Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,2,Mod(47,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.n (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.638803216170\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.47 |
Dual form | 80.2.n.b.63.1 |
$q$-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 \(\left(\mathbb{Z}/80\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | −1.73205 | − | 1.73205i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | − | 2.00000i | −0.447214 | − | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 1.73205i | 0.654654 | − | 0.654654i | −0.299456 | − | 0.954110i | \(-0.596805\pi\) |
0.954110 | + | 0.299456i | \(0.0968053\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | − | 1.00000i | 0.277350 | − | 0.277350i | −0.554700 | − | 0.832050i | \(-0.687167\pi\) |
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.73205 | + | 5.19615i | −0.447214 | + | 1.34164i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | + | 1.00000i | 0.242536 | + | 0.242536i | 0.817898 | − | 0.575363i | \(-0.195139\pi\) |
−0.575363 | + | 0.817898i | \(0.695139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.92820 | 1.58944 | 0.794719 | − | 0.606977i | \(-0.207618\pi\) | ||||
0.794719 | + | 0.606977i | \(0.207618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.00000 | −1.30931 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.73205 | − | 1.73205i | −0.361158 | − | 0.361158i | 0.503081 | − | 0.864239i | \(-0.332200\pi\) |
−0.864239 | + | 0.503081i | \(0.832200\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | + | 4.00000i | −0.600000 | + | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.00000i | − | 0.742781i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) | ||
0.928477 | − | 0.371391i | \(-0.121119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.00000 | − | 6.00000i | 1.04447 | − | 1.04447i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.19615 | − | 1.73205i | −0.878310 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | + | 5.00000i | 0.821995 | + | 0.821995i | 0.986394 | − | 0.164399i | \(-0.0525685\pi\) |
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.46410 | −0.554700 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.73205 | − | 1.73205i | −0.264135 | − | 0.264135i | 0.562596 | − | 0.826732i | \(-0.309803\pi\) |
−0.826732 | + | 0.562596i | \(0.809803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.00000 | − | 3.00000i | 0.894427 | − | 0.447214i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.73205 | − | 1.73205i | 0.252646 | − | 0.252646i | −0.569409 | − | 0.822054i | \(-0.692828\pi\) |
0.822054 | + | 0.569409i | \(0.192828\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 3.46410i | − | 0.485071i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.00000 | + | 7.00000i | −0.961524 | + | 0.961524i | −0.999287 | − | 0.0377628i | \(-0.987977\pi\) |
0.0377628 | + | 0.999287i | \(0.487977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.92820 | − | 3.46410i | 0.934199 | − | 0.467099i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.0000 | − | 12.0000i | −1.58944 | − | 1.58944i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.92820 | −0.901975 | −0.450988 | − | 0.892530i | \(-0.648928\pi\) | ||||
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.19615 | + | 5.19615i | 0.654654 | + | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | − | 1.00000i | −0.372104 | − | 0.124035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.19615 | + | 5.19615i | −0.634811 | + | 0.634811i | −0.949271 | − | 0.314460i | \(-0.898177\pi\) |
0.314460 | + | 0.949271i | \(0.398177\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000i | 0.722315i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.3923i | 1.23334i | 0.787222 | + | 0.616670i | \(0.211519\pi\) | ||||
−0.787222 | + | 0.616670i | \(0.788481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | + | 7.00000i | −0.819288 | + | 0.819288i | −0.986005 | − | 0.166717i | \(-0.946683\pi\) |
0.166717 | + | 0.986005i | \(0.446683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.1244 | − | 1.73205i | 1.40000 | − | 0.200000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | + | 6.00000i | 0.683763 | + | 0.683763i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.1244 | + | 12.1244i | 1.33082 | + | 1.33082i | 0.904636 | + | 0.426185i | \(0.140143\pi\) |
0.426185 | + | 0.904636i | \(0.359857\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | − | 3.00000i | 0.108465 | − | 0.325396i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.92820 | + | 6.92820i | −0.742781 | + | 0.742781i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 8.00000i | − | 0.847998i | −0.905663 | − | 0.423999i | \(-0.860626\pi\) | ||
0.905663 | − | 0.423999i | \(-0.139374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.46410i | − | 0.363137i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.00000 | + | 6.00000i | −0.622171 | + | 0.622171i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.92820 | − | 13.8564i | −0.710819 | − | 1.42164i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | − | 7.00000i | −0.710742 | − | 0.710742i | 0.255948 | − | 0.966691i | \(-0.417612\pi\) |
−0.966691 | + | 0.255948i | \(0.917612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.3923 | −1.04447 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.73205 | − | 1.73205i | −0.170664 | − | 0.170664i | 0.616607 | − | 0.787271i | \(-0.288507\pi\) |
