Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2850,2,Mod(799,2850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2850, 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("2850.799");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2850.d (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: | \(22.7573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2850.799 |
Dual form | 2850.2.d.u.799.3 |
$q$-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 \(\left(\mathbb{Z}/2850\mathbb{Z}\right)^\times\).
\(n\) | \(1027\) | \(1351\) | \(1901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.732051i | 0.276689i | 0.990384 | + | 0.138345i | \(0.0441781\pi\) | ||||
−0.990384 | + | 0.138345i | \(0.955822\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.19615 | −1.56670 | −0.783349 | − | 0.621582i | \(-0.786490\pi\) | ||||
−0.783349 | + | 0.621582i | \(0.786490\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 1.26795i | 0.351666i | 0.984420 | + | 0.175833i | \(0.0562618\pi\) | ||||
−0.984420 | + | 0.175833i | \(0.943738\pi\) | |||||||
\(14\) | 0.732051 | 0.195649 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 0.732051i | − 0.177548i | −0.996052 | − | 0.0887742i | \(-0.971705\pi\) | ||||
0.996052 | − | 0.0887742i | \(-0.0282950\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.732051 | 0.159747 | ||||||||
\(22\) | 5.19615i | 1.10782i | ||||||||
\(23\) | 1.53590i | 0.320257i | 0.987096 | + | 0.160128i | \(0.0511909\pi\) | ||||
−0.987096 | + | 0.160128i | \(0.948809\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.26795 | 0.248665 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 0.732051i | − 0.138345i | ||||||||
\(29\) | −1.19615 | −0.222120 | −0.111060 | − | 0.993814i | \(-0.535425\pi\) | ||||
−0.111060 | + | 0.993814i | \(0.535425\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.92820 | 1.42395 | 0.711974 | − | 0.702206i | \(-0.247802\pi\) | ||||
0.711974 | + | 0.702206i | \(0.247802\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 5.19615i | 0.904534i | ||||||||
\(34\) | −0.732051 | −0.125546 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − 4.92820i | − 0.810192i | −0.914274 | − | 0.405096i | \(-0.867238\pi\) | ||||
0.914274 | − | 0.405096i | \(-0.132762\pi\) | |||||||
\(38\) | 1.00000i | 0.162221i | ||||||||
\(39\) | 1.26795 | 0.203034 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | − 0.732051i | − 0.112958i | ||||||||
\(43\) | 5.26795i | 0.803355i | 0.915781 | + | 0.401677i | \(0.131573\pi\) | ||||
−0.915781 | + | 0.401677i | \(0.868427\pi\) | |||||||
\(44\) | 5.19615 | 0.783349 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.53590 | 0.226456 | ||||||||
\(47\) | − 3.46410i | − 0.505291i | −0.967559 | − | 0.252646i | \(-0.918699\pi\) | ||||
0.967559 | − | 0.252646i | \(-0.0813007\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | 6.46410 | 0.923443 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.732051 | −0.102508 | ||||||||
\(52\) | − 1.26795i | − 0.175833i | ||||||||
\(53\) | 12.6603i | 1.73902i | 0.493916 | + | 0.869510i | \(0.335565\pi\) | ||||
−0.493916 | + | 0.869510i | \(0.664435\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.732051 | −0.0978244 | ||||||||
\(57\) | 1.00000i | 0.132453i | ||||||||
\(58\) | 1.19615i | 0.157063i | ||||||||
\(59\) | 8.19615 | 1.06705 | 0.533524 | − | 0.845785i | \(-0.320867\pi\) | ||||
0.533524 | + | 0.845785i | \(0.320867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7321 | 1.50214 | 0.751068 | − | 0.660225i | \(-0.229539\pi\) | ||||
0.751068 | + | 0.660225i | \(0.229539\pi\) | |||||||
\(62\) | − 7.92820i | − 1.00688i | ||||||||
\(63\) | − 0.732051i | − 0.0922297i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.19615 | 0.639602 | ||||||||
\(67\) | − 5.19615i | − 0.634811i | −0.948290 | − | 0.317406i | \(-0.897188\pi\) | ||||
0.948290 | − | 0.317406i | \(-0.102812\pi\) | |||||||
\(68\) | 0.732051i | 0.0887742i | ||||||||
\(69\) | 1.53590 | 0.184900 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.196152 | 0.0232790 | 0.0116395 | − | 0.999932i | \(-0.496295\pi\) | ||||
0.0116395 | + | 0.999932i | \(0.496295\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | 7.53590i | 0.882010i | 0.897505 | + | 0.441005i | \(0.145378\pi\) | ||||
−0.897505 | + | 0.441005i | \(0.854622\pi\) | |||||||
\(74\) | −4.92820 | −0.572892 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | − 3.80385i | − 0.433489i | ||||||||
\(78\) | − 1.26795i | − 0.143567i | ||||||||
\(79\) | 7.92820 | 0.891993 | 0.445996 | − | 0.895035i | \(-0.352849\pi\) | ||||
0.445996 | + | 0.895035i | \(0.352849\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 0.660254i | − 0.0724723i | −0.999343 | − | 0.0362361i | \(-0.988463\pi\) | ||||
0.999343 | − | 0.0362361i | \(-0.0115368\pi\) | |||||||
\(84\) | −0.732051 | −0.0798733 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.26795 | 0.568058 | ||||||||
\(87\) | 1.19615i | 0.128241i | ||||||||
\(88\) | − 5.19615i | − 0.553912i | ||||||||
\(89\) | 9.92820 | 1.05239 | 0.526194 | − | 0.850365i | \(-0.323619\pi\) | ||||
0.526194 | + | 0.850365i | \(0.323619\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.928203 | −0.0973021 | ||||||||
\(92\) | − 1.53590i | − 0.160128i | ||||||||
\(93\) | − 7.92820i | − 0.822116i | ||||||||
\(94\) | −3.46410 | −0.357295 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 7.12436i | 0.723369i | 0.932301 | + | 0.361684i | \(0.117798\pi\) | ||||
−0.932301 | + | 0.361684i | \(0.882202\pi\) | |||||||
\(98\) | − 6.46410i | − 0.652973i | ||||||||
\(99\) | 5.19615 | 0.522233 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.66025 | 0.563216 | 0.281608 | − | 0.959529i | \(-0.409132\pi\) | ||||
0.281608 | + | 0.959529i | \(0.409132\pi\) | |||||||
\(102\) | 0.732051i | 0.0724838i | ||||||||
\(103\) | 12.8564i | 1.26678i | 0.773833 | + | 0.633390i | \(0.218337\pi\) | ||||
−0.773833 | + | 0.633390i | \(0.781663\pi\) | |||||||
\(104\) | −1.26795 | −0.124333 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.6603 | 1.22967 | ||||||||
\(107\) | 6.19615i | 0.599005i | 0.954096 | + | 0.299502i | \(0.0968206\pi\) | ||||
−0.954096 | + | 0.299502i | \(0.903179\pi\) | |||||||
\(108\) | − 1.00000i | − 0.0962250i | ||||||||
\(109\) | −10.3923 | −0.995402 | −0.497701 | − | 0.867349i | \(-0.665822\pi\) | ||||
−0.497701 | + | 0.867349i | \(0.665822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.92820 | −0.467764 | ||||||||
\(112\) | 0.732051i | 0.0691723i | ||||||||
\(113\) | 20.3205i | 1.91159i | 0.294030 | + | 0.955796i | \(0.405004\pi\) | ||||
−0.294030 | + | 0.955796i | \(0.594996\pi\) | |||||||
