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 | 49.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.49 |
Dual form | 1950.2.y.d.199.1 |
$q$-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 | ||||||||
\(11\) | 0.232051 | − | 0.133975i | 0.0699660 | − | 0.0403949i | −0.464609 | − | 0.885516i | \(-0.653805\pi\) |
0.534575 | + | 0.845121i | \(0.320472\pi\) | |||||||
\(12\) | − | 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 | 0.857321 | − | 0.514782i | \(-0.172127\pi\) |
−0.0171533 | + | 0.999853i | \(0.505460\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.96410 | − | 2.86603i | −1.13884 | − | 0.657511i | −0.192699 | − | 0.981258i | \(-0.561724\pi\) |
−0.946144 | + | 0.323747i | \(0.895057\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000i | 0.654654i | ||||||||
\(22\) | −0.232051 | − | 0.133975i | −0.0494734 | − | 0.0285635i | ||||
\(23\) | 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 | ||||
\(29\) | 0.732051 | + | 1.26795i | 0.135938 | + | 0.235452i | 0.925956 | − | 0.377633i | \(-0.123262\pi\) |
−0.790017 | + | 0.613085i | \(0.789928\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.92820i | − | 0.885131i | −0.896736 | − | 0.442566i | \(-0.854068\pi\) | ||
0.896736 | − | 0.442566i | \(-0.145932\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −0.133975 | + | 0.232051i | −0.0233220 | + | 0.0403949i | ||||
\(34\) | − | 4.00000i | − | 0.685994i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | 2.96410 | + | 5.13397i | 0.487295 | + | 0.844020i | 0.999893 | − | 0.0146085i | \(-0.00465020\pi\) |
−0.512598 | + | 0.858629i | \(0.671317\pi\) | |||||||
\(38\) | 5.73205i | 0.929861i | ||||||||
\(39\) | −3.46410 | + | 1.00000i | −0.554700 | + | 0.160128i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.46410 | + | 2.00000i | −0.541002 | + | 0.312348i | −0.745485 | − | 0.666523i | \(-0.767782\pi\) |
0.204483 | + | 0.978870i | \(0.434449\pi\) | |||||||
\(42\) | 2.59808 | − | 1.50000i | 0.400892 | − | 0.231455i | ||||
\(43\) | −5.19615 | − | 3.00000i | −0.792406 | − | 0.457496i | 0.0484030 | − | 0.998828i | \(-0.484587\pi\) |
−0.840809 | + | 0.541332i | \(0.817920\pi\) | |||||||
\(44\) | 0.267949i | 0.0403949i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | − | 1.73205i | −0.442326 | − | 0.255377i | ||||
\(47\) | 6.46410 | 0.942886 | 0.471443 | − | 0.881897i | \(-0.343733\pi\) | ||||
0.471443 | + | 0.881897i | \(0.343733\pi\) | |||||||
\(48\) | 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 | ||||
\(53\) | − | 0.267949i | − | 0.0368057i | −0.999831 | − | 0.0184028i | \(-0.994142\pi\) | ||
0.999831 | − | 0.0184028i | \(-0.00585813\pi\) | |||||||
\(54\) | 0.866025 | − | 0.500000i | 0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.50000 | − | 2.59808i | 0.200446 | − | 0.347183i | ||||
\(57\) | 5.73205 | 0.759229 | ||||||||
\(58\) | 0.732051 | − | 1.26795i | 0.0961230 | − | 0.166490i | ||||
\(59\) | 9.92820 | + | 5.73205i | 1.29254 | + | 0.746249i | 0.979104 | − | 0.203359i | \(-0.0651859\pi\) |
0.313438 | + | 0.949609i | \(0.398519\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.267949 | − | 0.464102i | 0.0343074 | − | 0.0594221i | −0.848362 | − | 0.529417i | \(-0.822411\pi\) |
0.882669 | + | 0.469995i | \(0.155744\pi\) | |||||||
\(62\) | −4.26795 | + | 2.46410i | −0.542030 | + | 0.312941i | ||||
\(63\) | −1.50000 | − | 2.59808i | −0.188982 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.267949 | 0.0329823 | ||||||||
\(67\) | −0.732051 | − | 1.26795i | −0.0894342 | − | 0.154905i | 0.817838 | − | 0.575449i | \(-0.195173\pi\) |
−0.907272 | + | 0.420544i | \(0.861839\pi\) | |||||||
\(68\) | −3.46410 | + | 2.00000i | −0.420084 | + | 0.242536i | ||||
\(69\) | −1.73205 | + | 3.00000i | −0.208514 | + | 0.361158i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.1962 | − | 6.46410i | −1.32874 | − | 0.767148i | −0.343634 | − | 0.939104i | \(-0.611658\pi\) |
−0.985105 | + | 0.171956i | \(0.944991\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −6.92820 | −0.810885 | −0.405442 | − | 0.914121i | \(-0.632883\pi\) | ||||
−0.405442 | + | 0.914121i | \(0.632883\pi\) | |||||||
\(74\) | 2.96410 | − | 5.13397i | 0.344570 | − | 0.596812i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.96410 | − | 2.86603i | 0.569422 | − | 0.328756i | ||||
\(77\) | − | 0.803848i | − | 0.0916069i | ||||||
\(78\) | 2.59808 | + | 2.50000i | 0.294174 | + | 0.283069i | ||||
\(79\) | −3.07180 | −0.345604 | −0.172802 | − | 0.984957i | \(-0.555282\pi\) | ||||
−0.172802 | + | 0.984957i | \(0.555282\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 3.46410 | + | 2.00000i | 0.382546 | + | 0.220863i | ||||
\(83\) | 9.46410 | 1.03882 | 0.519410 | − | 0.854525i | \(-0.326152\pi\) | ||||
0.519410 | + | 0.854525i | \(0.326152\pi\) | |||||||
\(84\) | −2.59808 | − | 1.50000i | −0.283473 | − | 0.163663i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.00000i | 0.646997i | ||||||||
\(87\) | −1.26795 | − | 0.732051i | −0.135938 | − | 0.0784841i | ||||
\(88\) | 0.232051 | − | 0.133975i | 0.0247367 | − | 0.0142817i | ||||
\(89\) | 12.2321 | − | 7.06218i | 1.29659 | − | 0.748589i | 0.316780 | − | 0.948499i | \(-0.397398\pi\) |
0.979814 | + | 0.199910i | \(0.0640648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.50000 | − | 7.79423i | 0.786214 | − | 0.817057i | ||||
\(92\) | 3.46410i | 0.361158i | ||||||||
\(93\) | 2.46410 | + | 4.26795i | 0.255515 | + | 0.442566i | ||||
\(94\) | −3.23205 | − | 5.59808i | −0.333361 | − | 0.577397i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 4.19615 | − | 7.26795i | 0.426055 | − | 0.737948i | −0.570464 | − | 0.821323i | \(-0.693236\pi\) |
0.996518 | + | 0.0833745i | \(0.0265698\pi\) | |||||||
\(98\) | −1.00000 | + | 1.73205i | −0.101015 | + | 0.174964i | ||||
\(99\) | − | 0.267949i | − | 0.0269299i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.19615 | − | 10.7321i | −0.616540 | − | 1.06788i | −0.990112 | − | 0.140278i | \(-0.955200\pi\) |
0.373572 | − | 0.927601i | \(-0.378133\pi\) | |||||||
\(102\) | 2.00000 | + | 3.46410i | 0.198030 | + | 0.342997i | ||||
\(103\) | − | 11.5885i | − | 1.14184i | −0.821004 | − | 0.570922i | \(-0.806586\pi\) | ||
0.821004 | − | 0.570922i | \(-0.193414\pi\) | |||||||
\(104\) | 3.50000 | + | 0.866025i | 0.343203 | + | 0.0849208i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.232051 | + | 0.133975i | −0.0225388 | + | 0.0130128i | ||||
\(107\) | 11.1962 | − | 6.46410i | 1.08237 | − | 0.624908i | 0.150837 | − | 0.988559i | \(-0.451803\pi\) |
0.931536 | + | 0.363650i | \(0.118470\pi\) | |||||||
\(108\) | −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 | ||||||||
\(111\) | −5.13397 | − | 2.96410i | −0.487295 | − | 0.281340i | ||||
\(112\) | −3.00000 | −0.283473 | ||||||||
\(113\) | 10.3923 | + | 6.00000i | 0.977626 | + | 0.564433i | 0.901553 | − | 0.432670i | \(-0.142428\pi\) |
0.0760733 | + | 0.997102i | \(0.475762\pi\) | |||||||
\(114\) | −2.86603 | − | 4.96410i | −0.268428 | − | 0.464931i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.46410 | −0.135938 | ||||||||
\(117\) | 2.50000 | − | 2.59808i | 0.231125 | − | 0.240192i | ||||
\(118\) | − | 11.4641i | − | 1.05536i | ||||||
\(119\) | 10.3923 | − | 6.00000i | 0.952661 | − | 0.550019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.46410 | + | 9.46410i | −0.496737 | + | 0.860373i | ||||
\(122\) | −0.535898 | −0.0485180 | ||||||||
\(123\) | 2.00000 | − | 3.46410i | 0.180334 | − | 0.312348i | ||||
\(124\) | 4.26795 | + | 2.46410i | 0.383273 | + | 0.221283i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.50000 | + | 2.59808i | −0.133631 | + | 0.231455i | ||||
\(127\) | 10.9641 | − | 6.33013i | 0.972907 | − | 0.561708i | 0.0727855 | − | 0.997348i | \(-0.476811\pi\) |
0.900121 | + | 0.435640i | \(0.143478\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 6.00000 | 0.528271 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.3205 | 1.25119 | 0.625594 | − | 0.780149i | \(-0.284857\pi\) | ||||
0.625594 | + | 0.780149i | \(0.284857\pi\) | |||||||
\(132\) | −0.133975 | − | 0.232051i | −0.0116610 | − | 0.0201974i | ||||
\(133\) | −14.8923 | + | 8.59808i | −1.29133 | + | 0.745548i | ||||
\(134\) | −0.732051 | + | 1.26795i | −0.0632396 | + | 0.109534i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.46410 | + | 2.00000i | 0.297044 | + | 0.171499i | ||||
\(137\) | 6.73205 | − | 11.6603i | 0.575158 | − | 0.996203i | −0.420867 | − | 0.907123i | \(-0.638274\pi\) |
0.996024 | − | 0.0890802i | \(-0.0283927\pi\) | |||||||
\(138\) | 3.46410 | 0.294884 | ||||||||
