Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), 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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.3 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.e.2591.5 |
$q$-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 \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.82843i | − 1.26491i | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||||
0.774597 | − | 0.632456i | \(-0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.635674 | −0.191663 | −0.0958315 | − | 0.995398i | \(-0.530551\pi\) | ||||
−0.0958315 | + | 0.995398i | \(0.530551\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.550510 | 0.152684 | 0.0763420 | − | 0.997082i | \(-0.475676\pi\) | ||||
0.0763420 | + | 0.997082i | \(0.475676\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.14626i | 0.763081i | 0.924352 | + | 0.381541i | \(0.124606\pi\) | ||||
−0.924352 | + | 0.381541i | \(0.875394\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.00000i | − 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.14626 | −0.656041 | −0.328021 | − | 0.944671i | \(-0.606382\pi\) | ||||
−0.328021 | + | 0.944671i | \(0.606382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 5.19615i | − 0.964901i | −0.875923 | − | 0.482451i | \(-0.839747\pi\) | ||||
0.875923 | − | 0.482451i | \(-0.160253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.7980i | 1.93937i | 0.244357 | + | 0.969685i | \(0.421423\pi\) | ||||
−0.244357 | + | 0.969685i | \(0.578577\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.82843 | 0.478091 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.89898 | −1.46298 | −0.731492 | − | 0.681850i | \(-0.761175\pi\) | ||||
−0.731492 | + | 0.681850i | \(0.761175\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 3.46410i | − 0.541002i | −0.962720 | − | 0.270501i | \(-0.912811\pi\) | ||||
0.962720 | − | 0.270501i | \(-0.0871893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.550510i | 0.0839520i | 0.999119 | + | 0.0419760i | \(0.0133653\pi\) | ||||
−0.999119 | + | 0.0419760i | \(0.986635\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.27135 | −0.185445 | −0.0927227 | − | 0.995692i | \(-0.529557\pi\) | ||||
−0.0927227 | + | 0.995692i | \(0.529557\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 2.36773i | − 0.325232i | −0.986689 | − | 0.162616i | \(-0.948007\pi\) | ||||
0.986689 | − | 0.162616i | \(-0.0519932\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.79796i | 0.242437i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.4887 | −1.49570 | −0.747849 | − | 0.663868i | \(-0.768914\pi\) | ||||
−0.747849 | + | 0.663868i | \(0.768914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.10102 | 0.397045 | 0.198522 | − | 0.980096i | \(-0.436386\pi\) | ||||
0.198522 | + | 0.980096i | \(0.436386\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 1.55708i | − 0.193132i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.44949i | 0.177083i | 0.996072 | + | 0.0885417i | \(0.0282206\pi\) | ||||
−0.996072 | + | 0.0885417i | \(0.971779\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.97469 | −0.709065 | −0.354533 | − | 0.935044i | \(-0.615360\pi\) | ||||
−0.354533 | + | 0.935044i | \(0.615360\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 0.635674i | − 0.0724418i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0000i | 1.12509i | 0.826767 | + | 0.562544i | \(0.190177\pi\) | ||||
−0.826767 | + | 0.562544i | \(0.809823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.46410 | 0.380235 | 0.190117 | − | 0.981761i | \(-0.439113\pi\) | ||||
0.190117 | + | 0.981761i | \(0.439113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.89898 | 0.965230 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 13.5386i | − 1.43509i | −0.696514 | − | 0.717543i | \(-0.745267\pi\) | ||||
0.696514 | − | 0.717543i | \(-0.254733\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.550510i | 0.0577092i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.3137 | −1.16076 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.79796 | 0.385624 | 0.192812 | − | 0.981236i | \(-0.438239\pi\) | ||||
0.192812 | + | 0.981236i | \(0.438239\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.65685i | 0.562878i | 0.959579 | + | 0.281439i | \(0.0908117\pi\) | ||||
−0.959579 | + | 0.281439i | \(0.909188\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.89898i | 0.581244i | 0.956838 | + | 0.290622i | \(0.0938622\pi\) | ||||
−0.956838 | + | 0.290622i | \(0.906138\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.38551 | −0.423963 | −0.211981 | − | 0.977274i | \(-0.567992\pi\) | ||||
−0.211981 | + | 0.977274i | \(0.567992\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.00000 | −0.766261 | −0.383131 | − | 0.923694i | \(-0.625154\pi\) | ||||
−0.383131 | + | 0.923694i | \(0.625154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.48528i | 0.798228i | 0.916901 | + | 0.399114i | \(0.130682\pi\) | ||||
