Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(3497,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4028.3497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.c (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: | \(32.1637419342\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3497.18 | ||
Character | \(\chi\) | \(=\) | 4028.3497 |
Dual form | 4028.2.c.a.3497.65 |
$q$-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 \(\left(\mathbb{Z}/4028\mathbb{Z}\right)^\times\).
\(n\) | \(2015\) | \(2281\) | \(2757\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 2.07591i | − | 1.19853i | −0.800552 | − | 0.599264i | \(-0.795460\pi\) | ||
0.800552 | − | 0.599264i | \(-0.204540\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.80942i | − | 0.809196i | −0.914495 | − | 0.404598i | \(-0.867411\pi\) | ||
0.914495 | − | 0.404598i | \(-0.132589\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.11331 | 0.420793 | 0.210396 | − | 0.977616i | \(-0.432525\pi\) | ||||
0.210396 | + | 0.977616i | \(0.432525\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.30941 | −0.436469 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.61828 | 1.09095 | 0.545477 | − | 0.838126i | \(-0.316349\pi\) | ||||
0.545477 | + | 0.838126i | \(0.316349\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.43779 | 1.78552 | 0.892761 | − | 0.450530i | \(-0.148765\pi\) | ||||
0.892761 | + | 0.450530i | \(0.148765\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.75619 | −0.969844 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.97195 | −1.69095 | −0.845473 | − | 0.534019i | \(-0.820681\pi\) | ||||
−0.845473 | + | 0.534019i | \(0.820681\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.31114i | − | 0.504332i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.32108i | 1.31804i | 0.752127 | + | 0.659018i | \(0.229028\pi\) | ||||
−0.752127 | + | 0.659018i | \(0.770972\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.72601 | 0.345202 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.50952i | − | 0.675408i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.59306 | 0.295824 | 0.147912 | − | 0.989000i | \(-0.452745\pi\) | ||||
0.147912 | + | 0.989000i | \(0.452745\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.346279i | − | 0.0621935i | −0.999516 | − | 0.0310967i | \(-0.990100\pi\) | ||
0.999516 | − | 0.0310967i | \(-0.00989999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 7.51123i | − | 1.30754i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 2.01445i | − | 0.340504i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.84318 | 1.45381 | 0.726905 | − | 0.686738i | \(-0.240958\pi\) | ||||
0.726905 | + | 0.686738i | \(0.240958\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 13.3643i | − | 2.14000i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.2048i | − | 1.59372i | −0.604165 | − | 0.796859i | \(-0.706493\pi\) | ||
0.604165 | − | 0.796859i | \(-0.293507\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.64187 | −0.555380 | −0.277690 | − | 0.960671i | \(-0.589569\pi\) | ||||
−0.277690 | + | 0.960671i | \(0.589569\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.36926i | 0.353189i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.75561 | 0.693676 | 0.346838 | − | 0.937925i | \(-0.387255\pi\) | ||||
0.346838 | + | 0.937925i | \(0.387255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.76053 | −0.822934 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.4731i | 2.02664i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.70311 | + | 2.84048i | 0.920743 | + | 0.390169i | ||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6.54698i | − | 0.882795i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.07591 | −0.274961 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.2914 | 1.86059 | 0.930293 | − | 0.366818i | \(-0.119553\pi\) | ||||
0.930293 | + | 0.366818i | \(0.119553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.53081i | 0.964221i | 0.876110 | + | 0.482111i | \(0.160130\pi\) | ||||
−0.876110 | + | 0.482111i | \(0.839870\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.45778 | −0.183663 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 11.6487i | − | 1.44484i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.06783i | − | 0.619134i | −0.950878 | − | 0.309567i | \(-0.899816\pi\) | ||
0.950878 | − | 0.309567i | \(-0.100184\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.1220 | 1.57970 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.4007i | − | 1.35301i | −0.736437 | − | 0.676506i | \(-0.763493\pi\) | ||
0.736437 | − | 0.676506i | \(-0.236507\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.1518i | − | 1.30521i | −0.757696 | − | 0.652607i | \(-0.773675\pi\) | ||
0.757696 | − | 0.652607i | \(-0.226325\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 3.58304i | − | 0.413734i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.02828 | 0.459065 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.51640i | 0.733152i | 0.930388 | + | 0.366576i | \(0.119470\pi\) | ||||
−0.930388 | + | 0.366576i | \(0.880530\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.2137 | −1.24596 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.38380i | 0.371421i | 0.982605 | + | 0.185710i | \(0.0594586\pi\) | ||||
−0.982605 | + | 0.185710i | \(0.940541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.6152i | 1.36831i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.30706i | − | 0.354554i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.49994 | −0.582992 | −0.291496 | − | 0.956572i | \(-0.594153\pi\) | ||||
−0.291496 | + | 0.956572i | \(0.594153\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.16728 | 0.751335 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.718843 | −0.0745406 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.80942 | −0.185642 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.13179 | 0.724124 | 0.362062 | − | 0.932154i | \(-0.382073\pi\) | ||||
0.362062 | + | 0.932154i | \(0.382073\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.73780 | −0.476167 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.07135i | 0.305610i | 0.988256 | + | 0.152805i | \(0.0488307\pi\) | ||||
−0.988256 | + | 0.152805i | \(0.951169\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.51664i | 0.543571i | 0.962358 | + | 0.271785i | \(0.0876140\pi\) | ||||
−0.962358 | + | 0.271785i | \(0.912386\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.18181 | −0.408103 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.59900 | −0.154581 | −0.0772907 | − | 0.997009i | \(-0.524627\pi\) | ||||