\(139\) | −9.89230 | + | 17.1340i | −0.839054 | + | 1.45328i | 0.0516319 | + | 0.998666i | \(0.483558\pi\) |
−0.890686 | + | 0.454619i | \(0.849776\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.59808 | + | 3.23205i | −0.471443 | + | 0.272188i | ||||
\(142\) | 12.9282i | 1.08491i | ||||||||
\(143\) | 0.928203 | − | 0.267949i | 0.0776203 | − | 0.0224070i | ||||
\(144\) | −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 | ||||
\(148\) | −5.92820 | −0.487295 | ||||||||
\(149\) | −16.2679 | − | 9.39230i | −1.33272 | − | 0.769448i | −0.347006 | − | 0.937863i | \(-0.612802\pi\) |
−0.985716 | + | 0.168415i | \(0.946135\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 22.7846i | − | 1.85419i | −0.374832 | − | 0.927093i | \(-0.622300\pi\) | ||
0.374832 | − | 0.927093i | \(-0.377700\pi\) | |||||||
\(152\) | −4.96410 | − | 2.86603i | −0.402642 | − | 0.232465i | ||||
\(153\) | 3.46410 | − | 2.00000i | 0.280056 | − | 0.161690i | ||||
\(154\) | −0.696152 | + | 0.401924i | −0.0560976 | + | 0.0323879i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.866025 | − | 3.50000i | 0.0693375 | − | 0.280224i | ||||
\(157\) | − | 21.1962i | − | 1.69164i | −0.533471 | − | 0.845819i | \(-0.679113\pi\) | ||
0.533471 | − | 0.845819i | \(-0.320887\pi\) | |||||||
\(158\) | 1.53590 | + | 2.66025i | 0.122190 | + | 0.211638i | ||||
\(159\) | 0.133975 | + | 0.232051i | 0.0106249 | + | 0.0184028i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 10.3923i | − | 0.819028i | ||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | 1.46410 | − | 2.53590i | 0.114677 | − | 0.198627i | −0.802973 | − | 0.596015i | \(-0.796750\pi\) |
0.917651 | + | 0.397388i | \(0.130083\pi\) | |||||||
\(164\) | − | 4.00000i | − | 0.312348i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.73205 | − | 8.19615i | −0.367278 | − | 0.636145i | ||||
\(167\) | 0.232051 | + | 0.401924i | 0.0179566 | + | 0.0311018i | 0.874864 | − | 0.484368i | \(-0.160951\pi\) |
−0.856907 | + | 0.515470i | \(0.827617\pi\) | |||||||
\(168\) | 3.00000i | 0.231455i | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.96410 | + | 2.86603i | −0.379614 | + | 0.219170i | ||||
\(172\) | 5.19615 | − | 3.00000i | 0.396203 | − | 0.228748i | ||||
\(173\) | 1.83975 | + | 1.06218i | 0.139873 | + | 0.0807559i | 0.568304 | − | 0.822819i | \(-0.307600\pi\) |
−0.428430 | + | 0.903575i | \(0.640933\pi\) | |||||||
\(174\) | 1.46410i | 0.110993i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.232051 | − | 0.133975i | −0.0174915 | − | 0.0100987i | ||||
\(177\) | −11.4641 | −0.861695 | ||||||||
\(178\) | −12.2321 | − | 7.06218i | −0.916831 | − | 0.529333i | ||||
\(179\) | 4.53590 | + | 7.85641i | 0.339029 | + | 0.587215i | 0.984250 | − | 0.176780i | \(-0.0565682\pi\) |
−0.645221 | + | 0.763996i | \(0.723235\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.9282 | 1.25826 | 0.629132 | − | 0.777299i | \(-0.283411\pi\) | ||||
0.629132 | + | 0.777299i | \(0.283411\pi\) | |||||||
\(182\) | −10.5000 | − | 2.59808i | −0.778312 | − | 0.192582i | ||||
\(183\) | 0.535898i | 0.0396147i | ||||||||
\(184\) | 3.00000 | − | 1.73205i | 0.221163 | − | 0.127688i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.46410 | − | 4.26795i | 0.180677 | − | 0.312941i | ||||
\(187\) | 1.07180 | 0.0783775 | ||||||||
\(188\) | −3.23205 | + | 5.59808i | −0.235722 | + | 0.408282i | ||||
\(189\) | 2.59808 | + | 1.50000i | 0.188982 | + | 0.109109i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.66025 | − | 15.0000i | 0.626634 | − | 1.08536i | −0.361588 | − | 0.932338i | \(-0.617765\pi\) |
0.988222 | − | 0.153024i | \(-0.0489012\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −4.92820 | − | 8.53590i | −0.354740 | − | 0.614427i | 0.632334 | − | 0.774696i | \(-0.282097\pi\) |
−0.987073 | + | 0.160269i | \(0.948764\pi\) | |||||||
\(194\) | −8.39230 | −0.602532 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 5.69615 | + | 9.86603i | 0.405834 | + | 0.702925i | 0.994418 | − | 0.105511i | \(-0.0336478\pi\) |
−0.588584 | + | 0.808436i | \(0.700314\pi\) | |||||||
\(198\) | −0.232051 | + | 0.133975i | −0.0164911 | + | 0.00952116i | ||||
\(199\) | −12.4641 | + | 21.5885i | −0.883557 | + | 1.53037i | −0.0361978 | + | 0.999345i | \(0.511525\pi\) |
−0.847359 | + | 0.531021i | \(0.821809\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.26795 | + | 0.732051i | 0.0894342 | + | 0.0516349i | ||||
\(202\) | −6.19615 | + | 10.7321i | −0.435960 | + | 0.755104i | ||||
\(203\) | 4.39230 | 0.308279 | ||||||||
\(204\) | 2.00000 | − | 3.46410i | 0.140028 | − | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.0359 | + | 5.79423i | −0.699234 | + | 0.403703i | ||||
\(207\) | − | 3.46410i | − | 0.240772i | ||||||
\(208\) | −1.00000 | − | 3.46410i | −0.0693375 | − | 0.240192i | ||||
\(209\) | −1.53590 | −0.106240 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.03590 | + | 6.99038i | 0.277843 | + | 0.481238i | 0.970848 | − | 0.239694i | \(-0.0770473\pi\) |
−0.693006 | + | 0.720932i | \(0.743714\pi\) | |||||||
\(212\) | 0.232051 | + | 0.133975i | 0.0159373 | + | 0.00920141i | ||||
\(213\) | 12.9282 | 0.885826 | ||||||||
\(214\) | −11.1962 | − | 6.46410i | −0.765353 | − | 0.441877i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −12.8038 | − | 7.39230i | −0.869182 | − | 0.501822i | ||||
\(218\) | −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 | ||||
\(222\) | 5.92820i | 0.397875i | ||||||||
\(223\) | −9.42820 | − | 16.3301i | −0.631359 | − | 1.09355i | −0.987274 | − | 0.159028i | \(-0.949164\pi\) |
0.355915 | − | 0.934518i | \(-0.384169\pi\) | |||||||
\(224\) | 1.50000 | + | 2.59808i | 0.100223 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 12.0000i | − | 0.798228i | ||||||
\(227\) | 3.26795 | − | 5.66025i | 0.216901 | − | 0.375684i | −0.736958 | − | 0.675939i | \(-0.763738\pi\) |
0.953859 | + | 0.300255i | \(0.0970717\pi\) | |||||||
\(228\) | −2.86603 | + | 4.96410i | −0.189807 | + | 0.328756i | ||||
\(229\) | 4.53590i | 0.299741i | 0.988706 | + | 0.149870i | \(0.0478856\pi\) | ||||
−0.988706 | + | 0.149870i | \(0.952114\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.401924 | + | 0.696152i | 0.0264446 | + | 0.0458035i | ||||
\(232\) | 0.732051 | + | 1.26795i | 0.0480615 | + | 0.0832449i | ||||
\(233\) | 18.0000i | 1.17922i | 0.807688 | + | 0.589610i | \(0.200718\pi\) | ||||
−0.807688 | + | 0.589610i | \(0.799282\pi\) | |||||||
\(234\) | −3.50000 | − | 0.866025i | −0.228802 | − | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.92820 | + | 5.73205i | −0.646271 | + | 0.373125i | ||||
\(237\) | 2.66025 | − | 1.53590i | 0.172802 | − | 0.0997673i | ||||
\(238\) | −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 | ||||||||
\(241\) | −21.8205 | − | 12.5981i | −1.40558 | − | 0.811513i | −0.410624 | − | 0.911805i | \(-0.634689\pi\) |
−0.994958 | + | 0.100291i | \(0.968023\pi\) | |||||||
\(242\) | 10.9282 | 0.702492 | ||||||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 0.267949 | + | 0.464102i | 0.0171537 | + | 0.0297111i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.00000 | −0.255031 | ||||||||
\(247\) | −14.8923 | − | 14.3301i | −0.947575 | − | 0.911804i | ||||
\(248\) | − | 4.92820i | − | 0.312941i | ||||||
\(249\) | −8.19615 | + | 4.73205i | −0.519410 | + | 0.299882i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.76795 | + | 16.9186i | −0.616547 | + | 1.06789i | 0.373563 | + | 0.927605i | \(0.378136\pi\) |
−0.990111 | + | 0.140287i | \(0.955198\pi\) | |||||||
\(252\) | 3.00000 | 0.188982 | ||||||||
\(253\) | 0.464102 | − | 0.803848i | 0.0291778 | − | 0.0505375i | ||||
\(254\) | −10.9641 | − | 6.33013i | −0.687949 | − | 0.397187i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −12.5885 | + | 7.26795i | −0.785246 | + | 0.453362i | −0.838286 | − | 0.545230i | \(-0.816442\pi\) |
0.0530400 | + | 0.998592i | \(0.483109\pi\) | |||||||
\(258\) | −3.00000 | − | 5.19615i | −0.186772 | − | 0.323498i | ||||
\(259\) | 17.7846 | 1.10508 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.46410 | 0.0906256 | ||||||||
\(262\) | −7.16025 | − | 12.4019i | −0.442362 | − | 0.766193i | ||||
\(263\) | −21.2321 | + | 12.2583i | −1.30922 | + | 0.755881i | −0.981967 | − | 0.189054i | \(-0.939458\pi\) |
−0.327258 | + | 0.944935i | \(0.606125\pi\) | |||||||
\(264\) | −0.133975 | + | 0.232051i | −0.00824557 | + | 0.0142817i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.8923 | + | 8.59808i | 0.913106 | + | 0.527182i | ||||
\(267\) | −7.06218 | + | 12.2321i | −0.432198 | + | 0.748589i | ||||