−0.916901 | + | 0.399114i | \(0.869318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.89898i | 0.829834i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.14626 | −0.288418 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5959 | −0.963265 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 5.65685i | − 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1.10102i | − 0.0976998i | −0.998806 | − | 0.0488499i | \(-0.984444\pi\) | ||||
0.998806 | − | 0.0488499i | \(-0.0155556\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.02458 | 0.701111 | 0.350555 | − | 0.936542i | \(-0.385993\pi\) | ||||
0.350555 | + | 0.936542i | \(0.385993\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 8.19955i | − 0.700535i | −0.936650 | − | 0.350268i | \(-0.886091\pi\) | ||||
0.936650 | − | 0.350268i | \(-0.113909\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 3.79796i | − 0.322139i | −0.986943 | − | 0.161069i | \(-0.948506\pi\) | ||||
0.986943 | − | 0.161069i | \(-0.0514943\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.349945 | −0.0292639 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −14.6969 | −1.22051 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.36773i | 0.193972i | 0.995286 | + | 0.0969858i | \(0.0309201\pi\) | ||||
−0.995286 | + | 0.0969858i | \(0.969080\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.7980i | 1.12286i | 0.827524 | + | 0.561431i | \(0.189749\pi\) | ||||
−0.827524 | + | 0.561431i | \(0.810251\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 30.5412 | 2.45313 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.1464 | −1.44824 | −0.724121 | − | 0.689673i | \(-0.757754\pi\) | ||||
−0.724121 | + | 0.689673i | \(0.757754\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 3.14626i | − 0.247960i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 7.44949i | − 0.583489i | −0.956496 | − | 0.291745i | \(-0.905764\pi\) | ||||
0.956496 | − | 0.291745i | \(-0.0942357\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.73545 | 0.366440 | 0.183220 | − | 0.983072i | \(-0.441348\pi\) | ||||
0.183220 | + | 0.983072i | \(0.441348\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6969 | −0.976688 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.7060i | 1.65028i | 0.564930 | + | 0.825139i | \(0.308903\pi\) | ||||
−0.564930 | + | 0.825139i | \(0.691097\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.00000i | − 0.226779i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.6848 | 1.24708 | 0.623542 | − | 0.781790i | \(-0.285693\pi\) | ||||
0.623542 | + | 0.781790i | \(0.285693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.3485 | −1.80981 | −0.904904 | − | 0.425616i | \(-0.860057\pi\) | ||||
−0.904904 | + | 0.425616i | \(0.860057\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.1701i | 1.85054i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.00000i | − 0.146254i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.6848 | −1.20727 | −0.603636 | − | 0.797260i | \(-0.706282\pi\) | ||||
−0.603636 | + | 0.797260i | \(0.706282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.89898 | 0.424618 | 0.212309 | − | 0.977203i | \(-0.431902\pi\) | ||||
0.212309 | + | 0.977203i | \(0.431902\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 16.9706i | − 1.20910i | −0.796566 | − | 0.604551i | \(-0.793352\pi\) | ||||
0.796566 | − | 0.604551i | \(-0.206648\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 1.20204i | − 0.0852104i | −0.999092 | − | 0.0426052i | \(-0.986434\pi\) | ||||
0.999092 | − | 0.0426052i | \(-0.0135658\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.19615 | 0.364698 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.79796 | −0.684319 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.54270i | 0.175882i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.1464i | 1.38694i | 0.720487 | + | 0.693469i | \(0.243918\pi\) | ||||
−0.720487 | + | 0.693469i | \(0.756082\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.55708 | 0.106192 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.7980 | −0.733013 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.73205i | 0.116510i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.79796i | 0.656120i | 0.944657 | + | 0.328060i | \(0.106395\pi\) | ||||
−0.944657 | + | 0.328060i | \(0.893605\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.8530 | −0.720339 | −0.360170 | − | 0.932887i | \(-0.617281\pi\) | ||||
−0.360170 | + | 0.932887i | \(0.617281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.8990 | −0.852389 | −0.426194 | − | 0.904632i | \(-0.640146\pi\) | ||||
−0.426194 | + | 0.904632i | \(0.640146\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.4203i | 1.40329i | 0.712527 | + | 0.701645i | \(0.247551\pi\) | ||||
