Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(361,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.bs (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: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 361.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.361 |
Dual form | 1170.2.bs.d.901.2 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.59808 | − | 1.50000i | −0.981981 | − | 0.566947i | −0.0791130 | − | 0.996866i | \(-0.525209\pi\) |
−0.902867 | + | 0.429919i | \(0.858542\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 3.23205 | − | 1.86603i | 0.974500 | − | 0.562628i | 0.0738948 | − | 0.997266i | \(-0.476457\pi\) |
0.900605 | + | 0.434638i | \(0.143124\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.866025 | + | 3.50000i | −0.240192 | + | 0.970725i | ||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.00000 | − | 3.46410i | 0.485071 | − | 0.840168i | −0.514782 | − | 0.857321i | \(-0.672127\pi\) |
0.999853 | + | 0.0171533i | \(0.00546033\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.96410 | − | 1.13397i | −0.450596 | − | 0.260152i | 0.257486 | − | 0.966282i | \(-0.417106\pi\) |
−0.708082 | + | 0.706130i | \(0.750439\pi\) | |||||||
\(20\) | −0.866025 | − | 0.500000i | −0.193649 | − | 0.111803i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.86603 | − | 3.23205i | 0.397838 | − | 0.689076i | ||||
\(23\) | −1.73205 | − | 3.00000i | −0.361158 | − | 0.625543i | 0.626994 | − | 0.779024i | \(-0.284285\pi\) |
−0.988152 | + | 0.153481i | \(0.950952\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 1.00000 | + | 3.46410i | 0.196116 | + | 0.679366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.59808 | + | 1.50000i | −0.490990 | + | 0.283473i | ||||
\(29\) | −2.73205 | − | 4.73205i | −0.507329 | − | 0.878720i | −0.999964 | − | 0.00848369i | \(-0.997300\pi\) |
0.492635 | − | 0.870236i | \(-0.336034\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.92820i | − | 1.60355i | −0.597624 | − | 0.801776i | \(-0.703889\pi\) | ||
0.597624 | − | 0.801776i | \(-0.296111\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.00000i | − | 0.685994i | ||||||
\(35\) | −1.50000 | + | 2.59808i | −0.253546 | + | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.86603 | + | 3.96410i | −1.12877 | + | 0.651694i | −0.943625 | − | 0.331017i | \(-0.892608\pi\) |
−0.185143 | + | 0.982712i | \(0.559275\pi\) | |||||||
\(38\) | −2.26795 | −0.367910 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −3.46410 | + | 2.00000i | −0.541002 | + | 0.312348i | −0.745485 | − | 0.666523i | \(-0.767782\pi\) |
0.204483 | + | 0.978870i | \(0.434449\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00000 | + | 5.19615i | −0.457496 | + | 0.792406i | −0.998828 | − | 0.0484030i | \(-0.984587\pi\) |
0.541332 | + | 0.840809i | \(0.317920\pi\) | |||||||
\(44\) | − | 3.73205i | − | 0.562628i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | − | 1.73205i | −0.442326 | − | 0.255377i | ||||
\(47\) | − | 0.464102i | − | 0.0676962i | −0.999427 | − | 0.0338481i | \(-0.989224\pi\) | ||
0.999427 | − | 0.0338481i | \(-0.0107762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 1.73205i | 0.142857 | + | 0.247436i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.59808 | + | 2.50000i | 0.360288 | + | 0.346688i | ||||
\(53\) | 3.73205 | 0.512637 | 0.256318 | − | 0.966592i | \(-0.417490\pi\) | ||||
0.256318 | + | 0.966592i | \(0.417490\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.86603 | − | 3.23205i | −0.251615 | − | 0.435810i | ||||
\(56\) | −1.50000 | + | 2.59808i | −0.200446 | + | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.73205 | − | 2.73205i | −0.621349 | − | 0.358736i | ||||
\(59\) | −3.92820 | − | 2.26795i | −0.511409 | − | 0.295262i | 0.222004 | − | 0.975046i | \(-0.428740\pi\) |
−0.733412 | + | 0.679784i | \(0.762074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.73205 | − | 6.46410i | 0.477840 | − | 0.827643i | −0.521837 | − | 0.853045i | \(-0.674753\pi\) |
0.999677 | + | 0.0254017i | \(0.00808648\pi\) | |||||||
\(62\) | −4.46410 | − | 7.73205i | −0.566941 | − | 0.981971i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.50000 | + | 0.866025i | 0.434122 | + | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.73205 | − | 2.73205i | 0.578112 | − | 0.333773i | −0.182271 | − | 0.983248i | \(-0.558345\pi\) |
0.760383 | + | 0.649475i | \(0.225011\pi\) | |||||||
\(68\) | −2.00000 | − | 3.46410i | −0.242536 | − | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.00000i | 0.358569i | ||||||||
\(71\) | 0.803848 | + | 0.464102i | 0.0953992 | + | 0.0550787i | 0.546941 | − | 0.837171i | \(-0.315792\pi\) |
−0.451541 | + | 0.892250i | \(0.649126\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | −3.96410 | + | 6.86603i | −0.460817 | + | 0.798159i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.96410 | + | 1.13397i | −0.225298 | + | 0.130076i | ||||
\(77\) | −11.1962 | −1.27592 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.9282 | 1.90457 | 0.952286 | − | 0.305208i | \(-0.0987259\pi\) | ||||
0.952286 | + | 0.305208i | \(0.0987259\pi\) | |||||||
\(80\) | −0.866025 | + | 0.500000i | −0.0968246 | + | 0.0559017i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.00000 | + | 3.46410i | −0.220863 | + | 0.382546i | ||||
\(83\) | − | 2.53590i | − | 0.278351i | −0.990268 | − | 0.139176i | \(-0.955555\pi\) | ||
0.990268 | − | 0.139176i | \(-0.0444452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.46410 | − | 2.00000i | −0.375735 | − | 0.216930i | ||||
\(86\) | 6.00000i | 0.646997i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.86603 | − | 3.23205i | −0.198919 | − | 0.344538i | ||||
\(89\) | 8.76795 | − | 5.06218i | 0.929401 | − | 0.536590i | 0.0427788 | − | 0.999085i | \(-0.486379\pi\) |
0.886622 | + | 0.462495i | \(0.153046\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.50000 | − | 7.79423i | 0.786214 | − | 0.817057i | ||||
\(92\) | −3.46410 | −0.361158 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.232051 | − | 0.401924i | −0.0239342 | − | 0.0414553i | ||||
\(95\) | −1.13397 | + | 1.96410i | −0.116343 | + | 0.201513i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7321 | + | 6.19615i | 1.08967 | + | 0.629124i | 0.933490 | − | 0.358604i | \(-0.116747\pi\) |
0.156185 | + | 0.987728i | \(0.450080\pi\) | |||||||
\(98\) | 1.73205 | + | 1.00000i | 0.174964 | + | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −4.19615 | − | 7.26795i | −0.417533 | − | 0.723188i | 0.578158 | − | 0.815925i | \(-0.303772\pi\) |
−0.995691 | + | 0.0927369i | \(0.970438\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.5885 | 1.93011 | 0.965054 | − | 0.262051i | \(-0.0843989\pi\) | ||||
0.965054 | + | 0.262051i | \(0.0843989\pi\) | |||||||
\(104\) | 3.50000 | + | 0.866025i | 0.343203 | + | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.23205 | − | 1.86603i | 0.313925 | − | 0.181244i | ||||
\(107\) | 0.464102 | + | 0.803848i | 0.0448664 | + | 0.0777109i | 0.887587 | − | 0.460641i | \(-0.152380\pi\) |
−0.842720 | + | 0.538352i | \(0.819047\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.3923i | 0.995402i | 0.867349 | + | 0.497701i | \(0.165822\pi\) | ||||
−0.867349 | + | 0.497701i | \(0.834178\pi\) | |||||||
\(110\) | −3.23205 | − | 1.86603i | −0.308164 | − | 0.177919i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.00000i | 0.283473i | ||||||||
\(113\) | −6.00000 | + | 10.3923i | −0.564433 | + | 0.977626i | 0.432670 | + | 0.901553i | \(0.357572\pi\) |
−0.997102 | + | 0.0760733i | \(0.975762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | + | 1.73205i | −0.279751 | + | 0.161515i | ||||
\(116\) | −5.46410 | −0.507329 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.53590 | −0.417563 | ||||||||
\(119\) | −10.3923 | + | 6.00000i | −0.952661 | + | 0.550019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.46410 | − | 2.53590i | 0.133100 | − | 0.230536i | ||||
\(122\) | − | 7.46410i | − | 0.675768i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.73205 | − | 4.46410i | −0.694359 | − | 0.400888i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.33013 | − | 4.03590i | −0.206765 | − | 0.358128i | 0.743928 | − | 0.668259i | \(-0.232960\pi\) |
