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 | 91.6 | ||
Root | \(1.63139 + 1.15696i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.91 |
Dual form | 108.3.f.c.19.6 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.63139 | + | 1.15696i | 0.815695 | + | 0.578482i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.32286 | + | 3.77492i | 0.330716 | + | 0.943730i | ||||
\(5\) | −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 | −0.536094 | − | 0.844159i | \(-0.680101\pi\) |
0.463016 | + | 0.886350i | \(0.346767\pi\) | |||||||
\(8\) | −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 | 0.383088 | − | 0.923712i | \(-0.374861\pi\) |
0.991502 | + | 0.130092i | \(0.0415274\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.892255 | + | 1.54543i | −0.0686350 | + | 0.118879i | −0.898301 | − | 0.439381i | \(-0.855198\pi\) |
0.829666 | + | 0.558261i | \(0.188531\pi\) | |||||||
\(14\) | −1.17622 | − | 0.110024i | −0.0840160 | − | 0.00785882i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.5001 | + | 9.98742i | −0.781254 | + | 0.624214i | ||||
\(17\) | 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 | \(-0.828419\pi\) | ||
0.858203 | − | 0.513310i | \(-0.171581\pi\) | |||||||
\(20\) | −24.1656 | − | 4.56079i | −1.20828 | − | 0.228040i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 34.7675 | + | 3.25214i | 1.58034 | + | 0.147824i | ||||
\(23\) | −6.86778 | − | 3.96511i | −0.298599 | − | 0.172396i | 0.343214 | − | 0.939257i | \(-0.388484\pi\) |
−0.641813 | + | 0.766861i | \(0.721818\pi\) | |||||||
\(24\) | 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 | −0.0174873 | − | 0.999847i | \(-0.505567\pi\) |
−0.874637 | + | 0.484779i | \(0.838900\pi\) | |||||||
\(32\) | −31.9476 | + | 1.83125i | −0.998361 | + | 0.0572266i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 27.5984 | + | 19.5725i | 0.811717 | + | 0.575661i | ||||
\(35\) | − | 3.63153i | − | 0.103758i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 58.2834 | 1.57523 | 0.787614 | − | 0.616169i | \(-0.211316\pi\) | ||||
0.787614 | + | 0.616169i | \(0.211316\pi\) | |||||||
\(38\) | 22.5675 | − | 31.8215i | 0.593881 | − | 0.837408i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −34.1469 | − | 35.3992i | −0.853672 | − | 0.884980i | ||||
\(41\) | 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 | −0.0505290 | − | 0.998723i | \(-0.516091\pi\) |
0.839655 | + | 0.543121i | \(0.182757\pi\) | |||||||
\(44\) | 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 | −0.599047 | − | 0.800714i | \(-0.704454\pi\) |
0.393915 | + | 0.919147i | \(0.371120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.3255 | + | 42.1331i | −0.496440 | + | 0.859859i | ||||
\(50\) | 2.38396 | − | 25.4861i | 0.0476791 | − | 0.509721i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.01421 | − | 1.32380i | −0.134889 | − | 0.0254576i | ||||
\(53\) | −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 | ||||||||
\(56\) | −1.14066 | − | 4.58570i | −0.0203689 | − | 0.0818875i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.18285 | − | 12.6455i | 0.0203940 | − | 0.218026i | ||||
\(59\) | −20.8974 | − | 12.0651i | −0.354194 | − | 0.204494i | 0.312337 | − | 0.949971i | \(-0.398888\pi\) |
−0.666531 | + | 0.745477i | \(0.732222\pi\) | |||||||
\(60\) | 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 | 0.718299 | − | 0.695734i | \(-0.244921\pi\) |
−0.243374 | + | 0.969933i | \(0.578254\pi\) | |||||||
\(68\) | 22.3790 | + | 63.8607i | 0.329103 | + | 0.939128i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.20156 | − | 5.92445i | 0.0600222 | − | 0.0846350i | ||||
\(71\) | 87.8370i | 1.23714i | 0.785730 | + | 0.618570i | \(0.212288\pi\) | ||||
−0.785730 | + | 0.618570i | \(0.787712\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −60.0423 | −0.822498 | −0.411249 | − | 0.911523i | \(-0.634907\pi\) | ||||
−0.411249 | + | 0.911523i | \(0.634907\pi\) | |||||||
\(74\) | 95.0830 | + | 67.4319i | 1.28490 | + | 0.911241i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 73.6328 | − | 25.8035i | 0.968852 | − | 0.339520i | ||||
\(77\) | −5.15652 | + | 8.93136i | −0.0669678 | + | 0.115992i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −32.1841 | + | 18.5815i | −0.407394 | + | 0.235209i | −0.689669 | − | 0.724124i | \(-0.742244\pi\) |
0.282275 | + | 0.959333i | \(0.408911\pi\) | |||||||
\(80\) | −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 | −0.841902 | − | 0.539630i | \(-0.818564\pi\) |
0.0463824 | + | 0.998924i | \(0.485231\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −52.0037 | + | 90.0730i | −0.611808 | + | 1.05968i | ||||
\(86\) | 78.0229 | + | 7.29823i | 0.907243 | + | 0.0848632i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 33.7161 | + | 135.547i | 0.383138 | + | 1.54030i | ||||
\(89\) | 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 | ||||||
\(92\) | 5.88285 | − | 31.1706i | 0.0639440 | − | 0.338811i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −22.1686 | − | 2.07364i | −0.235836 | − | 0.0220600i | ||||
\(95\) | 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 | 0.580225 | − | 0.814457i | \(-0.302965\pi\) |
−0.415228 | + | 0.909717i | \(0.636298\pi\) | |||||||
\(104\) | −9.91133 | − | 10.2748i | −0.0953012 | − | 0.0987964i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −58.5294 | − | 41.5085i | −0.552164 | − | 0.391589i | ||||
\(107\) | − | 183.200i | − | 1.71215i | −0.516850 | − | 0.856076i | \(-0.672895\pi\) | ||
0.516850 | − | 0.856076i | \(-0.327105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 100.841 | 0.925147 | 0.462573 | − | 0.886581i | \(-0.346926\pi\) | ||||