−0.712527 | + | 0.701645i | \(0.752449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.59592i | 0.234572i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.82843 | −0.182956 | −0.0914779 | − | 0.995807i | \(-0.529159\pi\) | ||||
−0.0914779 | + | 0.995807i | \(0.529159\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.0000 | 0.901819 | 0.450910 | − | 0.892570i | \(-0.351100\pi\) | ||||
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.82843i | 0.180702i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2.20204i | − 0.140113i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0492 | 1.01301 | 0.506507 | − | 0.862236i | \(-0.330936\pi\) | ||||
0.506507 | + | 0.862236i | \(0.330936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.1633i | 1.19537i | 0.801729 | + | 0.597687i | \(0.203914\pi\) | ||||
−0.801729 | + | 0.597687i | \(0.796086\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 8.89898i | − 0.552956i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.1168 | 1.24046 | 0.620228 | − | 0.784421i | \(-0.287040\pi\) | ||||
0.620228 | + | 0.784421i | \(0.287040\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.69694 | −0.411390 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.1489i | 1.22850i | 0.789111 | + | 0.614251i | \(0.210542\pi\) | ||||
−0.789111 | + | 0.614251i | \(0.789458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.1010i | 1.22105i | 0.791997 | + | 0.610525i | \(0.209042\pi\) | ||||
−0.791997 | + | 0.610525i | \(0.790958\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.90702 | 0.114998 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.1010 | 1.26784 | 0.633919 | − | 0.773400i | \(-0.281445\pi\) | ||||
0.633919 | + | 0.773400i | \(0.281445\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 27.3629i | − 1.63233i | −0.577818 | − | 0.816166i | \(-0.696096\pi\) | ||||
0.577818 | − | 0.816166i | \(-0.303904\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7980i | 0.820204i | 0.912040 | + | 0.410102i | \(0.134507\pi\) | ||||
−0.912040 | + | 0.410102i | \(0.865493\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.46410 | 0.204479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.10102 | 0.417707 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 7.56388i | − 0.441886i | −0.975287 | − | 0.220943i | \(-0.929086\pi\) | ||||
0.975287 | − | 0.220943i | \(-0.0709136\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 32.4949i | 1.89193i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.73205 | −0.100167 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.550510 | −0.0317309 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 8.77101i | − 0.502227i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.69694i | 0.153922i | 0.997034 | + | 0.0769612i | \(0.0245218\pi\) | ||||
−0.997034 | + | 0.0769612i | \(0.975478\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.0771 | −1.53540 | −0.767702 | − | 0.640807i | \(-0.778600\pi\) | ||||
−0.767702 | + | 0.640807i | \(0.778600\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.5959 | −1.33372 | −0.666860 | − | 0.745183i | \(-0.732362\pi\) | ||||
−0.666860 | + | 0.745183i | \(0.732362\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.27135i | 0.0714061i | 0.999362 | + | 0.0357030i | \(0.0113670\pi\) | ||||
−0.999362 | + | 0.0357030i | \(0.988633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.30306i | 0.184936i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.5851 | 0.700251 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.65153 | −0.0916104 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 1.27135i | − 0.0700917i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.3485i | 1.11845i | 0.829015 | + | 0.559227i | \(0.188902\pi\) | ||||
−0.829015 | + | 0.559227i | \(0.811098\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.09978 | 0.223995 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.1010 | −0.550238 | −0.275119 | − | 0.961410i | \(-0.588717\pi\) | ||||
−0.275119 | + | 0.961410i | \(0.588717\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 6.86399i | − 0.371706i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.4921 | 0.777976 | 0.388988 | − | 0.921243i | \(-0.372825\pi\) | ||||
0.388988 | + | 0.921243i | \(0.372825\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.8434 | −1.86512 | −0.932561 | − | 0.361012i | \(-0.882431\pi\) | ||||
−0.932561 | + | 0.361012i | \(0.882431\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 15.3814i | − 0.818668i | −0.912385 | − | 0.409334i | \(-0.865761\pi\) | ||||
0.912385 | − | 0.409334i | \(-0.134239\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.8990i | 0.896905i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.78194 | −0.199603 | −0.0998015 | − | 0.995007i | \(-0.531821\pi\) | ||||
−0.0998015 | + | 0.995007i | \(0.531821\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.3137i | 0.592187i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 15.2020i | − 0.793540i | −0.917918 | − | 0.396770i | \(-0.870131\pi\) | ||||
