Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(376,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.376");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.bt (of order \(6\), 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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(54\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 376.9 | ||
Character | \(\chi\) | \(=\) | 585.376 |
Dual form | 585.2.bt.b.571.9 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.71224 | − | 0.988562i | −1.21074 | − | 0.699019i | −0.247816 | − | 0.968807i | \(-0.579713\pi\) |
−0.962920 | + | 0.269788i | \(0.913046\pi\) | |||||||
\(3\) | −1.13208 | − | 1.31087i | −0.653608 | − | 0.756834i | ||||
\(4\) | 0.954509 | + | 1.65326i | 0.477255 | + | 0.826629i | ||||
\(5\) | −0.866025 | + | 0.500000i | −0.387298 | + | 0.223607i | ||||
\(6\) | 0.642514 | + | 3.36366i | 0.262305 | + | 1.37321i | ||||
\(7\) | −3.18919 | − | 1.84128i | −1.20540 | − | 0.695938i | −0.243648 | − | 0.969864i | \(-0.578344\pi\) |
−0.961751 | + | 0.273926i | \(0.911678\pi\) | |||||||
\(8\) | 0.179881i | 0.0635976i | ||||||||
\(9\) | −0.436783 | + | 2.96803i | −0.145594 | + | 0.989344i | ||||
\(10\) | 1.97712 | 0.625221 | ||||||||
\(11\) | 1.59587 | + | 0.921379i | 0.481174 | + | 0.277806i | 0.720906 | − | 0.693033i | \(-0.243726\pi\) |
−0.239731 | + | 0.970839i | \(0.577059\pi\) | |||||||
\(12\) | 1.08663 | − | 3.12287i | 0.313684 | − | 0.901494i | ||||
\(13\) | −3.58458 | + | 0.388332i | −0.994183 | + | 0.107704i | ||||
\(14\) | 3.64043 | + | 6.30542i | 0.972947 | + | 1.68519i | ||||
\(15\) | 1.63585 | + | 0.569210i | 0.422374 | + | 0.146969i | ||||
\(16\) | 2.08684 | − | 3.61452i | 0.521711 | − | 0.903629i | ||||
\(17\) | 0.179874 | 0.0436259 | 0.0218129 | − | 0.999762i | \(-0.493056\pi\) | ||||
0.0218129 | + | 0.999762i | \(0.493056\pi\) | |||||||
\(18\) | 3.68196 | − | 4.65020i | 0.867847 | − | 1.09606i | ||||
\(19\) | 0.475894i | 0.109178i | 0.998509 | + | 0.0545888i | \(0.0173848\pi\) | ||||
−0.998509 | + | 0.0545888i | \(0.982615\pi\) | |||||||
\(20\) | −1.65326 | − | 0.954509i | −0.369680 | − | 0.213435i | ||||
\(21\) | 1.19674 | + | 6.26510i | 0.261149 | + | 1.36716i | ||||
\(22\) | −1.82168 | − | 3.15524i | −0.388383 | − | 0.672700i | ||||
\(23\) | 3.15723 | + | 5.46848i | 0.658328 | + | 1.14026i | 0.981048 | + | 0.193763i | \(0.0620694\pi\) |
−0.322720 | + | 0.946494i | \(0.604597\pi\) | |||||||
\(24\) | 0.235801 | − | 0.203640i | 0.0481328 | − | 0.0415678i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | 6.52155 | + | 2.87866i | 1.27898 | + | 0.564552i | ||||
\(27\) | 4.38519 | − | 2.78749i | 0.843931 | − | 0.536452i | ||||
\(28\) | − | 7.03007i | − | 1.32856i | ||||||
\(29\) | −0.00188512 | + | 0.00326513i | −0.000350059 | + | 0.000606320i | −0.866200 | − | 0.499697i | \(-0.833445\pi\) |
0.865850 | + | 0.500303i | \(0.166778\pi\) | |||||||
\(30\) | −2.23827 | − | 2.59176i | −0.408649 | − | 0.473189i | ||||
\(31\) | −1.31356 | + | 0.758387i | −0.235923 | + | 0.136210i | −0.613302 | − | 0.789849i | \(-0.710159\pi\) |
0.377378 | + | 0.926059i | \(0.376826\pi\) | |||||||
\(32\) | −6.83478 | + | 3.94606i | −1.20823 | + | 0.697572i | ||||
\(33\) | −0.598848 | − | 3.13507i | −0.104246 | − | 0.545745i | ||||
\(34\) | −0.307988 | − | 0.177817i | −0.0528194 | − | 0.0304953i | ||||
\(35\) | 3.68256 | 0.622465 | ||||||||
\(36\) | −5.32384 | + | 2.11090i | −0.887307 | + | 0.351817i | ||||
\(37\) | − | 5.39633i | − | 0.887151i | −0.896237 | − | 0.443575i | \(-0.853710\pi\) | ||
0.896237 | − | 0.443575i | \(-0.146290\pi\) | |||||||
\(38\) | 0.470451 | − | 0.814844i | 0.0763172 | − | 0.132185i | ||||
\(39\) | 4.56709 | + | 4.25931i | 0.731319 | + | 0.682035i | ||||
\(40\) | −0.0899405 | − | 0.155782i | −0.0142208 | − | 0.0246312i | ||||
\(41\) | 1.53334 | − | 0.885273i | 0.239467 | − | 0.138256i | −0.375465 | − | 0.926837i | \(-0.622517\pi\) |
0.614932 | + | 0.788580i | \(0.289184\pi\) | |||||||
\(42\) | 4.14434 | − | 11.9104i | 0.639486 | − | 1.83781i | ||||
\(43\) | 1.10082 | − | 1.90667i | 0.167873 | − | 0.290765i | −0.769799 | − | 0.638287i | \(-0.779643\pi\) |
0.937672 | + | 0.347522i | \(0.112977\pi\) | |||||||
\(44\) | 3.51786i | 0.530337i | ||||||||
\(45\) | −1.10575 | − | 2.78878i | −0.164836 | − | 0.415727i | ||||
\(46\) | − | 12.4845i | − | 1.84074i | ||||||
\(47\) | 7.86397 | + | 4.54027i | 1.14708 | + | 0.662266i | 0.948173 | − | 0.317753i | \(-0.102928\pi\) |
0.198904 | + | 0.980019i | \(0.436262\pi\) | |||||||
\(48\) | −7.10065 | + | 1.35634i | −1.02489 | + | 0.195771i | ||||
\(49\) | 3.28061 | + | 5.68218i | 0.468658 | + | 0.811740i | ||||
\(50\) | −1.71224 | + | 0.988562i | −0.242147 | + | 0.139804i | ||||
\(51\) | −0.203632 | − | 0.235792i | −0.0285142 | − | 0.0330175i | ||||
\(52\) | −4.06353 | − | 5.55557i | −0.563510 | − | 0.770419i | ||||
\(53\) | −9.08755 | −1.24827 | −0.624135 | − | 0.781316i | \(-0.714549\pi\) | ||||
−0.624135 | + | 0.781316i | \(0.714549\pi\) | |||||||
\(54\) | −10.2641 | + | 0.437811i | −1.39677 | + | 0.0595785i | ||||
\(55\) | −1.84276 | −0.248477 | ||||||||
\(56\) | 0.331211 | − | 0.573674i | 0.0442599 | − | 0.0766605i | ||||
\(57\) | 0.623837 | − | 0.538751i | 0.0826292 | − | 0.0713593i | ||||
\(58\) | 0.00645557 | − | 0.00372713i | 0.000847658 | − | 0.000489396i | ||||
\(59\) | 3.80390 | − | 2.19618i | 0.495226 | − | 0.285919i | −0.231514 | − | 0.972832i | \(-0.574368\pi\) |
0.726740 | + | 0.686913i | \(0.241035\pi\) | |||||||
\(60\) | 0.620382 | + | 3.24780i | 0.0800909 | + | 0.419289i | ||||
\(61\) | 3.04023 | − | 5.26583i | 0.389262 | − | 0.674221i | −0.603089 | − | 0.797674i | \(-0.706064\pi\) |
0.992350 | + | 0.123453i | \(0.0393968\pi\) | |||||||
\(62\) | 2.99885 | 0.380854 | ||||||||
\(63\) | 6.85796 | − | 8.66137i | 0.864021 | − | 1.09123i | ||||
\(64\) | 7.25635 | 0.907044 | ||||||||
\(65\) | 2.91017 | − | 2.12859i | 0.360962 | − | 0.264020i | ||||
\(66\) | −2.07384 | + | 5.95998i | −0.255272 | + | 0.733623i | ||||
\(67\) | 10.1270 | − | 5.84681i | 1.23721 | − | 0.714301i | 0.268684 | − | 0.963228i | \(-0.413411\pi\) |
0.968522 | + | 0.248927i | \(0.0800780\pi\) | |||||||
\(68\) | 0.171692 | + | 0.297378i | 0.0208207 | + | 0.0360624i | ||||
\(69\) | 3.59425 | − | 10.3295i | 0.432697 | − | 1.24353i | ||||
\(70\) | −6.30542 | − | 3.64043i | −0.753641 | − | 0.435115i | ||||
\(71\) | − | 12.0988i | − | 1.43586i | −0.696115 | − | 0.717930i | \(-0.745090\pi\) | ||
0.696115 | − | 0.717930i | \(-0.254910\pi\) | |||||||
\(72\) | −0.533893 | − | 0.0785690i | −0.0629199 | − | 0.00925945i | ||||
\(73\) | − | 4.31020i | − | 0.504471i | −0.967666 | − | 0.252235i | \(-0.918834\pi\) | ||
0.967666 | − | 0.252235i | \(-0.0811657\pi\) | |||||||
\(74\) | −5.33460 | + | 9.23980i | −0.620135 | + | 1.07411i | ||||
\(75\) | −1.70129 | + | 0.324974i | −0.196448 | + | 0.0375248i | ||||
\(76\) | −0.786776 | + | 0.454245i | −0.0902494 | + | 0.0521055i | ||||
\(77\) | −3.39303 | − | 5.87690i | −0.386671 | − | 0.669735i | ||||
\(78\) | −3.60936 | − | 11.8078i | −0.408680 | − | 1.33697i | ||||
\(79\) | −5.42831 | + | 9.40211i | −0.610732 | + | 1.05782i | 0.380385 | + | 0.924828i | \(0.375792\pi\) |
−0.991117 | + | 0.132991i | \(0.957542\pi\) | |||||||
\(80\) | 4.17368i | 0.466632i | ||||||||
\(81\) | −8.61844 | − | 2.59277i | −0.957605 | − | 0.288086i | ||||
\(82\) | −3.50059 | −0.386575 | ||||||||
\(83\) | 15.1698 | + | 8.75827i | 1.66510 | + | 0.961345i | 0.970222 | + | 0.242216i | \(0.0778744\pi\) |
0.694877 | + | 0.719129i | \(0.255459\pi\) | |||||||
\(84\) | −9.21554 | + | 7.95861i | −1.00550 | + | 0.868355i | ||||
\(85\) | −0.155776 | + | 0.0899371i | −0.0168962 | + | 0.00975504i | ||||
\(86\) | −3.76973 | + | 2.17645i | −0.406500 | + | 0.234693i | ||||
\(87\) | 0.00641429 | − | 0.00122523i | 0.000687684 | − | 0.000131359i | ||||
\(88\) | −0.165739 | + | 0.287068i | −0.0176678 | + | 0.0306015i | ||||
\(89\) | 2.06569i | 0.218963i | 0.993989 | + | 0.109481i | \(0.0349190\pi\) | ||||
−0.993989 | + | 0.109481i | \(0.965081\pi\) | |||||||
\(90\) | −0.863575 | + | 5.86817i | −0.0910288 | + | 0.618559i | ||||
\(91\) | 12.1469 | + | 5.36174i | 1.27334 | + | 0.562063i | ||||
\(92\) | −6.02721 | + | 10.4394i | −0.628380 | + | 1.08839i | ||||
\(93\) | 2.48121 | + | 0.863362i | 0.257290 | + | 0.0895265i | ||||
\(94\) | −8.97667 | − | 15.5480i | −0.925872 | − | 1.60366i | ||||
\(95\) | −0.237947 | − | 0.412136i | −0.0244128 | − | 0.0422843i | ||||
\(96\) | 12.9103 | + | 4.49228i | 1.31765 | + | 0.458491i | ||||
\(97\) | 9.54063 | + | 5.50829i | 0.968705 | + | 0.559282i | 0.898841 | − | 0.438275i | \(-0.144410\pi\) |
0.0698636 | + | 0.997557i | \(0.477744\pi\) | |||||||
\(98\) | − | 12.9723i | − | 1.31040i | ||||||
\(99\) | −3.43173 | + | 4.33417i | −0.344902 | + | 0.435600i | ||||
\(100\) | 1.90902 | 0.190902 | ||||||||
\(101\) | −2.14975 | + | 3.72348i | −0.213908 | + | 0.370500i | −0.952934 | − | 0.303177i | \(-0.901953\pi\) |
0.739026 | + | 0.673677i | \(0.235286\pi\) | |||||||
\(102\) | 0.115572 | + | 0.605036i | 0.0114433 | + | 0.0599075i | ||||
\(103\) | 8.61522 | + | 14.9220i | 0.848883 | + | 1.47031i | 0.882206 | + | 0.470864i | \(0.156058\pi\) |
−0.0333232 | + | 0.999445i | \(0.510609\pi\) | |||||||
\(104\) | −0.0698536 | − | 0.644798i | −0.00684971 | − | 0.0632276i | ||||
\(105\) | −4.16895 | − | 4.82737i | −0.406848 | − | 0.471103i | ||||
\(106\) | 15.5601 | + | 8.98361i | 1.51133 | + | 0.872565i | ||||
\(107\) | −8.40204 | −0.812256 | −0.406128 | − | 0.913816i | \(-0.633121\pi\) | ||||
−0.406128 | + | 0.913816i | \(0.633121\pi\) | |||||||
\(108\) | 8.79415 | + | 4.58918i | 0.846217 | + | 0.441594i | ||||
\(109\) | 17.0795i | 1.63592i | 0.575278 | + | 0.817958i | \(0.304894\pi\) | ||||
−0.575278 | + | 0.817958i | \(0.695106\pi\) | |||||||
\(110\) | 3.15524 | + | 1.82168i | 0.300841 | + | 0.173690i | ||||
\(111\) | −7.07391 | + | 6.10908i | −0.671426 | + | 0.579848i | ||||
\(112\) | −13.3107 | + | 7.68491i | −1.25774 | + | 0.726156i | ||||
\(113\) | 2.24214 | + | 3.88350i | 0.210923 | + | 0.365329i | 0.952004 | − | 0.306087i | \(-0.0990199\pi\) |
