Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(362,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.362");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.s (of order \(6\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 362.5 | ||
Character | \(\chi\) | \(=\) | 441.362 |
Dual form | 441.2.s.d.374.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61855 | + | 0.934468i | −1.14449 | + | 0.660769i | −0.947537 | − | 0.319645i | \(-0.896436\pi\) |
−0.196948 | + | 0.980414i | \(0.563103\pi\) | |||||||
\(3\) | −0.710525 | + | 1.57961i | −0.410222 | + | 0.911986i | ||||
\(4\) | 0.746462 | − | 1.29291i | 0.373231 | − | 0.646455i | ||||
\(5\) | 2.50573 | 1.12060 | 0.560299 | − | 0.828290i | \(-0.310686\pi\) | ||||
0.560299 | + | 0.828290i | \(0.310686\pi\) | |||||||
\(6\) | −0.326074 | − | 3.22063i | −0.133119 | − | 1.31482i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 0.947692i | − | 0.335060i | ||||||
\(9\) | −1.99031 | − | 2.24470i | −0.663436 | − | 0.748233i | ||||
\(10\) | −4.05565 | + | 2.34153i | −1.28251 | + | 0.740457i | ||||
\(11\) | 5.60957i | 1.69135i | 0.533698 | + | 0.845675i | \(0.320802\pi\) | ||||
−0.533698 | + | 0.845675i | \(0.679198\pi\) | |||||||
\(12\) | 1.51191 | + | 2.09776i | 0.436451 | + | 0.605572i | ||||
\(13\) | −0.384312 | + | 0.221883i | −0.106589 | + | 0.0615392i | −0.552347 | − | 0.833614i | \(-0.686268\pi\) |
0.445758 | + | 0.895154i | \(0.352934\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.78039 | + | 3.95807i | −0.459694 | + | 1.02197i | ||||
\(16\) | 2.37851 | + | 4.11970i | 0.594628 | + | 1.02993i | ||||
\(17\) | 1.53885 | + | 2.66536i | 0.373226 | + | 0.646446i | 0.990060 | − | 0.140647i | \(-0.0449184\pi\) |
−0.616834 | + | 0.787093i | \(0.711585\pi\) | |||||||
\(18\) | 5.31901 | + | 1.77327i | 1.25370 | + | 0.417963i | ||||
\(19\) | −2.22932 | − | 1.28710i | −0.511440 | − | 0.295280i | 0.221985 | − | 0.975050i | \(-0.428746\pi\) |
−0.733425 | + | 0.679770i | \(0.762080\pi\) | |||||||
\(20\) | 1.87044 | − | 3.23969i | 0.418242 | − | 0.724417i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.24197 | − | 9.07935i | −1.11759 | − | 1.93572i | ||||
\(23\) | 7.89210i | 1.64562i | 0.568319 | + | 0.822808i | \(0.307594\pi\) | ||||
−0.568319 | + | 0.822808i | \(0.692406\pi\) | |||||||
\(24\) | 1.49698 | + | 0.673359i | 0.305570 | + | 0.137449i | ||||
\(25\) | 1.27870 | 0.255741 | ||||||||
\(26\) | 0.414685 | − | 0.718255i | 0.0813264 | − | 0.140861i | ||||
\(27\) | 4.95990 | − | 1.54899i | 0.954534 | − | 0.298103i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.71041 | + | 1.56485i | 0.503310 | + | 0.290586i | 0.730079 | − | 0.683362i | \(-0.239483\pi\) |
−0.226770 | + | 0.973948i | \(0.572816\pi\) | |||||||
\(30\) | −0.817055 | − | 8.07004i | −0.149173 | − | 1.47338i | ||||
\(31\) | −9.06457 | − | 5.23343i | −1.62805 | − | 0.939952i | −0.984675 | − | 0.174397i | \(-0.944202\pi\) |
−0.643370 | − | 0.765556i | \(-0.722464\pi\) | |||||||
\(32\) | −6.05802 | − | 3.49760i | −1.07092 | − | 0.618294i | ||||
\(33\) | −8.86091 | − | 3.98574i | −1.54249 | − | 0.693828i | ||||
\(34\) | −4.98140 | − | 2.87601i | −0.854303 | − | 0.493232i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.38788 | + | 0.897709i | −0.731314 | + | 0.149618i | ||||
\(37\) | 0.708168 | − | 1.22658i | 0.116422 | − | 0.201649i | −0.801925 | − | 0.597424i | \(-0.796191\pi\) |
0.918347 | + | 0.395775i | \(0.129524\pi\) | |||||||
\(38\) | 4.81100 | 0.780448 | ||||||||
\(39\) | −0.0774239 | − | 0.764715i | −0.0123978 | − | 0.122452i | ||||
\(40\) | − | 2.37466i | − | 0.375467i | ||||||
\(41\) | −1.64665 | − | 2.85208i | −0.257163 | − | 0.445420i | 0.708318 | − | 0.705894i | \(-0.249455\pi\) |
−0.965481 | + | 0.260474i | \(0.916121\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.75676 | + | 8.23894i | −0.725398 | + | 1.25643i | 0.233411 | + | 0.972378i | \(0.425011\pi\) |
−0.958810 | + | 0.284049i | \(0.908322\pi\) | |||||||
\(44\) | 7.25268 | + | 4.18733i | 1.09338 | + | 0.631264i | ||||
\(45\) | −4.98718 | − | 5.62462i | −0.743446 | − | 0.838468i | ||||
\(46\) | −7.37492 | − | 12.7737i | −1.08737 | − | 1.88338i | ||||
\(47\) | 1.07190 | + | 1.85659i | 0.156353 | + | 0.270811i | 0.933551 | − | 0.358445i | \(-0.116693\pi\) |
−0.777198 | + | 0.629256i | \(0.783360\pi\) | |||||||
\(48\) | −8.19750 | + | 0.829960i | −1.18321 | + | 0.119794i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.06964 | + | 1.19491i | −0.292691 | + | 0.168985i | ||||
\(51\) | −5.30362 | + | 0.536967i | −0.742655 | + | 0.0751904i | ||||
\(52\) | 0.662509i | 0.0918734i | ||||||||
\(53\) | −4.20379 | + | 2.42706i | −0.577435 | + | 0.333382i | −0.760113 | − | 0.649791i | \(-0.774857\pi\) |
0.182678 | + | 0.983173i | \(0.441523\pi\) | |||||||
\(54\) | −6.58035 | + | 7.14198i | −0.895472 | + | 0.971901i | ||||
\(55\) | 14.0561i | 1.89532i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.61709 | − | 2.60693i | 0.479095 | − | 0.345296i | ||||
\(58\) | −5.84923 | −0.768041 | ||||||||
\(59\) | 3.65496 | − | 6.33057i | 0.475835 | − | 0.824170i | −0.523782 | − | 0.851852i | \(-0.675479\pi\) |
0.999617 | + | 0.0276824i | \(0.00881270\pi\) | |||||||
\(60\) | 3.78844 | + | 5.25643i | 0.489086 | + | 0.678602i | ||||
\(61\) | 7.40950 | − | 4.27788i | 0.948690 | − | 0.547726i | 0.0560160 | − | 0.998430i | \(-0.482160\pi\) |
0.892674 | + | 0.450704i | \(0.148827\pi\) | |||||||
\(62\) | 19.5619 | 2.48437 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.55953 | 0.444941 | ||||||||
\(65\) | −0.962984 | + | 0.555979i | −0.119443 | + | 0.0689607i | ||||
\(66\) | 18.0664 | − | 1.82914i | 2.22381 | − | 0.225151i | ||||
\(67\) | 0.934442 | − | 1.61850i | 0.114160 | − | 0.197731i | −0.803284 | − | 0.595597i | \(-0.796916\pi\) |
0.917444 | + | 0.397865i | \(0.130249\pi\) | |||||||
\(68\) | 4.59477 | 0.557198 | ||||||||
\(69\) | −12.4664 | − | 5.60753i | −1.50078 | − | 0.675067i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.95338i | − | 0.350501i | −0.984524 | − | 0.175251i | \(-0.943926\pi\) | ||
0.984524 | − | 0.175251i | \(-0.0560736\pi\) | |||||||
\(72\) | −2.12728 | + | 1.88620i | −0.250703 | + | 0.222291i | ||||
\(73\) | 7.37804 | − | 4.25971i | 0.863534 | − | 0.498562i | −0.00165984 | − | 0.999999i | \(-0.500528\pi\) |
0.865194 | + | 0.501437i | \(0.167195\pi\) | |||||||
\(74\) | 2.64704i | 0.307712i | ||||||||
\(75\) | −0.908550 | + | 2.01985i | −0.104910 | + | 0.233232i | ||||
\(76\) | −3.32820 | + | 1.92154i | −0.381771 | + | 0.220415i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.839916 | + | 1.16538i | 0.0951018 | + | 0.131953i | ||||
\(79\) | 0.287130 | + | 0.497324i | 0.0323047 | + | 0.0559533i | 0.881726 | − | 0.471762i | \(-0.156382\pi\) |
−0.849421 | + | 0.527716i | \(0.823049\pi\) | |||||||
\(80\) | 5.95992 | + | 10.3229i | 0.666339 | + | 1.15413i | ||||
\(81\) | −1.07734 | + | 8.93529i | −0.119705 | + | 0.992810i | ||||
\(82\) | 5.33036 | + | 3.07748i | 0.588639 | + | 0.339851i | ||||
\(83\) | −4.23521 | + | 7.33560i | −0.464875 | + | 0.805186i | −0.999196 | − | 0.0400951i | \(-0.987234\pi\) |
0.534321 | + | 0.845281i | \(0.320567\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.85595 | + | 6.67870i | 0.418236 | + | 0.724406i | ||||
\(86\) | − | 17.7802i | − | 1.91728i | ||||||
\(87\) | −4.39766 | + | 3.16951i | −0.471479 | + | 0.339807i | ||||
\(88\) | 5.31615 | 0.566703 | ||||||||
\(89\) | −3.78929 | + | 6.56325i | −0.401664 | + | 0.695703i | −0.993927 | − | 0.110042i | \(-0.964901\pi\) |
0.592263 | + | 0.805745i | \(0.298235\pi\) | |||||||
\(90\) | 13.3280 | + | 4.44334i | 1.40490 | + | 0.468369i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 10.2038 | + | 5.89115i | 1.06382 | + | 0.614195i | ||||
\(93\) | 14.7074 | − | 10.6000i | 1.52508 | − | 1.09917i | ||||
\(94\) | −3.46984 | − | 2.00332i | −0.357887 | − | 0.206626i | ||||
\(95\) | −5.58607 | − | 3.22512i | −0.573119 | − | 0.330890i | ||||
\(96\) | 9.82920 | − | 7.08415i | 1.00319 | − | 0.723023i | ||||
\(97\) | 3.22662 | + | 1.86289i | 0.327614 | + | 0.189148i | 0.654781 | − | 0.755818i | \(-0.272761\pi\) |
−0.327167 | + | 0.944966i | \(0.606094\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.5918 | − | 11.1648i | 1.26552 | − | 1.12210i | ||||
\(100\) | 0.954503 | − | 1.65325i | 0.0954503 | − | 0.165325i | ||||
\(101\) | −7.53449 | −0.749710 | −0.374855 | − | 0.927083i | \(-0.622308\pi\) | ||||
−0.374855 | + | 0.927083i | \(0.622308\pi\) | |||||||
\(102\) | 8.08237 | − | 5.82517i | 0.800274 | − | 0.576778i | ||||
\(103\) | 14.3235i | 1.41133i | 0.708545 | + | 0.705666i | \(0.249352\pi\) | ||||
−0.708545 | + | 0.705666i | \(0.750648\pi\) | |||||||
\(104\) | 0.210276 | + | 0.364210i | 0.0206193 | + | 0.0357137i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.53602 | − | 7.85662i | 0.440577 | − | 0.763102i | ||||
\(107\) | 11.6798 | + | 6.74331i | 1.12912 | + | 0.651900i | 0.943715 | − | 0.330761i | \(-0.107305\pi\) |
0.185410 | + | 0.982661i | \(0.440639\pi\) | |||||||
\(108\) | 1.69967 | − | 7.56897i | 0.163551 | − | 0.728325i | ||||
\(109\) | 0.459348 | + | 0.795613i | 0.0439975 | + | 0.0762059i | 0.887186 | − | 0.461413i | \(-0.152657\pi\) |
−0.843188 | + | 0.537619i | \(0.819324\pi\) | |||||||
\(110\) | −13.1350 | − | 22.7504i | −1.25237 | − | 2.16917i | ||||
\(111\) | 1.43435 | + | 1.99014i | 0.136142 | + | 0.188896i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.10412 | − | 2.36952i | 0.386083 | − | 0.222905i | −0.294378 | − | 0.955689i | \(-0.595113\pi\) |
0.680462 | + | 0.732784i | \(0.261779\pi\) | |||||||
\(114\) | −3.41834 | + | 7.59949i | −0.320157 | + | 0.711757i | ||||