0.917918 | − | 0.396770i | \(-0.129869\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.36773 | 0.122926 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 36.2929 | 1.87917 | 0.939586 | − | 0.342312i | \(-0.111210\pi\) | ||||
0.939586 | + | 0.342312i | \(0.111210\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2.86054i | − 0.147325i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000i | 0.513665i | 0.966456 | + | 0.256833i | \(0.0826790\pi\) | ||||
−0.966456 | + | 0.256833i | \(0.917321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −38.6766 | −1.97628 | −0.988140 | − | 0.153553i | \(-0.950928\pi\) | ||||
−0.988140 | + | 0.153553i | \(0.950928\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.79796 | −0.0916325 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.77101i | 0.444708i | 0.974966 | + | 0.222354i | \(0.0713741\pi\) | ||||
−0.974966 | + | 0.222354i | \(0.928626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 9.89898i | − 0.500613i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.2843 | 1.42314 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.8990 | −1.24964 | −0.624822 | − | 0.780767i | \(-0.714828\pi\) | ||||
−0.624822 | + | 0.780767i | \(0.714828\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.9774i | 1.14743i | 0.819053 | + | 0.573717i | \(0.194499\pi\) | ||||
−0.819053 | + | 0.573717i | \(0.805501\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.94439i | 0.296111i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.65685 | 0.280400 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.696938 | 0.0344614 | 0.0172307 | − | 0.999852i | \(-0.494515\pi\) | ||||
0.0172307 | + | 0.999852i | \(0.494515\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 11.4887i | − 0.565321i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 9.79796i | − 0.480963i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.2597 | −0.989751 | −0.494875 | − | 0.868964i | \(-0.664786\pi\) | ||||
−0.494875 | + | 0.868964i | \(0.664786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.59592 | 0.370202 | 0.185101 | − | 0.982719i | \(-0.440739\pi\) | ||||
0.185101 | + | 0.982719i | \(0.440739\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 9.43879i | − 0.457849i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.10102i | 0.150069i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.8708 | 0.619964 | 0.309982 | − | 0.950742i | \(-0.399677\pi\) | ||||
0.309982 | + | 0.950742i | \(0.399677\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.5959 | 0.941720 | 0.470860 | − | 0.882208i | \(-0.343944\pi\) | ||||
0.470860 | + | 0.882208i | \(0.343944\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12.5851i | 0.602025i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 37.4949i | − 1.78953i | −0.446534 | − | 0.894767i | \(-0.647342\pi\) | ||||
0.446534 | − | 0.894767i | \(-0.352658\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.9985 | 1.33025 | 0.665125 | − | 0.746732i | \(-0.268378\pi\) | ||||
0.665125 | + | 0.746732i | \(0.268378\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −38.2929 | −1.81526 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 12.2993i | − 0.580441i | −0.956960 | − | 0.290221i | \(-0.906271\pi\) | ||||
0.956960 | − | 0.290221i | \(-0.0937287\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.20204i | 0.103690i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.55708 | 0.0729969 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.6969 | −1.85694 | −0.928472 | − | 0.371402i | \(-0.878877\pi\) | ||||
−0.928472 | + | 0.371402i | \(0.878877\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 6.92820i | − 0.322679i | −0.986899 | − | 0.161339i | \(-0.948419\pi\) | ||||
0.986899 | − | 0.161339i | \(-0.0515813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.59592i | 0.353012i | 0.984300 | + | 0.176506i | \(0.0564795\pi\) | ||||
−0.984300 | + | 0.176506i | \(0.943520\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.7778 | 0.683835 | 0.341918 | − | 0.939730i | \(-0.388924\pi\) | ||||
0.341918 | + | 0.939730i | \(0.388924\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.44949 | −0.0669312 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 0.349945i | − 0.0160905i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000i | 0.550598i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.6554 | −1.53775 | −0.768877 | − | 0.639397i | \(-0.779184\pi\) | ||||
−0.768877 | + | 0.639397i | \(0.779184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.89898 | −0.223374 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 10.7423i | − 0.487780i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000i | 0.362515i | 0.983436 | + | 0.181257i | \(0.0580167\pi\) | ||||
−0.983436 | + | 0.181257i | \(0.941983\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.74983 | −0.169227 | −0.0846137 | − | 0.996414i | \(-0.526966\pi\) | ||||