−0.787271 | + | 0.616607i | \(0.788507\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | + | 12.0000i | 0.585540 | + | 1.17108i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.66025 | − | 8.66025i | 0.837218 | − | 0.837218i | −0.151274 | − | 0.988492i | \(-0.548337\pi\) |
0.988492 | + | 0.151274i | \(0.0483374\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.0000i | − | 1.14939i | −0.818367 | − | 0.574696i | \(-0.805120\pi\) | ||
0.818367 | − | 0.574696i | \(-0.194880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 17.3205i | − | 1.64399i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.00000 | − | 9.00000i | 0.846649 | − | 0.846649i | −0.143065 | − | 0.989713i | \(-0.545696\pi\) |
0.989713 | + | 0.143065i | \(0.0456957\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.73205 | + | 5.19615i | −0.161515 | + | 0.484544i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.00000 | + | 3.00000i | 0.277350 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.46410 | 0.317554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.46410 | − | 3.46410i | −0.312348 | − | 0.312348i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0000 | + | 2.00000i | 0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.1244 | + | 12.1244i | −1.07586 | + | 1.07586i | −0.0789869 | + | 0.996876i | \(0.525169\pi\) |
−0.996876 | + | 0.0789869i | \(0.974831\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000i | 0.528271i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 10.3923i | − | 0.907980i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000 | − | 12.0000i | 1.04053 | − | 1.04053i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.00000 | + | 9.00000i | 0.768922 | + | 0.768922i | 0.977917 | − | 0.208995i | \(-0.0670192\pi\) |
−0.208995 | + | 0.977917i | \(0.567019\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.46410 | + | 3.46410i | 0.289683 | + | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | + | 4.00000i | −0.664364 | + | 0.332182i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.73205 | − | 1.73205i | 0.142857 | − | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 4.00000i | − | 0.327693i | −0.986486 | − | 0.163846i | \(-0.947610\pi\) | ||
0.986486 | − | 0.163846i | \(-0.0523901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3923i | 0.845714i | 0.906196 | + | 0.422857i | \(0.138973\pi\) | ||||
−0.906196 | + | 0.422857i | \(0.861027\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.00000 | + | 3.00000i | −0.242536 | + | 0.242536i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.92820 | + | 3.46410i | −0.556487 | + | 0.278243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0000 | − | 11.0000i | −0.877896 | − | 0.877896i | 0.115421 | − | 0.993317i | \(-0.463178\pi\) |
−0.993317 | + | 0.115421i | \(0.963178\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.2487 | 1.92305 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.73205 | − | 1.73205i | −0.135665 | − | 0.135665i | 0.636013 | − | 0.771678i | \(-0.280582\pi\) |
−0.771678 | + | 0.636013i | \(0.780582\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.0000 | − | 6.00000i | −1.40130 | − | 0.467099i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.5885 | − | 15.5885i | 1.20627 | − | 1.20627i | 0.234045 | − | 0.972226i | \(-0.424804\pi\) |
0.972226 | − | 0.234045i | \(-0.0751964\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 20.7846i | 1.58944i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.0000 | + | 15.0000i | −1.14043 | + | 1.14043i | −0.152057 | + | 0.988372i | \(0.548590\pi\) |
−0.988372 | + | 0.152057i | \(0.951410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.73205 | + | 12.1244i | 0.130931 | + | 0.916515i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | + | 12.0000i | 0.901975 | + | 0.901975i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.92820 | 0.517838 | 0.258919 | − | 0.965899i | \(-0.416634\pi\) | ||||
0.258919 | + | 0.965899i | \(0.416634\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.3923 | − | 10.3923i | −0.768221 | − | 0.768221i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.00000 | − | 15.0000i | 0.367607 | − | 1.10282i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.46410 | + | 3.46410i | −0.253320 | + | 0.253320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.2487i | 1.75458i | 0.479965 | + | 0.877288i | \(0.340649\pi\) | ||||
−0.479965 | + | 0.877288i | \(0.659351\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00000 | − | 1.00000i | 0.0719816 | − | 0.0719816i | −0.670199 | − | 0.742181i | \(-0.733791\pi\) |
0.742181 | + | 0.670199i | \(0.233791\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.46410 | + | 6.92820i | 0.248069 | + | 0.496139i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | − | 3.00000i | −0.213741 | − | 0.213741i | 0.592113 | − | 0.805855i | \(-0.298294\pi\) |
−0.805855 | + | 0.592113i | \(0.798294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8564 | −0.982255 | −0.491127 | − | 0.871088i | \(-0.663415\pi\) | ||||
