Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(3005,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6012.3005");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.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: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3005.8 | ||
Character | \(\chi\) | \(=\) | 6012.3005 |
Dual form | 6012.2.h.a.3005.7 |
$q$-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 \(\left(\mathbb{Z}/6012\mathbb{Z}\right)^\times\).
\(n\) | \(3007\) | \(3341\) | \(4681\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | −3.30258 | −1.47696 | −0.738480 | − | 0.674276i | \(-0.764456\pi\) | ||||
−0.738480 | + | 0.674276i | \(0.764456\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.47594 | −1.69175 | −0.845874 | − | 0.533383i | \(-0.820920\pi\) | ||||
−0.845874 | + | 0.533383i | \(0.820920\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.74620i | 0.526501i | 0.964728 | + | 0.263250i | \(0.0847945\pi\) | ||||
−0.964728 | + | 0.263250i | \(0.915206\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.94627i | 0.817148i | 0.912725 | + | 0.408574i | \(0.133974\pi\) | ||||
−0.912725 | + | 0.408574i | \(0.866026\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.90566 | 0.704725 | 0.352362 | − | 0.935864i | \(-0.385378\pi\) | ||||
0.352362 | + | 0.935864i | \(0.385378\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.77245 | 0.865458 | 0.432729 | − | 0.901524i | \(-0.357551\pi\) | ||||
0.432729 | + | 0.901524i | \(0.357551\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.201252 | 0.0419640 | 0.0209820 | − | 0.999780i | \(-0.493321\pi\) | ||||
0.0209820 | + | 0.999780i | \(0.493321\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.90705 | 1.18141 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.23069i | − | 1.15701i | −0.815679 | − | 0.578505i | \(-0.803636\pi\) | ||
0.815679 | − | 0.578505i | \(-0.196364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.31658 | 0.775281 | 0.387640 | − | 0.921811i | \(-0.373290\pi\) | ||||
0.387640 | + | 0.921811i | \(0.373290\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 14.7822 | 2.49864 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.99423i | 0.985445i | 0.870187 | + | 0.492722i | \(0.163998\pi\) | ||||
−0.870187 | + | 0.492722i | \(0.836002\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.64706 | 1.03810 | 0.519048 | − | 0.854745i | \(-0.326286\pi\) | ||||
0.519048 | + | 0.854745i | \(0.326286\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.12658i | − | 0.934294i | −0.884180 | − | 0.467147i | \(-0.845282\pi\) | ||
0.884180 | − | 0.467147i | \(-0.154718\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.02820i | 0.733438i | 0.930332 | + | 0.366719i | \(0.119519\pi\) | ||||
−0.930332 | + | 0.366719i | \(0.880481\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.0341 | 1.86201 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.29277 | −0.314936 | −0.157468 | − | 0.987524i | \(-0.550333\pi\) | ||||
−0.157468 | + | 0.987524i | \(0.550333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.76699i | − | 0.777620i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.540391 | −0.0703530 | −0.0351765 | − | 0.999381i | \(-0.511199\pi\) | ||||
−0.0351765 | + | 0.999381i | \(0.511199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.87576 | −1.13642 | −0.568212 | − | 0.822882i | \(-0.692365\pi\) | ||||
−0.568212 | + | 0.822882i | \(0.692365\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 9.73030i | − | 1.20690i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.8297i | 1.56740i | 0.621138 | + | 0.783701i | \(0.286671\pi\) | ||||
−0.621138 | + | 0.783701i | \(0.713329\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.03751 | 0.597842 | 0.298921 | − | 0.954278i | \(-0.403373\pi\) | ||||
0.298921 | + | 0.954278i | \(0.403373\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.72315i | 0.552802i | 0.961042 | + | 0.276401i | \(0.0891419\pi\) | ||||
−0.961042 | + | 0.276401i | \(0.910858\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 7.81591i | − | 0.890706i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.282217i | 0.0317519i | 0.999874 | + | 0.0158759i | \(0.00505368\pi\) | ||||
−0.999874 | + | 0.0158759i | \(0.994946\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.56680 | 0.391507 | 0.195754 | − | 0.980653i | \(-0.437285\pi\) | ||||
0.195754 | + | 0.980653i | \(0.437285\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.59617 | −1.04085 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.81680i | 0.404580i | 0.979326 | + | 0.202290i | \(0.0648383\pi\) | ||||
−0.979326 | + | 0.202290i | \(0.935162\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 13.1873i | − | 1.38241i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.4588 | −1.27825 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.03056 | −0.815380 | −0.407690 | − | 0.913120i | \(-0.633666\pi\) | ||||
−0.407690 | + | 0.913120i | \(0.633666\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.01447 | −0.299951 | −0.149976 | − | 0.988690i | \(-0.547920\pi\) | ||||