−0.0846137 | + | 0.996414i | \(0.526966\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.3485 | 0.736298 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 5.97469i | − 0.268002i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 16.2020i | − 0.725303i | −0.931925 | − | 0.362651i | \(-0.881872\pi\) | ||||
0.931925 | − | 0.362651i | \(-0.118128\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.3417 | −0.996167 | −0.498083 | − | 0.867129i | \(-0.665963\pi\) | ||||
−0.498083 | + | 0.867129i | \(0.665963\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0000 | 0.711991 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.9985i | 1.24101i | 0.784201 | + | 0.620507i | \(0.213073\pi\) | ||||
−0.784201 | + | 0.620507i | \(0.786927\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 4.00000i | − 0.176950i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.6848 | 0.735222 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.808164 | 0.0355430 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 8.16744i | − 0.357822i | −0.983865 | − | 0.178911i | \(-0.942743\pi\) | ||||
0.983865 | − | 0.178911i | \(-0.0572575\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 0.202041i | − 0.00883464i | −0.999990 | − | 0.00441732i | \(-0.998594\pi\) | ||||
0.999990 | − | 0.00441732i | \(-0.00140608\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −33.9732 | −1.47990 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.1010 | −0.569610 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.90702i | − 0.0826024i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.4041i | 0.536275i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.635674 | 0.0273804 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.49490 | −0.365224 | −0.182612 | − | 0.983185i | \(-0.558455\pi\) | ||||
−0.182612 | + | 0.983185i | \(0.558455\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.6274i | 0.969252i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.3939i | 1.85539i | 0.373341 | + | 0.927694i | \(0.378212\pi\) | ||||
−0.373341 | + | 0.927694i | \(0.621788\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −20.7846 | −0.885454 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0000 | −0.425243 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 38.8515i | − 1.64619i | −0.567902 | − | 0.823096i | \(-0.692245\pi\) | ||||
0.567902 | − | 0.823096i | \(-0.307755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.303062i | 0.0128181i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −14.6028 | −0.615436 | −0.307718 | − | 0.951478i | \(-0.599565\pi\) | ||||
−0.307718 | + | 0.951478i | \(0.599565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.0000 | 1.00969 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 9.12096i | − 0.382370i | −0.981554 | − | 0.191185i | \(-0.938767\pi\) | ||||
0.981554 | − | 0.191185i | \(-0.0612331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.2474i | 0.554388i | 0.960814 | + | 0.277194i | \(0.0894046\pi\) | ||||
−0.960814 | + | 0.277194i | \(0.910595\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.43879 | 0.393625 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.6969 | 1.44445 | 0.722226 | − | 0.691657i | \(-0.243119\pi\) | ||||
0.722226 | + | 0.691657i | \(0.243119\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.46410i | 0.143715i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.50510i | 0.0623350i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.7026 | 0.771939 | 0.385970 | − | 0.922511i | \(-0.373867\pi\) | ||||
0.385970 | + | 0.922511i | \(0.373867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 43.1918 | 1.77969 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.1633i | 0.786943i | 0.919337 | + | 0.393472i | \(0.128726\pi\) | ||||
−0.919337 | + | 0.393472i | \(0.871274\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.89898i | 0.364823i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.4026 | −0.833626 | −0.416813 | − | 0.908992i | \(-0.636853\pi\) | ||||
−0.416813 | + | 0.908992i | \(0.636853\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.10102 | −0.289657 | −0.144828 | − | 0.989457i | \(-0.546263\pi\) | ||||
−0.144828 | + | 0.989457i | \(0.546263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 29.9698i | 1.21844i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 19.0000i | − 0.771186i | −0.922669 | − | 0.385593i | \(-0.873997\pi\) | ||||
0.922669 | − | 0.385593i | \(-0.126003\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.699891 | −0.0283145 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.0000 | −0.807792 | −0.403896 | − | 0.914805i | \(-0.632344\pi\) | ||||
−0.403896 | + | 0.914805i | \(0.632344\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 12.2993i | − 0.495152i | −0.968868 | − | 0.247576i | \(-0.920366\pi\) | ||||
0.968868 | − | 0.247576i | \(-0.0796340\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.59592i | 0.385693i | 0.981229 | + | 0.192846i | \(0.0617719\pi\) | ||||