−0.0772907 | + | 0.997009i | \(0.524627\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.2931i | 1.75217i | 0.482161 | + | 0.876083i | \(0.339852\pi\) | ||||
−0.482161 | + | 0.876083i | \(0.660148\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 18.3577i | − | 1.74243i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0175 | −1.41273 | −0.706363 | − | 0.707849i | \(-0.749666\pi\) | ||||
−0.706363 | + | 0.707849i | \(0.749666\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.4375 | 1.06655 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.42969 | −0.779325 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.76196 | −0.711537 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.09196 | 0.190179 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21.1842 | −1.91011 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 12.1702i | − | 1.08853i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.8012i | 1.66834i | 0.551508 | + | 0.834170i | \(0.314053\pi\) | ||||
−0.551508 | + | 0.834170i | \(0.685947\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.56020i | 0.665638i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.52680 | 0.220768 | 0.110384 | − | 0.993889i | \(-0.464792\pi\) | ||||
0.110384 | + | 0.993889i | \(0.464792\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 1.11331i | − | 0.0965365i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.35019 | −0.546537 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 0.301874i | − | 0.0257908i | −0.999917 | − | 0.0128954i | \(-0.995895\pi\) | ||
0.999917 | − | 0.0128954i | \(-0.00410485\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.5999i | − | 0.899070i | −0.893263 | − | 0.449535i | \(-0.851590\pi\) | ||
0.893263 | − | 0.449535i | \(-0.148410\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.87221i | − | 0.831390i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.2937 | 1.94792 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.88252i | − | 0.239380i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.9584i | 0.986309i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.7004 | −0.958536 | −0.479268 | − | 0.877669i | \(-0.659098\pi\) | ||||
−0.479268 | + | 0.877669i | \(0.659098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.200264i | 0.0162973i | 0.999967 | + | 0.00814863i | \(0.00259382\pi\) | ||||
−0.999967 | + | 0.00814863i | \(0.997406\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.12911 | 0.738045 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.626562 | −0.0503267 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.37658i | − | 0.508906i | −0.967085 | − | 0.254453i | \(-0.918105\pi\) | ||
0.967085 | − | 0.254453i | \(-0.0818955\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.89657 | − | 13.9151i | 0.467629 | − | 1.10354i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.03734i | 0.554620i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.91950 | −0.306999 | −0.153499 | − | 0.988149i | \(-0.549054\pi\) | ||||
−0.153499 | + | 0.988149i | \(0.549054\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.5910 | −1.05805 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.5709i | − | 1.35968i | −0.733362 | − | 0.679838i | \(-0.762050\pi\) | ||
0.733362 | − | 0.679838i | \(-0.237950\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.4452 | 2.18809 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.30941i | 0.100133i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 18.1021i | − | 1.37628i | −0.725580 | − | 0.688138i | \(-0.758429\pi\) | ||
0.725580 | − | 0.688138i | \(-0.241571\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.92159 | 0.145258 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 29.6677i | − | 2.22996i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.4269i | − | 0.928833i | −0.885617 | − | 0.464416i | \(-0.846264\pi\) | ||
0.885617 | − | 0.464416i | \(-0.153736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.03256i | 0.522726i | 0.965241 | + | 0.261363i | \(0.0841720\pi\) | ||||
−0.965241 | + | 0.261363i | \(0.915828\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.6333 | 1.15565 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 16.0010i | − | 1.17642i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −25.2265 | −1.84474 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 3.90720i | − | 0.284207i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.63409i | − | 0.624740i | −0.949960 | − | 0.312370i | \(-0.898877\pi\) | ||
0.949960 | − | 0.312370i | \(-0.101123\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.0817i | 1.08561i | 0.839860 | + | 0.542804i | \(0.182637\pi\) | ||||
−0.839860 | + | 0.542804i | \(0.817363\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24.1816 | −1.73168 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.24576 | −0.516239 | −0.258120 | − | 0.966113i | \(-0.583103\pi\) | ||||
−0.258120 | + | 0.966113i | \(0.583103\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.02486 | 0.0726504 | 0.0363252 | − | 0.999340i | \(-0.488435\pi\) | ||||
0.0363252 | + | 0.999340i | \(0.488435\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.5204 | −0.742050 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.77358 | 0.124481 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.4647 | −1.28963 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 8.27686i | − | 0.575282i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3.61828i | − | 0.250282i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.3791 | 1.67832 | 0.839162 | − | 0.543882i | \(-0.183046\pi\) | ||||
0.839162 | + | 0.543882i | \(0.183046\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.6668 | −1.62162 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.58966i | 0.449411i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.385516i | − | 0.0261706i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.1501 | −1.56434 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −44.8839 | −3.01922 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4371 | −0.832847 | −0.416424 | − | 0.909171i | \(-0.636717\pi\) | ||||
−0.416424 | + | 0.909171i | \(0.636717\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.26005 | −0.150670 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.7540 | −1.24475 | −0.622373 | − | 0.782721i | \(-0.713831\pi\) | ||||
−0.622373 | + | 0.782721i | \(0.713831\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.96459 | −0.394151 | −0.197076 | − | 0.980388i | \(-0.563144\pi\) | ||||