0.462573 | + | 0.886581i | \(0.346926\pi\) | |||||||
\(110\) | −124.192 | + | 175.118i | −1.12902 | + | 1.59198i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.44464 | − | 8.80076i | 0.0307557 | − | 0.0785782i | ||||
\(113\) | 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 | ||||
\(122\) | 14.1361 | − | 151.124i | 0.115870 | − | 1.23872i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 23.6896 | − | 125.521i | 0.191045 | − | 1.01227i | ||||
\(125\) | −75.0146 | −0.600117 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 164.386i | − | 1.29438i | −0.762331 | − | 0.647188i | \(-0.775945\pi\) | ||
0.762331 | − | 0.647188i | \(-0.224055\pi\) | |||||||
\(128\) | −49.1751 | − | 118.177i | −0.384181 | − | 0.923258i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.04358 | − | 21.8472i | 0.0157198 | − | 0.168055i | ||||
\(131\) | −123.421 | − | 71.2570i | −0.942143 | − | 0.543947i | −0.0515116 | − | 0.998672i | \(-0.516404\pi\) |
−0.890631 | + | 0.454726i | \(0.849737\pi\) | |||||||
\(132\) | 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 | 0.0806575 | − | 0.996742i | \(-0.474298\pi\) |
−0.822875 | + | 0.568222i | \(0.807631\pi\) | |||||||
\(140\) | 13.7088 | − | 4.80403i | 0.0979197 | − | 0.0343145i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −101.624 | + | 143.296i | −0.715664 | + | 1.00913i | ||||
\(143\) | 31.1569i | 0.217880i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 39.0423 | 0.269257 | ||||||||
\(146\) | −97.9524 | − | 69.4669i | −0.670907 | − | 0.475800i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 77.1011 | + | 220.015i | 0.520953 | + | 1.48659i | ||||
\(149\) | 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 | −0.858572 | − | 0.512693i | \(-0.828648\pi\) |
0.0147190 | + | 0.999892i | \(0.495315\pi\) | |||||||
\(152\) | 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 | \(0.102491\pi\) | |||||||
\(158\) | −74.0030 | − | 6.92221i | −0.468373 | − | 0.0438115i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 88.4575 | − | 175.730i | 0.552859 | − | 1.09831i | ||||
\(161\) | 4.68422 | 0.0290946 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 143.325i | − | 0.879292i | −0.898171 | − | 0.439646i | \(-0.855104\pi\) | ||
0.898171 | − | 0.439646i | \(-0.144896\pi\) | |||||||
\(164\) | 20.9854 | + | 3.96058i | 0.127960 | + | 0.0241499i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −151.823 | − | 14.2014i | −0.914595 | − | 0.0855508i | ||||
\(167\) | 150.531 | + | 86.9089i | 0.901381 | + | 0.520413i | 0.877648 | − | 0.479306i | \(-0.159111\pi\) |
0.0237332 | + | 0.999718i | \(0.492445\pi\) | |||||||
\(168\) | 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 | ||||
\(176\) | −101.819 | + | 260.138i | −0.578515 | + | 1.47806i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 45.0056 | + | 31.9175i | 0.252840 | + | 0.179312i | ||||
\(179\) | − | 96.0059i | − | 0.536346i | −0.963371 | − | 0.268173i | \(-0.913580\pi\) | ||
0.963371 | − | 0.268173i | \(-0.0864199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −328.757 | −1.81634 | −0.908170 | − | 0.418603i | \(-0.862520\pi\) | ||||
−0.908170 | + | 0.418603i | \(0.862520\pi\) | |||||||
\(182\) | 1.21953 | − | 1.71960i | 0.00670069 | − | 0.00944838i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 45.6605 | − | 44.0452i | 0.248155 | − | 0.239376i | ||||
\(185\) | −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 | −0.500921 | − | 0.865493i | \(-0.667005\pi\) |
0.499078 | + | 0.866557i | \(0.333672\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −31.2230 | + | 54.0798i | −0.161777 | + | 0.280206i | −0.935506 | − | 0.353311i | \(-0.885056\pi\) |
0.773729 | + | 0.633517i | \(0.218389\pi\) | |||||||
\(194\) | −4.86472 | + | 52.0071i | −0.0250759 | + | 0.268078i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −191.228 | − | 36.0906i | −0.975656 | − | 0.184136i | ||||
\(197\) | 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 | \(0.270707\pi\) | ||||
−0.659643 | + | 0.751579i | \(0.729293\pi\) | |||||||
\(200\) | 99.3616 | − | 24.7154i | 0.496808 | − | 0.123577i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.79938 | + | 51.3085i | −0.0237593 | + | 0.254003i | ||||
\(203\) | 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 | 0.796748 | − | 0.604311i | \(-0.206552\pi\) |
−0.124975 | + | 0.992160i | \(0.539885\pi\) | |||||||
\(212\) | −47.4605 | − | 135.433i | −0.223870 | − | 0.638835i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 211.956 | − | 298.871i | 0.990450 | − | 1.39659i | ||||
\(215\) | 240.892i | 1.12043i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.8629 | 0.0869257 | ||||||||
\(218\) | 164.511 | + | 116.669i | 0.754637 | + | 0.535181i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −405.211 | + | 142.000i | −1.84187 | + | 0.645455i | ||||
\(221\) | −15.0944 | + | 26.1442i | −0.0683003 | + | 0.118300i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −330.681 | + | 190.919i | −1.48287 | + | 0.856138i | −0.999811 | − | 0.0194478i | \(-0.993809\pi\) |
−0.483063 | + | 0.875586i | \(0.660476\pi\) | |||||||
\(224\) | 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 | −0.609224 | − | 0.792998i | \(-0.708519\pi\) |
0.382144 | + | 0.924103i | \(0.375186\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 64.4366 | − | 111.608i | 0.281383 | − | 0.487369i | −0.690343 | − | 0.723482i | \(-0.742540\pi\) |
0.971726 | + | 0.236113i | \(0.0758736\pi\) | |||||||
\(230\) | 97.0873 | + | 9.08150i | 0.422118 | + | 0.0394848i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 49.3005 | − | 12.2631i | 0.212502 | − | 0.0528582i | ||||
