Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(263,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.263");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.g (of order \(3\), degree \(2\), 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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 263.4 | ||
Root | \(1.37054 - 2.37385i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.263 |
Dual form | 637.2.g.j.373.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37054 | − | 2.37385i | 0.969119 | − | 1.67856i | 0.271003 | − | 0.962579i | \(-0.412645\pi\) |
0.698116 | − | 0.715984i | \(-0.254022\pi\) | |||||||
\(3\) | −1.36482 | −0.787979 | −0.393989 | − | 0.919115i | \(-0.628905\pi\) | ||||
−0.393989 | + | 0.919115i | \(0.628905\pi\) | |||||||
\(4\) | −2.75677 | − | 4.77486i | −1.37838 | − | 2.38743i | ||||
\(5\) | 0.370541 | + | 0.641796i | 0.165711 | + | 0.287020i | 0.936908 | − | 0.349577i | \(-0.113675\pi\) |
−0.771197 | + | 0.636597i | \(0.780341\pi\) | |||||||
\(6\) | −1.87054 | + | 3.23987i | −0.763645 | + | 1.32267i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −9.63087 | −3.40503 | ||||||||
\(9\) | −1.13727 | −0.379089 | ||||||||
\(10\) | 2.03137 | 0.642374 | ||||||||
\(11\) | −1.36482 | −0.411509 | −0.205754 | − | 0.978604i | \(-0.565965\pi\) | ||||
−0.205754 | + | 0.978604i | \(0.565965\pi\) | |||||||
\(12\) | 3.76249 | + | 6.51682i | 1.08614 | + | 1.88124i | ||||
\(13\) | −0.301907 | + | 3.59289i | −0.0837339 | + | 0.996488i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.505722 | − | 0.875935i | −0.130577 | − | 0.226166i | ||||
\(16\) | −7.68598 | + | 13.3125i | −1.92149 | + | 3.32813i | ||||
\(17\) | −2.07436 | − | 3.59289i | −0.503105 | − | 0.871404i | −0.999994 | − | 0.00358919i | \(-0.998858\pi\) |
0.496888 | − | 0.867814i | \(-0.334476\pi\) | |||||||
\(18\) | −1.55867 | + | 2.69970i | −0.367383 | + | 0.636325i | ||||
\(19\) | −7.26606 | −1.66695 | −0.833474 | − | 0.552559i | \(-0.813651\pi\) | ||||
−0.833474 | + | 0.552559i | \(0.813651\pi\) | |||||||
\(20\) | 2.04299 | − | 3.53856i | 0.456826 | − | 0.791246i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.87054 | + | 3.23987i | −0.398801 | + | 0.690743i | ||||
\(23\) | 1.16673 | − | 2.02083i | 0.243279 | − | 0.421372i | −0.718367 | − | 0.695664i | \(-0.755110\pi\) |
0.961646 | + | 0.274292i | \(0.0884435\pi\) | |||||||
\(24\) | 13.1444 | 2.68309 | ||||||||
\(25\) | 2.22540 | − | 3.85450i | 0.445080 | − | 0.770901i | ||||
\(26\) | 8.11519 | + | 5.64088i | 1.59152 | + | 1.10627i | ||||
\(27\) | 5.64662 | 1.08669 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.203815 | + | 0.353017i | 0.0378474 | + | 0.0655536i | 0.884329 | − | 0.466865i | \(-0.154617\pi\) |
−0.846481 | + | 0.532419i | \(0.821283\pi\) | |||||||
\(30\) | −2.77245 | −0.506178 | ||||||||
\(31\) | −1.38622 | + | 2.40101i | −0.248973 | + | 0.431234i | −0.963241 | − | 0.268638i | \(-0.913426\pi\) |
0.714268 | + | 0.699872i | \(0.246760\pi\) | |||||||
\(32\) | 11.4370 | + | 19.8095i | 2.02180 | + | 3.50186i | ||||
\(33\) | 1.86273 | 0.324260 | ||||||||
\(34\) | −11.3720 | −1.95027 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.13518 | + | 5.43029i | 0.522530 | + | 0.905049i | ||||
\(37\) | 3.05295 | − | 5.28787i | 0.501902 | − | 0.869320i | −0.498096 | − | 0.867122i | \(-0.665967\pi\) |
0.999998 | − | 0.00219764i | \(-0.000699531\pi\) | |||||||
\(38\) | −9.95843 | + | 17.2485i | −1.61547 | + | 2.79808i | ||||
\(39\) | 0.412049 | − | 4.90364i | 0.0659806 | − | 0.785212i | ||||
\(40\) | −3.56863 | − | 6.18106i | −0.564251 | − | 0.977311i | ||||
\(41\) | 0.627306 | + | 1.08653i | 0.0979688 | + | 0.169687i | 0.910844 | − | 0.412751i | \(-0.135432\pi\) |
−0.812875 | + | 0.582438i | \(0.802099\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.870541 | − | 1.50782i | 0.132756 | − | 0.229941i | −0.791982 | − | 0.610545i | \(-0.790951\pi\) |
0.924738 | + | 0.380604i | \(0.124284\pi\) | |||||||
\(44\) | 3.76249 | + | 6.51682i | 0.567216 | + | 0.982447i | ||||
\(45\) | −0.421404 | − | 0.729894i | −0.0628193 | − | 0.108806i | ||||
\(46\) | −3.19809 | − | 5.53926i | −0.471533 | − | 0.816719i | ||||
\(47\) | −2.92921 | − | 5.07355i | −0.427270 | − | 0.740053i | 0.569360 | − | 0.822089i | \(-0.307191\pi\) |
−0.996629 | + | 0.0820357i | \(0.973858\pi\) | |||||||
\(48\) | 10.4900 | − | 18.1692i | 1.51410 | − | 2.62249i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.10000 | − | 10.5655i | −0.862670 | − | 1.49419i | ||||
\(51\) | 2.83112 | + | 4.90364i | 0.396436 | + | 0.686648i | ||||
\(52\) | 17.9878 | − | 8.46319i | 2.49446 | − | 1.17363i | ||||
\(53\) | −2.28389 | + | 3.95582i | −0.313717 | + | 0.543373i | −0.979164 | − | 0.203072i | \(-0.934908\pi\) |
0.665447 | + | 0.746445i | \(0.268241\pi\) | |||||||
\(54\) | 7.73893 | − | 13.4042i | 1.05313 | − | 1.82408i | ||||
\(55\) | −0.505722 | − | 0.875935i | −0.0681915 | − | 0.118111i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.91685 | 1.31352 | ||||||||
\(58\) | 1.11734 | 0.146715 | ||||||||
\(59\) | −5.49213 | − | 9.51264i | −0.715014 | − | 1.23844i | −0.962954 | − | 0.269665i | \(-0.913087\pi\) |
0.247940 | − | 0.968775i | \(-0.420246\pi\) | |||||||
\(60\) | −2.78831 | + | 4.82950i | −0.359969 | + | 0.623485i | ||||
\(61\) | −6.52497 | −0.835437 | −0.417719 | − | 0.908576i | \(-0.637170\pi\) | ||||
−0.417719 | + | 0.908576i | \(0.637170\pi\) | |||||||
\(62\) | 3.79975 | + | 6.58137i | 0.482569 | + | 0.835834i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 31.9557 | 3.99446 | ||||||||
\(65\) | −2.41777 | + | 1.13755i | −0.299887 | + | 0.141096i | ||||
\(66\) | 2.55295 | − | 4.42184i | 0.314247 | − | 0.544291i | ||||
\(67\) | −13.7597 | −1.68101 | −0.840505 | − | 0.541804i | \(-0.817742\pi\) | ||||
−0.840505 | + | 0.541804i | \(0.817742\pi\) | |||||||
\(68\) | −11.4370 | + | 19.8095i | −1.38694 | + | 2.40226i | ||||
\(69\) | −1.59237 | + | 2.75807i | −0.191699 | + | 0.332032i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.40763 | − | 4.17014i | 0.285733 | − | 0.494904i | −0.687054 | − | 0.726607i | \(-0.741096\pi\) |
0.972787 | + | 0.231703i | \(0.0744296\pi\) | |||||||
\(72\) | 10.9529 | 1.29081 | ||||||||
\(73\) | 3.03494 | − | 5.25666i | 0.355212 | − | 0.615246i | −0.631942 | − | 0.775016i | \(-0.717742\pi\) |
0.987154 | + | 0.159770i | \(0.0510752\pi\) | |||||||
\(74\) | −8.36839 | − | 14.4945i | −0.972805 | − | 1.68495i | ||||
\(75\) | −3.03727 | + | 5.26070i | −0.350713 | + | 0.607453i | ||||
\(76\) | 20.0308 | + | 34.6944i | 2.29769 | + | 3.97972i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11.0758 | − | 7.69879i | −1.25408 | − | 0.871716i | ||||
\(79\) | 4.56291 | + | 7.90320i | 0.513368 | + | 0.889179i | 0.999880 | + | 0.0155052i | \(0.00493564\pi\) |
−0.486512 | + | 0.873674i | \(0.661731\pi\) | |||||||
\(80\) | −11.3919 | −1.27365 | ||||||||
\(81\) | −4.29482 | −0.477202 | ||||||||
\(82\) | 3.43900 | 0.379774 | ||||||||
\(83\) | −11.7368 | −1.28828 | −0.644139 | − | 0.764908i | \(-0.722784\pi\) | ||||
−0.644139 | + | 0.764908i | \(0.722784\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.53727 | − | 2.66263i | 0.166740 | − | 0.288802i | ||||
\(86\) | −2.38622 | − | 4.13306i | −0.257313 | − | 0.445679i | ||||
\(87\) | −0.278170 | − | 0.481805i | −0.0298230 | − | 0.0516549i | ||||
\(88\) | 13.1444 | 1.40120 | ||||||||
\(89\) | −0.880503 | + | 1.52508i | −0.0933331 | + | 0.161658i | −0.908912 | − | 0.416989i | \(-0.863085\pi\) |
0.815579 | + | 0.578646i | \(0.196419\pi\) | |||||||
\(90\) | −2.31021 | −0.243517 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.8656 | −1.34133 | ||||||||
\(93\) | 1.89195 | − | 3.27695i | 0.196186 | − | 0.339803i | ||||
\(94\) | −16.0584 | −1.65630 | ||||||||
\(95\) | −2.69237 | − | 4.66332i | −0.276231 | − | 0.478447i | ||||
\(96\) | −15.6095 | − | 27.0364i | −1.59313 | − | 2.75939i | ||||
\(97\) | 4.76691 | − | 8.25652i | 0.484006 | − | 0.838323i | −0.515825 | − | 0.856694i | \(-0.672515\pi\) |
0.999831 | + | 0.0183708i | \(0.00584795\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.55217 | 0.155998 | ||||||||
\(100\) | −24.5396 | −2.45396 | ||||||||
\(101\) | 7.49361 | 0.745642 | 0.372821 | − | 0.927903i | \(-0.378391\pi\) | ||||
0.372821 | + | 0.927903i | \(0.378391\pi\) | |||||||
\(102\) | 15.5207 | 1.53678 | ||||||||
\(103\) | 1.40424 | + | 2.43221i | 0.138364 | + | 0.239653i | 0.926877 | − | 0.375364i | \(-0.122482\pi\) |
−0.788514 | + | 0.615017i | \(0.789149\pi\) | |||||||
\(104\) | 2.90763 | − | 34.6027i | 0.285116 | − | 3.39307i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.26033 | + | 10.8432i | 0.608057 | + | 1.05319i | ||||
\(107\) | −0.743235 | + | 1.28732i | −0.0718512 | + | 0.124450i | −0.899713 | − | 0.436483i | \(-0.856224\pi\) |
0.827861 | + | 0.560933i | \(0.189557\pi\) | |||||||
\(108\) | −15.5664 | − | 26.9618i | −1.49788 | − | 2.59440i | ||||
\(109\) | −1.43561 | + | 2.48654i | −0.137506 | + | 0.238168i | −0.926552 | − | 0.376167i | \(-0.877242\pi\) |
0.789046 | + | 0.614334i | \(0.210575\pi\) | |||||||
\(110\) | −2.77245 | −0.264343 | ||||||||
\(111\) | −4.16673 | + | 7.21698i | −0.395488 | + | 0.685006i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.20972 | − | 10.7555i | 0.584161 | − | 1.01180i | −0.410819 | − | 0.911717i | \(-0.634757\pi\) |