−0.491127 | + | 0.871088i | \(0.663415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.0000 | 1.26962 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.92820 | − | 6.92820i | −0.486265 | − | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | − | 4.00000i | −0.139686 | − | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.19615 | − | 5.19615i | 0.361158 | − | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000i | 1.66011i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 10.3923i | − | 0.715436i | −0.933830 | − | 0.357718i | \(-0.883555\pi\) | ||
0.933830 | − | 0.357718i | \(-0.116445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.0000 | − | 18.0000i | 1.23334 | − | 1.23334i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.73205 | + | 5.19615i | −0.118125 | + | 0.354375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | − | 6.00000i | −0.407307 | − | 0.407307i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 24.2487 | 1.63858 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | 0.134535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.5885 | − | 15.5885i | −1.04388 | − | 1.04388i | −0.998992 | − | 0.0448883i | \(-0.985707\pi\) |
−0.0448883 | − | 0.998992i | \(-0.514293\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.0000 | − | 9.00000i | −0.800000 | − | 0.600000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.66025 | − | 8.66025i | 0.574801 | − | 0.574801i | −0.358665 | − | 0.933466i | \(-0.616768\pi\) |
0.933466 | + | 0.358665i | \(0.116768\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.0000i | 1.32164i | 0.750546 | + | 0.660819i | \(0.229791\pi\) | ||||
−0.750546 | + | 0.660819i | \(0.770209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 20.7846i | − | 1.36753i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.00000 | − | 1.00000i | 0.0655122 | − | 0.0655122i | −0.673592 | − | 0.739104i | \(-0.735249\pi\) |
0.739104 | + | 0.673592i | \(0.235249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.19615 | − | 1.73205i | −0.338960 | − | 0.112987i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.7128 | −1.79259 | −0.896296 | − | 0.443455i | \(-0.853752\pi\) | ||||
−0.896296 | + | 0.443455i | \(0.853752\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0000 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | − | 15.5885i | −1.00000 | − | 1.00000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.00000 | − | 1.00000i | 0.127775 | − | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.92820 | − | 6.92820i | 0.440831 | − | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 42.0000i | − | 2.66164i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.46410i | 0.218652i | 0.994006 | + | 0.109326i | \(0.0348693\pi\) | ||||
−0.994006 | + | 0.109326i | \(0.965131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | − | 6.00000i | 0.377217 | − | 0.377217i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.92820 | + | 3.46410i | −0.433861 | + | 0.216930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.00000 | + | 9.00000i | 0.561405 | + | 0.561405i | 0.929706 | − | 0.368302i | \(-0.120061\pi\) |
−0.368302 | + | 0.929706i | \(0.620061\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.3205 | 1.07624 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.0000 | 0.742781 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.1244 | + | 12.1244i | 0.747620 | + | 0.747620i | 0.974032 | − | 0.226412i | \(-0.0726995\pi\) |
−0.226412 | + | 0.974032i | \(0.572700\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.0000 | + | 7.00000i | 1.29002 | + | 0.430007i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.8564 | + | 13.8564i | −0.847998 | + | 0.847998i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.00000i | 0.243884i | 0.992537 | + | 0.121942i | \(0.0389122\pi\) | ||||
−0.992537 | + | 0.121942i | \(0.961088\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.46410i | − | 0.210429i | −0.994450 | − | 0.105215i | \(-0.966447\pi\) | ||
0.994450 | − | 0.105215i | \(-0.0335529\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00000 | + | 6.00000i | −0.363137 | + | 0.363137i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.8564 | − | 10.3923i | −0.835573 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0000 | + | 13.0000i | 0.781094 | + | 0.781094i | 0.980015 | − | 0.198921i | \(-0.0637438\pi\) |
−0.198921 | + | 0.980015i | \(0.563744\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.3923 | 0.622171 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.0000 | −0.835170 | −0.417585 | − | 0.908638i | \(-0.637123\pi\) | ||||
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1244 | + | 12.1244i | 0.720718 | + | 0.720718i | 0.968751 | − | 0.248033i | \(-0.0797843\pi\) |
−0.248033 | + | 0.968751i | \(0.579784\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.0000 | + | 36.0000i | −0.710819 | + | 2.13246i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.46410 | − | 3.46410i | 0.204479 | − | 0.204479i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 15.0000i | − | 0.882353i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 24.2487i | 1.42148i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.00000 | − | 9.00000i | 0.525786 | − | 0.525786i | −0.393527 | − | 0.919313i | \(-0.628745\pi\) |