−0.741081 | + | 0.671416i | \(0.765687\pi\) | |||||||
\(114\) | −1.60075 | + | 0.305768i | −0.149924 | + | 0.0286378i | ||||
\(115\) | −5.46848 | − | 3.15723i | −0.509939 | − | 0.294413i | ||||
\(116\) | −0.00719748 | −0.000668269 | ||||||||
\(117\) | 0.413101 | − | 10.8088i | 0.0381912 | − | 0.999270i | ||||
\(118\) | −8.68426 | −0.799451 | ||||||||
\(119\) | −0.573652 | − | 0.331198i | −0.0525866 | − | 0.0303609i | ||||
\(120\) | −0.102390 | + | 0.294258i | −0.00934689 | + | 0.0268620i | ||||
\(121\) | −3.80212 | − | 6.58547i | −0.345647 | − | 0.598679i | ||||
\(122\) | −10.4112 | + | 6.01091i | −0.942586 | + | 0.544203i | ||||
\(123\) | −2.89634 | − | 1.00781i | −0.261155 | − | 0.0908714i | ||||
\(124\) | −2.50762 | − | 1.44777i | −0.225191 | − | 0.130014i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −20.3048 | + | 8.05083i | −1.80889 | + | 0.717225i | ||||
\(127\) | 6.28102 | 0.557350 | 0.278675 | − | 0.960385i | \(-0.410105\pi\) | ||||
0.278675 | + | 0.960385i | \(0.410105\pi\) | |||||||
\(128\) | 1.24496 | + | 0.718780i | 0.110040 | + | 0.0635318i | ||||
\(129\) | −3.74563 | + | 0.715475i | −0.329784 | + | 0.0629941i | ||||
\(130\) | −7.08715 | + | 0.767781i | −0.621585 | + | 0.0673388i | ||||
\(131\) | 10.3974 | + | 18.0088i | 0.908423 | + | 1.57343i | 0.816255 | + | 0.577691i | \(0.196046\pi\) |
0.0921678 | + | 0.995743i | \(0.470620\pi\) | |||||||
\(132\) | 4.61147 | − | 3.98250i | 0.401377 | − | 0.346632i | ||||
\(133\) | 0.876253 | − | 1.51771i | 0.0759808 | − | 0.131603i | ||||
\(134\) | −23.1197 | −1.99724 | ||||||||
\(135\) | −2.40394 | + | 4.60663i | −0.206899 | + | 0.396476i | ||||
\(136\) | 0.0323559i | 0.00277450i | ||||||||
\(137\) | 6.19634 | + | 3.57746i | 0.529389 | + | 0.305643i | 0.740768 | − | 0.671761i | \(-0.234462\pi\) |
−0.211379 | + | 0.977404i | \(0.567795\pi\) | |||||||
\(138\) | −16.3656 | + | 14.1334i | −1.39313 | + | 1.20312i | ||||
\(139\) | 8.25510 | + | 14.2982i | 0.700188 | + | 1.21276i | 0.968400 | + | 0.249402i | \(0.0802340\pi\) |
−0.268212 | + | 0.963360i | \(0.586433\pi\) | |||||||
\(140\) | 3.51503 | + | 6.08822i | 0.297075 | + | 0.514548i | ||||
\(141\) | −2.95094 | − | 15.4486i | −0.248514 | − | 1.30101i | ||||
\(142\) | −11.9604 | + | 20.7160i | −1.00369 | + | 1.73845i | ||||
\(143\) | −6.07834 | − | 2.68302i | −0.508296 | − | 0.224366i | ||||
\(144\) | 9.81651 | + | 7.77258i | 0.818042 | + | 0.647715i | ||||
\(145\) | − | 0.00377025i | − | 0.000313102i | ||||||
\(146\) | −4.26090 | + | 7.38010i | −0.352635 | + | 0.610781i | ||||
\(147\) | 3.73471 | − | 10.7332i | 0.308034 | − | 0.885256i | ||||
\(148\) | 8.92153 | − | 5.15085i | 0.733345 | − | 0.423397i | ||||
\(149\) | −14.4350 | + | 8.33407i | −1.18256 | + | 0.682753i | −0.956606 | − | 0.291384i | \(-0.905884\pi\) |
−0.225957 | + | 0.974137i | \(0.572551\pi\) | |||||||
\(150\) | 3.23428 | + | 1.12540i | 0.264077 | + | 0.0918884i | ||||
\(151\) | −8.26158 | − | 4.76983i | −0.672318 | − | 0.388163i | 0.124636 | − | 0.992202i | \(-0.460224\pi\) |
−0.796954 | + | 0.604040i | \(0.793557\pi\) | |||||||
\(152\) | −0.0856043 | −0.00694343 | ||||||||
\(153\) | −0.0785660 | + | 0.533872i | −0.00635169 | + | 0.0431610i | ||||
\(154\) | 13.4169i | 1.08116i | ||||||||
\(155\) | 0.758387 | − | 1.31356i | 0.0609151 | − | 0.105508i | ||||
\(156\) | −2.68241 | + | 11.6161i | −0.214765 | + | 0.930035i | ||||
\(157\) | 4.32832 | + | 7.49686i | 0.345437 | + | 0.598315i | 0.985433 | − | 0.170064i | \(-0.0543973\pi\) |
−0.639996 | + | 0.768378i | \(0.721064\pi\) | |||||||
\(158\) | 18.5891 | − | 10.7324i | 1.47887 | − | 0.853827i | ||||
\(159\) | 10.2878 | + | 11.9126i | 0.815879 | + | 0.944733i | ||||
\(160\) | 3.94606 | − | 6.83478i | 0.311964 | − | 0.540337i | ||||
\(161\) | − | 23.2534i | − | 1.83262i | ||||||
\(162\) | 12.1937 | + | 12.9593i | 0.958029 | + | 1.01818i | ||||
\(163\) | 3.30102i | 0.258555i | 0.991608 | + | 0.129278i | \(0.0412659\pi\) | ||||
−0.991608 | + | 0.129278i | \(0.958734\pi\) | |||||||
\(164\) | 2.92717 | + | 1.69000i | 0.228574 | + | 0.131967i | ||||
\(165\) | 2.08615 | + | 2.41562i | 0.162407 | + | 0.188056i | ||||
\(166\) | −17.3162 | − | 29.9925i | −1.34400 | − | 2.32787i | ||||
\(167\) | −8.05426 | + | 4.65013i | −0.623257 | + | 0.359838i | −0.778136 | − | 0.628096i | \(-0.783835\pi\) |
0.154879 | + | 0.987933i | \(0.450501\pi\) | |||||||
\(168\) | −1.12697 | + | 0.215270i | −0.0869478 | + | 0.0166084i | ||||
\(169\) | 12.6984 | − | 2.78401i | 0.976800 | − | 0.214155i | ||||
\(170\) | 0.355633 | 0.0272758 | ||||||||
\(171\) | −1.41247 | − | 0.207863i | −0.108014 | − | 0.0158956i | ||||
\(172\) | 4.20297 | 0.320473 | ||||||||
\(173\) | 7.33343 | − | 12.7019i | 0.557550 | − | 0.965705i | −0.440150 | − | 0.897924i | \(-0.645075\pi\) |
0.997700 | − | 0.0677809i | \(-0.0215919\pi\) | |||||||
\(174\) | −0.0121940 | − | 0.00424303i | −0.000924427 | − | 0.000321663i | ||||
\(175\) | −3.18919 | + | 1.84128i | −0.241080 | + | 0.139188i | ||||
\(176\) | 6.66068 | − | 3.84554i | 0.502068 | − | 0.289869i | ||||
\(177\) | −7.18525 | − | 2.50018i | −0.540076 | − | 0.187925i | ||||
\(178\) | 2.04206 | − | 3.53696i | 0.153059 | − | 0.265106i | ||||
\(179\) | −3.91870 | −0.292897 | −0.146449 | − | 0.989218i | \(-0.546784\pi\) | ||||
−0.146449 | + | 0.989218i | \(0.546784\pi\) | |||||||
\(180\) | 3.55513 | − | 4.49001i | 0.264984 | − | 0.334666i | ||||
\(181\) | 18.4224 | 1.36933 | 0.684664 | − | 0.728858i | \(-0.259949\pi\) | ||||
0.684664 | + | 0.728858i | \(0.259949\pi\) | |||||||
\(182\) | −15.4980 | − | 21.1886i | −1.14879 | − | 1.57060i | ||||
\(183\) | −10.3446 | + | 1.97599i | −0.764698 | + | 0.146070i | ||||
\(184\) | −0.983677 | + | 0.567926i | −0.0725176 | + | 0.0418681i | ||||
\(185\) | 2.69816 | + | 4.67336i | 0.198373 | + | 0.343592i | ||||
\(186\) | −3.39494 | − | 3.93111i | −0.248929 | − | 0.288243i | ||||
\(187\) | 0.287057 | + | 0.165732i | 0.0209917 | + | 0.0121195i | ||||
\(188\) | 17.3349i | 1.26428i | ||||||||
\(189\) | −19.1177 | + | 0.815458i | −1.39061 | + | 0.0593159i | ||||
\(190\) | 0.940901i | 0.0682601i | ||||||||
\(191\) | 0.300236 | − | 0.520024i | 0.0217243 | − | 0.0376276i | −0.854959 | − | 0.518696i | \(-0.826418\pi\) |
0.876683 | + | 0.481068i | \(0.159751\pi\) | |||||||
\(192\) | −8.21478 | − | 9.51216i | −0.592850 | − | 0.686481i | ||||
\(193\) | 0.779254 | − | 0.449902i | 0.0560919 | − | 0.0323847i | −0.471692 | − | 0.881763i | \(-0.656356\pi\) |
0.527784 | + | 0.849379i | \(0.323023\pi\) | |||||||
\(194\) | −10.8906 | − | 18.8630i | −0.781897 | − | 1.35429i | ||||
\(195\) | −6.08487 | − | 1.40512i | −0.435746 | − | 0.100623i | ||||
\(196\) | −6.26274 | + | 10.8474i | −0.447339 | + | 0.774813i | ||||
\(197\) | 1.36267i | 0.0970863i | 0.998821 | + | 0.0485432i | \(0.0154578\pi\) | ||||
−0.998821 | + | 0.0485432i | \(0.984542\pi\) | |||||||
\(198\) | 10.1605 | − | 4.02865i | 0.722078 | − | 0.286304i | ||||
\(199\) | 25.1448 | 1.78247 | 0.891235 | − | 0.453542i | \(-0.149840\pi\) | ||||
0.891235 | + | 0.453542i | \(0.149840\pi\) | |||||||
\(200\) | 0.155782 | + | 0.0899405i | 0.0110154 | + | 0.00635976i | ||||
\(201\) | −19.1290 | − | 6.65612i | −1.34925 | − | 0.469486i | ||||
\(202\) | 7.36179 | − | 4.25033i | 0.517973 | − | 0.299052i | ||||
\(203\) | 0.0120240 | − | 0.00694208i | 0.000843921 | − | 0.000487238i | ||||
\(204\) | 0.195457 | − | 0.561723i | 0.0136847 | − | 0.0393285i | ||||
\(205\) | −0.885273 | + | 1.53334i | −0.0618301 | + | 0.107093i | ||||
\(206\) | − | 34.0667i | − | 2.37354i | ||||||
\(207\) | −17.6097 | + | 6.98222i | −1.22396 | + | 0.485298i | ||||
\(208\) | −6.07682 | + | 13.7669i | −0.421351 | + | 0.954563i | ||||
\(209\) | −0.438479 | + | 0.759467i | −0.0303302 | + | 0.0525334i | ||||
\(210\) | 2.36609 | + | 12.3869i | 0.163276 | + | 0.854776i | ||||
\(211\) | −11.5692 | − | 20.0385i | −0.796458 | − | 1.37951i | −0.921909 | − | 0.387405i | \(-0.873371\pi\) |
0.125452 | − | 0.992100i | \(-0.459962\pi\) | |||||||
\(212\) | −8.67415 | − | 15.0241i | −0.595743 | − | 1.03186i | ||||
\(213\) | −15.8600 | + | 13.6968i | −1.08671 | + | 0.938490i | ||||
\(214\) | 14.3863 | + | 8.30594i | 0.983428 | + | 0.567782i | ||||
\(215\) | 2.20164i | 0.150150i | ||||||||
\(216\) | 0.501416 | + | 0.788813i | 0.0341170 | + | 0.0536719i | ||||
\(217\) | 5.58560 | 0.379175 | ||||||||
\(218\) | 16.8841 | − | 29.2441i | 1.14354 | − | 1.98066i | ||||
\(219\) | −5.65013 | + | 4.87950i | −0.381801 | + | 0.329726i | ||||
\(220\) | −1.75893 | − | 3.04656i | −0.118587 | − | 0.205399i | ||||
\(221\) | −0.644773 | + | 0.0698509i | −0.0433721 | + | 0.00469868i | ||||
\(222\) | 18.1514 | − | 3.46722i | 1.21824 | − | 0.232704i | ||||
\(223\) | −3.91964 | − | 2.26301i | −0.262479 | − | 0.151542i | 0.362986 | − | 0.931795i | \(-0.381757\pi\) |
−0.625465 | + | 0.780252i | \(0.715091\pi\) | |||||||
\(224\) | 29.0632 | 1.94187 | ||||||||
\(225\) | 2.35200 | + | 1.86228i | 0.156800 | + | 0.124152i | ||||
\(226\) | − | 8.86597i | − | 0.589756i | ||||||
\(227\) | 20.0281 | + | 11.5632i | 1.32931 | + | 0.767478i | 0.985193 | − | 0.171448i | \(-0.0548446\pi\) |
0.344118 | + | 0.938926i | \(0.388178\pi\) | |||||||
\(228\) | 1.48615 | + | 0.517122i | 0.0984229 | + | 0.0342472i | ||||
\(229\) | −6.05063 | + | 3.49333i | −0.399837 | + | 0.230846i | −0.686413 | − | 0.727211i | \(-0.740816\pi\) |
0.286577 | + | 0.958057i | \(0.407483\pi\) | |||||||
\(230\) | 6.24224 | + | 10.8119i | 0.411601 | + | 0.712914i | ||||
\(231\) | −3.86269 | + | 11.1010i | −0.254146 | + | 0.730390i | ||||
\(232\) | −0.000587335 | 0 | 0.000339098i | −3.85605e−5 | 0 | 2.22629e-5i | ||||
\(233\) | −22.6754 | −1.48552 | −0.742758 | − | 0.669559i | \(-0.766483\pi\) | ||||
−0.742758 | + | 0.669559i | \(0.766483\pi\) | |||||||
\(234\) | −11.3925 | + | 18.0988i | −0.744748 | + | 1.18316i | ||||
\(235\) | −9.08053 | −0.592348 | ||||||||
\(236\) | 7.26172 | + | 4.19256i | 0.472698 | + | 0.272912i | ||||
\(237\) | 18.4703 | − | 3.52812i | 1.19977 | − | 0.229176i | ||||
\(238\) | 0.654820 | + | 1.13418i | 0.0424457 | + | 0.0735181i | ||||
