Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(49,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.y (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.5708283941\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.49 |
Dual form | 1950.2.y.d.199.2 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.866025 | − | 0.500000i | −0.353553 | − | 0.204124i | ||||
\(7\) | 1.50000 | − | 2.59808i | 0.566947 | − | 0.981981i | −0.429919 | − | 0.902867i | \(-0.641458\pi\) |
0.996866 | − | 0.0791130i | \(-0.0252088\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.23205 | + | 1.86603i | −0.974500 | + | 0.562628i | −0.900605 | − | 0.434638i | \(-0.856876\pi\) |
−0.0738948 | + | 0.997266i | \(0.523543\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 3.50000 | + | 0.866025i | 0.970725 | + | 0.240192i | ||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −3.46410 | − | 2.00000i | −0.840168 | − | 0.485071i | 0.0171533 | − | 0.999853i | \(-0.494540\pi\) |
−0.857321 | + | 0.514782i | \(0.827873\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.96410 | + | 1.13397i | 0.450596 | + | 0.260152i | 0.708082 | − | 0.706130i | \(-0.249561\pi\) |
−0.257486 | + | 0.966282i | \(0.582894\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.00000i | − | 0.654654i | ||||||
\(22\) | 3.23205 | + | 1.86603i | 0.689076 | + | 0.397838i | ||||
\(23\) | 3.00000 | − | 1.73205i | 0.625543 | − | 0.361158i | −0.153481 | − | 0.988152i | \(-0.549048\pi\) |
0.779024 | + | 0.626994i | \(0.215715\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00000 | − | 3.46410i | −0.196116 | − | 0.679366i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 1.50000 | + | 2.59808i | 0.283473 | + | 0.490990i | ||||
\(29\) | −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 | \(-0.296111\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.86603 | + | 3.23205i | −0.324833 | + | 0.562628i | ||||
\(34\) | 4.00000i | 0.685994i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | −3.96410 | − | 6.86603i | −0.651694 | − | 1.12877i | −0.982712 | − | 0.185143i | \(-0.940725\pi\) |
0.331017 | − | 0.943625i | \(-0.392608\pi\) | |||||||
\(38\) | − | 2.26795i | − | 0.367910i | ||||||
\(39\) | 3.46410 | − | 1.00000i | 0.554700 | − | 0.160128i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410 | − | 2.00000i | 0.541002 | − | 0.312348i | −0.204483 | − | 0.978870i | \(-0.565551\pi\) |
0.745485 | + | 0.666523i | \(0.232218\pi\) | |||||||
\(42\) | −2.59808 | + | 1.50000i | −0.400892 | + | 0.231455i | ||||
\(43\) | 5.19615 | + | 3.00000i | 0.792406 | + | 0.457496i | 0.840809 | − | 0.541332i | \(-0.182080\pi\) |
−0.0484030 | + | 0.998828i | \(0.515413\pi\) | |||||||
\(44\) | − | 3.73205i | − | 0.562628i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | − | 1.73205i | −0.442326 | − | 0.255377i | ||||
\(47\) | −0.464102 | −0.0676962 | −0.0338481 | − | 0.999427i | \(-0.510776\pi\) | ||||
−0.0338481 | + | 0.999427i | \(0.510776\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | −2.50000 | + | 2.59808i | −0.346688 | + | 0.360288i | ||||
\(53\) | 3.73205i | 0.512637i | 0.966592 | + | 0.256318i | \(0.0825095\pi\) | ||||
−0.966592 | + | 0.256318i | \(0.917490\pi\) | |||||||
\(54\) | −0.866025 | + | 0.500000i | −0.117851 | + | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.50000 | − | 2.59808i | 0.200446 | − | 0.347183i | ||||
\(57\) | 2.26795 | 0.300397 | ||||||||
\(58\) | −2.73205 | + | 4.73205i | −0.358736 | + | 0.621349i | ||||
\(59\) | −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 | \(0.00808648\pi\) | |||||||
\(62\) | −7.73205 | + | 4.46410i | −0.981971 | + | 0.566941i | ||||
\(63\) | −1.50000 | − | 2.59808i | −0.188982 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.73205 | 0.459384 | ||||||||
\(67\) | 2.73205 | + | 4.73205i | 0.333773 | + | 0.578112i | 0.983248 | − | 0.182271i | \(-0.0583447\pi\) |
−0.649475 | + | 0.760383i | \(0.725011\pi\) | |||||||
\(68\) | 3.46410 | − | 2.00000i | 0.420084 | − | 0.242536i | ||||
\(69\) | 1.73205 | − | 3.00000i | 0.208514 | − | 0.361158i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.803848 | − | 0.464102i | −0.0953992 | − | 0.0550787i | 0.451541 | − | 0.892250i | \(-0.350874\pi\) |
−0.546941 | + | 0.837171i | \(0.684208\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 6.92820 | 0.810885 | 0.405442 | − | 0.914121i | \(-0.367117\pi\) | ||||
0.405442 | + | 0.914121i | \(0.367117\pi\) | |||||||
\(74\) | −3.96410 | + | 6.86603i | −0.460817 | + | 0.798159i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.96410 | + | 1.13397i | −0.225298 | + | 0.130076i | ||||
\(77\) | 11.1962i | 1.27592i | ||||||||
\(78\) | −2.59808 | − | 2.50000i | −0.294174 | − | 0.283069i | ||||
\(79\) | −16.9282 | −1.90457 | −0.952286 | − | 0.305208i | \(-0.901274\pi\) | ||||
−0.952286 | + | 0.305208i | \(0.901274\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −3.46410 | − | 2.00000i | −0.382546 | − | 0.220863i | ||||
\(83\) | 2.53590 | 0.278351 | 0.139176 | − | 0.990268i | \(-0.455555\pi\) | ||||
0.139176 | + | 0.990268i | \(0.455555\pi\) | |||||||
\(84\) | 2.59808 | + | 1.50000i | 0.283473 | + | 0.163663i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 6.00000i | − | 0.646997i | ||||||
\(87\) | −4.73205 | − | 2.73205i | −0.507329 | − | 0.292907i | ||||
\(88\) | −3.23205 | + | 1.86603i | −0.344538 | + | 0.198919i | ||||
\(89\) | 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 | ||||
\(92\) | 3.46410i | 0.361158i | ||||||||
\(93\) | −4.46410 | − | 7.73205i | −0.462906 | − | 0.801776i | ||||
\(94\) | 0.232051 | + | 0.401924i | 0.0239342 | + | 0.0414553i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −6.19615 | + | 10.7321i | −0.629124 | + | 1.08967i | 0.358604 | + | 0.933490i | \(0.383253\pi\) |
−0.987728 | + | 0.156185i | \(0.950080\pi\) | |||||||
\(98\) | −1.00000 | + | 1.73205i | −0.101015 | + | 0.174964i | ||||
\(99\) | 3.73205i | 0.375085i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.19615 | + | 7.26795i | 0.417533 | + | 0.723188i | 0.995691 | − | 0.0927369i | \(-0.0295616\pi\) |
−0.578158 | + | 0.815925i | \(0.696228\pi\) | |||||||
\(102\) | 2.00000 | + | 3.46410i | 0.198030 | + | 0.342997i | ||||
\(103\) | − | 19.5885i | − | 1.93011i | −0.262051 | − | 0.965054i | \(-0.584399\pi\) | ||
0.262051 | − | 0.965054i | \(-0.415601\pi\) | |||||||
\(104\) | 3.50000 | + | 0.866025i | 0.343203 | + | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.23205 | − | 1.86603i | 0.313925 | − | 0.181244i | ||||
\(107\) | 0.803848 | − | 0.464102i | 0.0777109 | − | 0.0448664i | −0.460641 | − | 0.887587i | \(-0.652380\pi\) |
0.538352 | + | 0.842720i | \(0.319047\pi\) | |||||||
\(108\) | 0.866025 | + | 0.500000i | 0.0833333 | + | 0.0481125i | ||||
\(109\) | − | 10.3923i | − | 0.995402i | −0.867349 | − | 0.497701i | \(-0.834178\pi\) | ||
0.867349 | − | 0.497701i | \(-0.165822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.86603 | − | 3.96410i | −0.651694 | − | 0.376256i | ||||
\(112\) | −3.00000 | −0.283473 | ||||||||
\(113\) | −10.3923 | − | 6.00000i | −0.977626 | − | 0.564433i | −0.0760733 | − | 0.997102i | \(-0.524238\pi\) |
−0.901553 | + | 0.432670i | \(0.857572\pi\) | |||||||
\(114\) | −1.13397 | − | 1.96410i | −0.106206 | − | 0.183955i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.46410 | 0.507329 | ||||||||
\(117\) | 2.50000 | − | 2.59808i | 0.231125 | − | 0.240192i | ||||
\(118\) | 4.53590i | 0.417563i | ||||||||
\(119\) | −10.3923 | + | 6.00000i | −0.952661 | + | 0.550019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.46410 | − | 2.53590i | 0.133100 | − | 0.230536i | ||||
\(122\) | −7.46410 | −0.675768 | ||||||||
\(123\) | 2.00000 | − | 3.46410i | 0.180334 | − | 0.312348i | ||||
\(124\) | 7.73205 | + | 4.46410i | 0.694359 | + | 0.400888i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.50000 | + | 2.59808i | −0.133631 | + | 0.231455i | ||||
\(127\) | 4.03590 | − | 2.33013i | 0.358128 | − | 0.206765i | −0.310131 | − | 0.950694i | \(-0.600373\pi\) |
0.668259 | + | 0.743928i | \(0.267040\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.3205 | −1.77541 | −0.887706 | − | 0.460412i | \(-0.847702\pi\) | ||||
