Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [85,2,Mod(9,85)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(85, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("85.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 85 = 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 85.m (of order \(8\), degree \(4\), 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: | \(0.678728417181\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Character | \(\chi\) | \(=\) | 85.49 |
Dual form | 85.2.m.a.59.4 |
$q$-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 \(\left(\mathbb{Z}/85\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.176012 | − | 0.176012i | 0.124459 | − | 0.124459i | −0.642134 | − | 0.766593i | \(-0.721951\pi\) |
0.766593 | + | 0.642134i | \(0.221951\pi\) | |||||||
\(3\) | −1.51856 | + | 0.629010i | −0.876744 | + | 0.363159i | −0.775233 | − | 0.631675i | \(-0.782368\pi\) |
−0.101511 | + | 0.994834i | \(0.532368\pi\) | |||||||
\(4\) | 1.93804i | 0.969020i | ||||||||
\(5\) | 1.62749 | + | 1.53338i | 0.727837 | + | 0.685750i | ||||
\(6\) | −0.156572 | + | 0.377999i | −0.0639203 | + | 0.154317i | ||||
\(7\) | 0.547653 | − | 1.32215i | 0.206993 | − | 0.499726i | −0.785954 | − | 0.618286i | \(-0.787828\pi\) |
0.992947 | + | 0.118559i | \(0.0378275\pi\) | |||||||
\(8\) | 0.693142 | + | 0.693142i | 0.245063 | + | 0.245063i | ||||
\(9\) | −0.210935 | + | 0.210935i | −0.0703116 | + | 0.0703116i | ||||
\(10\) | 0.556352 | − | 0.0165642i | 0.175934 | − | 0.00523805i | ||||
\(11\) | 1.03080 | − | 2.48857i | 0.310798 | − | 0.750333i | −0.688878 | − | 0.724878i | \(-0.741896\pi\) |
0.999676 | − | 0.0254558i | \(-0.00810370\pi\) | |||||||
\(12\) | −1.21905 | − | 2.94304i | −0.351908 | − | 0.849582i | ||||
\(13\) | 0.174664 | 0.0484432 | 0.0242216 | − | 0.999707i | \(-0.492289\pi\) | ||||
0.0242216 | + | 0.999707i | \(0.492289\pi\) | |||||||
\(14\) | −0.136321 | − | 0.329108i | −0.0364333 | − | 0.0879578i | ||||
\(15\) | −3.43597 | − | 1.30483i | −0.887163 | − | 0.336907i | ||||
\(16\) | −3.63208 | −0.908019 | ||||||||
\(17\) | 2.27165 | − | 3.44088i | 0.550955 | − | 0.834535i | ||||
\(18\) | 0.0742541i | 0.0175019i | ||||||||
\(19\) | −2.69404 | − | 2.69404i | −0.618055 | − | 0.618055i | 0.326978 | − | 0.945032i | \(-0.393970\pi\) |
−0.945032 | + | 0.326978i | \(0.893970\pi\) | |||||||
\(20\) | −2.97176 | + | 3.15415i | −0.664506 | + | 0.705288i | ||||
\(21\) | 2.35225i | 0.513304i | ||||||||
\(22\) | −0.256585 | − | 0.619452i | −0.0547042 | − | 0.132068i | ||||
\(23\) | 2.54807 | + | 1.05544i | 0.531309 | + | 0.220075i | 0.632176 | − | 0.774825i | \(-0.282162\pi\) |
−0.100867 | + | 0.994900i | \(0.532162\pi\) | |||||||
\(24\) | −1.48857 | − | 0.616588i | −0.303854 | − | 0.125860i | ||||
\(25\) | 0.297464 | + | 4.99114i | 0.0594929 | + | 0.998229i | ||||
\(26\) | 0.0307430 | − | 0.0307430i | 0.00602920 | − | 0.00602920i | ||||
\(27\) | 2.07467 | − | 5.00869i | 0.399270 | − | 0.963923i | ||||
\(28\) | 2.56238 | + | 1.06137i | 0.484245 | + | 0.200581i | ||||
\(29\) | 5.94408 | − | 2.46212i | 1.10379 | − | 0.457204i | 0.244994 | − | 0.969525i | \(-0.421214\pi\) |
0.858794 | + | 0.512321i | \(0.171214\pi\) | |||||||
\(30\) | −0.834438 | + | 0.375105i | −0.152347 | + | 0.0684845i | ||||
\(31\) | −0.188417 | − | 0.454879i | −0.0338407 | − | 0.0816987i | 0.906056 | − | 0.423159i | \(-0.139079\pi\) |
−0.939896 | + | 0.341460i | \(0.889079\pi\) | |||||||
\(32\) | −2.02557 | + | 2.02557i | −0.358074 | + | 0.358074i | ||||
\(33\) | 4.42745i | 0.770719i | ||||||||
\(34\) | −0.205798 | − | 1.00547i | −0.0352941 | − | 0.172437i | ||||
\(35\) | 2.91867 | − | 1.31203i | 0.493345 | − | 0.221773i | ||||
\(36\) | −0.408800 | − | 0.408800i | −0.0681333 | − | 0.0681333i | ||||
\(37\) | −5.30576 | + | 2.19772i | −0.872261 | + | 0.361302i | −0.773490 | − | 0.633808i | \(-0.781491\pi\) |
−0.0987704 | + | 0.995110i | \(0.531491\pi\) | |||||||
\(38\) | −0.948365 | −0.153845 | ||||||||
\(39\) | −0.265239 | + | 0.109866i | −0.0424723 | + | 0.0175926i | ||||
\(40\) | 0.0652303 | + | 2.19094i | 0.0103138 | + | 0.346417i | ||||
\(41\) | 5.54000 | + | 2.29474i | 0.865203 | + | 0.358379i | 0.770740 | − | 0.637150i | \(-0.219887\pi\) |
0.0944627 | + | 0.995528i | \(0.469887\pi\) | |||||||
\(42\) | 0.414025 | + | 0.414025i | 0.0638854 | + | 0.0638854i | ||||
\(43\) | −8.00004 | − | 8.00004i | −1.22000 | − | 1.22000i | −0.967633 | − | 0.252363i | \(-0.918792\pi\) |
−0.252363 | − | 0.967633i | \(-0.581208\pi\) | |||||||
\(44\) | 4.82296 | + | 1.99773i | 0.727088 | + | 0.301170i | ||||
\(45\) | −0.666739 | + | 0.0198507i | −0.0993916 | + | 0.00295917i | ||||
\(46\) | 0.634261 | − | 0.262720i | 0.0935167 | − | 0.0387359i | ||||
\(47\) | 2.65291 | 0.386967 | 0.193483 | − | 0.981104i | \(-0.438021\pi\) | ||||
0.193483 | + | 0.981104i | \(0.438021\pi\) | |||||||
\(48\) | 5.51554 | − | 2.28461i | 0.796100 | − | 0.329756i | ||||
\(49\) | 3.50159 | + | 3.50159i | 0.500227 | + | 0.500227i | ||||
\(50\) | 0.930858 | + | 0.826143i | 0.131643 | + | 0.116834i | ||||
\(51\) | −1.28530 | + | 6.65408i | −0.179977 | + | 0.931758i | ||||
\(52\) | 0.338506i | 0.0469424i | ||||||||
\(53\) | −8.73501 | + | 8.73501i | −1.19985 | + | 1.19985i | −0.225633 | + | 0.974212i | \(0.572445\pi\) |
−0.974212 | + | 0.225633i | \(0.927555\pi\) | |||||||
\(54\) | −0.516423 | − | 1.24676i | −0.0702763 | − | 0.169662i | ||||
\(55\) | 5.49356 | − | 2.46952i | 0.740752 | − | 0.332990i | ||||
\(56\) | 1.29604 | − | 0.536837i | 0.173191 | − | 0.0717379i | ||||
\(57\) | 5.78565 | + | 2.39649i | 0.766328 | + | 0.317423i | ||||
\(58\) | 0.612867 | − | 1.47959i | 0.0804733 | − | 0.194280i | ||||
\(59\) | −5.72232 | + | 5.72232i | −0.744982 | + | 0.744982i | −0.973532 | − | 0.228550i | \(-0.926602\pi\) |
0.228550 | + | 0.973532i | \(0.426602\pi\) | |||||||
\(60\) | 2.52882 | − | 6.65904i | 0.326469 | − | 0.859679i | ||||
\(61\) | −6.41902 | − | 2.65884i | −0.821871 | − | 0.340430i | −0.0681914 | − | 0.997672i | \(-0.521723\pi\) |
−0.753679 | + | 0.657242i | \(0.771723\pi\) | |||||||
\(62\) | −0.113228 | − | 0.0469005i | −0.0143799 | − | 0.00595637i | ||||
\(63\) | 0.163369 | + | 0.394407i | 0.0205825 | + | 0.0496906i | ||||
\(64\) | − | 6.55110i | − | 0.818888i | ||||||
\(65\) | 0.284265 | + | 0.267828i | 0.0352587 | + | 0.0332199i | ||||
\(66\) | 0.779283 | + | 0.779283i | 0.0959231 | + | 0.0959231i | ||||
\(67\) | 12.3901i | 1.51369i | 0.653594 | + | 0.756845i | \(0.273260\pi\) | ||||
−0.653594 | + | 0.756845i | \(0.726740\pi\) | |||||||
\(68\) | 6.66855 | + | 4.40254i | 0.808681 | + | 0.533886i | ||||
\(69\) | −4.53329 | −0.545744 | ||||||||
\(70\) | 0.282788 | − | 0.744653i | 0.0337996 | − | 0.0890031i | ||||
\(71\) | −4.67878 | − | 11.2956i | −0.555269 | − | 1.34054i | −0.913474 | − | 0.406896i | \(-0.866611\pi\) |
0.358205 | − | 0.933643i | \(-0.383389\pi\) | |||||||
\(72\) | −0.292415 | −0.0344615 | ||||||||
\(73\) | −5.99425 | − | 14.4714i | −0.701574 | − | 1.69375i | −0.720052 | − | 0.693920i | \(-0.755882\pi\) |
0.0184781 | − | 0.999829i | \(-0.494118\pi\) | |||||||
\(74\) | −0.547052 | + | 1.32070i | −0.0635935 | + | 0.153528i | ||||
\(75\) | −3.59120 | − | 7.39227i | −0.414676 | − | 0.853586i | ||||
\(76\) | 5.22115 | − | 5.22115i | 0.598907 | − | 0.598907i | ||||
\(77\) | −2.72575 | − | 2.72575i | −0.310628 | − | 0.310628i | ||||
\(78\) | −0.0273476 | + | 0.0660229i | −0.00309650 | + | 0.00747562i | ||||
\(79\) | −4.94031 | + | 11.9270i | −0.555828 | + | 1.34189i | 0.357214 | + | 0.934022i | \(0.383727\pi\) |
−0.913042 | + | 0.407865i | \(0.866273\pi\) | |||||||
\(80\) | −5.91118 | − | 5.56937i | −0.660890 | − | 0.622674i | ||||
\(81\) | 8.01609i | 0.890677i | ||||||||
\(82\) | 1.37901 | − | 0.571204i | 0.152286 | − | 0.0630789i | ||||
\(83\) | 6.06390 | − | 6.06390i | 0.665600 | − | 0.665600i | −0.291094 | − | 0.956694i | \(-0.594019\pi\) |
0.956694 | + | 0.291094i | \(0.0940194\pi\) | |||||||
\(84\) | −4.55876 | −0.497401 | ||||||||
\(85\) | 8.97327 | − | 2.11669i | 0.973288 | − | 0.229588i | ||||
\(86\) | −2.81621 | −0.303679 | ||||||||
\(87\) | −7.47777 | + | 7.47777i | −0.801702 | + | 0.801702i | ||||
\(88\) | 2.43943 | − | 1.01044i | 0.260044 | − | 0.107714i | ||||
\(89\) | − | 11.4907i | − | 1.21801i | −0.793165 | − | 0.609006i | \(-0.791568\pi\) | ||
0.793165 | − | 0.609006i | \(-0.208432\pi\) | |||||||
\(90\) | −0.113860 | + | 0.120848i | −0.0120019 | + | 0.0127385i | ||||
\(91\) | 0.0956555 | − | 0.230933i | 0.0100274 | − | 0.0242083i | ||||
\(92\) | −2.04549 | + | 4.93826i | −0.213257 | + | 0.514849i | ||||
\(93\) | 0.572247 | + | 0.572247i | 0.0593393 | + | 0.0593393i | ||||
\(94\) | 0.466944 | − | 0.466944i | 0.0481616 | − | 0.0481616i | ||||
\(95\) | −0.253531 | − | 8.51552i | −0.0260117 | − | 0.873674i | ||||
\(96\) | 1.80186 | − | 4.35007i | 0.183901 | − | 0.443977i | ||||
\(97\) | −0.879757 | − | 2.12392i | −0.0893258 | − | 0.215651i | 0.872903 | − | 0.487894i | \(-0.162235\pi\) |
−0.962229 | + | 0.272242i | \(0.912235\pi\) | |||||||
\(98\) | 1.23264 | 0.124516 | ||||||||
\(99\) | 0.307495 | + | 0.742359i | 0.0309044 | + | 0.0746099i | ||||
\(100\) | −9.67303 | + | 0.576498i | −0.967303 | + | 0.0576498i | ||||
\(101\) | −0.890917 | −0.0886495 | −0.0443248 | − | 0.999017i | \(-0.514114\pi\) | ||||
−0.0443248 | + | 0.999017i | \(0.514114\pi\) | |||||||
\(102\) | 0.944970 | + | 1.39742i | 0.0935660 | + | 0.138366i | ||||
\(103\) | − | 0.367137i | − | 0.0361751i | −0.999836 | − | 0.0180875i | \(-0.994242\pi\) | ||
0.999836 | − | 0.0180875i | \(-0.00575776\pi\) | |||||||
\(104\) | 0.121067 | + | 0.121067i | 0.0118716 | + | 0.0118716i | ||||
\(105\) | −3.60691 | + | 3.82827i | −0.351998 | + | 0.373601i | ||||
\(106\) | 3.07493i | 0.298664i | ||||||||
\(107\) | 2.54389 | + | 6.14149i | 0.245927 | + | 0.593720i | 0.997851 | − | 0.0655301i | \(-0.0208738\pi\) |
−0.751924 | + | 0.659250i | \(0.770874\pi\) | |||||||
\(108\) | 9.70705 | + | 4.02079i | 0.934061 | + | 0.386901i | ||||
\(109\) | 8.16665 | + | 3.38274i | 0.782223 | + | 0.324007i | 0.737812 | − | 0.675006i | \(-0.235859\pi\) |
0.0444107 | + | 0.999013i | \(0.485859\pi\) | |||||||
\(110\) | 0.532267 | − | 1.40160i | 0.0507497 | − | 0.133637i | ||||
\(111\) | 6.67475 | − | 6.67475i | 0.633539 | − | 0.633539i | ||||
\(112\) | −1.98912 | + | 4.80216i | −0.187954 | + | 0.453761i | ||||
