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 | 2591.6 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.e.2591.4 |
$q$-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 | \(0.217953\pi\) | ||||
−0.774597 | + | 0.632456i | \(0.782047\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.29253 | 1.89727 | 0.948634 | − | 0.316374i | \(-0.102466\pi\) | ||||
0.948634 | + | 0.316374i | \(0.102466\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.44949 | 1.51142 | 0.755708 | − | 0.654908i | \(-0.227293\pi\) | ||||
0.755708 | + | 0.654908i | \(0.227293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.317837i | 0.0770869i | 0.999257 | + | 0.0385434i | \(0.0122718\pi\) | ||||
−0.999257 | + | 0.0385434i | \(0.987728\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.317837 | 0.0662736 | 0.0331368 | − | 0.999451i | \(-0.489450\pi\) | ||||
0.0331368 | + | 0.999451i | \(0.489450\pi\) | |||||||
\(24\) | 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 | ||||||||
\(31\) | 8.79796i | 1.58016i | 0.613004 | + | 0.790080i | \(0.289961\pi\) | ||||
−0.613004 | + | 0.790080i | \(0.710039\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.82843 | 0.478091 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.898979 | 0.147791 | 0.0738957 | − | 0.997266i | \(-0.476457\pi\) | ||||
0.0738957 | + | 0.997266i | \(0.476457\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | − 5.44949i | − 0.831039i | −0.909584 | − | 0.415520i | \(-0.863600\pi\) | ||||
0.909584 | − | 0.415520i | \(-0.136400\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.5851 | 1.83572 | 0.917860 | − | 0.396905i | \(-0.129916\pi\) | ||||
0.917860 | + | 0.396905i | \(0.129916\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 8.02458i | − 1.10226i | −0.834419 | − | 0.551130i | \(-0.814197\pi\) | ||||
0.834419 | − | 0.551130i | \(-0.185803\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.7980i | 2.39988i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.83183 | 0.759239 | 0.379620 | − | 0.925143i | \(-0.376055\pi\) | ||||
0.379620 | + | 0.925143i | \(0.376055\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.8990 | 1.65155 | 0.825773 | − | 0.564003i | \(-0.190739\pi\) | ||||
0.825773 | + | 0.564003i | \(0.190739\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 15.4135i | 1.91181i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.44949i | 0.421422i | 0.977548 | + | 0.210711i | \(0.0675779\pi\) | ||||
−0.977548 | + | 0.210711i | \(0.932422\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.51059 | −0.297952 | −0.148976 | − | 0.988841i | \(-0.547598\pi\) | ||||
−0.148976 | + | 0.988841i | \(0.547598\pi\) | |||||||
\(72\) | 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 | ||||||||
\(77\) | − 6.29253i | − 0.717100i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 10.0000i | − 1.12509i | −0.826767 | − | 0.562544i | \(-0.809823\pi\) | ||||
0.826767 | − | 0.562544i | \(-0.190177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.46410 | −0.380235 | −0.190117 | − | 0.981761i | \(-0.560887\pi\) | ||||
−0.190117 | + | 0.981761i | \(0.560887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.898979 | −0.0975080 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 10.7101i | − 1.13527i | −0.823279 | − | 0.567636i | \(-0.807858\pi\) | ||||
0.823279 | − | 0.567636i | \(-0.192142\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 5.44949i | − 0.571262i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.3137 | −1.16076 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.7980 | −1.60404 | −0.802020 | − | 0.597297i | \(-0.796241\pi\) | ||||
−0.802020 | + | 0.597297i | \(0.796241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 5.65685i | − 0.562878i | −0.959579 | − | 0.281439i | \(-0.909188\pi\) | ||||
0.959579 | − | 0.281439i | \(-0.0908117\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.89898i | 0.384178i | 0.981378 | + | 0.192089i | \(0.0615262\pi\) | ||||
−0.981378 | + | 0.192089i | \(0.938474\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.2419 | −1.76351 | −0.881756 | − | 0.471706i | \(-0.843638\pi\) | ||||
−0.881756 | + | 0.471706i | \(0.843638\pi\) | |||||||
\(108\) | 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 | \(-0.869318\pi\) | ||||
0.916901 | − | 0.399114i | \(-0.130682\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.898979i | 0.0838303i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.317837 | 0.0291361 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28.5959 | 2.59963 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.65685i | 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.8990i | 0.967128i | 0.875309 | + | 0.483564i | \(0.160658\pi\) | ||||
