Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(82,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.f (of order \(5\), 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: | \(7.11467082010\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 487.4 | ||
Character | \(\chi\) | \(=\) | 891.487 |
Dual form | 891.2.f.e.730.4 |
$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.537447 | + | 0.390478i | −0.380032 | + | 0.276109i | −0.761359 | − | 0.648331i | \(-0.775467\pi\) |
0.381327 | + | 0.924440i | \(0.375467\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.481658 | + | 1.48239i | −0.240829 | + | 0.741196i | ||||
\(5\) | 0.903367 | + | 0.656335i | 0.403998 | + | 0.293522i | 0.771168 | − | 0.636632i | \(-0.219673\pi\) |
−0.367169 | + | 0.930154i | \(0.619673\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.20657 | + | 3.71344i | −0.456041 | + | 1.40355i | 0.413869 | + | 0.910337i | \(0.364177\pi\) |
−0.869909 | + | 0.493212i | \(0.835823\pi\) | |||||||
\(8\) | −0.730548 | − | 2.24840i | −0.258288 | − | 0.794928i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.741796 | −0.234576 | ||||||||
\(11\) | 1.17816 | + | 3.10031i | 0.355230 | + | 0.934779i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.16655 | + | 1.57409i | −0.600893 | + | 0.436574i | −0.846196 | − | 0.532872i | \(-0.821113\pi\) |
0.245303 | + | 0.969447i | \(0.421113\pi\) | |||||||
\(14\) | −0.801549 | − | 2.46691i | −0.214223 | − | 0.659311i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.25142 | − | 0.909207i | −0.312854 | − | 0.227302i | ||||
\(17\) | 4.48727 | + | 3.26019i | 1.08832 | + | 0.790713i | 0.979115 | − | 0.203306i | \(-0.0651688\pi\) |
0.109207 | + | 0.994019i | \(0.465169\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.58598 | − | 4.88115i | −0.363849 | − | 1.11981i | −0.950699 | − | 0.310116i | \(-0.899632\pi\) |
0.586850 | − | 0.809696i | \(-0.300368\pi\) | |||||||
\(20\) | −1.40806 | + | 1.02301i | −0.314852 | + | 0.228753i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.84380 | − | 1.20620i | −0.393100 | − | 0.257164i | ||||
\(23\) | −2.11438 | −0.440878 | −0.220439 | − | 0.975401i | \(-0.570749\pi\) | ||||
−0.220439 | + | 0.975401i | \(0.570749\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.15979 | − | 3.56946i | −0.231958 | − | 0.713892i | ||||
\(26\) | 0.549758 | − | 1.69198i | 0.107816 | − | 0.331825i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.92362 | − | 3.57722i | −0.930476 | − | 0.676030i | ||||
\(29\) | −0.334678 | + | 1.03003i | −0.0621481 | + | 0.191272i | −0.977310 | − | 0.211814i | \(-0.932063\pi\) |
0.915162 | + | 0.403087i | \(0.132063\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.348009 | − | 0.252843i | 0.0625042 | − | 0.0454120i | −0.556094 | − | 0.831119i | \(-0.687701\pi\) |
0.618599 | + | 0.785707i | \(0.287701\pi\) | |||||||
\(32\) | 5.75580 | 1.01749 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.68470 | −0.631921 | ||||||||
\(35\) | −3.52724 | + | 2.56269i | −0.596212 | + | 0.433173i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.69024 | + | 8.27970i | −0.442273 | + | 1.36118i | 0.443175 | + | 0.896435i | \(0.353852\pi\) |
−0.885447 | + | 0.464740i | \(0.846148\pi\) | |||||||
\(38\) | 2.75836 | + | 2.00407i | 0.447465 | + | 0.325102i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.815747 | − | 2.51061i | 0.128981 | − | 0.396962i | ||||
\(41\) | 0.902044 | + | 2.77621i | 0.140876 | + | 0.433571i | 0.996458 | − | 0.0840968i | \(-0.0268005\pi\) |
−0.855582 | + | 0.517667i | \(0.826800\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.23257 | −0.340463 | −0.170232 | − | 0.985404i | \(-0.554452\pi\) | ||||
−0.170232 | + | 0.985404i | \(0.554452\pi\) | |||||||
\(44\) | −5.16335 | + | 0.253209i | −0.778404 | + | 0.0381728i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.13637 | − | 0.825618i | 0.167548 | − | 0.121731i | ||||
\(47\) | −3.96638 | − | 12.2073i | −0.578556 | − | 1.78061i | −0.623739 | − | 0.781633i | \(-0.714387\pi\) |
0.0451833 | − | 0.998979i | \(-0.485613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.67071 | − | 4.84655i | −0.952958 | − | 0.692365i | ||||
\(50\) | 2.01712 | + | 1.46552i | 0.285264 | + | 0.207256i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.28988 | − | 3.96985i | −0.178875 | − | 0.550519i | ||||
\(53\) | 4.56381 | − | 3.31581i | 0.626888 | − | 0.455461i | −0.228433 | − | 0.973560i | \(-0.573360\pi\) |
0.855321 | + | 0.518099i | \(0.173360\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.970527 | + | 3.57399i | −0.130866 | + | 0.481917i | ||||
\(56\) | 9.23074 | 1.23351 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.222333 | − | 0.684272i | −0.0291938 | − | 0.0898493i | ||||
\(59\) | 0.734030 | − | 2.25911i | 0.0955625 | − | 0.294111i | −0.891837 | − | 0.452356i | \(-0.850584\pi\) |
0.987400 | + | 0.158245i | \(0.0505836\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.30439 | + | 2.40078i | 0.423084 | + | 0.307389i | 0.778878 | − | 0.627176i | \(-0.215789\pi\) |
−0.355793 | + | 0.934565i | \(0.615789\pi\) | |||||||
\(62\) | −0.0883065 | + | 0.271779i | −0.0112149 | + | 0.0345160i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.590604 | + | 0.429099i | −0.0738255 | + | 0.0536374i | ||||
\(65\) | −2.99032 | −0.370904 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.75169 | −1.19136 | −0.595679 | − | 0.803223i | \(-0.703117\pi\) | ||||
−0.595679 | + | 0.803223i | \(0.703117\pi\) | |||||||
\(68\) | −6.99421 | + | 5.08159i | −0.848172 | + | 0.616233i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.895028 | − | 2.75461i | 0.106976 | − | 0.329239i | ||||
\(71\) | 5.11062 | + | 3.71308i | 0.606519 | + | 0.440662i | 0.848187 | − | 0.529697i | \(-0.177694\pi\) |
−0.241668 | + | 0.970359i | \(0.577694\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.60705 | + | 11.1014i | −0.422174 | + | 1.29932i | 0.483501 | + | 0.875344i | \(0.339365\pi\) |
−0.905675 | + | 0.423973i | \(0.860635\pi\) | |||||||
\(74\) | −1.78718 | − | 5.50038i | −0.207756 | − | 0.639406i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.99967 | 0.917625 | ||||||||
\(77\) | −12.9344 | + | 0.634298i | −1.47401 | + | 0.0722850i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.65248 | + | 2.65368i | −0.410936 | + | 0.298562i | −0.773980 | − | 0.633209i | \(-0.781737\pi\) |
0.363045 | + | 0.931772i | \(0.381737\pi\) | |||||||
\(80\) | −0.533744 | − | 1.64269i | −0.0596744 | − | 0.183659i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.56885 | − | 1.13983i | −0.173250 | − | 0.125874i | ||||
\(83\) | 0.389949 | + | 0.283315i | 0.0428025 | + | 0.0310978i | 0.608981 | − | 0.793185i | \(-0.291579\pi\) |
−0.566178 | + | 0.824283i | \(0.691579\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.91387 | + | 5.89030i | 0.207589 | + | 0.638893i | ||||
\(86\) | 1.19989 | − | 0.871768i | 0.129387 | − | 0.0940052i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.11002 | − | 4.91390i | 0.651330 | − | 0.523824i | ||||
\(89\) | −16.0830 | −1.70480 | −0.852399 | − | 0.522891i | \(-0.824853\pi\) | ||||
−0.852399 | + | 0.522891i | \(0.824853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23120 | − | 9.94461i | −0.338722 | − | 1.04248i | ||||
\(92\) | 1.01841 | − | 3.13433i | 0.106176 | − | 0.326777i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.89838 | + | 5.01197i | 0.711513 | + | 0.516945i | ||||
\(95\) | 1.77094 | − | 5.45040i | 0.181695 | − | 0.559199i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.48480 | + | 4.71148i | −0.658432 | + | 0.478379i | −0.866133 | − | 0.499814i | \(-0.833402\pi\) |
0.207701 | + | 0.978192i | \(0.433402\pi\) | |||||||
\(98\) | 5.47762 | 0.553323 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.84996 | 0.584996 | ||||||||
\(101\) | 1.42493 | − | 1.03527i | 0.141786 | − | 0.103014i | −0.514631 | − | 0.857412i | \(-0.672071\pi\) |
0.656417 | + | 0.754398i | \(0.272071\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.830534 | − | 2.55612i | 0.0818350 | − | 0.251862i | −0.901765 | − | 0.432227i | \(-0.857728\pi\) |
0.983600 | + | 0.180365i | \(0.0577279\pi\) | |||||||
\(104\) | 5.12195 | + | 3.72131i | 0.502248 | + | 0.364905i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.15806 | + | 3.56414i | −0.112481 | + | 0.346179i | ||||
\(107\) | 3.17558 | + | 9.77342i | 0.306995 | + | 0.944833i | 0.978925 | + | 0.204219i | \(0.0654653\pi\) |
−0.671931 | + | 0.740614i | \(0.734535\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.36284 | 0.226319 | 0.113160 | − | 0.993577i | \(-0.463903\pi\) | ||||
0.113160 | + | 0.993577i | \(0.463903\pi\) | |||||||
\(110\) | −0.873957 | − | 2.29980i | −0.0833285 | − | 0.219277i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.88620 | − | 3.55004i | 0.461703 | − | 0.335447i | ||||
\(113\) | −0.473548 | − | 1.45743i | −0.0445476 | − | 0.137103i | 0.926309 | − | 0.376765i | \(-0.122964\pi\) |