\(113\) | 5.27825 | + | 2.18632i | 0.496536 | + | 0.205672i | 0.616875 | − | 0.787061i | \(-0.288398\pi\) |
−0.120339 | + | 0.992733i | \(0.538398\pi\) | |||||||
\(114\) | 1.44015 | − | 0.596531i | 0.134883 | − | 0.0558703i | ||||
\(115\) | 2.52856 | + | 5.62490i | 0.235789 | + | 0.524524i | ||||
\(116\) | 4.77168 | + | 11.5199i | 0.443040 | + | 1.06959i | ||||
\(117\) | −0.0368428 | + | 0.0368428i | −0.00340612 | + | 0.00340612i | ||||
\(118\) | 2.01439i | 0.185440i | ||||||||
\(119\) | −3.30529 | − | 4.88787i | −0.302995 | − | 0.448070i | ||||
\(120\) | −1.47718 | − | 3.28605i | −0.134847 | − | 0.299974i | ||||
\(121\) | 2.64772 | + | 2.64772i | 0.240702 | + | 0.240702i | ||||
\(122\) | −1.59781 | + | 0.661835i | −0.144659 | + | 0.0599197i | ||||
\(123\) | −9.85627 | −0.888710 | ||||||||
\(124\) | 0.881574 | − | 0.365160i | 0.0791676 | − | 0.0327923i | ||||
\(125\) | −7.16922 | + | 8.57918i | −0.641235 | + | 0.767345i | ||||
\(126\) | 0.0981752 | + | 0.0406655i | 0.00874614 | + | 0.00362277i | ||||
\(127\) | 11.5590 | + | 11.5590i | 1.02569 | + | 1.02569i | 0.999661 | + | 0.0260300i | \(0.00828653\pi\) |
0.0260300 | + | 0.999661i | \(0.491713\pi\) | |||||||
\(128\) | −5.20422 | − | 5.20422i | −0.459992 | − | 0.459992i | ||||
\(129\) | 17.1807 | + | 7.11648i | 1.51268 | + | 0.626571i | ||||
\(130\) | 0.0971749 | − | 0.00289317i | 0.00852280 | − | 0.000253748i | ||||
\(131\) | −8.90518 | + | 3.68865i | −0.778049 | + | 0.322279i | −0.736128 | − | 0.676842i | \(-0.763348\pi\) |
−0.0419214 | + | 0.999121i | \(0.513348\pi\) | |||||||
\(132\) | −8.58057 | −0.746842 | ||||||||
\(133\) | −5.03733 | + | 2.08653i | −0.436791 | + | 0.180925i | ||||
\(134\) | 2.18080 | + | 2.18080i | 0.188393 | + | 0.188393i | ||||
\(135\) | 11.0568 | − | 4.97035i | 0.951614 | − | 0.427779i | ||||
\(136\) | 3.95959 | − | 0.810442i | 0.339532 | − | 0.0694949i | ||||
\(137\) | − | 6.60524i | − | 0.564324i | −0.959367 | − | 0.282162i | \(-0.908948\pi\) | ||
0.959367 | − | 0.282162i | \(-0.0910515\pi\) | |||||||
\(138\) | −0.797913 | + | 0.797913i | −0.0679229 | + | 0.0679229i | ||||
\(139\) | −1.75923 | − | 4.24715i | −0.149216 | − | 0.360239i | 0.831544 | − | 0.555459i | \(-0.187458\pi\) |
−0.980759 | + | 0.195221i | \(0.937458\pi\) | |||||||
\(140\) | 2.54277 | + | 5.65650i | 0.214903 | + | 0.478061i | ||||
\(141\) | −4.02862 | + | 1.66871i | −0.339271 | + | 0.140531i | ||||
\(142\) | −2.81168 | − | 1.16464i | −0.235951 | − | 0.0977340i | ||||
\(143\) | 0.180044 | − | 0.434665i | 0.0150561 | − | 0.0363485i | ||||
\(144\) | 0.766131 | − | 0.766131i | 0.0638443 | − | 0.0638443i | ||||
\(145\) | 13.4493 | + | 5.10748i | 1.11691 | + | 0.424153i | ||||
\(146\) | −3.60220 | − | 1.49208i | −0.298120 | − | 0.123485i | ||||
\(147\) | −7.51992 | − | 3.11485i | −0.620232 | − | 0.256909i | ||||
\(148\) | −4.25926 | − | 10.2828i | −0.350109 | − | 0.845238i | ||||
\(149\) | − | 11.6404i | − | 0.953619i | −0.879007 | − | 0.476810i | \(-0.841793\pi\) | ||
0.879007 | − | 0.476810i | \(-0.158207\pi\) | |||||||
\(150\) | −1.93322 | − | 0.669033i | −0.157847 | − | 0.0546263i | ||||
\(151\) | 0.0974235 | + | 0.0974235i | 0.00792821 | + | 0.00792821i | 0.711060 | − | 0.703132i | \(-0.248216\pi\) |
−0.703132 | + | 0.711060i | \(0.748216\pi\) | |||||||
\(152\) | − | 3.73470i | − | 0.302924i | ||||||
\(153\) | 0.246631 | + | 1.20497i | 0.0199390 | + | 0.0974160i | ||||
\(154\) | −0.959530 | −0.0773211 | ||||||||
\(155\) | 0.390857 | − | 1.02923i | 0.0313944 | − | 0.0826696i | ||||
\(156\) | −0.212924 | − | 0.514044i | −0.0170476 | − | 0.0411565i | ||||
\(157\) | 9.66489 | 0.771343 | 0.385671 | − | 0.922636i | \(-0.373970\pi\) | ||||
0.385671 | + | 0.922636i | \(0.373970\pi\) | |||||||
\(158\) | 1.22973 | + | 2.96884i | 0.0978323 | + | 0.236188i | ||||
\(159\) | 7.77027 | − | 18.7591i | 0.616222 | − | 1.48769i | ||||
\(160\) | −6.40259 | + | 0.190623i | −0.506169 | + | 0.0150701i | ||||
\(161\) | 2.79092 | − | 2.79092i | 0.219955 | − | 0.219955i | ||||
\(162\) | 1.41093 | + | 1.41093i | 0.110853 | + | 0.110853i | ||||
\(163\) | −4.75100 | + | 11.4699i | −0.372127 | + | 0.898394i | 0.621263 | + | 0.783602i | \(0.286620\pi\) |
−0.993390 | + | 0.114792i | \(0.963380\pi\) | |||||||
\(164\) | −4.44730 | + | 10.7367i | −0.347276 | + | 0.838399i | ||||
\(165\) | −6.78898 | + | 7.20564i | −0.528521 | + | 0.560958i | ||||
\(166\) | − | 2.13464i | − | 0.165680i | ||||||
\(167\) | −3.86872 | + | 1.60248i | −0.299371 | + | 0.124003i | −0.527313 | − | 0.849671i | \(-0.676800\pi\) |
0.227942 | + | 0.973675i | \(0.426800\pi\) | |||||||
\(168\) | −1.63045 | + | 1.63045i | −0.125792 | + | 0.125792i | ||||
\(169\) | −12.9695 | −0.997653 | ||||||||
\(170\) | 1.20684 | − | 1.95197i | 0.0925603 | − | 0.149709i | ||||
\(171\) | 1.13653 | 0.0869128 | ||||||||
\(172\) | 15.5044 | − | 15.5044i | 1.18220 | − | 1.18220i | ||||
\(173\) | 2.73000 | − | 1.13080i | 0.207558 | − | 0.0859733i | −0.276483 | − | 0.961019i | \(-0.589169\pi\) |
0.484040 | + | 0.875046i | \(0.339169\pi\) | |||||||
\(174\) | 2.63235i | 0.199558i | ||||||||
\(175\) | 6.76196 | + | 2.34012i | 0.511156 | + | 0.176897i | ||||
\(176\) | −3.74395 | + | 9.03869i | −0.282211 | + | 0.681317i | ||||
\(177\) | 5.09032 | − | 12.2891i | 0.382612 | − | 0.923706i | ||||
\(178\) | −2.02250 | − | 2.02250i | −0.151593 | − | 0.151593i | ||||
\(179\) | −16.4589 | + | 16.4589i | −1.23019 | + | 1.23019i | −0.266304 | + | 0.963889i | \(0.585803\pi\) |
−0.963889 | + | 0.266304i | \(0.914197\pi\) | |||||||
\(180\) | −0.0384714 | − | 1.29217i | −0.00286749 | − | 0.0963124i | ||||
\(181\) | 4.37037 | − | 10.5510i | 0.324847 | − | 0.784250i | −0.674112 | − | 0.738629i | \(-0.735474\pi\) |
0.998959 | − | 0.0456205i | \(-0.0145265\pi\) | |||||||
\(182\) | −0.0238104 | − | 0.0574834i | −0.00176495 | − | 0.00426096i | ||||
\(183\) | 11.4201 | 0.844200 | ||||||||
\(184\) | 1.03460 | + | 2.49775i | 0.0762717 | + | 0.184136i | ||||
\(185\) | −12.0050 | − | 4.55900i | −0.882627 | − | 0.335184i | ||||
\(186\) | 0.201445 | 0.0147706 | ||||||||
\(187\) | −6.22126 | − | 9.20002i | −0.454944 | − | 0.672772i | ||||
\(188\) | 5.14145i | 0.374978i | ||||||||
\(189\) | −5.48605 | − | 5.48605i | −0.399052 | − | 0.399052i | ||||
\(190\) | −1.54346 | − | 1.45421i | −0.111974 | − | 0.105499i | ||||
\(191\) | 3.08201i | 0.223007i | 0.993764 | + | 0.111503i | \(0.0355666\pi\) | ||||
−0.993764 | + | 0.111503i | \(0.964433\pi\) | |||||||
\(192\) | 4.12071 | + | 9.94828i | 0.297387 | + | 0.717955i | ||||
\(193\) | −14.7688 | − | 6.11743i | −1.06308 | − | 0.440343i | −0.218537 | − | 0.975829i | \(-0.570128\pi\) |
−0.844544 | + | 0.535486i | \(0.820128\pi\) | |||||||
\(194\) | −0.528683 | − | 0.218988i | −0.0379572 | − | 0.0157224i | ||||
\(195\) | −0.600141 | − | 0.227908i | −0.0429770 | − | 0.0163208i | ||||
\(196\) | −6.78621 | + | 6.78621i | −0.484729 | + | 0.484729i | ||||
\(197\) | 4.08460 | − | 9.86109i | 0.291015 | − | 0.702573i | −0.708981 | − | 0.705228i | \(-0.750845\pi\) |
0.999996 | + | 0.00265412i | \(0.000844833\pi\) | |||||||
\(198\) | 0.184787 | + | 0.0765412i | 0.0131322 | + | 0.00543954i | ||||
\(199\) | 14.6337 | − | 6.06147i | 1.03735 | − | 0.429686i | 0.201993 | − | 0.979387i | \(-0.435258\pi\) |
0.835362 | + | 0.549701i | \(0.185258\pi\) | |||||||
\(200\) | −3.25339 | + | 3.66576i | −0.230049 | + | 0.259208i | ||||
\(201\) | −7.79349 | − | 18.8152i | −0.549710 | − | 1.32712i | ||||
\(202\) | −0.156812 | + | 0.156812i | −0.0110333 | + | 0.0110333i | ||||
\(203\) | − | 9.20737i | − | 0.646230i | ||||||
\(204\) | −12.8959 | − | 2.49095i | −0.902892 | − | 0.174402i | ||||
\(205\) | 5.49759 | + | 12.2296i | 0.383968 | + | 0.854154i | ||||
\(206\) | −0.0646205 | − | 0.0646205i | −0.00450232 | − | 0.00450232i | ||||
\(207\) | −0.760106 | + | 0.314846i | −0.0528310 | + | 0.0218833i | ||||
\(208\) | −0.634394 | −0.0439873 | ||||||||
\(209\) | −9.48133 | + | 3.92729i | −0.655837 | + | 0.271657i | ||||
\(210\) | 0.0389631 | + | 1.30868i | 0.00268871 | + | 0.0903076i | ||||
\(211\) | −4.54512 | − | 1.88265i | −0.312899 | − | 0.129607i | 0.220707 | − | 0.975340i | \(-0.429164\pi\) |
−0.533606 | + | 0.845733i | \(0.679164\pi\) | |||||||
\(212\) | −16.9288 | − | 16.9288i | −1.16267 | − | 1.16267i | ||||
\(213\) | 14.2101 | + | 14.2101i | 0.973658 | + | 0.973658i | ||||
\(214\) | 1.52873 | + | 0.633221i | 0.104502 | + | 0.0432861i | ||||
\(215\) | −0.752870 | − | 25.2872i | −0.0513453 | − | 1.72457i | ||||
\(216\) | 4.90977 | − | 2.03370i | 0.334068 | − | 0.138375i | ||||
\(217\) | −0.704606 | −0.0478318 | ||||||||
\(218\) | 2.03283 | − | 0.842025i | 0.137681 | − | 0.0570292i | ||||
\(219\) | 18.2053 | + | 18.2053i | 1.23020 | + | 1.23020i | ||||
\(220\) | 4.78603 | + | 10.6467i | 0.322674 | + | 0.717803i | ||||
\(221\) | 0.396776 | − | 0.600998i | 0.0266900 | − | 0.0404275i | ||||
\(222\) | − | 2.34967i | − | 0.157700i | ||||||
\(223\) | 7.10210 | − | 7.10210i | 0.475592 | − | 0.475592i | −0.428127 | − | 0.903719i | \(-0.640826\pi\) |
0.903719 | + | 0.428127i | \(0.140826\pi\) | |||||||
\(224\) | 1.56880 | + | 3.78743i | 0.104820 | + | 0.253058i | ||||
\(225\) | −1.11555 | − | 0.990060i | −0.0743701 | − | 0.0660040i | ||||
\(226\) | 1.31385 | − | 0.544216i | 0.0873963 | − | 0.0362007i | ||||
\(227\) | −4.13654 | − | 1.71341i | −0.274552 | − | 0.113723i | 0.241160 | − | 0.970485i | \(-0.422472\pi\) |
−0.515711 | + | 0.856762i | \(0.672472\pi\) | |||||||
\(228\) | −4.64450 | + | 11.2128i | −0.307589 | + | 0.742587i | ||||
\(229\) | −0.847088 | + | 0.847088i | −0.0559771 | + | 0.0559771i | −0.734541 | − | 0.678564i | \(-0.762603\pi\) |
0.678564 | + | 0.734541i | \(0.262603\pi\) | |||||||
\(230\) | 1.43511 | + | 0.544992i | 0.0946280 | + | 0.0359357i | ||||
\(231\) | 5.85376 | + | 2.42471i | 0.385149 | + | 0.159534i | ||||
\(232\) | 5.82669 | + | 2.41349i | 0.382541 | + | 0.158454i | ||||
\(233\) | 9.74096 | + | 23.5168i | 0.638152 | + | 1.54063i | 0.829139 | + | 0.559042i | \(0.188831\pi\) |
−0.190987 | + | 0.981592i | \(0.561169\pi\) | |||||||
\(234\) | 0.0129695i | 0.000847845i | ||||||||
\(235\) | 4.31759 | + | 4.06793i | 0.281649 | + | 0.265363i | ||||
\(236\) | −11.0901 | − | 11.0901i | −0.721903 | − | 0.721903i | ||||
\(237\) | − | 21.2194i | − | 1.37835i | ||||||
\(238\) | −1.44209 | − | 0.278553i | −0.0934770 | − | 0.0180559i | ||||
\(239\) | 6.21407 | 0.401955 | 0.200977 | − | 0.979596i | \(-0.435588\pi\) | ||||