−0.950694 | + | 0.310131i | \(0.899627\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.46410 | − | 1.00000i | 0.303822 | − | 0.0877058i | ||||
\(131\) | 20.3205 | 1.77541 | 0.887706 | − | 0.460412i | \(-0.152298\pi\) | ||||
0.887706 | + | 0.460412i | \(0.152298\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.40192 | + | 5.89230i | 0.294984 | + | 0.510928i | ||||
\(134\) | 2.73205 | − | 4.73205i | 0.236013 | − | 0.408787i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.46410 | − | 2.00000i | −0.297044 | − | 0.171499i | ||||
\(137\) | 5.66025 | + | 3.26795i | 0.483588 | + | 0.279200i | 0.721911 | − | 0.691986i | \(-0.243264\pi\) |
−0.238322 | + | 0.971186i | \(0.576598\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.8923 | + | 18.8660i | −0.923873 | + | 1.60020i | −0.130510 | + | 0.991447i | \(0.541661\pi\) |
−0.793363 | + | 0.608748i | \(0.791672\pi\) | |||||||
\(140\) | 1.50000 | + | 2.59808i | 0.126773 | + | 0.219578i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.928203 | 0.0778931 | ||||||||
\(143\) | 3.73205 | + | 12.9282i | 0.312090 | + | 1.08111i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.73205 | + | 2.73205i | −0.392975 | + | 0.226884i | ||||
\(146\) | 3.46410 | + | 6.00000i | 0.286691 | + | 0.496564i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.92820i | 0.651694i | ||||||||
\(149\) | −19.7321 | − | 11.3923i | −1.61651 | − | 0.933294i | −0.987813 | − | 0.155646i | \(-0.950254\pi\) |
−0.628700 | − | 0.777648i | \(-0.716413\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 18.7846i | − | 1.52867i | −0.644819 | − | 0.764335i | \(-0.723067\pi\) | ||
0.644819 | − | 0.764335i | \(-0.276933\pi\) | |||||||
\(152\) | −1.13397 | + | 1.96410i | −0.0919775 | + | 0.159310i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.69615 | + | 5.59808i | −0.781338 | + | 0.451106i | ||||
\(155\) | −8.92820 | −0.717131 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.8038 | 0.862241 | 0.431120 | − | 0.902294i | \(-0.358118\pi\) | ||||
0.431120 | + | 0.902294i | \(0.358118\pi\) | |||||||
\(158\) | 14.6603 | − | 8.46410i | 1.16631 | − | 0.673368i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | 10.3923i | 0.819028i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.46410 | − | 5.46410i | −0.741286 | − | 0.427981i | 0.0812509 | − | 0.996694i | \(-0.474108\pi\) |
−0.822537 | + | 0.568712i | \(0.807442\pi\) | |||||||
\(164\) | 4.00000i | 0.312348i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.26795 | − | 2.19615i | −0.0984119 | − | 0.170454i | ||||
\(167\) | 5.59808 | − | 3.23205i | 0.433192 | − | 0.250104i | −0.267513 | − | 0.963554i | \(-0.586202\pi\) |
0.700706 | + | 0.713451i | \(0.252869\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | − | 6.06218i | −0.884615 | − | 0.466321i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.00000 | + | 5.19615i | 0.228748 | + | 0.396203i | ||||
\(173\) | 11.0622 | − | 19.1603i | 0.841042 | − | 1.45673i | −0.0479730 | − | 0.998849i | \(-0.515276\pi\) |
0.889015 | − | 0.457879i | \(-0.151391\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.59808 | + | 1.50000i | 0.196396 | + | 0.113389i | ||||
\(176\) | −3.23205 | − | 1.86603i | −0.243625 | − | 0.140657i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.06218 | − | 8.76795i | 0.379426 | − | 0.657186i | ||||
\(179\) | 11.4641 | + | 19.8564i | 0.856867 | + | 1.48414i | 0.874902 | + | 0.484300i | \(0.160926\pi\) |
−0.0180347 | + | 0.999837i | \(0.505741\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.07180 | 0.228325 | 0.114162 | − | 0.993462i | \(-0.463582\pi\) | ||||
0.114162 | + | 0.993462i | \(0.463582\pi\) | |||||||
\(182\) | 2.59808 | − | 10.5000i | 0.192582 | − | 0.778312i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.00000 | + | 1.73205i | −0.221163 | + | 0.127688i | ||||
\(185\) | 3.96410 | + | 6.86603i | 0.291447 | + | 0.504800i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 14.9282i | − | 1.09166i | ||||||
\(188\) | −0.401924 | − | 0.232051i | −0.0293133 | − | 0.0169240i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.26795i | 0.164534i | ||||||||
\(191\) | 8.66025 | − | 15.0000i | 0.626634 | − | 1.08536i | −0.361588 | − | 0.932338i | \(-0.617765\pi\) |
0.988222 | − | 0.153024i | \(-0.0489012\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.4641 | + | 8.92820i | −1.11313 | + | 0.642666i | −0.939638 | − | 0.342169i | \(-0.888838\pi\) |
−0.173492 | + | 0.984835i | \(0.555505\pi\) | |||||||
\(194\) | 12.3923 | 0.889716 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 8.13397 | − | 4.69615i | 0.579522 | − | 0.334587i | −0.181422 | − | 0.983405i | \(-0.558070\pi\) |
0.760943 | + | 0.648818i | \(0.224737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.53590 | − | 9.58846i | 0.392429 | − | 0.679708i | −0.600340 | − | 0.799745i | \(-0.704968\pi\) |
0.992769 | + | 0.120037i | \(0.0383014\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.26795 | − | 4.19615i | −0.511371 | − | 0.295240i | ||||
\(203\) | 16.3923i | 1.15051i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | + | 3.46410i | 0.139686 | + | 0.241943i | ||||
\(206\) | 16.9641 | − | 9.79423i | 1.18194 | − | 0.682396i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.46410 | − | 1.00000i | 0.240192 | − | 0.0693375i | ||||
\(209\) | −8.46410 | −0.585474 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.9641 | + | 18.9904i | 0.754800 | + | 1.30735i | 0.945474 | + | 0.325698i | \(0.105599\pi\) |
−0.190674 | + | 0.981653i | \(0.561067\pi\) | |||||||
\(212\) | 1.86603 | − | 3.23205i | 0.128159 | − | 0.221978i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.803848 | + | 0.464102i | 0.0549499 | + | 0.0317253i | ||||
\(215\) | 5.19615 | + | 3.00000i | 0.354375 | + | 0.204598i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.3923 | + | 23.1962i | −0.909129 | + | 1.57466i | ||||
\(218\) | 5.19615 | + | 9.00000i | 0.351928 | + | 0.609557i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.73205 | −0.251615 | ||||||||
\(221\) | 10.3923 | + | 10.0000i | 0.699062 | + | 0.672673i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.66987 | + | 4.42820i | −0.513613 | + | 0.296534i | −0.734317 | − | 0.678806i | \(-0.762498\pi\) |
0.220705 | + | 0.975341i | \(0.429164\pi\) | |||||||
\(224\) | 1.50000 | + | 2.59808i | 0.100223 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.0000i | 0.798228i | ||||||||
\(227\) | 11.6603 | + | 6.73205i | 0.773918 | + | 0.446822i | 0.834271 | − | 0.551355i | \(-0.185889\pi\) |
−0.0603523 | + | 0.998177i | \(0.519222\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4641i | 0.757569i | 0.925485 | + | 0.378785i | \(0.123658\pi\) | ||||
−0.925485 | + | 0.378785i | \(0.876342\pi\) | |||||||
\(230\) | −1.73205 | + | 3.00000i | −0.114208 | + | 0.197814i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.73205 | + | 2.73205i | −0.310674 | + | 0.179368i | ||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.464102 | −0.0302747 | ||||||||
\(236\) | −3.92820 | + | 2.26795i | −0.255704 | + | 0.147631i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.00000 | + | 10.3923i | −0.388922 | + | 0.673633i | ||||
\(239\) | − | 3.46410i | − | 0.224074i | −0.993704 | − | 0.112037i | \(-0.964262\pi\) | ||
0.993704 | − | 0.112037i | \(-0.0357375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.8205 | + | 7.40192i | 0.825842 | + | 0.476800i | 0.852427 | − | 0.522847i | \(-0.175130\pi\) |
−0.0265852 | + | 0.999647i | \(0.508463\pi\) | |||||||
\(242\) | − | 2.92820i | − | 0.188232i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.73205 | − | 6.46410i | −0.238920 | − | 0.413822i | ||||
\(245\) | 1.73205 | − | 1.00000i | 0.110657 | − | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.66987 | − | 5.89230i | 0.360765 | − | 0.374918i | ||||
\(248\) | −8.92820 | −0.566941 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 13.2321 | − | 22.9186i | 0.835200 | − | 1.44661i | −0.0586681 | − | 0.998278i | \(-0.518685\pi\) |
0.893868 | − | 0.448331i | \(-0.147981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.1962 | − | 6.46410i | −0.703896 | − | 0.406395i | ||||
\(254\) | −4.03590 | − | 2.33013i | −0.253235 | − | 0.146205i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 10.7321 | + | 18.5885i | 0.669447 | + | 1.15952i | 0.978059 | + | 0.208328i | \(0.0668022\pi\) |
