Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [36,3,Mod(7,36)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36, 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("36.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 36 = 2^{2} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 36.f (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.980928951697\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 7.2 | ||
Root | \(1.84233 + 0.778342i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 36.7 |
Dual form | 36.3.f.c.31.2 |
$q$-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 \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).
\(n\) | \(19\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.84233 | − | 0.778342i | −0.921166 | − | 0.389171i | ||||
\(3\) | 0.262217 | + | 2.98852i | 0.0874058 | + | 0.996173i | ||||
\(4\) | 2.78837 | + | 2.86793i | 0.697092 | + | 0.716982i | ||||
\(5\) | 1.10093 | + | 1.90686i | 0.220185 | + | 0.381372i | 0.954864 | − | 0.297043i | \(-0.0960005\pi\) |
−0.734679 | + | 0.678415i | \(0.762667\pi\) | |||||||
\(6\) | 1.84300 | − | 5.70994i | 0.307166 | − | 0.951656i | ||||
\(7\) | 7.23844 | + | 4.17912i | 1.03406 | + | 0.597017i | 0.918146 | − | 0.396242i | \(-0.129686\pi\) |
0.115917 | + | 0.993259i | \(0.463019\pi\) | |||||||
\(8\) | −2.90487 | − | 7.45397i | −0.363109 | − | 0.931747i | ||||
\(9\) | −8.86248 | + | 1.56728i | −0.984720 | + | 0.174143i | ||||
\(10\) | −0.544081 | − | 4.36996i | −0.0544081 | − | 0.436996i | ||||
\(11\) | −4.54769 | − | 2.62561i | −0.413426 | − | 0.238692i | 0.278835 | − | 0.960339i | \(-0.410052\pi\) |
−0.692261 | + | 0.721648i | \(0.743385\pi\) | |||||||
\(12\) | −7.83969 | + | 9.08511i | −0.653308 | + | 0.757092i | ||||
\(13\) | −7.37788 | − | 12.7789i | −0.567529 | − | 0.982990i | −0.996809 | − | 0.0798182i | \(-0.974566\pi\) |
0.429280 | − | 0.903171i | \(-0.358767\pi\) | |||||||
\(14\) | −10.0828 | − | 13.3333i | −0.720202 | − | 0.952379i | ||||
\(15\) | −5.41000 | + | 3.79015i | −0.360667 | + | 0.252676i | ||||
\(16\) | −0.450004 | + | 15.9937i | −0.0281253 | + | 0.999604i | ||||
\(17\) | 28.2789 | 1.66346 | 0.831732 | − | 0.555178i | \(-0.187350\pi\) | ||||
0.831732 | + | 0.555178i | \(0.187350\pi\) | |||||||
\(18\) | 17.5475 | + | 4.01059i | 0.974862 | + | 0.222810i | ||||
\(19\) | − | 19.1376i | − | 1.00724i | −0.863925 | − | 0.503620i | \(-0.832001\pi\) | ||
0.863925 | − | 0.503620i | \(-0.167999\pi\) | |||||||
\(20\) | −2.39894 | + | 8.47440i | −0.119947 | + | 0.423720i | ||||
\(21\) | −10.5913 | + | 22.7281i | −0.504349 | + | 1.08229i | ||||
\(22\) | 6.33472 | + | 8.37689i | 0.287942 | + | 0.380768i | ||||
\(23\) | 3.16702 | − | 1.82848i | 0.137696 | − | 0.0794990i | −0.429569 | − | 0.903034i | \(-0.641335\pi\) |
0.567266 | + | 0.823535i | \(0.308001\pi\) | |||||||
\(24\) | 21.5146 | − | 10.6358i | 0.896443 | − | 0.443159i | ||||
\(25\) | 10.0759 | − | 17.4520i | 0.403037 | − | 0.698081i | ||||
\(26\) | 3.64618 | + | 29.2854i | 0.140238 | + | 1.12636i | ||||
\(27\) | −7.00775 | − | 26.0747i | −0.259546 | − | 0.965731i | ||||
\(28\) | 8.19805 | + | 32.4122i | 0.292787 | + | 1.15758i | ||||
\(29\) | −12.3355 | + | 21.3657i | −0.425362 | + | 0.736748i | −0.996454 | − | 0.0841375i | \(-0.973187\pi\) |
0.571092 | + | 0.820886i | \(0.306520\pi\) | |||||||
\(30\) | 12.9170 | − | 2.77188i | 0.430568 | − | 0.0923959i | ||||
\(31\) | −32.9674 | + | 19.0338i | −1.06347 | + | 0.613992i | −0.926389 | − | 0.376568i | \(-0.877104\pi\) |
−0.137077 | + | 0.990560i | \(0.543771\pi\) | |||||||
\(32\) | 13.2776 | − | 29.1154i | 0.414925 | − | 0.909856i | ||||
\(33\) | 6.65419 | − | 14.2793i | 0.201642 | − | 0.432707i | ||||
\(34\) | −52.0991 | − | 22.0106i | −1.53233 | − | 0.647372i | ||||
\(35\) | 18.4036i | 0.525817i | ||||||||
\(36\) | −29.2067 | − | 21.0468i | −0.811298 | − | 0.584633i | ||||
\(37\) | −4.21977 | −0.114048 | −0.0570239 | − | 0.998373i | \(-0.518161\pi\) | ||||
−0.0570239 | + | 0.998373i | \(0.518161\pi\) | |||||||
\(38\) | −14.8956 | + | 35.2578i | −0.391989 | + | 0.927836i | ||||
\(39\) | 36.2553 | − | 25.3998i | 0.929622 | − | 0.651276i | ||||
\(40\) | 11.0156 | − | 13.7454i | 0.275391 | − | 0.343636i | ||||
\(41\) | −9.92483 | − | 17.1903i | −0.242069 | − | 0.419276i | 0.719235 | − | 0.694767i | \(-0.244493\pi\) |
−0.961303 | + | 0.275492i | \(0.911159\pi\) | |||||||
\(42\) | 37.2029 | − | 33.6289i | 0.885784 | − | 0.800689i | ||||
\(43\) | 20.1894 | + | 11.6564i | 0.469521 | + | 0.271078i | 0.716039 | − | 0.698060i | \(-0.245953\pi\) |
−0.246518 | + | 0.969138i | \(0.579286\pi\) | |||||||
\(44\) | −5.15057 | − | 20.3636i | −0.117058 | − | 0.462809i | ||||
\(45\) | −12.7455 | − | 15.1740i | −0.283234 | − | 0.337201i | ||||
\(46\) | −7.25787 | + | 0.903640i | −0.157780 | + | 0.0196444i | ||||
\(47\) | 25.8538 | + | 14.9267i | 0.550082 | + | 0.317590i | 0.749155 | − | 0.662395i | \(-0.230460\pi\) |
−0.199073 | + | 0.979985i | \(0.563793\pi\) | |||||||
\(48\) | −47.9154 | + | 2.84897i | −0.998237 | + | 0.0593536i | ||||
\(49\) | 10.4300 | + | 18.0654i | 0.212858 | + | 0.368681i | ||||
\(50\) | −32.1468 | + | 24.3099i | −0.642937 | + | 0.486198i | ||||
\(51\) | 7.41521 | + | 84.5120i | 0.145396 | + | 1.65710i | ||||
\(52\) | 16.0766 | − | 56.7914i | 0.309165 | − | 1.09214i | ||||
\(53\) | −32.1118 | −0.605883 | −0.302942 | − | 0.953009i | \(-0.597969\pi\) | ||||
−0.302942 | + | 0.953009i | \(0.597969\pi\) | |||||||
\(54\) | −7.38445 | + | 53.4927i | −0.136749 | + | 0.990606i | ||||
\(55\) | − | 11.5624i | − | 0.210225i | ||||||
\(56\) | 10.1243 | − | 66.0950i | 0.180791 | − | 1.18027i | ||||
\(57\) | 57.1930 | − | 5.01820i | 1.00339 | − | 0.0880387i | ||||
\(58\) | 39.3559 | − | 29.7615i | 0.678550 | − | 0.513129i | ||||
\(59\) | −7.96159 | + | 4.59663i | −0.134942 | + | 0.0779089i | −0.565951 | − | 0.824439i | \(-0.691491\pi\) |
0.431009 | + | 0.902348i | \(0.358158\pi\) | |||||||
\(60\) | −25.9549 | − | 4.94716i | −0.432582 | − | 0.0824526i | ||||
\(61\) | −40.8215 | + | 70.7049i | −0.669205 | + | 1.15910i | 0.308922 | + | 0.951087i | \(0.400032\pi\) |
−0.978127 | + | 0.208009i | \(0.933302\pi\) | |||||||
\(62\) | 75.5517 | − | 9.40656i | 1.21858 | − | 0.151719i | ||||
\(63\) | −70.7005 | − | 25.6927i | −1.12223 | − | 0.407820i | ||||
\(64\) | −47.1234 | + | 43.3057i | −0.736304 | + | 0.676651i | ||||
\(65\) | 16.2450 | − | 28.1372i | 0.249923 | − | 0.432879i | ||||
\(66\) | −23.3734 | + | 21.1280i | −0.354143 | + | 0.320121i | ||||
\(67\) | 6.86179 | − | 3.96166i | 0.102415 | − | 0.0591292i | −0.447918 | − | 0.894075i | \(-0.647834\pi\) |
0.550333 | + | 0.834946i | \(0.314501\pi\) | |||||||
\(68\) | 78.8519 | + | 81.1017i | 1.15959 | + | 1.19267i | ||||
\(69\) | 6.29489 | + | 8.98523i | 0.0912302 | + | 0.130221i | ||||
\(70\) | 14.3243 | − | 33.9055i | 0.204633 | − | 0.484364i | ||||
\(71\) | − | 62.9286i | − | 0.886318i | −0.896443 | − | 0.443159i | \(-0.853858\pi\) | ||
0.896443 | − | 0.443159i | \(-0.146142\pi\) | |||||||
\(72\) | 37.4269 | + | 61.5080i | 0.519817 | + | 0.854277i | ||||
\(73\) | 33.3218 | 0.456463 | 0.228232 | − | 0.973607i | \(-0.426706\pi\) | ||||
0.228232 | + | 0.973607i | \(0.426706\pi\) | |||||||
\(74\) | 7.77421 | + | 3.28442i | 0.105057 | + | 0.0443841i | ||||
\(75\) | 54.7978 | + | 25.5359i | 0.730637 | + | 0.340478i | ||||
\(76\) | 54.8852 | − | 53.3626i | 0.722173 | − | 0.702140i | ||||
\(77\) | −21.9454 | − | 38.0106i | −0.285006 | − | 0.493644i | ||||
\(78\) | −86.5639 | + | 18.5758i | −1.10979 | + | 0.238151i | ||||
\(79\) | 53.7133 | + | 31.0114i | 0.679916 | + | 0.392549i | 0.799823 | − | 0.600236i | \(-0.204927\pi\) |
−0.119908 | + | 0.992785i | \(0.538260\pi\) | |||||||
\(80\) | −30.9931 | + | 16.7497i | −0.387414 | + | 0.209372i | ||||
\(81\) | 76.0873 | − | 27.7800i | 0.939349 | − | 0.342963i | ||||
\(82\) | 4.90489 | + | 39.3951i | 0.0598157 | + | 0.480429i | ||||
\(83\) | −103.056 | − | 59.4995i | −1.24164 | − | 0.716861i | −0.272212 | − | 0.962237i | \(-0.587755\pi\) |
−0.969428 | + | 0.245376i | \(0.921089\pi\) | |||||||
\(84\) | −94.7149 | + | 32.9991i | −1.12756 | + | 0.392846i | ||||
\(85\) | 31.1329 | + | 53.9238i | 0.366270 | + | 0.634398i | ||||
\(86\) | −28.1230 | − | 37.1892i | −0.327011 | − | 0.432432i | ||||
\(87\) | −67.0864 | − | 31.2624i | −0.771108 | − | 0.359338i | ||||
\(88\) | −6.36077 | + | 41.5254i | −0.0722815 | + | 0.471879i | ||||
\(89\) | −107.361 | −1.20630 | −0.603152 | − | 0.797626i | \(-0.706089\pi\) | ||||
−0.603152 | + | 0.797626i | \(0.706089\pi\) | |||||||
\(90\) | 11.6709 | + | 37.8760i | 0.129676 | + | 0.420844i | ||||
\(91\) | − | 123.332i | − | 1.35530i | ||||||
\(92\) | 14.0747 | + | 3.98430i | 0.152986 | + | 0.0433076i | ||||
\(93\) | −65.5274 | − | 93.5328i | −0.704596 | − | 1.00573i | ||||
\(94\) | −36.0132 | − | 47.6231i | −0.383120 | − | 0.506629i | ||||
\(95\) | 36.4927 | − | 21.0690i | 0.384133 | − | 0.221779i | ||||
\(96\) | 90.4935 | + | 32.0458i | 0.942640 | + | 0.333810i | ||||
\(97\) | 1.78621 | − | 3.09380i | 0.0184145 | − | 0.0318949i | −0.856671 | − | 0.515863i | \(-0.827471\pi\) |
0.875086 | + | 0.483968i | \(0.160805\pi\) | |||||||
\(98\) | −5.15457 | − | 41.4005i | −0.0525976 | − | 0.422454i | ||||
\(99\) | 44.4189 | + | 16.1419i | 0.448675 | + | 0.163049i | ||||
\(100\) | 78.1465 | − | 19.7656i | 0.781465 | − | 0.197656i | ||||
\(101\) | 7.54688 | − | 13.0716i | 0.0747216 | − | 0.129422i | −0.826244 | − | 0.563313i | \(-0.809527\pi\) |
0.900965 | + | 0.433891i | \(0.142860\pi\) | |||||||
\(102\) | 52.1179 | − | 161.471i | 0.510960 | − | 1.58304i | ||||
\(103\) | −112.813 | + | 65.1324i | −1.09527 | + | 0.632353i | −0.934974 | − | 0.354716i | \(-0.884578\pi\) |
−0.160294 | + | 0.987069i | \(0.551244\pi\) | |||||||
\(104\) | −73.8215 | + | 92.1155i | −0.709822 | + | 0.885726i | ||||
\(105\) | −54.9995 | + | 4.82574i | −0.523804 | + | 0.0459594i | ||||
\(106\) | 59.1606 | + | 24.9940i | 0.558119 | + | 0.235792i | ||||
\(107\) | 51.2733i | 0.479190i | 0.970873 | + | 0.239595i | \(0.0770146\pi\) | ||||
−0.970873 | + | 0.239595i | \(0.922985\pi\) | |||||||
\(108\) | 55.2402 | − | 92.8037i | 0.511483 | − | 0.859293i | ||||
\(109\) | −25.4737 | −0.233704 | −0.116852 | − | 0.993149i | \(-0.537280\pi\) | ||||
−0.116852 | + | 0.993149i | \(0.537280\pi\) | |||||||
\(110\) | −8.99949 | + | 21.3018i | −0.0818136 | + | 0.193652i | ||||
\(111\) | −1.10650 | − | 12.6108i | −0.00996843 | − | 0.113611i | ||||
\(112\) | −70.0968 | + | 113.889i | −0.625864 | + | 1.01686i | ||||