−0.149976 | + | 0.988690i | \(0.547920\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.10909i | − | 0.109282i | −0.998506 | − | 0.0546408i | \(-0.982599\pi\) | ||
0.998506 | − | 0.0546408i | \(-0.0174014\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 18.0758i | − | 1.74745i | −0.486416 | − | 0.873727i | \(-0.661696\pi\) | ||
0.486416 | − | 0.873727i | \(-0.338304\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.8681i | 1.51989i | 0.649990 | + | 0.759943i | \(0.274773\pi\) | ||||
−0.649990 | + | 0.759943i | \(0.725227\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3715 | −1.06974 | −0.534869 | − | 0.844935i | \(-0.679639\pi\) | ||||
−0.534869 | + | 0.844935i | \(0.679639\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.664653 | −0.0619792 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.0055 | −1.19222 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.95077 | 0.722797 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.99561 | −0.267936 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.90908 | −0.258139 | −0.129070 | − | 0.991636i | \(-0.541199\pi\) | ||||
−0.129070 | + | 0.991636i | \(0.541199\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.21247 | 0.193305 | 0.0966523 | − | 0.995318i | \(-0.469187\pi\) | ||||
0.0966523 | + | 0.995318i | \(0.469187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.8852 | −1.46414 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 20.2993i | − | 1.73429i | −0.498056 | − | 0.867145i | \(-0.665953\pi\) | ||
0.498056 | − | 0.867145i | \(-0.334047\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0422i | 1.10623i | 0.833105 | + | 0.553115i | \(0.186561\pi\) | ||||
−0.833105 | + | 0.553115i | \(0.813439\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.14479 | −0.430229 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.5774i | 1.70886i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.97767 | −0.162017 | −0.0810086 | − | 0.996713i | \(-0.525814\pi\) | ||||
−0.0810086 | + | 0.996713i | \(0.525814\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.45460i | 0.606646i | 0.952888 | + | 0.303323i | \(0.0980962\pi\) | ||||
−0.952888 | + | 0.303323i | \(0.901904\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.2559 | −1.14506 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.89114 | −0.629782 | −0.314891 | − | 0.949128i | \(-0.601968\pi\) | ||||
−0.314891 | + | 0.949128i | \(0.601968\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.900794 | −0.0709925 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.36362i | − | 0.185133i | −0.995707 | − | 0.0925664i | \(-0.970493\pi\) | ||
0.995707 | − | 0.0925664i | \(-0.0295070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.47390 | − | 8.78893i | 0.733112 | − | 0.680108i | ||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.31949 | 0.332269 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 11.7117i | − | 0.890421i | −0.895426 | − | 0.445211i | \(-0.853129\pi\) | ||
0.895426 | − | 0.445211i | \(-0.146871\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −26.4396 | −1.99865 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1.05482i | − | 0.0788411i | −0.999223 | − | 0.0394205i | \(-0.987449\pi\) | ||
0.999223 | − | 0.0394205i | \(-0.0125512\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.3368 | −1.43729 | −0.718647 | − | 0.695375i | \(-0.755238\pi\) | ||||
−0.718647 | + | 0.695375i | \(0.755238\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 19.7964i | − | 1.45546i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.07387i | 0.371038i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.18869i | 0.520155i | 0.965588 | + | 0.260078i | \(0.0837482\pi\) | ||||
−0.965588 | + | 0.260078i | \(0.916252\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.5942i | 1.77033i | 0.465279 | + | 0.885164i | \(0.345954\pi\) | ||||
−0.465279 | + | 0.885164i | \(0.654046\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.7355 | −1.04986 | −0.524932 | − | 0.851144i | \(-0.675909\pi\) | ||||
−0.524932 | + | 0.851144i | \(0.675909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.1485 | −1.57007 | −0.785034 | − | 0.619453i | \(-0.787354\pi\) | ||||
−0.785034 | + | 0.619453i | \(0.787354\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 27.8882i | 1.95737i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.9525 | −1.53323 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.58746i | 0.455664i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9623 | 1.16773 | 0.583867 | − | 0.811849i | \(-0.301539\pi\) | ||||
0.583867 | + | 0.811849i | \(0.301539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.2335i | 1.37991i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.3208 | −1.31158 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.56084i | 0.575865i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.960326 | 0.0643082 | 0.0321541 | − | 0.999483i | \(-0.489763\pi\) | ||||
0.0321541 | + | 0.999483i | \(0.489763\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −26.3838 | −1.75115 | −0.875576 | − | 0.483081i | \(-0.839518\pi\) | ||||