−0.308612 | + | 0.951188i | \(0.599864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.7846 | 1.47790 | ||||||||
\(260\) | 2.50000 | − | 2.59808i | 0.155043 | − | 0.161126i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.5981 | − | 10.1603i | 1.08721 | − | 0.627703i | ||||
\(263\) | 10.2583 | + | 17.7679i | 0.632556 | + | 1.09562i | 0.987027 | + | 0.160552i | \(0.0513274\pi\) |
−0.354472 | + | 0.935067i | \(0.615339\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.73205i | − | 0.229258i | ||||||
\(266\) | 5.89230 | + | 3.40192i | 0.361280 | + | 0.208585i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 5.46410i | − | 0.333773i | ||||||
\(269\) | −15.4641 | + | 26.7846i | −0.942863 | + | 1.63309i | −0.182888 | + | 0.983134i | \(0.558545\pi\) |
−0.759975 | + | 0.649953i | \(0.774789\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.12436 | + | 1.80385i | −0.189791 | + | 0.109576i | −0.591885 | − | 0.806023i | \(-0.701616\pi\) |
0.402094 | + | 0.915599i | \(0.368283\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.53590 | 0.394848 | ||||||||
\(275\) | −3.23205 | + | 1.86603i | −0.194900 | + | 0.112526i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.79423 | − | 16.9641i | 0.588478 | − | 1.01927i | −0.405954 | − | 0.913894i | \(-0.633061\pi\) |
0.994432 | − | 0.105380i | \(-0.0336060\pi\) | |||||||
\(278\) | 21.7846i | 1.30655i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.59808 | + | 1.50000i | 0.155265 | + | 0.0896421i | ||||
\(281\) | − | 6.92820i | − | 0.413302i | −0.978415 | − | 0.206651i | \(-0.933744\pi\) | ||
0.978415 | − | 0.206651i | \(-0.0662565\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.19615 | − | 12.4641i | −0.427767 | − | 0.740914i | 0.568907 | − | 0.822402i | \(-0.307366\pi\) |
−0.996674 | + | 0.0814876i | \(0.974033\pi\) | |||||||
\(284\) | 0.803848 | − | 0.464102i | 0.0476996 | − | 0.0275394i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.69615 | + | 9.33013i | 0.573346 | + | 0.551702i | ||||
\(287\) | 12.0000 | 0.708338 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | −2.73205 | + | 4.73205i | −0.160432 | + | 0.277876i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.00000 | + | 3.46410i | 0.351123 | + | 0.202721i | ||||
\(293\) | −16.6699 | − | 9.62436i | −0.973864 | − | 0.562261i | −0.0734522 | − | 0.997299i | \(-0.523402\pi\) |
−0.900412 | + | 0.435038i | \(0.856735\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.26795 | + | 3.92820i | −0.132045 | + | 0.228709i | ||||
\(296\) | 3.96410 | + | 6.86603i | 0.230409 | + | 0.399080i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.7846 | −1.31988 | ||||||||
\(299\) | 12.0000 | − | 3.46410i | 0.693978 | − | 0.200334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.5885 | − | 9.00000i | 0.898504 | − | 0.518751i | ||||
\(302\) | −9.39230 | − | 16.2679i | −0.540466 | − | 0.936115i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.26795i | 0.130076i | ||||||||
\(305\) | −6.46410 | − | 3.73205i | −0.370133 | − | 0.213697i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.2487i | − | 1.15565i | −0.816159 | − | 0.577827i | \(-0.803901\pi\) | ||
0.816159 | − | 0.577827i | \(-0.196099\pi\) | |||||||
\(308\) | −5.59808 | + | 9.69615i | −0.318980 | + | 0.552490i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.73205 | + | 4.46410i | −0.439151 | + | 0.253544i | ||||
\(311\) | −5.07180 | −0.287595 | −0.143798 | − | 0.989607i | \(-0.545931\pi\) | ||||
−0.143798 | + | 0.989607i | \(0.545931\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.32051 | 0.0746395 | 0.0373198 | − | 0.999303i | \(-0.488118\pi\) | ||||
0.0373198 | + | 0.999303i | \(0.488118\pi\) | |||||||
\(314\) | 9.35641 | − | 5.40192i | 0.528013 | − | 0.304848i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.46410 | − | 14.6603i | 0.476143 | − | 0.824704i | ||||
\(317\) | 23.5359i | 1.32191i | 0.750427 | + | 0.660954i | \(0.229848\pi\) | ||||
−0.750427 | + | 0.660954i | \(0.770152\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.6603 | − | 10.1962i | −0.988784 | − | 0.570875i | ||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.19615 | + | 9.00000i | 0.289570 | + | 0.501550i | ||||
\(323\) | −7.85641 | + | 4.53590i | −0.437142 | + | 0.252384i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.866025 | − | 3.50000i | 0.0480384 | − | 0.194145i | ||||
\(326\) | −10.9282 | −0.605257 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.00000 | + | 3.46410i | 0.110432 | + | 0.191273i | ||||
\(329\) | −0.696152 | + | 1.20577i | −0.0383801 | + | 0.0664763i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.53590 | + | 3.19615i | 0.304280 | + | 0.175676i | 0.644364 | − | 0.764719i | \(-0.277122\pi\) |
−0.340084 | + | 0.940395i | \(0.610455\pi\) | |||||||
\(332\) | −2.19615 | − | 1.26795i | −0.120530 | − | 0.0695878i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.23205 | − | 5.59808i | 0.176850 | − | 0.306313i | ||||
\(335\) | −2.73205 | − | 4.73205i | −0.149268 | − | 0.258540i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.60770 | −0.305471 | −0.152735 | − | 0.988267i | \(-0.548808\pi\) | ||||
−0.152735 | + | 0.988267i | \(0.548808\pi\) | |||||||
\(338\) | −12.9904 | + | 0.500000i | −0.706584 | + | 0.0271964i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.46410 | + | 2.00000i | −0.187867 | + | 0.108465i | ||||
\(341\) | −16.6603 | − | 28.8564i | −0.902203 | − | 1.56266i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000i | 0.809924i | ||||||||
\(344\) | 5.19615 | + | 3.00000i | 0.280158 | + | 0.161749i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 22.1244i | − | 1.18941i | ||||||
\(347\) | −8.19615 | + | 14.1962i | −0.439993 | + | 0.762089i | −0.997688 | − | 0.0679560i | \(-0.978352\pi\) |
0.557696 | + | 0.830045i | \(0.311686\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.1244 | − | 8.73205i | 0.809588 | − | 0.467416i | −0.0372247 | − | 0.999307i | \(-0.511852\pi\) |
0.846813 | + | 0.531891i | \(0.178518\pi\) | |||||||
\(350\) | 3.00000 | 0.160357 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.73205 | −0.198919 | ||||||||
\(353\) | 24.5885 | − | 14.1962i | 1.30871 | − | 0.755585i | 0.326830 | − | 0.945083i | \(-0.394019\pi\) |
0.981881 | + | 0.189498i | \(0.0606861\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.464102 | − | 0.803848i | 0.0246320 | − | 0.0426638i | ||||
\(356\) | − | 10.1244i | − | 0.536590i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.8564 | + | 11.4641i | 1.04944 | + | 0.605897i | ||||
\(359\) | − | 12.9282i | − | 0.682324i | −0.940004 | − | 0.341162i | \(-0.889179\pi\) | ||
0.940004 | − | 0.341162i | \(-0.110821\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.92820 | − | 12.0000i | −0.364642 | − | 0.631579i | ||||
\(362\) | 2.66025 | − | 1.53590i | 0.139820 | − | 0.0807250i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.00000 | − | 10.3923i | −0.157243 | − | 0.544705i | ||||
\(365\) | 6.92820 | 0.362639 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.66025 | + | 11.5359i | 0.347662 | + | 0.602169i | 0.985834 | − | 0.167725i | \(-0.0536422\pi\) |
−0.638171 | + | 0.769894i | \(0.720309\pi\) | |||||||
\(368\) | −1.73205 | + | 3.00000i | −0.0902894 | + | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.86603 | + | 3.96410i | 0.356948 | + | 0.206084i | ||||
\(371\) | −9.69615 | − | 5.59808i | −0.503399 | − | 0.290638i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.4641 | + | 19.8564i | −0.593589 | + | 1.02813i | 0.400156 | + | 0.916447i | \(0.368956\pi\) |
−0.993744 | + | 0.111679i | \(0.964377\pi\) | |||||||
\(374\) | −7.46410 | − | 12.9282i | −0.385960 | − | 0.668501i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.464102 | −0.0239342 | ||||||||
\(377\) | 18.9282 | − | 5.46410i | 0.974852 | − | 0.281416i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.42820 | − | 3.13397i | 0.278828 | − | 0.160981i | −0.354065 | − | 0.935221i | \(-0.615201\pi\) |
0.632893 | + | 0.774239i | \(0.281867\pi\) | |||||||
\(380\) | 1.13397 | + | 1.96410i | 0.0581717 | + | 0.100756i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 17.3205i | − | 0.886194i | ||||||