−0.970857 | + | 0.239661i | \(0.922964\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.91006 | − | 1.38774i | −0.178114 | − | 0.129407i | ||||
\(116\) | −1.36571 | − | 0.992247i | −0.126803 | − | 0.0921279i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.487631 | + | 1.50077i | 0.0448901 | + | 0.138157i | ||||
\(119\) | −17.5207 | + | 12.7296i | −1.60612 | + | 1.16692i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.22386 | + | 7.30535i | −0.747624 | + | 0.664123i | ||||
\(122\) | −2.71339 | −0.245658 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.207191 | + | 0.637669i | 0.0186063 | + | 0.0572644i | ||||
\(125\) | 3.02032 | − | 9.29560i | 0.270146 | − | 0.831424i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.19006 | + | 4.49734i | 0.549279 | + | 0.399074i | 0.827519 | − | 0.561437i | \(-0.189751\pi\) |
−0.278241 | + | 0.960511i | \(0.589751\pi\) | |||||||
\(128\) | −3.40742 | + | 10.4869i | −0.301176 | + | 0.926924i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.60714 | − | 1.16765i | 0.140955 | − | 0.102410i | ||||
\(131\) | 5.35912 | 0.468229 | 0.234114 | − | 0.972209i | \(-0.424781\pi\) | ||||
0.234114 | + | 0.972209i | \(0.424781\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.0394 | 1.73764 | ||||||||
\(134\) | 5.24101 | − | 3.80782i | 0.452754 | − | 0.328945i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.05203 | − | 12.4709i | 0.347459 | − | 1.06937i | ||||
\(137\) | 13.5358 | + | 9.83435i | 1.15644 | + | 0.840205i | 0.989324 | − | 0.145731i | \(-0.0465535\pi\) |
0.167119 | + | 0.985937i | \(0.446554\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.24593 | − | 13.0676i | 0.360135 | − | 1.10838i | −0.592837 | − | 0.805323i | \(-0.701992\pi\) |
0.952972 | − | 0.303059i | \(-0.0980079\pi\) | |||||||
\(140\) | −2.09998 | − | 6.46308i | −0.177481 | − | 0.546230i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.19656 | −0.352168 | ||||||||
\(143\) | −7.43273 | − | 4.86244i | −0.621556 | − | 0.406618i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.978384 | + | 0.710837i | −0.0812503 | + | 0.0590318i | ||||
\(146\) | −2.39624 | − | 7.37487i | −0.198314 | − | 0.610348i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.9780 | − | 7.97597i | −0.902385 | − | 0.655621i | ||||
\(149\) | 4.49786 | + | 3.26788i | 0.368479 | + | 0.267716i | 0.756580 | − | 0.653901i | \(-0.226869\pi\) |
−0.388101 | + | 0.921617i | \(0.626869\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.0506502 | − | 0.155885i | −0.00412186 | − | 0.0126858i | 0.948974 | − | 0.315353i | \(-0.102123\pi\) |
−0.953096 | + | 0.302667i | \(0.902123\pi\) | |||||||
\(152\) | −9.81611 | + | 7.13182i | −0.796192 | + | 0.578467i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.70385 | − | 5.39148i | 0.540211 | − | 0.434458i | ||||
\(155\) | 0.480329 | 0.0385810 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.37099 | + | 22.6856i | 0.588269 | + | 1.81051i | 0.585727 | + | 0.810509i | \(0.300809\pi\) |
0.00254199 | + | 0.999997i | \(0.499191\pi\) | |||||||
\(158\) | 0.926808 | − | 2.85242i | 0.0737329 | − | 0.226926i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.19960 | + | 3.77773i | 0.411065 | + | 0.298656i | ||||
\(161\) | 2.55114 | − | 7.85161i | 0.201058 | − | 0.618794i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.39466 | − | 2.46636i | 0.265890 | − | 0.193180i | −0.446850 | − | 0.894609i | \(-0.647454\pi\) |
0.712740 | + | 0.701429i | \(0.247454\pi\) | |||||||
\(164\) | −4.54990 | −0.355288 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.320205 | −0.0248527 | ||||||||
\(167\) | 12.8151 | − | 9.31075i | 0.991666 | − | 0.720488i | 0.0313807 | − | 0.999508i | \(-0.490010\pi\) |
0.960285 | + | 0.279020i | \(0.0900096\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.80104 | + | 5.54304i | −0.138542 | + | 0.426387i | ||||
\(170\) | −3.32864 | − | 2.41840i | −0.255295 | − | 0.185482i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.07533 | − | 3.30954i | 0.0819935 | − | 0.252350i | ||||
\(173\) | 0.804337 | + | 2.47549i | 0.0611526 | + | 0.188208i | 0.976966 | − | 0.213396i | \(-0.0684526\pi\) |
−0.915813 | + | 0.401605i | \(0.868453\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.6543 | 1.10776 | ||||||||
\(176\) | 1.34445 | − | 4.95097i | 0.101342 | − | 0.373194i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.64378 | − | 6.28007i | 0.647878 | − | 0.470711i | ||||
\(179\) | −2.34483 | − | 7.21663i | −0.175261 | − | 0.539396i | 0.824385 | − | 0.566030i | \(-0.191521\pi\) |
−0.999645 | + | 0.0266334i | \(0.991521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.94179 | + | 1.41080i | 0.144332 | + | 0.104864i | 0.657608 | − | 0.753360i | \(-0.271568\pi\) |
−0.513276 | + | 0.858224i | \(0.671568\pi\) | |||||||
\(182\) | 5.61975 | + | 4.08298i | 0.416563 | + | 0.302651i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.54465 | + | 4.75396i | 0.113873 | + | 0.350466i | ||||
\(185\) | −7.86453 | + | 5.71392i | −0.578212 | + | 0.420095i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.82087 | + | 17.7530i | −0.352537 | + | 1.29823i | ||||
\(188\) | 20.0064 | 1.45911 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.17647 | + | 3.62081i | 0.0853504 | + | 0.262681i | ||||
\(191\) | 5.10442 | − | 15.7098i | 0.369343 | − | 1.13672i | −0.577874 | − | 0.816126i | \(-0.696118\pi\) |
0.947217 | − | 0.320594i | \(-0.103882\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.58132 | + | 4.78161i | 0.473734 | + | 0.344188i | 0.798895 | − | 0.601471i | \(-0.205418\pi\) |
−0.325161 | + | 0.945659i | \(0.605418\pi\) | |||||||
\(194\) | 1.64550 | − | 5.06434i | 0.118140 | − | 0.363598i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.3975 | − | 7.55422i | 0.742678 | − | 0.539587i | ||||
\(197\) | 22.9072 | 1.63207 | 0.816035 | − | 0.578003i | \(-0.196168\pi\) | ||||
0.816035 | + | 0.578003i | \(0.196168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.27177 | 0.657259 | 0.328629 | − | 0.944459i | \(-0.393413\pi\) | ||||
0.328629 | + | 0.944459i | \(0.393413\pi\) | |||||||
\(200\) | −7.17828 | + | 5.21532i | −0.507581 | + | 0.368779i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.361574 | + | 1.11281i | −0.0254402 | + | 0.0782970i | ||||
\(203\) | −3.42115 | − | 2.48561i | −0.240118 | − | 0.174456i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.00724 | + | 3.09998i | −0.0703489 | + | 0.216512i | ||||
\(206\) | 0.551741 | + | 1.69808i | 0.0384416 | + | 0.118311i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.14243 | 0.287226 | ||||||||
\(209\) | 13.2645 | − | 10.6678i | 0.917527 | − | 0.737909i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.40643 | + | 2.47491i | −0.234508 | + | 0.170380i | −0.698833 | − | 0.715285i | \(-0.746297\pi\) |
0.464325 | + | 0.885665i | \(0.346297\pi\) | |||||||
\(212\) | 2.71712 | + | 8.36244i | 0.186613 | + | 0.574335i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.52301 | − | 4.01270i | −0.377545 | − | 0.274303i | ||||
\(215\) | −2.01683 | − | 1.46531i | −0.137547 | − | 0.0999334i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.519021 | + | 1.59738i | 0.0352335 | + | 0.108437i | ||||
\(218\) | −1.26990 | + | 0.922637i | −0.0860086 | + | 0.0624889i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.83059 | − | 3.16014i | −0.325678 | − | 0.213057i | ||||
\(221\) | −14.8537 | −0.999170 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.11957 | − | 6.52335i | −0.141937 | − | 0.436836i | 0.854668 | − | 0.519175i | \(-0.173761\pi\) |
−0.996604 | + | 0.0823393i | \(0.973761\pi\) | |||||||
\(224\) | −6.94477 | + | 21.3738i | −0.464017 | + | 1.42810i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.823601 | + | 0.598381i | 0.0547851 | + | 0.0398037i | ||||
\(227\) | −8.69262 | + | 26.7531i | −0.576950 | + | 1.77567i | 0.0524933 | + | 0.998621i | \(0.483283\pi\) |
−0.629443 | + | 0.777047i | \(0.716717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3543 | − | 8.24939i | 0.750314 | − | 0.545135i | −0.145610 | − | 0.989342i | \(-0.546515\pi\) |
0.895924 | + | 0.444207i | \(0.146515\pi\) | |||||||
\(230\) | 1.56844 | 0.103420 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.56042 | 0.168100 | ||||||||
\(233\) | −11.7385 | + | 8.52854i | −0.769017 | + | 0.558723i | −0.901663 | − | 0.432440i | \(-0.857653\pi\) |
0.132646 | + | 0.991163i | \(0.457653\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.42895 | − | 13.6309i | 0.288913 | − | 0.889182i | ||||
\(236\) | 2.99534 | + | 2.17624i | 0.194980 | + | 0.141661i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.44585 | − | 13.6829i | 0.288181 | − | 0.886931i | ||||
\(239\) | 7.77120 | + | 23.9173i | 0.502677 | + | 1.54708i | 0.804641 | + | 0.593762i | \(0.202358\pi\) |
