.488913i | \(-0.162606\pi\) |
−0.993108 | + | 0.117205i | \(0.962606\pi\) | |||||||
\(228\) | 7.41641 | − | 22.8254i | 0.491164 | − | 1.51165i | ||||
\(229\) | 3.61803 | + | 2.62866i | 0.239086 | + | 0.173706i | 0.700876 | − | 0.713283i | \(-0.252793\pi\) |
−0.461790 | + | 0.886989i | \(0.652793\pi\) | |||||||
\(230\) | 11.0557 | 0.728993 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.9443 | 1.24375 | ||||||||
\(233\) | 7.61803 | + | 5.53483i | 0.499074 | + | 0.362598i | 0.808663 | − | 0.588272i | \(-0.200192\pi\) |
−0.309589 | + | 0.950870i | \(0.600192\pi\) | |||||||
\(234\) | −3.29180 | + | 10.1311i | −0.215191 | + | 0.662291i | ||||
\(235\) | −1.70820 | − | 5.25731i | −0.111431 | − | 0.342949i | ||||
\(236\) | 3.00000 | − | 2.17963i | 0.195283 | − | 0.141882i | ||||
\(237\) | 8.94427 | − | 6.49839i | 0.580993 | − | 0.422116i | ||||
\(238\) | 2.23607 | + | 6.88191i | 0.144943 | + | 0.446088i | ||||
\(239\) | 3.05573 | − | 9.40456i | 0.197659 | − | 0.608331i | −0.802277 | − | 0.596952i | \(-0.796378\pi\) |
0.999935 | − | 0.0113783i | \(-0.00362189\pi\) | |||||||
\(240\) | 2.00000 | + | 1.45309i | 0.129099 | + | 0.0937962i | ||||
\(241\) | 13.1246 | 0.845431 | 0.422715 | − | 0.906263i | \(-0.361077\pi\) | ||||
0.422715 | + | 0.906263i | \(0.361077\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5967 | −0.872232 | ||||||||
\(244\) | −17.5623 | − | 12.7598i | −1.12431 | − | 0.816860i | ||||
\(245\) | −0.618034 | + | 1.90211i | −0.0394847 | + | 0.121522i | ||||
\(246\) | 9.59675 | + | 29.5358i | 0.611866 | + | 1.88313i | ||||
\(247\) | −16.9443 | + | 12.3107i | −1.07814 | + | 0.783313i | ||||
\(248\) | −5.00000 | + | 3.63271i | −0.317500 | + | 0.230677i | ||||
\(249\) | −4.36068 | − | 13.4208i | −0.276347 | − | 0.850508i | ||||
\(250\) | −8.29180 | + | 25.5195i | −0.524419 | + | 1.61400i | ||||
\(251\) | −3.47214 | − | 2.52265i | −0.219159 | − | 0.159229i | 0.472789 | − | 0.881176i | \(-0.343247\pi\) |
−0.691948 | + | 0.721947i | \(0.743247\pi\) | |||||||
\(252\) | 4.41641 | 0.278208 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 6.83282 | 0.428729 | ||||||||
\(255\) | −6.47214 | − | 4.70228i | −0.405301 | − | 0.294468i | ||||
\(256\) | −2.78115 | + | 8.55951i | −0.173822 | + | 0.534969i | ||||
\(257\) | −1.85410 | − | 5.70634i | −0.115656 | − | 0.355952i | 0.876428 | − | 0.481534i | \(-0.159920\pi\) |
−0.992083 | + | 0.125582i | \(0.959920\pi\) | |||||||
\(258\) | 17.8885 | − | 12.9968i | 1.11369 | − | 0.809145i | ||||
\(259\) | −6.85410 | + | 4.97980i | −0.425893 | + | 0.309430i | ||||
\(260\) | 6.00000 | + | 18.4661i | 0.372104 | + | 1.14522i | ||||
\(261\) | 3.85410 | − | 11.8617i | 0.238563 | − | 0.734221i | ||||
\(262\) | −39.5967 | − | 28.7687i | −2.44630 | − | 1.77734i | ||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.944272 | 0.0580062 | ||||||||
\(266\) | 11.7082 | + | 8.50651i | 0.717876 | + | 0.521567i | ||||
\(267\) | −0.763932 | + | 2.35114i | −0.0467519 | + | 0.143887i | ||||
\(268\) | 13.4164 | + | 41.2915i | 0.819538 | + | 2.52228i | ||||
\(269\) | −10.8541 | + | 7.88597i | −0.661786 | + | 0.480816i | −0.867266 | − | 0.497846i | \(-0.834125\pi\) |
0.205479 | + | 0.978661i | \(0.434125\pi\) | |||||||
\(270\) | −20.0000 | + | 14.5309i | −1.21716 | + | 0.884319i | ||||
\(271\) | 3.23607 | + | 9.95959i | 0.196577 | + | 0.605002i | 0.999955 | + | 0.00953205i | \(0.00303419\pi\) |
−0.803377 | + | 0.595470i | \(0.796966\pi\) | |||||||
\(272\) | −1.00000 | + | 3.07768i | −0.0606339 | + | 0.186612i | ||||
\(273\) | 3.23607 | + | 2.35114i | 0.195856 | + | 0.142298i | ||||
\(274\) | −36.8328 | −2.22515 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.16718 | −0.551800 | ||||||||
\(277\) | −16.0902 | − | 11.6902i | −0.966765 | − | 0.702396i | −0.0120527 | − | 0.999927i | \(-0.503837\pi\) |
−0.954712 | + | 0.297532i | \(0.903837\pi\) | |||||||
\(278\) | −1.05573 | + | 3.24920i | −0.0633184 | + | 0.194874i | ||||
\(279\) | 1.25735 | + | 3.86974i | 0.0752758 | + | 0.231675i | ||||
\(280\) | 3.61803 | − | 2.62866i | 0.216219 | − | 0.157092i | ||||
\(281\) | −2.85410 | + | 2.07363i | −0.170261 | + | 0.123702i | −0.669653 | − | 0.742674i | \(-0.733557\pi\) |
0.499391 | + | 0.866377i | \(0.333557\pi\) | |||||||
\(282\) | 2.36068 | + | 7.26543i | 0.140576 | + | 0.432650i | ||||
\(283\) | −9.23607 | + | 28.4257i | −0.549027 | + | 1.68973i | 0.162190 | + | 0.986760i | \(0.448144\pi\) |
−0.711217 | + | 0.702973i | \(0.751856\pi\) | |||||||
\(284\) | 25.4164 | + | 18.4661i | 1.50819 | + | 1.09576i | ||||
\(285\) | −16.0000 | −0.947758 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.2361 | −0.663244 | ||||||||
\(288\) | 7.98936 | + | 5.80461i | 0.470777 | + | 0.342040i | ||||
\(289\) | −2.01722 | + | 6.20837i | −0.118660 | + | 0.365198i | ||||
\(290\) | −11.7082 | − | 36.0341i | −0.687529 | − | 2.11600i | ||||
\(291\) | 17.4164 | − | 12.6538i | 1.02097 | − | 0.741777i | ||||
\(292\) | −1.85410 | + | 1.34708i | −0.108503 | + | 0.0788321i | ||||
\(293\) | 7.76393 | + | 23.8949i | 0.453574 | + | 1.39596i | 0.872801 | + | 0.488075i | \(0.162301\pi\) |
−0.419228 | + | 0.907881i | \(0.637699\pi\) | |||||||
\(294\) | 0.854102 | − | 2.62866i | 0.0498122 | − | 0.153306i | ||||
\(295\) | −2.00000 | − | 1.45309i | −0.116445 | − | 0.0846019i | ||||
\(296\) | 18.9443 | 1.10111 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 31.3050 | 1.81345 | ||||||||
\(299\) | 6.47214 | + | 4.70228i | 0.374293 | + | 0.271940i | ||||
\(300\) | 1.14590 | − | 3.52671i | 0.0661585 | − | 0.203615i | ||||
\(301\) | 2.47214 | + | 7.60845i | 0.142492 | + | 0.438544i | ||||
\(302\) | −16.1803 | + | 11.7557i | −0.931074 | + | 0.676465i | ||||
\(303\) | 4.76393 | − | 3.46120i | 0.273681 | − | 0.198841i | ||||
\(304\) | 2.00000 | + | 6.15537i | 0.114708 | + | 0.353035i | ||||
\(305\) | −4.47214 | + | 13.7638i | −0.256074 | + | 0.788114i | ||||
\(306\) | −8.61803 | − | 6.26137i | −0.492660 | − | 0.357939i | ||||
\(307\) | 8.94427 | 0.510477 | 0.255238 | − | 0.966878i | \(-0.417846\pi\) | ||||
0.255238 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.52786 | −0.542021 | ||||||||
\(310\) | 10.0000 | + | 7.26543i | 0.567962 | + | 0.412648i | ||||
\(311\) | −2.56231 | + | 7.88597i | −0.145295 | + | 0.447172i | −0.997049 | − | 0.0767701i | \(-0.975539\pi\) |
0.851754 | + | 0.523942i | \(0.175539\pi\) | |||||||
\(312\) | −2.76393 | − | 8.50651i | −0.156477 | − | 0.481586i | ||||
\(313\) | −12.0902 | + | 8.78402i | −0.683377 | + | 0.496502i | −0.874476 | − | 0.485068i | \(-0.838795\pi\) |
0.191099 | + | 0.981571i | \(0.438795\pi\) | |||||||
\(314\) | 19.7984 | − | 14.3844i | 1.11729 | − | 0.811756i | ||||
\(315\) | −0.909830 | − | 2.80017i | −0.0512631 | − | 0.157772i | ||||
\(316\) | 8.29180 | − | 25.5195i | 0.466450 | − | 1.43559i | ||||
\(317\) | −11.3262 | − | 8.22899i | −0.636145 | − | 0.462186i | 0.222379 | − | 0.974960i | \(-0.428618\pi\) |
−0.858524 | + | 0.512774i | \(0.828618\pi\) | |||||||
\(318\) | −1.30495 | −0.0731781 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 26.0000 | 1.45344 | ||||||||
\(321\) | 4.00000 | + | 2.90617i | 0.223258 | + | 0.162207i | ||||
\(322\) | 1.70820 | − | 5.25731i | 0.0951945 | − | 0.292978i | ||||
\(323\) | −6.47214 | − | 19.9192i | −0.360119 | − | 1.10833i | ||||
\(324\) | 5.86475 | − | 4.26099i | 0.325819 | − | 0.236721i | ||||
\(325\) | −2.61803 | + | 1.90211i | −0.145222 | + | 0.105510i | ||||