−0.887706 | + | 0.460412i | \(0.847702\pi\) | |||||||
\(132\) | −1.86603 | − | 3.23205i | −0.162417 | − | 0.281314i | ||||
\(133\) | 5.89230 | − | 3.40192i | 0.510928 | − | 0.294984i | ||||
\(134\) | 2.73205 | − | 4.73205i | 0.236013 | − | 0.408787i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.46410 | − | 2.00000i | −0.297044 | − | 0.171499i | ||||
\(137\) | 3.26795 | − | 5.66025i | 0.279200 | − | 0.483588i | −0.691986 | − | 0.721911i | \(-0.743264\pi\) |
0.971186 | + | 0.238322i | \(0.0765975\pi\) | |||||||
\(138\) | −3.46410 | −0.294884 | ||||||||
\(139\) | 10.8923 | − | 18.8660i | 0.923873 | − | 1.60020i | 0.130510 | − | 0.991447i | \(-0.458339\pi\) |
0.793363 | − | 0.608748i | \(-0.208328\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.401924 | + | 0.232051i | −0.0338481 | + | 0.0195422i | ||||
\(142\) | 0.928203i | 0.0778931i | ||||||||
\(143\) | −12.9282 | + | 3.73205i | −1.08111 | + | 0.312090i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.46410 | − | 6.00000i | −0.286691 | − | 0.496564i | ||||
\(147\) | −1.73205 | − | 1.00000i | −0.142857 | − | 0.0824786i | ||||
\(148\) | 7.92820 | 0.651694 | ||||||||
\(149\) | −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 | \(-0.276933\pi\) | |||||||
\(152\) | 1.96410 | + | 1.13397i | 0.159310 | + | 0.0919775i | ||||
\(153\) | −3.46410 | + | 2.00000i | −0.280056 | + | 0.161690i | ||||
\(154\) | 9.69615 | − | 5.59808i | 0.781338 | − | 0.451106i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.866025 | + | 3.50000i | −0.0693375 | + | 0.280224i | ||||
\(157\) | 10.8038i | 0.862241i | 0.902294 | + | 0.431120i | \(0.141882\pi\) | ||||
−0.902294 | + | 0.431120i | \(0.858118\pi\) | |||||||
\(158\) | 8.46410 | + | 14.6603i | 0.673368 | + | 1.16631i | ||||
\(159\) | 1.86603 | + | 3.23205i | 0.147985 | + | 0.256318i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 10.3923i | − | 0.819028i | ||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −5.46410 | + | 9.46410i | −0.427981 | + | 0.741286i | −0.996694 | − | 0.0812509i | \(-0.974108\pi\) |
0.568712 | + | 0.822537i | \(0.307442\pi\) | |||||||
\(164\) | 4.00000i | 0.312348i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.26795 | − | 2.19615i | −0.0984119 | − | 0.170454i | ||||
\(167\) | −3.23205 | − | 5.59808i | −0.250104 | − | 0.433192i | 0.713451 | − | 0.700706i | \(-0.247131\pi\) |
−0.963554 | + | 0.267513i | \(0.913798\pi\) | |||||||
\(168\) | − | 3.00000i | − | 0.231455i | ||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.96410 | − | 1.13397i | 0.150199 | − | 0.0867172i | ||||
\(172\) | −5.19615 | + | 3.00000i | −0.396203 | + | 0.228748i | ||||
\(173\) | 19.1603 | + | 11.0622i | 1.45673 | + | 0.841042i | 0.998849 | − | 0.0479730i | \(-0.0152761\pi\) |
0.457879 | + | 0.889015i | \(0.348609\pi\) | |||||||
\(174\) | 5.46410i | 0.414232i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.23205 | + | 1.86603i | 0.243625 | + | 0.140657i | ||||
\(177\) | −4.53590 | −0.340939 | ||||||||
\(178\) | −8.76795 | − | 5.06218i | −0.657186 | − | 0.379426i | ||||
\(179\) | 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 | \(0.463582\pi\) | |||||||
\(182\) | −10.5000 | − | 2.59808i | −0.778312 | − | 0.192582i | ||||
\(183\) | − | 7.46410i | − | 0.551762i | ||||||
\(184\) | 3.00000 | − | 1.73205i | 0.221163 | − | 0.127688i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.46410 | + | 7.73205i | −0.327324 | + | 0.566941i | ||||
\(187\) | 14.9282 | 1.09166 | ||||||||
\(188\) | 0.232051 | − | 0.401924i | 0.0169240 | − | 0.0293133i | ||||
\(189\) | −2.59808 | − | 1.50000i | −0.188982 | − | 0.109109i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.66025 | + | 15.0000i | −0.626634 | + | 1.08536i | 0.361588 | + | 0.932338i | \(0.382235\pi\) |
−0.988222 | + | 0.153024i | \(0.951099\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 8.92820 | + | 15.4641i | 0.642666 | + | 1.11313i | 0.984835 | + | 0.173492i | \(0.0555051\pi\) |
−0.342169 | + | 0.939638i | \(0.611162\pi\) | |||||||
\(194\) | 12.3923 | 0.889716 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | −4.69615 | − | 8.13397i | −0.334587 | − | 0.579522i | 0.648818 | − | 0.760943i | \(-0.275263\pi\) |
−0.983405 | + | 0.181422i | \(0.941930\pi\) | |||||||
\(198\) | 3.23205 | − | 1.86603i | 0.229692 | − | 0.132613i | ||||
\(199\) | −5.53590 | + | 9.58846i | −0.392429 | + | 0.679708i | −0.992769 | − | 0.120037i | \(-0.961699\pi\) |
0.600340 | + | 0.799745i | \(0.295032\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.73205 | + | 2.73205i | 0.333773 | + | 0.192704i | ||||
\(202\) | 4.19615 | − | 7.26795i | 0.295240 | − | 0.511371i | ||||
\(203\) | −16.3923 | −1.15051 | ||||||||
\(204\) | 2.00000 | − | 3.46410i | 0.140028 | − | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.9641 | + | 9.79423i | −1.18194 | + | 0.682396i | ||||
\(207\) | − | 3.46410i | − | 0.240772i | ||||||
\(208\) | −1.00000 | − | 3.46410i | −0.0693375 | − | 0.240192i | ||||
\(209\) | −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 | \(0.561067\pi\) | |||||||
\(212\) | −3.23205 | − | 1.86603i | −0.221978 | − | 0.128159i | ||||
\(213\) | −0.928203 | −0.0635994 | ||||||||
\(214\) | −0.803848 | − | 0.464102i | −0.0549499 | − | 0.0317253i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −23.1962 | − | 13.3923i | −1.57466 | − | 0.909129i | ||||
\(218\) | −9.00000 | + | 5.19615i | −0.609557 | + | 0.351928i | ||||
\(219\) | 6.00000 | − | 3.46410i | 0.405442 | − | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.3923 | − | 10.0000i | −0.699062 | − | 0.672673i | ||||
\(222\) | 7.92820i | 0.532106i | ||||||||
\(223\) | 4.42820 | + | 7.66987i | 0.296534 | + | 0.513613i | 0.975341 | − | 0.220705i | \(-0.0708357\pi\) |
−0.678806 | + | 0.734317i | \(0.737502\pi\) | |||||||
\(224\) | 1.50000 | + | 2.59808i | 0.100223 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.0000i | 0.798228i | ||||||||
\(227\) | 6.73205 | − | 11.6603i | 0.446822 | − | 0.773918i | −0.551355 | − | 0.834271i | \(-0.685889\pi\) |
0.998177 | + | 0.0603523i | \(0.0192224\pi\) | |||||||
\(228\) | −1.13397 | + | 1.96410i | −0.0750993 | + | 0.130076i | ||||
\(229\) | − | 11.4641i | − | 0.757569i | −0.925485 | − | 0.378785i | \(-0.876342\pi\) | ||
0.925485 | − | 0.378785i | \(-0.123658\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.59808 | + | 9.69615i | 0.368326 | + | 0.637960i | ||||
\(232\) | −2.73205 | − | 4.73205i | −0.179368 | − | 0.310674i | ||||
\(233\) | − | 18.0000i | − | 1.17922i | −0.807688 | − | 0.589610i | \(-0.799282\pi\) | ||
0.807688 | − | 0.589610i | \(-0.200718\pi\) | |||||||
\(234\) | −3.50000 | − | 0.866025i | −0.228802 | − | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.92820 | − | 2.26795i | 0.255704 | − | 0.147631i | ||||
\(237\) | −14.6603 | + | 8.46410i | −0.952286 | + | 0.549802i | ||||
\(238\) | 10.3923 | + | 6.00000i | 0.673633 | + | 0.388922i | ||||
\(239\) | − | 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 | \(0.508463\pi\) | |||||||
\(242\) | −2.92820 | −0.188232 | ||||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 3.73205 | + | 6.46410i | 0.238920 | + | 0.413822i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.00000 | −0.255031 | ||||||||
\(247\) | 5.89230 | + | 5.66987i | 0.374918 | + | 0.360765i | ||||
\(248\) | − | 8.92820i | − | 0.566941i | ||||||
\(249\) | 2.19615 | − | 1.26795i | 0.139176 | − | 0.0803530i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.2321 | + | 22.9186i | −0.835200 | + | 1.44661i | 0.0586681 | + | 0.998278i | \(0.481315\pi\) |
−0.893868 | + | 0.448331i | \(0.852019\pi\) | |||||||
\(252\) | 3.00000 | 0.188982 | ||||||||
\(253\) | −6.46410 | + | 11.1962i | −0.406395 | + | 0.703896i | ||||
\(254\) | −4.03590 | − | 2.33013i | −0.253235 | − | 0.146205i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 18.5885 | − | 10.7321i | 1.15952 | − | 0.669447i | 0.208328 | − | 0.978059i | \(-0.433198\pi\) |
0.951188 | + | 0.308612i | \(0.0998645\pi\) | |||||||