−0.875309 | + | 0.483564i | \(0.839342\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.36773 | −0.206869 | −0.103435 | − | 0.994636i | \(-0.532983\pi\) | ||||
−0.103435 | + | 0.994636i | \(0.532983\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 19.5133i | − 1.66713i | −0.552421 | − | 0.833565i | \(-0.686296\pi\) | ||||
0.552421 | − | 0.833565i | \(-0.313704\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 15.7980i | − 1.33997i | −0.742377 | − | 0.669983i | \(-0.766302\pi\) | ||||
0.742377 | − | 0.669983i | \(-0.233698\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 34.2911 | 2.86756 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.6969 | 1.22051 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.02458i | 0.657399i | 0.944435 | + | 0.328700i | \(0.106610\pi\) | ||||
−0.944435 | + | 0.328700i | \(0.893390\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.79796i | 0.471831i | 0.971774 | + | 0.235916i | \(0.0758089\pi\) | ||||
−0.971774 | + | 0.235916i | \(0.924191\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24.8844 | −1.99876 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1464 | 1.28863 | 0.644313 | − | 0.764762i | \(-0.277144\pi\) | ||||
0.644313 | + | 0.764762i | \(0.277144\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 0.317837i | − 0.0250491i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.55051i | 0.199771i | 0.994999 | + | 0.0998857i | \(0.0318477\pi\) | ||||
−0.994999 | + | 0.0998857i | \(0.968152\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.0492 | −1.24192 | −0.620961 | − | 0.783842i | \(-0.713257\pi\) | ||||
−0.620961 | + | 0.783842i | \(0.713257\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.6969 | 1.28438 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 0.921404i | − 0.0700530i | −0.999386 | − | 0.0350265i | \(-0.988848\pi\) | ||||
0.999386 | − | 0.0350265i | \(-0.0111516\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.00000i | 0.226779i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.0280 | −0.824270 | −0.412135 | − | 0.911123i | \(-0.635217\pi\) | ||||
−0.412135 | + | 0.911123i | \(0.635217\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.65153 | −0.717393 | −0.358696 | − | 0.933454i | \(-0.616779\pi\) | ||||
−0.358696 | + | 0.933454i | \(0.616779\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.54270i | 0.186943i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000i | 0.146254i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.0280 | 0.797957 | 0.398978 | − | 0.916960i | \(-0.369365\pi\) | ||||
0.398978 | + | 0.916960i | \(0.369365\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.89898 | −0.280655 | −0.140327 | − | 0.990105i | \(-0.544815\pi\) | ||||
−0.140327 | + | 0.990105i | \(0.544815\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.9706i | 1.20910i | 0.796566 | + | 0.604551i | \(0.206648\pi\) | ||||
−0.796566 | + | 0.604551i | \(0.793352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.7980i | 1.47433i | 0.675714 | + | 0.737164i | \(0.263836\pi\) | ||||
−0.675714 | + | 0.737164i | \(0.736164\pi\) | |||||||
\(200\) | 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 | ||||||||
\(209\) | 25.1701i | 1.74105i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1464i | 0.973880i | 0.873435 | + | 0.486940i | \(0.161887\pi\) | ||||
−0.873435 | + | 0.486940i | \(0.838113\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.4135 | 1.05119 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.79796 | 0.597244 | ||||||||
\(218\) | 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 | ||||||||
\(227\) | −0.460702 | −0.0305779 | −0.0152889 | − | 0.999883i | \(-0.504867\pi\) | ||||
−0.0152889 | + | 0.999883i | \(0.504867\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.10102 | −0.204921 | −0.102461 | − | 0.994737i | \(-0.532672\pi\) | ||||
−0.102461 | + | 0.994737i | \(0.532672\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.0771i | 1.77388i | 0.461882 | + | 0.886941i | \(0.347174\pi\) | ||||
−0.461882 | + | 0.886941i | \(0.652826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 35.5959i | 2.32202i | ||||||||
\(236\) | 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 | ||||||||
\(247\) | 21.7980i | 1.38697i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.73545 | −0.298899 | −0.149449 | − | 0.988769i | \(-0.547750\pi\) | ||||
−0.149449 | + | 0.988769i | \(0.547750\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 26.0915i | − 1.62754i | −0.581184 | − | 0.813772i | \(-0.697410\pi\) | ||||
0.581184 | − | 0.813772i | \(-0.302590\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 0.898979i | − 0.0558599i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.6527 | 1.02685 | 0.513426 | − | 0.858134i | \(-0.328376\pi\) | ||||