\(383\) | −31.8564 | − | 18.3923i | −1.62779 | − | 0.939803i | −0.984752 | − | 0.173966i | \(-0.944342\pi\) |
−0.643035 | − | 0.765837i | \(-0.722325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.1962i | 0.570609i | ||||||||
\(386\) | −8.92820 | + | 15.4641i | −0.454434 | + | 0.787102i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.7321 | − | 6.19615i | 0.544837 | − | 0.314562i | ||||
\(389\) | 9.85641 | 0.499740 | 0.249870 | − | 0.968279i | \(-0.419612\pi\) | ||||
0.249870 | + | 0.968279i | \(0.419612\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.8564 | −0.700749 | ||||||||
\(392\) | 1.73205 | − | 1.00000i | 0.0874818 | − | 0.0505076i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.69615 | − | 8.13397i | 0.236589 | − | 0.409784i | ||||
\(395\) | − | 16.9282i | − | 0.851750i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.86603 | − | 3.96410i | −0.344596 | − | 0.198953i | 0.317707 | − | 0.948189i | \(-0.397087\pi\) |
−0.662303 | + | 0.749237i | \(0.730421\pi\) | |||||||
\(398\) | − | 11.0718i | − | 0.554979i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 1.83975 | − | 1.06218i | 0.0918725 | − | 0.0530426i | −0.453360 | − | 0.891328i | \(-0.649775\pi\) |
0.545232 | + | 0.838285i | \(0.316441\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.2487 | + | 7.73205i | 1.55661 | + | 0.385161i | ||||
\(404\) | −8.39230 | −0.417533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.19615 | + | 14.1962i | 0.406768 | + | 0.704543i | ||||
\(407\) | −14.7942 | + | 25.6244i | −0.733323 | + | 1.27015i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.820508 | + | 0.473721i | 0.0405715 | + | 0.0234240i | 0.520149 | − | 0.854076i | \(-0.325877\pi\) |
−0.479577 | + | 0.877500i | \(0.659210\pi\) | |||||||
\(410\) | 3.46410 | + | 2.00000i | 0.171080 | + | 0.0987730i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.79423 | − | 16.9641i | 0.482527 | − | 0.835761i | ||||
\(413\) | 6.80385 | + | 11.7846i | 0.334795 | + | 0.579883i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.53590 | −0.124482 | ||||||||
\(416\) | 2.50000 | − | 2.59808i | 0.122573 | − | 0.127381i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.33013 | + | 4.23205i | −0.358528 | + | 0.206996i | ||||
\(419\) | −8.92820 | − | 15.4641i | −0.436171 | − | 0.755471i | 0.561219 | − | 0.827667i | \(-0.310332\pi\) |
−0.997390 | + | 0.0721964i | \(0.976999\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.85641i | 0.285424i | 0.989764 | + | 0.142712i | \(0.0455822\pi\) | ||||
−0.989764 | + | 0.142712i | \(0.954418\pi\) | |||||||
\(422\) | 18.9904 | + | 10.9641i | 0.924437 | + | 0.533724i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 3.73205i | − | 0.181244i | ||||||
\(425\) | −2.00000 | + | 3.46410i | −0.0970143 | + | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.3923 | + | 11.1962i | −0.938459 | + | 0.541820i | ||||
\(428\) | 0.928203 | 0.0448664 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.00000 | 0.289346 | ||||||||
\(431\) | 12.0000 | − | 6.92820i | 0.578020 | − | 0.333720i | −0.182326 | − | 0.983238i | \(-0.558363\pi\) |
0.760346 | + | 0.649518i | \(0.225029\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.3923 | + | 28.3923i | −0.787764 | + | 1.36445i | 0.139570 | + | 0.990212i | \(0.455428\pi\) |
−0.927334 | + | 0.374235i | \(0.877905\pi\) | |||||||
\(434\) | 26.7846i | 1.28570i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.00000 | + | 5.19615i | 0.431022 | + | 0.248851i | ||||
\(437\) | 7.85641i | 0.375823i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.6603 | − | 18.4641i | −0.508786 | − | 0.881243i | −0.999948 | − | 0.0101753i | \(-0.996761\pi\) |
0.491162 | − | 0.871068i | \(-0.336572\pi\) | |||||||
\(440\) | −3.23205 | + | 1.86603i | −0.154082 | + | 0.0889593i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.0000 | + | 3.46410i | 0.665912 | + | 0.164771i | ||||
\(443\) | −7.85641 | −0.373269 | −0.186635 | − | 0.982429i | \(-0.559758\pi\) | ||||
−0.186635 | + | 0.982429i | \(0.559758\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.06218 | − | 8.76795i | −0.239970 | − | 0.415641i | ||||
\(446\) | −4.42820 | + | 7.66987i | −0.209682 | + | 0.363179i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.59808 | + | 1.50000i | 0.122748 | + | 0.0708683i | ||||
\(449\) | 15.6962 | + | 9.06218i | 0.740747 | + | 0.427671i | 0.822341 | − | 0.568995i | \(-0.192668\pi\) |
−0.0815937 | + | 0.996666i | \(0.526001\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.46410 | + | 12.9282i | −0.351471 | + | 0.608765i | ||||
\(452\) | 6.00000 | + | 10.3923i | 0.282216 | + | 0.488813i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.4641 | 0.631902 | ||||||||
\(455\) | −7.79423 | − | 7.50000i | −0.365399 | − | 0.351605i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.464102 | − | 0.267949i | 0.0217098 | − | 0.0125341i | −0.489106 | − | 0.872224i | \(-0.662677\pi\) |
0.510816 | + | 0.859690i | \(0.329343\pi\) | |||||||
\(458\) | 5.73205 | + | 9.92820i | 0.267841 | + | 0.463914i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.46410i | 0.161515i | ||||||||
\(461\) | −28.0526 | − | 16.1962i | −1.30654 | − | 0.754330i | −0.325021 | − | 0.945707i | \(-0.605371\pi\) |
−0.981517 | + | 0.191377i | \(0.938705\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.784610i | − | 0.0364639i | −0.999834 | − | 0.0182320i | \(-0.994196\pi\) | ||
0.999834 | − | 0.0182320i | \(-0.00580373\pi\) | |||||||
\(464\) | −2.73205 | + | 4.73205i | −0.126832 | + | 0.219680i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.5885 | + | 9.00000i | −0.722121 | + | 0.416917i | ||||
\(467\) | −3.60770 | −0.166944 | −0.0834721 | − | 0.996510i | \(-0.526601\pi\) | ||||
−0.0834721 | + | 0.996510i | \(0.526601\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.3923 | −0.756926 | ||||||||
\(470\) | −0.401924 | + | 0.232051i | −0.0185394 | + | 0.0107037i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.26795 | + | 3.92820i | −0.104391 | + | 0.180810i | ||||
\(473\) | 22.3923i | 1.02960i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.96410 | + | 1.13397i | 0.0901192 | + | 0.0520303i | ||||
\(476\) | 12.0000i | 0.550019i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.73205 | − | 3.00000i | −0.0792222 | − | 0.137217i | ||||
\(479\) | 22.7321 | − | 13.1244i | 1.03865 | − | 0.599667i | 0.119202 | − | 0.992870i | \(-0.461966\pi\) |
0.919452 | + | 0.393203i | \(0.128633\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.92820 | − | 27.4641i | −0.361495 | − | 1.25226i | ||||
\(482\) | 14.8038 | 0.674297 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.46410 | − | 2.53590i | −0.0665501 | − | 0.115268i | ||||
\(485\) | 6.19615 | − | 10.7321i | 0.281353 | − | 0.487317i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.1865 | − | 10.5000i | −0.824110 | − | 0.475800i | 0.0277214 | − | 0.999616i | \(-0.491175\pi\) |
−0.851832 | + | 0.523815i | \(0.824508\pi\) | |||||||
\(488\) | −6.46410 | − | 3.73205i | −0.292616 | − | 0.168942i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.00000 | − | 1.73205i | 0.0451754 | − | 0.0782461i | ||||
\(491\) | −7.69615 | − | 13.3301i | −0.347322 | − | 0.601580i | 0.638450 | − | 0.769663i | \(-0.279576\pi\) |
−0.985773 | + | 0.168083i | \(0.946242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.8564 | −0.984363 | ||||||||
\(494\) | 1.96410 | − | 7.93782i | 0.0883691 | − | 0.357140i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.73205 | + | 4.46410i | −0.347179 | + | 0.200444i | ||||
\(497\) | −1.39230 | − | 2.41154i | −0.0624534 | − | 0.108172i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.32051i | 0.0591141i | 0.999563 | + | 0.0295570i | \(0.00940967\pi\) | ||||
−0.999563 | + | 0.0295570i | \(0.990590\pi\) | |||||||
\(500\) | 0.866025 | + | 0.500000i | 0.0387298 | + | 0.0223607i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 26.4641i | − | 1.18115i | ||||||
\(503\) | 0.133975 | − | 0.232051i | 0.00597363 | − | 0.0103466i | −0.863023 | − | 0.505164i | \(-0.831432\pi\) |
0.868997 | + | 0.494818i | \(0.164765\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.26795 | + | 4.19615i | −0.323419 | + | 0.186726i | ||||