−0.875576 | + | 0.483081i | \(0.839518\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.90353 | 0.257953 | 0.128976 | − | 0.991648i | \(-0.458831\pi\) | ||||
0.128976 | + | 0.991648i | \(0.458831\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.848301i | 0.0555741i | 0.999614 | + | 0.0277870i | \(0.00884602\pi\) | ||||
−0.999614 | + | 0.0277870i | \(0.991154\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 16.6060i | − | 1.08326i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.93714i | 0.254672i | 0.991860 | + | 0.127336i | \(0.0406427\pi\) | ||||
−0.991860 | + | 0.127336i | \(0.959357\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.3587i | 0.860510i | 0.902707 | + | 0.430255i | \(0.141576\pi\) | ||||
−0.902707 | + | 0.430255i | \(0.858424\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −43.0461 | −2.75011 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.1146i | 0.707208i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.1441i | 1.14524i | 0.819820 | + | 0.572621i | \(0.194073\pi\) | ||||
−0.819820 | + | 0.572621i | \(0.805927\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.351428i | 0.0220941i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.1437 | −1.38129 | −0.690644 | − | 0.723195i | \(-0.742673\pi\) | ||||
−0.690644 | + | 0.723195i | \(0.742673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 26.8298i | − | 1.66712i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 12.8406i | − | 0.791785i | −0.918297 | − | 0.395893i | \(-0.870435\pi\) | ||
0.918297 | − | 0.395893i | \(-0.129565\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.57205 | 0.465147 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.4969 | 0.700976 | 0.350488 | − | 0.936567i | \(-0.386016\pi\) | ||||
0.350488 | + | 0.936567i | \(0.386016\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.6014i | 0.765482i | 0.923856 | + | 0.382741i | \(0.125020\pi\) | ||||
−0.923856 | + | 0.382741i | \(0.874980\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.3149i | 0.622013i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.4112i | 0.685632i | 0.939403 | + | 0.342816i | \(0.111381\pi\) | ||||
−0.939403 | + | 0.342816i | \(0.888619\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.4111i | − | 0.859694i | −0.902902 | − | 0.429847i | \(-0.858568\pi\) | ||
0.902902 | − | 0.429847i | \(-0.141432\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.27067 | 0.0755334 | 0.0377667 | − | 0.999287i | \(-0.487976\pi\) | ||||
0.0377667 | + | 0.999287i | \(0.487976\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.7519 | −1.75620 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.55717 | −0.503363 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6014i | 0.736183i | 0.929790 | + | 0.368092i | \(0.119989\pi\) | ||||
−0.929790 | + | 0.368092i | \(0.880011\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.78469 | 0.103909 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.592944i | 0.0342908i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.4222i | 1.58059i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 29.3129 | 1.67845 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 30.1036i | − | 1.71810i | −0.511888 | − | 0.859052i | \(-0.671054\pi\) | ||
0.511888 | − | 0.859052i | \(-0.328946\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.4913i | 1.27536i | 0.770300 | + | 0.637681i | \(0.220106\pi\) | ||||
−0.770300 | + | 0.637681i | \(0.779894\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.74957i | − | 0.0988917i | −0.998777 | − | 0.0494459i | \(-0.984254\pi\) | ||
0.998777 | − | 0.0494459i | \(-0.0157455\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 17.1405i | − | 0.962708i | −0.876526 | − | 0.481354i | \(-0.840145\pi\) | ||
0.876526 | − | 0.481354i | \(-0.159855\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.8801 | 0.609166 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.9614 | 0.609910 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.4038i | 0.965387i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 22.5059i | − | 1.24079i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 12.7118i | − | 0.698704i | −0.936991 | − | 0.349352i | \(-0.886402\pi\) | ||
0.936991 | − | 0.349352i | \(-0.113598\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 42.3713i | − | 2.31499i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.34572 | −0.182253 | −0.0911266 | − | 0.995839i | \(-0.529047\pi\) | ||||
−0.0911266 | + | 0.995839i | \(0.529047\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.53763i | 0.408186i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −27.0081 | −1.45830 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.3087 | 0.607085 | 0.303543 | − | 0.952818i | \(-0.401831\pi\) | ||||
0.303543 | + | 0.952818i | \(0.401831\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.81106i | − | 0.364588i | −0.983244 | − | 0.182294i | \(-0.941648\pi\) | ||