\(268\) | 1.46410 | 0.0894342 | ||||||||
\(269\) | −8.53590 | + | 14.7846i | −0.520443 | + | 0.901434i | 0.479275 | + | 0.877665i | \(0.340900\pi\) |
−0.999717 | + | 0.0237685i | \(0.992434\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1244 | − | 12.1962i | 1.28321 | − | 0.740863i | 0.305779 | − | 0.952103i | \(-0.401083\pi\) |
0.977434 | + | 0.211239i | \(0.0677499\pi\) | |||||||
\(272\) | − | 4.00000i | − | 0.242536i | ||||||
\(273\) | −2.59808 | + | 10.5000i | −0.157243 | + | 0.635489i | ||||
\(274\) | −13.4641 | −0.813396 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.73205 | − | 3.00000i | −0.104257 | − | 0.180579i | ||||
\(277\) | 10.0359 | + | 5.79423i | 0.602999 | + | 0.348141i | 0.770220 | − | 0.637778i | \(-0.220146\pi\) |
−0.167222 | + | 0.985919i | \(0.553480\pi\) | |||||||
\(278\) | 19.7846 | 1.18660 | ||||||||
\(279\) | −4.26795 | − | 2.46410i | −0.255515 | − | 0.147522i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.92820i | 0.413302i | 0.978415 | + | 0.206651i | \(0.0662565\pi\) | ||||
−0.978415 | + | 0.206651i | \(0.933744\pi\) | |||||||
\(282\) | 5.59808 | + | 3.23205i | 0.333361 | + | 0.192466i | ||||
\(283\) | −5.53590 | + | 3.19615i | −0.329075 | + | 0.189992i | −0.655430 | − | 0.755256i | \(-0.727513\pi\) |
0.326355 | + | 0.945247i | \(0.394179\pi\) | |||||||
\(284\) | 11.1962 | − | 6.46410i | 0.664369 | − | 0.383574i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.696152 | − | 0.669873i | −0.0411644 | − | 0.0396104i | ||||
\(287\) | 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 | ||||||||
\(291\) | 8.39230i | 0.491966i | ||||||||
\(292\) | 3.46410 | − | 6.00000i | 0.202721 | − | 0.351123i | ||||
\(293\) | −14.6244 | + | 25.3301i | −0.854364 | + | 1.47980i | 0.0228698 | + | 0.999738i | \(0.492720\pi\) |
−0.877234 | + | 0.480063i | \(0.840614\pi\) | |||||||
\(294\) | − | 2.00000i | − | 0.116642i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.96410 | + | 5.13397i | 0.172285 | + | 0.298406i | ||||
\(297\) | 0.133975 | + | 0.232051i | 0.00777399 | + | 0.0134650i | ||||
\(298\) | 18.7846i | 1.08816i | ||||||||
\(299\) | 12.0000 | − | 3.46410i | 0.693978 | − | 0.200334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.5885 | + | 9.00000i | −0.898504 | + | 0.518751i | ||||
\(302\) | −19.7321 | + | 11.3923i | −1.13545 | + | 0.655553i | ||||
\(303\) | 10.7321 | + | 6.19615i | 0.616540 | + | 0.355960i | ||||
\(304\) | 5.73205i | 0.328756i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.46410 | − | 2.00000i | −0.198030 | − | 0.114332i | ||||
\(307\) | −28.2487 | −1.61224 | −0.806120 | − | 0.591753i | \(-0.798436\pi\) | ||||
−0.806120 | + | 0.591753i | \(0.798436\pi\) | |||||||
\(308\) | 0.696152 | + | 0.401924i | 0.0396670 | + | 0.0229017i | ||||
\(309\) | 5.79423 | + | 10.0359i | 0.329622 | + | 0.570922i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.9282 | 1.07332 | 0.536660 | − | 0.843799i | \(-0.319686\pi\) | ||||
0.536660 | + | 0.843799i | \(0.319686\pi\) | |||||||
\(312\) | −3.46410 | + | 1.00000i | −0.196116 | + | 0.0566139i | ||||
\(313\) | − | 33.3205i | − | 1.88339i | −0.336473 | − | 0.941693i | \(-0.609234\pi\) | ||
0.336473 | − | 0.941693i | \(-0.390766\pi\) | |||||||
\(314\) | −18.3564 | + | 10.5981i | −1.03591 | + | 0.598084i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.53590 | − | 2.66025i | 0.0864010 | − | 0.149651i | ||||
\(317\) | 30.4641 | 1.71103 | 0.855517 | − | 0.517774i | \(-0.173239\pi\) | ||||
0.855517 | + | 0.517774i | \(0.173239\pi\) | |||||||
\(318\) | 0.133975 | − | 0.232051i | 0.00751292 | − | 0.0130128i | ||||
\(319\) | 0.339746 | + | 0.196152i | 0.0190221 | + | 0.0109824i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.46410 | + | 11.1962i | −0.360791 | + | 0.624908i | ||||
\(322\) | −9.00000 | + | 5.19615i | −0.501550 | + | 0.289570i | ||||
\(323\) | −11.4641 | − | 19.8564i | −0.637880 | − | 1.10484i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.92820 | −0.162178 | ||||||||
\(327\) | 5.19615 | + | 9.00000i | 0.287348 | + | 0.497701i | ||||
\(328\) | −3.46410 | + | 2.00000i | −0.191273 | + | 0.110432i | ||||
\(329\) | 9.69615 | − | 16.7942i | 0.534566 | − | 0.925896i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.4641 | + | 7.19615i | 0.685089 | + | 0.395536i | 0.801770 | − | 0.597633i | \(-0.203892\pi\) |
−0.116681 | + | 0.993169i | \(0.537225\pi\) | |||||||
\(332\) | −4.73205 | + | 8.19615i | −0.259705 | + | 0.449822i | ||||
\(333\) | 5.92820 | 0.324864 | ||||||||
\(334\) | 0.232051 | − | 0.401924i | 0.0126973 | − | 0.0219923i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.59808 | − | 1.50000i | 0.141737 | − | 0.0818317i | ||||
\(337\) | 26.3923i | 1.43768i | 0.695175 | + | 0.718840i | \(0.255327\pi\) | ||||
−0.695175 | + | 0.718840i | \(0.744673\pi\) | |||||||
\(338\) | −0.500000 | − | 12.9904i | −0.0271964 | − | 0.706584i | ||||
\(339\) | −12.0000 | −0.651751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.660254 | − | 1.14359i | −0.0357548 | − | 0.0619291i | ||||
\(342\) | 4.96410 | + | 2.86603i | 0.268428 | + | 0.154977i | ||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −5.19615 | − | 3.00000i | −0.280158 | − | 0.161749i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 2.12436i | − | 0.114206i | ||||||
\(347\) | 3.80385 | + | 2.19615i | 0.204201 | + | 0.117896i | 0.598614 | − | 0.801038i | \(-0.295719\pi\) |
−0.394412 | + | 0.918934i | \(0.629052\pi\) | |||||||
\(348\) | 1.26795 | − | 0.732051i | 0.0679692 | − | 0.0392420i | ||||
\(349\) | 9.12436 | − | 5.26795i | 0.488416 | − | 0.281987i | −0.235501 | − | 0.971874i | \(-0.575673\pi\) |
0.723917 | + | 0.689887i | \(0.242340\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.866025 | + | 3.50000i | −0.0462250 | + | 0.186816i | ||||
\(352\) | 0.267949i | 0.0142817i | ||||||||
\(353\) | 3.80385 | + | 6.58846i | 0.202458 | + | 0.350668i | 0.949320 | − | 0.314311i | \(-0.101774\pi\) |
−0.746862 | + | 0.664980i | \(0.768440\pi\) | |||||||
\(354\) | 5.73205 | + | 9.92820i | 0.304655 | + | 0.527678i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.1244i | 0.748589i | ||||||||
\(357\) | −6.00000 | + | 10.3923i | −0.317554 | + | 0.550019i | ||||
\(358\) | 4.53590 | − | 7.85641i | 0.239730 | − | 0.415224i | ||||
\(359\) | − | 0.928203i | − | 0.0489887i | −0.999700 | − | 0.0244943i | \(-0.992202\pi\) | ||
0.999700 | − | 0.0244943i | \(-0.00779757\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.92820 | + | 12.0000i | 0.364642 | + | 0.631579i | ||||
\(362\) | −8.46410 | − | 14.6603i | −0.444863 | − | 0.770526i | ||||
\(363\) | − | 10.9282i | − | 0.573582i | ||||||
\(364\) | 3.00000 | + | 10.3923i | 0.157243 | + | 0.544705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.464102 | − | 0.267949i | 0.0242590 | − | 0.0140059i | ||||
\(367\) | −18.4641 | + | 10.6603i | −0.963818 | + | 0.556461i | −0.897346 | − | 0.441328i | \(-0.854508\pi\) |
−0.0664722 | + | 0.997788i | \(0.521174\pi\) | |||||||
\(368\) | −3.00000 | − | 1.73205i | −0.156386 | − | 0.0902894i | ||||
\(369\) | 4.00000i | 0.208232i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.696152 | − | 0.401924i | −0.0361424 | − | 0.0208668i | ||||
\(372\) | −4.92820 | −0.255515 | ||||||||
\(373\) | −7.85641 | − | 4.53590i | −0.406789 | − | 0.234860i | 0.282620 | − | 0.959232i | \(-0.408796\pi\) |
−0.689409 | + | 0.724372i | \(0.742130\pi\) | |||||||
\(374\) | −0.535898 | − | 0.928203i | −0.0277106 | − | 0.0479962i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.46410 | 0.333361 | ||||||||
\(377\) | 1.46410 | + | 5.07180i | 0.0754051 | + | 0.261211i | ||||
\(378\) | − | 3.00000i | − | 0.154303i | ||||||
\(379\) | 8.42820 | − | 4.86603i | 0.432928 | − | 0.249951i | −0.267665 | − | 0.963512i | \(-0.586252\pi\) |
0.700593 | + | 0.713561i | \(0.252919\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.33013 | + | 10.9641i | −0.324302 | + | 0.561708i | ||||
\(382\) | −17.3205 | −0.886194 | ||||||||
\(383\) | −2.39230 | + | 4.14359i | −0.122241 | + | 0.211728i | −0.920651 | − | 0.390386i | \(-0.872341\pi\) |
0.798410 | + | 0.602114i | \(0.205675\pi\) | |||||||
\(384\) | 0.866025 | + | 0.500000i | 0.0441942 | + | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.92820 | + | 8.53590i | −0.250839 | + | 0.434466i | ||||
\(387\) | −5.19615 | + | 3.00000i | −0.264135 | + | 0.152499i | ||||
\(388\) | 4.19615 | + | 7.26795i | 0.213027 | + | 0.368974i | ||||
\(389\) | −17.8564 | −0.905356 | −0.452678 | − | 0.891674i | \(-0.649531\pi\) | ||||
