Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(19,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.f (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.94278685509\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 91.5 | ||
Root | \(0.186266 + 1.99131i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.91 |
Dual form | 108.3.f.c.19.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.186266 | + | 1.99131i | 0.0931330 | + | 0.995654i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.93061 | + | 0.741826i | −0.982652 | + | 0.185456i | ||||
\(5\) | −3.07403 | + | 5.32438i | −0.614806 | + | 1.06488i | 0.375612 | + | 0.926777i | \(0.377432\pi\) |
−0.990418 | + | 0.138099i | \(0.955901\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.511543 | − | 0.295340i | 0.0730776 | − | 0.0421914i | −0.463016 | − | 0.886350i | \(-0.653233\pi\) |
0.536094 | + | 0.844159i | \(0.319899\pi\) | |||||||
\(8\) | −2.20934 | − | 7.68888i | −0.276168 | − | 0.961109i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −11.1751 | − | 5.12959i | −1.11751 | − | 0.512959i | ||||
\(11\) | −15.1205 | + | 8.72982i | −1.37459 | + | 0.793620i | −0.991502 | − | 0.130092i | \(-0.958473\pi\) |
−0.383088 | + | 0.923712i | \(0.625139\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.892255 | + | 1.54543i | −0.0686350 | + | 0.118879i | −0.898301 | − | 0.439381i | \(-0.855198\pi\) |
0.829666 | + | 0.558261i | \(0.188531\pi\) | |||||||
\(14\) | 0.683395 | + | 0.963628i | 0.0488140 | + | 0.0688306i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.8994 | − | 5.83166i | 0.931212 | − | 0.364479i | ||||
\(17\) | 16.9171 | 0.995123 | 0.497562 | − | 0.867429i | \(-0.334229\pi\) | ||||
0.497562 | + | 0.867429i | \(0.334229\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.5058i | 1.02662i | 0.858203 | + | 0.513310i | \(0.171581\pi\) | ||||
−0.858203 | + | 0.513310i | \(0.828419\pi\) | |||||||
\(20\) | 8.13306 | − | 23.2084i | 0.406653 | − | 1.16042i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −20.2002 | − | 28.4835i | −0.918190 | − | 1.29470i | ||||
\(23\) | 6.86778 | + | 3.96511i | 0.298599 | + | 0.172396i | 0.641813 | − | 0.766861i | \(-0.278182\pi\) |
−0.343214 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.39933 | − | 11.0840i | −0.255973 | − | 0.443359i | ||||
\(26\) | −3.24362 | − | 1.48889i | −0.124755 | − | 0.0572651i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.79159 | + | 1.54034i | −0.0639852 | + | 0.0550122i | ||||
\(29\) | −3.17517 | − | 5.49956i | −0.109489 | − | 0.189640i | 0.806075 | − | 0.591814i | \(-0.201588\pi\) |
−0.915563 | + | 0.402174i | \(0.868255\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 27.6558 | + | 15.9671i | 0.892124 | + | 0.515068i | 0.874637 | − | 0.484779i | \(-0.161100\pi\) |
0.0174873 | + | 0.999847i | \(0.494433\pi\) | |||||||
\(32\) | 14.3879 | + | 28.5830i | 0.449621 | + | 0.893219i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.15108 | + | 33.6871i | 0.0926788 | + | 0.990798i | ||||
\(35\) | 3.63153i | 0.103758i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 58.2834 | 1.57523 | 0.787614 | − | 0.616169i | \(-0.211316\pi\) | ||||
0.787614 | + | 0.616169i | \(0.211316\pi\) | |||||||
\(38\) | −38.8420 | + | 3.63326i | −1.02216 | + | 0.0956122i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 47.7301 | + | 11.8725i | 1.19325 | + | 0.296812i | ||||
\(41\) | 2.66948 | − | 4.62368i | 0.0651093 | − | 0.112773i | −0.831633 | − | 0.555325i | \(-0.812594\pi\) |
0.896742 | + | 0.442553i | \(0.145927\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −33.9324 | + | 19.5909i | −0.789126 | + | 0.455602i | −0.839655 | − | 0.543121i | \(-0.817243\pi\) |
0.0505290 | + | 0.998723i | \(0.483909\pi\) | |||||||
\(44\) | 52.9567 | − | 45.5303i | 1.20356 | − | 1.03478i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.61653 | + | 14.4144i | −0.143838 | + | 0.313357i | ||||
\(47\) | 9.64117 | − | 5.56633i | 0.205131 | − | 0.118433i | −0.393915 | − | 0.919147i | \(-0.628880\pi\) |
0.599047 | + | 0.800714i | \(0.295546\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.3255 | + | 42.1331i | −0.496440 | + | 0.859859i | ||||
\(50\) | 20.8796 | − | 14.8076i | 0.417592 | − | 0.296152i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.36067 | − | 6.73638i | 0.0453974 | − | 0.129546i | ||||
\(53\) | −35.8770 | −0.676925 | −0.338462 | − | 0.940980i | \(-0.609907\pi\) | ||||
−0.338462 | + | 0.940980i | \(0.609907\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 107.343i | − | 1.95169i | ||||||
\(56\) | −3.40100 | − | 3.28069i | −0.0607322 | − | 0.0585837i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.3599 | − | 7.34713i | 0.178619 | − | 0.126675i | ||||
\(59\) | 20.8974 | + | 12.0651i | 0.354194 | + | 0.204494i | 0.666531 | − | 0.745477i | \(-0.267778\pi\) |
−0.312337 | + | 0.949971i | \(0.601112\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −37.9460 | − | 65.7244i | −0.622066 | − | 1.07745i | −0.989100 | − | 0.147243i | \(-0.952960\pi\) |
0.367034 | − | 0.930207i | \(-0.380373\pi\) | |||||||
\(62\) | −26.6441 | + | 58.0454i | −0.429743 | + | 0.936216i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −54.2376 | + | 33.9747i | −0.847463 | + | 0.530855i | ||||
\(65\) | −5.48564 | − | 9.50141i | −0.0843944 | − | 0.146175i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −31.8200 | − | 18.3713i | −0.474925 | − | 0.274198i | 0.243374 | − | 0.969933i | \(-0.421746\pi\) |
−0.718299 | + | 0.695734i | \(0.755079\pi\) | |||||||
\(68\) | −66.4945 | + | 12.5495i | −0.977860 | + | 0.184552i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.23150 | + | 0.676431i | −0.103307 | + | 0.00966331i | ||||
\(71\) | − | 87.8370i | − | 1.23714i | −0.785730 | − | 0.618570i | \(-0.787712\pi\) | ||
0.785730 | − | 0.618570i | \(-0.212288\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −60.0423 | −0.822498 | −0.411249 | − | 0.911523i | \(-0.634907\pi\) | ||||
−0.411249 | + | 0.911523i | \(0.634907\pi\) | |||||||
\(74\) | 10.8562 | + | 116.060i | 0.146706 | + | 1.56838i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −14.4699 | − | 76.6696i | −0.190393 | − | 1.00881i | ||||
\(77\) | −5.15652 | + | 8.93136i | −0.0669678 | + | 0.115992i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 32.1841 | − | 18.5815i | 0.407394 | − | 0.235209i | −0.282275 | − | 0.959333i | \(-0.591089\pi\) |
0.689669 | + | 0.724124i | \(0.257756\pi\) | |||||||
\(80\) | −14.7512 | + | 97.2567i | −0.184391 | + | 1.21571i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.70439 | + | 4.45452i | 0.118346 | + | 0.0543234i | ||||
\(83\) | 66.0281 | − | 38.1214i | 0.795520 | − | 0.459294i | −0.0463824 | − | 0.998924i | \(-0.514769\pi\) |
0.841902 | + | 0.539630i | \(0.181436\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −52.0037 | + | 90.0730i | −0.611808 | + | 1.05968i | ||||
\(86\) | −45.3319 | − | 63.9207i | −0.527115 | − | 0.743264i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 100.529 | + | 96.9724i | 1.14237 | + | 1.10196i | ||||
\(89\) | 27.5873 | 0.309969 | 0.154985 | − | 0.987917i | \(-0.450467\pi\) | ||||
0.154985 | + | 0.987917i | \(0.450467\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.05407i | 0.0115832i | ||||||||
\(92\) | −29.9360 | − | 10.4906i | −0.325391 | − | 0.114028i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.8801 | + | 18.1617i | 0.137022 | + | 0.193210i | ||||
\(95\) | −103.856 | − | 59.9614i | −1.09322 | − | 0.631172i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0585 | + | 22.6180i | 0.134624 | + | 0.233176i | 0.925454 | − | 0.378861i | \(-0.123684\pi\) |
−0.790830 | + | 0.612036i | \(0.790351\pi\) | |||||||
\(98\) | −88.4309 | − | 40.5917i | −0.902357 | − | 0.414201i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 33.3757 | + | 38.8196i | 0.333757 | + | 0.388196i | ||||
\(101\) | 12.8831 | + | 22.3142i | 0.127556 | + | 0.220933i | 0.922729 | − | 0.385449i | \(-0.125953\pi\) |
−0.795173 | + | 0.606382i | \(0.792620\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9947 | − | 9.81187i | −0.164997 | − | 0.0952609i | 0.415228 | − | 0.909717i | \(-0.363702\pi\) |
−0.580225 | + | 0.814457i | \(0.697035\pi\) | |||||||
\(104\) | 13.8539 | + | 3.44605i | 0.133211 | + | 0.0331351i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.68267 | − | 71.4422i | −0.0630441 | − | 0.673983i | ||||
\(107\) | 183.200i | 1.71215i | 0.516850 | + | 0.856076i | \(0.327105\pi\) | ||||
−0.516850 | + | 0.856076i | \(0.672895\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 100.841 | 0.925147 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(110\) | 213.753 | − | 19.9943i | 1.94321 | − | 0.181767i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.89936 | − | 7.38353i | 0.0526729 | − | 0.0659243i | ||||
\(113\) | 9.12484 | − | 15.8047i | 0.0807508 | − | 0.139865i | −0.822822 | − | 0.568299i | \(-0.807602\pi\) |
0.903573 | + | 0.428435i | \(0.140935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −42.2235 | + | 24.3778i | −0.367161 | + | 0.211981i | ||||