\(326\) | 2.36068 | + | 7.26543i | 0.130746 | + | 0.402395i | ||||
\(327\) | −1.70820 | + | 5.25731i | −0.0944639 | + | 0.290730i | ||||
\(328\) | 20.3262 | + | 14.7679i | 1.12233 | + | 0.815420i | ||||
\(329\) | −2.76393 | −0.152381 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.8885 | −0.763383 | −0.381692 | − | 0.924290i | \(-0.624658\pi\) | ||||
−0.381692 | + | 0.924290i | \(0.624658\pi\) | |||||||
\(332\) | −27.7082 | − | 20.1312i | −1.52069 | − | 1.10484i | ||||
\(333\) | 3.85410 | − | 11.8617i | 0.211203 | − | 0.650017i | ||||
\(334\) | 3.41641 | + | 10.5146i | 0.186938 | + | 0.575335i | ||||
\(335\) | 23.4164 | − | 17.0130i | 1.27938 | − | 0.929520i | ||||
\(336\) | 1.00000 | − | 0.726543i | 0.0545545 | − | 0.0396361i | ||||
\(337\) | 3.56231 | + | 10.9637i | 0.194051 | + | 0.597228i | 0.999986 | + | 0.00522430i | \(0.00166295\pi\) |
−0.805935 | + | 0.592004i | \(0.798337\pi\) | |||||||
\(338\) | 1.74671 | − | 5.37582i | 0.0950086 | − | 0.292406i | ||||
\(339\) | 2.00000 | + | 1.45309i | 0.108625 | + | 0.0789207i | ||||
\(340\) | −19.4164 | −1.05300 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −21.3050 | −1.15204 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | 5.52786 | − | 17.0130i | 0.298042 | − | 0.917280i | ||||
\(345\) | 1.88854 | + | 5.81234i | 0.101676 | + | 0.312926i | ||||
\(346\) | 23.0902 | − | 16.7760i | 1.24134 | − | 0.901883i | ||||
\(347\) | 16.9443 | − | 12.3107i | 0.909616 | − | 0.660875i | −0.0313016 | − | 0.999510i | \(-0.509965\pi\) |
0.940918 | + | 0.338635i | \(0.109965\pi\) | |||||||
\(348\) | 9.70820 | + | 29.8788i | 0.520414 | + | 1.60167i | ||||
\(349\) | 2.23607 | − | 6.88191i | 0.119694 | − | 0.368380i | −0.873203 | − | 0.487356i | \(-0.837961\pi\) |
0.992897 | + | 0.118976i | \(0.0379612\pi\) | |||||||
\(350\) | 1.80902 | + | 1.31433i | 0.0966960 | + | 0.0702538i | ||||
\(351\) | −17.8885 | −0.954820 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.8885 | 1.05856 | 0.529280 | − | 0.848447i | \(-0.322462\pi\) | ||||
0.529280 | + | 0.848447i | \(0.322462\pi\) | |||||||
\(354\) | 2.76393 | + | 2.00811i | 0.146901 | + | 0.106730i | ||||
\(355\) | 6.47214 | − | 19.9192i | 0.343505 | − | 1.05720i | ||||
\(356\) | 1.85410 | + | 5.70634i | 0.0982672 | + | 0.302435i | ||||
\(357\) | −3.23607 | + | 2.35114i | −0.171271 | + | 0.124436i | ||||
\(358\) | −16.1803 | + | 11.7557i | −0.855158 | + | 0.621308i | ||||
\(359\) | 7.70820 | + | 23.7234i | 0.406823 | + | 1.25207i | 0.919363 | + | 0.393410i | \(0.128705\pi\) |
−0.512540 | + | 0.858664i | \(0.671295\pi\) | |||||||
\(360\) | −2.03444 | + | 6.26137i | −0.107225 | + | 0.330003i | ||||
\(361\) | −18.5172 | − | 13.4535i | −0.974591 | − | 0.708082i | ||||
\(362\) | 56.8328 | 2.98707 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.70820 | 0.508848 | ||||||||
\(365\) | 1.23607 | + | 0.898056i | 0.0646988 | + | 0.0470064i | ||||
\(366\) | 6.18034 | − | 19.0211i | 0.323052 | − | 0.994250i | ||||
\(367\) | −7.14590 | − | 21.9928i | −0.373013 | − | 1.14802i | −0.944810 | − | 0.327620i | \(-0.893753\pi\) |
0.571797 | − | 0.820395i | \(-0.306247\pi\) | |||||||
\(368\) | 2.00000 | − | 1.45309i | 0.104257 | − | 0.0757473i | ||||
\(369\) | 13.3820 | − | 9.72257i | 0.696637 | − | 0.506137i | ||||
\(370\) | −11.7082 | − | 36.0341i | −0.608681 | − | 1.87333i | ||||
\(371\) | 0.145898 | − | 0.449028i | 0.00757465 | − | 0.0233124i | ||||
\(372\) | −8.29180 | − | 6.02434i | −0.429910 | − | 0.312348i | ||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.8328 | −0.765963 | ||||||||
\(376\) | 5.00000 | + | 3.63271i | 0.257855 | + | 0.187343i | ||||
\(377\) | 8.47214 | − | 26.0746i | 0.436337 | − | 1.34291i | ||||
\(378\) | 3.81966 | + | 11.7557i | 0.196462 | + | 0.604648i | ||||
\(379\) | −30.1803 | + | 21.9273i | −1.55026 | + | 1.12633i | −0.606795 | + | 0.794859i | \(0.707545\pi\) |
−0.943465 | + | 0.331471i | \(0.892455\pi\) | |||||||
\(380\) | −31.4164 | + | 22.8254i | −1.61163 | + | 1.17092i | ||||
\(381\) | 1.16718 | + | 3.59222i | 0.0597967 | + | 0.184035i | ||||
\(382\) | 2.11146 | − | 6.49839i | 0.108031 | − | 0.332487i | ||||
\(383\) | 3.76393 | + | 2.73466i | 0.192328 | + | 0.139734i | 0.679782 | − | 0.733414i | \(-0.262074\pi\) |
−0.487454 | + | 0.873149i | \(0.662074\pi\) | |||||||
\(384\) | −19.3475 | −0.987324 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.5836 | 1.35307 | ||||||||
\(387\) | −9.52786 | − | 6.92240i | −0.484329 | − | 0.351885i | ||||
\(388\) | 16.1459 | − | 49.6920i | 0.819684 | − | 2.52273i | ||||
\(389\) | 4.90983 | + | 15.1109i | 0.248938 | + | 0.766153i | 0.994964 | + | 0.100236i | \(0.0319597\pi\) |
−0.746025 | + | 0.665917i | \(0.768040\pi\) | |||||||
\(390\) | −14.4721 | + | 10.5146i | −0.732825 | + | 0.532429i | ||||
\(391\) | −6.47214 | + | 4.70228i | −0.327310 | + | 0.237805i | ||||
\(392\) | −0.690983 | − | 2.12663i | −0.0348999 | − | 0.107411i | ||||
\(393\) | 8.36068 | − | 25.7315i | 0.421741 | − | 1.29798i | ||||
\(394\) | 3.61803 | + | 2.62866i | 0.182274 | + | 0.132430i | ||||
\(395\) | −17.8885 | −0.900070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −35.8885 | −1.80119 | −0.900597 | − | 0.434655i | \(-0.856870\pi\) | ||||
−0.900597 | + | 0.434655i | \(0.856870\pi\) | |||||||
\(398\) | −3.94427 | − | 2.86568i | −0.197708 | − | 0.143644i | ||||
\(399\) | −2.47214 | + | 7.60845i | −0.123762 | + | 0.380899i | ||||
\(400\) | 0.309017 | + | 0.951057i | 0.0154508 | + | 0.0475528i | ||||
\(401\) | −18.5623 | + | 13.4863i | −0.926957 | + | 0.673474i | −0.945246 | − | 0.326359i | \(-0.894178\pi\) |
0.0182886 | + | 0.999833i | \(0.494178\pi\) | |||||||
\(402\) | −32.3607 | + | 23.5114i | −1.61400 | + | 1.17264i | ||||
\(403\) | 2.76393 | + | 8.50651i | 0.137681 | + | 0.423739i | ||||
\(404\) | 4.41641 | − | 13.5923i | 0.219725 | − | 0.676242i | ||||
\(405\) | −3.90983 | − | 2.84066i | −0.194281 | − | 0.141153i | ||||
\(406\) | −18.9443 | −0.940188 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 8.94427 | 0.442807 | ||||||||
\(409\) | 7.38197 | + | 5.36331i | 0.365015 | + | 0.265199i | 0.755141 | − | 0.655563i | \(-0.227569\pi\) |
−0.390126 | + | 0.920762i | \(0.627569\pi\) | |||||||
\(410\) | 15.5279 | − | 47.7899i | 0.766867 | − | 2.36017i | ||||
\(411\) | −6.29180 | − | 19.3642i | −0.310351 | − | 0.955163i | ||||
\(412\) | −18.7082 | + | 13.5923i | −0.921687 | + | 0.669645i | ||||
\(413\) | −1.00000 | + | 0.726543i | −0.0492068 | + | 0.0357508i | ||||
\(414\) | 2.51471 | + | 7.73948i | 0.123591 | + | 0.380375i | ||||
\(415\) | −7.05573 | + | 21.7153i | −0.346352 | + | 1.06596i | ||||
\(416\) | 17.5623 | + | 12.7598i | 0.861063 | + | 0.625599i | ||||
\(417\) | −1.88854 | −0.0924824 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.6525 | 1.20435 | 0.602176 | − | 0.798363i | \(-0.294300\pi\) | ||||
0.602176 | + | 0.798363i | \(0.294300\pi\) | |||||||
\(420\) | 6.00000 | + | 4.35926i | 0.292770 | + | 0.212710i | ||||
\(421\) | 6.90983 | − | 21.2663i | 0.336765 | − | 1.03645i | −0.629082 | − | 0.777339i | \(-0.716569\pi\) |
0.965846 | − | 0.259116i | \(-0.0834310\pi\) | |||||||
\(422\) | −9.59675 | − | 29.5358i | −0.467162 | − | 1.43778i | ||||
\(423\) | 3.29180 | − | 2.39163i | 0.160053 | − | 0.116285i | ||||
\(424\) | −0.854102 | + | 0.620541i | −0.0414789 | + | 0.0301362i | ||||
\(425\) | −1.00000 | − | 3.07768i | −0.0485071 | − | 0.149290i | ||||
\(426\) | −8.94427 | + | 27.5276i | −0.433351 | + | 1.33372i | ||||
