Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,2,Mod(149,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.j (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.79476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 249.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.249 |
Dual form | 350.2.j.e.149.1 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | −1.73205 | − | 1.00000i | −1.00000 | − | 0.577350i | −0.0917517 | − | 0.995782i | \(-0.529247\pi\) |
−0.908248 | + | 0.418432i | \(0.862580\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | −0.866025 | + | 2.50000i | −0.327327 | + | 0.944911i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | −1.73205 | + | 1.00000i | −0.500000 | + | 0.288675i | ||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | −0.500000 | − | 2.59808i | −0.133631 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.59808 | + | 1.50000i | 0.630126 | + | 0.363803i | 0.780801 | − | 0.624780i | \(-0.214811\pi\) |
−0.150675 | + | 0.988583i | \(0.548145\pi\) | |||||||
\(18\) | −0.866025 | − | 0.500000i | −0.204124 | − | 0.117851i | ||||
\(19\) | 4.00000 | + | 6.92820i | 0.917663 | + | 1.58944i | 0.802955 | + | 0.596040i | \(0.203260\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | − | 3.46410i | 0.872872 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.79423 | − | 4.50000i | 1.62521 | − | 0.938315i | 0.639713 | − | 0.768613i | \(-0.279053\pi\) |
0.985496 | − | 0.169701i | \(-0.0542803\pi\) | |||||||
\(24\) | 1.00000 | − | 1.73205i | 0.204124 | − | 0.353553i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.00000 | + | 1.73205i | 0.196116 | + | 0.339683i | ||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | 1.73205 | + | 2.00000i | 0.327327 | + | 0.377964i | ||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | + | 4.33013i | −0.449013 | + | 0.777714i | −0.998322 | − | 0.0579057i | \(-0.981558\pi\) |
0.549309 | + | 0.835619i | \(0.314891\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.00000 | −0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.92820 | − | 4.00000i | 1.13899 | − | 0.657596i | 0.192809 | − | 0.981236i | \(-0.438240\pi\) |
0.946180 | + | 0.323640i | \(0.104907\pi\) | |||||||
\(38\) | −6.92820 | − | 4.00000i | −1.12390 | − | 0.648886i | ||||
\(39\) | −2.00000 | + | 3.46410i | −0.320256 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | −1.73205 | + | 5.00000i | −0.267261 | + | 0.771517i | ||||
\(43\) | 10.0000i | 1.52499i | 0.646997 | + | 0.762493i | \(0.276025\pi\) | ||||
−0.646997 | + | 0.762493i | \(0.723975\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.50000 | + | 7.79423i | −0.663489 | + | 1.14920i | ||||
\(47\) | −2.59808 | + | 1.50000i | −0.378968 | + | 0.218797i | −0.677369 | − | 0.735643i | \(-0.736880\pi\) |
0.298401 | + | 0.954441i | \(0.403547\pi\) | |||||||
\(48\) | 2.00000i | 0.288675i | ||||||||
\(49\) | −5.50000 | − | 4.33013i | −0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.00000 | − | 5.19615i | −0.420084 | − | 0.727607i | ||||
\(52\) | −1.73205 | − | 1.00000i | −0.240192 | − | 0.138675i | ||||
\(53\) | 5.19615 | + | 3.00000i | 0.713746 | + | 0.412082i | 0.812447 | − | 0.583036i | \(-0.198135\pi\) |
−0.0987002 | + | 0.995117i | \(0.531468\pi\) | |||||||
\(54\) | −2.00000 | − | 3.46410i | −0.272166 | − | 0.471405i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.50000 | − | 0.866025i | −0.334077 | − | 0.115728i | ||||
\(57\) | − | 16.0000i | − | 2.11925i | ||||||
\(58\) | −5.19615 | + | 3.00000i | −0.682288 | + | 0.393919i | ||||
\(59\) | 6.00000 | − | 10.3923i | 0.781133 | − | 1.35296i | −0.150148 | − | 0.988663i | \(-0.547975\pi\) |
0.931282 | − | 0.364299i | \(-0.118692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | + | 3.46410i | 0.256074 | + | 0.443533i | 0.965187 | − | 0.261562i | \(-0.0842377\pi\) |
−0.709113 | + | 0.705095i | \(0.750904\pi\) | |||||||
\(62\) | − | 5.00000i | − | 0.635001i | ||||||
\(63\) | −2.59808 | + | 0.500000i | −0.327327 | + | 0.0629941i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.73205 | − | 1.00000i | −0.211604 | − | 0.122169i | 0.390453 | − | 0.920623i | \(-0.372318\pi\) |
−0.602056 | + | 0.798454i | \(0.705652\pi\) | |||||||
\(68\) | 2.59808 | − | 1.50000i | 0.315063 | − | 0.181902i | ||||
\(69\) | −18.0000 | −2.16695 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00000 | −1.06810 | −0.534052 | − | 0.845452i | \(-0.679331\pi\) | ||||
−0.534052 | + | 0.845452i | \(0.679331\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | −8.66025 | − | 5.00000i | −1.01361 | − | 0.585206i | −0.101361 | − | 0.994850i | \(-0.532320\pi\) |
−0.912245 | + | 0.409644i | \(0.865653\pi\) | |||||||
\(74\) | −4.00000 | + | 6.92820i | −0.464991 | + | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.00000 | 0.917663 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 4.00000i | − | 0.452911i | ||||||
\(79\) | 2.50000 | + | 4.33013i | 0.281272 | + | 0.487177i | 0.971698 | − | 0.236225i | \(-0.0759104\pi\) |
−0.690426 | + | 0.723403i | \(0.742577\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | − | 9.52628i | 0.611111 | − | 1.05848i | ||||
\(82\) | 2.59808 | − | 1.50000i | 0.286910 | − | 0.165647i | ||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | −1.00000 | − | 5.19615i | −0.109109 | − | 0.566947i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.00000 | − | 8.66025i | −0.539164 | − | 0.933859i | ||||
\(87\) | −10.3923 | − | 6.00000i | −1.11417 | − | 0.643268i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.50000 | + | 2.59808i | 0.159000 | + | 0.275396i | 0.934508 | − | 0.355942i | \(-0.115840\pi\) |
−0.775509 | + | 0.631337i | \(0.782506\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.00000 | + | 1.73205i | 0.524142 | + | 0.181568i | ||||
\(92\) | − | 9.00000i | − | 0.938315i | ||||||
\(93\) | 8.66025 | − | 5.00000i | 0.898027 | − | 0.518476i | ||||
\(94\) | 1.50000 | − | 2.59808i | 0.154713 | − | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | − | 1.73205i | −0.102062 | − | 0.176777i | ||||
\(97\) | 5.00000i | 0.507673i | 0.967247 | + | 0.253837i | \(0.0816925\pi\) | ||||
−0.967247 | + | 0.253837i | \(0.918307\pi\) | |||||||
\(98\) | 6.92820 | + | 1.00000i | 0.699854 | + | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 5.19615 | + | 3.00000i | 0.514496 | + | 0.297044i | ||||
\(103\) | −9.52628 | + | 5.50000i | −0.938652 | + | 0.541931i | −0.889538 | − | 0.456862i | \(-0.848973\pi\) |
−0.0491146 | + | 0.998793i | \(0.515640\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | 10.3923 | − | 6.00000i | 1.00466 | − | 0.580042i | 0.0950377 | − | 0.995474i | \(-0.469703\pi\) |
0.909624 | + | 0.415432i | \(0.136370\pi\) | |||||||
\(108\) | 3.46410 | + | 2.00000i | 0.333333 | + | 0.192450i | ||||
\(109\) | −5.00000 | + | 8.66025i | −0.478913 | + | 0.829502i | −0.999708 | − | 0.0241802i | \(-0.992302\pi\) |
0.520794 | + | 0.853682i | \(0.325636\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.0000 | −1.51865 | ||||||||
\(112\) | 2.59808 | − | 0.500000i | 0.245495 | − | 0.0472456i | ||||
\(113\) | − | 15.0000i | − | 1.41108i | −0.708669 | − | 0.705541i | \(-0.750704\pi\) | ||
0.708669 | − | 0.705541i | \(-0.249296\pi\) | |||||||
\(114\) | 8.00000 | + | 13.8564i | 0.749269 | + | 1.29777i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.00000 | − | 5.19615i | 0.278543 | − | 0.482451i | ||||
\(117\) | 1.73205 | − | 1.00000i | 0.160128 | − | 0.0924500i | ||||
\(118\) | 12.0000i | 1.10469i | ||||||||
\(119\) | −6.00000 | + | 5.19615i | −0.550019 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | −3.46410 | − | 2.00000i | −0.313625 | − | 0.181071i | ||||
\(123\) | 5.19615 | + | 3.00000i | 0.468521 | + | 0.270501i | ||||
\(124\) | 2.50000 | + | 4.33013i | 0.224507 | + | 0.388857i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | − | 1.73205i | 0.178174 | − | 0.154303i | ||||
\(127\) | 8.00000i | 0.709885i | 0.934888 | + | 0.354943i | \(0.115500\pi\) | ||||