\(506\) | −12.9282 | −0.574729 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.66025 | −0.206765 | ||||||||
\(509\) | −4.60770 | + | 2.66025i | −0.204232 | + | 0.117914i | −0.598628 | − | 0.801027i | \(-0.704287\pi\) |
0.394396 | + | 0.918941i | \(0.370954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.3923 | − | 18.0000i | 0.459728 | − | 0.796273i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.5885 | + | 10.7321i | 0.819902 | + | 0.473370i | ||||
\(515\) | − | 19.5885i | − | 0.863171i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.866025 | − | 1.50000i | −0.0380878 | − | 0.0659699i | ||||
\(518\) | 20.5981 | − | 11.8923i | 0.905028 | − | 0.522518i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.866025 | − | 3.50000i | 0.0379777 | − | 0.153485i | ||||
\(521\) | 27.3923 | 1.20008 | 0.600039 | − | 0.799970i | \(-0.295152\pi\) | ||||
0.600039 | + | 0.799970i | \(0.295152\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.85641 | − | 11.8756i | −0.299810 | − | 0.519286i | 0.676283 | − | 0.736642i | \(-0.263590\pi\) |
−0.976092 | + | 0.217357i | \(0.930257\pi\) | |||||||
\(524\) | 10.1603 | − | 17.5981i | 0.443853 | − | 0.768776i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.7679 | + | 10.2583i | 0.774719 | + | 0.447284i | ||||
\(527\) | −30.9282 | − | 17.8564i | −1.34725 | − | 0.777837i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.50000 | − | 9.52628i | 0.239130 | − | 0.414186i | ||||
\(530\) | −1.86603 | − | 3.23205i | −0.0810550 | − | 0.140391i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.80385 | 0.294984 | ||||||||
\(533\) | −4.00000 | − | 13.8564i | −0.173259 | − | 0.600188i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.803848 | − | 0.464102i | 0.0347534 | − | 0.0200649i | ||||
\(536\) | −2.73205 | − | 4.73205i | −0.118007 | − | 0.204393i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30.9282i | 1.33341i | ||||||||
\(539\) | 6.46410 | + | 3.73205i | 0.278429 | + | 0.160751i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.7846i | 1.15156i | 0.817605 | + | 0.575780i | \(0.195302\pi\) | ||||
−0.817605 | + | 0.575780i | \(0.804698\pi\) | |||||||
\(542\) | −1.80385 | + | 3.12436i | −0.0774819 | + | 0.134203i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.46410 | + | 2.00000i | −0.148522 | + | 0.0857493i | ||||
\(545\) | 10.3923 | 0.445157 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.3205 | 1.25365 | 0.626827 | − | 0.779158i | \(-0.284353\pi\) | ||||
0.626827 | + | 0.779158i | \(0.284353\pi\) | |||||||
\(548\) | 5.66025 | − | 3.26795i | 0.241794 | − | 0.139600i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.86603 | + | 3.23205i | −0.0795676 | + | 0.137815i | ||||
\(551\) | 12.3923i | 0.527930i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −43.9808 | − | 25.3923i | −1.87025 | − | 1.07979i | ||||
\(554\) | − | 19.5885i | − | 0.832234i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.8923 | + | 18.8660i | 0.461937 | + | 0.800098i | ||||
\(557\) | −37.5788 | + | 21.6962i | −1.59227 | + | 0.919295i | −0.599349 | + | 0.800488i | \(0.704574\pi\) |
−0.992917 | + | 0.118808i | \(0.962093\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.5885 | − | 15.0000i | −0.659321 | − | 0.634432i | ||||
\(560\) | 3.00000 | 0.126773 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.46410 | − | 6.00000i | −0.146124 | − | 0.253095i | ||||
\(563\) | 9.66025 | − | 16.7321i | 0.407131 | − | 0.705172i | −0.587436 | − | 0.809271i | \(-0.699863\pi\) |
0.994567 | + | 0.104099i | \(0.0331959\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.3923 | + | 6.00000i | 0.437208 | + | 0.252422i | ||||
\(566\) | −12.4641 | − | 7.19615i | −0.523905 | − | 0.302477i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.464102 | − | 0.803848i | 0.0194733 | − | 0.0337287i | ||||
\(569\) | 9.16025 | + | 15.8660i | 0.384018 | + | 0.665138i | 0.991632 | − | 0.129094i | \(-0.0412068\pi\) |
−0.607615 | + | 0.794232i | \(0.707873\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.8564 | −0.705419 | −0.352709 | − | 0.935733i | \(-0.614740\pi\) | ||||
−0.352709 | + | 0.935733i | \(0.614740\pi\) | |||||||
\(572\) | 13.0622 | + | 3.23205i | 0.546157 | + | 0.135139i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.3923 | − | 6.00000i | 0.433766 | − | 0.250435i | ||||
\(575\) | 1.73205 | + | 3.00000i | 0.0722315 | + | 0.125109i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 25.3205i | − | 1.05411i | −0.849832 | − | 0.527053i | \(-0.823297\pi\) | ||
0.849832 | − | 0.527053i | \(-0.176703\pi\) | |||||||
\(578\) | 0.866025 | + | 0.500000i | 0.0360219 | + | 0.0207973i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.46410i | 0.226884i | ||||||||
\(581\) | −3.80385 | + | 6.58846i | −0.157810 | + | 0.273335i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0622 | − | 6.96410i | 0.499564 | − | 0.288424i | ||||
\(584\) | 6.92820 | 0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.2487 | −0.795157 | ||||||||
\(587\) | 4.26795 | − | 2.46410i | 0.176157 | − | 0.101704i | −0.409329 | − | 0.912387i | \(-0.634237\pi\) |
0.585486 | + | 0.810683i | \(0.300904\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.1244 | + | 17.5359i | −0.417167 | + | 0.722554i | ||||
\(590\) | 4.53590i | 0.186740i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.86603 | + | 3.96410i | 0.282192 | + | 0.162924i | ||||
\(593\) | − | 3.21539i | − | 0.132040i | −0.997818 | − | 0.0660201i | \(-0.978970\pi\) | ||
0.997818 | − | 0.0660201i | \(-0.0210302\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | + | 10.3923i | 0.245976 | + | 0.426043i | ||||
\(596\) | −19.7321 | + | 11.3923i | −0.808256 | + | 0.466647i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.66025 | − | 9.00000i | 0.354144 | − | 0.368037i | ||||
\(599\) | −15.0718 | −0.615817 | −0.307908 | − | 0.951416i | \(-0.599629\pi\) | ||||
−0.307908 | + | 0.951416i | \(0.599629\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.3564 | + | 21.4019i | 0.504028 | + | 0.873003i | 0.999989 | + | 0.00465778i | \(0.00148262\pi\) |
−0.495961 | + | 0.868345i | \(0.665184\pi\) | |||||||
\(602\) | 9.00000 | − | 15.5885i | 0.366813 | − | 0.635338i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −16.2679 | − | 9.39230i | −0.661933 | − | 0.382167i | ||||
\(605\) | −2.53590 | − | 1.46410i | −0.103099 | − | 0.0595242i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.7224 | + | 32.4282i | −0.759920 | + | 1.31622i | 0.182971 | + | 0.983118i | \(0.441429\pi\) |
−0.942891 | + | 0.333102i | \(0.891905\pi\) | |||||||
\(608\) | 1.13397 | + | 1.96410i | 0.0459887 | + | 0.0796548i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.46410 | −0.302213 | ||||||||
\(611\) | 1.62436 | + | 0.401924i | 0.0657144 | + | 0.0162601i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.9711 | + | 22.5000i | −1.57403 | + | 0.908766i | −0.578362 | + | 0.815780i | \(0.696308\pi\) |
−0.995667 | + | 0.0929864i | \(0.970359\pi\) | |||||||
\(614\) | −10.1244 | − | 17.5359i | −0.408586 | − | 0.707691i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.1962i | 0.451106i | ||||||||
\(617\) | −24.7128 | − | 14.2679i | −0.994900 | − | 0.574406i | −0.0881649 | − | 0.996106i | \(-0.528100\pi\) |
−0.906735 | + | 0.421700i | \(0.861434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.5167i | 1.70889i | 0.519543 | + | 0.854444i | \(0.326102\pi\) | ||||
−0.519543 | + | 0.854444i | \(0.673898\pi\) | |||||||
\(620\) | −4.46410 | + | 7.73205i | −0.179283 | + | 0.310527i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.39230 | + | 2.53590i | −0.176115 | + | 0.101680i | ||||
\(623\) | −30.3731 | −1.21687 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.14359 | − | 0.660254i | 0.0457072 | − | 0.0263891i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.40192 | − | 9.35641i | 0.215560 | − | 0.373361i | ||||
\(629\) | 31.7128i | 1.26447i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.92820 | + | 4.00000i | 0.275807 | + | 0.159237i | 0.631524 | − | 0.775356i | \(-0.282430\pi\) |
−0.355716 | + | 0.934594i | \(0.615763\pi\) | |||||||
\(632\) | − | 16.9282i | − | 0.673368i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.7679 | + | 20.3827i | 0.467365 | + | 0.809500i | ||||