−0.301964 | + | 0.953319i | \(0.597642\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.7422 | 1.14288 | 0.571438 | − | 0.820645i | \(-0.306386\pi\) | ||||
0.571438 | + | 0.820645i | \(0.306386\pi\) | |||||||
\(242\) | 1.56731 | − | 7.13747i | 0.100750 | − | 0.458814i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.15048 | + | 3.74205i | −0.329726 | + | 0.239560i | ||||
\(245\) | −2.84514 | − | 8.75643i | −0.181769 | − | 0.559428i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.1195 | + | 8.07877i | 0.707515 | + | 0.514040i | ||||
\(248\) | −0.822729 | − | 0.597747i | −0.0522433 | − | 0.0379570i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.00646 | + | 6.17526i | 0.126900 | + | 0.390558i | ||||
\(251\) | −17.6993 | + | 12.8593i | −1.11717 | + | 0.811670i | −0.983777 | − | 0.179394i | \(-0.942586\pi\) |
−0.133390 | + | 0.991064i | \(0.542586\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.49108 | − | 6.55523i | −0.156613 | − | 0.412124i | ||||
\(254\) | −5.08294 | −0.318932 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.71480 | − | 8.35529i | −0.169675 | − | 0.522205i | ||||
\(257\) | −1.59568 | + | 4.91099i | −0.0995356 | + | 0.306339i | −0.988409 | − | 0.151814i | \(-0.951489\pi\) |
0.888874 | + | 0.458153i | \(0.151489\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.5002 | − | 19.9801i | −1.70878 | − | 1.24150i | ||||
\(260\) | 1.44031 | − | 4.43283i | 0.0893244 | − | 0.274912i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.88024 | + | 2.09262i | −0.177942 | + | 0.129282i | ||||
\(263\) | 27.8981 | 1.72027 | 0.860135 | − | 0.510066i | \(-0.170379\pi\) | ||||
0.860135 | + | 0.510066i | \(0.170379\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.29908 | 0.386949 | ||||||||
\(266\) | −10.7701 | + | 7.82496i | −0.660359 | + | 0.479779i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.69698 | − | 14.4558i | 0.286914 | − | 0.883029i | ||||
\(269\) | 2.44290 | + | 1.77487i | 0.148946 | + | 0.108216i | 0.659763 | − | 0.751474i | \(-0.270657\pi\) |
−0.510816 | + | 0.859690i | \(0.670657\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.84125 | + | 24.1329i | −0.476322 | + | 1.46597i | 0.367845 | + | 0.929887i | \(0.380096\pi\) |
−0.844167 | + | 0.536081i | \(0.819904\pi\) | |||||||
\(272\) | −2.65125 | − | 8.15971i | −0.160756 | − | 0.494755i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.1149 | −0.671474 | ||||||||
\(275\) | 9.70002 | − | 7.80111i | 0.584933 | − | 0.470425i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.54677 | − | 6.20959i | 0.513525 | − | 0.373098i | −0.300634 | − | 0.953740i | \(-0.597198\pi\) |
0.814159 | + | 0.580642i | \(0.197198\pi\) | |||||||
\(278\) | 2.82066 | + | 8.68109i | 0.169172 | + | 0.520657i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.33875 | + | 6.05845i | 0.498335 | + | 0.362062i | ||||
\(281\) | −18.2599 | − | 13.2666i | −1.08930 | − | 0.791420i | −0.110016 | − | 0.993930i | \(-0.535090\pi\) |
−0.979280 | + | 0.202510i | \(0.935090\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.81616 | − | 5.58958i | −0.107960 | − | 0.332266i | 0.882454 | − | 0.470399i | \(-0.155890\pi\) |
−0.990414 | + | 0.138133i | \(0.955890\pi\) | |||||||
\(284\) | −7.96581 | + | 5.78750i | −0.472684 | + | 0.343425i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.89337 | − | 0.289010i | 0.348482 | − | 0.0170895i | ||||
\(287\) | −11.3977 | −0.672782 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.25344 | + | 13.0907i | 0.250202 | + | 0.770044i | ||||
\(290\) | 0.248263 | − | 0.764074i | 0.0145785 | − | 0.0448680i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.7192 | − | 10.6941i | −0.861376 | − | 0.625827i | ||||
\(293\) | −2.19220 | + | 6.74690i | −0.128070 | + | 0.394158i | −0.994448 | − | 0.105230i | \(-0.966442\pi\) |
0.866378 | + | 0.499389i | \(0.166442\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.14583 | − | 1.55904i | 0.124935 | − | 0.0907707i | ||||
\(296\) | 20.5814 | 1.19627 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.69339 | −0.213953 | ||||||||
\(299\) | 4.58091 | − | 3.32822i | 0.264921 | − | 0.192476i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.69375 | − | 8.29051i | 0.155265 | − | 0.477857i | ||||
\(302\) | 0.0880915 | + | 0.0640022i | 0.00506910 | + | 0.00368292i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.45325 | + | 7.55033i | −0.140704 | + | 0.433041i | ||||
\(305\) | 1.40936 | + | 4.33757i | 0.0806999 | + | 0.248369i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.5370 | −1.05796 | −0.528981 | − | 0.848633i | \(-0.677426\pi\) | ||||
−0.528981 | + | 0.848633i | \(0.677426\pi\) | |||||||
\(308\) | 5.28966 | − | 19.4793i | 0.301406 | − | 1.10994i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.258151 | + | 0.187558i | −0.0146620 | + | 0.0106526i | ||||
\(311\) | −2.12487 | − | 6.53969i | −0.120491 | − | 0.370832i | 0.872562 | − | 0.488503i | \(-0.162457\pi\) |
−0.993053 | + | 0.117672i | \(0.962457\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.4890 | + | 14.8861i | 1.15811 | + | 0.841414i | 0.989537 | − | 0.144276i | \(-0.0460853\pi\) |
0.168569 | + | 0.985690i | \(0.446085\pi\) | |||||||
\(314\) | −12.8197 | − | 9.31407i | −0.723459 | − | 0.525624i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.17455 | − | 6.69256i | −0.122328 | − | 0.376486i | ||||
\(317\) | 8.88241 | − | 6.45345i | 0.498886 | − | 0.362462i | −0.309705 | − | 0.950833i | \(-0.600230\pi\) |
0.808591 | + | 0.588371i | \(0.200230\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.58773 | + | 0.175942i | −0.200874 | + | 0.00985083i | ||||
\(320\) | −0.815165 | −0.0455691 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.69478 | + | 5.21599i | 0.0944463 | + | 0.290676i | ||||
\(323\) | 8.79675 | − | 27.0736i | 0.489464 | − | 1.50642i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.13140 | + | 5.90780i | 0.451049 | + | 0.327706i | ||||
\(326\) | −0.861386 | + | 2.65107i | −0.0477078 | + | 0.146829i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.58302 | − | 4.05630i | 0.308271 | − | 0.223972i | ||||
\(329\) | 50.1166 | 2.76302 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.71025 | −0.203934 | −0.101967 | − | 0.994788i | \(-0.532514\pi\) | ||||
−0.101967 | + | 0.994788i | \(0.532514\pi\) | |||||||
\(332\) | −0.607805 | + | 0.441596i | −0.0333576 | + | 0.0242357i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.25182 | + | 10.0081i | −0.177931 | + | 0.547617i | ||||
\(335\) | −8.80935 | − | 6.40037i | −0.481306 | − | 0.349690i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.94885 | + | 30.6194i | −0.541948 | + | 1.66795i | 0.186189 | + | 0.982514i | \(0.440386\pi\) |
−0.728137 | + | 0.685432i | \(0.759614\pi\) | |||||||
\(338\) | −1.19647 | − | 3.68235i | −0.0650793 | − | 0.200294i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.65356 | −0.523538 | ||||||||
\(341\) | 1.19390 | + | 0.781045i | 0.0646535 | + | 0.0422960i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.93417 | − | 2.85834i | 0.212425 | − | 0.154336i | ||||
\(344\) | 1.63100 | + | 5.01970i | 0.0879375 | + | 0.270644i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.39891 | − | 1.01637i | −0.0752061 | − | 0.0546404i | ||||
\(347\) | −17.4121 | − | 12.6506i | −0.934728 | − | 0.679120i | 0.0124177 | − | 0.999923i | \(-0.496047\pi\) |
−0.947146 | + | 0.320803i | \(0.896047\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.19765 | − | 15.9967i | −0.278224 | − | 0.856285i | −0.988348 | − | 0.152209i | \(-0.951361\pi\) |
0.710124 | − | 0.704076i | \(-0.248639\pi\) | |||||||
\(350\) | −7.87593 | + | 5.72219i | −0.420986 | + | 0.305864i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.78127 | + | 17.8448i | 0.361443 | + | 0.951129i | ||||
\(353\) | −3.13085 | −0.166639 | −0.0833193 | − | 0.996523i | \(-0.526552\pi\) | ||||
−0.0833193 | + | 0.996523i | \(0.526552\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.17974 | + | 6.70855i | 0.115689 | + | 0.356053i | ||||
\(356\) | 7.74653 | − | 23.8414i | 0.410565 | − | 1.26359i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.07815 | + | 2.96295i | 0.215537 | + | 0.156597i | ||||
\(359\) | −2.62315 | + | 8.07323i | −0.138445 | + | 0.426089i | −0.996110 | − | 0.0881197i | \(-0.971914\pi\) |
0.857665 | + | 0.514208i | \(0.171914\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.93893 | + | 4.31489i | −0.312575 | + | 0.227099i | ||||
\(362\) | −1.59449 | −0.0838048 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.2981 | 0.854254 | ||||||||
\(365\) | −10.5447 | + | 7.66118i | −0.551935 | + | 0.401004i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.40258 | + | 10.4720i | −0.177613 | + | 0.546637i | −0.999743 | − | 0.0226630i | \(-0.992786\pi\) |
0.822130 | + | 0.569300i | \(0.192786\pi\) | |||||||
\(368\) | 2.64596 | + | 1.92241i | 0.137930 | + | 0.100212i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.99561 | − | 6.14185i | 0.103747 | − | 0.319300i | ||||