\(427\) | 5.85410 | + | 4.25325i | 0.283300 | + | 0.205829i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −35.7771 | −1.72532 | ||||||||
\(431\) | 9.70820 | + | 7.05342i | 0.467628 | + | 0.339751i | 0.796516 | − | 0.604617i | \(-0.206674\pi\) |
−0.328888 | + | 0.944369i | \(0.606674\pi\) | |||||||
\(432\) | −1.70820 | + | 5.25731i | −0.0821860 | + | 0.252942i | ||||
\(433\) | −2.61803 | − | 8.05748i | −0.125815 | − | 0.387218i | 0.868234 | − | 0.496155i | \(-0.165255\pi\) |
−0.994049 | + | 0.108937i | \(0.965255\pi\) | |||||||
\(434\) | 5.00000 | − | 3.63271i | 0.240008 | − | 0.174376i | ||||
\(435\) | 16.9443 | − | 12.3107i | 0.812416 | − | 0.590255i | ||||
\(436\) | 4.14590 | + | 12.7598i | 0.198553 | + | 0.611082i | ||||
\(437\) | −4.94427 | + | 15.2169i | −0.236517 | + | 0.727923i | ||||
\(438\) | −1.70820 | − | 1.24108i | −0.0816211 | − | 0.0593012i | ||||
\(439\) | −10.4721 | −0.499808 | −0.249904 | − | 0.968271i | \(-0.580399\pi\) | ||||
−0.249904 | + | 0.968271i | \(0.580399\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.47214 | −0.0701017 | ||||||||
\(442\) | −18.9443 | − | 13.7638i | −0.901087 | − | 0.654678i | ||||
\(443\) | −7.70820 | + | 23.7234i | −0.366228 | + | 1.12713i | 0.582981 | + | 0.812486i | \(0.301886\pi\) |
−0.949209 | + | 0.314647i | \(0.898114\pi\) | |||||||
\(444\) | 9.70820 | + | 29.8788i | 0.460731 | + | 1.41798i | ||||
\(445\) | 3.23607 | − | 2.35114i | 0.153404 | − | 0.111455i | ||||
\(446\) | −18.4164 | + | 13.3803i | −0.872042 | + | 0.633576i | ||||
\(447\) | 5.34752 | + | 16.4580i | 0.252929 | + | 0.778436i | ||||
\(448\) | 4.01722 | − | 12.3637i | 0.189796 | − | 0.584132i | ||||
\(449\) | 23.0344 | + | 16.7355i | 1.08706 | + | 0.789797i | 0.978901 | − | 0.204336i | \(-0.0655036\pi\) |
0.108162 | + | 0.994133i | \(0.465504\pi\) | |||||||
\(450\) | −3.29180 | −0.155177 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | −8.94427 | − | 6.49839i | −0.420239 | − | 0.305321i | ||||
\(454\) | 4.06888 | − | 12.5227i | 0.190962 | − | 0.587721i | ||||
\(455\) | −2.00000 | − | 6.15537i | −0.0937614 | − | 0.288568i | ||||
\(456\) | 14.4721 | − | 10.5146i | 0.677720 | − | 0.492392i | ||||
\(457\) | −23.3262 | + | 16.9475i | −1.09116 | + | 0.792771i | −0.979594 | − | 0.200987i | \(-0.935585\pi\) |
−0.111561 | + | 0.993758i | \(0.535585\pi\) | |||||||
\(458\) | 3.09017 | + | 9.51057i | 0.144394 | + | 0.444400i | ||||
\(459\) | 5.52786 | − | 17.0130i | 0.258019 | − | 0.794100i | ||||
\(460\) | 12.0000 | + | 8.71851i | 0.559503 | + | 0.406503i | ||||
\(461\) | 12.1803 | 0.567295 | 0.283647 | − | 0.958929i | \(-0.408455\pi\) | ||||
0.283647 | + | 0.958929i | \(0.408455\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.52786 | −0.256902 | −0.128451 | − | 0.991716i | \(-0.541000\pi\) | ||||
−0.128451 | + | 0.991716i | \(0.541000\pi\) | |||||||
\(464\) | −6.85410 | − | 4.97980i | −0.318194 | − | 0.231181i | ||||
\(465\) | −2.11146 | + | 6.49839i | −0.0979164 | + | 0.301356i | ||||
\(466\) | 6.50658 | + | 20.0252i | 0.301411 | + | 0.927649i | ||||
\(467\) | −19.4721 | + | 14.1473i | −0.901063 | + | 0.654661i | −0.938739 | − | 0.344629i | \(-0.888005\pi\) |
0.0376758 | + | 0.999290i | \(0.488005\pi\) | |||||||
\(468\) | −11.5623 | + | 8.40051i | −0.534468 | + | 0.388314i | ||||
\(469\) | −4.47214 | − | 13.7638i | −0.206504 | − | 0.635554i | ||||
\(470\) | 3.81966 | − | 11.7557i | 0.176188 | − | 0.542250i | ||||
\(471\) | 10.9443 | + | 7.95148i | 0.504285 | + | 0.366385i | ||||
\(472\) | 2.76393 | 0.127220 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 24.7214 | 1.13549 | ||||||||
\(475\) | −5.23607 | − | 3.80423i | −0.240247 | − | 0.174550i | ||||
\(476\) | −3.00000 | + | 9.23305i | −0.137505 | + | 0.423196i | ||||
\(477\) | 0.214782 | + | 0.661030i | 0.00983418 | + | 0.0302665i | ||||
\(478\) | 17.8885 | − | 12.9968i | 0.818203 | − | 0.594459i | ||||
\(479\) | 10.9443 | − | 7.95148i | 0.500057 | − | 0.363312i | −0.308982 | − | 0.951068i | \(-0.599988\pi\) |
0.809039 | + | 0.587756i | \(0.199988\pi\) | |||||||
\(480\) | 5.12461 | + | 15.7719i | 0.233905 | + | 0.719887i | ||||
\(481\) | 8.47214 | − | 26.0746i | 0.386296 | − | 1.18890i | ||||
\(482\) | 23.7426 | + | 17.2500i | 1.08145 | + | 0.785718i | ||||
\(483\) | 3.05573 | 0.139040 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −34.8328 | −1.58168 | ||||||||
\(486\) | −24.5967 | − | 17.8706i | −1.11573 | − | 0.810626i | ||||
\(487\) | −11.2361 | + | 34.5811i | −0.509155 | + | 1.56702i | 0.284517 | + | 0.958671i | \(0.408167\pi\) |
−0.793672 | + | 0.608346i | \(0.791833\pi\) | |||||||
\(488\) | −5.00000 | − | 15.3884i | −0.226339 | − | 0.696601i | ||||
\(489\) | −3.41641 | + | 2.48217i | −0.154495 | + | 0.112247i | ||||
\(490\) | −3.61803 | + | 2.62866i | −0.163446 | + | 0.118751i | ||||
\(491\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(492\) | −12.8754 | + | 39.6264i | −0.580467 | + | 1.78649i | ||||
\(493\) | 22.1803 | + | 16.1150i | 0.998952 | + | 0.725781i | ||||
\(494\) | −46.8328 | −2.10711 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.76393 | 0.124104 | ||||||||
\(497\) | −8.47214 | − | 6.15537i | −0.380027 | − | 0.276106i | ||||
\(498\) | 9.75078 | − | 30.0098i | 0.436943 | − | 1.34477i | ||||
\(499\) | 0.472136 | + | 1.45309i | 0.0211357 | + | 0.0650490i | 0.961068 | − | 0.276312i | \(-0.0891122\pi\) |
−0.939932 | + | 0.341361i | \(0.889112\pi\) | |||||||
\(500\) | −29.1246 | + | 21.1603i | −1.30249 | + | 0.946316i | ||||
\(501\) | −4.94427 | + | 3.59222i | −0.220894 | + | 0.160489i | ||||
\(502\) | −2.96556 | − | 9.12705i | −0.132359 | − | 0.407360i | ||||
\(503\) | −7.23607 | + | 22.2703i | −0.322640 | + | 0.992985i | 0.649854 | + | 0.760059i | \(0.274830\pi\) |
−0.972494 | + | 0.232926i | \(0.925170\pi\) | |||||||
\(504\) | 2.66312 | + | 1.93487i | 0.118625 | + | 0.0861859i | ||||
\(505\) | −9.52786 | −0.423984 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.12461 | 0.138769 | ||||||||
\(508\) | 7.41641 | + | 5.38834i | 0.329050 | + | 0.239069i | ||||
\(509\) | 12.5066 | − | 38.4913i | 0.554344 | − | 1.70610i | −0.143324 | − | 0.989676i | \(-0.545779\pi\) |
0.697669 | − | 0.716421i | \(-0.254221\pi\) | |||||||
\(510\) | −5.52786 | − | 17.0130i | −0.244778 | − | 0.753349i | ||||
\(511\) | 0.618034 | − | 0.449028i | 0.0273402 | − | 0.0198638i | ||||
\(512\) | 9.04508 | − | 6.57164i | 0.399740 | − | 0.290428i | ||||
\(513\) | −11.0557 | − | 34.0260i | −0.488122 | − | 1.50229i | ||||
\(514\) | 4.14590 | − | 12.7598i | 0.182868 | − | 0.562809i | ||||
\(515\) | 12.4721 | + | 9.06154i | 0.549588 | + | 0.399299i | ||||
\(516\) | 29.6656 | 1.30596 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −18.9443 | −0.832364 | ||||||||
\(519\) | 12.7639 | + | 9.27354i | 0.560274 | + | 0.407063i | ||||
\(520\) | −4.47214 | + | 13.7638i | −0.196116 | + | 0.603583i | ||||
\(521\) | 9.38197 | + | 28.8747i | 0.411031 | + | 1.26502i | 0.915753 | + | 0.401742i | \(0.131595\pi\) |
−0.504721 | + | 0.863282i | \(0.668405\pi\) | |||||||
\(522\) | 22.5623 | − | 16.3925i | 0.987525 | − | 0.717479i | ||||
\(523\) | 35.5967 | − | 25.8626i | 1.55654 | − | 1.13089i | 0.617759 | − | 0.786367i | \(-0.288041\pi\) |
0.938778 | − | 0.344523i | \(-0.111959\pi\) | |||||||
\(524\) | −20.2918 | − | 62.4517i | −0.886451 | − | 2.72822i | ||||
\(525\) | −0.381966 | + | 1.17557i | −0.0166704 | + | 0.0513061i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.94427 | −0.389619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 1.70820 | + | 1.24108i | 0.0741996 | + | 0.0539092i | ||||