0.994979 | − | 0.100079i | \(-0.0319096\pi\) | |||||||
\(114\) | 13.5915 | − | 23.5411i | 1.27296 | − | 2.20483i | ||||
\(115\) | 1.72928 | 0.161256 | ||||||||
\(116\) | 1.12374 | − | 1.94637i | 0.104336 | − | 0.180716i | ||||
\(117\) | 0.343349 | − | 4.08608i | 0.0317426 | − | 0.377758i | ||||
\(118\) | −30.1087 | −2.77173 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 4.87054 | + | 8.43602i | 0.444618 | + | 0.770100i | ||||
\(121\) | −9.13727 | −0.830661 | ||||||||
\(122\) | −8.94274 | + | 15.4893i | −0.809638 | + | 1.40233i | ||||
\(123\) | −0.856160 | − | 1.48291i | −0.0771973 | − | 0.133710i | ||||
\(124\) | 15.2860 | 1.37272 | ||||||||
\(125\) | 7.00382 | 0.626440 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.71526 | − | 4.70296i | −0.240940 | − | 0.417321i | 0.720042 | − | 0.693930i | \(-0.244122\pi\) |
−0.960982 | + | 0.276610i | \(0.910789\pi\) | |||||||
\(128\) | 20.9226 | − | 36.2390i | 1.84931 | − | 3.20310i | ||||
\(129\) | −1.18813 | + | 2.05790i | −0.104609 | + | 0.181188i | ||||
\(130\) | −0.613284 | + | 7.29847i | −0.0537886 | + | 0.640119i | ||||
\(131\) | −5.66100 | − | 9.80515i | −0.494604 | − | 0.856680i | 0.505376 | − | 0.862899i | \(-0.331354\pi\) |
−0.999981 | + | 0.00621925i | \(0.998020\pi\) | |||||||
\(132\) | −5.13512 | − | 8.89428i | −0.446954 | − | 0.774148i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −18.8582 | + | 32.6633i | −1.62910 | + | 2.82168i | ||||
\(135\) | 2.09231 | + | 3.62398i | 0.180077 | + | 0.311902i | ||||
\(136\) | 19.9779 | + | 34.6027i | 1.71309 | + | 2.96715i | ||||
\(137\) | 6.98771 | + | 12.1031i | 0.597000 | + | 1.03403i | 0.993261 | + | 0.115897i | \(0.0369741\pi\) |
−0.396261 | + | 0.918138i | \(0.629693\pi\) | |||||||
\(138\) | 4.36482 | + | 7.56009i | 0.371558 | + | 0.643558i | ||||
\(139\) | 5.21544 | − | 9.03340i | 0.442368 | − | 0.766203i | −0.555497 | − | 0.831518i | \(-0.687472\pi\) |
0.997865 | + | 0.0653153i | \(0.0208053\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.99785 | + | 6.92447i | 0.336679 | + | 0.583146i | ||||
\(142\) | −6.59951 | − | 11.4307i | −0.553818 | − | 0.959242i | ||||
\(143\) | 0.412049 | − | 4.90364i | 0.0344572 | − | 0.410063i | ||||
\(144\) | 8.74102 | − | 15.1399i | 0.728418 | − | 1.26166i | ||||
\(145\) | −0.151043 | + | 0.261615i | −0.0125435 | + | 0.0217259i | ||||
\(146\) | −8.31901 | − | 14.4089i | −0.688486 | − | 1.19249i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −33.6651 | −2.76725 | ||||||||
\(149\) | 8.16433 | 0.668848 | 0.334424 | − | 0.942423i | \(-0.391458\pi\) | ||||
0.334424 | + | 0.942423i | \(0.391458\pi\) | |||||||
\(150\) | 8.32540 | + | 14.4200i | 0.679766 | + | 1.17739i | ||||
\(151\) | 1.23094 | − | 2.13205i | 0.100173 | − | 0.173504i | −0.811583 | − | 0.584237i | \(-0.801394\pi\) |
0.911756 | + | 0.410733i | \(0.134727\pi\) | |||||||
\(152\) | 69.9785 | 5.67600 | ||||||||
\(153\) | 2.35910 | + | 4.08608i | 0.190722 | + | 0.330340i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.05461 | −0.165030 | ||||||||
\(156\) | −24.5501 | + | 11.5507i | −1.96558 | + | 0.924798i | ||||
\(157\) | −6.45991 | + | 11.1889i | −0.515557 | + | 0.892971i | 0.484280 | + | 0.874913i | \(0.339082\pi\) |
−0.999837 | + | 0.0180576i | \(0.994252\pi\) | |||||||
\(158\) | 25.0146 | 1.99006 | ||||||||
\(159\) | 3.11710 | − | 5.39897i | 0.247202 | − | 0.428167i | ||||
\(160\) | −8.47577 | + | 14.6805i | −0.670069 | + | 1.16059i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −5.88622 | + | 10.1952i | −0.462465 | + | 0.801014i | ||||
\(163\) | −6.02742 | −0.472104 | −0.236052 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236052 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(164\) | 3.45867 | − | 5.99060i | 0.270077 | − | 0.467787i | ||||
\(165\) | 0.690219 | + | 1.19549i | 0.0537334 | + | 0.0930691i | ||||
\(166\) | −16.0857 | + | 27.8613i | −1.24850 | + | 2.16246i | ||||
\(167\) | 3.82558 | + | 6.62610i | 0.296032 | + | 0.512743i | 0.975224 | − | 0.221218i | \(-0.0710031\pi\) |
−0.679192 | + | 0.733960i | \(0.737670\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8177 | − | 2.16944i | −0.985977 | − | 0.166880i | ||||
\(170\) | −4.21378 | − | 7.29847i | −0.323182 | − | 0.559767i | ||||
\(171\) | 8.26345 | 0.631922 | ||||||||
\(172\) | −9.59951 | −0.731956 | ||||||||
\(173\) | 0.164460 | 0.0125036 | 0.00625182 | − | 0.999980i | \(-0.498010\pi\) | ||||
0.00625182 | + | 0.999980i | \(0.498010\pi\) | |||||||
\(174\) | −1.52497 | −0.115608 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.4900 | − | 18.1692i | 0.790711 | − | 1.36955i | ||||
\(177\) | 7.49576 | + | 12.9830i | 0.563416 | + | 0.975865i | ||||
\(178\) | 2.41353 | + | 4.18036i | 0.180902 | + | 0.313331i | ||||
\(179\) | 0.768633 | 0.0574503 | 0.0287252 | − | 0.999587i | \(-0.490855\pi\) | ||||
0.0287252 | + | 0.999587i | \(0.490855\pi\) | |||||||
\(180\) | −2.32343 | + | 4.02429i | −0.173178 | + | 0.299953i | ||||
\(181\) | 9.92152 | 0.737461 | 0.368730 | − | 0.929536i | \(-0.379793\pi\) | ||||
0.368730 | + | 0.929536i | \(0.379793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.90541 | 0.658307 | ||||||||
\(184\) | −11.2366 | + | 19.4624i | −0.828373 | + | 1.43478i | ||||
\(185\) | 4.52497 | 0.332683 | ||||||||
\(186\) | −5.18598 | − | 8.98238i | −0.380254 | − | 0.658620i | ||||
\(187\) | 2.83112 | + | 4.90364i | 0.207032 | + | 0.358590i | ||||
\(188\) | −16.1503 | + | 27.9732i | −1.17788 | + | 2.04015i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.7600 | −1.07080 | ||||||||
\(191\) | 9.89693 | 0.716117 | 0.358058 | − | 0.933699i | \(-0.383439\pi\) | ||||
0.358058 | + | 0.933699i | \(0.383439\pi\) | |||||||
\(192\) | −43.6138 | −3.14755 | ||||||||
\(193\) | 8.70075 | 0.626293 | 0.313147 | − | 0.949705i | \(-0.398617\pi\) | ||||
0.313147 | + | 0.949705i | \(0.398617\pi\) | |||||||
\(194\) | −13.0665 | − | 22.6318i | −0.938119 | − | 1.62487i | ||||
\(195\) | 3.29982 | − | 1.55255i | 0.236305 | − | 0.111180i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.0093 | + | 22.5328i | 0.926874 | + | 1.60539i | 0.788520 | + | 0.615009i | \(0.210848\pi\) |
0.138354 | + | 0.990383i | \(0.455819\pi\) | |||||||
\(198\) | 2.12731 | − | 3.68460i | 0.151181 | − | 0.261853i | ||||
\(199\) | 5.06648 | + | 8.77540i | 0.359153 | + | 0.622072i | 0.987820 | − | 0.155603i | \(-0.0497322\pi\) |
−0.628666 | + | 0.777675i | \(0.716399\pi\) | |||||||
\(200\) | −21.4325 | + | 37.1222i | −1.51551 | + | 2.62494i | ||||
\(201\) | 18.7795 | 1.32460 | ||||||||
\(202\) | 10.2703 | − | 17.7887i | 0.722615 | − | 1.25161i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 15.6095 | − | 27.0364i | 1.09288 | − | 1.89293i | ||||
\(205\) | −0.464885 | + | 0.805205i | −0.0324690 | + | 0.0562380i | ||||
\(206\) | 7.69827 | 0.536364 | ||||||||
\(207\) | −1.32688 | + | 2.29822i | −0.0922246 | + | 0.159738i | ||||
\(208\) | −45.5099 | − | 31.6340i | −3.15554 | − | 2.19342i | ||||
\(209\) | 9.91685 | 0.685963 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.33911 | − | 14.4438i | −0.574088 | − | 0.994349i | −0.996140 | − | 0.0877779i | \(-0.972023\pi\) |
0.422052 | − | 0.906572i | \(-0.361310\pi\) | |||||||
\(212\) | 25.1846 | 1.72969 | ||||||||
\(213\) | −3.28598 | + | 5.69148i | −0.225152 | + | 0.389974i | ||||
\(214\) | 2.03727 | + | 3.52865i | 0.139265 | + | 0.241214i | ||||
\(215\) | 1.29028 | 0.0879967 | ||||||||
\(216\) | −54.3819 | −3.70022 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.93511 | + | 6.81582i | 0.266520 | + | 0.461625i | ||||
\(219\) | −4.14214 | + | 7.17439i | −0.279900 | + | 0.484801i | ||||
\(220\) | −2.78831 | + | 4.82950i | −0.187988 | + | 0.325605i | ||||
\(221\) | 13.5351 | − | 6.36821i | 0.910470 | − | 0.428372i | ||||
\(222\) | 11.4213 | + | 19.7823i | 0.766550 | + | 1.32770i | ||||
\(223\) | 0.535180 | + | 0.926959i | 0.0358383 | + | 0.0620738i | 0.883388 | − | 0.468642i | \(-0.155257\pi\) |
−0.847550 | + | 0.530716i | \(0.821923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.53087 | + | 4.38360i | −0.168725 | + | 0.292240i | ||||
\(226\) | −17.0213 | − | 29.4818i | −1.13224 | − | 1.96110i | ||||
\(227\) | −12.2332 | − | 21.1885i | −0.811947 | − | 1.40633i | −0.911500 | − | 0.411300i | \(-0.865075\pi\) |
0.0995534 | − | 0.995032i | \(-0.468259\pi\) | |||||||
\(228\) | −27.3384 | − | 47.3516i | −1.81053 | − | 3.13593i | ||||
\(229\) | 2.36482 | + | 4.09599i | 0.156272 | + | 0.270670i | 0.933521 | − | 0.358522i | \(-0.116719\pi\) |
−0.777250 | + | 0.629192i | \(0.783386\pi\) | |||||||
\(230\) | 2.37005 | − | 4.10505i | 0.156276 | − | 0.270679i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.96291 | − | 3.39986i | −0.128871 | − | 0.223212i | ||||
\(233\) | −10.2753 | − | 17.7974i | −0.673160 | − | 1.16595i | −0.977003 | − | 0.213226i | \(-0.931603\pi\) |
0.303843 | − | 0.952722i | \(-0.401730\pi\) | |||||||
\(234\) | −9.22915 | − | 6.41519i | −0.603328 | − | 0.419374i | ||||
\(235\) | 2.17079 | − | 3.75991i | 0.141607 | − | 0.245270i | ||||
\(236\) | −30.2810 | + | 52.4482i | −1.97113 | + | 3.41409i | ||||
\(237\) | −6.22755 | − | 10.7864i | −0.404523 | − | 0.700654i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.25461 | 0.404577 | 0.202289 | − | 0.979326i | \(-0.435162\pi\) | ||||