\(113\) | 76.1529 | + | 131.901i | 0.673919 | + | 1.16726i | 0.976783 | + | 0.214229i | \(0.0687238\pi\) |
−0.302864 | + | 0.953034i | \(0.597943\pi\) | |||||||
\(114\) | −109.274 | − | 35.2705i | −0.958547 | − | 0.309390i | ||||
\(115\) | 6.97330 | + | 4.02603i | 0.0606374 | + | 0.0350090i | ||||
\(116\) | −95.6712 | + | 24.1982i | −0.824751 | + | 0.208605i | ||||
\(117\) | 85.4144 | + | 101.689i | 0.730038 | + | 0.869139i | ||||
\(118\) | 18.2456 | − | 2.27167i | 0.154624 | − | 0.0192514i | ||||
\(119\) | 204.695 | + | 118.181i | 1.72013 | + | 0.993116i | ||||
\(120\) | 43.9670 | + | 29.3161i | 0.366392 | + | 0.244301i | ||||
\(121\) | −46.7124 | − | 80.9082i | −0.386053 | − | 0.668663i | ||||
\(122\) | 130.239 | − | 98.4888i | 1.06754 | − | 0.807285i | ||||
\(123\) | 48.7711 | − | 34.1681i | 0.396513 | − | 0.277790i | ||||
\(124\) | −146.513 | − | 41.4751i | −1.18156 | − | 0.334476i | ||||
\(125\) | 99.4176 | 0.795341 | ||||||||
\(126\) | 110.256 | + | 102.364i | 0.875047 | + | 0.812409i | ||||
\(127\) | 147.428i | 1.16085i | 0.814314 | + | 0.580425i | \(0.197114\pi\) | ||||
−0.814314 | + | 0.580425i | \(0.802886\pi\) | |||||||
\(128\) | 120.524 | − | 43.1052i | 0.941591 | − | 0.336760i | ||||
\(129\) | −29.5412 | + | 63.3929i | −0.229002 | + | 0.491418i | ||||
\(130\) | −51.8290 | + | 39.1938i | −0.398684 | + | 0.301491i | ||||
\(131\) | −112.889 | + | 65.1766i | −0.861750 | + | 0.497532i | −0.864598 | − | 0.502464i | \(-0.832427\pi\) |
0.00284803 | + | 0.999996i | \(0.499093\pi\) | |||||||
\(132\) | 59.5064 | − | 20.7323i | 0.450806 | − | 0.157063i | ||||
\(133\) | 79.9782 | − | 138.526i | 0.601340 | − | 1.04155i | ||||
\(134\) | −15.7252 | + | 1.95787i | −0.117352 | + | 0.0146109i | ||||
\(135\) | 42.0058 | − | 42.0691i | 0.311154 | − | 0.311623i | ||||
\(136\) | −82.1465 | − | 210.790i | −0.604018 | − | 1.54993i | ||||
\(137\) | 49.9179 | − | 86.4604i | 0.364364 | − | 0.631098i | −0.624310 | − | 0.781177i | \(-0.714620\pi\) |
0.988674 | + | 0.150079i | \(0.0479530\pi\) | |||||||
\(138\) | −4.60369 | − | 21.4533i | −0.0333600 | − | 0.155459i | ||||
\(139\) | 82.7828 | − | 47.7947i | 0.595560 | − | 0.343847i | −0.171733 | − | 0.985144i | \(-0.554937\pi\) |
0.767293 | + | 0.641297i | \(0.221603\pi\) | |||||||
\(140\) | −52.7801 | + | 51.3160i | −0.377001 | + | 0.366543i | ||||
\(141\) | −37.8295 | + | 81.1787i | −0.268294 | + | 0.575736i | ||||
\(142\) | −48.9799 | + | 115.935i | −0.344929 | + | 0.816445i | ||||
\(143\) | 77.4857i | 0.541858i | ||||||||
\(144\) | −21.0784 | − | 142.449i | −0.146378 | − | 0.989229i | ||||
\(145\) | −54.3218 | −0.374633 | ||||||||
\(146\) | −61.3898 | − | 25.9358i | −0.420478 | − | 0.177642i | ||||
\(147\) | −51.2538 | + | 35.9074i | −0.348665 | + | 0.244268i | ||||
\(148\) | −11.7663 | − | 12.1020i | −0.0795018 | − | 0.0817701i | ||||
\(149\) | 34.3382 | + | 59.4755i | 0.230458 | + | 0.399164i | 0.957943 | − | 0.286959i | \(-0.0926443\pi\) |
−0.727485 | + | 0.686123i | \(0.759311\pi\) | |||||||
\(150\) | −81.0800 | − | 89.6969i | −0.540533 | − | 0.597979i | ||||
\(151\) | −91.2633 | − | 52.6909i | −0.604393 | − | 0.348946i | 0.166375 | − | 0.986063i | \(-0.446794\pi\) |
−0.770768 | + | 0.637116i | \(0.780127\pi\) | |||||||
\(152\) | −142.651 | + | 55.5922i | −0.938493 | + | 0.365738i | ||||
\(153\) | −250.621 | + | 44.3210i | −1.63805 | + | 0.289680i | ||||
\(154\) | 10.8455 | + | 87.1092i | 0.0704255 | + | 0.565644i | ||||
\(155\) | −72.5894 | − | 41.9095i | −0.468319 | − | 0.270384i | ||||
\(156\) | 173.938 | + | 33.1535i | 1.11499 | + | 0.212523i | ||||
\(157\) | −107.502 | − | 186.200i | −0.684729 | − | 1.18598i | −0.973522 | − | 0.228593i | \(-0.926587\pi\) |
0.288794 | − | 0.957391i | \(-0.406746\pi\) | |||||||
\(158\) | −74.8203 | − | 98.9406i | −0.473546 | − | 0.626206i | ||||
\(159\) | −8.42027 | − | 95.9667i | −0.0529577 | − | 0.603564i | ||||
\(160\) | 70.1366 | − | 6.73536i | 0.438353 | − | 0.0420960i | ||||
\(161\) | 30.5657 | 0.189849 | ||||||||
\(162\) | −161.800 | − | 8.04186i | −0.998767 | − | 0.0496411i | ||||
\(163\) | − | 33.7439i | − | 0.207018i | −0.994629 | − | 0.103509i | \(-0.966993\pi\) | ||
0.994629 | − | 0.103509i | \(-0.0330071\pi\) | |||||||
\(164\) | 21.6265 | − | 76.3966i | 0.131869 | − | 0.465833i | ||||
\(165\) | 34.5544 | − | 3.03186i | 0.209421 | − | 0.0183749i | ||||
\(166\) | 143.553 | + | 189.831i | 0.864775 | + | 1.14356i | ||||
\(167\) | 131.565 | − | 75.9589i | 0.787812 | − | 0.454843i | −0.0513797 | − | 0.998679i | \(-0.516362\pi\) |
0.839192 | + | 0.543836i | \(0.183029\pi\) | |||||||
\(168\) | 200.181 | + | 12.9254i | 1.19155 | + | 0.0769367i | ||||
\(169\) | −24.3663 | + | 42.2036i | −0.144179 | + | 0.249726i | ||||
\(170\) | −15.3860 | − | 123.578i | −0.0905060 | − | 0.726927i | ||||
\(171\) | 29.9940 | + | 169.606i | 0.175403 | + | 0.991851i | ||||
\(172\) | 22.8659 | + | 90.4040i | 0.132941 | + | 0.525605i | ||||
\(173\) | −59.4003 | + | 102.884i | −0.343354 | + | 0.594707i | −0.985053 | − | 0.172249i | \(-0.944896\pi\) |
0.641699 | + | 0.766957i | \(0.278230\pi\) | |||||||
\(174\) | 99.2625 | + | 109.812i | 0.570474 | + | 0.631102i | ||||
\(175\) | 145.868 | − | 84.2170i | 0.833532 | − | 0.481240i | ||||
\(176\) | 44.0396 | − | 71.5526i | 0.250225 | − | 0.406549i | ||||
\(177\) | −15.8248 | − | 22.5881i | −0.0894055 | − | 0.127616i | ||||
\(178\) | 197.795 | + | 83.5636i | 1.11121 | + | 0.469458i | ||||
\(179\) | − | 218.189i | − | 1.21894i | −0.792811 | − | 0.609468i | \(-0.791383\pi\) | ||
0.792811 | − | 0.609468i | \(-0.208617\pi\) | |||||||
\(180\) | 7.97884 | − | 78.8640i | 0.0443269 | − | 0.438133i | ||||
\(181\) | 184.078 | 1.01701 | 0.508503 | − | 0.861060i | \(-0.330199\pi\) | ||||
0.508503 | + | 0.861060i | \(0.330199\pi\) | |||||||
\(182\) | −95.9945 | + | 227.219i | −0.527443 | + | 1.24845i | ||||
\(183\) | −222.007 | − | 103.456i | −1.21315 | − | 0.565332i | ||||
\(184\) | −22.8292 | − | 18.2954i | −0.124072 | − | 0.0994313i | ||||
\(185\) | −4.64565 | − | 8.04650i | −0.0251116 | − | 0.0434946i | ||||
\(186\) | 47.9226 | + | 223.321i | 0.257649 | + | 1.20065i | ||||
\(187\) | −128.603 | − | 74.2492i | −0.687719 | − | 0.397055i | ||||
\(188\) | 29.2813 | + | 115.768i | 0.155752 | + | 0.615788i | ||||
\(189\) | 58.2442 | − | 218.027i | 0.308170 | − | 1.15358i | ||||
\(190\) | −83.6305 | + | 10.4124i | −0.440160 | + | 0.0548021i | ||||
\(191\) | −215.775 | − | 124.578i | −1.12971 | − | 0.652239i | −0.185849 | − | 0.982578i | \(-0.559503\pi\) |
−0.943862 | + | 0.330339i | \(0.892837\pi\) | |||||||
\(192\) | −141.776 | − | 129.474i | −0.738419 | − | 0.674343i | ||||
\(193\) | 125.086 | + | 216.656i | 0.648115 | + | 1.12257i | 0.983573 | + | 0.180513i | \(0.0577758\pi\) |
−0.335457 | + | 0.942055i | \(0.608891\pi\) | |||||||
\(194\) | −5.69882 | + | 4.30953i | −0.0293754 | + | 0.0222141i | ||||
\(195\) | 88.3481 | + | 41.1704i | 0.453067 | + | 0.211130i | ||||
\(196\) | −22.7273 | + | 80.2855i | −0.115956 | + | 0.409620i | ||||
\(197\) | 255.674 | 1.29784 | 0.648919 | − | 0.760858i | \(-0.275221\pi\) | ||||
0.648919 | + | 0.760858i | \(0.275221\pi\) | |||||||
\(198\) | −69.2703 | − | 64.3118i | −0.349850 | − | 0.324807i | ||||
\(199\) | 309.110i | 1.55332i | 0.629921 | + | 0.776659i | \(0.283087\pi\) | ||||
−0.629921 | + | 0.776659i | \(0.716913\pi\) | |||||||
\(200\) | −159.356 | − | 24.4098i | −0.796781 | − | 0.122049i | ||||
\(201\) | 13.6388 | + | 19.4678i | 0.0678545 | + | 0.0968546i | ||||
\(202\) | −24.0780 | + | 18.2081i | −0.119198 | + | 0.0901392i | ||||
\(203\) | −178.580 | + | 103.103i | −0.879702 | + | 0.507896i | ||||
\(204\) | −221.698 | + | 256.917i | −1.08675 | + | 1.25940i | ||||
\(205\) | 21.8530 | − | 37.8505i | 0.106600 | − | 0.184636i | ||||
\(206\) | 258.533 | − | 32.1887i | 1.25502 | − | 0.156256i | ||||
\(207\) | −25.2019 | + | 21.1685i | −0.121748 | + | 0.102263i | ||||
\(208\) | 207.701 | − | 112.249i | 0.998563 | − | 0.539658i | ||||
\(209\) | −50.2478 | + | 87.0317i | −0.240420 | + | 0.416420i | ||||
\(210\) | 105.083 | + | 33.9178i | 0.500397 | + | 0.161513i | ||||
\(211\) | 341.158 | − | 196.968i | 1.61686 | − | 0.933497i | 0.629140 | − | 0.777292i | \(-0.283407\pi\) |
0.987725 | − | 0.156205i | \(-0.0499261\pi\) | |||||||
\(212\) | −89.5395 | − | 92.0943i | −0.422356 | − | 0.434407i | ||||
\(213\) | 188.063 | − | 16.5010i | 0.882926 | − | 0.0774693i | ||||
\(214\) | 39.9082 | − | 94.4624i | 0.186487 | − | 0.441413i | ||||
\(215\) | 51.3311i | 0.238750i | ||||||||
\(216\) | −174.004 | + | 127.979i | −0.805573 | + | 0.592497i | ||||
\(217\) | −318.177 | −1.46626 | ||||||||
\(218\) | 46.9310 | + | 19.8272i | 0.215280 | + | 0.0909506i | ||||
\(219\) | 8.73756 | + | 99.5829i | 0.0398975 | + | 0.454716i | ||||
\(220\) | 33.1601 | − | 32.2402i | 0.150728 | − | 0.146546i | ||||
\(221\) | −208.638 | − | 361.372i | −0.944064 | − | 1.63517i | ||||
\(222\) | −7.77702 | + | 24.0946i | −0.0350316 | + | 0.108534i | ||||
\(223\) | −89.4002 | − | 51.6152i | −0.400898 | − | 0.231458i | 0.285974 | − | 0.958238i | \(-0.407683\pi\) |
−0.686871 | + | 0.726779i | \(0.741016\pi\) | |||||||
\(224\) | 217.786 | − | 155.261i | 0.972258 | − | 0.693131i | ||||
\(225\) | −61.9455 | + | 170.460i | −0.275313 | + | 0.757600i | ||||
\(226\) | −37.6350 | − | 302.278i | −0.166527 | − | 1.33751i | ||||
\(227\) | 122.210 | + | 70.5578i | 0.538369 | + | 0.310828i | 0.744418 | − | 0.667714i | \(-0.232727\pi\) |
−0.206049 | + | 0.978542i | \(0.566061\pi\) | |||||||
\(228\) | 173.867 | + | 150.033i | 0.762575 | + | 0.658038i | ||||
\(229\) | 105.572 | + | 182.856i | 0.461012 | + | 0.798496i | 0.999012 | − | 0.0444490i | \(-0.0141532\pi\) |
−0.538000 | + | 0.842945i | \(0.680820\pi\) | |||||||
\(230\) | −9.71349 | − | 12.8449i | −0.0422326 | − | 0.0558474i | ||||
\(231\) | 107.841 | − | 75.5514i | 0.466844 | − | 0.327062i | ||||
\(232\) | 195.092 | + | 29.8838i | 0.840916 | + | 0.128810i | ||||
\(233\) | −280.109 | −1.20219 | −0.601093 | − | 0.799179i | \(-0.705268\pi\) | ||||
−0.601093 | + | 0.799179i | \(0.705268\pi\) | |||||||
\(234\) | −78.2127 | − | 253.827i | −0.334242 | − | 1.08473i | ||||
\(235\) | 65.7328i | 0.279714i | ||||||||
\(236\) | −35.3826 | − | 10.0162i | −0.149926 | − | 0.0424414i | ||||
\(237\) | −78.5936 | + | 168.655i | −0.331619 | + | 0.711624i | ||||
\(238\) | −285.131 | − | 377.051i | −1.19803 | − | 1.58425i | ||||
\(239\) | 339.349 | − | 195.923i | 1.41987 | − | 0.819762i | 0.423583 | − | 0.905857i | \(-0.360772\pi\) |