0.983244 | − | 0.182294i | \(-0.0583522\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.02447i | 0.107752i | 0.998548 | + | 0.0538759i | \(0.0171575\pi\) | ||||
−0.998548 | + | 0.0538759i | \(0.982842\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.6368 | −0.882989 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.7973i | 0.622640i | 0.950305 | + | 0.311320i | \(0.100771\pi\) | ||||
−0.950305 | + | 0.311320i | \(0.899229\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.76866 | −0.250982 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 15.5986i | − | 0.816467i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.29029 | −0.223952 | −0.111976 | − | 0.993711i | \(-0.535718\pi\) | ||||
−0.111976 | + | 0.993711i | \(0.535718\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.2623 | 0.532792 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.419097i | 0.0217000i | 0.999941 | + | 0.0108500i | \(0.00345373\pi\) | ||||
−0.999941 | + | 0.0108500i | \(0.996546\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.3573 | 0.945449 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 0.455203i | − | 0.0233822i | −0.999932 | − | 0.0116911i | \(-0.996279\pi\) | ||
0.999932 | − | 0.0116911i | \(-0.00372148\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 15.3395i | − | 0.783812i | −0.920005 | − | 0.391906i | \(-0.871816\pi\) | ||
0.920005 | − | 0.391906i | \(-0.128184\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.8127i | 1.31554i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.4909 | 0.633315 | 0.316658 | − | 0.948540i | \(-0.397439\pi\) | ||||
0.316658 | + | 0.948540i | \(0.397439\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.584770 | 0.0295731 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 0.932044i | − | 0.0468962i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.6895 | −1.74102 | −0.870509 | − | 0.492152i | \(-0.836210\pi\) | ||||
−0.870509 | + | 0.492152i | \(0.836210\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −38.4417 | −1.91969 | −0.959844 | − | 0.280534i | \(-0.909489\pi\) | ||||
−0.959844 | + | 0.280534i | \(0.909489\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.7178i | 0.633519i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.4671 | −0.518837 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0857 | 1.19096 | 0.595481 | − | 0.803370i | \(-0.296962\pi\) | ||||
0.595481 | + | 0.803370i | \(0.296962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.41876 | 0.119019 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.7797 | −0.578241 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.72636i | 0.279751i | 0.990169 | + | 0.139875i | \(0.0446702\pi\) | ||||
−0.990169 | + | 0.139875i | \(0.955330\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.0108 | 0.731584 | 0.365792 | − | 0.930697i | \(-0.380798\pi\) | ||||
0.365792 | + | 0.930697i | \(0.380798\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.1639 | 0.832569 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39.7274 | 1.92254 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.1945i | 0.731891i | 0.930636 | + | 0.365946i | \(0.119254\pi\) | ||||
−0.930636 | + | 0.365946i | \(0.880746\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.1293 | 0.630954 | 0.315477 | − | 0.948933i | \(-0.397835\pi\) | ||||
0.315477 | + | 0.948933i | \(0.397835\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.759214 | 0.0363181 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 0.946508i | − | 0.0451743i | −0.999745 | − | 0.0225872i | \(-0.992810\pi\) | ||
0.999745 | − | 0.0225872i | \(-0.00719033\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.4579 | −0.876961 | −0.438481 | − | 0.898741i | \(-0.644483\pi\) | ||||
−0.438481 | + | 0.898741i | \(0.644483\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 12.6053i | − | 0.597548i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.2668i | 0.767677i | 0.923400 | + | 0.383838i | \(0.125398\pi\) | ||||
−0.923400 | + | 0.383838i | \(0.874602\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.6071i | 0.546559i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 43.5523i | 2.04176i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.8957i | 0.556460i | 0.960515 | + | 0.278230i | \(0.0897477\pi\) | ||||
−0.960515 | + | 0.278230i | \(0.910252\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 31.3806i | − | 1.46154i | −0.682624 | − | 0.730770i | \(-0.739161\pi\) | ||
0.682624 | − | 0.730770i | \(-0.260839\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 35.6282i | − | 1.65578i | −0.560888 | − | 0.827891i | \(-0.689540\pi\) | ||
0.560888 | − | 0.827891i | \(-0.310460\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 8.27776i | − | 0.383049i | −0.981488 | − | 0.191524i | \(-0.938657\pi\) | ||
0.981488 | − | 0.191524i | \(-0.0613431\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 57.4252i | − | 2.65165i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.6983 | 0.491906 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22.2840 | 1.02246 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.39416 | 0.292157 | 0.146078 | − | 0.989273i | \(-0.453335\pi\) | ||||