0.202289 | + | 0.979326i | \(0.435162\pi\) | |||||||
\(240\) | 15.5479 | 1.00361 | ||||||||
\(241\) | −6.07220 | − | 10.5174i | −0.391145 | − | 0.677483i | 0.601456 | − | 0.798906i | \(-0.294588\pi\) |
−0.992601 | + | 0.121423i | \(0.961254\pi\) | |||||||
\(242\) | −12.5230 | + | 21.6905i | −0.805009 | + | 1.39432i | ||||
\(243\) | −11.0782 | −0.710668 | ||||||||
\(244\) | 17.9878 | + | 31.1558i | 1.15155 | + | 1.99455i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.69361 | −0.299254 | ||||||||
\(247\) | 2.19367 | − | 26.1061i | 0.139580 | − | 1.66109i | ||||
\(248\) | 13.3506 | − | 23.1238i | 0.847761 | − | 1.46836i | ||||
\(249\) | 16.0186 | 1.01514 | ||||||||
\(250\) | 9.59902 | − | 16.6260i | 0.607095 | − | 1.05152i | ||||
\(251\) | −3.15719 | + | 5.46842i | −0.199280 | + | 0.345163i | −0.948295 | − | 0.317390i | \(-0.897194\pi\) |
0.749015 | + | 0.662553i | \(0.230527\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.59237 | + | 2.75807i | −0.100112 | + | 0.173398i | ||||
\(254\) | −14.8855 | −0.933999 | ||||||||
\(255\) | −2.09809 | + | 3.63400i | −0.131388 | + | 0.227570i | ||||
\(256\) | −25.3948 | − | 43.9850i | −1.58717 | − | 2.74907i | ||||
\(257\) | 12.1781 | − | 21.0931i | 0.759649 | − | 1.31575i | −0.183380 | − | 0.983042i | \(-0.558704\pi\) |
0.943030 | − | 0.332709i | \(-0.107963\pi\) | |||||||
\(258\) | 3.25677 | + | 5.64088i | 0.202757 | + | 0.351186i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 12.0969 | + | 8.40855i | 0.750216 | + | 0.521476i | ||||
\(261\) | −0.231792 | − | 0.401475i | −0.0143475 | − | 0.0248507i | ||||
\(262\) | −31.0346 | −1.91732 | ||||||||
\(263\) | −9.57910 | −0.590672 | −0.295336 | − | 0.955393i | \(-0.595432\pi\) | ||||
−0.295336 | + | 0.955393i | \(0.595432\pi\) | |||||||
\(264\) | −17.9397 | −1.10411 | ||||||||
\(265\) | −3.38510 | −0.207945 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.20173 | − | 2.08145i | 0.0735445 | − | 0.127383i | ||||
\(268\) | 37.9322 | + | 65.7004i | 2.31708 | + | 4.01329i | ||||
\(269\) | 14.6995 | + | 25.4603i | 0.896245 | + | 1.55234i | 0.832256 | + | 0.554391i | \(0.187049\pi\) |
0.0639886 | + | 0.997951i | \(0.479618\pi\) | |||||||
\(270\) | 11.4704 | 0.698064 | ||||||||
\(271\) | −0.150192 | + | 0.260141i | −0.00912354 | + | 0.0158024i | −0.870551 | − | 0.492078i | \(-0.836237\pi\) |
0.861428 | + | 0.507880i | \(0.169571\pi\) | |||||||
\(272\) | 63.7738 | 3.86686 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 38.3078 | 2.31426 | ||||||||
\(275\) | −3.03727 | + | 5.26070i | −0.183154 | + | 0.317232i | ||||
\(276\) | 17.5592 | 1.05694 | ||||||||
\(277\) | 16.3855 | + | 28.3805i | 0.984509 | + | 1.70522i | 0.644100 | + | 0.764941i | \(0.277232\pi\) |
0.340408 | + | 0.940278i | \(0.389435\pi\) | |||||||
\(278\) | −14.2959 | − | 24.7613i | −0.857414 | − | 1.48508i | ||||
\(279\) | 1.57651 | − | 2.73059i | 0.0943831 | − | 0.163476i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.29482 | 0.256207 | 0.128104 | − | 0.991761i | \(-0.459111\pi\) | ||||
0.128104 | + | 0.991761i | \(0.459111\pi\) | |||||||
\(282\) | 21.9169 | 1.30513 | ||||||||
\(283\) | 21.1003 | 1.25428 | 0.627140 | − | 0.778907i | \(-0.284225\pi\) | ||||
0.627140 | + | 0.778907i | \(0.284225\pi\) | |||||||
\(284\) | −26.5491 | −1.57540 | ||||||||
\(285\) | 3.67460 | + | 6.36460i | 0.217665 | + | 0.377006i | ||||
\(286\) | −11.0758 | − | 7.69879i | −0.654924 | − | 0.455239i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −13.0070 | − | 22.5287i | −0.766442 | − | 1.32752i | ||||
\(289\) | −0.105901 | + | 0.183427i | −0.00622950 | + | 0.0107898i | ||||
\(290\) | 0.414022 | + | 0.717107i | 0.0243122 | + | 0.0421100i | ||||
\(291\) | −6.50597 | + | 11.2687i | −0.381387 | + | 0.660581i | ||||
\(292\) | −33.4664 | −1.95847 | ||||||||
\(293\) | 8.88192 | − | 15.3839i | 0.518887 | − | 0.898739i | −0.480872 | − | 0.876791i | \(-0.659680\pi\) |
0.999759 | − | 0.0219482i | \(-0.00698688\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.07012 | − | 7.04965i | 0.236971 | − | 0.410446i | ||||
\(296\) | −29.4026 | + | 50.9268i | −1.70899 | + | 2.96006i | ||||
\(297\) | −7.70662 | −0.447184 | ||||||||
\(298\) | 11.1895 | − | 19.3809i | 0.648193 | − | 1.12270i | ||||
\(299\) | 6.90837 | + | 4.80202i | 0.399522 | + | 0.277708i | ||||
\(300\) | 33.4921 | 1.93367 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.37411 | − | 5.84413i | −0.194158 | − | 0.336292i | ||||
\(303\) | −10.2274 | −0.587550 | ||||||||
\(304\) | 55.8467 | − | 96.7294i | 3.20303 | − | 5.54781i | ||||
\(305\) | −2.41777 | − | 4.18770i | −0.138441 | − | 0.239787i | ||||
\(306\) | 12.9330 | 0.739328 | ||||||||
\(307\) | −18.0156 | −1.02821 | −0.514103 | − | 0.857729i | \(-0.671875\pi\) | ||||
−0.514103 | + | 0.857729i | \(0.671875\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.91653 | − | 3.31953i | −0.109028 | − | 0.188842i | ||||
\(310\) | −2.81593 | + | 4.87733i | −0.159934 | + | 0.277014i | ||||
\(311\) | 8.62724 | − | 14.9428i | 0.489206 | − | 0.847330i | −0.510717 | − | 0.859749i | \(-0.670620\pi\) |
0.999923 | + | 0.0124194i | \(0.00395331\pi\) | |||||||
\(312\) | −3.96839 | + | 47.2264i | −0.224666 | + | 2.67367i | ||||
\(313\) | 3.40763 | + | 5.90219i | 0.192611 | + | 0.333611i | 0.946115 | − | 0.323832i | \(-0.104971\pi\) |
−0.753504 | + | 0.657443i | \(0.771638\pi\) | |||||||
\(314\) | 17.7071 | + | 30.6697i | 0.999272 | + | 1.73079i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.1578 | − | 43.5745i | 1.41523 | − | 2.45126i | ||||
\(317\) | 12.5385 | + | 21.7173i | 0.704233 | + | 1.21977i | 0.966968 | + | 0.254899i | \(0.0820421\pi\) |
−0.262735 | + | 0.964868i | \(0.584625\pi\) | |||||||
\(318\) | −8.54423 | − | 14.7990i | −0.479136 | − | 0.829889i | ||||
\(319\) | −0.278170 | − | 0.481805i | −0.0155745 | − | 0.0269759i | ||||
\(320\) | 11.8409 | + | 20.5090i | 0.661927 | + | 1.14649i | ||||
\(321\) | 1.01438 | − | 1.75696i | 0.0566172 | − | 0.0980639i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.0724 | + | 26.1061i | 0.838650 | + | 1.45258i | ||||
\(324\) | 11.8398 | + | 20.5071i | 0.657767 | + | 1.13929i | ||||
\(325\) | 13.1769 | + | 9.15931i | 0.730925 | + | 0.508067i | ||||
\(326\) | −8.26083 | + | 14.3082i | −0.457525 | + | 0.792456i | ||||
\(327\) | 1.95934 | − | 3.39368i | 0.108352 | − | 0.187671i | ||||
\(328\) | −6.04151 | − | 10.4642i | −0.333586 | − | 0.577789i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3.78389 | 0.208296 | ||||||||
\(331\) | −2.99534 | −0.164639 | −0.0823193 | − | 0.996606i | \(-0.526233\pi\) | ||||
−0.0823193 | + | 0.996606i | \(0.526233\pi\) | |||||||
\(332\) | 32.3555 | + | 56.0414i | 1.77574 | + | 3.07567i | ||||
\(333\) | −3.47202 | + | 6.01372i | −0.190266 | + | 0.329550i | ||||
\(334\) | 20.9724 | 1.14756 | ||||||||
\(335\) | −5.09852 | − | 8.83089i | −0.278562 | − | 0.482483i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.4888 | −1.60636 | −0.803179 | − | 0.595738i | \(-0.796860\pi\) | ||||
−0.803179 | + | 0.595738i | \(0.796860\pi\) | |||||||
\(338\) | −22.7171 | + | 27.4540i | −1.23565 | + | 1.49330i | ||||
\(339\) | −8.47514 | + | 14.6794i | −0.460306 | + | 0.797274i | ||||
\(340\) | −16.9515 | −0.919326 | ||||||||
\(341\) | 1.89195 | − | 3.27695i | 0.102455 | − | 0.177457i | ||||
\(342\) | 11.3254 | − | 19.6162i | 0.612407 | − | 1.06072i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.38407 | + | 14.5216i | −0.452039 | + | 0.782954i | ||||
\(345\) | −2.36015 | −0.127066 | ||||||||
\(346\) | 0.225399 | − | 0.390402i | 0.0121175 | − | 0.0209881i | ||||
\(347\) | 2.99343 | + | 5.18477i | 0.160696 | + | 0.278333i | 0.935118 | − | 0.354336i | \(-0.115293\pi\) |
−0.774423 | + | 0.632668i | \(0.781960\pi\) | |||||||
\(348\) | −1.53370 | + | 2.65644i | −0.0822149 | + | 0.142400i | ||||
\(349\) | −15.1681 | − | 26.2719i | −0.811929 | − | 1.40630i | −0.911513 | − | 0.411272i | \(-0.865085\pi\) |
0.0995840 | − | 0.995029i | \(-0.468249\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.70476 | + | 20.2877i | −0.0909931 | + | 1.08288i | ||||
\(352\) | −15.6095 | − | 27.0364i | −0.831988 | − | 1.44104i | ||||
\(353\) | 28.6063 | 1.52256 | 0.761280 | − | 0.648424i | \(-0.224572\pi\) | ||||
0.761280 | + | 0.648424i | \(0.224572\pi\) | |||||||
\(354\) | 41.0930 | 2.18407 | ||||||||
\(355\) | 3.56850 | 0.189396 | ||||||||
\(356\) | 9.70936 | 0.514595 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.05344 | − | 1.82462i | 0.0556762 | − | 0.0964340i | ||||
\(359\) | −11.7309 | − | 20.3185i | −0.619132 | − | 1.07237i | −0.989644 | − | 0.143540i | \(-0.954151\pi\) |
0.370513 | − | 0.928827i | \(-0.379182\pi\) | |||||||
\(360\) | 4.05849 | + | 7.02952i | 0.213901 | + | 0.370488i | ||||
\(361\) | 33.7956 | 1.77871 | ||||||||
\(362\) | 13.5978 | − | 23.5522i | 0.714687 | − | 1.23787i | ||||
\(363\) | 12.4707 | 0.654543 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.49827 | 0.235450 | ||||||||
\(366\) | 12.2052 | − | 21.1401i | 0.637978 | − | 1.10501i | ||||
\(367\) | −36.5197 | −1.90631 | −0.953156 | − | 0.302479i | \(-0.902186\pi\) | ||||
−0.953156 | + | 0.302479i | \(0.902186\pi\) | |||||||
\(368\) | 17.9349 | + | 31.0641i | 0.934920 | + | 1.61933i | ||||
\(369\) | −0.713415 | − | 1.23567i | −0.0371389 | − | 0.0643265i | ||||