0.513426 | + | 0.858134i | \(0.328376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.6969 | 1.39426 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.4921i | 0.883598i | 0.897114 | + | 0.441799i | \(0.145660\pi\) | ||||
−0.897114 | + | 0.441799i | \(0.854340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 29.8990i | − 1.81623i | −0.418717 | − | 0.908117i | \(-0.637520\pi\) | ||||
0.418717 | − | 0.908117i | \(-0.362480\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.8776 | −1.13836 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.8990 | 1.85654 | 0.928270 | − | 0.371907i | \(-0.121296\pi\) | ||||
0.928270 | + | 0.371907i | \(0.121296\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.57826i | 0.392426i | 0.980561 | + | 0.196213i | \(0.0628644\pi\) | ||||
−0.980561 | + | 0.196213i | \(0.937136\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.79796i | 0.344653i | 0.985040 | + | 0.172326i | \(0.0551284\pi\) | ||||
−0.985040 | + | 0.172326i | \(0.944872\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.46410 | −0.204479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8990 | 0.994058 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 13.2207i | − 0.772363i | −0.922423 | − | 0.386182i | \(-0.873794\pi\) | ||||
0.922423 | − | 0.386182i | \(-0.126206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.4949i | 0.960370i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.73205 | 0.100167 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.44949 | −0.314103 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.4838i | 2.08906i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.6969i | 1.52367i | 0.647768 | + | 0.761837i | \(0.275702\pi\) | ||||
−0.647768 | + | 0.761837i | \(0.724298\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.4203 | 1.21463 | 0.607316 | − | 0.794460i | \(-0.292246\pi\) | ||||
0.607316 | + | 0.794460i | \(0.292246\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.5959 | 0.881533 | 0.440767 | − | 0.897622i | \(-0.354707\pi\) | ||||
0.440767 | + | 0.897622i | \(0.354707\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.5851i | 0.706847i | 0.935463 | + | 0.353424i | \(0.114983\pi\) | ||||
−0.935463 | + | 0.353424i | \(0.885017\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 32.6969i | − 1.83068i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.27135 | −0.0707397 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.3485 | −0.906850 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 12.5851i | − 0.693837i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 5.65153i | − 0.310636i | −0.987865 | − | 0.155318i | \(-0.950360\pi\) | ||||
0.987865 | − | 0.155318i | \(-0.0496403\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.75663 | −0.533062 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.8990 | −1.08397 | −0.541983 | − | 0.840389i | \(-0.682326\pi\) | ||||
−0.541983 | + | 0.840389i | \(0.682326\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 55.3614i | 2.99799i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.1489 | −1.08165 | −0.540826 | − | 0.841135i | \(-0.681888\pi\) | ||||
−0.540826 | + | 0.841135i | \(0.681888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.8434 | 1.54395 | 0.771975 | − | 0.635653i | \(-0.219269\pi\) | ||||
0.771975 | + | 0.635653i | \(0.219269\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.7019i | 1.74055i | 0.492570 | + | 0.870273i | \(0.336058\pi\) | ||||
−0.492570 | + | 0.870273i | \(0.663942\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 7.10102i | − 0.376883i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.61037 | 0.348882 | 0.174441 | − | 0.984668i | \(-0.444188\pi\) | ||||
0.174441 | + | 0.984668i | \(0.444188\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 11.3137i | − 0.592187i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.7980i | 1.81644i | 0.418494 | + | 0.908219i | \(0.362558\pi\) | ||||
−0.418494 | + | 0.908219i | \(0.637442\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.02458 | −0.416615 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −32.2929 | −1.67206 | −0.836030 | − | 0.548683i | \(-0.815129\pi\) | ||||
−0.836030 | + | 0.548683i | \(0.815129\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 28.3164i | − 1.45837i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 10.0000i | − 0.513665i | −0.966456 | − | 0.256833i | \(-0.917321\pi\) | ||||
0.966456 | − | 0.256833i | \(-0.0826790\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8920 | −0.914237 | −0.457118 | − | 0.889406i | \(-0.651118\pi\) | ||||