0.200977 | + | 0.979596i | \(0.435588\pi\) | |||||||
\(240\) | 12.4797 | + | 4.73926i | 0.805561 | + | 0.305918i | ||||
\(241\) | 10.2576 | + | 24.7640i | 0.660750 | + | 1.59519i | 0.796631 | + | 0.604467i | \(0.206614\pi\) |
−0.135880 | + | 0.990725i | \(0.543386\pi\) | |||||||
\(242\) | 0.932062 | 0.0599152 | ||||||||
\(243\) | 1.18180 | + | 2.85312i | 0.0758126 | + | 0.183028i | ||||
\(244\) | 5.15294 | − | 12.4403i | 0.329883 | − | 0.796409i | ||||
\(245\) | 0.329528 | + | 11.0681i | 0.0210528 | + | 0.707114i | ||||
\(246\) | −1.73482 | + | 1.73482i | −0.110608 | + | 0.110608i | ||||
\(247\) | −0.470552 | − | 0.470552i | −0.0299405 | − | 0.0299405i | ||||
\(248\) | 0.184696 | − | 0.445895i | 0.0117282 | − | 0.0283144i | ||||
\(249\) | −5.39417 | + | 13.0227i | −0.341842 | + | 0.825279i | ||||
\(250\) | 0.248169 | + | 2.77191i | 0.0156956 | + | 0.175311i | ||||
\(251\) | 10.6052i | 0.669394i | 0.942326 | + | 0.334697i | \(0.108634\pi\) | ||||
−0.942326 | + | 0.334697i | \(0.891366\pi\) | |||||||
\(252\) | −0.764376 | + | 0.316615i | −0.0481512 | + | 0.0199449i | ||||
\(253\) | 5.25310 | − | 5.25310i | 0.330260 | − | 0.330260i | ||||
\(254\) | 4.06903 | 0.255313 | ||||||||
\(255\) | −12.2951 | + | 8.85862i | −0.769947 | + | 0.554748i | ||||
\(256\) | 11.2702 | 0.704387 | ||||||||
\(257\) | −1.08911 | + | 1.08911i | −0.0679369 | + | 0.0679369i | −0.740259 | − | 0.672322i | \(-0.765297\pi\) |
0.672322 | + | 0.740259i | \(0.265297\pi\) | |||||||
\(258\) | 4.27659 | − | 1.77142i | 0.266249 | − | 0.110284i | ||||
\(259\) | 8.21860i | 0.510679i | ||||||||
\(260\) | −0.519061 | + | 0.550917i | −0.0321908 | + | 0.0341664i | ||||
\(261\) | −0.734467 | + | 1.77316i | −0.0454624 | + | 0.109756i | ||||
\(262\) | −0.918172 | + | 2.21666i | −0.0567249 | + | 0.136946i | ||||
\(263\) | 0.301535 | + | 0.301535i | 0.0185935 | + | 0.0185935i | 0.716342 | − | 0.697749i | \(-0.245815\pi\) |
−0.697749 | + | 0.716342i | \(0.745815\pi\) | |||||||
\(264\) | −3.06885 | + | 3.06885i | −0.188875 | + | 0.188875i | ||||
\(265\) | −27.6103 | + | 0.822036i | −1.69609 | + | 0.0504973i | ||||
\(266\) | −0.519375 | + | 1.25388i | −0.0318449 | + | 0.0768805i | ||||
\(267\) | 7.22777 | + | 17.4494i | 0.442333 | + | 1.06789i | ||||
\(268\) | −24.0125 | −1.46680 | ||||||||
\(269\) | −6.54570 | − | 15.8027i | −0.399098 | − | 0.963508i | −0.987880 | − | 0.155217i | \(-0.950392\pi\) |
0.588782 | − | 0.808292i | \(-0.299608\pi\) | |||||||
\(270\) | 1.07128 | − | 2.82096i | 0.0651961 | − | 0.171678i | ||||
\(271\) | 16.0704 | 0.976208 | 0.488104 | − | 0.872785i | \(-0.337689\pi\) | ||||
0.488104 | + | 0.872785i | \(0.337689\pi\) | |||||||
\(272\) | −8.25079 | + | 12.4975i | −0.500278 | + | 0.757774i | ||||
\(273\) | 0.410855i | 0.0248661i | ||||||||
\(274\) | −1.16260 | − | 1.16260i | −0.0702353 | − | 0.0702353i | ||||
\(275\) | 12.7275 | + | 4.40461i | 0.767495 | + | 0.265608i | ||||
\(276\) | − | 8.78570i | − | 0.528837i | ||||||
\(277\) | −6.41483 | − | 15.4868i | −0.385430 | − | 0.930510i | −0.990895 | − | 0.134638i | \(-0.957013\pi\) |
0.605465 | − | 0.795872i | \(-0.292987\pi\) | |||||||
\(278\) | −1.05719 | − | 0.437904i | −0.0634063 | − | 0.0262637i | ||||
\(279\) | 0.135694 | + | 0.0562061i | 0.00812376 | + | 0.00336497i | ||||
\(280\) | 2.93247 | + | 1.11363i | 0.175249 | + | 0.0665521i | ||||
\(281\) | 5.54254 | − | 5.54254i | 0.330640 | − | 0.330640i | −0.522189 | − | 0.852830i | \(-0.674885\pi\) |
0.852830 | + | 0.522189i | \(0.174885\pi\) | |||||||
\(282\) | −0.415372 | + | 1.00280i | −0.0247350 | + | 0.0597157i | ||||
\(283\) | −6.07963 | − | 2.51826i | −0.361396 | − | 0.149695i | 0.194594 | − | 0.980884i | \(-0.437661\pi\) |
−0.555991 | + | 0.831189i | \(0.687661\pi\) | |||||||
\(284\) | 21.8913 | − | 9.06767i | 1.29901 | − | 0.538067i | ||||
\(285\) | 5.74135 | + | 12.7719i | 0.340088 | + | 0.756542i | ||||
\(286\) | −0.0448163 | − | 0.108196i | −0.00265004 | − | 0.00639777i | ||||
\(287\) | 6.06800 | − | 6.06800i | 0.358183 | − | 0.358183i | ||||
\(288\) | − | 0.854527i | − | 0.0503535i | ||||||
\(289\) | −6.67925 | − | 15.6329i | −0.392897 | − | 0.919582i | ||||
\(290\) | 3.26622 | − | 1.46826i | 0.191799 | − | 0.0862194i | ||||
\(291\) | 2.67194 | + | 2.67194i | 0.156632 | + | 0.156632i | ||||
\(292\) | 28.0461 | − | 11.6171i | 1.64128 | − | 0.679839i | ||||
\(293\) | −3.15115 | −0.184092 | −0.0920461 | − | 0.995755i | \(-0.529341\pi\) | ||||
−0.0920461 | + | 0.995755i | \(0.529341\pi\) | |||||||
\(294\) | −1.87185 | + | 0.775344i | −0.109168 | + | 0.0452190i | ||||
\(295\) | −18.0875 | + | 0.538517i | −1.05310 | + | 0.0313537i | ||||
\(296\) | −5.20097 | − | 2.15431i | −0.302300 | − | 0.125217i | ||||
\(297\) | −10.3259 | − | 10.3259i | −0.599171 | − | 0.599171i | ||||
\(298\) | −2.04885 | − | 2.04885i | −0.118687 | − | 0.118687i | ||||
\(299\) | 0.445057 | + | 0.184348i | 0.0257383 | + | 0.0106611i | ||||
\(300\) | 14.3265 | − | 6.95989i | 0.827141 | − | 0.401829i | ||||
\(301\) | −14.9585 | + | 6.19602i | −0.862195 | + | 0.357133i | ||||
\(302\) | 0.0342954 | 0.00197348 | ||||||||
\(303\) | 1.35292 | − | 0.560396i | 0.0777229 | − | 0.0321939i | ||||
\(304\) | 9.78495 | + | 9.78495i | 0.561205 | + | 0.561205i | ||||
\(305\) | −6.36987 | − | 14.1701i | −0.364738 | − | 0.811376i | ||||
\(306\) | 0.255499 | + | 0.168679i | 0.0146059 | + | 0.00964273i | ||||
\(307\) | 14.9905i | 0.855551i | 0.903885 | + | 0.427775i | \(0.140703\pi\) | ||||
−0.903885 | + | 0.427775i | \(0.859297\pi\) | |||||||
\(308\) | 5.28261 | − | 5.28261i | 0.301005 | − | 0.301005i | ||||
\(309\) | 0.230933 | + | 0.557521i | 0.0131373 | + | 0.0317163i | ||||
\(310\) | −0.112361 | − | 0.249952i | −0.00638167 | − | 0.0141963i | ||||
\(311\) | 9.26536 | − | 3.83784i | 0.525390 | − | 0.217624i | −0.104193 | − | 0.994557i | \(-0.533226\pi\) |
0.629583 | + | 0.776933i | \(0.283226\pi\) | |||||||
\(312\) | −0.260001 | − | 0.107696i | −0.0147196 | − | 0.00609708i | ||||
\(313\) | 1.35503 | − | 3.27134i | 0.0765910 | − | 0.184907i | −0.880946 | − | 0.473216i | \(-0.843093\pi\) |
0.957537 | + | 0.288309i | \(0.0930930\pi\) | |||||||
\(314\) | 1.70114 | − | 1.70114i | 0.0960007 | − | 0.0960007i | ||||
\(315\) | −0.338896 | + | 0.892401i | −0.0190946 | + | 0.0502811i | ||||
\(316\) | −23.1149 | − | 9.57451i | −1.30032 | − | 0.538608i | ||||
\(317\) | 11.2813 | + | 4.67288i | 0.633623 | + | 0.262455i | 0.676292 | − | 0.736634i | \(-0.263586\pi\) |
−0.0426686 | + | 0.999089i | \(0.513586\pi\) | |||||||
\(318\) | −1.93416 | − | 4.66948i | −0.108462 | − | 0.261851i | ||||
\(319\) | − | 17.3302i | − | 0.970307i | ||||||
\(320\) | 10.0454 | − | 10.6619i | 0.561553 | − | 0.596017i | ||||
\(321\) | −7.72612 | − | 7.72612i | −0.431230 | − | 0.431230i | ||||
\(322\) | − | 0.982469i | − | 0.0547508i | ||||||
\(323\) | −15.3897 | + | 3.14995i | −0.856308 | + | 0.175268i | ||||
\(324\) | −15.5355 | −0.863084 | ||||||||
\(325\) | 0.0519564 | + | 0.871775i | 0.00288203 | + | 0.0483574i | ||||
\(326\) | 1.18261 | + | 2.85508i | 0.0654988 | + | 0.158128i | ||||
\(327\) | −14.5294 | −0.803475 | ||||||||
\(328\) | 2.24942 | + | 5.43059i | 0.124204 | + | 0.299854i | ||||
\(329\) | 1.45288 | − | 3.50755i | 0.0800996 | − | 0.193378i | ||||
\(330\) | 0.0733369 | + | 2.46322i | 0.00403707 | + | 0.135596i | ||||
\(331\) | −13.0768 | + | 13.0768i | −0.718764 | + | 0.718764i | −0.968352 | − | 0.249588i | \(-0.919705\pi\) |
0.249588 | + | 0.968352i | \(0.419705\pi\) | |||||||
\(332\) | 11.7521 | + | 11.7521i | 0.644979 | + | 0.644979i | ||||
\(333\) | 0.655594 | − | 1.58274i | 0.0359263 | − | 0.0867338i | ||||
\(334\) | −0.398886 | + | 0.962996i | −0.0218261 | + | 0.0526928i | ||||
\(335\) | −18.9988 | + | 20.1648i | −1.03801 | + | 1.10172i | ||||
\(336\) | − | 8.54356i | − | 0.466090i | ||||||
\(337\) | −17.0378 | + | 7.05727i | −0.928106 | + | 0.384434i | −0.794960 | − | 0.606662i | \(-0.792508\pi\) |
−0.133146 | + | 0.991096i | \(0.542508\pi\) | |||||||
\(338\) | −2.28279 | + | 2.28279i | −0.124167 | + | 0.124167i | ||||
\(339\) | −9.39059 | −0.510027 | ||||||||
\(340\) | 4.10224 | + | 17.3906i | 0.222475 | + | 0.943135i | ||||
\(341\) | −1.32622 | −0.0718189 | ||||||||
\(342\) | 0.200043 | − | 0.200043i | 0.0108171 | − | 0.0108171i | ||||
\(343\) | 15.8023 | − | 6.54555i | 0.853247 | − | 0.353426i | ||||
\(344\) | − | 11.0903i | − | 0.597951i | ||||||
\(345\) | −7.37790 | − | 6.95128i | −0.397213 | − | 0.374244i | ||||
\(346\) | 0.281477 | − | 0.679547i | 0.0151323 | − | 0.0365327i | ||||
\(347\) | −1.94225 | + | 4.68901i | −0.104265 | + | 0.251719i | −0.967399 | − | 0.253256i | \(-0.918498\pi\) |
0.863134 | + | 0.504975i | \(0.168498\pi\) | |||||||
\(348\) | −14.4922 | − | 14.4922i | −0.776865 | − | 0.776865i | ||||
\(349\) | −17.2978 | + | 17.2978i | −0.925928 | + | 0.925928i | −0.997440 | − | 0.0715119i | \(-0.977218\pi\) |
0.0715119 | + | 0.997440i | \(0.477218\pi\) | |||||||
\(350\) | 1.60207 | − | 0.778296i | 0.0856345 | − | 0.0416017i | ||||
\(351\) | 0.362371 | − | 0.874840i | 0.0193419 | − | 0.0466955i | ||||
\(352\) | 2.95282 | + | 7.12875i | 0.157386 | + | 0.379964i | ||||
\(353\) | 17.5325 | 0.933161 | 0.466580 | − | 0.884479i | \(-0.345486\pi\) | ||||
0.466580 | + | 0.884479i | \(0.345486\pi\) | |||||||
\(354\) | −1.26707 | − | 3.05899i | −0.0673442 | − | 0.162583i | ||||
\(355\) | 9.70578 | − | 25.5579i | 0.515130 | − | 1.35647i | ||||
\(356\) | 22.2695 | 1.18028 | ||||||||
\(357\) | 8.09381 | + | 5.34349i | 0.428370 | + | 0.282807i | ||||
\(358\) | 5.79391i | 0.306218i | ||||||||
\(359\) | −1.42687 | − | 1.42687i | −0.0753076 | − | 0.0753076i | 0.668450 | − | 0.743757i | \(-0.266958\pi\) |
−0.743757 | + | 0.668450i | \(0.766958\pi\) | |||||||
\(360\) | −0.475904 | − | 0.448385i | −0.0250823 | − | 0.0236320i | ||||
\(361\) | − | 4.48433i | − | 0.236017i | ||||||
\(362\) | −1.08786 | − | 2.62634i | −0.0571769 | − | 0.138037i | ||||
\(363\) | −5.68619 | − | 2.35530i | −0.298447 | − | 0.123621i | ||||
\(364\) | 0.447557 | + | 0.185384i | 0.0234584 | + | 0.00971677i | ||||
\(365\) | 12.4346 | − | 32.7436i | 0.650858 | − | 1.71388i | ||||
\(366\) | 2.01008 | − | 2.01008i | 0.105069 | − | 0.105069i | ||||
\(367\) | −12.4008 | + | 29.9381i | −0.647315 | + | 1.56276i | 0.169294 | + | 0.985566i | \(0.445851\pi\) |
−0.816609 | + | 0.577191i | \(0.804149\pi\) | |||||||
\(368\) | −9.25478 | − | 3.83345i | −0.482439 | − | 0.199833i | ||||