0.996287 | + | 0.0860949i | \(0.0274388\pi\) | |||||||
\(240\) | −58.1838 | − | 88.2313i | −0.242433 | − | 0.367631i | ||||
\(241\) | −23.6786 | + | 41.0125i | −0.0982514 | + | 0.170176i | −0.910961 | − | 0.412493i | \(-0.864658\pi\) |
0.812710 | + | 0.582669i | \(0.197992\pi\) | |||||||
\(242\) | 23.0854 | + | 185.418i | 0.0953943 | + | 0.766190i | ||||
\(243\) | 102.973 | + | 220.104i | 0.423755 | + | 0.905777i | ||||
\(244\) | −316.602 | + | 80.0783i | −1.29755 | + | 0.328190i | ||||
\(245\) | −22.9654 | + | 39.7772i | −0.0937363 | + | 0.162356i | ||||
\(246\) | −116.447 | + | 24.9884i | −0.473362 | + | 0.101579i | ||||
\(247\) | −244.557 | + | 141.195i | −0.990107 | + | 0.571639i | ||||
\(248\) | 237.643 | + | 190.448i | 0.958239 | + | 0.767935i | ||||
\(249\) | 150.792 | − | 323.587i | 0.605591 | − | 1.29955i | ||||
\(250\) | −183.160 | − | 77.3809i | −0.732641 | − | 0.309524i | ||||
\(251\) | 389.416i | 1.55146i | 0.631065 | + | 0.775730i | \(0.282618\pi\) | ||||
−0.631065 | + | 0.775730i | \(0.717382\pi\) | |||||||
\(252\) | −123.454 | − | 274.404i | −0.489898 | − | 1.08891i | ||||
\(253\) | −19.2035 | −0.0759030 | ||||||||
\(254\) | 114.749 | − | 271.611i | 0.451769 | − | 1.06933i | ||||
\(255\) | −152.989 | + | 107.181i | −0.599956 | + | 0.420318i | ||||
\(256\) | −255.595 | − | 14.3944i | −0.998418 | − | 0.0562283i | ||||
\(257\) | −32.5409 | − | 56.3625i | −0.126618 | − | 0.219310i | 0.795746 | − | 0.605631i | \(-0.207079\pi\) |
−0.922364 | + | 0.386321i | \(0.873746\pi\) | |||||||
\(258\) | 103.766 | − | 93.7976i | 0.402194 | − | 0.363557i | ||||
\(259\) | −30.5445 | − | 17.6349i | −0.117933 | − | 0.0680884i | ||||
\(260\) | 125.992 | − | 31.8673i | 0.484586 | − | 0.122567i | ||||
\(261\) | 75.8370 | − | 208.686i | 0.290563 | − | 0.799565i | ||||
\(262\) | 258.709 | − | 32.2105i | 0.987439 | − | 0.122941i | ||||
\(263\) | 124.773 | + | 72.0378i | 0.474423 | + | 0.273908i | 0.718089 | − | 0.695951i | \(-0.245017\pi\) |
−0.243667 | + | 0.969859i | \(0.578350\pi\) | |||||||
\(264\) | −125.767 | − | 8.12060i | −0.476391 | − | 0.0307599i | ||||
\(265\) | −35.3527 | − | 61.2327i | −0.133406 | − | 0.231067i | ||||
\(266\) | −255.167 | + | 192.961i | −0.959275 | + | 0.725417i | ||||
\(267\) | −28.1519 | − | 320.850i | −0.105438 | − | 1.20169i | ||||
\(268\) | 30.4949 | + | 8.63255i | 0.113787 | + | 0.0322110i | ||||
\(269\) | −72.4113 | −0.269187 | −0.134593 | − | 0.990901i | \(-0.542973\pi\) | ||||
−0.134593 | + | 0.990901i | \(0.542973\pi\) | |||||||
\(270\) | −110.133 | + | 44.8104i | −0.407899 | + | 0.165964i | ||||
\(271\) | − | 35.4695i | − | 0.130884i | −0.997856 | − | 0.0654419i | \(-0.979154\pi\) | ||
0.997856 | − | 0.0654419i | \(-0.0208457\pi\) | |||||||
\(272\) | −12.7256 | + | 452.283i | −0.0467854 | + | 1.66281i | ||||
\(273\) | 368.580 | − | 32.3398i | 1.35011 | − | 0.118461i | ||||
\(274\) | −159.261 | + | 120.435i | −0.581245 | + | 0.439545i | ||||
\(275\) | −91.6443 | + | 52.9109i | −0.333252 | + | 0.192403i | ||||
\(276\) | −8.21651 | + | 43.1074i | −0.0297700 | + | 0.156186i | ||||
\(277\) | −166.922 | + | 289.118i | −0.602607 | + | 1.04375i | 0.389818 | + | 0.920892i | \(0.372538\pi\) |
−0.992425 | + | 0.122854i | \(0.960795\pi\) | |||||||
\(278\) | −189.714 | + | 23.6203i | −0.682424 | + | 0.0849651i | ||||
\(279\) | 262.342 | − | 220.356i | 0.940295 | − | 0.789806i | ||||
\(280\) | 137.180 | − | 53.4600i | 0.489928 | − | 0.190929i | ||||
\(281\) | −20.5385 | + | 35.5737i | −0.0730906 | + | 0.126597i | −0.900254 | − | 0.435364i | \(-0.856620\pi\) |
0.827164 | + | 0.561961i | \(0.189953\pi\) | |||||||
\(282\) | 132.879 | − | 120.114i | 0.471203 | − | 0.425936i | ||||
\(283\) | −218.583 | + | 126.199i | −0.772378 | + | 0.445933i | −0.833722 | − | 0.552184i | \(-0.813795\pi\) |
0.0613442 | + | 0.998117i | \(0.480461\pi\) | |||||||
\(284\) | 180.474 | − | 175.468i | 0.635474 | − | 0.617845i | ||||
\(285\) | 72.5342 | + | 103.534i | 0.254506 | + | 0.363278i | ||||
\(286\) | 60.3103 | − | 142.754i | 0.210875 | − | 0.499141i | ||||
\(287\) | − | 165.908i | − | 0.578077i | ||||||
\(288\) | −72.0405 | + | 278.844i | −0.250141 | + | 0.968210i | ||||
\(289\) | 510.695 | 1.76711 | ||||||||
\(290\) | 100.079 | + | 42.2809i | 0.345099 | + | 0.145796i | ||||
\(291\) | 9.71427 | + | 4.52687i | 0.0333824 | + | 0.0155562i | ||||
\(292\) | 92.9135 | + | 95.5646i | 0.318197 | + | 0.327276i | ||||
\(293\) | 20.3415 | + | 35.2325i | 0.0694248 | + | 0.120247i | 0.898648 | − | 0.438670i | \(-0.144550\pi\) |
−0.829223 | + | 0.558917i | \(0.811217\pi\) | |||||||
\(294\) | 122.375 | − | 26.2605i | 0.416240 | − | 0.0893213i | ||||
\(295\) | −17.5302 | − | 10.1211i | −0.0594245 | − | 0.0343088i | ||||
\(296\) | 12.2579 | + | 31.4540i | 0.0414117 | + | 0.106264i | ||||
\(297\) | −36.5930 | + | 136.979i | −0.123209 | + | 0.461210i | ||||
\(298\) | −16.9701 | − | 136.300i | −0.0569465 | − | 0.457384i | ||||
\(299\) | −46.7317 | − | 26.9806i | −0.156293 | − | 0.0902361i | ||||
\(300\) | 79.5613 | + | 228.359i | 0.265204 | + | 0.761198i | ||||
\(301\) | 97.4266 | + | 168.748i | 0.323677 | + | 0.560624i | ||||
\(302\) | 127.126 | + | 168.108i | 0.420946 | + | 0.556650i | ||||
\(303\) | 41.0436 | + | 19.1264i | 0.135457 | + | 0.0631234i | ||||
\(304\) | 306.080 | + | 8.61199i | 1.00684 | + | 0.0283289i | ||||
\(305\) | −179.766 | −0.589396 | ||||||||
\(306\) | 496.224 | + | 113.415i | 1.62165 | + | 0.370637i | ||||
\(307\) | − | 136.830i | − | 0.445701i | −0.974853 | − | 0.222850i | \(-0.928464\pi\) | ||
0.974853 | − | 0.222850i | \(-0.0715361\pi\) | |||||||
\(308\) | 47.8197 | − | 168.926i | 0.155259 | − | 0.548460i | ||||
\(309\) | −224.231 | − | 320.064i | −0.725666 | − | 1.03580i | ||||
\(310\) | 101.114 | + | 133.711i | 0.326174 | + | 0.431324i | ||||
\(311\) | −371.260 | + | 214.347i | −1.19376 | + | 0.689219i | −0.959158 | − | 0.282871i | \(-0.908713\pi\) |
−0.234605 | + | 0.972091i | \(0.575380\pi\) | |||||||
\(312\) | −294.646 | − | 196.463i | −0.944379 | − | 0.629688i | ||||
\(313\) | 5.98705 | − | 10.3699i | 0.0191280 | − | 0.0331306i | −0.856303 | − | 0.516474i | \(-0.827244\pi\) |
0.875431 | + | 0.483343i | \(0.160578\pi\) | |||||||
\(314\) | 53.1281 | + | 426.715i | 0.169198 | + | 1.35896i | ||||
\(315\) | −28.8436 | − | 163.101i | −0.0915670 | − | 0.517782i | ||||
\(316\) | 60.8341 | + | 240.517i | 0.192513 | + | 0.761130i | ||||
\(317\) | −23.5266 | + | 40.7493i | −0.0742164 | + | 0.128547i | −0.900745 | − | 0.434348i | \(-0.856979\pi\) |
0.826529 | + | 0.562894i | \(0.190312\pi\) | |||||||
\(318\) | −59.1820 | + | 183.356i | −0.186107 | + | 0.576592i | ||||
\(319\) | 112.196 | − | 64.7763i | 0.351711 | − | 0.203061i | ||||
\(320\) | −134.457 | − | 42.1814i | −0.420179 | − | 0.131817i | ||||
\(321\) | −153.231 | + | 13.4448i | −0.477356 | + | 0.0418840i | ||||
\(322\) | −56.3121 | − | 23.7906i | −0.174882 | − | 0.0738837i | ||||
\(323\) | − | 541.189i | − | 1.67551i | ||||||
\(324\) | 291.830 | + | 140.752i | 0.900711 | + | 0.434419i | ||||
\(325\) | −297.356 | −0.914941 | ||||||||
\(326\) | −26.2643 | + | 62.1675i | −0.0805654 | + | 0.190698i | ||||
\(327\) | −6.67964 | − | 76.1286i | −0.0204270 | − | 0.232809i | ||||
\(328\) | −99.3057 | + | 123.915i | −0.302761 | + | 0.377790i | ||||
\(329\) | 124.761 | + | 216.092i | 0.379213 | + | 0.656816i | ||||
\(330\) | −66.0205 | − | 21.3095i | −0.200062 | − | 0.0645741i | ||||
\(331\) | −73.1501 | − | 42.2332i | −0.220997 | − | 0.127593i | 0.385415 | − | 0.922743i | \(-0.374058\pi\) |
−0.606412 | + | 0.795151i | \(0.707392\pi\) | |||||||
\(332\) | −116.718 | − | 461.464i | −0.351561 | − | 1.38995i | ||||
\(333\) | 37.3976 | − | 6.61357i | 0.112305 | − | 0.0198606i | ||||
\(334\) | −301.508 | + | 37.5392i | −0.902717 | + | 0.112393i | ||||
\(335\) | 15.1086 | + | 8.72297i | 0.0451004 | + | 0.0260387i | ||||
\(336\) | −358.739 | − | 179.622i | −1.06768 | − | 0.534589i | ||||
\(337\) | −252.558 | − | 437.443i | −0.749430 | − | 1.29805i | −0.948096 | − | 0.317983i | \(-0.896994\pi\) |
0.198667 | − | 0.980067i | \(-0.436339\pi\) | |||||||
\(338\) | 77.7396 | − | 58.7877i | 0.229999 | − | 0.173928i | ||||
\(339\) | −374.219 | + | 262.171i | −1.10389 | + | 0.773366i | ||||
\(340\) | −67.8395 | + | 239.646i | −0.199528 | + | 0.704842i | ||||
\(341\) | 199.901 | 0.586219 | ||||||||
\(342\) | 76.7529 | − | 335.817i | 0.224424 | − | 0.981921i | ||||
\(343\) | − | 235.200i | − | 0.685714i | ||||||
\(344\) | 28.2386 | − | 184.352i | 0.0820889 | − | 0.535906i | ||||
\(345\) | −10.2034 | + | 21.8955i | −0.0295750 | + | 0.0634653i | ||||
\(346\) | 189.514 | − | 143.313i | 0.547729 | − | 0.414200i | ||||
\(347\) | 424.751 | − | 245.230i | 1.22407 | − | 0.706715i | 0.258284 | − | 0.966069i | \(-0.416843\pi\) |
0.965782 | + | 0.259354i | \(0.0835097\pi\) | |||||||
\(348\) | −97.4033 | − | 279.570i | −0.279894 | − | 0.803362i | ||||
\(349\) | 186.972 | − | 323.845i | 0.535736 | − | 0.927923i | −0.463391 | − | 0.886154i | \(-0.653367\pi\) |
0.999127 | − | 0.0417686i | \(-0.0132992\pi\) | |||||||
\(350\) | −334.287 | + | 41.6203i | −0.955105 | + | 0.118915i | ||||
\(351\) | −281.503 | + | 281.927i | −0.802003 | + | 0.803212i | ||||
\(352\) | −136.828 | + | 97.5458i | −0.388716 | + | 0.277119i | ||||
\(353\) | 297.026 | − | 514.465i | 0.841434 | − | 1.45741i | −0.0472483 | − | 0.998883i | \(-0.515045\pi\) |
0.888682 | − | 0.458523i | \(-0.151621\pi\) | |||||||
\(354\) | 11.5733 | + | 53.9318i | 0.0326928 | + | 0.152350i | ||||
\(355\) | 119.996 | − | 69.2796i | 0.338016 | − | 0.195154i | ||||
\(356\) | −299.362 | − | 307.904i | −0.840905 | − | 0.864898i | ||||
\(357\) | −299.511 | + | 642.724i | −0.838966 | + | 1.80035i | ||||
\(358\) | −169.826 | + | 401.977i | −0.474374 | + | 1.12284i | ||||
\(359\) | 410.893i | 1.14455i | 0.820062 | + | 0.572274i | \(0.193939\pi\) | ||||
−0.820062 | + | 0.572274i | \(0.806061\pi\) | |||||||
\(360\) | −76.0828 | + | 139.083i | −0.211341 | + | 0.386343i | ||||
\(361\) | −5.24690 | −0.0145343 | ||||||||
\(362\) | −339.133 | − | 143.276i | −0.936832 | − | 0.395789i | ||||
\(363\) | 229.547 | − | 160.816i | 0.632360 | − | 0.443020i | ||||
\(364\) | 353.707 | − | 343.895i | 0.971724 | − | 0.944768i | ||||
\(365\) | 36.6848 | + | 63.5400i | 0.100506 | + | 0.174082i | ||||
\(366\) | 328.487 | + | 363.397i | 0.897504 | + | 0.992888i | ||||
\(367\) | 466.176 | + | 269.147i | 1.27023 | + | 0.733370i | 0.975032 | − | 0.222064i | \(-0.0712795\pi\) |
0.295203 | + | 0.955435i | \(0.404613\pi\) | |||||||