−0.457118 | + | 0.889406i | \(0.651118\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.7980 | 0.907068 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 36.4838i | − 1.84980i | −0.380206 | − | 0.924902i | \(-0.624147\pi\) | ||||
0.380206 | − | 0.924902i | \(-0.375853\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.101021i | 0.00510883i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.2843 | 1.42314 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.1010 | −0.757898 | −0.378949 | − | 0.925417i | \(-0.623715\pi\) | ||||
−0.378949 | + | 0.925417i | \(0.623715\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.6637i | 0.582455i | 0.956654 | + | 0.291228i | \(0.0940637\pi\) | ||||
−0.956654 | + | 0.291228i | \(0.905936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 47.9444i | 2.38828i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.65685 | 0.280400 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.6969 | −1.41897 | −0.709486 | − | 0.704719i | \(-0.751073\pi\) | ||||
−0.709486 | + | 0.704719i | \(0.751073\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5.83183i | − 0.286965i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 9.79796i | − 0.480963i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.6520 | −1.49745 | −0.748724 | − | 0.662882i | \(-0.769333\pi\) | ||||
−0.748724 | + | 0.662882i | \(0.769333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.5959 | −1.53989 | −0.769945 | − | 0.638110i | \(-0.779717\pi\) | ||||
−0.769945 | + | 0.638110i | \(0.779717\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 0.953512i | − 0.0462521i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 12.8990i | − 0.624225i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.7272 | 1.28740 | 0.643702 | − | 0.765276i | \(-0.277398\pi\) | ||||
0.643702 | + | 0.765276i | \(0.277398\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.5959 | −0.941720 | −0.470860 | − | 0.882208i | \(-0.656056\pi\) | ||||
−0.470860 | + | 0.882208i | \(0.656056\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.27135i | 0.0608169i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 11.4949i | − 0.548622i | −0.961641 | − | 0.274311i | \(-0.911550\pi\) | ||||
0.961641 | − | 0.274311i | \(-0.0884497\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.285729 | 0.0135754 | 0.00678770 | − | 0.999977i | \(-0.497839\pi\) | ||||
0.00678770 | + | 0.999977i | \(0.497839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 30.2929 | 1.43602 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 29.2699i | − 1.38133i | −0.723174 | − | 0.690666i | \(-0.757318\pi\) | ||||
0.723174 | − | 0.690666i | \(-0.242682\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 21.7980i | − 1.02643i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.4135 | 0.722595 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.3031 | −0.481957 | −0.240978 | − | 0.970530i | \(-0.577468\pi\) | ||||
−0.240978 | + | 0.970530i | \(0.577468\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 31.5959i | 1.46839i | 0.678940 | + | 0.734193i | \(0.262439\pi\) | ||||
−0.678940 | + | 0.734193i | \(0.737561\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.84961 | 0.363236 | 0.181618 | − | 0.983369i | \(-0.441866\pi\) | ||||
0.181618 | + | 0.983369i | \(0.441866\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.44949 | 0.159283 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 34.2911i | − 1.57671i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 12.0000i | − 0.550598i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.94258 | −0.271524 | −0.135762 | − | 0.990742i | \(-0.543348\pi\) | ||||
−0.135762 | + | 0.990742i | \(0.543348\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.89898 | 0.223374 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 44.6834i | − 2.02897i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 8.00000i | − 0.362515i | −0.983436 | − | 0.181257i | \(-0.941983\pi\) | ||||
0.983436 | − | 0.181257i | \(-0.0580167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.5344 | −1.10722 | −0.553612 | − | 0.832775i | \(-0.686751\pi\) | ||||
−0.553612 | + | 0.832775i | \(0.686751\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.65153 | 0.0743812 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.51059i | 0.112615i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.7980i | 1.60254i | 0.598305 | + | 0.801268i | \(0.295841\pi\) | ||||
−0.598305 | + | 0.801268i | \(0.704159\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.37113 | 0.239487 | 0.119743 | − | 0.992805i | \(-0.461793\pi\) | ||||