\(635\) | −4.03590 | + | 2.33013i | −0.160160 | + | 0.0924683i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.92820 | + | 2.00000i | −0.274505 | + | 0.0792429i | ||||
\(638\) | −20.3923 | −0.807339 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 3.76795 | − | 6.52628i | 0.148825 | − | 0.257773i | −0.781968 | − | 0.623318i | \(-0.785784\pi\) |
0.930793 | + | 0.365546i | \(0.119118\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.9282 | + | 14.3923i | 0.983072 | + | 0.567577i | 0.903196 | − | 0.429228i | \(-0.141214\pi\) |
0.0798761 | + | 0.996805i | \(0.474548\pi\) | |||||||
\(644\) | 9.00000 | + | 5.19615i | 0.354650 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.53590 | + | 7.85641i | −0.178463 | + | 0.309106i | ||||
\(647\) | −16.1340 | − | 27.9449i | −0.634292 | − | 1.09863i | −0.986665 | − | 0.162766i | \(-0.947958\pi\) |
0.352373 | − | 0.935860i | \(-0.385375\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.9282 | −0.664490 | ||||||||
\(650\) | −1.00000 | − | 3.46410i | −0.0392232 | − | 0.135873i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.46410 | + | 5.46410i | −0.370643 | + | 0.213991i | ||||
\(653\) | 14.7942 | + | 25.6244i | 0.578943 | + | 1.00276i | 0.995601 | + | 0.0936952i | \(0.0298679\pi\) |
−0.416658 | + | 0.909063i | \(0.636799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 20.3205i | − | 0.793988i | ||||||
\(656\) | 3.46410 | + | 2.00000i | 0.135250 | + | 0.0780869i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.39230i | 0.0542777i | ||||||||
\(659\) | 7.85641 | − | 13.6077i | 0.306042 | − | 0.530081i | −0.671451 | − | 0.741049i | \(-0.734328\pi\) |
0.977493 | + | 0.210969i | \(0.0676618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.7128 | − | 21.1962i | 1.42796 | − | 0.824435i | 0.431003 | − | 0.902351i | \(-0.358160\pi\) |
0.996960 | + | 0.0779157i | \(0.0248265\pi\) | |||||||
\(662\) | 6.39230 | 0.248444 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.53590 | −0.0984119 | ||||||||
\(665\) | 5.89230 | − | 3.40192i | 0.228494 | − | 0.131921i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.46410 | + | 16.3923i | −0.366451 | + | 0.634713i | ||||
\(668\) | − | 6.46410i | − | 0.250104i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.73205 | − | 2.73205i | −0.182815 | − | 0.105548i | ||||
\(671\) | − | 27.8564i | − | 1.07538i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.3923 | − | 21.4641i | −0.477688 | − | 0.827380i | 0.521985 | − | 0.852955i | \(-0.325192\pi\) |
−0.999673 | + | 0.0255746i | \(0.991858\pi\) | |||||||
\(674\) | −4.85641 | + | 2.80385i | −0.187062 | + | 0.108000i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | 2.92820 | 0.112540 | 0.0562700 | − | 0.998416i | \(-0.482079\pi\) | ||||
0.0562700 | + | 0.998416i | \(0.482079\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.5885 | − | 32.1962i | −0.713360 | − | 1.23557i | ||||
\(680\) | −2.00000 | + | 3.46410i | −0.0766965 | + | 0.132842i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −28.8564 | − | 16.6603i | −1.10497 | − | 0.637954i | ||||
\(683\) | 5.78461 | + | 3.33975i | 0.221342 | + | 0.127792i | 0.606571 | − | 0.795029i | \(-0.292544\pi\) |
−0.385230 | + | 0.922821i | \(0.625878\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.26795 | − | 5.66025i | 0.124862 | − | 0.216267i | ||||
\(686\) | 7.50000 | + | 12.9904i | 0.286351 | + | 0.495975i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.00000 | 0.228748 | ||||||||
\(689\) | −3.23205 | + | 13.0622i | −0.123131 | + | 0.497629i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.9641 | − | 11.5263i | 0.759470 | − | 0.438480i | −0.0696353 | − | 0.997573i | \(-0.522184\pi\) |
0.829106 | + | 0.559092i | \(0.188850\pi\) | |||||||
\(692\) | −11.0622 | − | 19.1603i | −0.420521 | − | 0.728364i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.3923i | 0.622243i | ||||||||
\(695\) | 18.8660 | + | 10.8923i | 0.715629 | + | 0.413169i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.0000i | 0.606043i | ||||||||
\(698\) | 8.73205 | − | 15.1244i | 0.330513 | − | 0.572465i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.59808 | − | 1.50000i | 0.0981981 | − | 0.0566947i | ||||
\(701\) | −16.3923 | −0.619129 | −0.309564 | − | 0.950878i | \(-0.600183\pi\) | ||||
−0.309564 | + | 0.950878i | \(0.600183\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.9808 | 0.678157 | ||||||||
\(704\) | −3.23205 | + | 1.86603i | −0.121812 | + | 0.0703285i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.1962 | − | 24.5885i | 0.534279 | − | 0.925399i | ||||
\(707\) | 25.1769i | 0.946875i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.33975 | − | 3.66025i | −0.238094 | − | 0.137464i | 0.376206 | − | 0.926536i | \(-0.377228\pi\) |
−0.614300 | + | 0.789072i | \(0.710562\pi\) | |||||||
\(710\) | − | 0.928203i | − | 0.0348348i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.06218 | − | 8.76795i | −0.189713 | − | 0.328593i | ||||
\(713\) | −26.7846 | + | 15.4641i | −1.00309 | + | 0.579135i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.9282 | − | 3.73205i | 0.483487 | − | 0.139571i | ||||
\(716\) | 22.9282 | 0.856867 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.46410 | − | 11.1962i | −0.241238 | − | 0.417837i | ||||
\(719\) | 8.00000 | − | 13.8564i | 0.298350 | − | 0.516757i | −0.677409 | − | 0.735607i | \(-0.736897\pi\) |
0.975759 | + | 0.218850i | \(0.0702305\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.8923 | − | 29.3827i | −1.89533 | − | 1.09427i | ||||
\(722\) | −12.0000 | − | 6.92820i | −0.446594 | − | 0.257841i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.53590 | − | 2.66025i | 0.0570812 | − | 0.0988676i | ||||
\(725\) | 2.73205 | + | 4.73205i | 0.101466 | + | 0.175744i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.6603 | 0.469543 | 0.234771 | − | 0.972051i | \(-0.424566\pi\) | ||||
0.234771 | + | 0.972051i | \(0.424566\pi\) | |||||||
\(728\) | −7.79423 | − | 7.50000i | −0.288873 | − | 0.277968i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.00000 | − | 3.46410i | 0.222070 | − | 0.128212i | ||||
\(731\) | 12.0000 | + | 20.7846i | 0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.85641i | 0.253247i | 0.991951 | + | 0.126624i | \(0.0404140\pi\) | ||||
−0.991951 | + | 0.126624i | \(0.959586\pi\) | |||||||
\(734\) | 11.5359 | + | 6.66025i | 0.425798 | + | 0.245834i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.46410i | 0.127688i | ||||||||
\(737\) | 10.1962 | − | 17.6603i | 0.375580 | − | 0.650524i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.9641 | − | 21.9186i | 1.39653 | − | 0.806288i | 0.402505 | − | 0.915418i | \(-0.368140\pi\) |
0.994028 | + | 0.109130i | \(0.0348064\pi\) | |||||||
\(740\) | 7.92820 | 0.291447 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.1962 | −0.411024 | ||||||||
\(743\) | 2.53590 | − | 1.46410i | 0.0930331 | − | 0.0537127i | −0.452762 | − | 0.891632i | \(-0.649561\pi\) |
0.545795 | + | 0.837919i | \(0.316228\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.3923 | + | 19.7321i | −0.417382 | + | 0.722926i | ||||
\(746\) | 22.9282i | 0.839461i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.9282 | − | 7.46410i | −0.472702 | − | 0.272915i | ||||
\(749\) | − | 2.78461i | − | 0.101747i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5885 | − | 35.6603i | −0.751283 | − | 1.30126i | −0.947201 | − | 0.320641i | \(-0.896102\pi\) |
0.195917 | − | 0.980620i | \(-0.437232\pi\) | |||||||
\(752\) | −0.401924 | + | 0.232051i | −0.0146567 | + | 0.00846202i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.6603 | − | 14.1962i | 0.497477 | − | 0.516993i | ||||
\(755\) | −18.7846 | −0.683642 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.13397 | − | 15.8205i | −0.331980 | − | 0.575006i | 0.650920 | − | 0.759146i | \(-0.274383\pi\) |
−0.982900 | + | 0.184140i | \(0.941050\pi\) | |||||||
\(758\) | 3.13397 | − | 5.42820i | 0.113831 | − | 0.197161i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.96410 | + | 1.13397i | 0.0712455 | + | 0.0411336i | ||||
\(761\) | −38.0885 | − | 21.9904i | −1.38071 | − | 0.797151i | −0.388463 | − | 0.921465i | \(-0.626994\pi\) |
−0.992243 | + | 0.124314i | \(0.960327\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.5885 | − | 27.0000i | 0.564340 | − | 0.977466i | ||||