\(233\) | −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 | ||||||
\(236\) | 17.9005 | − | 94.8467i | 0.0758495 | − | 0.401893i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −19.8983 | − | 1.86128i | −0.0836063 | − | 0.00782050i | ||||
\(239\) | −315.244 | − | 182.006i | −1.31901 | − | 0.761532i | −0.335442 | − | 0.942061i | \(-0.608886\pi\) |
−0.983570 | + | 0.180529i | \(0.942219\pi\) | |||||||
\(240\) | 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 | ||||
\(248\) | 183.870 | − | 177.366i | 0.741413 | − | 0.715184i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −122.378 | − | 86.7892i | −0.489512 | − | 0.347157i | ||||
\(251\) | 281.883i | 1.12304i | 0.827463 | + | 0.561520i | \(0.189783\pi\) | ||||
−0.827463 | + | 0.561520i | \(0.810217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −138.459 | −0.547268 | ||||||||
\(254\) | 190.188 | − | 268.177i | 0.748773 | − | 1.05582i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 56.5028 | − | 249.687i | 0.220714 | − | 0.975339i | ||||
\(257\) | 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 | −0.687655 | − | 0.726037i | \(-0.741360\pi\) |
0.284939 | + | 0.958546i | \(0.408027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 110.287 | − | 191.023i | 0.416178 | − | 0.720841i | ||||
\(266\) | −2.14609 | + | 22.9432i | −0.00806802 | + | 0.0862525i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −27.2566 | + | 144.421i | −0.101704 | + | 0.538883i | ||||
\(269\) | −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 | \(0.0480146\pi\) | ||||
−0.988645 | + | 0.150271i | \(0.951985\pi\) | |||||||
\(272\) | −211.465 | + | 168.958i | −0.777443 | + | 0.621170i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.14805 | + | 12.2735i | −0.00418998 | + | 0.0447937i | ||||
\(275\) | −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 | 0.945941 | − | 0.324339i | \(-0.105142\pi\) |
0.192084 | + | 0.981378i | \(0.438475\pi\) | |||||||
\(284\) | −331.578 | + | 116.196i | −1.16753 | + | 0.409142i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −36.0474 | + | 50.8290i | −0.126040 | + | 0.177724i | ||||
\(287\) | 3.15361i | 0.0109882i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.81196 | −0.00972996 | ||||||||
\(290\) | 63.6932 | + | 45.1706i | 0.219632 | + | 0.155761i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −79.4279 | − | 226.655i | −0.272013 | − | 0.776216i | ||||
\(293\) | 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 | ||||
\(302\) | −292.989 | − | 27.4061i | −0.970163 | − | 0.0907486i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 194.812 | + | 243.823i | 0.640830 | + | 0.802050i | ||||
\(305\) | 466.589 | 1.52980 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 336.514i | − | 1.09614i | −0.836434 | − | 0.548068i | \(-0.815363\pi\) | ||
0.836434 | − | 0.548068i | \(-0.184637\pi\) | |||||||
\(308\) | −40.5366 | − | 7.65048i | −0.131612 | − | 0.0248392i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 390.960 | + | 36.5703i | 1.26116 | + | 0.117969i | ||||
\(311\) | 304.206 | + | 175.634i | 0.978156 | + | 0.564738i | 0.901713 | − | 0.432336i | \(-0.142310\pi\) |
0.0764428 | + | 0.997074i | \(0.475644\pi\) | |||||||
\(312\) | 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 | ||||
\(320\) | 347.622 | − | 184.342i | 1.08632 | − | 0.576069i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.64179 | + | 5.41948i | 0.0237323 | + | 0.0168307i | ||||
\(323\) | − | 329.981i | − | 1.02161i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.8393 | 0.0702749 | ||||||||
\(326\) | 165.821 | − | 233.818i | 0.508655 | − | 0.717234i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 29.6531 | + | 30.7406i | 0.0904057 | + | 0.0937213i | ||||
\(329\) | 3.28792 | − | 5.69484i | 0.00999368 | − | 0.0173096i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −384.104 | + | 221.763i | −1.16044 | + | 0.669978i | −0.951408 | − | 0.307932i | \(-0.900363\pi\) |
−0.209027 | + | 0.977910i | \(0.567030\pi\) | |||||||
\(332\) | −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 | \(0.894585\pi\) | |||||||
\(338\) | −30.8858 | + | 330.190i | −0.0913781 | + | 0.976893i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −408.812 | − | 77.1553i | −1.20239 | − | 0.226927i | ||||
\(341\) | −557.560 | −1.63507 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 57.6805i | − | 0.168165i | ||||||
\(344\) | 75.6636 | + | 304.185i | 0.219952 | + | 0.884259i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −46.8667 | + | 501.036i | −0.135453 | + | 1.44808i | ||||
\(347\) | 492.773 | + | 284.503i | 1.42010 | + | 0.819893i | 0.996307 | − | 0.0858678i | \(-0.0273663\pi\) |
0.423790 | + | 0.905761i | \(0.360700\pi\) | |||||||
\(348\) | 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 | ||||
\(356\) | 36.4942 | + | 104.140i | 0.102512 | + | 0.292527i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 111.076 | − | 156.623i | 0.310267 | − | 0.437495i | ||||
\(359\) | − | 303.196i | − | 0.844557i | −0.906466 | − | 0.422278i | \(-0.861230\pi\) | ||
0.906466 | − | 0.422278i | \(-0.138770\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.4752 | −0.0539480 | ||||||||
\(362\) | −536.331 | − | 380.361i | −1.48158 | − | 1.05072i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.97904 | − | 1.39440i | 0.0109314 | − | 0.00383076i | ||||
\(365\) | 184.572 | − | 319.688i | 0.505677 | − | 0.875858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 615.571 | − | 355.400i | 1.67730 | − | 0.968392i | 0.713936 | − | 0.700211i | \(-0.246911\pi\) |