−0.452678 | + | 0.891674i | \(0.649531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.8564 | 0.700749 | ||||||||
\(392\) | −1.00000 | − | 1.73205i | −0.0505076 | − | 0.0874818i | ||||
\(393\) | −12.4019 | + | 7.16025i | −0.625594 | + | 0.361187i | ||||
\(394\) | 5.69615 | − | 9.86603i | 0.286968 | − | 0.497043i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.232051 | + | 0.133975i | 0.0116610 | + | 0.00673248i | ||||
\(397\) | −2.96410 | + | 5.13397i | −0.148764 | + | 0.257667i | −0.930771 | − | 0.365603i | \(-0.880863\pi\) |
0.782007 | + | 0.623270i | \(0.214196\pi\) | |||||||
\(398\) | 24.9282 | 1.24954 | ||||||||
\(399\) | 8.59808 | − | 14.8923i | 0.430442 | − | 0.745548i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.1603 | + | 11.0622i | −0.956817 | + | 0.552419i | −0.895192 | − | 0.445681i | \(-0.852962\pi\) |
−0.0616254 | + | 0.998099i | \(0.519628\pi\) | |||||||
\(402\) | − | 1.46410i | − | 0.0730228i | ||||||
\(403\) | 4.26795 | − | 17.2487i | 0.212602 | − | 0.859220i | ||||
\(404\) | 12.3923 | 0.616540 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.19615 | − | 3.80385i | −0.108993 | − | 0.188782i | ||||
\(407\) | 1.37564 | + | 0.794229i | 0.0681882 | + | 0.0393685i | ||||
\(408\) | −4.00000 | −0.198030 | ||||||||
\(409\) | 33.8205 | + | 19.5263i | 1.67232 | + | 0.965512i | 0.966337 | + | 0.257280i | \(0.0828264\pi\) |
0.705980 | + | 0.708232i | \(0.250507\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.4641i | 0.664135i | ||||||||
\(412\) | 10.0359 | + | 5.79423i | 0.494433 | + | 0.285461i | ||||
\(413\) | 29.7846 | − | 17.1962i | 1.46560 | − | 0.846167i | ||||
\(414\) | −3.00000 | + | 1.73205i | −0.147442 | + | 0.0851257i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.50000 | + | 2.59808i | −0.122573 | + | 0.127381i | ||||
\(417\) | − | 19.7846i | − | 0.968857i | ||||||
\(418\) | 0.767949 | + | 1.33013i | 0.0375616 | + | 0.0650586i | ||||
\(419\) | 4.92820 | + | 8.53590i | 0.240758 | + | 0.417006i | 0.960931 | − | 0.276790i | \(-0.0892705\pi\) |
−0.720172 | + | 0.693795i | \(0.755937\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.8564i | 1.06522i | 0.846362 | + | 0.532608i | \(0.178788\pi\) | ||||
−0.846362 | + | 0.532608i | \(0.821212\pi\) | |||||||
\(422\) | 4.03590 | − | 6.99038i | 0.196464 | − | 0.340286i | ||||
\(423\) | 3.23205 | − | 5.59808i | 0.157148 | − | 0.272188i | ||||
\(424\) | − | 0.267949i | − | 0.0130128i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.46410 | − | 11.1962i | −0.313187 | − | 0.542455i | ||||
\(427\) | −0.803848 | − | 1.39230i | −0.0389009 | − | 0.0673784i | ||||
\(428\) | 12.9282i | 0.624908i | ||||||||
\(429\) | −0.669873 | + | 0.696152i | −0.0323418 | + | 0.0336106i | ||||
\(430\) | 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 | ||||
\(433\) | 7.60770 | + | 4.39230i | 0.365602 | + | 0.211081i | 0.671536 | − | 0.740972i | \(-0.265635\pi\) |
−0.305933 | + | 0.952053i | \(0.598968\pi\) | |||||||
\(434\) | 14.7846i | 0.709684i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.00000 | + | 5.19615i | 0.431022 | + | 0.248851i | ||||
\(437\) | −19.8564 | −0.949861 | ||||||||
\(438\) | −6.00000 | − | 3.46410i | −0.286691 | − | 0.165521i | ||||
\(439\) | −6.66025 | − | 11.5359i | −0.317877 | − | 0.550578i | 0.662168 | − | 0.749355i | \(-0.269636\pi\) |
−0.980045 | + | 0.198777i | \(0.936303\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | −0.0952381 | ||||||||
\(442\) | 3.46410 | − | 14.0000i | 0.164771 | − | 0.665912i | ||||
\(443\) | − | 19.8564i | − | 0.943406i | −0.881757 | − | 0.471703i | \(-0.843639\pi\) | ||
0.881757 | − | 0.471703i | \(-0.156361\pi\) | |||||||
\(444\) | 5.13397 | − | 2.96410i | 0.243648 | − | 0.140670i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.42820 | + | 16.3301i | −0.446438 | + | 0.773254i | ||||
\(447\) | 18.7846 | 0.888482 | ||||||||
\(448\) | 1.50000 | − | 2.59808i | 0.0708683 | − | 0.122748i | ||||
\(449\) | 5.30385 | + | 3.06218i | 0.250304 | + | 0.144513i | 0.619903 | − | 0.784678i | \(-0.287172\pi\) |
−0.369599 | + | 0.929191i | \(0.620505\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.535898 | + | 0.928203i | −0.0252345 | + | 0.0437074i | ||||
\(452\) | −10.3923 | + | 6.00000i | −0.488813 | + | 0.282216i | ||||
\(453\) | 11.3923 | + | 19.7321i | 0.535257 | + | 0.927093i | ||||
\(454\) | −6.53590 | −0.306745 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.73205 | 0.268428 | ||||||||
\(457\) | 3.73205 | + | 6.46410i | 0.174578 | + | 0.302378i | 0.940015 | − | 0.341133i | \(-0.110811\pi\) |
−0.765437 | + | 0.643511i | \(0.777477\pi\) | |||||||
\(458\) | 3.92820 | − | 2.26795i | 0.183553 | − | 0.105974i | ||||
\(459\) | −2.00000 | + | 3.46410i | −0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0526 | − | 5.80385i | −0.468194 | − | 0.270312i | 0.247289 | − | 0.968942i | \(-0.420460\pi\) |
−0.715484 | + | 0.698630i | \(0.753794\pi\) | |||||||
\(462\) | 0.401924 | − | 0.696152i | 0.0186992 | − | 0.0323879i | ||||
\(463\) | 40.7846 | 1.89542 | 0.947711 | − | 0.319131i | \(-0.103391\pi\) | ||||
0.947711 | + | 0.319131i | \(0.103391\pi\) | |||||||
\(464\) | 0.732051 | − | 1.26795i | 0.0339846 | − | 0.0588631i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.5885 | − | 9.00000i | 0.722121 | − | 0.416917i | ||||
\(467\) | − | 24.3923i | − | 1.12874i | −0.825522 | − | 0.564371i | \(-0.809119\pi\) | ||
0.825522 | − | 0.564371i | \(-0.190881\pi\) | |||||||
\(468\) | 1.00000 | + | 3.46410i | 0.0462250 | + | 0.160128i | ||||
\(469\) | −4.39230 | −0.202818 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.5981 | + | 18.3564i | 0.488334 | + | 0.845819i | ||||
\(472\) | 9.92820 | + | 5.73205i | 0.456983 | + | 0.263839i | ||||
\(473\) | −1.60770 | −0.0739219 | ||||||||
\(474\) | −2.66025 | − | 1.53590i | −0.122190 | − | 0.0705461i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0000i | 0.550019i | ||||||||
\(477\) | −0.232051 | − | 0.133975i | −0.0106249 | − | 0.00613428i | ||||
\(478\) | −3.00000 | + | 1.73205i | −0.137217 | + | 0.0792222i | ||||
\(479\) | 19.2679 | − | 11.1244i | 0.880375 | − | 0.508285i | 0.00959301 | − | 0.999954i | \(-0.496946\pi\) |
0.870782 | + | 0.491669i | \(0.163613\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.92820 | + | 20.5359i | 0.270303 | + | 0.936356i | ||||
\(482\) | 25.1962i | 1.14765i | ||||||||
\(483\) | 5.19615 | + | 9.00000i | 0.236433 | + | 0.409514i | ||||
\(484\) | −5.46410 | − | 9.46410i | −0.248368 | − | 0.430186i | ||||
\(485\) | 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 | \(0.00882512\pi\) | |||||||
\(488\) | 0.267949 | − | 0.464102i | 0.0121295 | − | 0.0210089i | ||||
\(489\) | 2.92820i | 0.132418i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.69615 | − | 4.66987i | −0.121676 | − | 0.210748i | 0.798753 | − | 0.601659i | \(-0.205493\pi\) |
−0.920429 | + | 0.390911i | \(0.872160\pi\) | |||||||
\(492\) | 2.00000 | + | 3.46410i | 0.0901670 | + | 0.156174i | ||||
\(493\) | 5.85641i | 0.263759i | ||||||||
\(494\) | −4.96410 | + | 20.0622i | −0.223345 | + | 0.902640i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.26795 | + | 2.46410i | −0.191637 | + | 0.110641i | ||||
\(497\) | −33.5885 | + | 19.3923i | −1.50665 | + | 0.869864i | ||||
\(498\) | 8.19615 | + | 4.73205i | 0.367278 | + | 0.212048i | ||||
\(499\) | − | 33.3205i | − | 1.49163i | −0.666153 | − | 0.745815i | \(-0.732060\pi\) | ||
0.666153 | − | 0.745815i | \(-0.267940\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.401924 | − | 0.232051i | −0.0179566 | − | 0.0103673i | ||||
\(502\) | 19.5359 | 0.871930 | ||||||||
\(503\) | −3.23205 | − | 1.86603i | −0.144110 | − | 0.0832020i | 0.426211 | − | 0.904624i | \(-0.359848\pi\) |
−0.570321 | + | 0.821422i | \(0.693181\pi\) | |||||||
\(504\) | −1.50000 | − | 2.59808i | −0.0668153 | − | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.928203 | −0.0412637 | ||||||||
\(507\) | −12.9904 | + | 0.500000i | −0.576923 | + | 0.0222058i | ||||
\(508\) | 12.6603i | 0.561708i | ||||||||
\(509\) | −25.3923 | + | 14.6603i | −1.12549 | + | 0.649804i | −0.942798 | − | 0.333365i | \(-0.891816\pi\) |
−0.182696 | + | 0.983169i | \(0.558483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.3923 | + | 18.0000i | −0.459728 | + | 0.796273i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.86603 | − | 4.96410i | 0.126538 | − | 0.219170i | ||||
\(514\) | 12.5885 | + | 7.26795i | 0.555253 | + | 0.320575i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.00000 | + | 5.19615i | −0.132068 | + | 0.228748i | ||||
