Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4900,2,Mod(2549,4900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4900.2549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4900.e (of order \(2\), degree \(1\), not 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: | \(39.1266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.4227136.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 22x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 700) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2549.3 | ||
Root | \(-2.19869i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4900.2549 |
Dual form | 4900.2.e.s.2549.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) | \(2451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 0.364448i | − 0.210414i | −0.994450 | − | 0.105207i | \(-0.966449\pi\) | ||||
0.994450 | − | 0.105207i | \(-0.0335505\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.86718 | 0.955726 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.36445 | 0.411397 | 0.205698 | − | 0.978615i | \(-0.434053\pi\) | ||||
0.205698 | + | 0.978615i | \(0.434053\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.63555i | − 0.730971i | −0.930817 | − | 0.365485i | \(-0.880903\pi\) | ||||
0.930817 | − | 0.365485i | \(-0.119097\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2.23163i | − 0.541249i | −0.962685 | − | 0.270624i | \(-0.912770\pi\) | ||||
0.962685 | − | 0.270624i | \(-0.0872301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.23163 | −1.42963 | −0.714816 | − | 0.699312i | \(-0.753490\pi\) | ||||
−0.714816 | + | 0.699312i | \(0.753490\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 6.59607i | − 1.37538i | −0.726006 | − | 0.687688i | \(-0.758626\pi\) | ||||
0.726006 | − | 0.687688i | \(-0.241374\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2.13828i | − 0.411512i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.50273 | −1.02183 | −0.510916 | − | 0.859631i | \(-0.670694\pi\) | ||||
−0.510916 | + | 0.859631i | \(0.670694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.50273 | −0.808714 | −0.404357 | − | 0.914601i | \(-0.632505\pi\) | ||||
−0.404357 | + | 0.914601i | \(0.632505\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 0.497270i | − 0.0865637i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.09334i | − 0.344144i | −0.985084 | − | 0.172072i | \(-0.944954\pi\) | ||||
0.985084 | − | 0.172072i | \(-0.0550461\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.960522 | −0.153807 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.32497 | −1.45632 | −0.728158 | − | 0.685410i | \(-0.759623\pi\) | ||||
−0.728158 | + | 0.685410i | \(0.759623\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.86718i | 0.284742i | 0.989813 | + | 0.142371i | \(0.0454726\pi\) | ||||
−0.989813 | + | 0.142371i | \(0.954527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.86718i | 1.00168i | 0.865540 | + | 0.500840i | \(0.166976\pi\) | ||||
−0.865540 | + | 0.500840i | \(0.833024\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.813312 | −0.113886 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.1383i | 1.39260i | 0.717751 | + | 0.696300i | \(0.245172\pi\) | ||||
−0.717751 | + | 0.696300i | \(0.754828\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.27110i | 0.300815i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.63555 | −0.212931 | −0.106465 | − | 0.994316i | \(-0.533953\pi\) | ||||
−0.106465 | + | 0.994316i | \(0.533953\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0394782 | −0.00505467 | −0.00252733 | − | 0.999997i | \(-0.500804\pi\) | ||||
−0.00252733 | + | 0.999997i | \(0.500804\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.72890i | − 0.822065i | −0.911621 | − | 0.411033i | \(-0.865168\pi\) | ||||
0.911621 | − | 0.411033i | \(-0.134832\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.40393 | −0.289399 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.27110 | −0.744243 | −0.372122 | − | 0.928184i | \(-0.621370\pi\) | ||||
−0.372122 | + | 0.928184i | \(0.621370\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 4.00000i | − 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.32497 | −0.599106 | −0.299553 | − | 0.954080i | \(-0.596838\pi\) | ||||
−0.299553 | + | 0.954080i | \(0.596838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.82224 | 0.869138 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 14.7738i | − 1.62164i | −0.585296 | − | 0.810819i | \(-0.699022\pi\) | ||||
0.585296 | − | 0.810819i | \(-0.300978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00546i | 0.215008i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.867178 | 0.0919206 | 0.0459603 | − | 0.998943i | \(-0.485365\pi\) | ||||
0.0459603 | + | 0.998943i | \(0.485365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.64101i | 0.170165i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0988i | 1.63459i | 0.576222 | + | 0.817293i | \(0.304526\pi\) | ||||
−0.576222 | + | 0.817293i | \(0.695474\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.91211 | 0.393182 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.6949 | 1.56170 | 0.780849 | − | 0.624719i | \(-0.214787\pi\) | ||||
0.780849 | + | 0.624719i | \(0.214787\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 13.3699i | − 1.31738i | −0.752416 | − | 0.658688i | \(-0.771112\pi\) | ||||