\(116\) | 16.5601 | + | 19.2612i | 0.142759 | + | 0.166045i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −20.1329 | + | 43.8606i | −0.170618 | + | 0.371700i | ||||
\(119\) | 8.65383 | − | 4.99629i | 0.0727212 | − | 0.0419856i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 91.9194 | − | 159.209i | 0.759664 | − | 1.31578i | ||||
\(122\) | 123.810 | − | 87.8044i | 1.01483 | − | 0.719708i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −120.549 | − | 42.2447i | −0.972170 | − | 0.340683i | ||||
\(125\) | −75.0146 | −0.600117 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 164.386i | 1.29438i | 0.762331 | + | 0.647188i | \(0.224055\pi\) | ||||
−0.762331 | + | 0.647188i | \(0.775945\pi\) | |||||||
\(128\) | −77.7567 | − | 101.675i | −0.607474 | − | 0.794339i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 17.8984 | − | 12.6934i | 0.137680 | − | 0.0976414i | ||||
\(131\) | 123.421 | + | 71.2570i | 0.942143 | + | 0.543947i | 0.890631 | − | 0.454726i | \(-0.150263\pi\) |
0.0515116 | + | 0.998672i | \(0.483596\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.76083 | + | 9.97805i | 0.0433145 | + | 0.0750229i | ||||
\(134\) | 30.6559 | − | 66.7853i | 0.228775 | − | 0.498398i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −37.3757 | − | 130.073i | −0.274821 | − | 0.956422i | ||||
\(137\) | 3.08176 | + | 5.33777i | 0.0224946 | + | 0.0389618i | 0.877054 | − | 0.480393i | \(-0.159506\pi\) |
−0.854559 | + | 0.519354i | \(0.826172\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 103.168 | + | 59.5642i | 0.742218 | + | 0.428519i | 0.822875 | − | 0.568222i | \(-0.192369\pi\) |
−0.0806575 | + | 0.996742i | \(0.525702\pi\) | |||||||
\(140\) | −2.69397 | − | 14.2741i | −0.0192426 | − | 0.101958i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 174.910 | − | 16.3610i | 1.23176 | − | 0.115219i | ||||
\(143\) | − | 31.1569i | − | 0.217880i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 39.0423 | 0.269257 | ||||||||
\(146\) | −11.1838 | − | 119.563i | −0.0766017 | − | 0.818923i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −229.089 | + | 43.2361i | −1.54790 | + | 0.292136i | ||||
\(149\) | 103.365 | − | 179.034i | 0.693726 | − | 1.20157i | −0.276882 | − | 0.960904i | \(-0.589301\pi\) |
0.970608 | − | 0.240665i | \(-0.0773657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 127.422 | − | 73.5670i | 0.843853 | − | 0.487199i | −0.0147190 | − | 0.999892i | \(-0.504685\pi\) |
0.858572 | + | 0.512693i | \(0.171352\pi\) | |||||||
\(152\) | 149.977 | − | 43.0949i | 0.986694 | − | 0.283519i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −18.7456 | − | 8.60461i | −0.121724 | − | 0.0558741i | ||||
\(155\) | −170.030 | + | 98.1668i | −1.09697 | + | 0.633334i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 31.4395 | − | 54.4548i | 0.200251 | − | 0.346846i | −0.748358 | − | 0.663295i | \(-0.769157\pi\) |
0.948609 | + | 0.316449i | \(0.102491\pi\) | |||||||
\(158\) | 42.9963 | + | 60.6274i | 0.272129 | + | 0.383718i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −196.416 | − | 11.2586i | −1.22760 | − | 0.0703665i | ||||
\(161\) | 4.68422 | 0.0290946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 143.325i | 0.879292i | 0.898171 | + | 0.439646i | \(0.144896\pi\) | ||||
−0.898171 | + | 0.439646i | \(0.855104\pi\) | |||||||
\(164\) | −7.06272 | + | 20.1542i | −0.0430654 | + | 0.122891i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 88.2102 | + | 124.382i | 0.531386 | + | 0.749287i | ||||
\(167\) | −150.531 | − | 86.9089i | −0.901381 | − | 0.520413i | −0.0237332 | − | 0.999718i | \(-0.507555\pi\) |
−0.877648 | + | 0.479306i | \(0.840889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 82.9078 | + | 143.600i | 0.490578 | + | 0.849707i | ||||
\(170\) | −189.050 | − | 86.7777i | −1.11206 | − | 0.510457i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 118.842 | − | 102.176i | 0.690942 | − | 0.594047i | ||||
\(173\) | 125.806 | + | 217.902i | 0.727201 | + | 1.25955i | 0.958062 | + | 0.286562i | \(0.0925125\pi\) |
−0.230861 | + | 0.972987i | \(0.574154\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.54707 | − | 3.77995i | −0.0374118 | − | 0.0215997i | ||||
\(176\) | −174.377 | + | 218.246i | −0.990777 | + | 1.24004i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.13857 | + | 54.9347i | 0.0288684 | + | 0.308622i | ||||
\(179\) | 96.0059i | 0.536346i | 0.963371 | + | 0.268173i | \(0.0864199\pi\) | ||||
−0.963371 | + | 0.268173i | \(0.913580\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −328.757 | −1.81634 | −0.908170 | − | 0.418603i | \(-0.862520\pi\) | ||||
−0.908170 | + | 0.418603i | \(0.862520\pi\) | |||||||
\(182\) | −2.09898 | + | 0.196338i | −0.0115329 | + | 0.00107878i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.3140 | − | 61.5658i | 0.0832282 | − | 0.334597i | ||||
\(185\) | −179.165 | + | 310.323i | −0.968460 | + | 1.67742i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −255.795 | + | 147.683i | −1.36789 | + | 0.789749i | ||||
\(188\) | −33.7664 | + | 29.0312i | −0.179609 | + | 0.154421i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 100.057 | − | 217.978i | 0.526614 | − | 1.14725i | ||||
\(191\) | 0.351914 | − | 0.203178i | 0.00184248 | − | 0.00106376i | −0.499078 | − | 0.866557i | \(-0.666328\pi\) |
0.500921 | + | 0.865493i | \(0.332995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −31.2230 | + | 54.0798i | −0.161777 | + | 0.280206i | −0.935506 | − | 0.353311i | \(-0.885056\pi\) |
0.773729 | + | 0.633517i | \(0.218389\pi\) | |||||||
\(194\) | −42.6071 | + | 30.2165i | −0.219624 | + | 0.155755i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 64.3588 | − | 183.654i | 0.328361 | − | 0.937010i | ||||
\(197\) | 207.861 | 1.05513 | 0.527566 | − | 0.849514i | \(-0.323105\pi\) | ||||
0.527566 | + | 0.849514i | \(0.323105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 299.128i | − | 1.50316i | −0.659643 | − | 0.751579i | \(-0.729293\pi\) | ||
0.659643 | − | 0.751579i | \(-0.270707\pi\) | |||||||
\(200\) | −71.0849 | + | 73.6919i | −0.355425 | + | 0.368460i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −42.0348 | + | 29.8107i | −0.208093 | + | 0.147578i | ||||
\(203\) | −3.24848 | − | 1.87551i | −0.0160024 | − | 0.00923896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.4121 | + | 28.4266i | 0.0800592 | + | 0.138667i | ||||
\(206\) | 16.3729 | − | 35.6692i | 0.0794802 | − | 0.173152i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.28163 | + | 28.2293i | −0.0205848 | + | 0.135718i | ||||
\(209\) | −170.282 | − | 294.937i | −0.814746 | − | 1.41118i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −141.744 | − | 81.8360i | −0.671773 | − | 0.387848i | 0.124975 | − | 0.992160i | \(-0.460115\pi\) |
−0.796748 | + | 0.604311i | \(0.793448\pi\) | |||||||
\(212\) | 141.019 | − | 26.6145i | 0.665182 | − | 0.125540i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −364.808 | + | 34.1240i | −1.70471 | + | 0.159458i | ||||
\(215\) | − | 240.892i | − | 1.12043i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.8629 | 0.0869257 | ||||||||
\(218\) | 18.7833 | + | 200.805i | 0.0861617 | + | 0.921126i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 79.6297 | + | 421.923i | 0.361953 | + | 1.91783i | ||||
\(221\) | −15.0944 | + | 26.1442i | −0.0683003 | + | 0.118300i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 330.681 | − | 190.919i | 1.48287 | − | 0.856138i | 0.483063 | − | 0.875586i | \(-0.339524\pi\) |
0.999811 | + | 0.0194478i | \(0.00619081\pi\) | |||||||
\(224\) | 15.8017 | + | 10.3721i | 0.0705434 | + | 0.0463042i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 33.1717 | + | 15.2265i | 0.146777 | + | 0.0673739i | ||||
\(227\) | 51.5472 | − | 29.7608i | 0.227080 | − | 0.131105i | −0.382144 | − | 0.924103i | \(-0.624814\pi\) |
0.609224 | + | 0.792998i | \(0.291481\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 64.4366 | − | 111.608i | 0.281383 | − | 0.487369i | −0.690343 | − | 0.723482i | \(-0.742540\pi\) |
0.971726 | + | 0.236113i | \(0.0758736\pi\) | |||||||
\(230\) | −56.4084 | − | 79.5393i | −0.245254 | − | 0.345823i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −35.2704 | + | 36.5639i | −0.152028 | + | 0.157603i | ||||
\(233\) | −14.9939 | −0.0643513 | −0.0321757 | − | 0.999482i | \(-0.510244\pi\) | ||||
−0.0321757 | + | 0.999482i | \(0.510244\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 68.4443i | 0.291252i | ||||||||
\(236\) | −91.0899 | − | 31.9211i | −0.385974 | − | 0.135259i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.5611 | + | 16.3018i | 0.0485759 | + | 0.0684949i | ||||
\(239\) | 315.244 | + | 182.006i | 1.31901 | + | 0.761532i | 0.983570 | − | 0.180529i | \(-0.0577811\pi\) |
0.335442 | + | 0.942061i | \(0.391114\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −40.5235 | − | 70.1888i | −0.168147 | − | 0.291240i | 0.769621 | − | 0.638501i | \(-0.220445\pi\) |