\(517\) | 1.50000 | − | 0.866025i | 0.0659699 | − | 0.0380878i | ||||
\(518\) | −8.89230 | − | 15.4019i | −0.390705 | − | 0.676722i | ||||
\(519\) | −2.12436 | −0.0932489 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.60770 | −0.289488 | −0.144744 | − | 0.989469i | \(-0.546236\pi\) | ||||
−0.144744 | + | 0.989469i | \(0.546236\pi\) | |||||||
\(522\) | −0.732051 | − | 1.26795i | −0.0320410 | − | 0.0554966i | ||||
\(523\) | −36.1244 | + | 20.8564i | −1.57961 | + | 0.911987i | −0.584694 | + | 0.811254i | \(0.698786\pi\) |
−0.994913 | + | 0.100733i | \(0.967881\pi\) | |||||||
\(524\) | −7.16025 | + | 12.4019i | −0.312797 | + | 0.541781i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.2321 | + | 12.2583i | 0.925761 | + | 0.534489i | ||||
\(527\) | 9.85641 | − | 17.0718i | 0.429352 | − | 0.743659i | ||||
\(528\) | 0.267949 | 0.0116610 | ||||||||
\(529\) | −5.50000 | + | 9.52628i | −0.239130 | + | 0.414186i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.92820 | − | 5.73205i | 0.430847 | − | 0.248750i | ||||
\(532\) | − | 17.1962i | − | 0.745548i | ||||||
\(533\) | −13.8564 | + | 4.00000i | −0.600188 | + | 0.173259i | ||||
\(534\) | 14.1244 | 0.611221 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.732051 | − | 1.26795i | −0.0316198 | − | 0.0547671i | ||||
\(537\) | −7.85641 | − | 4.53590i | −0.339029 | − | 0.195738i | ||||
\(538\) | 17.0718 | 0.736017 | ||||||||
\(539\) | −0.464102 | − | 0.267949i | −0.0199903 | − | 0.0115414i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7846i | 0.635640i | 0.948151 | + | 0.317820i | \(0.102951\pi\) | ||||
−0.948151 | + | 0.317820i | \(0.897049\pi\) | |||||||
\(542\) | −21.1244 | − | 12.1962i | −0.907369 | − | 0.523870i | ||||
\(543\) | −14.6603 | + | 8.46410i | −0.629132 | + | 0.363229i | ||||
\(544\) | −3.46410 | + | 2.00000i | −0.148522 | + | 0.0857493i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.3923 | − | 3.00000i | 0.444750 | − | 0.128388i | ||||
\(547\) | 5.32051i | 0.227488i | 0.993510 | + | 0.113744i | \(0.0362844\pi\) | ||||
−0.993510 | + | 0.113744i | \(0.963716\pi\) | |||||||
\(548\) | 6.73205 | + | 11.6603i | 0.287579 | + | 0.498101i | ||||
\(549\) | −0.267949 | − | 0.464102i | −0.0114358 | − | 0.0198074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 8.39230i | − | 0.357524i | ||||||
\(552\) | −1.73205 | + | 3.00000i | −0.0737210 | + | 0.127688i | ||||
\(553\) | −4.60770 | + | 7.98076i | −0.195939 | + | 0.339377i | ||||
\(554\) | − | 11.5885i | − | 0.492346i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.89230 | − | 17.1340i | −0.419527 | − | 0.726642i | ||||
\(557\) | 11.3038 | + | 19.5788i | 0.478959 | + | 0.829582i | 0.999709 | − | 0.0241275i | \(-0.00768078\pi\) |
−0.520749 | + | 0.853710i | \(0.674347\pi\) | |||||||
\(558\) | 4.92820i | 0.208627i | ||||||||
\(559\) | −15.5885 | − | 15.0000i | −0.659321 | − | 0.634432i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.928203 | + | 0.535898i | −0.0391888 | + | 0.0226256i | ||||
\(562\) | 6.00000 | − | 3.46410i | 0.253095 | − | 0.146124i | ||||
\(563\) | 13.2679 | + | 7.66025i | 0.559177 | + | 0.322841i | 0.752815 | − | 0.658232i | \(-0.228695\pi\) |
−0.193638 | + | 0.981073i | \(0.562029\pi\) | |||||||
\(564\) | − | 6.46410i | − | 0.272188i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.53590 | + | 3.19615i | 0.232691 | + | 0.134344i | ||||
\(567\) | −3.00000 | −0.125988 | ||||||||
\(568\) | −11.1962 | − | 6.46410i | −0.469780 | − | 0.271228i | ||||
\(569\) | −8.16025 | − | 14.1340i | −0.342096 | − | 0.592527i | 0.642726 | − | 0.766096i | \(-0.277803\pi\) |
−0.984822 | + | 0.173569i | \(0.944470\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.8564 | 0.454326 | 0.227163 | − | 0.973857i | \(-0.427055\pi\) | ||||
0.227163 | + | 0.973857i | \(0.427055\pi\) | |||||||
\(572\) | −0.232051 | + | 0.937822i | −0.00970253 | + | 0.0392123i | ||||
\(573\) | 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 | ||||
\(577\) | −9.32051 | −0.388018 | −0.194009 | − | 0.981000i | \(-0.562149\pi\) | ||||
−0.194009 | + | 0.981000i | \(0.562149\pi\) | |||||||
\(578\) | −0.500000 | + | 0.866025i | −0.0207973 | + | 0.0360219i | ||||
\(579\) | 8.53590 | + | 4.92820i | 0.354740 | + | 0.204809i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.1962 | − | 24.5885i | 0.588956 | − | 1.02010i | ||||
\(582\) | 7.26795 | − | 4.19615i | 0.301266 | − | 0.173936i | ||||
\(583\) | −0.0358984 | − | 0.0621778i | −0.00148676 | − | 0.00257514i | ||||
\(584\) | −6.92820 | −0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.2487 | 1.20825 | ||||||||
\(587\) | 4.46410 | + | 7.73205i | 0.184253 | + | 0.319136i | 0.943325 | − | 0.331871i | \(-0.107680\pi\) |
−0.759071 | + | 0.651007i | \(0.774347\pi\) | |||||||
\(588\) | −1.73205 | + | 1.00000i | −0.0714286 | + | 0.0412393i | ||||
\(589\) | −14.1244 | + | 24.4641i | −0.581984 | + | 1.00803i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.86603 | − | 5.69615i | −0.405834 | − | 0.234308i | ||||
\(592\) | 2.96410 | − | 5.13397i | 0.121824 | − | 0.211005i | ||||
\(593\) | 44.7846 | 1.83908 | 0.919542 | − | 0.392992i | \(-0.128560\pi\) | ||||
0.919542 | + | 0.392992i | \(0.128560\pi\) | |||||||
\(594\) | 0.133975 | − | 0.232051i | 0.00549704 | − | 0.00952116i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.2679 | − | 9.39230i | 0.666361 | − | 0.384724i | ||||
\(597\) | − | 24.9282i | − | 1.02024i | ||||||
\(598\) | −9.00000 | − | 8.66025i | −0.368037 | − | 0.354144i | ||||
\(599\) | −28.9282 | −1.18197 | −0.590987 | − | 0.806681i | \(-0.701262\pi\) | ||||
−0.590987 | + | 0.806681i | \(0.701262\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.3564 | − | 26.5981i | −0.626401 | − | 1.08496i | −0.988268 | − | 0.152729i | \(-0.951194\pi\) |
0.361867 | − | 0.932230i | \(-0.382139\pi\) | |||||||
\(602\) | 15.5885 | + | 9.00000i | 0.635338 | + | 0.366813i | ||||
\(603\) | −1.46410 | −0.0596228 | ||||||||
\(604\) | 19.7321 | + | 11.3923i | 0.802886 | + | 0.463546i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 12.3923i | − | 0.503403i | ||||||
\(607\) | −18.5718 | − | 10.7224i | −0.753806 | − | 0.435210i | 0.0732615 | − | 0.997313i | \(-0.476659\pi\) |
−0.827067 | + | 0.562103i | \(0.809993\pi\) | |||||||
\(608\) | 4.96410 | − | 2.86603i | 0.201321 | − | 0.116233i | ||||
\(609\) | −3.80385 | + | 2.19615i | −0.154140 | + | 0.0889926i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.6244 | + | 5.59808i | 0.915283 | + | 0.226474i | ||||
\(612\) | 4.00000i | 0.161690i | ||||||||
\(613\) | 22.5000 | + | 38.9711i | 0.908766 | + | 1.57403i | 0.815780 | + | 0.578362i | \(0.196308\pi\) |
0.0929864 | + | 0.995667i | \(0.470359\pi\) | |||||||
\(614\) | 14.1244 | + | 24.4641i | 0.570013 | + | 0.987291i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 0.803848i | − | 0.0323879i | ||||||
\(617\) | −17.7321 | + | 30.7128i | −0.713865 | + | 1.23645i | 0.249530 | + | 0.968367i | \(0.419724\pi\) |
−0.963395 | + | 0.268084i | \(0.913609\pi\) | |||||||
\(618\) | 5.79423 | − | 10.0359i | 0.233078 | − | 0.403703i | ||||
\(619\) | − | 2.51666i | − | 0.101153i | −0.998720 | − | 0.0505766i | \(-0.983894\pi\) | ||
0.998720 | − | 0.0505766i | \(-0.0161059\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.73205 | + | 3.00000i | 0.0695048 | + | 0.120386i | ||||
\(622\) | −9.46410 | − | 16.3923i | −0.379476 | − | 0.657272i | ||||
\(623\) | − | 42.3731i | − | 1.69764i | ||||||
\(624\) | 2.59808 | + | 2.50000i | 0.104006 | + | 0.100080i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −28.8564 | + | 16.6603i | −1.15333 | + | 0.665878i | ||||
\(627\) | 1.33013 | − | 0.767949i | 0.0531202 | − | 0.0306689i | ||||
\(628\) | 18.3564 | + | 10.5981i | 0.732500 | + | 0.422909i | ||||
\(629\) | 23.7128i | 0.945492i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.92820 | − | 4.00000i | −0.275807 | − | 0.159237i | 0.355716 | − | 0.934594i | \(-0.384237\pi\) |
−0.631524 | + | 0.775356i | \(0.717570\pi\) | |||||||
\(632\) | −3.07180 | −0.122190 | ||||||||
\(633\) | −6.99038 | − | 4.03590i | −0.277843 | − | 0.160413i | ||||
\(634\) | −15.2321 | − | 26.3827i | −0.604942 | − | 1.04779i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.267949 | −0.0106249 | ||||||||
\(637\) | −2.00000 | − | 6.92820i | −0.0792429 | − | 0.274505i | ||||
\(638\) | − | 0.392305i | − | 0.0155315i | ||||||
\(639\) | −11.1962 | + | 6.46410i | −0.442913 | + | 0.255716i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.23205 | + | 12.5263i | −0.285649 | + | 0.494758i | −0.972766 | − | 0.231788i | \(-0.925542\pi\) |
