Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 165.1 | ||
Character | \(\chi\) | \(=\) | 784.165 |
Dual form | 784.2.x.o.765.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41419 | + | 0.00789795i | −0.999984 | + | 0.00558469i | ||||
\(3\) | −0.814813 | − | 3.04092i | −0.470433 | − | 1.75568i | −0.638218 | − | 0.769855i | \(-0.720328\pi\) |
0.167786 | − | 0.985823i | \(-0.446338\pi\) | |||||||
\(4\) | 1.99988 | − | 0.0223384i | 0.999938 | − | 0.0111692i | ||||
\(5\) | −0.501787 | + | 1.87270i | −0.224406 | + | 0.837495i | 0.758235 | + | 0.651981i | \(0.226062\pi\) |
−0.982642 | + | 0.185514i | \(0.940605\pi\) | |||||||
\(6\) | 1.17632 | + | 4.29401i | 0.480230 | + | 1.75302i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82803 | + | 0.0473857i | −0.999860 | + | 0.0167534i | ||||
\(9\) | −5.98523 | + | 3.45557i | −1.99508 | + | 1.15186i | ||||
\(10\) | 0.694833 | − | 2.65231i | 0.219726 | − | 0.838735i | ||||
\(11\) | −1.11913 | + | 0.299871i | −0.337431 | + | 0.0904145i | −0.423556 | − | 0.905870i | \(-0.639218\pi\) |
0.0861247 | + | 0.996284i | \(0.472552\pi\) | |||||||
\(12\) | −1.69745 | − | 6.06327i | −0.490013 | − | 1.75031i | ||||
\(13\) | −0.00680742 | + | 0.00680742i | −0.00188804 | + | 0.00188804i | −0.708050 | − | 0.706162i | \(-0.750425\pi\) |
0.706162 | + | 0.708050i | \(0.250425\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.10359 | 1.57594 | ||||||||
\(16\) | 3.99900 | − | 0.0893481i | 0.999750 | − | 0.0223370i | ||||
\(17\) | −1.52290 | + | 2.63774i | −0.369357 | + | 0.639745i | −0.989465 | − | 0.144771i | \(-0.953755\pi\) |
0.620108 | + | 0.784516i | \(0.287089\pi\) | |||||||
\(18\) | 8.43697 | − | 4.93411i | 1.98861 | − | 1.16298i | ||||
\(19\) | 4.64620 | + | 1.24495i | 1.06591 | + | 0.285610i | 0.748812 | − | 0.662782i | \(-0.230625\pi\) |
0.317099 | + | 0.948392i | \(0.397291\pi\) | |||||||
\(20\) | −0.961679 | + | 3.75637i | −0.215038 | + | 0.839949i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.58030 | − | 0.432914i | 0.336921 | − | 0.0922975i | ||||
\(23\) | 4.27392 | − | 2.46755i | 0.891174 | − | 0.514520i | 0.0168479 | − | 0.999858i | \(-0.494637\pi\) |
0.874326 | + | 0.485338i | \(0.161304\pi\) | |||||||
\(24\) | 2.44841 | + | 8.56122i | 0.499780 | + | 1.74755i | ||||
\(25\) | 1.07493 | + | 0.620609i | 0.214985 | + | 0.124122i | ||||
\(26\) | 0.00957323 | − | 0.00968076i | 0.00187746 | − | 0.00189855i | ||||
\(27\) | 8.70665 | + | 8.70665i | 1.67559 | + | 1.67559i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.45434 | + | 1.45434i | −0.270064 | + | 0.270064i | −0.829126 | − | 0.559062i | \(-0.811161\pi\) |
0.559062 | + | 0.829126i | \(0.311161\pi\) | |||||||
\(30\) | −8.63165 | + | 0.0482059i | −1.57592 | + | 0.00880114i | ||||
\(31\) | −2.60906 | + | 4.51902i | −0.468600 | + | 0.811639i | −0.999356 | − | 0.0358855i | \(-0.988575\pi\) |
0.530756 | + | 0.847525i | \(0.321908\pi\) | |||||||
\(32\) | −5.65465 | + | 0.157939i | −0.999610 | + | 0.0279200i | ||||
\(33\) | 1.82377 | + | 3.15886i | 0.317478 | + | 0.549887i | ||||
\(34\) | 2.13284 | − | 3.74229i | 0.365778 | − | 0.641798i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11.8925 | + | 7.04442i | −1.98209 | + | 1.17407i | ||||
\(37\) | 2.28095 | − | 8.51263i | 0.374986 | − | 1.39947i | −0.478379 | − | 0.878154i | \(-0.658775\pi\) |
0.853365 | − | 0.521314i | \(-0.174558\pi\) | |||||||
\(38\) | −6.58045 | − | 1.72390i | −1.06749 | − | 0.279653i | ||||
\(39\) | 0.0262476 | + | 0.0151541i | 0.00420298 | + | 0.00242659i | ||||
\(40\) | 1.33033 | − | 5.31982i | 0.210344 | − | 0.841137i | ||||
\(41\) | 6.02687i | 0.941238i | 0.882336 | + | 0.470619i | \(0.155969\pi\) | ||||
−0.882336 | + | 0.470619i | \(0.844031\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.17315 | + | 7.17315i | 1.09389 | + | 1.09389i | 0.995109 | + | 0.0987862i | \(0.0314960\pi\) |
0.0987862 | + | 0.995109i | \(0.468504\pi\) | |||||||
\(44\) | −2.23143 | + | 0.624704i | −0.336400 | + | 0.0941777i | ||||
\(45\) | −3.46793 | − | 12.9425i | −0.516968 | − | 1.92935i | ||||
\(46\) | −6.02466 | + | 3.52334i | −0.888287 | + | 0.519489i | ||||
\(47\) | −0.796989 | − | 1.38043i | −0.116253 | − | 0.201356i | 0.802027 | − | 0.597288i | \(-0.203755\pi\) |
−0.918280 | + | 0.395932i | \(0.870422\pi\) | |||||||
\(48\) | −3.53014 | − | 12.0879i | −0.509532 | − | 1.74473i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.52505 | − | 0.869170i | −0.215675 | − | 0.122919i | ||||
\(51\) | 9.26203 | + | 2.48175i | 1.29694 | + | 0.347515i | ||||
\(52\) | −0.0134619 | + | 0.0137661i | −0.00186683 | + | 0.00190901i | ||||
\(53\) | −0.787777 | + | 0.211084i | −0.108209 | + | 0.0289946i | −0.312517 | − | 0.949912i | \(-0.601172\pi\) |
0.204308 | + | 0.978907i | \(0.434506\pi\) | |||||||
\(54\) | −12.3816 | − | 12.2441i | −1.68493 | − | 1.66621i | ||||
\(55\) | − | 2.24627i | − | 0.302887i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 15.1431i | − | 2.00576i | ||||||
\(58\) | 2.04523 | − | 2.06820i | 0.268552 | − | 0.271568i | ||||
\(59\) | 7.25156 | − | 1.94305i | 0.944073 | − | 0.252964i | 0.246228 | − | 0.969212i | \(-0.420809\pi\) |
0.697845 | + | 0.716248i | \(0.254142\pi\) | |||||||
\(60\) | 12.2064 | − | 0.136345i | 1.57584 | − | 0.0176020i | ||||
\(61\) | 9.21796 | + | 2.46994i | 1.18024 | + | 0.316244i | 0.795021 | − | 0.606582i | \(-0.207460\pi\) |
0.385217 | + | 0.922826i | \(0.374126\pi\) | |||||||
\(62\) | 3.65401 | − | 6.41136i | 0.464060 | − | 0.814244i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.99551 | − | 0.268016i | 0.999439 | − | 0.0335021i | ||||
\(65\) | −0.00933235 | − | 0.0161641i | −0.00115754 | − | 0.00200491i | ||||
\(66\) | −2.60411 | − | 4.45283i | −0.320544 | − | 0.548106i | ||||
\(67\) | −1.70317 | − | 6.35630i | −0.208075 | − | 0.776546i | −0.988490 | − | 0.151284i | \(-0.951659\pi\) |
0.780416 | − | 0.625261i | \(-0.215008\pi\) | |||||||
\(68\) | −2.98668 | + | 5.30916i | −0.362188 | + | 0.643830i | ||||
\(69\) | −10.9861 | − | 10.9861i | −1.32257 | − | 1.32257i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.77044i | 0.803504i | 0.915749 | + | 0.401752i | \(0.131599\pi\) | ||||
−0.915749 | + | 0.401752i | \(0.868401\pi\) | |||||||
\(72\) | 16.7627 | − | 10.0561i | 1.97550 | − | 1.18512i | ||||
\(73\) | 3.43645 | + | 1.98403i | 0.402206 | + | 0.232214i | 0.687435 | − | 0.726246i | \(-0.258737\pi\) |
−0.285230 | + | 0.958459i | \(0.592070\pi\) | |||||||
\(74\) | −3.15847 | + | 12.0565i | −0.367165 | + | 1.40154i | ||||
\(75\) | 1.01136 | − | 3.77445i | 0.116782 | − | 0.435836i | ||||
\(76\) | 9.31963 | + | 2.38595i | 1.06903 | + | 0.273687i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.0372388 | − | 0.0212235i | −0.00421647 | − | 0.00240308i | ||||
\(79\) | −2.81227 | − | 4.87099i | −0.316405 | − | 0.548029i | 0.663330 | − | 0.748327i | \(-0.269142\pi\) |
−0.979735 | + | 0.200298i | \(0.935809\pi\) | |||||||
\(80\) | −1.83933 | + | 7.53375i | −0.205643 | + | 0.842299i | ||||
\(81\) | 9.01525 | − | 15.6149i | 1.00169 | − | 1.73499i | ||||
\(82\) | −0.0475999 | − | 8.52314i | −0.00525653 | − | 0.941224i | ||||
\(83\) | 11.3733 | − | 11.3733i | 1.24838 | − | 1.24838i | 0.291940 | − | 0.956437i | \(-0.405699\pi\) |
0.956437 | − | 0.291940i | \(-0.0943007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.17551 | − | 4.17551i | −0.452897 | − | 0.452897i | ||||
\(86\) | −10.2009 | − | 10.0876i | −1.09999 | − | 1.08777i | ||||
\(87\) | 5.60755 | + | 3.23752i | 0.601193 | + | 0.347099i | ||||
\(88\) | 3.15073 | − | 0.901075i | 0.335869 | − | 0.0960549i | ||||
\(89\) | −3.59386 | + | 2.07492i | −0.380948 | + | 0.219941i | −0.678231 | − | 0.734849i | \(-0.737253\pi\) |
0.297282 | + | 0.954790i | \(0.403920\pi\) | |||||||
\(90\) | 5.00653 | + | 18.2758i | 0.527735 | + | 1.92643i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.49219 | − | 5.03026i | 0.885372 | − | 0.524441i | ||||
\(93\) | 15.8679 | + | 4.25179i | 1.64542 | + | 0.440890i | ||||
\(94\) | 1.13800 | + | 1.94589i | 0.117376 | + | 0.200703i | ||||
\(95\) | −4.66281 | + | 8.07622i | −0.478394 | + | 0.828603i | ||||
\(96\) | 5.08777 | + | 17.0667i | 0.519268 | + | 1.74186i | ||||
\(97\) | −0.390669 | −0.0396664 | −0.0198332 | − | 0.999803i | \(-0.506314\pi\) | ||||
−0.0198332 | + | 0.999803i | \(0.506314\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.66204 | − | 5.66204i | 0.569057 | − | 0.569057i | ||||
\(100\) | 2.16358 | + | 1.21713i | 0.216358 | + | 0.121713i | ||||
\(101\) | −3.75110 | + | 1.00511i | −0.373249 | + | 0.100012i | −0.440567 | − | 0.897720i | \(-0.645222\pi\) |
0.0673179 | + | 0.997732i | \(0.478556\pi\) | |||||||
\(102\) | −13.1179 | − | 3.43653i | −1.29886 | − | 0.340267i | ||||
\(103\) | 1.83121 | − | 1.05725i | 0.180434 | − | 0.104174i | −0.407062 | − | 0.913400i | \(-0.633447\pi\) |
0.587497 | + | 0.809227i | \(0.300113\pi\) | |||||||
\(104\) | 0.0189290 | − | 0.0195742i | 0.00185614 | − | 0.00191940i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.11240 | − | 0.304735i | 0.108046 | − | 0.0295985i | ||||
\(107\) | −3.89744 | + | 14.5454i | −0.376779 | + | 1.40616i | 0.473948 | + | 0.880553i | \(0.342828\pi\) |
−0.850728 | + | 0.525607i | \(0.823838\pi\) | |||||||
\(108\) | 17.6067 | + | 17.2177i | 1.69421 | + | 1.65678i | ||||
\(109\) | −0.887009 | − | 3.31036i | −0.0849600 | − | 0.317075i | 0.910347 | − | 0.413847i | \(-0.135815\pi\) |
−0.995307 | + | 0.0967715i | \(0.969148\pi\) | |||||||
\(110\) | 0.0177409 | + | 3.17665i | 0.00169153 | + | 0.302882i | ||||
\(111\) | −27.7448 | −2.63342 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.54270 | −0.239197 | −0.119599 | − | 0.992822i | \(-0.538161\pi\) | ||||
−0.119599 | + | 0.992822i | \(0.538161\pi\) | |||||||
\(114\) | 0.119600 | + | 21.4153i | 0.0112015 | + | 2.00573i | ||||
\(115\) | 2.47637 | + | 9.24194i | 0.230923 | + | 0.861816i | ||||
\(116\) | −2.87601 | + | 2.94098i | −0.267031 | + | 0.273064i | ||||
\(117\) | 0.0172204 | − | 0.0642675i | 0.00159203 | − | 0.00594153i | ||||