0.963369 | − | 0.268181i | \(-0.0864224\pi\) | |||||||
\(368\) | 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 | \(0.0191501\pi\) | |||||||
\(374\) | 588.165 | + | 55.0167i | 1.57263 | + | 0.147103i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −21.4982 | − | 86.4277i | −0.0571761 | − | 0.229861i | ||||
\(377\) | 11.3323 | 0.0300590 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 662.686i | 1.74851i | 0.485465 | + | 0.874256i | \(0.338650\pi\) | ||||
−0.485465 | + | 0.874256i | \(0.661350\pi\) | |||||||
\(380\) | −88.9618 | + | 471.369i | −0.234110 | + | 1.24045i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.809179 | − | 0.0756903i | −0.00211827 | − | 0.000198142i | ||||
\(383\) | −69.9008 | − | 40.3572i | −0.182509 | − | 0.105371i | 0.405962 | − | 0.913890i | \(-0.366936\pi\) |
−0.588471 | + | 0.808518i | \(0.700270\pi\) | |||||||
\(384\) | 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 | ||||
\(392\) | −270.213 | − | 280.123i | −0.689318 | − | 0.714598i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 339.102 | + | 240.488i | 0.860665 | + | 0.610375i | ||||
\(395\) | − | 228.481i | − | 0.578432i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 657.713 | 1.65671 | 0.828354 | − | 0.560206i | \(-0.189278\pi\) | ||||
0.828354 | + | 0.560206i | \(0.189278\pi\) | |||||||
\(398\) | −346.081 | + | 487.995i | −0.869550 | + | 1.22612i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 190.692 | + | 74.6374i | 0.476731 | + | 0.186594i | ||||
\(401\) | −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 | \(0.295955\pi\) | |||||||
\(410\) | −6.11405 | + | 65.3632i | −0.0149123 | + | 0.159422i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.5574 | + | 77.1333i | −0.0353335 | + | 0.187217i | ||||
\(413\) | 14.2533 | 0.0345115 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 468.745i | − | 1.12951i | ||||||
\(416\) | 25.6753 | − | 51.0067i | 0.0617195 | − | 0.122612i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 63.4354 | − | 678.167i | 0.151759 | − | 1.62241i | ||||
\(419\) | −222.744 | − | 128.601i | −0.531608 | − | 0.306924i | 0.210063 | − | 0.977688i | \(-0.432633\pi\) |
−0.741671 | + | 0.670764i | \(0.765967\pi\) | |||||||
\(420\) | 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 | ||||
\(428\) | 691.567 | − | 242.349i | 1.61581 | − | 0.566237i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −278.703 | + | 392.989i | −0.648148 | + | 0.913927i | ||||
\(431\) | − | 144.348i | − | 0.334914i | −0.985879 | − | 0.167457i | \(-0.946445\pi\) | ||
0.985879 | − | 0.167457i | \(-0.0535555\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 395.353 | 0.913057 | 0.456528 | − | 0.889709i | \(-0.349093\pi\) | ||||
0.456528 | + | 0.889709i | \(0.349093\pi\) | |||||||
\(434\) | 30.7727 | + | 21.8237i | 0.0709049 | + | 0.0502850i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 133.399 | + | 380.667i | 0.305961 | + | 0.873089i | ||||
\(437\) | −77.3426 | + | 133.961i | −0.176985 | + | 0.306548i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 194.776 | − | 112.454i | 0.443682 | − | 0.256160i | −0.261476 | − | 0.965210i | \(-0.584209\pi\) |
0.705158 | + | 0.709050i | \(0.250876\pi\) | |||||||
\(440\) | −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 | −0.855006 | − | 0.518618i | \(-0.826447\pi\) |
0.0216335 | + | 0.999766i | \(0.493113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −84.8041 | + | 146.885i | −0.190571 | + | 0.330079i | ||||
\(446\) | −760.356 | − | 71.1233i | −1.70483 | − | 0.159469i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 37.7790 | + | 1.36102i | 0.0843281 | + | 0.00303799i | ||||
\(449\) | 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 | ||||||
\(452\) | 71.7324 | + | 13.5381i | 0.158700 | + | 0.0299515i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −118.526 | − | 11.0869i | −0.261070 | − | 0.0244204i | ||||
\(455\) | 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 | 0.230503 | − | 0.973072i | \(-0.425963\pi\) |
−0.727453 | + | 0.686157i | \(0.759296\pi\) | |||||||
\(464\) | 94.6163 | + | 37.0330i | 0.203914 | + | 0.0798126i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.4608 | − | 17.3474i | −0.0524910 | − | 0.0372261i | ||||
\(467\) | 794.598i | 1.70149i | 0.525575 | + | 0.850747i | \(0.323850\pi\) | ||||
−0.525575 | + | 0.850747i | \(0.676150\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −21.7031 | −0.0462752 | ||||||||
\(470\) | 79.1877 | − | 111.659i | 0.168484 | − | 0.237573i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 138.937 | − | 134.022i | 0.294358 | − | 0.283944i | ||||
\(473\) | 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 | −0.959698 | − | 0.281033i | \(-0.909323\pi\) |
−0.236468 | + | 0.971639i | \(0.575990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −52.0037 | + | 90.0730i | −0.108116 | + | 0.187262i | ||||
\(482\) | 15.0963 | − | 161.390i | 0.0313202 | − | 0.334833i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 722.599 | + | 136.376i | 1.49297 | + | 0.281769i | ||||
\(485\) | −160.569 | −0.331071 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 57.1525i | − | 0.117356i | −0.998277 | − | 0.0586781i | \(-0.981311\pi\) | ||
0.998277 | − | 0.0586781i | \(-0.0186886\pi\) | |||||||
\(488\) | 589.183 | − | 146.554i | 1.20734 | − | 0.300317i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 55.7140 | − | 595.620i | 0.113702 | − | 1.21555i | ||||
\(491\) | 48.6600 | + | 28.0939i | 0.0991040 | + | 0.0572177i | 0.548733 | − | 0.835998i | \(-0.315110\pi\) |
−0.449629 | + | 0.893215i | \(0.648444\pi\) | |||||||