\(114\) | 1.00000 | 0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.19615 | 0.111060 | ||||||||
\(117\) | − 1.26795i | − 0.117222i | ||||||||
\(118\) | − 8.19615i | − 0.754517i | ||||||||
\(119\) | 0.535898 | 0.0491257 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.0000 | 1.45455 | ||||||||
\(122\) | − 11.7321i | − 1.06217i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.92820 | −0.711974 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.732051 | −0.0652163 | ||||||||
\(127\) | − 11.3923i | − 1.01090i | −0.862855 | − | 0.505452i | \(-0.831326\pi\) | ||||
0.862855 | − | 0.505452i | \(-0.168674\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 5.26795 | 0.463817 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.803848 | −0.0702325 | −0.0351162 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351162 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(132\) | − 5.19615i | − 0.452267i | ||||||||
\(133\) | − 0.732051i | − 0.0634769i | ||||||||
\(134\) | −5.19615 | −0.448879 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.732051 | 0.0627728 | ||||||||
\(137\) | 4.39230i | 0.375260i | 0.982240 | + | 0.187630i | \(0.0600806\pi\) | ||||
−0.982240 | + | 0.187630i | \(0.939919\pi\) | |||||||
\(138\) | − 1.53590i | − 0.130744i | ||||||||
\(139\) | 14.1962 | 1.20410 | 0.602051 | − | 0.798458i | \(-0.294350\pi\) | ||||
0.602051 | + | 0.798458i | \(0.294350\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.46410 | −0.291730 | ||||||||
\(142\) | − 0.196152i | − 0.0164607i | ||||||||
\(143\) | − 6.58846i | − 0.550954i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.53590 | 0.623675 | ||||||||
\(147\) | − 6.46410i | − 0.533150i | ||||||||
\(148\) | 4.92820i | 0.405096i | ||||||||
\(149\) | −5.85641 | −0.479776 | −0.239888 | − | 0.970801i | \(-0.577111\pi\) | ||||
−0.239888 | + | 0.970801i | \(0.577111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.3923 | −0.845714 | −0.422857 | − | 0.906196i | \(-0.638973\pi\) | ||||
−0.422857 | + | 0.906196i | \(0.638973\pi\) | |||||||
\(152\) | − 1.00000i | − 0.0811107i | ||||||||
\(153\) | 0.732051i | 0.0591828i | ||||||||
\(154\) | −3.80385 | −0.306523 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.26795 | −0.101517 | ||||||||
\(157\) | 5.85641i | 0.467392i | 0.972310 | + | 0.233696i | \(0.0750821\pi\) | ||||
−0.972310 | + | 0.233696i | \(0.924918\pi\) | |||||||
\(158\) | − 7.92820i | − 0.630734i | ||||||||
\(159\) | 12.6603 | 1.00402 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.12436 | −0.0886116 | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 10.0000i | − 0.783260i | −0.920123 | − | 0.391630i | \(-0.871911\pi\) | ||||
0.920123 | − | 0.391630i | \(-0.128089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.660254 | −0.0512457 | ||||||||
\(167\) | − 2.00000i | − 0.154765i | −0.997001 | − | 0.0773823i | \(-0.975344\pi\) | ||||
0.997001 | − | 0.0773823i | \(-0.0246562\pi\) | |||||||
\(168\) | 0.732051i | 0.0564789i | ||||||||
\(169\) | 11.3923 | 0.876331 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | − 5.26795i | − 0.401677i | ||||||||
\(173\) | 5.33975i | 0.405973i | 0.979181 | + | 0.202987i | \(0.0650648\pi\) | ||||
−0.979181 | + | 0.202987i | \(0.934935\pi\) | |||||||
\(174\) | 1.19615 | 0.0906801 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.19615 | −0.391675 | ||||||||
\(177\) | − 8.19615i | − 0.616061i | ||||||||
\(178\) | − 9.92820i | − 0.744150i | ||||||||
\(179\) | −17.8564 | −1.33465 | −0.667325 | − | 0.744766i | \(-0.732561\pi\) | ||||
−0.667325 | + | 0.744766i | \(0.732561\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.7321 | 1.68966 | 0.844830 | − | 0.535035i | \(-0.179702\pi\) | ||||
0.844830 | + | 0.535035i | \(0.179702\pi\) | |||||||
\(182\) | 0.928203i | 0.0688030i | ||||||||
\(183\) | − 11.7321i | − 0.867258i | ||||||||
\(184\) | −1.53590 | −0.113228 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.92820 | −0.581324 | ||||||||
\(187\) | 3.80385i | 0.278165i | ||||||||
\(188\) | 3.46410i | 0.252646i | ||||||||
\(189\) | −0.732051 | −0.0532489 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.5359 | −1.26885 | −0.634427 | − | 0.772983i | \(-0.718764\pi\) | ||||
−0.634427 | + | 0.772983i | \(0.718764\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 0.196152i | 0.0141194i | 0.999975 | + | 0.00705968i | \(0.00224718\pi\) | ||||
−0.999975 | + | 0.00705968i | \(0.997753\pi\) | |||||||
\(194\) | 7.12436 | 0.511499 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.46410 | −0.461722 | ||||||||
\(197\) | − 17.6603i | − 1.25824i | −0.777308 | − | 0.629121i | \(-0.783415\pi\) | ||||
0.777308 | − | 0.629121i | \(-0.216585\pi\) | |||||||
\(198\) | − 5.19615i | − 0.369274i | ||||||||
\(199\) | −16.9282 | −1.20001 | −0.600004 | − | 0.799997i | \(-0.704834\pi\) | ||||
−0.600004 | + | 0.799997i | \(0.704834\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.19615 | −0.366508 | ||||||||
\(202\) | − 5.66025i | − 0.398254i | ||||||||
\(203\) | − 0.875644i | − 0.0614582i | ||||||||
\(204\) | 0.732051 | 0.0512538 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.8564 | 0.895748 | ||||||||
\(207\) | − 1.53590i | − 0.106752i | ||||||||
\(208\) | 1.26795i | 0.0879165i | ||||||||
\(209\) | 5.19615 | 0.359425 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.19615 | −0.220032 | −0.110016 | − | 0.993930i | \(-0.535090\pi\) | ||||
−0.110016 | + | 0.993930i | \(0.535090\pi\) | |||||||
\(212\) | − 12.6603i | − 0.869510i | ||||||||
\(213\) | − 0.196152i | − 0.0134401i | ||||||||
\(214\) | 6.19615 | 0.423560 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 5.80385i | 0.393991i | ||||||||
\(218\) | 10.3923i | 0.703856i | ||||||||
\(219\) | 7.53590 | 0.509229 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.928203 | 0.0624377 | ||||||||
\(222\) | 4.92820i | 0.330759i | ||||||||
\(223\) | 4.07180i | 0.272668i | 0.990663 | + | 0.136334i | \(0.0435320\pi\) | ||||
−0.990663 | + | 0.136334i | \(0.956468\pi\) | |||||||
\(224\) | 0.732051 | 0.0489122 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 20.3205 | 1.35170 | ||||||||
\(227\) | − 2.00000i | − 0.132745i | −0.997795 | − | 0.0663723i | \(-0.978857\pi\) | ||||
0.997795 | − | 0.0663723i | \(-0.0211425\pi\) | |||||||
\(228\) | − 1.00000i | − 0.0662266i | ||||||||
\(229\) | 5.19615 | 0.343371 | 0.171686 | − | 0.985152i | \(-0.445079\pi\) | ||||
0.171686 | + | 0.985152i | \(0.445079\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.80385 | −0.250275 | ||||||||
\(232\) | − 1.19615i | − 0.0785313i | ||||||||
\(233\) | − 0.339746i | − 0.0222575i | −0.999938 | − | 0.0111287i | \(-0.996458\pi\) | ||||
0.999938 | − | 0.0111287i | \(-0.00354246\pi\) | |||||||