\(368\) | 27.8189 | + | 51.4750i | 0.0755948 | + | 0.139878i | ||||
\(369\) | 114.901 | + | 136.794i | 0.311384 | + | 0.370715i | ||||
\(370\) | 2.29590 | + | 18.4402i | 0.00620512 | + | 0.0498384i | ||||
\(371\) | −232.440 | − | 134.199i | −0.626522 | − | 0.361722i | ||||
\(372\) | 85.5308 | − | 448.732i | 0.229922 | − | 1.20627i | ||||
\(373\) | −74.9606 | − | 129.836i | −0.200967 | − | 0.348085i | 0.747873 | − | 0.663841i | \(-0.231075\pi\) |
−0.948840 | + | 0.315757i | \(0.897742\pi\) | |||||||
\(374\) | 179.139 | + | 236.889i | 0.478981 | + | 0.633393i | ||||
\(375\) | 26.0690 | + | 297.111i | 0.0695174 | + | 0.792297i | ||||
\(376\) | 36.1613 | − | 236.074i | 0.0961737 | − | 0.627857i | ||||
\(377\) | 364.039 | 0.965621 | ||||||||
\(378\) | −277.004 | + | 356.343i | −0.732816 | + | 0.942708i | ||||
\(379\) | 184.361i | 0.486442i | 0.969971 | + | 0.243221i | \(0.0782040\pi\) | ||||
−0.969971 | + | 0.243221i | \(0.921796\pi\) | |||||||
\(380\) | 162.179 | + | 45.9100i | 0.426788 | + | 0.120816i | ||||
\(381\) | −440.591 | + | 38.6582i | −1.15641 | + | 0.101465i | ||||
\(382\) | 300.565 | + | 397.460i | 0.786818 | + | 1.04047i | ||||
\(383\) | −180.514 | + | 104.220i | −0.471315 | + | 0.272114i | −0.716790 | − | 0.697289i | \(-0.754389\pi\) |
0.245475 | + | 0.969403i | \(0.421056\pi\) | |||||||
\(384\) | 160.424 | + | 348.884i | 0.417771 | + | 0.908552i | ||||
\(385\) | 48.3206 | − | 83.6937i | 0.125508 | − | 0.217386i | ||||
\(386\) | −61.8181 | − | 496.511i | −0.160150 | − | 1.28630i | ||||
\(387\) | −197.197 | − | 71.6618i | −0.509554 | − | 0.185173i | ||||
\(388\) | 13.8534 | − | 3.50395i | 0.0357047 | − | 0.00903080i | ||||
\(389\) | −150.914 | + | 261.390i | −0.387953 | + | 0.671954i | −0.992174 | − | 0.124863i | \(-0.960151\pi\) |
0.604221 | + | 0.796816i | \(0.293484\pi\) | |||||||
\(390\) | −130.722 | − | 144.615i | −0.335184 | − | 0.370807i | ||||
\(391\) | 89.5597 | − | 51.7073i | 0.229053 | − | 0.132244i | ||||
\(392\) | 104.361 | − | 130.223i | 0.266227 | − | 0.332201i | ||||
\(393\) | −224.383 | − | 320.281i | −0.570949 | − | 0.814965i | ||||
\(394\) | −471.036 | − | 199.002i | −1.19552 | − | 0.505081i | ||||
\(395\) | 136.565i | 0.345734i | ||||||||
\(396\) | 77.5624 | + | 172.400i | 0.195865 | + | 0.435352i | ||||
\(397\) | −246.672 | −0.621341 | −0.310670 | − | 0.950518i | \(-0.600553\pi\) | ||||
−0.310670 | + | 0.950518i | \(0.600553\pi\) | |||||||
\(398\) | 240.593 | − | 569.483i | 0.604506 | − | 1.43086i | ||||
\(399\) | 434.960 | + | 202.692i | 1.09013 | + | 0.508001i | ||||
\(400\) | 274.588 | + | 169.005i | 0.686469 | + | 0.422511i | ||||
\(401\) | 377.516 | + | 653.877i | 0.941437 | + | 1.63062i | 0.762734 | + | 0.646713i | \(0.223857\pi\) |
0.178703 | + | 0.983903i | \(0.442810\pi\) | |||||||
\(402\) | −9.97454 | − | 46.4817i | −0.0248123 | − | 0.115626i | ||||
\(403\) | 486.460 | + | 280.858i | 1.20710 | + | 0.696917i | ||||
\(404\) | 58.5318 | − | 14.8045i | 0.144881 | − | 0.0366447i | ||||
\(405\) | 136.739 | + | 114.504i | 0.337627 | + | 0.282726i | ||||
\(406\) | 409.252 | − | 50.9539i | 1.00801 | − | 0.125502i | ||||
\(407\) | 19.1902 | + | 11.0794i | 0.0471503 | + | 0.0272222i | ||||
\(408\) | 608.410 | − | 300.769i | 1.49120 | − | 0.737179i | ||||
\(409\) | 130.730 | + | 226.432i | 0.319634 | + | 0.553622i | 0.980412 | − | 0.196959i | \(-0.0631067\pi\) |
−0.660778 | + | 0.750582i | \(0.729773\pi\) | |||||||
\(410\) | −69.7210 | + | 52.7240i | −0.170051 | + | 0.128595i | ||||
\(411\) | 271.478 | + | 126.509i | 0.660530 | + | 0.307808i | ||||
\(412\) | −501.358 | − | 141.925i | −1.21689 | − | 0.344479i | ||||
\(413\) | −76.8394 | −0.186052 | ||||||||
\(414\) | 62.9065 | − | 19.3836i | 0.151948 | − | 0.0468204i | ||||
\(415\) | − | 262.018i | − | 0.631369i | ||||||
\(416\) | −470.022 | + | 45.1372i | −1.12986 | + | 0.108503i | ||||
\(417\) | 164.542 | + | 234.865i | 0.394586 | + | 0.563226i | ||||
\(418\) | 160.313 | − | 121.231i | 0.383525 | − | 0.290027i | ||||
\(419\) | −340.246 | + | 196.441i | −0.812043 | + | 0.468833i | −0.847665 | − | 0.530532i | \(-0.821992\pi\) |
0.0356217 | + | 0.999365i | \(0.488659\pi\) | |||||||
\(420\) | −167.199 | − | 144.278i | −0.398092 | − | 0.343520i | ||||
\(421\) | 102.451 | − | 177.450i | 0.243351 | − | 0.421496i | −0.718316 | − | 0.695717i | \(-0.755087\pi\) |
0.961667 | + | 0.274221i | \(0.0884200\pi\) | |||||||
\(422\) | −781.835 | + | 97.3423i | −1.85269 | + | 0.230669i | ||||
\(423\) | −252.524 | − | 91.7676i | −0.596983 | − | 0.216945i | ||||
\(424\) | 93.2807 | + | 239.361i | 0.220002 | + | 0.564530i | ||||
\(425\) | 284.936 | − | 493.524i | 0.670438 | − | 1.16123i | ||||
\(426\) | −359.318 | − | 115.977i | −0.843469 | − | 0.272247i | ||||
\(427\) | −590.968 | + | 341.196i | −1.38400 | + | 0.799053i | ||||
\(428\) | −147.048 | + | 142.969i | −0.343570 | + | 0.334039i | ||||
\(429\) | −231.567 | + | 20.3181i | −0.539784 | + | 0.0473615i | ||||
\(430\) | 39.9532 | − | 94.5690i | 0.0929144 | − | 0.219928i | ||||
\(431\) | − | 462.725i | − | 1.07361i | −0.843707 | − | 0.536803i | \(-0.819632\pi\) | ||
0.843707 | − | 0.536803i | \(-0.180368\pi\) | |||||||
\(432\) | 420.184 | − | 100.346i | 0.972648 | − | 0.232282i | ||||
\(433\) | 190.574 | 0.440126 | 0.220063 | − | 0.975486i | \(-0.429374\pi\) | ||||
0.220063 | + | 0.975486i | \(0.429374\pi\) | |||||||
\(434\) | 586.188 | + | 247.651i | 1.35066 | + | 0.570624i | ||||
\(435\) | −14.2441 | − | 162.342i | −0.0327451 | − | 0.373200i | ||||
\(436\) | −71.0300 | − | 73.0567i | −0.162913 | − | 0.167561i | ||||
\(437\) | −34.9926 | − | 60.6090i | −0.0800747 | − | 0.138693i | ||||
\(438\) | 61.4120 | − | 190.265i | 0.140210 | − | 0.434396i | ||||
\(439\) | −379.279 | − | 218.977i | −0.863962 | − | 0.498809i | 0.00137479 | − | 0.999999i | \(-0.499562\pi\) |
−0.865337 | + | 0.501190i | \(0.832896\pi\) | |||||||
\(440\) | −86.1858 | + | 33.5873i | −0.195877 | + | 0.0763347i | ||||
\(441\) | −120.750 | − | 143.757i | −0.273809 | − | 0.325980i | ||||
\(442\) | 103.110 | + | 828.159i | 0.233280 | + | 1.87366i | ||||
\(443\) | 721.993 | + | 416.843i | 1.62978 | + | 0.940954i | 0.984157 | + | 0.177297i | \(0.0567354\pi\) |
0.645623 | + | 0.763657i | \(0.276598\pi\) | |||||||
\(444\) | 33.0817 | − | 38.3370i | 0.0745083 | − | 0.0863447i | ||||
\(445\) | −118.196 | − | 204.722i | −0.265610 | − | 0.460050i | ||||
\(446\) | 124.530 | + | 164.676i | 0.279216 | + | 0.369229i | ||||
\(447\) | −168.740 | + | 118.216i | −0.377493 | + | 0.264465i | ||||
\(448\) | −522.080 | + | 116.531i | −1.16536 | + | 0.260114i | ||||
\(449\) | −480.789 | −1.07080 | −0.535399 | − | 0.844599i | \(-0.679839\pi\) | ||||
−0.535399 | + | 0.844599i | \(0.679839\pi\) | |||||||
\(450\) | 246.800 | − | 265.829i | 0.548445 | − | 0.590731i | ||||
\(451\) | 104.235i | 0.231119i | ||||||||
\(452\) | −165.939 | + | 586.189i | −0.367122 | + | 1.29688i | ||||
\(453\) | 133.537 | − | 286.559i | 0.294784 | − | 0.632580i | ||||
\(454\) | −170.233 | − | 225.112i | −0.374962 | − | 0.495841i | ||||
\(455\) | 235.177 | − | 135.779i | 0.516872 | − | 0.298416i | ||||
\(456\) | −203.544 | − | 411.738i | −0.446368 | − | 0.902934i | ||||
\(457\) | 109.313 | − | 189.336i | 0.239197 | − | 0.414302i | −0.721287 | − | 0.692636i | \(-0.756449\pi\) |
0.960484 | + | 0.278334i | \(0.0897824\pi\) | |||||||
\(458\) | −52.1739 | − | 419.051i | −0.113917 | − | 0.914959i | ||||
\(459\) | −198.171 | − | 737.364i | −0.431746 | − | 1.60646i | ||||
\(460\) | 7.89775 | + | 31.2250i | 0.0171690 | + | 0.0678804i | ||||
\(461\) | −358.474 | + | 620.894i | −0.777600 | + | 1.34684i | 0.155722 | + | 0.987801i | \(0.450230\pi\) |
−0.933322 | + | 0.359042i | \(0.883104\pi\) | |||||||
\(462\) | −257.484 | + | 55.2536i | −0.557324 | + | 0.119597i | ||||
\(463\) | 26.6250 | − | 15.3719i | 0.0575053 | − | 0.0332007i | −0.470972 | − | 0.882148i | \(-0.656097\pi\) |
0.528477 | + | 0.848948i | \(0.322763\pi\) | |||||||
\(464\) | −336.165 | − | 206.904i | −0.724494 | − | 0.445915i | ||||
\(465\) | 106.213 | − | 227.924i | 0.228415 | − | 0.490159i | ||||
\(466\) | 516.054 | + | 218.021i | 1.10741 | + | 0.467856i | ||||
\(467\) | 458.639i | 0.982096i | 0.871133 | + | 0.491048i | \(0.163386\pi\) | ||||
−0.871133 | + | 0.491048i | \(0.836614\pi\) | |||||||
\(468\) | −53.4704 | + | 528.509i | −0.114253 | + | 1.12929i | ||||
\(469\) | 66.2249 | 0.141204 | ||||||||
\(470\) | 51.1626 | − | 121.102i | 0.108857 | − | 0.257663i | ||||
\(471\) | 528.272 | − | 370.098i | 1.12160 | − | 0.785770i | ||||
\(472\) | 57.3905 | + | 45.9929i | 0.121590 | + | 0.0974426i | ||||
\(473\) | −61.2101 | − | 106.019i | −0.129408 | − | 0.224142i | ||||
\(474\) | 276.067 | − | 249.546i | 0.582419 | − | 0.526468i | ||||
\(475\) | −333.989 | − | 192.829i | −0.703135 | − | 0.405955i | ||||
\(476\) | 231.832 | + | 916.582i | 0.487041 | + | 1.92559i | ||||
\(477\) | 284.590 | − | 50.3283i | 0.596626 | − | 0.105510i | ||||
\(478\) | −777.688 | + | 96.8260i | −1.62696 | + | 0.202565i | ||||
\(479\) | −570.477 | − | 329.365i | −1.19098 | − | 0.687610i | −0.232448 | − | 0.972609i | \(-0.574674\pi\) |
−0.958528 | + | 0.284999i | \(0.908007\pi\) | |||||||
\(480\) | 38.5198 | + | 207.838i | 0.0802495 | + | 0.432996i | ||||
\(481\) | 31.1329 | + | 53.9238i | 0.0647254 | + | 0.112108i | ||||
\(482\) | 75.5456 | − | 57.1286i | 0.156734 | − | 0.118524i | ||||
\(483\) | 8.01485 | + | 91.3461i | 0.0165939 | + | 0.189122i | ||||
\(484\) | 101.787 | − | 359.570i | 0.210305 | − | 0.742912i | ||||
\(485\) | 7.86593 | 0.0162184 | ||||||||
\(486\) | −18.3936 | − | 485.652i | −0.0378469 | − | 0.999284i | ||||
\(487\) | − | 715.589i | − | 1.46938i | −0.678402 | − | 0.734691i | \(-0.737327\pi\) | ||
0.678402 | − | 0.734691i | \(-0.262673\pi\) | |||||||
\(488\) | 645.614 | + | 98.8937i | 1.32298 | + | 0.202651i | ||||
\(489\) | 100.844 | − | 8.84825i | 0.206226 | − | 0.0180946i | ||||
\(490\) | 73.2702 | − | 55.4079i | 0.149531 | − | 0.113077i | ||||
\(491\) | 574.179 | − | 331.502i | 1.16941 | − | 0.675157i | 0.215866 | − | 0.976423i | \(-0.430742\pi\) |
0.953540 | + | 0.301266i | \(0.0974091\pi\) | |||||||
\(492\) | 233.983 | + | 44.5986i | 0.475576 | + | 0.0906475i | ||||
\(493\) | −348.834 | + | 604.198i | −0.707574 | + | 1.22555i | ||||
\(494\) | 560.452 | − | 69.7790i | 1.13452 | − | 0.141253i | ||||
\(495\) | 18.1215 | + | 102.472i | 0.0366092 | + | 0.207013i | ||||
\(496\) | −289.584 | − | 535.836i | −0.583839 | − | 1.08031i | ||||
\(497\) | 262.986 | − | 455.505i | 0.529147 | − | 0.916509i | ||||