−0.937769 | + | 0.347261i | \(0.887112\pi\) | |||||||
\(242\) | 334.156 | + | 153.385i | 1.38081 | + | 0.633820i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 197.907 | + | 230.188i | 0.811095 | + | 0.943393i | ||||
\(245\) | −149.555 | − | 259.037i | −0.610428 | − | 1.05729i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.1448 | − | 17.4041i | −0.122044 | − | 0.0704620i | ||||
\(248\) | 61.6679 | − | 247.919i | 0.248661 | − | 0.999674i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.9727 | − | 149.377i | −0.0558907 | − | 0.597508i | ||||
\(251\) | − | 281.883i | − | 1.12304i | −0.827463 | − | 0.561520i | \(-0.810217\pi\) | ||
0.827463 | − | 0.561520i | \(-0.189783\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −138.459 | −0.547268 | ||||||||
\(254\) | −327.342 | + | 30.6195i | −1.28875 | + | 0.120549i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 187.984 | − | 173.776i | 0.734311 | − | 0.678813i | ||||
\(257\) | 37.6564 | − | 65.2227i | 0.146523 | − | 0.253785i | −0.783417 | − | 0.621496i | \(-0.786525\pi\) |
0.929940 | + | 0.367711i | \(0.119858\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.8145 | − | 17.2134i | 0.115114 | − | 0.0664610i | ||||
\(260\) | 28.6103 | + | 33.2769i | 0.110040 | + | 0.127988i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −118.905 | + | 259.041i | −0.453838 | + | 0.988708i | ||||
\(263\) | 105.914 | − | 61.1497i | 0.402716 | − | 0.232508i | −0.284939 | − | 0.958546i | \(-0.591973\pi\) |
0.687655 | + | 0.726037i | \(0.258640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 110.287 | − | 191.023i | 0.416178 | − | 0.720841i | ||||
\(266\) | −18.7963 | + | 13.3302i | −0.0706628 | + | 0.0501134i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 138.700 | + | 48.6054i | 0.517538 | + | 0.181364i | ||||
\(269\) | −280.452 | −1.04257 | −0.521287 | − | 0.853382i | \(-0.674548\pi\) | ||||
−0.521287 | + | 0.853382i | \(0.674548\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 81.4468i | − | 0.300542i | −0.988645 | − | 0.150271i | \(-0.951985\pi\) | ||
0.988645 | − | 0.150271i | \(-0.0480146\pi\) | |||||||
\(272\) | 252.054 | − | 98.6547i | 0.926670 | − | 0.362701i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.0551 | + | 7.13098i | −0.0366975 | + | 0.0260255i | ||||
\(275\) | 193.522 | + | 111.730i | 0.703716 | + | 0.406291i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 224.861 | + | 389.471i | 0.811774 | + | 1.40603i | 0.911622 | + | 0.411031i | \(0.134831\pi\) |
−0.0998479 | + | 0.995003i | \(0.531836\pi\) | |||||||
\(278\) | −99.3939 | + | 216.534i | −0.357532 | + | 0.778901i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 27.9224 | − | 8.02330i | 0.0997229 | − | 0.0286546i | ||||
\(281\) | 37.8649 | + | 65.5838i | 0.134750 | + | 0.233394i | 0.925502 | − | 0.378743i | \(-0.123643\pi\) |
−0.790752 | + | 0.612137i | \(0.790310\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −322.061 | − | 185.942i | −1.13803 | − | 0.657039i | −0.192084 | − | 0.981378i | \(-0.561525\pi\) |
−0.945941 | + | 0.324339i | \(0.894858\pi\) | |||||||
\(284\) | 65.1597 | + | 345.253i | 0.229436 | + | 1.21568i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 62.0429 | − | 5.80347i | 0.216933 | − | 0.0202919i | ||||
\(287\) | − | 3.15361i | − | 0.0109882i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.81196 | −0.00972996 | ||||||||
\(290\) | 7.27226 | + | 77.7453i | 0.0250768 | + | 0.268087i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 236.003 | − | 44.5409i | 0.808229 | − | 0.152537i | ||||
\(293\) | 66.3946 | − | 114.999i | 0.226603 | − | 0.392488i | −0.730196 | − | 0.683237i | \(-0.760571\pi\) |
0.956799 | + | 0.290750i | \(0.0939047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −128.479 | + | 74.1772i | −0.435521 | + | 0.251448i | ||||
\(296\) | −128.768 | − | 448.134i | −0.435027 | − | 1.51397i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 375.765 | + | 172.484i | 1.26096 | + | 0.578806i | ||||
\(299\) | −12.2556 | + | 7.07579i | −0.0409887 | + | 0.0236648i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.5719 | + | 20.0432i | −0.0384450 | + | 0.0665886i | ||||
\(302\) | 170.229 | + | 240.033i | 0.563672 | + | 0.794811i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 113.751 | + | 290.624i | 0.374181 | + | 0.956000i | ||||
\(305\) | 466.589 | 1.52980 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 336.514i | 1.09614i | 0.836434 | + | 0.548068i | \(0.184637\pi\) | ||||
−0.836434 | + | 0.548068i | \(0.815363\pi\) | |||||||
\(308\) | 13.6428 | − | 38.9309i | 0.0442947 | − | 0.126399i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −227.151 | − | 320.296i | −0.732745 | − | 1.03321i | ||||
\(311\) | −304.206 | − | 175.634i | −0.978156 | − | 0.564738i | −0.0764428 | − | 0.997074i | \(-0.524356\pi\) |
−0.901713 | + | 0.432336i | \(0.857690\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −95.4299 | − | 165.289i | −0.304888 | − | 0.528081i | 0.672349 | − | 0.740235i | \(-0.265286\pi\) |
−0.977236 | + | 0.212154i | \(0.931952\pi\) | |||||||
\(314\) | 114.292 | + | 52.4626i | 0.363988 | + | 0.167078i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −112.719 | + | 96.9117i | −0.356706 | + | 0.306683i | ||||
\(317\) | 202.797 | + | 351.255i | 0.639738 | + | 1.10806i | 0.985490 | + | 0.169733i | \(0.0542906\pi\) |
−0.345752 | + | 0.938326i | \(0.612376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 96.0203 | + | 55.4374i | 0.301004 | + | 0.173785i | ||||
\(320\) | −14.1661 | − | 393.221i | −0.0442692 | − | 1.22882i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.872512 | + | 9.32773i | 0.00270966 | + | 0.0289681i | ||||
\(323\) | 329.981i | 1.02161i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.8393 | 0.0702749 | ||||||||
\(326\) | −285.403 | + | 26.6965i | −0.875470 | + | 0.0818911i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −41.4487 | − | 10.3100i | −0.126368 | − | 0.0314330i | ||||
\(329\) | 3.28792 | − | 5.69484i | 0.00999368 | − | 0.0173096i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 384.104 | − | 221.763i | 1.16044 | − | 0.669978i | 0.209027 | − | 0.977910i | \(-0.432970\pi\) |
0.951408 | + | 0.307932i | \(0.0996370\pi\) | |||||||
\(332\) | −231.251 | + | 198.822i | −0.696541 | + | 0.598860i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 145.024 | − | 315.941i | 0.434203 | − | 0.945931i | ||||
\(335\) | 195.631 | − | 112.948i | 0.583974 | − | 0.337158i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −254.239 | + | 440.356i | −0.754420 | + | 1.30669i | 0.191243 | + | 0.981543i | \(0.438748\pi\) |
−0.945662 | + | 0.325150i | \(0.894585\pi\) | |||||||
\(338\) | −270.510 | + | 191.843i | −0.800325 | + | 0.567582i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 137.588 | − | 392.619i | 0.404670 | − | 1.15476i | ||||
\(341\) | −557.560 | −1.63507 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 57.6805i | 0.168165i | ||||||||
\(344\) | 225.600 | + | 217.619i | 0.655814 | + | 0.632614i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −410.476 | + | 291.106i | −1.18635 | + | 0.841346i | ||||
\(347\) | −492.773 | − | 284.503i | −1.42010 | − | 0.819893i | −0.423790 | − | 0.905761i | \(-0.639300\pi\) |
−0.996307 | + | 0.0858678i | \(0.972634\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −206.901 | − | 358.363i | −0.592840 | − | 1.02683i | −0.993848 | − | 0.110754i | \(-0.964673\pi\) |
0.401008 | − | 0.916074i | \(-0.368660\pi\) | |||||||
\(350\) | 6.30755 | − | 13.7413i | 0.0180216 | − | 0.0392609i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −467.076 | − | 306.586i | −1.32692 | − | 0.870982i | ||||
\(353\) | −62.3070 | − | 107.919i | −0.176507 | − | 0.305719i | 0.764175 | − | 0.645009i | \(-0.223147\pi\) |
−0.940682 | + | 0.339290i | \(0.889813\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 467.677 | + | 270.014i | 1.31740 | + | 0.760602i | ||||
\(356\) | −108.435 | + | 20.4649i | −0.304592 | + | 0.0574858i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −191.177 | + | 17.8826i | −0.534015 | + | 0.0499515i | ||||
\(359\) | 303.196i | 0.844557i | 0.906466 | + | 0.422278i | \(0.138770\pi\) | ||||
−0.906466 | + | 0.422278i | \(0.861230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.4752 | −0.0539480 | ||||||||
\(362\) | −61.2363 | − | 654.657i | −0.169161 | − | 1.80844i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.781939 | − | 4.14315i | −0.00214818 | − | 0.0113823i | ||||
\(365\) | 184.572 | − | 319.688i | 0.505677 | − | 0.875858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −615.571 | + | 355.400i | −1.67730 | + | 0.968392i | −0.713936 | + | 0.700211i | \(0.753089\pi\) |
−0.963369 | + | 0.268181i | \(0.913578\pi\) | |||||||
\(368\) | 125.449 | + | 19.0273i | 0.340894 | + | 0.0517045i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −651.321 | − | 298.970i | −1.76033 | − | 0.808027i | ||||
