Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(127,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 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("720.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.x (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: | \(5.74922894553\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 703.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.703 |
Dual form | 720.2.x.d.127.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 2.00000i | 0.447214 | − | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | + | 1.73205i | 0.654654 | + | 0.654654i | 0.954110 | − | 0.299456i | \(-0.0968053\pi\) |
−0.299456 | + | 0.954110i | \(0.596805\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) |
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | + | 1.00000i | −0.242536 | + | 0.242536i | −0.817898 | − | 0.575363i | \(-0.804861\pi\) |
0.575363 | + | 0.817898i | \(0.304861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.92820 | 1.58944 | 0.794719 | − | 0.606977i | \(-0.207618\pi\) | ||||
0.794719 | + | 0.606977i | \(0.207618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.73205 | − | 1.73205i | 0.361158 | − | 0.361158i | −0.503081 | − | 0.864239i | \(-0.667800\pi\) |
0.864239 | + | 0.503081i | \(0.167800\pi\) | |||||||
\(24\) | 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 | \(0.100693\pi\) | ||||
−0.950382 | + | 0.311086i | \(0.899307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.19615 | − | 1.73205i | 0.878310 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | − | 5.00000i | 0.821995 | − | 0.821995i | −0.164399 | − | 0.986394i | \(-0.552568\pi\) |
0.986394 | + | 0.164399i | \(0.0525685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.73205 | + | 1.73205i | −0.264135 | + | 0.264135i | −0.826732 | − | 0.562596i | \(-0.809803\pi\) |
0.562596 | + | 0.826732i | \(0.309803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.73205 | − | 1.73205i | −0.252646 | − | 0.252646i | 0.569409 | − | 0.822054i | \(-0.307172\pi\) |
−0.822054 | + | 0.569409i | \(0.807172\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.00000 | + | 7.00000i | 0.961524 | + | 0.961524i | 0.999287 | − | 0.0377628i | \(-0.0120231\pi\) |
−0.0377628 | + | 0.999287i | \(0.512023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.92820 | + | 3.46410i | 0.934199 | + | 0.467099i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.92820 | 0.901975 | 0.450988 | − | 0.892530i | \(-0.351072\pi\) | ||||
0.450988 | + | 0.892530i | \(0.351072\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | − | 1.00000i | 0.372104 | − | 0.124035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.19615 | − | 5.19615i | −0.634811 | − | 0.634811i | 0.314460 | − | 0.949271i | \(-0.398177\pi\) |
−0.949271 | + | 0.314460i | \(0.898177\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | 0.166717 | − | 0.986005i | \(-0.446683\pi\) |
−0.986005 | + | 0.166717i | \(0.946683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.1244 | + | 12.1244i | −1.33082 | + | 1.33082i | −0.426185 | + | 0.904636i | \(0.640143\pi\) |
−0.904636 | + | 0.426185i | \(0.859857\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | + | 3.00000i | 0.108465 | + | 0.325396i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.92820 | − | 13.8564i | 0.710819 | − | 1.42164i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | + | 7.00000i | −0.710742 | + | 0.710742i | −0.966691 | − | 0.255948i | \(-0.917612\pi\) |
0.255948 | + | 0.966691i | \(0.417612\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.73205 | + | 1.73205i | −0.170664 | + | 0.170664i | −0.787271 | − | 0.616607i | \(-0.788507\pi\) |
0.616607 | + | 0.787271i | \(0.288507\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.66025 | − | 8.66025i | −0.837218 | − | 0.837218i | 0.151274 | − | 0.988492i | \(-0.451663\pi\) |
−0.988492 | + | 0.151274i | \(0.951663\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.0000i | 1.14939i | 0.818367 | + | 0.574696i | \(0.194880\pi\) | ||||
−0.818367 | + | 0.574696i | \(0.805120\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.00000 | − | 9.00000i | −0.846649 | − | 0.846649i | 0.143065 | − | 0.989713i | \(-0.454304\pi\) |
−0.989713 | + | 0.143065i | \(0.954304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.73205 | − | 5.19615i | −0.161515 | − | 0.484544i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.46410 | −0.317554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.1244 | − | 12.1244i | −1.07586 | − | 1.07586i | −0.996876 | − | 0.0789869i | \(-0.974831\pi\) |