\(498\) | −529.670 | + | 478.786i | −1.06360 | + | 0.961419i | ||||
\(499\) | −458.706 | + | 264.834i | −0.919251 | + | 0.530730i | −0.883396 | − | 0.468627i | \(-0.844749\pi\) |
−0.0358546 | + | 0.999357i | \(0.511415\pi\) | |||||||
\(500\) | 277.213 | + | 285.122i | 0.554426 | + | 0.570245i | ||||
\(501\) | 261.503 | + | 373.266i | 0.521962 | + | 0.745041i | ||||
\(502\) | 303.099 | − | 717.434i | 0.603783 | − | 1.42915i | ||||
\(503\) | 68.3537i | 0.135892i | 0.997689 | + | 0.0679460i | \(0.0216446\pi\) | ||||
−0.997689 | + | 0.0679460i | \(0.978355\pi\) | |||||||
\(504\) | 13.8632 | + | 601.633i | 0.0275063 | + | 1.19372i | ||||
\(505\) | 33.2342 | 0.0658103 | ||||||||
\(506\) | 35.3791 | + | 14.9469i | 0.0699192 | + | 0.0295392i | ||||
\(507\) | −132.516 | − | 61.7525i | −0.261372 | − | 0.121800i | ||||
\(508\) | −422.812 | + | 411.083i | −0.832308 | + | 0.809219i | ||||
\(509\) | −400.473 | − | 693.640i | −0.786784 | − | 1.36275i | −0.927927 | − | 0.372761i | \(-0.878411\pi\) |
0.141143 | − | 0.989989i | \(-0.454922\pi\) | |||||||
\(510\) | 365.279 | − | 78.3856i | 0.716234 | − | 0.153697i | ||||
\(511\) | 241.198 | + | 139.256i | 0.472012 | + | 0.272516i | ||||
\(512\) | 459.687 | + | 225.460i | 0.897826 | + | 0.440351i | ||||
\(513\) | −499.007 | + | 134.111i | −0.972723 | + | 0.261426i | ||||
\(514\) | 16.0818 | + | 129.166i | 0.0312876 | + | 0.251297i | ||||
\(515\) | −248.396 | − | 143.412i | −0.482323 | − | 0.278469i | ||||
\(516\) | −264.178 | + | 92.0408i | −0.511973 | + | 0.178374i | ||||
\(517\) | −78.3834 | − | 135.764i | −0.151612 | − | 0.262600i | ||||
\(518\) | 42.5472 | + | 56.2634i | 0.0821374 | + | 0.108617i | ||||
\(519\) | −323.047 | − | 150.541i | −0.622442 | − | 0.290059i | ||||
\(520\) | −256.923 | − | 39.3549i | −0.494083 | − | 0.0756826i | ||||
\(521\) | −208.227 | −0.399668 | −0.199834 | − | 0.979830i | \(-0.564040\pi\) | ||||
−0.199834 | + | 0.979830i | \(0.564040\pi\) | |||||||
\(522\) | −302.146 | + | 325.442i | −0.578824 | + | 0.623453i | ||||
\(523\) | − | 30.5350i | − | 0.0583843i | −0.999574 | − | 0.0291921i | \(-0.990707\pi\) | ||
0.999574 | − | 0.0291921i | \(-0.00929347\pi\) | |||||||
\(524\) | −501.699 | − | 142.022i | −0.957440 | − | 0.271034i | ||||
\(525\) | 289.933 | + | 413.846i | 0.552254 | + | 0.788279i | ||||
\(526\) | −173.803 | − | 229.834i | −0.330425 | − | 0.436946i | ||||
\(527\) | −932.283 | + | 538.254i | −1.76904 | + | 1.02135i | ||||
\(528\) | 225.384 | + | 112.851i | 0.426864 | + | 0.213732i | ||||
\(529\) | −257.813 | + | 446.546i | −0.487360 | + | 0.844132i | ||||
\(530\) | 17.4714 | + | 140.327i | 0.0329650 | + | 0.264769i | ||||
\(531\) | 63.3553 | − | 53.2156i | 0.119313 | − | 0.100218i | ||||
\(532\) | 620.292 | − | 156.891i | 1.16596 | − | 0.294907i | ||||
\(533\) | −146.448 | + | 253.656i | −0.274762 | + | 0.475903i | ||||
\(534\) | −197.866 | + | 613.025i | −0.370536 | + | 1.14799i | ||||
\(535\) | −97.7710 | + | 56.4481i | −0.182749 | + | 0.105510i | ||||
\(536\) | −49.4627 | − | 39.6395i | −0.0922811 | − | 0.0739543i | ||||
\(537\) | 652.063 | − | 57.2130i | 1.21427 | − | 0.106542i | ||||
\(538\) | 133.406 | + | 56.3607i | 0.247966 | + | 0.104760i | ||||
\(539\) | − | 109.541i | − | 0.203230i | ||||||
\(540\) | 237.779 | + | 3.16539i | 0.440331 | + | 0.00586183i | ||||
\(541\) | 526.091 | 0.972442 | 0.486221 | − | 0.873836i | \(-0.338375\pi\) | ||||
0.486221 | + | 0.873836i | \(0.338375\pi\) | |||||||
\(542\) | −27.6074 | + | 65.3466i | −0.0509361 | + | 0.120566i | ||||
\(543\) | 48.2685 | + | 550.121i | 0.0888923 | + | 1.01311i | ||||
\(544\) | 375.476 | − | 823.350i | 0.690213 | − | 1.51351i | ||||
\(545\) | −28.0446 | − | 48.5747i | −0.0514580 | − | 0.0891279i | ||||
\(546\) | −704.219 | − | 227.301i | −1.28978 | − | 0.416302i | ||||
\(547\) | 823.276 | + | 475.318i | 1.50507 | + | 0.868955i | 0.999983 | + | 0.00588962i | \(0.00187474\pi\) |
0.505092 | + | 0.863066i | \(0.331459\pi\) | |||||||
\(548\) | 387.151 | − | 97.9224i | 0.706481 | − | 0.178691i | ||||
\(549\) | 250.965 | − | 690.600i | 0.457132 | − | 1.25792i | ||||
\(550\) | 210.022 | − | 26.1487i | 0.381858 | − | 0.0475432i | ||||
\(551\) | 408.888 | + | 236.071i | 0.742083 | + | 0.428442i | ||||
\(552\) | 48.6898 | − | 73.0228i | 0.0882062 | − | 0.132288i | ||||
\(553\) | 259.201 | + | 448.949i | 0.468717 | + | 0.811842i | ||||
\(554\) | 532.558 | − | 402.728i | 0.961297 | − | 0.726946i | ||||
\(555\) | 22.8289 | − | 15.9935i | 0.0411332 | − | 0.0288172i | ||||
\(556\) | 367.901 | + | 104.146i | 0.661692 | + | 0.187313i | ||||
\(557\) | 978.257 | 1.75630 | 0.878148 | − | 0.478390i | \(-0.158779\pi\) | ||||
0.878148 | + | 0.478390i | \(0.158779\pi\) | |||||||
\(558\) | −654.833 | + | 201.776i | −1.17354 | + | 0.361606i | ||||
\(559\) | − | 343.997i | − | 0.615379i | ||||||
\(560\) | −294.341 | − | 8.28169i | −0.525609 | − | 0.0147887i | ||||
\(561\) | 188.173 | − | 403.803i | 0.335425 | − | 0.719792i | ||||
\(562\) | 65.5271 | − | 49.5525i | 0.116596 | − | 0.0881718i | ||||
\(563\) | 925.131 | − | 534.125i | 1.64322 | − | 0.948712i | 0.663538 | − | 0.748143i | \(-0.269054\pi\) |
0.979680 | − | 0.200569i | \(-0.0642792\pi\) | |||||||
\(564\) | −338.297 | + | 117.864i | −0.599818 | + | 0.208979i | ||||
\(565\) | −167.677 | + | 290.426i | −0.296774 | + | 0.514028i | ||||
\(566\) | 500.928 | − | 62.3680i | 0.885032 | − | 0.110191i | ||||
\(567\) | 666.849 | + | 116.893i | 1.17610 | + | 0.206161i | ||||
\(568\) | −469.068 | + | 182.799i | −0.825824 | + | 0.321830i | ||||
\(569\) | −481.775 | + | 834.459i | −0.846705 | + | 1.46654i | 0.0374271 | + | 0.999299i | \(0.488084\pi\) |
−0.884132 | + | 0.467237i | \(0.845250\pi\) | |||||||
\(570\) | −53.0470 | − | 247.201i | −0.0930649 | − | 0.433686i | ||||
\(571\) | −243.132 | + | 140.372i | −0.425800 | + | 0.245836i | −0.697556 | − | 0.716531i | \(-0.745729\pi\) |
0.271756 | + | 0.962366i | \(0.412396\pi\) | |||||||
\(572\) | −222.223 | + | 216.059i | −0.388502 | + | 0.377725i | ||||
\(573\) | 315.723 | − | 677.513i | 0.550999 | − | 1.18240i | ||||
\(574\) | −129.133 | + | 305.658i | −0.224971 | + | 0.532505i | ||||
\(575\) | − | 73.6944i | − | 0.128164i | ||||||
\(576\) | 349.759 | − | 457.652i | 0.607220 | − | 0.794534i | ||||
\(577\) | −552.228 | −0.957068 | −0.478534 | − | 0.878069i | \(-0.658832\pi\) | ||||
−0.478534 | + | 0.878069i | \(0.658832\pi\) | |||||||
\(578\) | −940.869 | − | 397.495i | −1.62780 | − | 0.687708i | ||||
\(579\) | −614.680 | + | 430.633i | −1.06162 | + | 0.743754i | ||||
\(580\) | −151.469 | − | 155.791i | −0.261154 | − | 0.268605i | ||||
\(581\) | −497.311 | − | 861.367i | −0.855956 | − | 1.48256i | ||||
\(582\) | −14.3734 | − | 15.9010i | −0.0246966 | − | 0.0273213i | ||||
\(583\) | 146.034 | + | 84.3130i | 0.250488 | + | 0.144619i | ||||
\(584\) | −96.7956 | − | 248.380i | −0.165746 | − | 0.425308i | ||||
\(585\) | −99.8721 | + | 274.826i | −0.170722 | + | 0.469787i | ||||
\(586\) | −10.0528 | − | 80.7425i | −0.0171550 | − | 0.137786i | ||||
\(587\) | 141.476 | + | 81.6811i | 0.241015 | + | 0.139150i | 0.615643 | − | 0.788025i | \(-0.288896\pi\) |
−0.374628 | + | 0.927175i | \(0.622230\pi\) | |||||||
\(588\) | −245.894 | − | 46.8688i | −0.418188 | − | 0.0797089i | ||||
\(589\) | 364.260 | + | 630.917i | 0.618438 | + | 1.07117i | ||||
\(590\) | 24.4188 | + | 32.2909i | 0.0413879 | + | 0.0547304i | ||||
\(591\) | 67.0421 | + | 764.086i | 0.113438 | + | 1.29287i | ||||
\(592\) | 1.89891 | − | 67.4895i | 0.00320762 | − | 0.114003i | ||||
\(593\) | −818.460 | −1.38020 | −0.690101 | − | 0.723713i | \(-0.742434\pi\) | ||||
−0.690101 | + | 0.723713i | \(0.742434\pi\) | |||||||
\(594\) | 174.033 | − | 223.879i | 0.292985 | − | 0.376901i | ||||
\(595\) | 520.433i | 0.874677i | ||||||||
\(596\) | −74.8238 | + | 264.319i | −0.125543 | + | 0.443488i | ||||
\(597\) | −923.782 | + | 81.0541i | −1.54737 | + | 0.135769i | ||||
\(598\) | 65.0952 | + | 86.0804i | 0.108855 | + | 0.143947i | ||||
\(599\) | −398.849 | + | 230.275i | −0.665857 | + | 0.384433i | −0.794505 | − | 0.607257i | \(-0.792270\pi\) |
0.128648 | + | 0.991690i | \(0.458936\pi\) | |||||||
\(600\) | 31.1633 | − | 482.639i | 0.0519388 | − | 0.804399i | ||||
\(601\) | 162.324 | − | 281.153i | 0.270090 | − | 0.467809i | −0.698795 | − | 0.715322i | \(-0.746280\pi\) |
0.968885 | + | 0.247513i | \(0.0796132\pi\) | |||||||
\(602\) | −48.1486 | − | 386.721i | −0.0799811 | − | 0.642393i | ||||
\(603\) | −54.6035 | + | 45.8645i | −0.0905530 | + | 0.0760605i | ||||
\(604\) | −103.362 | − | 408.658i | −0.171129 | − | 0.676587i | ||||
\(605\) | 102.854 | − | 178.148i | 0.170006 | − | 0.294459i | ||||
\(606\) | −60.7290 | − | 67.1831i | −0.100213 | − | 0.110863i | ||||
\(607\) | 764.054 | − | 441.127i | 1.25874 | − | 0.726733i | 0.285909 | − | 0.958257i | \(-0.407705\pi\) |
0.972829 | + | 0.231524i | \(0.0743712\pi\) | |||||||
\(608\) | −557.198 | − | 254.101i | −0.916444 | − | 0.417929i | ||||
\(609\) | −354.952 | − | 506.653i | −0.582844 | − | 0.831942i | ||||
\(610\) | 331.188 | + | 139.919i | 0.542931 | + | 0.229376i | ||||
\(611\) | − | 440.510i | − | 0.720966i | ||||||
\(612\) | −825.933 | − | 595.180i | −1.34956 | − | 0.972516i | ||||
\(613\) | 19.4869 | 0.0317895 | 0.0158947 | − | 0.999874i | \(-0.494940\pi\) | ||||
0.0158947 | + | 0.999874i | \(0.494940\pi\) | |||||||
\(614\) | −106.501 | + | 252.086i | −0.173454 | + | 0.410564i | ||||
\(615\) | 118.847 | + | 55.3830i | 0.193247 | + | 0.0900537i | ||||
\(616\) | −219.582 | + | 273.997i | −0.356464 | + | 0.444800i | ||||
\(617\) | −48.3314 | − | 83.7124i | −0.0783329 | − | 0.135677i | 0.824198 | − | 0.566302i | \(-0.191626\pi\) |
−0.902531 | + | 0.430625i | \(0.858293\pi\) | |||||||
\(618\) | 163.988 | + | 764.191i | 0.265353 | + | 1.23656i | ||||
\(619\) | −363.937 | − | 210.119i | −0.587944 | − | 0.339449i | 0.176340 | − | 0.984329i | \(-0.443574\pi\) |
−0.764284 | + | 0.644880i | \(0.776907\pi\) | |||||||
\(620\) | −82.2126 | − | 325.040i | −0.132601 | − | 0.524258i | ||||
\(621\) | −69.8707 | − | 69.7656i | −0.112513 | − | 0.112344i | ||||
\(622\) | 850.820 | − | 105.931i | 1.36788 | − | 0.170307i | ||||
\(623\) | −777.127 | − | 448.674i | −1.24739 | − | 0.720184i | ||||
\(624\) | 389.921 | + | 591.285i | 0.624873 | + | 0.947572i | ||||
\(625\) | −142.447 | − | 246.725i | −0.227915 | − | 0.394760i | ||||
\(626\) | −19.1014 | + | 14.4448i | −0.0305135 | + | 0.0230747i | ||||
\(627\) | −273.272 | − | 127.345i | −0.435840 | − | 0.203102i | ||||