\(371\) | −18.3527 | + | 10.5959i | −0.0494681 | + | 0.0285604i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 166.740 | − | 288.803i | 0.447025 | − | 0.774271i | −0.551166 | − | 0.834396i | \(-0.685817\pi\) |
0.998191 | + | 0.0601254i | \(0.0191501\pi\) | |||||||
\(374\) | −341.728 | − | 481.857i | −0.913712 | − | 1.28839i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −64.0995 | − | 61.8318i | −0.170477 | − | 0.164446i | ||||
\(377\) | 11.3323 | 0.0300590 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 662.686i | − | 1.74851i | −0.485465 | − | 0.874256i | \(-0.661350\pi\) | ||
0.485465 | − | 0.874256i | \(-0.338650\pi\) | |||||||
\(380\) | 452.699 | + | 158.642i | 1.19131 | + | 0.417478i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.470139 | + | 0.662924i | 0.00123073 | + | 0.00173540i | ||||
\(383\) | 69.9008 | + | 40.3572i | 0.182509 | + | 0.105371i | 0.588471 | − | 0.808518i | \(-0.299730\pi\) |
−0.405962 | + | 0.913890i | \(0.633064\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.7026 | − | 54.9106i | −0.0823445 | − | 0.142625i | ||||
\(386\) | −113.505 | − | 52.1013i | −0.294055 | − | 0.134977i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −68.1066 | − | 79.2155i | −0.175533 | − | 0.204164i | ||||
\(389\) | 346.006 | + | 599.301i | 0.889476 | + | 1.54062i | 0.840495 | + | 0.541819i | \(0.182264\pi\) |
0.0489809 | + | 0.998800i | \(0.484403\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 116.183 | + | 67.0782i | 0.297143 | + | 0.171556i | ||||
\(392\) | 377.700 | + | 93.9497i | 0.963519 | + | 0.239668i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 38.7174 | + | 413.915i | 0.0982675 | + | 1.05055i | ||||
\(395\) | 228.481i | 0.578432i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 657.713 | 1.65671 | 0.828354 | − | 0.560206i | \(-0.189278\pi\) | ||||
0.828354 | + | 0.560206i | \(0.189278\pi\) | |||||||
\(398\) | 595.657 | − | 55.7175i | 1.49662 | − | 0.139994i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −159.984 | − | 127.826i | −0.399960 | − | 0.319564i | ||||
\(401\) | −296.433 | + | 513.437i | −0.739235 | + | 1.28039i | 0.213606 | + | 0.976920i | \(0.431479\pi\) |
−0.952840 | + | 0.303472i | \(0.901854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −49.3521 | + | 28.4935i | −0.122462 | + | 0.0707034i | ||||
\(404\) | −67.1918 | − | 78.1515i | −0.166316 | − | 0.193444i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.12963 | − | 6.81806i | 0.00770846 | − | 0.0167933i | ||||
\(407\) | −881.274 | + | 508.804i | −2.16529 | + | 1.25013i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −161.594 | + | 279.889i | −0.395095 | + | 0.684325i | −0.993113 | − | 0.117157i | \(-0.962622\pi\) |
0.598018 | + | 0.801483i | \(0.295955\pi\) | |||||||
\(410\) | −53.5492 | + | 37.9765i | −0.130608 | + | 0.0926257i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 74.0781 | + | 25.9596i | 0.179801 | + | 0.0630086i | ||||
\(413\) | 14.2533 | 0.0345115 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 468.745i | 1.12951i | ||||||||
\(416\) | −57.0107 | − | 3.26788i | −0.137045 | − | 0.00785549i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 555.592 | − | 394.020i | 1.32917 | − | 0.942632i | ||||
\(419\) | 222.744 | + | 128.601i | 0.531608 | + | 0.306924i | 0.741671 | − | 0.670764i | \(-0.234033\pi\) |
−0.210063 | + | 0.977688i | \(0.567367\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 41.9905 | + | 72.7297i | 0.0997400 | + | 0.172755i | 0.911577 | − | 0.411129i | \(-0.134866\pi\) |
−0.811837 | + | 0.583884i | \(0.801532\pi\) | |||||||
\(422\) | 136.559 | − | 297.499i | 0.323598 | − | 0.704975i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 79.2646 | + | 275.854i | 0.186945 | + | 0.650599i | ||||
\(425\) | −108.258 | − | 187.509i | −0.254725 | − | 0.441197i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −38.8221 | − | 22.4139i | −0.0909182 | − | 0.0524917i | ||||
\(428\) | −135.903 | − | 720.089i | −0.317530 | − | 1.68245i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 479.690 | − | 44.8700i | 1.11556 | − | 0.104349i | ||||
\(431\) | 144.348i | 0.334914i | 0.985879 | + | 0.167457i | \(0.0535555\pi\) | ||||
−0.985879 | + | 0.167457i | \(0.946445\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 395.353 | 0.913057 | 0.456528 | − | 0.889709i | \(-0.349093\pi\) | ||||
0.456528 | + | 0.889709i | \(0.349093\pi\) | |||||||
\(434\) | 3.51351 | + | 37.5618i | 0.00809566 | + | 0.0865479i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −396.367 | + | 74.8065i | −0.909098 | + | 0.171574i | ||||
\(437\) | −77.3426 | + | 133.961i | −0.176985 | + | 0.306548i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −194.776 | + | 112.454i | −0.443682 | + | 0.256160i | −0.705158 | − | 0.709050i | \(-0.749124\pi\) |
0.261476 | + | 0.965210i | \(0.415791\pi\) | |||||||
\(440\) | −825.346 | + | 237.157i | −1.87579 | + | 0.538994i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −54.8727 | − | 25.1877i | −0.124146 | − | 0.0569858i | ||||
\(443\) | 369.184 | − | 213.148i | 0.833373 | − | 0.481148i | −0.0216335 | − | 0.999766i | \(-0.506887\pi\) |
0.855006 | + | 0.518618i | \(0.173553\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −84.8041 | + | 146.885i | −0.190571 | + | 0.330079i | ||||
\(446\) | 441.772 | + | 622.926i | 0.990521 | + | 1.39669i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −17.7108 | + | 33.3981i | −0.0395331 | + | 0.0745493i | ||||
\(449\) | 406.744 | 0.905888 | 0.452944 | − | 0.891539i | \(-0.350374\pi\) | ||||
0.452944 | + | 0.891539i | \(0.350374\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 93.2163i | 0.206688i | ||||||||
\(452\) | −24.1419 | + | 68.8911i | −0.0534112 | + | 0.152414i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 68.8644 | + | 97.1029i | 0.151684 | + | 0.213883i | ||||
\(455\) | −5.61228 | − | 3.24025i | −0.0123347 | − | 0.00712144i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −159.600 | − | 276.435i | −0.349234 | − | 0.604891i | 0.636879 | − | 0.770963i | \(-0.280225\pi\) |
−0.986114 | + | 0.166072i | \(0.946892\pi\) | |||||||
\(458\) | 234.247 | + | 107.524i | 0.511457 | + | 0.234770i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 147.880 | − | 127.142i | 0.321479 | − | 0.276396i | ||||
\(461\) | −293.888 | − | 509.029i | −0.637501 | − | 1.10418i | −0.985979 | − | 0.166867i | \(-0.946635\pi\) |
0.348478 | − | 0.937317i | \(-0.386698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 230.088 | + | 132.841i | 0.496950 | + | 0.286914i | 0.727453 | − | 0.686157i | \(-0.240704\pi\) |
−0.230503 | + | 0.973072i | \(0.574037\pi\) | |||||||
\(464\) | −79.3797 | − | 63.4236i | −0.171077 | − | 0.136689i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.79285 | − | 29.8574i | −0.00599323 | − | 0.0640716i | ||||
\(467\) | − | 794.598i | − | 1.70149i | −0.525575 | − | 0.850747i | \(-0.676150\pi\) | ||
0.525575 | − | 0.850747i | \(-0.323850\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.7031 | −0.0462752 | ||||||||
\(470\) | −136.294 | + | 12.7489i | −0.289987 | + | 0.0271252i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 46.5978 | − | 187.334i | 0.0987241 | − | 0.396894i | ||||
\(473\) | 342.050 | − | 592.447i | 0.723149 | − | 1.25253i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 216.201 | − | 124.824i | 0.455161 | − | 0.262787i | ||||
\(476\) | −30.3084 | + | 26.0581i | −0.0636732 | + | 0.0547439i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −303.711 | + | 661.649i | −0.635378 | + | 1.38420i | ||||
\(479\) | 572.964 | − | 330.801i | 1.19617 | − | 0.690607i | 0.236468 | − | 0.971639i | \(-0.424010\pi\) |
0.959698 | + | 0.281033i | \(0.0906769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −52.0037 | + | 90.0730i | −0.108116 | + | 0.187262i | ||||
\(482\) | 132.219 | − | 93.7686i | 0.274314 | − | 0.194541i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −243.194 | + | 693.977i | −0.502467 | + | 1.43384i | ||||
\(485\) | −160.569 | −0.331071 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 57.1525i | 0.117356i | 0.998277 | + | 0.0586781i | \(0.0186886\pi\) | ||||
−0.998277 | + | 0.0586781i | \(0.981311\pi\) | |||||||
\(488\) | −421.511 | + | 436.970i | −0.863753 | + | 0.895430i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 487.965 | − | 346.060i | 0.995847 | − | 0.706244i | ||||
\(491\) | −48.6600 | − | 28.0939i | −0.0991040 | − | 0.0572177i | 0.449629 | − | 0.893215i | \(-0.351556\pi\) |
−0.548733 | + | 0.835998i | \(0.684890\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −53.7147 | − | 93.0366i | −0.108955 | − | 0.188715i | ||||
\(494\) | 29.0420 | − | 63.2694i | 0.0587895 | − | 0.128076i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 505.170 | + | 76.6208i | 1.01849 | + | 0.154477i | ||||
\(497\) | −25.9417 | − | 44.9324i | −0.0521967 | − | 0.0904073i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 522.225 | + | 301.507i | 1.04654 | + | 0.604222i | 0.921679 | − | 0.387952i | \(-0.126817\pi\) |