−0.0789869 | − | 0.996876i | \(-0.525169\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | \(-0.932981\pi\) |
0.208995 | + | 0.977917i | \(0.432981\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 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 | \(-0.861027\pi\) | ||
0.906196 | − | 0.422857i | \(-0.138973\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.92820 | + | 3.46410i | 0.556487 | + | 0.278243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.0000 | + | 11.0000i | −0.877896 | + | 0.877896i | −0.993317 | − | 0.115421i | \(-0.963178\pi\) |
0.115421 | + | 0.993317i | \(0.463178\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.73205 | + | 1.73205i | −0.135665 | + | 0.135665i | −0.771678 | − | 0.636013i | \(-0.780582\pi\) |
0.636013 | + | 0.771678i | \(0.280582\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.5885 | − | 15.5885i | −1.20627 | − | 1.20627i | −0.972226 | − | 0.234045i | \(-0.924804\pi\) |
−0.234045 | − | 0.972226i | \(-0.575196\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.0000i | − | 0.846154i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.0000 | + | 15.0000i | 1.14043 | + | 1.14043i | 0.988372 | + | 0.152057i | \(0.0485898\pi\) |
0.152057 | + | 0.988372i | \(0.451410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.73205 | − | 12.1244i | 0.130931 | − | 0.916515i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.92820 | −0.517838 | −0.258919 | − | 0.965899i | \(-0.583366\pi\) | ||||
−0.258919 | + | 0.965899i | \(0.583366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | 0.742181 | − | 0.670199i | \(-0.233791\pi\) |
−0.670199 | + | 0.742181i | \(0.733791\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.00000 | − | 3.00000i | 0.213741 | − | 0.213741i | −0.592113 | − | 0.805855i | \(-0.701706\pi\) |
0.805855 | + | 0.592113i | \(0.201706\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8564 | −0.982255 | −0.491127 | − | 0.871088i | \(-0.663415\pi\) | ||||
−0.491127 | + | 0.871088i | \(0.663415\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000i | 1.66011i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3923i | 0.715436i | 0.933830 | + | 0.357718i | \(0.116445\pi\) | ||||
−0.933830 | + | 0.357718i | \(0.883555\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 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 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.00000 | −0.134535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.5885 | + | 15.5885i | −1.04388 | + | 1.04388i | −0.0448883 | + | 0.998992i | \(0.514293\pi\) |
−0.998992 | + | 0.0448883i | \(0.985707\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.66025 | − | 8.66025i | −0.574801 | − | 0.574801i | 0.358665 | − | 0.933466i | \(-0.383232\pi\) |
−0.933466 | + | 0.358665i | \(0.883232\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 20.0000i | − | 1.32164i | −0.750546 | − | 0.660819i | \(-0.770209\pi\) | ||
0.750546 | − | 0.660819i | \(-0.229791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.00000 | − | 1.00000i | −0.0655122 | − | 0.0655122i | 0.673592 | − | 0.739104i | \(-0.264751\pi\) |
−0.739104 | + | 0.673592i | \(0.764751\pi\) | |||||||
\(234\) | 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 | \(-0.146248\pi\) | ||||
0.896296 | + | 0.443455i | \(0.146248\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.0000 | −1.41714 | −0.708572 | − | 0.705638i | \(-0.750660\pi\) | ||||
−0.708572 | + | 0.705638i | \(0.750660\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 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 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | + | 9.00000i | −0.561405 | + | 0.561405i | −0.929706 | − | 0.368302i | \(-0.879939\pi\) |
0.368302 | + | 0.929706i | \(0.379939\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.3205 | 1.07624 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.1244 | + | 12.1244i | −0.747620 | + | 0.747620i | −0.974032 | − | 0.226412i | \(-0.927300\pi\) |
0.226412 | + | 0.974032i | \(0.427300\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.0000 | − | 7.00000i | 1.29002 | − | 0.430007i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 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 | \(0.0335529\pi\) | ||||