\(628\) | 234.250 | − | 827.502i | 0.373010 | − | 1.31768i | ||||
\(629\) | −119.330 | −0.189714 | ||||||||
\(630\) | −73.8092 | + | 322.937i | −0.117157 | + | 0.512599i | ||||
\(631\) | 483.230i | 0.765816i | 0.923787 | + | 0.382908i | \(0.125077\pi\) | ||||
−0.923787 | + | 0.382908i | \(0.874923\pi\) | |||||||
\(632\) | 75.1279 | − | 490.462i | 0.118873 | − | 0.776047i | ||||
\(633\) | 678.100 | + | 967.910i | 1.07125 | + | 1.52908i | ||||
\(634\) | 75.0607 | − | 56.7619i | 0.118392 | − | 0.0895299i | ||||
\(635\) | −281.124 | + | 162.307i | −0.442715 | + | 0.255602i | ||||
\(636\) | 251.747 | − | 291.739i | 0.395828 | − | 0.458710i | ||||
\(637\) | 153.903 | − | 266.568i | 0.241606 | − | 0.418475i | ||||
\(638\) | −257.120 | + | 32.0127i | −0.403010 | + | 0.0501767i | ||||
\(639\) | 98.6268 | + | 557.703i | 0.154346 | + | 0.872775i | ||||
\(640\) | 214.883 | + | 182.366i | 0.335755 | + | 0.284947i | ||||
\(641\) | −45.2967 | + | 78.4562i | −0.0706657 | + | 0.122397i | −0.899193 | − | 0.437552i | \(-0.855846\pi\) |
0.828528 | + | 0.559948i | \(0.189179\pi\) | |||||||
\(642\) | 292.767 | + | 94.4966i | 0.456024 | + | 0.147191i | ||||
\(643\) | 453.773 | − | 261.986i | 0.705713 | − | 0.407444i | −0.103759 | − | 0.994602i | \(-0.533087\pi\) |
0.809472 | + | 0.587159i | \(0.199754\pi\) | |||||||
\(644\) | 85.2284 | + | 87.6602i | 0.132342 | + | 0.136118i | ||||
\(645\) | −153.404 | + | 13.4599i | −0.237836 | + | 0.0208681i | ||||
\(646\) | −421.230 | + | 997.050i | −0.652059 | + | 1.54342i | ||||
\(647\) | − | 31.3018i | − | 0.0483799i | −0.999707 | − | 0.0241900i | \(-0.992299\pi\) | ||
0.999707 | − | 0.0241900i | \(-0.00770066\pi\) | |||||||
\(648\) | −428.095 | − | 486.455i | −0.660641 | − | 0.750702i | ||||
\(649\) | 48.2758 | 0.0743848 | ||||||||
\(650\) | 547.828 | + | 231.445i | 0.842813 | + | 0.356069i | ||||
\(651\) | −83.4316 | − | 950.879i | −0.128159 | − | 1.46064i | ||||
\(652\) | 96.7752 | − | 94.0906i | 0.148428 | − | 0.144311i | ||||
\(653\) | 445.115 | + | 770.961i | 0.681646 | + | 1.18065i | 0.974478 | + | 0.224481i | \(0.0720688\pi\) |
−0.292833 | + | 0.956164i | \(0.594598\pi\) | |||||||
\(654\) | −46.9479 | + | 145.453i | −0.0717858 | + | 0.222405i | ||||
\(655\) | −248.565 | − | 143.509i | −0.379489 | − | 0.219098i | ||||
\(656\) | 279.402 | − | 150.999i | 0.425918 | − | 0.230181i | ||||
\(657\) | −295.314 | + | 52.2247i | −0.449489 | + | 0.0794897i | ||||
\(658\) | −61.6574 | − | 495.221i | −0.0937042 | − | 0.752615i | ||||
\(659\) | 41.1783 | + | 23.7743i | 0.0624860 | + | 0.0360763i | 0.530918 | − | 0.847423i | \(-0.321847\pi\) |
−0.468432 | + | 0.883500i | \(0.655181\pi\) | |||||||
\(660\) | 105.046 | + | 90.6456i | 0.159160 | + | 0.137342i | ||||
\(661\) | −24.8421 | − | 43.0278i | −0.0375826 | − | 0.0650950i | 0.846622 | − | 0.532194i | \(-0.178632\pi\) |
−0.884205 | + | 0.467099i | \(0.845299\pi\) | |||||||
\(662\) | 101.895 | + | 134.743i | 0.153920 | + | 0.203540i | ||||
\(663\) | 1025.26 | − | 718.277i | 1.54639 | − | 1.08337i | ||||
\(664\) | −144.143 | + | 941.016i | −0.217083 | + | 1.41719i | ||||
\(665\) | 352.200 | 0.529624 | ||||||||
\(666\) | −74.0464 | − | 16.9237i | −0.111181 | − | 0.0254110i | ||||
\(667\) | 90.2207i | 0.135263i | ||||||||
\(668\) | 584.695 | + | 165.516i | 0.875292 | + | 0.247779i | ||||
\(669\) | 130.811 | − | 280.709i | 0.195532 | − | 0.419594i | ||||
\(670\) | −21.0457 | − | 27.8303i | −0.0314114 | − | 0.0415377i | ||||
\(671\) | 371.287 | − | 214.362i | 0.553333 | − | 0.319467i | ||||
\(672\) | 521.109 | + | 610.144i | 0.775459 | + | 0.907953i | ||||
\(673\) | −16.4365 | + | 28.4688i | −0.0244227 | + | 0.0423013i | −0.877978 | − | 0.478700i | \(-0.841108\pi\) |
0.853556 | + | 0.521002i | \(0.174441\pi\) | |||||||
\(674\) | 124.815 | + | 1002.49i | 0.185185 | + | 1.48738i | ||||
\(675\) | −525.666 | − | 140.428i | −0.778765 | − | 0.208041i | ||||
\(676\) | −188.979 | + | 47.7986i | −0.279555 | + | 0.0707079i | ||||
\(677\) | 457.417 | − | 792.269i | 0.675653 | − | 1.17026i | −0.300625 | − | 0.953742i | \(-0.597195\pi\) |
0.976278 | − | 0.216522i | \(-0.0694714\pi\) | |||||||
\(678\) | 893.494 | − | 191.735i | 1.31784 | − | 0.282796i | ||||
\(679\) | 25.8587 | − | 14.9296i | 0.0380836 | − | 0.0219876i | ||||
\(680\) | 311.510 | − | 388.706i | 0.458102 | − | 0.571626i | ||||
\(681\) | −178.818 | + | 383.728i | −0.262581 | + | 0.563477i | ||||
\(682\) | −368.283 | − | 155.591i | −0.540005 | − | 0.228139i | ||||
\(683\) | 870.646i | 1.27474i | 0.770559 | + | 0.637369i | \(0.219977\pi\) | ||||
−0.770559 | + | 0.637369i | \(0.780023\pi\) | |||||||
\(684\) | −402.785 | + | 558.946i | −0.588866 | + | 0.817172i | ||||
\(685\) | 219.824 | 0.320910 | ||||||||
\(686\) | −183.066 | + | 433.316i | −0.266860 | + | 0.631656i | ||||
\(687\) | −518.784 | + | 363.451i | −0.755145 | + | 0.529041i | ||||
\(688\) | −195.513 | + | 317.657i | −0.284176 | + | 0.461711i | ||||
\(689\) | 236.917 | + | 410.352i | 0.343856 | + | 0.595577i | ||||
\(690\) | 35.8402 | − | 32.3971i | 0.0519423 | − | 0.0469523i | ||||
\(691\) | −800.188 | − | 461.988i | −1.15801 | − | 0.668580i | −0.207187 | − | 0.978301i | \(-0.566431\pi\) |
−0.950827 | + | 0.309722i | \(0.899764\pi\) | |||||||
\(692\) | −460.695 | + | 116.524i | −0.665744 | + | 0.168387i | ||||
\(693\) | 254.065 | + | 302.474i | 0.366616 | + | 0.436470i | ||||
\(694\) | −973.405 | + | 121.194i | −1.40260 | + | 0.174631i | ||||
\(695\) | 182.275 | + | 105.237i | 0.262267 | + | 0.151420i | ||||
\(696\) | −38.1518 | + | 590.873i | −0.0548158 | + | 0.848956i | ||||
\(697\) | −280.663 | − | 486.123i | −0.402673 | − | 0.697450i | ||||
\(698\) | −596.526 | + | 451.102i | −0.854622 | + | 0.646277i | ||||
\(699\) | −73.4495 | − | 837.112i | −0.105078 | − | 1.19758i | ||||
\(700\) | 648.262 | + | 183.511i | 0.926089 | + | 0.262159i | ||||
\(701\) | 1191.44 | 1.69963 | 0.849815 | − | 0.527082i | \(-0.176714\pi\) | ||||
0.849815 | + | 0.527082i | \(0.176714\pi\) | |||||||
\(702\) | 738.058 | − | 300.298i | 1.05136 | − | 0.427775i | ||||
\(703\) | 80.7561i | 0.114874i | ||||||||
\(704\) | 328.006 | − | 73.2129i | 0.465918 | − | 0.103996i | ||||
\(705\) | −196.444 | + | 17.2363i | −0.278644 | + | 0.0244486i | ||||
\(706\) | −947.650 | + | 716.626i | −1.34228 | + | 1.01505i | ||||
\(707\) | 109.255 | − | 63.0786i | 0.154534 | − | 0.0892201i | ||||
\(708\) | 20.6556 | − | 108.368i | 0.0291745 | − | 0.153062i | ||||
\(709\) | 655.954 | − | 1136.15i | 0.925182 | − | 1.60246i | 0.133914 | − | 0.990993i | \(-0.457246\pi\) |
0.791268 | − | 0.611469i | \(-0.209421\pi\) | |||||||
\(710\) | −274.995 | + | 34.2383i | −0.387317 | + | 0.0482229i | ||||
\(711\) | −524.637 | − | 190.654i | −0.737886 | − | 0.268149i | ||||
\(712\) | 311.870 | + | 800.266i | 0.438020 | + | 1.12397i | ||||
\(713\) | −69.6056 | + | 120.560i | −0.0976236 | + | 0.169089i | ||||
\(714\) | 1052.06 | − | 950.989i | 1.47347 | − | 1.33192i | ||||
\(715\) | −147.754 | + | 85.3059i | −0.206649 | + | 0.119309i | ||||
\(716\) | 625.751 | − | 608.392i | 0.873954 | − | 0.849710i | ||||
\(717\) | 674.503 | + | 962.776i | 0.940730 | + | 1.34278i | ||||
\(718\) | 319.815 | − | 757.001i | 0.445425 | − | 1.05432i | ||||
\(719\) | − | 245.763i | − | 0.341813i | −0.985287 | − | 0.170906i | \(-0.945330\pi\) | ||
0.985287 | − | 0.170906i | \(-0.0546695\pi\) | |||||||
\(720\) | 248.424 | − | 197.019i | 0.345034 | − | 0.273638i | ||||
\(721\) | −1088.78 | −1.51010 | ||||||||
\(722\) | 9.66652 | + | 4.08388i | 0.0133885 | + | 0.00565634i | ||||
\(723\) | −128.776 | − | 60.0097i | −0.178113 | − | 0.0830010i | ||||
\(724\) | 513.278 | + | 527.923i | 0.708947 | + | 0.729175i | ||||
\(725\) | 248.583 | + | 430.559i | 0.342873 | + | 0.593874i | ||||
\(726\) | −548.071 | + | 117.611i | −0.754919 | + | 0.161999i | ||||
\(727\) | −1041.96 | − | 601.573i | −1.43323 | − | 0.827473i | −0.435860 | − | 0.900014i | \(-0.643556\pi\) |
−0.997365 | + | 0.0725411i | \(0.976889\pi\) | |||||||
\(728\) | −919.314 | + | 358.264i | −1.26279 | + | 0.492121i | ||||
\(729\) | −630.783 | + | 365.450i | −0.865271 | + | 0.501304i | ||||
\(730\) | −18.1298 | − | 145.615i | −0.0248353 | − | 0.199473i | ||||
\(731\) | 570.934 | + | 329.629i | 0.781032 | + | 0.450929i | ||||
\(732\) | −322.334 | − | 925.172i | −0.440347 | − | 1.26390i | ||||
\(733\) | −510.693 | − | 884.546i | −0.696716 | − | 1.20675i | −0.969599 | − | 0.244700i | \(-0.921310\pi\) |
0.272883 | − | 0.962047i | \(-0.412023\pi\) | |||||||
\(734\) | −649.363 | − | 858.702i | −0.884690 | − | 1.16989i | ||||
\(735\) | −124.897 | − | 58.2023i | −0.169928 | − | 0.0791867i | ||||
\(736\) | −11.1865 | − | 116.487i | −0.0151990 | − | 0.158270i | ||||
\(737\) | −41.6070 | −0.0564546 | ||||||||
\(738\) | −105.213 | − | 341.451i | −0.142565 | − | 0.462671i | ||||
\(739\) | 259.300i | 0.350879i | 0.984490 | + | 0.175439i | \(0.0561346\pi\) | ||||
−0.984490 | + | 0.175439i | \(0.943865\pi\) | |||||||
\(740\) | 10.1230 | − | 35.7600i | 0.0136797 | − | 0.0483243i | ||||
\(741\) | −486.090 | − | 693.838i | −0.655992 | − | 0.936354i | ||||
\(742\) | 323.778 | + | 428.156i | 0.436358 | + | 0.577030i | ||||
\(743\) | −100.270 | + | 57.8907i | −0.134953 | + | 0.0779149i | −0.565956 | − | 0.824435i | \(-0.691493\pi\) |
0.431004 | + | 0.902350i | \(0.358160\pi\) | |||||||
\(744\) | −506.843 | + | 760.140i | −0.681240 | + | 1.02169i | ||||
\(745\) | −75.6076 | + | 130.956i | −0.101487 | + | 0.175780i | ||||
\(746\) | 37.0458 | + | 297.545i | 0.0496593 | + | 0.398854i | ||||
\(747\) | 1006.59 | + | 365.795i | 1.34750 | + | 0.489686i | ||||
\(748\) | −145.652 | − | 575.859i | −0.194723 | − | 0.769866i | ||||
\(749\) | −214.277 | + | 371.139i | −0.286084 | + | 0.495513i | ||||
\(750\) | 183.226 | − | 567.668i | 0.244302 | − | 0.756891i | ||||
\(751\) | 543.581 | − | 313.837i | 0.723809 | − | 0.417891i | −0.0923438 | − | 0.995727i | \(-0.529436\pi\) |
0.816153 | + | 0.577836i | \(0.196103\pi\) | |||||||
\(752\) | −250.367 | + | 406.781i | −0.332935 | + | 0.540932i | ||||
\(753\) | −1163.78 | + | 102.112i | −1.54552 | + | 0.135607i | ||||
\(754\) | −670.681 | − | 283.347i | −0.889497 | − | 0.375792i | ||||
\(755\) | − | 232.035i | − | 0.307331i | ||||||
\(756\) | 787.691 | − | 440.899i | 1.04192 | − | 0.583199i | ||||
\(757\) | 49.5546 | 0.0654618 | 0.0327309 | − | 0.999464i | \(-0.489580\pi\) | ||||
0.0327309 | + | 0.999464i | \(0.489580\pi\) | |||||||
\(758\) | 143.496 | − | 339.655i | 0.189309 | − | 0.448093i | ||||