−0.934888 | + | 0.354943i | \(0.884500\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 10.0000 | − | 17.3205i | 0.880451 | − | 1.52499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.7846 | + | 4.00000i | −1.80225 | + | 0.346844i | ||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50000 | + | 2.59808i | −0.128624 | + | 0.222783i | ||||
\(137\) | −7.79423 | − | 4.50000i | −0.665906 | − | 0.384461i | 0.128618 | − | 0.991694i | \(-0.458946\pi\) |
−0.794524 | + | 0.607233i | \(0.792279\pi\) | |||||||
\(138\) | 15.5885 | − | 9.00000i | 1.32698 | − | 0.766131i | ||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 7.79423 | − | 4.50000i | 0.654077 | − | 0.377632i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.500000 | − | 0.866025i | 0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 5.19615 | + | 13.0000i | 0.428571 | + | 1.07222i | ||||
\(148\) | − | 8.00000i | − | 0.657596i | ||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | − | 3.46410i | 0.162758 | − | 0.281905i | −0.773099 | − | 0.634285i | \(-0.781294\pi\) |
0.935857 | + | 0.352381i | \(0.114628\pi\) | |||||||
\(152\) | −6.92820 | + | 4.00000i | −0.561951 | + | 0.324443i | ||||
\(153\) | 3.00000i | 0.242536i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | + | 3.46410i | 0.160128 | + | 0.277350i | ||||
\(157\) | −1.73205 | − | 1.00000i | −0.138233 | − | 0.0798087i | 0.429289 | − | 0.903167i | \(-0.358764\pi\) |
−0.567521 | + | 0.823359i | \(0.692098\pi\) | |||||||
\(158\) | −4.33013 | − | 2.50000i | −0.344486 | − | 0.198889i | ||||
\(159\) | −6.00000 | − | 10.3923i | −0.475831 | − | 0.824163i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.50000 | + | 23.3827i | 0.354650 | + | 1.84281i | ||||
\(162\) | 11.0000i | 0.864242i | ||||||||
\(163\) | −6.92820 | + | 4.00000i | −0.542659 | + | 0.313304i | −0.746156 | − | 0.665771i | \(-0.768103\pi\) |
0.203497 | + | 0.979076i | \(0.434769\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | − | 5.19615i | −0.232845 | − | 0.403300i | ||||
\(167\) | 24.0000i | 1.85718i | 0.371113 | + | 0.928588i | \(0.378976\pi\) | ||||
−0.371113 | + | 0.928588i | \(0.621024\pi\) | |||||||
\(168\) | 3.46410 | + | 4.00000i | 0.267261 | + | 0.308607i | ||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | + | 6.92820i | −0.305888 | + | 0.529813i | ||||
\(172\) | 8.66025 | + | 5.00000i | 0.660338 | + | 0.381246i | ||||
\(173\) | 10.3923 | − | 6.00000i | 0.790112 | − | 0.456172i | −0.0498898 | − | 0.998755i | \(-0.515887\pi\) |
0.840002 | + | 0.542583i | \(0.182554\pi\) | |||||||
\(174\) | 12.0000 | 0.909718 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −20.7846 | + | 12.0000i | −1.56227 | + | 0.901975i | ||||
\(178\) | −2.59808 | − | 1.50000i | −0.194734 | − | 0.112430i | ||||
\(179\) | 12.0000 | − | 20.7846i | 0.896922 | − | 1.55351i | 0.0655145 | − | 0.997852i | \(-0.479131\pi\) |
0.831408 | − | 0.555663i | \(-0.187536\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | −5.19615 | + | 1.00000i | −0.385164 | + | 0.0741249i | ||||
\(183\) | − | 8.00000i | − | 0.591377i | ||||||
\(184\) | 4.50000 | + | 7.79423i | 0.331744 | + | 0.574598i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.00000 | + | 8.66025i | −0.366618 | + | 0.635001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.00000i | 0.218797i | ||||||||
\(189\) | −10.0000 | − | 3.46410i | −0.727393 | − | 0.251976i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.50000 | − | 12.9904i | −0.542681 | − | 0.939951i | −0.998749 | − | 0.0500060i | \(-0.984076\pi\) |
0.456068 | − | 0.889945i | \(-0.349257\pi\) | |||||||
\(192\) | 1.73205 | + | 1.00000i | 0.125000 | + | 0.0721688i | ||||
\(193\) | 4.33013 | + | 2.50000i | 0.311689 | + | 0.179954i | 0.647682 | − | 0.761911i | \(-0.275738\pi\) |
−0.335993 | + | 0.941865i | \(0.609072\pi\) | |||||||
\(194\) | −2.50000 | − | 4.33013i | −0.179490 | − | 0.310885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | + | 2.59808i | −0.464286 | + | 0.185577i | ||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.50000 | − | 14.7224i | 0.602549 | − | 1.04365i | −0.389885 | − | 0.920864i | \(-0.627485\pi\) |
0.992434 | − | 0.122782i | \(-0.0391815\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.00000 | + | 3.46410i | 0.141069 | + | 0.244339i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.19615 | + | 15.0000i | −0.364698 | + | 1.05279i | ||||
\(204\) | −6.00000 | −0.420084 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.50000 | − | 9.52628i | 0.383203 | − | 0.663727i | ||||
\(207\) | 7.79423 | + | 4.50000i | 0.541736 | + | 0.312772i | ||||
\(208\) | −1.73205 | + | 1.00000i | −0.120096 | + | 0.0693375i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | 5.19615 | − | 3.00000i | 0.356873 | − | 0.206041i | ||||
\(213\) | 15.5885 | + | 9.00000i | 1.06810 | + | 0.616670i | ||||
\(214\) | −6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | −0.272166 | ||||||||
\(217\) | −8.66025 | − | 10.0000i | −0.587896 | − | 0.678844i | ||||
\(218\) | − | 10.0000i | − | 0.677285i | ||||||
\(219\) | 10.0000 | + | 17.3205i | 0.675737 | + | 1.17041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | − | 5.19615i | 0.201802 | − | 0.349531i | ||||
\(222\) | 13.8564 | − | 8.00000i | 0.929981 | − | 0.536925i | ||||
\(223\) | − | 23.0000i | − | 1.54019i | −0.637927 | − | 0.770097i | \(-0.720208\pi\) | ||
0.637927 | − | 0.770097i | \(-0.279792\pi\) | |||||||
\(224\) | −2.00000 | + | 1.73205i | −0.133631 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.50000 | + | 12.9904i | 0.498893 | + | 0.864107i | ||||
\(227\) | −15.5885 | − | 9.00000i | −1.03464 | − | 0.597351i | −0.116331 | − | 0.993210i | \(-0.537113\pi\) |
−0.918311 | + | 0.395860i | \(0.870447\pi\) | |||||||
\(228\) | −13.8564 | − | 8.00000i | −0.917663 | − | 0.529813i | ||||
\(229\) | 10.0000 | + | 17.3205i | 0.660819 | + | 1.14457i | 0.980401 | + | 0.197013i | \(0.0631241\pi\) |
−0.319582 | + | 0.947559i | \(0.603543\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000i | 0.393919i | ||||||||
\(233\) | 5.19615 | − | 3.00000i | 0.340411 | − | 0.196537i | −0.320043 | − | 0.947403i | \(-0.603697\pi\) |
0.660454 | + | 0.750867i | \(0.270364\pi\) | |||||||
\(234\) | −1.00000 | + | 1.73205i | −0.0653720 | + | 0.113228i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.00000 | − | 10.3923i | −0.390567 | − | 0.676481i | ||||
\(237\) | − | 10.0000i | − | 0.649570i | ||||||
\(238\) | 2.59808 | − | 7.50000i | 0.168408 | − | 0.486153i | ||||
\(239\) | −15.0000 | −0.970269 | −0.485135 | − | 0.874439i | \(-0.661229\pi\) | ||||
−0.485135 | + | 0.874439i | \(0.661229\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0000 | − | 19.0526i | 0.708572 | − | 1.22728i | −0.256814 | − | 0.966461i | \(-0.582673\pi\) |
0.965387 | − | 0.260822i | \(-0.0839937\pi\) | |||||||
\(242\) | −9.52628 | − | 5.50000i | −0.612372 | − | 0.353553i | ||||
\(243\) | −8.66025 | + | 5.00000i | −0.555556 | + | 0.320750i | ||||
\(244\) | 4.00000 | 0.256074 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 13.8564 | − | 8.00000i | 0.881662 | − | 0.509028i | ||||
\(248\) | −4.33013 | − | 2.50000i | −0.274963 | − | 0.158750i | ||||
\(249\) | 6.00000 | − | 10.3923i | 0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −0.866025 | + | 2.50000i | −0.0545545 | + | 0.157485i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.00000 | − | 6.92820i | −0.250982 | − | 0.434714i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 15.5885 | − | 9.00000i | 0.972381 | − | 0.561405i | 0.0724199 | − | 0.997374i | \(-0.476928\pi\) |
0.899961 | + | 0.435970i | \(0.143595\pi\) | |||||||
\(258\) | 20.0000i | 1.24515i | ||||||||
\(259\) | 4.00000 | + | 20.7846i | 0.248548 | + | 1.29149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | + | 5.19615i | 0.185695 | + | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.79423 | + | 4.50000i | 0.480613 | + | 0.277482i | 0.720672 | − | 0.693276i | \(-0.243833\pi\) |