\(258\) | −3.00000 | − | 5.19615i | −0.186772 | − | 0.323498i | ||||
\(259\) | −23.7846 | −1.47790 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.46410 | −0.338219 | ||||||||
\(262\) | 10.1603 | + | 17.5981i | 0.627703 | + | 1.08721i | ||||
\(263\) | −17.7679 | + | 10.2583i | −1.09562 | + | 0.632556i | −0.935067 | − | 0.354472i | \(-0.884661\pi\) |
−0.160552 | + | 0.987027i | \(0.551327\pi\) | |||||||
\(264\) | −1.86603 | + | 3.23205i | −0.114846 | + | 0.198919i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.89230 | − | 3.40192i | −0.361280 | − | 0.208585i | ||||
\(267\) | 5.06218 | − | 8.76795i | 0.309800 | − | 0.536590i | ||||
\(268\) | −5.46410 | −0.333773 | ||||||||
\(269\) | −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 | \(0.368283\pi\) | |||||||
\(272\) | 4.00000i | 0.242536i | ||||||||
\(273\) | 2.59808 | − | 10.5000i | 0.157243 | − | 0.635489i | ||||
\(274\) | −6.53590 | −0.394848 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.73205 | + | 3.00000i | 0.104257 | + | 0.180579i | ||||
\(277\) | 16.9641 | + | 9.79423i | 1.01927 | + | 0.588478i | 0.913894 | − | 0.405954i | \(-0.133061\pi\) |
0.105380 | + | 0.994432i | \(0.466394\pi\) | |||||||
\(278\) | −21.7846 | −1.30655 | ||||||||
\(279\) | −7.73205 | − | 4.46410i | −0.462906 | − | 0.267259i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.92820i | 0.413302i | 0.978415 | + | 0.206651i | \(0.0662565\pi\) | ||||
−0.978415 | + | 0.206651i | \(0.933744\pi\) | |||||||
\(282\) | 0.401924 | + | 0.232051i | 0.0239342 | + | 0.0138184i | ||||
\(283\) | −12.4641 | + | 7.19615i | −0.740914 | + | 0.427767i | −0.822402 | − | 0.568907i | \(-0.807366\pi\) |
0.0814876 | + | 0.996674i | \(0.474033\pi\) | |||||||
\(284\) | 0.803848 | − | 0.464102i | 0.0476996 | − | 0.0275394i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.69615 | + | 9.33013i | 0.573346 | + | 0.551702i | ||||
\(287\) | − | 12.0000i | − | 0.708338i | ||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.3923i | 0.726450i | ||||||||
\(292\) | −3.46410 | + | 6.00000i | −0.202721 | + | 0.351123i | ||||
\(293\) | 9.62436 | − | 16.6699i | 0.562261 | − | 0.973864i | −0.435038 | − | 0.900412i | \(-0.643265\pi\) |
0.997299 | − | 0.0734522i | \(-0.0234016\pi\) | |||||||
\(294\) | 2.00000i | 0.116642i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.96410 | − | 6.86603i | −0.230409 | − | 0.399080i | ||||
\(297\) | 1.86603 | + | 3.23205i | 0.108278 | + | 0.187543i | ||||
\(298\) | 22.7846i | 1.31988i | ||||||||
\(299\) | 12.0000 | − | 3.46410i | 0.693978 | − | 0.200334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.5885 | − | 9.00000i | 0.898504 | − | 0.518751i | ||||
\(302\) | −16.2679 | + | 9.39230i | −0.936115 | + | 0.540466i | ||||
\(303\) | 7.26795 | + | 4.19615i | 0.417533 | + | 0.241063i | ||||
\(304\) | − | 2.26795i | − | 0.130076i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.46410 | + | 2.00000i | 0.198030 | + | 0.114332i | ||||
\(307\) | 20.2487 | 1.15565 | 0.577827 | − | 0.816159i | \(-0.303901\pi\) | ||||
0.577827 | + | 0.816159i | \(0.303901\pi\) | |||||||
\(308\) | −9.69615 | − | 5.59808i | −0.552490 | − | 0.318980i | ||||
\(309\) | −9.79423 | − | 16.9641i | −0.557174 | − | 0.965054i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.07180 | 0.287595 | 0.143798 | − | 0.989607i | \(-0.454069\pi\) | ||||
0.143798 | + | 0.989607i | \(0.454069\pi\) | |||||||
\(312\) | 3.46410 | − | 1.00000i | 0.196116 | − | 0.0566139i | ||||
\(313\) | − | 1.32051i | − | 0.0746395i | −0.999303 | − | 0.0373198i | \(-0.988118\pi\) | ||
0.999303 | − | 0.0373198i | \(-0.0118820\pi\) | |||||||
\(314\) | 9.35641 | − | 5.40192i | 0.528013 | − | 0.304848i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.46410 | − | 14.6603i | 0.476143 | − | 0.824704i | ||||
\(317\) | 23.5359 | 1.32191 | 0.660954 | − | 0.750427i | \(-0.270152\pi\) | ||||
0.660954 | + | 0.750427i | \(0.270152\pi\) | |||||||
\(318\) | 1.86603 | − | 3.23205i | 0.104642 | − | 0.181244i | ||||
\(319\) | 17.6603 | + | 10.1962i | 0.988784 | + | 0.570875i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.464102 | − | 0.803848i | 0.0259036 | − | 0.0448664i | ||||
\(322\) | −9.00000 | + | 5.19615i | −0.501550 | + | 0.289570i | ||||
\(323\) | −4.53590 | − | 7.85641i | −0.252384 | − | 0.437142i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.9282 | 0.605257 | ||||||||
\(327\) | −5.19615 | − | 9.00000i | −0.287348 | − | 0.497701i | ||||
\(328\) | 3.46410 | − | 2.00000i | 0.191273 | − | 0.110432i | ||||
\(329\) | −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 | \(0.610455\pi\) | |||||||
\(332\) | −1.26795 | + | 2.19615i | −0.0695878 | + | 0.120530i | ||||
\(333\) | −7.92820 | −0.434463 | ||||||||
\(334\) | −3.23205 | + | 5.59808i | −0.176850 | + | 0.306313i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.59808 | + | 1.50000i | −0.141737 | + | 0.0818317i | ||||
\(337\) | − | 5.60770i | − | 0.305471i | −0.988267 | − | 0.152735i | \(-0.951192\pi\) | ||
0.988267 | − | 0.152735i | \(-0.0488082\pi\) | |||||||
\(338\) | −0.500000 | − | 12.9904i | −0.0271964 | − | 0.706584i | ||||
\(339\) | −12.0000 | −0.651751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.6603 | + | 28.8564i | 0.902203 | + | 1.56266i | ||||
\(342\) | −1.96410 | − | 1.13397i | −0.106206 | − | 0.0613183i | ||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 5.19615 | + | 3.00000i | 0.280158 | + | 0.161749i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 22.1244i | − | 1.18941i | ||||||
\(347\) | 14.1962 | + | 8.19615i | 0.762089 | + | 0.439993i | 0.830045 | − | 0.557696i | \(-0.188314\pi\) |
−0.0679560 | + | 0.997688i | \(0.521648\pi\) | |||||||
\(348\) | 4.73205 | − | 2.73205i | 0.253665 | − | 0.146453i | ||||
\(349\) | −15.1244 | + | 8.73205i | −0.809588 | + | 0.467416i | −0.846813 | − | 0.531891i | \(-0.821482\pi\) |
0.0372247 | + | 0.999307i | \(0.488148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.866025 | − | 3.50000i | 0.0462250 | − | 0.186816i | ||||
\(352\) | − | 3.73205i | − | 0.198919i | ||||||
\(353\) | 14.1962 | + | 24.5885i | 0.755585 | + | 1.30871i | 0.945083 | + | 0.326830i | \(0.105981\pi\) |
−0.189498 | + | 0.981881i | \(0.560686\pi\) | |||||||
\(354\) | 2.26795 | + | 3.92820i | 0.120540 | + | 0.208782i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.1244i | 0.536590i | ||||||||
\(357\) | −6.00000 | + | 10.3923i | −0.317554 | + | 0.550019i | ||||
\(358\) | 11.4641 | − | 19.8564i | 0.605897 | − | 1.04944i | ||||
\(359\) | − | 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 | ||||
\(362\) | −1.53590 | − | 2.66025i | −0.0807250 | − | 0.139820i | ||||
\(363\) | − | 2.92820i | − | 0.153691i | ||||||
\(364\) | 3.00000 | + | 10.3923i | 0.157243 | + | 0.544705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.46410 | + | 3.73205i | −0.337884 | + | 0.195077i | ||||
\(367\) | −11.5359 | + | 6.66025i | −0.602169 | + | 0.347662i | −0.769894 | − | 0.638171i | \(-0.779691\pi\) |
0.167725 | + | 0.985834i | \(0.446358\pi\) | |||||||
\(368\) | −3.00000 | − | 1.73205i | −0.156386 | − | 0.0902894i | ||||
\(369\) | − | 4.00000i | − | 0.208232i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.69615 | + | 5.59808i | 0.503399 | + | 0.290638i | ||||
\(372\) | 8.92820 | 0.462906 | ||||||||
\(373\) | 19.8564 | + | 11.4641i | 1.02813 | + | 0.593589i | 0.916447 | − | 0.400156i | \(-0.131044\pi\) |
0.111679 | + | 0.993744i | \(0.464377\pi\) | |||||||
\(374\) | −7.46410 | − | 12.9282i | −0.385960 | − | 0.668501i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.464102 | −0.0239342 | ||||||||
\(377\) | −5.46410 | − | 18.9282i | −0.281416 | − | 0.974852i | ||||
\(378\) | 3.00000i | 0.154303i | ||||||||
\(379\) | −5.42820 | + | 3.13397i | −0.278828 | + | 0.160981i | −0.632893 | − | 0.774239i | \(-0.718133\pi\) |
0.354065 | + | 0.935221i | \(0.384799\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.33013 | − | 4.03590i | 0.119376 | − | 0.206765i | ||||
\(382\) | 17.3205 | 0.886194 | ||||||||
\(383\) | 18.3923 | − | 31.8564i | 0.939803 | − | 1.62779i | 0.173966 | − | 0.984752i | \(-0.444342\pi\) |