0.124863 | + | 0.992174i | \(0.460151\pi\) | |||||||
\(500\) | 294.853 | − | 55.6477i | 0.589706 | − | 0.111295i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 561.316 | − | 52.5052i | 1.11816 | − | 0.104592i | ||||
\(503\) | 549.354i | 1.09216i | 0.837734 | + | 0.546078i | \(0.183880\pi\) | ||||
−0.837734 | + | 0.546078i | \(0.816120\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −158.413 | −0.313688 | ||||||||
\(506\) | −25.7902 | − | 275.714i | −0.0509687 | − | 0.544890i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −121.946 | − | 646.136i | −0.240050 | − | 1.27192i | ||||
\(509\) | 119.464 | − | 206.918i | 0.234704 | − | 0.406519i | −0.724483 | − | 0.689293i | \(-0.757921\pi\) |
0.959187 | + | 0.282774i | \(0.0912547\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.7143 | + | 17.7329i | −0.0601062 | + | 0.0347023i | ||||
\(512\) | 381.057 | + | 341.964i | 0.744252 | + | 0.667899i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 136.893 | + | 62.8366i | 0.266328 | + | 0.122250i | ||||
\(515\) | 104.484 | − | 60.3240i | 0.202882 | − | 0.117134i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −97.1862 | + | 168.331i | −0.187981 | + | 0.325593i | ||||
\(518\) | 39.8306 | + | 56.1636i | 0.0768931 | + | 0.108424i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −60.9355 | + | 63.1703i | −0.117184 | + | 0.121481i | ||||
\(521\) | 567.711 | 1.08966 | 0.544828 | − | 0.838548i | \(-0.316595\pi\) | ||||
0.544828 | + | 0.838548i | \(0.316595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 941.999i | − | 1.80114i | −0.434706 | − | 0.900572i | \(-0.643148\pi\) | ||
0.434706 | − | 0.900572i | \(-0.356852\pi\) | |||||||
\(524\) | −537.979 | − | 188.527i | −1.02668 | − | 0.359784i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 141.496 | + | 199.518i | 0.269004 | + | 0.379312i | ||||
\(527\) | 467.856 | + | 270.117i | 0.887773 | + | 0.512556i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −233.056 | − | 403.664i | −0.440559 | − | 0.763071i | ||||
\(530\) | 400.928 | + | 184.034i | 0.756468 | + | 0.347235i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −30.0456 | − | 34.9463i | −0.0564766 | − | 0.0656885i | ||||
\(533\) | 4.76372 | + | 8.25100i | 0.00893755 | + | 0.0154803i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −975.428 | − | 563.163i | −1.82323 | − | 1.05264i | ||||
\(536\) | −70.9532 | + | 285.248i | −0.132375 | + | 0.532180i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −52.2387 | − | 558.467i | −0.0970980 | − | 1.03804i | ||||
\(539\) | − | 849.430i | − | 1.57594i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −242.245 | −0.447772 | −0.223886 | − | 0.974615i | \(-0.571874\pi\) | ||||
−0.223886 | + | 0.974615i | \(0.571874\pi\) | |||||||
\(542\) | 162.186 | − | 15.1708i | 0.299235 | − | 0.0279904i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 243.401 | + | 483.542i | 0.447428 | + | 0.888863i | ||||
\(545\) | −309.988 | + | 536.915i | −0.568786 | + | 0.985166i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −170.503 | + | 98.4402i | −0.311706 | + | 0.179964i | −0.647690 | − | 0.761904i | \(-0.724265\pi\) |
0.335983 | + | 0.941868i | \(0.390931\pi\) | |||||||
\(548\) | −16.0729 | − | 18.6945i | −0.0293301 | − | 0.0341141i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −186.442 | + | 406.173i | −0.338986 | + | 0.738497i | ||||
\(551\) | 107.273 | − | 61.9342i | 0.194688 | − | 0.112403i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.9757 | − | 19.0105i | 0.0198476 | − | 0.0343770i | ||||
\(554\) | −733.673 | + | 520.313i | −1.32432 | + | 0.939194i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −449.700 | − | 157.591i | −0.808814 | − | 0.283437i | ||||
\(557\) | −958.121 | −1.72015 | −0.860073 | − | 0.510171i | \(-0.829582\pi\) | ||||
−0.860073 | + | 0.510171i | \(0.829582\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 69.9202i | − | 0.125081i | ||||||
\(560\) | 21.1779 | + | 54.1076i | 0.0378176 | + | 0.0966208i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −123.545 | + | 87.6166i | −0.219830 | + | 0.155901i | ||||
\(563\) | −165.774 | − | 95.7097i | −0.294448 | − | 0.169999i | 0.345498 | − | 0.938419i | \(-0.387710\pi\) |
−0.639946 | + | 0.768420i | \(0.721043\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 56.1001 | + | 97.1682i | 0.0992922 | + | 0.171979i | ||||
\(566\) | 310.279 | − | 675.957i | 0.548196 | − | 1.19427i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −675.368 | + | 194.062i | −1.18903 | + | 0.341658i | ||||
\(569\) | −228.215 | − | 395.280i | −0.401081 | − | 0.694693i | 0.592775 | − | 0.805368i | \(-0.298032\pi\) |
−0.993857 | + | 0.110675i | \(0.964699\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −842.764 | − | 486.570i | −1.47594 | − | 0.852136i | −0.476312 | − | 0.879276i | \(-0.658027\pi\) |
−0.999632 | + | 0.0271399i | \(0.991360\pi\) | |||||||
\(572\) | 23.1130 | + | 122.466i | 0.0404073 | + | 0.214101i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.27982 | − | 0.587411i | 0.0109404 | − | 0.00102336i | ||||
\(575\) | − | 101.496i | − | 0.176515i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 138.527 | 0.240081 | 0.120040 | − | 0.992769i | \(-0.461698\pi\) | ||||
0.120040 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(578\) | −0.523773 | − | 5.59948i | −0.000906181 | − | 0.00968768i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −153.460 | + | 28.9626i | −0.264586 | + | 0.0499355i | ||||
\(581\) | 22.5175 | − | 39.0015i | 0.0387565 | − | 0.0671282i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 542.478 | − | 313.200i | 0.930494 | − | 0.537221i | ||||
\(584\) | 132.654 | + | 461.658i | 0.227147 | + | 0.790510i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 241.365 | + | 110.792i | 0.411886 | + | 0.189064i | ||||
\(587\) | −620.808 | + | 358.424i | −1.05759 | + | 0.610602i | −0.924766 | − | 0.380537i | \(-0.875739\pi\) |
−0.132829 | + | 0.991139i | \(0.542406\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −311.451 | + | 539.449i | −0.528779 | + | 0.915872i | ||||
\(590\) | −171.641 | − | 242.024i | −0.290917 | − | 0.410210i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 868.387 | − | 339.889i | 1.46687 | − | 0.574137i | ||||
\(593\) | −542.129 | −0.914214 | −0.457107 | − | 0.889412i | \(-0.651114\pi\) | ||||
−0.457107 | + | 0.889412i | \(0.651114\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 61.4350i | 0.103252i | ||||||||
\(596\) | −273.477 | + | 780.391i | −0.458853 | + | 1.30938i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.3729 | − | 23.0867i | −0.0273794 | − | 0.0386066i | ||||
\(599\) | 245.527 | + | 141.755i | 0.409895 | + | 0.236653i | 0.690744 | − | 0.723099i | \(-0.257283\pi\) |
−0.280850 | + | 0.959752i | \(0.590616\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 377.424 | + | 653.717i | 0.627993 | + | 1.08772i | 0.987954 | + | 0.154748i | \(0.0494567\pi\) |
−0.359961 | + | 0.932967i | \(0.617210\pi\) | |||||||
\(602\) | −42.0676 | − | 19.3099i | −0.0698797 | − | 0.0320763i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −446.272 | + | 383.688i | −0.738860 | + | 0.635245i | ||||
\(605\) | 565.126 | + | 978.827i | 0.934093 | + | 1.61790i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 77.2227 | + | 44.5845i | 0.127220 | + | 0.0734506i | 0.562260 | − | 0.826961i | \(-0.309932\pi\) |
−0.435039 | + | 0.900411i | \(0.643266\pi\) | |||||||
\(608\) | −557.534 | + | 280.647i | −0.916997 | + | 0.461590i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 86.9097 | + | 929.122i | 0.142475 | + | 1.52315i | ||||
\(611\) | 19.8664i | 0.0325145i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −316.779 | −0.516769 | −0.258385 | − | 0.966042i | \(-0.583190\pi\) | ||||
−0.258385 | + | 0.966042i | \(0.583190\pi\) | |||||||
\(614\) | −670.103 | + | 62.6811i | −1.09137 | + | 0.102087i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 80.0646 | + | 19.9154i | 0.129975 | + | 0.0323302i | ||||
\(617\) | −534.934 | + | 926.533i | −0.866992 | + | 1.50167i | −0.00193565 | + | 0.999998i | \(0.500616\pi\) |
−0.865056 | + | 0.501675i | \(0.832717\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 578.542 | − | 334.021i | 0.934640 | − | 0.539615i | 0.0463638 | − | 0.998925i | \(-0.485237\pi\) |
0.888276 | + | 0.459310i | \(0.151903\pi\) | |||||||
\(620\) | 595.498 | − | 511.988i | 0.960481 | − | 0.825787i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 293.077 | − | 638.483i | 0.471185 | − | 1.02650i | ||||
\(623\) | 14.1121 | − | 8.14762i | 0.0226518 | − | 0.0130780i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390.580 | − | 676.505i | 0.624929 | − | 1.08241i | ||||
\(626\) | 311.367 | − | 220.818i | 0.497391 | − | 0.352744i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −83.1804 | + | 237.363i | −0.132453 | + | 0.377967i | ||||
\(629\) | 985.986 | 1.56755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 150.631i | 0.238718i | 0.992851 | + | 0.119359i | \(0.0380839\pi\) | ||||