\(239\) | 22.3254 | − | 12.8896i | 1.44411 | − | 0.833756i | 0.445987 | − | 0.895039i | \(-0.352853\pi\) |
0.998120 | + | 0.0612833i | \(0.0195193\pi\) | |||||||
\(240\) | 5.47118 | − | 4.72495i | 0.353163 | − | 0.304994i | ||||
\(241\) | −5.14460 | − | 2.97024i | −0.331393 | − | 0.191330i | 0.325067 | − | 0.945691i | \(-0.394613\pi\) |
−0.656459 | + | 0.754361i | \(0.727947\pi\) | |||||||
\(242\) | 15.0345i | 0.966456i | ||||||||
\(243\) | 6.35797 | + | 14.2329i | 0.407864 | + | 0.913043i | ||||
\(244\) | 11.6077 | 0.743108 | ||||||||
\(245\) | −5.68218 | − | 3.28061i | −0.363021 | − | 0.209590i | ||||
\(246\) | 3.96295 | + | 4.58883i | 0.252669 | + | 0.292573i | ||||
\(247\) | −0.184805 | − | 1.70588i | −0.0117589 | − | 0.108542i | ||||
\(248\) | −0.136419 | − | 0.236285i | −0.00866264 | − | 0.0150041i | ||||
\(249\) | −5.69242 | − | 29.8007i | −0.360743 | − | 1.88855i | ||||
\(250\) | 0.988562 | − | 1.71224i | 0.0625221 | − | 0.108292i | ||||
\(251\) | 20.7925 | 1.31241 | 0.656206 | − | 0.754582i | \(-0.272160\pi\) | ||||
0.656206 | + | 0.754582i | \(0.272160\pi\) | |||||||
\(252\) | 20.8655 | + | 3.07062i | 1.31440 | + | 0.193431i | ||||
\(253\) | 11.6360i | 0.731551i | ||||||||
\(254\) | −10.7546 | − | 6.20918i | −0.674804 | − | 0.389598i | ||||
\(255\) | 0.294247 | + | 0.102386i | 0.0184264 | + | 0.00641167i | ||||
\(256\) | −8.67747 | − | 15.0298i | −0.542342 | − | 0.939363i | ||||
\(257\) | 2.10977 | + | 3.65423i | 0.131604 | + | 0.227945i | 0.924295 | − | 0.381679i | \(-0.124654\pi\) |
−0.792691 | + | 0.609624i | \(0.791321\pi\) | |||||||
\(258\) | 7.12070 | + | 2.47772i | 0.443315 | + | 0.154256i | ||||
\(259\) | −9.93614 | + | 17.2099i | −0.617402 | + | 1.06937i | ||||
\(260\) | 6.29690 | + | 2.77950i | 0.390517 | + | 0.172377i | ||||
\(261\) | −0.00886763 | − | 0.00702127i | −0.000548892 | − | 0.000434606i | ||||
\(262\) | − | 41.1138i | − | 2.54002i | ||||||
\(263\) | −15.4548 | + | 26.7685i | −0.952985 | + | 1.65062i | −0.214072 | + | 0.976818i | \(0.568673\pi\) |
−0.738913 | + | 0.673801i | \(0.764661\pi\) | |||||||
\(264\) | 0.563939 | − | 0.107721i | 0.0347081 | − | 0.00662980i | ||||
\(265\) | 7.87005 | − | 4.54377i | 0.483453 | − | 0.279122i | ||||
\(266\) | −3.00071 | + | 1.73246i | −0.183985 | + | 0.106224i | ||||
\(267\) | 2.70786 | − | 2.33853i | 0.165718 | − | 0.143116i | ||||
\(268\) | 19.3326 | + | 11.1617i | 1.18092 | + | 0.681807i | ||||
\(269\) | 1.86363 | 0.113628 | 0.0568138 | − | 0.998385i | \(-0.481906\pi\) | ||||
0.0568138 | + | 0.998385i | \(0.481906\pi\) | |||||||
\(270\) | 8.67007 | − | 5.51121i | 0.527644 | − | 0.335401i | ||||
\(271\) | 5.61519i | 0.341098i | 0.985349 | + | 0.170549i | \(0.0545542\pi\) | ||||
−0.985349 | + | 0.170549i | \(0.945446\pi\) | |||||||
\(272\) | 0.375369 | − | 0.650158i | 0.0227601 | − | 0.0394216i | ||||
\(273\) | −6.72273 | − | 21.9930i | −0.406878 | − | 1.33108i | ||||
\(274\) | −7.07308 | − | 12.2509i | −0.427300 | − | 0.740106i | ||||
\(275\) | 1.59587 | − | 0.921379i | 0.0962349 | − | 0.0555612i | ||||
\(276\) | 20.5081 | − | 3.91738i | 1.23444 | − | 0.235798i | ||||
\(277\) | 0.341185 | − | 0.590950i | 0.0204998 | − | 0.0355067i | −0.855593 | − | 0.517648i | \(-0.826808\pi\) |
0.876093 | + | 0.482142i | \(0.160141\pi\) | |||||||
\(278\) | − | 32.6427i | − | 1.95778i | ||||||
\(279\) | −1.67717 | − | 4.22995i | −0.100410 | − | 0.253241i | ||||
\(280\) | 0.662422i | 0.0395873i | ||||||||
\(281\) | 22.9981 | + | 13.2780i | 1.37195 | + | 0.792097i | 0.991174 | − | 0.132569i | \(-0.0423227\pi\) |
0.380778 | + | 0.924666i | \(0.375656\pi\) | |||||||
\(282\) | −10.2192 | + | 29.3689i | −0.608545 | + | 1.74889i | ||||
\(283\) | −13.9923 | − | 24.2353i | −0.831755 | − | 1.44064i | −0.896646 | − | 0.442749i | \(-0.854003\pi\) |
0.0648907 | − | 0.997892i | \(-0.479330\pi\) | |||||||
\(284\) | 20.0024 | − | 11.5484i | 1.18692 | − | 0.685271i | ||||
\(285\) | −0.270883 | + | 0.778490i | −0.0160458 | + | 0.0461138i | ||||
\(286\) | 7.75524 | + | 10.6028i | 0.458577 | + | 0.626956i | ||||
\(287\) | −6.52013 | −0.384871 | ||||||||
\(288\) | −8.72673 | − | 22.0094i | −0.514228 | − | 1.29692i | ||||
\(289\) | −16.9676 | −0.998097 | ||||||||
\(290\) | −0.00372713 | + | 0.00645557i | −0.000218864 | + | 0.000379084i | ||||
\(291\) | −3.58010 | − | 18.7424i | −0.209869 | − | 1.09870i | ||||
\(292\) | 7.12588 | − | 4.11413i | 0.417010 | − | 0.240761i | ||||
\(293\) | −3.52118 | + | 2.03295i | −0.205710 | + | 0.118766i | −0.599316 | − | 0.800513i | \(-0.704561\pi\) |
0.393606 | + | 0.919279i | \(0.371227\pi\) | |||||||
\(294\) | −17.0051 | + | 14.6857i | −0.991758 | + | 0.856490i | ||||
\(295\) | −2.19618 | + | 3.80390i | −0.127867 | + | 0.221472i | ||||
\(296\) | 0.970697 | 0.0564206 | ||||||||
\(297\) | 9.56655 | − | 0.408057i | 0.555108 | − | 0.0236779i | ||||
\(298\) | 32.9550 | 1.90903 | ||||||||
\(299\) | −13.4409 | − | 18.3762i | −0.777309 | − | 1.06272i | ||||
\(300\) | −2.16116 | − | 2.50248i | −0.124775 | − | 0.144481i | ||||
\(301\) | −7.02143 | + | 4.05383i | −0.404709 | + | 0.233659i | ||||
\(302\) | 9.43054 | + | 16.3342i | 0.542666 | + | 0.939926i | ||||
\(303\) | 7.31471 | − | 1.39723i | 0.420219 | − | 0.0802687i | ||||
\(304\) | 1.72013 | + | 0.993116i | 0.0986560 | + | 0.0569591i | ||||
\(305\) | 6.08046i | 0.348166i | ||||||||
\(306\) | 0.662290 | − | 0.836450i | 0.0378606 | − | 0.0478167i | ||||
\(307\) | − | 17.1314i | − | 0.977739i | −0.872357 | − | 0.488870i | \(-0.837409\pi\) | ||
0.872357 | − | 0.488870i | \(-0.162591\pi\) | |||||||
\(308\) | 6.47736 | − | 11.2191i | 0.369082 | − | 0.639268i | ||||
\(309\) | 9.80774 | − | 28.1864i | 0.557943 | − | 1.60347i | ||||
\(310\) | −2.59708 | + | 1.49942i | −0.147504 | + | 0.0851616i | ||||
\(311\) | 1.95051 | + | 3.37838i | 0.110603 | + | 0.191570i | 0.916014 | − | 0.401147i | \(-0.131388\pi\) |
−0.805410 | + | 0.592717i | \(0.798055\pi\) | |||||||
\(312\) | −0.766169 | + | 0.821533i | −0.0433758 | + | 0.0465101i | ||||
\(313\) | 5.78100 | − | 10.0130i | 0.326762 | − | 0.565968i | −0.655106 | − | 0.755537i | \(-0.727376\pi\) |
0.981867 | + | 0.189569i | \(0.0607092\pi\) | |||||||
\(314\) | − | 17.1152i | − | 0.965868i | ||||||
\(315\) | −1.60848 | + | 10.9299i | −0.0906275 | + | 0.615833i | ||||
\(316\) | −20.7255 | −1.16590 | ||||||||
\(317\) | −10.1371 | − | 5.85264i | −0.569354 | − | 0.328717i | 0.187537 | − | 0.982258i | \(-0.439950\pi\) |
−0.756891 | + | 0.653541i | \(0.773283\pi\) | |||||||
\(318\) | −5.83888 | − | 30.5675i | −0.327428 | − | 1.71414i | ||||
\(319\) | −0.00601685 | + | 0.00347383i | −0.000336879 | + | 0.000194497i | ||||
\(320\) | −6.28418 | + | 3.62817i | −0.351296 | + | 0.202821i | ||||
\(321\) | 9.51180 | + | 11.0140i | 0.530897 | + | 0.614743i | ||||
\(322\) | −22.9874 | + | 39.8153i | −1.28104 | + | 2.21882i | ||||
\(323\) | 0.0856010i | 0.00476297i | ||||||||
\(324\) | −3.93986 | − | 16.7233i | −0.218881 | − | 0.929074i | ||||
\(325\) | −1.45598 | + | 3.29850i | −0.0807634 | + | 0.182968i | ||||
\(326\) | 3.26326 | − | 5.65213i | 0.180735 | − | 0.313042i | ||||
\(327\) | 22.3890 | − | 19.3353i | 1.23812 | − | 1.06925i | ||||
\(328\) | 0.159244 | + | 0.275818i | 0.00879277 | + | 0.0152295i | ||||
\(329\) | −16.7198 | − | 28.9595i | −0.921791 | − | 1.59659i | ||||
\(330\) | −1.18400 | − | 6.19842i | −0.0651769 | − | 0.341212i | ||||
\(331\) | −14.8937 | − | 8.59889i | −0.818633 | − | 0.472638i | 0.0313119 | − | 0.999510i | \(-0.490031\pi\) |
−0.849945 | + | 0.526872i | \(0.823365\pi\) | |||||||
\(332\) | 33.4394i | 1.83523i | ||||||||
\(333\) | 16.0165 | + | 2.35703i | 0.877698 | + | 0.129164i | ||||
\(334\) | 18.3878 | 1.00613 | ||||||||
\(335\) | −5.84681 | + | 10.1270i | −0.319445 | + | 0.553295i | ||||
\(336\) | 25.1427 | + | 8.74866i | 1.37165 | + | 0.477278i | ||||
\(337\) | 9.49177 | + | 16.4402i | 0.517050 | + | 0.895557i | 0.999804 | + | 0.0198007i | \(0.00630319\pi\) |
−0.482754 | + | 0.875756i | \(0.660363\pi\) | |||||||
\(338\) | −24.4949 | − | 7.78625i | −1.33235 | − | 0.423516i | ||||
\(339\) | 2.55249 | − | 7.33560i | 0.138632 | − | 0.398415i | ||||
\(340\) | −0.297378 | − | 0.171692i | −0.0161276 | − | 0.00931128i | ||||
\(341\) | −2.79505 | −0.151360 | ||||||||
\(342\) | 2.21300 | + | 1.75222i | 0.119665 | + | 0.0947494i | ||||
\(343\) | 1.61585i | 0.0872477i | ||||||||
\(344\) | 0.342975 | + | 0.198016i | 0.0184919 | + | 0.0106763i | ||||
\(345\) | 2.05204 | + | 10.7427i | 0.110478 | + | 0.578370i | ||||
\(346\) | −25.1132 | + | 14.4991i | −1.35009 | + | 0.779476i | ||||
\(347\) | −11.9344 | − | 20.6711i | −0.640674 | − | 1.10968i | −0.985282 | − | 0.170934i | \(-0.945322\pi\) |
0.344608 | − | 0.938747i | \(-0.388012\pi\) | |||||||
\(348\) | 0.00814813 | + | 0.00943499i | 0.000436786 | + | 0.000505768i | ||||
\(349\) | 25.2213 | + | 14.5615i | 1.35006 | + | 0.779460i | 0.988258 | − | 0.152794i | \(-0.0488270\pi\) |
0.361806 | + | 0.932253i | \(0.382160\pi\) | |||||||
\(350\) | 7.28087 | 0.389179 | ||||||||
\(351\) | −14.6366 | + | 11.6949i | −0.781244 | + | 0.624226i | ||||
\(352\) | −14.5433 | −0.775160 | ||||||||
\(353\) | 1.85874 | + | 1.07314i | 0.0989308 | + | 0.0571177i | 0.548649 | − | 0.836053i | \(-0.315142\pi\) |
−0.449718 | + | 0.893170i | \(0.648476\pi\) | |||||||
\(354\) | 9.83128 | + | 11.3840i | 0.522527 | + | 0.605051i | ||||
\(355\) | 6.04939 | + | 10.4779i | 0.321068 | + | 0.556107i | ||||
\(356\) | −3.41512 | + | 1.97172i | −0.181001 | + | 0.104501i | ||||
\(357\) | 0.215262 | + | 1.12693i | 0.0113929 | + | 0.0596434i | ||||
\(358\) | 6.70975 | + | 3.87388i | 0.354621 | + | 0.204741i | ||||
\(359\) | − | 2.98854i | − | 0.157729i | −0.996885 | − | 0.0788646i | \(-0.974871\pi\) | ||
0.996885 | − | 0.0788646i | \(-0.0251295\pi\) | |||||||
\(360\) | 0.501649 | − | 0.198904i | 0.0264392 | − | 0.0104831i | ||||
\(361\) | 18.7735 | 0.988080 | ||||||||
\(362\) | −31.5436 | − | 18.2117i | −1.65790 | − | 0.957187i | ||||
\(363\) | −4.32841 | + | 12.4394i | −0.227183 | + | 0.652899i | ||||
\(364\) | 2.73000 | + | 25.1998i | 0.143091 | + | 1.32083i | ||||