\(531\) | 0.562306 | − | 1.73060i | 0.0244020 | − | 0.0751016i | ||||
\(532\) | 6.00000 | + | 18.4661i | 0.260133 | + | 0.800607i | ||||
\(533\) | 29.4164 | − | 21.3723i | 1.27417 | − | 0.925736i | ||||
\(534\) | −4.47214 | + | 3.24920i | −0.193528 | + | 0.140607i | ||||
\(535\) | −2.47214 | − | 7.60845i | −0.106880 | − | 0.328942i | ||||
\(536\) | −10.0000 | + | 30.7768i | −0.431934 | + | 1.32936i | ||||
\(537\) | −8.94427 | − | 6.49839i | −0.385974 | − | 0.280426i | ||||
\(538\) | −30.0000 | −1.29339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −33.1672 | −1.42729 | ||||||||
\(541\) | 16.8541 | + | 12.2452i | 0.724614 | + | 0.526463i | 0.887855 | − | 0.460123i | \(-0.152195\pi\) |
−0.163241 | + | 0.986586i | \(0.552195\pi\) | |||||||
\(542\) | −7.23607 | + | 22.2703i | −0.310816 | + | 0.956592i | ||||
\(543\) | 9.70820 | + | 29.8788i | 0.416619 | + | 1.28222i | ||||
\(544\) | −17.5623 | + | 12.7598i | −0.752978 | + | 0.547070i | ||||
\(545\) | 7.23607 | − | 5.25731i | 0.309959 | − | 0.225198i | ||||
\(546\) | 2.76393 | + | 8.50651i | 0.118285 | + | 0.364045i | ||||
\(547\) | −8.65248 | + | 26.6296i | −0.369953 | + | 1.13860i | 0.576868 | + | 0.816838i | \(0.304275\pi\) |
−0.946821 | + | 0.321761i | \(0.895725\pi\) | |||||||
\(548\) | −39.9787 | − | 29.0462i | −1.70781 | − | 1.24079i | ||||
\(549\) | −10.6525 | −0.454637 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 54.8328 | 2.33596 | ||||||||
\(552\) | −5.52786 | − | 4.01623i | −0.235282 | − | 0.170942i | ||||
\(553\) | −2.76393 | + | 8.50651i | −0.117534 | + | 0.361734i | ||||
\(554\) | −13.7426 | − | 42.2955i | −0.583869 | − | 1.79696i | ||||
\(555\) | 16.9443 | − | 12.3107i | 0.719244 | − | 0.522562i | ||||
\(556\) | −3.70820 | + | 2.69417i | −0.157263 | + | 0.114258i | ||||
\(557\) | 12.0344 | + | 37.0382i | 0.509916 | + | 1.56936i | 0.792346 | + | 0.610071i | \(0.208859\pi\) |
−0.282431 | + | 0.959288i | \(0.591141\pi\) | |||||||
\(558\) | −2.81153 | + | 8.65300i | −0.119022 | + | 0.366311i | ||||
\(559\) | −20.9443 | − | 15.2169i | −0.885848 | − | 0.643606i | ||||
\(560\) | −2.00000 | −0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.88854 | −0.332758 | ||||||||
\(563\) | 10.1803 | + | 7.39645i | 0.429050 | + | 0.311723i | 0.781269 | − | 0.624194i | \(-0.214573\pi\) |
−0.352219 | + | 0.935918i | \(0.614573\pi\) | |||||||
\(564\) | −3.16718 | + | 9.74759i | −0.133363 | + | 0.410448i | ||||
\(565\) | −1.23607 | − | 3.80423i | −0.0520018 | − | 0.160045i | ||||
\(566\) | −54.0689 | + | 39.2833i | −2.27268 | + | 1.65120i | ||||
\(567\) | −1.95492 | + | 1.42033i | −0.0820987 | + | 0.0596482i | ||||
\(568\) | 7.23607 | + | 22.2703i | 0.303619 | + | 0.934442i | ||||
\(569\) | −2.32624 | + | 7.15942i | −0.0975210 | + | 0.300139i | −0.987902 | − | 0.155076i | \(-0.950438\pi\) |
0.890382 | + | 0.455215i | \(0.150438\pi\) | |||||||
\(570\) | −28.9443 | − | 21.0292i | −1.21234 | − | 0.880818i | ||||
\(571\) | 15.0557 | 0.630063 | 0.315031 | − | 0.949081i | \(-0.397985\pi\) | ||||
0.315031 | + | 0.949081i | \(0.397985\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.77709 | 0.157790 | ||||||||
\(574\) | −20.3262 | − | 14.7679i | −0.848401 | − | 0.616399i | ||||
\(575\) | −0.763932 | + | 2.35114i | −0.0318582 | + | 0.0980494i | ||||
\(576\) | 5.91390 | + | 18.2011i | 0.246412 | + | 0.758379i | ||||
\(577\) | 15.7984 | − | 11.4782i | 0.657695 | − | 0.477843i | −0.208189 | − | 0.978089i | \(-0.566757\pi\) |
0.865884 | + | 0.500245i | \(0.166757\pi\) | |||||||
\(578\) | −11.8090 | + | 8.57975i | −0.491190 | + | 0.356871i | ||||
\(579\) | 4.54102 | + | 13.9758i | 0.188718 | + | 0.580815i | ||||
\(580\) | 15.7082 | − | 48.3449i | 0.652248 | − | 2.00741i | ||||
\(581\) | 9.23607 | + | 6.71040i | 0.383177 | + | 0.278394i | ||||
\(582\) | 48.1378 | 1.99537 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.70820 | −0.0706860 | ||||||||
\(585\) | 7.70820 | + | 5.60034i | 0.318695 | + | 0.231545i | ||||
\(586\) | −17.3607 | + | 53.4307i | −0.717163 | + | 2.20720i | ||||
\(587\) | 8.38197 | + | 25.7970i | 0.345961 | + | 1.06476i | 0.961067 | + | 0.276314i | \(0.0891129\pi\) |
−0.615107 | + | 0.788444i | \(0.710887\pi\) | |||||||
\(588\) | 3.00000 | − | 2.17963i | 0.123718 | − | 0.0898863i | ||||
\(589\) | −14.4721 | + | 10.5146i | −0.596314 | + | 0.433247i | ||||
\(590\) | −1.70820 | − | 5.25731i | −0.0703256 | − | 0.216440i | ||||
\(591\) | −0.763932 | + | 2.35114i | −0.0314240 | + | 0.0967130i | ||||
\(592\) | −6.85410 | − | 4.97980i | −0.281702 | − | 0.204668i | ||||
\(593\) | 45.7082 | 1.87701 | 0.938505 | − | 0.345264i | \(-0.112211\pi\) | ||||
0.938505 | + | 0.345264i | \(0.112211\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.47214 | 0.265332 | ||||||||
\(596\) | 33.9787 | + | 24.6870i | 1.39182 | + | 1.01122i | ||||
\(597\) | 0.832816 | − | 2.56314i | 0.0340849 | − | 0.104902i | ||||
\(598\) | 5.52786 | + | 17.0130i | 0.226051 | + | 0.695714i | ||||
\(599\) | 18.9443 | − | 13.7638i | 0.774042 | − | 0.562374i | −0.129143 | − | 0.991626i | \(-0.541223\pi\) |
0.903185 | + | 0.429252i | \(0.141223\pi\) | |||||||
\(600\) | 2.23607 | − | 1.62460i | 0.0912871 | − | 0.0663240i | ||||
\(601\) | 11.4721 | + | 35.3076i | 0.467958 | + | 1.44023i | 0.855224 | + | 0.518259i | \(0.173420\pi\) |
−0.387266 | + | 0.921968i | \(0.626580\pi\) | |||||||
\(602\) | −5.52786 | + | 17.0130i | −0.225299 | + | 0.693399i | ||||
\(603\) | 17.2361 | + | 12.5227i | 0.701907 | + | 0.509965i | ||||
\(604\) | −26.8328 | −1.09181 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.1672 | 0.534880 | ||||||||
\(607\) | 10.4721 | + | 7.60845i | 0.425051 | + | 0.308818i | 0.779667 | − | 0.626194i | \(-0.215388\pi\) |
−0.354616 | + | 0.935012i | \(0.615388\pi\) | |||||||
\(608\) | −13.4164 | + | 41.2915i | −0.544107 | + | 1.67459i | ||||
\(609\) | −3.23607 | − | 9.95959i | −0.131132 | − | 0.403583i | ||||
\(610\) | −26.1803 | + | 19.0211i | −1.06001 | + | 0.770143i | ||||
\(611\) | 7.23607 | − | 5.25731i | 0.292740 | − | 0.212688i | ||||
\(612\) | −4.41641 | − | 13.5923i | −0.178523 | − | 0.549436i | ||||
\(613\) | −4.72949 | + | 14.5559i | −0.191022 | + | 0.587906i | 0.808978 | + | 0.587839i | \(0.200021\pi\) |
−1.00000 | 6.68672e-5i | \(0.999979\pi\) | ||||||||
\(614\) | 16.1803 | + | 11.7557i | 0.652985 | + | 0.474422i | ||||
\(615\) | 27.7771 | 1.12008 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.58359 | 0.265045 | 0.132523 | − | 0.991180i | \(-0.457692\pi\) | ||||
0.132523 | + | 0.991180i | \(0.457692\pi\) | |||||||
\(618\) | −17.2361 | − | 12.5227i | −0.693336 | − | 0.503738i | ||||
\(619\) | 3.43769 | − | 10.5801i | 0.138173 | − | 0.425252i | −0.857897 | − | 0.513821i | \(-0.828230\pi\) |
0.996070 | + | 0.0885695i | \(0.0282295\pi\) | |||||||
\(620\) | 5.12461 | + | 15.7719i | 0.205809 | + | 0.633416i | ||||
\(621\) | −11.0557 | + | 8.03246i | −0.443651 | + | 0.322331i | ||||
\(622\) | −15.0000 | + | 10.8981i | −0.601445 | + | 0.436976i | ||||
\(623\) | −0.618034 | − | 1.90211i | −0.0247610 | − | 0.0762065i | ||||
\(624\) | −1.23607 | + | 3.80423i | −0.0494823 | + | 0.152291i | ||||
\(625\) | 15.3713 | + | 11.1679i | 0.614853 | + | 0.446717i | ||||
\(626\) | −33.4164 | −1.33559 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 32.8328 | 1.31017 | ||||||||
\(629\) | 22.1803 | + | 16.1150i | 0.884388 | + | 0.642546i | ||||