\(118\) | −10.2398 | + | 2.80512i | −0.942646 | + | 0.258232i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −17.2611 | + | 0.289223i | −1.57572 | + | 0.0264023i | ||||
\(121\) | −8.36374 | + | 4.82881i | −0.760340 | + | 0.438983i | ||||
\(122\) | −13.0555 | − | 3.42017i | −1.18199 | − | 0.309648i | ||||
\(123\) | 18.3272 | − | 4.91077i | 1.65251 | − | 0.442789i | ||||
\(124\) | −5.11684 | + | 9.09575i | −0.459506 | + | 0.816823i | ||||
\(125\) | −8.55614 | + | 8.55614i | −0.765285 | + | 0.765285i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.663876 | −0.0589095 | −0.0294547 | − | 0.999566i | \(-0.509377\pi\) | ||||
−0.0294547 | + | 0.999566i | \(0.509377\pi\) | |||||||
\(128\) | −11.3051 | + | 0.442175i | −0.999236 | + | 0.0390831i | ||||
\(129\) | 15.9682 | − | 27.6578i | 1.40592 | − | 2.43513i | ||||
\(130\) | 0.0133254 | + | 0.0227854i | 0.00116871 | + | 0.00199841i | ||||
\(131\) | 4.20367 | + | 1.12637i | 0.367276 | + | 0.0984113i | 0.437737 | − | 0.899103i | \(-0.355780\pi\) |
−0.0704606 | + | 0.997515i | \(0.522447\pi\) | |||||||
\(132\) | 3.71788 | + | 6.27659i | 0.323600 | + | 0.546307i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.45880 | + | 8.97557i | 0.212408 | + | 0.775372i | ||||
\(135\) | −20.6738 | + | 11.9360i | −1.77932 | + | 1.02729i | ||||
\(136\) | 4.18181 | − | 7.53176i | 0.358587 | − | 0.645843i | ||||
\(137\) | 12.1604 | + | 7.02081i | 1.03893 | + | 0.599828i | 0.919531 | − | 0.393018i | \(-0.128569\pi\) |
0.119402 | + | 0.992846i | \(0.461902\pi\) | |||||||
\(138\) | 15.6232 | + | 15.4497i | 1.32993 | + | 1.31516i | ||||
\(139\) | 9.59908 | + | 9.59908i | 0.814183 | + | 0.814183i | 0.985258 | − | 0.171075i | \(-0.0547239\pi\) |
−0.171075 | + | 0.985258i | \(0.554724\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.54837 | + | 3.54837i | −0.298827 | + | 0.298827i | ||||
\(142\) | −0.0534726 | − | 9.57471i | −0.00448732 | − | 0.803491i | ||||
\(143\) | 0.00557706 | − | 0.00965975i | 0.000466377 | − | 0.000807789i | ||||
\(144\) | −23.6262 | + | 14.3536i | −1.96885 | + | 1.19613i | ||||
\(145\) | −1.99377 | − | 3.45330i | −0.165573 | − | 0.286781i | ||||
\(146\) | −4.87546 | − | 2.77866i | −0.403496 | − | 0.229964i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.37146 | − | 17.0751i | 0.359332 | − | 1.40357i | ||||
\(149\) | 1.23001 | − | 4.59048i | 0.100767 | − | 0.376067i | −0.897064 | − | 0.441901i | \(-0.854304\pi\) |
0.997831 | + | 0.0658345i | \(0.0209709\pi\) | |||||||
\(150\) | −1.40045 | + | 5.34578i | −0.114346 | + | 0.436481i | ||||
\(151\) | −9.37492 | − | 5.41261i | −0.762920 | − | 0.440472i | 0.0674232 | − | 0.997724i | \(-0.478522\pi\) |
−0.830343 | + | 0.557252i | \(0.811856\pi\) | |||||||
\(152\) | −13.1986 | − | 3.30058i | −1.07055 | − | 0.267712i | ||||
\(153\) | − | 21.0499i | − | 1.70179i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.15355 | − | 7.15355i | −0.574587 | − | 0.574587i | ||||
\(156\) | 0.0528305 | + | 0.0297199i | 0.00422982 | + | 0.00237950i | ||||
\(157\) | −0.113562 | − | 0.423817i | −0.00906320 | − | 0.0338243i | 0.961246 | − | 0.275692i | \(-0.0889068\pi\) |
−0.970309 | + | 0.241867i | \(0.922240\pi\) | |||||||
\(158\) | 4.01556 | + | 6.86630i | 0.319460 | + | 0.546254i | ||||
\(159\) | 1.28378 | + | 2.22358i | 0.101811 | + | 0.176341i | ||||
\(160\) | 2.54166 | − | 10.6687i | 0.200936 | − | 0.843434i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −12.6260 | + | 22.1536i | −0.991989 | + | 1.74055i | ||||
\(163\) | 13.0407 | + | 3.49423i | 1.02142 | + | 0.273689i | 0.730395 | − | 0.683025i | \(-0.239336\pi\) |
0.291028 | + | 0.956715i | \(0.406003\pi\) | |||||||
\(164\) | 0.134631 | + | 12.0530i | 0.0105129 | + | 0.941179i | ||||
\(165\) | −6.83073 | + | 1.83029i | −0.531772 | + | 0.142488i | ||||
\(166\) | −15.9941 | + | 16.1738i | −1.24139 | + | 1.25533i | ||||
\(167\) | 3.70883i | 0.286998i | 0.989650 | + | 0.143499i | \(0.0458353\pi\) | ||||
−0.989650 | + | 0.143499i | \(0.954165\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9999i | 0.999993i | ||||||||
\(170\) | 5.93795 | + | 5.87199i | 0.455420 | + | 0.450361i | ||||
\(171\) | −32.1106 | + | 8.60400i | −2.45556 | + | 0.657964i | ||||
\(172\) | 14.5056 | + | 14.1852i | 1.10604 | + | 1.08161i | ||||
\(173\) | 5.15933 | + | 1.38244i | 0.392257 | + | 0.105105i | 0.449556 | − | 0.893252i | \(-0.351582\pi\) |
−0.0572992 | + | 0.998357i | \(0.518249\pi\) | |||||||
\(174\) | −7.95572 | − | 4.53419i | −0.603122 | − | 0.343736i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.44862 | + | 1.29918i | −0.335328 | + | 0.0979291i | ||||
\(177\) | −11.8173 | − | 20.4682i | −0.888246 | − | 1.53849i | ||||
\(178\) | 5.06602 | − | 2.96271i | 0.379714 | − | 0.222065i | ||||
\(179\) | 0.926668 | + | 3.45837i | 0.0692624 | + | 0.258491i | 0.991871 | − | 0.127246i | \(-0.0406139\pi\) |
−0.922609 | + | 0.385737i | \(0.873947\pi\) | |||||||
\(180\) | −7.22453 | − | 25.8059i | −0.538485 | − | 1.92346i | ||||
\(181\) | 10.2442 | + | 10.2442i | 0.761447 | + | 0.761447i | 0.976584 | − | 0.215137i | \(-0.0690199\pi\) |
−0.215137 | + | 0.976584i | \(0.569020\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 30.0437i | − | 2.22089i | ||||||
\(184\) | −11.9699 | + | 7.18083i | −0.882429 | + | 0.529378i | ||||
\(185\) | 14.7970 | + | 8.54306i | 1.08790 | + | 0.628098i | ||||
\(186\) | −22.4738 | − | 5.88752i | −1.64786 | − | 0.431694i | ||||
\(187\) | 0.913345 | − | 3.40865i | 0.0667904 | − | 0.249265i | ||||
\(188\) | −1.62472 | − | 2.74288i | −0.118495 | − | 0.200045i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.53032 | − | 11.4581i | 0.473759 | − | 0.831262i | ||||
\(191\) | 8.01270 | + | 13.8784i | 0.579779 | + | 1.00421i | 0.995504 | + | 0.0947160i | \(0.0301943\pi\) |
−0.415726 | + | 0.909490i | \(0.636472\pi\) | |||||||
\(192\) | −7.32987 | − | 24.0954i | −0.528988 | − | 1.73893i | ||||
\(193\) | −3.59186 | + | 6.22128i | −0.258548 | + | 0.447818i | −0.965853 | − | 0.259090i | \(-0.916577\pi\) |
0.707305 | + | 0.706908i | \(0.249911\pi\) | |||||||
\(194\) | 0.552481 | − | 0.00308548i | 0.0396658 | − | 0.000221525i | ||||
\(195\) | −0.0415497 | + | 0.0415497i | −0.00297544 | + | 0.00297544i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.9009 | + | 13.9009i | 0.990395 | + | 0.990395i | 0.999954 | − | 0.00955923i | \(-0.00304285\pi\) |
−0.00955923 | + | 0.999954i | \(0.503043\pi\) | |||||||
\(198\) | −7.96249 | + | 8.05193i | −0.565870 | + | 0.572226i | ||||
\(199\) | −23.8518 | − | 13.7709i | −1.69081 | − | 0.976191i | −0.953863 | − | 0.300242i | \(-0.902933\pi\) |
−0.736949 | − | 0.675949i | \(-0.763734\pi\) | |||||||
\(200\) | −3.06933 | − | 1.70416i | −0.217035 | − | 0.120503i | ||||
\(201\) | −17.9413 | + | 10.3584i | −1.26548 | + | 0.730625i | ||||
\(202\) | 5.29684 | − | 1.45104i | 0.372684 | − | 0.102095i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 18.5784 | + | 4.75630i | 1.30074 | + | 0.333008i | ||||
\(205\) | −11.2865 | − | 3.02421i | −0.788283 | − | 0.211220i | ||||
\(206\) | −2.58133 | + | 1.50962i | −0.179850 | + | 0.105180i | ||||
\(207\) | −17.0536 | + | 29.5377i | −1.18531 | + | 2.05301i | ||||
\(208\) | −0.0266146 | + | 0.0278311i | −0.00184539 | + | 0.00192974i | ||||
\(209\) | −5.57304 | −0.385495 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.278791 | + | 0.278791i | −0.0191928 | + | 0.0191928i | −0.716638 | − | 0.697445i | \(-0.754320\pi\) |
0.697445 | + | 0.716638i | \(0.254320\pi\) | |||||||
\(212\) | −1.57074 | + | 0.439740i | −0.107879 | + | 0.0302014i | ||||
\(213\) | 20.5884 | − | 5.51665i | 1.41069 | − | 0.377995i | ||||
\(214\) | 5.39684 | − | 20.6008i | 0.368920 | − | 1.40824i | ||||
\(215\) | −17.0325 | + | 9.83373i | −1.16161 | + | 0.670655i | ||||
\(216\) | −25.0352 | − | 24.2101i | −1.70343 | − | 1.64729i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.28055 | + | 4.67448i | 0.0867295 | + | 0.316596i | ||||
\(219\) | 3.23323 | − | 12.0666i | 0.218482 | − | 0.815385i | ||||
\(220\) | −0.0501781 | − | 4.49226i | −0.00338301 | − | 0.302868i | ||||
\(221\) | −0.00758917 | − | 0.0283232i | −0.000510503 | − | 0.00190522i | ||||
\(222\) | 39.2365 | − | 0.219127i | 2.63338 | − | 0.0147068i | ||||
\(223\) | 17.0225 | 1.13991 | 0.569956 | − | 0.821676i | \(-0.306960\pi\) | ||||
0.569956 | + | 0.821676i | \(0.306960\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.57824 | −0.571883 | ||||||||
\(226\) | 3.59587 | − | 0.0200821i | 0.239193 | − | 0.00133584i | ||||
\(227\) | −0.584192 | − | 2.18023i | −0.0387742 | − | 0.144707i | 0.943825 | − | 0.330445i | \(-0.107199\pi\) |
−0.982599 | + | 0.185738i | \(0.940532\pi\) | |||||||
\(228\) | −0.338274 | − | 30.2844i | −0.0224027 | − | 2.00563i | ||||
\(229\) | 3.59412 | − | 13.4134i | 0.237506 | − | 0.886384i | −0.739497 | − | 0.673160i | \(-0.764937\pi\) |
0.977003 | − | 0.213225i | \(-0.0683966\pi\) | |||||||
\(230\) | −3.57506 | − | 13.0503i | −0.235732 | − | 0.860513i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.04400 | − | 4.18183i | 0.265502 | − | 0.274551i | ||||
\(233\) | 1.84701 | − | 1.06637i | 0.121002 | − | 0.0698605i | −0.438277 | − | 0.898840i | \(-0.644411\pi\) |
0.559279 | + | 0.828979i | \(0.311078\pi\) | |||||||
\(234\) | −0.0238454 | + | 0.0910225i | −0.00155882 | + | 0.00595033i | ||||
\(235\) | 2.98504 | − | 0.799838i | 0.194722 | − | 0.0521757i | ||||
\(236\) | 14.4588 | − | 4.04785i | 0.941189 | − | 0.263492i | ||||
\(237\) | −12.5208 | + | 12.5208i | −0.813316 | + | 0.813316i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.5943 | −1.13808 | −0.569041 | − | 0.822309i | \(-0.692685\pi\) | ||||
−0.569041 | + | 0.822309i | \(0.692685\pi\) | |||||||
\(240\) | 24.4083 | − | 0.545344i | 1.57555 | − | 0.0352018i | ||||
\(241\) | −4.20427 | + | 7.28200i | −0.270821 | + | 0.469075i | −0.969072 | − | 0.246777i | \(-0.920628\pi\) |
0.698252 | + | 0.715852i | \(0.253962\pi\) | |||||||
\(242\) | 11.7898 | − | 6.89492i | 0.757877 | − | 0.443222i | ||||
\(243\) | −19.1489 | − | 5.13093i | −1.22840 | − | 0.329149i | ||||