\(371\) | 6.80648 | + | 20.9482i | 0.353375 | + | 1.08758i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0068 | 0.569912 | 0.284956 | − | 0.958541i | \(-0.408021\pi\) | ||||
0.284956 | + | 0.958541i | \(0.408021\pi\) | |||||||
\(374\) | −4.34118 | − | 11.4237i | −0.224477 | − | 0.590706i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −24.5491 | + | 17.8360i | −1.26602 | + | 0.919820i | ||||
\(377\) | −0.896269 | − | 2.75843i | −0.0461602 | − | 0.142067i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.5384 | − | 14.9220i | −1.05499 | − | 0.766492i | −0.0818315 | − | 0.996646i | \(-0.526077\pi\) |
−0.973154 | + | 0.230154i | \(0.926077\pi\) | |||||||
\(380\) | 7.22664 | + | 5.25046i | 0.370719 | + | 0.269343i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.39097 | + | 10.4363i | 0.173497 | + | 0.533969i | ||||
\(383\) | −9.80103 | + | 7.12086i | −0.500809 | + | 0.363859i | −0.809326 | − | 0.587360i | \(-0.800167\pi\) |
0.308517 | + | 0.951219i | \(0.400167\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.1008 | − | 7.91626i | −0.616713 | − | 0.403450i | ||||
\(386\) | −5.40422 | −0.275068 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.86080 | − | 11.8823i | −0.196003 | − | 0.603234i | ||||
\(389\) | −4.43473 | + | 13.6487i | −0.224850 | + | 0.692016i | 0.773457 | + | 0.633849i | \(0.218526\pi\) |
−0.998307 | + | 0.0581676i | \(0.981474\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.48778 | − | 6.89328i | −0.479818 | − | 0.348608i | ||||
\(392\) | −6.02370 | + | 18.5390i | −0.304243 | + | 0.936362i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.3114 | + | 8.94475i | −0.620239 | + | 0.450630i | ||||
\(395\) | −5.04123 | −0.253652 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.03882 | −0.252891 | −0.126446 | − | 0.991974i | \(-0.540357\pi\) | ||||
−0.126446 | + | 0.991974i | \(0.540357\pi\) | |||||||
\(398\) | −4.98308 | + | 3.62042i | −0.249779 | + | 0.181475i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.79400 | + | 5.52136i | −0.0897000 | + | 0.276068i | ||||
\(401\) | −14.7243 | − | 10.6978i | −0.735294 | − | 0.534223i | 0.155940 | − | 0.987767i | \(-0.450159\pi\) |
−0.891234 | + | 0.453544i | \(0.850159\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.355980 | + | 1.09560i | −0.0177327 | + | 0.0545755i | ||||
\(404\) | 0.848352 | + | 2.61096i | 0.0422071 | + | 0.129900i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.80926 | 0.139421 | ||||||||
\(407\) | −28.8392 | + | 1.41427i | −1.42951 | + | 0.0701027i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.2925 | + | 9.65758i | −0.657273 | + | 0.477537i | −0.865741 | − | 0.500493i | \(-0.833152\pi\) |
0.208468 | + | 0.978029i | \(0.433152\pi\) | |||||||
\(410\) | −0.669133 | − | 2.05938i | −0.0330461 | − | 0.101705i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.38914 | + | 2.46235i | 0.166971 | + | 0.121311i | ||||
\(413\) | 7.50342 | + | 5.45155i | 0.369219 | + | 0.268253i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.166318 | + | 0.511874i | 0.00816423 | + | 0.0251269i | ||||
\(416\) | −12.4702 | + | 9.06015i | −0.611403 | + | 0.444211i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.96343 | + | 10.9129i | −0.144946 | + | 0.533767i | ||||
\(419\) | 17.4065 | 0.850362 | 0.425181 | − | 0.905108i | \(-0.360210\pi\) | ||||
0.425181 | + | 0.905108i | \(0.360210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.40561 | + | 4.32602i | 0.0685052 | + | 0.210837i | 0.979449 | − | 0.201694i | \(-0.0646447\pi\) |
−0.910943 | + | 0.412531i | \(0.864645\pi\) | |||||||
\(422\) | 0.864374 | − | 2.66027i | 0.0420771 | − | 0.129500i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.7893 | − | 7.83890i | −0.523976 | − | 0.380691i | ||||
\(425\) | 6.43284 | − | 19.7983i | 0.312039 | − | 0.960356i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.9021 | + | 9.37395i | −0.624378 | + | 0.453637i | ||||
\(428\) | −16.0176 | −0.774239 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.65611 | 0.0798647 | ||||||||
\(431\) | 10.1004 | − | 7.33838i | 0.486520 | − | 0.353477i | −0.317325 | − | 0.948317i | \(-0.602784\pi\) |
0.803844 | + | 0.594840i | \(0.202784\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.86451 | − | 27.2822i | 0.426001 | − | 1.31110i | −0.476031 | − | 0.879428i | \(-0.657925\pi\) |
0.902032 | − | 0.431668i | \(-0.142075\pi\) | |||||||
\(434\) | −0.902689 | − | 0.655842i | −0.0433304 | − | 0.0314814i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.13808 | + | 3.50266i | −0.0545042 | + | 0.167747i | ||||
\(437\) | 3.35336 | + | 10.3206i | 0.160413 | + | 0.493701i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.10807 | −0.196068 | −0.0980338 | − | 0.995183i | \(-0.531255\pi\) | ||||
−0.0980338 | + | 0.995183i | \(0.531255\pi\) | |||||||
\(440\) | 8.74476 | − | 0.428841i | 0.416890 | − | 0.0204442i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.98309 | − | 5.80005i | 0.379717 | − | 0.275880i | ||||
\(443\) | 6.56034 | + | 20.1906i | 0.311691 | + | 0.959287i | 0.977095 | + | 0.212803i | \(0.0682593\pi\) |
−0.665404 | + | 0.746483i | \(0.731741\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.5289 | − | 10.5559i | −0.688736 | − | 0.500396i | ||||
\(446\) | 3.68638 | + | 2.67831i | 0.174555 | + | 0.126822i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.880828 | − | 2.71091i | −0.0416152 | − | 0.128078i | ||||
\(449\) | 20.9494 | − | 15.2206i | 0.988663 | − | 0.718306i | 0.0290350 | − | 0.999578i | \(-0.490757\pi\) |
0.959628 | + | 0.281273i | \(0.0907566\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.54435 | + | 6.06744i | −0.355249 | + | 0.285705i | ||||
\(452\) | 2.38857 | 0.112349 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.77469 | − | 17.7727i | −0.271019 | − | 0.834112i | ||||
\(455\) | 3.60803 | − | 11.1044i | 0.169147 | − | 0.520581i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.33600 | + | 6.05645i | 0.389941 | + | 0.283309i | 0.765431 | − | 0.643517i | \(-0.222526\pi\) |
−0.375490 | + | 0.926826i | \(0.622526\pi\) | |||||||
\(458\) | −2.88113 | + | 8.86721i | −0.134626 | + | 0.414338i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.97717 | − | 2.16304i | 0.138811 | − | 0.100852i | ||||
\(461\) | 25.4532 | 1.18548 | 0.592738 | − | 0.805395i | \(-0.298047\pi\) | ||||
0.592738 | + | 0.805395i | \(0.298047\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.8554 | −1.85224 | −0.926119 | − | 0.377231i | \(-0.876876\pi\) | ||||
−0.926119 | + | 0.377231i | \(0.876876\pi\) | |||||||
\(464\) | 1.35533 | − | 0.984708i | 0.0629198 | − | 0.0457139i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.97863 | − | 9.16727i | 0.137982 | − | 0.424666i | ||||
\(467\) | −14.0582 | − | 10.2139i | −0.650537 | − | 0.472643i | 0.212917 | − | 0.977070i | \(-0.431704\pi\) |
−0.863454 | + | 0.504427i | \(0.831704\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.7661 | − | 36.2123i | 0.543308 | − | 1.67213i | ||||
\(470\) | 2.94224 | + | 9.05529i | 0.135716 | + | 0.417689i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.61562 | −0.258480 | ||||||||
\(473\) | −2.63033 | − | 6.92165i | −0.120943 | − | 0.318258i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.5837 | + | 11.3222i | −0.715027 | + | 0.519498i | ||||
\(476\) | −10.4312 | − | 32.1039i | −0.478112 | − | 1.47148i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.5158 | − | 9.81979i | −0.618197 | − | 0.449147i | ||||
\(479\) | −17.7142 | − | 12.8701i | −0.809383 | − | 0.588051i | 0.104269 | − | 0.994549i | \(-0.466750\pi\) |
−0.913652 | + | 0.406498i | \(0.866750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.20447 | − | 22.1731i | −0.328496 | − | 1.01101i | ||||
\(482\) | −9.53548 | + | 6.92794i | −0.434329 | + | 0.315559i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.86830 | − | 15.7097i | −0.312195 | − | 0.714075i | ||||
\(485\) | −8.95046 | −0.406420 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.01084 | + | 3.11106i | 0.0458057 | + | 0.140975i | 0.971344 | − | 0.237679i | \(-0.0763867\pi\) |
−0.925538 | + | 0.378655i | \(0.876387\pi\) | |||||||
\(488\) | 2.98389 | − | 9.18347i | 0.135074 | − | 0.415716i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.94830 | + | 3.59515i | 0.223542 | + | 0.162412i | ||||
\(491\) | 2.23231 | − | 6.87034i | 0.100743 | − | 0.310054i | −0.887965 | − | 0.459911i | \(-0.847881\pi\) |
0.988708 | + | 0.149857i | \(0.0478813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.85989 | + | 3.53092i | −0.218879 | + | 0.159025i | ||||
\(494\) | −9.13071 | −0.410810 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.665390 | −0.0298769 | ||||||||
\(497\) | −19.9546 | + | 14.4979i | −0.895087 | + | 0.650319i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.58412 | − | 14.1085i | 0.205213 | − | 0.631581i | −0.794491 | − | 0.607275i | \(-0.792262\pi\) |