−0.981229 | + | 0.192846i | \(0.938228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.5386 | 0.542411 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 27.9985i | − 1.11637i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.4949i | 0.497414i | 0.968579 | + | 0.248707i | \(0.0800056\pi\) | ||||
−0.968579 | + | 0.248707i | \(0.919994\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.11416 | −0.123582 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.550510 | −0.0218120 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 14.4921i | − 0.572403i | −0.958169 | − | 0.286201i | \(-0.907607\pi\) | ||||
0.958169 | − | 0.286201i | \(-0.0923926\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 0.494897i | − 0.0195168i | −0.999952 | − | 0.00975842i | \(-0.996894\pi\) | ||||
0.999952 | − | 0.00975842i | \(-0.00310625\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.6554 | −1.32313 | −0.661565 | − | 0.749888i | \(-0.730107\pi\) | ||||
−0.661565 | + | 0.749888i | \(0.730107\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.30306 | 0.286670 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 19.6882i | − 0.770460i | −0.922821 | − | 0.385230i | \(-0.874122\pi\) | ||||
0.922821 | − | 0.385230i | \(-0.125878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 22.6969i | − 0.886843i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7846 | −0.809653 | −0.404827 | − | 0.914393i | \(-0.632668\pi\) | ||||
−0.404827 | + | 0.914393i | \(0.632668\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.10102 | 0.120616 | 0.0603079 | − | 0.998180i | \(-0.480792\pi\) | ||||
0.0603079 | + | 0.998180i | \(0.480792\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 11.3137i | − 0.438727i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.3485i | 0.633015i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.97124 | −0.0760989 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.5959 | 0.408443 | 0.204221 | − | 0.978925i | \(-0.434534\pi\) | ||||
0.204221 | + | 0.978925i | \(0.434534\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 34.0053i | − 1.30693i | −0.756956 | − | 0.653466i | \(-0.773314\pi\) | ||||
0.756956 | − | 0.653466i | \(-0.226686\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.79796i | 0.145752i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.1845 | −0.925394 | −0.462697 | − | 0.886516i | \(-0.653118\pi\) | ||||
−0.462697 | + | 0.886516i | \(0.653118\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.1918 | −0.886115 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1.30346i | − 0.0496578i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 47.7980i | − 1.81832i | −0.416447 | − | 0.909160i | \(-0.636725\pi\) | ||||
0.416447 | − | 0.909160i | \(-0.363275\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.7423 | −0.407477 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.8990 | 0.412828 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 5.65685i | − 0.213656i | −0.994277 | − | 0.106828i | \(-0.965931\pi\) | ||||
0.994277 | − | 0.106828i | \(-0.0340695\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.5959i | 1.34253i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.65685 | −0.212748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.40408 | −0.0902872 | −0.0451436 | − | 0.998981i | \(-0.514375\pi\) | ||||
−0.0451436 | + | 0.998981i | \(0.514375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 33.9732i | − 1.27231i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.989795i | 0.0370162i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.2631 | 0.867567 | 0.433783 | − | 0.901017i | \(-0.357178\pi\) | ||||
0.433783 | + | 0.901017i | \(0.357178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.89898 | −0.219689 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.5885i | 0.578941i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 39.4949i | − 1.46478i | −0.680883 | − | 0.732392i | \(-0.738404\pi\) | ||||
0.680883 | − | 0.732392i | \(-0.261596\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.73205 | −0.0640622 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.3485 | −0.529973 | −0.264986 | − | 0.964252i | \(-0.585367\pi\) | ||||
−0.264986 | + | 0.964252i | \(0.585367\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 0.921404i | − 0.0339403i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.2020i | 0.890286i | 0.895459 | + | 0.445143i | \(0.146847\pi\) | ||||
−0.895459 | + | 0.445143i | \(0.853153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.08885 | 0.333437 | 0.166719 | − | 0.986004i | \(-0.446683\pi\) | ||||
0.166719 | + | 0.986004i | \(0.446683\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.69694 | 0.245357 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 4.38551i | − 0.160243i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 35.1010i | − 1.28085i | −0.768019 | − | 0.640427i | \(-0.778757\pi\) | ||||