0.752416 | − | 0.658688i | \(-0.228888\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.40393i | 0.522417i | 0.965282 | + | 0.261209i | \(0.0841211\pi\) | ||||
−0.965282 | + | 0.261209i | \(0.915879\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.8277 | 1.51602 | 0.758009 | − | 0.652244i | \(-0.226172\pi\) | ||||
0.758009 | + | 0.652244i | \(0.226172\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.762915 | −0.0724127 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 18.4238i | − 1.73316i | −0.499036 | − | 0.866581i | \(-0.666312\pi\) | ||||
0.499036 | − | 0.866581i | \(-0.333688\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 7.55660i | − 0.698608i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.13828 | −0.830753 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.39847i | 0.306429i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.32497i | 0.472515i | 0.971691 | + | 0.236257i | \(0.0759208\pi\) | ||||
−0.971691 | + | 0.236257i | \(0.924079\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.680489 | 0.0599137 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.2371 | −1.41864 | −0.709320 | − | 0.704886i | \(-0.750998\pi\) | ||||
−0.709320 | + | 0.704886i | \(0.750998\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.40939i | 0.376719i | 0.982100 | + | 0.188360i | \(0.0603170\pi\) | ||||
−0.982100 | + | 0.188360i | \(0.939683\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.3699 | −1.89739 | −0.948695 | − | 0.316192i | \(-0.897596\pi\) | ||||
−0.948695 | + | 0.316192i | \(0.897596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.50273 | 0.210768 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 3.59607i | − 0.300719i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.5082 | −1.84394 | −0.921971 | − | 0.387258i | \(-0.873422\pi\) | ||||
−0.921971 | + | 0.387258i | \(0.873422\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.5027 | 1.09884 | 0.549418 | − | 0.835547i | \(-0.314849\pi\) | ||||
0.549418 | + | 0.835547i | \(0.314849\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 6.39847i | − 0.517285i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5566i | 1.24155i | 0.783988 | + | 0.620776i | \(0.213182\pi\) | ||||
−0.783988 | + | 0.620776i | \(0.786818\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.69488 | 0.293023 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 4.40393i | − 0.344942i | −0.985015 | − | 0.172471i | \(-0.944825\pi\) | ||||
0.985015 | − | 0.172471i | \(-0.0551751\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.09880i | 0.704087i | 0.935984 | + | 0.352043i | \(0.114513\pi\) | ||||
−0.935984 | + | 0.352043i | \(0.885487\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.05387 | 0.465682 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.8672 | −1.36634 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 19.9605i | − 1.51757i | −0.651341 | − | 0.758785i | \(-0.725793\pi\) | ||||
0.651341 | − | 0.758785i | \(-0.274207\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.596074i | 0.0448036i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.1921 | 0.986027 | 0.493014 | − | 0.870022i | \(-0.335895\pi\) | ||||
0.493014 | + | 0.870022i | \(0.335895\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2316 | −0.760511 | −0.380255 | − | 0.924882i | \(-0.624164\pi\) | ||||
−0.380255 | + | 0.924882i | \(0.624164\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0143878i | 0.00106357i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3.04494i | − 0.222668i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.0055 | 1.01340 | 0.506700 | − | 0.862123i | \(-0.330865\pi\) | ||||
0.506700 | + | 0.862123i | \(0.330865\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.4094i | 1.03721i | 0.855014 | + | 0.518605i | \(0.173549\pi\) | ||||
−0.855014 | + | 0.518605i | \(0.826451\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 11.5566i | − 0.823373i | −0.911325 | − | 0.411687i | \(-0.864940\pi\) | ||||
0.911325 | − | 0.411687i | \(-0.135060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.40939 | −0.383461 | −0.191731 | − | 0.981448i | \(-0.561410\pi\) | ||||
−0.191731 | + | 0.981448i | \(0.561410\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.45233 | −0.172974 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 18.9121i | − 1.31448i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.50273 | −0.588146 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.9660 | −0.754929 | −0.377465 | − | 0.926024i | \(-0.623204\pi\) | ||||
−0.377465 | + | 0.926024i | \(0.623204\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.28549i | 0.156599i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.45779 | −0.0985085 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.88157 | −0.395637 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 21.5566i | − 1.44354i | −0.692135 | − | 0.721768i | \(-0.743330\pi\) | ||||
0.692135 | − | 0.721768i | \(-0.256670\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 12.4238i | − 0.824595i | −0.911049 | − | 0.412297i | \(-0.864726\pi\) | ||||
0.911049 | − | 0.412297i | \(-0.135274\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.36445 | −0.552738 | −0.276369 | − | 0.961052i | \(-0.589131\pi\) | ||||