0.999705 | − | 0.0243059i | \(-0.00773756\pi\) | |||||||
\(500\) | 12.3250 | + | 8.95460i | 0.551189 | + | 0.400462i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.49115 | − | 13.8223i | 0.200450 | − | 0.616921i | ||||
\(503\) | 10.1918 | + | 31.3671i | 0.454430 | + | 1.39859i | 0.871803 | + | 0.489856i | \(0.162951\pi\) |
−0.417374 | + | 0.908735i | \(0.637049\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.96673 | 0.0875181 | ||||||||
\(506\) | 3.89850 | + | 2.55037i | 0.173309 | + | 0.113378i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.64831 | + | 7.00990i | −0.428074 | + | 0.311014i | ||||
\(509\) | −11.9495 | − | 36.7768i | −0.529652 | − | 1.63010i | −0.754929 | − | 0.655807i | \(-0.772329\pi\) |
0.225277 | − | 0.974295i | \(-0.427671\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −36.8721 | − | 26.7892i | −1.63113 | − | 1.18508i | ||||
\(512\) | −13.1198 | − | 9.53213i | −0.579821 | − | 0.421264i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.06004 | − | 3.26247i | −0.0467564 | − | 0.143901i | ||||
\(515\) | 2.42795 | − | 1.76401i | 0.106988 | − | 0.0777315i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.1733 | − | 26.6792i | 1.45896 | − | 1.17335i | ||||
\(518\) | 22.5817 | 0.992182 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.18457 | + | 6.72343i | 0.0957999 | + | 0.294842i | ||||
\(521\) | 5.40297 | − | 16.6286i | 0.236708 | − | 0.728514i | −0.760182 | − | 0.649710i | \(-0.774890\pi\) |
0.996890 | − | 0.0788032i | \(-0.0251099\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.7211 | − | 8.51591i | −0.512530 | − | 0.372375i | 0.301253 | − | 0.953544i | \(-0.402595\pi\) |
−0.813782 | + | 0.581170i | \(0.802595\pi\) | |||||||
\(524\) | −2.58126 | + | 7.94431i | −0.112763 | + | 0.347049i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.9937 | + | 10.8936i | −0.653758 | + | 0.474983i | ||||
\(527\) | 2.38593 | 0.103933 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.5294 | −0.805626 | ||||||||
\(530\) | −3.38542 | + | 2.45965i | −0.147053 | + | 0.106840i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.65216 | + | 29.7063i | −0.418474 | + | 1.28793i | ||||
\(533\) | −6.32433 | − | 4.59489i | −0.273937 | − | 0.199027i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.54592 | + | 10.9132i | −0.153304 | + | 0.471820i | ||||
\(536\) | 7.12408 | + | 21.9256i | 0.307713 | + | 0.947044i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.00597 | −0.0864837 | ||||||||
\(539\) | 7.16664 | − | 26.3913i | 0.308689 | − | 1.13675i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.7771 | + | 19.4547i | −1.15124 | + | 0.836422i | −0.988645 | − | 0.150272i | \(-0.951985\pi\) |
−0.162591 | + | 0.986694i | \(0.551985\pi\) | |||||||
\(542\) | −5.20910 | − | 16.0320i | −0.223750 | − | 0.688632i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 25.8278 | + | 18.7650i | 1.10736 | + | 0.804543i | ||||
\(545\) | 2.13451 | + | 1.55082i | 0.0914325 | + | 0.0664296i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.84732 | + | 8.76316i | 0.121743 | + | 0.374686i | 0.993294 | − | 0.115619i | \(-0.0368853\pi\) |
−0.871551 | + | 0.490305i | \(0.836885\pi\) | |||||||
\(548\) | −21.0980 | + | 15.3286i | −0.901262 | + | 0.654805i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.16708 | + | 7.98032i | −0.0924046 | + | 0.340282i | ||||
\(551\) | 5.55853 | 0.236802 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.44731 | − | 16.7651i | −0.231643 | − | 0.712925i | ||||
\(554\) | −2.16872 | + | 6.67464i | −0.0921402 | + | 0.283578i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.3262 | + | 12.5883i | 0.734796 | + | 0.533861i | ||||
\(557\) | −11.4496 | + | 35.2384i | −0.485137 | + | 1.49310i | 0.346645 | + | 0.937996i | \(0.387321\pi\) |
−0.831782 | + | 0.555102i | \(0.812679\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.83697 | − | 3.51427i | 0.204582 | − | 0.148638i | ||||
\(560\) | 6.74405 | 0.284988 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.9941 | 0.632486 | ||||||||
\(563\) | −21.8387 | + | 15.8667i | −0.920390 | + | 0.668702i | −0.943621 | − | 0.331028i | \(-0.892605\pi\) |
0.0232313 | + | 0.999730i | \(0.492605\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.528774 | − | 1.62740i | 0.0222457 | − | 0.0684652i | ||||
\(566\) | 3.15870 | + | 2.29493i | 0.132770 | + | 0.0964630i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.61492 | − | 14.2033i | 0.193638 | − | 0.595956i | ||||
\(569\) | 8.49046 | + | 26.1310i | 0.355939 | + | 1.09547i | 0.955463 | + | 0.295110i | \(0.0953564\pi\) |
−0.599524 | + | 0.800356i | \(0.704644\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.0103 | −1.63253 | −0.816266 | − | 0.577676i | \(-0.803960\pi\) | ||||
−0.816266 | + | 0.577676i | \(0.803960\pi\) | |||||||
\(572\) | 10.7881 | − | 8.67617i | 0.451072 | − | 0.362769i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.12563 | − | 4.45053i | 0.255679 | − | 0.185762i | ||||
\(575\) | 2.45223 | + | 7.54719i | 0.102265 | + | 0.314739i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.5957 | + | 17.1433i | 0.982302 | + | 0.713684i | 0.958222 | − | 0.286026i | \(-0.0923344\pi\) |
0.0240800 | + | 0.999710i | \(0.492334\pi\) | |||||||
\(578\) | −7.39764 | − | 5.37470i | −0.307701 | − | 0.223558i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.582493 | − | 1.79273i | −0.0241867 | − | 0.0744390i | ||||
\(581\) | −1.52257 | + | 1.10621i | −0.0631670 | + | 0.0458935i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.6569 | + | 10.2427i | 0.648445 | + | 0.424209i | ||||
\(584\) | 27.5954 | 1.14191 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.45632 | − | 4.48210i | −0.0601602 | − | 0.185154i | ||||
\(587\) | 1.57226 | − | 4.83891i | 0.0648940 | − | 0.199723i | −0.913352 | − | 0.407170i | \(-0.866516\pi\) |
0.978246 | + | 0.207447i | \(0.0665155\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.78610 | − | 1.29768i | −0.0735950 | − | 0.0534699i | ||||
\(590\) | −0.544500 | + | 1.67580i | −0.0224167 | + | 0.0689916i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.8946 | − | 7.91537i | 0.447764 | − | 0.325320i | ||||
\(593\) | −3.46422 | −0.142258 | −0.0711292 | − | 0.997467i | \(-0.522660\pi\) | ||||
−0.0711292 | + | 0.997467i | \(0.522660\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.1825 | −0.991386 | ||||||||
\(596\) | −7.01071 | + | 5.09358i | −0.287170 | + | 0.208641i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.16240 | + | 3.57748i | −0.0475339 | + | 0.146294i | ||||
\(599\) | 20.1242 | + | 14.6211i | 0.822251 | + | 0.597400i | 0.917356 | − | 0.398067i | \(-0.130319\pi\) |
−0.0951054 | + | 0.995467i | \(0.530319\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.42024 | − | 10.5264i | 0.139514 | − | 0.429381i | −0.856750 | − | 0.515731i | \(-0.827520\pi\) |
0.996265 | + | 0.0863500i | \(0.0275203\pi\) | |||||||
\(602\) | 1.78951 | + | 5.50755i | 0.0729351 | + | 0.224471i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.255479 | 0.0103953 | ||||||||
\(605\) | −12.2239 | + | 1.20181i | −0.496973 | + | 0.0488604i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.6209 | − | 16.4351i | 0.918155 | − | 0.667079i | −0.0249090 | − | 0.999690i | \(-0.507930\pi\) |
0.943064 | + | 0.332611i | \(0.107930\pi\) | |||||||
\(608\) | −9.12859 | − | 28.0949i | −0.370213 | − | 1.13940i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.45118 | − | 1.78089i | −0.0992455 | − | 0.0721061i | ||||
\(611\) | 27.8087 | + | 20.2042i | 1.12502 | + | 0.817375i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.39680 | + | 10.4543i | 0.137196 | + | 0.422245i | 0.995925 | − | 0.0901845i | \(-0.0287457\pi\) |
−0.858729 | + | 0.512429i | \(0.828746\pi\) | |||||||
\(614\) | 9.96265 | − | 7.23829i | 0.402060 | − | 0.292114i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.8753 | + | 28.6182i | 0.438179 | + | 1.15306i | ||||
\(617\) | −18.6262 | −0.749864 | −0.374932 | − | 0.927052i | \(-0.622334\pi\) | ||||
−0.374932 | + | 0.927052i | \(0.622334\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.830787 | + | 2.55690i | 0.0333921 | + | 0.102770i | 0.966363 | − | 0.257180i | \(-0.0827935\pi\) |
−0.932971 | + | 0.359951i | \(0.882793\pi\) | |||||||
\(620\) | −0.231355 | + | 0.712036i | −0.00929142 | + | 0.0285961i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.69561 | + | 2.68502i | 0.148180 | + | 0.107659i | ||||
\(623\) | 19.4053 | − | 59.7234i | 0.777457 | − | 2.39277i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.35233 | + | 4.61524i | −0.254093 | + | 0.184610i | ||||
\(626\) | −16.8244 | −0.672440 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −37.1792 | −1.48361 | ||||||||
\(629\) | −39.0652 | + | 28.3826i | −1.55763 | + | 1.13169i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1224 | + | 37.3089i | −0.482585 | + | 1.48524i | 0.352863 | + | 0.935675i | \(0.385208\pi\) |