\(244\) | 18.4899 | + | 4.73366i | 1.18370 | + | 0.303042i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −25.8794 | + | 7.08952i | −1.65001 | + | 0.452011i | ||||
\(247\) | −0.0401035 | + | 0.0231537i | −0.00255172 | + | 0.00147324i | ||||
\(248\) | 7.16435 | − | 12.9035i | 0.454937 | − | 0.819376i | ||||
\(249\) | −43.8523 | − | 25.3181i | −2.77903 | − | 1.60447i | ||||
\(250\) | 12.0324 | − | 12.1676i | 0.760999 | − | 0.769546i | ||||
\(251\) | −5.35828 | − | 5.35828i | −0.338212 | − | 0.338212i | 0.517482 | − | 0.855694i | \(-0.326869\pi\) |
−0.855694 | + | 0.517482i | \(0.826869\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.04314 | + | 4.04314i | −0.254190 | + | 0.254190i | ||||
\(254\) | 0.938848 | − | 0.00524326i | 0.0589086 | − | 0.000328991i | ||||
\(255\) | −9.29515 | + | 16.0997i | −0.582085 | + | 1.00820i | ||||
\(256\) | 15.9840 | − | 0.714607i | 0.999002 | − | 0.0446629i | ||||
\(257\) | −0.615501 | − | 1.06608i | −0.0383939 | − | 0.0665002i | 0.846190 | − | 0.532881i | \(-0.178891\pi\) |
−0.884584 | + | 0.466381i | \(0.845557\pi\) | |||||||
\(258\) | −22.3637 | + | 39.2395i | −1.39230 | + | 2.44295i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.0190246 | − | 0.0321177i | −0.00117986 | − | 0.00199186i | ||||
\(261\) | 3.67898 | − | 13.7301i | 0.227723 | − | 0.849873i | ||||
\(262\) | −5.95368 | − | 1.55970i | −0.367820 | − | 0.0963586i | ||||
\(263\) | −17.4432 | − | 10.0709i | −1.07560 | − | 0.620996i | −0.145891 | − | 0.989301i | \(-0.546605\pi\) |
−0.929705 | + | 0.368305i | \(0.879938\pi\) | |||||||
\(264\) | −5.30736 | − | 8.84693i | −0.326645 | − | 0.544491i | ||||
\(265\) | − | 1.58119i | − | 0.0971315i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.23799 | + | 9.23799i | 0.565356 | + | 0.565356i | ||||
\(268\) | −3.54811 | − | 12.6738i | −0.216735 | − | 0.774173i | ||||
\(269\) | 3.23015 | + | 12.0551i | 0.196946 | + | 0.735011i | 0.991755 | + | 0.128151i | \(0.0409044\pi\) |
−0.794809 | + | 0.606860i | \(0.792429\pi\) | |||||||
\(270\) | 29.1424 | − | 17.0431i | 1.77355 | − | 1.03721i | ||||
\(271\) | 13.7567 | + | 23.8273i | 0.835660 | + | 1.44741i | 0.893492 | + | 0.449079i | \(0.148248\pi\) |
−0.0578325 | + | 0.998326i | \(0.518419\pi\) | |||||||
\(272\) | −5.85439 | + | 10.6844i | −0.354975 | + | 0.647836i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −17.2526 | − | 9.83273i | −1.04227 | − | 0.594017i | ||||
\(275\) | −1.38909 | − | 0.372205i | −0.0837652 | − | 0.0224448i | ||||
\(276\) | −22.2162 | − | 21.7254i | −1.33726 | − | 1.30771i | ||||
\(277\) | 5.53100 | − | 1.48203i | 0.332326 | − | 0.0890464i | −0.0887978 | − | 0.996050i | \(-0.528303\pi\) |
0.421124 | + | 0.907003i | \(0.361636\pi\) | |||||||
\(278\) | −13.6508 | − | 13.4991i | −0.818718 | − | 0.809624i | ||||
\(279\) | − | 36.0631i | − | 2.15904i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.6051i | 0.930919i | 0.885069 | + | 0.465460i | \(0.154111\pi\) | ||||
−0.885069 | + | 0.465460i | \(0.845889\pi\) | |||||||
\(282\) | 4.99005 | − | 5.04610i | 0.297153 | − | 0.300491i | ||||
\(283\) | −8.14066 | + | 2.18128i | −0.483912 | + | 0.129664i | −0.492524 | − | 0.870299i | \(-0.663925\pi\) |
0.00861163 | + | 0.999963i | \(0.497259\pi\) | |||||||
\(284\) | 0.151241 | + | 13.5400i | 0.00897450 | + | 0.803454i | ||||
\(285\) | 28.3585 | + | 7.59864i | 1.67981 | + | 0.450104i | ||||
\(286\) | −0.00781074 | + | 0.0137048i | −0.000461859 | + | 0.000810381i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 33.2986 | − | 20.4854i | 1.96214 | − | 1.20711i | ||||
\(289\) | 3.86157 | + | 6.68843i | 0.227151 | + | 0.393437i | ||||
\(290\) | 2.84684 | + | 4.86789i | 0.167172 | + | 0.285852i | ||||
\(291\) | 0.318322 | + | 1.18800i | 0.0186604 | + | 0.0696415i | ||||
\(292\) | 6.91679 | + | 3.89106i | 0.404774 | + | 0.227707i | ||||
\(293\) | −10.7837 | − | 10.7837i | −0.629991 | − | 0.629991i | 0.318075 | − | 0.948066i | \(-0.396964\pi\) |
−0.948066 | + | 0.318075i | \(0.896964\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.5550i | 0.847423i | ||||||||
\(296\) | −6.04722 | + | 24.1821i | −0.351488 | + | 1.40555i | ||||
\(297\) | −12.3548 | − | 7.13303i | −0.716896 | − | 0.413900i | ||||
\(298\) | −1.70322 | + | 6.50153i | −0.0986649 | + | 0.376623i | ||||
\(299\) | −0.0122967 | + | 0.0458920i | −0.000711138 | + | 0.00265400i | ||||
\(300\) | 1.93828 | − | 7.57102i | 0.111907 | − | 0.437113i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 13.3007 | + | 7.58043i | 0.765368 | + | 0.436205i | ||||
\(303\) | 6.11290 | + | 10.5879i | 0.351177 | + | 0.608256i | ||||
\(304\) | 18.6914 | + | 4.56341i | 1.07202 | + | 0.261729i | ||||
\(305\) | −9.25091 | + | 16.0230i | −0.529706 | + | 0.917477i | ||||
\(306\) | 0.166251 | + | 29.7686i | 0.00950395 | + | 1.70176i | ||||
\(307\) | −12.4028 | + | 12.4028i | −0.707863 | + | 0.707863i | −0.966085 | − | 0.258223i | \(-0.916863\pi\) |
0.258223 | + | 0.966085i | \(0.416863\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.70711 | − | 4.70711i | −0.267778 | − | 0.267778i | ||||
\(310\) | 10.1730 | + | 10.0600i | 0.577787 | + | 0.571369i | ||||
\(311\) | 30.2727 | + | 17.4780i | 1.71661 | + | 0.991084i | 0.924922 | + | 0.380157i | \(0.124130\pi\) |
0.791687 | + | 0.610927i | \(0.209203\pi\) | |||||||
\(312\) | −0.0749471 | − | 0.0416124i | −0.00424305 | − | 0.00235584i | ||||
\(313\) | 6.83406 | − | 3.94565i | 0.386284 | − | 0.223021i | −0.294265 | − | 0.955724i | \(-0.595075\pi\) |
0.680549 | + | 0.732703i | \(0.261741\pi\) | |||||||
\(314\) | 0.163945 | + | 0.598462i | 0.00925196 | + | 0.0337732i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.73299 | − | 9.67855i | −0.322506 | − | 0.544461i | ||||
\(317\) | −6.72441 | − | 1.80180i | −0.377681 | − | 0.101199i | 0.0649843 | − | 0.997886i | \(-0.479300\pi\) |
−0.442665 | + | 0.896687i | \(0.645967\pi\) | |||||||
\(318\) | −1.83308 | − | 3.13442i | −0.102794 | − | 0.175770i | ||||
\(319\) | 1.19149 | − | 2.06371i | 0.0667104 | − | 0.115546i | ||||
\(320\) | −3.51013 | + | 15.1076i | −0.196222 | + | 0.844543i | ||||
\(321\) | 47.4072 | 2.64601 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3595 | + | 10.3595i | −0.576419 | + | 0.576419i | ||||
\(324\) | 17.6806 | − | 31.4292i | 0.982253 | − | 1.74607i | ||||
\(325\) | −0.0115422 | + | 0.00309273i | −0.000640247 | + | 0.000171554i | ||||
\(326\) | −18.4696 | − | 4.83852i | −1.02294 | − | 0.267981i | ||||
\(327\) | −9.34382 | + | 5.39465i | −0.516714 | + | 0.298325i | ||||
\(328\) | −0.285587 | − | 17.0442i | −0.0157689 | − | 0.941106i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 9.64551 | − | 2.64233i | 0.530968 | − | 0.145455i | ||||
\(331\) | −0.541330 | + | 2.02027i | −0.0297542 | + | 0.111044i | −0.979206 | − | 0.202869i | \(-0.934973\pi\) |
0.949452 | + | 0.313913i | \(0.101640\pi\) | |||||||
\(332\) | 22.4910 | − | 22.9991i | 1.23436 | − | 1.26224i | ||||
\(333\) | 15.7640 | + | 58.8320i | 0.863861 | + | 3.22397i | ||||
\(334\) | −0.0292921 | − | 5.24499i | −0.00160279 | − | 0.286993i | ||||
\(335\) | 12.7580 | 0.697047 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 35.7263 | 1.94613 | 0.973066 | − | 0.230525i | \(-0.0740442\pi\) | ||||
0.973066 | + | 0.230525i | \(0.0740442\pi\) | |||||||
\(338\) | −0.102673 | − | 18.3844i | −0.00558465 | − | 0.999977i | ||||
\(339\) | 2.07183 | + | 7.73216i | 0.112526 | + | 0.419953i | ||||
\(340\) | −8.44377 | − | 8.25722i | −0.457928 | − | 0.447811i | ||||
\(341\) | 1.56476 | − | 5.83976i | 0.0847365 | − | 0.316241i | ||||
\(342\) | 45.3425 | − | 12.4213i | 2.45184 | − | 0.671667i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −20.6258 | − | 19.9460i | −1.11207 | − | 1.07541i | ||||
\(345\) | 26.0863 | − | 15.0609i | 1.40444 | − | 0.810853i | ||||
\(346\) | −7.30720 | − | 1.91428i | −0.392838 | − | 0.102913i | ||||
\(347\) | 20.1610 | − | 5.40213i | 1.08230 | − | 0.290002i | 0.326763 | − | 0.945106i | \(-0.394042\pi\) |
0.755538 | + | 0.655105i | \(0.227375\pi\) | |||||||
\(348\) | 11.2867 | + | 6.34937i | 0.605032 | + | 0.340362i | ||||
\(349\) | −10.2714 | + | 10.2714i | −0.549813 | + | 0.549813i | −0.926387 | − | 0.376574i | \(-0.877102\pi\) |
0.376574 | + | 0.926387i | \(0.377102\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.118540 | −0.00632717 | ||||||||
\(352\) | 6.28094 | − | 1.87242i | 0.334775 | − | 0.0998003i | ||||
\(353\) | −15.0632 | + | 26.0903i | −0.801735 | + | 1.38865i | 0.116739 | + | 0.993163i | \(0.462756\pi\) |
−0.918473 | + | 0.395483i | \(0.870577\pi\) | |||||||
\(354\) | 16.8736 | + | 28.8527i | 0.896824 | + | 1.53350i | ||||
\(355\) | −12.6790 | − | 3.39732i | −0.672931 | − | 0.180311i | ||||
\(356\) | −7.14092 | + | 4.22986i | −0.378468 | + | 0.224182i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.33780 | − | 4.88348i | −0.0707049 | − | 0.258100i | ||||
\(359\) | 18.1770 | − | 10.4945i | 0.959347 | − | 0.553879i | 0.0633748 | − | 0.997990i | \(-0.479814\pi\) |
0.895972 | + | 0.444111i | \(0.146480\pi\) | |||||||
\(360\) | 10.4207 | + | 36.4374i | 0.549218 | + | 1.92042i | ||||
\(361\) | 3.58279 | + | 2.06853i | 0.188568 | + | 0.108870i | ||||
\(362\) | −14.5682 | − | 14.4064i | −0.765687 | − | 0.757182i | ||||
\(363\) | 21.4989 | + | 21.4989i | 1.12840 | + | 1.12840i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.43986 | + | 5.43986i | −0.284735 | + | 0.284735i | ||||
\(366\) | 0.237283 | + | 42.4875i | 0.0124030 | + | 2.22086i | ||||
\(367\) | 3.31261 | − | 5.73760i | 0.172917 | − | 0.299500i | −0.766522 | − | 0.642218i | \(-0.778014\pi\) |
0.939438 | + | 0.342718i | \(0.111348\pi\) | |||||||
\(368\) | 16.8710 | − | 10.2496i | 0.879459 | − | 0.534298i | ||||
\(369\) | −20.8263 | − | 36.0722i | −1.08417 | − | 1.87784i | ||||
\(370\) | −20.9933 | − | 11.9647i | −1.09139 | − | 0.622013i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 31.8288 | + | 8.14858i | 1.65024 | + | 0.422484i | ||||
\(373\) | −5.63908 | + | 21.0453i | −0.291981 | + | 1.08969i | 0.651605 | + | 0.758558i | \(0.274096\pi\) |
−0.943586 | + | 0.331128i | \(0.892571\pi\) | |||||||