\(365\) | 2.15510 | + | 3.73274i | 0.112803 | + | 0.195381i | ||||
\(366\) | 19.6659 | + | 6.84294i | 1.02795 | + | 0.357686i | ||||
\(367\) | −15.8370 | + | 27.4306i | −0.826687 | + | 1.43186i | 0.0739360 | + | 0.997263i | \(0.476444\pi\) |
−0.900623 | + | 0.434601i | \(0.856889\pi\) | |||||||
\(368\) | 26.3546 | 1.37383 | ||||||||
\(369\) | 1.95778 | + | 4.93767i | 0.101918 | + | 0.257045i | ||||
\(370\) | − | 10.6692i | − | 0.554666i | ||||||
\(371\) | 28.9819 | + | 16.7327i | 1.50466 | + | 0.868719i | ||||
\(372\) | 0.940978 | + | 4.92617i | 0.0487875 | + | 0.255410i | ||||
\(373\) | 9.20545 | + | 15.9443i | 0.476640 | + | 0.825565i | 0.999642 | − | 0.0267670i | \(-0.00852122\pi\) |
−0.523002 | + | 0.852332i | \(0.675188\pi\) | |||||||
\(374\) | −0.327673 | − | 0.567546i | −0.0169436 | − | 0.0293471i | ||||
\(375\) | 1.31087 | − | 1.13208i | 0.0676933 | − | 0.0584604i | ||||
\(376\) | −0.816708 | + | 1.41458i | −0.0421185 | + | 0.0729514i | ||||
\(377\) | 0.00548942 | − | 0.0124362i | 0.000282720 | − | 0.000640496i | ||||
\(378\) | 33.5403 | + | 17.5028i | 1.72513 | + | 0.900247i | ||||
\(379\) | − | 21.6000i | − | 1.10952i | −0.832011 | − | 0.554760i | \(-0.812810\pi\) | ||
0.832011 | − | 0.554760i | \(-0.187190\pi\) | |||||||
\(380\) | 0.454245 | − | 0.786776i | 0.0233023 | − | 0.0403607i | ||||
\(381\) | −7.11062 | − | 8.23363i | −0.364288 | − | 0.421821i | ||||
\(382\) | −1.02815 | + | 0.593604i | −0.0526049 | + | 0.0303714i | ||||
\(383\) | −22.9806 | + | 13.2679i | −1.17426 | + | 0.677957i | −0.954679 | − | 0.297638i | \(-0.903801\pi\) |
−0.219577 | + | 0.975595i | \(0.570468\pi\) | |||||||
\(384\) | −0.467170 | − | 2.44571i | −0.0238401 | − | 0.124807i | ||||
\(385\) | 5.87690 | + | 3.39303i | 0.299514 | + | 0.172925i | ||||
\(386\) | −1.77903 | −0.0905500 | ||||||||
\(387\) | 5.17825 | + | 4.10007i | 0.263225 | + | 0.208418i | ||||
\(388\) | 21.0309i | 1.06768i | ||||||||
\(389\) | 17.9599 | − | 31.1075i | 0.910605 | − | 1.57721i | 0.0973928 | − | 0.995246i | \(-0.468950\pi\) |
0.813212 | − | 0.581968i | \(-0.197717\pi\) | |||||||
\(390\) | 9.02970 | + | 8.42118i | 0.457237 | + | 0.426423i | ||||
\(391\) | 0.567904 | + | 0.983639i | 0.0287201 | + | 0.0497448i | ||||
\(392\) | −1.02212 | + | 0.590119i | −0.0516247 | + | 0.0298055i | ||||
\(393\) | 11.8366 | − | 34.0171i | 0.597076 | − | 1.71593i | ||||
\(394\) | 1.34709 | − | 2.33322i | 0.0678652 | − | 0.117546i | ||||
\(395\) | − | 10.8566i | − | 0.546256i | ||||||
\(396\) | −10.4411 | − | 1.53654i | −0.524686 | − | 0.0772141i | ||||
\(397\) | − | 14.4262i | − | 0.724031i | −0.932172 | − | 0.362016i | \(-0.882089\pi\) | ||
0.932172 | − | 0.362016i | \(-0.117911\pi\) | |||||||
\(398\) | −43.0540 | − | 24.8572i | −2.15810 | − | 1.24598i | ||||
\(399\) | −2.98152 | + | 0.569519i | −0.149263 | + | 0.0285116i | ||||
\(400\) | −2.08684 | − | 3.61452i | −0.104342 | − | 0.180726i | ||||
\(401\) | −32.5154 | + | 18.7728i | −1.62374 | + | 0.937469i | −0.637838 | + | 0.770171i | \(0.720171\pi\) |
−0.985906 | + | 0.167298i | \(0.946496\pi\) | |||||||
\(402\) | 26.1734 | + | 30.3071i | 1.30541 | + | 1.51158i | ||||
\(403\) | 4.41407 | − | 3.22860i | 0.219880 | − | 0.160828i | ||||
\(404\) | −8.20784 | −0.408355 | ||||||||
\(405\) | 8.76018 | − | 2.06381i | 0.435297 | − | 0.102552i | ||||
\(406\) | −0.0274507 | −0.00136235 | ||||||||
\(407\) | 4.97206 | − | 8.61186i | 0.246456 | − | 0.426874i | ||||
\(408\) | 0.0424146 | − | 0.0366296i | 0.00209983 | − | 0.00181343i | ||||
\(409\) | −21.8998 | + | 12.6439i | −1.08288 | + | 0.625199i | −0.931671 | − | 0.363304i | \(-0.881649\pi\) |
−0.151205 | + | 0.988502i | \(0.548315\pi\) | |||||||
\(410\) | 3.03160 | − | 1.75029i | 0.149720 | − | 0.0864409i | ||||
\(411\) | −2.32516 | − | 12.1726i | −0.114692 | − | 0.600430i | ||||
\(412\) | −16.4466 | + | 28.4864i | −0.810267 | + | 1.40342i | ||||
\(413\) | −16.1751 | −0.795927 | ||||||||
\(414\) | 37.0543 | + | 5.45301i | 1.82112 | + | 0.268001i | ||||
\(415\) | −17.5165 | −0.859853 | ||||||||
\(416\) | 22.9674 | − | 16.7991i | 1.12607 | − | 0.823646i | ||||
\(417\) | 9.39777 | − | 27.0082i | 0.460211 | − | 1.32260i | ||||
\(418\) | 1.50156 | − | 0.866926i | 0.0734437 | − | 0.0424028i | ||||
\(419\) | −17.4957 | − | 30.3034i | −0.854721 | − | 1.48042i | −0.876904 | − | 0.480666i | \(-0.840395\pi\) |
0.0221830 | − | 0.999754i | \(-0.492938\pi\) | |||||||
\(420\) | 4.00158 | − | 11.5001i | 0.195257 | − | 0.561149i | ||||
\(421\) | −23.1033 | − | 13.3387i | −1.12599 | − | 0.650088i | −0.183064 | − | 0.983101i | \(-0.558601\pi\) |
−0.942922 | + | 0.333013i | \(0.891935\pi\) | |||||||
\(422\) | 45.7475i | 2.22696i | ||||||||
\(423\) | −16.9105 | + | 21.3574i | −0.822217 | + | 1.03843i | ||||
\(424\) | − | 1.63468i | − | 0.0793870i | ||||||
\(425\) | 0.0899371 | − | 0.155776i | 0.00436259 | − | 0.00755622i | ||||
\(426\) | 40.6962 | − | 7.77364i | 1.97174 | − | 0.376634i | ||||
\(427\) | −19.3917 | + | 11.1958i | −0.938432 | + | 0.541804i | ||||
\(428\) | −8.01983 | − | 13.8908i | −0.387653 | − | 0.671435i | ||||
\(429\) | 3.36407 | + | 11.0053i | 0.162419 | + | 0.531343i | ||||
\(430\) | 2.17645 | − | 3.76973i | 0.104958 | − | 0.181793i | ||||
\(431\) | 26.5012i | 1.27652i | 0.769821 | + | 0.638260i | \(0.220346\pi\) | ||||
−0.769821 | + | 0.638260i | \(0.779654\pi\) | |||||||
\(432\) | −0.924213 | − | 21.6674i | −0.0444662 | − | 1.04247i | ||||
\(433\) | −10.2308 | −0.491659 | −0.245829 | − | 0.969313i | \(-0.579060\pi\) | ||||
−0.245829 | + | 0.969313i | \(0.579060\pi\) | |||||||
\(434\) | −9.56389 | − | 5.52171i | −0.459081 | − | 0.265051i | ||||
\(435\) | −0.00494232 | + | 0.00426823i | −0.000236966 | + | 0.000204646i | ||||
\(436\) | −28.2368 | + | 16.3025i | −1.35230 | + | 0.780748i | ||||
\(437\) | −2.60242 | + | 1.50251i | −0.124491 | + | 0.0718747i | ||||
\(438\) | 14.4981 | − | 2.76936i | 0.692744 | − | 0.132325i | ||||
\(439\) | 7.70352 | − | 13.3429i | 0.367669 | − | 0.636821i | −0.621532 | − | 0.783389i | \(-0.713489\pi\) |
0.989201 | + | 0.146568i | \(0.0468226\pi\) | |||||||
\(440\) | − | 0.331477i | − | 0.0158026i | ||||||
\(441\) | −18.2978 | + | 7.25507i | −0.871324 | + | 0.345480i | ||||
\(442\) | 1.17306 | + | 0.517796i | 0.0557966 | + | 0.0246291i | ||||
\(443\) | −12.0434 | + | 20.8597i | −0.572198 | + | 0.991076i | 0.424142 | + | 0.905596i | \(0.360576\pi\) |
−0.996340 | + | 0.0854802i | \(0.972758\pi\) | |||||||
\(444\) | −16.8520 | − | 5.86382i | −0.799761 | − | 0.278285i | ||||
\(445\) | −1.03285 | − | 1.78894i | −0.0489616 | − | 0.0848039i | ||||
\(446\) | 4.47424 | + | 7.74962i | 0.211862 | + | 0.366955i | ||||
\(447\) | 27.2665 | + | 9.48766i | 1.28966 | + | 0.448751i | ||||
\(448\) | −23.1418 | − | 13.3610i | −1.09335 | − | 0.631246i | ||||
\(449\) | 21.2128i | 1.00109i | 0.865710 | + | 0.500546i | \(0.166868\pi\) | ||||
−0.865710 | + | 0.500546i | \(0.833132\pi\) | |||||||
\(450\) | −2.18621 | − | 5.51377i | −0.103059 | − | 0.259922i | ||||
\(451\) | 3.26269 | 0.153634 | ||||||||
\(452\) | −4.28028 | + | 7.41367i | −0.201328 | + | 0.348710i | ||||
\(453\) | 3.10014 | + | 16.2297i | 0.145657 | + | 0.762539i | ||||
\(454\) | −22.8619 | − | 39.5980i | −1.07296 | − | 1.85843i | ||||
\(455\) | −13.2004 | + | 1.43005i | −0.618845 | + | 0.0670420i | ||||
\(456\) | 0.0969110 | + | 0.112216i | 0.00453828 | + | 0.00525502i | ||||
\(457\) | 4.57485 | + | 2.64129i | 0.214002 | + | 0.123554i | 0.603170 | − | 0.797613i | \(-0.293904\pi\) |
−0.389168 | + | 0.921167i | \(0.627237\pi\) | |||||||
\(458\) | 13.8135 | 0.645462 | ||||||||
\(459\) | 0.788783 | − | 0.501397i | 0.0368172 | − | 0.0234032i | ||||
\(460\) | − | 12.0544i | − | 0.562041i | ||||||
\(461\) | −19.7917 | − | 11.4268i | −0.921793 | − | 0.532197i | −0.0375860 | − | 0.999293i | \(-0.511967\pi\) |
−0.884206 | + | 0.467096i | \(0.845300\pi\) | |||||||
\(462\) | 17.5878 | − | 15.1890i | 0.818260 | − | 0.706656i | ||||
\(463\) | 12.7675 | − | 7.37130i | 0.593355 | − | 0.342574i | −0.173068 | − | 0.984910i | \(-0.555368\pi\) |
0.766423 | + | 0.642336i | \(0.222035\pi\) | |||||||
\(464\) | 0.00786792 | + | 0.0136276i | 0.000365259 | + | 0.000632647i | ||||
\(465\) | −2.58047 | + | 0.492912i | −0.119667 | + | 0.0228582i | ||||
\(466\) | 38.8258 | + | 22.4161i | 1.79857 | + | 1.03840i | ||||
\(467\) | 30.2235 | 1.39858 | 0.699288 | − | 0.714840i | \(-0.253501\pi\) | ||||
0.699288 | + | 0.714840i | \(0.253501\pi\) | |||||||
\(468\) | 18.2640 | − | 9.63410i | 0.844253 | − | 0.445337i | ||||
\(469\) | −43.0624 | −1.98844 | ||||||||
\(470\) | 15.5480 | + | 8.97667i | 0.717178 | + | 0.414063i | ||||
\(471\) | 4.92744 | − | 14.1609i | 0.227044 | − | 0.652501i | ||||
\(472\) | 0.395052 | + | 0.684250i | 0.0181837 | + | 0.0314952i | ||||
\(473\) | 3.51354 | − | 2.02854i | 0.161553 | − | 0.0932725i | ||||
\(474\) | −35.1133 | − | 12.2180i | −1.61281 | − | 0.561192i | ||||
\(475\) | 0.412136 | + | 0.237947i | 0.0189101 | + | 0.0109178i | ||||
\(476\) | − | 1.26453i | − | 0.0579595i | ||||||
\(477\) | 3.96929 | − | 26.9721i | 0.181741 | − | 1.23497i | ||||
\(478\) | −50.9685 | −2.33124 | ||||||||
\(479\) | −11.6401 | − | 6.72044i | −0.531852 | − | 0.307065i | 0.209918 | − | 0.977719i | \(-0.432680\pi\) |
−0.741770 | + | 0.670654i | \(0.766013\pi\) | |||||||
\(480\) | −13.4268 | + | 2.56474i | −0.612847 | + | 0.117064i | ||||
\(481\) | 2.09557 | + | 19.3436i | 0.0955496 | + | 0.881990i | ||||
\(482\) | 5.87252 | + | 10.1715i | 0.267486 | + | 0.463300i | ||||
\(483\) | −30.4822 | + | 26.3247i | −1.38699 | + | 1.19782i | ||||
\(484\) | 7.25832 | − | 12.5718i | 0.329924 | − | 0.571445i | ||||
\(485\) | −11.0166 | −0.500237 | ||||||||
\(486\) | 3.18375 | − | 30.6554i | 0.144418 | − | 1.39056i | ||||
\(487\) | 14.5660i | 0.660048i | 0.943973 | + | 0.330024i | \(0.107057\pi\) | ||||
−0.943973 | + | 0.330024i | \(0.892943\pi\) | |||||||
\(488\) | 0.947224 | + | 0.546880i | 0.0428788 | + | 0.0247561i | ||||
\(489\) | 4.32722 | − | 3.73702i | 0.195684 | − | 0.168994i | ||||
\(490\) | 6.48617 | + | 11.2344i | 0.293015 | + | 0.507517i | ||||