\(234\) | −1.26795 | −0.0828884 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.19615 | −0.533524 | ||||||||
\(237\) | − 7.92820i | − 0.514992i | ||||||||
\(238\) | − 0.535898i | − 0.0347371i | ||||||||
\(239\) | 20.9282 | 1.35373 | 0.676866 | − | 0.736106i | \(-0.263337\pi\) | ||||
0.676866 | + | 0.736106i | \(0.263337\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1962 | 1.17212 | 0.586059 | − | 0.810269i | \(-0.300679\pi\) | ||||
0.586059 | + | 0.810269i | \(0.300679\pi\) | |||||||
\(242\) | − 16.0000i | − 1.02852i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −11.7321 | −0.751068 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.26795i | − 0.0806777i | ||||||||
\(248\) | 7.92820i | 0.503441i | ||||||||
\(249\) | −0.660254 | −0.0418419 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.46410 | −0.218652 | −0.109326 | − | 0.994006i | \(-0.534869\pi\) | ||||
−0.109326 | + | 0.994006i | \(0.534869\pi\) | |||||||
\(252\) | 0.732051i | 0.0461149i | ||||||||
\(253\) | − 7.98076i | − 0.501746i | ||||||||
\(254\) | −11.3923 | −0.714817 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.07180i | 0.129235i | 0.997910 | + | 0.0646176i | \(0.0205828\pi\) | ||||
−0.997910 | + | 0.0646176i | \(0.979417\pi\) | |||||||
\(258\) | − 5.26795i | − 0.327968i | ||||||||
\(259\) | 3.60770 | 0.224171 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.19615 | 0.0740400 | ||||||||
\(262\) | 0.803848i | 0.0496619i | ||||||||
\(263\) | 5.53590i | 0.341358i | 0.985327 | + | 0.170679i | \(0.0545961\pi\) | ||||
−0.985327 | + | 0.170679i | \(0.945404\pi\) | |||||||
\(264\) | −5.19615 | −0.319801 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.732051 | −0.0448849 | ||||||||
\(267\) | − 9.92820i | − 0.607596i | ||||||||
\(268\) | 5.19615i | 0.317406i | ||||||||
\(269\) | −8.53590 | −0.520443 | −0.260221 | − | 0.965549i | \(-0.583796\pi\) | ||||
−0.260221 | + | 0.965549i | \(0.583796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.875644 | −0.0531916 | −0.0265958 | − | 0.999646i | \(-0.508467\pi\) | ||||
−0.0265958 | + | 0.999646i | \(0.508467\pi\) | |||||||
\(272\) | − 0.732051i | − 0.0443871i | ||||||||
\(273\) | 0.928203i | 0.0561774i | ||||||||
\(274\) | 4.39230 | 0.265349 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.53590 | −0.0924502 | ||||||||
\(277\) | − 20.5167i | − 1.23273i | −0.787462 | − | 0.616363i | \(-0.788605\pi\) | ||||
0.787462 | − | 0.616363i | \(-0.211395\pi\) | |||||||
\(278\) | − 14.1962i | − 0.851429i | ||||||||
\(279\) | −7.92820 | −0.474649 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0000 | −0.656205 | −0.328102 | − | 0.944642i | \(-0.606409\pi\) | ||||
−0.328102 | + | 0.944642i | \(0.606409\pi\) | |||||||
\(282\) | 3.46410i | 0.206284i | ||||||||
\(283\) | − 4.00000i | − 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | −0.196152 | −0.0116395 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.58846 | −0.389584 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 16.4641 | 0.968477 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.12436 | 0.417637 | ||||||||
\(292\) | − 7.53590i | − 0.441005i | ||||||||
\(293\) | − 9.33975i | − 0.545634i | −0.962066 | − | 0.272817i | \(-0.912045\pi\) | ||||
0.962066 | − | 0.272817i | \(-0.0879553\pi\) | |||||||
\(294\) | −6.46410 | −0.376994 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.92820 | 0.286446 | ||||||||
\(297\) | − 5.19615i | − 0.301511i | ||||||||
\(298\) | 5.85641i | 0.339253i | ||||||||
\(299\) | −1.94744 | −0.112623 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.85641 | −0.222280 | ||||||||
\(302\) | 10.3923i | 0.598010i | ||||||||
\(303\) | − 5.66025i | − 0.325173i | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.732051 | 0.0418486 | ||||||||
\(307\) | 12.6603i | 0.722559i | 0.932458 | + | 0.361279i | \(0.117660\pi\) | ||||
−0.932458 | + | 0.361279i | \(0.882340\pi\) | |||||||
\(308\) | 3.80385i | 0.216744i | ||||||||
\(309\) | 12.8564 | 0.731375 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.53590 | −0.484026 | −0.242013 | − | 0.970273i | \(-0.577808\pi\) | ||||
−0.242013 | + | 0.970273i | \(0.577808\pi\) | |||||||
\(312\) | 1.26795i | 0.0717835i | ||||||||
\(313\) | 22.8564i | 1.29192i | 0.763371 | + | 0.645960i | \(0.223543\pi\) | ||||
−0.763371 | + | 0.645960i | \(0.776457\pi\) | |||||||
\(314\) | 5.85641 | 0.330496 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.92820 | −0.445996 | ||||||||
\(317\) | 15.0526i | 0.845436i | 0.906261 | + | 0.422718i | \(0.138924\pi\) | ||||
−0.906261 | + | 0.422718i | \(0.861076\pi\) | |||||||
\(318\) | − 12.6603i | − 0.709952i | ||||||||
\(319\) | 6.21539 | 0.347995 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.19615 | 0.345836 | ||||||||
\(322\) | 1.12436i | 0.0626579i | ||||||||
\(323\) | 0.732051i | 0.0407324i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.0000 | −0.553849 | ||||||||
\(327\) | 10.3923i | 0.574696i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.53590 | 0.139809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.80385 | 0.483903 | 0.241952 | − | 0.970288i | \(-0.422212\pi\) | ||||
0.241952 | + | 0.970288i | \(0.422212\pi\) | |||||||
\(332\) | 0.660254i | 0.0362361i | ||||||||
\(333\) | 4.92820i | 0.270064i | ||||||||
\(334\) | −2.00000 | −0.109435 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.732051 | 0.0399366 | ||||||||
\(337\) | 19.3205i | 1.05246i | 0.850344 | + | 0.526228i | \(0.176394\pi\) | ||||
−0.850344 | + | 0.526228i | \(0.823606\pi\) | |||||||
\(338\) | − 11.3923i | − 0.619660i | ||||||||
\(339\) | 20.3205 | 1.10366 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −41.1962 | −2.23090 | ||||||||
\(342\) | − 1.00000i | − 0.0540738i | ||||||||
\(343\) | 9.85641i | 0.532196i | ||||||||
\(344\) | −5.26795 | −0.284029 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.33975 | 0.287067 | ||||||||
\(347\) | − 14.9282i | − 0.801388i | −0.916212 | − | 0.400694i | \(-0.868769\pi\) | ||||
0.916212 | − | 0.400694i | \(-0.131231\pi\) | |||||||
\(348\) | − 1.19615i | − 0.0641205i | ||||||||
\(349\) | −17.5885 | −0.941489 | −0.470744 | − | 0.882270i | \(-0.656015\pi\) | ||||
−0.470744 | + | 0.882270i | \(0.656015\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.26795 | −0.0676781 | ||||||||
\(352\) | 5.19615i | 0.276956i | ||||||||
\(353\) | − 34.5885i | − 1.84096i | −0.390792 | − | 0.920479i | \(-0.627799\pi\) | ||||
0.390792 | − | 0.920479i | \(-0.372201\pi\) | |||||||
\(354\) | −8.19615 | −0.435621 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.92820 | −0.526194 | ||||||||
\(357\) | − 0.535898i | − 0.0283628i | ||||||||
\(358\) | 17.8564i | 0.943740i | ||||||||