\(115\) | 19.7755i | 1.84407i | ||||||||
\(116\) | 4.04643 | − | 2.33621i | 0.375702 | − | 0.216912i | ||||
\(117\) | 1.26296 | + | 0.421050i | 0.116761 | + | 0.0389261i | ||||
\(118\) | 13.6618i | 1.25767i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.75103 | + | 1.68726i | 0.342421 | + | 0.154025i | ||||
\(121\) | −20.4673 | −1.86066 | ||||||||
\(122\) | −7.99508 | + | 13.8479i | −0.723841 | + | 1.25373i | ||||
\(123\) | 5.67515 | − | 0.574583i | 0.511711 | − | 0.0518084i | ||||
\(124\) | −13.5327 | + | 7.81312i | −1.21527 | + | 0.701639i | ||||
\(125\) | −9.32458 | −0.834016 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.37245 | 0.654200 | 0.327100 | − | 0.944990i | \(-0.393929\pi\) | ||||
0.327100 | + | 0.944990i | \(0.393929\pi\) | |||||||
\(128\) | 6.35477 | − | 3.66893i | 0.561688 | − | 0.324291i | ||||
\(129\) | −9.63449 | − | 13.3678i | −0.848269 | − | 1.17697i | ||||
\(130\) | 1.03909 | − | 1.79976i | 0.0911342 | − | 0.157849i | ||||
\(131\) | 7.86300 | 0.686993 | 0.343497 | − | 0.939154i | \(-0.388389\pi\) | ||||
0.343497 | + | 0.939154i | \(0.388389\pi\) | |||||||
\(132\) | −11.7675 | + | 8.48116i | −1.02423 | + | 0.738191i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.49283i | 0.301734i | ||||||||
\(135\) | 12.4282 | − | 3.88136i | 1.06965 | − | 0.334054i | ||||
\(136\) | 2.52594 | − | 1.45835i | 0.216598 | − | 0.125053i | ||||
\(137\) | 11.5698i | 0.988477i | 0.869326 | + | 0.494238i | \(0.164553\pi\) | ||||
−0.869326 | + | 0.494238i | \(0.835447\pi\) | |||||||
\(138\) | 25.4175 | − | 2.57341i | 2.16368 | − | 0.219063i | ||||
\(139\) | 16.9741 | − | 9.79999i | 1.43972 | − | 0.831224i | 0.441893 | − | 0.897068i | \(-0.354307\pi\) |
0.997830 | + | 0.0658437i | \(0.0209739\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.69429 | + | 0.374030i | −0.311115 | + | 0.0314990i | ||||
\(142\) | 2.75984 | + | 4.78018i | 0.231600 | + | 0.401144i | ||||
\(143\) | −1.24467 | − | 2.15583i | −0.104084 | − | 0.180279i | ||||
\(144\) | 4.51352 | − | 13.5385i | 0.376127 | − | 1.12821i | ||||
\(145\) | 6.79156 | + | 3.92111i | 0.564008 | + | 0.325630i | ||||
\(146\) | −7.96114 | + | 13.7891i | −0.658868 | + | 1.14119i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.05724 | − | 1.83120i | −0.0869047 | − | 0.150523i | ||||
\(149\) | − | 15.7402i | − | 1.28949i | −0.764397 | − | 0.644746i | \(-0.776963\pi\) | ||
0.764397 | − | 0.644746i | \(-0.223037\pi\) | |||||||
\(150\) | −0.416952 | − | 4.11823i | −0.0340440 | − | 0.336252i | ||||
\(151\) | −1.98271 | −0.161350 | −0.0806752 | − | 0.996740i | \(-0.525708\pi\) | ||||
−0.0806752 | + | 0.996740i | \(0.525708\pi\) | |||||||
\(152\) | −1.21977 | + | 2.11270i | −0.0989364 | + | 0.171363i | ||||
\(153\) | 2.92015 | − | 8.75915i | 0.236081 | − | 0.708135i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.7134 | − | 13.1136i | −1.82438 | − | 1.05331i | ||||
\(156\) | −1.04650 | − | 0.470729i | −0.0837872 | − | 0.0376885i | ||||
\(157\) | 7.26790 | + | 4.19612i | 0.580041 | + | 0.334887i | 0.761150 | − | 0.648576i | \(-0.224635\pi\) |
−0.181108 | + | 0.983463i | \(0.557969\pi\) | |||||||
\(158\) | −0.929468 | − | 0.536628i | −0.0739445 | − | 0.0426919i | ||||
\(159\) | −0.846899 | − | 8.36481i | −0.0671635 | − | 0.663373i | ||||
\(160\) | −15.1798 | − | 8.76405i | −1.20007 | − | 0.692859i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.60602 | − | 15.4689i | −0.519018 | − | 1.21535i | ||||
\(163\) | 0.537054 | − | 0.930204i | 0.0420653 | − | 0.0728592i | −0.844226 | − | 0.535987i | \(-0.819940\pi\) |
0.886291 | + | 0.463128i | \(0.153273\pi\) | |||||||
\(164\) | −4.91665 | −0.383926 | ||||||||
\(165\) | −22.2031 | − | 9.98721i | −1.72851 | − | 0.777503i | ||||
\(166\) | − | 15.8307i | − | 1.22870i | ||||||
\(167\) | 3.99731 | + | 6.92354i | 0.309321 | + | 0.535760i | 0.978214 | − | 0.207599i | \(-0.0665649\pi\) |
−0.668893 | + | 0.743359i | \(0.733232\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.40154 | + | 11.0878i | −0.492426 | + | 0.852907i | ||||
\(170\) | −12.4821 | − | 7.20652i | −0.957330 | − | 0.552715i | ||||
\(171\) | 1.54788 | + | 7.56586i | 0.118370 | + | 0.578576i | ||||
\(172\) | 7.10148 | + | 12.3001i | 0.541483 | + | 0.937875i | ||||
\(173\) | 0.501744 | + | 0.869046i | 0.0381469 | + | 0.0660723i | 0.884468 | − | 0.466600i | \(-0.154521\pi\) |
−0.846322 | + | 0.532672i | \(0.821188\pi\) | |||||||
\(174\) | 4.15602 | − | 9.23947i | 0.315067 | − | 0.700442i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −23.1098 | + | 13.3424i | −1.74197 | + | 1.00572i | ||||
\(177\) | 7.40287 | + | 10.2714i | 0.556434 | + | 0.772047i | ||||
\(178\) | − | 14.1639i | − | 1.06163i | ||||||
\(179\) | 1.27773 | − | 0.737695i | 0.0955017 | − | 0.0551379i | −0.451489 | − | 0.892277i | \(-0.649107\pi\) |
0.546990 | + | 0.837139i | \(0.315773\pi\) | |||||||
\(180\) | −10.9949 | + | 2.24942i | −0.819509 | + | 0.167662i | ||||
\(181\) | − | 15.0440i | − | 1.11821i | −0.829096 | − | 0.559106i | \(-0.811145\pi\) | ||
0.829096 | − | 0.559106i | \(-0.188855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.49273 | + | 14.7436i | 0.110345 | + | 1.08988i | ||||
\(184\) | 7.47928 | 0.551380 | ||||||||
\(185\) | 1.77448 | − | 3.07349i | 0.130462 | − | 0.225967i | ||||
\(186\) | −13.8992 | + | 30.9001i | −1.01914 | + | 2.26571i | ||||
\(187\) | −14.9516 | + | 8.63229i | −1.09337 | + | 0.631255i | ||||
\(188\) | 3.20054 | 0.233423 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 12.0551 | 0.874568 | ||||||||
\(191\) | −11.4521 | + | 6.61187i | −0.828644 | + | 0.478418i | −0.853388 | − | 0.521276i | \(-0.825456\pi\) |
0.0247439 | + | 0.999694i | \(0.492123\pi\) | |||||||
\(192\) | −2.52913 | + | 5.62265i | −0.182524 | + | 0.405780i | ||||
\(193\) | 0.777855 | − | 1.34728i | 0.0559912 | − | 0.0969796i | −0.836671 | − | 0.547705i | \(-0.815501\pi\) |
0.892662 | + | 0.450726i | \(0.148835\pi\) | |||||||
\(194\) | −6.96325 | −0.499932 | ||||||||
\(195\) | −0.194004 | − | 1.91617i | −0.0138929 | − | 0.137220i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.96185i | − | 0.353517i | −0.984254 | − | 0.176759i | \(-0.943439\pi\) | ||
0.984254 | − | 0.176759i | \(-0.0565612\pi\) | |||||||
\(198\) | −9.94728 | + | 29.8374i | −0.706922 | + | 2.12045i | ||||
\(199\) | 9.69273 | − | 5.59610i | 0.687100 | − | 0.396697i | −0.115425 | − | 0.993316i | \(-0.536823\pi\) |
0.802525 | + | 0.596619i | \(0.203490\pi\) | |||||||
\(200\) | − | 1.21182i | − | 0.0856883i | ||||||
\(201\) | 1.89265 | + | 2.62604i | 0.133497 | + | 0.185226i | ||||
\(202\) | 12.1949 | − | 7.04074i | 0.858032 | − | 0.495385i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3.26470 | + | 7.25793i | −0.228575 | + | 0.508157i | ||||
\(205\) | −4.12606 | − | 7.14655i | −0.288177 | − | 0.499137i | ||||
\(206\) | −13.3848 | − | 23.1832i | −0.932565 | − | 1.61525i | ||||
\(207\) | 17.7154 | − | 15.7077i | 1.23130 | − | 1.09176i | ||||
\(208\) | −1.82818 | − | 1.05550i | −0.126762 | − | 0.0731859i | ||||
\(209\) | 7.22006 | − | 12.5055i | 0.499422 | − | 0.865024i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.68026 | + | 13.3026i | 0.528731 | + | 0.915789i | 0.999439 | + | 0.0334999i | \(0.0106654\pi\) |
−0.470708 | + | 0.882289i | \(0.656001\pi\) | |||||||
\(212\) | 7.24683i | 0.497714i | ||||||||
\(213\) | 4.66517 | + | 2.09845i | 0.319652 | + | 0.143783i | ||||
\(214\) | −25.2056 | −1.72302 | ||||||||
\(215\) | −11.9192 | + | 20.6446i | −0.812880 | + | 1.40795i | ||||
\(216\) | −1.46796 | − | 4.70046i | −0.0998824 | − | 0.319826i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.48695 | − | 0.858492i | −0.100709 | − | 0.0581444i | ||||
\(219\) | 1.48639 | + | 14.6810i | 0.100441 | + | 0.992052i | ||||
\(220\) | 18.1733 | + | 10.4923i | 1.22524 | + | 0.707394i | ||||
\(221\) | −1.18280 | − | 0.682888i | −0.0795635 | − | 0.0459360i | ||||
\(222\) | −4.18128 | − | 1.88079i | −0.280629 | − | 0.126230i | ||||
\(223\) | −2.76845 | − | 1.59837i | −0.185389 | − | 0.107034i | 0.404433 | − | 0.914568i | \(-0.367469\pi\) |
−0.589822 | + | 0.807533i | \(0.700802\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.54501 | − | 2.87030i | −0.169668 | − | 0.191353i | ||||
\(226\) | −4.42848 | + | 7.67035i | −0.294578 | + | 0.510224i | ||||
\(227\) | 14.6699 | 0.973675 | 0.486837 | − | 0.873493i | \(-0.338150\pi\) | ||||
0.486837 | + | 0.873493i | \(0.338150\pi\) | |||||||
\(228\) | −0.670502 | − | 6.62254i | −0.0444051 | − | 0.438589i | ||||
\(229\) | 3.37807i | 0.223229i | 0.993752 | + | 0.111615i | \(0.0356022\pi\) | ||||
−0.993752 | + | 0.111615i | \(0.964398\pi\) | |||||||
\(230\) | −18.4796 | − | 32.0076i | −1.21851 | − | 2.11052i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.48300 | − | 2.56863i | 0.0973637 | − | 0.168639i | ||||
\(233\) | 4.22628 | + | 2.44005i | 0.276873 | + | 0.159853i | 0.632007 | − | 0.774963i | \(-0.282231\pi\) |
−0.355134 | + | 0.934815i | \(0.615565\pi\) | |||||||
\(234\) | −2.43762 | + | 0.498707i | −0.159352 | + | 0.0326015i | ||||
\(235\) | 2.68590 | + | 4.65211i | 0.175209 | + | 0.303470i | ||||
\(236\) | −5.45657 | − | 9.45106i | −0.355193 | − | 0.615212i | ||||
\(237\) | −0.989589 | + | 0.100191i | −0.0642807 | + | 0.00650813i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.6253 | − | 7.86657i | 0.881347 | − | 0.508846i | 0.0102448 | − | 0.999948i | \(-0.496739\pi\) |
0.871102 | + | 0.491101i | \(0.163406\pi\) | |||||||
\(240\) | −20.5408 | + | 2.07966i | −1.32590 | + | 0.134241i | ||||
\(241\) | 0.769383i | 0.0495603i | 0.999693 | + | 0.0247801i | \(0.00788857\pi\) | ||||
−0.999693 | + | 0.0247801i | \(0.992111\pi\) | |||||||