0.765837 | − | 0.643035i | \(-0.222325\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.92820 | − | 15.4641i | 0.454434 | − | 0.787102i | ||||
\(387\) | 5.19615 | − | 3.00000i | 0.264135 | − | 0.152499i | ||||
\(388\) | −6.19615 | − | 10.7321i | −0.314562 | − | 0.544837i | ||||
\(389\) | 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 | ||||||||
\(392\) | −1.00000 | − | 1.73205i | −0.0505076 | − | 0.0874818i | ||||
\(393\) | −17.5981 | + | 10.1603i | −0.887706 | + | 0.512517i | ||||
\(394\) | −4.69615 | + | 8.13397i | −0.236589 | + | 0.409784i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.23205 | − | 1.86603i | −0.162417 | − | 0.0937713i | ||||
\(397\) | 3.96410 | − | 6.86603i | 0.198953 | − | 0.344596i | −0.749237 | − | 0.662303i | \(-0.769579\pi\) |
0.948189 | + | 0.317707i | \(0.102913\pi\) | |||||||
\(398\) | 11.0718 | 0.554979 | ||||||||
\(399\) | 3.40192 | − | 5.89230i | 0.170309 | − | 0.294984i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.83975 | + | 1.06218i | −0.0918725 | + | 0.0530426i | −0.545232 | − | 0.838285i | \(-0.683559\pi\) |
0.453360 | + | 0.891328i | \(0.350225\pi\) | |||||||
\(402\) | − | 5.46410i | − | 0.272525i | ||||||
\(403\) | 7.73205 | − | 31.2487i | 0.385161 | − | 1.55661i | ||||
\(404\) | −8.39230 | −0.417533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.19615 | + | 14.1962i | 0.406768 | + | 0.704543i | ||||
\(407\) | 25.6244 | + | 14.7942i | 1.27015 | + | 0.733323i | ||||
\(408\) | −4.00000 | −0.198030 | ||||||||
\(409\) | −0.820508 | − | 0.473721i | −0.0405715 | − | 0.0234240i | 0.479577 | − | 0.877500i | \(-0.340790\pi\) |
−0.520149 | + | 0.854076i | \(0.674123\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.53590i | − | 0.322392i | ||||||
\(412\) | 16.9641 | + | 9.79423i | 0.835761 | + | 0.482527i | ||||
\(413\) | −11.7846 | + | 6.80385i | −0.579883 | + | 0.334795i | ||||
\(414\) | −3.00000 | + | 1.73205i | −0.147442 | + | 0.0851257i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.50000 | + | 2.59808i | −0.122573 | + | 0.127381i | ||||
\(417\) | − | 21.7846i | − | 1.06680i | ||||||
\(418\) | 4.23205 | + | 7.33013i | 0.206996 | + | 0.358528i | ||||
\(419\) | −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 | \(0.954418\pi\) | |||||||
\(422\) | 10.9641 | − | 18.9904i | 0.533724 | − | 0.924437i | ||||
\(423\) | −0.232051 | + | 0.401924i | −0.0112827 | + | 0.0195422i | ||||
\(424\) | 3.73205i | 0.181244i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.464102 | + | 0.803848i | 0.0224858 | + | 0.0389465i | ||||
\(427\) | −11.1962 | − | 19.3923i | −0.541820 | − | 0.938459i | ||||
\(428\) | 0.928203i | 0.0448664i | ||||||||
\(429\) | −9.33013 | + | 9.69615i | −0.450463 | + | 0.468135i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.0000 | + | 6.92820i | −0.578020 | + | 0.333720i | −0.760346 | − | 0.649518i | \(-0.774971\pi\) |
0.182326 | + | 0.983238i | \(0.441637\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 28.3923 | + | 16.3923i | 1.36445 | + | 0.787764i | 0.990212 | − | 0.139570i | \(-0.0445720\pi\) |
0.374235 | + | 0.927334i | \(0.377905\pi\) | |||||||
\(434\) | 26.7846i | 1.28570i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.00000 | + | 5.19615i | 0.431022 | + | 0.248851i | ||||
\(437\) | 7.85641 | 0.375823 | ||||||||
\(438\) | −6.00000 | − | 3.46410i | −0.286691 | − | 0.165521i | ||||
\(439\) | 10.6603 | + | 18.4641i | 0.508786 | + | 0.881243i | 0.999948 | + | 0.0101753i | \(0.00323895\pi\) |
−0.491162 | + | 0.871068i | \(0.663428\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | −3.46410 | + | 14.0000i | −0.164771 | + | 0.665912i | ||||
\(443\) | − | 7.85641i | − | 0.373269i | −0.982429 | − | 0.186635i | \(-0.940242\pi\) | ||
0.982429 | − | 0.186635i | \(-0.0597580\pi\) | |||||||
\(444\) | 6.86603 | − | 3.96410i | 0.325847 | − | 0.188128i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.42820 | − | 7.66987i | 0.209682 | − | 0.363179i | ||||
\(447\) | −22.7846 | −1.07768 | ||||||||
\(448\) | 1.50000 | − | 2.59808i | 0.0708683 | − | 0.122748i | ||||
\(449\) | 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 | ||||
\(452\) | 10.3923 | − | 6.00000i | 0.488813 | − | 0.282216i | ||||
\(453\) | −9.39230 | − | 16.2679i | −0.441289 | − | 0.764335i | ||||
\(454\) | −13.4641 | −0.631902 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.26795 | 0.106206 | ||||||||
\(457\) | 0.267949 | + | 0.464102i | 0.0125341 | + | 0.0217098i | 0.872224 | − | 0.489106i | \(-0.162677\pi\) |
−0.859690 | + | 0.510816i | \(0.829343\pi\) | |||||||
\(458\) | −9.92820 | + | 5.73205i | −0.463914 | + | 0.267841i | ||||
\(459\) | −2.00000 | + | 3.46410i | −0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.0526 | + | 16.1962i | 1.30654 | + | 0.754330i | 0.981517 | − | 0.191377i | \(-0.0612952\pi\) |
0.325021 | + | 0.945707i | \(0.394629\pi\) | |||||||
\(462\) | 5.59808 | − | 9.69615i | 0.260446 | − | 0.451106i | ||||
\(463\) | −0.784610 | −0.0364639 | −0.0182320 | − | 0.999834i | \(-0.505804\pi\) | ||||
−0.0182320 | + | 0.999834i | \(0.505804\pi\) | |||||||
\(464\) | −2.73205 | + | 4.73205i | −0.126832 | + | 0.219680i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.5885 | + | 9.00000i | −0.722121 | + | 0.416917i | ||||
\(467\) | 3.60770i | 0.166944i | 0.996510 | + | 0.0834721i | \(0.0266010\pi\) | ||||
−0.996510 | + | 0.0834721i | \(0.973399\pi\) | |||||||
\(468\) | 1.00000 | + | 3.46410i | 0.0462250 | + | 0.160128i | ||||
\(469\) | 16.3923 | 0.756926 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.40192 | + | 9.35641i | 0.248908 | + | 0.431120i | ||||
\(472\) | −3.92820 | − | 2.26795i | −0.180810 | − | 0.104391i | ||||
\(473\) | −22.3923 | −1.02960 | ||||||||
\(474\) | 14.6603 | + | 8.46410i | 0.673368 | + | 0.388769i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 12.0000i | − | 0.550019i | ||||||
\(477\) | 3.23205 | + | 1.86603i | 0.147985 | + | 0.0854394i | ||||
\(478\) | −3.00000 | + | 1.73205i | −0.137217 | + | 0.0792222i | ||||
\(479\) | 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 | ||||
\(482\) | − | 14.8038i | − | 0.674297i | ||||||
\(483\) | −5.19615 | − | 9.00000i | −0.236433 | − | 0.409514i | ||||
\(484\) | 1.46410 | + | 2.53590i | 0.0665501 | + | 0.115268i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 10.5000 | − | 18.1865i | 0.475800 | − | 0.824110i | −0.523815 | − | 0.851832i | \(-0.675492\pi\) |
0.999616 | + | 0.0277214i | \(0.00882512\pi\) | |||||||
\(488\) | 3.73205 | − | 6.46410i | 0.168942 | − | 0.292616i | ||||
\(489\) | 10.9282i | 0.494190i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.69615 | + | 13.3301i | 0.347322 | + | 0.601580i | 0.985773 | − | 0.168083i | \(-0.0537576\pi\) |
−0.638450 | + | 0.769663i | \(0.720424\pi\) | |||||||
\(492\) | 2.00000 | + | 3.46410i | 0.0901670 | + | 0.156174i | ||||
\(493\) | 21.8564i | 0.984363i | ||||||||
\(494\) | 1.96410 | − | 7.93782i | 0.0883691 | − | 0.357140i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.73205 | + | 4.46410i | −0.347179 | + | 0.200444i | ||||
\(497\) | −2.41154 | + | 1.39230i | −0.108172 | + | 0.0624534i | ||||
\(498\) | −2.19615 | − | 1.26795i | −0.0984119 | − | 0.0568182i | ||||
\(499\) | − | 1.32051i | − | 0.0591141i | −0.999563 | − | 0.0295570i | \(-0.990590\pi\) | ||
0.999563 | − | 0.0295570i | \(-0.00940967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.59808 | − | 3.23205i | −0.250104 | − | 0.144397i | ||||
\(502\) | 26.4641 | 1.18115 | ||||||||
\(503\) | 0.232051 | + | 0.133975i | 0.0103466 | + | 0.00597363i | 0.505164 | − | 0.863023i | \(-0.331432\pi\) |
−0.494818 | + | 0.868997i | \(0.664765\pi\) | |||||||
\(504\) | −1.50000 | − | 2.59808i | −0.0668153 | − | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12.9282 | 0.574729 | ||||||||
\(507\) | 12.9904 | − | 0.500000i | 0.576923 | − | 0.0222058i | ||||
\(508\) | 4.66025i | 0.206765i | ||||||||
\(509\) | −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 | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.13397 | − | 1.96410i | 0.0500662 | − | 0.0867172i | ||||