−0.240059 | + | 0.970758i | \(0.577167\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 16.0000 | − | 13.8564i | 0.981023 | − | 0.849591i | ||||
\(267\) | − | 6.00000i | − | 0.367194i | ||||||
\(268\) | −1.73205 | + | 1.00000i | −0.105802 | + | 0.0610847i | ||||
\(269\) | −15.0000 | + | 25.9808i | −0.914566 | + | 1.58408i | −0.107031 | + | 0.994256i | \(0.534134\pi\) |
−0.807535 | + | 0.589819i | \(0.799199\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.50000 | − | 9.52628i | −0.334101 | − | 0.578680i | 0.649211 | − | 0.760609i | \(-0.275099\pi\) |
−0.983312 | + | 0.181928i | \(0.941766\pi\) | |||||||
\(272\) | − | 3.00000i | − | 0.181902i | ||||||
\(273\) | −6.92820 | − | 8.00000i | −0.419314 | − | 0.484182i | ||||
\(274\) | 9.00000 | 0.543710 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.00000 | + | 15.5885i | −0.541736 | + | 0.938315i | ||||
\(277\) | 3.46410 | + | 2.00000i | 0.208138 | + | 0.120168i | 0.600446 | − | 0.799666i | \(-0.294990\pi\) |
−0.392308 | + | 0.919834i | \(0.628323\pi\) | |||||||
\(278\) | 1.73205 | − | 1.00000i | 0.103882 | − | 0.0599760i | ||||
\(279\) | −5.00000 | −0.299342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | −5.19615 | + | 3.00000i | −0.309426 | + | 0.178647i | ||||
\(283\) | 1.73205 | + | 1.00000i | 0.102960 | + | 0.0594438i | 0.550596 | − | 0.834772i | \(-0.314401\pi\) |
−0.447636 | + | 0.894216i | \(0.647734\pi\) | |||||||
\(284\) | −4.50000 | + | 7.79423i | −0.267026 | + | 0.462502i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.59808 | − | 7.50000i | 0.153360 | − | 0.442711i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −4.00000 | − | 6.92820i | −0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | − | 8.66025i | 0.293105 | − | 0.507673i | ||||
\(292\) | −8.66025 | + | 5.00000i | −0.506803 | + | 0.292603i | ||||
\(293\) | − | 6.00000i | − | 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | −11.0000 | − | 8.66025i | −0.641533 | − | 0.505076i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.00000 | + | 6.92820i | 0.232495 | + | 0.402694i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.00000 | − | 15.5885i | −0.520483 | − | 0.901504i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.0000 | − | 8.66025i | −1.44098 | − | 0.499169i | ||||
\(302\) | 4.00000i | 0.230174i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00000 | − | 6.92820i | 0.229416 | − | 0.397360i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.50000 | − | 2.59808i | −0.0857493 | − | 0.148522i | ||||
\(307\) | − | 16.0000i | − | 0.913168i | −0.889680 | − | 0.456584i | \(-0.849073\pi\) | ||
0.889680 | − | 0.456584i | \(-0.150927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.0000 | 1.25154 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.5000 | + | 18.1865i | −0.595400 | + | 1.03126i | 0.398090 | + | 0.917346i | \(0.369673\pi\) |
−0.993490 | + | 0.113917i | \(0.963660\pi\) | |||||||
\(312\) | −3.46410 | − | 2.00000i | −0.196116 | − | 0.113228i | ||||
\(313\) | −14.7224 | + | 8.50000i | −0.832161 | + | 0.480448i | −0.854592 | − | 0.519300i | \(-0.826193\pi\) |
0.0224310 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(314\) | 2.00000 | 0.112867 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.00000 | 0.281272 | ||||||||
\(317\) | −10.3923 | + | 6.00000i | −0.583690 | + | 0.336994i | −0.762598 | − | 0.646872i | \(-0.776077\pi\) |
0.178908 | + | 0.983866i | \(0.442743\pi\) | |||||||
\(318\) | 10.3923 | + | 6.00000i | 0.582772 | + | 0.336463i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0000 | −1.33955 | ||||||||
\(322\) | −15.5885 | − | 18.0000i | −0.868711 | − | 1.00310i | ||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | −5.50000 | − | 9.52628i | −0.305556 | − | 0.529238i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.00000 | − | 6.92820i | 0.221540 | − | 0.383718i | ||||
\(327\) | 17.3205 | − | 10.0000i | 0.957826 | − | 0.553001i | ||||
\(328\) | − | 3.00000i | − | 0.165647i | ||||||
\(329\) | −1.50000 | − | 7.79423i | −0.0826977 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.00000 | − | 12.1244i | −0.384755 | − | 0.666415i | 0.606980 | − | 0.794717i | \(-0.292381\pi\) |
−0.991735 | + | 0.128302i | \(0.959047\pi\) | |||||||
\(332\) | 5.19615 | + | 3.00000i | 0.285176 | + | 0.164646i | ||||
\(333\) | 6.92820 | + | 4.00000i | 0.379663 | + | 0.219199i | ||||
\(334\) | −12.0000 | − | 20.7846i | −0.656611 | − | 1.13728i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.00000 | − | 1.73205i | −0.272772 | − | 0.0944911i | ||||
\(337\) | − | 13.0000i | − | 0.708155i | −0.935216 | − | 0.354078i | \(-0.884795\pi\) | ||
0.935216 | − | 0.354078i | \(-0.115205\pi\) | |||||||
\(338\) | −7.79423 | + | 4.50000i | −0.423950 | + | 0.244768i | ||||
\(339\) | −15.0000 | + | 25.9808i | −0.814688 | + | 1.41108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | − | 8.00000i | − | 0.432590i | ||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | −10.0000 | −0.539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.00000 | + | 10.3923i | −0.322562 | + | 0.558694i | ||||
\(347\) | 5.19615 | + | 3.00000i | 0.278944 | + | 0.161048i | 0.632945 | − | 0.774197i | \(-0.281846\pi\) |
−0.354001 | + | 0.935245i | \(0.615179\pi\) | |||||||
\(348\) | −10.3923 | + | 6.00000i | −0.557086 | + | 0.321634i | ||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.00000 | 0.427008 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.79423 | − | 4.50000i | −0.414845 | − | 0.239511i | 0.278024 | − | 0.960574i | \(-0.410320\pi\) |
−0.692869 | + | 0.721063i | \(0.743654\pi\) | |||||||
\(354\) | 12.0000 | − | 20.7846i | 0.637793 | − | 1.10469i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.00000 | 0.159000 | ||||||||
\(357\) | 15.5885 | − | 3.00000i | 0.825029 | − | 0.158777i | ||||
\(358\) | 24.0000i | 1.26844i | ||||||||
\(359\) | −12.0000 | − | 20.7846i | −0.633336 | − | 1.09697i | −0.986865 | − | 0.161546i | \(-0.948352\pi\) |
0.353529 | − | 0.935423i | \(-0.384981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.5000 | + | 38.9711i | −1.18421 | + | 2.05111i | ||||
\(362\) | −17.3205 | + | 10.0000i | −0.910346 | + | 0.525588i | ||||
\(363\) | − | 22.0000i | − | 1.15470i | ||||||
\(364\) | 4.00000 | − | 3.46410i | 0.209657 | − | 0.181568i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.00000 | + | 6.92820i | 0.209083 | + | 0.362143i | ||||
\(367\) | −6.92820 | − | 4.00000i | −0.361649 | − | 0.208798i | 0.308155 | − | 0.951336i | \(-0.400289\pi\) |
−0.669804 | + | 0.742538i | \(0.733622\pi\) | |||||||
\(368\) | −7.79423 | − | 4.50000i | −0.406302 | − | 0.234579i | ||||
\(369\) | −1.50000 | − | 2.59808i | −0.0780869 | − | 0.135250i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | + | 10.3923i | −0.623009 | + | 0.539542i | ||||
\(372\) | − | 10.0000i | − | 0.518476i | ||||||
\(373\) | −1.73205 | + | 1.00000i | −0.0896822 | + | 0.0517780i | −0.544170 | − | 0.838975i | \(-0.683156\pi\) |
0.454488 | + | 0.890753i | \(0.349822\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.50000 | − | 2.59808i | −0.0773566 | − | 0.133986i | ||||
\(377\) | − | 12.0000i | − | 0.618031i | ||||||
\(378\) | 10.3923 | − | 2.00000i | 0.534522 | − | 0.102869i | ||||
\(379\) | −8.00000 | −0.410932 | −0.205466 | − | 0.978664i | \(-0.565871\pi\) | ||||
−0.205466 | + | 0.978664i | \(0.565871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | − | 13.8564i | 0.409852 | − | 0.709885i | ||||
\(382\) | 12.9904 | + | 7.50000i | 0.664646 | + | 0.383733i | ||||
\(383\) | −7.79423 | + | 4.50000i | −0.398266 | + | 0.229939i | −0.685736 | − | 0.727851i | \(-0.740519\pi\) |
0.287469 | + | 0.957790i | \(0.407186\pi\) | |||||||
\(384\) | −2.00000 | −0.102062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.00000 | −0.254493 | ||||||||
\(387\) | −8.66025 | + | 5.00000i | −0.440225 | + | 0.254164i | ||||
\(388\) | 4.33013 | + | 2.50000i | 0.219829 | + | 0.126918i | ||||
\(389\) | −9.00000 | + | 15.5885i | −0.456318 | + | 0.790366i | −0.998763 | − | 0.0497253i | \(-0.984165\pi\) |