\(359\) | 7.85641 | 0.414645 | 0.207323 | − | 0.978273i | \(-0.433525\pi\) | ||||
0.207323 | + | 0.978273i | \(0.433525\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − 22.7321i | − 1.19477i | ||||||||
\(363\) | − 16.0000i | − 0.839782i | ||||||||
\(364\) | 0.928203 | 0.0486511 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −11.7321 | −0.613244 | ||||||||
\(367\) | 15.5167i | 0.809963i | 0.914325 | + | 0.404982i | \(0.132722\pi\) | ||||
−0.914325 | + | 0.404982i | \(0.867278\pi\) | |||||||
\(368\) | 1.53590i | 0.0800642i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.26795 | −0.481168 | ||||||||
\(372\) | 7.92820i | 0.411058i | ||||||||
\(373\) | 10.3397i | 0.535372i | 0.963506 | + | 0.267686i | \(0.0862589\pi\) | ||||
−0.963506 | + | 0.267686i | \(0.913741\pi\) | |||||||
\(374\) | 3.80385 | 0.196692 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.46410 | 0.178647 | ||||||||
\(377\) | − 1.51666i | − 0.0781120i | ||||||||
\(378\) | 0.732051i | 0.0376526i | ||||||||
\(379\) | −33.1769 | −1.70418 | −0.852092 | − | 0.523392i | \(-0.824666\pi\) | ||||
−0.852092 | + | 0.523392i | \(0.824666\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3923 | −0.583645 | ||||||||
\(382\) | 17.5359i | 0.897215i | ||||||||
\(383\) | − 34.0526i | − 1.74000i | −0.493048 | − | 0.870002i | \(-0.664117\pi\) | ||||
0.493048 | − | 0.870002i | \(-0.335883\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.196152 | 0.00998390 | ||||||||
\(387\) | − 5.26795i | − 0.267785i | ||||||||
\(388\) | − 7.12436i | − 0.361684i | ||||||||
\(389\) | 0.928203 | 0.0470618 | 0.0235309 | − | 0.999723i | \(-0.492509\pi\) | ||||
0.0235309 | + | 0.999723i | \(0.492509\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.12436 | 0.0568611 | ||||||||
\(392\) | 6.46410i | 0.326486i | ||||||||
\(393\) | 0.803848i | 0.0405487i | ||||||||
\(394\) | −17.6603 | −0.889711 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.19615 | −0.261116 | ||||||||
\(397\) | 9.87564i | 0.495644i | 0.968806 | + | 0.247822i | \(0.0797149\pi\) | ||||
−0.968806 | + | 0.247822i | \(0.920285\pi\) | |||||||
\(398\) | 16.9282i | 0.848534i | ||||||||
\(399\) | −0.732051 | −0.0366484 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.7128 | −1.83335 | −0.916675 | − | 0.399633i | \(-0.869138\pi\) | ||||
−0.916675 | + | 0.399633i | \(0.869138\pi\) | |||||||
\(402\) | 5.19615i | 0.259161i | ||||||||
\(403\) | 10.0526i | 0.500754i | ||||||||
\(404\) | −5.66025 | −0.281608 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.875644 | −0.0434575 | ||||||||
\(407\) | 25.6077i | 1.26933i | ||||||||
\(408\) | − 0.732051i | − 0.0362419i | ||||||||
\(409\) | 17.3205 | 0.856444 | 0.428222 | − | 0.903674i | \(-0.359140\pi\) | ||||
0.428222 | + | 0.903674i | \(0.359140\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.39230 | 0.216656 | ||||||||
\(412\) | − 12.8564i | − 0.633390i | ||||||||
\(413\) | 6.00000i | 0.295241i | ||||||||
\(414\) | −1.53590 | −0.0754853 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.26795 | 0.0621663 | ||||||||
\(417\) | − 14.1962i | − 0.695189i | ||||||||
\(418\) | − 5.19615i | − 0.254152i | ||||||||
\(419\) | −21.8564 | −1.06776 | −0.533878 | − | 0.845562i | \(-0.679266\pi\) | ||||
−0.533878 | + | 0.845562i | \(0.679266\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 3.19615i | 0.155586i | ||||||||
\(423\) | 3.46410i | 0.168430i | ||||||||
\(424\) | −12.6603 | −0.614836 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.196152 | −0.00950362 | ||||||||
\(427\) | 8.58846i | 0.415625i | ||||||||
\(428\) | − 6.19615i | − 0.299502i | ||||||||
\(429\) | −6.58846 | −0.318094 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.3923 | −1.07860 | −0.539300 | − | 0.842114i | \(-0.681311\pi\) | ||||
−0.539300 | + | 0.842114i | \(0.681311\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 16.1962i | 0.778337i | 0.921166 | + | 0.389169i | \(0.127238\pi\) | ||||
−0.921166 | + | 0.389169i | \(0.872762\pi\) | |||||||
\(434\) | 5.80385 | 0.278594 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.3923 | 0.497701 | ||||||||
\(437\) | − 1.53590i | − 0.0734720i | ||||||||
\(438\) | − 7.53590i | − 0.360079i | ||||||||
\(439\) | 17.3923 | 0.830089 | 0.415045 | − | 0.909801i | \(-0.363766\pi\) | ||||
0.415045 | + | 0.909801i | \(0.363766\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.46410 | −0.307814 | ||||||||
\(442\) | − 0.928203i | − 0.0441501i | ||||||||
\(443\) | 24.5167i | 1.16482i | 0.812895 | + | 0.582411i | \(0.197890\pi\) | ||||
−0.812895 | + | 0.582411i | \(0.802110\pi\) | |||||||
\(444\) | 4.92820 | 0.233882 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.07180 | 0.192805 | ||||||||
\(447\) | 5.85641i | 0.276999i | ||||||||
\(448\) | − 0.732051i | − 0.0345861i | ||||||||
\(449\) | 6.46410 | 0.305060 | 0.152530 | − | 0.988299i | \(-0.451258\pi\) | ||||
0.152530 | + | 0.988299i | \(0.451258\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 20.3205i | − 0.955796i | ||||||||
\(453\) | 10.3923i | 0.488273i | ||||||||
\(454\) | −2.00000 | −0.0938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | 32.0000i | 1.49690i | 0.663193 | + | 0.748448i | \(0.269201\pi\) | ||||
−0.663193 | + | 0.748448i | \(0.730799\pi\) | |||||||
\(458\) | − 5.19615i | − 0.242800i | ||||||||
\(459\) | 0.732051 | 0.0341692 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.8564 | 1.20425 | 0.602126 | − | 0.798401i | \(-0.294320\pi\) | ||||
0.602126 | + | 0.798401i | \(0.294320\pi\) | |||||||
\(462\) | 3.80385i | 0.176971i | ||||||||
\(463\) | 32.3923i | 1.50540i | 0.658365 | + | 0.752699i | \(0.271248\pi\) | ||||
−0.658365 | + | 0.752699i | \(0.728752\pi\) | |||||||
\(464\) | −1.19615 | −0.0555300 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.339746 | −0.0157384 | ||||||||
\(467\) | 0.660254i | 0.0305529i | 0.999883 | + | 0.0152765i | \(0.00486284\pi\) | ||||
−0.999883 | + | 0.0152765i | \(0.995137\pi\) | |||||||
\(468\) | 1.26795i | 0.0586110i | ||||||||
\(469\) | 3.80385 | 0.175645 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.85641 | 0.269849 | ||||||||
\(472\) | 8.19615i | 0.377258i | ||||||||
\(473\) | − 27.3731i | − 1.25861i | ||||||||
\(474\) | −7.92820 | −0.364154 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.535898 | −0.0245629 | ||||||||
\(477\) | − 12.6603i | − 0.579673i | ||||||||
\(478\) | − 20.9282i | − 0.957234i | ||||||||
\(479\) | 37.3923 | 1.70850 | 0.854249 | − | 0.519864i | \(-0.174017\pi\) | ||||
0.854249 | + | 0.519864i | \(0.174017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.24871 | 0.284917 | ||||||||
\(482\) | − 18.1962i | − 0.828812i | ||||||||
\(483\) | 1.12436i | 0.0511600i | ||||||||