0.119743 | + | 0.992805i | \(0.461793\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.0000 | 0.711991 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 0.285729i | − 0.0126647i | −0.999980 | − | 0.00633236i | \(-0.997984\pi\) | ||||
0.999980 | − | 0.00633236i | \(-0.00201567\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.00000i | 0.176950i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.0280 | −0.485951 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 79.1918 | 3.48285 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.6315i | 0.509587i | 0.966995 | + | 0.254794i | \(0.0820075\pi\) | ||||
−0.966995 | + | 0.254794i | \(0.917992\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.7980i | 0.865704i | 0.901465 | + | 0.432852i | \(0.142493\pi\) | ||||
−0.901465 | + | 0.432852i | \(0.857507\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.79632 | −0.121810 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8990 | −0.995608 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 18.8776i | − 0.817679i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 51.5959i | − 2.23069i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.29253 | −0.271038 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.4949 | 1.74101 | 0.870506 | − | 0.492158i | \(-0.163792\pi\) | ||||
0.870506 | + | 0.492158i | \(0.163792\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 22.6274i | − 0.969252i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.3939i | 0.658195i | 0.944296 | + | 0.329097i | \(0.106744\pi\) | ||||
−0.944296 | + | 0.329097i | \(0.893256\pi\) | |||||||
\(548\) | 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 | ||||||||
\(557\) | 0.746431i | 0.0316273i | 0.999875 | + | 0.0158136i | \(0.00503385\pi\) | ||||
−0.999875 | + | 0.0158136i | \(0.994966\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 29.6969i | − 1.25605i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.9951 | −1.05342 | −0.526710 | − | 0.850045i | \(-0.676575\pi\) | ||||
−0.526710 | + | 0.850045i | \(0.676575\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.0000 | 1.00969 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.19275i | 0.0919250i | 0.998943 | + | 0.0459625i | \(0.0146355\pi\) | ||||
−0.998943 | + | 0.0459625i | \(0.985365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.2474i | 0.470691i | 0.971912 | + | 0.235346i | \(0.0756222\pi\) | ||||
−0.971912 | + | 0.235346i | \(0.924378\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.953512 | −0.0397642 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.30306 | 0.220769 | 0.110385 | − | 0.993889i | \(-0.464792\pi\) | ||||
0.110385 | + | 0.993889i | \(0.464792\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.46410i | 0.143715i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 50.4949i | − 2.09128i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.2385 | 0.628961 | 0.314480 | − | 0.949264i | \(-0.398170\pi\) | ||||
0.314480 | + | 0.949264i | \(0.398170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.1918 | −1.45005 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 26.0915i | − 1.07145i | −0.844392 | − | 0.535725i | \(-0.820038\pi\) | ||||
0.844392 | − | 0.535725i | \(-0.179962\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.898979i | 0.0368546i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.6513 | −1.82440 | −0.912201 | − | 0.409744i | \(-0.865618\pi\) | ||||
−0.912201 | + | 0.409744i | \(0.865618\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.8990 | −0.689324 | −0.344662 | − | 0.938727i | \(-0.612006\pi\) | ||||
−0.344662 | + | 0.938727i | \(0.612006\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 80.8815i | 3.28830i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.0000i | 0.771186i | 0.922669 | + | 0.385593i | \(0.126003\pi\) | ||||
−0.922669 | + | 0.385593i | \(0.873997\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 68.5821 | 2.77454 | ||||||||
\(612\) | 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 | ||||||||
\(617\) | − 29.2699i | − 1.17836i | −0.808001 | − | 0.589181i | \(-0.799451\pi\) | ||||
0.808001 | − | 0.589181i | \(-0.200549\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.5959i | 1.18956i | 0.803888 | + | 0.594780i | \(0.202761\pi\) | ||||
−0.803888 | + | 0.594780i | \(0.797239\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.7101 | −0.429093 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.285729i | 0.0113928i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.4949i | 1.45284i | 0.687252 | + | 0.726419i | \(0.258817\pi\) | ||||
−0.687252 | + | 0.726419i | \(0.741183\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.8270 | −1.22333 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.44949 | −0.215917 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 20.1489i | − 0.795835i | −0.917421 | − | 0.397918i | \(-0.869733\pi\) | ||||