−0.835448 | + | 0.549569i | \(0.814792\pi\) | |||||||
\(632\) | 8.63483 | + | 6.27357i | 0.343475 | + | 0.249549i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.25389 | + | 6.93677i | −0.0895135 | + | 0.275494i | ||||
\(635\) | 2.64013 | + | 8.12550i | 0.104771 | + | 0.322451i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.0813 | 0.874895 | ||||||||
\(638\) | 1.85951 | − | 1.49549i | 0.0736187 | − | 0.0592069i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.96109 | + | 7.23716i | −0.393747 | + | 0.286074i | ||||
\(641\) | −7.95687 | − | 24.4887i | −0.314277 | − | 0.967246i | −0.976051 | − | 0.217542i | \(-0.930196\pi\) |
0.661773 | − | 0.749704i | \(-0.269804\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.7859 | + | 7.83639i | 0.425353 | + | 0.309037i | 0.779788 | − | 0.626044i | \(-0.215327\pi\) |
−0.354435 | + | 0.935081i | \(0.615327\pi\) | |||||||
\(644\) | 10.4104 | + | 7.56359i | 0.410227 | + | 0.298047i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.84386 | + | 17.9856i | 0.229924 | + | 0.707632i | ||||
\(647\) | 19.2955 | − | 14.0190i | 0.758585 | − | 0.551145i | −0.139891 | − | 0.990167i | \(-0.544675\pi\) |
0.898476 | + | 0.439022i | \(0.144675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.86876 | − | 0.385882i | 0.308876 | − | 0.0151472i | ||||
\(650\) | −6.67706 | −0.261896 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.02105 | + | 6.22015i | 0.0791504 | + | 0.243600i | ||||
\(653\) | −3.93222 | + | 12.1021i | −0.153880 | + | 0.473593i | −0.998046 | − | 0.0624889i | \(-0.980096\pi\) |
0.844166 | + | 0.536082i | \(0.180096\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.84125 | + | 3.51738i | 0.189163 | + | 0.137435i | ||||
\(656\) | 1.39531 | − | 4.29433i | 0.0544778 | − | 0.167666i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −26.9350 | + | 19.5694i | −1.05004 | + | 0.762896i | ||||
\(659\) | 27.2527 | 1.06161 | 0.530806 | − | 0.847493i | \(-0.321889\pi\) | ||||
0.530806 | + | 0.847493i | \(0.321889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.6440 | 1.69755 | 0.848777 | − | 0.528751i | \(-0.177339\pi\) | ||||
0.848777 | + | 0.528751i | \(0.177339\pi\) | |||||||
\(662\) | 1.99406 | − | 1.44877i | 0.0775014 | − | 0.0563081i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.352127 | − | 1.08373i | 0.0136652 | − | 0.0420571i | ||||
\(665\) | 18.1030 | + | 13.1526i | 0.702003 | + | 0.510035i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.707636 | − | 2.17788i | 0.0273998 | − | 0.0843278i | ||||
\(668\) | 7.62965 | + | 23.4817i | 0.295200 | + | 0.908533i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.23376 | 0.279465 | ||||||||
\(671\) | −3.55005 | + | 13.0732i | −0.137048 | + | 0.504684i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.5900 | − | 15.6860i | 0.832233 | − | 0.604652i | −0.0879575 | − | 0.996124i | \(-0.528034\pi\) |
0.920190 | + | 0.391472i | \(0.128034\pi\) | |||||||
\(674\) | −6.60922 | − | 20.3411i | −0.254578 | − | 0.783510i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.34946 | − | 5.33970i | −0.282672 | − | 0.205373i | ||||
\(677\) | 21.9107 | + | 15.9190i | 0.842095 | + | 0.611818i | 0.922955 | − | 0.384908i | \(-0.125767\pi\) |
−0.0808602 | + | 0.996725i | \(0.525767\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.67144 | − | 29.7656i | −0.371156 | − | 1.14230i | ||||
\(680\) | 11.8455 | − | 8.60629i | 0.454256 | − | 0.330036i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.946640 | + | 0.0464231i | −0.0362487 | + | 0.00177763i | ||||
\(683\) | 16.7343 | 0.640322 | 0.320161 | − | 0.947363i | \(-0.396263\pi\) | ||||
0.320161 | + | 0.947363i | \(0.396263\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.77319 | + | 17.7681i | 0.220582 | + | 0.678883i | ||||
\(686\) | −0.998288 | + | 3.07242i | −0.0381148 | + | 0.117305i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.79387 | + | 2.02987i | 0.106515 | + | 0.0773879i | ||||
\(689\) | −4.66836 | + | 14.3677i | −0.177850 | + | 0.547367i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.3540 | − | 22.0534i | 1.15472 | − | 0.838953i | 0.165618 | − | 0.986190i | \(-0.447038\pi\) |
0.989101 | + | 0.147237i | \(0.0470381\pi\) | |||||||
\(692\) | −4.05707 | −0.154226 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.2978 | 0.542738 | ||||||||
\(695\) | 12.4124 | − | 9.01811i | 0.470828 | − | 0.342077i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.00325 | + | 15.3984i | −0.189512 | + | 0.583257i | ||||
\(698\) | 9.03983 | + | 6.56782i | 0.342163 | + | 0.248596i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.05838 | + | 21.7235i | −0.266782 | + | 0.821070i | ||||
\(701\) | −3.15219 | − | 9.70143i | −0.119056 | − | 0.366418i | 0.873715 | − | 0.486438i | \(-0.161704\pi\) |
−0.992771 | + | 0.120020i | \(0.961704\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.6811 | 1.68518 | ||||||||
\(704\) | −2.02617 | − | 1.32551i | −0.0763641 | − | 0.0499569i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.68267 | − | 1.22253i | 0.0633280 | − | 0.0460105i | ||||
\(707\) | 2.12515 | + | 6.54054i | 0.0799245 | + | 0.245982i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.7289 | + | 8.52152i | 0.440487 | + | 0.320032i | 0.785828 | − | 0.618445i | \(-0.212237\pi\) |
−0.345342 | + | 0.938477i | \(0.612237\pi\) | |||||||
\(710\) | −3.79104 | − | 2.75435i | −0.142275 | − | 0.103369i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.7494 | + | 36.1610i | 0.440329 | + | 1.35519i | ||||
\(713\) | −0.735822 | + | 0.534606i | −0.0275568 | + | 0.0200212i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.52309 | − | 9.27093i | −0.131756 | − | 0.346713i | ||||
\(716\) | 11.8273 | 0.442006 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.74261 | − | 5.36321i | −0.0650337 | − | 0.200153i | ||||
\(719\) | −5.94135 | + | 18.2856i | −0.221575 | + | 0.681938i | 0.777046 | + | 0.629444i | \(0.216717\pi\) |
−0.998621 | + | 0.0524943i | \(0.983283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.48991 | + | 6.16828i | 0.316181 | + | 0.229719i | ||||
\(722\) | 1.50699 | − | 4.63804i | 0.0560844 | − | 0.172610i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3.02663 | + | 2.19898i | −0.112484 | + | 0.0817243i | ||||
\(725\) | 4.06482 | 0.150964 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.726827 | 0.0269565 | 0.0134783 | − | 0.999909i | \(-0.495710\pi\) | ||||
0.0134783 | + | 0.999909i | \(0.495710\pi\) | |||||||
\(728\) | −19.9989 | + | 14.5300i | −0.741207 | + | 0.538519i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.67570 | − | 8.23495i | 0.0990320 | − | 0.304789i | ||||
\(731\) | −10.0181 | − | 7.27860i | −0.370534 | − | 0.269209i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.579681 | + | 1.78408i | −0.0214110 | + | 0.0658964i | −0.961191 | − | 0.275883i | \(-0.911030\pi\) |
0.939780 | + | 0.341780i | \(0.111030\pi\) | |||||||
\(734\) | −2.26040 | − | 6.95680i | −0.0834329 | − | 0.256780i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.1699 | −0.448590 | ||||||||
\(737\) | −11.4891 | − | 30.2333i | −0.423206 | − | 1.11366i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.5402 | − | 30.9073i | 1.56487 | − | 1.13694i | 0.632993 | − | 0.774157i | \(-0.281826\pi\) |
0.931873 | − | 0.362784i | \(-0.118174\pi\) | |||||||
\(740\) | −4.68224 | − | 14.4105i | −0.172123 | − | 0.529739i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.8379 | − | 8.60076i | −0.434584 | − | 0.315744i | ||||
\(743\) | −26.9668 | − | 19.5925i | −0.989316 | − | 0.718780i | −0.0295450 | − | 0.999563i | \(-0.509406\pi\) |
−0.959771 | + | 0.280783i | \(0.909406\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.91839 | + | 5.90420i | 0.0702844 | + | 0.216313i | ||||
\(746\) | −5.91558 | + | 4.29792i | −0.216585 | + | 0.157358i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −23.9948 | − | 15.6973i | −0.877338 | − | 0.573949i | ||||
\(749\) | −40.1246 | −1.46612 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.21990 | − | 22.2206i | −0.263458 | − | 0.810840i | −0.992045 | − | 0.125886i | \(-0.959823\pi\) |
0.728587 | − | 0.684953i | \(-0.240177\pi\) | |||||||
\(752\) | −6.13533 | + | 18.8826i | −0.223732 | + | 0.688578i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.55880 | + | 1.13254i | 0.0567683 | + | 0.0412446i | ||||
\(755\) | 0.0565572 | − | 0.174065i | 0.00205833 | − | 0.00633488i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.3472 | − | 19.8689i | 0.993952 | − | 0.722148i | 0.0331687 | − | 0.999450i | \(-0.489440\pi\) |
0.960783 | + | 0.277302i | \(0.0894401\pi\) | |||||||
\(758\) | 16.8650 | 0.612564 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.5484 | −0.491453 | ||||||||
\(761\) | 16.2709 | − | 11.8215i | 0.589819 | − | 0.428528i | −0.252432 | − | 0.967615i | \(-0.581230\pi\) |