\(630\) | 2.03444 | − | 6.26137i | 0.0810541 | − | 0.249459i | ||||
\(631\) | −7.41641 | − | 22.8254i | −0.295243 | − | 0.908663i | −0.983140 | − | 0.182855i | \(-0.941466\pi\) |
0.687897 | − | 0.725808i | \(-0.258534\pi\) | |||||||
\(632\) | 16.1803 | − | 11.7557i | 0.643619 | − | 0.467617i | ||||
\(633\) | 13.8885 | − | 10.0906i | 0.552020 | − | 0.401066i | ||||
\(634\) | −9.67376 | − | 29.7728i | −0.384194 | − | 1.18243i | ||||
\(635\) | 1.88854 | − | 5.81234i | 0.0749446 | − | 0.230656i | ||||
\(636\) | −1.41641 | − | 1.02908i | −0.0561642 | − | 0.0408057i | ||||
\(637\) | −3.23607 | −0.128218 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.4164 | 0.609864 | ||||||||
\(640\) | 25.3262 | + | 18.4006i | 1.00111 | + | 0.727347i | ||||
\(641\) | −4.79837 | + | 14.7679i | −0.189524 | + | 0.583296i | −0.999997 | − | 0.00248057i | \(-0.999210\pi\) |
0.810473 | + | 0.585777i | \(0.199210\pi\) | |||||||
\(642\) | 3.41641 | + | 10.5146i | 0.134835 | + | 0.414979i | ||||
\(643\) | −9.00000 | + | 6.53888i | −0.354925 | + | 0.257868i | −0.750932 | − | 0.660379i | \(-0.770396\pi\) |
0.396007 | + | 0.918247i | \(0.370396\pi\) | |||||||
\(644\) | 6.00000 | − | 4.35926i | 0.236433 | − | 0.171779i | ||||
\(645\) | −6.11146 | − | 18.8091i | −0.240638 | − | 0.740609i | ||||
\(646\) | 14.4721 | − | 44.5407i | 0.569399 | − | 1.75243i | ||||
\(647\) | −29.1803 | − | 21.2008i | −1.14720 | − | 0.833488i | −0.159092 | − | 0.987264i | \(-0.550857\pi\) |
−0.988106 | + | 0.153776i | \(0.950857\pi\) | |||||||
\(648\) | 5.40325 | 0.212260 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −7.23607 | −0.283822 | ||||||||
\(651\) | 2.76393 | + | 2.00811i | 0.108327 | + | 0.0787042i | ||||
\(652\) | −3.16718 | + | 9.74759i | −0.124037 | + | 0.381745i | ||||
\(653\) | 7.74265 | + | 23.8294i | 0.302993 | + | 0.932517i | 0.980418 | + | 0.196925i | \(0.0630957\pi\) |
−0.677425 | + | 0.735592i | \(0.736904\pi\) | |||||||
\(654\) | −10.0000 | + | 7.26543i | −0.391031 | + | 0.284101i | ||||
\(655\) | −35.4164 | + | 25.7315i | −1.38383 | + | 1.00541i | ||||
\(656\) | −3.47214 | − | 10.6861i | −0.135564 | − | 0.417224i | ||||
\(657\) | −0.347524 | + | 1.06957i | −0.0135582 | + | 0.0417279i | ||||
\(658\) | −5.00000 | − | 3.63271i | −0.194920 | − | 0.141618i | ||||
\(659\) | 17.8885 | 0.696839 | 0.348419 | − | 0.937339i | \(-0.386719\pi\) | ||||
0.348419 | + | 0.937339i | \(0.386719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.8328 | −1.58821 | −0.794106 | − | 0.607779i | \(-0.792061\pi\) | ||||
−0.794106 | + | 0.607779i | \(0.792061\pi\) | |||||||
\(662\) | −25.1246 | − | 18.2541i | −0.976496 | − | 0.709466i | ||||
\(663\) | 4.00000 | − | 12.3107i | 0.155347 | − | 0.478109i | ||||
\(664\) | −7.88854 | − | 24.2784i | −0.306135 | − | 0.942186i | ||||
\(665\) | 10.4721 | − | 7.60845i | 0.406092 | − | 0.295043i | ||||
\(666\) | 22.5623 | − | 16.3925i | 0.874272 | − | 0.635195i | ||||
\(667\) | −6.47214 | − | 19.9192i | −0.250602 | − | 0.771274i | ||||
\(668\) | −4.58359 | + | 14.1068i | −0.177345 | + | 0.545810i | ||||
\(669\) | −10.1803 | − | 7.39645i | −0.393595 | − | 0.285963i | ||||
\(670\) | 64.7214 | 2.50040 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 8.29180 | 0.319863 | ||||||||
\(673\) | −17.3262 | − | 12.5882i | −0.667877 | − | 0.485241i | 0.201437 | − | 0.979502i | \(-0.435439\pi\) |
−0.869314 | + | 0.494260i | \(0.835439\pi\) | |||||||
\(674\) | −7.96556 | + | 24.5155i | −0.306822 | + | 0.944301i | ||||
\(675\) | −1.70820 | − | 5.25731i | −0.0657488 | − | 0.202354i | ||||
\(676\) | 6.13525 | − | 4.45752i | 0.235971 | − | 0.171443i | ||||
\(677\) | −7.85410 | + | 5.70634i | −0.301858 | + | 0.219312i | −0.728395 | − | 0.685158i | \(-0.759733\pi\) |
0.426537 | + | 0.904470i | \(0.359733\pi\) | |||||||
\(678\) | 1.70820 | + | 5.25731i | 0.0656032 | + | 0.201906i | ||||
\(679\) | −5.38197 | + | 16.5640i | −0.206541 | + | 0.635668i | ||||
\(680\) | −11.7082 | − | 8.50651i | −0.448989 | − | 0.326210i | ||||
\(681\) | 7.27864 | 0.278918 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.88854 | −0.225319 | −0.112659 | − | 0.993634i | \(-0.535937\pi\) | ||||
−0.112659 | + | 0.993634i | \(0.535937\pi\) | |||||||
\(684\) | −23.1246 | − | 16.8010i | −0.884192 | − | 0.642403i | ||||
\(685\) | −10.1803 | + | 31.3319i | −0.388971 | + | 1.19713i | ||||
\(686\) | 0.690983 | + | 2.12663i | 0.0263819 | + | 0.0811950i | ||||
\(687\) | −4.47214 | + | 3.24920i | −0.170623 | + | 0.123965i | ||||
\(688\) | −6.47214 | + | 4.70228i | −0.246748 | + | 0.179273i | ||||
\(689\) | 0.472136 | + | 1.45309i | 0.0179869 | + | 0.0553581i | ||||
\(690\) | −4.22291 | + | 12.9968i | −0.160764 | + | 0.494779i | ||||
\(691\) | −15.0000 | − | 10.8981i | −0.570627 | − | 0.414585i | 0.264706 | − | 0.964329i | \(-0.414725\pi\) |
−0.835333 | + | 0.549744i | \(0.814725\pi\) | |||||||
\(692\) | 38.2918 | 1.45564 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 46.8328 | 1.77775 | ||||||||
\(695\) | 2.47214 | + | 1.79611i | 0.0937735 | + | 0.0681304i | ||||
\(696\) | −7.23607 | + | 22.2703i | −0.274282 | + | 0.844155i | ||||
\(697\) | 11.2361 | + | 34.5811i | 0.425596 | + | 1.30985i | ||||
\(698\) | 13.0902 | − | 9.51057i | 0.495470 | − | 0.359980i | ||||
\(699\) | −9.41641 | + | 6.84142i | −0.356161 | + | 0.258766i | ||||
\(700\) | 0.927051 | + | 2.85317i | 0.0350392 | + | 0.107840i | ||||
\(701\) | 4.79837 | − | 14.7679i | 0.181232 | − | 0.557775i | −0.818631 | − | 0.574320i | \(-0.805267\pi\) |
0.999863 | + | 0.0165448i | \(0.00526661\pi\) | |||||||
\(702\) | −32.3607 | − | 23.5114i | −1.22138 | − | 0.887381i | ||||
\(703\) | 54.8328 | 2.06806 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.83282 | 0.257339 | ||||||||
\(706\) | 35.9787 | + | 26.1401i | 1.35408 | + | 0.983794i | ||||
\(707\) | −1.47214 | + | 4.53077i | −0.0553654 | + | 0.170397i | ||||
\(708\) | 1.41641 | + | 4.35926i | 0.0532319 | + | 0.163831i | ||||
\(709\) | 12.0902 | − | 8.78402i | 0.454056 | − | 0.329891i | −0.337139 | − | 0.941455i | \(-0.609459\pi\) |
0.791195 | + | 0.611564i | \(0.209459\pi\) | |||||||
\(710\) | 37.8885 | − | 27.5276i | 1.42193 | − | 1.03309i | ||||
\(711\) | −4.06888 | − | 12.5227i | −0.152595 | − | 0.469639i | ||||
\(712\) | −1.38197 | + | 4.25325i | −0.0517914 | + | 0.159397i | ||||
\(713\) | 5.52786 | + | 4.01623i | 0.207020 | + | 0.150409i | ||||
\(714\) | −8.94427 | −0.334731 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −26.8328 | −1.00279 | ||||||||
\(717\) | 9.88854 | + | 7.18445i | 0.369294 | + | 0.268308i | ||||
\(718\) | −17.2361 | + | 53.0472i | −0.643244 | + | 1.97970i | ||||
\(719\) | −15.9098 | − | 48.9654i | −0.593337 | − | 1.82610i | −0.562838 | − | 0.826567i | \(-0.690290\pi\) |
−0.0304986 | − | 0.999535i | \(-0.509710\pi\) | |||||||
\(720\) | 2.38197 | − | 1.73060i | 0.0887706 | − | 0.0644956i | ||||
\(721\) | 6.23607 | − | 4.53077i | 0.232243 | − | 0.168735i | ||||
\(722\) | −15.8156 | − | 48.6754i | −0.588595 | − | 1.81151i | ||||
\(723\) | −5.01316 | + | 15.4289i | −0.186441 | + | 0.573807i | ||||
\(724\) | 61.6869 | + | 44.8182i | 2.29258 | + | 1.66565i | ||||
\(725\) | 8.47214 | 0.314647 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.0132 | 0.927687 | 0.463843 | − | 0.885917i | \(-0.346470\pi\) | ||||
0.463843 | + | 0.885917i | \(0.346470\pi\) | |||||||
\(728\) | 5.85410 | + | 4.25325i | 0.216967 | + | 0.157636i | ||||