−0.992851 | + | 0.119359i | \(0.961916\pi\) | |||||||
\(632\) | −213.977 | − | 206.407i | −0.338571 | − | 0.326593i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −661.682 | + | 469.258i | −1.04366 | + | 0.740155i | ||||
\(635\) | −875.252 | − | 505.327i | −1.37835 | − | 0.795790i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −43.4092 | − | 75.1869i | −0.0681463 | − | 0.118033i | ||||
\(638\) | −92.5075 | + | 201.532i | −0.144996 | + | 0.315881i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 780.385 | − | 101.453i | 1.21935 | − | 0.158520i | ||||
\(641\) | −351.521 | − | 608.852i | −0.548395 | − | 0.949847i | −0.998385 | − | 0.0568139i | \(-0.981906\pi\) |
0.449990 | − | 0.893034i | \(-0.351427\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 742.057 | + | 428.427i | 1.15405 | + | 0.666293i | 0.949872 | − | 0.312639i | \(-0.101213\pi\) |
0.204182 | + | 0.978933i | \(0.434546\pi\) | |||||||
\(644\) | −18.4119 | + | 3.47488i | −0.0285898 | + | 0.00539577i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −657.094 | + | 61.4643i | −1.01717 | + | 0.0951459i | ||||
\(647\) | − | 156.257i | − | 0.241510i | −0.992682 | − | 0.120755i | \(-0.961468\pi\) | ||
0.992682 | − | 0.120755i | \(-0.0385316\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −421.306 | −0.649162 | ||||||||
\(650\) | 4.25419 | + | 45.4802i | 0.00654491 | + | 0.0699695i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −106.322 | − | 563.353i | −0.163070 | − | 0.864038i | ||||
\(653\) | 441.773 | − | 765.173i | 0.676528 | − | 1.17178i | −0.299492 | − | 0.954099i | \(-0.596817\pi\) |
0.976020 | − | 0.217682i | \(-0.0698495\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −758.798 | + | 438.092i | −1.15847 | + | 0.668843i | ||||
\(656\) | 12.8099 | − | 84.4574i | 0.0195273 | − | 0.128746i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.9526 | + | 5.48650i | 0.0181651 | + | 0.00833815i | ||||
\(659\) | 379.533 | − | 219.123i | 0.575922 | − | 0.332509i | −0.183589 | − | 0.983003i | \(-0.558772\pi\) |
0.759511 | + | 0.650494i | \(0.225438\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 233.924 | − | 405.168i | 0.353894 | − | 0.612963i | −0.633034 | − | 0.774124i | \(-0.718191\pi\) |
0.986928 | + | 0.161161i | \(0.0515239\pi\) | |||||||
\(662\) | 513.143 | + | 723.562i | 0.775140 | + | 1.09299i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −438.989 | − | 423.459i | −0.661128 | − | 0.637739i | ||||
\(665\) | −70.8359 | −0.106520 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 50.3597i | − | 0.0755018i | ||||||
\(668\) | 656.149 | + | 229.938i | 0.982259 | + | 0.344218i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 261.353 | + | 368.524i | 0.390079 | + | 0.550035i | ||||
\(671\) | 1147.52 | + | 662.524i | 1.71017 | + | 0.987368i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 273.302 | + | 473.372i | 0.406094 | + | 0.703376i | 0.994448 | − | 0.105227i | \(-0.0335571\pi\) |
−0.588354 | + | 0.808604i | \(0.700224\pi\) | |||||||
\(674\) | −924.240 | − | 424.246i | −1.37128 | − | 0.629444i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −432.405 | − | 502.934i | −0.639652 | − | 0.743986i | ||||
\(677\) | −227.606 | − | 394.225i | −0.336198 | − | 0.582312i | 0.647516 | − | 0.762052i | \(-0.275808\pi\) |
−0.983714 | + | 0.179740i | \(0.942475\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.3600 | + | 7.71341i | 0.0196760 | + | 0.0113600i | ||||
\(680\) | 807.454 | + | 200.848i | 1.18743 | + | 0.295364i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −103.854 | − | 1110.27i | −0.152279 | − | 1.62797i | ||||
\(683\) | − | 123.214i | − | 0.180400i | −0.995924 | − | 0.0902002i | \(-0.971249\pi\) | ||
0.995924 | − | 0.0902002i | \(-0.0287507\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.8937 | −0.0553193 | ||||||||
\(686\) | −114.860 | + | 10.7439i | −0.167434 | + | 0.0156617i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −391.325 | + | 489.774i | −0.568786 | + | 0.711881i | ||||
\(689\) | 32.0115 | − | 55.4455i | 0.0464607 | − | 0.0804724i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −163.326 | + | 94.2965i | −0.236362 | + | 0.136464i | −0.613504 | − | 0.789692i | \(-0.710240\pi\) |
0.377141 | + | 0.926156i | \(0.376907\pi\) | |||||||
\(692\) | −656.139 | − | 763.162i | −0.948177 | − | 1.10283i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 474.746 | − | 1034.26i | 0.684071 | − | 1.49028i | ||||
\(695\) | −634.285 | + | 366.204i | −0.912640 | + | 0.526913i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.1599 | − | 78.2192i | 0.0647918 | − | 0.112223i | ||||
\(698\) | 675.073 | − | 478.754i | 0.967153 | − | 0.685895i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 28.5381 | + | 10.0007i | 0.0407686 | + | 0.0142868i | ||||
\(701\) | 810.064 | 1.15558 | 0.577792 | − | 0.816184i | \(-0.303915\pi\) | ||||
0.577792 | + | 0.816184i | \(0.303915\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1136.86i | 1.61716i | ||||||||
\(704\) | 523.506 | − | 987.199i | 0.743616 | − | 1.40227i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 203.294 | − | 144.174i | 0.287952 | − | 0.204212i | ||||
\(707\) | 13.1806 | + | 7.60980i | 0.0186429 | + | 0.0107635i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −651.819 | − | 1128.98i | −0.919349 | − | 1.59236i | −0.800406 | − | 0.599459i | \(-0.795382\pi\) |
−0.118944 | − | 0.992901i | \(-0.537951\pi\) | |||||||
\(710\) | −450.568 | + | 981.583i | −0.634602 | + | 1.38251i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −60.9497 | − | 212.115i | −0.0856035 | − | 0.297914i | ||||
\(713\) | 126.623 | + | 219.317i | 0.177592 | + | 0.307598i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 165.891 | + | 95.7772i | 0.232015 | + | 0.133954i | ||||
\(716\) | −71.2197 | − | 377.362i | −0.0994688 | − | 0.527042i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −603.756 | + | 56.4751i | −0.840886 | + | 0.0786561i | ||||
\(719\) | 788.981i | 1.09733i | 0.836042 | + | 0.548666i | \(0.184864\pi\) | ||||
−0.836042 | + | 0.548666i | \(0.815136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.5913 | −0.0160768 | ||||||||
\(722\) | −3.62757 | − | 38.7812i | −0.00502434 | − | 0.0537135i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1292.22 | − | 243.881i | 1.78483 | − | 0.336852i | ||||
\(725\) | −40.6380 | + | 70.3870i | −0.0560524 | + | 0.0970856i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −232.676 | + | 134.335i | −0.320049 | + | 0.184780i | −0.651414 | − | 0.758722i | \(-0.725824\pi\) |
0.331365 | + | 0.943502i | \(0.392491\pi\) | |||||||
\(728\) | 8.10464 | − | 2.32881i | 0.0111327 | − | 0.00319891i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 670.977 | + | 307.992i | 0.919146 | + | 0.421907i | ||||
\(731\) | −574.038 | + | 331.421i | −0.785277 | + | 0.453380i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.8343 | + | 63.7989i | −0.0502514 | + | 0.0870380i | −0.890057 | − | 0.455849i | \(-0.849336\pi\) |
0.839806 | + | 0.542887i | \(0.182669\pi\) | |||||||
\(734\) | −822.370 | − | 1159.59i | −1.12040 | − | 1.57982i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.5222 | + | 253.351i | −0.0197313 | + | 0.344227i | ||||
\(737\) | 641.512 | 0.870437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 448.249i | 0.606562i | 0.952901 | + | 0.303281i | \(0.0980820\pi\) | ||||
−0.952901 | + | 0.303281i | \(0.901918\pi\) | |||||||
\(740\) | 474.022 | − | 1352.67i | 0.640571 | − | 1.82793i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −24.5182 | − | 34.5721i | −0.0330434 | − | 0.0465932i | ||||
\(743\) | −656.602 | − | 379.089i | −0.883718 | − | 0.510215i | −0.0118352 | − | 0.999930i | \(-0.503767\pi\) |
−0.871882 | + | 0.489715i | \(0.837101\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 635.496 | + | 1100.71i | 0.853015 | + | 1.47746i | ||||
\(746\) | 606.153 | + | 278.237i | 0.812538 | + | 0.372972i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 895.874 | − | 770.240i | 1.19769 | − | 1.02973i | ||||
\(749\) | 54.1063 | + | 93.7149i | 0.0722381 | + | 0.125120i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1141.58 | + | 659.091i | 1.52008 | + | 0.877618i | 0.999720 | + | 0.0236697i | \(0.00753501\pi\) |
0.520358 | + | 0.853948i | \(0.325798\pi\) | |||||||
\(752\) | 111.187 | − | 139.159i | 0.147855 | − | 0.185052i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.11081 | + | 22.5660i | 0.00279949 | + | 0.0299284i | ||||
\(755\) | 904.589i | 1.19813i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 587.874 | 0.776583 | 0.388292 | − | 0.921537i | \(-0.373065\pi\) | ||||
0.388292 | + | 0.921537i | \(0.373065\pi\) | |||||||
\(758\) | 1319.61 | − | 123.436i | 1.74091 | − | 0.162844i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −231.582 | + | 931.012i | −0.304713 | + | 1.22502i | ||||
\(761\) | 188.496 | − | 326.485i | 0.247695 | − | 0.429021i | −0.715191 | − | 0.698929i | \(-0.753660\pi\) |