−0.197076 | + | 0.980388i | \(0.563144\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 8.36235i | − | 0.550202i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 14.5654i | − | 0.954210i | −0.878846 | − | 0.477105i | \(-0.841686\pi\) | ||
0.878846 | − | 0.477105i | \(-0.158314\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 8.60488i | − | 0.561320i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.5275 | 0.878703 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.2877i | 1.63573i | 0.575412 | + | 0.817864i | \(0.304842\pi\) | ||||
−0.575412 | + | 0.817864i | \(0.695158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.3921 | −1.57123 | −0.785616 | − | 0.618715i | \(-0.787654\pi\) | ||||
−0.785616 | + | 0.618715i | \(0.787654\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.7500i | 0.817914i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.4232i | 0.665915i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.43779i | − | 0.409627i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.02448 | 0.445158 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.51779i | − | 0.0958023i | −0.998852 | − | 0.0479012i | \(-0.984747\pi\) | ||
0.998852 | − | 0.0479012i | \(-0.0152533\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.8715i | 1.43792i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 26.1880 | 1.63995 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.9365i | 0.869337i | 0.900590 | + | 0.434669i | \(0.143134\pi\) | ||||
−0.900590 | + | 0.434669i | \(0.856866\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.84523 | 0.611753 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.08597 | −0.129118 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.1130i | 1.36355i | 0.731562 | + | 0.681775i | \(0.238791\pi\) | ||||
−0.731562 | + | 0.681775i | \(0.761209\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.13961 | − | 12.1287i | 0.315724 | − | 0.745062i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.4174i | 0.698733i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.6401 | −0.648737 | −0.324368 | − | 0.945931i | \(-0.605152\pi\) | ||||
−0.324368 | + | 0.945931i | \(0.605152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.9844 | −1.69993 | −0.849967 | − | 0.526836i | \(-0.823378\pi\) | ||||
−0.849967 | + | 0.526836i | \(0.823378\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 14.8786i | − | 0.900495i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.24518 | 0.376599 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 24.1032i | − | 1.44822i | −0.689683 | − | 0.724112i | \(-0.742250\pi\) | ||
0.689683 | − | 0.724112i | \(-0.257750\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.453419i | 0.0271455i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.5683 | −1.28666 | −0.643330 | − | 0.765589i | \(-0.722448\pi\) | ||||
−0.643330 | + | 0.765589i | \(0.722448\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.64733i | 0.514030i | 0.966407 | + | 0.257015i | \(0.0827390\pi\) | ||||
−0.966407 | + | 0.257015i | \(0.917261\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.75619i | 0.222497i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 11.3611i | − | 0.670625i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.6080 | 1.85930 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 14.8050i | − | 0.867883i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.75977 | 0.570172 | 0.285086 | − | 0.958502i | \(-0.407978\pi\) | ||||
0.285086 | + | 0.958502i | \(0.407978\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 25.8592i | − | 1.50558i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 12.6984i | − | 0.736838i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 40.6938i | 2.35338i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.05454 | −0.233700 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.37584 | 0.366283 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.6264 | 0.780244 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.210125 | −0.0119925 | −0.00599623 | − | 0.999982i | \(-0.501909\pi\) | ||||
−0.00599623 | + | 0.999982i | \(0.501909\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.4520 | 0.651484 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.2791 | 1.43345 | 0.716724 | − | 0.697357i | \(-0.245641\pi\) | ||||
0.716724 | + | 0.697357i | \(0.245641\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 16.9644i | − | 0.958883i | −0.877574 | − | 0.479441i | \(-0.840839\pi\) | ||
0.877574 | − | 0.479441i | \(-0.159161\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.63773i | 0.148619i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.5277 | −1.54611 | −0.773054 | − | 0.634340i | \(-0.781272\pi\) | ||||
−0.773054 | + | 0.634340i | \(0.781272\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.76415 | 0.322731 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.31939i | 0.185270i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.97195i | 0.387929i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.1117 | 0.616365 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 37.9749 | 2.10002 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.29448 | 0.291894 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.1765 | 0.724246 | 0.362123 | − | 0.932130i | \(-0.382052\pi\) | ||||
0.362123 | + | 0.932130i | \(0.382052\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.5793 | −0.634543 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.16983 | −0.501001 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.8326i | 1.13482i | 0.823435 | + | 0.567411i | \(0.192055\pi\) | ||||
−0.823435 | + | 0.567411i | \(0.807945\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.1750i | 1.69319i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.25293i | − | 0.0678502i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2065 | −0.767077 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 23.7432i | − | 1.27829i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.7844 | −1.16945 | −0.584723 | − | 0.811233i | \(-0.698797\pi\) | ||||
−0.584723 | + | 0.811233i | \(0.698797\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4.10963i | − | 0.219983i | −0.993933 | − | 0.109992i | \(-0.964918\pi\) | ||
0.993933 | − | 0.109992i | \(-0.0350824\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 22.5936i | − | 1.20596i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.9921i | 1.54309i | 0.636172 | + | 0.771547i | \(0.280517\pi\) | ||||