\(759\) | −5.03548 | − | 57.3899i | −0.00663436 | − | 0.0756125i | ||||
\(760\) | −263.055 | − | 210.812i | −0.346124 | − | 0.277385i | ||||
\(761\) | −13.0738 | − | 22.6446i | −0.0171798 | − | 0.0297563i | 0.857308 | − | 0.514804i | \(-0.172135\pi\) |
−0.874488 | + | 0.485048i | \(0.838802\pi\) | |||||||
\(762\) | 841.804 | + | 271.709i | 1.10473 | + | 0.356574i | ||||
\(763\) | −184.390 | − | 106.458i | −0.241664 | − | 0.139525i | ||||
\(764\) | −244.380 | − | 966.195i | −0.319869 | − | 1.26465i | ||||
\(765\) | −360.429 | − | 429.105i | −0.471149 | − | 0.560921i | ||||
\(766\) | 413.684 | − | 51.5057i | 0.540058 | − | 0.0672398i | ||||
\(767\) | 117.479 | + | 67.8267i | 0.153167 | + | 0.0884312i | ||||
\(768\) | −24.0034 | − | 767.625i | −0.0312544 | − | 0.999511i | ||||
\(769\) | 93.5875 | + | 162.098i | 0.121700 | + | 0.210791i | 0.920438 | − | 0.390888i | \(-0.127832\pi\) |
−0.798738 | + | 0.601679i | \(0.794499\pi\) | |||||||
\(770\) | −154.165 | + | 116.582i | −0.200214 | + | 0.151405i | ||||
\(771\) | 159.908 | − | 112.028i | 0.207403 | − | 0.145303i | ||||
\(772\) | −272.566 | + | 962.854i | −0.353065 | + | 1.24722i | ||||
\(773\) | −877.069 | −1.13463 | −0.567315 | − | 0.823501i | \(-0.692018\pi\) | ||||
−0.567315 | + | 0.823501i | \(0.692018\pi\) | |||||||
\(774\) | 307.525 | + | 285.512i | 0.397319 | + | 0.368878i | ||||
\(775\) | 767.131i | 0.989847i | ||||||||
\(776\) | −28.2498 | − | 4.32725i | −0.0364044 | − | 0.00557635i | ||||
\(777\) | 44.6929 | − | 95.9071i | 0.0575198 | − | 0.123433i | ||||
\(778\) | 481.483 | − | 364.105i | 0.618873 | − | 0.468001i | ||||
\(779\) | −328.981 | + | 189.937i | −0.422312 | + | 0.243822i | ||||
\(780\) | 128.273 | + | 368.174i | 0.164453 | + | 0.472018i | ||||
\(781\) | −165.226 | + | 286.179i | −0.211557 | + | 0.366427i | ||||
\(782\) | −205.245 | + | 25.5539i | −0.262461 | + | 0.0326777i | ||||
\(783\) | 643.549 | + | 171.919i | 0.821902 | + | 0.219565i | ||||
\(784\) | −293.625 | + | 158.685i | −0.374522 | + | 0.202405i | ||||
\(785\) | 236.704 | − | 409.984i | 0.301534 | − | 0.522272i | ||||
\(786\) | 164.100 | + | 764.711i | 0.208778 | + | 0.972914i | ||||
\(787\) | 577.106 | − | 333.192i | 0.733298 | − | 0.423370i | −0.0863293 | − | 0.996267i | \(-0.527514\pi\) |
0.819628 | + | 0.572897i | \(0.194180\pi\) | |||||||
\(788\) | 712.913 | + | 733.254i | 0.904712 | + | 0.930526i | ||||
\(789\) | −182.569 | + | 391.776i | −0.231392 | + | 0.496548i | ||||
\(790\) | 106.294 | − | 251.598i | 0.134550 | − | 0.318478i | ||||
\(791\) | 1273.01i | 1.60936i | ||||||||
\(792\) | −8.70978 | − | 377.987i | −0.0109972 | − | 0.477256i | ||||
\(793\) | 1204.70 | 1.51917 | ||||||||
\(794\) | 454.452 | + | 191.995i | 0.572358 | + | 0.241808i | ||||
\(795\) | 173.725 | − | 121.708i | 0.218522 | − | 0.153092i | ||||
\(796\) | −886.505 | + | 861.913i | −1.11370 | + | 1.08281i | ||||
\(797\) | 90.8816 | + | 157.412i | 0.114030 | + | 0.197505i | 0.917391 | − | 0.397986i | \(-0.130291\pi\) |
−0.803362 | + | 0.595491i | \(0.796957\pi\) | |||||||
\(798\) | −643.577 | − | 711.974i | −0.806487 | − | 0.892198i | ||||
\(799\) | 731.118 | + | 422.111i | 0.915041 | + | 0.528299i | ||||
\(800\) | −374.338 | − | 525.085i | −0.467923 | − | 0.656357i | ||||
\(801\) | 951.486 | − | 168.265i | 1.18787 | − | 0.210069i | ||||
\(802\) | −186.570 | − | 1498.49i | −0.232631 | − | 1.86845i | ||||
\(803\) | −151.537 | − | 87.4900i | −0.188714 | − | 0.108954i | ||||
\(804\) | −17.8022 | + | 93.3983i | −0.0221421 | + | 0.116167i | ||||
\(805\) | 33.6505 | + | 58.2844i | 0.0418019 | + | 0.0724030i | ||||
\(806\) | −677.617 | − | 896.065i | −0.840716 | − | 1.11174i | ||||
\(807\) | −18.9875 | − | 216.402i | −0.0235285 | − | 0.268157i | ||||
\(808\) | −119.358 | − | 18.2830i | −0.147720 | − | 0.0226275i | ||||
\(809\) | 114.921 | 0.142053 | 0.0710266 | − | 0.997474i | \(-0.477372\pi\) | ||||
0.0710266 | + | 0.997474i | \(0.477372\pi\) | |||||||
\(810\) | −162.795 | − | 317.384i | −0.200982 | − | 0.391832i | ||||
\(811\) | 1378.48i | 1.69973i | 0.526997 | + | 0.849867i | \(0.323318\pi\) | ||||
−0.526997 | + | 0.849867i | \(0.676682\pi\) | |||||||
\(812\) | −793.637 | − | 224.664i | −0.977386 | − | 0.276680i | ||||
\(813\) | 106.001 | − | 9.30072i | 0.130383 | − | 0.0114400i | ||||
\(814\) | −26.7310 | − | 35.3485i | −0.0328391 | − | 0.0434257i | ||||
\(815\) | 64.3449 | − | 37.1496i | 0.0789508 | − | 0.0455823i | ||||
\(816\) | −1354.99 | + | 80.5657i | −1.66053 | + | 0.0987325i | ||||
\(817\) | 223.075 | − | 386.377i | 0.273041 | − | 0.472921i | ||||
\(818\) | −64.6074 | − | 518.915i | −0.0789822 | − | 0.634370i | ||||
\(819\) | 193.296 | + | 1093.03i | 0.236015 | + | 1.33459i | ||||
\(820\) | 169.487 | − | 42.8683i | 0.206691 | − | 0.0522784i | ||||
\(821\) | −160.807 | + | 278.526i | −0.195867 | + | 0.339252i | −0.947184 | − | 0.320689i | \(-0.896085\pi\) |
0.751317 | + | 0.659941i | \(0.229419\pi\) | |||||||
\(822\) | −401.684 | − | 444.374i | −0.488667 | − | 0.540601i | ||||
\(823\) | −56.6805 | + | 32.7245i | −0.0688706 | + | 0.0397625i | −0.534040 | − | 0.845459i | \(-0.679327\pi\) |
0.465169 | + | 0.885222i | \(0.345993\pi\) | |||||||
\(824\) | 813.201 | + | 651.701i | 0.986895 | + | 0.790899i | ||||
\(825\) | −182.156 | − | 260.007i | −0.220795 | − | 0.315159i | ||||
\(826\) | 141.564 | + | 59.8073i | 0.171385 | + | 0.0724059i | ||||
\(827\) | − | 778.406i | − | 0.941240i | −0.882336 | − | 0.470620i | \(-0.844030\pi\) | ||
0.882336 | − | 0.470620i | \(-0.155970\pi\) | |||||||
\(828\) | −130.982 | − | 13.2517i | −0.158191 | − | 0.0160045i | ||||
\(829\) | −81.3426 | −0.0981214 | −0.0490607 | − | 0.998796i | \(-0.515623\pi\) | ||||
−0.0490607 | + | 0.998796i | \(0.515623\pi\) | |||||||
\(830\) | −203.940 | + | 482.724i | −0.245710 | + | 0.581595i | ||||
\(831\) | −907.803 | − | 423.038i | −1.09242 | − | 0.509071i | ||||
\(832\) | 901.068 | + | 282.680i | 1.08301 | + | 0.339760i | ||||
\(833\) | 294.950 | + | 510.869i | 0.354082 | + | 0.613288i | ||||
\(834\) | −120.336 | − | 560.770i | −0.144288 | − | 0.672386i | ||||
\(835\) | 289.686 | + | 167.250i | 0.346929 | + | 0.200299i | ||||
\(836\) | −389.710 | + | 98.5695i | −0.466160 | + | 0.117906i | ||||
\(837\) | 727.328 | + | 726.233i | 0.868970 | + | 0.867662i | ||||
\(838\) | 779.744 | − | 97.0820i | 0.930483 | − | 0.115850i | ||||
\(839\) | −553.733 | − | 319.698i | −0.659992 | − | 0.381046i | 0.132282 | − | 0.991212i | \(-0.457769\pi\) |
−0.792274 | + | 0.610166i | \(0.791103\pi\) | |||||||
\(840\) | 195.737 | + | 395.946i | 0.233021 | + | 0.471365i | ||||
\(841\) | 116.171 | + | 201.214i | 0.138135 | + | 0.239256i | ||||
\(842\) | −326.865 | + | 247.180i | −0.388200 | + | 0.293563i | ||||
\(843\) | −111.698 | − | 52.0515i | −0.132501 | − | 0.0617456i | ||||
\(844\) | 1516.16 | + | 429.198i | 1.79640 | + | 0.508529i | ||||
\(845\) | −107.302 | −0.126984 | ||||||||
\(846\) | 393.806 | + | 365.616i | 0.465491 | + | 0.432170i | ||||
\(847\) | − | 780.866i | − | 0.921920i | ||||||
\(848\) | 14.4505 | − | 513.586i | 0.0170406 | − | 0.605643i | ||||
\(849\) | −434.464 | − | 620.148i | −0.511736 | − | 0.730445i | ||||
\(850\) | −909.076 | + | 687.456i | −1.06950 | + | 0.808772i | ||||
\(851\) | −13.3641 | + | 7.71575i | −0.0157040 | + | 0.00906668i | ||||
\(852\) | 571.713 | + | 493.341i | 0.671024 | + | 0.579038i | ||||
\(853\) | −38.8069 | + | 67.2155i | −0.0454946 | + | 0.0787989i | −0.887876 | − | 0.460083i | \(-0.847820\pi\) |
0.842381 | + | 0.538882i | \(0.181153\pi\) | |||||||
\(854\) | 1354.33 | − | 168.620i | 1.58586 | − | 0.197448i | ||||
\(855\) | −290.394 | + | 243.918i | −0.339643 | + | 0.285285i | ||||
\(856\) | 382.190 | − | 148.942i | 0.446484 | − | 0.173998i | ||||
\(857\) | 436.010 | − | 755.192i | 0.508763 | − | 0.881204i | −0.491185 | − | 0.871055i | \(-0.663436\pi\) |
0.999948 | − | 0.0101489i | \(-0.00323056\pi\) | |||||||
\(858\) | 442.438 | + | 142.806i | 0.515662 | + | 0.166440i | ||||
\(859\) | −136.909 | + | 79.0444i | −0.159382 | + | 0.0920191i | −0.577570 | − | 0.816342i | \(-0.695999\pi\) |
0.418188 | + | 0.908361i | \(0.362665\pi\) | |||||||
\(860\) | −147.214 | + | 143.130i | −0.171179 | + | 0.166430i | ||||
\(861\) | 495.819 | − | 43.5040i | 0.575865 | − | 0.0505273i | ||||
\(862\) | −360.158 | + | 852.492i | −0.417816 | + | 0.988970i | ||||
\(863\) | − | 685.963i | − | 0.794859i | −0.917633 | − | 0.397429i | \(-0.869902\pi\) | ||
0.917633 | − | 0.397429i | \(-0.130098\pi\) | |||||||
\(864\) | −852.222 | − | 142.176i | −0.986368 | − | 0.164556i | ||||
\(865\) | −261.581 | −0.302406 | ||||||||
\(866\) | −351.101 | − | 148.332i | −0.405429 | − | 0.171284i | ||||
\(867\) | 133.913 | + | 1526.22i | 0.154456 | + | 1.76035i | ||||
\(868\) | −887.196 | − | 912.509i | −1.02211 | − | 1.05128i | ||||
\(869\) | −162.848 | − | 282.060i | −0.187396 | − | 0.324580i | ||||
\(870\) | −100.115 | + | 310.174i | −0.115075 | + | 0.356522i | ||||
\(871\) | −101.251 | − | 58.4573i | −0.116247 | − | 0.0671151i | ||||
\(872\) | 73.9978 | + | 189.880i | 0.0848598 | + | 0.217752i | ||||
\(873\) | −10.9814 | + | 30.2183i | −0.0125789 | + | 0.0346143i | ||||
\(874\) | 17.2935 | + | 138.898i | 0.0197866 | + | 0.158922i | ||||
\(875\) | 719.629 | + | 415.478i | 0.822433 | + | 0.474832i | ||||
\(876\) | −261.233 | + | 302.732i | −0.298211 | + | 0.345585i | ||||
\(877\) | 458.905 | + | 794.847i | 0.523267 | + | 0.906325i | 0.999633 | + | 0.0270780i | \(0.00862025\pi\) |
−0.476366 | + | 0.879247i | \(0.658046\pi\) | |||||||
\(878\) | 528.319 | + | 698.637i | 0.601731 | + | 0.795715i | ||||
\(879\) | −99.9590 | + | 70.0294i | −0.113719 | + | 0.0796694i | ||||
\(880\) | 184.925 | + | 5.20313i | 0.210142 | + | 0.00591264i | ||||
\(881\) | −657.430 | −0.746231 | −0.373116 | − | 0.927785i | \(-0.621711\pi\) | ||||
−0.373116 | + | 0.927785i | \(0.621711\pi\) | |||||||
\(882\) | 110.569 | + | 358.833i | 0.125361 | + | 0.406840i | ||||
\(883\) | − | 618.879i | − | 0.700882i | −0.936585 | − | 0.350441i | \(-0.886032\pi\) | ||
0.936585 | − | 0.350441i | \(-0.113968\pi\) | |||||||
\(884\) | 454.628 | − | 1606.00i | 0.514285 | − | 1.81674i | ||||
\(885\) | 25.6503 | − | 55.0434i | 0.0289834 | − | 0.0621959i | ||||
\(886\) | −1005.70 | − | 1329.92i | −1.13511 | − | 1.50104i | ||||
\(887\) | 110.844 | − | 63.9959i | 0.124965 | − | 0.0721487i | −0.436214 | − | 0.899843i | \(-0.643681\pi\) |
0.561180 | + | 0.827694i | \(0.310348\pi\) | |||||||
\(888\) | −90.7867 | + | 44.8807i | −0.102237 | + | 0.0505413i | ||||