0.919313 | + | 0.393527i | \(0.128745\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.92820 | + | 13.8564i | 0.403376 | + | 0.806751i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.46410 | −0.200334 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | −0.345834 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.3205 | + | 17.3205i | 0.995037 | + | 0.995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.00000 | − | 12.0000i | −0.343559 | − | 0.687118i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.19615 | + | 5.19615i | −0.296560 | + | 0.296560i | −0.839665 | − | 0.543105i | \(-0.817249\pi\) |
0.543105 | + | 0.839665i | \(0.317249\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000i | 0.341328i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 17.3205i | − | 0.982156i | −0.871116 | − | 0.491078i | \(-0.836603\pi\) | ||
0.871116 | − | 0.491078i | \(-0.163397\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.00000 | + | 7.00000i | −0.395663 | + | 0.395663i | −0.876700 | − | 0.481037i | \(-0.840260\pi\) |
0.481037 | + | 0.876700i | \(0.340260\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.19615 | − | 15.5885i | 0.292770 | − | 0.878310i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.0000 | − | 19.0000i | −1.06715 | − | 1.06715i | −0.997577 | − | 0.0695692i | \(-0.977838\pi\) |
−0.0695692 | − | 0.997577i | \(-0.522162\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.8564 | 0.775810 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.0000 | −1.67444 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.92820 | + | 6.92820i | 0.385496 | + | 0.385496i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | + | 7.00000i | 0.0554700 | + | 0.388290i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −20.7846 | + | 20.7846i | −1.14939 | + | 1.14939i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.00000i | − | 0.330791i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 24.2487i | − | 1.33283i | −0.745581 | − | 0.666415i | \(-0.767828\pi\) | ||
0.745581 | − | 0.666415i | \(-0.232172\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.0000 | + | 15.0000i | −0.821995 | + | 0.821995i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.5885 | + | 5.19615i | 0.851688 | + | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.00000 | + | 1.00000i | 0.0544735 | + | 0.0544735i | 0.733819 | − | 0.679345i | \(-0.237736\pi\) |
−0.679345 | + | 0.733819i | \(0.737736\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −31.1769 | −1.69330 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.8564 | + | 13.8564i | 0.748176 | + | 0.748176i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.0000 | − | 6.00000i | 0.646058 | − | 0.323029i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.19615 | + | 5.19615i | −0.278944 | + | 0.278944i | −0.832687 | − | 0.553743i | \(-0.813199\pi\) |
0.553743 | + | 0.832687i | \(0.313199\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0000i | 0.642345i | 0.947021 | + | 0.321173i | \(0.104077\pi\) | ||||
−0.947021 | + | 0.321173i | \(0.895923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.00000 | − | 1.00000i | 0.0532246 | − | 0.0532246i | −0.679994 | − | 0.733218i | \(-0.738017\pi\) |
0.733218 | + | 0.679994i | \(0.238017\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.7846 | − | 10.3923i | 1.10313 | − | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.00000 | − | 6.00000i | −0.317554 | − | 0.317554i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.8564 | −0.731313 | −0.365657 | − | 0.930750i | \(-0.619156\pi\) | ||||
−0.365657 | + | 0.930750i | \(0.619156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.0000 | 1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.73205 | + | 1.73205i | 0.0909091 | + | 0.0909091i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.0000 | + | 7.00000i | 1.09919 | + | 0.366397i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.5885 | − | 15.5885i | 0.813711 | − | 0.813711i | −0.171477 | − | 0.985188i | \(-0.554854\pi\) |
0.985188 | + | 0.171477i | \(0.0548540\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.00000i | 0.312348i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.2487i | 1.25893i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.00000 | − | 1.00000i | 0.0517780 | − | 0.0517780i | −0.680744 | − | 0.732522i | \(-0.738343\pi\) |
0.732522 | + | 0.680744i | \(0.238343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.5885 | − | 22.5167i | −0.804984 | − | 1.16276i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.00000 | − | 4.00000i | −0.206010 | − | 0.206010i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.92820 | −0.355878 | −0.177939 | − | 0.984042i | \(-0.556943\pi\) | ||||
−0.177939 | + | 0.984042i | \(0.556943\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 42.0000 | 2.15173 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.5885 | − | 15.5885i | −0.796533 | − | 0.796533i | 0.186014 | − | 0.982547i | \(-0.440443\pi\) |
−0.982547 | + | 0.186014i | \(0.940443\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | − | 18.0000i | 0.305788 | − | 0.917365i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.19615 | − | 5.19615i | 0.264135 | − | 0.264135i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 20.0000i | − | 1.01404i | −0.861934 | − | 0.507020i | \(-0.830747\pi\) | ||
0.861934 | − | 0.507020i | \(-0.169253\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.46410i | − | 0.175187i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.0000 | + | 18.0000i | −0.907980 | + | 0.907980i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0000 | − | 11.0000i | −0.552074 | − | 0.552074i | 0.374965 | − | 0.927039i | \(-0.377655\pi\) |