\(242\) | 33.1273 | − | 19.1260i | 2.12950 | − | 1.22947i | ||||
\(243\) | −13.3488 | − | 8.05052i | −0.856323 | − | 0.516441i | ||||
\(244\) | − | 12.7731i | − | 0.817714i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.64856 | + | 6.23323i | −0.551412 | + | 0.397416i | ||||
\(247\) | 1.14234 | 0.0726852 | ||||||||
\(248\) | −4.95968 | + | 8.59042i | −0.314940 | + | 0.545492i | ||||
\(249\) | −8.57813 | − | 11.9021i | −0.543617 | − | 0.754264i | ||||
\(250\) | 15.0923 | − | 8.71353i | 0.954519 | − | 0.551092i | ||||
\(251\) | 1.14544 | 0.0722996 | 0.0361498 | − | 0.999346i | \(-0.488491\pi\) | ||||
0.0361498 | + | 0.999346i | \(0.488491\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −44.2713 | −2.78331 | ||||||||
\(254\) | −11.9327 | + | 6.88933i | −0.748722 | + | 0.432275i | ||||
\(255\) | −13.2895 | + | 1.34550i | −0.832218 | + | 0.0842583i | ||||
\(256\) | −10.4165 | + | 18.0420i | −0.651033 | + | 1.12762i | ||||
\(257\) | 28.9835 | 1.80794 | 0.903969 | − | 0.427598i | \(-0.140640\pi\) | ||||
0.903969 | + | 0.427598i | \(0.140640\pi\) | |||||||
\(258\) | 28.0856 | + | 12.6332i | 1.74853 | + | 0.786511i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.66007i | 0.102953i | ||||||||
\(261\) | −1.88192 | − | 9.19859i | −0.116488 | − | 0.569378i | ||||
\(262\) | −12.7266 | + | 7.34772i | −0.786254 | + | 0.453944i | ||||
\(263\) | − | 13.6998i | − | 0.844763i | −0.906418 | − | 0.422381i | \(-0.861194\pi\) | ||
0.906418 | − | 0.422381i | \(-0.138806\pi\) | |||||||
\(264\) | −3.77725 | + | 8.39742i | −0.232474 | + | 0.516825i | ||||
\(265\) | −10.5336 | + | 6.08156i | −0.647072 | + | 0.373587i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.67496 | − | 10.6489i | −0.469700 | − | 0.651704i | ||||
\(268\) | −1.39505 | − | 2.41630i | −0.0852163 | − | 0.147599i | ||||
\(269\) | −5.23973 | − | 9.07548i | −0.319472 | − | 0.553342i | 0.660906 | − | 0.750469i | \(-0.270172\pi\) |
−0.980378 | + | 0.197127i | \(0.936839\pi\) | |||||||
\(270\) | −16.4886 | + | 17.8959i | −1.00346 | + | 1.08911i | ||||
\(271\) | −5.66907 | − | 3.27304i | −0.344371 | − | 0.198823i | 0.317832 | − | 0.948147i | \(-0.397045\pi\) |
−0.662203 | + | 0.749324i | \(0.730379\pi\) | |||||||
\(272\) | −7.32034 | + | 12.6792i | −0.443861 | + | 0.768790i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.8116 | − | 18.7263i | −0.653155 | − | 1.13130i | ||||
\(275\) | 7.17298i | 0.432547i | ||||||||
\(276\) | −16.5557 | + | 11.9321i | −0.996538 | + | 0.718230i | ||||
\(277\) | 22.4313 | 1.34777 | 0.673883 | − | 0.738838i | \(-0.264625\pi\) | ||||
0.673883 | + | 0.738838i | \(0.264625\pi\) | |||||||
\(278\) | −18.3156 | + | 31.7235i | −1.09849 | + | 1.90265i | ||||
\(279\) | 6.29382 | + | 30.7634i | 0.376801 | + | 1.84176i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.3552 | + | 11.1747i | 1.15463 | + | 0.666627i | 0.950012 | − | 0.312214i | \(-0.101071\pi\) |
0.204621 | + | 0.978841i | \(0.434404\pi\) | |||||||
\(282\) | 5.62986 | − | 4.05758i | 0.335253 | − | 0.241625i | ||||
\(283\) | −16.4296 | − | 9.48563i | −0.976638 | − | 0.563862i | −0.0753848 | − | 0.997155i | \(-0.524019\pi\) |
−0.901254 | + | 0.433292i | \(0.857352\pi\) | |||||||
\(284\) | −3.81845 | − | 2.20459i | −0.226584 | − | 0.130818i | ||||
\(285\) | 9.06346 | − | 6.53226i | 0.536873 | − | 0.386938i | ||||
\(286\) | 4.02910 | + | 2.32620i | 0.238246 | + | 0.137551i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.20627 | + | 20.5597i | 0.247857 | + | 1.21149i | ||||
\(289\) | 3.76389 | − | 6.51924i | 0.221405 | − | 0.383485i | ||||
\(290\) | −14.6566 | −0.860665 | ||||||||
\(291\) | −5.23523 | + | 3.77316i | −0.306895 | + | 0.221187i | ||||
\(292\) | − | 12.7189i | − | 0.744315i | ||||||
\(293\) | −4.41136 | − | 7.64069i | −0.257714 | − | 0.446374i | 0.707915 | − | 0.706298i | \(-0.249636\pi\) |
−0.965629 | + | 0.259924i | \(0.916303\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.15835 | − | 15.8627i | 0.533220 | − | 0.923563i | ||||
\(296\) | −1.16242 | − | 0.671125i | −0.0675644 | − | 0.0390083i | ||||
\(297\) | 8.68917 | + | 27.8229i | 0.504197 | + | 1.61445i | ||||
\(298\) | 14.7088 | + | 25.4763i | 0.852056 | + | 1.47580i | ||||
\(299\) | −1.75112 | − | 3.03303i | −0.101270 | − | 0.175405i | ||||
\(300\) | 1.93328 | + | 2.68241i | 0.111618 | + | 0.154869i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.20910 | − | 1.85278i | 0.184663 | − | 0.106615i | ||||
\(303\) | 5.35344 | − | 11.9015i | 0.307547 | − | 0.683725i | ||||
\(304\) | − | 12.2455i | − | 0.702327i | ||||||
\(305\) | 18.5662 | − | 10.7192i | 1.06310 | − | 0.613781i | ||||
\(306\) | 3.45874 | + | 16.9059i | 0.197723 | + | 0.966445i | ||||
\(307\) | − | 28.7533i | − | 1.64104i | −0.571620 | − | 0.820519i | \(-0.693685\pi\) | ||
0.571620 | − | 0.820519i | \(-0.306315\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −22.6254 | − | 10.1772i | −1.28712 | − | 0.578959i | ||||
\(310\) | 49.0169 | 2.78398 | ||||||||
\(311\) | 6.64294 | − | 11.5059i | 0.376687 | − | 0.652441i | −0.613891 | − | 0.789391i | \(-0.710397\pi\) |
0.990578 | + | 0.136950i | \(0.0437300\pi\) | |||||||
\(312\) | −0.724714 | + | 0.0733740i | −0.0410289 | + | 0.00415399i | ||||
\(313\) | 27.3227 | − | 15.7748i | 1.54437 | − | 0.891643i | 0.545815 | − | 0.837905i | \(-0.316220\pi\) |
0.998555 | − | 0.0537372i | \(-0.0171133\pi\) | |||||||
\(314\) | −15.6846 | −0.885132 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.857328 | 0.0482285 | ||||||||
\(317\) | −17.3819 | + | 10.0354i | −0.976264 | + | 0.563646i | −0.901140 | − | 0.433528i | \(-0.857268\pi\) |
−0.0751236 | + | 0.997174i | \(0.523935\pi\) | |||||||
\(318\) | 9.18740 | + | 12.7474i | 0.515204 | + | 0.714841i | ||||
\(319\) | −8.77816 | + | 15.2042i | −0.491483 | + | 0.851273i | ||||
\(320\) | 8.91923 | 0.498600 | ||||||||
\(321\) | −18.9505 | + | 13.6581i | −1.05772 | + | 0.762322i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.92259i | − | 0.440824i | ||||||
\(324\) | 10.7483 | + | 8.06276i | 0.597130 | + | 0.447931i | ||||
\(325\) | −0.491421 | + | 0.283722i | −0.0272591 | + | 0.0157381i | ||||
\(326\) | 2.00744i | 0.111182i | ||||||||
\(327\) | −1.58313 | + | 0.160285i | −0.0875475 | + | 0.00886378i | ||||
\(328\) | −2.70289 | + | 1.56052i | −0.149242 | + | 0.0861651i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 45.2695 | − | 4.58333i | 2.49200 | − | 0.252304i | ||||
\(331\) | −0.623957 | − | 1.08073i | −0.0342958 | − | 0.0594020i | 0.848368 | − | 0.529407i | \(-0.177585\pi\) |
−0.882664 | + | 0.470005i | \(0.844252\pi\) | |||||||
\(332\) | 6.32285 | + | 10.9515i | 0.347011 | + | 0.601041i | ||||
\(333\) | −4.16278 | + | 0.851655i | −0.228119 | + | 0.0466704i | ||||
\(334\) | −12.9397 | − | 7.47072i | −0.708027 | − | 0.408780i | ||||
\(335\) | 2.34146 | − | 4.05553i | 0.127928 | − | 0.221577i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.58745 | + | 11.4098i | 0.358842 | + | 0.621532i | 0.987768 | − | 0.155933i | \(-0.0498385\pi\) |
−0.628926 | + | 0.777465i | \(0.716505\pi\) | |||||||
\(338\) | − | 23.9281i | − | 1.30152i | ||||||
\(339\) | 0.826821 | + | 8.16650i | 0.0449067 | + | 0.443543i | ||||
\(340\) | 11.5133 | 0.624395 | ||||||||
\(341\) | 29.3573 | − | 50.8484i | 1.58979 | − | 2.75359i | ||||
\(342\) | −9.57538 | − | 10.7992i | −0.517777 | − | 0.583956i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 7.80798 | + | 4.50794i | 0.420978 | + | 0.243052i | ||||
\(345\) | −31.2375 | − | 14.0510i | −1.68177 | − | 0.756479i | ||||
\(346\) | −1.62419 | − | 0.937727i | −0.0873171 | − | 0.0504125i | ||||
\(347\) | 23.4411 | + | 13.5337i | 1.25838 | + | 0.726529i | 0.972760 | − | 0.231813i | \(-0.0744658\pi\) |
0.285624 | + | 0.958342i | \(0.407799\pi\) | |||||||
\(348\) | 0.815198 | + | 8.05170i | 0.0436992 | + | 0.431616i | ||||
\(349\) | 30.3413 | + | 17.5176i | 1.62413 | + | 0.937694i | 0.985798 | + | 0.167936i | \(0.0537101\pi\) |
0.638336 | + | 0.769758i | \(0.279623\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.56246 | + | 1.69581i | −0.0833978 | + | 0.0905158i | ||||
\(352\) | 19.6200 | − | 33.9829i | 1.04575 | − | 1.81129i | ||||
\(353\) | −2.52512 | −0.134398 | −0.0671992 | − | 0.997740i | \(-0.521406\pi\) | ||||
−0.0671992 | + | 0.997740i | \(0.521406\pi\) | |||||||
\(354\) | −21.5802 | − | 9.70702i | −1.14697 | − | 0.515922i | ||||
\(355\) | − | 7.40038i | − | 0.392771i | ||||||
\(356\) | 5.65713 | + | 9.79843i | 0.299827 | + | 0.519316i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.37871 | + | 2.38799i | −0.0728669 | + | 0.126209i | ||||
\(359\) | 6.29395 | + | 3.63381i | 0.332182 | + | 0.191785i | 0.656809 | − | 0.754057i | \(-0.271906\pi\) |
−0.324628 | + | 0.945842i | \(0.605239\pi\) | |||||||
\(360\) | −5.33040 | + | 4.72631i | −0.280937 | + | 0.249099i | ||||
\(361\) | −6.18677 | − | 10.7158i | −0.325619 | − | 0.563989i | ||||
\(362\) | 14.0581 | + | 24.3494i | 0.738880 | + | 1.27978i | ||||
\(363\) | 14.5425 | − | 32.3303i | 0.763285 | − | 1.69690i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.4874 | − | 10.6737i | 0.967675 | − | 0.558688i | ||||
\(366\) | −16.1935 | − | 22.4684i | −0.846448 | − | 1.17444i | ||||
\(367\) | 13.4770i | 0.703492i | 0.936095 | + | 0.351746i | \(0.114412\pi\) | ||||
−0.936095 | + | 0.351746i | \(0.885588\pi\) | |||||||
\(368\) | −32.5131 | + | 18.7715i | −1.69486 | + | 0.978530i | ||||
\(369\) | −3.12472 | + | 9.37275i | −0.162666 | + | 0.487926i | ||||
\(370\) | 6.63278i | 0.344822i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.72632 | − | 26.9278i | −0.141353 | − | 1.39614i | ||||