−0.994450 | + | 0.105215i | \(0.966447\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.8564 | − | 10.3923i | 0.835573 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0000 | − | 13.0000i | 0.781094 | − | 0.781094i | −0.198921 | − | 0.980015i | \(-0.563744\pi\) |
0.980015 | + | 0.198921i | \(0.0637438\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.0000 | 0.835170 | 0.417585 | − | 0.908638i | \(-0.362877\pi\) | ||||
0.417585 | + | 0.908638i | \(0.362877\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1244 | − | 12.1244i | 0.720718 | − | 0.720718i | −0.248033 | − | 0.968751i | \(-0.579784\pi\) |
0.968751 | + | 0.248033i | \(0.0797843\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.46410 | − | 3.46410i | −0.204479 | − | 0.204479i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.0000i | 0.882353i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.00000 | − | 9.00000i | −0.525786 | − | 0.525786i | 0.393527 | − | 0.919313i | \(-0.371255\pi\) |
−0.919313 | + | 0.393527i | \(0.871255\pi\) | |||||||
\(294\) | 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 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.00000 | − | 12.0000i | 0.343559 | − | 0.687118i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.19615 | − | 5.19615i | −0.296560 | − | 0.296560i | 0.543105 | − | 0.839665i | \(-0.317249\pi\) |
−0.839665 | + | 0.543105i | \(0.817249\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | 0.481037 | − | 0.876700i | \(-0.340260\pi\) |
−0.876700 | + | 0.481037i | \(0.840260\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.0000 | − | 19.0000i | 1.06715 | − | 1.06715i | 0.0695692 | − | 0.997577i | \(-0.477838\pi\) |
0.997577 | − | 0.0695692i | \(-0.0221625\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.8564 | 0.775810 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 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 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.00000i | − | 0.330791i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.2487i | 1.33283i | 0.745581 | + | 0.666415i | \(0.232172\pi\) | ||||
−0.745581 | + | 0.666415i | \(0.767828\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.5885 | + | 5.19615i | −0.851688 | + | 0.283896i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.00000 | − | 1.00000i | 0.0544735 | − | 0.0544735i | −0.679345 | − | 0.733819i | \(-0.737736\pi\) |
0.733819 | + | 0.679345i | \(0.237736\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.0000 | −0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.8564 | − | 13.8564i | 0.748176 | − | 0.748176i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.19615 | + | 5.19615i | 0.278944 | + | 0.278944i | 0.832687 | − | 0.553743i | \(-0.186801\pi\) |
−0.553743 | + | 0.832687i | \(0.686801\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12.0000i | − | 0.642345i | −0.947021 | − | 0.321173i | \(-0.895923\pi\) | ||
0.947021 | − | 0.321173i | \(-0.104077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.00000 | − | 1.00000i | −0.0532246 | − | 0.0532246i | 0.679994 | − | 0.733218i | \(-0.261983\pi\) |
−0.733218 | + | 0.679994i | \(0.761983\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.7846 | + | 10.3923i | 1.10313 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.8564 | 0.731313 | 0.365657 | − | 0.930750i | \(-0.380844\pi\) | ||||
0.365657 | + | 0.930750i | \(0.380844\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.0000 | 1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −21.0000 | + | 7.00000i | −1.09919 | + | 0.366397i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.5885 | + | 15.5885i | 0.813711 | + | 0.813711i | 0.985188 | − | 0.171477i | \(-0.0548540\pi\) |
−0.171477 | + | 0.985188i | \(0.554854\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.2487i | 1.25893i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.00000 | + | 1.00000i | 0.0517780 | + | 0.0517780i | 0.732522 | − | 0.680744i | \(-0.238343\pi\) |
−0.680744 | + | 0.732522i | \(0.738343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.5885 | − | 15.5885i | 0.796533 | − | 0.796533i | −0.186014 | − | 0.982547i | \(-0.559557\pi\) |
0.982547 | + | 0.186014i | \(0.0595570\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | + | 18.0000i | 0.305788 | + | 0.917365i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 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 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0000 | + | 11.0000i | −0.552074 | + | 0.552074i | −0.927039 | − | 0.374965i | \(-0.877655\pi\) |