\(764\) | −8.66025 | − | 15.0000i | −0.313317 | − | 0.542681i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36.7846 | −1.32908 | ||||||||
\(767\) | 11.3397 | − | 11.7846i | 0.409454 | − | 0.425518i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.3923 | − | 19.8564i | 1.24022 | − | 0.716040i | 0.271080 | − | 0.962557i | \(-0.412619\pi\) |
0.969139 | + | 0.246517i | \(0.0792860\pi\) | |||||||
\(770\) | 5.59808 | + | 9.69615i | 0.201741 | + | 0.349425i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.8564i | 0.642666i | ||||||||
\(773\) | −46.2391 | − | 26.6962i | −1.66310 | − | 0.960194i | −0.971220 | − | 0.238186i | \(-0.923447\pi\) |
−0.691885 | − | 0.722008i | \(-0.743220\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.92820i | 0.320711i | ||||||||
\(776\) | 6.19615 | − | 10.7321i | 0.222429 | − | 0.385258i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.53590 | − | 4.92820i | 0.306027 | − | 0.176685i | ||||
\(779\) | 9.07180 | 0.325031 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.46410 | 0.123955 | ||||||||
\(782\) | −12.0000 | + | 6.92820i | −0.429119 | + | 0.247752i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | − | 1.73205i | 0.0357143 | − | 0.0618590i | ||||
\(785\) | − | 10.8038i | − | 0.385606i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.73205 | + | 2.73205i | 0.168679 | + | 0.0973871i | 0.581963 | − | 0.813215i | \(-0.302285\pi\) |
−0.413284 | + | 0.910602i | \(0.635618\pi\) | |||||||
\(788\) | − | 9.39230i | − | 0.334587i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.46410 | − | 14.6603i | −0.301139 | − | 0.521588i | ||||
\(791\) | 31.1769 | − | 18.0000i | 1.10852 | − | 0.640006i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.3923 | + | 18.6603i | 0.688641 | + | 0.662645i | ||||
\(794\) | −7.92820 | −0.281361 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.53590 | − | 9.58846i | −0.196215 | − | 0.339854i | ||||
\(797\) | −18.9282 | + | 32.7846i | −0.670471 | + | 1.16129i | 0.307299 | + | 0.951613i | \(0.400575\pi\) |
−0.977771 | + | 0.209678i | \(0.932759\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.60770 | − | 0.928203i | −0.0568762 | − | 0.0328375i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.06218 | − | 1.83975i | 0.0375068 | − | 0.0649637i | ||||
\(803\) | 12.9282 | + | 22.3923i | 0.456226 | + | 0.790207i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.3923 | 0.366281 | ||||||||
\(806\) | 30.9282 | − | 8.92820i | 1.08940 | − | 0.314483i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.26795 | + | 4.19615i | −0.255686 | + | 0.147620i | ||||
\(809\) | 17.3923 | + | 30.1244i | 0.611481 | + | 1.05912i | 0.990991 | + | 0.133928i | \(0.0427592\pi\) |
−0.379510 | + | 0.925188i | \(0.623907\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.58846i | 0.266467i | 0.991085 | + | 0.133233i | \(0.0425360\pi\) | ||||
−0.991085 | + | 0.133233i | \(0.957464\pi\) | |||||||
\(812\) | 14.1962 | + | 8.19615i | 0.498187 | + | 0.287629i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.5885i | 1.03707i | ||||||||
\(815\) | −5.46410 | + | 9.46410i | −0.191399 | + | 0.331513i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.7846 | − | 6.80385i | 0.412291 | − | 0.238036i | ||||
\(818\) | 0.947441 | 0.0331265 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.00000 | 0.139686 | ||||||||
\(821\) | −42.7128 | + | 24.6603i | −1.49069 | + | 0.860649i | −0.999943 | − | 0.0106549i | \(-0.996608\pi\) |
−0.490744 | + | 0.871304i | \(0.663275\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.7942 | − | 34.2846i | 0.689983 | − | 1.19509i | −0.281859 | − | 0.959456i | \(-0.590951\pi\) |
0.971843 | − | 0.235631i | \(-0.0757155\pi\) | |||||||
\(824\) | − | 19.5885i | − | 0.682396i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.7846 | + | 6.80385i | 0.410039 | + | 0.236736i | ||||
\(827\) | − | 50.4974i | − | 1.75597i | −0.478690 | − | 0.877984i | \(-0.658888\pi\) | ||
0.478690 | − | 0.877984i | \(-0.341112\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.6603 | + | 34.0526i | 0.682829 | + | 1.18269i | 0.974114 | + | 0.226058i | \(0.0725839\pi\) |
−0.291285 | + | 0.956636i | \(0.594083\pi\) | |||||||
\(830\) | −2.19615 | + | 1.26795i | −0.0762296 | + | 0.0440112i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.866025 | − | 3.50000i | 0.0300240 | − | 0.121341i | ||||
\(833\) | 8.00000 | 0.277184 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.23205 | − | 5.59808i | −0.111850 | − | 0.193729i | ||||
\(836\) | −4.23205 | + | 7.33013i | −0.146369 | + | 0.253518i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.4641 | − | 8.92820i | −0.534199 | − | 0.308420i | ||||
\(839\) | −37.3923 | − | 21.5885i | −1.29093 | − | 0.745316i | −0.312107 | − | 0.950047i | \(-0.601035\pi\) |
−0.978818 | + | 0.204731i | \(0.934368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.428203 | + | 0.741670i | −0.0147656 | + | 0.0255748i | ||||
\(842\) | 2.92820 | + | 5.07180i | 0.100913 | + | 0.174786i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 21.9282 | 0.754800 | ||||||||
\(845\) | −6.06218 | + | 11.5000i | −0.208545 | + | 0.395612i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.60770 | + | 4.39230i | −0.261403 | + | 0.150921i | ||||
\(848\) | −1.86603 | − | 3.23205i | −0.0640796 | − | 0.110989i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.00000i | 0.137199i | ||||||||
\(851\) | 23.7846 | + | 13.7321i | 0.815326 | + | 0.470729i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 44.6410i | − | 1.52848i | −0.644932 | − | 0.764240i | \(-0.723114\pi\) | ||
0.644932 | − | 0.764240i | \(-0.276886\pi\) | |||||||
\(854\) | −11.1962 | + | 19.3923i | −0.383124 | + | 0.663591i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.803848 | − | 0.464102i | 0.0274749 | − | 0.0158627i | ||||
\(857\) | 15.0718 | 0.514843 | 0.257421 | − | 0.966299i | \(-0.417127\pi\) | ||||
0.257421 | + | 0.966299i | \(0.417127\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.9282 | −0.679942 | −0.339971 | − | 0.940436i | \(-0.610417\pi\) | ||||
−0.339971 | + | 0.940436i | \(0.610417\pi\) | |||||||
\(860\) | 5.19615 | − | 3.00000i | 0.177187 | − | 0.102299i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.92820 | − | 12.0000i | 0.235976 | − | 0.408722i | ||||
\(863\) | − | 10.9282i | − | 0.372000i | −0.982550 | − | 0.186000i | \(-0.940447\pi\) | ||
0.982550 | − | 0.186000i | \(-0.0595525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.1603 | − | 11.0622i | −0.651468 | − | 0.376125i | ||||
\(866\) | 32.7846i | 1.11407i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.3923 | + | 23.1962i | 0.454564 | + | 0.787329i | ||||
\(869\) | 54.7128 | − | 31.5885i | 1.85601 | − | 1.07157i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.46410 | + | 18.9282i | 0.185144 | + | 0.641358i | ||||
\(872\) | 10.3923 | 0.351928 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.92820 | + | 6.80385i | 0.132873 | + | 0.230144i | ||||
\(875\) | 1.50000 | − | 2.59808i | 0.0507093 | − | 0.0878310i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.1962 | + | 16.8564i | 0.985884 | + | 0.569200i | 0.904041 | − | 0.427445i | \(-0.140586\pi\) |
0.0818426 | + | 0.996645i | \(0.473920\pi\) | |||||||
\(878\) | −18.4641 | − | 10.6603i | −0.623133 | − | 0.359766i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.86603 | + | 3.23205i | −0.0629037 | + | 0.108952i | ||||
\(881\) | −18.5526 | − | 32.1340i | −0.625052 | − | 1.08262i | −0.988531 | − | 0.151019i | \(-0.951745\pi\) |
0.363479 | − | 0.931602i | \(-0.381589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.3205 | 0.717492 | 0.358746 | − | 0.933435i | \(-0.383204\pi\) | ||||
0.358746 | + | 0.933435i | \(0.383204\pi\) | |||||||
\(884\) | 13.8564 | − | 4.00000i | 0.466041 | − | 0.134535i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.80385 | + | 3.92820i | −0.228580 | + | 0.131971i | ||||
\(887\) | 26.1340 | + | 45.2654i | 0.877493 | + | 1.51986i | 0.854083 | + | 0.520136i | \(0.174119\pi\) |
0.0234098 | + | 0.999726i | \(0.492548\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.9808i | 0.468900i | ||||||||