\(370\) | 6.20166 | − | 10.7416i | 0.322409 | − | 0.558429i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −20.8626 | −1.08168 | ||||||||
\(373\) | −13.0498 | −0.675694 | −0.337847 | − | 0.941201i | \(-0.609699\pi\) | ||||
−0.337847 | + | 0.941201i | \(0.609699\pi\) | |||||||
\(374\) | 15.5207 | 0.802555 | ||||||||
\(375\) | −9.55894 | −0.493622 | ||||||||
\(376\) | 28.2109 | + | 48.8627i | 1.45487 | + | 2.51990i | ||||
\(377\) | −1.32988 | + | 0.625705i | −0.0684925 | + | 0.0322254i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3018 | − | 26.5036i | −0.786003 | − | 1.36140i | −0.928398 | − | 0.371587i | \(-0.878814\pi\) |
0.142395 | − | 0.989810i | \(-0.454520\pi\) | |||||||
\(380\) | −14.8445 | + | 25.7114i | −0.761505 | + | 1.31897i | ||||
\(381\) | 3.70584 | + | 6.41870i | 0.189856 | + | 0.328840i | ||||
\(382\) | 13.5641 | − | 23.4938i | 0.694002 | − | 1.20205i | ||||
\(383\) | 4.88598 | 0.249662 | 0.124831 | − | 0.992178i | \(-0.460161\pi\) | ||||
0.124831 | + | 0.992178i | \(0.460161\pi\) | |||||||
\(384\) | −28.5555 | + | 49.4596i | −1.45722 | + | 2.52398i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.9247 | − | 20.6542i | 0.606953 | − | 1.05127i | ||||
\(387\) | −0.990038 | + | 1.71480i | −0.0503265 | + | 0.0871680i | ||||
\(388\) | −52.5650 | −2.66858 | ||||||||
\(389\) | 0.927126 | − | 1.60583i | 0.0470072 | − | 0.0814188i | −0.841564 | − | 0.540157i | \(-0.818365\pi\) |
0.888572 | + | 0.458738i | \(0.151698\pi\) | |||||||
\(390\) | 0.837022 | − | 9.96110i | 0.0423842 | − | 0.504400i | ||||
\(391\) | −9.68082 | −0.489580 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.72625 | + | 13.3823i | 0.389738 | + | 0.675046i | ||||
\(394\) | 71.3191 | 3.59300 | ||||||||
\(395\) | −3.38149 | + | 5.85692i | −0.170141 | + | 0.294693i | ||||
\(396\) | −4.27896 | − | 7.41137i | −0.215026 | − | 0.372435i | ||||
\(397\) | −21.5134 | −1.07973 | −0.539863 | − | 0.841753i | \(-0.681524\pi\) | ||||
−0.539863 | + | 0.841753i | \(0.681524\pi\) | |||||||
\(398\) | 27.7753 | 1.39225 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 34.2087 | + | 59.2513i | 1.71044 | + | 2.96256i | ||||
\(401\) | 7.28266 | − | 12.6139i | 0.363678 | − | 0.629910i | −0.624885 | − | 0.780717i | \(-0.714854\pi\) |
0.988563 | + | 0.150808i | \(0.0481874\pi\) | |||||||
\(402\) | 25.7380 | − | 44.5795i | 1.28370 | − | 2.22343i | ||||
\(403\) | −8.20805 | − | 5.70543i | −0.408872 | − | 0.284208i | ||||
\(404\) | −20.6581 | − | 35.7809i | −1.02778 | − | 1.78017i | ||||
\(405\) | −1.59141 | − | 2.75640i | −0.0790776 | − | 0.136966i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.16673 | + | 7.21698i | −0.206537 | + | 0.357733i | ||||
\(408\) | −27.2662 | − | 47.2264i | −1.34988 | − | 2.33805i | ||||
\(409\) | −11.0645 | − | 19.1643i | −0.547105 | − | 0.947613i | −0.998471 | − | 0.0552745i | \(-0.982397\pi\) |
0.451366 | − | 0.892339i | \(-0.350937\pi\) | |||||||
\(410\) | 1.27429 | + | 2.20713i | 0.0629326 | + | 0.109003i | ||||
\(411\) | −9.53696 | − | 16.5185i | −0.470423 | − | 0.814797i | ||||
\(412\) | 7.74232 | − | 13.4101i | 0.381437 | − | 0.660668i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.63709 | + | 6.29962i | 0.178753 | + | 0.309610i | ||||
\(415\) | −4.34896 | − | 7.53261i | −0.213482 | − | 0.369761i | ||||
\(416\) | −74.6263 | + | 35.1113i | −3.65885 | + | 1.72147i | ||||
\(417\) | −7.11813 | + | 12.3290i | −0.348576 | + | 0.603752i | ||||
\(418\) | 13.5915 | − | 23.5411i | 0.664780 | − | 1.15143i | ||||
\(419\) | 1.68795 | + | 2.92362i | 0.0824618 | + | 0.142828i | 0.904307 | − | 0.426883i | \(-0.140388\pi\) |
−0.821845 | + | 0.569711i | \(0.807055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.1101 | −1.22379 | −0.611895 | − | 0.790939i | \(-0.709593\pi\) | ||||
−0.611895 | + | 0.790939i | \(0.709593\pi\) | |||||||
\(422\) | −45.7164 | −2.22544 | ||||||||
\(423\) | 3.33130 | + | 5.76998i | 0.161973 | + | 0.280546i | ||||
\(424\) | 21.9959 | − | 38.0980i | 1.06821 | − | 1.85020i | ||||
\(425\) | −18.4651 | −0.895688 | ||||||||
\(426\) | 9.00714 | + | 15.6008i | 0.436397 | + | 0.755862i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 8.19570 | 0.396154 | ||||||||
\(429\) | −0.562372 | + | 6.69259i | −0.0271516 | + | 0.323121i | ||||
\(430\) | 1.76839 | − | 3.06294i | 0.0852792 | − | 0.147708i | ||||
\(431\) | 10.7948 | 0.519969 | 0.259985 | − | 0.965613i | \(-0.416282\pi\) | ||||
0.259985 | + | 0.965613i | \(0.416282\pi\) | |||||||
\(432\) | −43.3998 | + | 75.1707i | −2.08808 | + | 3.61665i | ||||
\(433\) | −7.25910 | + | 12.5731i | −0.348850 | + | 0.604226i | −0.986045 | − | 0.166476i | \(-0.946761\pi\) |
0.637195 | + | 0.770702i | \(0.280094\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.206147 | − | 0.357057i | 0.00988398 | − | 0.0171196i | ||||
\(436\) | 15.8305 | 0.758144 | ||||||||
\(437\) | −8.47750 | + | 14.6835i | −0.405534 | + | 0.702405i | ||||
\(438\) | 11.3539 | + | 19.6656i | 0.542512 | + | 0.939659i | ||||
\(439\) | −7.21544 | + | 12.4975i | −0.344374 | + | 0.596473i | −0.985240 | − | 0.171180i | \(-0.945242\pi\) |
0.640866 | + | 0.767653i | \(0.278575\pi\) | |||||||
\(440\) | 4.87054 | + | 8.43602i | 0.232194 | + | 0.402172i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.43327 | − | 40.8582i | 0.163304 | − | 1.94343i | ||||
\(443\) | 15.1215 | + | 26.1912i | 0.718445 | + | 1.24438i | 0.961616 | + | 0.274400i | \(0.0884792\pi\) |
−0.243171 | + | 0.969984i | \(0.578187\pi\) | |||||||
\(444\) | 45.9467 | 2.18054 | ||||||||
\(445\) | −1.30505 | −0.0618653 | ||||||||
\(446\) | 2.93395 | 0.138926 | ||||||||
\(447\) | −11.1428 | −0.527038 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.6380 | + | 27.0858i | −0.738003 | + | 1.27826i | 0.215390 | + | 0.976528i | \(0.430898\pi\) |
−0.953393 | + | 0.301731i | \(0.902435\pi\) | |||||||
\(450\) | 6.93733 | + | 12.0158i | 0.327029 | + | 0.566431i | ||||
\(451\) | −0.856160 | − | 1.48291i | −0.0403150 | − | 0.0698276i | ||||
\(452\) | −68.4749 | −3.22079 | ||||||||
\(453\) | −1.68001 | + | 2.90987i | −0.0789338 | + | 0.136717i | ||||
\(454\) | −67.0645 | −3.14749 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −95.5080 | −4.47257 | ||||||||
\(457\) | −10.3233 | + | 17.8805i | −0.482904 | + | 0.836415i | −0.999807 | − | 0.0196293i | \(-0.993751\pi\) |
0.516903 | + | 0.856044i | \(0.327085\pi\) | |||||||
\(458\) | 12.9643 | 0.605783 | ||||||||
\(459\) | −11.7131 | − | 20.2877i | −0.546721 | − | 0.946948i | ||||
\(460\) | −4.76722 | − | 8.25707i | −0.222273 | − | 0.384988i | ||||
\(461\) | 13.6480 | − | 23.6391i | 0.635653 | − | 1.10098i | −0.350724 | − | 0.936479i | \(-0.614064\pi\) |
0.986376 | − | 0.164504i | \(-0.0526022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.65977 | 0.263032 | 0.131516 | − | 0.991314i | \(-0.458016\pi\) | ||||
0.131516 | + | 0.991314i | \(0.458016\pi\) | |||||||
\(464\) | −6.26606 | −0.290894 | ||||||||
\(465\) | 2.80417 | 0.130040 | ||||||||
\(466\) | −56.3311 | −2.60949 | ||||||||
\(467\) | 21.1073 | + | 36.5588i | 0.976727 | + | 1.69174i | 0.674114 | + | 0.738628i | \(0.264526\pi\) |
0.302614 | + | 0.953113i | \(0.402141\pi\) | |||||||
\(468\) | −20.4570 | + | 9.62491i | −0.945624 | + | 0.444912i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.95031 | − | 10.3062i | −0.274467 | − | 0.475391i | ||||
\(471\) | 8.81661 | − | 15.2708i | 0.406248 | − | 0.703642i | ||||
\(472\) | 52.8940 | + | 91.6151i | 2.43464 | + | 4.21692i | ||||
\(473\) | −1.18813 | + | 2.05790i | −0.0546303 | + | 0.0946225i | ||||
\(474\) | −34.1405 | −1.56812 | ||||||||
\(475\) | −16.1699 | + | 28.0070i | −0.741925 | + | 1.28505i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.59740 | − | 4.49882i | 0.118927 | − | 0.205987i | ||||
\(478\) | 8.57220 | − | 14.8475i | 0.392083 | − | 0.679108i | ||||
\(479\) | −32.5316 | −1.48641 | −0.743204 | − | 0.669065i | \(-0.766695\pi\) | ||||
−0.743204 | + | 0.669065i | \(0.766695\pi\) | |||||||
\(480\) | 11.5679 | − | 20.0362i | 0.528000 | − | 0.914523i | ||||
\(481\) | 18.0770 | + | 12.5654i | 0.824241 | + | 0.572931i | ||||
\(482\) | −33.2888 | −1.51626 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 25.1893 | + | 43.6292i | 1.14497 | + | 1.98314i | ||||
\(485\) | 7.06534 | 0.320820 | ||||||||
\(486\) | −15.1832 | + | 26.2980i | −0.688722 | + | 1.19290i | ||||
\(487\) | −13.4291 | − | 23.2600i | −0.608533 | − | 1.05401i | −0.991482 | − | 0.130240i | \(-0.958425\pi\) |
0.382950 | − | 0.923769i | \(-0.374908\pi\) | |||||||
\(488\) | 62.8412 | 2.84469 | ||||||||
\(489\) | 8.22634 | 0.372008 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.8439 | − | 37.8348i | −0.985802 | − | 1.70746i | −0.638317 | − | 0.769774i | \(-0.720369\pi\) |
−0.347485 | − | 0.937685i | \(-0.612964\pi\) | |||||||
\(492\) | −4.72046 | + | 8.17608i | −0.212815 | + | 0.368606i | ||||
\(493\) | 0.845567 | − | 1.46457i | 0.0380824 | − | 0.0659607i | ||||
\(494\) | −58.9654 | − | 40.9870i | −2.65298 | − | 1.84409i | ||||
\(495\) | 0.575141 | + | 0.996173i | 0.0258507 | + | 0.0447747i | ||||
\(496\) | −21.3090 | − | 36.9082i | −0.956801 | − | 1.65723i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 21.9541 | − | 38.0257i | 0.983788 | − | 1.70397i | ||||
\(499\) | 9.05098 | + | 15.6768i | 0.405177 | + | 0.701788i | 0.994342 | − | 0.106225i | \(-0.0338764\pi\) |