0.542445 | + | 0.840091i | \(0.317499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.0000 | 1.36545 | ||||||||
\(392\) | 4.33013 | − | 5.50000i | 0.218704 | − | 0.277792i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.00000 | − | 15.5885i | −0.453413 | − | 0.785335i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.73205 | − | 1.00000i | 0.0869291 | − | 0.0501886i | −0.455905 | − | 0.890028i | \(-0.650684\pi\) |
0.542834 | + | 0.839840i | \(0.317351\pi\) | |||||||
\(398\) | 17.0000i | 0.852133i | ||||||||
\(399\) | 40.0000 | + | 13.8564i | 2.00250 | + | 0.693688i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.00000 | − | 15.5885i | −0.449439 | − | 0.778450i | 0.548911 | − | 0.835881i | \(-0.315043\pi\) |
−0.998350 | + | 0.0574304i | \(0.981709\pi\) | |||||||
\(402\) | −3.46410 | − | 2.00000i | −0.172774 | − | 0.0997509i | ||||
\(403\) | 8.66025 | + | 5.00000i | 0.431398 | + | 0.249068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.00000 | − | 15.5885i | −0.148888 | − | 0.773642i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 5.19615 | − | 3.00000i | 0.257248 | − | 0.148522i | ||||
\(409\) | −3.50000 | + | 6.06218i | −0.173064 | + | 0.299755i | −0.939490 | − | 0.342578i | \(-0.888700\pi\) |
0.766426 | + | 0.642333i | \(0.222033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.00000 | + | 15.5885i | 0.443937 | + | 0.768922i | ||||
\(412\) | 11.0000i | 0.541931i | ||||||||
\(413\) | 20.7846 | + | 24.0000i | 1.02274 | + | 1.18096i | ||||
\(414\) | −9.00000 | −0.442326 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00000 | − | 1.73205i | 0.0490290 | − | 0.0849208i | ||||
\(417\) | 3.46410 | + | 2.00000i | 0.169638 | + | 0.0979404i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0000 | 1.46560 | 0.732798 | − | 0.680446i | \(-0.238214\pi\) | ||||
0.732798 | + | 0.680446i | \(0.238214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | −1.73205 | + | 1.00000i | −0.0843149 | + | 0.0486792i | ||||
\(423\) | −2.59808 | − | 1.50000i | −0.126323 | − | 0.0729325i | ||||
\(424\) | −3.00000 | + | 5.19615i | −0.145693 | + | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −18.0000 | −0.872103 | ||||||||
\(427\) | −10.3923 | + | 2.00000i | −0.502919 | + | 0.0967868i | ||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.50000 | − | 2.59808i | 0.0722525 | − | 0.125145i | −0.827636 | − | 0.561266i | \(-0.810315\pi\) |
0.899888 | + | 0.436121i | \(0.143648\pi\) | |||||||
\(432\) | 3.46410 | − | 2.00000i | 0.166667 | − | 0.0962250i | ||||
\(433\) | − | 29.0000i | − | 1.39365i | −0.717241 | − | 0.696826i | \(-0.754595\pi\) | ||
0.717241 | − | 0.696826i | \(-0.245405\pi\) | |||||||
\(434\) | 12.5000 | + | 4.33013i | 0.600019 | + | 0.207853i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | + | 8.66025i | 0.239457 | + | 0.414751i | ||||
\(437\) | 62.3538 | + | 36.0000i | 2.98279 | + | 1.72211i | ||||
\(438\) | −17.3205 | − | 10.0000i | −0.827606 | − | 0.477818i | ||||
\(439\) | 11.5000 | + | 19.9186i | 0.548865 | + | 0.950662i | 0.998353 | + | 0.0573756i | \(0.0182733\pi\) |
−0.449488 | + | 0.893287i | \(0.648393\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | − | 6.92820i | 0.0476190 | − | 0.329914i | ||||
\(442\) | 6.00000i | 0.285391i | ||||||||
\(443\) | 10.3923 | − | 6.00000i | 0.493753 | − | 0.285069i | −0.232377 | − | 0.972626i | \(-0.574650\pi\) |
0.726130 | + | 0.687557i | \(0.241317\pi\) | |||||||
\(444\) | −8.00000 | + | 13.8564i | −0.379663 | + | 0.657596i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.5000 | + | 19.9186i | 0.544541 | + | 0.943172i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.866025 | − | 2.50000i | 0.0409159 | − | 0.118114i | ||||
\(449\) | 27.0000 | 1.27421 | 0.637104 | − | 0.770778i | \(-0.280132\pi\) | ||||
0.637104 | + | 0.770778i | \(0.280132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −12.9904 | − | 7.50000i | −0.611016 | − | 0.352770i | ||||
\(453\) | −6.92820 | + | 4.00000i | −0.325515 | + | 0.187936i | ||||
\(454\) | 18.0000 | 0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16.0000 | 0.749269 | ||||||||
\(457\) | −19.0526 | + | 11.0000i | −0.891241 | + | 0.514558i | −0.874348 | − | 0.485299i | \(-0.838711\pi\) |
−0.0168929 | + | 0.999857i | \(0.505377\pi\) | |||||||
\(458\) | −17.3205 | − | 10.0000i | −0.809334 | − | 0.467269i | ||||
\(459\) | −6.00000 | + | 10.3923i | −0.280056 | + | 0.485071i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.0000 | −1.11779 | −0.558896 | − | 0.829238i | \(-0.688775\pi\) | ||||
−0.558896 | + | 0.829238i | \(0.688775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.0000i | 1.16185i | 0.813958 | + | 0.580924i | \(0.197309\pi\) | ||||
−0.813958 | + | 0.580924i | \(0.802691\pi\) | |||||||
\(464\) | −3.00000 | − | 5.19615i | −0.139272 | − | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | −5.19615 | + | 3.00000i | −0.240449 | + | 0.138823i | −0.615383 | − | 0.788228i | \(-0.710999\pi\) |
0.374934 | + | 0.927052i | \(0.377665\pi\) | |||||||
\(468\) | − | 2.00000i | − | 0.0924500i | ||||||
\(469\) | 4.00000 | − | 3.46410i | 0.184703 | − | 0.159957i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.00000 | + | 3.46410i | 0.0921551 | + | 0.159617i | ||||
\(472\) | 10.3923 | + | 6.00000i | 0.478345 | + | 0.276172i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 5.00000 | + | 8.66025i | 0.229658 | + | 0.397779i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.50000 | + | 7.79423i | 0.0687524 | + | 0.357248i | ||||
\(477\) | 6.00000i | 0.274721i | ||||||||
\(478\) | 12.9904 | − | 7.50000i | 0.594166 | − | 0.343042i | ||||
\(479\) | −13.5000 | + | 23.3827i | −0.616831 | + | 1.06838i | 0.373230 | + | 0.927739i | \(0.378250\pi\) |
−0.990060 | + | 0.140643i | \(0.955083\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | − | 13.8564i | −0.364769 | − | 0.631798i | ||||
\(482\) | 22.0000i | 1.00207i | ||||||||
\(483\) | 15.5885 | − | 45.0000i | 0.709299 | − | 2.04757i | ||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.00000 | − | 8.66025i | 0.226805 | − | 0.392837i | ||||
\(487\) | −9.52628 | − | 5.50000i | −0.431677 | − | 0.249229i | 0.268384 | − | 0.963312i | \(-0.413510\pi\) |
−0.700061 | + | 0.714083i | \(0.746844\pi\) | |||||||
\(488\) | −3.46410 | + | 2.00000i | −0.156813 | + | 0.0905357i | ||||
\(489\) | 16.0000 | 0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 42.0000 | 1.89543 | 0.947717 | − | 0.319113i | \(-0.103385\pi\) | ||||
0.947717 | + | 0.319113i | \(0.103385\pi\) | |||||||
\(492\) | 5.19615 | − | 3.00000i | 0.234261 | − | 0.135250i | ||||
\(493\) | 15.5885 | + | 9.00000i | 0.702069 | + | 0.405340i | ||||
\(494\) | −8.00000 | + | 13.8564i | −0.359937 | + | 0.623429i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.00000 | 0.224507 | ||||||||
\(497\) | 7.79423 | − | 22.5000i | 0.349619 | − | 1.00926i | ||||
\(498\) | 12.0000i | 0.537733i | ||||||||
\(499\) | −17.0000 | − | 29.4449i | −0.761025 | − | 1.31813i | −0.942323 | − | 0.334705i | \(-0.891363\pi\) |
0.181298 | − | 0.983428i | \(-0.441970\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.0000 | − | 41.5692i | 1.07224 | − | 1.85718i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | −0.500000 | − | 2.59808i | −0.0222718 | − | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.5885 | − | 9.00000i | −0.692308 | − | 0.399704i | ||||
\(508\) | 6.92820 | + | 4.00000i | 0.307389 | + | 0.177471i | ||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | − | 17.3205i | 0.884748 | − | 0.766214i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −27.7128 | + | 16.0000i | −1.22355 | + | 0.706417i | ||||
\(514\) | −9.00000 | + | 15.5885i | −0.396973 | + | 0.687577i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −10.0000 | − | 17.3205i | −0.440225 | − | 0.762493i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −13.8564 | − | 16.0000i | −0.608816 | − | 0.703000i | ||||