−0.636172 | + | 0.771547i | \(0.719483\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.6286 | −1.09485 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.1131i | 0.852797i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.7496i | 0.884009i | 0.897013 | + | 0.442005i | \(0.145733\pi\) | ||||
−0.897013 | + | 0.442005i | \(0.854267\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 4.34273i | − | 0.227934i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.1782 | −1.05617 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.07482 | −0.212704 | −0.106352 | − | 0.994329i | \(-0.533917\pi\) | ||||
−0.106352 | + | 0.994329i | \(0.533917\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 13.3622i | 0.695608i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.46266 | + | 3.16234i | 0.387442 | + | 0.164180i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.39014i | − | 0.123757i | −0.998084 | − | 0.0618783i | \(-0.980291\pi\) | ||
0.998084 | − | 0.0618783i | \(-0.0197091\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −25.2642 | −1.30464 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.2558 | 0.528201 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.6785i | 1.57585i | 0.615773 | + | 0.787924i | \(0.288844\pi\) | ||||
−0.615773 | + | 0.787924i | \(0.711156\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 39.0297 | 1.99955 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.9732i | 1.22497i | 0.790481 | + | 0.612486i | \(0.209830\pi\) | ||||
−0.790481 | + | 0.612486i | \(0.790170\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 7.28884i | − | 0.371474i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.76869 | 0.242406 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2.00795i | − | 0.101807i | −0.998704 | − | 0.0509035i | \(-0.983790\pi\) | ||
0.998704 | − | 0.0509035i | \(-0.0162101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 44.0702i | − | 2.22873i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5.24542i | − | 0.264596i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.7909 | 0.593264 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.6928i | 1.69100i | 0.533979 | + | 0.845498i | \(0.320696\pi\) | ||||
−0.533979 | + | 0.845498i | \(0.679304\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.31114 | −0.115702 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 32.6847i | − | 1.63220i | −0.577912 | − | 0.816099i | \(-0.696132\pi\) | ||
0.577912 | − | 0.816099i | \(-0.303868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2.22927i | − | 0.111048i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.2902i | 1.00823i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 31.9971 | 1.58604 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.7668 | −1.81800 | −0.909000 | − | 0.416797i | \(-0.863153\pi\) | ||||
−0.909000 | + | 0.416797i | \(0.863153\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.626663 | −0.0309110 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.9108 | 0.782921 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.12272 | 0.300552 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.0044 | −1.07756 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 1.73470i | − | 0.0847458i | −0.999102 | − | 0.0423729i | \(-0.986508\pi\) | ||
0.999102 | − | 0.0423729i | \(-0.0134918\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 16.1548i | − | 0.787335i | −0.919253 | − | 0.393667i | \(-0.871206\pi\) | ||
0.919253 | − | 0.393667i | \(-0.128794\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.22702 | −0.302768 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.0336 | −0.583717 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.38415i | 0.405737i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 48.3557i | − | 2.33464i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.470516 | −0.0226640 | −0.0113320 | − | 0.999936i | \(-0.503607\pi\) | ||||
−0.0113320 | + | 0.999936i | \(0.503607\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.49971 | 0.120128 | 0.0600641 | − | 0.998195i | \(-0.480869\pi\) | ||||
0.0600641 | + | 0.998195i | \(0.480869\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.98385 | −0.286904 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.32108 | 0.302378 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.9522 | 1.19090 | 0.595452 | − | 0.803391i | \(-0.296973\pi\) | ||||
0.595452 | + | 0.803391i | \(0.296973\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.54288 | 0.359185 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.11705i | 0.433164i | 0.976264 | + | 0.216582i | \(0.0694909\pi\) | ||||
−0.976264 | + | 0.216582i | \(0.930509\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.95169i | 0.471755i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 24.2890i | 1.14883i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.5551 | −0.875669 | −0.437834 | − | 0.899056i | \(-0.644254\pi\) | ||||
−0.437834 | + | 0.899056i | \(0.644254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 36.9237i | − | 1.73867i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.415731 | 0.0195327 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 12.9686i | − | 0.607977i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.5736i | − | 0.494612i | −0.968937 | − | 0.247306i | \(-0.920455\pi\) | ||
0.968937 | − | 0.247306i | \(-0.0795454\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 24.4682i | 1.14208i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.83054 | 0.0852568 | 0.0426284 | − | 0.999091i | \(-0.486427\pi\) | ||||
0.0426284 | + | 0.999091i | \(0.486427\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 11.2235i | − | 0.521599i | −0.965393 | − | 0.260799i | \(-0.916014\pi\) | ||
0.965393 | − | 0.260799i | \(-0.0839861\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.30069i | 0.0603180i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.55857 | 0.118397 | 0.0591983 | − | 0.998246i | \(-0.481146\pi\) | ||||
0.0591983 | + | 0.998246i | \(0.481146\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.64208i | − | 0.260527i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.2372 | −0.609938 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.1773 | −0.605894 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.72601i | − | 0.0791947i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.77710 | − | 3.71934i | −0.401876 | − | 0.170297i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.1251i | 0.508318i | 0.967162 | + | 0.254159i | \(0.0817987\pi\) | ||||