\(491\) | 18.7197 | + | 32.4236i | 0.844810 | + | 1.46325i | 0.885786 | + | 0.464094i | \(0.153620\pi\) |
−0.0409752 | + | 0.999160i | \(0.513046\pi\) | |||||||
\(492\) | −1.09841 | − | 5.75037i | −0.0495203 | − | 0.259247i | ||||
\(493\) | −0.000339085 | 0 | 0.000587313i | −1.52716e−5 | 0 | 2.64512e-5i | ||||
\(494\) | −1.36994 | + | 3.10356i | −0.0616364 | + | 0.139636i | ||||
\(495\) | 0.804886 | − | 5.46937i | 0.0361769 | − | 0.245830i | ||||
\(496\) | 6.33053i | 0.284249i | ||||||||
\(497\) | −22.2772 | + | 38.5853i | −0.999270 | + | 1.73079i | ||||
\(498\) | −19.7131 | + | 56.6533i | −0.883365 | + | 2.53870i | ||||
\(499\) | 30.8555 | − | 17.8144i | 1.38128 | − | 0.797483i | 0.388969 | − | 0.921251i | \(-0.372831\pi\) |
0.992311 | + | 0.123768i | \(0.0394979\pi\) | |||||||
\(500\) | −1.65326 | + | 0.954509i | −0.0739360 | + | 0.0426870i | ||||
\(501\) | 15.2138 | + | 5.29380i | 0.679703 | + | 0.236509i | ||||
\(502\) | −35.6018 | − | 20.5547i | −1.58898 | − | 0.917401i | ||||
\(503\) | −4.68505 | −0.208896 | −0.104448 | − | 0.994530i | \(-0.533308\pi\) | ||||
−0.104448 | + | 0.994530i | \(0.533308\pi\) | |||||||
\(504\) | 1.55802 | + | 1.23362i | 0.0693996 | + | 0.0549496i | ||||
\(505\) | − | 4.29951i | − | 0.191326i | ||||||
\(506\) | 11.5029 | − | 19.9237i | 0.511368 | − | 0.885715i | ||||
\(507\) | −18.0251 | − | 13.4943i | −0.800523 | − | 0.599302i | ||||
\(508\) | 5.99529 | + | 10.3841i | 0.265998 | + | 0.460722i | ||||
\(509\) | 17.9569 | − | 10.3674i | 0.795926 | − | 0.459528i | −0.0461186 | − | 0.998936i | \(-0.514685\pi\) |
0.842045 | + | 0.539408i | \(0.181352\pi\) | |||||||
\(510\) | −0.402606 | − | 0.466191i | −0.0178277 | − | 0.0206433i | ||||
\(511\) | −7.93628 | + | 13.7460i | −0.351080 | + | 0.608089i | ||||
\(512\) | 31.4377i | 1.38936i | ||||||||
\(513\) | 1.32655 | + | 2.08689i | 0.0585685 | + | 0.0921383i | ||||
\(514\) | − | 8.34256i | − | 0.367975i | ||||||
\(515\) | −14.9220 | − | 8.61522i | −0.657542 | − | 0.379632i | ||||
\(516\) | −4.75810 | − | 5.50956i | −0.209464 | − | 0.242545i | ||||
\(517\) | 8.36661 | + | 14.4914i | 0.367963 | + | 0.637331i | ||||
\(518\) | 34.0261 | − | 19.6450i | 1.49502 | − | 0.863151i | ||||
\(519\) | −24.9526 | + | 4.76635i | −1.09530 | + | 0.209219i | ||||
\(520\) | 0.382894 | + | 0.523484i | 0.0167910 | + | 0.0229563i | ||||
\(521\) | 3.45022 | 0.151157 | 0.0755784 | − | 0.997140i | \(-0.475920\pi\) | ||||
0.0755784 | + | 0.997140i | \(0.475920\pi\) | |||||||
\(522\) | 0.00824255 | + | 0.0207883i | 0.000360766 | + | 0.000909879i | ||||
\(523\) | −19.4273 | −0.849494 | −0.424747 | − | 0.905312i | \(-0.639637\pi\) | ||||
−0.424747 | + | 0.905312i | \(0.639637\pi\) | |||||||
\(524\) | −19.8488 | + | 34.3791i | −0.867098 | + | 1.50186i | ||||
\(525\) | 6.02410 | + | 2.09615i | 0.262913 | + | 0.0914833i | ||||
\(526\) | 52.9247 | − | 30.5561i | 2.30763 | − | 1.33231i | ||||
\(527\) | −0.236276 | + | 0.136414i | −0.0102924 | + | 0.00594229i | ||||
\(528\) | −12.5815 | − | 4.37784i | −0.547538 | − | 0.190521i | ||||
\(529\) | −8.43622 | + | 14.6120i | −0.366792 | + | 0.635302i | ||||
\(530\) | −17.9672 | −0.780446 | ||||||||
\(531\) | 4.85687 | + | 12.2494i | 0.210770 | + | 0.531577i | ||||
\(532\) | 3.34557 | 0.145049 | ||||||||
\(533\) | −5.15259 | + | 3.76877i | −0.223183 | + | 0.163244i | ||||
\(534\) | −6.94829 | + | 1.32724i | −0.300682 | + | 0.0574351i | ||||
\(535\) | 7.27638 | − | 4.20102i | 0.314586 | − | 0.181626i | ||||
\(536\) | 1.05173 | + | 1.82165i | 0.0454278 | + | 0.0786833i | ||||
\(537\) | 4.43629 | + | 5.13692i | 0.191440 | + | 0.221675i | ||||
\(538\) | −3.19098 | − | 1.84231i | −0.137573 | − | 0.0794278i | ||||
\(539\) | 12.0907i | 0.520785i | ||||||||
\(540\) | −9.91054 | + | 0.422730i | −0.426482 | + | 0.0181914i | ||||
\(541\) | − | 10.9817i | − | 0.472139i | −0.971736 | − | 0.236069i | \(-0.924141\pi\) | ||
0.971736 | − | 0.236069i | \(-0.0758592\pi\) | |||||||
\(542\) | 5.55096 | − | 9.61454i | 0.238434 | − | 0.412980i | ||||
\(543\) | −20.8557 | − | 24.1495i | −0.895004 | − | 1.03635i | ||||
\(544\) | −1.22940 | + | 0.709795i | −0.0527101 | + | 0.0304322i | ||||
\(545\) | −8.53973 | − | 14.7912i | −0.365802 | − | 0.633587i | ||||
\(546\) | −10.2305 | + | 44.3031i | −0.437826 | + | 1.89600i | ||||
\(547\) | 17.6658 | − | 30.5981i | 0.755335 | − | 1.30828i | −0.189872 | − | 0.981809i | \(-0.560807\pi\) |
0.945208 | − | 0.326470i | \(-0.105859\pi\) | |||||||
\(548\) | 13.6589i | 0.583478i | ||||||||
\(549\) | 14.3012 | + | 11.3235i | 0.610362 | + | 0.483277i | ||||
\(550\) | −3.64336 | −0.155353 | ||||||||
\(551\) | −0.00155386 | 0.000897119i | −6.61965e−5 | 3.82186e-5i | ||||||
\(552\) | 1.85808 | + | 0.646538i | 0.0790852 | + | 0.0275185i | ||||
\(553\) | 34.6238 | − | 19.9900i | 1.47235 | − | 0.850063i | ||||
\(554\) | −1.16838 | + | 0.674565i | −0.0496398 | + | 0.0286595i | ||||
\(555\) | 3.07164 | − | 8.82757i | 0.130384 | − | 0.374710i | ||||
\(556\) | −15.7591 | + | 27.2956i | −0.668336 | + | 1.15759i | ||||
\(557\) | 10.1075i | 0.428267i | 0.976804 | + | 0.214134i | \(0.0686928\pi\) | ||||
−0.976804 | + | 0.214134i | \(0.931307\pi\) | |||||||
\(558\) | −1.30985 | + | 8.90068i | −0.0554503 | + | 0.376796i | ||||
\(559\) | −3.20555 | + | 7.26210i | −0.135580 | + | 0.307154i | ||||
\(560\) | 7.68491 | − | 13.3107i | 0.324747 | − | 0.562478i | ||||
\(561\) | −0.107717 | − | 0.563917i | −0.00454783 | − | 0.0238086i | ||||
\(562\) | −26.2522 | − | 45.4701i | −1.10738 | − | 1.91804i | ||||
\(563\) | 18.2497 | + | 31.6093i | 0.769131 | + | 1.33217i | 0.938034 | + | 0.346542i | \(0.112644\pi\) |
−0.168903 | + | 0.985633i | \(0.554023\pi\) | |||||||
\(564\) | 22.7239 | − | 19.6245i | 0.956848 | − | 0.826341i | ||||
\(565\) | −3.88350 | − | 2.24214i | −0.163380 | − | 0.0943275i | ||||
\(566\) | 55.3289i | 2.32565i | ||||||||
\(567\) | 22.7118 | + | 24.1378i | 0.953806 | + | 1.01369i | ||||
\(568\) | 2.17634 | 0.0913173 | ||||||||
\(569\) | −4.37142 | + | 7.57152i | −0.183259 | + | 0.317415i | −0.942989 | − | 0.332825i | \(-0.891998\pi\) |
0.759729 | + | 0.650240i | \(0.225331\pi\) | |||||||
\(570\) | 1.23340 | − | 1.06518i | 0.0516616 | − | 0.0446153i | ||||
\(571\) | 10.5346 | + | 18.2464i | 0.440859 | + | 0.763590i | 0.997753 | − | 0.0669932i | \(-0.0213406\pi\) |
−0.556894 | + | 0.830583i | \(0.688007\pi\) | |||||||
\(572\) | −1.36610 | − | 12.6100i | −0.0571194 | − | 0.527252i | ||||
\(573\) | −1.02158 | + | 0.195138i | −0.0426770 | + | 0.00815200i | ||||
\(574\) | 11.1640 | + | 6.44556i | 0.465978 | + | 0.269032i | ||||
\(575\) | 6.31446 | 0.263331 | ||||||||
\(576\) | −3.16945 | + | 21.5371i | −0.132061 | + | 0.897378i | ||||
\(577\) | 23.6128i | 0.983014i | 0.870874 | + | 0.491507i | \(0.163554\pi\) | ||||
−0.870874 | + | 0.491507i | \(0.836446\pi\) | |||||||
\(578\) | 29.0527 | + | 16.7736i | 1.20843 | + | 0.697688i | ||||
\(579\) | −1.47194 | − | 0.512178i | −0.0611719 | − | 0.0212854i | ||||
\(580\) | 0.00623320 | − | 0.00359874i | 0.000258819 | − | 0.000149429i | ||||
\(581\) | −32.2528 | − | 55.8635i | −1.33807 | − | 2.31761i | ||||
\(582\) | −12.3980 | + | 35.6306i | −0.513915 | + | 1.47694i | ||||
\(583\) | −14.5026 | − | 8.37308i | −0.600636 | − | 0.346777i | ||||
\(584\) | 0.775323 | 0.0320831 | ||||||||
\(585\) | 5.04663 | + | 9.56721i | 0.208652 | + | 0.395556i | ||||
\(586\) | 8.03880 | 0.332080 | ||||||||
\(587\) | 1.83805 | + | 1.06120i | 0.0758643 | + | 0.0438003i | 0.537452 | − | 0.843294i | \(-0.319387\pi\) |
−0.461588 | + | 0.887094i | \(0.652720\pi\) | |||||||
\(588\) | 21.3095 | − | 4.07046i | 0.878789 | − | 0.167863i | ||||
\(589\) | −0.360912 | − | 0.625117i | −0.0148711 | − | 0.0257575i | ||||
\(590\) | 7.52079 | − | 4.34213i | 0.309626 | − | 0.178763i | ||||
\(591\) | 1.78629 | − | 1.54266i | 0.0734782 | − | 0.0634564i | ||||
\(592\) | −19.5051 | − | 11.2613i | −0.801655 | − | 0.462836i | ||||
\(593\) | − | 11.5522i | − | 0.474391i | −0.971462 | − | 0.237196i | \(-0.923772\pi\) | ||
0.971462 | − | 0.237196i | \(-0.0762282\pi\) | |||||||
\(594\) | −16.7836 | − | 8.75844i | −0.688640 | − | 0.359363i | ||||
\(595\) | 0.662396 | 0.0271556 | ||||||||
\(596\) | −27.5567 | − | 15.9099i | −1.12877 | − | 0.651694i | ||||
\(597\) | −28.4660 | − | 32.9617i | −1.16504 | − | 1.34903i | ||||
\(598\) | 4.84812 | + | 44.7516i | 0.198254 | + | 1.83003i | ||||
\(599\) | 20.3446 | + | 35.2379i | 0.831258 | + | 1.43978i | 0.897041 | + | 0.441947i | \(0.145712\pi\) |
−0.0657834 | + | 0.997834i | \(0.520955\pi\) | |||||||
\(600\) | −0.0584567 | − | 0.306030i | −0.00238648 | − | 0.0124936i | ||||
\(601\) | −5.12863 | + | 8.88304i | −0.209201 | + | 0.362347i | −0.951463 | − | 0.307763i | \(-0.900420\pi\) |
0.742262 | + | 0.670110i | \(0.233753\pi\) | |||||||
\(602\) | 16.0298 | 0.653327 | ||||||||
\(603\) | 12.9302 | + | 32.6110i | 0.526559 | + | 1.32802i | ||||
\(604\) | − | 18.2114i | − | 0.741010i | ||||||
\(605\) | 6.58547 | + | 3.80212i | 0.267737 | + | 0.154578i | ||||
\(606\) | −13.9058 | − | 4.83866i | −0.564884 | − | 0.196557i | ||||
\(607\) | −17.1143 | − | 29.6428i | −0.694648 | − | 1.20317i | −0.970299 | − | 0.241908i | \(-0.922227\pi\) |
0.275651 | − | 0.961258i | \(-0.411106\pi\) | |||||||
\(608\) | −1.87791 | − | 3.25263i | −0.0761592 | − | 0.131912i | ||||
\(609\) | −0.0227124 | − | 0.00790300i | −0.000920352 | − | 0.000320246i | ||||
\(610\) | 6.01091 | − | 10.4112i | 0.243375 | − | 0.421537i | ||||
\(611\) | −29.9521 | − | 13.2211i | −1.21173 | − | 0.534869i | ||||
\(612\) | −0.957621 | + | 0.379696i | −0.0387095 | + | 0.0153483i | ||||
\(613\) | − | 48.3073i | − | 1.95111i | −0.219752 | − | 0.975556i | \(-0.570525\pi\) | ||
0.219752 | − | 0.975556i | \(-0.429475\pi\) | |||||||
\(614\) | −16.9354 | + | 29.3330i | −0.683458 | + | 1.18378i | ||||
\(615\) | 3.01221 | − | 0.575382i | 0.121464 | − | 0.0232016i | ||||
\(616\) | 1.05714 | − | 0.610342i | 0.0425935 | − | 0.0245914i | ||||
\(617\) | 1.19929 | − | 0.692413i | 0.0482818 | − | 0.0278755i | −0.475665 | − | 0.879627i | \(-0.657792\pi\) |
0.523947 | + | 0.851751i | \(0.324459\pi\) | |||||||