−0.927039 | + | 0.374965i | \(0.877655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −41.5692 | −2.08106 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.46410 | − | 3.46410i | −0.172559 | − | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.00000 | − | 18.0000i | −0.447214 | − | 0.894427i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.3205 | + | 17.3205i | −0.858546 | + | 0.858546i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 31.1769i | − | 1.53784i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | + | 12.0000i | −0.590481 | + | 0.590481i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.1244 | − | 36.3731i | 0.595161 | − | 1.78548i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0000 | + | 12.0000i | 0.587643 | + | 0.587643i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.92820 | 0.338465 | 0.169232 | − | 0.985576i | \(-0.445871\pi\) | ||||
0.169232 | + | 0.985576i | \(0.445871\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.19615 | + | 5.19615i | 0.252646 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.00000 | + | 1.00000i | −0.339550 | + | 0.0485071i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.3923 | − | 10.3923i | 0.502919 | − | 0.502919i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 12.0000i | − | 0.579365i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3.46410i | − | 0.166860i | −0.996514 | − | 0.0834300i | \(-0.973413\pi\) | ||
0.996514 | − | 0.0834300i | \(-0.0265875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.00000 | + | 7.00000i | −0.336399 | + | 0.336399i | −0.855010 | − | 0.518611i | \(-0.826449\pi\) |
0.518611 | + | 0.855010i | \(0.326449\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.7846 | + | 6.92820i | 0.996546 | + | 0.332182i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.0000 | − | 12.0000i | −0.574038 | − | 0.574038i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.8564 | 0.661330 | 0.330665 | − | 0.943748i | \(-0.392727\pi\) | ||||
0.330665 | + | 0.943748i | \(0.392727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.1244 | + | 12.1244i | 0.576046 | + | 0.576046i | 0.933811 | − | 0.357766i | \(-0.116461\pi\) |
−0.357766 | + | 0.933811i | \(0.616461\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.0000 | + | 8.00000i | −0.758473 | + | 0.379236i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.92820 | + | 6.92820i | −0.327693 | + | 0.327693i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.00000i | 0.377543i | 0.982021 | + | 0.188772i | \(0.0604506\pi\) | ||||
−0.982021 | + | 0.188772i | \(0.939549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.92820i | 0.326236i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.0000 | − | 18.0000i | 0.845714 | − | 0.845714i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.92820 | + | 3.46410i | −0.324799 | + | 0.162400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.0000 | + | 17.0000i | 0.795226 | + | 0.795226i | 0.982339 | − | 0.187112i | \(-0.0599128\pi\) |
−0.187112 | + | 0.982339i | \(0.559913\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.00000 | −0.0931493 | −0.0465746 | − | 0.998915i | \(-0.514831\pi\) | ||||
−0.0465746 | + | 0.998915i | \(0.514831\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.73205 | − | 1.73205i | −0.0804952 | − | 0.0804952i | 0.665713 | − | 0.746208i | \(-0.268128\pi\) |
−0.746208 | + | 0.665713i | \(0.768128\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.0000 | + | 6.00000i | 0.834730 | + | 0.278243i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.0526 | + | 19.0526i | −0.881647 | + | 0.881647i | −0.993702 | − | 0.112055i | \(-0.964257\pi\) |
0.112055 | + | 0.993702i | \(0.464257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.0000i | 0.831163i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 38.1051i | 1.75579i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.00000 | − | 6.00000i | 0.275880 | − | 0.275880i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.7846 | + | 27.7128i | −0.953663 | + | 1.27155i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.0000 | − | 21.0000i | −0.961524 | − | 0.961524i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.7128 | 1.26623 | 0.633115 | − | 0.774057i | \(-0.281776\pi\) | ||||
0.633115 | + | 0.774057i | \(0.281776\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0000 | 0.455961 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.3923 | + | 10.3923i | 0.472866 | + | 0.472866i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.00000 | + | 21.0000i | −0.317854 | + | 0.953561i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.73205 | − | 1.73205i | 0.0784867 | − | 0.0784867i | −0.666774 | − | 0.745260i | \(-0.732325\pi\) |
0.745260 | + | 0.666774i | \(0.232325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.00000i | 0.271329i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 24.2487i | − | 1.09433i | −0.837025 | − | 0.547165i | \(-0.815707\pi\) | ||
0.837025 | − | 0.547165i | \(-0.184293\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | − | 4.00000i | 0.180151 | − | 0.180151i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.3923 | + | 20.7846i | 0.467099 | + | 0.934199i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.0000 | + | 18.0000i | 0.807410 | + | 0.807410i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.7846 | −0.930447 | −0.465223 | − | 0.885193i | \(-0.654026\pi\) | ||||