0.768019 | − | 0.640427i | \(-0.221243\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.0265 | 1.42032 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.1918 | 1.64253 | 0.821263 | − | 0.570550i | \(-0.193270\pi\) | ||||
0.821263 | + | 0.570550i | \(0.193270\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 16.9385i | − 0.614019i | −0.951707 | − | 0.307009i | \(-0.900672\pi\) | ||||
0.951707 | − | 0.307009i | \(-0.0993283\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 8.00000i | − 0.289619i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.32464 | −0.228369 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.89898 | 0.176662 | 0.0883309 | − | 0.996091i | \(-0.471847\pi\) | ||||
0.0883309 | + | 0.996091i | \(0.471847\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 3.17837i | − 0.114318i | −0.998365 | − | 0.0571591i | \(-0.981796\pi\) | ||||
0.998365 | − | 0.0571591i | \(-0.0182042\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 32.3939i | − 1.16362i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.8564 | −0.496457 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.79796 | 0.135902 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 51.3258i | 1.83190i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 17.5959i | − 0.627227i | −0.949551 | − | 0.313613i | \(-0.898460\pi\) | ||||
0.949551 | − | 0.313613i | \(-0.101540\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.48528 | −0.301702 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.70714 | 0.0606224 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.4558i | 0.901692i | 0.892602 | + | 0.450846i | \(0.148878\pi\) | ||||
−0.892602 | + | 0.450846i | \(0.851122\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 4.00000i | − 0.141510i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.54270 | 0.0897299 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.89898 | −0.313648 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 34.5768i | − 1.21566i | −0.794069 | − | 0.607828i | \(-0.792041\pi\) | ||||
0.794069 | − | 0.607828i | \(-0.207959\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 24.4949i | − 0.860132i | −0.902797 | − | 0.430066i | \(-0.858490\pi\) | ||||
0.902797 | − | 0.430066i | \(-0.141510\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.0703 | −0.738062 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.20204 | 0.0770397 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 42.6656i | − 1.48904i | −0.667600 | − | 0.744520i | \(-0.732679\pi\) | ||||
0.667600 | − | 0.744520i | \(-0.267321\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.8990i | 1.07707i | 0.842603 | + | 0.538535i | \(0.181022\pi\) | ||||
−0.842603 | + | 0.538535i | \(0.818978\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.81405 | 0.132627 | 0.0663137 | − | 0.997799i | \(-0.478876\pi\) | ||||
0.0663137 | + | 0.997799i | \(0.478876\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.3031 | −0.600960 | −0.300480 | − | 0.953788i | \(-0.597147\pi\) | ||||
−0.300480 | + | 0.953788i | \(0.597147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 3.14626i | − 0.109012i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 13.3939i | − 0.463514i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.46410 | −0.119594 | −0.0597970 | − | 0.998211i | \(-0.519045\pi\) | ||||
−0.0597970 | + | 0.998211i | \(0.519045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | 0.0689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 35.9124i | 1.23542i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 10.5959i | − 0.364080i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.9985 | 0.959778 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.3485 | −1.58694 | −0.793471 | − | 0.608608i | \(-0.791728\pi\) | ||||
−0.793471 | + | 0.608608i | \(0.791728\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 13.5386i | − 0.462469i | −0.972898 | − | 0.231234i | \(-0.925724\pi\) | ||||
0.972898 | − | 0.231234i | \(-0.0742764\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 26.2929i | − 0.897101i | −0.893758 | − | 0.448550i | \(-0.851940\pi\) | ||||
0.893758 | − | 0.448550i | \(-0.148060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34.2590 | 1.16619 | 0.583094 | − | 0.812404i | \(-0.301842\pi\) | ||||
0.583094 | + | 0.812404i | \(0.301842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 61.3939 | 2.08745 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 6.35674i | − 0.215638i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.797959i | 0.0270378i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.65685 | 0.191237 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.8990 | 1.31353 | 0.656763 | − | 0.754097i | \(-0.271925\pi\) | ||||
0.656763 | + | 0.754097i | \(0.271925\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.4244i | 0.351207i | 0.984461 | + | 0.175604i | \(0.0561877\pi\) | ||||