−0.276369 | + | 0.961052i | \(0.589131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 14.0055i | − 0.917528i | −0.888558 | − | 0.458764i | \(-0.848292\pi\) | ||||
0.888558 | − | 0.458764i | \(-0.151708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.94067i | 0.126060i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.9605 | −1.09708 | −0.548542 | − | 0.836123i | \(-0.684817\pi\) | ||||
−0.548542 | + | 0.836123i | \(0.684817\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.3304 | −0.665441 | −0.332721 | − | 0.943025i | \(-0.607967\pi\) | ||||
−0.332721 | + | 0.943025i | \(0.607967\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 9.26564i | − 0.594391i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.4238i | 1.04502i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.38429 | −0.341216 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.5082 | −1.23135 | −0.615673 | − | 0.788002i | \(-0.711116\pi\) | ||||
−0.615673 | + | 0.788002i | \(0.711116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.00000i | − 0.565825i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.4633i | 1.77549i | 0.460337 | + | 0.887744i | \(0.347729\pi\) | ||||
−0.460337 | + | 0.887744i | \(0.652271\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.7773 | −0.976591 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.5621i | 1.76121i | 0.473849 | + | 0.880606i | \(0.342864\pi\) | ||||
−0.473849 | + | 0.880606i | \(0.657136\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 0.316041i | − 0.0193414i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.19761 | −0.560788 | −0.280394 | − | 0.959885i | \(-0.590465\pi\) | ||||
−0.280394 | + | 0.959885i | \(0.590465\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.86172 | −0.234583 | −0.117291 | − | 0.993098i | \(-0.537421\pi\) | ||||
−0.117291 | + | 0.993098i | \(0.537421\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 10.6410i | − 0.639356i | −0.947526 | − | 0.319678i | \(-0.896425\pi\) | ||||
0.947526 | − | 0.319678i | \(-0.103575\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.9101 | −0.772909 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.73436 | 0.103463 | 0.0517315 | − | 0.998661i | \(-0.483526\pi\) | ||||
0.0517315 | + | 0.998661i | \(0.483526\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.91211i | 0.351439i | 0.984440 | + | 0.175719i | \(0.0562251\pi\) | ||||
−0.984440 | + | 0.175719i | \(0.943775\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.0198 | 0.707050 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.86718 | 0.343940 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 24.3250i | − 1.42108i | −0.703657 | − | 0.710540i | \(-0.748451\pi\) | ||||
0.703657 | − | 0.710540i | \(-0.251549\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.91757i | − 0.169295i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.3843 | −1.00536 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 5.71997i | − 0.328604i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 23.5226i | − 1.34250i | −0.741229 | − | 0.671252i | \(-0.765757\pi\) | ||||
0.741229 | − | 0.671252i | \(-0.234243\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.87264 | −0.277195 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.81877 | 0.500067 | 0.250033 | − | 0.968237i | \(-0.419558\pi\) | ||||
0.250033 | + | 0.968237i | \(0.419558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.0933442i | 0.00527612i | 0.999997 | + | 0.00263806i | \(0.000839722\pi\) | ||||
−0.999997 | + | 0.00263806i | \(0.999160\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3.54221i | − 0.198950i | −0.995040 | − | 0.0994751i | \(-0.968284\pi\) | ||||
0.995040 | − | 0.0994751i | \(-0.0317164\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.50819 | −0.420378 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.96945 | 0.109924 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.9067i | 0.773787i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 5.76837i | − 0.318992i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.6499 | −1.08006 | −0.540029 | − | 0.841646i | \(-0.681587\pi\) | ||||
−0.540029 | + | 0.841646i | \(0.681587\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 6.00199i | − 0.328907i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0449i | 1.25534i | 0.778480 | + | 0.627669i | \(0.215991\pi\) | ||||
−0.778480 | + | 0.627669i | \(0.784009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.71451 | −0.364682 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.14374 | −0.332702 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.5621i | 1.21119i | 0.795771 | + | 0.605597i | \(0.207066\pi\) | ||||
−0.795771 | + | 0.605597i | \(0.792934\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3250 | 0.766798 | 0.383399 | − | 0.923583i | \(-0.374753\pi\) | ||||
0.383399 | + | 0.923583i | \(0.374753\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.63555 | −0.300804 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 32.7003i | − 1.74046i | −0.492643 | − | 0.870232i | \(-0.663969\pi\) | ||||
0.492643 | − | 0.870232i | \(-0.336031\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.1581 | 1.38057 | 0.690287 | − | 0.723536i | \(-0.257484\pi\) | ||||