0.687117 | + | 0.726546i | \(0.258876\pi\) | |||||||
\(642\) | 12.9282 | 0.510235 | ||||||||
\(643\) | −6.39230 | + | 11.0718i | −0.252088 | + | 0.436629i | −0.964100 | − | 0.265538i | \(-0.914451\pi\) |
0.712013 | + | 0.702167i | \(0.247784\pi\) | |||||||
\(644\) | 9.00000 | + | 5.19615i | 0.354650 | + | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.4641 | + | 19.8564i | −0.451049 | + | 0.781240i | ||||
\(647\) | 30.9449 | − | 17.8660i | 1.21657 | − | 0.702386i | 0.252386 | − | 0.967627i | \(-0.418785\pi\) |
0.964182 | + | 0.265241i | \(0.0854514\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 3.07180 | 0.120579 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 14.7846 | 0.579455 | ||||||||
\(652\) | 1.46410 | + | 2.53590i | 0.0573386 | + | 0.0993134i | ||||
\(653\) | −1.37564 | + | 0.794229i | −0.0538331 | + | 0.0310806i | −0.526675 | − | 0.850067i | \(-0.676562\pi\) |
0.472842 | + | 0.881147i | \(0.343228\pi\) | |||||||
\(654\) | 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 | ||||
\(658\) | −19.3923 | −0.755991 | ||||||||
\(659\) | −19.8564 | + | 34.3923i | −0.773496 | + | 1.33973i | 0.162140 | + | 0.986768i | \(0.448160\pi\) |
−0.935636 | + | 0.352966i | \(0.885173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.7128 | + | 10.8038i | −0.727844 | + | 0.420221i | −0.817633 | − | 0.575740i | \(-0.804714\pi\) |
0.0897889 | + | 0.995961i | \(0.471381\pi\) | |||||||
\(662\) | − | 14.3923i | − | 0.559373i | ||||||
\(663\) | −14.0000 | − | 3.46410i | −0.543715 | − | 0.134535i | ||||
\(664\) | 9.46410 | 0.367278 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.96410 | − | 5.13397i | −0.114857 | − | 0.198937i | ||||
\(667\) | 4.39230 | + | 2.53590i | 0.170071 | + | 0.0981904i | ||||
\(668\) | −0.464102 | −0.0179566 | ||||||||
\(669\) | 16.3301 | + | 9.42820i | 0.631359 | + | 0.364515i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 0.143594i | − | 0.00554337i | ||||||
\(672\) | −2.59808 | − | 1.50000i | −0.100223 | − | 0.0578638i | ||||
\(673\) | −14.5359 | + | 8.39230i | −0.560318 | + | 0.323500i | −0.753273 | − | 0.657708i | \(-0.771526\pi\) |
0.192955 | + | 0.981208i | \(0.438193\pi\) | |||||||
\(674\) | 22.8564 | − | 13.1962i | 0.880396 | − | 0.508297i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | + | 6.92820i | −0.423077 | + | 0.266469i | ||||
\(677\) | − | 10.9282i | − | 0.420005i | −0.977701 | − | 0.210002i | \(-0.932653\pi\) | ||
0.977701 | − | 0.210002i | \(-0.0673472\pi\) | |||||||
\(678\) | 6.00000 | + | 10.3923i | 0.230429 | + | 0.399114i | ||||
\(679\) | −12.5885 | − | 21.8038i | −0.483101 | − | 0.836755i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.53590i | 0.250456i | ||||||||
\(682\) | −0.660254 | + | 1.14359i | −0.0252824 | + | 0.0437905i | ||||
\(683\) | −20.6603 | + | 35.7846i | −0.790543 | + | 1.36926i | 0.135089 | + | 0.990834i | \(0.456868\pi\) |
−0.925631 | + | 0.378427i | \(0.876465\pi\) | |||||||
\(684\) | − | 5.73205i | − | 0.219170i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.50000 | − | 12.9904i | −0.286351 | − | 0.495975i | ||||
\(687\) | −2.26795 | − | 3.92820i | −0.0865277 | − | 0.149870i | ||||
\(688\) | 6.00000i | 0.228748i | ||||||||
\(689\) | 0.232051 | − | 0.937822i | 0.00884043 | − | 0.0357282i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0359 | − | 7.52628i | 0.495909 | − | 0.286313i | −0.231114 | − | 0.972927i | \(-0.574237\pi\) |
0.727023 | + | 0.686614i | \(0.240904\pi\) | |||||||
\(692\) | −1.83975 | + | 1.06218i | −0.0699366 | + | 0.0403779i | ||||
\(693\) | −0.696152 | − | 0.401924i | −0.0264446 | − | 0.0152678i | ||||
\(694\) | − | 4.39230i | − | 0.166730i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.26795 | − | 0.732051i | −0.0480615 | − | 0.0277483i | ||||
\(697\) | −16.0000 | −0.606043 | ||||||||
\(698\) | −9.12436 | − | 5.26795i | −0.345362 | − | 0.199395i | ||||
\(699\) | −9.00000 | − | 15.5885i | −0.340411 | − | 0.589610i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.39230 | −0.165895 | −0.0829475 | − | 0.996554i | \(-0.526433\pi\) | ||||
−0.0829475 | + | 0.996554i | \(0.526433\pi\) | |||||||
\(702\) | 3.46410 | − | 1.00000i | 0.130744 | − | 0.0377426i | ||||
\(703\) | − | 33.9808i | − | 1.28161i | ||||||
\(704\) | 0.232051 | − | 0.133975i | 0.00874574 | − | 0.00504936i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.80385 | − | 6.58846i | 0.143160 | − | 0.247960i | ||||
\(707\) | −37.1769 | −1.39818 | ||||||||
\(708\) | 5.73205 | − | 9.92820i | 0.215424 | − | 0.373125i | ||||
\(709\) | 23.6603 | + | 13.6603i | 0.888579 | + | 0.513022i | 0.873478 | − | 0.486864i | \(-0.161859\pi\) |
0.0151019 | + | 0.999886i | \(0.495193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.53590 | + | 2.66025i | −0.0576007 | + | 0.0997673i | ||||
\(712\) | 12.2321 | − | 7.06218i | 0.458415 | − | 0.264666i | ||||
\(713\) | −8.53590 | − | 14.7846i | −0.319672 | − | 0.553688i | ||||
\(714\) | 12.0000 | 0.449089 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.07180 | −0.339029 | ||||||||
\(717\) | 1.73205 | + | 3.00000i | 0.0646846 | + | 0.112037i | ||||
\(718\) | −0.803848 | + | 0.464102i | −0.0299993 | + | 0.0173201i | ||||
\(719\) | 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 | ||||||||
\(721\) | −30.1077 | − | 17.3827i | −1.12127 | − | 0.647365i | ||||
\(722\) | 6.92820 | − | 12.0000i | 0.257841 | − | 0.446594i | ||||
\(723\) | 25.1962 | 0.937055 | ||||||||
\(724\) | −8.46410 | + | 14.6603i | −0.314566 | + | 0.544844i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.46410 | + | 5.46410i | −0.351246 | + | 0.202792i | ||||
\(727\) | 4.66025i | 0.172839i | 0.996259 | + | 0.0864196i | \(0.0275426\pi\) | ||||
−0.996259 | + | 0.0864196i | \(0.972457\pi\) | |||||||
\(728\) | 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 | ||||
\(732\) | −0.464102 | − | 0.267949i | −0.0171537 | − | 0.00990369i | ||||
\(733\) | −20.8564 | −0.770349 | −0.385174 | − | 0.922844i | \(-0.625859\pi\) | ||||
−0.385174 | + | 0.922844i | \(0.625859\pi\) | |||||||
\(734\) | 18.4641 | + | 10.6603i | 0.681522 | + | 0.393477i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.46410i | 0.127688i | ||||||||
\(737\) | −0.339746 | − | 0.196152i | −0.0125147 | − | 0.00722537i | ||||
\(738\) | 3.46410 | − | 2.00000i | 0.127515 | − | 0.0736210i | ||||
\(739\) | −31.0359 | + | 17.9186i | −1.14167 | + | 0.659146i | −0.946845 | − | 0.321691i | \(-0.895749\pi\) |
−0.194829 | + | 0.980837i | \(0.562415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.0622 | + | 4.96410i | 0.737003 | + | 0.182361i | ||||
\(742\) | 0.803848i | 0.0295102i | ||||||||
\(743\) | −5.46410 | − | 9.46410i | −0.200458 | − | 0.347204i | 0.748218 | − | 0.663453i | \(-0.230910\pi\) |
−0.948676 | + | 0.316249i | \(0.897576\pi\) | |||||||
\(744\) | 2.46410 | + | 4.26795i | 0.0903383 | + | 0.156471i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.07180i | 0.332142i | ||||||||
\(747\) | 4.73205 | − | 8.19615i | 0.173137 | − | 0.299882i | ||||
\(748\) | −0.535898 | + | 0.928203i | −0.0195944 | + | 0.0339385i | ||||
\(749\) | − | 38.7846i | − | 1.41716i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.5885 | + | 18.3397i | 0.386378 | + | 0.669227i | 0.991959 | − | 0.126557i | \(-0.0403926\pi\) |
−0.605581 | + | 0.795784i | \(0.707059\pi\) | |||||||
\(752\) | −3.23205 | − | 5.59808i | −0.117861 | − | 0.204141i | ||||
\(753\) | − | 19.5359i | − | 0.711928i | ||||||
\(754\) | 3.66025 | − | 3.80385i | 0.133299 | − | 0.138528i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.59808 | + | 1.50000i | −0.0944911 | + | 0.0545545i | ||||
\(757\) | −18.8205 | + | 10.8660i | −0.684043 | + | 0.394932i | −0.801377 | − | 0.598160i | \(-0.795899\pi\) |
0.117334 | + | 0.993093i | \(0.462565\pi\) | |||||||
\(758\) | −8.42820 | − | 4.86603i | −0.306126 | − | 0.176742i | ||||
\(759\) | 0.928203i | 0.0336916i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.91154 | + | 3.99038i | 0.250543 | + | 0.144651i | 0.620013 | − | 0.784592i | \(-0.287127\pi\) |
−0.369470 | + | 0.929243i | \(0.620461\pi\) | |||||||
\(762\) | 12.6603 | 0.458633 | ||||||||
\(763\) | −27.0000 | − | 15.5885i | −0.977466 | − | 0.564340i | ||||
\(764\) | 8.66025 | + | 15.0000i | 0.313317 | + | 0.542681i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.78461 | 0.172875 | ||||||||
\(767\) | 29.7846 | + | 28.6603i | 1.07546 | + | 1.03486i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −13.6077 | + | 7.85641i | −0.490706 | + | 0.283309i | −0.724867 | − | 0.688889i | \(-0.758099\pi\) |