\(729\) | 7.43363 | − | 22.8784i | 0.275320 | − | 0.847347i | ||||
\(730\) | 1.05573 | + | 3.24920i | 0.0390742 | + | 0.120258i | ||||
\(731\) | 20.9443 | − | 15.2169i | 0.774652 | − | 0.562818i | ||||
\(732\) | 21.7082 | − | 15.7719i | 0.802358 | − | 0.582947i | ||||
\(733\) | −2.70820 | − | 8.33499i | −0.100030 | − | 0.307860i | 0.888502 | − | 0.458873i | \(-0.151747\pi\) |
−0.988532 | + | 0.151013i | \(0.951747\pi\) | |||||||
\(734\) | 15.9787 | − | 49.1774i | 0.589785 | − | 1.81517i | ||||
\(735\) | −2.00000 | − | 1.45309i | −0.0737711 | − | 0.0535978i | ||||
\(736\) | 16.5836 | 0.611279 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 36.9868 | 1.36150 | ||||||||
\(739\) | 20.1803 | + | 14.6619i | 0.742346 | + | 0.539346i | 0.893445 | − | 0.449173i | \(-0.148281\pi\) |
−0.151099 | + | 0.988519i | \(0.548281\pi\) | |||||||
\(740\) | 15.7082 | − | 48.3449i | 0.577445 | − | 1.77719i | ||||
\(741\) | −8.00000 | − | 24.6215i | −0.293887 | − | 0.904492i | ||||
\(742\) | 0.854102 | − | 0.620541i | 0.0313551 | − | 0.0227808i | ||||
\(743\) | 1.52786 | − | 1.11006i | 0.0560519 | − | 0.0407241i | −0.559407 | − | 0.828893i | \(-0.688971\pi\) |
0.615458 | + | 0.788169i | \(0.288971\pi\) | |||||||
\(744\) | −2.36068 | − | 7.26543i | −0.0865467 | − | 0.266363i | ||||
\(745\) | 8.65248 | − | 26.6296i | 0.317002 | − | 0.975632i | ||||
\(746\) | −10.8541 | − | 7.88597i | −0.397397 | − | 0.288726i | ||||
\(747\) | −16.8065 | −0.614918 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | −26.8328 | − | 19.4952i | −0.979796 | − | 0.711863i | ||||
\(751\) | 9.12461 | − | 28.0827i | 0.332962 | − | 1.02475i | −0.634756 | − | 0.772713i | \(-0.718899\pi\) |
0.967717 | − | 0.252038i | \(-0.0811008\pi\) | |||||||
\(752\) | −0.854102 | − | 2.62866i | −0.0311459 | − | 0.0958572i | ||||
\(753\) | 4.29180 | − | 3.11817i | 0.156402 | − | 0.113633i | ||||
\(754\) | 49.5967 | − | 36.0341i | 1.80621 | − | 1.31229i | ||||
\(755\) | 5.52786 | + | 17.0130i | 0.201180 | + | 0.619167i | ||||
\(756\) | −5.12461 | + | 15.7719i | −0.186380 | + | 0.573620i | ||||
\(757\) | −12.8541 | − | 9.33905i | −0.467190 | − | 0.339434i | 0.329155 | − | 0.944276i | \(-0.393236\pi\) |
−0.796345 | + | 0.604842i | \(0.793236\pi\) | |||||||
\(758\) | −83.4164 | −3.02982 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −28.9443 | −1.04992 | ||||||||
\(761\) | −25.5623 | − | 18.5721i | −0.926633 | − | 0.673238i | 0.0185332 | − | 0.999828i | \(-0.494100\pi\) |
−0.945166 | + | 0.326590i | \(0.894100\pi\) | |||||||
\(762\) | −2.60990 | + | 8.03246i | −0.0945468 | + | 0.290985i | ||||
\(763\) | −1.38197 | − | 4.25325i | −0.0500305 | − | 0.153978i | ||||
\(764\) | 7.41641 | − | 5.38834i | 0.268316 | − | 0.194943i | ||||
\(765\) | −7.70820 | + | 5.60034i | −0.278691 | + | 0.202481i | ||||
\(766\) | 3.21478 | + | 9.89408i | 0.116155 | + | 0.357488i | ||||
\(767\) | 1.23607 | − | 3.80423i | 0.0446318 | − | 0.137363i | ||||
\(768\) | −9.00000 | − | 6.53888i | −0.324760 | − | 0.235952i | ||||
\(769\) | −18.2918 | −0.659619 | −0.329810 | − | 0.944047i | \(-0.606985\pi\) | ||||
−0.329810 | + | 0.944047i | \(0.606985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.41641 | 0.267095 | ||||||||
\(772\) | 28.8541 | + | 20.9637i | 1.03848 | + | 0.754501i | ||||
\(773\) | −11.8541 | + | 36.4832i | −0.426362 | + | 1.31221i | 0.475321 | + | 0.879812i | \(0.342332\pi\) |
−0.901684 | + | 0.432396i | \(0.857668\pi\) | |||||||
\(774\) | −8.13777 | − | 25.0455i | −0.292506 | − | 0.900241i | ||||
\(775\) | −2.23607 | + | 1.62460i | −0.0803219 | + | 0.0583573i | ||||
\(776\) | 31.5066 | − | 22.8909i | 1.13102 | − | 0.821734i | ||||
\(777\) | −3.23607 | − | 9.95959i | −0.116093 | − | 0.357298i | ||||
\(778\) | −10.9787 | + | 33.7890i | −0.393606 | + | 1.21139i | ||||
\(779\) | 58.8328 | + | 42.7445i | 2.10790 | + | 1.53148i | ||||
\(780\) | −24.0000 | −0.859338 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −17.8885 | −0.639693 | ||||||||
\(783\) | 37.8885 | + | 27.5276i | 1.35403 | + | 0.983758i | ||||
\(784\) | −0.309017 | + | 0.951057i | −0.0110363 | + | 0.0339663i | ||||
\(785\) | −6.76393 | − | 20.8172i | −0.241415 | − | 0.742999i | ||||
\(786\) | 48.9443 | − | 35.5601i | 1.74578 | − | 1.26839i | ||||
\(787\) | −35.1246 | + | 25.5195i | −1.25206 | + | 0.909673i | −0.998339 | − | 0.0576055i | \(-0.981653\pi\) |
−0.253718 | + | 0.967278i | \(0.581653\pi\) | |||||||
\(788\) | 1.85410 | + | 5.70634i | 0.0660496 | + | 0.203280i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.3607 | − | 23.5114i | −1.15134 | − | 0.836498i | ||||
\(791\) | −2.00000 | −0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −23.4164 | −0.831541 | ||||||||
\(794\) | −64.9230 | − | 47.1693i | −2.30403 | − | 1.67398i | ||||
\(795\) | −0.360680 | + | 1.11006i | −0.0127920 | + | 0.0393697i | ||||
\(796\) | −2.02129 | − | 6.22088i | −0.0716426 | − | 0.220493i | ||||
\(797\) | 12.0902 | − | 8.78402i | 0.428256 | − | 0.311146i | −0.352695 | − | 0.935738i | \(-0.614735\pi\) |
0.780951 | + | 0.624592i | \(0.214735\pi\) | |||||||
\(798\) | −14.4721 | + | 10.5146i | −0.512308 | + | 0.372214i | ||||
\(799\) | 2.76393 | + | 8.50651i | 0.0977809 | + | 0.300939i | ||||
\(800\) | −2.07295 | + | 6.37988i | −0.0732898 | + | 0.225563i | ||||
\(801\) | 2.38197 | + | 1.73060i | 0.0841626 | + | 0.0611477i | ||||
\(802\) | −51.3050 | −1.81164 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −53.6656 | −1.89264 | ||||||||
\(805\) | −4.00000 | − | 2.90617i | −0.140981 | − | 0.102429i | ||||
\(806\) | −6.18034 | + | 19.0211i | −0.217693 | + | 0.669991i | ||||
\(807\) | −5.12461 | − | 15.7719i | −0.180395 | − | 0.555198i | ||||
\(808\) | 8.61803 | − | 6.26137i | 0.303181 | − | 0.220274i | ||||
\(809\) | 17.0344 | − | 12.3762i | 0.598899 | − | 0.435126i | −0.246589 | − | 0.969120i | \(-0.579310\pi\) |
0.845488 | + | 0.533995i | \(0.179310\pi\) | |||||||
\(810\) | −3.33939 | − | 10.2776i | −0.117334 | − | 0.361118i | ||||
\(811\) | 10.7639 | − | 33.1280i | 0.377973 | − | 1.16328i | −0.563478 | − | 0.826131i | \(-0.690537\pi\) |
0.941451 | − | 0.337150i | \(-0.109463\pi\) | |||||||
\(812\) | −20.5623 | − | 14.9394i | −0.721595 | − | 0.524270i | ||||
\(813\) | −12.9443 | −0.453975 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.83282 | 0.239343 | ||||||||
\(816\) | −3.23607 | − | 2.35114i | −0.113285 | − | 0.0823064i | ||||
\(817\) | 16.0000 | − | 49.2429i | 0.559769 | − | 1.72279i | ||||
\(818\) | 6.30495 | + | 19.4046i | 0.220447 | + | 0.678468i | ||||
\(819\) | 3.85410 | − | 2.80017i | 0.134673 | − | 0.0978458i | ||||
\(820\) | 54.5410 | − | 39.6264i | 1.90466 | − | 1.38381i | ||||
\(821\) | −13.8541 | − | 42.6385i | −0.483511 | − | 1.48810i | −0.834125 | − | 0.551575i | \(-0.814027\pi\) |
0.350614 | − | 0.936520i | \(-0.385973\pi\) | |||||||
\(822\) | 14.0689 | − | 43.2996i | 0.490709 | − | 1.51025i | ||||
\(823\) | 11.4164 | + | 8.29451i | 0.397951 | + | 0.289128i | 0.768706 | − | 0.639602i | \(-0.220901\pi\) |
−0.370755 | + | 0.928731i | \(0.620901\pi\) | |||||||
\(824\) | −17.2361 | −0.600447 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.76393 | −0.0961695 | ||||||||
\(827\) | −10.4721 | − | 7.60845i | −0.364152 | − | 0.264572i | 0.390630 | − | 0.920548i | \(-0.372257\pi\) |
−0.754782 | + | 0.655976i | \(0.772257\pi\) | |||||||
\(828\) | −3.37384 | + | 10.3836i | −0.117249 | + | 0.360855i | ||||
\(829\) | 11.3820 | + | 35.0301i | 0.395312 | + | 1.21665i | 0.928718 | + | 0.370786i | \(0.120912\pi\) |