0.962886 | + | 0.269908i | \(0.0869934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.5845 | − | 29.7823i | 0.0676075 | − | 0.0390332i | ||||
\(764\) | −1.23252 | + | 1.05967i | −0.00161324 | + | 0.00138701i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −67.3435 | + | 146.711i | −0.0879158 | + | 0.191529i | ||||
\(767\) | −37.2917 | + | 21.5304i | −0.0486202 | + | 0.0280709i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 643.939 | − | 1115.34i | 0.837372 | − | 1.45037i | −0.0547122 | − | 0.998502i | \(-0.517424\pi\) |
0.892084 | − | 0.451869i | \(-0.149243\pi\) | |||||||
\(770\) | 103.439 | − | 73.3576i | 0.134336 | − | 0.0952697i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 82.6075 | − | 235.728i | 0.107005 | − | 0.305348i | ||||
\(773\) | −778.578 | −1.00722 | −0.503608 | − | 0.863932i | \(-0.667994\pi\) | ||||
−0.503608 | + | 0.863932i | \(0.667994\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 408.715i | − | 0.527375i | ||||||
\(776\) | 145.057 | − | 150.376i | 0.186929 | − | 0.193784i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1128.94 | + | 800.634i | −1.45108 | + | 1.02909i | ||||
\(779\) | 90.1884 | + | 52.0703i | 0.115775 | + | 0.0668425i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 766.801 | + | 1328.14i | 0.981819 | + | 1.70056i | ||||
\(782\) | −111.932 | + | 243.850i | −0.143136 | + | 0.311829i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −116.730 | + | 769.615i | −0.148890 | + | 0.981652i | ||||
\(785\) | 193.292 | + | 334.791i | 0.246232 | + | 0.426486i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −390.283 | − | 225.330i | −0.495913 | − | 0.286315i | 0.231111 | − | 0.972927i | \(-0.425764\pi\) |
−0.727024 | + | 0.686612i | \(0.759097\pi\) | |||||||
\(788\) | −817.020 | + | 154.197i | −1.03683 | + | 0.195681i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −454.975 | + | 42.5582i | −0.575918 | + | 0.0538711i | ||||
\(791\) | − | 10.7797i | − | 0.0136280i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 135.430 | 0.170782 | ||||||||
\(794\) | 122.510 | + | 1309.71i | 0.154294 | + | 1.64951i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 221.901 | + | 1175.76i | 0.278770 | + | 1.47708i | ||||
\(797\) | 182.891 | − | 316.776i | 0.229474 | − | 0.397461i | −0.728178 | − | 0.685388i | \(-0.759633\pi\) |
0.957652 | + | 0.287927i | \(0.0929661\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 163.101 | − | 94.1662i | 0.204131 | − | 0.117855i | ||||
\(800\) | 224.741 | − | 342.387i | 0.280926 | − | 0.427984i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1077.63 | − | 494.653i | −1.34367 | − | 0.616775i | ||||
\(803\) | 907.869 | − | 524.158i | 1.13060 | − | 0.652750i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.3994 | + | 24.9406i | −0.0178875 | + | 0.0309821i | ||||
\(806\) | −65.9319 | − | 92.9679i | −0.0818013 | − | 0.115345i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 143.108 | − | 148.357i | 0.177114 | − | 0.183610i | ||||
\(809\) | −1167.70 | −1.44339 | −0.721695 | − | 0.692212i | \(-0.756636\pi\) | ||||
−0.721695 | + | 0.692212i | \(0.756636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 810.121i | 0.998916i | 0.866338 | + | 0.499458i | \(0.166467\pi\) | ||||
−0.866338 | + | 0.499458i | \(0.833533\pi\) | |||||||
\(812\) | 14.1598 | + | 4.96209i | 0.0174382 | + | 0.00611095i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1177.34 | − | 1660.11i | −1.44636 | − | 2.03945i | ||||
\(815\) | −763.114 | − | 440.584i | −0.936336 | − | 0.540594i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −382.135 | − | 661.878i | −0.467730 | − | 0.810132i | ||||
\(818\) | −587.445 | − | 269.650i | −0.718148 | − | 0.329645i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −85.5973 | − | 99.5591i | −0.104387 | − | 0.121414i | ||||
\(821\) | 280.513 | + | 485.862i | 0.341672 | + | 0.591793i | 0.984743 | − | 0.174013i | \(-0.0556734\pi\) |
−0.643071 | + | 0.765806i | \(0.722340\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1016.04 | − | 586.612i | −1.23456 | − | 0.712773i | −0.266583 | − | 0.963812i | \(-0.585895\pi\) |
−0.967977 | + | 0.251039i | \(0.919228\pi\) | |||||||
\(824\) | −37.8952 | + | 152.348i | −0.0459894 | + | 0.184888i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.65490 | + | 28.3826i | 0.00321416 | + | 0.0343615i | ||||
\(827\) | − | 267.739i | − | 0.323747i | −0.986811 | − | 0.161874i | \(-0.948246\pi\) | ||
0.986811 | − | 0.161874i | \(-0.0517537\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −432.474 | −0.521682 | −0.260841 | − | 0.965382i | \(-0.584000\pi\) | ||||
−0.260841 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(830\) | −933.415 | + | 87.3113i | −1.12460 | + | 0.105194i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.11180 | − | 114.135i | −0.00494207 | − | 0.137181i | ||||
\(833\) | −411.518 | + | 712.769i | −0.494019 | + | 0.855665i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 925.472 | − | 534.321i | 1.10835 | − | 0.639906i | ||||
\(836\) | 888.103 | + | 1032.96i | 1.06232 | + | 1.23560i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −214.595 | + | 467.506i | −0.256080 | + | 0.557883i | ||||
\(839\) | 459.103 | − | 265.063i | 0.547202 | − | 0.315927i | −0.200790 | − | 0.979634i | \(-0.564351\pi\) |
0.747993 | + | 0.663707i | \(0.231018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 400.337 | − | 693.403i | 0.476024 | − | 0.824499i | ||||
\(842\) | −137.006 | + | 97.1632i | −0.162715 | + | 0.115396i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 617.849 | + | 216.516i | 0.732049 | + | 0.256536i | ||||
\(845\) | −1019.44 | −1.20644 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 108.590i | − | 0.128205i | ||||||
\(848\) | −534.546 | + | 209.222i | −0.630361 | + | 0.246725i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 353.222 | − | 250.502i | 0.415556 | − | 0.294708i | ||||
\(851\) | 400.278 | + | 231.100i | 0.470361 | + | 0.271563i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 88.3868 | + | 153.090i | 0.103619 | + | 0.179473i | 0.913173 | − | 0.407572i | \(-0.133624\pi\) |
−0.809554 | + | 0.587045i | \(0.800291\pi\) | |||||||
\(854\) | 37.4018 | − | 81.4816i | 0.0437960 | − | 0.0954118i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1408.60 | − | 404.752i | 1.64557 | − | 0.472841i | ||||
\(857\) | 194.859 | + | 337.505i | 0.227373 | + | 0.393821i | 0.957029 | − | 0.289993i | \(-0.0936531\pi\) |
−0.729656 | + | 0.683815i | \(0.760320\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −503.279 | − | 290.568i | −0.585889 | − | 0.338263i | 0.177581 | − | 0.984106i | \(-0.443173\pi\) |
−0.763470 | + | 0.645843i | \(0.776506\pi\) | |||||||
\(860\) | 178.700 | + | 946.852i | 0.207791 | + | 1.10099i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −287.441 | + | 26.8871i | −0.333458 | + | 0.0311915i | ||||
\(863\) | 827.326i | 0.958663i | 0.877634 | + | 0.479331i | \(0.159121\pi\) | ||||
−0.877634 | + | 0.479331i | \(0.840879\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1546.92 | −1.78835 | ||||||||
\(866\) | 73.6409 | + | 787.270i | 0.0850357 | + | 0.909088i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −74.1426 | + | 13.9930i | −0.0854178 | + | 0.0161209i | ||||
\(869\) | −324.426 | + | 561.923i | −0.373333 | + | 0.646632i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.7831 | − | 32.7837i | 0.0651930 | − | 0.0376392i | ||||
\(872\) | −222.792 | − | 775.354i | −0.255496 | − | 0.889167i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −281.165 | − | 129.060i | −0.321699 | − | 0.147666i | ||||
\(875\) | −38.3732 | + | 22.1548i | −0.0438551 | + | 0.0253198i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −279.815 | + | 484.653i | −0.319059 | + | 0.552626i | −0.980292 | − | 0.197554i | \(-0.936700\pi\) |
0.661233 | + | 0.750181i | \(0.270033\pi\) | |||||||
\(878\) | −260.211 | − | 366.913i | −0.296368 | − | 0.417897i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −625.987 | − | 1599.34i | −0.711349 | − | 1.81744i | ||||
\(881\) | 957.127 | 1.08641 | 0.543205 | − | 0.839600i | \(-0.317211\pi\) | ||||
0.543205 | + | 0.839600i | \(0.317211\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 625.252i | − | 0.708100i | −0.935227 | − | 0.354050i | \(-0.884804\pi\) | ||
0.935227 | − | 0.354050i | \(-0.115196\pi\) | |||||||
\(884\) | 39.9356 | − | 113.960i | 0.0451760 | − | 0.128914i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 493.211 | + | 695.457i | 0.556671 | + | 0.784940i | ||||
\(887\) | −921.187 | − | 531.847i | −1.03854 | − | 0.599602i | −0.119122 | − | 0.992880i | \(-0.538008\pi\) |
−0.919420 | + | 0.393277i | \(0.871341\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.5496 | + | 84.0904i | 0.0546115 | + | 0.0945899i | ||||
\(890\) | −308.289 | − | 141.511i | −0.346393 | − | 0.159002i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1158.15 | + | 995.735i | −1.29837 | + | 1.11629i | ||||