−0.967162 | + | 0.254159i | \(0.918201\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.9306 | 2.59581 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.6089 | 0.664727 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 12.9044i | − | 0.585958i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.5147 | 1.06555 | 0.532777 | − | 0.846256i | \(-0.321149\pi\) | ||||
0.532777 | + | 0.846256i | \(0.321149\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.13652i | 0.367946i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 20.9397i | − | 0.944995i | −0.881332 | − | 0.472498i | \(-0.843353\pi\) | ||
0.881332 | − | 0.472498i | \(-0.156647\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.1067 | −0.500223 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.57266i | 0.385312i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 12.6925i | − | 0.569338i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0171i | 0.806557i | 0.915077 | + | 0.403279i | \(0.132129\pi\) | ||||
−0.915077 | + | 0.403279i | \(0.867871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −36.4756 | −1.62961 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 8.50820i | − | 0.379362i | −0.981846 | − | 0.189681i | \(-0.939255\pi\) | ||
0.981846 | − | 0.189681i | \(-0.0607453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.55735 | 0.247299 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 59.0496i | − | 2.62249i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.4527i | 0.906549i | 0.891371 | + | 0.453275i | \(0.149744\pi\) | ||||
−0.891371 | + | 0.453275i | \(0.850256\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 12.4154i | − | 0.549225i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.50952 | −0.154949 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.98190 | 0.439855 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.2071 | 0.756768 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −37.5783 | −1.64950 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.1086 | −1.18765 | −0.593824 | − | 0.804595i | \(-0.702382\pi\) | ||||
−0.593824 | + | 0.804595i | \(0.702382\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.3889 | 1.59117 | 0.795587 | − | 0.605839i | \(-0.207162\pi\) | ||||
0.795587 | + | 0.605839i | \(0.207162\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 3.98904i | − | 0.174096i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.41424i | 0.105166i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.9561 | −0.737220 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.7133 | −0.812088 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 65.6962i | − | 2.84562i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.89326i | 0.125087i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.7972 | −1.11323 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20.8432 | −0.897782 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 25.3899 | 1.09160 | 0.545798 | − | 0.837917i | \(-0.316226\pi\) | ||||
0.545798 | + | 0.837917i | \(0.316226\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.5990 | 0.626502 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.0999 | 1.41785 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.6208 | 1.56579 | 0.782896 | − | 0.622153i | \(-0.213742\pi\) | ||||
0.782896 | + | 0.622153i | \(0.213742\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 9.86089i | − | 0.420852i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.59306i | − | 0.0678668i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.25479i | 0.308505i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −33.2167 | −1.40997 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 33.9146i | − | 1.43701i | −0.695523 | − | 0.718504i | \(-0.744827\pi\) | ||
0.695523 | − | 0.718504i | \(-0.255173\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.4456 | −0.991643 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 52.3679i | 2.21097i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1.23922i | − | 0.0522268i | −0.999659 | − | 0.0261134i | \(-0.991687\pi\) | ||
0.999659 | − | 0.0261134i | \(-0.00831309\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.1729i | 1.14317i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.4843 | −0.524292 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 17.4079i | − | 0.729779i | −0.931051 | − | 0.364889i | \(-0.881107\pi\) | ||
0.931051 | − | 0.364889i | \(-0.118893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.41087i | 0.100892i | 0.998727 | + | 0.0504458i | \(0.0160642\pi\) | ||||
−0.998727 | + | 0.0504458i | \(0.983936\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.9236 | −0.748769 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.9102i | 0.454988i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.3394 | 1.09652 | 0.548261 | − | 0.836307i | \(-0.315290\pi\) | ||||
0.548261 | + | 0.836307i | \(0.315290\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 31.3083 | 1.30113 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.76723i | 0.156291i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.2537 | + | 10.2776i | 1.00449 | + | 0.425656i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.2528i | 0.630627i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.00249 | 0.123926 | 0.0619630 | − | 0.998078i | \(-0.480264\pi\) | ||||
0.0619630 | + | 0.998078i | \(0.480264\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.346279 | −0.0142682 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.0416i | 0.618727i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.8221 | 0.813996 | 0.406998 | − | 0.913429i | \(-0.366576\pi\) | ||||
0.406998 | + | 0.913429i | \(0.366576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.0446i | 0.575773i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 2.12752i | − | 0.0870735i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.53257 | 0.348632 | 0.174316 | − | 0.984690i | \(-0.444229\pi\) | ||||
0.174316 | + | 0.984690i | \(0.444229\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 21.0541i | − | 0.858815i | −0.903111 | − | 0.429408i | \(-0.858722\pi\) | ||
0.903111 | − | 0.429408i | \(-0.141278\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.63585i | 0.270233i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 3.78524i | − | 0.153892i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.28330 | 0.173854 | 0.0869269 | − | 0.996215i | \(-0.472295\pi\) | ||||
0.0869269 | + | 0.996215i | \(0.472295\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 3.68179i | − | 0.149194i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.6156 | 1.23857 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 19.3708i | − | 0.782378i | −0.920310 | − | 0.391189i | \(-0.872064\pi\) | ||