\(369\) | −1.65262 | + | 0.684538i | −0.0860320 | + | 0.0356356i | ||||
\(370\) | −2.91546 | + | 1.31059i | −0.151568 | + | 0.0681343i | ||||
\(371\) | 6.76525 | + | 16.3328i | 0.351234 | + | 0.847955i | ||||
\(372\) | −1.10904 | + | 1.10904i | −0.0575009 | + | 0.0575009i | ||||
\(373\) | − | 20.6108i | − | 1.06719i | −0.845741 | − | 0.533593i | \(-0.820841\pi\) | ||
0.845741 | − | 0.533593i | \(-0.179159\pi\) | |||||||
\(374\) | −2.71433 | − | 0.524297i | −0.140355 | − | 0.0271107i | ||||
\(375\) | 5.49054 | − | 17.5375i | 0.283530 | − | 0.905635i | ||||
\(376\) | 1.83884 | + | 1.83884i | 0.0948311 | + | 0.0948311i | ||||
\(377\) | 1.03822 | − | 0.430044i | 0.0534710 | − | 0.0221484i | ||||
\(378\) | −1.93122 | −0.0993313 | ||||||||
\(379\) | 15.3385 | − | 6.35343i | 0.787887 | − | 0.326354i | 0.0477935 | − | 0.998857i | \(-0.484781\pi\) |
0.740094 | + | 0.672504i | \(0.234781\pi\) | |||||||
\(380\) | 16.5034 | − | 0.491353i | 0.846607 | − | 0.0252059i | ||||
\(381\) | −24.8237 | − | 10.2823i | −1.27176 | − | 0.526779i | ||||
\(382\) | 0.542471 | + | 0.542471i | 0.0277552 | + | 0.0277552i | ||||
\(383\) | 16.4274 | + | 16.4274i | 0.839401 | + | 0.839401i | 0.988780 | − | 0.149379i | \(-0.0477274\pi\) |
−0.149379 | + | 0.988780i | \(0.547727\pi\) | |||||||
\(384\) | 11.1764 | + | 4.62944i | 0.570346 | + | 0.236245i | ||||
\(385\) | −0.256516 | − | 8.61577i | −0.0130732 | − | 0.439100i | ||||
\(386\) | −3.67622 | + | 1.52274i | −0.187115 | + | 0.0775055i | ||||
\(387\) | 3.37498 | 0.171560 | ||||||||
\(388\) | 4.11624 | − | 1.70500i | 0.208971 | − | 0.0865584i | ||||
\(389\) | 25.9259 | + | 25.9259i | 1.31450 | + | 1.31450i | 0.918064 | + | 0.396433i | \(0.129752\pi\) |
0.396433 | + | 0.918064i | \(0.370248\pi\) | |||||||
\(390\) | −0.145747 | + | 0.0655174i | −0.00738016 | + | 0.00331760i | ||||
\(391\) | 9.41996 | − | 6.36999i | 0.476388 | − | 0.322144i | ||||
\(392\) | 4.85419i | 0.245174i | ||||||||
\(393\) | 11.2029 | − | 11.2029i | 0.565112 | − | 0.565112i | ||||
\(394\) | −1.01673 | − | 2.45461i | −0.0512222 | − | 0.123661i | ||||
\(395\) | −26.3289 | + | 11.8356i | −1.32475 | + | 0.595516i | ||||
\(396\) | −1.43872 | + | 0.595938i | −0.0722984 | + | 0.0299470i | ||||
\(397\) | −9.06522 | − | 3.75494i | −0.454970 | − | 0.188455i | 0.143416 | − | 0.989662i | \(-0.454191\pi\) |
−0.598386 | + | 0.801208i | \(0.704191\pi\) | |||||||
\(398\) | 1.50881 | − | 3.64259i | 0.0756299 | − | 0.182587i | ||||
\(399\) | 6.33706 | − | 6.33706i | 0.317250 | − | 0.317250i | ||||
\(400\) | −1.08041 | − | 18.1282i | −0.0540207 | − | 0.906411i | ||||
\(401\) | 19.8539 | + | 8.22376i | 0.991457 | + | 0.410675i | 0.818657 | − | 0.574282i | \(-0.194719\pi\) |
0.172799 | + | 0.984957i | \(0.444719\pi\) | |||||||
\(402\) | −4.68344 | − | 1.93994i | −0.233589 | − | 0.0967556i | ||||
\(403\) | −0.0329097 | − | 0.0794512i | −0.00163935 | − | 0.00395774i | ||||
\(404\) | − | 1.72663i | − | 0.0859032i | ||||||
\(405\) | −12.2918 | + | 13.0461i | −0.610782 | + | 0.648267i | ||||
\(406\) | −1.62061 | − | 1.62061i | −0.0804293 | − | 0.0804293i | ||||
\(407\) | 15.4692i | 0.766779i | ||||||||
\(408\) | −5.50311 | + | 3.72133i | −0.272445 | + | 0.184233i | ||||
\(409\) | −31.2735 | −1.54638 | −0.773189 | − | 0.634176i | \(-0.781339\pi\) | ||||
−0.773189 | + | 0.634176i | \(0.781339\pi\) | |||||||
\(410\) | 3.12020 | + | 1.18492i | 0.154096 | + | 0.0585190i | ||||
\(411\) | 4.15476 | + | 10.0305i | 0.204939 | + | 0.494767i | ||||
\(412\) | 0.711526 | 0.0350544 | ||||||||
\(413\) | 4.43193 | + | 10.6996i | 0.218081 | + | 0.526494i | ||||
\(414\) | −0.0783710 | + | 0.189204i | −0.00385173 | + | 0.00929889i | ||||
\(415\) | 19.1673 | − | 0.570663i | 0.940883 | − | 0.0280128i | ||||
\(416\) | −0.353795 | + | 0.353795i | −0.0173462 | + | 0.0173462i | ||||
\(417\) | 5.34300 | + | 5.34300i | 0.261648 | + | 0.261648i | ||||
\(418\) | −0.977576 | + | 2.36008i | −0.0478148 | + | 0.115435i | ||||
\(419\) | −7.78615 | + | 18.7974i | −0.380378 | + | 0.918314i | 0.611514 | + | 0.791234i | \(0.290561\pi\) |
−0.991892 | + | 0.127081i | \(0.959439\pi\) | |||||||
\(420\) | −7.41935 | − | 6.99033i | −0.362027 | − | 0.341093i | ||||
\(421\) | − | 1.80862i | − | 0.0881467i | −0.999028 | − | 0.0440733i | \(-0.985966\pi\) | ||
0.999028 | − | 0.0440733i | \(-0.0140335\pi\) | |||||||
\(422\) | −1.13136 | + | 0.468626i | −0.0550740 | + | 0.0228124i | ||||
\(423\) | −0.559591 | + | 0.559591i | −0.0272083 | + | 0.0272083i | ||||
\(424\) | −12.1092 | −0.588075 | ||||||||
\(425\) | 17.8496 | + | 10.3146i | 0.865835 | + | 0.500330i | ||||
\(426\) | 5.00228 | 0.242361 | ||||||||
\(427\) | −7.03079 | + | 7.03079i | −0.340244 | + | 0.340244i | ||||
\(428\) | −11.9024 | + | 4.93016i | −0.575327 | + | 0.238308i | ||||
\(429\) | 0.773317i | 0.0373361i | ||||||||
\(430\) | −4.58335 | − | 4.31833i | −0.221029 | − | 0.208248i | ||||
\(431\) | 6.37695 | − | 15.3953i | 0.307167 | − | 0.741566i | −0.692628 | − | 0.721295i | \(-0.743547\pi\) |
0.999795 | − | 0.0202708i | \(-0.00645283\pi\) | |||||||
\(432\) | −7.53536 | + | 18.1920i | −0.362545 | + | 0.875261i | ||||
\(433\) | 11.5388 | + | 11.5388i | 0.554519 | + | 0.554519i | 0.927742 | − | 0.373222i | \(-0.121747\pi\) |
−0.373222 | + | 0.927742i | \(0.621747\pi\) | |||||||
\(434\) | −0.124019 | + | 0.124019i | −0.00595311 | + | 0.00595311i | ||||
\(435\) | −23.6363 | + | 0.703720i | −1.13328 | + | 0.0337408i | ||||
\(436\) | −6.55588 | + | 15.8273i | −0.313970 | + | 0.757990i | ||||
\(437\) | −4.02118 | − | 9.70800i | −0.192359 | − | 0.464396i | ||||
\(438\) | 6.40870 | 0.306220 | ||||||||
\(439\) | 9.19489 | + | 22.1984i | 0.438848 | + | 1.05947i | 0.976347 | + | 0.216209i | \(0.0693692\pi\) |
−0.537499 | + | 0.843264i | \(0.680631\pi\) | |||||||
\(440\) | 5.51955 | + | 2.09609i | 0.263134 | + | 0.0999271i | ||||
\(441\) | −1.47721 | −0.0703434 | ||||||||
\(442\) | −0.0359457 | − | 0.175620i | −0.00170976 | − | 0.00835340i | ||||
\(443\) | − | 21.2757i | − | 1.01084i | −0.862874 | − | 0.505419i | \(-0.831338\pi\) | ||
0.862874 | − | 0.505419i | \(-0.168662\pi\) | |||||||
\(444\) | 12.9359 | + | 12.9359i | 0.613912 | + | 0.613912i | ||||
\(445\) | 17.6197 | − | 18.7010i | 0.835253 | − | 0.886515i | ||||
\(446\) | − | 2.50011i | − | 0.118384i | ||||||
\(447\) | 7.32193 | + | 17.6767i | 0.346316 | + | 0.836080i | ||||
\(448\) | −8.66156 | − | 3.58773i | −0.409220 | − | 0.169504i | ||||
\(449\) | 26.9783 | + | 11.1748i | 1.27318 | + | 0.527370i | 0.913931 | − | 0.405870i | \(-0.133031\pi\) |
0.359253 | + | 0.933240i | \(0.383031\pi\) | |||||||
\(450\) | −0.370613 | + | 0.0220879i | −0.0174709 | + | 0.00104124i | ||||
\(451\) | 11.4213 | − | 11.4213i | 0.537807 | − | 0.537807i | ||||
\(452\) | −4.23718 | + | 10.2295i | −0.199300 | + | 0.481153i | ||||
\(453\) | −0.209224 | − | 0.0866636i | −0.00983022 | − | 0.00407181i | ||||
\(454\) | −1.02966 | + | 0.426500i | −0.0483244 | + | 0.0200166i | ||||
\(455\) | 0.509787 | − | 0.229165i | 0.0238992 | − | 0.0107434i | ||||
\(456\) | 2.34916 | + | 5.67138i | 0.110010 | + | 0.265587i | ||||
\(457\) | 0.734055 | − | 0.734055i | 0.0343376 | − | 0.0343376i | −0.689729 | − | 0.724067i | \(-0.742271\pi\) |
0.724067 | + | 0.689729i | \(0.242271\pi\) | |||||||
\(458\) | 0.298195i | 0.0139337i | ||||||||
\(459\) | −12.5214 | − | 18.5167i | −0.584448 | − | 0.864283i | ||||
\(460\) | −10.9013 | + | 4.90045i | −0.508274 | + | 0.228485i | ||||
\(461\) | 0.0496372 | + | 0.0496372i | 0.00231183 | + | 0.00231183i | 0.708262 | − | 0.705950i | \(-0.249480\pi\) |
−0.705950 | + | 0.708262i | \(0.749480\pi\) | |||||||
\(462\) | 1.45711 | − | 0.603554i | 0.0677908 | − | 0.0280799i | ||||
\(463\) | 40.0649 | 1.86197 | 0.930987 | − | 0.365051i | \(-0.118949\pi\) | ||||
0.930987 | + | 0.365051i | \(0.118949\pi\) | |||||||
\(464\) | −21.5894 | + | 8.94260i | −1.00226 | + | 0.415150i | ||||
\(465\) | 0.0538532 | + | 1.80880i | 0.00249738 | + | 0.0838812i | ||||
\(466\) | 5.85376 | + | 2.42471i | 0.271170 | + | 0.112322i | ||||
\(467\) | 16.0563 | + | 16.0563i | 0.742997 | + | 0.742997i | 0.973154 | − | 0.230156i | \(-0.0739238\pi\) |
−0.230156 | + | 0.973154i | \(0.573924\pi\) | |||||||
\(468\) | −0.0714028 | − | 0.0714028i | −0.00330059 | − | 0.00330059i | ||||
\(469\) | 16.3816 | + | 6.78547i | 0.756431 | + | 0.313324i | ||||
\(470\) | 1.47595 | − | 0.0439433i | 0.0680806 | − | 0.00202695i | ||||
\(471\) | −14.6768 | + | 6.07932i | −0.676270 | + | 0.280120i | ||||
\(472\) | −7.93276 | −0.365135 | ||||||||
\(473\) | −28.1552 | + | 11.6622i | −1.29458 | + | 0.536231i | ||||
\(474\) | −3.73486 | − | 3.73486i | −0.171548 | − | 0.171548i | ||||
\(475\) | 12.6449 | − | 14.2477i | 0.580190 | − | 0.653730i | ||||
\(476\) | 9.47288 | − | 6.40578i | 0.434189 | − | 0.293608i | ||||
\(477\) | − | 3.68503i | − | 0.168726i | ||||||
\(478\) | 1.09375 | − | 1.09375i | 0.0500270 | − | 0.0500270i | ||||
\(479\) | −8.90144 | − | 21.4900i | −0.406717 | − | 0.981902i | −0.985995 | − | 0.166772i | \(-0.946665\pi\) |
0.579278 | − | 0.815130i | \(-0.303335\pi\) | |||||||
\(480\) | 9.60284 | − | 4.31676i | 0.438308 | − | 0.197032i | ||||
\(481\) | −0.926726 | + | 0.383863i | −0.0422551 | + | 0.0175026i | ||||
\(482\) | 6.16422 | + | 2.55331i | 0.280773 | + | 0.116300i | ||||
\(483\) | −2.48267 | + | 5.99370i | −0.112965 | + | 0.272723i | ||||
\(484\) | −5.13139 | + | 5.13139i | −0.233245 | + | 0.233245i | ||||
\(485\) | 1.82499 | − | 4.80567i | 0.0828685 | − | 0.218214i | ||||
\(486\) | 0.710195 | + | 0.294172i | 0.0322151 | + | 0.0133439i | ||||
\(487\) | −15.6248 | − | 6.47199i | −0.708026 | − | 0.293274i | −0.000538564 | − | 1.00000i | \(-0.500171\pi\) |
−0.707488 | + | 0.706726i | \(0.750171\pi\) | |||||||
\(488\) | −2.60633 | − | 6.29224i | −0.117983 | − | 0.284837i | ||||
\(489\) | − | 20.4063i | − | 0.922803i | ||||||
\(490\) | 2.00611 | + | 1.89011i | 0.0906270 | + | 0.0853866i | ||||
\(491\) | −14.8915 | − | 14.8915i | −0.672045 | − | 0.672045i | 0.286142 | − | 0.958187i | \(-0.407627\pi\) |
−0.958187 | + | 0.286142i | \(0.907627\pi\) | |||||||
\(492\) | − | 19.1018i | − | 0.861177i | ||||||
\(493\) | 5.03100 | − | 26.0459i | 0.226585 | − | 1.17305i | ||||
\(494\) | −0.165646 | −0.00745275 | ||||||||
\(495\) | −0.637875 | + | 1.67969i | −0.0286704 | + | 0.0754965i | ||||
\(496\) | 0.684345 | + | 1.65216i | 0.0307280 | + | 0.0741840i | ||||
\(497\) | −17.4968 | −0.784840 | ||||||||