0.842251 | + | 0.539086i | \(0.181230\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.85093 | + | 8.77427i | −0.103211 | + | 0.317650i | ||||
\(764\) | 20.8294 | + | 15.1335i | 0.753583 | + | 0.547510i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.48699 | − | 7.65417i | 0.0898586 | − | 0.276556i | ||||
\(767\) | 1.96573 | + | 6.04991i | 0.0709786 | + | 0.218450i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.626999 | 0.0226102 | 0.0113051 | − | 0.999936i | \(-0.496401\pi\) | ||||
0.0113051 | + | 0.999936i | \(0.496401\pi\) | |||||||
\(770\) | 9.59465 | − | 0.470520i | 0.345767 | − | 0.0169564i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.2582 | + | 7.45299i | −0.369199 | + | 0.268239i | ||||
\(773\) | −8.88046 | − | 27.3313i | −0.319408 | − | 0.983037i | −0.973902 | − | 0.226970i | \(-0.927118\pi\) |
0.654494 | − | 0.756067i | \(-0.272882\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.30613 | − | 0.948959i | −0.0469176 | − | 0.0340876i | ||||
\(776\) | 15.3307 | + | 11.1384i | 0.550341 | + | 0.399846i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.94608 | − | 9.06711i | −0.105622 | − | 0.325072i | ||||
\(779\) | 12.1204 | − | 8.80602i | 0.434260 | − | 0.315508i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.49056 | + | 20.2191i | −0.196468 | + | 0.723497i | ||||
\(782\) | 7.79085 | 0.278600 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.94131 | + | 12.1301i | 0.140761 | + | 0.433218i | ||||
\(785\) | −8.23062 | + | 25.3312i | −0.293763 | + | 0.904110i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.4095 | + | 8.28950i | 0.406705 | + | 0.295489i | 0.772267 | − | 0.635298i | \(-0.219123\pi\) |
−0.365561 | + | 0.930787i | \(0.619123\pi\) | |||||||
\(788\) | −11.0334 | + | 33.9574i | −0.393050 | + | 1.20968i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.70939 | − | 1.96849i | 0.0963958 | − | 0.0700357i | ||||
\(791\) | 5.98345 | 0.212747 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9382 | −0.388426 | ||||||||
\(794\) | 2.70810 | − | 1.96755i | 0.0961068 | − | 0.0698257i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.46582 | + | 13.7444i | −0.158287 | + | 0.487157i | ||||
\(797\) | 21.1596 | + | 15.3733i | 0.749511 | + | 0.544552i | 0.895675 | − | 0.444709i | \(-0.146693\pi\) |
−0.146164 | + | 0.989260i | \(0.546693\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.9998 | − | 67.7084i | 0.778297 | − | 2.39535i | ||||
\(800\) | −6.67551 | − | 20.5451i | −0.236015 | − | 0.726379i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.0908 | 0.426939 | ||||||||
\(803\) | −38.6674 | + | 1.89624i | −1.36454 | + | 0.0669169i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.45791 | − | 5.41849i | 0.262857 | − | 0.190977i | ||||
\(806\) | −0.236485 | − | 0.727826i | −0.00832983 | − | 0.0256366i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.36869 | − | 2.44750i | −0.118510 | − | 0.0861026i | ||||
\(809\) | 12.8256 | + | 9.31836i | 0.450925 | + | 0.327616i | 0.789961 | − | 0.613157i | \(-0.210101\pi\) |
−0.339036 | + | 0.940773i | \(0.610101\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.2255 | − | 34.5484i | −0.394179 | − | 1.21316i | −0.929599 | − | 0.368573i | \(-0.879846\pi\) |
0.535420 | − | 0.844586i | \(-0.320154\pi\) | |||||||
\(812\) | 5.33248 | − | 3.87427i | 0.187133 | − | 0.135960i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.9473 | − | 12.0212i | 0.523902 | − | 0.421342i | ||||
\(815\) | 4.68538 | 0.164122 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.54081 | + | 10.8975i | 0.123877 | + | 0.381255i | ||||
\(818\) | 3.37295 | − | 10.3809i | 0.117932 | − | 0.362958i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.11023 | − | 2.98626i | −0.143535 | − | 0.104285i | ||||
\(821\) | 5.05451 | − | 15.5562i | 0.176404 | − | 0.542914i | −0.823291 | − | 0.567619i | \(-0.807865\pi\) |
0.999695 | + | 0.0247048i | \(0.00786458\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.1756 | − | 15.3850i | 0.738136 | − | 0.536287i | −0.153991 | − | 0.988072i | \(-0.549213\pi\) |
0.892127 | + | 0.451785i | \(0.149213\pi\) | |||||||
\(824\) | −6.35392 | −0.221349 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.16139 | −0.214382 | ||||||||
\(827\) | 4.48139 | − | 3.25592i | 0.155833 | − | 0.113219i | −0.507136 | − | 0.861866i | \(-0.669296\pi\) |
0.662969 | + | 0.748647i | \(0.269296\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.71784 | − | 17.5977i | 0.198589 | − | 0.611194i | −0.801327 | − | 0.598227i | \(-0.795872\pi\) |
0.999916 | − | 0.0129672i | \(-0.00412771\pi\) | |||||||
\(830\) | −0.289263 | − | 0.210162i | −0.0100405 | − | 0.00729481i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.604133 | − | 1.85933i | 0.0209445 | − | 0.0644606i | ||||
\(833\) | −14.1326 | − | 43.4956i | −0.489664 | − | 1.50703i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.6878 | 0.612110 | ||||||||
\(836\) | 9.42492 | + | 24.8015i | 0.325968 | + | 0.857776i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.35505 | + | 6.79684i | −0.323165 | + | 0.234793i | ||||
\(839\) | 5.55158 | + | 17.0860i | 0.191662 | + | 0.589875i | 0.999999 | + | 0.00115518i | \(0.000367705\pi\) |
−0.808337 | + | 0.588719i | \(0.799632\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.5125 | + | 16.3563i | 0.776294 | + | 0.564011i | ||||
\(842\) | −2.44465 | − | 1.77614i | −0.0842483 | − | 0.0612100i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.02806 | − | 6.24172i | −0.0698086 | − | 0.214849i | ||||
\(845\) | −5.26509 | + | 3.82531i | −0.181125 | + | 0.131595i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.2053 | − | 39.3532i | −0.591182 | − | 1.35219i | ||||
\(848\) | −8.72598 | −0.299651 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.27347 | + | 13.1524i | 0.146579 | + | 0.451123i | ||||
\(851\) | 5.68818 | − | 17.5064i | 0.194988 | − | 0.600112i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −22.5822 | − | 16.4069i | −0.773199 | − | 0.561762i | 0.129732 | − | 0.991549i | \(-0.458588\pi\) |
−0.902930 | + | 0.429788i | \(0.858588\pi\) | |||||||
\(854\) | 3.27389 | − | 10.0760i | 0.112030 | − | 0.344794i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.6546 | − | 14.2799i | 0.671781 | − | 0.488077i | ||||
\(857\) | 8.49967 | 0.290343 | 0.145172 | − | 0.989406i | \(-0.453627\pi\) | ||||
0.145172 | + | 0.989406i | \(0.453627\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.8517 | 0.950289 | 0.475145 | − | 0.879908i | \(-0.342396\pi\) | ||||
0.475145 | + | 0.879908i | \(0.342396\pi\) | |||||||
\(860\) | 3.14359 | − | 2.28395i | 0.107195 | − | 0.0778820i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.56296 | + | 7.88797i | −0.0872947 | + | 0.268665i | ||||
\(863\) | 10.9978 | + | 7.99035i | 0.374368 | + | 0.271995i | 0.759020 | − | 0.651067i | \(-0.225678\pi\) |
−0.384652 | + | 0.923062i | \(0.625678\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.898141 | + | 2.76419i | −0.0305377 | + | 0.0939854i | ||||
\(866\) | 5.88887 | + | 18.1241i | 0.200112 | + | 0.615882i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.61794 | −0.0888586 | ||||||||
\(869\) | −12.5304 | − | 8.19734i | −0.425066 | − | 0.278076i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.1275 | − | 15.3500i | 0.715879 | − | 0.520117i | ||||
\(872\) | −1.72617 | − | 5.31260i | −0.0584555 | − | 0.179907i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.83221 | − | 4.23735i | −0.197278 | − | 0.143331i | ||||
\(875\) | 30.8744 | + | 22.4316i | 1.04375 | + | 0.758326i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.1796 | + | 34.4073i | 0.377509 | + | 1.16185i | 0.941771 | + | 0.336256i | \(0.109161\pi\) |
−0.564262 | + | 0.825596i | \(0.690839\pi\) | |||||||
\(878\) | 2.20787 | − | 1.60411i | 0.0745120 | − | 0.0541361i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.46403 | − | 3.59014i | 0.150482 | − | 0.121023i | ||||
\(881\) | −26.6423 | −0.897601 | −0.448800 | − | 0.893632i | \(-0.648149\pi\) | ||||
−0.448800 | + | 0.893632i | \(0.648149\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.32757 | − | 19.4743i | −0.212940 | − | 0.655361i | −0.999293 | − | 0.0375844i | \(-0.988034\pi\) |
0.786354 | − | 0.617776i | \(-0.211966\pi\) | |||||||
\(884\) | 7.15442 | − | 22.0190i | 0.240629 | − | 0.740581i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.4098 | − | 8.28973i | −0.383321 | − | 0.278499i | ||||
\(887\) | 9.88890 | − | 30.4349i | 0.332037 | − | 1.02190i | −0.636126 | − | 0.771585i | \(-0.719464\pi\) |
0.968163 | − | 0.250320i | \(-0.0805357\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.1693 | + | 17.5600i | −0.810613 | + | 0.588945i | ||||
\(890\) | 11.9303 | 0.399906 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.6911 | 0.357963 | ||||||||