\(519\) | −24.0000 | −1.05348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.50000 | − | 2.59808i | 0.0657162 | − | 0.113824i | −0.831295 | − | 0.555831i | \(-0.812400\pi\) |
0.897011 | + | 0.442007i | \(0.145733\pi\) | |||||||
\(522\) | −5.19615 | − | 3.00000i | −0.227429 | − | 0.131306i | ||||
\(523\) | 29.4449 | − | 17.0000i | 1.28753 | − | 0.743358i | 0.309320 | − | 0.950958i | \(-0.399899\pi\) |
0.978214 | + | 0.207600i | \(0.0665652\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.00000 | −0.392419 | ||||||||
\(527\) | −12.9904 | + | 7.50000i | −0.565870 | + | 0.326705i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.0000 | − | 50.2295i | 1.26087 | − | 2.18389i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | −6.92820 | + | 20.0000i | −0.300376 | + | 0.867110i | ||||
\(533\) | 6.00000i | 0.259889i | ||||||||
\(534\) | 3.00000 | + | 5.19615i | 0.129823 | + | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.00000 | − | 1.73205i | 0.0431934 | − | 0.0748132i | ||||
\(537\) | −41.5692 | + | 24.0000i | −1.79384 | + | 1.03568i | ||||
\(538\) | − | 30.0000i | − | 1.29339i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.00000 | + | 8.66025i | 0.214967 | + | 0.372333i | 0.953262 | − | 0.302144i | \(-0.0977023\pi\) |
−0.738296 | + | 0.674477i | \(0.764369\pi\) | |||||||
\(542\) | 9.52628 | + | 5.50000i | 0.409189 | + | 0.236245i | ||||
\(543\) | −34.6410 | − | 20.0000i | −1.48659 | − | 0.858282i | ||||
\(544\) | 1.50000 | + | 2.59808i | 0.0643120 | + | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 10.0000 | + | 3.46410i | 0.427960 | + | 0.148250i | ||||
\(547\) | 8.00000i | 0.342055i | 0.985266 | + | 0.171028i | \(0.0547087\pi\) | ||||
−0.985266 | + | 0.171028i | \(0.945291\pi\) | |||||||
\(548\) | −7.79423 | + | 4.50000i | −0.332953 | + | 0.192230i | ||||
\(549\) | −2.00000 | + | 3.46410i | −0.0853579 | + | 0.147844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.0000 | + | 41.5692i | 1.02243 | + | 1.77091i | ||||
\(552\) | − | 18.0000i | − | 0.766131i | ||||||
\(553\) | −12.9904 | + | 2.50000i | −0.552407 | + | 0.106311i | ||||
\(554\) | −4.00000 | −0.169944 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | + | 1.73205i | −0.0424094 | + | 0.0734553i | ||||
\(557\) | −20.7846 | − | 12.0000i | −0.880672 | − | 0.508456i | −0.00979220 | − | 0.999952i | \(-0.503117\pi\) |
−0.870880 | + | 0.491496i | \(0.836450\pi\) | |||||||
\(558\) | 4.33013 | − | 2.50000i | 0.183309 | − | 0.105833i | ||||
\(559\) | 20.0000 | 0.845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.59808 | + | 1.50000i | −0.109593 | + | 0.0632737i | ||||
\(563\) | −5.19615 | − | 3.00000i | −0.218992 | − | 0.126435i | 0.386492 | − | 0.922293i | \(-0.373687\pi\) |
−0.605483 | + | 0.795858i | \(0.707020\pi\) | |||||||
\(564\) | 3.00000 | − | 5.19615i | 0.126323 | − | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.00000 | −0.0840663 | ||||||||
\(567\) | 19.0526 | + | 22.0000i | 0.800132 | + | 0.923913i | ||||
\(568\) | − | 9.00000i | − | 0.377632i | ||||||
\(569\) | −1.50000 | − | 2.59808i | −0.0628833 | − | 0.108917i | 0.832870 | − | 0.553469i | \(-0.186696\pi\) |
−0.895753 | + | 0.444552i | \(0.853363\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.0000i | 1.25327i | ||||||||
\(574\) | 1.50000 | + | 7.79423i | 0.0626088 | + | 0.325325i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 29.4449 | + | 17.0000i | 1.22581 | + | 0.707719i | 0.966150 | − | 0.257982i | \(-0.0830575\pi\) |
0.259656 | + | 0.965701i | \(0.416391\pi\) | |||||||
\(578\) | 6.92820 | + | 4.00000i | 0.288175 | + | 0.166378i | ||||
\(579\) | −5.00000 | − | 8.66025i | −0.207793 | − | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.0000 | − | 5.19615i | −0.622305 | − | 0.215573i | ||||
\(582\) | 10.0000i | 0.414513i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 5.00000 | − | 8.66025i | 0.206901 | − | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.00000 | + | 5.19615i | 0.123929 | + | 0.214651i | ||||
\(587\) | 12.0000i | 0.495293i | 0.968850 | + | 0.247647i | \(0.0796572\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(588\) | 13.8564 | + | 2.00000i | 0.571429 | + | 0.0824786i | ||||
\(589\) | −40.0000 | −1.64817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0000 | − | 31.1769i | 0.740421 | − | 1.28245i | ||||
\(592\) | −6.92820 | − | 4.00000i | −0.284747 | − | 0.164399i | ||||
\(593\) | −2.59808 | + | 1.50000i | −0.106690 | + | 0.0615976i | −0.552396 | − | 0.833582i | \(-0.686286\pi\) |
0.445705 | + | 0.895180i | \(0.352953\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.4449 | + | 17.0000i | −1.20510 | + | 0.695764i | ||||
\(598\) | 15.5885 | + | 9.00000i | 0.637459 | + | 0.368037i | ||||
\(599\) | 10.5000 | − | 18.1865i | 0.429018 | − | 0.743082i | −0.567768 | − | 0.823189i | \(-0.692193\pi\) |
0.996786 | + | 0.0801071i | \(0.0255262\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 25.9808 | − | 5.00000i | 1.05890 | − | 0.203785i | ||||
\(603\) | − | 2.00000i | − | 0.0814463i | ||||||
\(604\) | −2.00000 | − | 3.46410i | −0.0813788 | − | 0.140952i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.6506 | + | 12.5000i | −0.878772 | + | 0.507359i | −0.870253 | − | 0.492604i | \(-0.836045\pi\) |
−0.00851879 | + | 0.999964i | \(0.502712\pi\) | |||||||
\(608\) | 8.00000i | 0.324443i | ||||||||
\(609\) | 24.0000 | − | 20.7846i | 0.972529 | − | 0.842235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00000 | + | 5.19615i | 0.121367 | + | 0.210214i | ||||
\(612\) | 2.59808 | + | 1.50000i | 0.105021 | + | 0.0606339i | ||||
\(613\) | 1.73205 | + | 1.00000i | 0.0699569 | + | 0.0403896i | 0.534570 | − | 0.845124i | \(-0.320473\pi\) |
−0.464614 | + | 0.885514i | \(0.653807\pi\) | |||||||
\(614\) | 8.00000 | + | 13.8564i | 0.322854 | + | 0.559199i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.0000i | 0.603877i | 0.953327 | + | 0.301939i | \(0.0976338\pi\) | ||||
−0.953327 | + | 0.301939i | \(0.902366\pi\) | |||||||
\(618\) | −19.0526 | + | 11.0000i | −0.766406 | + | 0.442485i | ||||
\(619\) | −5.00000 | + | 8.66025i | −0.200967 | + | 0.348085i | −0.948840 | − | 0.315757i | \(-0.897742\pi\) |
0.747873 | + | 0.663842i | \(0.231075\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.0000 | + | 31.1769i | 0.722315 | + | 1.25109i | ||||
\(622\) | − | 21.0000i | − | 0.842023i | ||||||
\(623\) | −7.79423 | + | 1.50000i | −0.312269 | + | 0.0600962i | ||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.50000 | − | 14.7224i | 0.339728 | − | 0.588427i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.73205 | + | 1.00000i | −0.0691164 | + | 0.0399043i | ||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0000 | −0.756378 | −0.378189 | − | 0.925728i | \(-0.623453\pi\) | ||||
−0.378189 | + | 0.925728i | \(0.623453\pi\) | |||||||
\(632\) | −4.33013 | + | 2.50000i | −0.172243 | + | 0.0994447i | ||||
\(633\) | −3.46410 | − | 2.00000i | −0.137686 | − | 0.0794929i | ||||
\(634\) | 6.00000 | − | 10.3923i | 0.238290 | − | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.0000 | −0.475831 | ||||||||
\(637\) | −8.66025 | + | 11.0000i | −0.343132 | + | 0.435836i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.50000 | − | 7.79423i | −0.178017 | − | 0.308335i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.5000 | + | 38.9711i | −0.888697 | + | 1.53927i | −0.0472793 | + | 0.998882i | \(0.515055\pi\) |
−0.841417 | + | 0.540386i | \(0.818278\pi\) | |||||||
\(642\) | 20.7846 | − | 12.0000i | 0.820303 | − | 0.473602i | ||||
\(643\) | − | 20.0000i | − | 0.788723i | −0.918955 | − | 0.394362i | \(-0.870966\pi\) | ||
0.918955 | − | 0.394362i | \(-0.129034\pi\) | |||||||
\(644\) | 22.5000 | + | 7.79423i | 0.886624 | + | 0.307136i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | − | 20.7846i | −0.472134 | − | 0.817760i | ||||
\(647\) | −20.7846 | − | 12.0000i | −0.817127 | − | 0.471769i | 0.0322975 | − | 0.999478i | \(-0.489718\pi\) |
−0.849425 | + | 0.527710i | \(0.823051\pi\) | |||||||