\(374\) | −1.26472 | + | 4.82770i | −0.0653973 | + | 0.249634i | ||||
\(375\) | 32.9902 | + | 19.0469i | 1.70361 | + | 0.983579i | ||||
\(376\) | 2.31932 | + | 3.86612i | 0.119610 | + | 0.199380i | ||||
\(377\) | − | 0.0198006i | − | 0.00101978i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.217504 | − | 0.217504i | −0.0111724 | − | 0.0111724i | 0.701499 | − | 0.712671i | \(-0.252515\pi\) |
−0.712671 | + | 0.701499i | \(0.752515\pi\) | |||||||
\(380\) | −9.14462 | + | 16.2556i | −0.469109 | + | 0.833894i | ||||
\(381\) | 0.540935 | + | 2.01880i | 0.0277129 | + | 0.103426i | ||||
\(382\) | −11.4411 | − | 19.5634i | −0.585378 | − | 1.00095i | ||||
\(383\) | −11.0347 | − | 19.1127i | −0.563848 | − | 0.976614i | −0.997156 | − | 0.0753677i | \(-0.975987\pi\) |
0.433308 | − | 0.901246i | \(-0.357346\pi\) | |||||||
\(384\) | 10.5561 | + | 34.0176i | 0.538691 | + | 1.73595i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.03044 | − | 8.82645i | 0.256043 | − | 0.449255i | ||||
\(387\) | −67.7203 | − | 18.1456i | −3.44241 | − | 0.922392i | ||||
\(388\) | −0.781289 | + | 0.00872693i | −0.0396640 | + | 0.000443043i | ||||
\(389\) | 32.8412 | − | 8.79977i | 1.66511 | − | 0.446166i | 0.701327 | − | 0.712840i | \(-0.252591\pi\) |
0.963787 | + | 0.266674i | \(0.0859246\pi\) | |||||||
\(390\) | 0.0584311 | − | 0.0590874i | 0.00295877 | − | 0.00299201i | ||||
\(391\) | 15.0313i | 0.760166i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 13.7008i | − | 0.691114i | ||||||
\(394\) | −19.7683 | − | 19.5487i | −0.995911 | − | 0.984849i | ||||
\(395\) | 10.5330 | − | 2.82232i | 0.529975 | − | 0.142006i | ||||
\(396\) | 11.1969 | − | 11.4499i | 0.562665 | − | 0.575377i | ||||
\(397\) | −36.3522 | − | 9.74055i | −1.82447 | − | 0.488864i | −0.827144 | − | 0.561991i | \(-0.810036\pi\) |
−0.997323 | + | 0.0731264i | \(0.976702\pi\) | |||||||
\(398\) | 33.8398 | + | 19.2863i | 1.69624 | + | 0.966733i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.35408 | + | 2.38577i | 0.217704 | + | 0.119289i | ||||
\(401\) | −14.3983 | − | 24.9385i | −0.719015 | − | 1.24537i | −0.961390 | − | 0.275188i | \(-0.911260\pi\) |
0.242375 | − | 0.970183i | \(-0.422073\pi\) | |||||||
\(402\) | 25.2906 | − | 14.7905i | 1.26138 | − | 0.737681i | ||||
\(403\) | −0.0130019 | − | 0.0485238i | −0.000647671 | − | 0.00241714i | ||||
\(404\) | −7.47929 | + | 2.09388i | −0.372108 | + | 0.104174i | ||||
\(405\) | 24.7182 | + | 24.7182i | 1.22826 | + | 1.22826i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.2108i | 0.506128i | ||||||||
\(408\) | −26.3109 | − | 6.57959i | −1.30258 | − | 0.325738i | ||||
\(409\) | −17.3533 | − | 10.0189i | −0.858066 | − | 0.495405i | 0.00529806 | − | 0.999986i | \(-0.498314\pi\) |
−0.863364 | + | 0.504581i | \(0.831647\pi\) | |||||||
\(410\) | 15.9851 | + | 4.18767i | 0.789450 | + | 0.206814i | ||||
\(411\) | 11.4413 | − | 42.6995i | 0.564358 | − | 2.10621i | ||||
\(412\) | 3.63857 | − | 2.15527i | 0.179260 | − | 0.106183i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 23.8838 | − | 41.9066i | 1.17382 | − | 2.05960i | ||||
\(415\) | 15.5917 | + | 27.0056i | 0.765366 | + | 1.32565i | ||||
\(416\) | 0.0374184 | − | 0.0395687i | 0.00183459 | − | 0.00194002i | ||||
\(417\) | 21.3686 | − | 37.0115i | 1.04643 | − | 1.81246i | ||||
\(418\) | 7.88134 | − | 0.0440156i | 0.385489 | − | 0.00215287i | ||||
\(419\) | 11.3829 | − | 11.3829i | 0.556093 | − | 0.556093i | −0.372100 | − | 0.928193i | \(-0.621362\pi\) |
0.928193 | + | 0.372100i | \(0.121362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.3916 | − | 28.3916i | −1.38372 | − | 1.38372i | −0.837905 | − | 0.545816i | \(-0.816220\pi\) |
−0.545816 | − | 0.837905i | \(-0.683780\pi\) | |||||||
\(422\) | 0.392062 | − | 0.396466i | 0.0190853 | − | 0.0192997i | ||||
\(423\) | 9.54032 | + | 5.50811i | 0.463866 | + | 0.267813i | ||||
\(424\) | 2.21785 | − | 0.634282i | 0.107708 | − | 0.0308034i | ||||
\(425\) | −3.27401 | + | 1.89025i | −0.158813 | + | 0.0916905i | ||||
\(426\) | −29.0724 | + | 7.96420i | −1.40856 | + | 0.385867i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.46946 | + | 29.1761i | −0.361050 | + | 1.41028i | ||||
\(429\) | −0.0339188 | − | 0.00908853i | −0.00163762 | − | 0.000438798i | ||||
\(430\) | 24.0096 | − | 14.0413i | 1.15785 | − | 0.677132i | ||||
\(431\) | 11.6251 | − | 20.1352i | 0.559961 | − | 0.969880i | −0.437538 | − | 0.899200i | \(-0.644150\pi\) |
0.997499 | − | 0.0706806i | \(-0.0225171\pi\) | |||||||
\(432\) | 35.5958 | + | 34.0400i | 1.71260 | + | 1.63775i | ||||
\(433\) | −19.0385 | −0.914932 | −0.457466 | − | 0.889227i | \(-0.651243\pi\) | ||||
−0.457466 | + | 0.889227i | \(0.651243\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.87669 | + | 8.87669i | −0.425605 | + | 0.425605i | ||||
\(436\) | −1.84786 | − | 6.60050i | −0.0884962 | − | 0.316106i | ||||
\(437\) | 22.9295 | − | 6.14393i | 1.09686 | − | 0.293904i | ||||
\(438\) | −4.47711 | + | 17.0900i | −0.213925 | + | 0.816592i | ||||
\(439\) | 22.9131 | − | 13.2289i | 1.09358 | − | 0.631380i | 0.159055 | − | 0.987270i | \(-0.449155\pi\) |
0.934528 | + | 0.355889i | \(0.115822\pi\) | |||||||
\(440\) | 0.106441 | + | 6.35251i | 0.00507438 | + | 0.302844i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.0109562 | + | 0.0399944i | 0.000521135 | + | 0.00190234i | ||||
\(443\) | 8.64233 | − | 32.2536i | 0.410609 | − | 1.53241i | −0.382861 | − | 0.923806i | \(-0.625061\pi\) |
0.793470 | − | 0.608609i | \(-0.208272\pi\) | |||||||
\(444\) | −55.4862 | + | 0.619775i | −2.63326 | + | 0.0294132i | ||||
\(445\) | −2.08233 | − | 7.77138i | −0.0987121 | − | 0.368399i | ||||
\(446\) | −24.0731 | + | 0.134443i | −1.13989 | + | 0.00636605i | ||||
\(447\) | −14.9615 | −0.707656 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.6036 | −1.34989 | −0.674945 | − | 0.737868i | \(-0.735833\pi\) | ||||
−0.674945 | + | 0.737868i | \(0.735833\pi\) | |||||||
\(450\) | 12.1313 | − | 0.0677505i | 0.571874 | − | 0.00319379i | ||||
\(451\) | −1.80728 | − | 6.74486i | −0.0851015 | − | 0.317603i | ||||
\(452\) | −5.08508 | + | 0.0567999i | −0.239182 | + | 0.00267164i | ||||
\(453\) | −8.82054 | + | 32.9187i | −0.414425 | + | 1.54665i | ||||
\(454\) | 0.843378 | + | 3.07865i | 0.0395817 | + | 0.144488i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.717569 | + | 42.8253i | 0.0336032 | + | 2.00548i | ||||
\(457\) | −28.3772 | + | 16.3836i | −1.32743 | + | 0.766392i | −0.984902 | − | 0.173115i | \(-0.944617\pi\) |
−0.342529 | + | 0.939507i | \(0.611283\pi\) | |||||||
\(458\) | −4.97683 | + | 18.9975i | −0.232552 | + | 0.887697i | ||||
\(459\) | −36.2252 | + | 9.70650i | −1.69085 | + | 0.453061i | ||||
\(460\) | 5.15888 | + | 18.4274i | 0.240534 | + | 0.859183i | ||||
\(461\) | −17.2919 | + | 17.2919i | −0.805362 | + | 0.805362i | −0.983928 | − | 0.178566i | \(-0.942854\pi\) |
0.178566 | + | 0.983928i | \(0.442854\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.66786 | 0.0775121 | 0.0387560 | − | 0.999249i | \(-0.487660\pi\) | ||||
0.0387560 | + | 0.999249i | \(0.487660\pi\) | |||||||
\(464\) | −5.68596 | + | 5.94585i | −0.263964 | + | 0.276029i | ||||
\(465\) | −15.9246 | + | 27.5822i | −0.738486 | + | 1.27910i | ||||
\(466\) | −2.60361 | + | 1.52265i | −0.120610 | + | 0.0705352i | ||||
\(467\) | −2.87255 | − | 0.769699i | −0.132926 | − | 0.0356174i | 0.191743 | − | 0.981445i | \(-0.438586\pi\) |
−0.324669 | + | 0.945828i | \(0.605253\pi\) | |||||||
\(468\) | 0.0330030 | − | 0.128912i | 0.00152557 | − | 0.00595894i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.21510 | + | 1.15470i | −0.194428 | + | 0.0532623i | ||||
\(471\) | −1.19627 | + | 0.690664i | −0.0551210 | + | 0.0318241i | ||||
\(472\) | −20.4156 | + | 5.83863i | −0.939703 | + | 0.268745i | ||||
\(473\) | −10.1787 | − | 5.87669i | −0.468018 | − | 0.270211i | ||||
\(474\) | 17.6080 | − | 17.8058i | 0.808761 | − | 0.817845i | ||||
\(475\) | 4.22170 | + | 4.22170i | 0.193705 | + | 0.193705i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.98561 | − | 3.98561i | 0.182488 | − | 0.182488i | ||||
\(478\) | 24.8817 | − | 0.138959i | 1.13806 | − | 0.00635584i | ||||
\(479\) | 3.91759 | − | 6.78546i | 0.178999 | − | 0.310035i | −0.762539 | − | 0.646942i | \(-0.776047\pi\) |
0.941538 | + | 0.336907i | \(0.109381\pi\) | |||||||
\(480\) | −34.5137 | + | 0.963997i | −1.57533 | + | 0.0440002i | ||||
\(481\) | 0.0424216 | + | 0.0734764i | 0.00193426 | + | 0.00335023i | ||||
\(482\) | 5.88813 | − | 10.3314i | 0.268197 | − | 0.470580i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.6186 | + | 9.84385i | −0.755390 | + | 0.447448i | ||||
\(485\) | 0.196033 | − | 0.731604i | 0.00890139 | − | 0.0332204i | ||||
\(486\) | 27.1207 | + | 7.10488i | 1.23022 | + | 0.322284i | ||||
\(487\) | −14.2879 | − | 8.24910i | −0.647445 | − | 0.373802i | 0.140032 | − | 0.990147i | \(-0.455279\pi\) |
−0.787477 | + | 0.616345i | \(0.788613\pi\) | |||||||
\(488\) | −26.1857 | − | 6.54828i | −1.18537 | − | 0.296427i | ||||
\(489\) | − | 42.5028i | − | 1.92204i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4608 | − | 13.4608i | −0.607477 | − | 0.607477i | 0.334809 | − | 0.942286i | \(-0.391328\pi\) |
−0.942286 | + | 0.334809i | \(0.891328\pi\) | |||||||
\(492\) | 36.5425 | − | 10.2303i | 1.64746 | − | 0.461219i | ||||
\(493\) | −1.62135 | − | 6.05097i | −0.0730221 | − | 0.272522i | ||||
\(494\) | 0.0565311 | − | 0.0330606i | 0.00254346 | − | 0.00148747i | ||||
\(495\) | 7.76214 | + | 13.4444i | 0.348882 | + | 0.604282i | ||||
\(496\) | −10.0299 | + | 18.3047i | −0.450354 | + | 0.821904i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 62.2155 | + | 35.4583i | 2.78794 | + | 1.58893i | ||||
\(499\) | 13.4940 | + | 3.61570i | 0.604074 | + | 0.161861i | 0.547877 | − | 0.836559i | \(-0.315436\pi\) |
0.0561963 | + | 0.998420i | \(0.482103\pi\) | |||||||
\(500\) | −16.9201 | + | 17.3023i | −0.756689 | + | 0.773784i | ||||
\(501\) | 11.2783 | − | 3.02200i | 0.503876 | − | 0.135013i | ||||
\(502\) | 7.61995 | + | 7.53531i | 0.340095 | + | 0.336318i | ||||