\(498\) | 1.34271 | + | 3.24159i | 0.0601682 | + | 0.145259i | ||||
\(499\) | 8.62028 | − | 20.8112i | 0.385897 | − | 0.931637i | −0.604903 | − | 0.796299i | \(-0.706788\pi\) |
0.990800 | − | 0.135338i | \(-0.0432120\pi\) | |||||||
\(500\) | −16.6268 | − | 13.8942i | −0.743572 | − | 0.621369i | ||||
\(501\) | 4.86693 | − | 4.86693i | 0.217438 | − | 0.217438i | ||||
\(502\) | 1.86664 | + | 1.86664i | 0.0833122 | + | 0.0833122i | ||||
\(503\) | 11.1063 | − | 26.8129i | 0.495204 | − | 1.19553i | −0.456835 | − | 0.889551i | \(-0.651017\pi\) |
0.952039 | − | 0.305977i | \(-0.0989829\pi\) | |||||||
\(504\) | −0.160142 | + | 0.386618i | −0.00713330 | + | 0.0172213i | ||||
\(505\) | −1.44996 | − | 1.36612i | −0.0645224 | − | 0.0607915i | ||||
\(506\) | − | 1.84922i | − | 0.0822077i | ||||||
\(507\) | 19.6950 | − | 8.15794i | 0.874686 | − | 0.362307i | ||||
\(508\) | −22.4017 | + | 22.4017i | −0.993915 | + | 0.993915i | ||||
\(509\) | −4.38401 | −0.194318 | −0.0971589 | − | 0.995269i | \(-0.530976\pi\) | ||||
−0.0971589 | + | 0.995269i | \(0.530976\pi\) | |||||||
\(510\) | −0.604857 | + | 3.72330i | −0.0267835 | + | 0.164871i | ||||
\(511\) | −22.4162 | −0.991633 | ||||||||
\(512\) | 12.3921 | − | 12.3921i | 0.547660 | − | 0.547660i | ||||
\(513\) | −19.0828 | + | 7.90437i | −0.842528 | + | 0.348987i | ||||
\(514\) | 0.383393i | 0.0169107i | ||||||||
\(515\) | 0.562962 | − | 0.597513i | 0.0248071 | − | 0.0263295i | ||||
\(516\) | −13.7920 | + | 33.2969i | −0.607160 | + | 1.46581i | ||||
\(517\) | 2.73462 | − | 6.60196i | 0.120269 | − | 0.290354i | ||||
\(518\) | 1.44657 | + | 1.44657i | 0.0635587 | + | 0.0635587i | ||||
\(519\) | −3.43439 | + | 3.43439i | −0.150753 | + | 0.150753i | ||||
\(520\) | 0.0113934 | + | 0.382678i | 0.000499634 | + | 0.0167816i | ||||
\(521\) | −1.22242 | + | 2.95118i | −0.0535551 | + | 0.129294i | −0.948393 | − | 0.317099i | \(-0.897291\pi\) |
0.894837 | + | 0.446392i | \(0.147291\pi\) | |||||||
\(522\) | 0.182822 | + | 0.441372i | 0.00800192 | + | 0.0193183i | ||||
\(523\) | −34.0520 | −1.48899 | −0.744494 | − | 0.667629i | \(-0.767309\pi\) | ||||
−0.744494 | + | 0.667629i | \(0.767309\pi\) | |||||||
\(524\) | −7.14875 | − | 17.2586i | −0.312294 | − | 0.753945i | ||||
\(525\) | −11.7404 | + | 0.699712i | −0.512395 | + | 0.0305379i | ||||
\(526\) | 0.106148 | 0.00462825 | ||||||||
\(527\) | −1.99320 | − | 0.385004i | −0.0868251 | − | 0.0167710i | ||||
\(528\) | − | 16.0808i | − | 0.699828i | ||||||
\(529\) | −10.8848 | − | 10.8848i | −0.473251 | − | 0.473251i | ||||
\(530\) | −4.71505 | + | 5.00443i | −0.204809 | + | 0.217378i | ||||
\(531\) | − | 2.41407i | − | 0.104762i | ||||||
\(532\) | −4.04377 | − | 9.76254i | −0.175320 | − | 0.423260i | ||||
\(533\) | 0.967641 | + | 0.400810i | 0.0419132 | + | 0.0173610i | ||||
\(534\) | 4.34347 | + | 1.79913i | 0.187961 | + | 0.0778558i | ||||
\(535\) | −5.27710 | + | 13.8960i | −0.228149 | + | 0.600776i | ||||
\(536\) | −8.58809 | + | 8.58809i | −0.370949 | + | 0.370949i | ||||
\(537\) | 14.6411 | − | 35.3467i | 0.631808 | − | 1.52532i | ||||
\(538\) | −3.93359 | − | 1.62934i | −0.169589 | − | 0.0702460i | ||||
\(539\) | 12.3234 | − | 5.10452i | 0.530806 | − | 0.219867i | ||||
\(540\) | 9.63273 | + | 21.4284i | 0.414527 | + | 0.922133i | ||||
\(541\) | −10.3587 | − | 25.0081i | −0.445355 | − | 1.07518i | −0.974042 | − | 0.226366i | \(-0.927315\pi\) |
0.528687 | − | 0.848817i | \(-0.322685\pi\) | |||||||
\(542\) | 2.82859 | − | 2.82859i | 0.121498 | − | 0.121498i | ||||
\(543\) | 18.7714i | 0.805557i | ||||||||
\(544\) | 2.36836 | + | 11.5711i | 0.101543 | + | 0.496108i | ||||
\(545\) | 8.10412 | + | 18.0280i | 0.347143 | + | 0.772234i | ||||
\(546\) | 0.0723153 | + | 0.0723153i | 0.00309481 | + | 0.00309481i | ||||
\(547\) | −12.5020 | + | 5.17849i | −0.534546 | + | 0.221416i | −0.633593 | − | 0.773667i | \(-0.718421\pi\) |
0.0990470 | + | 0.995083i | \(0.468421\pi\) | |||||||
\(548\) | 12.8012 | 0.546841 | ||||||||
\(549\) | 1.91484 | − | 0.793151i | 0.0817232 | − | 0.0338509i | ||||
\(550\) | 3.01545 | − | 1.46492i | 0.128579 | − | 0.0624644i | ||||
\(551\) | −22.6466 | − | 9.38053i | −0.964778 | − | 0.399624i | ||||
\(552\) | −3.14221 | − | 3.14221i | −0.133742 | − | 0.133742i | ||||
\(553\) | 13.0637 | + | 13.0637i | 0.555524 | + | 0.555524i | ||||
\(554\) | −3.85494 | − | 1.59677i | −0.163781 | − | 0.0678402i | ||||
\(555\) | 21.0981 | − | 0.628149i | 0.895563 | − | 0.0266634i | ||||
\(556\) | 8.23114 | − | 3.40945i | 0.349078 | − | 0.144593i | ||||
\(557\) | 30.5182 | 1.29310 | 0.646548 | − | 0.762873i | \(-0.276212\pi\) | ||||
0.646548 | + | 0.762873i | \(0.276212\pi\) | |||||||
\(558\) | 0.0337766 | − | 0.0139907i | 0.00142988 | − | 0.000592275i | ||||
\(559\) | −1.39732 | − | 1.39732i | −0.0591005 | − | 0.0591005i | ||||
\(560\) | −10.6008 | + | 4.76539i | −0.447967 | + | 0.201375i | ||||
\(561\) | 15.2343 | + | 10.0576i | 0.643192 | + | 0.424632i | ||||
\(562\) | − | 1.95111i | − | 0.0823024i | ||||||
\(563\) | 5.73355 | − | 5.73355i | 0.241640 | − | 0.241640i | −0.575888 | − | 0.817529i | \(-0.695344\pi\) |
0.817529 | + | 0.575888i | \(0.195344\pi\) | |||||||
\(564\) | −3.23402 | − | 7.80762i | −0.136177 | − | 0.328760i | ||||
\(565\) | 5.23784 | + | 11.6518i | 0.220358 | + | 0.490196i | ||||
\(566\) | −1.51333 | + | 0.626842i | −0.0636101 | + | 0.0263481i | ||||
\(567\) | 10.5985 | + | 4.39004i | 0.445095 | + | 0.184364i | ||||
\(568\) | 4.58638 | − | 11.0725i | 0.192440 | − | 0.464592i | ||||
\(569\) | −2.71124 | + | 2.71124i | −0.113661 | + | 0.113661i | −0.761650 | − | 0.647989i | \(-0.775610\pi\) |
0.647989 | + | 0.761650i | \(0.275610\pi\) | |||||||
\(570\) | 3.25855 | + | 1.23746i | 0.136486 | + | 0.0518315i | ||||
\(571\) | 6.06730 | + | 2.51316i | 0.253909 | + | 0.105172i | 0.506007 | − | 0.862529i | \(-0.331121\pi\) |
−0.252099 | + | 0.967701i | \(0.581121\pi\) | |||||||
\(572\) | 0.842398 | + | 0.348933i | 0.0352224 | + | 0.0145896i | ||||
\(573\) | −1.93862 | − | 4.68023i | −0.0809869 | − | 0.195520i | ||||
\(574\) | − | 2.13608i | − | 0.0891583i | ||||||
\(575\) | −4.50991 | + | 13.0317i | −0.188076 | + | 0.543461i | ||||
\(576\) | 1.38186 | + | 1.38186i | 0.0575773 | + | 0.0575773i | ||||
\(577\) | 23.2880i | 0.969493i | 0.874655 | + | 0.484746i | \(0.161088\pi\) | ||||
−0.874655 | + | 0.484746i | \(0.838912\pi\) | |||||||
\(578\) | −3.92720 | − | 1.57595i | −0.163350 | − | 0.0655508i | ||||
\(579\) | 26.2753 | 1.09196 | ||||||||
\(580\) | −9.89850 | + | 26.0653i | −0.411013 | + | 1.08230i | ||||
\(581\) | −4.69649 | − | 11.3383i | −0.194843 | − | 0.470393i | ||||
\(582\) | 0.940585 | 0.0389885 | ||||||||
\(583\) | 12.7337 | + | 30.7418i | 0.527374 | + | 1.27319i | ||||
\(584\) | 5.87587 | − | 14.1856i | 0.243145 | − | 0.587004i | ||||
\(585\) | −0.116456 | + | 0.00346721i | −0.00481484 | + | 0.000143351i | ||||
\(586\) | −0.554640 | + | 0.554640i | −0.0229120 | + | 0.0229120i | ||||
\(587\) | −26.0085 | − | 26.0085i | −1.07348 | − | 1.07348i | −0.997077 | − | 0.0764077i | \(-0.975655\pi\) |
−0.0764077 | − | 0.997077i | \(-0.524345\pi\) | |||||||
\(588\) | 6.03671 | − | 14.5739i | 0.248950 | − | 0.601017i | ||||
\(589\) | −0.717858 | + | 1.73306i | −0.0295788 | + | 0.0714096i | ||||
\(590\) | −3.08884 | + | 3.27841i | −0.127165 | + | 0.134970i | ||||
\(591\) | 17.5440i | 0.721662i | ||||||||
\(592\) | 19.2709 | − | 7.98227i | 0.792030 | − | 0.328069i | ||||
\(593\) | −19.1275 | + | 19.1275i | −0.785474 | + | 0.785474i | −0.980749 | − | 0.195275i | \(-0.937440\pi\) |
0.195275 | + | 0.980749i | \(0.437440\pi\) | |||||||
\(594\) | −3.63497 | −0.149145 | ||||||||
\(595\) | 2.11565 | − | 13.0232i | 0.0867332 | − | 0.533901i | ||||
\(596\) | 22.5596 | 0.924076 | ||||||||
\(597\) | −18.4095 | + | 18.4095i | −0.753450 | + | 0.753450i | ||||
\(598\) | 0.110783 | − | 0.0458877i | 0.00453025 | − | 0.00187649i | ||||
\(599\) | − | 12.2973i | − | 0.502456i | −0.967928 | − | 0.251228i | \(-0.919166\pi\) | ||
0.967928 | − | 0.251228i | \(-0.0808344\pi\) | |||||||
\(600\) | 2.63468 | − | 7.61310i | 0.107560 | − | 0.310804i | ||||
\(601\) | −3.08883 | + | 7.45710i | −0.125996 | + | 0.304181i | −0.974273 | − | 0.225372i | \(-0.927640\pi\) |
0.848277 | + | 0.529553i | \(0.177640\pi\) | |||||||
\(602\) | −1.54230 | + | 3.72345i | −0.0628596 | + | 0.151757i | ||||
\(603\) | −2.61350 | − | 2.61350i | −0.106430 | − | 0.106430i | ||||
\(604\) | −0.188811 | + | 0.188811i | −0.00768260 | + | 0.00768260i | ||||
\(605\) | 0.249173 | + | 8.36913i | 0.0101303 | + | 0.340254i | ||||
\(606\) | 0.139493 | − | 0.336765i | 0.00566651 | − | 0.0136802i | ||||
\(607\) | −9.22388 | − | 22.2684i | −0.374386 | − | 0.903847i | −0.992996 | − | 0.118149i | \(-0.962304\pi\) |
0.618610 | − | 0.785698i | \(-0.287696\pi\) | |||||||
\(608\) | 10.9139 | 0.442619 | ||||||||
\(609\) | 5.79153 | + | 13.9820i | 0.234685 | + | 0.566579i | ||||
\(610\) | −3.61527 | − | 1.37293i | −0.146378 | − | 0.0555882i | ||||
\(611\) | 0.463369 | 0.0187459 | ||||||||
\(612\) | −2.33528 | + | 0.477981i | −0.0943980 | + | 0.0193212i | ||||
\(613\) | 39.8359i | 1.60896i | 0.593983 | + | 0.804478i | \(0.297555\pi\) | ||||
−0.593983 | + | 0.804478i | \(0.702445\pi\) | |||||||
\(614\) | 2.63850 | + | 2.63850i | 0.106481 | + | 0.106481i | ||||
\(615\) | −16.0410 | − | 15.1134i | −0.646836 | − | 0.609433i | ||||
\(616\) | − | 3.77867i | − | 0.152247i | ||||||
\(617\) | −9.87155 | − | 23.8320i | −0.397414 | − | 0.959442i | −0.988277 | − | 0.152670i | \(-0.951213\pi\) |
0.590863 | − | 0.806772i | \(-0.298787\pi\) | |||||||
\(618\) | 0.138777 | + | 0.0574834i | 0.00558244 | + | 0.00231232i | ||||
\(619\) | −3.48155 | − | 1.44210i | −0.139935 | − | 0.0579630i | 0.311617 | − | 0.950208i | \(-0.399129\pi\) |
−0.451552 | + | 0.892245i | \(0.649129\pi\) | |||||||
\(620\) | 1.99468 | + | 0.757496i | 0.0801085 | + | 0.0304218i | ||||
\(621\) | 10.5728 | − | 10.5728i | 0.424272 | − | 0.424272i | ||||
\(622\) | 0.955308 | − | 2.30632i | 0.0383044 | − | 0.0924749i | ||||
\(623\) | −15.1925 | − | 6.29293i | −0.608673 | − | 0.252121i | ||||
\(624\) | 0.963369 | − | 0.399041i | 0.0385656 | − | 0.0159744i | ||||
\(625\) | −24.8230 | + | 2.96938i | −0.992921 | + | 0.118775i | ||||
\(626\) | −0.337293 | − | 0.814297i | −0.0134809 | − | 0.0325459i | ||||
\(627\) | 11.9277 | − | 11.9277i | 0.476347 | − | 0.476347i | ||||
\(628\) | 18.7309i | 0.747446i | ||||||||