\(373\) | 23.7639 | 1.23045 | 0.615224 | − | 0.788352i | \(-0.289065\pi\) | ||||
0.615224 | + | 0.788352i | \(0.289065\pi\) | |||||||
\(374\) | 16.1332 | − | 27.9435i | 0.834228 | − | 1.44492i | ||||
\(375\) | 6.62535 | − | 14.7292i | 0.342131 | − | 0.760611i | ||||
\(376\) | 1.75947 | − | 1.01583i | 0.0907379 | − | 0.0523875i | ||||
\(377\) | −1.38886 | −0.0715297 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2283 | 1.09042 | 0.545211 | − | 0.838299i | \(-0.316449\pi\) | ||||
0.545211 | + | 0.838299i | \(0.316449\pi\) | |||||||
\(380\) | −8.33958 | + | 4.81486i | −0.427812 | + | 0.246997i | ||||
\(381\) | −5.23831 | + | 11.6456i | −0.268367 | + | 0.596621i | ||||
\(382\) | 12.3572 | − | 21.4032i | 0.632248 | − | 1.09509i | ||||
\(383\) | −12.9586 | −0.662154 | −0.331077 | − | 0.943604i | \(-0.607412\pi\) | ||||
−0.331077 | + | 0.943604i | \(0.607412\pi\) | |||||||
\(384\) | 1.28024 | + | 12.6449i | 0.0653319 | + | 0.645282i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.90752i | 0.147989i | ||||||||
\(387\) | 27.9614 | − | 5.72056i | 1.42136 | − | 0.290792i | ||||
\(388\) | 4.81710 | − | 2.78116i | 0.244551 | − | 0.141192i | ||||
\(389\) | − | 10.9470i | − | 0.555035i | −0.960721 | − | 0.277517i | \(-0.910488\pi\) | ||
0.960721 | − | 0.277517i | \(-0.0895116\pi\) | |||||||
\(390\) | 2.10461 | + | 2.92012i | 0.106571 | + | 0.147866i | ||||
\(391\) | −21.0353 | + | 12.1447i | −1.06380 | + | 0.614186i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.58685 | + | 12.4204i | −0.281819 | + | 0.626528i | ||||
\(394\) | 4.63669 | + | 8.03098i | 0.233593 | + | 0.404595i | ||||
\(395\) | 0.719472 | + | 1.24616i | 0.0362006 | + | 0.0627012i | ||||
\(396\) | −5.03576 | − | 24.6142i | −0.253057 | − | 1.23691i | ||||
\(397\) | −25.8856 | − | 14.9451i | −1.29916 | − | 0.750071i | −0.318901 | − | 0.947788i | \(-0.603314\pi\) |
−0.980259 | + | 0.197717i | \(0.936647\pi\) | |||||||
\(398\) | −10.4588 | + | 18.1151i | −0.524250 | + | 0.908028i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.04141 | + | 5.26788i | 0.152071 | + | 0.263394i | ||||
\(401\) | 19.1949i | 0.958547i | 0.877666 | + | 0.479273i | \(0.159100\pi\) | ||||
−0.877666 | + | 0.479273i | \(0.840900\pi\) | |||||||
\(402\) | −5.51729 | − | 2.48174i | −0.275177 | − | 0.123778i | ||||
\(403\) | 4.64483 | 0.231376 | ||||||||
\(404\) | −5.62421 | + | 9.74142i | −0.279815 | + | 0.484654i | ||||
\(405\) | −2.69953 | + | 22.3894i | −0.134141 | + | 1.11254i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.88060 | + | 3.97252i | 0.341059 | + | 0.196910i | ||||
\(408\) | 0.508879 | + | 5.02619i | 0.0251933 | + | 0.248834i | ||||
\(409\) | 24.9737 | + | 14.4186i | 1.23487 | + | 0.712953i | 0.968041 | − | 0.250790i | \(-0.0806905\pi\) |
0.266830 | + | 0.963744i | \(0.414024\pi\) | |||||||
\(410\) | 13.3565 | + | 7.71135i | 0.659628 | + | 0.380837i | ||||
\(411\) | −18.2758 | − | 8.22065i | −0.901477 | − | 0.405495i | ||||
\(412\) | 18.5190 | + | 10.6919i | 0.912363 | + | 0.526753i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −13.9948 | + | 41.9781i | −0.687807 | + | 2.06311i | ||||
\(415\) | −10.6123 | + | 18.3811i | −0.520938 | + | 0.902290i | ||||
\(416\) | 3.10423 | 0.152197 | ||||||||
\(417\) | 3.41961 | + | 33.7755i | 0.167459 | + | 1.65399i | ||||
\(418\) | 26.9877i | 1.32001i | ||||||||
\(419\) | 5.06390 | + | 8.77094i | 0.247388 | + | 0.428488i | 0.962800 | − | 0.270214i | \(-0.0870945\pi\) |
−0.715412 | + | 0.698702i | \(0.753761\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.7094 | − | 22.0134i | 0.619419 | − | 1.07287i | −0.370173 | − | 0.928963i | \(-0.620702\pi\) |
0.989592 | − | 0.143902i | \(-0.0459651\pi\) | |||||||
\(422\) | −24.8617 | − | 14.3539i | −1.21025 | − | 0.698738i | ||||
\(423\) | 2.03406 | − | 6.10128i | 0.0988996 | − | 0.296654i | ||||
\(424\) | 2.30010 | + | 3.98390i | 0.111703 | + | 0.193475i | ||||
\(425\) | 1.96773 | + | 3.40821i | 0.0954490 | + | 0.165322i | ||||
\(426\) | −9.51173 | + | 0.963020i | −0.460845 | + | 0.0466585i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 17.4370 | − | 10.0673i | 0.842849 | − | 0.486619i | ||||
\(429\) | 4.28972 | − | 0.434315i | 0.207110 | − | 0.0209689i | ||||
\(430\) | − | 44.5523i | − | 2.14850i | ||||||
\(431\) | 9.39066 | − | 5.42170i | 0.452332 | − | 0.261154i | −0.256482 | − | 0.966549i | \(-0.582564\pi\) |
0.708815 | + | 0.705395i | \(0.249230\pi\) | |||||||
\(432\) | 18.1786 | + | 16.7490i | 0.874617 | + | 0.805839i | ||||
\(433\) | 13.0519i | 0.627233i | 0.949550 | + | 0.313616i | \(0.101541\pi\) | ||||
−0.949550 | + | 0.313616i | \(0.898459\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.0194 | + | 7.94194i | −0.528338 | + | 0.380787i | ||||
\(436\) | 1.37154 | 0.0656850 | ||||||||
\(437\) | 10.1579 | − | 17.5940i | 0.485918 | − | 0.841634i | ||||
\(438\) | −16.1247 | − | 22.3730i | −0.770470 | − | 1.06902i | ||||
\(439\) | −27.6736 | + | 15.9773i | −1.32079 | + | 0.762557i | −0.983854 | − | 0.178972i | \(-0.942723\pi\) |
−0.336933 | + | 0.941529i | \(0.609389\pi\) | |||||||
\(440\) | 13.3208 | 0.635046 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.55255 | 0.121412 | ||||||||
\(443\) | −21.4748 | + | 12.3985i | −1.02030 | + | 0.589068i | −0.914190 | − | 0.405286i | \(-0.867172\pi\) |
−0.106107 | + | 0.994355i | \(0.533838\pi\) | |||||||
\(444\) | 3.64376 | − | 0.368914i | 0.172925 | − | 0.0175079i | ||||
\(445\) | −9.49496 | + | 16.4458i | −0.450104 | + | 0.779603i | ||||
\(446\) | 5.97449 | 0.282900 | ||||||||
\(447\) | 24.8634 | + | 11.1838i | 1.17600 | + | 0.528977i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.7710i | 0.649892i | 0.945733 | + | 0.324946i | \(0.105346\pi\) | ||||
−0.945733 | + | 0.324946i | \(0.894654\pi\) | |||||||
\(450\) | 6.80143 | + | 2.26748i | 0.320622 | + | 0.106890i | ||||
\(451\) | 15.9989 | − | 9.23700i | 0.753361 | − | 0.434953i | ||||
\(452\) | − | 7.07502i | − | 0.332781i | ||||||
\(453\) | 1.40876 | − | 3.13189i | 0.0661894 | − | 0.147149i | ||||
\(454\) | −23.7439 | + | 13.7085i | −1.11436 | + | 0.643374i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.47056 | − | 3.42789i | −0.115695 | − | 0.160525i | ||||
\(457\) | −13.6554 | − | 23.6518i | −0.638771 | − | 1.10638i | −0.985703 | − | 0.168494i | \(-0.946110\pi\) |
0.346931 | − | 0.937890i | \(-0.387224\pi\) | |||||||
\(458\) | −3.15670 | − | 5.46757i | −0.147503 | − | 0.255483i | ||||
\(459\) | 11.7612 | + | 10.8363i | 0.548964 | + | 0.505795i | ||||
\(460\) | 25.5680 | + | 14.7617i | 1.19211 | + | 0.688266i | ||||
\(461\) | −5.51822 | + | 9.55784i | −0.257009 | + | 0.445153i | −0.965439 | − | 0.260628i | \(-0.916070\pi\) |
0.708430 | + | 0.705781i | \(0.249404\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.2346 | − | 21.1910i | −0.568591 | − | 0.984829i | −0.996706 | − | 0.0811042i | \(-0.974155\pi\) |
0.428115 | − | 0.903724i | \(-0.359178\pi\) | |||||||
\(464\) | 14.8881i | 0.691163i | ||||||||
\(465\) | 36.8527 | − | 26.5607i | 1.70901 | − | 1.23172i | ||||
\(466\) | −9.12059 | −0.422503 | ||||||||
\(467\) | −7.95241 | + | 13.7740i | −0.367994 | + | 0.637384i | −0.989252 | − | 0.146222i | \(-0.953289\pi\) |
0.621258 | + | 0.783606i | \(0.286622\pi\) | |||||||
\(468\) | 1.48713 | − | 1.31860i | 0.0687427 | − | 0.0609521i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.69451 | − | 5.01978i | −0.401048 | − | 0.231545i | ||||
\(471\) | −11.7922 | + | 8.49896i | −0.543358 | + | 0.391612i | ||||
\(472\) | −5.99943 | − | 3.46377i | −0.276146 | − | 0.159433i | ||||
\(473\) | −46.2169 | − | 26.6834i | −2.12506 | − | 1.22690i | ||||
\(474\) | 1.50807 | − | 1.08690i | 0.0692680 | − | 0.0499232i | ||||
\(475\) | −2.85063 | − | 1.64581i | −0.130796 | − | 0.0755151i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.8149 | + | 4.60564i | 0.632539 | + | 0.210878i | ||||
\(478\) | −14.7021 | + | 25.4648i | −0.672459 | + | 1.16473i | ||||
\(479\) | 13.8537 | 0.632991 | 0.316496 | − | 0.948594i | \(-0.397494\pi\) | ||||
0.316496 | + | 0.948594i | \(0.397494\pi\) | |||||||
\(480\) | 24.6294 | − | 17.7510i | 1.12417 | − | 0.810218i | ||||
\(481\) | 0.628521i | 0.0286581i | ||||||||
\(482\) | −0.718964 | − | 1.24528i | −0.0327479 | − | 0.0567210i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15.2781 | + | 26.4624i | −0.694458 | + | 1.20284i | ||||
\(485\) | 8.08506 | + | 4.66791i | 0.367123 | + | 0.211959i | ||||
\(486\) | 29.1285 | + | 0.556150i | 1.32130 | + | 0.0252275i | ||||
\(487\) | −14.3993 | − | 24.9404i | −0.652496 | − | 1.13016i | −0.982515 | − | 0.186182i | \(-0.940389\pi\) |
0.330020 | − | 0.943974i | \(-0.392945\pi\) | |||||||
\(488\) | −4.05411 | − | 7.02193i | −0.183521 | − | 0.317868i | ||||
\(489\) | 1.08777 | + | 1.50927i | 0.0491905 | + | 0.0682514i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.5627 | + | 19.3774i | −1.51466 | + | 0.874492i | −0.514812 | + | 0.857303i | \(0.672138\pi\) |
−0.999852 | + | 0.0171884i | \(0.994528\pi\) | |||||||
\(492\) | 3.49340 | − | 7.76636i | 0.157495 | − | 0.350135i | ||||
\(493\) | 9.63230i | 0.433817i | ||||||||
\(494\) | −1.84893 | + | 1.06748i | −0.0831872 | + | 0.0480281i | ||||
\(495\) | 31.5517 | − | 27.9760i | 1.41814 | − | 1.25743i | ||||
\(496\) | − | 49.7911i | − | 2.23569i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 25.0062 | + | 11.2481i | 1.12056 | + | 0.504039i | ||||
\(499\) | −3.46667 | −0.155189 | −0.0775946 | − | 0.996985i | \(-0.524724\pi\) | ||||
−0.0775946 | + | 0.996985i | \(0.524724\pi\) | |||||||
\(500\) | −6.96045 | + | 12.0558i | −0.311281 | + | 0.539154i | ||||
\(501\) | −13.7767 | + | 1.39482i | −0.615496 | + | 0.0623161i | ||||