\(503\) | − | 31.1020i | − | 1.38677i | −0.720568 | − | 0.693384i | \(-0.756119\pi\) | ||
0.720568 | − | 0.693384i | \(-0.243881\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 7.52903i | − | 0.335037i | ||||||
\(506\) | 5.68584 | − | 5.74971i | 0.252767 | − | 0.255606i | ||||
\(507\) | 39.5317 | − | 10.5925i | 1.75567 | − | 0.470429i | ||||
\(508\) | −1.32767 | + | 0.0148299i | −0.0589058 | + | 0.000657972i | ||||
\(509\) | −39.7462 | − | 10.6500i | −1.76172 | − | 0.472051i | −0.774655 | − | 0.632383i | \(-0.782077\pi\) |
−0.987063 | + | 0.160332i | \(0.948743\pi\) | |||||||
\(510\) | 13.0180 | − | 22.8414i | 0.576445 | − | 1.01144i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.5988 | + | 1.13683i | −0.998737 | + | 0.0502413i | ||||
\(513\) | 29.6135 | + | 51.2921i | 1.30747 | + | 2.26460i | ||||
\(514\) | 0.878856 | + | 1.50278i | 0.0387647 | + | 0.0662847i | ||||
\(515\) | 1.06103 | + | 3.95981i | 0.0467545 | + | 0.174490i | ||||
\(516\) | 31.3166 | − | 55.6688i | 1.37864 | − | 2.45068i | ||||
\(517\) | 1.30589 | + | 1.30589i | 0.0574328 | + | 0.0574328i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 16.8156i | − | 0.738122i | ||||||
\(520\) | 0.0271581 | + | 0.0452703i | 0.00119096 | + | 0.00198524i | ||||
\(521\) | 6.59720 | + | 3.80889i | 0.289028 | + | 0.166871i | 0.637504 | − | 0.770447i | \(-0.279967\pi\) |
−0.348475 | + | 0.937318i | \(0.613300\pi\) | |||||||
\(522\) | −5.09434 | + | 19.4461i | −0.222973 | + | 0.851132i | ||||
\(523\) | 5.14314 | − | 19.1945i | 0.224894 | − | 0.839315i | −0.757553 | − | 0.652773i | \(-0.773605\pi\) |
0.982447 | − | 0.186542i | \(-0.0597280\pi\) | |||||||
\(524\) | 8.43197 | + | 2.15869i | 0.368352 | + | 0.0943030i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.7476 | + | 14.1044i | 1.07905 | + | 0.614979i | ||||
\(527\) | −7.94665 | − | 13.7640i | −0.346161 | − | 0.599569i | ||||
\(528\) | 7.57550 | + | 12.4693i | 0.329681 | + | 0.542658i | ||||
\(529\) | 0.677604 | − | 1.17365i | 0.0294611 | − | 0.0510281i | ||||
\(530\) | 0.0124881 | + | 2.23610i | 0.000542449 | + | 0.0971299i | ||||
\(531\) | −36.6879 | + | 36.6879i | −1.59212 | + | 1.59212i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0410274 | − | 0.0410274i | −0.00177709 | − | 0.00177709i | ||||
\(534\) | −13.1373 | − | 12.9913i | −0.568504 | − | 0.562190i | ||||
\(535\) | −25.2835 | − | 14.5974i | −1.09310 | − | 0.631102i | ||||
\(536\) | 5.11780 | + | 17.8951i | 0.221055 | + | 0.772951i | ||||
\(537\) | 9.76158 | − | 5.63585i | 0.421243 | − | 0.243205i | ||||
\(538\) | −4.66326 | − | 17.0227i | −0.201047 | − | 0.733900i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −41.0784 | + | 24.3324i | −1.76773 | + | 1.04710i | ||||
\(541\) | 15.2423 | + | 4.08415i | 0.655316 | + | 0.175591i | 0.571131 | − | 0.820859i | \(-0.306505\pi\) |
0.0841847 | + | 0.996450i | \(0.473171\pi\) | |||||||
\(542\) | −19.6428 | − | 33.5877i | −0.843730 | − | 1.44272i | ||||
\(543\) | 22.8048 | − | 39.4990i | 0.978646 | − | 1.69507i | ||||
\(544\) | 8.19485 | − | 15.1560i | 0.351351 | − | 0.649808i | ||||
\(545\) | 6.64439 | 0.284615 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.04855 | − | 8.04855i | 0.344131 | − | 0.344131i | −0.513787 | − | 0.857918i | \(-0.671758\pi\) |
0.857918 | + | 0.513787i | \(0.171758\pi\) | |||||||
\(548\) | 24.4761 | + | 13.7691i | 1.04557 | + | 0.588187i | ||||
\(549\) | −63.7066 | + | 17.0701i | −2.71893 | + | 0.728536i | ||||
\(550\) | 1.96738 | + | 0.515398i | 0.0838892 | + | 0.0219767i | ||||
\(551\) | −8.56772 | + | 4.94658i | −0.364997 | + | 0.210731i | ||||
\(552\) | 31.5896 | + | 30.5484i | 1.34454 | + | 1.30023i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −7.81019 | + | 2.13956i | −0.331823 | + | 0.0909010i | ||||
\(555\) | 13.9220 | − | 51.9576i | 0.590956 | − | 2.20548i | ||||
\(556\) | 19.4114 | + | 18.9825i | 0.823226 | + | 0.805039i | ||||
\(557\) | 7.81587 | + | 29.1692i | 0.331169 | + | 1.23594i | 0.907963 | + | 0.419050i | \(0.137637\pi\) |
−0.576794 | + | 0.816890i | \(0.695696\pi\) | |||||||
\(558\) | 0.284825 | + | 51.0002i | 0.0120576 | + | 2.15901i | ||||
\(559\) | −0.0976612 | −0.00413063 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.1097 | −0.469050 | ||||||||
\(562\) | −0.123248 | − | 22.0685i | −0.00519890 | − | 0.930905i | ||||
\(563\) | 0.151794 | + | 0.566504i | 0.00639736 | + | 0.0238753i | 0.969051 | − | 0.246862i | \(-0.0793993\pi\) |
−0.962653 | + | 0.270737i | \(0.912733\pi\) | |||||||
\(564\) | −7.01704 | + | 7.17557i | −0.295471 | + | 0.302146i | ||||
\(565\) | 1.27590 | − | 4.76171i | 0.0536773 | − | 0.200326i | ||||
\(566\) | 11.4952 | − | 3.14905i | 0.483180 | − | 0.132364i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.320822 | − | 19.1470i | −0.0134614 | − | 0.803391i | ||||
\(569\) | 30.9006 | − | 17.8405i | 1.29542 | − | 0.747912i | 0.315812 | − | 0.948822i | \(-0.397723\pi\) |
0.979610 | + | 0.200910i | \(0.0643898\pi\) | |||||||
\(570\) | −40.1644 | − | 10.5220i | −1.68230 | − | 0.440716i | ||||
\(571\) | 12.8771 | − | 3.45040i | 0.538888 | − | 0.144395i | 0.0208985 | − | 0.999782i | \(-0.493347\pi\) |
0.517989 | + | 0.855387i | \(0.326681\pi\) | |||||||
\(572\) | 0.0109376 | − | 0.0194429i | 0.000457326 | − | 0.000812948i | ||||
\(573\) | 35.6743 | − | 35.6743i | 1.49032 | − | 1.49032i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.12553 | 0.255452 | ||||||||
\(576\) | −46.9288 | + | 29.2332i | −1.95537 | + | 1.21805i | ||||
\(577\) | 6.90735 | − | 11.9639i | 0.287557 | − | 0.498063i | −0.685669 | − | 0.727913i | \(-0.740490\pi\) |
0.973226 | + | 0.229850i | \(0.0738237\pi\) | |||||||
\(578\) | −5.51382 | − | 9.42822i | −0.229345 | − | 0.392162i | ||||
\(579\) | 21.8451 | + | 5.85339i | 0.907853 | + | 0.243259i | ||||
\(580\) | −4.06443 | − | 6.86164i | −0.168766 | − | 0.284914i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.459551 | − | 1.67754i | −0.0190490 | − | 0.0695362i | ||||
\(583\) | 0.818329 | − | 0.472462i | 0.0338917 | − | 0.0195674i | ||||
\(584\) | −9.81239 | − | 5.44807i | −0.406040 | − | 0.225443i | ||||
\(585\) | 0.111712 | + | 0.0644972i | 0.00461874 | + | 0.00266663i | ||||
\(586\) | 15.3354 | + | 15.1651i | 0.633499 | + | 0.626462i | ||||
\(587\) | −26.0019 | − | 26.0019i | −1.07321 | − | 1.07321i | −0.997099 | − | 0.0761137i | \(-0.975749\pi\) |
−0.0761137 | − | 0.997099i | \(-0.524251\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.7481 | + | 17.7481i | −0.731298 | + | 0.731298i | ||||
\(590\) | −0.114954 | − | 20.5835i | −0.00473260 | − | 0.847410i | ||||
\(591\) | 30.9449 | − | 53.5981i | 1.27290 | − | 2.20473i | ||||
\(592\) | 8.36094 | − | 34.2458i | 0.343633 | − | 1.40749i | ||||
\(593\) | 19.0574 | + | 33.0084i | 0.782593 | + | 1.35549i | 0.930426 | + | 0.366479i | \(0.119437\pi\) |
−0.147833 | + | 0.989012i | \(0.547230\pi\) | |||||||
\(594\) | 17.5283 | + | 9.98989i | 0.719197 | + | 0.409890i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.35733 | − | 9.20786i | 0.0965601 | − | 0.377169i | ||||
\(597\) | −22.4414 | + | 83.7523i | −0.918464 | + | 3.42775i | ||||
\(598\) | 0.0170275 | − | 0.0649972i | 0.000696305 | − | 0.00265793i | ||||
\(599\) | −29.1573 | − | 16.8340i | −1.19133 | − | 0.687817i | −0.232725 | − | 0.972543i | \(-0.574764\pi\) |
−0.958609 | + | 0.284726i | \(0.908098\pi\) | |||||||
\(600\) | −2.68130 | + | 10.7222i | −0.109464 | + | 0.437731i | ||||
\(601\) | − | 27.9742i | − | 1.14109i | −0.821265 | − | 0.570546i | \(-0.806731\pi\) | ||
0.821265 | − | 0.570546i | \(-0.193269\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.1585 | + | 32.1585i | 1.30959 | + | 1.30959i | ||||
\(604\) | −18.8696 | − | 10.6151i | −0.767792 | − | 0.431923i | ||||
\(605\) | −4.84607 | − | 18.0858i | −0.197021 | − | 0.735292i | ||||
\(606\) | −8.72843 | − | 14.9250i | −0.354568 | − | 0.606286i | ||||
\(607\) | −2.51294 | − | 4.35254i | −0.101997 | − | 0.176664i | 0.810510 | − | 0.585724i | \(-0.199190\pi\) |
−0.912507 | + | 0.409060i | \(0.865857\pi\) | |||||||
\(608\) | −26.4692 | − | 6.30591i | −1.07347 | − | 0.255738i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.9560 | − | 22.7327i | 0.524573 | − | 0.920421i | ||||
\(611\) | 0.0148226 | + | 0.00397170i | 0.000599657 | + | 0.000160678i | ||||
\(612\) | −0.470222 | − | 42.0972i | −0.0190076 | − | 1.70168i | ||||
\(613\) | −32.2373 | + | 8.63795i | −1.30205 | + | 0.348883i | −0.842225 | − | 0.539126i | \(-0.818755\pi\) |
−0.459825 | + | 0.888009i | \(0.652088\pi\) | |||||||
\(614\) | 17.4419 | − | 17.6378i | 0.703898 | − | 0.711805i | ||||
\(615\) | 36.7855i | 1.48334i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 37.6332i | − | 1.51506i | −0.652803 | − | 0.757528i | \(-0.726407\pi\) | ||
0.652803 | − | 0.757528i | \(-0.273593\pi\) | |||||||
\(618\) | 6.69393 | + | 6.61958i | 0.269269 | + | 0.266278i | ||||
\(619\) | 5.08719 | − | 1.36311i | 0.204471 | − | 0.0547879i | −0.155130 | − | 0.987894i | \(-0.549580\pi\) |
0.359601 | + | 0.933106i | \(0.382913\pi\) | |||||||
\(620\) | −14.4660 | − | 14.1464i | −0.580969 | − | 0.568134i | ||||
\(621\) | 58.6956 | + | 15.7274i | 2.35537 | + | 0.631120i | ||||
\(622\) | −42.9495 | − | 24.4781i | −1.72212 | − | 0.981482i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.106318 | + | 0.0582560i | 0.00425614 | + | 0.00233211i | ||||
\(625\) | −8.62664 | − | 14.9418i | −0.345066 | − | 0.597671i | ||||
\(626\) | −9.63351 | + | 5.63388i | −0.385033 | + | 0.225175i | ||||
\(627\) | 4.54099 | + | 16.9472i | 0.181350 | + | 0.676806i | ||||
\(628\) | −0.236576 | − | 0.845045i | −0.00944042 | − | 0.0337210i | ||||
\(629\) | 18.9804 | + | 18.9804i | 0.756798 | + | 0.756798i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.9681i | 1.63091i | 0.578818 | + | 0.815457i | \(0.303514\pi\) | ||||
−0.578818 | + | 0.815457i | \(0.696486\pi\) | |||||||
\(632\) | 8.18399 | + | 13.6420i | 0.325542 | + | 0.542651i | ||||
\(633\) | 1.07495 | + | 0.620620i | 0.0427253 | + | 0.0246674i | ||||
\(634\) | 9.52384 | + | 2.49498i | 0.378240 | + | 0.0990884i | ||||