−0.533406 | + | 0.845859i | \(0.679088\pi\) | |||||||
\(830\) | −41.3050 | + | 30.0098i | −1.43372 | + | 1.04166i | ||||
\(831\) | 19.8885 | − | 14.4499i | 0.689926 | − | 0.501261i | ||||
\(832\) | 13.0000 | + | 40.0099i | 0.450694 | + | 1.38709i | ||||
\(833\) | 1.00000 | − | 3.07768i | 0.0346479 | − | 0.106635i | ||||
\(834\) | −3.41641 | − | 2.48217i | −0.118301 | − | 0.0859504i | ||||
\(835\) | 9.88854 | 0.342207 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.2786 | −0.528107 | ||||||||
\(838\) | 44.5967 | + | 32.4014i | 1.54057 | + | 1.11929i | ||||
\(839\) | 13.6180 | − | 41.9120i | 0.470147 | − | 1.44696i | −0.382246 | − | 0.924061i | \(-0.624849\pi\) |
0.852393 | − | 0.522902i | \(-0.175151\pi\) | |||||||
\(840\) | 1.70820 | + | 5.25731i | 0.0589386 | + | 0.181394i | ||||
\(841\) | −34.6074 | + | 25.1437i | −1.19336 | + | 0.867026i | ||||
\(842\) | 40.4508 | − | 29.3893i | 1.39403 | − | 1.01282i | ||||
\(843\) | −1.34752 | − | 4.14725i | −0.0464112 | − | 0.142839i | ||||
\(844\) | 12.8754 | − | 39.6264i | 0.443189 | − | 1.36400i | ||||
\(845\) | −4.09017 | − | 2.97168i | −0.140706 | − | 0.102229i | ||||
\(846\) | 9.09830 | 0.312806 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.472136 | 0.0162132 | ||||||||
\(849\) | −29.8885 | − | 21.7153i | −1.02577 | − | 0.745267i | ||||
\(850\) | 2.23607 | − | 6.88191i | 0.0766965 | − | 0.236048i | ||||
\(851\) | −6.47214 | − | 19.9192i | −0.221862 | − | 0.682821i | ||||
\(852\) | −31.4164 | + | 22.8254i | −1.07631 | + | 0.781984i | ||||
\(853\) | −24.7984 | + | 18.0171i | −0.849080 | + | 0.616893i | −0.924892 | − | 0.380229i | \(-0.875845\pi\) |
0.0758121 | + | 0.997122i | \(0.475845\pi\) | |||||||
\(854\) | 5.00000 | + | 15.3884i | 0.171096 | + | 0.526581i | ||||
\(855\) | −5.88854 | + | 18.1231i | −0.201384 | + | 0.619796i | ||||
\(856\) | 7.23607 | + | 5.25731i | 0.247324 | + | 0.179691i | ||||
\(857\) | −15.2361 | −0.520454 | −0.260227 | − | 0.965547i | \(-0.583797\pi\) | ||||
−0.260227 | + | 0.965547i | \(0.583797\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.5410 | −0.905568 | −0.452784 | − | 0.891620i | \(-0.649569\pi\) | ||||
−0.452784 | + | 0.891620i | \(0.649569\pi\) | |||||||
\(860\) | −38.8328 | − | 28.2137i | −1.32419 | − | 0.962079i | ||||
\(861\) | 4.29180 | − | 13.2088i | 0.146264 | − | 0.450154i | ||||
\(862\) | 8.29180 | + | 25.5195i | 0.282420 | + | 0.869198i | ||||
\(863\) | 2.47214 | − | 1.79611i | 0.0841525 | − | 0.0611404i | −0.544914 | − | 0.838492i | \(-0.683438\pi\) |
0.629066 | + | 0.777352i | \(0.283438\pi\) | |||||||
\(864\) | −30.0000 | + | 21.7963i | −1.02062 | + | 0.741524i | ||||
\(865\) | −7.88854 | − | 24.2784i | −0.268219 | − | 0.825492i | ||||
\(866\) | 5.85410 | − | 18.0171i | 0.198930 | − | 0.612245i | ||||
\(867\) | −6.52786 | − | 4.74277i | −0.221698 | − | 0.161073i | ||||
\(868\) | 8.29180 | 0.281442 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 46.8328 | 1.58778 | ||||||||
\(871\) | 37.8885 | + | 27.5276i | 1.28380 | + | 0.932738i | ||||
\(872\) | −3.09017 | + | 9.51057i | −0.104646 | + | 0.322068i | ||||
\(873\) | −7.92299 | − | 24.3844i | −0.268152 | − | 0.825288i | ||||
\(874\) | −28.9443 | + | 21.0292i | −0.979055 | + | 0.711325i | ||||
\(875\) | 9.70820 | − | 7.05342i | 0.328197 | − | 0.238449i | ||||
\(876\) | −0.875388 | − | 2.69417i | −0.0295766 | − | 0.0910275i | ||||
\(877\) | −4.50658 | + | 13.8698i | −0.152176 | + | 0.468351i | −0.997864 | − | 0.0653278i | \(-0.979191\pi\) |
0.845688 | + | 0.533678i | \(0.179191\pi\) | |||||||
\(878\) | −18.9443 | − | 13.7638i | −0.639338 | − | 0.464506i | ||||
\(879\) | −31.0557 | −1.04748 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.58359 | 0.0870434 | 0.0435217 | − | 0.999052i | \(-0.486142\pi\) | ||||
0.0435217 | + | 0.999052i | \(0.486142\pi\) | |||||||
\(882\) | −2.66312 | − | 1.93487i | −0.0896719 | − | 0.0651504i | ||||
\(883\) | −2.76393 | + | 8.50651i | −0.0930137 | + | 0.286267i | −0.986731 | − | 0.162364i | \(-0.948088\pi\) |
0.893717 | + | 0.448631i | \(0.148088\pi\) | |||||||
\(884\) | −9.70820 | − | 29.8788i | −0.326522 | − | 1.00493i | ||||
\(885\) | 2.47214 | − | 1.79611i | 0.0830999 | − | 0.0603756i | ||||
\(886\) | −45.1246 | + | 32.7849i | −1.51599 | + | 1.10143i | ||||
\(887\) | 1.34752 | + | 4.14725i | 0.0452454 | + | 0.139251i | 0.971127 | − | 0.238562i | \(-0.0766761\pi\) |
−0.925882 | + | 0.377813i | \(0.876676\pi\) | |||||||
\(888\) | −7.23607 | + | 22.2703i | −0.242827 | + | 0.747343i | ||||
\(889\) | −2.47214 | − | 1.79611i | −0.0829128 | − | 0.0602397i | ||||
\(890\) | 8.94427 | 0.299813 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30.5410 | −1.02259 | ||||||||
\(893\) | 14.4721 | + | 10.5146i | 0.484292 | + | 0.351858i | ||||
\(894\) | −11.9574 | + | 36.8012i | −0.399916 | + | 1.23082i | ||||
\(895\) | 5.52786 | + | 17.0130i | 0.184776 | + | 0.568682i | ||||
\(896\) | 12.6631 | − | 9.20029i | 0.423045 | − | 0.307360i | ||||
\(897\) | −8.00000 | + | 5.81234i | −0.267112 | + | 0.194068i | ||||
\(898\) | 19.6738 | + | 60.5496i | 0.656522 | + | 2.02057i | ||||
\(899\) | 7.23607 | − | 22.2703i | 0.241336 | − | 0.742757i | ||||
\(900\) | −3.57295 | − | 2.59590i | −0.119098 | − | 0.0865300i | ||||
\(901\) | −1.52786 | −0.0509005 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.88854 | −0.329070 | ||||||||
\(904\) | 3.61803 | + | 2.62866i | 0.120334 | + | 0.0874278i | ||||
\(905\) | 15.7082 | − | 48.3449i | 0.522158 | − | 1.60704i | ||||
\(906\) | −7.63932 | − | 23.5114i | −0.253799 | − | 0.781114i | ||||
\(907\) | −18.1803 | + | 13.2088i | −0.603668 | + | 0.438591i | −0.847179 | − | 0.531308i | \(-0.821701\pi\) |
0.243511 | + | 0.969898i | \(0.421701\pi\) | |||||||
\(908\) | 14.2918 | − | 10.3836i | 0.474290 | − | 0.344592i | ||||
\(909\) | −2.16718 | − | 6.66991i | −0.0718810 | − | 0.221227i | ||||
\(910\) | 4.47214 | − | 13.7638i | 0.148250 | − | 0.456266i | ||||
\(911\) | −34.3607 | − | 24.9645i | −1.13842 | − | 0.827111i | −0.151522 | − | 0.988454i | \(-0.548417\pi\) |
−0.986898 | + | 0.161343i | \(0.948417\pi\) | |||||||
\(912\) | −8.00000 | −0.264906 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −64.4721 | −2.13255 | ||||||||
\(915\) | −14.4721 | − | 10.5146i | −0.478434 | − | 0.347603i | ||||
\(916\) | −4.14590 | + | 12.7598i | −0.136984 | + | 0.421594i | ||||
\(917\) | 6.76393 | + | 20.8172i | 0.223365 | + | 0.687446i | ||||
\(918\) | 32.3607 | − | 23.5114i | 1.06806 | − | 0.775992i | ||||
\(919\) | 33.8885 | − | 24.6215i | 1.11788 | − | 0.812187i | 0.133994 | − | 0.990982i | \(-0.457220\pi\) |
0.983886 | + | 0.178795i | \(0.0572199\pi\) | |||||||
\(920\) | 3.41641 | + | 10.5146i | 0.112636 | + | 0.346657i | ||||
\(921\) | −3.41641 | + | 10.5146i | −0.112574 | + | 0.346469i | ||||
\(922\) | 22.0344 | + | 16.0090i | 0.725666 | + | 0.527227i | ||||
\(923\) | 33.8885 | 1.11546 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.47214 | 0.278562 | ||||||||
\(926\) | −10.0000 | − | 7.26543i | −0.328620 | − | 0.238757i | ||||
\(927\) | −3.50658 | + | 10.7921i | −0.115171 | + | 0.354460i | ||||
\(928\) | −17.5623 | − | 54.0512i | −0.576511 | − | 1.77432i | ||||
\(929\) | 42.2705 | − | 30.7113i | 1.38685 | − | 1.00761i | 0.390648 | − | 0.920540i | \(-0.372251\pi\) |
0.996203 | − | 0.0870656i | \(-0.0277490\pi\) | |||||||
\(930\) | −12.3607 | + | 8.98056i | −0.405323 | + | 0.294484i | ||||