\(648\) | 9.52628 | + | 5.50000i | 0.374228 | + | 0.216060i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.00000 | + | 25.9808i | 0.195965 | + | 1.01827i | ||||
\(652\) | 8.00000i | 0.313304i | ||||||||
\(653\) | −15.5885 | + | 9.00000i | −0.610023 | + | 0.352197i | −0.772975 | − | 0.634437i | \(-0.781232\pi\) |
0.162951 | + | 0.986634i | \(0.447899\pi\) | |||||||
\(654\) | −10.0000 | + | 17.3205i | −0.391031 | + | 0.677285i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.50000 | + | 2.59808i | 0.0585652 | + | 0.101438i | ||||
\(657\) | − | 10.0000i | − | 0.390137i | ||||||
\(658\) | 5.19615 | + | 6.00000i | 0.202567 | + | 0.233904i | ||||
\(659\) | −30.0000 | −1.16863 | −0.584317 | − | 0.811525i | \(-0.698638\pi\) | ||||
−0.584317 | + | 0.811525i | \(0.698638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.00000 | − | 13.8564i | 0.311164 | − | 0.538952i | −0.667451 | − | 0.744654i | \(-0.732615\pi\) |
0.978615 | + | 0.205702i | \(0.0659478\pi\) | |||||||
\(662\) | 12.1244 | + | 7.00000i | 0.471226 | + | 0.272063i | ||||
\(663\) | −10.3923 | + | 6.00000i | −0.403604 | + | 0.233021i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.00000 | −0.309994 | ||||||||
\(667\) | 46.7654 | − | 27.0000i | 1.81076 | − | 1.04544i | ||||
\(668\) | 20.7846 | + | 12.0000i | 0.804181 | + | 0.464294i | ||||
\(669\) | −23.0000 | + | 39.8372i | −0.889231 | + | 1.54019i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5.19615 | − | 1.00000i | 0.200446 | − | 0.0385758i | ||||
\(673\) | − | 5.00000i | − | 0.192736i | −0.995346 | − | 0.0963679i | \(-0.969277\pi\) | ||
0.995346 | − | 0.0963679i | \(-0.0307225\pi\) | |||||||
\(674\) | 6.50000 | + | 11.2583i | 0.250371 | + | 0.433655i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | − | 7.79423i | 0.173077 | − | 0.299778i | ||||
\(677\) | 36.3731 | − | 21.0000i | 1.39793 | − | 0.807096i | 0.403755 | − | 0.914867i | \(-0.367705\pi\) |
0.994176 | + | 0.107772i | \(0.0343715\pi\) | |||||||
\(678\) | − | 30.0000i | − | 1.15214i | ||||||
\(679\) | −12.5000 | − | 4.33013i | −0.479706 | − | 0.166175i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.0000 | + | 31.1769i | 0.689761 | + | 1.19470i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.9808 | − | 15.0000i | −0.994126 | − | 0.573959i | −0.0876211 | − | 0.996154i | \(-0.527926\pi\) |
−0.906505 | + | 0.422195i | \(0.861260\pi\) | |||||||
\(684\) | 4.00000 | + | 6.92820i | 0.152944 | + | 0.264906i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | − | 40.0000i | − | 1.52610i | ||||||
\(688\) | 8.66025 | − | 5.00000i | 0.330169 | − | 0.190623i | ||||
\(689\) | 6.00000 | − | 10.3923i | 0.228582 | − | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.0000 | − | 43.3013i | −0.951045 | − | 1.64726i | −0.743170 | − | 0.669102i | \(-0.766679\pi\) |
−0.207875 | − | 0.978155i | \(-0.566655\pi\) | |||||||
\(692\) | − | 12.0000i | − | 0.456172i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.00000 | −0.227757 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.00000 | − | 10.3923i | 0.227429 | − | 0.393919i | ||||
\(697\) | −7.79423 | − | 4.50000i | −0.295227 | − | 0.170450i | ||||
\(698\) | 22.5167 | − | 13.0000i | 0.852268 | − | 0.492057i | ||||
\(699\) | −12.0000 | −0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.0000 | −1.35970 | −0.679851 | − | 0.733351i | \(-0.737955\pi\) | ||||
−0.679851 | + | 0.733351i | \(0.737955\pi\) | |||||||
\(702\) | −6.92820 | + | 4.00000i | −0.261488 | + | 0.150970i | ||||
\(703\) | 55.4256 | + | 32.0000i | 2.09042 | + | 1.20690i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.00000 | 0.338719 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 24.0000i | 0.901975i | ||||||||
\(709\) | −2.00000 | − | 3.46410i | −0.0751116 | − | 0.130097i | 0.826023 | − | 0.563636i | \(-0.190598\pi\) |
−0.901135 | + | 0.433539i | \(0.857265\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.50000 | + | 4.33013i | −0.0937573 | + | 0.162392i | ||||
\(712\) | −2.59808 | + | 1.50000i | −0.0973670 | + | 0.0562149i | ||||
\(713\) | 45.0000i | 1.68526i | ||||||||
\(714\) | −12.0000 | + | 10.3923i | −0.449089 | + | 0.388922i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | − | 20.7846i | −0.448461 | − | 0.776757i | ||||
\(717\) | 25.9808 | + | 15.0000i | 0.970269 | + | 0.560185i | ||||
\(718\) | 20.7846 | + | 12.0000i | 0.775675 | + | 0.447836i | ||||
\(719\) | −7.50000 | − | 12.9904i | −0.279703 | − | 0.484459i | 0.691608 | − | 0.722273i | \(-0.256903\pi\) |
−0.971311 | + | 0.237814i | \(0.923569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.50000 | − | 28.5788i | −0.204831 | − | 1.06433i | ||||
\(722\) | − | 45.0000i | − | 1.67473i | ||||||
\(723\) | −38.1051 | + | 22.0000i | −1.41714 | + | 0.818189i | ||||
\(724\) | 10.0000 | − | 17.3205i | 0.371647 | − | 0.643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 11.0000 | + | 19.0526i | 0.408248 | + | 0.707107i | ||||
\(727\) | − | 31.0000i | − | 1.14973i | −0.818250 | − | 0.574863i | \(-0.805055\pi\) | ||
0.818250 | − | 0.574863i | \(-0.194945\pi\) | |||||||
\(728\) | −1.73205 | + | 5.00000i | −0.0641941 | + | 0.185312i | ||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.0000 | + | 25.9808i | −0.554795 | + | 0.960933i | ||||
\(732\) | −6.92820 | − | 4.00000i | −0.256074 | − | 0.147844i | ||||
\(733\) | 29.4449 | − | 17.0000i | 1.08757 | − | 0.627909i | 0.154642 | − | 0.987971i | \(-0.450578\pi\) |
0.932929 | + | 0.360061i | \(0.117244\pi\) | |||||||
\(734\) | 8.00000 | 0.295285 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9.00000 | 0.331744 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.59808 | + | 1.50000i | 0.0956365 | + | 0.0552158i | ||||
\(739\) | 4.00000 | − | 6.92820i | 0.147142 | − | 0.254858i | −0.783028 | − | 0.621987i | \(-0.786326\pi\) |
0.930170 | + | 0.367129i | \(0.119659\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32.0000 | −1.17555 | ||||||||
\(742\) | 5.19615 | − | 15.0000i | 0.190757 | − | 0.550667i | ||||
\(743\) | − | 33.0000i | − | 1.21065i | −0.795977 | − | 0.605326i | \(-0.793043\pi\) | ||
0.795977 | − | 0.605326i | \(-0.206957\pi\) | |||||||
\(744\) | 5.00000 | + | 8.66025i | 0.183309 | + | 0.317500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.00000 | − | 1.73205i | 0.0366126 | − | 0.0634149i | ||||
\(747\) | −5.19615 | + | 3.00000i | −0.190117 | + | 0.109764i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.00000 | + | 31.1769i | 0.219235 | + | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.00000 | + | 13.8564i | 0.291924 | + | 0.505627i | 0.974265 | − | 0.225407i | \(-0.0723712\pi\) |
−0.682341 | + | 0.731034i | \(0.739038\pi\) | |||||||
\(752\) | 2.59808 | + | 1.50000i | 0.0947421 | + | 0.0546994i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00000 | + | 10.3923i | 0.218507 | + | 0.378465i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.00000 | + | 6.92820i | −0.290957 | + | 0.251976i | ||||
\(757\) | 26.0000i | 0.944986i | 0.881334 | + | 0.472493i | \(0.156646\pi\) | ||||
−0.881334 | + | 0.472493i | \(0.843354\pi\) | |||||||
\(758\) | 6.92820 | − | 4.00000i | 0.251644 | − | 0.145287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.5000 | − | 38.9711i | −0.815624 | − | 1.41270i | −0.908879 | − | 0.417061i | \(-0.863060\pi\) |
0.0932544 | − | 0.995642i | \(-0.470273\pi\) | |||||||
\(762\) | 16.0000i | 0.579619i | ||||||||
\(763\) | −17.3205 | − | 20.0000i | −0.627044 | − | 0.724049i | ||||
\(764\) | −15.0000 | −0.542681 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.50000 | − | 7.79423i | 0.162592 | − | 0.281617i | ||||
\(767\) | −20.7846 | − | 12.0000i | −0.750489 | − | 0.433295i | ||||
\(768\) | 1.73205 | − | 1.00000i | 0.0625000 | − | 0.0360844i | ||||
\(769\) | −14.0000 | −0.504853 | −0.252426 | − | 0.967616i | \(-0.581229\pi\) | ||||
−0.252426 | + | 0.967616i | \(0.581229\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36.0000 | −1.29651 | ||||||||