−0.589165 | + | 0.808013i | \(0.700543\pi\) | |||||||
\(500\) | −19.3079 | − | 33.4422i | −0.863474 | − | 1.49558i | ||||
\(501\) | −5.22122 | − | 9.04343i | −0.233267 | − | 0.404030i | ||||
\(502\) | 8.65412 | + | 14.9894i | 0.386252 | + | 0.669009i | ||||
\(503\) | −14.2077 | + | 24.6085i | −0.633492 | + | 1.09724i | 0.353341 | + | 0.935495i | \(0.385046\pi\) |
−0.986833 | + | 0.161745i | \(0.948288\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.77669 | + | 4.80937i | 0.123561 | + | 0.214014i | ||||
\(506\) | 4.36482 | + | 7.56009i | 0.194040 | + | 0.336087i | ||||
\(507\) | 17.4939 | + | 2.96089i | 0.776929 | + | 0.131498i | ||||
\(508\) | −14.9707 | + | 25.9299i | −0.664215 | + | 1.15045i | ||||
\(509\) | 8.73956 | − | 15.1374i | 0.387374 | − | 0.670952i | −0.604721 | − | 0.796437i | \(-0.706715\pi\) |
0.992095 | + | 0.125485i | \(0.0400488\pi\) | |||||||
\(510\) | 5.75104 | + | 9.96110i | 0.254660 | + | 0.441085i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −55.5280 | −2.45402 | ||||||||
\(513\) | −41.0287 | −1.81146 | ||||||||
\(514\) | −33.3812 | − | 57.8179i | −1.47238 | − | 2.55024i | ||||
\(515\) | −1.04066 | + | 1.80247i | −0.0458568 | + | 0.0794263i | ||||
\(516\) | 13.1016 | 0.576766 | ||||||||
\(517\) | 3.99785 | + | 6.92447i | 0.175825 | + | 0.304538i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.224458 | −0.00985260 | ||||||||
\(520\) | 23.2852 | − | 10.9556i | 1.02113 | − | 0.480435i | ||||
\(521\) | 9.65437 | − | 16.7219i | 0.422966 | − | 0.732598i | −0.573263 | − | 0.819372i | \(-0.694322\pi\) |
0.996228 | + | 0.0867740i | \(0.0276558\pi\) | |||||||
\(522\) | −1.27072 | −0.0556179 | ||||||||
\(523\) | −5.01144 | + | 8.68007i | −0.219135 | + | 0.379553i | −0.954544 | − | 0.298071i | \(-0.903657\pi\) |
0.735409 | + | 0.677624i | \(0.236990\pi\) | |||||||
\(524\) | −31.2121 | + | 54.0610i | −1.36351 | + | 2.36167i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.1285 | + | 22.7393i | −0.572432 | + | 0.991481i | ||||
\(527\) | 11.5021 | 0.501039 | ||||||||
\(528\) | −14.3169 | + | 24.7976i | −0.623064 | + | 1.07918i | ||||
\(529\) | 8.77750 | + | 15.2031i | 0.381630 | + | 0.661003i | ||||
\(530\) | −4.63942 | + | 8.03571i | −0.201524 | + | 0.349049i | ||||
\(531\) | 6.24602 | + | 10.8184i | 0.271054 | + | 0.469479i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.09316 | + | 1.92581i | −0.177294 | + | 0.0834162i | ||||
\(534\) | −3.29403 | − | 5.70543i | −0.142547 | − | 0.246898i | ||||
\(535\) | −1.10160 | −0.0476261 | ||||||||
\(536\) | 132.518 | 5.72389 | ||||||||
\(537\) | −1.04904 | −0.0452696 | ||||||||
\(538\) | 80.5851 | 3.47427 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 11.5360 | − | 19.9809i | 0.496430 | − | 0.859842i | ||||
\(541\) | −8.80763 | − | 15.2553i | −0.378670 | − | 0.655875i | 0.612199 | − | 0.790703i | \(-0.290285\pi\) |
−0.990869 | + | 0.134829i | \(0.956952\pi\) | |||||||
\(542\) | 0.411690 | + | 0.713067i | 0.0176836 | + | 0.0306289i | ||||
\(543\) | −13.5411 | −0.581103 | ||||||||
\(544\) | 47.4489 | − | 82.1839i | 2.03435 | − | 3.52361i | ||||
\(545\) | −2.12780 | −0.0911451 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.98425 | 0.127597 | 0.0637987 | − | 0.997963i | \(-0.479678\pi\) | ||||
0.0637987 | + | 0.997963i | \(0.479678\pi\) | |||||||
\(548\) | 38.5269 | − | 66.7306i | 1.64579 | − | 2.85059i | ||||
\(549\) | 7.42064 | 0.316705 | ||||||||
\(550\) | 8.32540 | + | 14.4200i | 0.354996 | + | 0.614871i | ||||
\(551\) | −1.48093 | − | 2.56504i | −0.0630896 | − | 0.109274i | ||||
\(552\) | 15.3359 | − | 26.5626i | 0.652740 | − | 1.13058i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 89.8279 | 3.81642 | ||||||||
\(555\) | −6.17577 | −0.262147 | ||||||||
\(556\) | −57.5109 | −2.43901 | ||||||||
\(557\) | 7.25596 | 0.307445 | 0.153722 | − | 0.988114i | \(-0.450874\pi\) | ||||
0.153722 | + | 0.988114i | \(0.450874\pi\) | |||||||
\(558\) | −4.32134 | − | 7.48478i | −0.182937 | − | 0.316856i | ||||
\(559\) | 5.15461 | + | 3.58298i | 0.218017 | + | 0.151544i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.86397 | − | 6.69259i | −0.163137 | − | 0.282561i | ||||
\(562\) | 5.88622 | − | 10.1952i | 0.248295 | − | 0.430060i | ||||
\(563\) | 2.13967 | + | 3.70601i | 0.0901762 | + | 0.156190i | 0.907585 | − | 0.419868i | \(-0.137924\pi\) |
−0.817409 | + | 0.576058i | \(0.804590\pi\) | |||||||
\(564\) | 22.0423 | − | 38.1783i | 0.928146 | − | 1.60760i | ||||
\(565\) | 9.20382 | 0.387207 | ||||||||
\(566\) | 28.9188 | − | 50.0888i | 1.21555 | − | 2.10539i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −23.1876 | + | 40.1621i | −0.972929 | + | 1.68516i | ||||
\(569\) | 9.88131 | − | 17.1149i | 0.414246 | − | 0.717495i | −0.581103 | − | 0.813830i | \(-0.697379\pi\) |
0.995349 | + | 0.0963347i | \(0.0307119\pi\) | |||||||
\(570\) | 20.1448 | 0.843771 | ||||||||
\(571\) | 9.96182 | − | 17.2544i | 0.416889 | − | 0.722073i | −0.578736 | − | 0.815515i | \(-0.696454\pi\) |
0.995625 | + | 0.0934422i | \(0.0297870\pi\) | |||||||
\(572\) | −24.5501 | + | 11.5507i | −1.02649 | + | 0.482960i | ||||
\(573\) | −13.5075 | −0.564285 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.19286 | − | 8.99430i | −0.216557 | − | 0.375088i | ||||
\(576\) | −36.3422 | −1.51426 | ||||||||
\(577\) | −14.3650 | + | 24.8809i | −0.598023 | + | 1.03581i | 0.395090 | + | 0.918642i | \(0.370713\pi\) |
−0.993113 | + | 0.117163i | \(0.962620\pi\) | |||||||
\(578\) | 0.290284 | + | 0.502787i | 0.0120742 | + | 0.0209132i | ||||
\(579\) | −11.8749 | −0.493506 | ||||||||
\(580\) | 1.66556 | 0.0691587 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.8334 | + | 30.8883i | 0.739218 | + | 1.28036i | ||||
\(583\) | 3.11710 | − | 5.39897i | 0.129097 | − | 0.223603i | ||||
\(584\) | −29.2291 | + | 50.6263i | −1.20951 | + | 2.09493i | ||||
\(585\) | 2.74965 | − | 1.29370i | 0.113684 | − | 0.0534879i | ||||
\(586\) | −24.3461 | − | 42.1686i | −1.00573 | − | 1.74197i | ||||
\(587\) | 15.7694 | + | 27.3134i | 0.650872 | + | 1.12734i | 0.982912 | + | 0.184078i | \(0.0589299\pi\) |
−0.332040 | + | 0.943265i | \(0.607737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0724 | − | 17.4459i | 0.415025 | − | 0.718845i | ||||
\(590\) | −11.1565 | − | 19.3237i | −0.459307 | − | 0.795542i | ||||
\(591\) | −17.7553 | − | 30.7531i | −0.730357 | − | 1.26502i | ||||
\(592\) | 46.9298 | + | 81.2848i | 1.92880 | + | 3.34079i | ||||
\(593\) | −5.55903 | − | 9.62852i | −0.228282 | − | 0.395396i | 0.729017 | − | 0.684496i | \(-0.239977\pi\) |
−0.957299 | + | 0.289099i | \(0.906644\pi\) | |||||||
\(594\) | −10.5622 | + | 18.2943i | −0.433374 | + | 0.750626i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.5071 | − | 38.9835i | −0.921928 | − | 1.59683i | ||||
\(597\) | −6.91483 | − | 11.9768i | −0.283005 | − | 0.490179i | ||||
\(598\) | 20.8675 | − | 9.81805i | 0.853334 | − | 0.401490i | ||||
\(599\) | 3.64786 | − | 6.31828i | 0.149048 | − | 0.258158i | −0.781828 | − | 0.623494i | \(-0.785713\pi\) |
0.930876 | + | 0.365336i | \(0.119046\pi\) | |||||||
\(600\) | 29.2515 | − | 50.6652i | 1.19419 | − | 2.06840i | ||||
\(601\) | −0.586291 | − | 1.01548i | −0.0239153 | − | 0.0414225i | 0.853820 | − | 0.520568i | \(-0.174280\pi\) |
−0.877735 | + | 0.479146i | \(0.840947\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.6484 | 0.637253 | ||||||||
\(604\) | −13.5737 | −0.552304 | ||||||||
\(605\) | −3.38573 | − | 5.86426i | −0.137650 | − | 0.238416i | ||||
\(606\) | −14.0171 | + | 24.2783i | −0.569406 | + | 0.986240i | ||||
\(607\) | −0.633838 | −0.0257267 | −0.0128633 | − | 0.999917i | \(-0.504095\pi\) | ||||
−0.0128633 | + | 0.999917i | \(0.504095\pi\) | |||||||
\(608\) | −83.1020 | − | 143.937i | −3.37023 | − | 5.83741i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.2546 | −0.536664 | ||||||||
\(611\) | 19.1130 | − | 8.99260i | 0.773231 | − | 0.363802i | ||||
\(612\) | 13.0070 | − | 22.5287i | 0.525775 | − | 0.910669i | ||||
\(613\) | −30.8550 | −1.24622 | −0.623110 | − | 0.782134i | \(-0.714131\pi\) | ||||
−0.623110 | + | 0.782134i | \(0.714131\pi\) | |||||||
\(614\) | −24.6911 | + | 42.7663i | −0.996453 | + | 1.72591i | ||||
\(615\) | 0.634485 | − | 1.09896i | 0.0255849 | − | 0.0443143i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.9105 | + | 29.2898i | −0.680790 | + | 1.17916i | 0.293951 | + | 0.955821i | \(0.405030\pi\) |
−0.974740 | + | 0.223341i | \(0.928304\pi\) | |||||||
\(618\) | −10.5068 | −0.422644 | ||||||||
\(619\) | −0.202399 | + | 0.350565i | −0.00813509 | + | 0.0140904i | −0.870064 | − | 0.492938i | \(-0.835923\pi\) |
0.861929 | + | 0.507029i | \(0.169256\pi\) | |||||||
\(620\) | 5.66408 | + | 9.81048i | 0.227475 | + | 0.393998i | ||||
\(621\) | 6.58807 | − | 11.4109i | 0.264370 | − | 0.457902i | ||||
\(622\) | −23.6480 | − | 40.9595i | −0.948197 | − | 1.64233i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 62.1128 | + | 43.1747i | 2.48650 | + | 1.72837i | ||||
\(625\) | −8.53179 | − | 14.7775i | −0.341272 | − | 0.591100i | ||||
\(626\) | 18.6812 | 0.746650 | ||||||||
\(627\) | −13.5347 | −0.540524 | ||||||||
\(628\) | 71.2338 | 2.84254 | ||||||||
\(629\) | −25.3316 | −1.01004 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.2254 | + | 26.3712i | −0.606114 | + | 1.04982i | 0.385761 | + | 0.922599i | \(0.373939\pi\) |