0.920310 | − | 0.391189i | \(-0.127936\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 38.3311i | 1.54566i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.6768i | 0.631124i | 0.948905 | + | 0.315562i | \(0.102193\pi\) | ||||
−0.948905 | + | 0.315562i | \(0.897807\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.02148 | −0.0812500 | −0.0406250 | − | 0.999174i | \(-0.512935\pi\) | ||||
−0.0406250 | + | 0.999174i | \(0.512935\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.1840 | 0.890212 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.12315 | −0.245319 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.3909 | −0.535634 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.51123 | −0.299970 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −61.6542 | −2.45831 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.2114i | 0.963842i | 0.876215 | + | 0.481921i | \(0.160061\pi\) | ||||
−0.876215 | + | 0.481921i | \(0.839939\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 50.6087i | − | 2.01152i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34.0193 | 1.35001 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.0851 | −1.46937 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.9281i | 0.590548i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 25.8246i | − | 1.02001i | −0.860172 | − | 0.510004i | \(-0.829644\pi\) | ||
0.860172 | − | 0.510004i | \(-0.170356\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.9182 | 1.53478 | 0.767392 | − | 0.641178i | \(-0.221554\pi\) | ||||
0.767392 | + | 0.641178i | \(0.221554\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.6796 | 0.538632 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.1605 | 0.910534 | 0.455267 | − | 0.890355i | \(-0.349544\pi\) | ||||
0.455267 | + | 0.890355i | \(0.349544\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.7104 | 2.02981 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.800298 | −0.0313661 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.7838 | 0.539400 | 0.269700 | − | 0.962944i | \(-0.413075\pi\) | ||||
0.269700 | + | 0.962944i | \(0.413075\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4.57204i | − | 0.178645i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.6022i | 0.569685i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.0183i | 1.28621i | 0.765777 | + | 0.643106i | \(0.222355\pi\) | ||||
−0.765777 | + | 0.643106i | \(0.777645\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.25752 | −0.243389 | −0.121695 | − | 0.992568i | \(-0.538833\pi\) | ||||
−0.121695 | + | 0.992568i | \(0.538833\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 93.1751i | 3.61862i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.01445 | −0.0781169 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0699i | 0.389907i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25.8182i | 0.998191i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.2486i | 1.05192i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.1994 | −0.701536 | −0.350768 | − | 0.936462i | \(-0.614079\pi\) | ||||
−0.350768 | + | 0.936462i | \(0.614079\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 6.05746i | − | 0.233152i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.18112i | 0.352859i | 0.984313 | + | 0.176429i | \(0.0564548\pi\) | ||||
−0.984313 | + | 0.176429i | \(0.943545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.93992 | 0.304706 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 38.9316i | 1.49186i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.1304 | 1.26770 | 0.633849 | − | 0.773457i | \(-0.281474\pi\) | ||||
0.633849 | + | 0.773457i | \(0.281474\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.546215 | −0.0208698 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.3820i | 0.472401i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 43.1532 | + | 18.2864i | 1.64401 | + | 0.696656i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.4262i | 0.472714i | 0.971666 | + | 0.236357i | \(0.0759536\pi\) | ||||
−0.971666 | + | 0.236357i | \(0.924046\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.27465 | −0.200368 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.1796 | −0.727524 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 71.1471i | 2.69489i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.2364 | −1.14365 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.92468i | − | 0.261542i | −0.991413 | − | 0.130771i | \(-0.958255\pi\) | ||
0.991413 | − | 0.130771i | \(-0.0417452\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 8.84318i | − | 0.333527i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.8630 | −0.672758 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.41937i | 0.128599i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 7.46483i | − | 0.280347i | −0.990127 | − | 0.140174i | \(-0.955234\pi\) | ||
0.990127 | − | 0.140174i | \(-0.0447661\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 8.53261i | − | 0.319998i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.18885 | 0.0819733 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 42.1481i | − | 1.57625i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 52.4951 | 1.96047 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 18.5673i | − | 0.692444i | −0.938153 | − | 0.346222i | \(-0.887464\pi\) | ||
0.938153 | − | 0.346222i | \(-0.112536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.14174i | 0.228730i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 50.6358i | 1.88316i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.74964 | 0.102119 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.5615 | 1.61561 | 0.807803 | − | 0.589453i | \(-0.200657\pi\) | ||||
0.807803 | + | 0.589453i | \(0.200657\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.17311 | −0.265671 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.3909 | 0.939117 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.2011 | −1.30018 | −0.650092 | − | 0.759856i | \(-0.725270\pi\) | ||||
−0.650092 | + | 0.759856i | \(0.725270\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.6377 | 0.798117 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 18.3369i | − | 0.675447i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.7783i | 1.31613i | 0.752963 | + | 0.658063i | \(0.228624\pi\) | ||||
−0.752963 | + | 0.658063i | \(0.771376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.3643 | −0.490949 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.21910 | −0.301530 | −0.150765 | − | 0.988570i | \(-0.548174\pi\) | ||||