0.234161 | + | 0.972198i | \(0.424766\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.26795 | − | 12.5885i | 0.261749 | − | 0.453362i | ||||
\(772\) | 9.85641 | 0.354740 | ||||||||
\(773\) | 16.3038 | − | 28.2391i | 0.586409 | − | 1.01569i | −0.408290 | − | 0.912852i | \(-0.633875\pi\) |
0.994698 | − | 0.102837i | \(-0.0327920\pi\) | |||||||
\(774\) | 5.19615 | + | 3.00000i | 0.186772 | + | 0.107833i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.19615 | − | 7.26795i | 0.150633 | − | 0.260904i | ||||
\(777\) | −15.4019 | + | 8.89230i | −0.552541 | + | 0.319010i | ||||
\(778\) | 8.92820 | + | 15.4641i | 0.320092 | + | 0.554415i | ||||
\(779\) | 22.9282 | 0.821488 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.46410 | −0.123955 | ||||||||
\(782\) | −6.92820 | − | 12.0000i | −0.247752 | − | 0.429119i | ||||
\(783\) | −1.26795 | + | 0.732051i | −0.0453128 | + | 0.0261614i | ||||
\(784\) | −1.00000 | + | 1.73205i | −0.0357143 | + | 0.0618590i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.4019 | + | 7.16025i | 0.442362 | + | 0.255398i | ||||
\(787\) | 0.732051 | − | 1.26795i | 0.0260948 | − | 0.0451975i | −0.852683 | − | 0.522428i | \(-0.825026\pi\) |
0.878778 | + | 0.477231i | \(0.158359\pi\) | |||||||
\(788\) | −11.3923 | −0.405834 | ||||||||
\(789\) | 12.2583 | − | 21.2321i | 0.436408 | − | 0.755881i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.1769 | − | 18.0000i | 1.10852 | − | 0.640006i | ||||
\(792\) | − | 0.267949i | − | 0.00952116i | ||||||
\(793\) | 1.33975 | − | 1.39230i | 0.0475758 | − | 0.0494422i | ||||
\(794\) | 5.92820 | 0.210384 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.4641 | − | 21.5885i | −0.441778 | − | 0.765183i | ||||
\(797\) | −8.78461 | − | 5.07180i | −0.311167 | − | 0.179652i | 0.336282 | − | 0.941761i | \(-0.390831\pi\) |
−0.647449 | + | 0.762109i | \(0.724164\pi\) | |||||||
\(798\) | −17.1962 | −0.608737 | ||||||||
\(799\) | 22.3923 | + | 12.9282i | 0.792183 | + | 0.457367i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 14.1244i | − | 0.499060i | ||||||
\(802\) | 19.1603 | + | 11.0622i | 0.676572 | + | 0.390619i | ||||
\(803\) | −1.60770 | + | 0.928203i | −0.0567343 | + | 0.0327556i | ||||
\(804\) | −1.26795 | + | 0.732051i | −0.0447171 | + | 0.0258174i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −17.0718 | + | 4.92820i | −0.601328 | + | 0.173589i | ||||
\(807\) | − | 17.0718i | − | 0.600956i | ||||||
\(808\) | −6.19615 | − | 10.7321i | −0.217980 | − | 0.377552i | ||||
\(809\) | −3.39230 | − | 5.87564i | −0.119267 | − | 0.206577i | 0.800210 | − | 0.599719i | \(-0.204721\pi\) |
−0.919477 | + | 0.393143i | \(0.871388\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.5885i | 0.828303i | 0.910208 | + | 0.414151i | \(0.135922\pi\) | ||||
−0.910208 | + | 0.414151i | \(0.864078\pi\) | |||||||
\(812\) | −2.19615 | + | 3.80385i | −0.0770698 | + | 0.133489i | ||||
\(813\) | −12.1962 | + | 21.1244i | −0.427738 | + | 0.740863i | ||||
\(814\) | − | 1.58846i | − | 0.0556754i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | 17.1962 | + | 29.7846i | 0.601617 | + | 1.04203i | ||||
\(818\) | − | 39.0526i | − | 1.36544i | ||||||
\(819\) | −3.00000 | − | 10.3923i | −0.104828 | − | 0.363137i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.7128 | + | 7.33975i | −0.443680 | + | 0.256159i | −0.705157 | − | 0.709051i | \(-0.749124\pi\) |
0.261477 | + | 0.965210i | \(0.415790\pi\) | |||||||
\(822\) | 11.6603 | − | 6.73205i | 0.406698 | − | 0.234807i | ||||
\(823\) | 7.28461 | + | 4.20577i | 0.253926 | + | 0.146604i | 0.621560 | − | 0.783366i | \(-0.286499\pi\) |
−0.367635 | + | 0.929970i | \(0.619832\pi\) | |||||||
\(824\) | − | 11.5885i | − | 0.403703i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −29.7846 | − | 17.1962i | −1.03634 | − | 0.598331i | ||||
\(827\) | 46.4974 | 1.61687 | 0.808437 | − | 0.588583i | \(-0.200314\pi\) | ||||
0.808437 | + | 0.588583i | \(0.200314\pi\) | |||||||
\(828\) | 3.00000 | + | 1.73205i | 0.104257 | + | 0.0601929i | ||||
\(829\) | −2.33975 | − | 4.05256i | −0.0812627 | − | 0.140751i | 0.822530 | − | 0.568722i | \(-0.192562\pi\) |
−0.903793 | + | 0.427971i | \(0.859229\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.5885 | −0.401999 | ||||||||
\(832\) | 3.50000 | + | 0.866025i | 0.121341 | + | 0.0300240i | ||||
\(833\) | − | 8.00000i | − | 0.277184i | ||||||
\(834\) | −17.1340 | + | 9.89230i | −0.593301 | + | 0.342543i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.767949 | − | 1.33013i | 0.0265601 | − | 0.0460034i | ||||
\(837\) | 4.92820 | 0.170344 | ||||||||
\(838\) | 4.92820 | − | 8.53590i | 0.170242 | − | 0.294868i | ||||
\(839\) | −16.6077 | − | 9.58846i | −0.573361 | − | 0.331030i | 0.185129 | − | 0.982714i | \(-0.440730\pi\) |
−0.758491 | + | 0.651684i | \(0.774063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.4282 | − | 23.2583i | 0.463041 | − | 0.802011i | ||||
\(842\) | 18.9282 | − | 10.9282i | 0.652309 | − | 0.376611i | ||||
\(843\) | −3.46410 | − | 6.00000i | −0.119310 | − | 0.206651i | ||||
\(844\) | −8.07180 | −0.277843 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.46410 | −0.222240 | ||||||||
\(847\) | 16.3923 | + | 28.3923i | 0.563246 | + | 0.975571i | ||||
\(848\) | −0.232051 | + | 0.133975i | −0.00796866 | + | 0.00460071i | ||||
\(849\) | 3.19615 | − | 5.53590i | 0.109692 | − | 0.189992i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.7846 | + | 10.2679i | 0.609649 | + | 0.351981i | ||||
\(852\) | −6.46410 | + | 11.1962i | −0.221456 | + | 0.383574i | ||||
\(853\) | 24.6410 | 0.843692 | 0.421846 | − | 0.906667i | \(-0.361382\pi\) | ||||
0.421846 | + | 0.906667i | \(0.361382\pi\) | |||||||
\(854\) | −0.803848 | + | 1.39230i | −0.0275071 | + | 0.0476437i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.1962 | − | 6.46410i | 0.382677 | − | 0.220938i | ||||
\(857\) | 28.9282i | 0.988169i | 0.869414 | + | 0.494084i | \(0.164497\pi\) | ||||
−0.869414 | + | 0.494084i | \(0.835503\pi\) | |||||||
\(858\) | 0.937822 | + | 0.232051i | 0.0320167 | + | 0.00792208i | ||||
\(859\) | 6.07180 | 0.207167 | 0.103584 | − | 0.994621i | \(-0.466969\pi\) | ||||
0.103584 | + | 0.994621i | \(0.466969\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.00000 | − | 10.3923i | −0.204479 | − | 0.354169i | ||||
\(862\) | 12.0000 | + | 6.92820i | 0.408722 | + | 0.235976i | ||||
\(863\) | −2.92820 | −0.0996772 | −0.0498386 | − | 0.998757i | \(-0.515871\pi\) | ||||
−0.0498386 | + | 0.998757i | \(0.515871\pi\) | |||||||
\(864\) | −0.866025 | − | 0.500000i | −0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 8.78461i | − | 0.298513i | ||||||
\(867\) | 0.866025 | + | 0.500000i | 0.0294118 | + | 0.0169809i | ||||
\(868\) | 12.8038 | − | 7.39230i | 0.434591 | − | 0.250911i | ||||
\(869\) | −0.712813 | + | 0.411543i | −0.0241805 | + | 0.0139606i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.46410 | − | 5.07180i | −0.0496092 | − | 0.171851i | ||||
\(872\) | − | 10.3923i | − | 0.351928i | ||||||
\(873\) | −4.19615 | − | 7.26795i | −0.142018 | − | 0.245983i | ||||
\(874\) | 9.92820 | + | 17.1962i | 0.335826 | + | 0.581669i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.92820i | 0.234082i | ||||||||
\(877\) | 10.8564 | − | 18.8038i | 0.366595 | − | 0.634961i | −0.622436 | − | 0.782671i | \(-0.713857\pi\) |
0.989031 | + | 0.147710i | \(0.0471902\pi\) | |||||||
\(878\) | −6.66025 | + | 11.5359i | −0.224773 | + | 0.389318i | ||||
\(879\) | − | 29.2487i | − | 0.986535i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.5526 | − | 33.8660i | −0.658742 | − | 1.14098i | −0.980941 | − | 0.194303i | \(-0.937755\pi\) |
0.322199 | − | 0.946672i | \(-0.395578\pi\) | |||||||
\(882\) | 1.00000 | + | 1.73205i | 0.0336718 | + | 0.0583212i | ||||
\(883\) | − | 13.3205i | − | 0.448271i | −0.974558 | − | 0.224135i | \(-0.928044\pi\) | ||
0.974558 | − | 0.224135i | \(-0.0719558\pi\) | |||||||
\(884\) | −13.8564 | + | 4.00000i | −0.466041 | + | 0.134535i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.1962 | + | 9.92820i | −0.577716 | + | 0.333545i | ||||
\(887\) | −48.2654 | + | 27.8660i | −1.62059 | + | 0.935650i | −0.633831 | + | 0.773472i | \(0.718519\pi\) |
−0.986762 | + | 0.162178i | \(0.948148\pi\) | |||||||
\(888\) | −5.13397 | − | 2.96410i | −0.172285 | − | 0.0994687i | ||||
\(889\) | − | 37.9808i | − | 1.27383i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.232051 | − | 0.133975i | −0.00777399 | − | 0.00448832i | ||||
\(892\) | 18.8564 | 0.631359 | ||||||||
\(893\) | −32.0885 | − | 18.5263i | −1.07380 | − | 0.619958i | ||||