\(618\) | −44.6572 | + | 38.5663i | −1.79638 | + | 1.55136i | ||||
\(619\) | 11.0458 | + | 6.37731i | 0.443969 | + | 0.256326i | 0.705280 | − | 0.708929i | \(-0.250821\pi\) |
−0.261311 | + | 0.965255i | \(0.584155\pi\) | |||||||
\(620\) | 2.89555 | 0.116288 | ||||||||
\(621\) | 29.0884 | + | 15.1796i | 1.16728 | + | 0.609137i | ||||
\(622\) | − | 7.71279i | − | 0.309255i | ||||||
\(623\) | 3.80351 | − | 6.58788i | 0.152384 | − | 0.263938i | ||||
\(624\) | 24.9261 | − | 7.61932i | 0.997844 | − | 0.305017i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −19.7969 | + | 11.4298i | −0.791244 | + | 0.456825i | ||||
\(627\) | 1.49196 | − | 0.284988i | 0.0595831 | − | 0.0113813i | ||||
\(628\) | −8.26284 | + | 14.3117i | −0.329723 | + | 0.571097i | ||||
\(629\) | − | 0.970660i | − | 0.0387027i | ||||||
\(630\) | 13.5590 | − | 17.1246i | 0.540205 | − | 0.682261i | ||||
\(631\) | 36.8152i | 1.46559i | 0.680449 | + | 0.732796i | \(0.261785\pi\) | ||||
−0.680449 | + | 0.732796i | \(0.738215\pi\) | |||||||
\(632\) | −1.69126 | − | 0.976450i | −0.0672747 | − | 0.0388411i | ||||
\(633\) | −13.1706 | + | 37.8510i | −0.523485 | + | 1.50444i | ||||
\(634\) | 11.5714 | + | 20.0422i | 0.459559 | + | 0.795979i | ||||
\(635\) | −5.43952 | + | 3.14051i | −0.215861 | + | 0.124627i | ||||
\(636\) | −9.87482 | + | 28.3792i | −0.391562 | + | 1.12531i | ||||
\(637\) | −13.9662 | − | 19.0942i | −0.553360 | − | 0.756542i | ||||
\(638\) | 0.0137364 | 0.000543828 | ||||||||
\(639\) | 35.9096 | + | 5.28455i | 1.42056 | + | 0.209053i | ||||
\(640\) | −1.43756 | −0.0568245 | ||||||||
\(641\) | −3.25193 | + | 5.63250i | −0.128443 | + | 0.222470i | −0.923074 | − | 0.384623i | \(-0.874331\pi\) |
0.794630 | + | 0.607094i | \(0.207665\pi\) | |||||||
\(642\) | −5.39843 | − | 28.2616i | −0.213059 | − | 1.11540i | ||||
\(643\) | 18.8197 | − | 10.8655i | 0.742175 | − | 0.428495i | −0.0806847 | − | 0.996740i | \(-0.525711\pi\) |
0.822860 | + | 0.568245i | \(0.192377\pi\) | |||||||
\(644\) | 38.4438 | − | 22.1955i | 1.51490 | − | 0.874627i | ||||
\(645\) | 2.88607 | − | 2.49243i | 0.113639 | − | 0.0981394i | ||||
\(646\) | 0.0846219 | − | 0.146569i | 0.00332940 | − | 0.00576670i | ||||
\(647\) | 2.31013 | 0.0908207 | 0.0454104 | − | 0.998968i | \(-0.485540\pi\) | ||||
0.0454104 | + | 0.998968i | \(0.485540\pi\) | |||||||
\(648\) | 0.466391 | − | 1.55029i | 0.0183216 | − | 0.0609013i | ||||
\(649\) | 8.09407 | 0.317720 | ||||||||
\(650\) | 5.75377 | − | 4.20849i | 0.225681 | − | 0.165071i | ||||
\(651\) | −6.32336 | − | 7.32202i | −0.247832 | − | 0.286973i | ||||
\(652\) | −5.45743 | + | 3.15085i | −0.213730 | + | 0.123397i | ||||
\(653\) | 6.74124 | + | 11.6762i | 0.263805 | + | 0.456924i | 0.967250 | − | 0.253826i | \(-0.0816890\pi\) |
−0.703445 | + | 0.710750i | \(0.748356\pi\) | |||||||
\(654\) | −57.4496 | + | 10.9738i | −2.24646 | + | 0.429109i | ||||
\(655\) | −18.0088 | − | 10.3974i | −0.703661 | − | 0.406259i | ||||
\(656\) | − | 7.38970i | − | 0.288519i | ||||||
\(657\) | 12.7928 | + | 1.88262i | 0.499095 | + | 0.0734481i | ||||
\(658\) | 66.1141i | 2.57740i | ||||||||
\(659\) | 4.46412 | − | 7.73208i | 0.173897 | − | 0.301199i | −0.765882 | − | 0.642981i | \(-0.777697\pi\) |
0.939779 | + | 0.341782i | \(0.111031\pi\) | |||||||
\(660\) | −2.00240 | + | 5.75468i | −0.0779433 | + | 0.224001i | ||||
\(661\) | −28.3029 | + | 16.3407i | −1.10085 | + | 0.635579i | −0.936445 | − | 0.350813i | \(-0.885905\pi\) |
−0.164409 | + | 0.986392i | \(0.552572\pi\) | |||||||
\(662\) | 17.0011 | + | 29.4467i | 0.660766 | + | 1.14448i | ||||
\(663\) | 0.821501 | + | 0.766139i | 0.0319045 | + | 0.0297544i | ||||
\(664\) | −1.57545 | + | 2.72876i | −0.0611392 | + | 0.105896i | ||||
\(665\) | 1.75251i | 0.0679593i | ||||||||
\(666\) | −25.0940 | − | 19.8691i | −0.972372 | − | 0.769911i | ||||
\(667\) | −0.0238071 | −0.000921815 | ||||||||
\(668\) | −15.3757 | − | 8.87718i | −0.594905 | − | 0.343469i | ||||
\(669\) | 1.47084 | + | 7.70007i | 0.0568658 | + | 0.297702i | ||||
\(670\) | 20.0223 | − | 11.5599i | 0.773528 | − | 0.446596i | ||||
\(671\) | 9.70366 | − | 5.60241i | 0.374606 | − | 0.216279i | ||||
\(672\) | −32.9019 | − | 38.0982i | −1.26922 | − | 1.46967i | ||||
\(673\) | 20.0752 | − | 34.7712i | 0.773842 | − | 1.34033i | −0.161602 | − | 0.986856i | \(-0.551666\pi\) |
0.935443 | − | 0.353477i | \(-0.115001\pi\) | |||||||
\(674\) | − | 37.5328i | − | 1.44571i | ||||||
\(675\) | −0.221438 | − | 5.19143i | −0.00852316 | − | 0.199818i | ||||
\(676\) | 16.7234 | + | 18.3364i | 0.643209 | + | 0.705245i | ||||
\(677\) | 19.1300 | − | 33.1342i | 0.735227 | − | 1.27345i | −0.219397 | − | 0.975636i | \(-0.570409\pi\) |
0.954624 | − | 0.297814i | \(-0.0962577\pi\) | |||||||
\(678\) | −11.6222 | + | 10.0370i | −0.446347 | + | 0.385469i | ||||
\(679\) | −20.2846 | − | 35.1339i | −0.778451 | − | 1.34832i | ||||
\(680\) | −0.0161780 | − | 0.0280211i | −0.000620397 | − | 0.00107456i | ||||
\(681\) | −7.51550 | − | 39.3448i | −0.287994 | − | 1.50770i | ||||
\(682\) | 4.78579 | + | 2.76308i | 0.183257 | + | 0.105804i | ||||
\(683\) | − | 18.5501i | − | 0.709801i | −0.934904 | − | 0.354901i | \(-0.884515\pi\) | ||
0.934904 | − | 0.354901i | \(-0.115485\pi\) | |||||||
\(684\) | −1.00456 | − | 2.53358i | −0.0384105 | − | 0.0968740i | ||||
\(685\) | −7.15492 | −0.273375 | ||||||||
\(686\) | 1.59737 | − | 2.76672i | 0.0609878 | − | 0.105634i | ||||
\(687\) | 11.4291 | + | 3.97688i | 0.436048 | + | 0.151727i | ||||
\(688\) | −4.59447 | − | 7.95786i | −0.175163 | − | 0.303390i | ||||
\(689\) | 32.5750 | − | 3.52899i | 1.24101 | − | 0.134444i | ||||
\(690\) | 7.10629 | − | 20.4227i | 0.270532 | − | 0.777479i | ||||
\(691\) | 38.8399 | + | 22.4242i | 1.47754 | + | 0.853058i | 0.999678 | − | 0.0253767i | \(-0.00807852\pi\) |
0.477862 | + | 0.878435i | \(0.341412\pi\) | |||||||
\(692\) | 27.9993 | 1.06437 | ||||||||
\(693\) | 18.9248 | − | 7.50369i | 0.718895 | − | 0.285042i | ||||
\(694\) | 47.1917i | 1.79137i | ||||||||
\(695\) | −14.2982 | − | 8.25510i | −0.542364 | − | 0.313134i | ||||
\(696\) | 0.000220396 | 0.00115381i | 8.35410e−6 | 4.37350e-5i | ||||||
\(697\) | 0.275808 | − | 0.159238i | 0.0104470 | − | 0.00603156i | ||||
\(698\) | −28.7899 | − | 49.8656i | −1.08971 | − | 1.88744i | ||||
\(699\) | 25.6704 | + | 29.7246i | 0.970945 | + | 1.12429i | ||||
\(700\) | −6.08822 | − | 3.51503i | −0.230113 | − | 0.132856i | ||||
\(701\) | −32.7223 | −1.23591 | −0.617953 | − | 0.786215i | \(-0.712038\pi\) | ||||
−0.617953 | + | 0.786215i | \(0.712038\pi\) | |||||||
\(702\) | 36.6225 | − | 5.55525i | 1.38223 | − | 0.209669i | ||||
\(703\) | 2.56808 | 0.0968569 | ||||||||
\(704\) | 11.5802 | + | 6.68585i | 0.436446 | + | 0.251982i | ||||
\(705\) | 10.2799 | + | 11.9034i | 0.387163 | + | 0.448309i | ||||
\(706\) | −2.12174 | − | 3.67496i | −0.0798528 | − | 0.138309i | ||||
\(707\) | 13.7119 | − | 7.91659i | 0.515690 | − | 0.297734i | ||||
\(708\) | −2.72494 | − | 14.2655i | −0.102410 | − | 0.536131i | ||||
\(709\) | 9.06616 | + | 5.23435i | 0.340487 | + | 0.196580i | 0.660487 | − | 0.750837i | \(-0.270350\pi\) |
−0.320001 | + | 0.947417i | \(0.603683\pi\) | |||||||
\(710\) | − | 23.9208i | − | 0.897731i | ||||||
\(711\) | −25.5348 | − | 20.2181i | −0.957629 | − | 0.758237i | ||||
\(712\) | −0.371579 | −0.0139255 | ||||||||
\(713\) | −8.29445 | − | 4.78880i | −0.310630 | − | 0.179342i | ||||
\(714\) | 0.745460 | − | 2.14237i | 0.0278981 | − | 0.0801763i | ||||
\(715\) | 6.60551 | − | 0.715602i | 0.247032 | − | 0.0267620i | ||||
\(716\) | −3.74043 | − | 6.47862i | −0.139787 | − | 0.242118i | ||||
\(717\) | −42.1707 | − | 14.6737i | −1.57489 | − | 0.548000i | ||||
\(718\) | −2.95436 | + | 5.11710i | −0.110256 | + | 0.190969i | ||||
\(719\) | −10.0212 | −0.373727 | −0.186864 | − | 0.982386i | \(-0.559832\pi\) | ||||
−0.186864 | + | 0.982386i | \(0.559832\pi\) | |||||||
\(720\) | −12.3876 | − | 1.82300i | −0.461660 | − | 0.0679390i | ||||
\(721\) | − | 63.4520i | − | 2.36308i | ||||||
\(722\) | −32.1448 | − | 18.5588i | −1.19630 | − | 0.690687i | ||||
\(723\) | 1.93050 | + | 10.1065i | 0.0717960 | + | 0.375864i | ||||
\(724\) | 17.5844 | + | 30.4571i | 0.653519 | + | 1.13193i | ||||
\(725\) | 0.00188512 | + | 0.00326513i | 7.00118e−5 | + | 0.000121264i | ||||
\(726\) | 19.7084 | − | 17.0203i | 0.731447 | − | 0.631683i | ||||
\(727\) | 22.6535 | − | 39.2370i | 0.840171 | − | 1.45522i | −0.0495795 | − | 0.998770i | \(-0.515788\pi\) |
0.889750 | − | 0.456448i | \(-0.150879\pi\) | |||||||
\(728\) | −0.964475 | + | 2.18500i | −0.0357458 | + | 0.0809815i | ||||
\(729\) | 11.4598 | − | 24.4473i | 0.424438 | − | 0.905457i | ||||
\(730\) | − | 8.52180i | − | 0.315406i | ||||||
\(731\) | 0.198009 | − | 0.342961i | 0.00732362 | − | 0.0126849i | ||||
\(732\) | −13.1409 | − | 15.2163i | −0.485701 | − | 0.562409i | ||||
\(733\) | −0.358019 | + | 0.206702i | −0.0132237 | + | 0.00763473i | −0.506597 | − | 0.862183i | \(-0.669097\pi\) |
0.493374 | + | 0.869818i | \(0.335764\pi\) | |||||||
\(734\) | 54.2336 | − | 31.3118i | 2.00180 | − | 1.15574i | ||||
\(735\) | 2.13222 | + | 11.1625i | 0.0786483 | + | 0.411736i | ||||
\(736\) | −43.1580 | − | 24.9173i | −1.59082 | − | 0.918463i | ||||
\(737\) | 21.5485 | 0.793749 | ||||||||
\(738\) | 1.52900 | − | 10.3899i | 0.0562832 | − | 0.382456i | ||||
\(739\) | 8.98933i | 0.330678i | 0.986237 | + | 0.165339i | \(0.0528718\pi\) | ||||
−0.986237 | + | 0.165339i | \(0.947128\pi\) | |||||||
\(740\) | −5.15085 | + | 8.92153i | −0.189349 | + | 0.327962i | ||||
\(741\) | −2.02698 | + | 2.17345i | −0.0744629 | + | 0.0798437i | ||||
\(742\) | −33.0826 | − | 57.3008i | −1.21450 | − | 2.10358i | ||||
\(743\) | 6.96651 | − | 4.02211i | 0.255576 | − | 0.147557i | −0.366739 | − | 0.930324i | \(-0.619526\pi\) |
0.622315 | + | 0.782767i | \(0.286192\pi\) | |||||||
\(744\) | −0.155303 | + | 0.446323i | −0.00569367 | + | 0.0163630i | ||||
\(745\) | 8.33407 | − | 14.4350i | 0.305337 | − | 0.528858i | ||||
\(746\) | − | 36.4006i | − | 1.33272i | ||||||
\(747\) | −32.6207 | + | 41.1989i | −1.19353 | + | 1.50739i | ||||