0.146078 | + | 0.989273i | \(0.453335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.6606 | −0.805254 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.5216 | 1.20428 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.5822i | 1.06861i | 0.845292 | + | 0.534305i | \(0.179426\pi\) | ||||
−0.845292 | + | 0.534305i | \(0.820574\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.84530i | 0.263795i | 0.991263 | + | 0.131897i | \(0.0421069\pi\) | ||||
−0.991263 | + | 0.131897i | \(0.957893\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 18.1042i | − | 0.815374i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.5476 | −1.01140 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 33.4438i | − | 1.49715i | −0.663051 | − | 0.748574i | \(-0.730739\pi\) | ||
0.663051 | − | 0.748574i | \(-0.269261\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 12.0827i | − | 0.538741i | −0.963037 | − | 0.269371i | \(-0.913184\pi\) | ||
0.963037 | − | 0.269371i | \(-0.0868157\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.95555 | 0.443016 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.0315i | 0.754908i | 0.926028 | + | 0.377454i | \(0.123200\pi\) | ||||
−0.926028 | + | 0.377454i | \(0.876800\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 21.1405i | − | 0.935202i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.66285i | 0.161405i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.78026 | −0.386155 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.9883 | 1.83954 | 0.919770 | − | 0.392457i | \(-0.128375\pi\) | ||||
0.919770 | + | 0.392457i | \(0.128375\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.1413 | −0.705810 | −0.352905 | − | 0.935659i | \(-0.614806\pi\) | ||||
−0.352905 | + | 0.935659i | \(0.614806\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.5425 | 0.546360 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9595 | −0.998239 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.5840i | 0.848279i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 59.6968i | 2.58092i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.7601i | 0.980348i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 10.0272i | − | 0.431105i | −0.976492 | − | 0.215552i | \(-0.930845\pi\) | ||
0.976492 | − | 0.215552i | \(-0.0691552\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 52.4056i | − | 2.24481i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.1458i | 1.75927i | 0.475650 | + | 0.879635i | \(0.342213\pi\) | ||||
−0.475650 | + | 0.879635i | \(0.657787\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 23.5049i | − | 1.00134i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.26319i | − | 0.0537162i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 8.92681i | − | 0.378241i | −0.981954 | − | 0.189120i | \(-0.939436\pi\) | ||
0.981954 | − | 0.189120i | \(-0.0605637\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.0505 | 0.763457 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 4.92539i | − | 0.207581i | −0.994599 | − | 0.103790i | \(-0.966903\pi\) | ||
0.994599 | − | 0.103790i | \(-0.0330971\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.5552 | 1.57996 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −36.2533 | −1.51982 | −0.759908 | − | 0.650030i | \(-0.774756\pi\) | ||||
−0.759908 | + | 0.650030i | \(0.774756\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.17787i | 0.300384i | 0.988657 | + | 0.150192i | \(0.0479892\pi\) | ||||
−0.988657 | + | 0.150192i | \(0.952011\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.18881 | 0.0495767 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.7645 | 1.19748 | 0.598741 | − | 0.800943i | \(-0.295668\pi\) | ||||
0.598741 | + | 0.800943i | \(0.295668\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.9648 | −0.662331 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.00364i | − | 0.165814i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.99976 | 0.0825390 | 0.0412695 | − | 0.999148i | \(-0.486860\pi\) | ||||
0.0412695 | + | 0.999148i | \(0.486860\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.2841 | 0.670973 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.97200 | 0.163110 | 0.0815552 | − | 0.996669i | \(-0.474011\pi\) | ||||
0.0815552 | + | 0.996669i | \(0.474011\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 42.9519 | 1.76086 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 48.6269i | − | 1.98684i | −0.114524 | − | 0.993420i | \(-0.536534\pi\) | ||
0.114524 | − | 0.993420i | \(-0.463466\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.9517 | −0.732264 | −0.366132 | − | 0.930563i | \(-0.619318\pi\) | ||||
−0.366132 | + | 0.930563i | \(0.619318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −26.2581 | −1.06754 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.2026i | 1.30706i | 0.756900 | + | 0.653531i | \(0.226713\pi\) | ||||
−0.756900 | + | 0.653531i | \(0.773287\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −14.8144 | −0.599328 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.7854 | −1.93003 | −0.965017 | − | 0.262189i | \(-0.915556\pi\) | ||||