−0.991874 | + | 0.127221i | \(0.959394\pi\) | |||||||
\(632\) | −43.9448 | − | 76.1147i | −1.74803 | − | 3.02768i | ||||
\(633\) | 11.3814 | + | 19.7131i | 0.452369 | + | 0.783526i | ||||
\(634\) | 68.7381 | 2.72994 | ||||||||
\(635\) | 2.01223 | − | 3.48528i | 0.0798529 | − | 0.138309i | ||||
\(636\) | −34.3724 | −1.36296 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.52497 | −0.0603743 | ||||||||
\(639\) | −2.73812 | + | 4.74256i | −0.108318 | + | 0.187613i | ||||
\(640\) | 31.0107 | 1.22581 | ||||||||
\(641\) | −4.82282 | − | 8.35337i | −0.190490 | − | 0.329938i | 0.754923 | − | 0.655814i | \(-0.227674\pi\) |
−0.945413 | + | 0.325875i | \(0.894341\pi\) | |||||||
\(642\) | −2.78050 | − | 4.81597i | −0.109738 | − | 0.190071i | ||||
\(643\) | 4.06648 | − | 7.04335i | 0.160366 | − | 0.277763i | −0.774634 | − | 0.632410i | \(-0.782066\pi\) |
0.935000 | + | 0.354647i | \(0.115399\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.76101 | −0.0693395 | ||||||||
\(646\) | 82.6293 | 3.25101 | ||||||||
\(647\) | 11.5227 | 0.453005 | 0.226503 | − | 0.974011i | \(-0.427271\pi\) | ||||
0.226503 | + | 0.974011i | \(0.427271\pi\) | |||||||
\(648\) | 41.3629 | 1.62489 | ||||||||
\(649\) | 7.49576 | + | 12.9830i | 0.294234 | + | 0.509629i | ||||
\(650\) | 39.8023 | − | 18.7268i | 1.56118 | − | 0.734526i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.6162 | + | 28.7801i | 0.650740 | + | 1.12711i | ||||
\(653\) | −21.2020 | + | 36.7229i | −0.829697 | + | 1.43708i | 0.0685797 | + | 0.997646i | \(0.478153\pi\) |
−0.898276 | + | 0.439431i | \(0.855180\pi\) | |||||||
\(654\) | −5.37072 | − | 9.30236i | −0.210012 | − | 0.363751i | ||||
\(655\) | 4.19527 | − | 7.26642i | 0.163923 | − | 0.283922i | ||||
\(656\) | −19.2858 | −0.752986 | ||||||||
\(657\) | −3.45153 | + | 5.97823i | −0.134657 | + | 0.233233i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.25044 | − | 2.16582i | 0.0487101 | − | 0.0843684i | −0.840642 | − | 0.541591i | \(-0.817822\pi\) |
0.889352 | + | 0.457222i | \(0.151156\pi\) | |||||||
\(660\) | 3.80554 | − | 6.59139i | 0.148130 | − | 0.256570i | ||||
\(661\) | −14.8394 | −0.577184 | −0.288592 | − | 0.957452i | \(-0.593187\pi\) | ||||
−0.288592 | + | 0.957452i | \(0.593187\pi\) | |||||||
\(662\) | −4.10523 | + | 7.11047i | −0.159554 | + | 0.276356i | ||||
\(663\) | −18.4730 | + | 8.69146i | −0.717431 | + | 0.337548i | ||||
\(664\) | 113.035 | 4.38663 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.51710 | + | 16.4841i | 0.368780 | + | 0.638746i | ||||
\(667\) | 0.951183 | 0.0368300 | ||||||||
\(668\) | 21.0924 | − | 36.5332i | 0.816091 | − | 1.41351i | ||||
\(669\) | −0.730424 | − | 1.26513i | −0.0282398 | − | 0.0489128i | ||||
\(670\) | −27.9509 | −1.07984 | ||||||||
\(671\) | 8.90541 | 0.343790 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.8046 | − | 34.3025i | −0.763410 | − | 1.32226i | −0.941083 | − | 0.338175i | \(-0.890190\pi\) |
0.177674 | − | 0.984089i | \(-0.443143\pi\) | |||||||
\(674\) | −40.4156 | + | 70.0019i | −1.55675 | + | 2.69637i | ||||
\(675\) | 12.5660 | − | 21.7649i | 0.483665 | − | 0.837733i | ||||
\(676\) | 24.9766 | + | 67.1833i | 0.960640 | + | 2.58397i | ||||
\(677\) | 8.51604 | + | 14.7502i | 0.327298 | + | 0.566897i | 0.981975 | − | 0.189012i | \(-0.0605285\pi\) |
−0.654677 | + | 0.755909i | \(0.727195\pi\) | |||||||
\(678\) | 23.2311 | + | 40.2374i | 0.892183 | + | 1.54531i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −14.8052 | + | 25.6434i | −0.567755 | + | 0.983380i | ||||
\(681\) | 16.6961 | + | 28.9185i | 0.639797 | + | 1.10816i | ||||
\(682\) | −5.18598 | − | 8.98238i | −0.198581 | − | 0.343953i | ||||
\(683\) | −16.4456 | − | 28.4846i | −0.629272 | − | 1.08993i | −0.987698 | − | 0.156374i | \(-0.950020\pi\) |
0.358426 | − | 0.933558i | \(-0.383314\pi\) | |||||||
\(684\) | −22.7804 | − | 39.4568i | −0.871030 | − | 1.50867i | ||||
\(685\) | −5.17846 | + | 8.96936i | −0.197859 | + | 0.342702i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.22755 | − | 5.59028i | −0.123139 | − | 0.213283i | ||||
\(688\) | 13.3819 | + | 23.1782i | 0.510181 | + | 0.883659i | ||||
\(689\) | −13.5233 | − | 9.40006i | −0.515196 | − | 0.358114i | ||||
\(690\) | −3.23469 | + | 5.60265i | −0.123143 | + | 0.213289i | ||||
\(691\) | −11.8961 | + | 20.6047i | −0.452550 | + | 0.783839i | −0.998544 | − | 0.0539500i | \(-0.982819\pi\) |
0.545994 | + | 0.837789i | \(0.316152\pi\) | |||||||
\(692\) | −0.453377 | − | 0.785272i | −0.0172348 | − | 0.0298515i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.4105 | 0.622933 | ||||||||
\(695\) | 7.73013 | 0.293221 | ||||||||
\(696\) | 2.67902 | + | 4.64020i | 0.101548 | + | 0.175886i | ||||
\(697\) | 2.60251 | − | 4.50768i | 0.0985772 | − | 0.170741i | ||||
\(698\) | −83.1539 | −3.14742 | ||||||||
\(699\) | 14.0240 | + | 24.2903i | 0.530436 | + | 0.918742i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.7796 | 1.12476 | 0.562380 | − | 0.826879i | \(-0.309886\pi\) | ||||
0.562380 | + | 0.826879i | \(0.309886\pi\) | |||||||
\(702\) | 45.8234 | + | 31.8519i | 1.72949 | + | 1.20217i | ||||
\(703\) | −22.1829 | + | 38.4219i | −0.836644 | + | 1.44911i | ||||
\(704\) | −43.6138 | −1.64376 | ||||||||
\(705\) | −2.96273 | + | 5.13160i | −0.111583 | + | 0.193267i | ||||
\(706\) | 39.2061 | − | 67.9069i | 1.47554 | − | 2.55571i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 41.3281 | − | 71.5824i | 1.55321 | − | 2.69023i | ||||
\(709\) | 11.9304 | 0.448054 | 0.224027 | − | 0.974583i | \(-0.428080\pi\) | ||||
0.224027 | + | 0.974583i | \(0.428080\pi\) | |||||||
\(710\) | 4.89078 | − | 8.47107i | 0.183548 | − | 0.317914i | ||||
\(711\) | −5.18925 | − | 8.98805i | −0.194612 | − | 0.337078i | ||||
\(712\) | 8.48001 | − | 14.6878i | 0.317802 | − | 0.550449i | ||||
\(713\) | 3.23469 | + | 5.60265i | 0.121140 | + | 0.209821i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.29982 | − | 1.55255i | 0.123406 | − | 0.0580621i | ||||
\(716\) | −2.11894 | − | 3.67011i | −0.0791885 | − | 0.137159i | ||||
\(717\) | −8.53642 | −0.318798 | ||||||||
\(718\) | −64.3106 | −2.40005 | ||||||||
\(719\) | −32.3638 | −1.20697 | −0.603484 | − | 0.797375i | \(-0.706221\pi\) | ||||
−0.603484 | + | 0.797375i | \(0.706221\pi\) | |||||||
\(720\) | 12.9556 | 0.482827 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 46.3182 | − | 80.2255i | 1.72379 | − | 2.98568i | ||||
\(723\) | 8.28746 | + | 14.3543i | 0.308214 | + | 0.533842i | ||||
\(724\) | −27.3513 | − | 47.3738i | −1.01650 | − | 1.76063i | ||||
\(725\) | 1.81427 | 0.0673805 | ||||||||
\(726\) | 17.0916 | − | 29.6036i | 0.634330 | − | 1.09869i | ||||
\(727\) | 31.4897 | 1.16789 | 0.583943 | − | 0.811794i | \(-0.301509\pi\) | ||||
0.583943 | + | 0.811794i | \(0.301509\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.0042 | 1.03719 | ||||||||
\(730\) | 6.16507 | − | 10.6782i | 0.228179 | − | 0.395218i | ||||
\(731\) | −7.22325 | −0.267161 | ||||||||
\(732\) | −24.5501 | − | 42.5221i | −0.907399 | − | 1.57166i | ||||
\(733\) | 1.33112 | + | 2.30557i | 0.0491661 | + | 0.0851581i | 0.889561 | − | 0.456816i | \(-0.151010\pi\) |
−0.840395 | + | 0.541974i | \(0.817677\pi\) | |||||||
\(734\) | −50.0517 | + | 86.6921i | −1.84744 | + | 3.19986i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 53.3755 | 1.96745 | ||||||||
\(737\) | 18.7795 | 0.691750 | ||||||||
\(738\) | −3.91106 | −0.143968 | ||||||||
\(739\) | −35.5828 | −1.30893 | −0.654467 | − | 0.756091i | \(-0.727107\pi\) | ||||
−0.654467 | + | 0.756091i | \(0.727107\pi\) | |||||||
\(740\) | −12.4743 | − | 21.6061i | −0.458564 | − | 0.794256i | ||||
\(741\) | −2.99397 | + | 35.6302i | −0.109986 | + | 1.30891i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.1203 | − | 20.9929i | −0.444650 | − | 0.770156i | 0.553378 | − | 0.832930i | \(-0.313339\pi\) |
−0.998028 | + | 0.0627740i | \(0.980005\pi\) | |||||||
\(744\) | −18.2211 | + | 31.5599i | −0.668018 | + | 1.15704i | ||||
\(745\) | 3.02522 | + | 5.23983i | 0.110835 | + | 0.191973i | ||||
\(746\) | −17.8853 | + | 30.9783i | −0.654828 | + | 1.13419i | ||||
\(747\) | 13.3479 | 0.488373 | ||||||||
\(748\) | 15.6095 | − | 27.0364i | 0.570739 | − | 0.988549i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −13.1009 | + | 22.6915i | −0.478378 | + | 0.828575i | ||||
\(751\) | 14.5705 | − | 25.2368i | 0.531684 | − | 0.920904i | −0.467632 | − | 0.883923i | \(-0.654893\pi\) |
0.999316 | − | 0.0369807i | \(-0.0117740\pi\) | |||||||
\(752\) | 90.0555 | 3.28399 | ||||||||
\(753\) | 4.30900 | − | 7.46340i | 0.157029 | − | 0.271981i | ||||
\(754\) | −0.337334 | + | 4.01449i | −0.0122850 | + | 0.146199i | ||||
\(755\) | 1.82446 | 0.0663988 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.49495 | + | 4.32138i | 0.0906805 | + | 0.157063i | 0.907798 | − | 0.419408i | \(-0.137762\pi\) |
−0.817117 | + | 0.576472i | \(0.804429\pi\) | |||||||
\(758\) | −83.8872 | −3.04692 | ||||||||
\(759\) | 2.17330 | − | 3.76426i | 0.0788858 | − | 0.136634i | ||||
\(760\) | 25.9299 | + | 44.9119i | 0.940576 | + | 1.62913i | ||||
\(761\) | 11.8372 | 0.429097 | 0.214548 | − | 0.976713i | \(-0.431172\pi\) | ||||
0.214548 | + | 0.976713i | \(0.431172\pi\) | |||||||