\(514\) | −18.5885 | − | 10.7321i | −0.819902 | − | 0.473370i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.00000 | + | 5.19615i | −0.132068 | + | 0.228748i | ||||
\(517\) | 1.50000 | − | 0.866025i | 0.0659699 | − | 0.0380878i | ||||
\(518\) | 11.8923 | + | 20.5981i | 0.522518 | + | 0.905028i | ||||
\(519\) | 22.1244 | 0.971151 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.3923 | −1.20008 | −0.600039 | − | 0.799970i | \(-0.704848\pi\) | ||||
−0.600039 | + | 0.799970i | \(0.704848\pi\) | |||||||
\(522\) | 2.73205 | + | 4.73205i | 0.119579 | + | 0.207116i | ||||
\(523\) | −11.8756 | + | 6.85641i | −0.519286 | + | 0.299810i | −0.736642 | − | 0.676283i | \(-0.763590\pi\) |
0.217357 | + | 0.976092i | \(0.430257\pi\) | |||||||
\(524\) | 10.1603 | − | 17.5981i | 0.443853 | − | 0.768776i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.7679 | + | 10.2583i | 0.774719 | + | 0.447284i | ||||
\(527\) | −17.8564 | + | 30.9282i | −0.777837 | + | 1.34725i | ||||
\(528\) | 3.73205 | 0.162417 | ||||||||
\(529\) | −5.50000 | + | 9.52628i | −0.239130 | + | 0.414186i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.92820 | + | 2.26795i | −0.170470 | + | 0.0984206i | ||||
\(532\) | 6.80385i | 0.294984i | ||||||||
\(533\) | 13.8564 | − | 4.00000i | 0.600188 | − | 0.173259i | ||||
\(534\) | −10.1244 | −0.438124 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.73205 | + | 4.73205i | 0.118007 | + | 0.204393i | ||||
\(537\) | 19.8564 | + | 11.4641i | 0.856867 | + | 0.494713i | ||||
\(538\) | 30.9282 | 1.33341 | ||||||||
\(539\) | 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 | \(0.804698\pi\) | |||||||
\(542\) | 3.12436 | + | 1.80385i | 0.134203 | + | 0.0774819i | ||||
\(543\) | 2.66025 | − | 1.53590i | 0.114162 | − | 0.0659117i | ||||
\(544\) | 3.46410 | − | 2.00000i | 0.148522 | − | 0.0857493i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.3923 | + | 3.00000i | −0.444750 | + | 0.128388i | ||||
\(547\) | 29.3205i | 1.25365i | 0.779158 | + | 0.626827i | \(0.215647\pi\) | ||||
−0.779158 | + | 0.626827i | \(0.784353\pi\) | |||||||
\(548\) | 3.26795 | + | 5.66025i | 0.139600 | + | 0.241794i | ||||
\(549\) | −3.73205 | − | 6.46410i | −0.159280 | − | 0.275881i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 12.3923i | − | 0.527930i | ||||||
\(552\) | 1.73205 | − | 3.00000i | 0.0737210 | − | 0.127688i | ||||
\(553\) | −25.3923 | + | 43.9808i | −1.07979 | + | 1.87025i | ||||
\(554\) | − | 19.5885i | − | 0.832234i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.8923 | + | 18.8660i | 0.461937 | + | 0.800098i | ||||
\(557\) | 21.6962 | + | 37.5788i | 0.919295 | + | 1.59227i | 0.800488 | + | 0.599349i | \(0.204574\pi\) |
0.118808 | + | 0.992917i | \(0.462093\pi\) | |||||||
\(558\) | 8.92820i | 0.377961i | ||||||||
\(559\) | 15.5885 | + | 15.0000i | 0.659321 | + | 0.634432i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.9282 | − | 7.46410i | 0.545829 | − | 0.315135i | ||||
\(562\) | 6.00000 | − | 3.46410i | 0.253095 | − | 0.146124i | ||||
\(563\) | 16.7321 | + | 9.66025i | 0.705172 | + | 0.407131i | 0.809271 | − | 0.587436i | \(-0.199863\pi\) |
−0.104099 | + | 0.994567i | \(0.533196\pi\) | |||||||
\(564\) | − | 0.464102i | − | 0.0195422i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12.4641 | + | 7.19615i | 0.523905 | + | 0.302477i | ||||
\(567\) | −3.00000 | −0.125988 | ||||||||
\(568\) | −0.803848 | − | 0.464102i | −0.0337287 | − | 0.0194733i | ||||
\(569\) | 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 | \(0.614740\pi\) | |||||||
\(572\) | 3.23205 | − | 13.0622i | 0.135139 | − | 0.546157i | ||||
\(573\) | 17.3205i | 0.723575i | ||||||||
\(574\) | −10.3923 | + | 6.00000i | −0.433766 | + | 0.250435i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 25.3205 | 1.05411 | 0.527053 | − | 0.849832i | \(-0.323297\pi\) | ||||
0.527053 | + | 0.849832i | \(0.323297\pi\) | |||||||
\(578\) | −0.500000 | + | 0.866025i | −0.0207973 | + | 0.0360219i | ||||
\(579\) | 15.4641 | + | 8.92820i | 0.642666 | + | 0.371043i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.80385 | − | 6.58846i | 0.157810 | − | 0.273335i | ||||
\(582\) | 10.7321 | − | 6.19615i | 0.444858 | − | 0.256839i | ||||
\(583\) | −6.96410 | − | 12.0622i | −0.288424 | − | 0.499564i | ||||
\(584\) | 6.92820 | 0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.2487 | −0.795157 | ||||||||
\(587\) | −2.46410 | − | 4.26795i | −0.101704 | − | 0.176157i | 0.810683 | − | 0.585486i | \(-0.199096\pi\) |
−0.912387 | + | 0.409329i | \(0.865763\pi\) | |||||||
\(588\) | 1.73205 | − | 1.00000i | 0.0714286 | − | 0.0412393i | ||||
\(589\) | 10.1244 | − | 17.5359i | 0.417167 | − | 0.722554i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.13397 | − | 4.69615i | −0.334587 | − | 0.193174i | ||||
\(592\) | −3.96410 | + | 6.86603i | −0.162924 | + | 0.282192i | ||||
\(593\) | 3.21539 | 0.132040 | 0.0660201 | − | 0.997818i | \(-0.478970\pi\) | ||||
0.0660201 | + | 0.997818i | \(0.478970\pi\) | |||||||
\(594\) | 1.86603 | − | 3.23205i | 0.0765639 | − | 0.132613i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.7321 | − | 11.3923i | 0.808256 | − | 0.466647i | ||||
\(597\) | 11.0718i | 0.453138i | ||||||||
\(598\) | −9.00000 | − | 8.66025i | −0.368037 | − | 0.354144i | ||||
\(599\) | −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 | \(0.665184\pi\) | |||||||
\(602\) | −15.5885 | − | 9.00000i | −0.635338 | − | 0.366813i | ||||
\(603\) | 5.46410 | 0.222515 | ||||||||
\(604\) | 16.2679 | + | 9.39230i | 0.661933 | + | 0.382167i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 8.39230i | − | 0.340914i | ||||||
\(607\) | −32.4282 | − | 18.7224i | −1.31622 | − | 0.759920i | −0.333102 | − | 0.942891i | \(-0.608095\pi\) |
−0.983118 | + | 0.182971i | \(0.941429\pi\) | |||||||
\(608\) | −1.96410 | + | 1.13397i | −0.0796548 | + | 0.0459887i | ||||
\(609\) | −14.1962 | + | 8.19615i | −0.575257 | + | 0.332125i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.62436 | − | 0.401924i | −0.0657144 | − | 0.0162601i | ||||
\(612\) | − | 4.00000i | − | 0.161690i | ||||||
\(613\) | 22.5000 | + | 38.9711i | 0.908766 | + | 1.57403i | 0.815780 | + | 0.578362i | \(0.196308\pi\) |
0.0929864 | + | 0.995667i | \(0.470359\pi\) | |||||||
\(614\) | −10.1244 | − | 17.5359i | −0.408586 | − | 0.707691i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.1962i | 0.451106i | ||||||||
\(617\) | −14.2679 | + | 24.7128i | −0.574406 | + | 0.994900i | 0.421700 | + | 0.906735i | \(0.361434\pi\) |
−0.996106 | + | 0.0881649i | \(0.971900\pi\) | |||||||
\(618\) | −9.79423 | + | 16.9641i | −0.393982 | + | 0.682396i | ||||
\(619\) | − | 42.5167i | − | 1.70889i | −0.519543 | − | 0.854444i | \(-0.673898\pi\) | ||
0.519543 | − | 0.854444i | \(-0.326102\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.73205 | − | 3.00000i | −0.0695048 | − | 0.120386i | ||||
\(622\) | −2.53590 | − | 4.39230i | −0.101680 | − | 0.176115i | ||||
\(623\) | − | 30.3731i | − | 1.21687i | ||||||
\(624\) | −2.59808 | − | 2.50000i | −0.104006 | − | 0.100080i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.14359 | + | 0.660254i | −0.0457072 | + | 0.0263891i | ||||
\(627\) | −7.33013 | + | 4.23205i | −0.292737 | + | 0.169012i | ||||
\(628\) | −9.35641 | − | 5.40192i | −0.373361 | − | 0.215560i | ||||
\(629\) | 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 | \(0.615763\pi\) | |||||||
\(632\) | −16.9282 | −0.673368 | ||||||||
\(633\) | 18.9904 | + | 10.9641i | 0.754800 | + | 0.435784i | ||||
\(634\) | −11.7679 | − | 20.3827i | −0.467365 | − | 0.809500i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.73205 | −0.147985 | ||||||||
\(637\) | −2.00000 | − | 6.92820i | −0.0792429 | − | 0.274505i | ||||
\(638\) | − | 20.3923i | − | 0.807339i | ||||||
\(639\) | −0.803848 | + | 0.464102i | −0.0317997 | + | 0.0183596i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.76795 | + | 6.52628i | −0.148825 | + | 0.257773i | −0.930793 | − | 0.365546i | \(-0.880882\pi\) |
0.781968 | + | 0.623318i | \(0.214216\pi\) | |||||||
\(642\) | −0.928203 | −0.0366333 | ||||||||