\(484\) | −16.0000 | −0.727273 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 26.9282i | 1.22023i | 0.792312 | + | 0.610117i | \(0.208877\pi\) | ||||
−0.792312 | + | 0.610117i | \(0.791123\pi\) | |||||||
\(488\) | 11.7321i | 0.531085i | ||||||||
\(489\) | −10.0000 | −0.452216 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.0718 | −0.950957 | −0.475478 | − | 0.879727i | \(-0.657725\pi\) | ||||
−0.475478 | + | 0.879727i | \(0.657725\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.875644i | 0.0394370i | ||||||||
\(494\) | −1.26795 | −0.0570477 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.92820 | 0.355987 | ||||||||
\(497\) | 0.143594i | 0.00644105i | ||||||||
\(498\) | 0.660254i | 0.0295867i | ||||||||
\(499\) | 11.1244 | 0.497995 | 0.248997 | − | 0.968504i | \(-0.419899\pi\) | ||||
0.248997 | + | 0.968504i | \(0.419899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.00000 | −0.0893534 | ||||||||
\(502\) | 3.46410i | 0.154610i | ||||||||
\(503\) | 28.7846i | 1.28344i | 0.766938 | + | 0.641721i | \(0.221779\pi\) | ||||
−0.766938 | + | 0.641721i | \(0.778221\pi\) | |||||||
\(504\) | 0.732051 | 0.0326081 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.98076 | −0.354788 | ||||||||
\(507\) | − 11.3923i | − 0.505950i | ||||||||
\(508\) | 11.3923i | 0.505452i | ||||||||
\(509\) | −3.73205 | −0.165420 | −0.0827101 | − | 0.996574i | \(-0.526358\pi\) | ||||
−0.0827101 | + | 0.996574i | \(0.526358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.51666 | −0.244043 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | − 1.00000i | − 0.0441511i | ||||||||
\(514\) | 2.07180 | 0.0913830 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.26795 | −0.231909 | ||||||||
\(517\) | 18.0000i | 0.791639i | ||||||||
\(518\) | − 3.60770i | − 0.158513i | ||||||||
\(519\) | 5.33975 | 0.234389 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.3205 | 1.67885 | 0.839426 | − | 0.543474i | \(-0.182891\pi\) | ||||
0.839426 | + | 0.543474i | \(0.182891\pi\) | |||||||
\(522\) | − 1.19615i | − 0.0523542i | ||||||||
\(523\) | − 9.85641i | − 0.430991i | −0.976505 | − | 0.215495i | \(-0.930863\pi\) | ||||
0.976505 | − | 0.215495i | \(-0.0691366\pi\) | |||||||
\(524\) | 0.803848 | 0.0351162 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.53590 | 0.241377 | ||||||||
\(527\) | − 5.80385i | − 0.252820i | ||||||||
\(528\) | 5.19615i | 0.226134i | ||||||||
\(529\) | 20.6410 | 0.897435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.19615 | −0.355683 | ||||||||
\(532\) | 0.732051i | 0.0317384i | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −9.92820 | −0.429635 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.19615 | 0.224440 | ||||||||
\(537\) | 17.8564i | 0.770561i | ||||||||
\(538\) | 8.53590i | 0.368009i | ||||||||
\(539\) | −33.5885 | −1.44676 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.66025 | −0.372333 | −0.186167 | − | 0.982518i | \(-0.559606\pi\) | ||||
−0.186167 | + | 0.982518i | \(0.559606\pi\) | |||||||
\(542\) | 0.875644i | 0.0376121i | ||||||||
\(543\) | − 22.7321i | − 0.975526i | ||||||||
\(544\) | −0.732051 | −0.0313864 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.928203 | 0.0397234 | ||||||||
\(547\) | 27.5885i | 1.17960i | 0.807550 | + | 0.589799i | \(0.200793\pi\) | ||||
−0.807550 | + | 0.589799i | \(0.799207\pi\) | |||||||
\(548\) | − 4.39230i | − 0.187630i | ||||||||
\(549\) | −11.7321 | −0.500712 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.19615 | 0.0509578 | ||||||||
\(552\) | 1.53590i | 0.0653722i | ||||||||
\(553\) | 5.80385i | 0.246805i | ||||||||
\(554\) | −20.5167 | −0.871669 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.1962 | −0.602051 | ||||||||
\(557\) | 7.41154i | 0.314037i | 0.987596 | + | 0.157019i | \(0.0501883\pi\) | ||||
−0.987596 | + | 0.157019i | \(0.949812\pi\) | |||||||
\(558\) | 7.92820i | 0.335628i | ||||||||
\(559\) | −6.67949 | −0.282512 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.80385 | 0.160599 | ||||||||
\(562\) | 11.0000i | 0.464007i | ||||||||
\(563\) | − 21.8038i | − 0.918923i | −0.888198 | − | 0.459461i | \(-0.848042\pi\) | ||||
0.888198 | − | 0.459461i | \(-0.151958\pi\) | |||||||
\(564\) | 3.46410 | 0.145865 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0.732051i | 0.0307432i | ||||||||
\(568\) | 0.196152i | 0.00823037i | ||||||||
\(569\) | 41.7128 | 1.74869 | 0.874346 | − | 0.485303i | \(-0.161291\pi\) | ||||
0.874346 | + | 0.485303i | \(0.161291\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.26795 | −0.304154 | −0.152077 | − | 0.988369i | \(-0.548596\pi\) | ||||
−0.152077 | + | 0.988369i | \(0.548596\pi\) | |||||||
\(572\) | 6.58846i | 0.275477i | ||||||||
\(573\) | 17.5359i | 0.732573i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − 14.3205i | − 0.596171i | −0.954539 | − | 0.298085i | \(-0.903652\pi\) | ||||
0.954539 | − | 0.298085i | \(-0.0963480\pi\) | |||||||
\(578\) | − 16.4641i | − 0.684816i | ||||||||
\(579\) | 0.196152 | 0.00815182 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.483340 | 0.0200523 | ||||||||
\(582\) | − 7.12436i | − 0.295314i | ||||||||
\(583\) | − 65.7846i | − 2.72452i | ||||||||
\(584\) | −7.53590 | −0.311838 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.33975 | −0.385821 | ||||||||
\(587\) | 21.7321i | 0.896978i | 0.893788 | + | 0.448489i | \(0.148038\pi\) | ||||
−0.893788 | + | 0.448489i | \(0.851962\pi\) | |||||||
\(588\) | 6.46410i | 0.266575i | ||||||||
\(589\) | −7.92820 | −0.326676 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.6603 | −0.726446 | ||||||||
\(592\) | − 4.92820i | − 0.202548i | ||||||||
\(593\) | 18.2487i | 0.749385i | 0.927149 | + | 0.374692i | \(0.122252\pi\) | ||||
−0.927149 | + | 0.374692i | \(0.877748\pi\) | |||||||
\(594\) | −5.19615 | −0.213201 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.85641 | 0.239888 | ||||||||
\(597\) | 16.9282i | 0.692825i | ||||||||
\(598\) | 1.94744i | 0.0796368i | ||||||||
\(599\) | −34.9808 | −1.42928 | −0.714638 | − | 0.699495i | \(-0.753408\pi\) | ||||
−0.714638 | + | 0.699495i | \(0.753408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.1962 | 1.47647 | 0.738236 | − | 0.674543i | \(-0.235659\pi\) | ||||
0.738236 | + | 0.674543i | \(0.235659\pi\) | |||||||
\(602\) | 3.85641i | 0.157175i | ||||||||
\(603\) | 5.19615i | 0.211604i | ||||||||
\(604\) | 10.3923 | 0.422857 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.66025 | −0.229932 | ||||||||
\(607\) | − 41.1051i | − 1.66841i | −0.551458 | − | 0.834203i | \(-0.685928\pi\) | ||||
0.551458 | − | 0.834203i | \(-0.314072\pi\) | |||||||
\(608\) | 1.00000i | 0.0405554i | ||||||||
\(609\) | −0.875644 | −0.0354829 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.39230 | 0.177694 | ||||||||