\(762\) | 20.3160 | 0.735971 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −27.2835 | − | 47.2564i | −0.987083 | − | 1.70968i | ||||
\(765\) | −1.74828 | + | 3.02812i | −0.0632094 | + | 0.109482i | ||||
\(766\) | 6.69643 | − | 11.5986i | 0.241952 | − | 0.419073i | ||||
\(767\) | 35.8360 | − | 16.8607i | 1.29396 | − | 0.608803i | ||||
\(768\) | 34.6593 | + | 60.0316i | 1.25066 | + | 2.16621i | ||||
\(769\) | −17.9092 | − | 31.0196i | −0.645821 | − | 1.11859i | −0.984111 | − | 0.177553i | \(-0.943182\pi\) |
0.338291 | − | 0.941042i | \(-0.390151\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.6209 | + | 28.7883i | −0.598588 | + | 1.03678i | ||||
\(772\) | −23.9859 | − | 41.5448i | −0.863272 | − | 1.49523i | ||||
\(773\) | −9.97669 | − | 17.2801i | −0.358837 | − | 0.621523i | 0.628930 | − | 0.777462i | \(-0.283493\pi\) |
−0.987767 | + | 0.155939i | \(0.950160\pi\) | |||||||
\(774\) | 2.71378 | + | 4.70040i | 0.0975447 | + | 0.168952i | ||||
\(775\) | 6.16980 | + | 10.6864i | 0.221626 | + | 0.383867i | ||||
\(776\) | −45.9095 | + | 79.5176i | −1.64805 | + | 2.85451i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.54133 | − | 4.40171i | −0.0911110 | − | 0.157809i | ||||
\(779\) | −4.55804 | − | 7.89476i | −0.163309 | − | 0.282859i | ||||
\(780\) | −16.5100 | − | 11.4762i | −0.591154 | − | 0.410912i | ||||
\(781\) | −3.28598 | + | 5.69148i | −0.117582 | + | 0.203657i | ||||
\(782\) | −13.2680 | + | 22.9808i | −0.474461 | + | 0.821791i | ||||
\(783\) | 1.15086 | + | 1.99335i | 0.0411285 | + | 0.0712367i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.57464 | −0.341734 | ||||||||
\(786\) | 42.3566 | 1.51081 | ||||||||
\(787\) | 1.39809 | + | 2.42157i | 0.0498367 | + | 0.0863196i | 0.889868 | − | 0.456219i | \(-0.150797\pi\) |
−0.840031 | + | 0.542539i | \(0.817463\pi\) | |||||||
\(788\) | 71.7271 | − | 124.235i | 2.55517 | − | 4.42569i | ||||
\(789\) | 13.0737 | 0.465437 | ||||||||
\(790\) | 9.26895 | + | 16.0543i | 0.329774 | + | 0.571186i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −14.9487 | −0.531179 | ||||||||
\(793\) | 1.96994 | − | 23.4435i | 0.0699545 | − | 0.832503i | ||||
\(794\) | −29.4850 | + | 51.0695i | −1.04638 | + | 1.81239i | ||||
\(795\) | 4.62005 | 0.163856 | ||||||||
\(796\) | 27.9342 | − | 48.3835i | 0.990101 | − | 1.71491i | ||||
\(797\) | 0.842809 | − | 1.45979i | 0.0298538 | − | 0.0517083i | −0.850712 | − | 0.525631i | \(-0.823829\pi\) |
0.880566 | + | 0.473923i | \(0.157162\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.1525 | + | 21.0487i | −0.429923 | + | 0.744649i | ||||
\(800\) | 101.808 | 3.59945 | ||||||||
\(801\) | 1.00137 | − | 1.73442i | 0.0353816 | − | 0.0612827i | ||||
\(802\) | −19.9624 | − | 34.5758i | −0.704895 | − | 1.22091i | ||||
\(803\) | −4.14214 | + | 7.17439i | −0.146173 | + | 0.253179i | ||||
\(804\) | −51.7705 | − | 89.6692i | −1.82581 | − | 3.16239i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24.7933 | + | 11.6651i | −0.873307 | + | 0.410887i | ||||
\(807\) | −20.0622 | − | 34.7487i | −0.706222 | − | 1.22321i | ||||
\(808\) | −72.1700 | −2.53893 | ||||||||
\(809\) | −43.4372 | −1.52717 | −0.763585 | − | 0.645708i | \(-0.776562\pi\) | ||||
−0.763585 | + | 0.645708i | \(0.776562\pi\) | |||||||
\(810\) | −8.72435 | −0.306542 | ||||||||
\(811\) | −5.60812 | −0.196928 | −0.0984639 | − | 0.995141i | \(-0.531393\pi\) | ||||
−0.0984639 | + | 0.995141i | \(0.531393\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.204986 | − | 0.355045i | 0.00718916 | − | 0.0124520i | ||||
\(814\) | 11.4213 | + | 19.7823i | 0.400318 | + | 0.693371i | ||||
\(815\) | −2.23341 | − | 3.86837i | −0.0782328 | − | 0.135503i | ||||
\(816\) | −87.0397 | −3.04700 | ||||||||
\(817\) | −6.32540 | + | 10.9559i | −0.221298 | + | 0.383299i | ||||
\(818\) | −60.6574 | −2.12084 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.12632 | 0.179019 | ||||||||
\(821\) | 11.9724 | − | 20.7368i | 0.417839 | − | 0.723718i | −0.577883 | − | 0.816120i | \(-0.696121\pi\) |
0.995722 | + | 0.0924014i | \(0.0294543\pi\) | |||||||
\(822\) | −52.2832 | −1.82358 | ||||||||
\(823\) | −17.7058 | − | 30.6674i | −0.617187 | − | 1.06900i | −0.989997 | − | 0.141091i | \(-0.954939\pi\) |
0.372810 | − | 0.927908i | \(-0.378394\pi\) | |||||||
\(824\) | −13.5241 | − | 23.4244i | −0.471133 | − | 0.816026i | ||||
\(825\) | 4.14532 | − | 7.17991i | 0.144322 | − | 0.249972i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.1563 | −0.561811 | −0.280905 | − | 0.959735i | \(-0.590635\pi\) | ||||
−0.280905 | + | 0.959735i | \(0.590635\pi\) | |||||||
\(828\) | 14.6316 | 0.508483 | ||||||||
\(829\) | 52.7010 | 1.83038 | 0.915190 | − | 0.403022i | \(-0.132040\pi\) | ||||
0.915190 | + | 0.403022i | \(0.132040\pi\) | |||||||
\(830\) | −23.8417 | −0.827557 | ||||||||
\(831\) | −22.3632 | − | 38.7343i | −0.775772 | − | 1.34368i | ||||
\(832\) | −9.64766 | + | 114.813i | −0.334472 | + | 3.98044i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.5114 | + | 33.7947i | 0.675624 | + | 1.17021i | ||||
\(835\) | −2.83507 | + | 4.91048i | −0.0981116 | + | 0.169934i | ||||
\(836\) | −27.3384 | − | 47.3516i | −0.945520 | − | 1.63769i | ||||
\(837\) | −7.82749 | + | 13.5576i | −0.270558 | + | 0.468619i | ||||
\(838\) | 9.25363 | 0.319661 | ||||||||
\(839\) | −11.2169 | + | 19.4283i | −0.387251 | + | 0.670738i | −0.992079 | − | 0.125618i | \(-0.959909\pi\) |
0.604828 | + | 0.796356i | \(0.293242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4169 | − | 24.9708i | 0.497135 | − | 0.861063i | ||||
\(842\) | −34.4144 | + | 59.6075i | −1.18600 | + | 2.05421i | ||||
\(843\) | −5.86165 | −0.201886 | ||||||||
\(844\) | −45.9779 | + | 79.6361i | −1.58263 | + | 2.74119i | ||||
\(845\) | −3.35715 | − | 9.03021i | −0.115489 | − | 0.310649i | ||||
\(846\) | 18.2627 | 0.627886 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −35.1079 | − | 60.8086i | −1.20561 | − | 2.08818i | ||||
\(849\) | −28.7980 | −0.988346 | ||||||||
\(850\) | −25.3071 | + | 43.8333i | −0.868028 | + | 1.50347i | ||||
\(851\) | −7.12392 | − | 12.3390i | −0.244205 | − | 0.422975i | ||||
\(852\) | 36.2347 | 1.24138 | ||||||||
\(853\) | −30.8521 | −1.05635 | −0.528177 | − | 0.849134i | \(-0.677124\pi\) | ||||
−0.528177 | + | 0.849134i | \(0.677124\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.06195 | + | 5.30345i | 0.104716 | + | 0.181374i | ||||
\(856\) | 7.15800 | − | 12.3980i | 0.244655 | − | 0.423756i | ||||
\(857\) | 13.3700 | − | 23.1575i | 0.456710 | − | 0.791045i | −0.542075 | − | 0.840330i | \(-0.682361\pi\) |
0.998785 | + | 0.0492854i | \(0.0156944\pi\) | |||||||
\(858\) | 15.1164 | + | 10.5075i | 0.516066 | + | 0.358719i | ||||
\(859\) | −2.57902 | − | 4.46699i | −0.0879950 | − | 0.152412i | 0.818669 | − | 0.574266i | \(-0.194713\pi\) |
−0.906664 | + | 0.421855i | \(0.861379\pi\) | |||||||
\(860\) | −3.55701 | − | 6.16092i | −0.121293 | − | 0.210086i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.7948 | − | 25.6253i | 0.503912 | − | 0.872801i | ||||
\(863\) | −4.08407 | − | 7.07382i | −0.139023 | − | 0.240796i | 0.788104 | − | 0.615542i | \(-0.211063\pi\) |
−0.927127 | + | 0.374747i | \(0.877730\pi\) | |||||||
\(864\) | 64.5806 | + | 111.857i | 2.19708 | + | 3.80545i | ||||
\(865\) | 0.0609391 | + | 0.105550i | 0.00207199 | + | 0.00358879i | ||||
\(866\) | 19.8978 | + | 34.4640i | 0.676154 | + | 1.17113i | ||||
\(867\) | 0.144536 | − | 0.250344i | 0.00490871 | − | 0.00850214i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.22755 | − | 10.7864i | −0.211255 | − | 0.365905i | ||||
\(870\) | −0.565065 | − | 0.978722i | −0.0191575 | − | 0.0331818i | ||||
\(871\) | 4.15414 | − | 49.4369i | 0.140758 | − | 1.67511i | ||||
\(872\) | 13.8261 | − | 23.9476i | 0.468212 | − | 0.810968i | ||||
\(873\) | −5.42125 | + | 9.38988i | −0.183481 | + | 0.317799i | ||||
\(874\) | 23.2375 | + | 40.2486i | 0.786021 | + | 1.36143i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 45.6756 | 1.54324 | ||||||||
\(877\) | 15.6184 | 0.527398 | 0.263699 | − | 0.964605i | \(-0.415058\pi\) | ||||
0.263699 | + | 0.964605i | \(0.415058\pi\) | |||||||
\(878\) | 19.7781 | + | 34.2567i | 0.667479 | + | 1.15611i | ||||
\(879\) | −12.1222 | + | 20.9963i | −0.408872 | + | 0.708187i | ||||
\(880\) | 15.5479 | 0.524118 | ||||||||
\(881\) | −23.2188 | − | 40.2161i | −0.782260 | − | 1.35491i | −0.930622 | − | 0.365981i | \(-0.880734\pi\) |
0.148362 | − | 0.988933i | \(-0.452600\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.6588 | 0.526960 | 0.263480 | − | 0.964665i | \(-0.415130\pi\) | ||||
0.263480 | + | 0.964665i | \(0.415130\pi\) | |||||||
\(884\) | −67.7204 | − | 47.0726i | −2.27768 | − | 1.58322i | ||||
\(885\) | −5.55497 | + | 9.62149i | −0.186728 | + | 0.323423i | ||||
\(886\) | 82.8986 | 2.78503 | ||||||||
\(887\) | 15.7554 | − | 27.2891i | 0.529013 | − | 0.916278i | −0.470414 | − | 0.882446i | \(-0.655896\pi\) |
0.999428 | − | 0.0338320i | \(-0.0107711\pi\) | |||||||
\(888\) | 40.1292 | − | 69.5059i | 1.34665 | − | 2.33246i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.78862 | + | 3.09799i | −0.0599548 | + | 0.103845i | ||||
\(891\) | 5.86165 | 0.196373 | ||||||||
\(892\) | 2.95073 | − | 5.11082i | 0.0987978 | − | 0.171123i | ||||
\(893\) | 21.2838 | + | 36.8647i | 0.712236 | + | 1.23363i | ||||
\(894\) | −15.2717 | + | 26.4514i | −0.510762 | + | 0.884666i | ||||