\(635\) | 0.333125 | − | 1.24324i | 0.0132197 | − | 0.0493364i | ||||
\(636\) | 2.61707 | + | 4.41820i | 0.103774 | + | 0.175193i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.66869 | + | 2.92790i | −0.0660640 | + | 0.115916i | ||||
\(639\) | −23.3958 | − | 40.5227i | −0.925522 | − | 1.60305i | ||||
\(640\) | 4.84468 | − | 21.3928i | 0.191503 | − | 0.845626i | ||||
\(641\) | −7.08895 | + | 12.2784i | −0.279997 | + | 0.484968i | −0.971384 | − | 0.237516i | \(-0.923667\pi\) |
0.691387 | + | 0.722485i | \(0.257000\pi\) | |||||||
\(642\) | −67.0429 | + | 0.374420i | −2.64597 | + | 0.0147772i | ||||
\(643\) | 0.705913 | − | 0.705913i | 0.0278385 | − | 0.0278385i | −0.693051 | − | 0.720889i | \(-0.743734\pi\) |
0.720889 | + | 0.693051i | \(0.243734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 43.7820 | + | 43.7820i | 1.72391 | + | 1.72391i | ||||
\(646\) | 14.5685 | − | 14.7322i | 0.573191 | − | 0.579629i | ||||
\(647\) | 0.498838 | + | 0.288004i | 0.0196113 | + | 0.0113226i | 0.509774 | − | 0.860309i | \(-0.329729\pi\) |
−0.490162 | + | 0.871631i | \(0.663062\pi\) | |||||||
\(648\) | −24.7555 | + | 44.5865i | −0.972487 | + | 1.75152i | ||||
\(649\) | −7.53280 | + | 4.34906i | −0.295688 | + | 0.170716i | ||||
\(650\) | 0.0162985 | − | 0.00446487i | 0.000639279 | − | 0.000175127i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 26.1577 | + | 6.69672i | 1.02442 | + | 0.262264i | ||||
\(653\) | −18.1467 | − | 4.86239i | −0.710135 | − | 0.190280i | −0.114369 | − | 0.993438i | \(-0.536485\pi\) |
−0.595766 | + | 0.803158i | \(0.703151\pi\) | |||||||
\(654\) | 13.1713 | − | 7.70287i | 0.515040 | − | 0.301206i | ||||
\(655\) | −4.21869 | + | 7.30699i | −0.164838 | + | 0.285508i | ||||
\(656\) | 0.538489 | + | 24.1014i | 0.0210245 | + | 0.941003i | ||||
\(657\) | −27.4239 | −1.06991 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26.5183 | − | 26.5183i | 1.03301 | − | 1.03301i | 0.0335689 | − | 0.999436i | \(-0.489313\pi\) |
0.999436 | − | 0.0335689i | \(-0.0106873\pi\) | |||||||
\(660\) | −13.6197 | + | 3.81294i | −0.530147 | + | 0.148418i | ||||
\(661\) | −41.9426 | + | 11.2385i | −1.63138 | + | 0.437127i | −0.954316 | − | 0.298798i | \(-0.903414\pi\) |
−0.677063 | + | 0.735925i | \(0.736748\pi\) | |||||||
\(662\) | 0.749588 | − | 2.86133i | 0.0291336 | − | 0.111209i | ||||
\(663\) | −0.0799449 | + | 0.0461562i | −0.00310480 | + | 0.00179256i | ||||
\(664\) | −31.6250 | + | 32.7028i | −1.22729 | + | 1.26912i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −22.7580 | − | 83.0752i | −0.881853 | − | 3.21910i | ||||
\(667\) | −2.62708 | + | 9.80439i | −0.101721 | + | 0.379627i | ||||
\(668\) | 0.0828493 | + | 7.41719i | 0.00320554 | + | 0.286980i | ||||
\(669\) | −13.8702 | − | 51.7642i | −0.536251 | − | 2.00132i | ||||
\(670\) | −18.0423 | + | 0.100762i | −0.697036 | + | 0.00389279i | ||||
\(671\) | −11.0568 | −0.426842 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.5484 | 1.17756 | 0.588778 | − | 0.808295i | \(-0.299609\pi\) | ||||
0.588778 | + | 0.808295i | \(0.299609\pi\) | |||||||
\(674\) | −50.5238 | + | 0.282164i | −1.94610 | + | 0.0108686i | ||||
\(675\) | 3.95558 | + | 14.7624i | 0.152250 | + | 0.568206i | ||||
\(676\) | 0.290397 | + | 25.9982i | 0.0111691 | + | 0.999930i | ||||
\(677\) | 9.54210 | − | 35.6116i | 0.366733 | − | 1.36867i | −0.498324 | − | 0.866991i | \(-0.666051\pi\) |
0.865056 | − | 0.501675i | \(-0.167283\pi\) | |||||||
\(678\) | −2.99103 | − | 10.9184i | −0.114870 | − | 0.419318i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.0063 | + | 11.6106i | 0.460421 | + | 0.445246i | ||||
\(681\) | −6.15392 | + | 3.55297i | −0.235819 | + | 0.136150i | ||||
\(682\) | −2.16675 | + | 8.27090i | −0.0829690 | + | 0.316709i | ||||
\(683\) | −5.87766 | + | 1.57491i | −0.224902 | + | 0.0602624i | −0.369510 | − | 0.929227i | \(-0.620475\pi\) |
0.144608 | + | 0.989489i | \(0.453808\pi\) | |||||||
\(684\) | −64.0249 | + | 17.9242i | −2.44805 | + | 0.685350i | ||||
\(685\) | −19.2498 | + | 19.2498i | −0.735496 | + | 0.735496i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.7178 | −1.66794 | ||||||||
\(688\) | 29.3263 | + | 28.0445i | 1.11806 | + | 1.06919i | ||||
\(689\) | 0.00392579 | − | 0.00679966i | 0.000149561 | − | 0.000259046i | ||||
\(690\) | −36.7720 | + | 21.5050i | −1.39989 | + | 0.818683i | ||||
\(691\) | 0.492824 | + | 0.132052i | 0.0187479 | + | 0.00502349i | 0.268181 | − | 0.963369i | \(-0.413578\pi\) |
−0.249433 | + | 0.968392i | \(0.580244\pi\) | |||||||
\(692\) | 10.3489 | + | 2.64945i | 0.393406 | + | 0.100717i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −28.4689 | + | 7.79888i | −1.08066 | + | 0.296042i | ||||
\(695\) | −22.7929 | + | 13.1595i | −0.864583 | + | 0.499167i | ||||
\(696\) | −16.0117 | − | 8.89009i | −0.606923 | − | 0.336978i | ||||
\(697\) | −15.8973 | − | 9.17830i | −0.602152 | − | 0.347653i | ||||
\(698\) | 14.4445 | − | 14.6068i | 0.546734 | − | 0.552875i | ||||
\(699\) | −4.74774 | − | 4.74774i | −0.179576 | − | 0.179576i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.72808 | − | 6.72808i | 0.254116 | − | 0.254116i | −0.568540 | − | 0.822656i | \(-0.692491\pi\) |
0.822656 | + | 0.568540i | \(0.192491\pi\) | |||||||
\(702\) | 0.167638 | 0.000936219i | 0.00632707 | 3.53353e-5i | ||||||
\(703\) | 21.1955 | − | 36.7117i | 0.799404 | − | 1.38461i | ||||
\(704\) | −8.86767 | + | 2.69757i | −0.334213 | + | 0.101668i | ||||
\(705\) | −4.86450 | − | 8.42556i | −0.183208 | − | 0.317325i | ||||
\(706\) | 21.0962 | − | 37.0156i | 0.793967 | − | 1.39310i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −24.0904 | − | 40.6699i | −0.905374 | − | 1.52847i | ||||
\(709\) | −0.751876 | + | 2.80604i | −0.0282373 | + | 0.105383i | −0.978606 | − | 0.205742i | \(-0.934039\pi\) |
0.950369 | + | 0.311125i | \(0.100706\pi\) | |||||||
\(710\) | 17.9573 | + | 4.70433i | 0.673927 | + | 0.176550i | ||||
\(711\) | 33.6641 | + | 19.4360i | 1.26250 | + | 0.728907i | ||||
\(712\) | 10.0652 | − | 6.03822i | 0.377210 | − | 0.226292i | ||||
\(713\) | 25.7519i | 0.964416i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0152913 | + | 0.0152913i | 0.000571862 | + | 0.000571862i | ||||
\(716\) | 1.93047 | + | 6.89561i | 0.0721452 | + | 0.257701i | ||||
\(717\) | 14.3361 | + | 53.5030i | 0.535391 | + | 1.99811i | ||||
\(718\) | −25.6229 | + | 14.9848i | −0.956239 | + | 0.559228i | ||||
\(719\) | 11.0995 | + | 19.2250i | 0.413943 | + | 0.716970i | 0.995317 | − | 0.0966665i | \(-0.0308180\pi\) |
−0.581374 | + | 0.813636i | \(0.697485\pi\) | |||||||
\(720\) | −15.0246 | − | 51.4471i | −0.559935 | − | 1.91732i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −5.08309 | − | 2.89699i | −0.189173 | − | 0.107815i | ||||
\(723\) | 25.5697 | + | 6.85139i | 0.950948 | + | 0.254806i | ||||
\(724\) | 20.7160 | + | 20.2583i | 0.769904 | + | 0.752894i | ||||
\(725\) | −2.46588 | + | 0.660731i | −0.0915806 | + | 0.0245390i | ||||
\(726\) | −30.5734 | − | 30.2338i | −1.13469 | − | 1.12208i | ||||
\(727\) | 11.9796i | 0.444300i | 0.975013 | + | 0.222150i | \(0.0713074\pi\) | ||||
−0.975013 | + | 0.222150i | \(0.928693\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.31959i | 0.308133i | ||||||||
\(730\) | 7.65004 | − | 7.73597i | 0.283141 | − | 0.286321i | ||||
\(731\) | −29.8448 | + | 7.99690i | −1.10385 | + | 0.295776i | ||||
\(732\) | −0.671128 | − | 60.0836i | −0.0248056 | − | 2.22075i | ||||
\(733\) | 20.0603 | + | 5.37515i | 0.740945 | + | 0.198536i | 0.609498 | − | 0.792787i | \(-0.291371\pi\) |
0.131447 | + | 0.991323i | \(0.458038\pi\) | |||||||
\(734\) | −4.63935 | + | 8.14023i | −0.171241 | + | 0.300461i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −23.7778 | + | 14.6281i | −0.876461 | + | 0.539201i | ||||
\(737\) | 3.81214 | + | 6.60282i | 0.140422 | + | 0.243218i | ||||
\(738\) | 29.7372 | + | 50.8485i | 1.09464 | + | 1.87176i | ||||
\(739\) | 11.5688 | + | 43.1754i | 0.425565 | + | 1.58823i | 0.762686 | + | 0.646769i | \(0.223880\pi\) |
−0.337120 | + | 0.941462i | \(0.609453\pi\) | |||||||
\(740\) | 29.7830 | + | 16.7545i | 1.09485 | + | 0.615908i | ||||
\(741\) | 0.103086 | + | 0.103086i | 0.00378695 | + | 0.00378695i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.9156i | 0.547200i | 0.961844 | + | 0.273600i | \(0.0882144\pi\) | ||||
−0.961844 | + | 0.273600i | \(0.911786\pi\) | |||||||
\(744\) | −45.0763 | − | 11.2723i | −1.65258 | − | 0.413261i | ||||
\(745\) | 7.97936 | + | 4.60689i | 0.292341 | + | 0.168783i | ||||
\(746\) | 7.80853 | − | 29.8067i | 0.285890 | − | 1.09130i | ||||
\(747\) | −28.7704 | + | 107.373i | −1.05265 | + | 3.92856i | ||||
\(748\) | 1.75043 | − | 6.83728i | 0.0640022 | − | 0.249996i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −46.8049 | − | 26.6754i | −1.70908 | − | 0.974049i | ||||
\(751\) | 10.0879 | + | 17.4727i | 0.368111 | + | 0.637587i | 0.989270 | − | 0.146097i | \(-0.0466712\pi\) |
−0.621159 | + | 0.783685i | \(0.713338\pi\) | |||||||
\(752\) | −3.31050 | − | 5.44912i | −0.120721 | − | 0.198709i | ||||
\(753\) | −11.9281 | + | 20.6601i | −0.434685 | + | 0.752897i | ||||
\(754\) | 0.000156384 | 0.0280018i | 5.69517e−6 | 0.00101977i | ||||||
\(755\) | 14.8404 | − | 14.8404i | 0.540097 | − | 0.540097i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.2417 | − | 15.2417i | −0.553968 | − | 0.553968i | 0.373615 | − | 0.927584i | \(-0.378118\pi\) |
−0.927584 | + | 0.373615i | \(0.878118\pi\) | |||||||
\(758\) | 0.309310 | + | 0.305874i | 0.0112346 | + | 0.0111098i | ||||
\(759\) | 15.5893 | + | 9.00048i | 0.565856 | + | 0.326697i | ||||
\(760\) | 12.8039 | − | 23.0607i | 0.464445 | − | 0.836501i | ||||
\(761\) | 27.5359 | − | 15.8978i | 0.998174 | − | 0.576296i | 0.0904666 | − | 0.995899i | \(-0.471164\pi\) |
0.907708 | + | 0.419603i | \(0.137831\pi\) | |||||||
\(762\) | −0.780930 | − | 2.85069i | −0.0282901 | − | 0.103270i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.3344 | + | 27.5761i | 0.590959 | + | 0.997668i | ||||
\(765\) | 39.4201 | + | 10.5626i | 1.42524 | + | 0.381891i | ||||