0.690287 | + | 0.723536i | \(0.257484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.8332 | 1.04385 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.33043i | 0.174802i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 25.2316i | − 1.31708i | −0.752546 | − | 0.658540i | \(-0.771174\pi\) | ||||
0.752546 | − | 0.658540i | \(-0.228826\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −26.7363 | −1.39184 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 5.69488i | − 0.294870i | −0.989072 | − | 0.147435i | \(-0.952898\pi\) | ||||
0.989072 | − | 0.147435i | \(-0.0471017\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.5027i | 0.746929i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9660 | −0.768751 | −0.384375 | − | 0.923177i | \(-0.625583\pi\) | ||||
−0.384375 | + | 0.923177i | \(0.625583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.94067 | 0.0994238 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.4776i | 1.25075i | 0.780325 | + | 0.625374i | \(0.215054\pi\) | ||||
−0.780325 | + | 0.625374i | \(0.784946\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.35353i | 0.272135i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.2460 | 1.58424 | 0.792118 | − | 0.610368i | \(-0.208978\pi\) | ||||
0.792118 | + | 0.610368i | \(0.208978\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.7200 | −0.744421 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.91757i | 0.298502i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.13282i | − 0.0568547i | −0.999596 | − | 0.0284274i | \(-0.990950\pi\) | ||||
0.999596 | − | 0.0284274i | \(-0.00904993\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.82224 | −0.190874 | −0.0954368 | − | 0.995435i | \(-0.530425\pi\) | ||||
−0.0954368 | + | 0.995435i | \(0.530425\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8672i | 0.591146i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.85626i | − 0.141580i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.6609 | 1.66442 | 0.832211 | − | 0.554459i | \(-0.187075\pi\) | ||||
0.832211 | + | 0.554459i | \(0.187075\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.60699 | 0.0792671 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.15267i | 0.399238i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.497270 | −0.0242933 | −0.0121466 | − | 0.999926i | \(-0.503866\pi\) | ||||
−0.0121466 | + | 0.999926i | \(0.503866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.28003 | −0.0623850 | −0.0311925 | − | 0.999513i | \(-0.509930\pi\) | ||||
−0.0311925 | + | 0.999513i | \(0.509930\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.6894i | 0.957332i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.31058 | −0.0632755 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.2910 | −0.495698 | −0.247849 | − | 0.968799i | \(-0.579724\pi\) | ||||
−0.247849 | + | 0.968799i | \(0.579724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 29.8870i | − 1.43628i | −0.695899 | − | 0.718139i | \(-0.744994\pi\) | ||||
0.695899 | − | 0.718139i | \(-0.255006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 41.1043i | 1.96628i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.04841 | −0.240947 | −0.120474 | − | 0.992717i | \(-0.538441\pi\) | ||||
−0.120474 | + | 0.992717i | \(0.538441\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 11.7738i | − 0.559392i | −0.960089 | − | 0.279696i | \(-0.909766\pi\) | ||||
0.960089 | − | 0.279696i | \(-0.0902336\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.20307i | 0.387992i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.3843 | 0.537258 | 0.268629 | − | 0.963244i | \(-0.413429\pi\) | ||||
0.268629 | + | 0.963244i | \(0.413429\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.7234 | −0.599123 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 4.92104i | − 0.231211i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 37.2515i | − 1.74255i | −0.490795 | − | 0.871275i | \(-0.663294\pi\) | ||||
0.490795 | − | 0.871275i | \(-0.336706\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.77184 | −0.222731 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.0449 | 0.700713 | 0.350356 | − | 0.936616i | \(-0.386061\pi\) | ||||
0.350356 | + | 0.936616i | \(0.386061\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 31.2031i | − 1.45013i | −0.688681 | − | 0.725065i | \(-0.741810\pi\) | ||||
0.688681 | − | 0.725065i | \(-0.258190\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.7684i | 0.868497i | 0.900793 | + | 0.434248i | \(0.142986\pi\) | ||||
−0.900793 | + | 0.434248i | \(0.857014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.66957 | 0.261240 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.54767i | 0.117142i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.0683i | 1.33094i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.714508 | −0.0326467 | −0.0163234 | − | 0.999867i | \(-0.505196\pi\) | ||||
−0.0163234 | + | 0.999867i | \(0.505196\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.51712 | −0.251559 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 16.6949i | − 0.756517i | −0.925700 | − | 0.378259i | \(-0.876523\pi\) | ||||
0.925700 | − | 0.378259i | \(-0.123477\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.60500 | −0.0725807 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.19761 | 0.279694 | 0.139847 | − | 0.990173i | \(-0.455339\pi\) | ||||