\(895\) | 0.284810 | + | 0.493305i | 0.00952015 | + | 0.0164894i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.42868 | − | 6.55389i | −0.314815 | − | 0.218828i | ||||
\(898\) | 42.8651 | + | 74.2445i | 1.43043 | + | 2.47757i | ||||
\(899\) | −1.13013 | −0.0376920 | ||||||||
\(900\) | 27.9081 | 0.930270 | ||||||||
\(901\) | 18.9504 | 0.631330 | ||||||||
\(902\) | −4.69361 | −0.156280 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −59.8050 | + | 103.585i | −1.98908 | + | 3.44520i | ||||
\(905\) | 3.67633 | + | 6.36759i | 0.122205 | + | 0.211666i | ||||
\(906\) | 4.60505 | + | 7.97618i | 0.152993 | + | 0.264991i | ||||
\(907\) | −0.747991 | −0.0248366 | −0.0124183 | − | 0.999923i | \(-0.503953\pi\) | ||||
−0.0124183 | + | 0.999923i | \(0.503953\pi\) | |||||||
\(908\) | −67.4482 | + | 116.824i | −2.23835 | + | 3.87693i | ||||
\(909\) | −8.52224 | −0.282665 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.9000 | 0.824973 | 0.412486 | − | 0.910964i | \(-0.364660\pi\) | ||||
0.412486 | + | 0.910964i | \(0.364660\pi\) | |||||||
\(912\) | −76.2207 | + | 132.018i | −2.52392 | + | 4.37156i | ||||
\(913\) | 16.0186 | 0.530138 | ||||||||
\(914\) | 28.2970 | + | 49.0119i | 0.935983 | + | 1.62117i | ||||
\(915\) | 3.29982 | + | 5.71546i | 0.109089 | + | 0.188947i | ||||
\(916\) | 13.0385 | − | 22.5834i | 0.430804 | − | 0.746175i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −64.2132 | −2.11935 | ||||||||
\(919\) | 0.586495 | 0.0193467 | 0.00967334 | − | 0.999953i | \(-0.496921\pi\) | ||||
0.00967334 | + | 0.999953i | \(0.496921\pi\) | |||||||
\(920\) | −16.6545 | −0.549082 | ||||||||
\(921\) | 24.5881 | 0.810204 | ||||||||
\(922\) | −37.4104 | − | 64.7967i | −1.23205 | − | 2.13397i | ||||
\(923\) | 14.2560 | + | 9.90934i | 0.469240 | + | 0.326170i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.5881 | − | 23.5352i | −0.446773 | − | 0.773833i | ||||
\(926\) | 7.75694 | − | 13.4354i | 0.254909 | − | 0.441515i | ||||
\(927\) | −1.59700 | − | 2.76608i | −0.0524523 | − | 0.0908500i | ||||
\(928\) | −4.66206 | + | 8.07493i | −0.153040 | + | 0.265073i | ||||
\(929\) | 50.1949 | 1.64684 | 0.823421 | − | 0.567431i | \(-0.192062\pi\) | ||||
0.823421 | + | 0.567431i | \(0.192062\pi\) | |||||||
\(930\) | 3.84324 | − | 6.65668i | 0.126025 | − | 0.218281i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −56.6534 | + | 98.1266i | −1.85574 | + | 3.21424i | ||||
\(933\) | −11.7746 | + | 20.3943i | −0.385484 | + | 0.667678i | ||||
\(934\) | 115.713 | 3.78626 | ||||||||
\(935\) | −2.09809 | + | 3.63400i | −0.0686150 | + | 0.118845i | ||||
\(936\) | −3.30675 | + | 39.3525i | −0.108085 | + | 1.28628i | ||||
\(937\) | −22.7130 | −0.742003 | −0.371001 | − | 0.928632i | \(-0.620985\pi\) | ||||
−0.371001 | + | 0.928632i | \(0.620985\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.65080 | − | 8.05542i | −0.151773 | − | 0.262879i | ||||
\(940\) | −23.9374 | −0.780752 | ||||||||
\(941\) | −24.9367 | + | 43.1916i | −0.812914 | + | 1.40801i | 0.0979030 | + | 0.995196i | \(0.468787\pi\) |
−0.910816 | + | 0.412812i | \(0.864547\pi\) | |||||||
\(942\) | −24.1670 | − | 41.8586i | −0.787405 | − | 1.36383i | ||||
\(943\) | 2.92758 | 0.0953351 | ||||||||
\(944\) | 168.849 | 5.49558 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.25677 | + | 5.64088i | 0.105887 | + | 0.183401i | ||||
\(947\) | −0.133207 | + | 0.230722i | −0.00432865 | + | 0.00749745i | −0.868182 | − | 0.496247i | \(-0.834711\pi\) |
0.863853 | + | 0.503744i | \(0.168045\pi\) | |||||||
\(948\) | −34.3358 | + | 59.4713i | −1.11517 | + | 1.93154i | ||||
\(949\) | 17.9703 | + | 12.4912i | 0.583342 | + | 0.405482i | ||||
\(950\) | 44.3229 | + | 76.7696i | 1.43803 | + | 2.49073i | ||||
\(951\) | −17.1128 | − | 29.6402i | −0.554920 | − | 0.961150i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.91014 | + | 6.77257i | −0.126662 | + | 0.219385i | −0.922381 | − | 0.386281i | \(-0.873760\pi\) |
0.795719 | + | 0.605665i | \(0.207093\pi\) | |||||||
\(954\) | −7.11968 | − | 12.3316i | −0.230508 | − | 0.399252i | ||||
\(955\) | 3.66722 | + | 6.35181i | 0.118668 | + | 0.205540i | ||||
\(956\) | −17.2425 | − | 29.8649i | −0.557662 | − | 0.965899i | ||||
\(957\) | 0.379652 | + | 0.657576i | 0.0122724 | + | 0.0212564i | ||||
\(958\) | −44.5859 | + | 77.2251i | −1.44051 | + | 2.49503i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −16.1607 | − | 27.9911i | −0.521584 | − | 0.903410i | ||||
\(961\) | 11.6568 | + | 20.1901i | 0.376025 | + | 0.651294i | ||||
\(962\) | 54.6035 | − | 25.6907i | 1.76049 | − | 0.828302i | ||||
\(963\) | 0.845257 | − | 1.46403i | 0.0272380 | − | 0.0471776i | ||||
\(964\) | −33.4793 | + | 57.9878i | −1.07829 | + | 1.86766i | ||||
\(965\) | 3.22398 | + | 5.58410i | 0.103784 | + | 0.179759i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.8224 | 1.28060 | 0.640301 | − | 0.768124i | \(-0.278810\pi\) | ||||
0.640301 | + | 0.768124i | \(0.278810\pi\) | |||||||
\(968\) | 87.9999 | 2.82842 | ||||||||
\(969\) | −20.5711 | − | 35.6302i | −0.660838 | − | 1.14461i | ||||
\(970\) | 9.68333 | − | 16.7720i | 0.310913 | − | 0.538517i | ||||
\(971\) | 45.9295 | 1.47395 | 0.736974 | − | 0.675921i | \(-0.236254\pi\) | ||||
0.736974 | + | 0.675921i | \(0.236254\pi\) | |||||||
\(972\) | 30.5401 | + | 52.8969i | 0.979573 | + | 1.69667i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −73.6208 | −2.35896 | ||||||||
\(975\) | −17.9841 | − | 12.5008i | −0.575954 | − | 0.400346i | ||||
\(976\) | 50.1508 | − | 86.8637i | 1.60529 | − | 2.78044i | ||||
\(977\) | −28.6627 | −0.917002 | −0.458501 | − | 0.888694i | \(-0.651613\pi\) | ||||
−0.458501 | + | 0.888694i | \(0.651613\pi\) | |||||||
\(978\) | 11.2745 | − | 19.5281i | 0.360520 | − | 0.624439i | ||||
\(979\) | 1.20173 | − | 2.08145i | 0.0384074 | − | 0.0665235i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.63267 | − | 2.82787i | 0.0521271 | − | 0.0902868i | ||||
\(982\) | −119.752 | −3.82144 | ||||||||
\(983\) | −23.0600 | + | 39.9411i | −0.735500 | + | 1.27392i | 0.219003 | + | 0.975724i | \(0.429720\pi\) |
−0.954503 | + | 0.298200i | \(0.903614\pi\) | |||||||
\(984\) | 8.24557 | + | 14.2817i | 0.262859 | + | 0.455285i | ||||
\(985\) | −9.64095 | + | 16.6986i | −0.307186 | + | 0.532062i | ||||
\(986\) | −2.31777 | − | 4.01449i | −0.0738128 | − | 0.127848i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −130.700 | + | 61.4940i | −4.15814 | + | 1.95638i | ||||
\(989\) | −2.03137 | − | 3.51843i | −0.0645937 | − | 0.111880i | ||||
\(990\) | 3.15302 | 0.100209 | ||||||||
\(991\) | 37.8249 | 1.20155 | 0.600773 | − | 0.799419i | \(-0.294859\pi\) | ||||
0.600773 | + | 0.799419i | \(0.294859\pi\) | |||||||
\(992\) | −63.4171 | −2.01350 | ||||||||
\(993\) | 4.08809 | 0.129732 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.75468 | + | 6.50329i | −0.119031 | + | 0.206168i | ||||
\(996\) | −44.1595 | − | 76.4864i | −1.39925 | − | 2.42357i | ||||
\(997\) | 19.1874 | + | 33.2335i | 0.607671 | + | 1.05252i | 0.991623 | + | 0.129164i | \(0.0412293\pi\) |
−0.383952 | + | 0.923353i | \(0.625437\pi\) | |||||||
\(998\) | 49.6189 | 1.57066 | ||||||||
\(999\) | 17.2389 | − | 29.8586i | 0.545414 | − | 0.944684i |
(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 | 637.2.g.j.263.4 | 8 | ||
7.2 | even | 3 | 637.2.h.i.471.1 | 8 | |||
7.3 | odd | 6 | 91.2.f.c.29.4 | yes | 8 | ||
7.4 | even | 3 | 637.2.f.i.393.4 | 8 | |||
7.5 | odd | 6 | 637.2.h.h.471.1 | 8 | |||
7.6 | odd | 2 | 637.2.g.k.263.4 | 8 | |||
13.9 | even | 3 | 637.2.h.i.165.1 | 8 | |||
21.17 | even | 6 | 819.2.o.h.757.1 | 8 | |||
28.3 | even | 6 | 1456.2.s.q.1121.3 | 8 | |||
91.3 | odd | 6 | 1183.2.a.k.1.1 | 4 | |||
91.9 | even | 3 | inner | 637.2.g.j.373.4 | 8 | ||
91.10 | odd | 6 | 1183.2.a.l.1.4 | 4 | |||
91.24 | even | 12 | 1183.2.c.g.337.1 | 8 | |||
91.48 | odd | 6 | 637.2.h.h.165.1 | 8 | |||
91.61 | odd | 6 | 637.2.g.k.373.4 | 8 | |||
91.74 | even | 3 | 637.2.f.i.295.4 | 8 | |||
91.80 | even | 12 | 1183.2.c.g.337.8 | 8 | |||
91.81 | even | 3 | 8281.2.a.bp.1.1 | 4 | |||
91.87 | odd | 6 | 91.2.f.c.22.4 | ✓ | 8 | ||
91.88 | even | 6 | 8281.2.a.bt.1.4 | 4 | |||
273.269 | even | 6 | 819.2.o.h.568.1 | 8 | |||
364.87 | even | 6 | 1456.2.s.q.113.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.f.c.22.4 | ✓ | 8 | 91.87 | odd | 6 | ||
91.2.f.c.29.4 | yes | 8 | 7.3 | odd | 6 | ||
637.2.f.i.295.4 | 8 | 91.74 | even | 3 | |||
637.2.f.i.393.4 | 8 | 7.4 | even | 3 | |||
637.2.g.j.263.4 | 8 | 1.1 | even | 1 | trivial | ||
637.2.g.j.373.4 | 8 | 91.9 | even | 3 | inner | ||
637.2.g.k.263.4 | 8 | 7.6 | odd | 2 | |||
637.2.g.k.373.4 | 8 | 91.61 | odd | 6 | |||
637.2.h.h.165.1 | 8 | 91.48 | odd | 6 | |||
637.2.h.h.471.1 | 8 | 7.5 | odd | 6 | |||
637.2.h.i.165.1 | 8 | 13.9 | even | 3 | |||
637.2.h.i.471.1 | 8 | 7.2 | even | 3 | |||
819.2.o.h.568.1 | 8 | 273.269 | even | 6 | |||
819.2.o.h.757.1 | 8 | 21.17 | even | 6 | |||
1183.2.a.k.1.1 | 4 | 91.3 | odd | 6 | |||
1183.2.a.l.1.4 | 4 | 91.10 | odd | 6 | |||
1183.2.c.g.337.1 | 8 | 91.24 | even | 12 | |||
1183.2.c.g.337.8 | 8 | 91.80 | even | 12 | |||
1456.2.s.q.113.3 | 8 | 364.87 | even | 6 | |||
1456.2.s.q.1121.3 | 8 | 28.3 | even | 6 | |||
8281.2.a.bp.1.1 | 4 | 91.81 | even | 3 | |||
8281.2.a.bt.1.4 | 4 | 91.88 | even | 6 |