−0.965017 | + | 0.262189i | \(0.915556\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 2.53524i | − | 0.102065i | −0.998697 | − | 0.0510325i | \(-0.983749\pi\) | ||
0.998697 | − | 0.0510325i | \(-0.0162512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 48.3473i | − | 1.94324i | −0.236542 | − | 0.971621i | \(-0.576014\pi\) | ||
0.236542 | − | 0.971621i | \(-0.423986\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 17.0838i | − | 0.684447i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.6420 | −0.785680 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.4172i | 0.694467i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.4366 | 0.415474 | 0.207737 | − | 0.978185i | \(-0.433390\pi\) | ||||
0.207737 | + | 0.978185i | \(0.433390\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.60748 | 0.381261 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 38.4019i | 1.52154i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.677992 | −0.0267791 | −0.0133895 | − | 0.999910i | \(-0.504262\pi\) | ||||
−0.0133895 | + | 0.999910i | \(0.504262\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.9191i | 1.25876i | 0.777096 | + | 0.629382i | \(0.216692\pi\) | ||||
−0.777096 | + | 0.629382i | \(0.783308\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.1454 | 1.14583 | 0.572913 | − | 0.819616i | \(-0.305813\pi\) | ||||
0.572913 | + | 0.819616i | \(0.305813\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.943634i | − | 0.0370409i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 38.1069i | − | 1.49124i | −0.666372 | − | 0.745619i | \(-0.732154\pi\) | ||
0.666372 | − | 0.745619i | \(-0.267846\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.30687 | −0.285503 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.0667 | 0.742732 | 0.371366 | − | 0.928487i | \(-0.378890\pi\) | ||||
0.371366 | + | 0.928487i | \(0.378890\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 16.2058i | − | 0.630331i | −0.949037 | − | 0.315166i | \(-0.897940\pi\) | ||
0.949037 | − | 0.315166i | \(-0.102060\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 55.7649 | 2.16247 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.25394i | − | 0.0485528i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 15.4989i | − | 0.598328i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.76689i | 0.183750i | 0.995771 | + | 0.0918750i | \(0.0292860\pi\) | ||||
−0.995771 | + | 0.0918750i | \(0.970714\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.5383i | 1.09682i | 0.836211 | + | 0.548408i | \(0.184766\pi\) | ||||
−0.836211 | + | 0.548408i | \(0.815234\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.9443 | 1.37942 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.6812 | 1.02093 | 0.510464 | − | 0.859899i | \(-0.329474\pi\) | ||||
0.510464 | + | 0.859899i | \(0.329474\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 67.0402i | 2.56148i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 6.75511i | − | 0.257349i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 29.2893i | − | 1.11422i | −0.830440 | − | 0.557109i | \(-0.811911\pi\) | ||
0.830440 | − | 0.557109i | \(-0.188089\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 43.0731i | − | 1.63386i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.3141 | 0.731573 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.2439i | 0.802370i | 0.915997 | + | 0.401185i | \(0.131402\pi\) | ||||
−0.915997 | + | 0.401185i | \(0.868598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.6129i | 0.852861i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.4926 | 0.507442 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2.54912i | − | 0.0957342i | −0.998854 | − | 0.0478671i | \(-0.984758\pi\) | ||
0.998854 | − | 0.0478671i | \(-0.0152424\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.868722 | 0.0325339 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.9911 | 0.635431 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.7150 | −1.07089 | −0.535445 | − | 0.844570i | \(-0.679856\pi\) | ||||
−0.535445 | + | 0.844570i | \(0.679856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.96421i | 0.184877i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 36.8050i | − | 1.36690i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.0147i | 1.33571i | 0.744290 | + | 0.667856i | \(0.232788\pi\) | ||||
−0.744290 | + | 0.667856i | \(0.767212\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 17.8017i | − | 0.658420i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.00576 | −0.332635 | −0.166318 | − | 0.986072i | \(-0.553188\pi\) | ||||
−0.166318 | + | 0.986072i | \(0.553188\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22.4034 | −0.825238 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 41.7652i | − | 1.53636i | −0.640236 | − | 0.768179i | \(-0.721163\pi\) | ||
0.640236 | − | 0.768179i | \(-0.278837\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.2569i | 0.633093i | 0.948577 | + | 0.316547i | \(0.102523\pi\) | ||||