\(629\) | −4.49073 | + | 23.2489i | −0.179057 | + | 0.926994i | ||||
\(630\) | 0.0974235 | + | 0.216723i | 0.00388145 | + | 0.00863445i | ||||
\(631\) | 13.6572 | + | 13.6572i | 0.543685 | + | 0.543685i | 0.924607 | − | 0.380922i | \(-0.124393\pi\) |
−0.380922 | + | 0.924607i | \(0.624393\pi\) | |||||||
\(632\) | −11.6914 | + | 4.84274i | −0.465059 | + | 0.192634i | ||||
\(633\) | 8.08627 | 0.321400 | ||||||||
\(634\) | 2.80813 | − | 1.16317i | 0.111525 | − | 0.0461952i | ||||
\(635\) | 1.08779 | + | 36.5364i | 0.0431677 | + | 1.44990i | ||||
\(636\) | 36.3558 | + | 15.0591i | 1.44160 | + | 0.597131i | ||||
\(637\) | 0.611602 | + | 0.611602i | 0.0242326 | + | 0.0242326i | ||||
\(638\) | −3.05033 | − | 3.05033i | −0.120764 | − | 0.120764i | ||||
\(639\) | 3.36955 | + | 1.39571i | 0.133297 | + | 0.0552136i | ||||
\(640\) | −0.489760 | − | 16.4499i | −0.0193594 | − | 0.650239i | ||||
\(641\) | 19.0839 | − | 7.90483i | 0.753770 | − | 0.312222i | 0.0274914 | − | 0.999622i | \(-0.491248\pi\) |
0.726279 | + | 0.687400i | \(0.241248\pi\) | |||||||
\(642\) | −2.71978 | −0.107341 | ||||||||
\(643\) | 26.8106 | − | 11.1053i | 1.05731 | − | 0.437951i | 0.214813 | − | 0.976655i | \(-0.431086\pi\) |
0.842495 | + | 0.538704i | \(0.181086\pi\) | |||||||
\(644\) | 5.40890 | + | 5.40890i | 0.213141 | + | 0.213141i | ||||
\(645\) | 17.0492 | + | 37.9266i | 0.671310 | + | 1.49336i | ||||
\(646\) | −2.15435 | + | 3.26321i | −0.0847618 | + | 0.128389i | ||||
\(647\) | − | 41.2848i | − | 1.62307i | −0.584302 | − | 0.811536i | \(-0.698632\pi\) | ||
0.584302 | − | 0.811536i | \(-0.301368\pi\) | |||||||
\(648\) | −5.55629 | + | 5.55629i | −0.218272 | + | 0.218272i | ||||
\(649\) | 8.34184 | + | 20.1390i | 0.327446 | + | 0.790524i | ||||
\(650\) | 0.162588 | + | 0.144298i | 0.00637721 | + | 0.00565983i | ||||
\(651\) | 1.06999 | − | 0.443205i | 0.0419362 | − | 0.0173706i | ||||
\(652\) | −22.2292 | − | 9.20763i | −0.870562 | − | 0.360598i | ||||
\(653\) | 9.39804 | − | 22.6889i | 0.367774 | − | 0.887884i | −0.626341 | − | 0.779549i | \(-0.715448\pi\) |
0.994114 | − | 0.108335i | \(-0.0345519\pi\) | |||||||
\(654\) | −2.55734 | + | 2.55734i | −0.0999999 | + | 0.0999999i | ||||
\(655\) | −20.1492 | − | 7.65182i | −0.787296 | − | 0.298981i | ||||
\(656\) | −20.1217 | − | 8.33468i | −0.785621 | − | 0.325415i | ||||
\(657\) | 4.31692 | + | 1.78813i | 0.168419 | + | 0.0697614i | ||||
\(658\) | −0.361647 | − | 0.873094i | −0.0140985 | − | 0.0340368i | ||||
\(659\) | 17.7024i | 0.689588i | 0.938678 | + | 0.344794i | \(0.112051\pi\) | ||||
−0.938678 | + | 0.344794i | \(0.887949\pi\) | |||||||
\(660\) | −13.9648 | − | 13.1573i | −0.543579 | − | 0.512147i | ||||
\(661\) | 10.0305 | + | 10.0305i | 0.390141 | + | 0.390141i | 0.874738 | − | 0.484597i | \(-0.161034\pi\) |
−0.484597 | + | 0.874738i | \(0.661034\pi\) | |||||||
\(662\) | 4.60333i | 0.178914i | ||||||||
\(663\) | −0.224495 | + | 1.16223i | −0.00871867 | + | 0.0451373i | ||||
\(664\) | 8.40629 | 0.326227 | ||||||||
\(665\) | −11.3977 | − | 4.32835i | −0.441982 | − | 0.167846i | ||||
\(666\) | −0.163189 | − | 0.393974i | −0.00632346 | − | 0.0152662i | ||||
\(667\) | 17.7445 | 0.687072 | ||||||||
\(668\) | −3.10566 | − | 7.49773i | −0.120162 | − | 0.290096i | ||||
\(669\) | −6.31771 | + | 15.2523i | −0.244257 | + | 0.589688i | ||||
\(670\) | 0.205231 | + | 6.89325i | 0.00792878 | + | 0.266309i | ||||
\(671\) | −13.2335 | + | 13.2335i | −0.510872 | + | 0.510872i | ||||
\(672\) | −4.76466 | − | 4.76466i | −0.183801 | − | 0.183801i | ||||
\(673\) | 0.124393 | − | 0.300312i | 0.00479501 | − | 0.0115762i | −0.921464 | − | 0.388464i | \(-0.873006\pi\) |
0.926259 | + | 0.376888i | \(0.123006\pi\) | |||||||
\(674\) | −1.75668 | + | 4.24101i | −0.0676650 | + | 0.163358i | ||||
\(675\) | 25.6162 | + | 8.86506i | 0.985970 | + | 0.341216i | ||||
\(676\) | − | 25.1354i | − | 0.966746i | ||||||
\(677\) | 15.9805 | − | 6.61933i | 0.614180 | − | 0.254402i | −0.0538347 | − | 0.998550i | \(-0.517144\pi\) |
0.668014 | + | 0.744148i | \(0.267144\pi\) | |||||||
\(678\) | −1.65286 | + | 1.65286i | −0.0634775 | + | 0.0634775i | ||||
\(679\) | −3.28995 | −0.126257 | ||||||||
\(680\) | 7.68692 | + | 4.75258i | 0.294780 | + | 0.182253i | ||||
\(681\) | 7.35936 | 0.282011 | ||||||||
\(682\) | −0.233431 | + | 0.233431i | −0.00893852 | + | 0.00893852i | ||||
\(683\) | −31.8570 | + | 13.1956i | −1.21898 | + | 0.504916i | −0.897084 | − | 0.441860i | \(-0.854319\pi\) |
−0.321891 | + | 0.946777i | \(0.604319\pi\) | |||||||
\(684\) | 2.20264i | 0.0842202i | ||||||||
\(685\) | 10.1284 | − | 10.7500i | 0.386985 | − | 0.410736i | ||||
\(686\) | 1.62931 | − | 3.93350i | 0.0622072 | − | 0.150182i | ||||
\(687\) | 0.753531 | − | 1.81919i | 0.0287490 | − | 0.0694062i | ||||
\(688\) | 29.0568 | + | 29.0568i | 1.10778 | + | 1.10778i | ||||
\(689\) | −1.52569 | + | 1.52569i | −0.0581243 | + | 0.0581243i | ||||
\(690\) | −2.52211 | + | 0.0750902i | −0.0960149 | + | 0.00285863i | ||||
\(691\) | 16.1221 | − | 38.9223i | 0.613315 | − | 1.48067i | −0.246022 | − | 0.969264i | \(-0.579124\pi\) |
0.859337 | − | 0.511409i | \(-0.170876\pi\) | |||||||
\(692\) | 2.19154 | + | 5.29084i | 0.0833098 | + | 0.201128i | ||||
\(693\) | 1.14991 | 0.0436815 | ||||||||
\(694\) | 0.483462 | + | 1.16718i | 0.0183520 | + | 0.0443056i | ||||
\(695\) | 3.64938 | − | 9.60978i | 0.138429 | − | 0.364520i | ||||
\(696\) | −10.3663 | −0.392934 | ||||||||
\(697\) | 20.4808 | − | 13.8496i | 0.775767 | − | 0.524591i | ||||
\(698\) | 6.08922i | 0.230481i | ||||||||
\(699\) | −29.5846 | − | 29.5846i | −1.11899 | − | 1.11899i | ||||
\(700\) | −4.53525 | + | 13.1049i | −0.171416 | + | 0.495320i | ||||
\(701\) | 29.6266i | 1.11898i | 0.828836 | + | 0.559491i | \(0.189003\pi\) | ||||
−0.828836 | + | 0.559491i | \(0.810997\pi\) | |||||||
\(702\) | −0.0902007 | − | 0.217764i | −0.00340441 | − | 0.00821897i | ||||
\(703\) | 20.2146 | + | 8.37317i | 0.762409 | + | 0.315800i | ||||
\(704\) | −16.3029 | − | 6.75289i | −0.614439 | − | 0.254509i | ||||
\(705\) | −9.11531 | − | 3.46161i | −0.343303 | − | 0.130372i | ||||
\(706\) | 3.08593 | − | 3.08593i | 0.116140 | − | 0.116140i | ||||
\(707\) | −0.487914 | + | 1.17793i | −0.0183499 | + | 0.0443005i | ||||
\(708\) | 23.8168 | + | 9.86523i | 0.895089 | + | 0.370758i | ||||
\(709\) | 15.0352 | − | 6.22777i | 0.564657 | − | 0.233889i | −0.0820483 | − | 0.996628i | \(-0.526146\pi\) |
0.646706 | + | 0.762740i | \(0.276146\pi\) | |||||||
\(710\) | −2.79015 | − | 6.20682i | −0.104713 | − | 0.232938i | ||||
\(711\) | −1.47373 | − | 3.55789i | −0.0552691 | − | 0.133431i | ||||
\(712\) | 7.96469 | − | 7.96469i | 0.298489 | − | 0.298489i | ||||
\(713\) | − | 1.35793i | − | 0.0508547i | ||||||
\(714\) | 2.36512 | − | 0.484090i | 0.0885125 | − | 0.0181166i | ||||
\(715\) | 0.959530 | − | 0.431337i | 0.0358844 | − | 0.0161311i | ||||
\(716\) | −31.8979 | − | 31.8979i | −1.19208 | − | 1.19208i | ||||
\(717\) | −9.43647 | + | 3.90871i | −0.352411 | + | 0.145974i | ||||
\(718\) | −0.502294 | −0.0187454 | ||||||||
\(719\) | −29.0292 | + | 12.0243i | −1.08261 | + | 0.448430i | −0.851423 | − | 0.524480i | \(-0.824260\pi\) |
−0.231184 | + | 0.972910i | \(0.574260\pi\) | |||||||
\(720\) | 2.42165 | − | 0.0720992i | 0.0902495 | − | 0.00268698i | ||||
\(721\) | −0.485411 | − | 0.201064i | −0.0180776 | − | 0.00748800i | ||||
\(722\) | −0.789295 | − | 0.789295i | −0.0293745 | − | 0.0293745i | ||||
\(723\) | −31.1537 | − | 31.1537i | −1.15862 | − | 1.15862i | ||||
\(724\) | 20.4483 | + | 8.46994i | 0.759953 | + | 0.314783i | ||||
\(725\) | 14.0569 | + | 28.9354i | 0.522062 | + | 1.07463i | ||||
\(726\) | −1.41540 | + | 0.586276i | −0.0525303 | + | 0.0217588i | ||||
\(727\) | −21.6544 | −0.803118 | −0.401559 | − | 0.915833i | \(-0.631532\pi\) | ||||
−0.401559 | + | 0.915833i | \(0.631532\pi\) | |||||||
\(728\) | 0.226372 | − | 0.0937664i | 0.00838991 | − | 0.00347521i | ||||
\(729\) | −20.5940 | − | 20.5940i | −0.762740 | − | 0.762740i | ||||
\(730\) | −3.57462 | − | 7.95190i | −0.132303 | − | 0.294313i | ||||
\(731\) | −45.7004 | + | 9.35389i | −1.69029 | + | 0.345966i | ||||
\(732\) | 22.1327i | 0.818047i | ||||||||
\(733\) | −22.2422 | + | 22.2422i | −0.821534 | + | 0.821534i | −0.986328 | − | 0.164794i | \(-0.947304\pi\) |
0.164794 | + | 0.986328i | \(0.447304\pi\) | |||||||
\(734\) | 3.08678 | + | 7.45215i | 0.113935 | + | 0.275064i | ||||
\(735\) | −7.46235 | − | 16.6003i | −0.275253 | − | 0.612312i | ||||
\(736\) | −7.29917 | + | 3.02342i | −0.269051 | + | 0.111445i | ||||
\(737\) | 30.8337 | + | 12.7717i | 1.13577 | + | 0.470452i | ||||
\(738\) | −0.170394 | + | 0.411368i | −0.00627229 | + | 0.0151426i | ||||
\(739\) | −9.68961 | + | 9.68961i | −0.356438 | + | 0.356438i | −0.862498 | − | 0.506060i | \(-0.831101\pi\) |
0.506060 | + | 0.862498i | \(0.331101\pi\) | |||||||
\(740\) | 8.83552 | − | 23.2662i | 0.324800 | − | 0.855283i | ||||
\(741\) | 1.01055 | + | 0.418582i | 0.0371233 | + | 0.0153770i | ||||
\(742\) | 4.06552 | + | 1.68400i | 0.149250 | + | 0.0618214i | ||||
\(743\) | −6.20770 | − | 14.9867i | −0.227738 | − | 0.549809i | 0.768163 | − | 0.640254i | \(-0.221171\pi\) |
−0.995901 | + | 0.0904453i | \(0.971171\pi\) | |||||||
\(744\) | 0.793297i | 0.0290837i | ||||||||
\(745\) | 17.8492 | − | 18.9447i | 0.653945 | − | 0.694079i | ||||
\(746\) | −3.62775 | − | 3.62775i | −0.132821 | − | 0.132821i | ||||
\(747\) | 2.55818i | 0.0935988i | ||||||||
\(748\) | 17.8300 | − | 12.0570i | 0.651929 | − | 0.440849i | ||||
\(749\) | 9.51315 | 0.347603 | ||||||||
\(750\) | −2.12042 | − | 4.05322i | −0.0774267 | − | 0.148003i | ||||
\(751\) | −4.26568 | − | 10.2983i | −0.155657 | − | 0.375789i | 0.826743 | − | 0.562580i | \(-0.190191\pi\) |
−0.982400 | + | 0.186791i | \(0.940191\pi\) | |||||||
\(752\) | −9.63558 | −0.351373 | ||||||||
\(753\) | −6.67077 | − | 16.1047i | −0.243096 | − | 0.586887i | ||||
\(754\) | 0.107046 | − | 0.258432i | 0.00389838 | − | 0.00941153i | ||||
\(755\) | 0.00916835 | + | 0.307944i | 0.000333671 | + | 0.0112072i | ||||
\(756\) | 10.6322 | − | 10.6322i | 0.386689 | − | 0.386689i | ||||
\(757\) | −14.0667 | − | 14.0667i | −0.511262 | − | 0.511262i | 0.403651 | − | 0.914913i | \(-0.367741\pi\) |
−0.914913 | + | 0.403651i | \(0.867741\pi\) | |||||||
\(758\) | 1.58149 | − | 3.81804i | 0.0574421 | − | 0.138678i | ||||
\(759\) | −4.67292 | + | 11.2814i | −0.169616 | + | 0.409490i | ||||