−0.465223 | + | 0.885193i | \(0.654026\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −54.0000 | −2.41254 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.73205 | − | 1.73205i | −0.0772283 | − | 0.0772283i | 0.667437 | − | 0.744666i | \(-0.267391\pi\) |
−0.744666 | + | 0.667437i | \(0.767391\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | + | 20.0000i | 0.444994 | + | 0.889988i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.0526 | − | 19.0526i | 0.846154 | − | 0.846154i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 20.0000i | − | 0.886484i | −0.896402 | − | 0.443242i | \(-0.853828\pi\) | ||
0.896402 | − | 0.443242i | \(-0.146172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.2487i | 1.07270i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.73205 | + | 5.19615i | −0.0763233 | + | 0.228970i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.00000 | + | 6.00000i | 0.263880 | + | 0.263880i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 51.9615 | 2.28086 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.0000 | −1.66481 | −0.832405 | − | 0.554168i | \(-0.813037\pi\) | ||||
−0.832405 | + | 0.554168i | \(0.813037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.1244 | + | 12.1244i | 0.530161 | + | 0.530161i | 0.920620 | − | 0.390459i | \(-0.127684\pi\) |
−0.390459 | + | 0.920620i | \(0.627684\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.0000 | − | 24.0000i | 0.785584 | − | 1.04745i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.46410 | − | 3.46410i | 0.150899 | − | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 17.0000i | − | 0.739130i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 20.7846i | − | 0.901975i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.00000 | − | 2.00000i | 0.0866296 | − | 0.0866296i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.9808 | − | 8.66025i | −1.12325 | − | 0.374415i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | − | 12.0000i | −0.517838 | − | 0.517838i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.46410 | −0.149209 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.3923 | − | 10.3923i | −0.445976 | − | 0.445976i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.0000 | + | 12.0000i | −1.02805 | + | 0.514024i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.66025 | − | 8.66025i | 0.370286 | − | 0.370286i | −0.497296 | − | 0.867581i | \(-0.665674\pi\) |
0.867581 | + | 0.497296i | \(0.165674\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18.0000i | 0.768221i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 27.7128i | − | 1.18061i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −34.6410 | + | 17.3205i | −1.47043 | + | 0.735215i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.0000 | + | 29.0000i | 1.22877 | + | 1.22877i | 0.964430 | + | 0.264340i | \(0.0851541\pi\) |
0.264340 | + | 0.964430i | \(0.414846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.46410 | −0.146516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.0000 | 0.506640 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.4449 | − | 29.4449i | −1.24095 | − | 1.24095i | −0.959606 | − | 0.281347i | \(-0.909219\pi\) |
−0.281347 | − | 0.959606i | \(-0.590781\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.0000 | − | 9.00000i | −1.13590 | − | 0.378633i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.5885 | − | 15.5885i | 0.654654 | − | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.0000i | 0.670755i | 0.942084 | + | 0.335377i | \(0.108864\pi\) | ||||
−0.942084 | + | 0.335377i | \(0.891136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.1769i | 1.30471i | 0.757912 | + | 0.652357i | \(0.226220\pi\) | ||||
−0.757912 | + | 0.652357i | \(0.773780\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 42.0000 | − | 42.0000i | 1.75458 | − | 1.75458i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.1244 | − | 1.73205i | 0.505621 | − | 0.0722315i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.00000 | − | 7.00000i | −0.291414 | − | 0.291414i | 0.546225 | − | 0.837639i | \(-0.316064\pi\) |
−0.837639 | + | 0.546225i | \(0.816064\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.46410 | −0.143963 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 42.0000 | 1.74245 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.2487 | − | 24.2487i | −1.00428 | − | 1.00428i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.00000 | − | 9.00000i | 0.124035 | − | 0.372104i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.19615 | + | 5.19615i | −0.214468 | + | 0.214468i | −0.806162 | − | 0.591694i | \(-0.798459\pi\) |
0.591694 | + | 0.806162i | \(0.298459\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 24.0000i | − | 0.988903i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.3923i | 0.427482i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.0000 | − | 33.0000i | 1.35515 | − | 1.35515i | 0.475352 | − | 0.879796i | \(-0.342321\pi\) |
0.879796 | − | 0.475352i | \(-0.157679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.46410 | − | 6.92820i | −0.142014 | − | 0.284029i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.0000 | + | 24.0000i | 0.982255 | + | 0.982255i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.8564 | 0.566157 | 0.283079 | − | 0.959097i | \(-0.408644\pi\) | ||||