\(931\) | −2.00000 | − | 6.15537i | −0.0655474 | − | 0.201734i | ||||
\(932\) | −8.72949 | + | 26.8666i | −0.285944 | + | 0.880045i | ||||
\(933\) | −8.29180 | − | 6.02434i | −0.271461 | − | 0.197228i | ||||
\(934\) | −53.8197 | −1.76103 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.6525 | −0.348187 | ||||||||
\(937\) | −8.61803 | − | 6.26137i | −0.281539 | − | 0.204550i | 0.438049 | − | 0.898951i | \(-0.355669\pi\) |
−0.719588 | + | 0.694401i | \(0.755669\pi\) | |||||||
\(938\) | 10.0000 | − | 30.7768i | 0.326512 | − | 1.00490i | ||||
\(939\) | −5.70820 | − | 17.5680i | −0.186280 | − | 0.573311i | ||||
\(940\) | 13.4164 | − | 9.74759i | 0.437595 | − | 0.317931i | ||||
\(941\) | 6.14590 | − | 4.46526i | 0.200351 | − | 0.145563i | −0.483087 | − | 0.875573i | \(-0.660484\pi\) |
0.683437 | + | 0.730009i | \(0.260484\pi\) | |||||||
\(942\) | 9.34752 | + | 28.7687i | 0.304559 | + | 0.937336i | ||||
\(943\) | 8.58359 | − | 26.4176i | 0.279520 | − | 0.860275i | ||||
\(944\) | −1.00000 | − | 0.726543i | −0.0325472 | − | 0.0236469i | ||||
\(945\) | 11.0557 | 0.359643 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.16718 | −0.167911 | −0.0839555 | − | 0.996470i | \(-0.526755\pi\) | ||||
−0.0839555 | + | 0.996470i | \(0.526755\pi\) | |||||||
\(948\) | 26.8328 | + | 19.4952i | 0.871489 | + | 0.633174i | ||||
\(949\) | −0.763932 | + | 2.35114i | −0.0247983 | + | 0.0763213i | ||||
\(950\) | −4.47214 | − | 13.7638i | −0.145095 | − | 0.446557i | ||||
\(951\) | 14.0000 | − | 10.1716i | 0.453981 | − | 0.329837i | ||||
\(952\) | −5.85410 | + | 4.25325i | −0.189733 | + | 0.137849i | ||||
\(953\) | −7.09017 | − | 21.8213i | −0.229673 | − | 0.706861i | −0.997784 | − | 0.0665438i | \(-0.978803\pi\) |
0.768110 | − | 0.640317i | \(-0.221197\pi\) | |||||||
\(954\) | −0.480267 | + | 1.47811i | −0.0155492 | + | 0.0478555i | ||||
\(955\) | −4.94427 | − | 3.59222i | −0.159993 | − | 0.116242i | ||||
\(956\) | 29.6656 | 0.959455 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.2492 | 0.977308 | ||||||||
\(959\) | 13.3262 | + | 9.68208i | 0.430327 | + | 0.312651i | ||||
\(960\) | −9.93112 | + | 30.5648i | −0.320525 | + | 0.986476i | ||||
\(961\) | −7.21885 | − | 22.2173i | −0.232866 | − | 0.716688i | ||||
\(962\) | 49.5967 | − | 36.0341i | 1.59906 | − | 1.16179i | ||||
\(963\) | 4.76393 | − | 3.46120i | 0.153516 | − | 0.111536i | ||||
\(964\) | 12.1672 | + | 37.4467i | 0.391879 | + | 1.20608i | ||||
\(965\) | 7.34752 | − | 22.6134i | 0.236525 | − | 0.727950i | ||||
\(966\) | 5.52786 | + | 4.01623i | 0.177856 | + | 0.129220i | ||||
\(967\) | 13.8885 | 0.446625 | 0.223313 | − | 0.974747i | \(-0.428313\pi\) | ||||
0.223313 | + | 0.974747i | \(0.428313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.8885 | 0.831660 | ||||||||
\(970\) | −63.0132 | − | 45.7817i | −2.02323 | − | 1.46996i | ||||
\(971\) | 3.43769 | − | 10.5801i | 0.110321 | − | 0.339533i | −0.880622 | − | 0.473820i | \(-0.842875\pi\) |
0.990942 | + | 0.134288i | \(0.0428746\pi\) | |||||||
\(972\) | −12.6049 | − | 38.7938i | −0.404302 | − | 1.24431i | ||||
\(973\) | 1.23607 | − | 0.898056i | 0.0396265 | − | 0.0287904i | ||||
\(974\) | −65.7771 | + | 47.7899i | −2.10763 | + | 1.53129i | ||||
\(975\) | −1.23607 | − | 3.80423i | −0.0395859 | − | 0.121833i | ||||
\(976\) | −2.23607 | + | 6.88191i | −0.0715748 | + | 0.220285i | ||||
\(977\) | −18.5623 | − | 13.4863i | −0.593861 | − | 0.431465i | 0.249834 | − | 0.968289i | \(-0.419624\pi\) |
−0.843694 | + | 0.536824i | \(0.819624\pi\) | |||||||
\(978\) | −9.44272 | −0.301945 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | 5.32624 | + | 3.86974i | 0.170054 | + | 0.123551i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.74265 | + | 20.7517i | 0.215057 | + | 0.661877i | 0.999150 | + | 0.0412335i | \(0.0131287\pi\) |
−0.784093 | + | 0.620644i | \(0.786871\pi\) | |||||||
\(984\) | −25.1246 | + | 18.2541i | −0.800943 | + | 0.581919i | ||||
\(985\) | 3.23607 | − | 2.35114i | 0.103110 | − | 0.0749136i | ||||
\(986\) | 18.9443 | + | 58.3045i | 0.603309 | + | 1.85679i | ||||
\(987\) | 1.05573 | − | 3.24920i | 0.0336042 | − | 0.103423i | ||||
\(988\) | −50.8328 | − | 36.9322i | −1.61721 | − | 1.17497i | ||||
\(989\) | −19.7771 | −0.628875 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.2492 | 1.72328 | 0.861642 | − | 0.507517i | \(-0.169437\pi\) | ||||
0.861642 | + | 0.507517i | \(0.169437\pi\) | |||||||
\(992\) | 15.0000 | + | 10.8981i | 0.476250 | + | 0.346016i | ||||
\(993\) | 5.30495 | − | 16.3270i | 0.168348 | − | 0.518120i | ||||
\(994\) | −7.23607 | − | 22.2703i | −0.229514 | − | 0.706372i | ||||
\(995\) | −3.52786 | + | 2.56314i | −0.111841 | + | 0.0812571i | ||||
\(996\) | 34.2492 | − | 24.8835i | 1.08523 | − | 0.788464i | ||||
\(997\) | −0.416408 | − | 1.28157i | −0.0131878 | − | 0.0405878i | 0.944246 | − | 0.329241i | \(-0.106793\pi\) |
−0.957434 | + | 0.288653i | \(0.906793\pi\) | |||||||
\(998\) | −1.05573 | + | 3.24920i | −0.0334185 | + | 0.102852i | ||||
\(999\) | 37.8885 | + | 27.5276i | 1.19874 | + | 0.870936i |
(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 | 847.2.f.m.323.1 | 4 | ||
11.2 | odd | 10 | 847.2.f.n.148.1 | 4 | |||
11.3 | even | 5 | inner | 847.2.f.m.729.1 | 4 | ||
11.4 | even | 5 | 847.2.f.b.372.1 | 4 | |||
11.5 | even | 5 | 847.2.a.f.1.1 | 2 | |||
11.6 | odd | 10 | 77.2.a.d.1.2 | ✓ | 2 | ||
11.7 | odd | 10 | 847.2.f.n.372.1 | 4 | |||
11.8 | odd | 10 | 847.2.f.a.729.1 | 4 | |||
11.9 | even | 5 | 847.2.f.b.148.1 | 4 | |||
11.10 | odd | 2 | 847.2.f.a.323.1 | 4 | |||
33.5 | odd | 10 | 7623.2.a.bl.1.2 | 2 | |||
33.17 | even | 10 | 693.2.a.h.1.1 | 2 | |||
44.39 | even | 10 | 1232.2.a.m.1.2 | 2 | |||
55.17 | even | 20 | 1925.2.b.h.1849.3 | 4 | |||
55.28 | even | 20 | 1925.2.b.h.1849.2 | 4 | |||
55.39 | odd | 10 | 1925.2.a.r.1.1 | 2 | |||
77.6 | even | 10 | 539.2.a.f.1.2 | 2 | |||
77.17 | even | 30 | 539.2.e.j.177.1 | 4 | |||
77.27 | odd | 10 | 5929.2.a.m.1.1 | 2 | |||
77.39 | odd | 30 | 539.2.e.i.177.1 | 4 | |||
77.61 | even | 30 | 539.2.e.j.67.1 | 4 | |||
77.72 | odd | 30 | 539.2.e.i.67.1 | 4 | |||
88.61 | odd | 10 | 4928.2.a.bm.1.2 | 2 | |||
88.83 | even | 10 | 4928.2.a.bv.1.1 | 2 | |||
231.83 | odd | 10 | 4851.2.a.y.1.1 | 2 | |||
308.83 | odd | 10 | 8624.2.a.ce.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.d.1.2 | ✓ | 2 | 11.6 | odd | 10 | ||
539.2.a.f.1.2 | 2 | 77.6 | even | 10 | |||
539.2.e.i.67.1 | 4 | 77.72 | odd | 30 | |||
539.2.e.i.177.1 | 4 | 77.39 | odd | 30 | |||
539.2.e.j.67.1 | 4 | 77.61 | even | 30 | |||
539.2.e.j.177.1 | 4 | 77.17 | even | 30 | |||
693.2.a.h.1.1 | 2 | 33.17 | even | 10 | |||
847.2.a.f.1.1 | 2 | 11.5 | even | 5 | |||
847.2.f.a.323.1 | 4 | 11.10 | odd | 2 | |||
847.2.f.a.729.1 | 4 | 11.8 | odd | 10 | |||
847.2.f.b.148.1 | 4 | 11.9 | even | 5 | |||
847.2.f.b.372.1 | 4 | 11.4 | even | 5 | |||
847.2.f.m.323.1 | 4 | 1.1 | even | 1 | trivial | ||
847.2.f.m.729.1 | 4 | 11.3 | even | 5 | inner | ||
847.2.f.n.148.1 | 4 | 11.2 | odd | 10 | |||
847.2.f.n.372.1 | 4 | 11.7 | odd | 10 | |||
1232.2.a.m.1.2 | 2 | 44.39 | even | 10 | |||
1925.2.a.r.1.1 | 2 | 55.39 | odd | 10 | |||
1925.2.b.h.1849.2 | 4 | 55.28 | even | 20 | |||
1925.2.b.h.1849.3 | 4 | 55.17 | even | 20 | |||
4851.2.a.y.1.1 | 2 | 231.83 | odd | 10 | |||
4928.2.a.bm.1.2 | 2 | 88.61 | odd | 10 | |||
4928.2.a.bv.1.1 | 2 | 88.83 | even | 10 | |||
5929.2.a.m.1.1 | 2 | 77.27 | odd | 10 | |||
7623.2.a.bl.1.2 | 2 | 33.5 | odd | 10 | |||
8624.2.a.ce.1.1 | 2 | 308.83 | odd | 10 |