\(760\) | 5.72673 | − | 6.07820i | 0.207730 | − | 0.220479i | ||||
\(761\) | 45.4255i | 1.64667i | 0.567553 | + | 0.823337i | \(0.307890\pi\) | ||||
−0.567553 | + | 0.823337i | \(0.692110\pi\) | |||||||
\(762\) | −6.17908 | + | 2.55946i | −0.223844 | + | 0.0927194i | ||||
\(763\) | 8.94498 | − | 8.94498i | 0.323830 | − | 0.323830i | ||||
\(764\) | −5.97306 | −0.216098 | ||||||||
\(765\) | −1.44629 | + | 2.33926i | −0.0522908 | + | 0.0845761i | ||||
\(766\) | 5.78284 | 0.208942 | ||||||||
\(767\) | −0.999485 | + | 0.999485i | −0.0360893 | + | 0.0360893i | ||||
\(768\) | −17.1145 | + | 7.08907i | −0.617567 | + | 0.255805i | ||||
\(769\) | 5.98158i | 0.215701i | 0.994167 | + | 0.107851i | \(0.0343968\pi\) | ||||
−0.994167 | + | 0.107851i | \(0.965603\pi\) | |||||||
\(770\) | −1.56163 | − | 1.47133i | −0.0562771 | − | 0.0530230i | ||||
\(771\) | 0.968824 | − | 2.33895i | 0.0348913 | − | 0.0842352i | ||||
\(772\) | 11.8558 | − | 28.6225i | 0.426701 | − | 1.03015i | ||||
\(773\) | −9.29889 | − | 9.29889i | −0.334458 | − | 0.334458i | 0.519819 | − | 0.854277i | \(-0.325999\pi\) |
−0.854277 | + | 0.519819i | \(0.825999\pi\) | |||||||
\(774\) | 0.594036 | − | 0.594036i | 0.0213522 | − | 0.0213522i | ||||
\(775\) | 2.21432 | − | 1.07573i | 0.0795407 | − | 0.0386413i | ||||
\(776\) | 0.862382 | − | 2.08197i | 0.0309577 | − | 0.0747385i | ||||
\(777\) | −5.16958 | − | 12.4805i | −0.185458 | − | 0.447735i | ||||
\(778\) | 9.12654 | 0.327202 | ||||||||
\(779\) | −8.74284 | − | 21.1071i | −0.313245 | − | 0.756240i | ||||
\(780\) | 0.441695 | − | 1.16310i | 0.0158152 | − | 0.0416456i | ||||
\(781\) | −32.9328 | −1.17843 | ||||||||
\(782\) | 0.536831 | − | 2.77922i | 0.0191970 | − | 0.0993847i | ||||
\(783\) | − | 34.8802i | − | 1.24652i | ||||||
\(784\) | −12.7180 | − | 12.7180i | −0.454215 | − | 0.454215i | ||||
\(785\) | 15.7295 | + | 14.8200i | 0.561412 | + | 0.528948i | ||||
\(786\) | − | 3.94369i | − | 0.140667i | ||||||
\(787\) | −9.83375 | − | 23.7408i | −0.350535 | − | 0.846267i | −0.996554 | − | 0.0829458i | \(-0.973567\pi\) |
0.646019 | − | 0.763322i | \(-0.276433\pi\) | |||||||
\(788\) | 19.1112 | + | 7.91611i | 0.680808 | + | 0.282000i | ||||
\(789\) | −0.647570 | − | 0.268232i | −0.0230541 | − | 0.00954932i | ||||
\(790\) | −2.55099 | + | 6.71742i | −0.0907601 | + | 0.238995i | ||||
\(791\) | 5.78130 | − | 5.78130i | 0.205560 | − | 0.205560i | ||||
\(792\) | −0.301422 | + | 0.727698i | −0.0107106 | + | 0.0258576i | ||||
\(793\) | −1.12117 | − | 0.464405i | −0.0398140 | − | 0.0164915i | ||||
\(794\) | −2.25650 | + | 0.934673i | −0.0800802 | + | 0.0331703i | ||||
\(795\) | 41.4109 | − | 18.6155i | 1.46869 | − | 0.660222i | ||||
\(796\) | 11.7474 | + | 28.3607i | 0.416375 | + | 1.00522i | ||||
\(797\) | −35.6691 | + | 35.6691i | −1.26347 | + | 1.26347i | −0.314064 | + | 0.949402i | \(0.601691\pi\) |
−0.949402 | + | 0.314064i | \(0.898309\pi\) | |||||||
\(798\) | − | 2.23080i | − | 0.0789693i | ||||||
\(799\) | 6.02647 | − | 9.12834i | 0.213201 | − | 0.322937i | ||||
\(800\) | −10.7125 | − | 9.50739i | −0.378743 | − | 0.336137i | ||||
\(801\) | 2.42379 | + | 2.42379i | 0.0856404 | + | 0.0856404i | ||||
\(802\) | 4.94200 | − | 2.04704i | 0.174508 | − | 0.0722836i | ||||
\(803\) | −42.1920 | −1.48892 | ||||||||
\(804\) | 36.4645 | − | 15.1041i | 1.28600 | − | 0.532680i | ||||
\(805\) | 8.82174 | − | 0.262648i | 0.310926 | − | 0.00925713i | ||||
\(806\) | −0.0197769 | − | 0.00819184i | −0.000696610 | − | 0.000288545i | ||||
\(807\) | 19.8801 | + | 19.8801i | 0.699814 | + | 0.699814i | ||||
\(808\) | −0.617532 | − | 0.617532i | −0.0217247 | − | 0.0217247i | ||||
\(809\) | −8.50125 | − | 3.52133i | −0.298888 | − | 0.123803i | 0.228200 | − | 0.973614i | \(-0.426716\pi\) |
−0.527088 | + | 0.849811i | \(0.676716\pi\) | |||||||
\(810\) | 0.132780 | + | 4.45977i | 0.00466541 | + | 0.156700i | ||||
\(811\) | 9.89831 | − | 4.10002i | 0.347577 | − | 0.143971i | −0.202064 | − | 0.979372i | \(-0.564765\pi\) |
0.549640 | + | 0.835401i | \(0.314765\pi\) | |||||||
\(812\) | 17.8442 | 0.626210 | ||||||||
\(813\) | −24.4040 | + | 10.1085i | −0.855885 | + | 0.354519i | ||||
\(814\) | 2.72276 | + | 2.72276i | 0.0954327 | + | 0.0954327i | ||||
\(815\) | −25.3200 | + | 11.3821i | −0.886922 | + | 0.398698i | ||||
\(816\) | 4.66829 | − | 24.1681i | 0.163423 | − | 0.846054i | ||||
\(817\) | 43.1048i | 1.50805i | ||||||||
\(818\) | −5.50452 | + | 5.50452i | −0.192461 | + | 0.192461i | ||||
\(819\) | 0.0285347 | + | 0.0688888i | 0.000997083 | + | 0.00240717i | ||||
\(820\) | −23.7015 | + | 10.6545i | −0.827692 | + | 0.372073i | ||||
\(821\) | 26.0334 | − | 10.7834i | 0.908572 | − | 0.376343i | 0.121062 | − | 0.992645i | \(-0.461370\pi\) |
0.787510 | + | 0.616302i | \(0.211370\pi\) | |||||||
\(822\) | 2.49677 | + | 1.03420i | 0.0870849 | + | 0.0360718i | ||||
\(823\) | −13.5250 | + | 32.6522i | −0.471452 | + | 1.13819i | 0.492070 | + | 0.870556i | \(0.336240\pi\) |
−0.963522 | + | 0.267630i | \(0.913760\pi\) | |||||||
\(824\) | 0.254478 | − | 0.254478i | 0.00886516 | − | 0.00886516i | ||||
\(825\) | −22.0980 | + | 1.31701i | −0.769354 | + | 0.0458523i | ||||
\(826\) | 2.66333 | + | 1.10319i | 0.0926692 | + | 0.0383848i | ||||
\(827\) | 36.2562 | + | 15.0178i | 1.26075 | + | 0.522221i | 0.910140 | − | 0.414300i | \(-0.135974\pi\) |
0.350612 | + | 0.936521i | \(0.385974\pi\) | |||||||
\(828\) | −0.610184 | − | 1.47312i | −0.0212054 | − | 0.0511943i | ||||
\(829\) | − | 17.4130i | − | 0.604779i | −0.953184 | − | 0.302389i | \(-0.902216\pi\) | ||
0.953184 | − | 0.302389i | \(-0.0977843\pi\) | |||||||
\(830\) | 3.27322 | − | 3.47411i | 0.113615 | − | 0.120588i | ||||
\(831\) | 19.4827 | + | 19.4827i | 0.675846 | + | 0.675846i | ||||
\(832\) | − | 1.14424i | − | 0.0396695i | ||||||
\(833\) | 20.0029 | − | 4.09416i | 0.693059 | − | 0.141854i | ||||
\(834\) | 1.88086 | 0.0651290 | ||||||||
\(835\) | −8.75353 | − | 3.32422i | −0.302928 | − | 0.115039i | ||||
\(836\) | −7.61125 | − | 18.3752i | −0.263241 | − | 0.635519i | ||||
\(837\) | −2.66925 | −0.0922629 | ||||||||
\(838\) | 1.93812 | + | 4.67903i | 0.0669511 | + | 0.161634i | ||||
\(839\) | −10.2960 | + | 24.8566i | −0.355456 | + | 0.858147i | 0.640471 | + | 0.767982i | \(0.278739\pi\) |
−0.995927 | + | 0.0901643i | \(0.971261\pi\) | |||||||
\(840\) | −5.15364 | + | 0.153438i | −0.177817 | + | 0.00529412i | ||||
\(841\) | 8.76397 | − | 8.76397i | 0.302206 | − | 0.302206i | ||||
\(842\) | −0.318338 | − | 0.318338i | −0.0109707 | − | 0.0109707i | ||||
\(843\) | −4.93039 | + | 11.9030i | −0.169812 | + | 0.409962i | ||||
\(844\) | 3.64865 | − | 8.80862i | 0.125592 | − | 0.303205i | ||||
\(845\) | −21.1078 | − | 19.8872i | −0.726129 | − | 0.684141i | ||||
\(846\) | 0.196989i | 0.00677263i | ||||||||
\(847\) | 4.95073 | − | 2.05066i | 0.170109 | − | 0.0704615i | ||||
\(848\) | 31.7262 | − | 31.7262i | 1.08948 | − | 1.08948i | ||||
\(849\) | 10.8163 | 0.371215 | ||||||||
\(850\) | 4.95724 | − | 1.32626i | 0.170032 | − | 0.0454904i | ||||
\(851\) | −15.8390 | −0.542954 | ||||||||
\(852\) | −27.5397 | + | 27.5397i | −0.943494 | + | 0.943494i | ||||
\(853\) | 15.1019 | − | 6.25540i | 0.517078 | − | 0.214181i | −0.108855 | − | 0.994058i | \(-0.534718\pi\) |
0.625933 | + | 0.779877i | \(0.284718\pi\) | |||||||
\(854\) | 2.47501i | 0.0846930i | ||||||||
\(855\) | 1.84970 | + | 1.74274i | 0.0632583 | + | 0.0596005i | ||||
\(856\) | −2.49365 | + | 6.02020i | −0.0852311 | + | 0.205766i | ||||
\(857\) | −1.47991 | + | 3.57282i | −0.0505527 | + | 0.122045i | −0.947138 | − | 0.320825i | \(-0.896040\pi\) |
0.896586 | + | 0.442870i | \(0.146040\pi\) | |||||||
\(858\) | 0.136113 | + | 0.136113i | 0.00464682 | + | 0.00464682i | ||||
\(859\) | 27.6000 | − | 27.6000i | 0.941701 | − | 0.941701i | −0.0566905 | − | 0.998392i | \(-0.518055\pi\) |
0.998392 | + | 0.0566905i | \(0.0180548\pi\) | |||||||
\(860\) | 49.0075 | − | 1.45909i | 1.67114 | − | 0.0497546i | ||||
\(861\) | −5.39782 | + | 13.0315i | −0.183957 | + | 0.444112i | ||||
\(862\) | −1.58734 | − | 3.83218i | −0.0540650 | − | 0.130524i | ||||
\(863\) | −22.1279 | −0.753243 | −0.376621 | − | 0.926367i | \(-0.622914\pi\) | ||||
−0.376621 | + | 0.926367i | \(0.622914\pi\) | |||||||
\(864\) | 5.94308 | + | 14.3479i | 0.202188 | + | 0.488124i | ||||
\(865\) | 6.17700 | + | 2.34576i | 0.210024 | + | 0.0797583i | ||||
\(866\) | 4.06193 | 0.138030 | ||||||||
\(867\) | 19.9761 | + | 19.5383i | 0.678425 | + | 0.663554i | ||||
\(868\) | − | 1.36556i | − | 0.0463500i | ||||||
\(869\) | 24.5886 | + | 24.5886i | 0.834112 | + | 0.834112i | ||||
\(870\) | −4.03641 | + | 4.28414i | −0.136847 | + | 0.145246i | ||||
\(871\) | 2.16411i | 0.0733280i | ||||||||
\(872\) | 3.31593 | + | 8.00536i | 0.112292 | + | 0.271096i | ||||
\(873\) | 0.633580 | + | 0.262437i | 0.0214434 | + | 0.00888216i | ||||
\(874\) | −2.41650 | − | 1.00095i | −0.0817393 | − | 0.0338575i | ||||
\(875\) | 7.41673 | + | 14.1772i | 0.250731 | + | 0.479277i | ||||
\(876\) | −35.2826 | + | 35.2826i | −1.19209 | + | 1.19209i | ||||
\(877\) | −7.55317 | + | 18.2350i | −0.255052 | + | 0.615751i | −0.998598 | − | 0.0529342i | \(-0.983143\pi\) |
0.743546 | + | 0.668685i | \(0.233143\pi\) | |||||||
\(878\) | 5.52560 | + | 2.28878i | 0.186480 | + | 0.0772425i | ||||
\(879\) | 4.78523 | − | 1.98211i | 0.161402 | − | 0.0668548i | ||||
\(880\) | −19.9530 | + | 8.96949i | −0.672617 | + | 0.302362i | ||||
\(881\) | 4.37489 | + | 10.5619i | 0.147394 | + | 0.355840i | 0.980283 | − | 0.197600i | \(-0.0633147\pi\) |
−0.832889 | + | 0.553440i | \(0.813315\pi\) | |||||||
\(882\) | −0.260007 | + | 0.260007i | −0.00875489 | + | 0.00875489i | ||||
\(883\) | 13.2658i | 0.446431i | 0.974769 | + | 0.223216i | \(0.0716554\pi\) | ||||
−0.974769 | + | 0.223216i | \(0.928345\pi\) | |||||||
\(884\) | 1.16476 | + | 0.768967i | 0.0391751 | + | 0.0258631i | ||||
\(885\) | 27.1284 | − | 12.1950i | 0.911911 | − | 0.409931i | ||||
\(886\) | −3.74477 | − | 3.74477i | −0.125808 | − | 0.125808i | ||||
\(887\) | −28.2772 | + | 11.7128i | −0.949455 | + | 0.393277i | −0.803026 | − | 0.595944i | \(-0.796778\pi\) |
−0.146429 | + | 0.989221i | \(0.546778\pi\) | |||||||
\(888\) | 9.25310 | 0.310514 | ||||||||
\(889\) | 21.6130 | − | 8.95239i | 0.724876 | − | 0.300254i | ||||
\(890\) | −0.190334 | − | 6.39288i | −0.00638001 | − | 0.214290i | ||||
\(891\) | 19.9486 | + | 8.26300i | 0.668305 | + | 0.276821i | ||||