\(492\) | 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 | −0.124863 | − | 0.992174i | \(-0.539849\pi\) |
−0.921679 | + | 0.387952i | \(0.873183\pi\) | |||||||
\(500\) | −99.2341 | − | 283.174i | −0.198468 | − | 0.566348i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −326.129 | + | 459.861i | −0.649659 | + | 0.916058i | ||||
\(503\) | − | 549.354i | − | 1.09216i | −0.837734 | − | 0.546078i | \(-0.816120\pi\) | ||
0.837734 | − | 0.546078i | \(-0.183880\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −158.413 | −0.313688 | ||||||||
\(506\) | −225.880 | − | 160.192i | −0.446404 | − | 0.316585i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 620.543 | − | 217.460i | 1.22154 | − | 0.428071i | ||||
\(509\) | 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 | ||||
\(518\) | −68.5544 | − | 6.41255i | −0.132344 | − | 0.0123794i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 85.1748 | − | 21.1865i | 0.163798 | − | 0.0407433i | ||||
\(521\) | 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 | \(0.356852\pi\) | ||||
−0.434706 | + | 0.900572i | \(0.643148\pi\) | |||||||
\(524\) | 105.721 | − | 560.167i | 0.201757 | − | 1.06902i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −243.536 | − | 22.7802i | −0.462996 | − | 0.0433084i | ||||
\(527\) | −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 | ||||
\(536\) | −211.556 | + | 204.072i | −0.394694 | + | 0.380730i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −457.527 | − | 324.473i | −0.850422 | − | 0.603110i | ||||
\(539\) | 849.430i | 1.57594i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −242.245 | −0.447772 | −0.223886 | − | 0.974615i | \(-0.571874\pi\) | ||||
−0.223886 | + | 0.974615i | \(0.571874\pi\) | |||||||
\(542\) | −94.2311 | + | 132.871i | −0.173858 | + | 0.245150i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −540.460 | + | 30.9794i | −0.993492 | + | 0.0569475i | ||||
\(545\) | −309.988 | + | 536.915i | −0.568786 | + | 0.985166i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 170.503 | − | 98.4402i | 0.311706 | − | 0.179964i | −0.335983 | − | 0.941868i | \(-0.609069\pi\) |
0.647690 | + | 0.761904i | \(0.275735\pi\) | |||||||
\(548\) | −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 | ||||
\(554\) | −83.7681 | + | 895.536i | −0.151206 | + | 1.61649i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 88.3725 | − | 468.247i | 0.158943 | − | 0.842171i | ||||
\(557\) | −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 | ||||||||
\(560\) | 36.2697 | + | 45.3944i | 0.0647672 | + | 0.0810614i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.1059 | + | 150.801i | −0.0250994 | + | 0.268329i | ||||
\(563\) | 165.774 | + | 95.7097i | 0.294448 | + | 0.169999i | 0.639946 | − | 0.768420i | \(-0.278957\pi\) |
−0.345498 | + | 0.938419i | \(0.612290\pi\) | |||||||
\(564\) | 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 | 0.999632 | − | 0.0271399i | \(-0.00863995\pi\) |
0.476312 | + | 0.879276i | \(0.341973\pi\) | |||||||
\(572\) | −117.615 | + | 41.2164i | −0.205620 | + | 0.0720566i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.64862 | + | 5.14477i | −0.00635648 | + | 0.00896302i | ||||
\(575\) | 101.496i | 0.176515i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 138.527 | 0.240081 | 0.120040 | − | 0.992769i | \(-0.461698\pi\) | ||||
0.120040 | + | 0.992769i | \(0.461698\pi\) | |||||||
\(578\) | −4.58740 | − | 3.25334i | −0.00793668 | − | 0.00562861i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 51.6477 | + | 147.382i | 0.0890478 | + | 0.254106i | ||||
\(581\) | 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 | 0.132829 | − | 0.991139i | \(-0.457594\pi\) |
0.924766 | + | 0.380537i | \(0.124261\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −311.451 | + | 539.449i | −0.528779 | + | 0.915872i | ||||
\(590\) | 295.419 | + | 27.6334i | 0.500711 | + | 0.0468363i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −728.546 | + | 582.101i | −1.23065 | + | 0.983279i | ||||
\(593\) | −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 | ||||||
\(596\) | 812.577 | + | 153.358i | 1.36338 | + | 0.257312i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 28.1801 | + | 2.63596i | 0.0471240 | + | 0.00440796i | ||||
\(599\) | −245.527 | − | 141.755i | −0.409895 | − | 0.236653i | 0.280850 | − | 0.959752i | \(-0.409384\pi\) |
−0.690744 | + | 0.723099i | \(0.742717\pi\) | |||||||
\(600\) | 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 | 0.435039 | − | 0.900411i | \(-0.356734\pi\) |
−0.562260 | + | 0.826961i | \(0.690068\pi\) | |||||||
\(608\) | 35.7200 | + | 623.162i | 0.0587499 | + | 1.02494i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 761.189 | + | 539.827i | 1.24785 | + | 0.884962i | ||||
\(611\) | − | 19.8664i | − | 0.0325145i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −316.779 | −0.516769 | −0.258385 | − | 0.966042i | \(-0.583190\pi\) | ||||
−0.258385 | + | 0.966042i | \(0.583190\pi\) | |||||||
\(614\) | 389.335 | − | 548.985i | 0.634096 | − | 0.894113i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −57.2796 | − | 59.3803i | −0.0929863 | − | 0.0963966i | ||||
\(617\) | −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 | −0.888276 | − | 0.459310i | \(-0.848097\pi\) |
−0.0463638 | + | 0.998925i | \(0.514763\pi\) | |||||||
\(620\) | 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 | ||||
\(626\) | 35.5507 | − | 380.060i | 0.0567902 | − | 0.607125i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 247.153 | + | 46.6452i | 0.393555 | + | 0.0742759i | ||||