0.917421 | − | 0.397918i | \(-0.130267\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 48.4949i | − 1.91245i | −0.292629 | − | 0.956226i | \(-0.594530\pi\) | ||||
0.292629 | − | 0.956226i | \(-0.405470\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.94258 | −0.233627 | −0.116814 | − | 0.993154i | \(-0.537268\pi\) | ||||
−0.116814 | + | 0.993154i | \(0.537268\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.6969 | 1.44048 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 25.3451i | − 0.991830i | −0.868371 | − | 0.495915i | \(-0.834833\pi\) | ||||
0.868371 | − | 0.495915i | \(-0.165167\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 6.69694i | − 0.261671i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.7846 | 0.809653 | 0.404827 | − | 0.914393i | \(-0.367332\pi\) | ||||
0.404827 | + | 0.914393i | \(0.367332\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8990 | 0.501712 | 0.250856 | − | 0.968024i | \(-0.419288\pi\) | ||||
0.250856 | + | 0.968024i | \(0.419288\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.3137i | 0.438727i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 1.65153i | − 0.0639475i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 81.1672 | 3.13342 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.5959 | −1.10229 | −0.551146 | − | 0.834409i | \(-0.685809\pi\) | ||||
−0.551146 | + | 0.834409i | \(0.685809\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 28.3485i | − 1.08952i | −0.838592 | − | 0.544760i | \(-0.816621\pi\) | ||||
0.838592 | − | 0.544760i | \(-0.183379\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.7980i | 0.606270i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.0409 | −1.45559 | −0.727797 | − | 0.685792i | \(-0.759456\pi\) | ||||
−0.727797 | + | 0.685792i | \(0.759456\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 55.1918 | 2.10877 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 43.7299i | − 1.66598i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.2020i | 1.07286i | 0.843946 | + | 0.536428i | \(0.180227\pi\) | ||||
−0.843946 | + | 0.536428i | \(0.819773\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 44.6834 | 1.69494 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.10102 | 0.0417041 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.65685i | 0.213656i | 0.994277 | + | 0.106828i | \(0.0340695\pi\) | ||||
−0.994277 | + | 0.106828i | \(0.965931\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.59592i | 0.135623i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.65685 | −0.212748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.5959 | −1.56217 | −0.781084 | − | 0.624426i | \(-0.785333\pi\) | ||||
−0.781084 | + | 0.624426i | \(0.785333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.79632i | 0.104723i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 96.9898i | 3.62721i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.3349 | 0.609189 | 0.304594 | − | 0.952482i | \(-0.401479\pi\) | ||||
0.304594 | + | 0.952482i | \(0.401479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.89898 | 0.145206 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.5885i | 0.578941i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 9.49490i | − 0.352146i | −0.984377 | − | 0.176073i | \(-0.943660\pi\) | ||||
0.984377 | − | 0.176073i | \(-0.0563395\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.73205 | 0.0640622 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.348469 | 0.0128710 | 0.00643550 | − | 0.999979i | \(-0.497952\pi\) | ||||
0.00643550 | + | 0.999979i | \(0.497952\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.7060i | 0.799551i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 43.7980i | − 1.61113i | −0.592505 | − | 0.805567i | \(-0.701861\pi\) | ||||
0.592505 | − | 0.805567i | \(-0.298139\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.3376 | 1.22304 | 0.611518 | − | 0.791230i | \(-0.290559\pi\) | ||||
0.611518 | + | 0.791230i | \(0.290559\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.6969 | −0.831551 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.2419i | 0.666545i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 44.8990i | 1.63839i | 0.573517 | + | 0.819194i | \(0.305579\pi\) | ||||
−0.573517 | + | 0.819194i | \(0.694421\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.3991 | −0.596825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.1918 | −1.20638 | −0.603189 | − | 0.797598i | \(-0.706103\pi\) | ||||