\(772\) | 4.33013 | − | 2.50000i | 0.155845 | − | 0.0899770i | ||||
\(773\) | −10.3923 | − | 6.00000i | −0.373785 | − | 0.215805i | 0.301326 | − | 0.953521i | \(-0.402571\pi\) |
−0.675111 | + | 0.737716i | \(0.735904\pi\) | |||||||
\(774\) | 5.00000 | − | 8.66025i | 0.179721 | − | 0.311286i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.00000 | −0.179490 | ||||||||
\(777\) | 13.8564 | − | 40.0000i | 0.497096 | − | 1.43499i | ||||
\(778\) | − | 18.0000i | − | 0.645331i | ||||||
\(779\) | −12.0000 | − | 20.7846i | −0.429945 | − | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −23.3827 | + | 13.5000i | −0.836163 | + | 0.482759i | ||||
\(783\) | 24.0000i | 0.857690i | ||||||||
\(784\) | −1.00000 | + | 6.92820i | −0.0357143 | + | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.8564 | + | 8.00000i | 0.493928 | + | 0.285169i | 0.726202 | − | 0.687481i | \(-0.241284\pi\) |
−0.232275 | + | 0.972650i | \(0.574617\pi\) | |||||||
\(788\) | 15.5885 | + | 9.00000i | 0.555316 | + | 0.320612i | ||||
\(789\) | −9.00000 | − | 15.5885i | −0.320408 | − | 0.554964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 37.5000 | + | 12.9904i | 1.33335 | + | 0.461885i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.92820 | − | 4.00000i | 0.246028 | − | 0.142044i | ||||
\(794\) | −1.00000 | + | 1.73205i | −0.0354887 | + | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.50000 | − | 14.7224i | −0.301275 | − | 0.521823i | ||||
\(797\) | − | 12.0000i | − | 0.425062i | −0.977154 | − | 0.212531i | \(-0.931829\pi\) | ||
0.977154 | − | 0.212531i | \(-0.0681706\pi\) | |||||||
\(798\) | −41.5692 | + | 8.00000i | −1.47153 | + | 0.283197i | ||||
\(799\) | −9.00000 | −0.318397 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.50000 | + | 2.59808i | −0.0529999 | + | 0.0917985i | ||||
\(802\) | 15.5885 | + | 9.00000i | 0.550448 | + | 0.317801i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 4.00000 | 0.141069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.0000 | −0.352235 | ||||||||
\(807\) | 51.9615 | − | 30.0000i | 1.82913 | − | 1.05605i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.0000 | + | 25.9808i | −0.527372 | + | 0.913435i | 0.472119 | + | 0.881535i | \(0.343489\pi\) |
−0.999491 | + | 0.0319002i | \(0.989844\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.0000 | 0.912983 | 0.456492 | − | 0.889728i | \(-0.349106\pi\) | ||||
0.456492 | + | 0.889728i | \(0.349106\pi\) | |||||||
\(812\) | 10.3923 | + | 12.0000i | 0.364698 | + | 0.421117i | ||||
\(813\) | 22.0000i | 0.771574i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.00000 | + | 5.19615i | −0.105021 | + | 0.181902i | ||||
\(817\) | −69.2820 | + | 40.0000i | −2.42387 | + | 1.39942i | ||||
\(818\) | − | 7.00000i | − | 0.244749i | ||||||
\(819\) | 1.00000 | + | 5.19615i | 0.0349428 | + | 0.181568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.00000 | + | 10.3923i | 0.209401 | + | 0.362694i | 0.951526 | − | 0.307568i | \(-0.0995151\pi\) |
−0.742125 | + | 0.670262i | \(0.766182\pi\) | |||||||
\(822\) | −15.5885 | − | 9.00000i | −0.543710 | − | 0.313911i | ||||
\(823\) | 17.3205 | + | 10.0000i | 0.603755 | + | 0.348578i | 0.770517 | − | 0.637419i | \(-0.219998\pi\) |
−0.166762 | + | 0.985997i | \(0.553331\pi\) | |||||||
\(824\) | −5.50000 | − | 9.52628i | −0.191602 | − | 0.331864i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.0000 | − | 10.3923i | −1.04383 | − | 0.361595i | ||||
\(827\) | − | 18.0000i | − | 0.625921i | −0.949766 | − | 0.312961i | \(-0.898679\pi\) | ||
0.949766 | − | 0.312961i | \(-0.101321\pi\) | |||||||
\(828\) | 7.79423 | − | 4.50000i | 0.270868 | − | 0.156386i | ||||
\(829\) | 22.0000 | − | 38.1051i | 0.764092 | − | 1.32345i | −0.176634 | − | 0.984277i | \(-0.556521\pi\) |
0.940726 | − | 0.339169i | \(-0.110146\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | − | 6.92820i | −0.138758 | − | 0.240337i | ||||
\(832\) | 2.00000i | 0.0693375i | ||||||||
\(833\) | −7.79423 | − | 19.5000i | −0.270054 | − | 0.675635i | ||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.3205 | − | 10.0000i | −0.598684 | − | 0.345651i | ||||
\(838\) | −25.9808 | + | 15.0000i | −0.897491 | + | 0.518166i | ||||
\(839\) | 33.0000 | 1.13929 | 0.569643 | − | 0.821892i | \(-0.307081\pi\) | ||||
0.569643 | + | 0.821892i | \(0.307081\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 3.46410 | − | 2.00000i | 0.119381 | − | 0.0689246i | ||||
\(843\) | −5.19615 | − | 3.00000i | −0.178965 | − | 0.103325i | ||||
\(844\) | 1.00000 | − | 1.73205i | 0.0344214 | − | 0.0596196i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.00000 | 0.103142 | ||||||||
\(847\) | −28.5788 | + | 5.50000i | −0.981981 | + | 0.188982i | ||||
\(848\) | − | 6.00000i | − | 0.206041i | ||||||
\(849\) | −2.00000 | − | 3.46410i | −0.0686398 | − | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.0000 | − | 62.3538i | 1.23406 | − | 2.13746i | ||||
\(852\) | 15.5885 | − | 9.00000i | 0.534052 | − | 0.308335i | ||||
\(853\) | 10.0000i | 0.342393i | 0.985237 | + | 0.171197i | \(0.0547634\pi\) | ||||
−0.985237 | + | 0.171197i | \(0.945237\pi\) | |||||||
\(854\) | 8.00000 | − | 6.92820i | 0.273754 | − | 0.237078i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | + | 10.3923i | 0.205076 | + | 0.355202i | ||||
\(857\) | −46.7654 | − | 27.0000i | −1.59747 | − | 0.922302i | −0.991972 | − | 0.126459i | \(-0.959639\pi\) |
−0.605503 | − | 0.795843i | \(-0.707028\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.0000 | − | 34.6410i | −0.682391 | − | 1.18194i | −0.974249 | − | 0.225475i | \(-0.927607\pi\) |
0.291858 | − | 0.956462i | \(-0.405727\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | + | 10.3923i | −0.408959 | + | 0.354169i | ||||
\(862\) | 3.00000i | 0.102180i | ||||||||
\(863\) | −18.1865 | + | 10.5000i | −0.619077 | + | 0.357424i | −0.776509 | − | 0.630106i | \(-0.783012\pi\) |
0.157433 | + | 0.987530i | \(0.449678\pi\) | |||||||
\(864\) | −2.00000 | + | 3.46410i | −0.0680414 | + | 0.117851i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.5000 | + | 25.1147i | 0.492730 | + | 0.853433i | ||||
\(867\) | 16.0000i | 0.543388i | ||||||||
\(868\) | −12.9904 | + | 2.50000i | −0.440922 | + | 0.0848555i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.00000 | + | 3.46410i | −0.0677674 | + | 0.117377i | ||||
\(872\) | −8.66025 | − | 5.00000i | −0.293273 | − | 0.169321i | ||||
\(873\) | −4.33013 | + | 2.50000i | −0.146553 | + | 0.0846122i | ||||
\(874\) | −72.0000 | −2.43544 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.0000 | 0.675737 | ||||||||
\(877\) | −13.8564 | + | 8.00000i | −0.467898 | + | 0.270141i | −0.715359 | − | 0.698757i | \(-0.753737\pi\) |
0.247462 | + | 0.968898i | \(0.420404\pi\) | |||||||
\(878\) | −19.9186 | − | 11.5000i | −0.672220 | − | 0.388106i | ||||
\(879\) | −6.00000 | + | 10.3923i | −0.202375 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.0000 | 0.909653 | 0.454827 | − | 0.890580i | \(-0.349701\pi\) | ||||
0.454827 | + | 0.890580i | \(0.349701\pi\) | |||||||
\(882\) | 2.59808 | + | 6.50000i | 0.0874818 | + | 0.218866i | ||||
\(883\) | − | 26.0000i | − | 0.874970i | −0.899226 | − | 0.437485i | \(-0.855869\pi\) | ||
0.899226 | − | 0.437485i | \(-0.144131\pi\) | |||||||
\(884\) | −3.00000 | − | 5.19615i | −0.100901 | − | 0.174766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.00000 | + | 10.3923i | −0.201574 | + | 0.349136i | ||||
\(887\) | 31.1769 | − | 18.0000i | 1.04682 | − | 0.604381i | 0.125061 | − | 0.992149i | \(-0.460087\pi\) |
0.921757 | + | 0.387768i | \(0.126754\pi\) | |||||||
\(888\) | − | 16.0000i | − | 0.536925i | ||||||
\(889\) | −20.0000 | − | 6.92820i | −0.670778 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.9186 | − | 11.5000i | −0.666924 | − | 0.385048i | ||||
\(893\) | −20.7846 | − | 12.0000i | −0.695530 | − | 0.401565i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | + | 2.59808i | 0.0167038 | + | 0.0867956i | ||||
\(897\) | 36.0000i | 1.20201i | ||||||||