0.374965 | + | 0.927039i | \(0.377655\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.00000 | −0.0998752 | −0.0499376 | − | 0.998752i | \(-0.515902\pi\) | ||||
−0.0499376 | + | 0.998752i | \(0.515902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.46410 | + | 3.46410i | −0.172559 | + | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 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 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.92820 | −0.338465 | −0.169232 | − | 0.985576i | \(-0.554129\pi\) | ||||
−0.169232 | + | 0.985576i | \(0.554129\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 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 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | 0.518611 | − | 0.855010i | \(-0.326449\pi\) |
−0.855010 | + | 0.518611i | \(0.826449\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.1244 | + | 12.1244i | −0.576046 | + | 0.576046i | −0.933811 | − | 0.357766i | \(-0.883539\pi\) |
0.357766 | + | 0.933811i | \(0.383539\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.0000 | − | 8.00000i | −0.758473 | − | 0.379236i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 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 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.92820 | + | 3.46410i | 0.324799 | + | 0.162400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.0000 | − | 17.0000i | 0.795226 | − | 0.795226i | −0.187112 | − | 0.982339i | \(-0.559913\pi\) |
0.982339 | + | 0.187112i | \(0.0599128\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.73205 | + | 1.73205i | −0.0804952 | + | 0.0804952i | −0.746208 | − | 0.665713i | \(-0.768128\pi\) |
0.665713 | + | 0.746208i | \(0.268128\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19.0526 | + | 19.0526i | 0.881647 | + | 0.881647i | 0.993702 | − | 0.112055i | \(-0.0357432\pi\) |
−0.112055 | + | 0.993702i | \(0.535743\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 18.0000i | − | 0.831163i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 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 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.7128 | −1.26623 | −0.633115 | − | 0.774057i | \(-0.718224\pi\) | ||||
−0.633115 | + | 0.774057i | \(0.718224\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.0000 | 0.455961 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.00000 | + | 21.0000i | 0.317854 | + | 0.953561i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.73205 | + | 1.73205i | 0.0784867 | + | 0.0784867i | 0.745260 | − | 0.666774i | \(-0.232325\pi\) |
−0.666774 | + | 0.745260i | \(0.732325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.73205 | − | 1.73205i | 0.0772283 | − | 0.0772283i | −0.667437 | − | 0.744666i | \(-0.732609\pi\) |
0.744666 | + | 0.667437i | \(0.232609\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | − | 20.0000i | 0.444994 | − | 0.889988i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.0000 | 1.66481 | 0.832405 | − | 0.554168i | \(-0.186963\pi\) | ||||
0.832405 | + | 0.554168i | \(0.186963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.1244 | − | 12.1244i | 0.530161 | − | 0.530161i | −0.390459 | − | 0.920620i | \(-0.627684\pi\) |
0.920620 | + | 0.390459i | \(0.127684\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.46410 | − | 3.46410i | −0.150899 | − | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.0000i | 0.739130i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 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 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.0000 | + | 12.0000i | 1.02805 | + | 0.514024i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.66025 | + | 8.66025i | 0.370286 | + | 0.370286i | 0.867581 | − | 0.497296i | \(-0.165674\pi\) |
−0.497296 | + | 0.867581i | \(0.665674\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 27.7128i | − | 1.18061i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.0000 | + | 29.0000i | −1.22877 | + | 1.22877i | −0.264340 | + | 0.964430i | \(0.585154\pi\) |
−0.964430 | + | 0.264340i | \(0.914846\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.46410 | −0.146516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 29.4449 | − | 29.4449i | 1.24095 | − | 1.24095i | 0.281347 | − | 0.959606i | \(-0.409219\pi\) |