0.139847 | + | 0.990173i | \(0.455339\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.2800i | 0.553065i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.4687 | −0.647708 | −0.323854 | − | 0.946107i | \(-0.604979\pi\) | ||||
−0.323854 | + | 0.946107i | \(0.604979\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.31604 | 0.148150 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.6949i | 1.36862i | 0.729193 | + | 0.684308i | \(0.239896\pi\) | ||||
−0.729193 | + | 0.684308i | \(0.760104\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 2.20632i | − 0.0979861i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 44.4742 | 1.97128 | 0.985641 | − | 0.168852i | \(-0.0540059\pi\) | ||||
0.985641 | + | 0.168852i | \(0.0540059\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.3250i | 0.588312i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.36991i | 0.412088i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.27457 | −0.319318 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6499 | 0.554204 | 0.277102 | − | 0.960841i | \(-0.410626\pi\) | ||||
0.277102 | + | 0.960841i | \(0.410626\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 10.2711i | − 0.449124i | −0.974460 | − | 0.224562i | \(-0.927905\pi\) | ||||
0.974460 | − | 0.224562i | \(-0.0720951\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.0484i | 0.437715i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.5082 | −0.891660 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.68942 | −0.203503 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.5764i | 1.06452i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 4.80785i | − 0.207474i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.13828 | −0.0919319 | −0.0459660 | − | 0.998943i | \(-0.514637\pi\) | ||||
−0.0459660 | + | 0.998943i | \(0.514637\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.72890i | 0.160022i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 32.0198i | − 1.36907i | −0.728980 | − | 0.684535i | \(-0.760005\pi\) | ||||
0.728980 | − | 0.684535i | \(-0.239995\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.113191 | −0.00483088 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.2910 | 1.46084 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 8.33043i | − 0.352972i | −0.984303 | − | 0.176486i | \(-0.943527\pi\) | ||||
0.984303 | − | 0.176486i | \(-0.0564730\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.92104 | 0.208138 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.10972 | −0.0468525 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 19.4633i | − 0.820278i | −0.912023 | − | 0.410139i | \(-0.865480\pi\) | ||||
0.912023 | − | 0.410139i | \(-0.134520\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.8925 | −0.792014 | −0.396007 | − | 0.918247i | \(-0.629604\pi\) | ||||
−0.396007 | + | 0.918247i | \(0.629604\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.6301 | −0.779645 | −0.389823 | − | 0.920890i | \(-0.627464\pi\) | ||||
−0.389823 | + | 0.920890i | \(0.627464\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 5.10426i | − 0.213234i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.5926i | 0.774020i | 0.922075 | + | 0.387010i | \(0.126492\pi\) | ||||
−0.922075 | + | 0.387010i | \(0.873508\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.25147 | 0.218244 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.8332i | 0.572911i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 10.1383i | − 0.418452i | −0.977867 | − | 0.209226i | \(-0.932906\pi\) | ||||
0.977867 | − | 0.209226i | \(-0.0670944\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0593 | 1.15616 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.21178 | −0.173249 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 17.0055i | − 0.698331i | −0.937061 | − | 0.349165i | \(-0.886465\pi\) | ||||
0.937061 | − | 0.349165i | \(-0.113535\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.97144i | 0.0806857i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.18669 | 0.334499 | 0.167250 | − | 0.985915i | \(-0.446511\pi\) | ||||
0.167250 | + | 0.985915i | \(0.446511\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.3359 | 1.44138 | 0.720690 | − | 0.693257i | \(-0.243825\pi\) | ||||
0.720690 | + | 0.693257i | \(0.243825\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 19.2929i | − 0.785669i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 28.2316i | − 1.14589i | −0.819595 | − | 0.572943i | \(-0.805802\pi\) | ||||
0.819595 | − | 0.572943i | \(-0.194198\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0988 | 0.732199 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 31.1581i | − 1.25846i | −0.777217 | − | 0.629232i | \(-0.783369\pi\) | ||||
0.777217 | − | 0.629232i | \(-0.216631\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 39.1527i | − 1.57623i | −0.615530 | − | 0.788114i | \(-0.711058\pi\) | ||||
0.615530 | − | 0.788114i | \(-0.288942\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.3843 | −1.58299 | −0.791494 | − | 0.611177i | \(-0.790696\pi\) | ||||