\(894\) | −9.39230 | − | 16.2679i | −0.314126 | − | 0.544082i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.00000 | −0.100223 | ||||||||
\(897\) | −8.66025 | + | 9.00000i | −0.289157 | + | 0.300501i | ||||
\(898\) | − | 6.12436i | − | 0.204372i | ||||||
\(899\) | 6.24871 | − | 3.60770i | 0.208406 | − | 0.120323i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.535898 | − | 0.928203i | 0.0178534 | − | 0.0309229i | ||||
\(902\) | 1.07180 | 0.0356869 | ||||||||
\(903\) | 9.00000 | − | 15.5885i | 0.299501 | − | 0.518751i | ||||
\(904\) | 10.3923 | + | 6.00000i | 0.345643 | + | 0.199557i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.3923 | − | 19.7321i | 0.378484 | − | 0.655553i | ||||
\(907\) | −18.1244 | + | 10.4641i | −0.601809 | + | 0.347455i | −0.769753 | − | 0.638342i | \(-0.779621\pi\) |
0.167944 | + | 0.985797i | \(0.446287\pi\) | |||||||
\(908\) | 3.26795 | + | 5.66025i | 0.108451 | + | 0.187842i | ||||
\(909\) | −12.3923 | −0.411027 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.7846 | 0.423573 | 0.211787 | − | 0.977316i | \(-0.432072\pi\) | ||||
0.211787 | + | 0.977316i | \(0.432072\pi\) | |||||||
\(912\) | −2.86603 | − | 4.96410i | −0.0949036 | − | 0.164378i | ||||
\(913\) | 2.19615 | − | 1.26795i | 0.0726820 | − | 0.0419630i | ||||
\(914\) | 3.73205 | − | 6.46410i | 0.123445 | − | 0.213813i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.92820 | − | 2.26795i | −0.129791 | − | 0.0749352i | ||||
\(917\) | 21.4808 | − | 37.2058i | 0.709357 | − | 1.22864i | ||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | −23.9808 | + | 41.5359i | −0.791052 | + | 1.37014i | 0.134264 | + | 0.990946i | \(0.457133\pi\) |
−0.925316 | + | 0.379197i | \(0.876200\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.4641 | − | 14.1244i | 0.806120 | − | 0.465413i | ||||
\(922\) | 11.6077i | 0.382279i | ||||||||
\(923\) | −33.5885 | − | 32.3205i | −1.10558 | − | 1.06384i | ||||
\(924\) | −0.803848 | −0.0264446 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20.3923 | − | 35.3205i | −0.670133 | − | 1.16070i | ||||
\(927\) | −10.0359 | − | 5.79423i | −0.329622 | − | 0.190307i | ||||
\(928\) | −1.46410 | −0.0480615 | ||||||||
\(929\) | −50.1051 | − | 28.9282i | −1.64390 | − | 0.949104i | −0.979430 | − | 0.201785i | \(-0.935326\pi\) |
−0.664466 | − | 0.747319i | \(-0.731341\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.4641i | 0.375721i | ||||||||
\(932\) | −15.5885 | − | 9.00000i | −0.510617 | − | 0.294805i | ||||
\(933\) | −16.3923 | + | 9.46410i | −0.536660 | + | 0.309841i | ||||
\(934\) | −21.1244 | + | 12.1962i | −0.691210 | + | 0.399070i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.50000 | − | 2.59808i | 0.0817151 | − | 0.0849208i | ||||
\(937\) | 21.7128i | 0.709327i | 0.934994 | + | 0.354663i | \(0.115405\pi\) | ||||
−0.934994 | + | 0.354663i | \(0.884595\pi\) | |||||||
\(938\) | 2.19615 | + | 3.80385i | 0.0717069 | + | 0.124200i | ||||
\(939\) | 16.6603 | + | 28.8564i | 0.543687 | + | 0.941693i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 60.4974i | − | 1.97216i | −0.166273 | − | 0.986080i | \(-0.553173\pi\) | ||
0.166273 | − | 0.986080i | \(-0.446827\pi\) | |||||||
\(942\) | 10.5981 | − | 18.3564i | 0.345304 | − | 0.598084i | ||||
\(943\) | −6.92820 | + | 12.0000i | −0.225613 | + | 0.390774i | ||||
\(944\) | − | 11.4641i | − | 0.373125i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.803848 | + | 1.39230i | 0.0261353 | + | 0.0452677i | ||||
\(947\) | −17.1962 | − | 29.7846i | −0.558800 | − | 0.967870i | −0.997597 | − | 0.0692836i | \(-0.977929\pi\) |
0.438797 | − | 0.898586i | \(-0.355405\pi\) | |||||||
\(948\) | 3.07180i | 0.0997673i | ||||||||
\(949\) | −24.2487 | − | 6.00000i | −0.787146 | − | 0.194768i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.3827 | + | 15.2321i | −0.855517 | + | 0.493933i | ||||
\(952\) | 10.3923 | − | 6.00000i | 0.336817 | − | 0.194461i | ||||
\(953\) | 46.1769 | + | 26.6603i | 1.49582 | + | 0.863610i | 0.999988 | − | 0.00481009i | \(-0.00153111\pi\) |
0.495829 | + | 0.868420i | \(0.334864\pi\) | |||||||
\(954\) | 0.267949i | 0.00867518i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | + | 1.73205i | 0.0970269 | + | 0.0560185i | ||||
\(957\) | −0.392305 | −0.0126814 | ||||||||
\(958\) | −19.2679 | − | 11.1244i | −0.622519 | − | 0.359412i | ||||
\(959\) | −20.1962 | − | 34.9808i | −0.652168 | − | 1.12959i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.71281 | 0.216542 | ||||||||
\(962\) | 14.8205 | − | 15.4019i | 0.477832 | − | 0.496578i | ||||
\(963\) | − | 12.9282i | − | 0.416606i | ||||||
\(964\) | 21.8205 | − | 12.5981i | 0.702791 | − | 0.405757i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.19615 | − | 9.00000i | 0.167183 | − | 0.289570i | ||||
\(967\) | −1.14359 | −0.0367755 | −0.0183877 | − | 0.999831i | \(-0.505853\pi\) | ||||
−0.0183877 | + | 0.999831i | \(0.505853\pi\) | |||||||
\(968\) | −5.46410 | + | 9.46410i | −0.175623 | + | 0.304188i | ||||
\(969\) | 19.8564 | + | 11.4641i | 0.637880 | + | 0.368280i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.6962 | − | 35.8468i | 0.664171 | − | 1.15038i | −0.315338 | − | 0.948979i | \(-0.602118\pi\) |
0.979509 | − | 0.201399i | \(-0.0645487\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | 29.6769 | + | 51.4019i | 0.951398 | + | 1.64787i | ||||
\(974\) | −21.0000 | −0.672883 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.535898 | −0.0171537 | ||||||||
\(977\) | 2.73205 | + | 4.73205i | 0.0874060 | + | 0.151392i | 0.906414 | − | 0.422391i | \(-0.138809\pi\) |
−0.819008 | + | 0.573782i | \(0.805476\pi\) | |||||||
\(978\) | 2.53590 | − | 1.46410i | 0.0810891 | − | 0.0468168i | ||||
\(979\) | 1.89230 | − | 3.27757i | 0.0604783 | − | 0.104752i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.00000 | − | 5.19615i | −0.287348 | − | 0.165900i | ||||
\(982\) | −2.69615 | + | 4.66987i | −0.0860377 | + | 0.149022i | ||||
\(983\) | −46.1769 | −1.47281 | −0.736407 | − | 0.676538i | \(-0.763479\pi\) | ||||
−0.736407 | + | 0.676538i | \(0.763479\pi\) | |||||||
\(984\) | 2.00000 | − | 3.46410i | 0.0637577 | − | 0.110432i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.07180 | − | 2.92820i | 0.161519 | − | 0.0932530i | ||||
\(987\) | 19.3923i | 0.617264i | ||||||||
\(988\) | 19.8564 | − | 5.73205i | 0.631716 | − | 0.182361i | ||||
\(989\) | −20.7846 | −0.660912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.5885 | − | 33.9282i | −0.622248 | − | 1.07776i | −0.989066 | − | 0.147472i | \(-0.952886\pi\) |
0.366818 | − | 0.930293i | \(-0.380447\pi\) | |||||||
\(992\) | 4.26795 | + | 2.46410i | 0.135508 | + | 0.0782353i | ||||
\(993\) | −14.3923 | −0.456726 | ||||||||
\(994\) | 33.5885 | + | 19.3923i | 1.06536 | + | 0.615087i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 9.46410i | − | 0.299882i | ||||||
\(997\) | 53.6769 | + | 30.9904i | 1.69996 | + | 0.981475i | 0.945777 | + | 0.324817i | \(0.105303\pi\) |
0.754188 | + | 0.656659i | \(0.228031\pi\) | |||||||
\(998\) | −28.8564 | + | 16.6603i | −0.913434 | + | 0.527371i | ||||
\(999\) | −5.13397 | + | 2.96410i | −0.162432 | + | 0.0937800i |
(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.49.1 | 4 | ||
5.2 | odd | 4 | 390.2.bb.a.361.2 | yes | 4 | ||
5.3 | odd | 4 | 1950.2.bc.a.751.1 | 4 | |||
5.4 | even | 2 | 1950.2.y.e.49.2 | 4 | |||
13.4 | even | 6 | 1950.2.y.e.199.2 | 4 | |||
15.2 | even | 4 | 1170.2.bs.d.361.1 | 4 | |||
65.2 | even | 12 | 5070.2.a.be.1.2 | 2 | |||
65.4 | even | 6 | inner | 1950.2.y.d.199.1 | 4 | ||
65.17 | odd | 12 | 390.2.bb.a.121.2 | ✓ | 4 | ||
65.37 | even | 12 | 5070.2.a.ba.1.1 | 2 | |||
65.42 | odd | 12 | 5070.2.b.p.1351.3 | 4 | |||
65.43 | odd | 12 | 1950.2.bc.a.901.1 | 4 | |||
65.62 | odd | 12 | 5070.2.b.p.1351.2 | 4 | |||
195.17 | even | 12 | 1170.2.bs.d.901.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.a.121.2 | ✓ | 4 | 65.17 | odd | 12 | ||
390.2.bb.a.361.2 | yes | 4 | 5.2 | odd | 4 | ||
1170.2.bs.d.361.1 | 4 | 15.2 | even | 4 | |||
1170.2.bs.d.901.1 | 4 | 195.17 | even | 12 | |||
1950.2.y.d.49.1 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.y.d.199.1 | 4 | 65.4 | even | 6 | inner | ||
1950.2.y.e.49.2 | 4 | 5.4 | even | 2 | |||
1950.2.y.e.199.2 | 4 | 13.4 | even | 6 | |||
1950.2.bc.a.751.1 | 4 | 5.3 | odd | 4 | |||
1950.2.bc.a.901.1 | 4 | 65.43 | odd | 12 | |||
5070.2.a.ba.1.1 | 2 | 65.37 | even | 12 | |||
5070.2.a.be.1.2 | 2 | 65.2 | even | 12 | |||
5070.2.b.p.1351.2 | 4 | 65.62 | odd | 12 | |||
5070.2.b.p.1351.3 | 4 | 65.42 | odd | 12 |