\(629\) | 985.986 | 1.56755 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 150.631i | − | 0.238718i | −0.992851 | − | 0.119359i | \(-0.961916\pi\) | ||
0.992851 | − | 0.119359i | \(-0.0380839\pi\) | |||||||
\(632\) | −71.7652 | − | 288.513i | −0.113553 | − | 0.456507i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −75.5484 | + | 807.662i | −0.119162 | + | 1.27392i | ||||
\(635\) | 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 | −0.204182 | − | 0.978933i | \(-0.565454\pi\) |
−0.949872 | + | 0.312639i | \(0.898787\pi\) | |||||||
\(644\) | 6.19659 | + | 17.6826i | 0.00962204 | + | 0.0274574i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 381.776 | − | 538.328i | 0.590985 | − | 0.833324i | ||||
\(647\) | 156.257i | 0.241510i | 0.992682 | + | 0.120755i | \(0.0385316\pi\) | ||||
−0.992682 | + | 0.120755i | \(0.961468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −421.306 | −0.649162 | ||||||||
\(650\) | 37.2599 | + | 26.4243i | 0.0573229 | + | 0.0406528i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 541.039 | − | 189.599i | 0.829814 | − | 0.290796i | ||||
\(653\) | 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 | −0.759511 | − | 0.650494i | \(-0.774562\pi\) |
0.183589 | + | 0.983003i | \(0.441228\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 233.924 | − | 405.168i | 0.353894 | − | 0.612963i | −0.633034 | − | 0.774124i | \(-0.718191\pi\) |
0.986928 | + | 0.161161i | \(0.0515239\pi\) | |||||||
\(662\) | −883.195 | − | 82.6137i | −1.33413 | − | 0.124794i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −147.232 | − | 591.905i | −0.221734 | − | 0.891424i | ||||
\(665\) | −70.8359 | −0.106520 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 50.3597i | 0.0755018i | ||||||||
\(668\) | −128.943 | + | 683.210i | −0.193028 | + | 1.02277i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −449.827 | − | 42.0767i | −0.671384 | − | 0.0628010i | ||||
\(671\) | −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 | ||||
\(680\) | −577.666 | − | 598.852i | −0.849509 | − | 0.880664i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −909.597 | − | 645.077i | −1.33372 | − | 0.945861i | ||||
\(683\) | 123.214i | 0.180400i | 0.995924 | + | 0.0902002i | \(0.0287507\pi\) | ||||
−0.995924 | + | 0.0902002i | \(0.971249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.8937 | −0.0553193 | ||||||||
\(686\) | 66.7343 | − | 94.0994i | 0.0972803 | − | 0.137171i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −228.495 | + | 583.784i | −0.332114 | + | 0.848524i | ||||
\(689\) | 32.0115 | − | 55.4455i | 0.0464607 | − | 0.0804724i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 163.326 | − | 94.2965i | 0.236362 | − | 0.136464i | −0.377141 | − | 0.926156i | \(-0.623093\pi\) |
0.613504 | + | 0.789692i | \(0.289760\pi\) | |||||||
\(692\) | −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 | ||||
\(698\) | 77.0773 | − | 824.007i | 0.110426 | − | 1.18053i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.60814 | + | 29.7150i | −0.00801162 | + | 0.0424501i | ||||
\(701\) | 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 | ||||||
\(704\) | −1116.69 | − | 40.2298i | −1.58621 | − | 0.0571447i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.2114 | − | 248.145i | 0.0328773 | − | 0.351480i | ||||
\(707\) | −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 | ||||
\(716\) | 362.415 | − | 127.003i | 0.506166 | − | 0.177378i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 350.787 | − | 494.631i | 0.488561 | − | 0.688901i | ||||
\(719\) | − | 788.981i | − | 1.09733i | −0.836042 | − | 0.548666i | \(-0.815136\pi\) | ||
0.836042 | − | 0.548666i | \(-0.184864\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.5913 | −0.0160768 | ||||||||
\(722\) | −31.7717 | − | 22.5321i | −0.0440051 | − | 0.0312080i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −434.902 | − | 1241.03i | −0.600693 | − | 1.71413i | ||||
\(725\) | −40.6380 | + | 70.3870i | −0.0560524 | + | 0.0970856i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 232.676 | − | 134.335i | 0.320049 | − | 0.184780i | −0.331365 | − | 0.943502i | \(-0.607509\pi\) |
0.651414 | + | 0.758722i | \(0.274176\pi\) | |||||||
\(728\) | 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 | \(0.182669\pi\) | |||||||
\(734\) | 1415.42 | + | 132.398i | 1.92837 | + | 0.180379i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 226.670 | + | 114.099i | 0.307975 | + | 0.155026i | ||||
\(737\) | 641.512 | 0.870437 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 448.249i | − | 0.606562i | −0.952901 | − | 0.303281i | \(-0.901918\pi\) | ||
0.952901 | − | 0.303281i | \(-0.0980820\pi\) | |||||||
\(740\) | −1408.46 | − | 265.818i | −1.90332 | − | 0.359214i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 42.1994 | + | 3.94732i | 0.0568725 | + | 0.00531983i | ||||
\(743\) | 656.602 | + | 379.089i | 0.883718 | + | 0.510215i | 0.871882 | − | 0.489715i | \(-0.162899\pi\) |
0.0118352 | + | 0.999930i | \(0.496233\pi\) | |||||||
\(744\) | 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 | \(-0.992465\pi\) |
−0.520358 | − | 0.853948i | \(-0.674202\pi\) | |||||||
\(752\) | 64.9219 | − | 165.870i | 0.0863323 | − | 0.220572i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.4873 | + | 13.1110i | 0.0245190 | + | 0.0173886i | ||||
\(755\) | − | 904.589i | − | 1.19813i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 587.874 | 0.776583 | 0.388292 | − | 0.921537i | \(-0.373065\pi\) | ||||
0.388292 | + | 0.921537i | \(0.373065\pi\) | |||||||