−0.948577 | + | 0.316547i | \(0.897477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.53143 | 0.239293 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 80.9063i | 2.95625i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.6483i | 0.680487i | 0.940337 | + | 0.340244i | \(0.110510\pi\) | ||||
−0.940337 | + | 0.340244i | \(0.889490\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 24.6194i | − | 0.895992i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.8340 | −0.648186 | −0.324093 | − | 0.946025i | \(-0.605059\pi\) | ||||
−0.324093 | + | 0.946025i | \(0.605059\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.4205i | 0.921492i | 0.887532 | + | 0.460746i | \(0.152418\pi\) | ||||
−0.887532 | + | 0.460746i | \(0.847582\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 71.0246i | − | 2.57126i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1.59214i | − | 0.0574888i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.8535i | 0.499569i | 0.968301 | + | 0.249784i | \(0.0803598\pi\) | ||||
−0.968301 | + | 0.249784i | \(0.919640\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.0966 | −0.938631 | −0.469315 | − | 0.883031i | \(-0.655499\pi\) | ||||
−0.469315 | + | 0.883031i | \(0.655499\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.4983 | 0.915924 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.0757 | 0.898429 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.79652i | 0.314764i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.0611 | 0.930162 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.19066i | 0.185027i | 0.995711 | + | 0.0925136i | \(0.0294902\pi\) | ||||
−0.995711 | + | 0.0925136i | \(0.970510\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 50.8981 | 1.80973 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 26.1504i | − | 0.928627i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.5481 | −1.04665 | −0.523324 | − | 0.852134i | \(-0.675308\pi\) | ||||
−0.523324 | + | 0.852134i | \(0.675308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.6102i | 0.516872i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.24758 | −0.291051 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.97495 | 0.104853 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.9149i | 0.946277i | 0.880988 | + | 0.473138i | \(0.156879\pi\) | ||||
−0.880988 | + | 0.473138i | \(0.843121\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.3461i | 0.925135i | 0.886584 | + | 0.462568i | \(0.153072\pi\) | ||||
−0.886584 | + | 0.462568i | \(0.846928\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.80604i | 0.273434i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 23.1122i | − | 0.808592i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.2721 | −1.89411 | −0.947056 | − | 0.321070i | \(-0.895958\pi\) | ||||
−0.947056 | + | 0.321070i | \(0.895958\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.7665i | 1.21188i | 0.795509 | + | 0.605941i | \(0.207203\pi\) | ||||
−0.795509 | + | 0.605941i | \(0.792797\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.1080 | −0.977412 | −0.488706 | − | 0.872448i | \(-0.662531\pi\) | ||||
−0.488706 | + | 0.872448i | \(0.662531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 35.1274i | − | 1.22002i | −0.792392 | − | 0.610012i | \(-0.791165\pi\) | ||
0.792392 | − | 0.610012i | \(-0.208835\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.8725 | 1.31220 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.2883 | + | 29.0262i | −1.08278 | + | 1.00449i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 44.8685i | − | 1.54903i | −0.632554 | − | 0.774516i | \(-0.717993\pi\) | ||
0.632554 | − | 0.774516i | \(-0.282007\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.82150 | −0.338673 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.2655 | −0.490748 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.5872 | −1.22279 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.20635i | 0.0413532i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.0582 | 1.06341 | 0.531705 | − | 0.846929i | \(-0.321551\pi\) | ||||
0.531705 | + | 0.846929i | \(0.321551\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 46.7685i | 1.59758i | 0.601609 | + | 0.798791i | \(0.294527\pi\) | ||||
−0.601609 | + | 0.798791i | \(0.705473\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.84253 | 0.301703 | 0.150852 | − | 0.988556i | \(-0.451798\pi\) | ||||
0.150852 | + | 0.988556i | \(0.451798\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 6.59372i | − | 0.224453i | −0.993683 | − | 0.112226i | \(-0.964202\pi\) | ||
0.993683 | − | 0.112226i | \(-0.0357982\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 38.6787i | 1.31512i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.492808 | −0.0167174 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.7999 | −1.28080 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.4082 | 0.453279 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42.7745 | −1.44439 | −0.722197 | − | 0.691688i | \(-0.756867\pi\) | ||||