\(502\) | −1.85395 | + | 1.07038i | −0.0827458 | + | 0.0477733i | ||||
\(503\) | −28.2202 | −1.25828 | −0.629138 | − | 0.777293i | \(-0.716592\pi\) | ||||
−0.629138 | + | 0.777293i | \(0.716592\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.8794 | −0.840124 | ||||||||
\(506\) | 71.6552 | − | 41.3701i | 3.18546 | − | 1.83913i | ||||
\(507\) | −12.9659 | − | 17.9901i | −0.575835 | − | 0.798966i | ||||
\(508\) | 5.50326 | − | 9.53193i | 0.244168 | − | 0.422911i | ||||
\(509\) | −35.8124 | −1.58736 | −0.793678 | − | 0.608338i | \(-0.791836\pi\) | ||||
−0.793678 | + | 0.608338i | \(0.791836\pi\) | |||||||
\(510\) | 20.2523 | − | 14.5963i | 0.896786 | − | 0.646336i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 24.2599i | − | 1.07215i | ||||||
\(513\) | −13.0509 | − | 2.93068i | −0.576211 | − | 0.129393i | ||||
\(514\) | −46.9111 | + | 27.0841i | −2.06916 | + | 1.19463i | ||||
\(515\) | 35.8908i | 1.58154i | ||||||||
\(516\) | −24.4751 | + | 2.47799i | −1.07746 | + | 0.109088i | ||||
\(517\) | −10.4147 | + | 6.01291i | −0.458036 | + | 0.264447i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.72925 | + | 0.175079i | −0.0759057 | + | 0.00768511i | ||||
\(520\) | 0.526897 | + | 0.912612i | 0.0231060 | + | 0.0400207i | ||||
\(521\) | 13.4608 | + | 23.3148i | 0.589729 | + | 1.02144i | 0.994268 | + | 0.106920i | \(0.0340989\pi\) |
−0.404538 | + | 0.914521i | \(0.632568\pi\) | |||||||
\(522\) | 11.6418 | + | 13.1297i | 0.509546 | + | 0.574673i | ||||
\(523\) | −7.82181 | − | 4.51593i | −0.342024 | − | 0.197468i | 0.319143 | − | 0.947707i | \(-0.396605\pi\) |
−0.661167 | + | 0.750239i | \(0.729938\pi\) | |||||||
\(524\) | 5.86943 | − | 10.1662i | 0.256407 | − | 0.444110i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.8020 | + | 22.1737i | 0.558193 | + | 0.966819i | ||||
\(527\) | − | 32.2139i | − | 1.40326i | ||||||
\(528\) | −4.65572 | − | 45.9845i | −0.202614 | − | 2.00122i | ||||
\(529\) | −39.2852 | −1.70805 | ||||||||
\(530\) | 11.3661 | − | 19.6866i | 0.493710 | − | 0.855131i | ||||
\(531\) | −21.4847 | + | 4.39552i | −0.932357 | + | 0.190749i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.26565 | + | 0.730726i | 0.0548216 | + | 0.0316513i | ||||
\(534\) | 22.3734 | + | 10.0638i | 0.968190 | + | 0.435503i | ||||
\(535\) | 29.2664 | + | 16.8969i | 1.26530 | + | 0.730518i | ||||
\(536\) | −1.53384 | − | 0.885563i | −0.0662518 | − | 0.0382505i | ||||
\(537\) | 0.257412 | + | 2.54245i | 0.0111081 | + | 0.109715i | ||||
\(538\) | 16.9615 | + | 9.79273i | 0.731262 | + | 0.422195i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.25893 | − | 18.9658i | 0.183275 | − | 0.816159i | ||||
\(541\) | −5.66792 | + | 9.81713i | −0.243683 | + | 0.422071i | −0.961760 | − | 0.273892i | \(-0.911689\pi\) |
0.718078 | + | 0.695963i | \(0.245022\pi\) | |||||||
\(542\) | 12.2342 | 0.525504 | ||||||||
\(543\) | 23.7636 | + | 10.6891i | 1.01979 | + | 0.458715i | ||||
\(544\) | − | 21.5291i | − | 0.923053i | ||||||
\(545\) | 1.15100 | + | 1.99360i | 0.0493035 | + | 0.0853962i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4246 | − | 33.6444i | 0.830537 | − | 1.43853i | −0.0670762 | − | 0.997748i | \(-0.521367\pi\) |
0.897613 | − | 0.440784i | \(-0.145300\pi\) | |||||||
\(548\) | 14.9587 | + | 8.63644i | 0.639006 | + | 0.368930i | ||||
\(549\) | −24.3497 | − | 8.11780i | −1.03922 | − | 0.346459i | ||||
\(550\) | −6.70292 | − | 11.6098i | −0.285813 | − | 0.495043i | ||||
\(551\) | −4.02823 | − | 6.97711i | −0.171609 | − | 0.297235i | ||||
\(552\) | −5.31421 | + | 11.8143i | −0.226188 | + | 0.502850i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −36.3061 | + | 20.9613i | −1.54250 | + | 0.890562i | ||||
\(555\) | 3.59409 | + | 4.98677i | 0.152561 | + | 0.211677i | ||||
\(556\) | − | 29.2613i | − | 1.24096i | ||||||
\(557\) | 6.29167 | − | 3.63249i | 0.266586 | − | 0.153914i | −0.360749 | − | 0.932663i | \(-0.617479\pi\) |
0.627335 | + | 0.778749i | \(0.284146\pi\) | |||||||
\(558\) | −38.9342 | − | 43.9106i | −1.64822 | − | 1.85888i | ||||
\(559\) | − | 4.22177i | − | 0.178562i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.01216 | − | 29.7510i | −0.127173 | − | 1.25609i | ||||
\(562\) | −41.7697 | −1.76195 | ||||||||
\(563\) | −11.5409 | + | 19.9894i | −0.486390 | + | 0.842453i | −0.999878 | − | 0.0156446i | \(-0.995020\pi\) |
0.513487 | + | 0.858097i | \(0.328353\pi\) | |||||||
\(564\) | −2.27406 | + | 5.05558i | −0.0957552 | + | 0.212879i | ||||
\(565\) | 10.2838 | − | 5.93738i | 0.432644 | − | 0.249787i | ||||
\(566\) | 35.4561 | 1.49033 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.79889 | −0.117439 | ||||||||
\(569\) | 15.5482 | − | 8.97677i | 0.651815 | − | 0.376326i | −0.137336 | − | 0.990525i | \(-0.543854\pi\) |
0.789151 | + | 0.614199i | \(0.210521\pi\) | |||||||
\(570\) | −8.56544 | + | 19.0423i | −0.358767 | + | 0.797594i | ||||
\(571\) | 7.04234 | − | 12.1977i | 0.294713 | − | 0.510457i | −0.680205 | − | 0.733022i | \(-0.738109\pi\) |
0.974918 | + | 0.222564i | \(0.0714427\pi\) | |||||||
\(572\) | −3.71639 | −0.155390 | ||||||||
\(573\) | −2.30715 | − | 22.7877i | −0.0963826 | − | 0.951969i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.0916i | 0.420851i | ||||||||
\(576\) | −7.08456 | − | 7.99007i | −0.295190 | − | 0.332919i | ||||
\(577\) | −26.0392 | + | 15.0337i | −1.08403 | + | 0.625862i | −0.931979 | − | 0.362511i | \(-0.881919\pi\) |
−0.152046 | + | 0.988373i | \(0.548586\pi\) | |||||||
\(578\) | 14.0689i | 0.585190i | ||||||||
\(579\) | 1.57549 | + | 2.18598i | 0.0654752 | + | 0.0908463i | ||||
\(580\) | 10.1393 | − | 5.85392i | 0.421011 | − | 0.243071i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.94756 | − | 10.9992i | 0.205083 | − | 0.455931i | ||||
\(583\) | −13.6148 | − | 23.5815i | −0.563866 | − | 0.976644i | ||||
\(584\) | −4.03690 | − | 6.99211i | −0.167048 | − | 0.289336i | ||||
\(585\) | 3.16464 | + | 1.05504i | 0.130842 | + | 0.0436205i | ||||
\(586\) | 14.2800 | + | 8.24455i | 0.589900 | + | 0.340579i | ||||
\(587\) | 18.0979 | − | 31.3465i | 0.746981 | − | 1.29381i | −0.202283 | − | 0.979327i | \(-0.564836\pi\) |
0.949264 | − | 0.314481i | \(-0.101831\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.4719 | + | 23.3339i | 0.555098 | + | 0.961459i | ||||
\(590\) | 34.2327i | 1.40934i | ||||||||
\(591\) | 7.83776 | + | 3.52552i | 0.322403 | + | 0.145020i | ||||
\(592\) | 6.73755 | 0.276911 | ||||||||
\(593\) | 1.02158 | − | 1.76943i | 0.0419514 | − | 0.0726620i | −0.844287 | − | 0.535891i | \(-0.819976\pi\) |
0.886239 | + | 0.463229i | \(0.153309\pi\) | |||||||
\(594\) | −40.0635 | − | 36.9130i | −1.64382 | − | 1.51456i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −20.3507 | − | 11.7495i | −0.833598 | − | 0.481278i | ||||
\(597\) | 1.95271 | + | 19.2869i | 0.0799190 | + | 0.789359i | ||||
\(598\) | 5.66854 | + | 3.27273i | 0.231804 | + | 0.133832i | ||||
\(599\) | 15.7873 | + | 9.11478i | 0.645050 | + | 0.372420i | 0.786557 | − | 0.617517i | \(-0.211861\pi\) |
−0.141507 | + | 0.989937i | \(0.545195\pi\) | |||||||
\(600\) | 1.91419 | + | 0.861025i | 0.0781466 | + | 0.0351512i | ||||
\(601\) | −32.1713 | − | 18.5741i | −1.31230 | − | 0.757654i | −0.329820 | − | 0.944044i | \(-0.606988\pi\) |
−0.982476 | + | 0.186390i | \(0.940321\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.49287 | + | 1.12378i | −0.223687 | + | 0.0457637i | ||||
\(604\) | −1.48002 | + | 2.56346i | −0.0602210 | + | 0.104306i | ||||
\(605\) | −51.2856 | −2.08506 | ||||||||
\(606\) | 2.45680 | + | 24.2658i | 0.0998008 | + | 0.985731i | ||||
\(607\) | 19.8296i | 0.804860i | 0.915451 | + | 0.402430i | \(0.131834\pi\) | ||||
−0.915451 | + | 0.402430i | \(0.868166\pi\) | |||||||
\(608\) | 9.00349 | + | 15.5945i | 0.365140 | + | 0.632440i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.0336 | + | 34.6991i | −0.811135 | + | 1.40493i | ||||
\(611\) | −0.823890 | − | 0.475673i | −0.0333310 | − | 0.0192437i | ||||
\(612\) | −9.14501 | − | 10.3139i | −0.369665 | − | 0.416914i | ||||
\(613\) | 6.34412 | + | 10.9883i | 0.256237 | + | 0.443815i | 0.965231 | − | 0.261400i | \(-0.0841840\pi\) |
−0.708994 | + | 0.705214i | \(0.750851\pi\) | |||||||
\(614\) | 26.8690 | + | 46.5385i | 1.08435 | + | 1.87814i | ||||
\(615\) | 14.2204 | − | 1.43975i | 0.573422 | − | 0.0580564i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.37247 | − | 2.52445i | 0.176029 | − | 0.101630i | −0.409397 | − | 0.912357i | \(-0.634261\pi\) |
0.585426 | + | 0.810726i | \(0.300927\pi\) | |||||||
\(618\) | 46.1305 | − | 4.67051i | 1.85564 | − | 0.187875i | ||||
\(619\) | − | 0.267890i | − | 0.0107674i | −0.999986 | − | 0.00538370i | \(-0.998286\pi\) | ||
0.999986 | − | 0.00538370i | \(-0.00171369\pi\) | |||||||
\(620\) | −33.9094 | + | 19.5776i | −1.36183 | + | 0.786255i | ||||
\(621\) | 12.2248 | + | 39.1440i | 0.490563 | + | 1.57080i | ||||
\(622\) | 24.8305i | 0.995611i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.96625 | − | 2.13785i | 0.118745 | − | 0.0855824i | ||||
\(625\) | −29.7584 | −1.19034 | ||||||||
\(626\) | −29.4820 | + | 51.0644i | −1.17834 | + | 2.04094i | ||||
\(627\) | 14.6237 | + | 20.2903i | 0.584016 | + | 0.810317i | ||||
\(628\) | 10.8504 | − | 6.26449i | 0.432979 | − | 0.249981i | ||||
\(629\) | 4.35905 | 0.173807 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.7899 | 1.50439 | 0.752197 | − | 0.658938i | \(-0.228994\pi\) | ||||
0.752197 | + | 0.658938i | \(0.228994\pi\) | |||||||
\(632\) | 0.471310 | − | 0.272111i | 0.0187477 | − | 0.0108240i | ||||
\(633\) | −26.4699 | + | 2.67996i | −1.05208 | + | 0.106519i | ||||