−0.603189 | + | 0.797598i | \(0.706103\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.1154i | 1.74418i | 0.489345 | + | 0.872090i | \(0.337236\pi\) | ||||
−0.489345 | + | 0.872090i | \(0.662764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000i | 0.289619i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31.7805 | 1.14753 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.89898 | −0.176662 | −0.0883309 | − | 0.996091i | \(-0.528153\pi\) | ||||
−0.0883309 | + | 0.996091i | \(0.528153\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 31.4626i | − 1.13163i | −0.824531 | − | 0.565816i | \(-0.808561\pi\) | ||||
0.824531 | − | 0.565816i | \(-0.191439\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 26.3939i | − 0.948096i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.8564 | 0.496457 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.7980 | −0.565295 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 45.6690i | 1.63000i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 21.5959i | − 0.769811i | −0.922956 | − | 0.384906i | \(-0.874234\pi\) | ||||
0.922956 | − | 0.384906i | \(-0.125766\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.48528 | −0.301702 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 70.2929 | 2.49617 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 25.4558i | − 0.901692i | −0.892602 | − | 0.450846i | \(-0.851122\pi\) | ||||
0.892602 | − | 0.450846i | \(-0.148878\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000i | 0.141510i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.1701 | −0.888234 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.898979 | 0.0316849 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.6486i | 0.972073i | 0.873939 | + | 0.486036i | \(0.161558\pi\) | ||||
−0.873939 | + | 0.486036i | \(0.838442\pi\) | |||||||
\(810\) | 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 | ||||||||
\(815\) | −7.21393 | −0.252693 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.7980 | 0.762614 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 37.0087i | − 1.29161i | −0.763501 | − | 0.645807i | \(-0.776521\pi\) | ||||
0.763501 | − | 0.645807i | \(-0.223479\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 21.1010i | − 0.735535i | −0.929918 | − | 0.367768i | \(-0.880122\pi\) | ||||
0.929918 | − | 0.367768i | \(-0.119878\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.7552 | −1.31288 | −0.656438 | − | 0.754380i | \(-0.727938\pi\) | ||||
−0.656438 | + | 0.754380i | \(0.727938\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.6969 | −1.62185 | −0.810926 | − | 0.585149i | \(-0.801036\pi\) | ||||
−0.810926 | + | 0.585149i | \(0.801036\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.317837i | − 0.0110124i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 45.3939i | − 1.57092i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.46410 | 0.119594 | 0.0597970 | − | 0.998211i | \(-0.480955\pi\) | ||||
0.0597970 | + | 0.998211i | \(0.480955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | 0.0689655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 47.2261i | 1.62463i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 28.5959i | − 0.982567i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.285729 | 0.00979467 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.6515 | −1.08373 | −0.541864 | − | 0.840466i | \(-0.682281\pi\) | ||||
−0.541864 | + | 0.840466i | \(0.682281\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 10.7101i | − 0.365851i | −0.983127 | − | 0.182926i | \(-0.941443\pi\) | ||||
0.983127 | − | 0.182926i | \(-0.0585568\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 42.2929i | − 1.44301i | −0.692407 | − | 0.721507i | \(-0.743450\pi\) | ||||
0.692407 | − | 0.721507i | \(-0.256550\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.7949 | 1.04827 | 0.524135 | − | 0.851635i | \(-0.324389\pi\) | ||||
0.524135 | + | 0.851635i | \(0.324389\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.60612 | 0.0886108 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 62.9253i | − 2.13459i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.7980i | 0.636945i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.65685 | 0.191237 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.1010 | 0.982672 | 0.491336 | − | 0.870970i | \(-0.336509\pi\) | ||||
0.491336 | + | 0.870970i | \(0.336509\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.5371i | 1.39942i | 0.714427 | + | 0.699710i | \(0.246688\pi\) | ||||
−0.714427 | + | 0.699710i | \(0.753312\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1.65153i | − 0.0555784i | −0.999614 | − | 0.0277892i | \(-0.991153\pi\) | ||||