\(893\) | −53.2948 | + | 38.7209i | −1.78344 | + | 1.29575i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.61829 | − | 8.05826i | 0.0875197 | − | 0.269358i | ||||
\(896\) | −34.8314 | − | 25.3065i | −1.16363 | − | 0.845430i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.31586 | + | 16.3605i | −0.177393 | + | 0.545958i | ||||
\(899\) | 0.143966 | + | 0.443082i | 0.00480153 | + | 0.0147776i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31.2892 | 1.04239 | ||||||||
\(902\) | 1.68548 | − | 6.20683i | 0.0561204 | − | 0.206665i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.93093 | + | 2.12944i | −0.0974813 | + | 0.0708243i | ||||
\(905\) | 0.828198 | + | 2.54893i | 0.0275302 | + | 0.0847294i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.6825 | + | 28.8310i | 1.31764 | + | 0.957318i | 0.999958 | + | 0.00911935i | \(0.00290282\pi\) |
0.317677 | + | 0.948199i | \(0.397097\pi\) | |||||||
\(908\) | −35.4717 | − | 25.7717i | −1.17717 | − | 0.855265i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.39689 | + | 7.37687i | 0.0794561 | + | 0.244541i | ||||
\(911\) | −18.9159 | + | 13.7432i | −0.626710 | + | 0.455332i | −0.855259 | − | 0.518201i | \(-0.826602\pi\) |
0.228549 | + | 0.973532i | \(0.426602\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.418940 | + | 1.54275i | −0.0138649 | + | 0.0510577i | ||||
\(914\) | −6.84506 | −0.226415 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.75993 | + | 20.8049i | 0.223354 | + | 0.687414i | ||||
\(917\) | −6.46615 | + | 19.9008i | −0.213531 | + | 0.657181i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.14797 | + | 4.46676i | 0.202803 | + | 0.147345i | 0.684551 | − | 0.728965i | \(-0.259998\pi\) |
−0.481749 | + | 0.876309i | \(0.659998\pi\) | |||||||
\(920\) | −1.72480 | + | 5.30838i | −0.0568649 | + | 0.175012i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.6798 | + | 9.93893i | −0.450519 | + | 0.327321i | ||||
\(923\) | −16.9171 | −0.556835 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.6742 | 1.07432 | ||||||||
\(926\) | 21.4202 | − | 15.5627i | 0.703910 | − | 0.511421i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.92634 | + | 5.92866i | −0.0632352 | + | 0.194618i | ||||
\(929\) | −12.0355 | − | 8.74433i | −0.394873 | − | 0.286892i | 0.372576 | − | 0.928002i | \(-0.378475\pi\) |
−0.767450 | + | 0.641109i | \(0.778475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.0771 | + | 40.2472i | −0.428585 | + | 1.31905i | ||||
\(932\) | −6.98867 | − | 21.5089i | −0.228922 | − | 0.704548i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.5438 | 0.377726 | ||||||||
\(935\) | −16.0069 | + | 12.8733i | −0.523482 | + | 0.421003i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.4192 | + | 10.4762i | −0.471056 | + | 0.342242i | −0.797853 | − | 0.602853i | \(-0.794031\pi\) |
0.326797 | + | 0.945095i | \(0.394031\pi\) | |||||||
\(938\) | 7.81646 | + | 24.0566i | 0.255216 | + | 0.785475i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18.0731 | + | 13.1309i | 0.589479 | + | 0.428282i | ||||
\(941\) | 34.5120 | + | 25.0744i | 1.12506 | + | 0.817402i | 0.984968 | − | 0.172737i | \(-0.0552609\pi\) |
0.140090 | + | 0.990139i | \(0.455261\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.90726 | − | 5.86995i | −0.0621090 | − | 0.191152i | ||||
\(944\) | −2.97257 | + | 2.15970i | −0.0967491 | + | 0.0702923i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.11641 | + | 2.69293i | 0.133836 | + | 0.0875548i | ||||
\(947\) | −6.89340 | −0.224006 | −0.112003 | − | 0.993708i | \(-0.535727\pi\) | ||||
−0.112003 | + | 0.993708i | \(0.535727\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.65971 | − | 29.7295i | −0.313567 | − | 0.965061i | ||||
\(950\) | 3.95432 | − | 12.1701i | 0.128295 | − | 0.394852i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 41.4208 | + | 30.0940i | 1.34246 | + | 0.975351i | ||||
\(953\) | 7.31766 | − | 22.5214i | 0.237042 | − | 0.729541i | −0.759802 | − | 0.650155i | \(-0.774704\pi\) |
0.996844 | − | 0.0793863i | \(-0.0252960\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.9220 | − | 10.8415i | 0.482866 | − | 0.350822i | ||||
\(956\) | −39.1978 | −1.26775 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14.5459 | 0.469958 | ||||||||
\(959\) | −52.8512 | + | 38.3986i | −1.70665 | + | 1.23996i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.52235 | + | 29.3068i | −0.307172 | + | 0.945380i | ||||
\(962\) | 12.5301 | + | 9.10366i | 0.403987 | + | 0.293514i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.54567 | + | 26.3009i | −0.275238 | + | 0.847094i | ||||
\(965\) | 2.80701 | + | 8.63910i | 0.0903610 | + | 0.278102i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.1399 | −1.00139 | −0.500696 | − | 0.865623i | \(-0.666923\pi\) | ||||
−0.500696 | + | 0.865623i | \(0.666923\pi\) | |||||||
\(968\) | 22.4332 | + | 13.1536i | 0.721032 | + | 0.422772i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.81040 | − | 3.49496i | 0.154453 | − | 0.112216i | ||||
\(971\) | −4.12687 | − | 12.7012i | −0.132438 | − | 0.407601i | 0.862745 | − | 0.505639i | \(-0.168743\pi\) |
−0.995183 | + | 0.0980383i | \(0.968743\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43.4028 | + | 31.5340i | 1.39143 | + | 1.01093i | ||||
\(974\) | −1.75807 | − | 1.27732i | −0.0563323 | − | 0.0409278i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.95236 | − | 6.00875i | −0.0624936 | − | 0.192335i | ||||
\(977\) | −7.21314 | + | 5.24065i | −0.230769 | + | 0.167663i | −0.697161 | − | 0.716915i | \(-0.745554\pi\) |
0.466392 | + | 0.884578i | \(0.345554\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.9485 | − | 49.8624i | −0.605595 | − | 1.59361i | ||||
\(980\) | 14.3508 | 0.458421 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.48297 | + | 4.56411i | 0.0473234 | + | 0.145647i | ||||
\(983\) | 5.20958 | − | 16.0334i | 0.166160 | − | 0.511387i | −0.832960 | − | 0.553333i | \(-0.813356\pi\) |
0.999120 | + | 0.0419459i | \(0.0133557\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.6936 | + | 15.0348i | 0.659353 | + | 0.479048i | ||||
\(986\) | 1.23319 | − | 3.79536i | 0.0392727 | − | 0.120869i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17.3317 | + | 12.5922i | −0.551394 | + | 0.400612i | ||||
\(989\) | 4.72049 | 0.150103 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.5356 | −1.06529 | −0.532647 | − | 0.846338i | \(-0.678803\pi\) | ||||
−0.532647 | + | 0.846338i | \(0.678803\pi\) | |||||||
\(992\) | 2.00307 | − | 1.45531i | 0.0635975 | − | 0.0462063i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.06344 | − | 15.5837i | 0.160603 | − | 0.494284i | ||||
\(995\) | 8.37582 | + | 6.08539i | 0.265531 | + | 0.192920i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.00235 | + | 3.08492i | −0.0317447 | + | 0.0977003i | −0.965673 | − | 0.259759i | \(-0.916357\pi\) |
0.933929 | + | 0.357459i | \(0.116357\pi\) | |||||||
\(998\) | 3.04532 | + | 9.37254i | 0.0963980 | + | 0.296682i | ||||
\(999\) | 0 | 0 |
(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 | 891.2.f.e.487.4 | 36 | ||
3.2 | odd | 2 | 891.2.f.f.487.6 | 36 | |||
9.2 | odd | 6 | 99.2.m.b.58.4 | yes | 72 | ||
9.4 | even | 3 | 297.2.n.b.289.4 | 72 | |||
9.5 | odd | 6 | 99.2.m.b.25.6 | yes | 72 | ||
9.7 | even | 3 | 297.2.n.b.91.6 | 72 | |||
11.2 | odd | 10 | 9801.2.a.cn.1.8 | 18 | |||
11.4 | even | 5 | inner | 891.2.f.e.730.4 | 36 | ||
11.9 | even | 5 | 9801.2.a.cp.1.11 | 18 | |||
33.2 | even | 10 | 9801.2.a.co.1.11 | 18 | |||
33.20 | odd | 10 | 9801.2.a.cm.1.8 | 18 | |||
33.26 | odd | 10 | 891.2.f.f.730.6 | 36 | |||
99.2 | even | 30 | 1089.2.e.o.364.8 | 36 | |||
99.4 | even | 15 | 297.2.n.b.235.6 | 72 | |||
99.20 | odd | 30 | 1089.2.e.p.364.11 | 36 | |||
99.59 | odd | 30 | 99.2.m.b.70.4 | yes | 72 | ||
99.68 | even | 30 | 1089.2.e.o.727.8 | 36 | |||
99.70 | even | 15 | 297.2.n.b.37.4 | 72 | |||
99.86 | odd | 30 | 1089.2.e.p.727.11 | 36 | |||
99.92 | odd | 30 | 99.2.m.b.4.6 | ✓ | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.4.6 | ✓ | 72 | 99.92 | odd | 30 | ||
99.2.m.b.25.6 | yes | 72 | 9.5 | odd | 6 | ||
99.2.m.b.58.4 | yes | 72 | 9.2 | odd | 6 | ||
99.2.m.b.70.4 | yes | 72 | 99.59 | odd | 30 | ||
297.2.n.b.37.4 | 72 | 99.70 | even | 15 | |||
297.2.n.b.91.6 | 72 | 9.7 | even | 3 | |||
297.2.n.b.235.6 | 72 | 99.4 | even | 15 | |||
297.2.n.b.289.4 | 72 | 9.4 | even | 3 | |||
891.2.f.e.487.4 | 36 | 1.1 | even | 1 | trivial | ||
891.2.f.e.730.4 | 36 | 11.4 | even | 5 | inner | ||
891.2.f.f.487.6 | 36 | 3.2 | odd | 2 | |||
891.2.f.f.730.6 | 36 | 33.26 | odd | 10 | |||
1089.2.e.o.364.8 | 36 | 99.2 | even | 30 | |||
1089.2.e.o.727.8 | 36 | 99.68 | even | 30 | |||
1089.2.e.p.364.11 | 36 | 99.20 | odd | 30 | |||
1089.2.e.p.727.11 | 36 | 99.86 | odd | 30 | |||
9801.2.a.cm.1.8 | 18 | 33.20 | odd | 10 | |||
9801.2.a.cn.1.8 | 18 | 11.2 | odd | 10 | |||
9801.2.a.co.1.11 | 18 | 33.2 | even | 10 | |||
9801.2.a.cp.1.11 | 18 | 11.9 | even | 5 |