\(643\) | 14.3923 | − | 24.9282i | 0.567577 | − | 0.983072i | −0.429228 | − | 0.903196i | \(-0.641214\pi\) |
0.996805 | − | 0.0798761i | \(-0.0254525\pi\) | |||||||
\(644\) | 9.00000 | + | 5.19615i | 0.354650 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.53590 | + | 7.85641i | −0.178463 | + | 0.309106i | ||||
\(647\) | −27.9449 | + | 16.1340i | −1.09863 | + | 0.634292i | −0.935860 | − | 0.352373i | \(-0.885375\pi\) |
−0.162766 | + | 0.986665i | \(0.552042\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 16.9282 | 0.664490 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −26.7846 | −1.04977 | ||||||||
\(652\) | −5.46410 | − | 9.46410i | −0.213991 | − | 0.370643i | ||||
\(653\) | −25.6244 | + | 14.7942i | −1.00276 | + | 0.578943i | −0.909063 | − | 0.416658i | \(-0.863201\pi\) |
−0.0936952 | + | 0.995601i | \(0.529868\pi\) | |||||||
\(654\) | −5.19615 | + | 9.00000i | −0.203186 | + | 0.351928i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.46410 | − | 2.00000i | −0.135250 | − | 0.0780869i | ||||
\(657\) | 3.46410 | − | 6.00000i | 0.135147 | − | 0.234082i | ||||
\(658\) | 1.39230 | 0.0542777 | ||||||||
\(659\) | 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 | \(0.0248265\pi\) | |||||||
\(662\) | − | 6.39230i | − | 0.248444i | ||||||
\(663\) | −14.0000 | − | 3.46410i | −0.543715 | − | 0.134535i | ||||
\(664\) | 2.53590 | 0.0984119 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.96410 | + | 6.86603i | 0.153606 | + | 0.266053i | ||||
\(667\) | −16.3923 | − | 9.46410i | −0.634713 | − | 0.366451i | ||||
\(668\) | 6.46410 | 0.250104 | ||||||||
\(669\) | 7.66987 | + | 4.42820i | 0.296534 | + | 0.171204i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.8564i | 1.07538i | ||||||||
\(672\) | 2.59808 | + | 1.50000i | 0.100223 | + | 0.0578638i | ||||
\(673\) | −21.4641 | + | 12.3923i | −0.827380 | + | 0.477688i | −0.852955 | − | 0.521985i | \(-0.825192\pi\) |
0.0255746 | + | 0.999673i | \(0.491858\pi\) | |||||||
\(674\) | −4.85641 | + | 2.80385i | −0.187062 | + | 0.108000i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | − | 2.92820i | − | 0.112540i | −0.998416 | − | 0.0562700i | \(-0.982079\pi\) | ||
0.998416 | − | 0.0562700i | \(-0.0179208\pi\) | |||||||
\(678\) | 6.00000 | + | 10.3923i | 0.230429 | + | 0.399114i | ||||
\(679\) | 18.5885 | + | 32.1962i | 0.713360 | + | 1.23557i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 13.4641i | − | 0.515945i | ||||||
\(682\) | 16.6603 | − | 28.8564i | 0.637954 | − | 1.10497i | ||||
\(683\) | −3.33975 | + | 5.78461i | −0.127792 | + | 0.221342i | −0.922821 | − | 0.385230i | \(-0.874122\pi\) |
0.795029 | + | 0.606571i | \(0.207456\pi\) | |||||||
\(684\) | 2.26795i | 0.0867172i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.50000 | − | 12.9904i | −0.286351 | − | 0.495975i | ||||
\(687\) | −5.73205 | − | 9.92820i | −0.218691 | − | 0.378785i | ||||
\(688\) | − | 6.00000i | − | 0.228748i | ||||||
\(689\) | −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 | \(0.188850\pi\) | |||||||
\(692\) | −19.1603 | + | 11.0622i | −0.728364 | + | 0.420521i | ||||
\(693\) | 9.69615 | + | 5.59808i | 0.368326 | + | 0.212653i | ||||
\(694\) | − | 16.3923i | − | 0.622243i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.73205 | − | 2.73205i | −0.179368 | − | 0.103558i | ||||
\(697\) | −16.0000 | −0.606043 | ||||||||
\(698\) | 15.1244 | + | 8.73205i | 0.572465 | + | 0.330513i | ||||
\(699\) | −9.00000 | − | 15.5885i | −0.340411 | − | 0.589610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.3923 | 0.619129 | 0.309564 | − | 0.950878i | \(-0.399817\pi\) | ||||
0.309564 | + | 0.950878i | \(0.399817\pi\) | |||||||
\(702\) | −3.46410 | + | 1.00000i | −0.130744 | + | 0.0377426i | ||||
\(703\) | − | 17.9808i | − | 0.678157i | ||||||
\(704\) | −3.23205 | + | 1.86603i | −0.121812 | + | 0.0703285i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.1962 | − | 24.5885i | 0.534279 | − | 0.925399i | ||||
\(707\) | 25.1769 | 0.946875 | ||||||||
\(708\) | 2.26795 | − | 3.92820i | 0.0852348 | − | 0.147631i | ||||
\(709\) | 6.33975 | + | 3.66025i | 0.238094 | + | 0.137464i | 0.614300 | − | 0.789072i | \(-0.289438\pi\) |
−0.376206 | + | 0.926536i | \(0.622772\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.46410 | + | 14.6603i | −0.317429 | + | 0.549802i | ||||
\(712\) | 8.76795 | − | 5.06218i | 0.328593 | − | 0.189713i | ||||
\(713\) | −15.4641 | − | 26.7846i | −0.579135 | − | 1.00309i | ||||
\(714\) | 12.0000 | 0.449089 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.9282 | −0.856867 | ||||||||
\(717\) | −1.73205 | − | 3.00000i | −0.0646846 | − | 0.112037i | ||||
\(718\) | −11.1962 | + | 6.46410i | −0.417837 | + | 0.241238i | ||||
\(719\) | 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 | ||||
\(722\) | −6.92820 | + | 12.0000i | −0.257841 | + | 0.446594i | ||||
\(723\) | 14.8038 | 0.550561 | ||||||||
\(724\) | −1.53590 | + | 2.66025i | −0.0570812 | + | 0.0988676i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.53590 | + | 1.46410i | −0.0941160 | + | 0.0543379i | ||||
\(727\) | 12.6603i | 0.469543i | 0.972051 | + | 0.234771i | \(0.0754342\pi\) | ||||
−0.972051 | + | 0.234771i | \(0.924566\pi\) | |||||||
\(728\) | 7.50000 | − | 7.79423i | 0.277968 | − | 0.288873i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | − | 20.7846i | −0.443836 | − | 0.768747i | ||||
\(732\) | 6.46410 | + | 3.73205i | 0.238920 | + | 0.137941i | ||||
\(733\) | 6.85641 | 0.253247 | 0.126624 | − | 0.991951i | \(-0.459586\pi\) | ||||
0.126624 | + | 0.991951i | \(0.459586\pi\) | |||||||
\(734\) | 11.5359 | + | 6.66025i | 0.425798 | + | 0.245834i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.46410i | 0.127688i | ||||||||
\(737\) | −17.6603 | − | 10.1962i | −0.650524 | − | 0.375580i | ||||
\(738\) | −3.46410 | + | 2.00000i | −0.127515 | + | 0.0736210i | ||||
\(739\) | −37.9641 | + | 21.9186i | −1.39653 | + | 0.806288i | −0.994028 | − | 0.109130i | \(-0.965194\pi\) |
−0.402505 | + | 0.915418i | \(0.631860\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.93782 | + | 1.96410i | 0.291603 | + | 0.0721531i | ||||
\(742\) | − | 11.1962i | − | 0.411024i | ||||||
\(743\) | 1.46410 | + | 2.53590i | 0.0537127 | + | 0.0930331i | 0.891632 | − | 0.452762i | \(-0.149561\pi\) |
−0.837919 | + | 0.545795i | \(0.816228\pi\) | |||||||
\(744\) | −4.46410 | − | 7.73205i | −0.163662 | − | 0.283471i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 22.9282i | − | 0.839461i | ||||||
\(747\) | 1.26795 | − | 2.19615i | 0.0463918 | − | 0.0803530i | ||||
\(748\) | −7.46410 | + | 12.9282i | −0.272915 | + | 0.472702i | ||||
\(749\) | − | 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 | \(-0.437232\pi\) | |||||||
\(752\) | 0.232051 | + | 0.401924i | 0.00846202 | + | 0.0146567i | ||||
\(753\) | 26.4641i | 0.964405i | ||||||||
\(754\) | −13.6603 | + | 14.1962i | −0.497477 | + | 0.516993i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.59808 | − | 1.50000i | 0.0944911 | − | 0.0545545i | ||||
\(757\) | 15.8205 | − | 9.13397i | 0.575006 | − | 0.331980i | −0.184140 | − | 0.982900i | \(-0.558950\pi\) |
0.759146 | + | 0.650920i | \(0.225617\pi\) | |||||||
\(758\) | 5.42820 | + | 3.13397i | 0.197161 | + | 0.113831i | ||||
\(759\) | 12.9282i | 0.469264i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.0885 | + | 21.9904i | 1.38071 | + | 0.797151i | 0.992243 | − | 0.124314i | \(-0.0396730\pi\) |
0.388463 | + | 0.921465i | \(0.373006\pi\) | |||||||
\(762\) | −4.66025 | −0.168823 | ||||||||
\(763\) | −27.0000 | − | 15.5885i | −0.977466 | − | 0.564340i | ||||
\(764\) | −8.66025 | − | 15.0000i | −0.313317 | − | 0.542681i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36.7846 | −1.32908 | ||||||||
\(767\) | −11.7846 | − | 11.3397i | −0.425518 | − | 0.409454i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −34.3923 | + | 19.8564i | −1.24022 | + | 0.716040i | −0.969139 | − | 0.246517i | \(-0.920714\pi\) |
−0.271080 | + | 0.962557i | \(0.587381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.7321 | − | 18.5885i | 0.386505 | − | 0.669447i | ||||
\(772\) | −17.8564 | −0.642666 | ||||||||