0.999614 | − | 0.0277892i | \(-0.00884672\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.3991 | 0.550628 | 0.275314 | − | 0.961354i | \(-0.411218\pi\) | ||||
0.275314 | + | 0.961354i | \(0.411218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.8990 | 0.365540 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 50.3402i | 1.68457i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 31.1918i | − 1.04263i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.7155 | 1.52470 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.55051 | 0.0849698 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 27.2987i | − 0.907438i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 41.1918i | − 1.36775i | −0.729598 | − | 0.683876i | \(-0.760293\pi\) | ||||
0.729598 | − | 0.683876i | \(-0.239707\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19.2275 | 0.637037 | 0.318518 | − | 0.947917i | \(-0.396815\pi\) | ||||
0.318518 | + | 0.947917i | \(0.396815\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.7980 | −0.721407 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.36773i | 0.0781892i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 21.5959i | − 0.712384i | −0.934413 | − | 0.356192i | \(-0.884075\pi\) | ||||
0.934413 | − | 0.356192i | \(-0.115925\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.6814 | −0.450330 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.69694 | −0.0886748 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 56.9185i | 1.86744i | 0.358011 | + | 0.933718i | \(0.383455\pi\) | ||||
−0.358011 | + | 0.933718i | \(0.616545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 4.00000i | − 0.131095i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.65685 | −0.184999 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.3031 | 0.565266 | 0.282633 | − | 0.959228i | \(-0.408792\pi\) | ||||
0.282633 | + | 0.959228i | \(0.408792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.4203i | 0.698281i | 0.937070 | + | 0.349141i | \(0.113526\pi\) | ||||
−0.937070 | + | 0.349141i | \(0.886474\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.10102i | − 0.0358542i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.38551 | 0.142510 | 0.0712549 | − | 0.997458i | \(-0.477300\pi\) | ||||
0.0712549 | + | 0.997458i | \(0.477300\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.7980 | −0.707592 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.5065i | 0.437517i | 0.975779 | + | 0.218759i | \(0.0702007\pi\) | ||||
−0.975779 | + | 0.218759i | \(0.929799\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.1918i | 1.00934i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19.5133 | −0.630116 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −46.4041 | −1.49691 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 11.0280i | − 0.355003i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 19.1010i | − 0.614247i | −0.951670 | − | 0.307124i | \(-0.900633\pi\) | ||||
0.951670 | − | 0.307124i | \(-0.0993665\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.38891 | −0.237121 | −0.118561 | − | 0.992947i | \(-0.537828\pi\) | ||||
−0.118561 | + | 0.992947i | \(0.537828\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.7980 | −0.506459 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.1278i | 0.483980i | 0.970279 | + | 0.241990i | \(0.0778001\pi\) | ||||
−0.970279 | + | 0.241990i | \(0.922200\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 67.3939i | − 2.15392i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.09978 | −0.130763 | −0.0653813 | − | 0.997860i | \(-0.520826\pi\) | ||||
−0.0653813 | + | 0.997860i | \(0.520826\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −48.0000 | −1.52941 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.73205i | − 0.0550760i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.4949i | 1.47696i | 0.674276 | + | 0.738480i | \(0.264456\pi\) | ||||
−0.674276 | + | 0.738480i | \(0.735544\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −58.8255 | −1.86489 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.4495 | 0.996015 | 0.498008 | − | 0.867173i | \(-0.334065\pi\) | ||||
0.498008 | + | 0.867173i | \(0.334065\pi\) | |||||||
\(998\) | 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.2591.6 | yes | 8 | |
3.2 | odd | 2 | inner | 6048.2.h.e.2591.1 | ✓ | 8 | |
4.3 | odd | 2 | inner | 6048.2.h.e.2591.7 | yes | 8 | |
12.11 | even | 2 | inner | 6048.2.h.e.2591.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.e.2591.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
6048.2.h.e.2591.4 | yes | 8 | 12.11 | even | 2 | inner | |
6048.2.h.e.2591.6 | yes | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.e.2591.7 | yes | 8 | 4.3 | odd | 2 | inner |