\(634\) | 18.7556 | − | 32.4856i | 0.744880 | − | 1.29017i | ||||
\(635\) | 18.4734 | 0.733095 | ||||||||
\(636\) | −11.4471 | − | 5.14905i | −0.453908 | − | 0.204173i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 32.8117i | − | 1.29903i | ||||||
\(639\) | −6.62944 | + | 5.87813i | −0.262257 | + | 0.232535i | ||||
\(640\) | 15.9234 | − | 9.19336i | 0.629426 | − | 0.363400i | ||||
\(641\) | − | 34.4090i | − | 1.35907i | −0.733641 | − | 0.679537i | \(-0.762181\pi\) | ||
0.733641 | − | 0.679537i | \(-0.237819\pi\) | |||||||
\(642\) | 17.9092 | − | 39.8150i | 0.706821 | − | 1.57137i | ||||
\(643\) | 0.676278 | − | 0.390449i | 0.0266698 | − | 0.0153978i | −0.486606 | − | 0.873622i | \(-0.661765\pi\) |
0.513276 | + | 0.858224i | \(0.328432\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.1415 | − | 33.4961i | −0.950569 | − | 1.31891i | ||||
\(646\) | 7.40341 | + | 12.8231i | 0.291283 | + | 0.504517i | ||||
\(647\) | 9.82182 | + | 17.0119i | 0.386136 | + | 0.668807i | 0.991926 | − | 0.126818i | \(-0.0404763\pi\) |
−0.605790 | + | 0.795624i | \(0.707143\pi\) | |||||||
\(648\) | 8.46790 | + | 1.02099i | 0.332650 | + | 0.0401082i | ||||
\(649\) | 35.5118 | + | 20.5027i | 1.39396 | + | 0.804803i | ||||
\(650\) | 0.530259 | − | 0.918435i | 0.0207985 | − | 0.0360240i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.801781 | − | 1.38872i | −0.0314001 | − | 0.0543867i | ||||
\(653\) | 3.20545i | 0.125439i | 0.998031 | + | 0.0627194i | \(0.0199773\pi\) | ||||
−0.998031 | + | 0.0627194i | \(0.980023\pi\) | |||||||
\(654\) | 2.41259 | − | 1.73882i | 0.0943399 | − | 0.0679931i | ||||
\(655\) | 19.7026 | 0.769843 | ||||||||
\(656\) | 7.83315 | − | 13.5674i | 0.305833 | − | 0.529719i | ||||
\(657\) | −24.2464 | − | 8.08333i | −0.945940 | − | 0.315361i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.2959 | − | 14.0273i | −0.946435 | − | 0.546425i | −0.0544636 | − | 0.998516i | \(-0.517345\pi\) |
−0.891972 | + | 0.452091i | \(0.850678\pi\) | |||||||
\(660\) | −29.4863 | + | 21.2515i | −1.14775 | + | 0.827215i | ||||
\(661\) | −28.0490 | − | 16.1941i | −1.09098 | − | 0.629878i | −0.157143 | − | 0.987576i | \(-0.550228\pi\) |
−0.933837 | + | 0.357698i | \(0.883562\pi\) | |||||||
\(662\) | 2.01981 | + | 1.16614i | 0.0785020 | + | 0.0453232i | ||||
\(663\) | 1.91910 | − | 1.38314i | 0.0745317 | − | 0.0537169i | ||||
\(664\) | 6.95189 | + | 4.01367i | 0.269785 | + | 0.155761i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.94181 | − | 5.26843i | 0.230240 | − | 0.204148i | ||||
\(667\) | −12.3500 | + | 21.3908i | −0.478193 | + | 0.828255i | ||||
\(668\) | 11.9354 | 0.461793 | ||||||||
\(669\) | 4.49184 | − | 3.23738i | 0.173665 | − | 0.125164i | ||||
\(670\) | 8.75209i | 0.338123i | ||||||||
\(671\) | 23.9971 | + | 41.5641i | 0.926397 | + | 1.60457i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.3088 | + | 17.8554i | −0.397375 | + | 0.688273i | −0.993401 | − | 0.114692i | \(-0.963412\pi\) |
0.596026 | + | 0.802965i | \(0.296745\pi\) | |||||||
\(674\) | −21.3242 | − | 12.3115i | −0.821378 | − | 0.474223i | ||||
\(675\) | 6.34224 | − | 1.98070i | 0.244113 | − | 0.0762371i | ||||
\(676\) | 9.55701 | + | 16.5532i | 0.367577 | + | 0.636663i | ||||
\(677\) | −25.1655 | − | 43.5880i | −0.967190 | − | 1.67522i | −0.703612 | − | 0.710585i | \(-0.748431\pi\) |
−0.263578 | − | 0.964638i | \(-0.584903\pi\) | |||||||
\(678\) | −8.96958 | − | 12.4452i | −0.344475 | − | 0.477956i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.32935 | − | 3.65425i | 0.242719 | − | 0.140134i | ||||
\(681\) | −10.4233 | + | 23.1726i | −0.399422 | + | 0.887977i | ||||
\(682\) | 109.734i | 4.20193i | ||||||||
\(683\) | −11.9031 | + | 6.87227i | −0.455460 | + | 0.262960i | −0.710133 | − | 0.704067i | \(-0.751365\pi\) |
0.254673 | + | 0.967027i | \(0.418032\pi\) | |||||||
\(684\) | 10.9374 | + | 3.64635i | 0.418203 | + | 0.139422i | ||||
\(685\) | 28.9909i | 1.10769i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.33602 | − | 2.40020i | −0.203582 | − | 0.0915735i | ||||
\(688\) | −45.2560 | −1.72537 | ||||||||
\(689\) | 1.07705 | − | 1.86550i | 0.0410321 | − | 0.0710698i | ||||
\(690\) | 63.6895 | − | 6.44828i | 2.42462 | − | 0.245482i | ||||
\(691\) | −25.4328 | + | 14.6837i | −0.967511 | + | 0.558593i | −0.898476 | − | 0.439022i | \(-0.855325\pi\) |
−0.0690343 | + | 0.997614i | \(0.521992\pi\) | |||||||
\(692\) | 1.49813 | 0.0569504 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −50.5874 | −1.92027 | ||||||||
\(695\) | 42.5325 | − | 24.5562i | 1.61335 | − | 0.931468i | ||||
\(696\) | 3.00371 | + | 4.16763i | 0.113856 | + | 0.157974i | ||||
\(697\) | 5.06789 | − | 8.77784i | 0.191960 | − | 0.332484i | ||||
\(698\) | −65.4785 | −2.47840 | ||||||||
\(699\) | −6.85719 | + | 4.94215i | −0.259363 | + | 0.186929i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.2011i | 1.66945i | 0.550666 | + | 0.834726i | \(0.314374\pi\) | ||||
−0.550666 | + | 0.834726i | \(0.685626\pi\) | |||||||
\(702\) | 0.944227 | − | 4.20482i | 0.0356375 | − | 0.158701i | ||||
\(703\) | −3.15746 | + | 1.82296i | −0.119086 | + | 0.0687542i | ||||
\(704\) | 19.9674i | 0.752551i | ||||||||
\(705\) | −9.25691 | + | 0.937220i | −0.348635 | + | 0.0352977i | ||||
\(706\) | 4.08702 | − | 2.35964i | 0.153817 | − | 0.0888063i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 18.8060 | − | 1.90402i | 0.706772 | − | 0.0715575i | ||||
\(709\) | 5.66629 | + | 9.81430i | 0.212802 | + | 0.368584i | 0.952590 | − | 0.304256i | \(-0.0984077\pi\) |
−0.739788 | + | 0.672840i | \(0.765074\pi\) | |||||||
\(710\) | 6.91542 | + | 11.9779i | 0.259531 | + | 0.449521i | ||||
\(711\) | 0.544865 | − | 1.63435i | 0.0204340 | − | 0.0612929i | ||||
\(712\) | 6.21994 | + | 3.59108i | 0.233102 | + | 0.134581i | ||||
\(713\) | 41.3028 | − | 71.5385i | 1.54680 | − | 2.67914i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.11881 | − | 5.40193i | −0.116637 | − | 0.202021i | ||||
\(716\) | − | 2.20265i | − | 0.0823168i | ||||||
\(717\) | 2.74497 | + | 27.1120i | 0.102513 | + | 1.01252i | ||||
\(718\) | −13.5827 | −0.506903 | ||||||||
\(719\) | 18.0647 | − | 31.2890i | 0.673700 | − | 1.16688i | −0.303147 | − | 0.952944i | \(-0.598037\pi\) |
0.976847 | − | 0.213939i | \(-0.0686294\pi\) | |||||||
\(720\) | 11.3097 | − | 33.9240i | 0.421487 | − | 1.26427i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 20.0271 | + | 11.5627i | 0.745333 | + | 0.430318i | ||||
\(723\) | −1.21532 | − | 0.546665i | −0.0451983 | − | 0.0203307i | ||||
\(724\) | −19.4505 | − | 11.2298i | −0.722874 | − | 0.417351i | ||||
\(725\) | 3.46580 | + | 2.00098i | 0.128717 | + | 0.0743146i | ||||
\(726\) | 6.67386 | + | 65.9176i | 0.247690 | + | 2.44643i | ||||
\(727\) | −6.20547 | − | 3.58273i | −0.230148 | − | 0.132876i | 0.380492 | − | 0.924784i | \(-0.375755\pi\) |
−0.610640 | + | 0.791908i | \(0.709088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.2013 | − | 15.3657i | 0.822269 | − | 0.569099i | ||||
\(730\) | −19.9485 | + | 34.5518i | −0.738327 | + | 1.27882i | ||||
\(731\) | −29.2797 | −1.08295 | ||||||||
\(732\) | 20.1765 | + | 9.07560i | 0.745744 | + | 0.335444i | ||||
\(733\) | 47.8498i | 1.76737i | 0.468081 | + | 0.883685i | \(0.344945\pi\) | ||||
−0.468081 | + | 0.883685i | \(0.655055\pi\) | |||||||
\(734\) | −12.5938 | − | 21.8131i | −0.464846 | − | 0.805136i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.6034 | − | 47.8105i | 1.01747 | − | 1.76232i | ||||
\(737\) | 9.07910 | + | 5.24182i | 0.334433 | + | 0.193085i | ||||
\(738\) | −3.70104 | − | 18.0902i | −0.136237 | − | 0.665909i | ||||
\(739\) | −7.67416 | − | 13.2920i | −0.282299 | − | 0.488956i | 0.689652 | − | 0.724141i | \(-0.257764\pi\) |
−0.971951 | + | 0.235185i | \(0.924430\pi\) | |||||||
\(740\) | −2.64917 | − | 4.58849i | −0.0973853 | − | 0.168676i | ||||
\(741\) | −0.811659 | + | 1.80444i | −0.0298170 | + | 0.0662879i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.9422 | − | 20.1739i | 1.28191 | − | 0.740109i | 0.304709 | − | 0.952445i | \(-0.401441\pi\) |
0.977197 | + | 0.212337i | \(0.0681073\pi\) | |||||||
\(744\) | −10.0455 | − | 13.9380i | −0.368286 | − | 0.510994i | ||||
\(745\) | − | 39.4409i | − | 1.44500i | ||||||
\(746\) | −38.4630 | + | 22.2066i | −1.40823 | + | 0.813042i | ||||
\(747\) | 24.8956 | − | 5.09334i | 0.910882 | − | 0.186355i | ||||
\(748\) | 25.7747i | 0.942417i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.04050 | + | 30.0310i | 0.111023 | + | 1.09658i | ||||
\(751\) | 33.8898 | 1.23665 | 0.618327 | − | 0.785921i | \(-0.287811\pi\) | ||||
0.618327 | + | 0.785921i | \(0.287811\pi\) | |||||||
\(752\) | −5.09906 | + | 8.83183i | −0.185944 | + | 0.322064i | ||||
\(753\) | −0.813864 | + | 1.80935i | −0.0296589 | + | 0.0659362i | ||||
\(754\) | 2.24793 | − | 1.29784i | 0.0818647 | − | 0.0472646i | ||||
\(755\) | −4.96814 | −0.180809 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.73237 | −0.208346 | −0.104173 | − | 0.994559i | \(-0.533220\pi\) | ||||
−0.104173 | + | 0.994559i | \(0.533220\pi\) | |||||||
\(758\) | −34.3589 | + | 19.8371i | −1.24797 | + | 0.720517i | ||||
\(759\) | 31.4559 | − | 69.9312i | 1.14178 | − | 2.53834i | ||||
\(760\) | −3.05642 | + | 5.29387i | −0.110868 | + | 0.192029i | ||||
\(761\) | −26.5332 | −0.961828 | −0.480914 | − | 0.876768i | \(-0.659695\pi\) | ||||
−0.480914 | + | 0.876768i | \(0.659695\pi\) | |||||||
\(762\) | −2.40397 | − | 23.7439i | −0.0870865 | − | 0.860152i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 19.7420i | 0.714242i | ||||||||
\(765\) | 7.31713 | − | 21.9481i | 0.264551 | − | 0.793535i | ||||
\(766\) | 20.9741 | − | 12.1094i | 0.757825 | − | 0.437531i | ||||