\(893\) | 108.576 | + | 188.059i | 0.121585 | + | 0.210592i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −511.172 | − | 295.125i | −0.571142 | − | 0.329749i | ||||
\(896\) | −69.8047 | − | 29.0467i | −0.0779071 | − | 0.0324182i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 75.7625 | + | 809.951i | 0.0843681 | + | 0.901950i | ||||
\(899\) | − | 202.793i | − | 0.225577i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −606.935 | −0.673624 | ||||||||
\(902\) | −185.622 | + | 17.3630i | −0.205790 | + | 0.0192495i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −141.680 | − | 35.2418i | −0.156726 | − | 0.0389843i | ||||
\(905\) | 1010.61 | − | 1750.43i | 1.11670 | − | 1.93418i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 207.207 | − | 119.631i | 0.228453 | − | 0.131898i | −0.381405 | − | 0.924408i | \(-0.624560\pi\) |
0.609858 | + | 0.792510i | \(0.291226\pi\) | |||||||
\(908\) | −180.535 | + | 155.217i | −0.198827 | + | 0.170944i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.40696 | − | 11.7793i | 0.00594172 | − | 0.0129443i | ||||
\(911\) | −175.804 | + | 101.501i | −0.192980 | + | 0.111417i | −0.593377 | − | 0.804925i | \(-0.702206\pi\) |
0.400397 | + | 0.916342i | \(0.368872\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −665.585 | + | 1152.83i | −0.729009 | + | 1.26268i | ||||
\(914\) | 520.740 | − | 369.303i | 0.569737 | − | 0.404052i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −170.482 | + | 486.486i | −0.186116 | + | 0.531099i | ||||
\(917\) | 84.1801 | 0.0917994 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 878.708i | − | 0.956156i | −0.878317 | − | 0.478078i | \(-0.841334\pi\) | ||
0.878317 | − | 0.478078i | \(-0.158666\pi\) | |||||||
\(920\) | 280.724 | + | 270.793i | 0.305135 | + | 0.294340i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 958.892 | − | 680.036i | 1.04001 | − | 0.737566i | ||||
\(923\) | 135.746 | + | 78.3730i | 0.147070 | + | 0.0849111i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −372.975 | − | 646.011i | −0.403216 | − | 0.698391i | ||||
\(926\) | −221.670 | + | 482.920i | −0.239385 | + | 0.521512i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 111.510 | − | 169.883i | 0.120162 | − | 0.183064i | ||||
\(929\) | −300.259 | − | 520.064i | −0.323207 | − | 0.559810i | 0.657941 | − | 0.753069i | \(-0.271428\pi\) |
−0.981148 | + | 0.193259i | \(0.938094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −821.838 | − | 474.489i | −0.882748 | − | 0.509655i | ||||
\(932\) | 58.9350 | − | 11.1228i | 0.0632350 | − | 0.0119344i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1582.29 | − | 148.007i | 1.69410 | − | 0.158465i | ||||
\(935\) | − | 1815.93i | − | 1.94217i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −184.325 | −0.196718 | −0.0983589 | − | 0.995151i | \(-0.531359\pi\) | ||||
−0.0983589 | + | 0.995151i | \(0.531359\pi\) | |||||||
\(938\) | −4.04255 | − | 43.2175i | −0.00430975 | − | 0.0460741i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −50.7738 | − | 269.028i | −0.0540147 | − | 0.286200i | ||||
\(941\) | 377.587 | − | 653.999i | 0.401261 | − | 0.695005i | −0.592617 | − | 0.805484i | \(-0.701905\pi\) |
0.993878 | + | 0.110479i | \(0.0352386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.6668 | − | 21.1696i | 0.0388831 | − | 0.0224492i | ||||
\(944\) | 381.719 | + | 57.8966i | 0.404363 | + | 0.0613311i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1243.46 | + | 570.773i | 1.31444 | + | 0.603354i | ||||
\(947\) | 769.965 | − | 444.539i | 0.813057 | − | 0.469419i | −0.0349595 | − | 0.999389i | \(-0.511130\pi\) |
0.848016 | + | 0.529970i | \(0.177797\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53.5731 | − | 92.7913i | 0.0564521 | − | 0.0977779i | ||||
\(950\) | 288.834 | + | 407.273i | 0.304036 | + | 0.428708i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −57.5351 | − | 55.4997i | −0.0604360 | − | 0.0582980i | ||||
\(953\) | −15.5920 | −0.0163610 | −0.00818050 | − | 0.999967i | \(-0.502604\pi\) | ||||
−0.00818050 | + | 0.999967i | \(0.502604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.49830i | 0.00261602i | ||||||||
\(956\) | −1374.12 | − | 481.539i | −1.43736 | − | 0.503702i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 765.449 | + | 1079.33i | 0.799008 | + | 1.12665i | ||||
\(959\) | 3.15291 | + | 1.82033i | 0.00328770 | + | 0.00189816i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.3970 | + | 50.9172i | 0.0305900 | + | 0.0529835i | ||||
\(962\) | −189.050 | − | 86.7777i | −0.196517 | − | 0.0902056i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 211.350 | + | 245.824i | 0.219243 | + | 0.255004i | ||||
\(965\) | −191.961 | − | 332.486i | −0.198923 | − | 0.344545i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 847.921 | + | 489.548i | 0.876858 | + | 0.506254i | 0.869621 | − | 0.493720i | \(-0.164363\pi\) |
0.00723669 | + | 0.999974i | \(0.497696\pi\) | |||||||
\(968\) | −1427.22 | − | 355.009i | −1.47440 | − | 0.366745i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −29.9086 | − | 319.743i | −0.0308336 | − | 0.329632i | ||||
\(971\) | 67.3838i | 0.0693963i | 0.999398 | + | 0.0346982i | \(0.0110470\pi\) | ||||
−0.999398 | + | 0.0346982i | \(0.988953\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 70.3667 | 0.0723193 | ||||||||
\(974\) | −113.808 | + | 10.6456i | −0.116846 | + | 0.0109297i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −948.655 | − | 757.966i | −0.971983 | − | 0.776604i | ||||
\(977\) | −353.710 | + | 612.644i | −0.362037 | + | 0.627067i | −0.988296 | − | 0.152549i | \(-0.951252\pi\) |
0.626259 | + | 0.779615i | \(0.284585\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −417.133 | + | 240.832i | −0.426081 | + | 0.245998i | ||||
\(980\) | 780.002 | + | 907.229i | 0.795921 | + | 0.925744i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 46.8799 | − | 102.130i | 0.0477392 | − | 0.104002i | ||||
\(983\) | 338.829 | − | 195.623i | 0.344689 | − | 0.199006i | −0.317655 | − | 0.948206i | \(-0.602895\pi\) |
0.662343 | + | 0.749200i | \(0.269562\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −638.971 | + | 1106.73i | −0.648701 | + | 1.12358i | ||||
\(986\) | 175.259 | − | 124.292i | 0.177748 | − | 0.126057i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 131.398 | + | 46.0466i | 0.132994 | + | 0.0466059i | ||||
\(989\) | −310.720 | −0.314176 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 104.988i | − | 0.105941i | −0.998596 | − | 0.0529706i | \(-0.983131\pi\) | ||
0.998596 | − | 0.0529706i | \(-0.0168690\pi\) | |||||||
\(992\) | −58.4795 | + | 1020.22i | −0.0589512 | + | 1.02845i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 84.6422 | − | 60.0274i | 0.0851531 | − | 0.0603897i | ||||
\(995\) | 1592.67 | + | 919.530i | 1.60068 | + | 0.924151i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.0028 | − | 67.5547i | −0.0391201 | − | 0.0677580i | 0.845802 | − | 0.533496i | \(-0.179122\pi\) |
−0.884923 | + | 0.465738i | \(0.845789\pi\) | |||||||
\(998\) | −503.120 | + | 1096.07i | −0.504128 | + | 1.09827i | ||||
\(999\) | 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 | 108.3.f.c.91.5 | 16 | ||
3.2 | odd | 2 | 36.3.f.c.31.4 | yes | 16 | ||
4.3 | odd | 2 | inner | 108.3.f.c.91.6 | 16 | ||
8.3 | odd | 2 | 1728.3.o.g.1279.7 | 16 | |||
8.5 | even | 2 | 1728.3.o.g.1279.8 | 16 | |||
9.2 | odd | 6 | 36.3.f.c.7.3 | ✓ | 16 | ||
9.4 | even | 3 | 324.3.d.g.163.1 | 8 | |||
9.5 | odd | 6 | 324.3.d.i.163.8 | 8 | |||
9.7 | even | 3 | inner | 108.3.f.c.19.6 | 16 | ||
12.11 | even | 2 | 36.3.f.c.31.3 | yes | 16 | ||
24.5 | odd | 2 | 576.3.o.g.319.7 | 16 | |||
24.11 | even | 2 | 576.3.o.g.319.2 | 16 | |||
36.7 | odd | 6 | inner | 108.3.f.c.19.5 | 16 | ||
36.11 | even | 6 | 36.3.f.c.7.4 | yes | 16 | ||
36.23 | even | 6 | 324.3.d.i.163.7 | 8 | |||
36.31 | odd | 6 | 324.3.d.g.163.2 | 8 | |||
72.11 | even | 6 | 576.3.o.g.511.7 | 16 | |||
72.29 | odd | 6 | 576.3.o.g.511.2 | 16 | |||
72.43 | odd | 6 | 1728.3.o.g.127.8 | 16 | |||
72.61 | even | 6 | 1728.3.o.g.127.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.3 | ✓ | 16 | 9.2 | odd | 6 | ||
36.3.f.c.7.4 | yes | 16 | 36.11 | even | 6 | ||
36.3.f.c.31.3 | yes | 16 | 12.11 | even | 2 | ||
36.3.f.c.31.4 | yes | 16 | 3.2 | odd | 2 | ||
108.3.f.c.19.5 | 16 | 36.7 | odd | 6 | inner | ||
108.3.f.c.19.6 | 16 | 9.7 | even | 3 | inner | ||
108.3.f.c.91.5 | 16 | 1.1 | even | 1 | trivial | ||
108.3.f.c.91.6 | 16 | 4.3 | odd | 2 | inner | ||
324.3.d.g.163.1 | 8 | 9.4 | even | 3 | |||
324.3.d.g.163.2 | 8 | 36.31 | odd | 6 | |||
324.3.d.i.163.7 | 8 | 36.23 | even | 6 | |||
324.3.d.i.163.8 | 8 | 9.5 | odd | 6 | |||
576.3.o.g.319.2 | 16 | 24.11 | even | 2 | |||
576.3.o.g.319.7 | 16 | 24.5 | odd | 2 | |||
576.3.o.g.511.2 | 16 | 72.29 | odd | 6 | |||
576.3.o.g.511.7 | 16 | 72.11 | even | 6 | |||
1728.3.o.g.127.7 | 16 | 72.61 | even | 6 | |||
1728.3.o.g.127.8 | 16 | 72.43 | odd | 6 | |||
1728.3.o.g.1279.7 | 16 | 8.3 | odd | 2 | |||
1728.3.o.g.1279.8 | 16 | 8.5 | even | 2 |