\(766\) | 15.7562 | + | 26.9419i | 0.569294 | + | 0.973450i | ||||
\(767\) | −0.0361373 | + | 0.0625916i | −0.00130484 | + | 0.00226005i | ||||
\(768\) | −15.1971 | − | 48.0240i | −0.548377 | − | 1.73292i | ||||
\(769\) | 28.1015 | 1.01336 | 0.506682 | − | 0.862133i | \(-0.330872\pi\) | ||||
0.506682 | + | 0.862133i | \(0.330872\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.74035 | + | 2.74035i | −0.0986912 | + | 0.0986912i | ||||
\(772\) | −7.04429 | + | 12.5220i | −0.253530 | + | 0.450677i | ||||
\(773\) | 21.6810 | − | 5.80940i | 0.779811 | − | 0.208950i | 0.153109 | − | 0.988209i | \(-0.451071\pi\) |
0.626701 | + | 0.779260i | \(0.284405\pi\) | |||||||
\(774\) | 95.9127 | + | 25.1265i | 3.44751 | + | 0.903153i | ||||
\(775\) | −5.60908 | + | 3.23841i | −0.201484 | + | 0.116327i | ||||
\(776\) | 1.10482 | − | 0.0185121i | 0.0396609 | − | 0.000664547i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −46.3742 | + | 12.7039i | −1.66260 | + | 0.455458i | ||||
\(779\) | −7.50312 | + | 28.0020i | −0.268827 | + | 1.00328i | ||||
\(780\) | −0.0821660 | + | 0.0840224i | −0.00294202 | + | 0.00300848i | ||||
\(781\) | −2.03026 | − | 7.57703i | −0.0726484 | − | 0.271127i | ||||
\(782\) | −0.118716 | − | 21.2571i | −0.00424529 | − | 0.760154i | ||||
\(783\) | −25.3248 | −0.905036 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.850665 | 0.0303615 | ||||||||
\(786\) | 0.108208 | + | 19.3756i | 0.00385966 | + | 0.691104i | ||||
\(787\) | −1.24497 | − | 4.64629i | −0.0443784 | − | 0.165622i | 0.940180 | − | 0.340677i | \(-0.110656\pi\) |
−0.984559 | + | 0.175055i | \(0.943990\pi\) | |||||||
\(788\) | 28.1105 | + | 27.4895i | 1.00140 | + | 0.979271i | ||||
\(789\) | −16.4117 | + | 61.2495i | −0.584274 | + | 2.18054i | ||||
\(790\) | −14.8735 | + | 4.07449i | −0.529174 | + | 0.144964i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −15.7441 | + | 16.2807i | −0.559443 | + | 0.578510i | ||||
\(793\) | −0.0795644 | + | 0.0459365i | −0.00282541 | + | 0.00163125i | ||||
\(794\) | 51.4859 | + | 13.4879i | 1.82717 | + | 0.478668i | ||||
\(795\) | −4.80827 | + | 1.28837i | −0.170532 | + | 0.0456938i | ||||
\(796\) | −48.0083 | − | 27.0072i | −1.70161 | − | 0.957245i | ||||
\(797\) | 0.757921 | − | 0.757921i | 0.0268469 | − | 0.0268469i | −0.693556 | − | 0.720403i | \(-0.743957\pi\) |
0.720403 | + | 0.693556i | \(0.243957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.85493 | 0.171755 | ||||||||
\(800\) | −6.17635 | − | 3.33955i | −0.218367 | − | 0.118071i | ||||
\(801\) | 14.3401 | − | 24.8377i | 0.506681 | − | 0.877597i | ||||
\(802\) | 20.5589 | + | 35.1541i | 0.725959 | + | 1.24134i | ||||
\(803\) | −4.44080 | − | 1.18991i | −0.156712 | − | 0.0419909i | ||||
\(804\) | −35.6489 | + | 21.1163i | −1.25724 | + | 0.744714i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.0187704 | + | 0.0685192i | 0.000661160 | + | 0.00241349i | ||||
\(807\) | 34.0266 | − | 19.6453i | 1.19779 | − | 0.691547i | ||||
\(808\) | 10.5606 | − | 3.02022i | 0.371521 | − | 0.106251i | ||||
\(809\) | 28.2323 | + | 16.2999i | 0.992593 | + | 0.573074i | 0.906048 | − | 0.423174i | \(-0.139084\pi\) |
0.0865449 | + | 0.996248i | \(0.472417\pi\) | |||||||
\(810\) | −35.1514 | − | 34.7610i | −1.23510 | − | 1.22138i | ||||
\(811\) | −10.5979 | − | 10.5979i | −0.372144 | − | 0.372144i | 0.496113 | − | 0.868258i | \(-0.334760\pi\) |
−0.868258 | + | 0.496113i | \(0.834760\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 61.2479 | − | 61.2479i | 2.14806 | − | 2.14806i | ||||
\(814\) | −0.0806440 | − | 14.4400i | −0.00282657 | − | 0.506120i | ||||
\(815\) | −13.0873 | + | 22.6678i | −0.458427 | + | 0.794019i | ||||
\(816\) | 37.2606 | + | 9.09700i | 1.30438 | + | 0.318459i | ||||
\(817\) | 24.3977 | + | 42.2581i | 0.853567 | + | 1.47842i | ||||
\(818\) | 24.6200 | + | 14.0316i | 0.860819 | + | 0.490605i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22.6391 | − | 5.79591i | −0.790592 | − | 0.202402i | ||||
\(821\) | 2.77480 | − | 10.3557i | 0.0968411 | − | 0.361416i | −0.900451 | − | 0.434957i | \(-0.856763\pi\) |
0.997292 | + | 0.0735415i | \(0.0234301\pi\) | |||||||
\(822\) | −15.8430 | + | 60.4757i | −0.552586 | + | 2.10933i | ||||
\(823\) | −35.5874 | − | 20.5464i | −1.24050 | − | 0.716202i | −0.271303 | − | 0.962494i | \(-0.587455\pi\) |
−0.969196 | + | 0.246291i | \(0.920788\pi\) | |||||||
\(824\) | −5.12862 | + | 3.07671i | −0.178664 | + | 0.107182i | ||||
\(825\) | 4.52739i | 0.157624i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.5960 | − | 10.5960i | −0.368458 | − | 0.368458i | 0.498457 | − | 0.866915i | \(-0.333900\pi\) |
−0.866915 | + | 0.498457i | \(0.833900\pi\) | |||||||
\(828\) | −33.4452 | + | 59.4527i | −1.16230 | + | 2.06612i | ||||
\(829\) | 2.76435 | + | 10.3167i | 0.0960097 | + | 0.358313i | 0.997171 | − | 0.0751716i | \(-0.0239504\pi\) |
−0.901161 | + | 0.433485i | \(0.857284\pi\) | |||||||
\(830\) | −22.2629 | − | 38.0679i | −0.772757 | − | 1.32136i | ||||
\(831\) | −9.01347 | − | 15.6118i | −0.312674 | − | 0.541567i | ||||
\(832\) | −0.0526043 | + | 0.0562533i | −0.00182372 | + | 0.00195023i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −29.9270 | + | 52.5102i | −1.03629 | + | 1.81828i | ||||
\(835\) | −6.94550 | − | 1.86104i | −0.240359 | − | 0.0644040i | ||||
\(836\) | −11.1454 | + | 0.124493i | −0.385471 | + | 0.00430568i | ||||
\(837\) | −62.0616 | + | 16.6294i | −2.14516 | + | 0.574795i | ||||
\(838\) | −16.0078 | + | 16.1876i | −0.552979 | + | 0.559190i | ||||
\(839\) | − | 23.6761i | − | 0.817391i | −0.912671 | − | 0.408696i | \(-0.865984\pi\) | ||
0.912671 | − | 0.408696i | \(-0.134016\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.7698i | 0.854131i | ||||||||
\(842\) | 40.3754 | + | 39.9269i | 1.39143 | + | 1.37597i | ||||
\(843\) | 47.4538 | − | 12.7152i | 1.63440 | − | 0.437935i | ||||
\(844\) | −0.551320 | + | 0.563775i | −0.0189772 | + | 0.0194059i | ||||
\(845\) | −24.3449 | − | 6.52319i | −0.837489 | − | 0.224405i | ||||
\(846\) | −13.5353 | − | 7.71417i | −0.465355 | − | 0.265219i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.13146 | + | 0.914512i | −0.107535 | + | 0.0314045i | ||||
\(849\) | 13.2662 | + | 22.9778i | 0.455296 | + | 0.788596i | ||||
\(850\) | 4.61514 | − | 2.69903i | 0.158298 | − | 0.0925760i | ||||
\(851\) | −11.2567 | − | 42.0107i | −0.385876 | − | 1.44011i | ||||
\(852\) | 41.0510 | − | 11.4925i | 1.40638 | − | 0.393727i | ||||
\(853\) | −10.1928 | − | 10.1928i | −0.348995 | − | 0.348995i | 0.510740 | − | 0.859735i | \(-0.329372\pi\) |
−0.859735 | + | 0.510740i | \(0.829372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 64.4507i | − | 2.20417i | ||||||
\(856\) | 10.3328 | − | 41.3196i | 0.353168 | − | 1.41227i | ||||
\(857\) | −37.5171 | − | 21.6605i | −1.28156 | − | 0.739909i | −0.304426 | − | 0.952536i | \(-0.598465\pi\) |
−0.977133 | + | 0.212627i | \(0.931798\pi\) | |||||||
\(858\) | 0.0480395 | + | 0.0125850i | 0.00164004 | + | 0.000429646i | ||||
\(859\) | −2.92018 | + | 10.8983i | −0.0996352 | + | 0.371844i | −0.997681 | − | 0.0680575i | \(-0.978320\pi\) |
0.898046 | + | 0.439901i | \(0.144987\pi\) | |||||||
\(860\) | −33.8433 | + | 20.0467i | −1.15405 | + | 0.683587i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.2811 | + | 28.5669i | −0.554536 | + | 0.972993i | ||||
\(863\) | −7.41990 | − | 12.8516i | −0.252576 | − | 0.437475i | 0.711658 | − | 0.702526i | \(-0.247945\pi\) |
−0.964234 | + | 0.265051i | \(0.914611\pi\) | |||||||
\(864\) | −50.6082 | − | 47.8579i | −1.72172 | − | 1.62816i | ||||
\(865\) | −5.17778 | + | 8.96817i | −0.176050 | + | 0.304927i | ||||
\(866\) | 26.9241 | − | 0.150365i | 0.914918 | − | 0.00510962i | ||||
\(867\) | 17.1926 | − | 17.1926i | 0.583890 | − | 0.583890i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.60797 | + | 4.60797i | 0.156315 | + | 0.156315i | ||||
\(870\) | 12.4832 | − | 12.6235i | 0.423221 | − | 0.427975i | ||||
\(871\) | 0.0548641 | + | 0.0316758i | 0.00185900 | + | 0.00107329i | ||||
\(872\) | 2.66535 | + | 9.31977i | 0.0902602 | + | 0.315607i | ||||
\(873\) | 2.33824 | − | 1.34999i | 0.0791375 | − | 0.0456901i | ||||
\(874\) | −32.3781 | + | 8.86979i | −1.09521 | + | 0.300025i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.19652 | − | 24.2039i | 0.209361 | − | 0.817774i | ||||
\(877\) | −26.1904 | − | 7.01770i | −0.884387 | − | 0.236971i | −0.212088 | − | 0.977251i | \(-0.568026\pi\) |
−0.672299 | + | 0.740280i | \(0.734693\pi\) | |||||||
\(878\) | −32.2990 | + | 18.8891i | −1.09004 | + | 0.637478i | ||||
\(879\) | −24.0057 | + | 41.5791i | −0.809693 | + | 1.40243i | ||||
\(880\) | −0.200700 | − | 8.98283i | −0.00676559 | − | 0.302811i | ||||
\(881\) | 5.53387 | 0.186441 | 0.0932204 | − | 0.995645i | \(-0.470284\pi\) | ||||
0.0932204 | + | 0.995645i | \(0.470284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.6942 | + | 27.6942i | −0.931985 | + | 0.931985i | −0.997830 | − | 0.0658444i | \(-0.979026\pi\) |
0.0658444 | + | 0.997830i | \(0.479026\pi\) | |||||||
\(884\) | −0.0158101 | − | 0.0564733i | −0.000531751 | − | 0.00189940i | ||||
\(885\) | 44.2606 | − | 11.8596i | 1.48780 | − | 0.398656i | ||||
\(886\) | −11.9672 | + | 45.6810i | −0.402045 | + | 1.53468i | ||||
\(887\) | −29.1956 | + | 16.8561i | −0.980291 | + | 0.565971i | −0.902358 | − | 0.430987i | \(-0.858165\pi\) |
−0.0779332 | + | 0.996959i | \(0.524832\pi\) | |||||||
\(888\) | 78.4632 | − | 1.31471i | 2.63305 | − | 0.0441187i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.00620 | + | 10.9738i | 0.100768 | + | 0.367842i | ||||
\(891\) | −5.40682 | + | 20.1785i | −0.181135 | + | 0.676006i | ||||
\(892\) | 34.0429 | − | 0.380256i | 1.13984 | − | 0.0127319i | ||||
\(893\) | −1.98442 | − | 7.40594i | −0.0664059 | − | 0.247830i | ||||
\(894\) | 21.1585 | − | 0.118165i | 0.707645 | − | 0.00395204i | ||||
\(895\) | −6.94147 | −0.232028 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.149574 | 0.00499412 | ||||||||
\(898\) | 40.4510 | − | 0.225910i | 1.34987 | − | 0.00753872i | ||||