\(773\) | 26.6962 | − | 46.2391i | 0.960194 | − | 1.66310i | 0.238186 | − | 0.971220i | \(-0.423447\pi\) |
0.722008 | − | 0.691885i | \(-0.243220\pi\) | |||||||
\(774\) | −5.19615 | − | 3.00000i | −0.186772 | − | 0.107833i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.19615 | + | 10.7321i | −0.222429 | + | 0.385258i | ||||
\(777\) | −20.5981 | + | 11.8923i | −0.738952 | + | 0.426634i | ||||
\(778\) | −4.92820 | − | 8.53590i | −0.176685 | − | 0.306027i | ||||
\(779\) | 9.07180 | 0.325031 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.46410 | 0.123955 | ||||||||
\(782\) | 6.92820 | + | 12.0000i | 0.247752 | + | 0.429119i | ||||
\(783\) | −4.73205 | + | 2.73205i | −0.169110 | + | 0.0976355i | ||||
\(784\) | −1.00000 | + | 1.73205i | −0.0357143 | + | 0.0618590i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 17.5981 | + | 10.1603i | 0.627703 | + | 0.362404i | ||||
\(787\) | −2.73205 | + | 4.73205i | −0.0973871 | + | 0.168679i | −0.910602 | − | 0.413284i | \(-0.864382\pi\) |
0.813215 | + | 0.581963i | \(0.197715\pi\) | |||||||
\(788\) | 9.39230 | 0.334587 | ||||||||
\(789\) | −10.2583 | + | 17.7679i | −0.365206 | + | 0.632556i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −31.1769 | + | 18.0000i | −1.10852 | + | 0.640006i | ||||
\(792\) | 3.73205i | 0.132613i | ||||||||
\(793\) | 18.6603 | − | 19.3923i | 0.662645 | − | 0.688641i | ||||
\(794\) | −7.92820 | −0.281361 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.53590 | − | 9.58846i | −0.196215 | − | 0.339854i | ||||
\(797\) | 32.7846 | + | 18.9282i | 1.16129 | + | 0.670471i | 0.951613 | − | 0.307299i | \(-0.0994253\pi\) |
0.209678 | + | 0.977771i | \(0.432759\pi\) | |||||||
\(798\) | −6.80385 | −0.240854 | ||||||||
\(799\) | 1.60770 | + | 0.928203i | 0.0568762 | + | 0.0328375i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 10.1244i | − | 0.357727i | ||||||
\(802\) | 1.83975 | + | 1.06218i | 0.0649637 | + | 0.0375068i | ||||
\(803\) | −22.3923 | + | 12.9282i | −0.790207 | + | 0.456226i | ||||
\(804\) | −4.73205 | + | 2.73205i | −0.166887 | + | 0.0963520i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −30.9282 | + | 8.92820i | −1.08940 | + | 0.314483i | ||||
\(807\) | 30.9282i | 1.08872i | ||||||||
\(808\) | 4.19615 | + | 7.26795i | 0.147620 | + | 0.255686i | ||||
\(809\) | 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 | \(0.957464\pi\) | |||||||
\(812\) | 8.19615 | − | 14.1962i | 0.287629 | − | 0.498187i | ||||
\(813\) | −1.80385 | + | 3.12436i | −0.0632637 | + | 0.109576i | ||||
\(814\) | − | 29.5885i | − | 1.03707i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | 6.80385 | + | 11.7846i | 0.238036 | + | 0.412291i | ||||
\(818\) | 0.947441i | 0.0331265i | ||||||||
\(819\) | −3.00000 | − | 10.3923i | −0.104828 | − | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.7128 | − | 24.6603i | 1.49069 | − | 0.860649i | 0.490744 | − | 0.871304i | \(-0.336725\pi\) |
0.999943 | + | 0.0106549i | \(0.00339162\pi\) | |||||||
\(822\) | −5.66025 | + | 3.26795i | −0.197424 | + | 0.113983i | ||||
\(823\) | −34.2846 | − | 19.7942i | −1.19509 | − | 0.689983i | −0.235631 | − | 0.971843i | \(-0.575716\pi\) |
−0.959456 | + | 0.281859i | \(0.909049\pi\) | |||||||
\(824\) | − | 19.5885i | − | 0.682396i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.7846 | + | 6.80385i | 0.410039 | + | 0.236736i | ||||
\(827\) | −50.4974 | −1.75597 | −0.877984 | − | 0.478690i | \(-0.841112\pi\) | ||||
−0.877984 | + | 0.478690i | \(0.841112\pi\) | |||||||
\(828\) | 3.00000 | + | 1.73205i | 0.104257 | + | 0.0601929i | ||||
\(829\) | −19.6603 | − | 34.0526i | −0.682829 | − | 1.18269i | −0.974114 | − | 0.226058i | \(-0.927416\pi\) |
0.291285 | − | 0.956636i | \(-0.405917\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.5885 | 0.679516 | ||||||||
\(832\) | 3.50000 | + | 0.866025i | 0.121341 | + | 0.0300240i | ||||
\(833\) | 8.00000i | 0.277184i | ||||||||
\(834\) | −18.8660 | + | 10.8923i | −0.653277 | + | 0.377170i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.23205 | − | 7.33013i | 0.146369 | − | 0.253518i | ||||
\(837\) | −8.92820 | −0.308604 | ||||||||
\(838\) | −8.92820 | + | 15.4641i | −0.308420 | + | 0.534199i | ||||
\(839\) | −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 | ||||
\(842\) | 5.07180 | − | 2.92820i | 0.174786 | − | 0.100913i | ||||
\(843\) | 3.46410 | + | 6.00000i | 0.119310 | + | 0.206651i | ||||
\(844\) | −21.9282 | −0.754800 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.464102 | 0.0159561 | ||||||||
\(847\) | −4.39230 | − | 7.60770i | −0.150921 | − | 0.261403i | ||||
\(848\) | 3.23205 | − | 1.86603i | 0.110989 | − | 0.0640796i | ||||
\(849\) | −7.19615 | + | 12.4641i | −0.246971 | + | 0.427767i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.7846 | − | 13.7321i | −0.815326 | − | 0.470729i | ||||
\(852\) | 0.464102 | − | 0.803848i | 0.0158999 | − | 0.0275394i | ||||
\(853\) | −44.6410 | −1.52848 | −0.764240 | − | 0.644932i | \(-0.776886\pi\) | ||||
−0.764240 | + | 0.644932i | \(0.776886\pi\) | |||||||
\(854\) | −11.1962 | + | 19.3923i | −0.383124 | + | 0.663591i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.803848 | − | 0.464102i | 0.0274749 | − | 0.0158627i | ||||
\(857\) | − | 15.0718i | − | 0.514843i | −0.966299 | − | 0.257421i | \(-0.917127\pi\) | ||
0.966299 | − | 0.257421i | \(-0.0828728\pi\) | |||||||
\(858\) | 13.0622 | + | 3.23205i | 0.445935 | + | 0.110340i | ||||
\(859\) | 19.9282 | 0.679942 | 0.339971 | − | 0.940436i | \(-0.389583\pi\) | ||||
0.339971 | + | 0.940436i | \(0.389583\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.00000 | − | 10.3923i | −0.204479 | − | 0.354169i | ||||
\(862\) | 12.0000 | + | 6.92820i | 0.408722 | + | 0.235976i | ||||
\(863\) | 10.9282 | 0.372000 | 0.186000 | − | 0.982550i | \(-0.440447\pi\) | ||||
0.186000 | + | 0.982550i | \(0.440447\pi\) | |||||||
\(864\) | 0.866025 | + | 0.500000i | 0.0294628 | + | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 32.7846i | − | 1.11407i | ||||||
\(867\) | −0.866025 | − | 0.500000i | −0.0294118 | − | 0.0169809i | ||||
\(868\) | 23.1962 | − | 13.3923i | 0.787329 | − | 0.454564i | ||||
\(869\) | 54.7128 | − | 31.5885i | 1.85601 | − | 1.07157i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.46410 | + | 18.9282i | 0.185144 | + | 0.641358i | ||||
\(872\) | − | 10.3923i | − | 0.351928i | ||||||
\(873\) | 6.19615 | + | 10.7321i | 0.209708 | + | 0.363225i | ||||
\(874\) | −3.92820 | − | 6.80385i | −0.132873 | − | 0.230144i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.92820i | 0.234082i | ||||||||
\(877\) | −16.8564 | + | 29.1962i | −0.569200 | + | 0.985884i | 0.427445 | + | 0.904041i | \(0.359414\pi\) |
−0.996645 | + | 0.0818426i | \(0.973920\pi\) | |||||||
\(878\) | 10.6603 | − | 18.4641i | 0.359766 | − | 0.623133i | ||||
\(879\) | − | 19.2487i | − | 0.649243i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.5526 | + | 32.1340i | 0.625052 | + | 1.08262i | 0.988531 | + | 0.151019i | \(0.0482554\pi\) |
−0.363479 | + | 0.931602i | \(0.618411\pi\) | |||||||
\(882\) | 1.00000 | + | 1.73205i | 0.0336718 | + | 0.0583212i | ||||
\(883\) | − | 21.3205i | − | 0.717492i | −0.933435 | − | 0.358746i | \(-0.883204\pi\) | ||
0.933435 | − | 0.358746i | \(-0.116796\pi\) | |||||||
\(884\) | 13.8564 | − | 4.00000i | 0.466041 | − | 0.134535i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.80385 | + | 3.92820i | −0.228580 | + | 0.131971i | ||||
\(887\) | 45.2654 | − | 26.1340i | 1.51986 | − | 0.877493i | 0.520136 | − | 0.854083i | \(-0.325881\pi\) |
0.999726 | − | 0.0234098i | \(-0.00745226\pi\) | |||||||
\(888\) | −6.86603 | − | 3.96410i | −0.230409 | − | 0.133027i | ||||
\(889\) | − | 13.9808i | − | 0.468900i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.23205 | + | 1.86603i | 0.108278 | + | 0.0625142i | ||||
\(892\) | −8.85641 | −0.296534 | ||||||||
\(893\) | −0.911543 | − | 0.526279i | −0.0305036 | − | 0.0176113i | ||||
\(894\) | 11.3923 | + | 19.7321i | 0.381016 | + | 0.659939i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | 8.66025 | − | 9.00000i | 0.289157 | − | 0.300501i | ||||