−0.791494 | + | 0.611177i | \(0.790696\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.1043 | −0.565985 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.09880i | 0.123754i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.67156 | −0.186267 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.7003 | 0.903686 | 0.451843 | − | 0.892097i | \(-0.350767\pi\) | ||||
0.451843 | + | 0.892097i | \(0.350767\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.99653i | 0.158848i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.9804 | −0.711292 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.41285 | 0.332288 | 0.166144 | − | 0.986102i | \(-0.446868\pi\) | ||||
0.166144 | + | 0.986102i | \(0.446868\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.7398i | 1.17282i | 0.810013 | + | 0.586412i | \(0.199460\pi\) | ||||
−0.810013 | + | 0.586412i | \(0.800540\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 21.6859i | − 0.852563i | −0.904591 | − | 0.426281i | \(-0.859823\pi\) | ||||
0.904591 | − | 0.426281i | \(-0.140177\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.23163 | −0.0875990 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.0702i | 1.17674i | 0.808592 | + | 0.588370i | \(0.200230\pi\) | ||||
−0.808592 | + | 0.588370i | \(0.799770\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 11.4687i | − 0.447437i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.37537 | −0.0925311 | −0.0462656 | − | 0.998929i | \(-0.514732\pi\) | ||||
−0.0462656 | + | 0.998929i | \(0.514732\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.4633 | 0.562555 | 0.281278 | − | 0.959626i | \(-0.409242\pi\) | ||||
0.281278 | + | 0.959626i | \(0.409242\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.14353i | 0.0832476i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.2964i | 1.40540i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.85626 | −0.303741 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.0538660 | −0.00207947 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.99653i | 0.346791i | 0.984852 | + | 0.173395i | \(0.0554738\pi\) | ||||
−0.984852 | + | 0.173395i | \(0.944526\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.49181i | 0.287934i | 0.989583 | + | 0.143967i | \(0.0459859\pi\) | ||||
−0.989583 | + | 0.143967i | \(0.954014\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.52782 | −0.173506 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 42.3250i | − 1.61952i | −0.586761 | − | 0.809760i | \(-0.699597\pi\) | ||||
0.586761 | − | 0.809760i | \(-0.300403\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.04841i | 0.116304i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.7200 | 1.01795 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.6465 | −1.08976 | −0.544882 | − | 0.838513i | \(-0.683425\pi\) | ||||
−0.544882 | + | 0.838513i | \(0.683425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.8098i | 0.788229i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.10426 | −0.193061 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.4292 | −0.771601 | −0.385801 | − | 0.922582i | \(-0.626075\pi\) | ||||
−0.385801 | + | 0.922582i | \(0.626075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.0449i | 0.491999i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.8277 | −1.08265 | −0.541323 | − | 0.840814i | \(-0.682077\pi\) | ||||
−0.541323 | + | 0.840814i | \(0.682077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.2676 | −0.572581 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.7003i | 1.11229i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.18123i | 0.230842i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.3106 | 1.16769 | 0.583844 | − | 0.811866i | \(-0.301548\pi\) | ||||
0.583844 | + | 0.811866i | \(0.301548\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.76490i | 0.140018i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 8.17230i | − 0.303094i | −0.988450 | − | 0.151547i | \(-0.951575\pi\) | ||||
0.988450 | − | 0.151547i | \(-0.0484255\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.0899 | 0.744069 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.16684 | 0.154116 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.4183i | 0.791103i | 0.918444 | + | 0.395552i | \(0.129447\pi\) | ||||
−0.918444 | + | 0.395552i | \(0.870553\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 9.18123i | − 0.338195i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.35006 | −0.160020 | −0.0800098 | − | 0.996794i | \(-0.525495\pi\) | ||||
−0.0800098 | + | 0.996794i | \(0.525495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.98561 | 0.219887 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.53328i | 0.239683i | 0.992793 | + | 0.119841i | \(0.0382386\pi\) | ||||
−0.992793 | + | 0.119841i | \(0.961761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 42.3592i | − 1.54984i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.4831 | 1.25831 | 0.629153 | − | 0.777281i | \(-0.283402\pi\) | ||||
0.629153 | + | 0.777281i | \(0.283402\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.10972i | 0.259093i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.2425i | 1.60802i | 0.594614 | + | 0.804011i | \(0.297305\pi\) | ||||
−0.594614 | + | 0.804011i | \(0.702695\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.28003 | −0.119058 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.8188 | 0.863430 | 0.431715 | − | 0.902010i | \(-0.357909\pi\) | ||||