\(748\) | 0.632772i | 0.0231364i | ||||||||
\(749\) | 26.7957 | + | 15.4705i | 0.979093 | + | 0.565280i | ||||
\(750\) | −3.36366 | + | 0.642514i | −0.122824 | + | 0.0234613i | ||||
\(751\) | −3.76057 | − | 6.51349i | −0.137225 | − | 0.237681i | 0.789220 | − | 0.614110i | \(-0.210485\pi\) |
−0.926445 | + | 0.376430i | \(0.877152\pi\) | |||||||
\(752\) | 32.8217 | − | 18.9496i | 1.19689 | − | 0.691022i | ||||
\(753\) | −23.5388 | − | 27.2564i | −0.857802 | − | 0.993277i | ||||
\(754\) | −0.0216931 | + | 0.0158671i | −0.000790017 | + | 0.000577845i | ||||
\(755\) | 9.53965 | 0.347183 | ||||||||
\(756\) | −19.5962 | − | 30.8282i | −0.712708 | − | 1.12121i | ||||
\(757\) | −38.3328 | −1.39323 | −0.696614 | − | 0.717446i | \(-0.745311\pi\) | ||||
−0.696614 | + | 0.717446i | \(0.745311\pi\) | |||||||
\(758\) | −21.3530 | + | 36.9844i | −0.775575 | + | 1.34334i | ||||
\(759\) | 15.2534 | − | 13.1729i | 0.553662 | − | 0.478147i | ||||
\(760\) | 0.0741355 | − | 0.0428021i | 0.00268918 | − | 0.00155260i | ||||
\(761\) | −11.3676 | + | 6.56308i | −0.412075 | + | 0.237912i | −0.691681 | − | 0.722203i | \(-0.743129\pi\) |
0.279606 | + | 0.960115i | \(0.409796\pi\) | |||||||
\(762\) | 4.03564 | + | 21.1272i | 0.146196 | + | 0.765359i | ||||
\(763\) | 31.4480 | − | 54.4696i | 1.13850 | − | 1.97193i | ||||
\(764\) | 1.14631 | 0.0414721 | ||||||||
\(765\) | −0.198896 | − | 0.501630i | −0.00719110 | − | 0.0181365i | ||||
\(766\) | 52.4645 | 1.89562 | ||||||||
\(767\) | −12.7825 | + | 9.34957i | −0.461551 | + | 0.337593i | ||||
\(768\) | −9.87860 | + | 28.3900i | −0.356463 | + | 1.02444i | ||||
\(769\) | 36.5074 | − | 21.0776i | 1.31649 | − | 0.760077i | 0.333329 | − | 0.942811i | \(-0.391828\pi\) |
0.983162 | + | 0.182734i | \(0.0584947\pi\) | |||||||
\(770\) | −6.70844 | − | 11.6194i | −0.241755 | − | 0.418732i | ||||
\(771\) | 2.40181 | − | 6.90254i | 0.0864989 | − | 0.248589i | ||||
\(772\) | 1.48761 | + | 0.858872i | 0.0535403 | + | 0.0309115i | ||||
\(773\) | 2.91191i | 0.104734i | 0.998628 | + | 0.0523671i | \(0.0166766\pi\) | ||||
−0.998628 | + | 0.0523671i | \(0.983323\pi\) | |||||||
\(774\) | −4.81323 | − | 12.1393i | −0.173008 | − | 0.436339i | ||||
\(775\) | 1.51677i | 0.0544841i | ||||||||
\(776\) | −0.990837 | + | 1.71618i | −0.0355690 | + | 0.0616073i | ||||
\(777\) | 33.8085 | − | 6.45797i | 1.21287 | − | 0.231679i | ||||
\(778\) | −61.5034 | + | 35.5090i | −2.20500 | + | 1.27306i | ||||
\(779\) | 0.421296 | + | 0.729706i | 0.0150945 | + | 0.0261444i | ||||
\(780\) | −3.48503 | − | 11.4011i | −0.124784 | − | 0.408224i | ||||
\(781\) | 11.1476 | − | 19.3081i | 0.398891 | − | 0.690900i | ||||
\(782\) | − | 2.24563i | − | 0.0803037i | ||||||
\(783\) | 0.000834877 | 0.0195730i | 2.98361e−5 | 0.000699482i | ||||||
\(784\) | 27.3844 | 0.978016 | ||||||||
\(785\) | −7.49686 | − | 4.32832i | −0.267574 | − | 0.154484i | ||||
\(786\) | −53.8950 | + | 46.5442i | −1.92237 | + | 1.66018i | ||||
\(787\) | −18.7041 | + | 10.7988i | −0.666730 | + | 0.384937i | −0.794836 | − | 0.606824i | \(-0.792443\pi\) |
0.128107 | + | 0.991760i | \(0.459110\pi\) | |||||||
\(788\) | −2.25285 | + | 1.30068i | −0.0802544 | + | 0.0463349i | ||||
\(789\) | 52.5863 | − | 10.0448i | 1.87212 | − | 0.357606i | ||||
\(790\) | −10.7324 | + | 18.5891i | −0.381843 | + | 0.661371i | ||||
\(791\) | − | 16.5136i | − | 0.587156i | ||||||
\(792\) | −0.779634 | − | 0.617304i | −0.0277031 | − | 0.0219349i | ||||
\(793\) | −8.85305 | + | 20.0564i | −0.314381 | + | 0.712224i | ||||
\(794\) | −14.2612 | + | 24.7012i | −0.506112 | + | 0.876611i | ||||
\(795\) | −14.8659 | − | 5.17272i | −0.527237 | − | 0.183458i | ||||
\(796\) | 24.0010 | + | 41.5709i | 0.850692 | + | 1.47344i | ||||
\(797\) | 2.33705 | + | 4.04788i | 0.0827824 | + | 0.143383i | 0.904444 | − | 0.426592i | \(-0.140286\pi\) |
−0.821662 | + | 0.569976i | \(0.806953\pi\) | |||||||
\(798\) | 5.66809 | + | 1.97227i | 0.200648 | + | 0.0698175i | ||||
\(799\) | 1.41452 | + | 0.816676i | 0.0500423 | + | 0.0288919i | ||||
\(800\) | 7.89213i | 0.279029i | ||||||||
\(801\) | −6.13104 | − | 0.902260i | −0.216630 | − | 0.0318798i | ||||
\(802\) | 74.2323 | 2.62123 | ||||||||
\(803\) | 3.97133 | − | 6.87854i | 0.140145 | − | 0.242738i | ||||
\(804\) | −7.25450 | − | 37.9785i | −0.255847 | − | 1.33940i | ||||
\(805\) | 11.6267 | + | 20.1380i | 0.409787 | + | 0.709771i | ||||
\(806\) | −10.7496 | + | 1.16455i | −0.378639 | + | 0.0410195i | ||||
\(807\) | −2.10978 | − | 2.44299i | −0.0742679 | − | 0.0859972i | ||||
\(808\) | −0.669784 | − | 0.386700i | −0.0235629 | − | 0.0136041i | ||||
\(809\) | −18.0978 | −0.636284 | −0.318142 | − | 0.948043i | \(-0.603059\pi\) | ||||
−0.318142 | + | 0.948043i | \(0.603059\pi\) | |||||||
\(810\) | −17.0397 | − | 5.12624i | −0.598715 | − | 0.180118i | ||||
\(811\) | − | 2.20322i | − | 0.0773655i | −0.999252 | − | 0.0386828i | \(-0.987684\pi\) | ||
0.999252 | − | 0.0386828i | \(-0.0123162\pi\) | |||||||
\(812\) | 0.0229541 | + | 0.0132526i | 0.000805531 | + | 0.000465074i | ||||
\(813\) | 7.36080 | − | 6.35685i | 0.258155 | − | 0.222944i | ||||
\(814\) | −17.0267 | + | 9.83038i | −0.596786 | + | 0.344555i | ||||
\(815\) | −1.65051 | − | 2.85876i | −0.0578148 | − | 0.100138i | ||||
\(816\) | −1.27722 | + | 0.243970i | −0.0447118 | + | 0.00854067i | ||||
\(817\) | 0.907374 | + | 0.523873i | 0.0317450 | + | 0.0183280i | ||||
\(818\) | 49.9970 | 1.74810 | ||||||||
\(819\) | −21.2194 | + | 33.7105i | −0.741466 | + | 1.17794i | ||||
\(820\) | −3.38001 | −0.118035 | ||||||||
\(821\) | −19.9180 | − | 11.4997i | −0.695145 | − | 0.401342i | 0.110392 | − | 0.993888i | \(-0.464789\pi\) |
−0.805536 | + | 0.592546i | \(0.798123\pi\) | |||||||
\(822\) | −8.05213 | + | 23.1410i | −0.280850 | + | 0.807134i | ||||
\(823\) | 17.9342 | + | 31.0629i | 0.625146 | + | 1.08278i | 0.988513 | + | 0.151138i | \(0.0482939\pi\) |
−0.363367 | + | 0.931646i | \(0.618373\pi\) | |||||||
\(824\) | −2.68418 | + | 1.54971i | −0.0935080 | + | 0.0539869i | ||||
\(825\) | −3.01447 | − | 1.04892i | −0.104950 | − | 0.0365186i | ||||
\(826\) | 27.6957 | + | 15.9901i | 0.963657 | + | 0.556368i | ||||
\(827\) | 40.7759i | 1.41792i | 0.705250 | + | 0.708959i | \(0.250835\pi\) | ||||
−0.705250 | + | 0.708959i | \(0.749165\pi\) | |||||||
\(828\) | −28.3520 | − | 22.4487i | −0.985301 | − | 0.780148i | ||||
\(829\) | 19.0813 | 0.662720 | 0.331360 | − | 0.943504i | \(-0.392492\pi\) | ||||
0.331360 | + | 0.943504i | \(0.392492\pi\) | |||||||
\(830\) | 29.9925 | + | 17.3162i | 1.04106 | + | 0.601054i | ||||
\(831\) | −1.16091 | + | 0.221753i | −0.0402715 | + | 0.00769251i | ||||
\(832\) | −26.0109 | + | 2.81787i | −0.901767 | + | 0.0976922i | ||||
\(833\) | 0.590096 | + | 1.02208i | 0.0204456 | + | 0.0354129i | ||||
\(834\) | −42.7905 | + | 36.9542i | −1.48171 | + | 1.27962i | ||||
\(835\) | 4.65013 | − | 8.05426i | 0.160924 | − | 0.278729i | ||||
\(836\) | −1.67413 | −0.0579009 | ||||||||
\(837\) | −3.64624 | + | 6.98722i | −0.126032 | + | 0.241513i | ||||
\(838\) | 69.1823i | 2.38986i | ||||||||
\(839\) | −14.2583 | − | 8.23204i | −0.492252 | − | 0.284202i | 0.233257 | − | 0.972415i | \(-0.425062\pi\) |
−0.725508 | + | 0.688214i | \(0.758395\pi\) | |||||||
\(840\) | 0.868352 | − | 0.749916i | 0.0299610 | − | 0.0258745i | ||||
\(841\) | 14.5000 | + | 25.1147i | 0.500000 | + | 0.866025i | ||||
\(842\) | 26.3723 | + | 45.6781i | 0.908848 | + | 1.57417i | ||||
\(843\) | −8.62999 | − | 45.1794i | −0.297233 | − | 1.55606i | ||||
\(844\) | 22.0858 | − | 38.2538i | 0.760226 | − | 1.31675i | ||||
\(845\) | −9.60513 | + | 8.76022i | −0.330426 | + | 0.301361i | ||||
\(846\) | 50.0680 | − | 19.8519i | 1.72137 | − | 0.682523i | ||||
\(847\) | 28.0031i | 0.962196i | ||||||||
\(848\) | −18.9643 | + | 32.8471i | −0.651236 | + | 1.12797i | ||||
\(849\) | −15.9291 | + | 45.7785i | −0.546685 | + | 1.57111i | ||||
\(850\) | −0.307988 | + | 0.177817i | −0.0105639 | + | 0.00609906i | ||||
\(851\) | 29.5097 | − | 17.0375i | 1.01158 | − | 0.584036i | ||||
\(852\) | −37.7829 | − | 13.1469i | −1.29442 | − | 0.450406i | ||||
\(853\) | 45.0815 | + | 26.0278i | 1.54356 | + | 0.891176i | 0.998610 | + | 0.0527094i | \(0.0167857\pi\) |
0.544953 | + | 0.838467i | \(0.316548\pi\) | |||||||
\(854\) | 44.2710 | 1.51492 | ||||||||
\(855\) | 1.32717 | − | 0.526220i | 0.0453881 | − | 0.0179964i | ||||
\(856\) | − | 1.51137i | − | 0.0516575i | ||||||
\(857\) | −3.08305 | + | 5.34000i | −0.105315 | + | 0.182411i | −0.913867 | − | 0.406014i | \(-0.866918\pi\) |
0.808552 | + | 0.588425i | \(0.200252\pi\) | |||||||
\(858\) | 5.11937 | − | 22.1694i | 0.174773 | − | 0.756850i | ||||
\(859\) | 3.61022 | + | 6.25308i | 0.123179 | + | 0.213352i | 0.921020 | − | 0.389516i | \(-0.127358\pi\) |
−0.797841 | + | 0.602868i | \(0.794024\pi\) | |||||||
\(860\) | −3.63988 | + | 2.10148i | −0.124119 | + | 0.0716600i | ||||
\(861\) | 7.38132 | + | 8.54708i | 0.251555 | + | 0.291284i | ||||
\(862\) | 26.1981 | − | 45.3765i | 0.892312 | − | 1.54553i | ||||
\(863\) | 4.07628i | 0.138758i | 0.997590 | + | 0.0693791i | \(0.0221018\pi\) | ||||
−0.997590 | + | 0.0693791i | \(0.977898\pi\) | |||||||
\(864\) | −18.9722 | + | 36.3561i | −0.645449 | + | 1.23686i | ||||
\(865\) | 14.6669i | 0.498688i | ||||||||
\(866\) | 17.5175 | + | 10.1137i | 0.595269 | + | 0.343679i | ||||
\(867\) | 19.2088 | + | 22.2425i | 0.652364 | + | 0.755393i | ||||
\(868\) | 5.33151 | + | 9.23445i | 0.180963 | + | 0.313438i | ||||
\(869\) | −17.3258 | + | 10.0031i | −0.587738 | + | 0.339330i | ||||
\(870\) | 0.0126819 | − | 0.00242244i | 0.000429955 | − | 8.21283e-5i | ||||
\(871\) | −34.0304 | + | 24.8910i | −1.15308 | + | 0.843398i | ||||
\(872\) | −3.07227 | −0.104040 | ||||||||
\(873\) | −20.5160 | + | 25.9110i | −0.694360 | + | 0.876954i | ||||
\(874\) | 5.94128 | 0.200967 | ||||||||
\(875\) | 1.84128 | − | 3.18919i | 0.0622465 | − | 0.107814i | ||||
\(876\) | −13.4602 | − | 4.68360i | −0.454777 | − | 0.158244i | ||||
\(877\) | 43.7145 | − | 25.2386i | 1.47613 | − | 0.852246i | 0.476496 | − | 0.879177i | \(-0.341907\pi\) |