\(612\) | − 0.732051i | − 0.0295914i | ||||||||
\(613\) | 20.9282i | 0.845282i | 0.906297 | + | 0.422641i | \(0.138897\pi\) | ||||
−0.906297 | + | 0.422641i | \(0.861103\pi\) | |||||||
\(614\) | 12.6603 | 0.510926 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.80385 | 0.153261 | ||||||||
\(617\) | 33.3205i | 1.34143i | 0.741714 | + | 0.670717i | \(0.234013\pi\) | ||||
−0.741714 | + | 0.670717i | \(0.765987\pi\) | |||||||
\(618\) | − 12.8564i | − 0.517161i | ||||||||
\(619\) | 24.9808 | 1.00406 | 0.502031 | − | 0.864850i | \(-0.332586\pi\) | ||||
0.502031 | + | 0.864850i | \(0.332586\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.53590 | −0.0616335 | ||||||||
\(622\) | 8.53590i | 0.342258i | ||||||||
\(623\) | 7.26795i | 0.291184i | ||||||||
\(624\) | 1.26795 | 0.0507586 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 22.8564 | 0.913526 | ||||||||
\(627\) | − 5.19615i | − 0.207514i | ||||||||
\(628\) | − 5.85641i | − 0.233696i | ||||||||
\(629\) | −3.60770 | −0.143848 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.9282 | 0.435045 | 0.217522 | − | 0.976055i | \(-0.430202\pi\) | ||||
0.217522 | + | 0.976055i | \(0.430202\pi\) | |||||||
\(632\) | 7.92820i | 0.315367i | ||||||||
\(633\) | 3.19615i | 0.127036i | ||||||||
\(634\) | 15.0526 | 0.597813 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.6603 | −0.502012 | ||||||||
\(637\) | 8.19615i | 0.324743i | ||||||||
\(638\) | − 6.21539i | − 0.246070i | ||||||||
\(639\) | −0.196152 | −0.00775967 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.39230 | 0.331476 | 0.165738 | − | 0.986170i | \(-0.446999\pi\) | ||||
0.165738 | + | 0.986170i | \(0.446999\pi\) | |||||||
\(642\) | − 6.19615i | − 0.244543i | ||||||||
\(643\) | 19.0718i | 0.752118i | 0.926596 | + | 0.376059i | \(0.122721\pi\) | ||||
−0.926596 | + | 0.376059i | \(0.877279\pi\) | |||||||
\(644\) | 1.12436 | 0.0443058 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.732051 | 0.0288022 | ||||||||
\(647\) | 0.0717968i | 0.00282262i | 0.999999 | + | 0.00141131i | \(0.000449234\pi\) | ||||
−0.999999 | + | 0.00141131i | \(0.999551\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −42.5885 | −1.67174 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.80385 | 0.227471 | ||||||||
\(652\) | 10.0000i | 0.391630i | ||||||||
\(653\) | − 37.1769i | − 1.45485i | −0.686190 | − | 0.727423i | \(-0.740718\pi\) | ||||
0.686190 | − | 0.727423i | \(-0.259282\pi\) | |||||||
\(654\) | 10.3923 | 0.406371 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 7.53590i | − 0.294003i | ||||||||
\(658\) | − 2.53590i | − 0.0988596i | ||||||||
\(659\) | 10.7321 | 0.418061 | 0.209031 | − | 0.977909i | \(-0.432969\pi\) | ||||
0.209031 | + | 0.977909i | \(0.432969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.0718 | 0.508434 | 0.254217 | − | 0.967147i | \(-0.418182\pi\) | ||||
0.254217 | + | 0.967147i | \(0.418182\pi\) | |||||||
\(662\) | − 8.80385i | − 0.342171i | ||||||||
\(663\) | − 0.928203i | − 0.0360484i | ||||||||
\(664\) | 0.660254 | 0.0256228 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.92820 | 0.190964 | ||||||||
\(667\) | − 1.83717i | − 0.0711355i | ||||||||
\(668\) | 2.00000i | 0.0773823i | ||||||||
\(669\) | 4.07180 | 0.157425 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −60.9615 | −2.35339 | ||||||||
\(672\) | − 0.732051i | − 0.0282395i | ||||||||
\(673\) | − 32.7321i | − 1.26173i | −0.775893 | − | 0.630864i | \(-0.782701\pi\) | ||||
0.775893 | − | 0.630864i | \(-0.217299\pi\) | |||||||
\(674\) | 19.3205 | 0.744198 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.3923 | −0.438166 | ||||||||
\(677\) | 48.1244i | 1.84957i | 0.380491 | + | 0.924785i | \(0.375755\pi\) | ||||
−0.380491 | + | 0.924785i | \(0.624245\pi\) | |||||||
\(678\) | − 20.3205i | − 0.780404i | ||||||||
\(679\) | −5.21539 | −0.200148 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.00000 | −0.0766402 | ||||||||
\(682\) | 41.1962i | 1.57748i | ||||||||
\(683\) | − 45.1244i | − 1.72664i | −0.504661 | − | 0.863318i | \(-0.668382\pi\) | ||||
0.504661 | − | 0.863318i | \(-0.331618\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.85641 | 0.376319 | ||||||||
\(687\) | − 5.19615i | − 0.198246i | ||||||||
\(688\) | 5.26795i | 0.200839i | ||||||||
\(689\) | −16.0526 | −0.611554 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.12436 | −0.194940 | −0.0974698 | − | 0.995238i | \(-0.531075\pi\) | ||||
−0.0974698 | + | 0.995238i | \(0.531075\pi\) | |||||||
\(692\) | − 5.33975i | − 0.202987i | ||||||||
\(693\) | 3.80385i | 0.144496i | ||||||||
\(694\) | −14.9282 | −0.566667 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.19615 | −0.0453400 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 17.5885i | 0.665733i | ||||||||
\(699\) | −0.339746 | −0.0128504 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.67949 | 0.327820 | 0.163910 | − | 0.986475i | \(-0.447589\pi\) | ||||
0.163910 | + | 0.986475i | \(0.447589\pi\) | |||||||
\(702\) | 1.26795i | 0.0478557i | ||||||||
\(703\) | 4.92820i | 0.185871i | ||||||||
\(704\) | 5.19615 | 0.195837 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34.5885 | −1.30175 | ||||||||
\(707\) | 4.14359i | 0.155836i | ||||||||
\(708\) | 8.19615i | 0.308030i | ||||||||
\(709\) | −29.4449 | −1.10583 | −0.552913 | − | 0.833239i | \(-0.686484\pi\) | ||||
−0.552913 | + | 0.833239i | \(0.686484\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.92820 | −0.297331 | ||||||||
\(712\) | 9.92820i | 0.372075i | ||||||||
\(713\) | 12.1769i | 0.456029i | ||||||||
\(714\) | −0.535898 | −0.0200555 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17.8564 | 0.667325 | ||||||||
\(717\) | − 20.9282i | − 0.781578i | ||||||||
\(718\) | − 7.85641i | − 0.293198i | ||||||||
\(719\) | −42.5692 | −1.58756 | −0.793782 | − | 0.608202i | \(-0.791891\pi\) | ||||
−0.793782 | + | 0.608202i | \(0.791891\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.41154 | −0.350504 | ||||||||
\(722\) | − 1.00000i | − 0.0372161i | ||||||||
\(723\) | − 18.1962i | − 0.676722i | ||||||||
\(724\) | −22.7321 | −0.844830 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −16.0000 | −0.593816 | ||||||||
\(727\) | − 3.46410i | − 0.128476i | −0.997935 | − | 0.0642382i | \(-0.979538\pi\) | ||||
0.997935 | − | 0.0642382i | \(-0.0204617\pi\) | |||||||
\(728\) | − 0.928203i | − 0.0344015i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.85641 | 0.142634 | ||||||||
\(732\) | 11.7321i | 0.433629i | ||||||||
\(733\) | − 8.26795i | − 0.305384i | −0.988274 | − | 0.152692i | \(-0.951206\pi\) | ||||
0.988274 | − | 0.152692i | \(-0.0487942\pi\) | |||||||