0.431715 | + | 0.902010i | \(0.357909\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.31058i | 0.155646i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.158128 | −0.00570225 | −0.00285113 | − | 0.999996i | \(-0.500908\pi\) | ||||
−0.00285113 | + | 0.999996i | \(0.500908\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3734 | 0.373588 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.7991i | 0.640191i | 0.947385 | + | 0.320095i | \(0.103715\pi\) | ||||
−0.947385 | + | 0.320095i | \(0.896285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58.1097 | 2.08200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.55660 | −0.306179 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.7664i | 0.420496i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 41.5226i | − 1.48012i | −0.672541 | − | 0.740060i | \(-0.734797\pi\) | ||||
0.672541 | − | 0.740060i | \(-0.265203\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.4094 | 0.370584 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.104047i | 0.00369481i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0933i | 0.888852i | 0.895816 | + | 0.444426i | \(0.146592\pi\) | ||||
−0.895816 | + | 0.444426i | \(0.853408\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.3250 | 0.542158 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.48635 | 0.0878509 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 5.45779i | − 0.192601i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.35205i | 0.117998i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.6949 | −0.446328 | −0.223164 | − | 0.974781i | \(-0.571639\pi\) | ||||
−0.223164 | + | 0.974781i | \(0.571639\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.9749 | −0.631184 | −0.315592 | − | 0.948895i | \(-0.602203\pi\) | ||||
−0.315592 | + | 0.948895i | \(0.602203\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.40740i | 0.0493595i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 11.6356i | − 0.407076i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.0683 | 0.700387 | 0.350193 | − | 0.936677i | \(-0.386116\pi\) | ||||
0.350193 | + | 0.936677i | \(0.386116\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 10.6105i | − 0.369857i | −0.982752 | − | 0.184929i | \(-0.940795\pi\) | ||||
0.982752 | − | 0.184929i | \(-0.0592054\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 34.7793i | − 1.20939i | −0.796455 | − | 0.604697i | \(-0.793294\pi\) | ||||
0.796455 | − | 0.604697i | \(-0.206706\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.2282 | −0.910942 | −0.455471 | − | 0.890251i | \(-0.650529\pi\) | ||||
−0.455471 | + | 0.890251i | \(0.650529\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.87810 | −0.134530 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.62810i | 0.332796i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.9210 | 1.17108 | 0.585542 | − | 0.810642i | \(-0.300882\pi\) | ||||
0.585542 | + | 0.810642i | \(0.300882\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.28003 | 0.0441391 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 0.632082i | − 0.0217701i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.15466 | 0.0739477 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.8079 | −0.473327 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 57.6698i | 1.97458i | 0.158942 | + | 0.987288i | \(0.449192\pi\) | ||||
−0.158942 | + | 0.987288i | \(0.550808\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.4039i | 1.20938i | 0.796463 | + | 0.604688i | \(0.206702\pi\) | ||||
−0.796463 | + | 0.604688i | \(0.793298\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.4434 | −0.458683 | −0.229342 | − | 0.973346i | \(-0.573657\pi\) | ||||
−0.229342 | + | 0.973346i | \(0.573657\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 7.06478i | − 0.240488i | −0.992744 | − | 0.120244i | \(-0.961632\pi\) | ||||
0.992744 | − | 0.120244i | \(-0.0383677\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 4.38061i | − 0.148773i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.26564 | −0.246470 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.7344 | −0.600906 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.1581i | 1.56222i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 15.0055i | − 0.506698i | −0.967375 | − | 0.253349i | \(-0.918468\pi\) | ||||
0.967375 | − | 0.253349i | \(-0.0815322\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.86519 | −0.299015 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.3699 | 1.32641 | 0.663203 | − | 0.748440i | \(-0.269197\pi\) | ||||
0.663203 | + | 0.748440i | \(0.269197\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 58.2229i | 1.95936i | 0.200574 | + | 0.979679i | \(0.435719\pi\) | ||||
−0.200574 | + | 0.979679i | \(0.564281\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.2460i | 0.847678i | 0.905738 | + | 0.423839i | \(0.139318\pi\) | ||||
−0.905738 | + | 0.423839i | \(0.860682\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.6730 | 0.357560 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 42.7937i | − 1.43204i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.33567i | 0.211542i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.7773 | 0.826369 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.6248 | 0.753743 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 27.1867i | − 0.902719i | −0.892342 | − | 0.451360i | \(-0.850939\pi\) | ||||