\(898\) | − | 18.1244i | − | 0.604818i | ||||||
\(899\) | −42.2487 | + | 24.3923i | −1.40907 | + | 0.813529i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.46410 | − | 12.9282i | 0.248665 | − | 0.430701i | ||||
\(902\) | 14.9282 | 0.497055 | ||||||||
\(903\) | 9.00000 | − | 15.5885i | 0.299501 | − | 0.518751i | ||||
\(904\) | −10.3923 | − | 6.00000i | −0.345643 | − | 0.199557i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.39230 | + | 16.2679i | −0.312038 | + | 0.540466i | ||||
\(907\) | 6.12436 | − | 3.53590i | 0.203356 | − | 0.117408i | −0.394864 | − | 0.918740i | \(-0.629208\pi\) |
0.598220 | + | 0.801332i | \(0.295875\pi\) | |||||||
\(908\) | 6.73205 | + | 11.6603i | 0.223411 | + | 0.386959i | ||||
\(909\) | 8.39230 | 0.278355 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.7846 | −0.953677 | −0.476838 | − | 0.878991i | \(-0.658217\pi\) | ||||
−0.476838 | + | 0.878991i | \(0.658217\pi\) | |||||||
\(912\) | −1.13397 | − | 1.96410i | −0.0375497 | − | 0.0650379i | ||||
\(913\) | −8.19615 | + | 4.73205i | −0.271253 | + | 0.156608i | ||||
\(914\) | 0.267949 | − | 0.464102i | 0.00886297 | − | 0.0153511i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.92820 | + | 5.73205i | 0.328037 | + | 0.189392i | ||||
\(917\) | −30.4808 | + | 52.7942i | −1.00656 | + | 1.74342i | ||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | 27.9808 | − | 48.4641i | 0.923000 | − | 1.59868i | 0.128254 | − | 0.991741i | \(-0.459063\pi\) |
0.794746 | − | 0.606942i | \(-0.207604\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.5359 | − | 10.1244i | 0.577827 | − | 0.333609i | ||||
\(922\) | − | 32.3923i | − | 1.06678i | ||||||
\(923\) | −2.41154 | − | 2.32051i | −0.0793769 | − | 0.0763805i | ||||
\(924\) | −11.1962 | −0.368326 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.392305 | + | 0.679492i | 0.0128919 | + | 0.0223295i | ||||
\(927\) | −16.9641 | − | 9.79423i | −0.557174 | − | 0.321685i | ||||
\(928\) | 5.46410 | 0.179368 | ||||||||
\(929\) | 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 | ||||||
\(932\) | 15.5885 | + | 9.00000i | 0.510617 | + | 0.294805i | ||||
\(933\) | 4.39230 | − | 2.53590i | 0.143798 | − | 0.0830216i | ||||
\(934\) | 3.12436 | − | 1.80385i | 0.102232 | − | 0.0590237i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.50000 | − | 2.59808i | 0.0817151 | − | 0.0849208i | ||||
\(937\) | 33.7128i | 1.10135i | 0.834720 | + | 0.550675i | \(0.185630\pi\) | ||||
−0.834720 | + | 0.550675i | \(0.814370\pi\) | |||||||
\(938\) | −8.19615 | − | 14.1962i | −0.267614 | − | 0.463521i | ||||
\(939\) | −0.660254 | − | 1.14359i | −0.0215466 | − | 0.0373198i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 36.4974i | − | 1.18978i | −0.803806 | − | 0.594891i | \(-0.797195\pi\) | ||
0.803806 | − | 0.594891i | \(-0.202805\pi\) | |||||||
\(942\) | 5.40192 | − | 9.35641i | 0.176004 | − | 0.304848i | ||||
\(943\) | 6.92820 | − | 12.0000i | 0.225613 | − | 0.390774i | ||||
\(944\) | 4.53590i | 0.147631i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.1962 | + | 19.3923i | 0.364018 | + | 0.630498i | ||||
\(947\) | −6.80385 | − | 11.7846i | −0.221095 | − | 0.382948i | 0.734046 | − | 0.679100i | \(-0.237630\pi\) |
−0.955141 | + | 0.296152i | \(0.904297\pi\) | |||||||
\(948\) | − | 16.9282i | − | 0.549802i | ||||||
\(949\) | 24.2487 | + | 6.00000i | 0.787146 | + | 0.194768i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.3827 | − | 11.7679i | 0.660954 | − | 0.381602i | ||||
\(952\) | −10.3923 | + | 6.00000i | −0.336817 | + | 0.194461i | ||||
\(953\) | −16.1769 | − | 9.33975i | −0.524022 | − | 0.302544i | 0.214557 | − | 0.976711i | \(-0.431169\pi\) |
−0.738579 | + | 0.674167i | \(0.764503\pi\) | |||||||
\(954\) | − | 3.73205i | − | 0.120830i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | + | 1.73205i | 0.0970269 | + | 0.0560185i | ||||
\(957\) | 20.3923 | 0.659190 | ||||||||
\(958\) | −22.7321 | − | 13.1244i | −0.734439 | − | 0.424029i | ||||
\(959\) | −9.80385 | − | 16.9808i | −0.316583 | − | 0.548337i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −48.7128 | −1.57138 | ||||||||
\(962\) | −19.8205 | + | 20.5981i | −0.639039 | + | 0.664109i | ||||
\(963\) | − | 0.928203i | − | 0.0299109i | ||||||
\(964\) | −12.8205 | + | 7.40192i | −0.412921 | + | 0.238400i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.19615 | + | 9.00000i | −0.167183 | + | 0.289570i | ||||
\(967\) | −28.8564 | −0.927959 | −0.463980 | − | 0.885846i | \(-0.653579\pi\) | ||||
−0.463980 | + | 0.885846i | \(0.653579\pi\) | |||||||
\(968\) | 1.46410 | − | 2.53590i | 0.0470580 | − | 0.0815069i | ||||
\(969\) | −7.85641 | − | 4.53590i | −0.252384 | − | 0.145714i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.3038 | − | 17.8468i | 0.330666 | − | 0.572731i | −0.651976 | − | 0.758239i | \(-0.726060\pi\) |
0.982643 | + | 0.185509i | \(0.0593932\pi\) | |||||||
\(972\) | 0.866025 | − | 0.500000i | 0.0277778 | − | 0.0160375i | ||||
\(973\) | −32.6769 | − | 56.5981i | −1.04757 | − | 1.81445i | ||||
\(974\) | −21.0000 | −0.672883 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.46410 | −0.238920 | ||||||||
\(977\) | −0.732051 | − | 1.26795i | −0.0234204 | − | 0.0405653i | 0.854078 | − | 0.520145i | \(-0.174122\pi\) |
−0.877498 | + | 0.479580i | \(0.840789\pi\) | |||||||
\(978\) | 9.46410 | − | 5.46410i | 0.302629 | − | 0.174723i | ||||
\(979\) | −18.8923 | + | 32.7224i | −0.603801 | + | 1.04581i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.00000 | − | 5.19615i | −0.287348 | − | 0.165900i | ||||
\(982\) | 7.69615 | − | 13.3301i | 0.245594 | − | 0.425381i | ||||
\(983\) | 16.1769 | 0.515963 | 0.257982 | − | 0.966150i | \(-0.416943\pi\) | ||||
0.257982 | + | 0.966150i | \(0.416943\pi\) | |||||||
\(984\) | 2.00000 | − | 3.46410i | 0.0637577 | − | 0.110432i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.9282 | − | 10.9282i | 0.602797 | − | 0.348025i | ||||
\(987\) | 1.39230i | 0.0443176i | ||||||||
\(988\) | −7.85641 | + | 2.26795i | −0.249946 | + | 0.0721531i | ||||
\(989\) | 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 | \(0.713335\pi\) | |||||||
\(992\) | 7.73205 | + | 4.46410i | 0.245493 | + | 0.141735i | ||||
\(993\) | 6.39230 | 0.202854 | ||||||||
\(994\) | 2.41154 | + | 1.39230i | 0.0764895 | + | 0.0441612i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.53590i | 0.0803530i | ||||||||
\(997\) | −8.67691 | − | 5.00962i | −0.274801 | − | 0.158656i | 0.356267 | − | 0.934384i | \(-0.384049\pi\) |
−0.631067 | + | 0.775728i | \(0.717383\pi\) | |||||||
\(998\) | −1.14359 | + | 0.660254i | −0.0361998 | + | 0.0209000i | ||||
\(999\) | −6.86603 | + | 3.96410i | −0.217231 | + | 0.125419i |
(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 | 1950.2.y.d.49.2 | 4 | ||
5.2 | odd | 4 | 1950.2.bc.a.751.2 | 4 | |||
5.3 | odd | 4 | 390.2.bb.a.361.1 | yes | 4 | ||
5.4 | even | 2 | 1950.2.y.e.49.1 | 4 | |||
13.4 | even | 6 | 1950.2.y.e.199.1 | 4 | |||
15.8 | even | 4 | 1170.2.bs.d.361.2 | 4 | |||
65.3 | odd | 12 | 5070.2.b.p.1351.1 | 4 | |||
65.4 | even | 6 | inner | 1950.2.y.d.199.2 | 4 | ||
65.17 | odd | 12 | 1950.2.bc.a.901.2 | 4 | |||
65.23 | odd | 12 | 5070.2.b.p.1351.4 | 4 | |||
65.28 | even | 12 | 5070.2.a.ba.1.2 | 2 | |||
65.43 | odd | 12 | 390.2.bb.a.121.1 | ✓ | 4 | ||
65.63 | even | 12 | 5070.2.a.be.1.1 | 2 | |||
195.173 | even | 12 | 1170.2.bs.d.901.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.a.121.1 | ✓ | 4 | 65.43 | odd | 12 | ||
390.2.bb.a.361.1 | yes | 4 | 5.3 | odd | 4 | ||
1170.2.bs.d.361.2 | 4 | 15.8 | even | 4 | |||
1170.2.bs.d.901.2 | 4 | 195.173 | even | 12 | |||
1950.2.y.d.49.2 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.y.d.199.2 | 4 | 65.4 | even | 6 | inner | ||
1950.2.y.e.49.1 | 4 | 5.4 | even | 2 | |||
1950.2.y.e.199.1 | 4 | 13.4 | even | 6 | |||
1950.2.bc.a.751.2 | 4 | 5.2 | odd | 4 | |||
1950.2.bc.a.901.2 | 4 | 65.17 | odd | 12 | |||
5070.2.a.ba.1.2 | 2 | 65.28 | even | 12 | |||
5070.2.a.be.1.1 | 2 | 65.63 | even | 12 | |||
5070.2.b.p.1351.1 | 4 | 65.3 | odd | 12 | |||
5070.2.b.p.1351.4 | 4 | 65.23 | odd | 12 |