\(899\) | −2.77773 | − | 10.3666i | −0.0926425 | − | 0.345747i | ||||
\(900\) | −17.1554 | + | 0.191624i | −0.571847 | + | 0.00638748i | ||||
\(901\) | 0.642919 | − | 2.39941i | 0.0214187 | − | 0.0799358i | ||||
\(902\) | 2.60911 | + | 9.52426i | 0.0868739 | + | 0.317123i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.19083 | − | 0.120488i | 0.239164 | − | 0.00400736i | ||||
\(905\) | −24.3247 | + | 14.0439i | −0.808581 | + | 0.466835i | ||||
\(906\) | 12.2139 | − | 46.6230i | 0.405781 | − | 1.54895i | ||||
\(907\) | 14.8478 | − | 3.97846i | 0.493013 | − | 0.132102i | −0.00374236 | − | 0.999993i | \(-0.501191\pi\) |
0.496756 | + | 0.867891i | \(0.334525\pi\) | |||||||
\(908\) | −1.21701 | − | 4.34714i | −0.0403880 | − | 0.144265i | ||||
\(909\) | 18.9780 | − | 18.9780i | 0.629460 | − | 0.629460i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.1727 | 1.79482 | 0.897411 | − | 0.441196i | \(-0.145446\pi\) | ||||
0.897411 | + | 0.441196i | \(0.145446\pi\) | |||||||
\(912\) | −1.35301 | − | 60.5574i | −0.0448027 | − | 2.00526i | ||||
\(913\) | −9.31768 | + | 16.1387i | −0.308370 | + | 0.534113i | ||||
\(914\) | 40.0014 | − | 23.3937i | 1.32313 | − | 0.773793i | ||||
\(915\) | 56.2626 | + | 15.0755i | 1.85999 | + | 0.498382i | ||||
\(916\) | 6.88815 | − | 26.9055i | 0.227591 | − | 0.888982i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 51.1527 | − | 14.0130i | 1.68829 | − | 0.462497i | ||||
\(919\) | −24.5003 | + | 14.1453i | −0.808191 | + | 0.466609i | −0.846327 | − | 0.532663i | \(-0.821191\pi\) |
0.0381361 | + | 0.999273i | \(0.487858\pi\) | |||||||
\(920\) | −7.44119 | − | 26.0191i | −0.245329 | − | 0.857826i | ||||
\(921\) | 47.8218 | + | 27.6099i | 1.57578 | + | 0.909778i | ||||
\(922\) | 24.3174 | − | 24.5906i | 0.800852 | − | 0.809847i | ||||
\(923\) | −0.0460892 | − | 0.0460892i | −0.00151705 | − | 0.00151705i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.73487 | − | 7.73487i | 0.254321 | − | 0.254321i | ||||
\(926\) | −2.35867 | + | 0.0131727i | −0.0775109 | + | 0.000432881i | ||||
\(927\) | −7.30680 | + | 12.6558i | −0.239987 | + | 0.415669i | ||||
\(928\) | 7.99408 | − | 8.45347i | 0.262419 | − | 0.277499i | ||||
\(929\) | −8.48566 | − | 14.6976i | −0.278406 | − | 0.482212i | 0.692583 | − | 0.721338i | \(-0.256473\pi\) |
−0.970989 | + | 0.239126i | \(0.923139\pi\) | |||||||
\(930\) | 22.3026 | − | 39.1323i | 0.731331 | − | 1.28320i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.66998 | − | 2.17387i | 0.120214 | − | 0.0712076i | ||||
\(933\) | 28.4826 | − | 106.298i | 0.932477 | − | 3.48005i | ||||
\(934\) | 4.06842 | + | 1.06581i | 0.133123 | + | 0.0348745i | ||||
\(935\) | 5.92506 | + | 3.42084i | 0.193770 | + | 0.111873i | ||||
\(936\) | −0.0456545 | + | 0.182566i | −0.00149226 | + | 0.00596737i | ||||
\(937\) | 47.8526i | 1.56328i | 0.623732 | + | 0.781639i | \(0.285616\pi\) | ||||
−0.623732 | + | 0.781639i | \(0.714384\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.5669 | − | 17.5669i | −0.573274 | − | 0.573274i | ||||
\(940\) | 5.95183 | − | 1.66626i | 0.194127 | − | 0.0543473i | ||||
\(941\) | −8.56722 | − | 31.9733i | −0.279283 | − | 1.04230i | −0.952916 | − | 0.303234i | \(-0.901934\pi\) |
0.673633 | − | 0.739066i | \(-0.264733\pi\) | |||||||
\(942\) | 1.68629 | − | 0.986180i | 0.0549424 | − | 0.0321315i | ||||
\(943\) | 14.8716 | + | 25.7583i | 0.484286 | + | 0.838807i | ||||
\(944\) | 28.8254 | − | 8.41818i | 0.938187 | − | 0.273988i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.4411 | + | 8.23037i | 0.469520 | + | 0.267593i | ||||
\(947\) | −25.7374 | − | 6.89633i | −0.836355 | − | 0.224101i | −0.184871 | − | 0.982763i | \(-0.559187\pi\) |
−0.651484 | + | 0.758662i | \(0.725853\pi\) | |||||||
\(948\) | −24.7604 | + | 25.3198i | −0.804181 | + | 0.822349i | ||||
\(949\) | −0.0368995 | + | 0.00988718i | −0.00119781 | + | 0.000320952i | ||||
\(950\) | −6.00363 | − | 5.93695i | −0.194784 | − | 0.192620i | ||||
\(951\) | 21.9166i | 0.710693i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.1790i | 0.880415i | 0.897896 | + | 0.440207i | \(0.145095\pi\) | ||||
−0.897896 | + | 0.440207i | \(0.854905\pi\) | |||||||
\(954\) | −5.60493 | + | 5.66789i | −0.181466 | + | 0.183505i | ||||
\(955\) | −30.0107 | + | 8.04134i | −0.971124 | + | 0.260212i | ||||
\(956\) | −35.1865 | + | 0.393029i | −1.13801 | + | 0.0127115i | ||||
\(957\) | −7.24643 | − | 1.94168i | −0.234244 | − | 0.0627655i | ||||
\(958\) | −5.48663 | + | 9.62688i | −0.177265 | + | 0.311030i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 48.8013 | − | 1.63586i | 1.57506 | − | 0.0527973i | ||||
\(961\) | 1.88566 | + | 3.26606i | 0.0608278 | + | 0.105357i | ||||
\(962\) | −0.0605726 | − | 0.103575i | −0.00195294 | − | 0.00333938i | ||||
\(963\) | −26.9357 | − | 100.526i | −0.867992 | − | 3.23939i | ||||
\(964\) | −8.24534 | + | 14.6570i | −0.265565 | + | 0.472071i | ||||
\(965\) | −9.84822 | − | 9.84822i | −0.317025 | − | 0.317025i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 53.5349i | − | 1.72157i | −0.508971 | − | 0.860784i | \(-0.669974\pi\) | ||
0.508971 | − | 0.860784i | \(-0.330026\pi\) | |||||||
\(968\) | 23.4241 | − | 14.0523i | 0.752879 | − | 0.451659i | ||||
\(969\) | 39.9436 | + | 23.0615i | 1.28317 | + | 0.740841i | ||||
\(970\) | −0.271450 | + | 1.03618i | −0.00871573 | + | 0.0332696i | ||||
\(971\) | 3.64148 | − | 13.5902i | 0.116861 | − | 0.436129i | −0.882559 | − | 0.470202i | \(-0.844181\pi\) |
0.999419 | + | 0.0340726i | \(0.0108477\pi\) | |||||||
\(972\) | −38.4100 | − | 9.83346i | −1.23200 | − | 0.315408i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20.2709 | + | 11.5530i | 0.649522 | + | 0.370181i | ||||
\(975\) | 0.0188095 | + | 0.0325790i | 0.000602386 | + | 0.00104336i | ||||
\(976\) | 37.0833 | + | 9.05370i | 1.18701 | + | 0.289802i | ||||
\(977\) | −21.9868 | + | 38.0823i | −0.703421 | + | 1.21836i | 0.263837 | + | 0.964567i | \(0.415012\pi\) |
−0.967258 | + | 0.253794i | \(0.918322\pi\) | |||||||
\(978\) | 0.335685 | + | 60.1071i | 0.0107340 | + | 1.92201i | ||||
\(979\) | 3.39980 | − | 3.39980i | 0.108658 | − | 0.108658i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.7481 | + | 16.7481i | 0.534727 | + | 0.534727i | ||||
\(982\) | 19.1424 | + | 18.9298i | 0.610860 | + | 0.604075i | ||||
\(983\) | −25.0685 | − | 14.4733i | −0.799561 | − | 0.461627i | 0.0437566 | − | 0.999042i | \(-0.486067\pi\) |
−0.843318 | + | 0.537415i | \(0.819401\pi\) | |||||||
\(984\) | −51.5973 | + | 14.7563i | −1.64486 | + | 0.470412i | ||||
\(985\) | −33.0074 | + | 19.0568i | −1.05170 | + | 0.607200i | ||||
\(986\) | 2.34069 | + | 8.54443i | 0.0745429 | + | 0.272110i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.0796847 | + | 0.0472005i | −0.00253511 | + | 0.00150165i | ||||
\(989\) | 48.3576 | + | 12.9574i | 1.53768 | + | 0.412021i | ||||
\(990\) | −11.0833 | − | 18.9517i | −0.352252 | − | 0.602324i | ||||
\(991\) | 10.8966 | − | 18.8735i | 0.346143 | − | 0.599537i | −0.639418 | − | 0.768860i | \(-0.720825\pi\) |
0.985561 | + | 0.169322i | \(0.0541579\pi\) | |||||||
\(992\) | 14.0396 | − | 25.9655i | 0.445757 | − | 0.824406i | ||||
\(993\) | 6.58458 | 0.208955 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 37.7572 | − | 37.7572i | 1.19698 | − | 1.19698i | ||||
\(996\) | −88.2647 | − | 49.6535i | −2.79677 | − | 1.57333i | ||||
\(997\) | −6.84507 | + | 1.83413i | −0.216785 | + | 0.0580875i | −0.365577 | − | 0.930781i | \(-0.619128\pi\) |
0.148792 | + | 0.988869i | \(0.452462\pi\) | |||||||
\(998\) | −19.1116 | − | 5.00672i | −0.604968 | − | 0.158485i | ||||
\(999\) | 93.9759 | − | 54.2570i | 2.97327 | − | 1.71662i |
(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 | 784.2.x.o.165.1 | 48 | ||
7.2 | even | 3 | inner | 784.2.x.o.373.9 | 48 | ||
7.3 | odd | 6 | 784.2.m.j.197.7 | 24 | |||
7.4 | even | 3 | 784.2.m.k.197.7 | 24 | |||
7.5 | odd | 6 | 112.2.w.c.37.9 | ✓ | 48 | ||
7.6 | odd | 2 | 112.2.w.c.53.1 | yes | 48 | ||
16.13 | even | 4 | inner | 784.2.x.o.557.9 | 48 | ||
28.19 | even | 6 | 448.2.ba.c.177.12 | 48 | |||
28.27 | even | 2 | 448.2.ba.c.305.1 | 48 | |||
56.5 | odd | 6 | 896.2.ba.f.737.12 | 48 | |||
56.13 | odd | 2 | 896.2.ba.f.865.1 | 48 | |||
56.19 | even | 6 | 896.2.ba.e.737.1 | 48 | |||
56.27 | even | 2 | 896.2.ba.e.865.12 | 48 | |||
112.5 | odd | 12 | 896.2.ba.f.289.1 | 48 | |||
112.13 | odd | 4 | 112.2.w.c.109.9 | yes | 48 | ||
112.19 | even | 12 | 448.2.ba.c.401.1 | 48 | |||
112.27 | even | 4 | 896.2.ba.e.417.1 | 48 | |||
112.45 | odd | 12 | 784.2.m.j.589.7 | 24 | |||
112.61 | odd | 12 | 112.2.w.c.93.1 | yes | 48 | ||
112.69 | odd | 4 | 896.2.ba.f.417.12 | 48 | |||
112.75 | even | 12 | 896.2.ba.e.289.12 | 48 | |||
112.83 | even | 4 | 448.2.ba.c.81.12 | 48 | |||
112.93 | even | 12 | inner | 784.2.x.o.765.1 | 48 | ||
112.109 | even | 12 | 784.2.m.k.589.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.c.37.9 | ✓ | 48 | 7.5 | odd | 6 | ||
112.2.w.c.53.1 | yes | 48 | 7.6 | odd | 2 | ||
112.2.w.c.93.1 | yes | 48 | 112.61 | odd | 12 | ||
112.2.w.c.109.9 | yes | 48 | 112.13 | odd | 4 | ||
448.2.ba.c.81.12 | 48 | 112.83 | even | 4 | |||
448.2.ba.c.177.12 | 48 | 28.19 | even | 6 | |||
448.2.ba.c.305.1 | 48 | 28.27 | even | 2 | |||
448.2.ba.c.401.1 | 48 | 112.19 | even | 12 | |||
784.2.m.j.197.7 | 24 | 7.3 | odd | 6 | |||
784.2.m.j.589.7 | 24 | 112.45 | odd | 12 | |||
784.2.m.k.197.7 | 24 | 7.4 | even | 3 | |||
784.2.m.k.589.7 | 24 | 112.109 | even | 12 | |||
784.2.x.o.165.1 | 48 | 1.1 | even | 1 | trivial | ||
784.2.x.o.373.9 | 48 | 7.2 | even | 3 | inner | ||
784.2.x.o.557.9 | 48 | 16.13 | even | 4 | inner | ||
784.2.x.o.765.1 | 48 | 112.93 | even | 12 | inner | ||
896.2.ba.e.289.12 | 48 | 112.75 | even | 12 | |||
896.2.ba.e.417.1 | 48 | 112.27 | even | 4 | |||
896.2.ba.e.737.1 | 48 | 56.19 | even | 6 | |||
896.2.ba.e.865.12 | 48 | 56.27 | even | 2 | |||
896.2.ba.f.289.1 | 48 | 112.5 | odd | 12 | |||
896.2.ba.f.417.12 | 48 | 112.69 | odd | 4 | |||
896.2.ba.f.737.12 | 48 | 56.5 | odd | 6 | |||
896.2.ba.f.865.1 | 48 | 56.13 | odd | 2 |