\(758\) | −766.705 | + | 1081.10i | −1.01148 | + | 1.42625i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −690.489 | + | 666.062i | −0.908538 | + | 0.876397i | ||||
\(761\) | 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 | \(-0.149243\pi\) | |||||||
\(770\) | 11.8102 | − | 126.259i | 0.0153380 | − | 0.163973i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −245.451 | − | 46.3240i | −0.317941 | − | 0.0600052i | ||||
\(773\) | −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 | ||||||||
\(776\) | −202.758 | + | 50.4344i | −0.261286 | + | 0.0649928i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −128.898 | + | 1378.01i | −0.165679 | + | 1.77122i | ||||
\(779\) | −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 | 0.727024 | − | 0.686612i | \(-0.240903\pi\) |
−0.231111 | + | 0.972927i | \(0.574236\pi\) | |||||||
\(788\) | 274.972 | + | 784.658i | 0.348949 | + | 0.995759i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 264.344 | − | 372.741i | 0.334613 | − | 0.471824i | ||||
\(791\) | 10.7797i | 0.0136280i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 135.430 | 0.170782 | ||||||||
\(794\) | 1072.99 | + | 760.950i | 1.35137 | + | 0.958376i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1129.19 | + | 395.707i | −1.41858 | + | 0.497119i | ||||
\(797\) | 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 | ||||
\(806\) | 113.478 | + | 10.6147i | 0.140792 | + | 0.0131696i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −200.035 | + | 49.7570i | −0.247568 | + | 0.0615804i | ||||
\(809\) | −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 | \(-0.833533\pi\) | ||
0.866338 | − | 0.499458i | \(-0.166467\pi\) | |||||||
\(812\) | −2.78260 | + | 14.7438i | −0.00342685 | + | 0.0181574i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2026.37 | + | 189.546i | 2.48940 | + | 0.232857i | ||||
\(815\) | 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 | 0.967977 | − | 0.251039i | \(-0.0807722\pi\) |
0.266583 | + | 0.963812i | \(0.414105\pi\) | |||||||
\(824\) | −112.989 | + | 108.992i | −0.137123 | + | 0.132272i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 23.2526 | + | 16.4905i | 0.0281509 | + | 0.0199643i | ||||
\(827\) | 267.739i | 0.323747i | 0.986811 | + | 0.161874i | \(0.0517537\pi\) | ||||
−0.986811 | + | 0.161874i | \(0.948246\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −432.474 | −0.521682 | −0.260841 | − | 0.965382i | \(-0.584000\pi\) | ||||
−0.260841 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(830\) | 542.321 | − | 764.706i | 0.653399 | − | 0.921332i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 100.899 | − | 53.5064i | 0.121273 | − | 0.0643105i | ||||
\(833\) | −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 | −0.747993 | − | 0.663707i | \(-0.768982\pi\) |
0.200790 | + | 0.979634i | \(0.435649\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 400.337 | − | 693.403i | 0.476024 | − | 0.824499i | ||||
\(842\) | −15.6428 | + | 167.232i | −0.0185782 | + | 0.198613i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −121.416 | + | 643.331i | −0.143858 | + | 0.762240i | ||||
\(845\) | −1019.44 | −1.20644 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 108.590i | 0.128205i | ||||||||
\(848\) | 448.465 | − | 358.319i | 0.528850 | − | 0.422546i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 40.3296 | − | 431.150i | 0.0474466 | − | 0.507236i | ||||
\(851\) | −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 | 0.763470 | − | 0.645843i | \(-0.223494\pi\) |
−0.177581 | + | 0.984106i | \(0.556827\pi\) | |||||||
\(860\) | −909.348 | + | 318.667i | −1.05738 | + | 0.370544i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 167.005 | − | 235.488i | 0.193742 | − | 0.273187i | ||||
\(863\) | − | 827.326i | − | 0.958663i | −0.877634 | − | 0.479331i | \(-0.840879\pi\) | ||
0.877634 | − | 0.479331i | \(-0.159121\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1546.92 | −1.78835 | ||||||||
\(866\) | 644.976 | + | 457.410i | 0.744776 | + | 0.528187i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24.9530 | + | 71.2059i | 0.0287478 | + | 0.0820344i | ||||
\(869\) | −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 | \(0.270033\pi\) | |||||||
\(878\) | 447.862 | + | 41.8928i | 0.510093 | + | 0.0477139i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1072.08 | − | 1341.79i | −1.21827 | − | 1.52476i | ||||
\(881\) | 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 | \(0.115196\pi\) | ||||
−0.935227 | + | 0.354050i | \(0.884804\pi\) | |||||||
\(884\) | −118.660 | − | 22.3948i | −0.134231 | − | 0.0253335i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −848.888 | − | 79.4047i | −0.958113 | − | 0.0896215i | ||||
\(887\) | 921.187 | + | 531.847i | 1.03854 | + | 0.599602i | 0.919420 | − | 0.393277i | \(-0.128659\pi\) |
0.119122 | + | 0.992880i | \(0.461992\pi\) | |||||||
\(888\) | 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 | ||||
\(896\) | 60.0576 | + | 45.9293i | 0.0670285 | + | 0.0512604i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 663.557 | + | 470.588i | 0.738928 | + | 0.524040i | ||||
\(899\) | 202.793i | 0.225577i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −606.935 | −0.673624 | ||||||||
\(902\) | 107.848 | − | 152.072i | 0.119565 | − | 0.168594i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 101.360 | + | 105.078i | 0.112124 | + | 0.116236i | ||||
\(905\) | 1010.61 | − | 1750.43i | 1.11670 | − | 1.93418i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −207.207 | + | 119.631i | −0.228453 | + | 0.131898i | −0.609858 | − | 0.792510i | \(-0.708774\pi\) |
0.381405 | + | 0.924408i | \(0.375440\pi\) | |||||||