\(890\) | −8.76795 | − | 5.06218i | −0.293902 | − | 0.169685i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.85641i | 0.296534i | ||||||||
\(893\) | −0.526279 | + | 0.911543i | −0.0176113 | + | 0.0305036i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.8564 | − | 11.4641i | 0.663726 | − | 0.383203i | ||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.1244 | 0.604818 | ||||||||
\(899\) | −42.2487 | + | 24.3923i | −1.40907 | + | 0.813529i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.46410 | − | 12.9282i | 0.248665 | − | 0.430701i | ||||
\(902\) | 14.9282i | 0.497055i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.3923 | + | 6.00000i | 0.345643 | + | 0.199557i | ||||
\(905\) | − | 3.07180i | − | 0.102110i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.53590 | − | 6.12436i | −0.117408 | − | 0.203356i | 0.801332 | − | 0.598220i | \(-0.204125\pi\) |
−0.918740 | + | 0.394864i | \(0.870792\pi\) | |||||||
\(908\) | 11.6603 | − | 6.73205i | 0.386959 | − | 0.223411i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.5000 | − | 2.59808i | −0.348072 | − | 0.0861254i | ||||
\(911\) | 28.7846 | 0.953677 | 0.476838 | − | 0.878991i | \(-0.341783\pi\) | ||||
0.476838 | + | 0.878991i | \(0.341783\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.73205 | − | 8.19615i | −0.156608 | − | 0.271253i | ||||
\(914\) | 0.267949 | − | 0.464102i | 0.00886297 | − | 0.0153511i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.92820 | + | 5.73205i | 0.328037 | + | 0.189392i | ||||
\(917\) | −52.7942 | − | 30.4808i | −1.74342 | − | 1.00656i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.9808 | + | 48.4641i | −0.923000 | + | 1.59868i | −0.128254 | + | 0.991741i | \(0.540937\pi\) |
−0.794746 | + | 0.606942i | \(0.792396\pi\) | |||||||
\(920\) | 1.73205 | + | 3.00000i | 0.0571040 | + | 0.0989071i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −32.3923 | −1.06678 | ||||||||
\(923\) | −2.32051 | + | 2.41154i | −0.0763805 | + | 0.0793769i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.86603 | − | 3.96410i | 0.225754 | − | 0.130339i | ||||
\(926\) | −0.392305 | − | 0.679492i | −0.0128919 | − | 0.0223295i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.46410i | 0.179368i | ||||||||
\(929\) | 26.1051 | + | 15.0718i | 0.856481 | + | 0.494490i | 0.862832 | − | 0.505490i | \(-0.168688\pi\) |
−0.00635120 | + | 0.999980i | \(0.502022\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 4.53590i | − | 0.148658i | ||||||
\(932\) | −9.00000 | + | 15.5885i | −0.294805 | + | 0.510617i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.12436 | + | 1.80385i | −0.102232 | + | 0.0590237i | ||||
\(935\) | −14.9282 | −0.488204 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.7128 | 1.10135 | 0.550675 | − | 0.834720i | \(-0.314370\pi\) | ||||
0.550675 | + | 0.834720i | \(0.314370\pi\) | |||||||
\(938\) | −14.1962 | + | 8.19615i | −0.463521 | + | 0.267614i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.232051 | + | 0.401924i | −0.00756866 | + | 0.0131093i | ||||
\(941\) | 36.4974i | 1.18978i | 0.803806 | + | 0.594891i | \(0.202805\pi\) | ||||
−0.803806 | + | 0.594891i | \(0.797195\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.0000 | + | 6.92820i | 0.390774 | + | 0.225613i | ||||
\(944\) | 4.53590i | 0.147631i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.1962 | + | 19.3923i | 0.364018 | + | 0.630498i | ||||
\(947\) | 11.7846 | − | 6.80385i | 0.382948 | − | 0.221095i | −0.296152 | − | 0.955141i | \(-0.595703\pi\) |
0.679100 | + | 0.734046i | \(0.262370\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.2487 | − | 6.00000i | −0.787146 | − | 0.194768i | ||||
\(950\) | 2.26795 | 0.0735820 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.00000 | + | 10.3923i | 0.194461 | + | 0.336817i | ||||
\(953\) | −9.33975 | + | 16.1769i | −0.302544 | + | 0.524022i | −0.976711 | − | 0.214557i | \(-0.931169\pi\) |
0.674167 | + | 0.738579i | \(0.264503\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.0000 | − | 8.66025i | −0.485389 | − | 0.280239i | ||||
\(956\) | −3.00000 | − | 1.73205i | −0.0970269 | − | 0.0560185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.1244 | − | 22.7321i | 0.424029 | − | 0.734439i | ||||
\(959\) | −9.80385 | − | 16.9808i | −0.316583 | − | 0.548337i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −48.7128 | −1.57138 | ||||||||
\(962\) | −20.5981 | − | 19.8205i | −0.664109 | − | 0.639039i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.8205 | − | 7.40192i | 0.412921 | − | 0.238400i | ||||
\(965\) | 8.92820 | + | 15.4641i | 0.287409 | + | 0.497807i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.8564i | 0.927959i | 0.885846 | + | 0.463980i | \(0.153579\pi\) | ||||
−0.885846 | + | 0.463980i | \(0.846421\pi\) | |||||||
\(968\) | −2.53590 | − | 1.46410i | −0.0815069 | − | 0.0470580i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 12.3923i | − | 0.397893i | ||||||
\(971\) | −10.3038 | + | 17.8468i | −0.330666 | + | 0.572731i | −0.982643 | − | 0.185509i | \(-0.940607\pi\) |
0.651976 | + | 0.758239i | \(0.273940\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 56.5981 | − | 32.6769i | 1.81445 | − | 1.04757i | ||||
\(974\) | −21.0000 | −0.672883 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.46410 | −0.238920 | ||||||||
\(977\) | 1.26795 | − | 0.732051i | 0.0405653 | − | 0.0234204i | −0.479580 | − | 0.877498i | \(-0.659211\pi\) |
0.520145 | + | 0.854078i | \(0.325878\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.8923 | − | 32.7224i | 0.603801 | − | 1.04581i | ||||
\(980\) | − | 2.00000i | − | 0.0638877i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.3301 | − | 7.69615i | −0.425381 | − | 0.245594i | ||||
\(983\) | − | 16.1769i | − | 0.515963i | −0.966150 | − | 0.257982i | \(-0.916943\pi\) | ||
0.966150 | − | 0.257982i | \(-0.0830574\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.69615 | − | 8.13397i | −0.149632 | − | 0.259170i | ||||
\(986\) | −18.9282 | + | 10.9282i | −0.602797 | + | 0.348025i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.26795 | − | 7.85641i | −0.0721531 | − | 0.249946i | ||||
\(989\) | 20.7846 | 0.660912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.5885 | + | 20.0718i | 0.368119 | + | 0.637602i | 0.989272 | − | 0.146088i | \(-0.0466684\pi\) |
−0.621152 | + | 0.783690i | \(0.713335\pi\) | |||||||
\(992\) | −4.46410 | + | 7.73205i | −0.141735 | + | 0.245493i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.41154 | − | 1.39230i | −0.0764895 | − | 0.0441612i | ||||
\(995\) | −9.58846 | − | 5.53590i | −0.303975 | − | 0.175500i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.00962 | + | 8.67691i | −0.158656 | + | 0.274801i | −0.934384 | − | 0.356267i | \(-0.884049\pi\) |
0.775728 | + | 0.631067i | \(0.217383\pi\) | |||||||
\(998\) | 0.660254 | + | 1.14359i | 0.0209000 | + | 0.0361998i | ||||
\(999\) | 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 | 1170.2.bs.d.361.2 | 4 | ||
3.2 | odd | 2 | 390.2.bb.a.361.1 | yes | 4 | ||
13.4 | even | 6 | inner | 1170.2.bs.d.901.2 | 4 | ||
15.2 | even | 4 | 1950.2.y.d.49.2 | 4 | |||
15.8 | even | 4 | 1950.2.y.e.49.1 | 4 | |||
15.14 | odd | 2 | 1950.2.bc.a.751.2 | 4 | |||
39.2 | even | 12 | 5070.2.a.ba.1.2 | 2 | |||
39.11 | even | 12 | 5070.2.a.be.1.1 | 2 | |||
39.17 | odd | 6 | 390.2.bb.a.121.1 | ✓ | 4 | ||
39.23 | odd | 6 | 5070.2.b.p.1351.4 | 4 | |||
39.29 | odd | 6 | 5070.2.b.p.1351.1 | 4 | |||
195.17 | even | 12 | 1950.2.y.e.199.1 | 4 | |||
195.134 | odd | 6 | 1950.2.bc.a.901.2 | 4 | |||
195.173 | even | 12 | 1950.2.y.d.199.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.a.121.1 | ✓ | 4 | 39.17 | odd | 6 | ||
390.2.bb.a.361.1 | yes | 4 | 3.2 | odd | 2 | ||
1170.2.bs.d.361.2 | 4 | 1.1 | even | 1 | trivial | ||
1170.2.bs.d.901.2 | 4 | 13.4 | even | 6 | inner | ||
1950.2.y.d.49.2 | 4 | 15.2 | even | 4 | |||
1950.2.y.d.199.2 | 4 | 195.173 | even | 12 | |||
1950.2.y.e.49.1 | 4 | 15.8 | even | 4 | |||
1950.2.y.e.199.1 | 4 | 195.17 | even | 12 | |||
1950.2.bc.a.751.2 | 4 | 15.14 | odd | 2 | |||
1950.2.bc.a.901.2 | 4 | 195.134 | odd | 6 | |||
5070.2.a.ba.1.2 | 2 | 39.2 | even | 12 | |||
5070.2.a.be.1.1 | 2 | 39.11 | even | 12 | |||
5070.2.b.p.1351.1 | 4 | 39.29 | odd | 6 | |||
5070.2.b.p.1351.4 | 4 | 39.23 | odd | 6 |