0.283079 | + | 0.959097i | \(0.408644\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0000 | 0.734235 | 0.367118 | − | 0.930175i | \(-0.380345\pi\) | ||||
0.367118 | + | 0.930175i | \(0.380345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.5885 | − | 15.5885i | −0.634811 | − | 0.634811i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.00000 | + | 2.00000i | 0.0406558 | + | 0.0813116i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.9808 | + | 25.9808i | −1.05453 | + | 1.05453i | −0.0561015 | + | 0.998425i | \(0.517867\pi\) |
−0.998425 | + | 0.0561015i | \(0.982133\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.0000i | 0.972529i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.46410i | − | 0.140143i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.0000 | + | 31.0000i | −1.25208 | + | 1.25208i | −0.297291 | + | 0.954787i | \(0.596083\pi\) |
−0.954787 | + | 0.297291i | \(0.903917\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.46410 | + | 10.3923i | −0.139686 | + | 0.419058i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.00000 | − | 7.00000i | −0.281809 | − | 0.281809i | 0.552021 | − | 0.833830i | \(-0.313857\pi\) |
−0.833830 | + | 0.552021i | \(0.813857\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.7846 | 0.835404 | 0.417702 | − | 0.908584i | \(-0.362836\pi\) | ||||
0.417702 | + | 0.908584i | \(0.362836\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.8564 | − | 13.8564i | −0.555145 | − | 0.555145i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 41.5692 | − | 41.5692i | 1.66011 | − | 1.66011i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.0000i | 0.398726i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 17.3205i | − | 0.689519i | −0.938691 | − | 0.344759i | \(-0.887961\pi\) | ||
0.938691 | − | 0.344759i | \(-0.112039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.0000 | + | 18.0000i | −0.715436 | + | 0.715436i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.3731 | + | 12.1244i | 1.44342 | + | 0.481140i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | + | 1.00000i | 0.0396214 | + | 0.0396214i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −31.1769 | −1.23334 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.0000 | 1.02694 | 0.513469 | − | 0.858108i | \(-0.328360\pi\) | ||||
0.513469 | + | 0.858108i | \(0.328360\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.5885 | − | 15.5885i | −0.614749 | − | 0.614749i | 0.329431 | − | 0.944180i | \(-0.393143\pi\) |
−0.944180 | + | 0.329431i | \(0.893143\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.0000 | − | 6.00000i | 0.472500 | − | 0.236250i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.73205 | − | 1.73205i | 0.0680939 | − | 0.0680939i | −0.672240 | − | 0.740334i | \(-0.734668\pi\) |
0.740334 | + | 0.672240i | \(0.234668\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 24.0000i | − | 0.942082i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.7846i | 0.814613i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.0000 | + | 23.0000i | −0.900060 | + | 0.900060i | −0.995441 | − | 0.0953813i | \(-0.969593\pi\) |
0.0953813 | + | 0.995441i | \(0.469593\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.7846 | + | 10.3923i | −0.812122 | + | 0.406061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.0000 | − | 21.0000i | −0.819288 | − | 0.819288i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.6410 | 1.34942 | 0.674711 | − | 0.738082i | \(-0.264268\pi\) | ||||
0.674711 | + | 0.738082i | \(0.264268\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0000 | −0.700119 | −0.350059 | − | 0.936727i | \(-0.613839\pi\) | ||||
−0.350059 | + | 0.936727i | \(0.613839\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.46410 | − | 3.46410i | −0.134535 | − | 0.134535i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −36.0000 | − | 12.0000i | −1.39602 | − | 0.465340i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.92820 | + | 6.92820i | −0.268261 | + | 0.268261i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 54.0000i | 2.08776i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.7846i | 0.802381i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.0000 | − | 25.0000i | 0.963679 | − | 0.963679i | −0.0356839 | − | 0.999363i | \(-0.511361\pi\) |
0.999363 | + | 0.0356839i | \(0.0113610\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.0000 | − | 35.0000i | −1.34516 | − | 1.34516i | −0.890838 | − | 0.454321i | \(-0.849882\pi\) |
−0.454321 | − | 0.890838i | \(-0.650118\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.2487 | −0.930580 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −30.0000 | −1.14960 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.73205 | − | 1.73205i | −0.0662751 | − | 0.0662751i | 0.673192 | − | 0.739467i | \(-0.264923\pi\) |
−0.739467 | + | 0.673192i | \(0.764923\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.00000 | − | 27.0000i | 0.343872 | − | 1.03162i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.6410 | − | 34.6410i | 1.32164 | − | 1.32164i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.0000i | 0.533358i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.0333i | 1.71315i | 0.516024 | + | 0.856574i | \(0.327412\pi\) | ||||