−0.150765 | + | 0.988570i | \(0.548174\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.1709i | 0.775643i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 4.43077i | − | 0.162114i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.78019 | −0.0650467 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.71438 | 0.208521 | 0.104260 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104260 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.15081 | −0.114822 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.362362 | 0.0131877 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.56822 | −0.347763 | −0.173881 | − | 0.984767i | \(-0.555631\pi\) | ||||
−0.173881 | + | 0.984767i | \(0.555631\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 47.4791 | 1.72338 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 4.28182i | − | 0.155216i | −0.996984 | − | 0.0776079i | \(-0.975272\pi\) | ||
0.996984 | − | 0.0776079i | \(-0.0247282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.3660i | 0.737298i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 16.5184i | − | 0.597223i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 92.0053 | 3.32212 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 30.1138i | − | 1.08593i | −0.839754 | − | 0.542966i | \(-0.817301\pi\) | ||
0.839754 | − | 0.542966i | \(-0.182699\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.9310 | 1.04192 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 25.6605i | − | 0.922943i | −0.887155 | − | 0.461471i | \(-0.847322\pi\) | ||
0.887155 | − | 0.461471i | \(-0.152678\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 0.597680i | − | 0.0214693i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 20.4378i | − | 0.733203i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.2048 | −0.365624 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 41.2509i | − | 1.47607i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 5.59089i | − | 0.199802i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.5379 | −0.411805 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.4167i | 0.478255i | 0.970988 | + | 0.239127i | \(0.0768614\pi\) | ||||
−0.970988 | + | 0.239127i | \(0.923139\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 45.9047 | 1.63425 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.7192 | −0.594465 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.4818i | 1.72164i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −25.1782 | − | 10.6694i | −0.892977 | − | 0.378403i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.166602i | 0.00590134i | 0.999996 | + | 0.00295067i | \(0.000939229\pi\) | ||||
−0.999996 | + | 0.00295067i | \(0.999061\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.1558 | −1.17297 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.20165 | 0.254458 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 40.3502i | − | 1.42393i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.7335 | 0.448796 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.0878i | 0.777529i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.6632i | 0.691322i | 0.938360 | + | 0.345661i | \(0.112345\pi\) | ||||
−0.938360 | + | 0.345661i | \(0.887655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.10444 | −0.109012 | −0.0545058 | − | 0.998513i | \(-0.517358\pi\) | ||||
−0.0545058 | + | 0.998513i | \(0.517358\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 58.0932i | 2.03742i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.09200i | 0.248422i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.64187i | 0.127413i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.38488 | −0.327934 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.5283i | 1.13525i | 0.823288 | + | 0.567623i | \(0.192137\pi\) | ||||
−0.823288 | + | 0.567623i | \(0.807863\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.04964 | −0.0714460 | −0.0357230 | − | 0.999362i | \(-0.511373\pi\) | ||||
−0.0357230 | + | 0.999362i | \(0.511373\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 12.9644i | − | 0.451364i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 43.0643i | − | 1.49749i | −0.662856 | − | 0.748747i | \(-0.730656\pi\) | ||
0.662856 | − | 0.748747i | \(-0.269344\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.1360i | 1.08140i | 0.841217 | + | 0.540698i | \(0.181840\pi\) | ||||
−0.841217 | + | 0.540698i | \(0.818160\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −50.0362 | −1.73574 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 40.1621 | 1.39154 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −31.7931 | −1.10024 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.21527 | −0.0420060 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.5149 | −1.60587 | −0.802936 | − | 0.596065i | \(-0.796730\pi\) | ||||
−0.802936 | + | 0.596065i | \(0.796730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4621 | −0.912488 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 44.7740i | 1.54210i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 51.4692i | − | 1.77059i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.32901 | 0.0800257 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.9511 | 0.616079 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 55.8985i | 1.91618i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 2.80122i | − | 0.0959120i | −0.998849 | − | 0.0479560i | \(-0.984729\pi\) | ||
0.998849 | − | 0.0479560i | \(-0.0152707\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.36926 | 0.0810271 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.8878 | −1.60166 | −0.800829 | − | 0.598893i | \(-0.795608\pi\) | ||||
−0.800829 | + | 0.598893i | \(0.795608\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.0424 | 0.683837 | 0.341918 | − | 0.939730i | \(-0.388923\pi\) | ||||
0.341918 | + | 0.939730i | \(0.388923\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −23.5846 | −0.803762 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.0913133 | −0.00310834 | −0.00155417 | − | 0.999999i | \(-0.500495\pi\) | ||||
−0.00155417 | + | 0.999999i | \(0.500495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.7542 | −1.11368 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 65.6155i | − | 2.22842i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.5782i | 0.799834i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 32.6257i | − | 1.10548i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.33841 | −0.316057 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 13.5492i | − | 0.458046i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 51.0677 | 1.72443 | 0.862217 | − | 0.506539i | \(-0.169075\pi\) | ||||