\(889\) | −616.119 | + | 1067.15i | −0.693047 | + | 1.20039i | ||||
\(890\) | 58.4131 | + | 469.164i | 0.0656327 | + | 0.527150i | ||||
\(891\) | −418.960 | − | 73.4404i | −0.470214 | − | 0.0824247i | ||||
\(892\) | −101.252 | − | 400.315i | −0.113511 | − | 0.448784i | ||||
\(893\) | 285.661 | − | 494.780i | 0.319890 | − | 0.554065i | ||||
\(894\) | 402.886 | − | 86.4557i | 0.450656 | − | 0.0967066i | ||||
\(895\) | 416.056 | − | 240.210i | 0.464867 | − | 0.268391i | ||||
\(896\) | 1052.55 | + | 191.668i | 1.17472 | + | 0.213915i | ||||
\(897\) | 68.3781 | − | 146.733i | 0.0762298 | − | 0.163582i | ||||
\(898\) | 885.772 | + | 374.218i | 0.986383 | + | 0.416724i | ||||
\(899\) | − | 939.164i | − | 1.04468i | ||||||
\(900\) | −661.594 | + | 297.650i | −0.735104 | + | 0.330723i | ||||
\(901\) | −908.086 | −1.00786 | ||||||||
\(902\) | 81.1303 | − | 192.035i | 0.0899449 | − | 0.212899i | ||||
\(903\) | −478.759 | + | 335.410i | −0.530187 | + | 0.371440i | ||||
\(904\) | 761.970 | − | 950.796i | 0.842887 | − | 1.05177i | ||||
\(905\) | 202.656 | + | 351.011i | 0.223930 | + | 0.387858i | ||||
\(906\) | −469.060 | + | 423.999i | −0.517726 | + | 0.467990i | ||||
\(907\) | 13.7946 | + | 7.96431i | 0.0152090 | + | 0.00878094i | 0.507585 | − | 0.861602i | \(-0.330538\pi\) |
−0.492376 | + | 0.870382i | \(0.663872\pi\) | |||||||
\(908\) | 138.411 | + | 547.230i | 0.152435 | + | 0.602676i | ||||
\(909\) | −46.3972 | + | 127.675i | −0.0510421 | + | 0.140456i | ||||
\(910\) | −538.957 | + | 67.1027i | −0.592260 | + | 0.0737393i | ||||
\(911\) | −43.9255 | − | 25.3604i | −0.0482168 | − | 0.0278380i | 0.475698 | − | 0.879609i | \(-0.342196\pi\) |
−0.523915 | + | 0.851771i | \(0.675529\pi\) | |||||||
\(912\) | 54.5224 | + | 916.984i | 0.0597833 | + | 1.00547i | ||||
\(913\) | 312.445 | + | 541.170i | 0.342218 | + | 0.592738i | ||||
\(914\) | −348.759 | + | 263.737i | −0.381575 | + | 0.288552i | ||||
\(915\) | −47.1377 | − | 537.233i | −0.0515166 | − | 0.587140i | ||||
\(916\) | −230.043 | + | 812.641i | −0.251139 | + | 0.887162i | ||||
\(917\) | −1089.52 | −1.18814 | ||||||||
\(918\) | −208.824 | + | 1512.71i | −0.227477 | + | 1.64784i | ||||
\(919\) | − | 1065.04i | − | 1.15892i | −0.815002 | − | 0.579458i | \(-0.803264\pi\) | ||
0.815002 | − | 0.579458i | \(-0.196736\pi\) | |||||||
\(920\) | 9.75343 | − | 63.6739i | 0.0106016 | − | 0.0692107i | ||||
\(921\) | 408.919 | − | 35.8792i | 0.443995 | − | 0.0389568i | ||||
\(922\) | 1143.70 | − | 864.878i | 1.24045 | − | 0.938046i | ||||
\(923\) | −804.156 | + | 464.279i | −0.871241 | + | 0.503011i | ||||
\(924\) | 517.376 | + | 98.6148i | 0.559931 | + | 0.106726i | ||||
\(925\) | −42.5181 | + | 73.6434i | −0.0459655 | + | 0.0796145i | ||||
\(926\) | −61.0166 | + | 7.59686i | −0.0658927 | + | 0.00820396i | ||||
\(927\) | 897.719 | − | 754.044i | 0.968413 | − | 0.813424i | ||||
\(928\) | 458.285 | + | 642.838i | 0.493841 | + | 0.692713i | ||||
\(929\) | 171.699 | − | 297.392i | 0.184822 | − | 0.320121i | −0.758695 | − | 0.651446i | \(-0.774163\pi\) |
0.943516 | + | 0.331326i | \(0.107496\pi\) | |||||||
\(930\) | −373.083 | + | 337.242i | −0.401164 | + | 0.362625i | ||||
\(931\) | 345.727 | − | 199.606i | 0.371351 | − | 0.214399i | ||||
\(932\) | −781.048 | − | 803.333i | −0.838034 | − | 0.861945i | ||||
\(933\) | −737.932 | − | 1053.31i | −0.790923 | − | 1.12895i | ||||
\(934\) | 356.978 | − | 844.964i | 0.382203 | − | 0.904673i | ||||
\(935\) | − | 326.971i | − | 0.349702i | ||||||
\(936\) | 509.871 | − | 932.071i | 0.544734 | − | 0.995803i | ||||
\(937\) | −267.742 | −0.285744 | −0.142872 | − | 0.989741i | \(-0.545634\pi\) | ||||
−0.142872 | + | 0.989741i | \(0.545634\pi\) | |||||||
\(938\) | −122.008 | − | 51.5456i | −0.130073 | − | 0.0549527i | ||||
\(939\) | 32.5605 | + | 15.1733i | 0.0346757 | + | 0.0161590i | ||||
\(940\) | −188.517 | + | 183.287i | −0.200550 | + | 0.194987i | ||||
\(941\) | −610.126 | − | 1056.77i | −0.648380 | − | 1.12303i | −0.983510 | − | 0.180855i | \(-0.942113\pi\) |
0.335130 | − | 0.942172i | \(-0.391220\pi\) | |||||||
\(942\) | −1261.31 | + | 270.666i | −1.33897 | + | 0.287331i | ||||
\(943\) | −62.8642 | − | 36.2946i | −0.0666640 | − | 0.0384885i | ||||
\(944\) | −69.9342 | − | 129.404i | −0.0740828 | − | 0.137080i | ||||
\(945\) | 479.868 | − | 128.968i | 0.507797 | − | 0.136474i | ||||
\(946\) | 30.2503 | + | 242.964i | 0.0319770 | + | 0.256833i | ||||
\(947\) | −1395.84 | − | 805.888i | −1.47396 | − | 0.850991i | −0.474390 | − | 0.880315i | \(-0.657331\pi\) |
−0.999570 | + | 0.0293240i | \(0.990665\pi\) | |||||||
\(948\) | −702.838 | + | 244.872i | −0.741390 | + | 0.258303i | ||||
\(949\) | −245.845 | − | 425.815i | −0.259056 | − | 0.448699i | ||||
\(950\) | 465.232 | + | 615.212i | 0.489718 | + | 0.647592i | ||||
\(951\) | −127.949 | − | 59.6245i | −0.134542 | − | 0.0626967i | ||||
\(952\) | 286.303 | − | 1869.09i | 0.300739 | − | 1.96333i | ||||
\(953\) | 242.459 | 0.254416 | 0.127208 | − | 0.991876i | \(-0.459398\pi\) | ||||
0.127208 | + | 0.991876i | \(0.459398\pi\) | |||||||
\(954\) | −563.482 | − | 128.787i | −0.590652 | − | 0.134997i | ||||
\(955\) | − | 548.603i | − | 0.574453i | ||||||
\(956\) | 1508.12 | + | 426.922i | 1.57753 | + | 0.446571i | ||||
\(957\) | 223.005 | + | 318.314i | 0.233025 | + | 0.332617i | ||||
\(958\) | 794.650 | + | 1050.83i | 0.829488 | + | 1.09690i | ||||
\(959\) | 722.656 | − | 417.226i | 0.753552 | − | 0.435063i | ||||
\(960\) | 90.8030 | − | 412.888i | 0.0945865 | − | 0.430092i | ||||
\(961\) | 244.068 | − | 422.739i | 0.253973 | − | 0.439895i | ||||
\(962\) | −15.3860 | − | 123.578i | −0.0159938 | − | 0.128459i | ||||
\(963\) | −80.3598 | − | 454.409i | −0.0834473 | − | 0.471868i | ||||
\(964\) | −183.646 | + | 46.4496i | −0.190504 | + | 0.0481842i | ||||
\(965\) | −275.421 | + | 477.043i | −0.285411 | + | 0.494346i | ||||
\(966\) | 56.3325 | − | 174.528i | 0.0583152 | − | 0.180671i | ||||
\(967\) | −1543.81 | + | 891.320i | −1.59650 | + | 0.921737i | −0.604340 | + | 0.796726i | \(0.706563\pi\) |
−0.992155 | + | 0.125011i | \(0.960103\pi\) | |||||||
\(968\) | −467.394 | + | 583.221i | −0.482845 | + | 0.602501i | ||||
\(969\) | 1617.35 | − | 141.909i | 1.66910 | − | 0.146449i | ||||
\(970\) | −14.4916 | − | 6.12238i | −0.0149398 | − | 0.00631173i | ||||
\(971\) | 645.136i | 0.664404i | 0.943208 | + | 0.332202i | \(0.107792\pi\) | ||||
−0.943208 | + | 0.332202i | \(0.892208\pi\) | |||||||
\(972\) | −344.116 | + | 909.048i | −0.354029 | + | 0.935235i | ||||
\(973\) | 798.958 | 0.821129 | ||||||||
\(974\) | −556.973 | + | 1318.35i | −0.571841 | + | 1.35354i | ||||
\(975\) | −77.9719 | − | 888.654i | −0.0799712 | − | 0.911440i | ||||
\(976\) | −1112.46 | − | 684.703i | −1.13982 | − | 0.701540i | ||||
\(977\) | −689.779 | − | 1194.73i | −0.706017 | − | 1.22286i | −0.966323 | − | 0.257331i | \(-0.917157\pi\) |
0.260306 | − | 0.965526i | \(-0.416176\pi\) | |||||||
\(978\) | −192.676 | − | 62.1900i | −0.197010 | − | 0.0635890i | ||||
\(979\) | 488.244 | + | 281.888i | 0.498717 | + | 0.287935i | ||||
\(980\) | −178.114 | + | 45.0505i | −0.181749 | + | 0.0459699i | ||||
\(981\) | 225.760 | − | 39.9245i | 0.230133 | − | 0.0406977i | ||||
\(982\) | −1315.85 | + | 163.830i | −1.33997 | + | 0.166833i | ||||
\(983\) | 639.804 | + | 369.391i | 0.650869 | + | 0.375779i | 0.788789 | − | 0.614664i | \(-0.210708\pi\) |
−0.137920 | + | 0.990443i | \(0.544042\pi\) | |||||||
\(984\) | −396.362 | − | 264.284i | −0.402807 | − | 0.268582i | ||||
\(985\) | 281.478 | + | 487.534i | 0.285764 | + | 0.494959i | ||||
\(986\) | 1112.94 | − | 841.621i | 1.12874 | − | 0.853571i | ||||
\(987\) | −613.082 | + | 429.514i | −0.621157 | + | 0.435171i | ||||
\(988\) | −1086.85 | − | 307.667i | −1.10005 | − | 0.311404i | ||||
\(989\) | 85.2536 | 0.0862018 | ||||||||
\(990\) | 46.3720 | − | 202.891i | 0.0468404 | − | 0.204941i | ||||
\(991\) | 1533.69i | 1.54762i | 0.633416 | + | 0.773811i | \(0.281652\pi\) | ||||
−0.633416 | + | 0.773811i | \(0.718348\pi\) | |||||||
\(992\) | 116.447 | + | 1212.58i | 0.117386 | + | 1.22236i | ||||
\(993\) | 107.034 | − | 229.685i | 0.107788 | − | 0.231304i | ||||
\(994\) | −839.045 | + | 634.498i | −0.844110 | + | 0.638328i | ||||
\(995\) | −589.430 | + | 340.307i | −0.592391 | + | 0.342017i | ||||
\(996\) | 1348.49 | − | 469.819i | 1.35390 | − | 0.471705i | ||||
\(997\) | −871.274 | + | 1509.09i | −0.873896 | + | 1.51363i | −0.0159621 | + | 0.999873i | \(0.505081\pi\) |
−0.857934 | + | 0.513760i | \(0.828252\pi\) | |||||||
\(998\) | 1051.22 | − | 130.882i | 1.05333 | − | 0.131144i | ||||
\(999\) | 29.5711 | + | 110.029i | 0.0296007 | + | 0.110139i |
(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 | 36.3.f.c.7.2 | ✓ | 16 | |
3.2 | odd | 2 | 108.3.f.c.19.7 | 16 | |||
4.3 | odd | 2 | inner | 36.3.f.c.7.8 | yes | 16 | |
8.3 | odd | 2 | 576.3.o.g.511.5 | 16 | |||
8.5 | even | 2 | 576.3.o.g.511.4 | 16 | |||
9.2 | odd | 6 | 324.3.d.g.163.5 | 8 | |||
9.4 | even | 3 | inner | 36.3.f.c.31.8 | yes | 16 | |
9.5 | odd | 6 | 108.3.f.c.91.1 | 16 | |||
9.7 | even | 3 | 324.3.d.i.163.4 | 8 | |||
12.11 | even | 2 | 108.3.f.c.19.1 | 16 | |||
24.5 | odd | 2 | 1728.3.o.g.127.4 | 16 | |||
24.11 | even | 2 | 1728.3.o.g.127.3 | 16 | |||
36.7 | odd | 6 | 324.3.d.i.163.3 | 8 | |||
36.11 | even | 6 | 324.3.d.g.163.6 | 8 | |||
36.23 | even | 6 | 108.3.f.c.91.7 | 16 | |||
36.31 | odd | 6 | inner | 36.3.f.c.31.2 | yes | 16 | |
72.5 | odd | 6 | 1728.3.o.g.1279.3 | 16 | |||
72.13 | even | 6 | 576.3.o.g.319.5 | 16 | |||
72.59 | even | 6 | 1728.3.o.g.1279.4 | 16 | |||
72.67 | odd | 6 | 576.3.o.g.319.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
36.3.f.c.7.8 | yes | 16 | 4.3 | odd | 2 | inner | |
36.3.f.c.31.2 | yes | 16 | 36.31 | odd | 6 | inner | |
36.3.f.c.31.8 | yes | 16 | 9.4 | even | 3 | inner | |
108.3.f.c.19.1 | 16 | 12.11 | even | 2 | |||
108.3.f.c.19.7 | 16 | 3.2 | odd | 2 | |||
108.3.f.c.91.1 | 16 | 9.5 | odd | 6 | |||
108.3.f.c.91.7 | 16 | 36.23 | even | 6 | |||
324.3.d.g.163.5 | 8 | 9.2 | odd | 6 | |||
324.3.d.g.163.6 | 8 | 36.11 | even | 6 | |||
324.3.d.i.163.3 | 8 | 36.7 | odd | 6 | |||
324.3.d.i.163.4 | 8 | 9.7 | even | 3 | |||
576.3.o.g.319.4 | 16 | 72.67 | odd | 6 | |||
576.3.o.g.319.5 | 16 | 72.13 | even | 6 | |||
576.3.o.g.511.4 | 16 | 8.5 | even | 2 | |||
576.3.o.g.511.5 | 16 | 8.3 | odd | 2 | |||
1728.3.o.g.127.3 | 16 | 24.11 | even | 2 | |||
1728.3.o.g.127.4 | 16 | 24.5 | odd | 2 | |||
1728.3.o.g.1279.3 | 16 | 72.5 | odd | 6 | |||
1728.3.o.g.1279.4 | 16 | 72.59 | even | 6 |