\(898\) | −23.3827 | + | 13.5000i | −0.780290 | + | 0.450501i | ||||
\(899\) | −15.0000 | + | 25.9808i | −0.500278 | + | 0.866507i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.00000 | + | 15.5885i | 0.299833 | + | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 34.6410 | + | 40.0000i | 1.15278 | + | 1.33112i | ||||
\(904\) | 15.0000 | 0.498893 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.00000 | − | 6.92820i | 0.132891 | − | 0.230174i | ||||
\(907\) | 34.6410 | + | 20.0000i | 1.15024 | + | 0.664089i | 0.948945 | − | 0.315442i | \(-0.102153\pi\) |
0.201291 | + | 0.979531i | \(0.435486\pi\) | |||||||
\(908\) | −15.5885 | + | 9.00000i | −0.517321 | + | 0.298675i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.00000 | 0.0993944 | 0.0496972 | − | 0.998764i | \(-0.484174\pi\) | ||||
0.0496972 | + | 0.998764i | \(0.484174\pi\) | |||||||
\(912\) | −13.8564 | + | 8.00000i | −0.458831 | + | 0.264906i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 11.0000 | − | 19.0526i | 0.363848 | − | 0.630203i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.0000 | 0.660819 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 12.0000i | − | 0.396059i | ||||||
\(919\) | 5.50000 | + | 9.52628i | 0.181428 | + | 0.314243i | 0.942367 | − | 0.334581i | \(-0.108595\pi\) |
−0.760939 | + | 0.648824i | \(0.775261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −16.0000 | + | 27.7128i | −0.527218 | + | 0.913168i | ||||
\(922\) | 20.7846 | − | 12.0000i | 0.684505 | − | 0.395199i | ||||
\(923\) | 18.0000i | 0.592477i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.5000 | − | 21.6506i | −0.410775 | − | 0.711484i | ||||
\(927\) | −9.52628 | − | 5.50000i | −0.312884 | − | 0.180644i | ||||
\(928\) | 5.19615 | + | 3.00000i | 0.170572 | + | 0.0984798i | ||||
\(929\) | 21.0000 | + | 36.3731i | 0.688988 | + | 1.19336i | 0.972166 | + | 0.234294i | \(0.0752779\pi\) |
−0.283178 | + | 0.959067i | \(0.591389\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.00000 | − | 55.4256i | 0.262189 | − | 1.81650i | ||||
\(932\) | − | 6.00000i | − | 0.196537i | ||||||
\(933\) | 36.3731 | − | 21.0000i | 1.19080 | − | 0.687509i | ||||
\(934\) | 3.00000 | − | 5.19615i | 0.0981630 | − | 0.170023i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.00000 | + | 1.73205i | 0.0326860 | + | 0.0566139i | ||||
\(937\) | − | 34.0000i | − | 1.11073i | −0.831606 | − | 0.555366i | \(-0.812578\pi\) | ||
0.831606 | − | 0.555366i | \(-0.187422\pi\) | |||||||
\(938\) | −1.73205 | + | 5.00000i | −0.0565535 | + | 0.163256i | ||||
\(939\) | 34.0000 | 1.10955 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.00000 | − | 5.19615i | 0.0977972 | − | 0.169390i | −0.812975 | − | 0.582298i | \(-0.802154\pi\) |
0.910773 | + | 0.412908i | \(0.135487\pi\) | |||||||
\(942\) | −3.46410 | − | 2.00000i | −0.112867 | − | 0.0651635i | ||||
\(943\) | −23.3827 | + | 13.5000i | −0.761445 | + | 0.439620i | ||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.3923 | + | 6.00000i | −0.337705 | + | 0.194974i | −0.659256 | − | 0.751918i | \(-0.729129\pi\) |
0.321552 | + | 0.946892i | \(0.395796\pi\) | |||||||
\(948\) | −8.66025 | − | 5.00000i | −0.281272 | − | 0.162392i | ||||
\(949\) | −10.0000 | + | 17.3205i | −0.324614 | + | 0.562247i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.0000 | 0.778253 | ||||||||
\(952\) | −5.19615 | − | 6.00000i | −0.168408 | − | 0.194461i | ||||
\(953\) | − | 54.0000i | − | 1.74923i | −0.484817 | − | 0.874616i | \(-0.661114\pi\) | ||
0.484817 | − | 0.874616i | \(-0.338886\pi\) | |||||||
\(954\) | −3.00000 | − | 5.19615i | −0.0971286 | − | 0.168232i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −7.50000 | + | 12.9904i | −0.242567 | + | 0.420139i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 27.0000i | − | 0.872330i | ||||||
\(959\) | 18.0000 | − | 15.5885i | 0.581250 | − | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | 13.8564 | + | 8.00000i | 0.446748 | + | 0.257930i | ||||
\(963\) | 10.3923 | + | 6.00000i | 0.334887 | + | 0.193347i | ||||
\(964\) | −11.0000 | − | 19.0526i | −0.354286 | − | 0.613642i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.00000 | + | 46.7654i | 0.289570 | + | 1.50465i | ||||
\(967\) | − | 7.00000i | − | 0.225105i | −0.993646 | − | 0.112552i | \(-0.964097\pi\) | ||
0.993646 | − | 0.112552i | \(-0.0359026\pi\) | |||||||
\(968\) | −9.52628 | + | 5.50000i | −0.306186 | + | 0.176777i | ||||
\(969\) | 24.0000 | − | 41.5692i | 0.770991 | − | 1.33540i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0000 | − | 25.9808i | −0.481373 | − | 0.833762i | 0.518399 | − | 0.855139i | \(-0.326528\pi\) |
−0.999771 | + | 0.0213768i | \(0.993195\pi\) | |||||||
\(972\) | 10.0000i | 0.320750i | ||||||||
\(973\) | 1.73205 | − | 5.00000i | 0.0555270 | − | 0.160293i | ||||
\(974\) | 11.0000 | 0.352463 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | − | 3.46410i | 0.0640184 | − | 0.110883i | ||||
\(977\) | 44.1673 | + | 25.5000i | 1.41304 | + | 0.815817i | 0.995673 | − | 0.0929223i | \(-0.0296208\pi\) |
0.417364 | + | 0.908740i | \(0.362954\pi\) | |||||||
\(978\) | −13.8564 | + | 8.00000i | −0.443079 | + | 0.255812i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | −36.3731 | + | 21.0000i | −1.16071 | + | 0.670137i | ||||
\(983\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(984\) | −3.00000 | + | 5.19615i | −0.0956365 | + | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −18.0000 | −0.573237 | ||||||||
\(987\) | −5.19615 | + | 15.0000i | −0.165395 | + | 0.477455i | ||||
\(988\) | − | 16.0000i | − | 0.509028i | ||||||
\(989\) | 45.0000 | + | 77.9423i | 1.43092 | + | 2.47842i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.5000 | + | 25.1147i | −0.460608 | + | 0.797796i | −0.998991 | − | 0.0449040i | \(-0.985702\pi\) |
0.538384 | + | 0.842700i | \(0.319035\pi\) | |||||||
\(992\) | −4.33013 | + | 2.50000i | −0.137482 | + | 0.0793751i | ||||
\(993\) | 28.0000i | 0.888553i | ||||||||
\(994\) | 4.50000 | + | 23.3827i | 0.142731 | + | 0.741654i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | − | 10.3923i | −0.190117 | − | 0.329293i | ||||
\(997\) | 3.46410 | + | 2.00000i | 0.109709 | + | 0.0633406i | 0.553851 | − | 0.832616i | \(-0.313158\pi\) |
−0.444141 | + | 0.895957i | \(0.646491\pi\) | |||||||
\(998\) | 29.4449 | + | 17.0000i | 0.932061 | + | 0.538126i | ||||
\(999\) | 16.0000 | + | 27.7128i | 0.506218 | + | 0.876795i |
(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 | 350.2.j.e.249.1 | 4 | ||
5.2 | odd | 4 | 350.2.e.a.151.1 | yes | 2 | ||
5.3 | odd | 4 | 350.2.e.k.151.1 | yes | 2 | ||
5.4 | even | 2 | inner | 350.2.j.e.249.2 | 4 | ||
7.2 | even | 3 | inner | 350.2.j.e.149.2 | 4 | ||
7.3 | odd | 6 | 2450.2.c.d.99.1 | 2 | |||
7.4 | even | 3 | 2450.2.c.o.99.1 | 2 | |||
35.2 | odd | 12 | 350.2.e.a.51.1 | ✓ | 2 | ||
35.3 | even | 12 | 2450.2.a.o.1.1 | 1 | |||
35.4 | even | 6 | 2450.2.c.o.99.2 | 2 | |||
35.9 | even | 6 | inner | 350.2.j.e.149.1 | 4 | ||
35.17 | even | 12 | 2450.2.a.u.1.1 | 1 | |||
35.18 | odd | 12 | 2450.2.a.e.1.1 | 1 | |||
35.23 | odd | 12 | 350.2.e.k.51.1 | yes | 2 | ||
35.24 | odd | 6 | 2450.2.c.d.99.2 | 2 | |||
35.32 | odd | 12 | 2450.2.a.be.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
350.2.e.a.51.1 | ✓ | 2 | 35.2 | odd | 12 | ||
350.2.e.a.151.1 | yes | 2 | 5.2 | odd | 4 | ||
350.2.e.k.51.1 | yes | 2 | 35.23 | odd | 12 | ||
350.2.e.k.151.1 | yes | 2 | 5.3 | odd | 4 | ||
350.2.j.e.149.1 | 4 | 35.9 | even | 6 | inner | ||
350.2.j.e.149.2 | 4 | 7.2 | even | 3 | inner | ||
350.2.j.e.249.1 | 4 | 1.1 | even | 1 | trivial | ||
350.2.j.e.249.2 | 4 | 5.4 | even | 2 | inner | ||
2450.2.a.e.1.1 | 1 | 35.18 | odd | 12 | |||
2450.2.a.o.1.1 | 1 | 35.3 | even | 12 | |||
2450.2.a.u.1.1 | 1 | 35.17 | even | 12 | |||
2450.2.a.be.1.1 | 1 | 35.32 | odd | 12 | |||
2450.2.c.d.99.1 | 2 | 7.3 | odd | 6 | |||
2450.2.c.d.99.2 | 2 | 35.24 | odd | 6 | |||
2450.2.c.o.99.1 | 2 | 7.4 | even | 3 | |||
2450.2.c.o.99.2 | 2 | 35.4 | even | 6 |