−0.984461 | + | 0.175604i | \(0.943812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.3485i | 0.550170i | 0.961420 | + | 0.275085i | \(0.0887060\pi\) | ||||
−0.961420 | + | 0.275085i | \(0.911294\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −39.0265 | −1.31038 | −0.655191 | − | 0.755463i | \(-0.727412\pi\) | ||||
−0.655191 | + | 0.755463i | \(0.727412\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.10102 | 0.0369270 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.08540i | 0.170176i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 47.1918i | − 1.57745i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 56.1078 | 1.87130 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.44949 | 0.248178 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 68.8679i | 2.28925i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 37.1918i | − 1.23493i | −0.786597 | − | 0.617467i | \(-0.788159\pi\) | ||||
0.786597 | − | 0.617467i | \(-0.211841\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.1981 | −1.19930 | −0.599648 | − | 0.800264i | \(-0.704693\pi\) | ||||
−0.599648 | + | 0.800264i | \(0.704693\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.20204 | −0.0728769 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.02458i | 0.264995i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 17.5959i | − 0.580436i | −0.956961 | − | 0.290218i | \(-0.906272\pi\) | ||||
0.956961 | − | 0.290218i | \(-0.0937278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.28913 | −0.108263 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.6969 | 0.877790 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 22.2775i | − 0.730900i | −0.930831 | − | 0.365450i | \(-0.880915\pi\) | ||||
0.930831 | − | 0.365450i | \(-0.119085\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000i | 0.131095i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.65685 | −0.184999 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.6969 | 1.52552 | 0.762761 | − | 0.646680i | \(-0.223843\pi\) | ||||
0.762761 | + | 0.646680i | \(0.223843\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0771i | 0.882689i | 0.897338 | + | 0.441345i | \(0.145498\pi\) | ||||
−0.897338 | + | 0.441345i | \(0.854502\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.8990i | 0.354920i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.2419 | 0.592782 | 0.296391 | − | 0.955067i | \(-0.404217\pi\) | ||||
0.296391 | + | 0.955067i | \(0.404217\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.20204 | −0.0714813 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 20.4347i | − 0.661944i | −0.943641 | − | 0.330972i | \(-0.892623\pi\) | ||||
0.943641 | − | 0.330972i | \(-0.107377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 47.1918i | 1.52709i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.19955 | 0.264777 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −85.5959 | −2.76116 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 16.6848i | − 0.537104i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.8990i | 0.929329i | 0.885487 | + | 0.464664i | \(0.153825\pi\) | ||||
−0.885487 | + | 0.464664i | \(0.846175\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.92480 | −0.125953 | −0.0629765 | − | 0.998015i | \(-0.520059\pi\) | ||||
−0.0629765 | + | 0.998015i | \(0.520059\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.79796 | 0.121757 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.4415i | 0.845937i | 0.906144 | + | 0.422969i | \(0.139012\pi\) | ||||
−0.906144 | + | 0.422969i | \(0.860988\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.60612i | 0.275053i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.75663 | 0.311188 | 0.155594 | − | 0.987821i | \(-0.450271\pi\) | ||||
0.155594 | + | 0.987821i | \(0.450271\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.0000 | −1.52941 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.73205i | − 0.0550760i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.49490i | 0.0792530i | 0.999215 | + | 0.0396265i | \(0.0126168\pi\) | ||||
−0.999215 | + | 0.0396265i | \(0.987383\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.39989 | −0.107784 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.5505 | 0.840863 | 0.420432 | − | 0.907324i | \(-0.361879\pi\) | ||||
0.420432 | + | 0.907324i | \(0.361879\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.h.e.2591.3 | yes | 8 | |
3.2 | odd | 2 | inner | 6048.2.h.e.2591.8 | yes | 8 | |
4.3 | odd | 2 | inner | 6048.2.h.e.2591.2 | ✓ | 8 | |
12.11 | even | 2 | inner | 6048.2.h.e.2591.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.e.2591.2 | ✓ | 8 | 4.3 | odd | 2 | inner | |
6048.2.h.e.2591.3 | yes | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.e.2591.5 | yes | 8 | 12.11 | even | 2 | inner | |
6048.2.h.e.2591.8 | yes | 8 | 3.2 | odd | 2 | inner |