0.999637 | + | 0.0269308i | \(0.00857338\pi\) | |||||||
\(878\) | −26.3805 | + | 15.2308i | −0.890300 | + | 0.514015i | ||||
\(879\) | 6.65121 | + | 2.31435i | 0.224340 | + | 0.0780612i | ||||
\(880\) | −3.84554 | + | 6.66068i | −0.129633 | + | 0.224531i | ||||
\(881\) | −23.9632 | −0.807340 | −0.403670 | − | 0.914905i | \(-0.632266\pi\) | ||||
−0.403670 | + | 0.914905i | \(0.632266\pi\) | |||||||
\(882\) | 38.5023 | + | 5.66610i | 1.29644 | + | 0.190787i | ||||
\(883\) | 23.2839 | 0.783564 | 0.391782 | − | 0.920058i | \(-0.371859\pi\) | ||||
0.391782 | + | 0.920058i | \(0.371859\pi\) | |||||||
\(884\) | −0.730923 | − | 0.999303i | −0.0245836 | − | 0.0336102i | ||||
\(885\) | 7.47270 | − | 1.42741i | 0.251192 | − | 0.0479817i | ||||
\(886\) | 41.2423 | − | 23.8112i | 1.38556 | − | 0.799954i | ||||
\(887\) | 8.34180 | + | 14.4484i | 0.280090 | + | 0.485130i | 0.971407 | − | 0.237422i | \(-0.0763023\pi\) |
−0.691316 | + | 0.722552i | \(0.742969\pi\) | |||||||
\(888\) | −1.09891 | − | 1.27246i | −0.0368769 | − | 0.0427010i | ||||
\(889\) | −20.0313 | − | 11.5651i | −0.671830 | − | 0.387881i | ||||
\(890\) | 4.08413i | 0.136900i | ||||||||
\(891\) | −11.3650 | − | 12.0786i | −0.380743 | − | 0.404648i | ||||
\(892\) | − | 8.64024i | − | 0.289297i | ||||||
\(893\) | −2.16068 | + | 3.74242i | −0.0723045 | + | 0.125235i | ||||
\(894\) | −37.3077 | − | 43.1998i | −1.24776 | − | 1.44482i | ||||
\(895\) | 3.39369 | − | 1.95935i | 0.113439 | − | 0.0654938i | ||||
\(896\) | −2.64695 | − | 4.58465i | −0.0884283 | − | 0.153162i | ||||
\(897\) | −8.87260 | + | 38.4227i | −0.296248 | + | 1.28290i | ||||
\(898\) | 20.9701 | − | 36.3214i | 0.699783 | − | 1.21206i | ||||
\(899\) | − | 0.00571861i | − | 0.000190726i | ||||||
\(900\) | −0.833828 | + | 5.66603i | −0.0277943 | + | 0.188868i | ||||
\(901\) | −1.63461 | −0.0544569 | ||||||||
\(902\) | −5.58650 | − | 3.22537i | −0.186010 | − | 0.107393i | ||||
\(903\) | 13.2629 | + | 4.61495i | 0.441361 | + | 0.153576i | ||||
\(904\) | −0.698568 | + | 0.403318i | −0.0232340 | + | 0.0134142i | ||||
\(905\) | −15.9543 | + | 9.21122i | −0.530339 | + | 0.306191i | ||||
\(906\) | 10.7359 | − | 30.8539i | 0.356677 | − | 1.02505i | ||||
\(907\) | 9.26718 | − | 16.0512i | 0.307712 | − | 0.532972i | −0.670150 | − | 0.742226i | \(-0.733770\pi\) |
0.977861 | + | 0.209254i | \(0.0671035\pi\) | |||||||
\(908\) | 44.1488i | 1.46513i | ||||||||
\(909\) | −10.1124 | − | 8.00689i | −0.335409 | − | 0.265572i | ||||
\(910\) | 24.0160 | + | 10.6008i | 0.796121 | + | 0.351414i | ||||
\(911\) | 1.92222 | − | 3.32938i | 0.0636859 | − | 0.110307i | −0.832424 | − | 0.554139i | \(-0.813048\pi\) |
0.896110 | + | 0.443831i | \(0.146381\pi\) | |||||||
\(912\) | −0.645474 | − | 3.37916i | −0.0213738 | − | 0.111895i | ||||
\(913\) | 16.1394 | + | 27.9542i | 0.534135 | + | 0.925149i | ||||
\(914\) | −5.22215 | − | 9.04504i | −0.172733 | − | 0.299183i | ||||
\(915\) | 7.97072 | − | 6.88358i | 0.263504 | − | 0.227564i | ||||
\(916\) | −11.5508 | − | 6.66883i | −0.381648 | − | 0.220344i | ||||
\(917\) | − | 76.5778i | − | 2.52882i | ||||||
\(918\) | −1.84625 | + | 0.0787508i | −0.0609352 | + | 0.00259916i | ||||
\(919\) | −37.5628 | −1.23908 | −0.619541 | − | 0.784964i | \(-0.712681\pi\) | ||||
−0.619541 | + | 0.784964i | \(0.712681\pi\) | |||||||
\(920\) | 0.567926 | − | 0.983677i | 0.0187240 | − | 0.0324309i | ||||
\(921\) | −22.4571 | + | 19.3941i | −0.739986 | + | 0.639058i | ||||
\(922\) | 22.5921 | + | 39.1307i | 0.744032 | + | 1.28870i | ||||
\(923\) | 4.69834 | + | 43.3690i | 0.154648 | + | 1.42751i | ||||
\(924\) | −22.0397 | + | 4.20995i | −0.725054 | + | 0.138497i | ||||
\(925\) | −4.67336 | − | 2.69816i | −0.153659 | − | 0.0887151i | ||||
\(926\) | −29.1480 | −0.957862 | ||||||||
\(927\) | −48.0520 | + | 19.0526i | −1.57823 | + | 0.625769i | ||||
\(928\) | − | 0.0297553i | − | 0.000976766i | ||||||
\(929\) | 15.6563 | + | 9.03915i | 0.513666 | + | 0.296565i | 0.734339 | − | 0.678783i | \(-0.237492\pi\) |
−0.220674 | + | 0.975348i | \(0.570826\pi\) | |||||||
\(930\) | 4.90566 | + | 1.70697i | 0.160863 | + | 0.0559739i | ||||
\(931\) | −2.70411 | + | 1.56122i | −0.0886238 | + | 0.0511670i | ||||
\(932\) | −21.6439 | − | 37.4884i | −0.708970 | − | 1.22797i | ||||
\(933\) | 2.22050 | − | 6.38147i | 0.0726957 | − | 0.208920i | ||||
\(934\) | −51.7498 | − | 29.8778i | −1.69331 | − | 0.977630i | ||||
\(935\) | −0.331464 | −0.0108400 | ||||||||
\(936\) | 1.94429 | + | 0.0743091i | 0.0635512 | + | 0.00242887i | ||||
\(937\) | −22.7662 | −0.743741 | −0.371870 | − | 0.928285i | \(-0.621283\pi\) | ||||
−0.371870 | + | 0.928285i | \(0.621283\pi\) | |||||||
\(938\) | 73.7331 | + | 42.5698i | 2.40747 | + | 1.38995i | ||||
\(939\) | −19.6703 | + | 3.75735i | −0.641917 | + | 0.122617i | ||||
\(940\) | −8.66745 | − | 15.0125i | −0.282701 | − | 0.489653i | ||||
\(941\) | −17.5655 | + | 10.1414i | −0.572619 | + | 0.330602i | −0.758195 | − | 0.652028i | \(-0.773918\pi\) |
0.185576 | + | 0.982630i | \(0.440585\pi\) | |||||||
\(942\) | −22.4359 | + | 19.3758i | −0.731002 | + | 0.631299i | ||||
\(943\) | 9.68220 | + | 5.59002i | 0.315296 | + | 0.182036i | ||||
\(944\) | − | 18.3324i | − | 0.596667i | ||||||
\(945\) | 16.1487 | − | 10.2651i | 0.525318 | − | 0.333923i | ||||
\(946\) | −8.02136 | −0.260797 | ||||||||
\(947\) | −1.68376 | − | 0.972120i | −0.0547149 | − | 0.0315896i | 0.472393 | − | 0.881388i | \(-0.343390\pi\) |
−0.527108 | + | 0.849798i | \(0.676724\pi\) | |||||||
\(948\) | 23.4629 | + | 27.1685i | 0.762041 | + | 0.882392i | ||||
\(949\) | 1.67379 | + | 15.4502i | 0.0543335 | + | 0.501536i | ||||
\(950\) | −0.470451 | − | 0.814844i | −0.0152634 | − | 0.0264370i | ||||
\(951\) | 3.80391 | + | 19.9141i | 0.123350 | + | 0.645758i | ||||
\(952\) | 0.0595763 | − | 0.103189i | 0.00193088 | − | 0.00334438i | ||||
\(953\) | 50.6834 | 1.64180 | 0.820898 | − | 0.571075i | \(-0.193474\pi\) | ||||
0.820898 | + | 0.571075i | \(0.193474\pi\) | |||||||
\(954\) | −33.4600 | + | 42.2589i | −1.08331 | + | 1.36818i | ||||
\(955\) | 0.600472i | 0.0194308i | ||||||||
\(956\) | 42.6195 | + | 24.6064i | 1.37841 | + | 0.795828i | ||||
\(957\) | 0.0113653 | + | 0.00395467i | 0.000367388 | + | 0.000127836i | ||||
\(958\) | 13.2871 | + | 23.0140i | 0.429288 | + | 0.743549i | ||||
\(959\) | −13.1742 | − | 22.8184i | −0.425417 | − | 0.736843i | ||||
\(960\) | 11.8703 | + | 4.13038i | 0.383112 | + | 0.133308i | ||||
\(961\) | −14.3497 | + | 24.8544i | −0.462894 | + | 0.801755i | ||||
\(962\) | 15.5342 | − | 35.1924i | 0.500842 | − | 1.13465i | ||||
\(963\) | 3.66987 | − | 24.9375i | 0.118260 | − | 0.803601i | ||||
\(964\) | − | 11.3405i | − | 0.365252i | ||||||
\(965\) | −0.449902 | + | 0.779254i | −0.0144829 | + | 0.0250851i | ||||
\(966\) | 78.2165 | − | 14.9406i | 2.51657 | − | 0.480706i | ||||
\(967\) | −19.0701 | + | 11.0101i | −0.613253 | + | 0.354062i | −0.774237 | − | 0.632895i | \(-0.781866\pi\) |
0.160985 | + | 0.986957i | \(0.448533\pi\) | |||||||
\(968\) | 1.18460 | − | 0.683930i | 0.0380745 | − | 0.0219823i | ||||
\(969\) | 0.112212 | − | 0.0969073i | 0.00360477 | − | 0.00311311i | ||||
\(970\) | 18.8630 | + | 10.8906i | 0.605655 | + | 0.349675i | ||||
\(971\) | −12.2478 | −0.393050 | −0.196525 | − | 0.980499i | \(-0.562966\pi\) | ||||
−0.196525 | + | 0.980499i | \(0.562966\pi\) | |||||||
\(972\) | −17.4620 | + | 24.0968i | −0.560093 | + | 0.772906i | ||||
\(973\) | − | 60.7997i | − | 1.94915i | ||||||
\(974\) | 14.3994 | − | 24.9405i | 0.461386 | − | 0.799144i | ||||
\(975\) | 5.97221 | − | 1.82556i | 0.191264 | − | 0.0584647i | ||||
\(976\) | −12.6890 | − | 21.9779i | −0.406164 | − | 0.703497i | ||||
\(977\) | 6.16072 | − | 3.55689i | 0.197099 | − | 0.113795i | −0.398203 | − | 0.917297i | \(-0.630366\pi\) |
0.595302 | + | 0.803502i | \(0.297033\pi\) | |||||||
\(978\) | −11.1035 | + | 2.12095i | −0.355051 | + | 0.0678205i | ||||
\(979\) | −1.90328 | + | 3.29659i | −0.0608292 | + | 0.105359i | ||||
\(980\) | − | 12.5255i | − | 0.400112i | ||||||
\(981\) | −50.6924 | − | 7.46002i | −1.61848 | − | 0.238180i | ||||
\(982\) | − | 74.0225i | − | 2.36215i | ||||||
\(983\) | −40.8515 | − | 23.5856i | −1.30296 | − | 0.752264i | −0.322049 | − | 0.946723i | \(-0.604371\pi\) |
−0.980911 | + | 0.194459i | \(0.937705\pi\) | |||||||
\(984\) | 0.181286 | − | 0.520998i | 0.00577920 | − | 0.0166088i | ||||
\(985\) | −0.681336 | − | 1.18011i | −0.0217092 | − | 0.0376014i | ||||
\(986\) | 0.00116119 | 0.000670413i | 3.69798e−5 | 2.13503e-5i | ||||||
\(987\) | −19.0341 | + | 54.7020i | −0.605863 | + | 1.74119i | ||||
\(988\) | 2.64386 | − | 1.93381i | 0.0841124 | − | 0.0615226i | ||||
\(989\) | 13.9022 | 0.442063 | ||||||||
\(990\) | −6.78496 | + | 8.56918i | −0.215640 | + | 0.272347i | ||||
\(991\) | −4.32831 | −0.137493 | −0.0687467 | − | 0.997634i | \(-0.521900\pi\) | ||||
−0.0687467 | + | 0.997634i | \(0.521900\pi\) | |||||||
\(992\) | 5.98529 | − | 10.3668i | 0.190033 | − | 0.329147i | ||||
\(993\) | 5.58883 | + | 29.2584i | 0.177356 | + | 0.928489i | ||||
\(994\) | 76.2879 | − | 44.0448i | 2.41970 | − | 1.39702i | ||||
\(995\) | −21.7761 | + | 12.5724i | −0.690348 | + | 0.398572i | ||||
\(996\) | 43.8349 | − | 37.8561i | 1.38896 | − | 1.19952i | ||||
\(997\) | 5.02697 | − | 8.70698i | 0.159206 | − | 0.275753i | −0.775377 | − | 0.631499i | \(-0.782440\pi\) |
0.934583 | + | 0.355746i | \(0.115773\pi\) | |||||||
\(998\) | −70.4426 | −2.22982 | ||||||||
\(999\) | −15.0422 | − | 23.6639i | −0.475914 | − | 0.748694i |
(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 | 585.2.bt.b.376.9 | ✓ | 108 | |
9.4 | even | 3 | inner | 585.2.bt.b.571.46 | yes | 108 | |
13.12 | even | 2 | inner | 585.2.bt.b.376.46 | yes | 108 | |
117.103 | even | 6 | inner | 585.2.bt.b.571.9 | yes | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.bt.b.376.9 | ✓ | 108 | 1.1 | even | 1 | trivial | |
585.2.bt.b.376.46 | yes | 108 | 13.12 | even | 2 | inner | |
585.2.bt.b.571.9 | yes | 108 | 117.103 | even | 6 | inner | |
585.2.bt.b.571.46 | yes | 108 | 9.4 | even | 3 | inner |