0.862217 | + | 0.506539i | \(0.169075\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 20.2604i | − | 0.683367i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.2222i | 1.25405i | 0.779000 | + | 0.627024i | \(0.215727\pi\) | ||||
−0.779000 | + | 0.627024i | \(0.784273\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 53.5955i | 1.80363i | 0.432119 | + | 0.901817i | \(0.357766\pi\) | ||||
−0.432119 | + | 0.901817i | \(0.642234\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −53.6813 | −1.80448 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.0832i | 1.04367i | 0.853046 | + | 0.521835i | \(0.174752\pi\) | ||||
−0.853046 | + | 0.521835i | \(0.825248\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.9316i | 0.702025i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.5742 | −1.35929 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 4.75561i | − | 0.159140i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.4855 | −0.751608 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 84.4767 | 2.82060 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 0.551644i | − | 0.0183983i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.7337 | − | 19.8036i | −1.55693 | − | 0.659755i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.41686i | 0.280096i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.7248 | 0.422988 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.5449 | −0.781795 | −0.390897 | − | 0.920434i | \(-0.627835\pi\) | ||||
−0.390897 | + | 0.920434i | \(0.627835\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 4.02164i | − | 0.133389i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.1271 | −0.832499 | −0.416249 | − | 0.909251i | \(-0.636656\pi\) | ||||
−0.416249 | + | 0.909251i | \(0.636656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.2436i | 0.405203i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 28.2871i | − | 0.935144i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.81312 | 0.0928975 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.3629i | 1.10054i | 0.834987 | + | 0.550270i | \(0.185475\pi\) | ||||
−0.834987 | + | 0.550270i | \(0.814525\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.436200i | 0.0143733i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 73.3953i | − | 2.41583i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.2634 | 0.501858 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 7.22352i | − | 0.237252i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.80316 | 0.288822 | 0.144411 | − | 0.989518i | \(-0.453871\pi\) | ||||
0.144411 | + | 0.989518i | \(0.453871\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.76053i | 0.188794i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 52.4772i | − | 1.71803i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 45.6452i | 1.49276i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.0788 | 0.590609 | 0.295304 | − | 0.955403i | \(-0.404579\pi\) | ||||
0.295304 | + | 0.955403i | \(0.404579\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35.2165 | −1.14925 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.9859 | −1.62949 | −0.814747 | − | 0.579817i | \(-0.803124\pi\) | ||||
−0.814747 | + | 0.579817i | \(0.803124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 64.5052 | 2.10058 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.06975 | −0.229979 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.8364 | −0.709588 | −0.354794 | − | 0.934945i | \(-0.615449\pi\) | ||||
−0.354794 | + | 0.934945i | \(0.615449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 71.7927i | − | 2.33049i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 57.1450i | 1.85305i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.86659 | 0.254824 | 0.127412 | − | 0.991850i | \(-0.459333\pi\) | ||||
0.127412 | + | 0.991850i | \(0.459333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.6227 | −0.505538 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 11.9659i | − | 0.386801i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 0.336080i | − | 0.0108526i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.8801 | 0.996132 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.09374 | 0.0674699 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.2892 | 0.878469 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.5809 | 1.17636 | 0.588181 | − | 0.808729i | \(-0.299844\pi\) | ||||
0.588181 | + | 0.808729i | \(0.299844\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.4731 | 0.464944 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.7963 | 0.699475 | 0.349737 | − | 0.936848i | \(-0.386271\pi\) | ||||
0.349737 | + | 0.936848i | \(0.386271\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 11.8010i | − | 0.378322i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 23.0669i | − | 0.738731i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.3745i | 0.875788i | 0.899027 | + | 0.437894i | \(0.144276\pi\) | ||||
−0.899027 | + | 0.437894i | \(0.855724\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.9003 | −0.636017 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 23.9532i | − | 0.764765i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.64589 | −0.116286 | −0.0581429 | − | 0.998308i | \(-0.518518\pi\) | ||||
−0.0581429 | + | 0.998308i | \(0.518518\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.1106i | 0.417739i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 10.9909i | − | 0.349843i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 23.0206i | − | 0.732011i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.7764 | 0.342324 | 0.171162 | − | 0.985243i | \(-0.445248\pi\) | ||||
0.171162 | + | 0.985243i | \(0.445248\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 27.3532i | − | 0.868028i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.85440i | − | 0.0587884i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 47.9952 | 1.52002 | 0.760011 | − | 0.649910i | \(-0.225194\pi\) | ||||
0.760011 | + | 0.649910i | \(0.225194\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 31.0354i | − | 0.981915i |
(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 | 4028.2.c.a.3497.18 | ✓ | 82 | |
53.52 | even | 2 | inner | 4028.2.c.a.3497.65 | yes | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.c.a.3497.18 | ✓ | 82 | 1.1 | even | 1 | trivial | |
4028.2.c.a.3497.65 | yes | 82 | 53.52 | even | 2 | inner |