\(734\) | 15.5167 | 0.572730 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.53590 | 0.0566140 | ||||||||
\(737\) | 27.0000i | 0.994558i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.2487 | −0.965574 | −0.482787 | − | 0.875738i | \(-0.660376\pi\) | ||||
−0.482787 | + | 0.875738i | \(0.660376\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.26795 | −0.0465793 | ||||||||
\(742\) | 9.26795i | 0.340237i | ||||||||
\(743\) | 24.7846i | 0.909259i | 0.890681 | + | 0.454630i | \(0.150228\pi\) | ||||
−0.890681 | + | 0.454630i | \(0.849772\pi\) | |||||||
\(744\) | 7.92820 | 0.290662 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.3397 | 0.378565 | ||||||||
\(747\) | 0.660254i | 0.0241574i | ||||||||
\(748\) | − 3.80385i | − 0.139082i | ||||||||
\(749\) | −4.53590 | −0.165738 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.5359 | 0.895328 | 0.447664 | − | 0.894202i | \(-0.352256\pi\) | ||||
0.447664 | + | 0.894202i | \(0.352256\pi\) | |||||||
\(752\) | − 3.46410i | − 0.126323i | ||||||||
\(753\) | 3.46410i | 0.126239i | ||||||||
\(754\) | −1.51666 | −0.0552335 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.732051 | 0.0266244 | ||||||||
\(757\) | 39.9808i | 1.45313i | 0.687100 | + | 0.726563i | \(0.258883\pi\) | ||||
−0.687100 | + | 0.726563i | \(0.741117\pi\) | |||||||
\(758\) | 33.1769i | 1.20504i | ||||||||
\(759\) | −7.98076 | −0.289683 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.5167 | 0.852478 | 0.426239 | − | 0.904611i | \(-0.359838\pi\) | ||||
0.426239 | + | 0.904611i | \(0.359838\pi\) | |||||||
\(762\) | 11.3923i | 0.412700i | ||||||||
\(763\) | − 7.60770i | − 0.275417i | ||||||||
\(764\) | 17.5359 | 0.634427 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34.0526 | −1.23037 | ||||||||
\(767\) | 10.3923i | 0.375244i | ||||||||
\(768\) | − 1.00000i | − 0.0360844i | ||||||||
\(769\) | −38.0718 | −1.37290 | −0.686452 | − | 0.727175i | \(-0.740833\pi\) | ||||
−0.686452 | + | 0.727175i | \(0.740833\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.07180 | 0.0746139 | ||||||||
\(772\) | − 0.196152i | − 0.00705968i | ||||||||
\(773\) | − 21.6077i | − 0.777175i | −0.921412 | − | 0.388587i | \(-0.872963\pi\) | ||||
0.921412 | − | 0.388587i | \(-0.127037\pi\) | |||||||
\(774\) | −5.26795 | −0.189353 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.12436 | −0.255749 | ||||||||
\(777\) | − 3.60770i | − 0.129425i | ||||||||
\(778\) | − 0.928203i | − 0.0332777i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.01924 | −0.0364712 | ||||||||
\(782\) | − 1.12436i | − 0.0402069i | ||||||||
\(783\) | − 1.19615i | − 0.0427470i | ||||||||
\(784\) | 6.46410 | 0.230861 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.803848 | 0.0286723 | ||||||||
\(787\) | 9.98076i | 0.355776i | 0.984051 | + | 0.177888i | \(0.0569264\pi\) | ||||
−0.984051 | + | 0.177888i | \(0.943074\pi\) | |||||||
\(788\) | 17.6603i | 0.629121i | ||||||||
\(789\) | 5.53590 | 0.197083 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.8756 | −0.528917 | ||||||||
\(792\) | 5.19615i | 0.184637i | ||||||||
\(793\) | 14.8756i | 0.528250i | ||||||||
\(794\) | 9.87564 | 0.350474 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.9282 | 0.600004 | ||||||||
\(797\) | 53.5692i | 1.89752i | 0.315999 | + | 0.948760i | \(0.397660\pi\) | ||||
−0.315999 | + | 0.948760i | \(0.602340\pi\) | |||||||
\(798\) | 0.732051i | 0.0259143i | ||||||||
\(799\) | −2.53590 | −0.0897136 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.92820 | −0.350796 | ||||||||
\(802\) | 36.7128i | 1.29637i | ||||||||
\(803\) | − 39.1577i | − 1.38184i | ||||||||
\(804\) | 5.19615 | 0.183254 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.0526 | 0.354086 | ||||||||
\(807\) | 8.53590i | 0.300478i | ||||||||
\(808\) | 5.66025i | 0.199127i | ||||||||
\(809\) | −5.12436 | −0.180163 | −0.0900814 | − | 0.995934i | \(-0.528713\pi\) | ||||
−0.0900814 | + | 0.995934i | \(0.528713\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.5167 | 0.931126 | 0.465563 | − | 0.885015i | \(-0.345852\pi\) | ||||
0.465563 | + | 0.885015i | \(0.345852\pi\) | |||||||
\(812\) | 0.875644i | 0.0307291i | ||||||||
\(813\) | 0.875644i | 0.0307102i | ||||||||
\(814\) | 25.6077 | 0.897549 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.732051 | −0.0256269 | ||||||||
\(817\) | − 5.26795i | − 0.184302i | ||||||||
\(818\) | − 17.3205i | − 0.605597i | ||||||||
\(819\) | 0.928203 | 0.0324340 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.8038 | 0.900560 | 0.450280 | − | 0.892887i | \(-0.351324\pi\) | ||||
0.450280 | + | 0.892887i | \(0.351324\pi\) | |||||||
\(822\) | − 4.39230i | − 0.153199i | ||||||||
\(823\) | 29.7128i | 1.03572i | 0.855464 | + | 0.517862i | \(0.173272\pi\) | ||||
−0.855464 | + | 0.517862i | \(0.826728\pi\) | |||||||
\(824\) | −12.8564 | −0.447874 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | 0.208767 | ||||||||
\(827\) | − 9.26795i | − 0.322278i | −0.986932 | − | 0.161139i | \(-0.948483\pi\) | ||||
0.986932 | − | 0.161139i | \(-0.0515168\pi\) | |||||||
\(828\) | 1.53590i | 0.0533762i | ||||||||
\(829\) | 3.26795 | 0.113501 | 0.0567503 | − | 0.998388i | \(-0.481926\pi\) | ||||
0.0567503 | + | 0.998388i | \(0.481926\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.5167 | −0.711715 | ||||||||
\(832\) | − 1.26795i | − 0.0439582i | ||||||||
\(833\) | − 4.73205i | − 0.163956i | ||||||||
\(834\) | −14.1962 | −0.491573 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −5.19615 | −0.179713 | ||||||||
\(837\) | 7.92820i | 0.274039i | ||||||||
\(838\) | 21.8564i | 0.755017i | ||||||||
\(839\) | −29.9090 | −1.03257 | −0.516286 | − | 0.856416i | \(-0.672686\pi\) | ||||
−0.516286 | + | 0.856416i | \(0.672686\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.5692 | −0.950663 | ||||||||
\(842\) | 2.00000i | 0.0689246i | ||||||||
\(843\) | 11.0000i | 0.378860i | ||||||||
\(844\) | 3.19615 | 0.110016 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.46410 | 0.119098 | ||||||||
\(847\) | 11.7128i | 0.402457i | ||||||||
\(848\) | 12.6603i | 0.434755i | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.56922 | 0.259469 | ||||||||
\(852\) | 0.196152i | 0.00672007i | ||||||||
\(853\) | 51.1769i | 1.75226i | 0.482071 | + | 0.876132i | \(0.339885\pi\) | ||||
−0.482071 | + | 0.876132i | \(0.660115\pi\) | |||||||
\(854\) | 8.58846 | 0.293891 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.19615 | −0.211780 | ||||||||
\(857\) | 13.8564i | 0.473326i | 0.971592 | + | 0.236663i | \(0.0760537\pi\) | ||||
−0.971592 | + | 0.236663i | \(0.923946\pi\) | |||||||
\(858\) | 6.58846i | 0.224926i | ||||||||
\(859\) | −10.7846 | −0.367966 | −0.183983 | − | 0.982929i | \(-0.558899\pi\) | ||||