\(767\) | 3.24389i | 0.117130i | ||||||||
\(768\) | −21.0980 | − | 29.2733i | −0.761307 | − | 1.05631i | ||||
\(769\) | 23.3944 | − | 13.5068i | 0.843623 | − | 0.487066i | −0.0148711 | − | 0.999889i | \(-0.504734\pi\) |
0.858494 | + | 0.512823i | \(0.171400\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.5935 | + | 45.7824i | −0.741655 | + | 1.64881i | ||||
\(772\) | −1.16128 | − | 2.01139i | −0.0417953 | − | 0.0723916i | ||||
\(773\) | 11.3009 | + | 19.5737i | 0.406464 | + | 0.704016i | 0.994491 | − | 0.104826i | \(-0.0334284\pi\) |
−0.588027 | + | 0.808841i | \(0.700095\pi\) | |||||||
\(774\) | −39.9111 | + | 35.3880i | −1.43457 | + | 1.27200i | ||||
\(775\) | −11.5909 | − | 6.69201i | −0.416357 | − | 0.240384i | ||||
\(776\) | 1.76545 | − | 3.05784i | 0.0633758 | − | 0.109770i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.2296 | + | 17.7182i | 0.366750 | + | 0.635229i | ||||
\(779\) | 8.47758i | 0.303741i | ||||||||
\(780\) | −2.62226 | − | 1.17952i | −0.0938918 | − | 0.0422336i | ||||
\(781\) | 16.5672 | 0.592821 | ||||||||
\(782\) | 22.6978 | − | 39.3137i | 0.811670 | − | 1.40585i | ||||
\(783\) | 15.8673 | + | 3.56313i | 0.567051 | + | 0.127336i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.2114 | + | 10.5144i | 0.649993 | + | 0.375274i | ||||
\(786\) | −2.56392 | − | 25.3238i | −0.0914519 | − | 0.903270i | ||||
\(787\) | −22.6864 | − | 13.0980i | −0.808683 | − | 0.466893i | 0.0378153 | − | 0.999285i | \(-0.487960\pi\) |
−0.846498 | + | 0.532391i | \(0.821293\pi\) | |||||||
\(788\) | −6.41523 | − | 3.70383i | −0.228533 | − | 0.131944i | ||||
\(789\) | 21.6402 | + | 9.73401i | 0.770412 | + | 0.346540i | ||||
\(790\) | −2.32900 | − | 1.34465i | −0.0828620 | − | 0.0478404i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −10.5808 | − | 11.9331i | −0.375971 | − | 0.424026i | ||||
\(793\) | −1.89838 | + | 3.28808i | −0.0674133 | + | 0.116763i | ||||
\(794\) | 55.8627 | 1.98249 | ||||||||
\(795\) | −2.12210 | − | 20.9600i | −0.0752633 | − | 0.743375i | ||||
\(796\) | − | 16.7091i | − | 0.592239i | ||||||
\(797\) | −5.96560 | − | 10.3327i | −0.211312 | − | 0.366004i | 0.740813 | − | 0.671711i | \(-0.234440\pi\) |
−0.952126 | + | 0.305707i | \(0.901107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.29899 | + | 5.71402i | −0.116710 | + | 0.202147i | ||||
\(800\) | −7.74640 | − | 4.47239i | −0.273877 | − | 0.158123i | ||||
\(801\) | 22.2744 | − | 4.55707i | 0.787026 | − | 0.161016i | ||||
\(802\) | −17.9370 | − | 31.0678i | −0.633378 | − | 1.09704i | ||||
\(803\) | 23.8952 | + | 41.3877i | 0.843242 | + | 1.46054i | ||||
\(804\) | 4.80802 | − | 0.486790i | 0.169566 | − | 0.0171678i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.51788 | + | 4.34045i | −0.264806 | + | 0.152886i | ||||
\(807\) | 18.0586 | − | 1.82836i | 0.635694 | − | 0.0643612i | ||||
\(808\) | 7.14038i | 0.251198i | ||||||||
\(809\) | −22.9399 | + | 13.2443i | −0.806522 | + | 0.465646i | −0.845747 | − | 0.533585i | \(-0.820845\pi\) |
0.0392244 | + | 0.999230i | \(0.487511\pi\) | |||||||
\(810\) | −16.5529 | − | 38.7610i | −0.581610 | − | 1.36192i | ||||
\(811\) | − | 13.7419i | − | 0.482544i | −0.970458 | − | 0.241272i | \(-0.922435\pi\) | ||
0.970458 | − | 0.241272i | \(-0.0775646\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.19812 | − | 6.62932i | 0.322592 | − | 0.232500i | ||||
\(814\) | −14.8488 | −0.520449 | ||||||||
\(815\) | 1.34571 | − | 2.33084i | 0.0471383 | − | 0.0816459i | ||||
\(816\) | −14.8269 | − | 20.5722i | −0.519044 | − | 0.720169i | ||||
\(817\) | 21.2086 | − | 12.2448i | 0.741996 | − | 0.428391i | ||||
\(818\) | −53.8949 | −1.88439 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.3198 | −0.430226 | ||||||||
\(821\) | 11.7493 | − | 6.78346i | 0.410053 | − | 0.236744i | −0.280759 | − | 0.959778i | \(-0.590586\pi\) |
0.690813 | + | 0.723034i | \(0.257253\pi\) | |||||||
\(822\) | 37.2621 | − | 3.77262i | 1.29967 | − | 0.131585i | ||||
\(823\) | −7.34857 | + | 12.7281i | −0.256155 | + | 0.443674i | −0.965209 | − | 0.261481i | \(-0.915789\pi\) |
0.709053 | + | 0.705155i | \(0.249122\pi\) | |||||||
\(824\) | 13.5742 | 0.472881 | ||||||||
\(825\) | −11.3305 | − | 5.09658i | −0.394476 | − | 0.177440i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.8787i | 1.42149i | 0.703449 | + | 0.710746i | \(0.251642\pi\) | ||||
−0.703449 | + | 0.710746i | \(0.748358\pi\) | |||||||
\(828\) | −7.08481 | − | 34.6296i | −0.246214 | − | 1.20346i | ||||
\(829\) | 17.7189 | − | 10.2300i | 0.615402 | − | 0.355302i | −0.159675 | − | 0.987170i | \(-0.551045\pi\) |
0.775077 | + | 0.631867i | \(0.217711\pi\) | |||||||
\(830\) | − | 39.6675i | − | 1.37688i | ||||||
\(831\) | −15.9380 | + | 35.4326i | −0.552883 | + | 1.22914i | ||||
\(832\) | −1.36797 | + | 0.789798i | −0.0474258 | + | 0.0273813i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −37.0969 | − | 51.4717i | −1.28456 | − | 1.78232i | ||||
\(835\) | 10.0162 | + | 17.3486i | 0.346625 | + | 0.600372i | ||||
\(836\) | −10.7790 | − | 18.6698i | −0.372800 | − | 0.645708i | ||||
\(837\) | −53.0659 | − | 11.9164i | −1.83423 | − | 0.411891i | ||||
\(838\) | −16.3923 | − | 9.46412i | −0.566264 | − | 0.326932i | ||||
\(839\) | −27.3475 | + | 47.3673i | −0.944141 | + | 1.63530i | −0.186680 | + | 0.982421i | \(0.559773\pi\) |
−0.757462 | + | 0.652880i | \(0.773561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.60247 | − | 16.6320i | −0.331120 | − | 0.573516i | ||||
\(842\) | 47.5062i | 1.63717i | ||||||||
\(843\) | −31.4040 | + | 22.6336i | −1.08161 | + | 0.779544i | ||||
\(844\) | 22.9321 | 0.789356 | ||||||||
\(845\) | −16.0405 | + | 27.7830i | −0.551812 | + | 0.955766i | ||||
\(846\) | 2.40922 | + | 11.7760i | 0.0828308 | + | 0.404866i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.9975 | − | 11.5456i | −0.686718 | − | 0.396477i | ||||
\(849\) | 26.6572 | − | 19.2125i | 0.914873 | − | 0.659372i | ||||
\(850\) | −6.36973 | − | 3.67756i | −0.218480 | − | 0.126139i | ||||
\(851\) | 9.68031 | + | 5.58893i | 0.331837 | + | 0.191586i | ||||
\(852\) | 6.19548 | − | 4.46524i | 0.212254 | − | 0.152977i | ||||
\(853\) | −11.0684 | − | 6.39037i | −0.378976 | − | 0.218802i | 0.298396 | − | 0.954442i | \(-0.403548\pi\) |
−0.677373 | + | 0.735640i | \(0.736882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.87859 | + | 18.9580i | 0.132645 | + | 0.648351i | ||||
\(856\) | 6.39058 | − | 11.0688i | 0.218426 | − | 0.378324i | ||||
\(857\) | 18.3240 | 0.625936 | 0.312968 | − | 0.949764i | \(-0.398677\pi\) | ||||
0.312968 | + | 0.949764i | \(0.398677\pi\) | |||||||
\(858\) | −6.53727 | + | 4.71157i | −0.223179 | + | 0.160850i | ||||
\(859\) | − | 38.6339i | − | 1.31817i | −0.752068 | − | 0.659085i | \(-0.770944\pi\) | ||
0.752068 | − | 0.659085i | \(-0.229056\pi\) | |||||||
\(860\) | 17.7944 | + | 30.8208i | 0.606784 | + | 1.05098i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.1328 | + | 17.5505i | −0.345125 | + | 0.597774i | ||||
\(863\) | 14.4626 | + | 8.35001i | 0.492314 | + | 0.284238i | 0.725534 | − | 0.688186i | \(-0.241593\pi\) |
−0.233220 | + | 0.972424i | \(0.574926\pi\) | |||||||
\(864\) | −35.4649 | − | 7.96394i | −1.20654 | − | 0.270939i | ||||
\(865\) | 1.25724 | + | 2.17760i | 0.0427473 | + | 0.0740405i | ||||
\(866\) | −12.1966 | − | 21.1251i | −0.414456 | − | 0.717859i | ||||
\(867\) | 7.62350 | + | 10.5775i | 0.258908 | + | 0.359232i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.78978 | + | 1.61068i | −0.0946367 | + | 0.0546385i | ||||
\(870\) | 10.4139 | − | 23.1517i | 0.353064 | − | 0.784915i | ||||
\(871\) | 0.829346i | 0.0281013i | ||||||||
\(872\) | 0.753996 | − | 0.435320i | 0.0255335 | − | 0.0147418i | ||||
\(873\) | −2.24035 | − | 10.9505i | −0.0758242 | − | 0.370619i | ||||
\(874\) | 37.9689i | 1.28432i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.0908 | + | 9.03707i | 0.678805 | + | 0.305334i | ||||
\(877\) | 33.5234 | 1.13200 | 0.566002 | − | 0.824404i | \(-0.308489\pi\) | ||||
0.566002 | + | 0.824404i | \(0.308489\pi\) | |||||||
\(878\) | 29.8606 | − | 51.7201i | 1.00775 | − | 1.74547i | ||||
\(879\) | 15.2037 | − | 1.53930i | 0.512807 | − | 0.0519194i | ||||
\(880\) | −57.9070 | + | 33.4326i | −1.95204 | + | 1.12701i | ||||
\(881\) | 28.6657 | 0.965771 | 0.482885 | − | 0.875684i | \(-0.339589\pi\) | ||||
0.482885 | + | 0.875684i | \(0.339589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.2091 | −1.28584 | −0.642919 | − | 0.765935i | \(-0.722277\pi\) | ||||
−0.642919 | + | 0.765935i | \(0.722277\pi\) | |||||||
\(884\) | −1.76583 | + | 1.01950i | −0.0593912 | + | 0.0342895i | ||||
\(885\) | 18.5496 | + | 25.7374i | 0.623539 | + | 0.865154i | ||||
\(886\) | 23.1719 | − | 40.1350i | 0.778476 | − | 1.34836i | ||||
\(887\) | 35.1828 | 1.18132 | 0.590662 | − | 0.806919i | \(-0.298867\pi\) | ||||
0.590662 | + | 0.806919i | \(0.298867\pi\) | |||||||
\(888\) | 1.88604 | − | 1.35932i | 0.0632915 | − | 0.0456157i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 35.4910i | − | 1.18966i | ||||||
\(891\) | −50.1231 | − | 6.04342i | −1.67919 | − | 0.202462i | ||||
\(892\) | −4.13309 | + | 2.38624i | −0.138386 | + | 0.0798972i | ||||
\(893\) | − | 5.51856i | − | 0.184672i | ||||||
\(894\) | −50.6935 | + | 5.13249i | −1.69544 | + | 0.171656i | ||||
\(895\) | 3.20164 | − | 1.84847i | 0.107019 | − | 0.0617875i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.03521 | − | 0.611037i | 0.201510 | − | 0.0204019i | ||||
\(898\) | −12.8685 | − | 22.2890i | −0.429429 | − | 0.743792i | ||||
\(899\) | −16.3791 | − | 28.3695i | −0.546274 | − | 0.946174i | ||||