\(892\) | 13.7642 | + | 13.7642i | 0.460858 | + | 0.460858i | ||||
\(893\) | −7.14704 | − | 7.14704i | −0.239167 | − | 0.239167i | ||||
\(894\) | 4.40006 | + | 1.82256i | 0.147160 | + | 0.0609557i | ||||
\(895\) | −52.0245 | + | 1.54891i | −1.73899 | + | 0.0517745i | ||||
\(896\) | −9.73087 | + | 4.03066i | −0.325086 | + | 0.134655i | ||||
\(897\) | −0.791804 | −0.0264376 | ||||||||
\(898\) | 6.71539 | − | 2.78161i | 0.224096 | − | 0.0928234i | ||||
\(899\) | −2.23993 | − | 2.23993i | −0.0747059 | − | 0.0747059i | ||||
\(900\) | 1.91878 | − | 2.16198i | 0.0639592 | − | 0.0720661i | ||||
\(901\) | 10.2132 | + | 49.8989i | 0.340252 | + | 1.66237i | ||||
\(902\) | − | 4.02056i | − | 0.133870i | ||||||
\(903\) | 18.8181 | − | 18.8181i | 0.626228 | − | 0.626228i | ||||
\(904\) | 2.14315 | + | 5.17401i | 0.0712799 | + | 0.172085i | ||||
\(905\) | 23.2915 | − | 10.4702i | 0.774235 | − | 0.348042i | ||||
\(906\) | −0.0520798 | + | 0.0215722i | −0.00173024 | + | 0.000716687i | ||||
\(907\) | −0.707707 | − | 0.293142i | −0.0234990 | − | 0.00973362i | 0.370903 | − | 0.928672i | \(-0.379048\pi\) |
−0.394402 | + | 0.918938i | \(0.629048\pi\) | |||||||
\(908\) | 3.32066 | − | 8.01678i | 0.110200 | − | 0.266046i | ||||
\(909\) | 0.187925 | − | 0.187925i | 0.00623309 | − | 0.00623309i | ||||
\(910\) | 0.0493929 | − | 0.130064i | 0.00163736 | − | 0.00431159i | ||||
\(911\) | 7.79323 | + | 3.22806i | 0.258201 | + | 0.106951i | 0.508029 | − | 0.861340i | \(-0.330374\pi\) |
−0.249828 | + | 0.968290i | \(0.580374\pi\) | |||||||
\(912\) | −21.0139 | − | 8.70425i | −0.695840 | − | 0.288226i | ||||
\(913\) | −8.83979 | − | 21.3412i | −0.292555 | − | 0.706289i | ||||
\(914\) | − | 0.258405i | − | 0.00854727i | ||||||
\(915\) | 18.5862 | + | 17.5115i | 0.614440 | + | 0.578911i | ||||
\(916\) | −1.64169 | − | 1.64169i | −0.0542430 | − | 0.0542430i | ||||
\(917\) | 13.7941i | 0.455522i | ||||||||
\(918\) | −5.46306 | − | 1.05524i | −0.180308 | − | 0.0348281i | ||||
\(919\) | −13.0143 | −0.429302 | −0.214651 | − | 0.976691i | \(-0.568861\pi\) | ||||
−0.214651 | + | 0.976691i | \(0.568861\pi\) | |||||||
\(920\) | −2.14620 | + | 5.65150i | −0.0707581 | + | 0.186324i | ||||
\(921\) | −9.42915 | − | 22.7640i | −0.310701 | − | 0.750099i | ||||
\(922\) | 0.0174735 | 0.000575458 | ||||||||
\(923\) | −0.817217 | − | 1.97294i | −0.0268990 | − | 0.0649400i | ||||
\(924\) | −4.69918 | + | 11.3448i | −0.154592 | + | 0.373217i | ||||
\(925\) | −12.5474 | − | 25.8280i | −0.412556 | − | 0.849221i | ||||
\(926\) | 7.05190 | − | 7.05190i | 0.231740 | − | 0.231740i | ||||
\(927\) | 0.0774419 | + | 0.0774419i | 0.00254353 | + | 0.00254353i | ||||
\(928\) | −7.05297 | + | 17.0274i | −0.231525 | + | 0.558951i | ||||
\(929\) | 9.89198 | − | 23.8814i | 0.324545 | − | 0.783522i | −0.674433 | − | 0.738336i | \(-0.735612\pi\) |
0.998979 | − | 0.0451859i | \(-0.0143880\pi\) | |||||||
\(930\) | 0.327850 | + | 0.308892i | 0.0107506 | + | 0.0101290i | ||||
\(931\) | − | 18.8668i | − | 0.618335i | ||||||
\(932\) | −45.5764 | + | 18.8784i | −1.49291 | + | 0.618382i | ||||
\(933\) | −11.6560 | + | 11.6560i | −0.381601 | + | 0.381601i | ||||
\(934\) | 5.65220 | 0.184946 | ||||||||
\(935\) | 3.98211 | − | 24.5125i | 0.130229 | − | 0.801646i | ||||
\(936\) | −0.0510746 | −0.00166942 | ||||||||
\(937\) | 0.615699 | − | 0.615699i | 0.0201140 | − | 0.0201140i | −0.696978 | − | 0.717092i | \(-0.745473\pi\) |
0.717092 | + | 0.696978i | \(0.245473\pi\) | |||||||
\(938\) | 4.07768 | − | 1.68903i | 0.133141 | − | 0.0551488i | ||||
\(939\) | 5.82007i | 0.189931i | ||||||||
\(940\) | −7.88381 | + | 8.36767i | −0.257142 | + | 0.272923i | ||||
\(941\) | 20.4139 | − | 49.2834i | 0.665473 | − | 1.60659i | −0.123627 | − | 0.992329i | \(-0.539453\pi\) |
0.789100 | − | 0.614265i | \(-0.210547\pi\) | |||||||
\(942\) | −1.51325 | + | 3.65332i | −0.0493045 | + | 0.119032i | ||||
\(943\) | 11.6943 | + | 11.6943i | 0.380820 | + | 0.380820i | ||||
\(944\) | 20.7839 | − | 20.7839i | 0.676458 | − | 0.676458i | ||||
\(945\) | −0.516283 | − | 17.3407i | −0.0167947 | − | 0.564094i | ||||
\(946\) | −2.90295 | + | 7.00834i | −0.0943830 | + | 0.227861i | ||||
\(947\) | 5.21997 | + | 12.6021i | 0.169626 | + | 0.409514i | 0.985717 | − | 0.168409i | \(-0.0538631\pi\) |
−0.816091 | + | 0.577924i | \(0.803863\pi\) | |||||||
\(948\) | 41.1240 | 1.33564 | ||||||||
\(949\) | −1.04698 | − | 2.52764i | −0.0339865 | − | 0.0820506i | ||||
\(950\) | −0.282105 | − | 4.73343i | −0.00915269 | − | 0.153573i | ||||
\(951\) | −20.0707 | −0.650838 | ||||||||
\(952\) | 1.09695 | − | 5.67902i | 0.0355525 | − | 0.184058i | ||||
\(953\) | − | 10.3660i | − | 0.335788i | −0.985805 | − | 0.167894i | \(-0.946303\pi\) | ||
0.985805 | − | 0.167894i | \(-0.0536967\pi\) | |||||||
\(954\) | −0.648610 | − | 0.648610i | −0.0209995 | − | 0.0209995i | ||||
\(955\) | −4.72591 | + | 5.01595i | −0.152927 | + | 0.162312i | ||||
\(956\) | 12.0431i | 0.389502i | ||||||||
\(957\) | 10.9009 | + | 26.3171i | 0.352376 | + | 0.850711i | ||||
\(958\) | −5.34925 | − | 2.21573i | −0.172827 | − | 0.0715871i | ||||
\(959\) | −8.73313 | − | 3.61738i | −0.282007 | − | 0.116811i | ||||
\(960\) | −8.54811 | + | 22.5094i | −0.275889 | + | 0.726487i | ||||
\(961\) | 21.7489 | − | 21.7489i | 0.701577 | − | 0.701577i | ||||
\(962\) | −0.0955505 | + | 0.230679i | −0.00308067 | + | 0.00743740i | ||||
\(963\) | −1.83205 | − | 0.758859i | −0.0590369 | − | 0.0244539i | ||||
\(964\) | −47.9937 | + | 19.8796i | −1.54577 | + | 0.640280i | ||||
\(965\) | −14.6557 | − | 32.6023i | −0.471784 | − | 1.04951i | ||||
\(966\) | 0.617983 | + | 1.49194i | 0.0198833 | + | 0.0480025i | ||||
\(967\) | −10.1327 | + | 10.1327i | −0.325847 | + | 0.325847i | −0.851005 | − | 0.525158i | \(-0.824006\pi\) |
0.525158 | + | 0.851005i | \(0.324006\pi\) | |||||||
\(968\) | 3.67050i | 0.117974i | ||||||||
\(969\) | 21.3890 | − | 14.4637i | 0.687113 | − | 0.464641i | ||||
\(970\) | −0.524635 | − | 1.16708i | −0.0168450 | − | 0.0374725i | ||||
\(971\) | 21.0309 | + | 21.0309i | 0.674913 | + | 0.674913i | 0.958845 | − | 0.283931i | \(-0.0916388\pi\) |
−0.283931 | + | 0.958845i | \(0.591639\pi\) | |||||||
\(972\) | −5.52946 | + | 2.29038i | −0.177358 | + | 0.0734639i | ||||
\(973\) | −6.57882 | −0.210907 | ||||||||
\(974\) | −3.88929 | + | 1.61100i | −0.124621 | + | 0.0516197i | ||||
\(975\) | −0.627255 | − | 1.29117i | −0.0200882 | − | 0.0413504i | ||||
\(976\) | 23.3144 | + | 9.65712i | 0.746274 | + | 0.309117i | ||||
\(977\) | −26.2437 | − | 26.2437i | −0.839611 | − | 0.839611i | 0.149196 | − | 0.988808i | \(-0.452331\pi\) |
−0.988808 | + | 0.149196i | \(0.952331\pi\) | |||||||
\(978\) | −3.59174 | − | 3.59174i | −0.114851 | − | 0.114851i | ||||
\(979\) | −28.5955 | − | 11.8446i | −0.913916 | − | 0.378556i | ||||
\(980\) | −21.4504 | + | 0.638638i | −0.685207 | + | 0.0204006i | ||||
\(981\) | −2.43617 | + | 1.00909i | −0.0777808 | + | 0.0322179i | ||||
\(982\) | −5.24217 | −0.167284 | ||||||||
\(983\) | 42.9257 | − | 17.7804i | 1.36912 | − | 0.567107i | 0.427568 | − | 0.903983i | \(-0.359371\pi\) |
0.941549 | + | 0.336877i | \(0.109371\pi\) | |||||||
\(984\) | −6.83179 | − | 6.83179i | −0.217790 | − | 0.217790i | ||||
\(985\) | 21.7685 | − | 9.78559i | 0.693602 | − | 0.311795i | ||||
\(986\) | −3.69887 | − | 5.46991i | −0.117796 | − | 0.174197i | ||||
\(987\) | 6.24032i | 0.198631i | ||||||||
\(988\) | 0.911949 | − | 0.911949i | 0.0290130 | − | 0.0290130i | ||||
\(989\) | −11.9411 | − | 28.8283i | −0.379703 | − | 0.916685i | ||||
\(990\) | 0.183372 | + | 0.407919i | 0.00582795 | + | 0.0129645i | ||||
\(991\) | −40.9290 | + | 16.9534i | −1.30015 | + | 0.538541i | −0.921996 | − | 0.387200i | \(-0.873442\pi\) |
−0.378158 | + | 0.925741i | \(0.623442\pi\) | |||||||
\(992\) | 1.30304 | + | 0.539738i | 0.0413717 | + | 0.0171367i | ||||
\(993\) | 11.6325 | − | 28.0833i | 0.369146 | − | 0.891198i | ||||
\(994\) | −3.07965 | + | 3.07965i | −0.0976806 | + | 0.0976806i | ||||
\(995\) | 33.1108 | + | 12.5741i | 1.04968 | + | 0.398625i | ||||
\(996\) | −25.2385 | − | 10.4541i | −0.799712 | − | 0.331252i | ||||
\(997\) | 22.7561 | + | 9.42589i | 0.720693 | + | 0.298521i | 0.712721 | − | 0.701447i | \(-0.247462\pi\) |
0.00797178 | + | 0.999968i | \(0.497462\pi\) | |||||||
\(998\) | −2.14575 | − | 5.18029i | −0.0679224 | − | 0.163979i | ||||
\(999\) | 31.1344i | 0.985050i |
(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 | 85.2.m.a.49.4 | yes | 24 | |
3.2 | odd | 2 | 765.2.bh.b.559.3 | 24 | |||
5.2 | odd | 4 | 425.2.m.e.151.4 | 24 | |||
5.3 | odd | 4 | 425.2.m.e.151.3 | 24 | |||
5.4 | even | 2 | inner | 85.2.m.a.49.3 | ✓ | 24 | |
15.14 | odd | 2 | 765.2.bh.b.559.4 | 24 | |||
17.5 | odd | 16 | 1445.2.b.i.579.13 | 24 | |||
17.8 | even | 8 | inner | 85.2.m.a.59.3 | yes | 24 | |
17.12 | odd | 16 | 1445.2.b.i.579.14 | 24 | |||
51.8 | odd | 8 | 765.2.bh.b.739.4 | 24 | |||
85.8 | odd | 8 | 425.2.m.e.76.3 | 24 | |||
85.12 | even | 16 | 7225.2.a.by.1.12 | 24 | |||
85.22 | even | 16 | 7225.2.a.by.1.11 | 24 | |||
85.29 | odd | 16 | 1445.2.b.i.579.11 | 24 | |||
85.39 | odd | 16 | 1445.2.b.i.579.12 | 24 | |||
85.42 | odd | 8 | 425.2.m.e.76.4 | 24 | |||
85.59 | even | 8 | inner | 85.2.m.a.59.4 | yes | 24 | |
85.63 | even | 16 | 7225.2.a.by.1.13 | 24 | |||
85.73 | even | 16 | 7225.2.a.by.1.14 | 24 | |||
255.59 | odd | 8 | 765.2.bh.b.739.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
85.2.m.a.49.3 | ✓ | 24 | 5.4 | even | 2 | inner | |
85.2.m.a.49.4 | yes | 24 | 1.1 | even | 1 | trivial | |
85.2.m.a.59.3 | yes | 24 | 17.8 | even | 8 | inner | |
85.2.m.a.59.4 | yes | 24 | 85.59 | even | 8 | inner | |
425.2.m.e.76.3 | 24 | 85.8 | odd | 8 | |||
425.2.m.e.76.4 | 24 | 85.42 | odd | 8 | |||
425.2.m.e.151.3 | 24 | 5.3 | odd | 4 | |||
425.2.m.e.151.4 | 24 | 5.2 | odd | 4 | |||
765.2.bh.b.559.3 | 24 | 3.2 | odd | 2 | |||
765.2.bh.b.559.4 | 24 | 15.14 | odd | 2 | |||
765.2.bh.b.739.3 | 24 | 255.59 | odd | 8 | |||
765.2.bh.b.739.4 | 24 | 51.8 | odd | 8 | |||
1445.2.b.i.579.11 | 24 | 85.29 | odd | 16 | |||
1445.2.b.i.579.12 | 24 | 85.39 | odd | 16 | |||
1445.2.b.i.579.13 | 24 | 17.5 | odd | 16 | |||
1445.2.b.i.579.14 | 24 | 17.12 | odd | 16 | |||
7225.2.a.by.1.11 | 24 | 85.22 | even | 16 | |||
7225.2.a.by.1.12 | 24 | 85.12 | even | 16 | |||
7225.2.a.by.1.13 | 24 | 85.63 | even | 16 | |||
7225.2.a.by.1.14 | 24 | 85.73 | even | 16 |