0.892342 | − | 0.451360i | \(-0.149061\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 45.0000 | 1.49256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.7882 | −1.35137 | −0.675687 | − | 0.737189i | \(-0.736153\pi\) | ||||
−0.675687 | + | 0.737189i | \(0.736153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 20.1581i | − 0.667137i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.0737 | 1.55282 | 0.776409 | − | 0.630229i | \(-0.217039\pi\) | ||||
0.776409 | + | 0.630229i | \(0.217039\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.57276 | −0.282482 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.5278i | 0.544020i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 38.3339i | − 1.25905i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.9911 | 0.590268 | 0.295134 | − | 0.955456i | \(-0.404636\pi\) | ||||
0.295134 | + | 0.955456i | \(0.404636\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 3.21398i | − 0.105221i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 37.7003i | − 1.23162i | −0.787896 | − | 0.615808i | \(-0.788830\pi\) | ||||
0.787896 | − | 0.615808i | \(-0.211170\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.0340191 | 0.00111017 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.83316 | −0.157556 | −0.0787782 | − | 0.996892i | \(-0.525102\pi\) | ||||
−0.0787782 | + | 0.996892i | \(0.525102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 61.5082i | 2.00298i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.83663i | − 0.0921780i | −0.998937 | − | 0.0460890i | \(-0.985324\pi\) | ||||
0.998937 | − | 0.0460890i | \(-0.0146758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.5422 | −0.342215 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.29095 | −0.0418619 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 17.7991i | − 0.576571i | −0.957545 | − | 0.288285i | \(-0.906915\pi\) | ||||
0.957545 | − | 0.288285i | \(-0.0930852\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.73634i | 0.0884535i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.7254 | −0.345982 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.4940i | 0.499288i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 15.1581i | − 0.487453i | −0.969844 | − | 0.243726i | \(-0.921630\pi\) | ||||
0.969844 | − | 0.243726i | \(-0.0783698\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.06825 | 0.162816 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.3843 | 1.52063 | 0.760317 | − | 0.649552i | \(-0.225044\pi\) | ||||
0.760317 | + | 0.649552i | \(0.225044\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.7200i | 0.758869i | 0.925219 | + | 0.379434i | \(0.123881\pi\) | ||||
−0.925219 | + | 0.379434i | \(0.876119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.18322 | 0.0378158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.3808 | 1.44890 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.4543i | 1.09892i | 0.835519 | + | 0.549461i | \(0.185167\pi\) | ||||
−0.835519 | + | 0.549461i | \(0.814833\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.3160 | 0.391627 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.6609 | −1.32340 | −0.661700 | − | 0.749768i | \(-0.730165\pi\) | ||||
−0.661700 | + | 0.749768i | \(0.730165\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.16138i | 0.227260i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 24.7882i | − 0.785051i | −0.919741 | − | 0.392525i | \(-0.871601\pi\) | ||||
0.919741 | − | 0.392525i | \(-0.128399\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.47616 | −0.141619 |
(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 | 4900.2.e.s.2549.3 | 6 | ||
5.2 | odd | 4 | 4900.2.a.bb.1.2 | 3 | |||
5.3 | odd | 4 | 4900.2.a.bd.1.2 | 3 | |||
5.4 | even | 2 | inner | 4900.2.e.s.2549.4 | 6 | ||
7.3 | odd | 6 | 700.2.r.d.149.4 | 12 | |||
7.5 | odd | 6 | 700.2.r.d.249.3 | 12 | |||
7.6 | odd | 2 | 4900.2.e.t.2549.4 | 6 | |||
35.3 | even | 12 | 700.2.i.e.401.2 | yes | 6 | ||
35.12 | even | 12 | 700.2.i.d.501.2 | yes | 6 | ||
35.13 | even | 4 | 4900.2.a.ba.1.2 | 3 | |||
35.17 | even | 12 | 700.2.i.d.401.2 | ✓ | 6 | ||
35.19 | odd | 6 | 700.2.r.d.249.4 | 12 | |||
35.24 | odd | 6 | 700.2.r.d.149.3 | 12 | |||
35.27 | even | 4 | 4900.2.a.bc.1.2 | 3 | |||
35.33 | even | 12 | 700.2.i.e.501.2 | yes | 6 | ||
35.34 | odd | 2 | 4900.2.e.t.2549.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
700.2.i.d.401.2 | ✓ | 6 | 35.17 | even | 12 | ||
700.2.i.d.501.2 | yes | 6 | 35.12 | even | 12 | ||
700.2.i.e.401.2 | yes | 6 | 35.3 | even | 12 | ||
700.2.i.e.501.2 | yes | 6 | 35.33 | even | 12 | ||
700.2.r.d.149.3 | 12 | 35.24 | odd | 6 | |||
700.2.r.d.149.4 | 12 | 7.3 | odd | 6 | |||
700.2.r.d.249.3 | 12 | 7.5 | odd | 6 | |||
700.2.r.d.249.4 | 12 | 35.19 | odd | 6 | |||
4900.2.a.ba.1.2 | 3 | 35.13 | even | 4 | |||
4900.2.a.bb.1.2 | 3 | 5.2 | odd | 4 | |||
4900.2.a.bc.1.2 | 3 | 35.27 | even | 4 | |||
4900.2.a.bd.1.2 | 3 | 5.3 | odd | 4 | |||
4900.2.e.s.2549.3 | 6 | 1.1 | even | 1 | trivial | ||
4900.2.e.s.2549.4 | 6 | 5.4 | even | 2 | inner | ||
4900.2.e.t.2549.3 | 6 | 35.34 | odd | 2 | |||
4900.2.e.t.2549.4 | 6 | 7.6 | odd | 2 |