−0.516024 | + | 0.856574i | \(0.672588\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.0000 | + | 18.0000i | −0.683763 | + | 0.683763i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.92820 | + | 13.8564i | 0.262802 | + | 0.525603i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.00000 | + | 2.00000i | 0.0757554 | + | 0.0757554i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.46410 | −0.131024 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.0000 | 1.43524 | 0.717620 | − | 0.696435i | \(-0.245231\pi\) | ||||
0.717620 | + | 0.696435i | \(0.245231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.6410 | + | 34.6410i | 1.30651 | + | 1.30651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.00000 | + | 12.0000i | 0.225973 | + | 0.451946i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.3205 | + | 17.3205i | −0.651405 | + | 0.651405i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000i | 0.150223i | 0.997175 | + | 0.0751116i | \(0.0239313\pi\) | ||||
−0.997175 | + | 0.0751116i | \(0.976069\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.00000 | + | 6.00000i | −0.224702 | + | 0.224702i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.46410 | − | 10.3923i | 0.129550 | − | 0.388650i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 48.0000 | + | 48.0000i | 1.79259 | + | 1.79259i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.7128 | 1.03351 | 0.516757 | − | 0.856132i | \(-0.327139\pi\) | ||||
0.516757 | + | 0.856132i | \(0.327139\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.00000 | −0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 38.1051 | + | 38.1051i | 1.41714 | + | 1.41714i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.0000 | + | 12.0000i | 0.594225 | + | 0.445669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.73205 | − | 1.73205i | 0.0642382 | − | 0.0642382i | −0.674258 | − | 0.738496i | \(-0.735536\pi\) |
0.738496 | + | 0.674258i | \(0.235536\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3.46410i | − | 0.128124i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.00000 | − | 1.00000i | 0.0369358 | − | 0.0369358i | −0.688398 | − | 0.725333i | \(-0.741686\pi\) |
0.725333 | + | 0.688398i | \(0.241686\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.19615 | − | 1.73205i | −0.191663 | − | 0.0638877i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.0000 | − | 18.0000i | −0.663039 | − | 0.663039i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.7846 | −0.764574 | −0.382287 | − | 0.924044i | \(-0.624863\pi\) | ||||
−0.382287 | + | 0.924044i | \(0.624863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.0000 | −0.881662 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.1244 | + | 12.1244i | 0.444799 | + | 0.444799i | 0.893621 | − | 0.448822i | \(-0.148156\pi\) |
−0.448822 | + | 0.893621i | \(0.648156\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.00000 | + | 4.00000i | −0.293097 | + | 0.146549i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −36.3731 | + | 36.3731i | −1.33082 | + | 1.33082i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 30.0000i | − | 1.09618i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.46410i | − | 0.126407i | −0.998001 | − | 0.0632034i | \(-0.979868\pi\) | ||
0.998001 | − | 0.0632034i | \(-0.0201317\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.00000 | − | 6.00000i | 0.218652 | − | 0.218652i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20.7846 | − | 10.3923i | 0.756429 | − | 0.378215i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.0000 | + | 29.0000i | 1.05402 | + | 1.05402i | 0.998455 | + | 0.0555680i | \(0.0176970\pi\) |
0.0555680 | + | 0.998455i | \(0.482303\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.7846 | −0.754434 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0000 | 0.362500 | 0.181250 | − | 0.983437i | \(-0.441986\pi\) | ||||
0.181250 | + | 0.983437i | \(0.441986\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.7846 | − | 20.7846i | −0.752453 | − | 0.752453i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.00000 | + | 3.00000i | 0.325396 | + | 0.108465i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.92820 | + | 6.92820i | −0.250163 | + | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 48.0000i | − | 1.73092i | −0.500974 | − | 0.865462i | \(-0.667025\pi\) | ||
0.500974 | − | 0.865462i | \(-0.332975\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 31.1769i | − | 1.12281i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.00000 | − | 1.00000i | 0.0359675 | − | 0.0359675i | −0.688894 | − | 0.724862i | \(-0.741904\pi\) |
0.724862 | + | 0.688894i | \(0.241904\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.8564 | + | 10.3923i | 0.497737 | + | 0.373303i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −30.0000 | − | 30.0000i | −1.07624 | − | 1.07624i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.8564 | 0.496457 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | −1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.0000 | + | 33.0000i | −0.392607 | + | 1.17782i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.19615 | + | 5.19615i | −0.185223 | + | 0.185223i | −0.793627 | − | 0.608404i | \(-0.791810\pi\) |
0.608404 | + | 0.793627i | \(0.291810\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 42.0000i | − | 1.49524i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 31.1769i | − | 1.10852i |