0.959606 | − | 0.281347i | \(-0.0907812\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.0000 | + | 9.00000i | −1.13590 | + | 0.378633i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 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 | \(-0.773780\pi\) | ||
0.757912 | − | 0.652357i | \(-0.226220\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.1244 | − | 1.73205i | −0.505621 | − | 0.0722315i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.00000 | + | 7.00000i | −0.291414 | + | 0.291414i | −0.837639 | − | 0.546225i | \(-0.816064\pi\) |
0.546225 | + | 0.837639i | \(0.316064\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −42.0000 | −1.74245 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.2487 | + | 24.2487i | −1.00428 | + | 1.00428i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.19615 | + | 5.19615i | 0.214468 | + | 0.214468i | 0.806162 | − | 0.591694i | \(-0.201541\pi\) |
−0.591694 | + | 0.806162i | \(0.701541\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0000i | 0.988903i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.0000 | − | 33.0000i | −1.35515 | − | 1.35515i | −0.879796 | − | 0.475352i | \(-0.842321\pi\) |
−0.475352 | − | 0.879796i | \(-0.657679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.46410 | + | 6.92820i | −0.142014 | + | 0.284029i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8564 | −0.566157 | −0.283079 | − | 0.959097i | \(-0.591356\pi\) | ||||
−0.283079 | + | 0.959097i | \(0.591356\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0000 | 0.734235 | 0.367118 | − | 0.930175i | \(-0.380345\pi\) | ||||
0.367118 | + | 0.930175i | \(0.380345\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | + | 2.00000i | −0.0406558 | + | 0.0813116i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.9808 | − | 25.9808i | −1.05453 | − | 1.05453i | −0.998425 | − | 0.0561015i | \(-0.982133\pi\) |
−0.0561015 | − | 0.998425i | \(-0.517867\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.46410i | − | 0.140143i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.0000 | − | 31.0000i | −1.25208 | − | 1.25208i | −0.954787 | − | 0.297291i | \(-0.903917\pi\) |
−0.297291 | − | 0.954787i | \(-0.596083\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.00000 | − | 7.00000i | 0.281809 | − | 0.281809i | −0.552021 | − | 0.833830i | \(-0.686143\pi\) |
0.833830 | + | 0.552021i | \(0.186143\pi\) | |||||||
\(618\) | 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 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.0000i | 0.398726i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.3205i | 0.689519i | 0.938691 | + | 0.344759i | \(0.112039\pi\) | ||||
−0.938691 | + | 0.344759i | \(0.887961\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 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 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.0000 | −1.02694 | −0.513469 | − | 0.858108i | \(-0.671640\pi\) | ||||
−0.513469 | + | 0.858108i | \(0.671640\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.5885 | + | 15.5885i | −0.614749 | + | 0.614749i | −0.944180 | − | 0.329431i | \(-0.893143\pi\) |
0.329431 | + | 0.944180i | \(0.393143\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.73205 | − | 1.73205i | −0.0680939 | − | 0.0680939i | 0.672240 | − | 0.740334i | \(-0.265332\pi\) |
−0.740334 | + | 0.672240i | \(0.765332\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000i | 0.942082i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.0000 | + | 23.0000i | 0.900060 | + | 0.900060i | 0.995441 | − | 0.0953813i | \(-0.0304070\pi\) |
−0.0953813 | + | 0.995441i | \(0.530407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.7846 | − | 10.3923i | −0.812122 | − | 0.406061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.6410 | −1.34942 | −0.674711 | − | 0.738082i | \(-0.735732\pi\) | ||||
−0.674711 | + | 0.738082i | \(0.735732\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0000 | −0.700119 | −0.350059 | − | 0.936727i | \(-0.613839\pi\) | ||||
−0.350059 | + | 0.936727i | \(0.613839\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 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 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.7846i | 0.802381i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.0000 | + | 25.0000i | 0.963679 | + | 0.963679i | 0.999363 | − | 0.0356839i | \(-0.0113610\pi\) |