−0.722197 | + | 0.691688i | \(0.756867\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.2813 | −1.59295 | −0.796474 | − | 0.604673i | \(-0.793304\pi\) | ||||
−0.796474 | + | 0.604673i | \(0.793304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.5367 | −0.926683 | −0.463342 | − | 0.886180i | \(-0.653350\pi\) | ||||
−0.463342 | + | 0.886180i | \(0.653350\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.1667 | 1.14720 | 0.573602 | − | 0.819134i | \(-0.305546\pi\) | ||||
0.573602 | + | 0.819134i | \(0.305546\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.0209 | 0.436706 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.9686i | 0.634760i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.48364i | 0.116445i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 26.8953i | − | 0.897007i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.66199 | −0.221943 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 63.8615 | 2.12283 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.5074 | −1.17900 | −0.589501 | − | 0.807768i | \(-0.700676\pi\) | ||||
−0.589501 | + | 0.807768i | \(0.700676\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.8628i | 0.525559i | 0.964856 | + | 0.262780i | \(0.0846392\pi\) | ||||
−0.964856 | + | 0.262780i | \(0.915361\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.22837i | 0.206129i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.90289 | −0.327022 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.9911 | 1.55009 | 0.775046 | − | 0.631904i | \(-0.217726\pi\) | ||||
0.775046 | + | 0.631904i | \(0.217726\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.8419i | 0.488526i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35.4082i | 1.16421i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 43.5736i | − | 1.42960i | −0.699328 | − | 0.714801i | \(-0.746517\pi\) | ||
0.699328 | − | 0.714801i | \(-0.253483\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49.1703 | 1.61149 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 16.7569i | − | 0.548008i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 32.1336i | − | 1.04976i | −0.851176 | − | 0.524880i | \(-0.824110\pi\) | ||
0.851176 | − | 0.524880i | \(-0.175890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.1950 | −0.919131 | −0.459566 | − | 0.888144i | \(-0.651995\pi\) | ||||
−0.459566 | + | 0.888144i | \(0.651995\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.33774 | 0.0435627 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 53.9801i | 1.75412i | 0.480384 | + | 0.877058i | \(0.340497\pi\) | ||||
−0.480384 | + | 0.877058i | \(0.659503\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.9157 | −0.451722 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.9058 | −0.644814 | −0.322407 | − | 0.946601i | \(-0.604492\pi\) | ||||
−0.322407 | + | 0.946601i | \(0.604492\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 23.7412i | − | 0.768248i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 90.8587i | 2.93398i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.3671 | −0.398940 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 81.2243i | − | 2.61470i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.7652 | −0.603449 | −0.301724 | − | 0.953395i | \(-0.597562\pi\) | ||||
−0.301724 | + | 0.953395i | \(0.597562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.7278 | −1.72421 | −0.862104 | − | 0.506732i | \(-0.830853\pi\) | ||||
−0.862104 | + | 0.506732i | \(0.830853\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 58.3764i | − | 1.87146i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.7057 | −0.918376 | −0.459188 | − | 0.888339i | \(-0.651860\pi\) | ||||
−0.459188 | + | 0.888339i | \(0.651860\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.66491 | −0.213012 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.2734 | −0.965570 | −0.482785 | − | 0.875739i | \(-0.660375\pi\) | ||||
−0.482785 | + | 0.875739i | \(0.660375\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.6653 | 1.55061 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.23299i | − | 0.0392067i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 14.0718i | − | 0.447006i | −0.974703 | − | 0.223503i | \(-0.928251\pi\) | ||
0.974703 | − | 0.223503i | \(-0.0717492\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 73.1473 | 2.31893 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.93389 | −0.251269 | −0.125634 | − | 0.992077i | \(-0.540097\pi\) | ||||
−0.125634 | + | 0.992077i | \(0.540097\pi\) | |||||||
\(998\) | 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 | 6012.2.h.a.3005.8 | yes | 56 | |
3.2 | odd | 2 | inner | 6012.2.h.a.3005.49 | yes | 56 | |
167.166 | odd | 2 | inner | 6012.2.h.a.3005.50 | yes | 56 | |
501.500 | even | 2 | inner | 6012.2.h.a.3005.7 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6012.2.h.a.3005.7 | ✓ | 56 | 501.500 | even | 2 | inner | |
6012.2.h.a.3005.8 | yes | 56 | 1.1 | even | 1 | trivial | |
6012.2.h.a.3005.49 | yes | 56 | 3.2 | odd | 2 | inner | |
6012.2.h.a.3005.50 | yes | 56 | 167.166 | odd | 2 | inner |