\(900\) | −5.61080 | + | 1.14790i | −0.187027 | + | 0.0382634i | ||||
\(901\) | −12.9380 | − | 7.46975i | −0.431027 | − | 0.248854i | ||||
\(902\) | −17.2634 | + | 29.9010i | −0.574807 | + | 0.995595i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.24557 | − | 3.88944i | −0.0746866 | − | 0.129361i | ||||
\(905\) | − | 37.6963i | − | 1.25307i | ||||||
\(906\) | 0.646509 | + | 6.38556i | 0.0214788 | + | 0.212146i | ||||
\(907\) | −42.5954 | −1.41436 | −0.707179 | − | 0.707034i | \(-0.750033\pi\) | ||||
−0.707179 | + | 0.707034i | \(0.750033\pi\) | |||||||
\(908\) | 10.9505 | − | 18.9669i | 0.363406 | − | 0.629437i | ||||
\(909\) | 14.9960 | + | 16.9127i | 0.497385 | + | 0.560958i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43.5221 | − | 25.1275i | −1.44195 | − | 0.832510i | −0.443970 | − | 0.896042i | \(-0.646430\pi\) |
−0.997980 | + | 0.0635313i | \(0.979764\pi\) | |||||||
\(912\) | 19.3431 | + | 8.70073i | 0.640513 | + | 0.288110i | ||||
\(913\) | −41.1496 | − | 23.7577i | −1.36185 | − | 0.786265i | ||||
\(914\) | 44.2037 | + | 25.5210i | 1.46213 | + | 0.844160i | ||||
\(915\) | 3.74037 | + | 36.9436i | 0.123653 | + | 1.22132i | ||||
\(916\) | 4.36754 | + | 2.52160i | 0.144308 | + | 0.0833161i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −29.1622 | − | 6.54860i | −0.962495 | − | 0.216136i | ||||
\(919\) | 29.3486 | − | 50.8333i | 0.968121 | − | 1.67684i | 0.267137 | − | 0.963658i | \(-0.413922\pi\) |
0.700984 | − | 0.713177i | \(-0.252744\pi\) | |||||||
\(920\) | 18.7411 | 0.617875 | ||||||||
\(921\) | 45.4189 | + | 20.4299i | 1.49660 | + | 0.673189i | ||||
\(922\) | − | 20.6264i | − | 0.679295i | ||||||
\(923\) | 0.655304 | + | 1.13502i | 0.0215696 | + | 0.0373596i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.905536 | − | 1.56843i | 0.0297738 | − | 0.0515698i | ||||
\(926\) | 39.6046 | + | 22.8657i | 1.30149 | + | 0.751415i | ||||
\(927\) | 32.1518 | − | 28.5081i | 1.05601 | − | 0.936329i | ||||
\(928\) | −10.9465 | − | 18.9598i | −0.359335 | − | 0.622387i | ||||
\(929\) | 7.19115 | + | 12.4554i | 0.235934 | + | 0.408650i | 0.959544 | − | 0.281560i | \(-0.0908518\pi\) |
−0.723610 | + | 0.690209i | \(0.757518\pi\) | |||||||
\(930\) | −34.8278 | + | 77.4275i | −1.14205 | + | 2.53895i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.30952 | − | 3.64281i | 0.206675 | − | 0.119324i | ||||
\(933\) | 13.4548 | + | 18.6685i | 0.440491 | + | 0.611178i | ||||
\(934\) | − | 29.7251i | − | 0.972636i | ||||||
\(935\) | −37.4646 | + | 21.6302i | −1.22522 | + | 0.707384i | ||||
\(936\) | 0.399025 | − | 1.19690i | 0.0130426 | − | 0.0391218i | ||||
\(937\) | 44.2981i | 1.44716i | 0.690243 | + | 0.723578i | \(0.257504\pi\) | ||||
−0.690243 | + | 0.723578i | \(0.742496\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.50446 | + | 54.3675i | 0.179631 | + | 1.77422i | ||||
\(940\) | 8.01969 | 0.261573 | ||||||||
\(941\) | 7.44400 | − | 12.8934i | 0.242667 | − | 0.420312i | −0.718806 | − | 0.695211i | \(-0.755311\pi\) |
0.961473 | + | 0.274899i | \(0.0886443\pi\) | |||||||
\(942\) | 11.1443 | − | 24.7754i | 0.363100 | − | 0.807228i | ||||
\(943\) | 22.5089 | − | 12.9955i | 0.732990 | − | 0.423192i | ||||
\(944\) | 34.7734 | 1.13178 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 99.7390 | 3.24280 | ||||||||
\(947\) | −36.3343 | + | 20.9776i | −1.18071 | + | 0.681681i | −0.956178 | − | 0.292787i | \(-0.905417\pi\) |
−0.224528 | + | 0.974468i | \(0.572084\pi\) | |||||||
\(948\) | −0.609153 | + | 1.35424i | −0.0197844 | + | 0.0439837i | ||||
\(949\) | −1.89031 | + | 3.27412i | −0.0613622 | + | 0.106282i | ||||
\(950\) | 6.15184 | 0.199592 | ||||||||
\(951\) | −3.50177 | − | 34.5869i | −0.113553 | − | 1.12156i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 13.9821i | − | 0.452926i | −0.974020 | − | 0.226463i | \(-0.927284\pi\) | ||
0.974020 | − | 0.226463i | \(-0.0727162\pi\) | |||||||
\(954\) | −26.6638 | + | 5.45510i | −0.863273 | + | 0.176615i | ||||
\(955\) | −28.6959 | + | 16.5676i | −0.928578 | + | 0.536115i | ||||
\(956\) | − | 23.4884i | − | 0.759669i | ||||||
\(957\) | −17.7796 | − | 24.6690i | −0.574732 | − | 0.797436i | ||||
\(958\) | −22.4228 | + | 12.9458i | −0.724449 | + | 0.418261i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6.33733 | + | 14.0889i | −0.204537 | + | 0.454716i | ||||
\(961\) | 39.2776 | + | 68.0309i | 1.26702 | + | 2.19454i | ||||
\(962\) | −0.587333 | − | 1.01729i | −0.0189364 | − | 0.0327988i | ||||
\(963\) | −8.10963 | − | 39.6388i | −0.261329 | − | 1.27734i | ||||
\(964\) | 0.994743 | + | 0.574315i | 0.0320385 | + | 0.0184974i | ||||
\(965\) | 1.94910 | − | 3.37593i | 0.0627436 | − | 0.108675i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.5757 | − | 20.0497i | −0.372249 | − | 0.644754i | 0.617662 | − | 0.786443i | \(-0.288080\pi\) |
−0.989911 | + | 0.141690i | \(0.954746\pi\) | |||||||
\(968\) | 19.3967i | 0.623433i | ||||||||
\(969\) | 12.5146 | + | 5.62919i | 0.402026 | + | 0.180836i | ||||
\(970\) | −17.4481 | −0.560223 | ||||||||
\(971\) | −21.6869 | + | 37.5628i | −0.695965 | + | 1.20545i | 0.273890 | + | 0.961761i | \(0.411690\pi\) |
−0.969854 | + | 0.243685i | \(0.921644\pi\) | |||||||
\(972\) | −20.3729 | + | 11.2493i | −0.653462 | + | 0.360823i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 46.6120 | + | 26.9114i | 1.49354 | + | 0.862298i | ||||
\(975\) | −0.0990022 | − | 0.977843i | −0.00317061 | − | 0.0313160i | ||||
\(976\) | 35.2472 | + | 20.3500i | 1.12824 | + | 0.651387i | ||||
\(977\) | 10.4210 | + | 6.01657i | 0.333397 | + | 0.192487i | 0.657348 | − | 0.753587i | \(-0.271678\pi\) |
−0.323951 | + | 0.946074i | \(0.605011\pi\) | |||||||
\(978\) | −3.17096 | − | 1.42633i | −0.101396 | − | 0.0456092i | ||||
\(979\) | −36.8170 | − | 21.2563i | −1.17668 | − | 0.679355i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.871668 | − | 2.61461i | 0.0278302 | − | 0.0834782i | ||||
\(982\) | 36.2152 | − | 62.7266i | 1.15567 | − | 2.00169i | ||||
\(983\) | 6.29658 | 0.200830 | 0.100415 | − | 0.994946i | \(-0.467983\pi\) | ||||
0.100415 | + | 0.994946i | \(0.467983\pi\) | |||||||
\(984\) | −0.544527 | − | 5.37829i | −0.0173589 | − | 0.171454i | ||||
\(985\) | − | 12.4331i | − | 0.396151i | ||||||
\(986\) | −9.00108 | − | 15.5903i | −0.286653 | − | 0.496497i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.852712 | − | 1.47694i | 0.0271284 | − | 0.0469877i | ||||
\(989\) | −65.0225 | − | 37.5408i | −2.06760 | − | 1.19373i | ||||
\(990\) | −24.9252 | + | 74.7645i | −0.792176 | + | 2.37617i | ||||
\(991\) | −16.7814 | − | 29.0662i | −0.533078 | − | 0.923317i | −0.999254 | − | 0.0386256i | \(-0.987702\pi\) |
0.466176 | − | 0.884692i | \(-0.345631\pi\) | |||||||
\(992\) | 36.6089 | + | 63.4085i | 1.16233 | + | 2.01322i | ||||
\(993\) | 2.15046 | − | 0.217724i | 0.0682427 | − | 0.00690926i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.2874 | − | 14.0223i | 0.769963 | − | 0.444538i | ||||
\(996\) | −21.7916 | + | 2.20630i | −0.690493 | + | 0.0699092i | ||||
\(997\) | − | 11.2565i | − | 0.356495i | −0.983986 | − | 0.178248i | \(-0.942957\pi\) | ||
0.983986 | − | 0.178248i | \(-0.0570428\pi\) | |||||||
\(998\) | 5.61096 | − | 3.23949i | 0.177612 | − | 0.102544i | ||||
\(999\) | 1.61248 | − | 7.18068i | 0.0510166 | − | 0.227187i |
(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 | 441.2.s.d.362.5 | 48 | ||
3.2 | odd | 2 | 1323.2.s.d.656.19 | 48 | |||
7.2 | even | 3 | 441.2.o.e.146.19 | ✓ | 48 | ||
7.3 | odd | 6 | 441.2.i.d.227.5 | 48 | |||
7.4 | even | 3 | 441.2.i.d.227.6 | 48 | |||
7.5 | odd | 6 | 441.2.o.e.146.20 | yes | 48 | ||
7.6 | odd | 2 | inner | 441.2.s.d.362.6 | 48 | ||
9.4 | even | 3 | 1323.2.i.d.1097.22 | 48 | |||
9.5 | odd | 6 | 441.2.i.d.68.19 | 48 | |||
21.2 | odd | 6 | 1323.2.o.e.440.6 | 48 | |||
21.5 | even | 6 | 1323.2.o.e.440.5 | 48 | |||
21.11 | odd | 6 | 1323.2.i.d.521.7 | 48 | |||
21.17 | even | 6 | 1323.2.i.d.521.22 | 48 | |||
21.20 | even | 2 | 1323.2.s.d.656.20 | 48 | |||
63.4 | even | 3 | 1323.2.s.d.962.20 | 48 | |||
63.5 | even | 6 | 441.2.o.e.293.19 | yes | 48 | ||
63.13 | odd | 6 | 1323.2.i.d.1097.7 | 48 | |||
63.23 | odd | 6 | 441.2.o.e.293.20 | yes | 48 | ||
63.31 | odd | 6 | 1323.2.s.d.962.19 | 48 | |||
63.32 | odd | 6 | inner | 441.2.s.d.374.6 | 48 | ||
63.40 | odd | 6 | 1323.2.o.e.881.6 | 48 | |||
63.41 | even | 6 | 441.2.i.d.68.20 | 48 | |||
63.58 | even | 3 | 1323.2.o.e.881.5 | 48 | |||
63.59 | even | 6 | inner | 441.2.s.d.374.5 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.i.d.68.19 | 48 | 9.5 | odd | 6 | |||
441.2.i.d.68.20 | 48 | 63.41 | even | 6 | |||
441.2.i.d.227.5 | 48 | 7.3 | odd | 6 | |||
441.2.i.d.227.6 | 48 | 7.4 | even | 3 | |||
441.2.o.e.146.19 | ✓ | 48 | 7.2 | even | 3 | ||
441.2.o.e.146.20 | yes | 48 | 7.5 | odd | 6 | ||
441.2.o.e.293.19 | yes | 48 | 63.5 | even | 6 | ||
441.2.o.e.293.20 | yes | 48 | 63.23 | odd | 6 | ||
441.2.s.d.362.5 | 48 | 1.1 | even | 1 | trivial | ||
441.2.s.d.362.6 | 48 | 7.6 | odd | 2 | inner | ||
441.2.s.d.374.5 | 48 | 63.59 | even | 6 | inner | ||
441.2.s.d.374.6 | 48 | 63.32 | odd | 6 | inner | ||
1323.2.i.d.521.7 | 48 | 21.11 | odd | 6 | |||
1323.2.i.d.521.22 | 48 | 21.17 | even | 6 | |||
1323.2.i.d.1097.7 | 48 | 63.13 | odd | 6 | |||
1323.2.i.d.1097.22 | 48 | 9.4 | even | 3 | |||
1323.2.o.e.440.5 | 48 | 21.5 | even | 6 | |||
1323.2.o.e.440.6 | 48 | 21.2 | odd | 6 | |||
1323.2.o.e.881.5 | 48 | 63.58 | even | 3 | |||
1323.2.o.e.881.6 | 48 | 63.40 | odd | 6 | |||
1323.2.s.d.656.19 | 48 | 3.2 | odd | 2 | |||
1323.2.s.d.656.20 | 48 | 21.20 | even | 2 | |||
1323.2.s.d.962.19 | 48 | 63.31 | odd | 6 | |||
1323.2.s.d.962.20 | 48 | 63.4 | even | 3 |