−0.0356839 | + | 0.999363i | \(0.511361\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.0000 | − | 35.0000i | 1.34516 | − | 1.34516i | 0.454321 | − | 0.890838i | \(-0.349882\pi\) |
0.890838 | − | 0.454321i | \(-0.150118\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.2487 | −0.930580 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.73205 | − | 1.73205i | 0.0662751 | − | 0.0662751i | −0.673192 | − | 0.739467i | \(-0.735077\pi\) |
0.739467 | + | 0.673192i | \(0.235077\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.00000 | + | 27.0000i | 0.343872 | + | 1.03162i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.0000i | 0.533358i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 45.0333i | − | 1.71315i | −0.516024 | − | 0.856574i | \(-0.672588\pi\) | ||
0.516024 | − | 0.856574i | \(-0.327412\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.0000 | −1.43524 | −0.717620 | − | 0.696435i | \(-0.754769\pi\) | ||||
−0.717620 | + | 0.696435i | \(0.754769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.6410 | − | 34.6410i | 1.30651 | − | 1.30651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.3205 | + | 17.3205i | 0.651405 | + | 0.651405i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 4.00000i | − | 0.150223i | −0.997175 | − | 0.0751116i | \(-0.976069\pi\) | ||
0.997175 | − | 0.0751116i | \(-0.0239313\pi\) | |||||||
\(710\) | 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 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.7128 | −1.03351 | −0.516757 | − | 0.856132i | \(-0.672861\pi\) | ||||
−0.516757 | + | 0.856132i | \(0.672861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.00000 | −0.223452 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16.0000 | + | 12.0000i | −0.594225 | + | 0.445669i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.73205 | + | 1.73205i | 0.0642382 | + | 0.0642382i | 0.738496 | − | 0.674258i | \(-0.235536\pi\) |
−0.674258 | + | 0.738496i | \(0.735536\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3.46410i | − | 0.128124i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.00000 | + | 1.00000i | 0.0369358 | + | 0.0369358i | 0.725333 | − | 0.688398i | \(-0.241686\pi\) |
−0.688398 | + | 0.725333i | \(0.741686\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.1244 | + | 12.1244i | −0.444799 | + | 0.444799i | −0.893621 | − | 0.448822i | \(-0.851844\pi\) |
0.448822 | + | 0.893621i | \(0.351844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.00000 | − | 4.00000i | −0.293097 | − | 0.146549i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 30.0000i | − | 1.09618i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.46410i | 0.126407i | 0.998001 | + | 0.0632034i | \(0.0201317\pi\) | ||||
−0.998001 | + | 0.0632034i | \(0.979868\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.7846 | − | 10.3923i | −0.756429 | − | 0.378215i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.0000 | − | 29.0000i | 1.05402 | − | 1.05402i | 0.0555680 | − | 0.998455i | \(-0.482303\pi\) |
0.998455 | − | 0.0555680i | \(-0.0176970\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.0000 | −0.362500 | −0.181250 | − | 0.983437i | \(-0.558014\pi\) | ||||
−0.181250 | + | 0.983437i | \(0.558014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.7846 | + | 20.7846i | −0.752453 | + | 0.752453i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.92820 | + | 6.92820i | 0.250163 | + | 0.250163i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.0000i | 1.73092i | 0.500974 | + | 0.865462i | \(0.332975\pi\) | ||||
−0.500974 | + | 0.865462i | \(0.667025\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.00000 | − | 1.00000i | −0.0359675 | − | 0.0359675i | 0.688894 | − | 0.724862i | \(-0.258096\pi\) |
−0.724862 | + | 0.688894i | \(0.758096\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.8564 | − | 10.3923i | 0.497737 | − | 0.373303i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | 0.608404 | − | 0.793627i | \(-0.291810\pi\) |
−0.793627 | + | 0.608404i | \(0.791810\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 31.1769i | − | 1.10852i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.00000 | + | 6.00000i | 0.213066 | + | 0.213066i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.00000 | − | 3.00000i | 0.106265 | − | 0.106265i | −0.651975 | − | 0.758240i | \(-0.726059\pi\) |
0.758240 | + | 0.651975i | \(0.226059\pi\) | |||||||