\(908\) | −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 | −0.400397 | − | 0.916342i | \(-0.631128\pi\) |
0.593377 | + | 0.804925i | \(0.297794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −665.585 | + | 1152.83i | −0.729009 | + | 1.26268i | ||||
\(914\) | 59.4561 | − | 635.625i | 0.0650505 | − | 0.695433i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 506.551 | + | 95.6015i | 0.553003 | + | 0.104368i | ||||
\(917\) | 84.1801 | 0.0917994 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 878.708i | 0.956156i | 0.878317 | + | 0.478078i | \(0.158666\pi\) | ||||
−0.878317 | + | 0.478078i | \(0.841334\pi\) | |||||||
\(920\) | 94.1514 | + | 378.510i | 0.102338 | + | 0.411424i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 109.483 | − | 1170.44i | 0.118745 | − | 1.26946i | ||||
\(923\) | −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 | ||||
\(932\) | −19.8348 | − | 56.6006i | −0.0212820 | − | 0.0607303i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −919.322 | + | 1296.30i | −0.984284 | + | 1.38790i | ||||
\(935\) | 1815.93i | 1.94217i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −184.325 | −0.196718 | −0.0983589 | − | 0.995151i | \(-0.531359\pi\) | ||||
−0.0983589 | + | 0.995151i | \(0.531359\pi\) | |||||||
\(938\) | −35.4062 | − | 25.1097i | −0.0377465 | − | 0.0267694i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 258.372 | − | 90.5426i | 0.274864 | − | 0.0963219i | ||||
\(941\) | 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 | −0.848016 | − | 0.529970i | \(-0.822203\pi\) |
0.0349595 | + | 0.999389i | \(0.488870\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 53.5731 | − | 92.7913i | 0.0564521 | − | 0.0977779i | ||||
\(950\) | −497.126 | − | 46.5009i | −0.523290 | − | 0.0489483i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −19.2966 | − | 77.5767i | −0.0202695 | − | 0.0814881i | ||||
\(953\) | −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 | ||||||
\(956\) | 270.034 | − | 1430.79i | 0.282462 | − | 1.49664i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1317.45 | − | 123.234i | −1.37521 | − | 0.128637i | ||||
\(959\) | −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 | −0.00723669 | − | 0.999974i | \(-0.502304\pi\) |
−0.869621 | + | 0.493720i | \(0.835637\pi\) | |||||||
\(968\) | 1021.06 | + | 1058.50i | 1.05481 | + | 1.09350i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −261.951 | − | 185.773i | −0.270053 | − | 0.191519i | ||||
\(971\) | − | 67.3838i | − | 0.0693963i | −0.999398 | − | 0.0346982i | \(-0.988953\pi\) | ||
0.999398 | − | 0.0346982i | \(-0.0110470\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 70.3667 | 0.0723193 | ||||||||
\(974\) | 66.1234 | − | 93.2379i | 0.0678885 | − | 0.0957268i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1130.75 | + | 442.576i | 1.15855 | + | 0.453459i | ||||
\(977\) | −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 | −0.662343 | − | 0.749200i | \(-0.730438\pi\) |
0.317655 | + | 0.948206i | \(0.397105\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −638.971 | + | 1106.73i | −0.648701 | + | 1.12358i | ||||
\(986\) | 20.0104 | − | 213.925i | 0.0202946 | − | 0.216962i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25.8217 | + | 136.818i | −0.0261353 | + | 0.138479i | ||||
\(989\) | −310.720 | −0.314176 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 104.988i | 0.105941i | 0.998596 | + | 0.0529706i | \(0.0168690\pi\) | ||||
−0.998596 | + | 0.0529706i | \(0.983131\pi\) | |||||||
\(992\) | 912.776 | + | 459.465i | 0.920137 | + | 0.463171i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.66413 | − | 103.316i | 0.00972247 | − | 0.103940i | ||||
\(995\) | −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.91.6 | 16 | ||
3.2 | odd | 2 | 36.3.f.c.31.3 | yes | 16 | ||
4.3 | odd | 2 | inner | 108.3.f.c.91.5 | 16 | ||
8.3 | odd | 2 | 1728.3.o.g.1279.8 | 16 | |||
8.5 | even | 2 | 1728.3.o.g.1279.7 | 16 | |||
9.2 | odd | 6 | 36.3.f.c.7.4 | yes | 16 | ||
9.4 | even | 3 | 324.3.d.g.163.2 | 8 | |||
9.5 | odd | 6 | 324.3.d.i.163.7 | 8 | |||
9.7 | even | 3 | inner | 108.3.f.c.19.5 | 16 | ||
12.11 | even | 2 | 36.3.f.c.31.4 | yes | 16 | ||
24.5 | odd | 2 | 576.3.o.g.319.2 | 16 | |||
24.11 | even | 2 | 576.3.o.g.319.7 | 16 | |||
36.7 | odd | 6 | inner | 108.3.f.c.19.6 | 16 | ||
36.11 | even | 6 | 36.3.f.c.7.3 | ✓ | 16 | ||
36.23 | even | 6 | 324.3.d.i.163.8 | 8 | |||
36.31 | odd | 6 | 324.3.d.g.163.1 | 8 | |||
72.11 | even | 6 | 576.3.o.g.511.2 | 16 | |||
72.29 | odd | 6 | 576.3.o.g.511.7 | 16 | |||
72.43 | odd | 6 | 1728.3.o.g.127.7 | 16 | |||
72.61 | even | 6 | 1728.3.o.g.127.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.3 | ✓ | 16 | 36.11 | even | 6 | ||
36.3.f.c.7.4 | yes | 16 | 9.2 | odd | 6 | ||
36.3.f.c.31.3 | yes | 16 | 3.2 | odd | 2 | ||
36.3.f.c.31.4 | yes | 16 | 12.11 | even | 2 | ||
108.3.f.c.19.5 | 16 | 9.7 | even | 3 | inner | ||
108.3.f.c.19.6 | 16 | 36.7 | odd | 6 | inner | ||
108.3.f.c.91.5 | 16 | 4.3 | odd | 2 | inner | ||
108.3.f.c.91.6 | 16 | 1.1 | even | 1 | trivial | ||
324.3.d.g.163.1 | 8 | 36.31 | odd | 6 | |||
324.3.d.g.163.2 | 8 | 9.4 | even | 3 | |||
324.3.d.i.163.7 | 8 | 9.5 | odd | 6 | |||
324.3.d.i.163.8 | 8 | 36.23 | even | 6 | |||
576.3.o.g.319.2 | 16 | 24.5 | odd | 2 | |||
576.3.o.g.319.7 | 16 | 24.11 | even | 2 | |||
576.3.o.g.511.2 | 16 | 72.11 | even | 6 | |||
576.3.o.g.511.7 | 16 | 72.29 | odd | 6 | |||
1728.3.o.g.127.7 | 16 | 72.43 | odd | 6 | |||
1728.3.o.g.127.8 | 16 | 72.61 | even | 6 | |||
1728.3.o.g.1279.7 | 16 | 8.5 | even | 2 | |||
1728.3.o.g.1279.8 | 16 | 8.3 | odd | 2 |