−0.183983 | + | 0.982929i | \(0.558899\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 22.3923i | 0.762685i | ||||||||
\(863\) | − 44.3923i | − 1.51113i | −0.655073 | − | 0.755566i | \(-0.727362\pi\) | ||||
0.655073 | − | 0.755566i | \(-0.272638\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.1962 | 0.550368 | ||||||||
\(867\) | − 16.4641i | − 0.559150i | ||||||||
\(868\) | − 5.80385i | − 0.196995i | ||||||||
\(869\) | −41.1962 | −1.39748 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.58846 | 0.223241 | ||||||||
\(872\) | − 10.3923i | − 0.351928i | ||||||||
\(873\) | − 7.12436i | − 0.241123i | ||||||||
\(874\) | −1.53590 | −0.0519525 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.53590 | −0.254614 | ||||||||
\(877\) | − 44.5359i | − 1.50387i | −0.659237 | − | 0.751935i | \(-0.729121\pi\) | ||||
0.659237 | − | 0.751935i | \(-0.270879\pi\) | |||||||
\(878\) | − 17.3923i | − 0.586962i | ||||||||
\(879\) | −9.33975 | −0.315022 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.3923 | 1.36085 | 0.680426 | − | 0.732817i | \(-0.261795\pi\) | ||||
0.680426 | + | 0.732817i | \(0.261795\pi\) | |||||||
\(882\) | 6.46410i | 0.217658i | ||||||||
\(883\) | − 21.9090i | − 0.737295i | −0.929569 | − | 0.368648i | \(-0.879821\pi\) | ||||
0.929569 | − | 0.368648i | \(-0.120179\pi\) | |||||||
\(884\) | −0.928203 | −0.0312189 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.5167 | 0.823653 | ||||||||
\(887\) | − 5.46410i | − 0.183467i | −0.995784 | − | 0.0917333i | \(-0.970759\pi\) | ||||
0.995784 | − | 0.0917333i | \(-0.0292407\pi\) | |||||||
\(888\) | − 4.92820i | − 0.165380i | ||||||||
\(889\) | 8.33975 | 0.279706 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.19615 | −0.174078 | ||||||||
\(892\) | − 4.07180i | − 0.136334i | ||||||||
\(893\) | 3.46410i | 0.115922i | ||||||||
\(894\) | 5.85641 | 0.195868 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.732051 | −0.0244561 | ||||||||
\(897\) | 1.94744i | 0.0650232i | ||||||||
\(898\) | − 6.46410i | − 0.215710i | ||||||||
\(899\) | −9.48334 | −0.316287 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.26795 | 0.308760 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.85641i | 0.128333i | ||||||||
\(904\) | −20.3205 | −0.675850 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 10.3923 | 0.345261 | ||||||||
\(907\) | − 41.3205i | − 1.37202i | −0.727590 | − | 0.686012i | \(-0.759360\pi\) | ||||
0.727590 | − | 0.686012i | \(-0.240640\pi\) | |||||||
\(908\) | 2.00000i | 0.0663723i | ||||||||
\(909\) | −5.66025 | −0.187739 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.3923 | −1.27199 | −0.635997 | − | 0.771692i | \(-0.719411\pi\) | ||||
−0.635997 | + | 0.771692i | \(0.719411\pi\) | |||||||
\(912\) | 1.00000i | 0.0331133i | ||||||||
\(913\) | 3.43078i | 0.113542i | ||||||||
\(914\) | 32.0000 | 1.05847 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.19615 | −0.171686 | ||||||||
\(917\) | − 0.588457i | − 0.0194326i | ||||||||
\(918\) | − 0.732051i | − 0.0241613i | ||||||||
\(919\) | 42.8372 | 1.41307 | 0.706534 | − | 0.707679i | \(-0.250258\pi\) | ||||
0.706534 | + | 0.707679i | \(0.250258\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.6603 | 0.417170 | ||||||||
\(922\) | − 25.8564i | − 0.851535i | ||||||||
\(923\) | 0.248711i | 0.00818643i | ||||||||
\(924\) | 3.80385 | 0.125137 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 32.3923 | 1.06448 | ||||||||
\(927\) | − 12.8564i | − 0.422260i | ||||||||
\(928\) | 1.19615i | 0.0392656i | ||||||||
\(929\) | −21.0718 | −0.691343 | −0.345672 | − | 0.938356i | \(-0.612349\pi\) | ||||
−0.345672 | + | 0.938356i | \(0.612349\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.46410 | −0.211852 | ||||||||
\(932\) | 0.339746i | 0.0111287i | ||||||||
\(933\) | 8.53590i | 0.279453i | ||||||||
\(934\) | 0.660254 | 0.0216042 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.26795 | 0.0414442 | ||||||||
\(937\) | − 46.7846i | − 1.52839i | −0.644987 | − | 0.764193i | \(-0.723137\pi\) | ||||
0.644987 | − | 0.764193i | \(-0.276863\pi\) | |||||||
\(938\) | − 3.80385i | − 0.124200i | ||||||||
\(939\) | 22.8564 | 0.745891 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.26795 | −0.139131 | −0.0695656 | − | 0.997577i | \(-0.522161\pi\) | ||||
−0.0695656 | + | 0.997577i | \(0.522161\pi\) | |||||||
\(942\) | − 5.85641i | − 0.190812i | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 8.19615 | 0.266762 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.3731 | −0.889975 | ||||||||
\(947\) | 2.14359i | 0.0696574i | 0.999393 | + | 0.0348287i | \(0.0110886\pi\) | ||||
−0.999393 | + | 0.0348287i | \(0.988911\pi\) | |||||||
\(948\) | 7.92820i | 0.257496i | ||||||||
\(949\) | −9.55514 | −0.310173 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.0526 | 0.488113 | ||||||||
\(952\) | 0.535898i | 0.0173686i | ||||||||
\(953\) | 13.3923i | 0.433819i | 0.976192 | + | 0.216910i | \(0.0695977\pi\) | ||||
−0.976192 | + | 0.216910i | \(0.930402\pi\) | |||||||
\(954\) | −12.6603 | −0.409891 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.9282 | −0.676866 | ||||||||
\(957\) | − 6.21539i | − 0.200915i | ||||||||
\(958\) | − 37.3923i | − 1.20809i | ||||||||
\(959\) | −3.21539 | −0.103830 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.8564 | 1.02763 | ||||||||
\(962\) | − 6.24871i | − 0.201467i | ||||||||
\(963\) | − 6.19615i | − 0.199668i | ||||||||
\(964\) | −18.1962 | −0.586059 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.12436 | 0.0361756 | ||||||||
\(967\) | − 41.0333i | − 1.31954i | −0.751466 | − | 0.659771i | \(-0.770653\pi\) | ||||
0.751466 | − | 0.659771i | \(-0.229347\pi\) | |||||||
\(968\) | 16.0000i | 0.514259i | ||||||||
\(969\) | 0.732051 | 0.0235169 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −44.1962 | −1.41832 | −0.709161 | − | 0.705047i | \(-0.750926\pi\) | ||||
−0.709161 | + | 0.705047i | \(0.750926\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 10.3923i | 0.333162i | ||||||||
\(974\) | 26.9282 | 0.862835 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.7321 | 0.375534 | ||||||||
\(977\) | 9.46410i | 0.302783i | 0.988474 | + | 0.151392i | \(0.0483755\pi\) | ||||
−0.988474 | + | 0.151392i | \(0.951625\pi\) | |||||||
\(978\) | 10.0000i | 0.319765i | ||||||||
\(979\) | −51.5885 | −1.64877 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.3923 | 0.331801 | ||||||||
\(982\) | 21.0718i | 0.672428i | ||||||||
\(983\) | 5.66025i | 0.180534i | 0.995918 | + | 0.0902670i | \(0.0287721\pi\) | ||||
−0.995918 | + | 0.0902670i | \(0.971228\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.875644 | 0.0278862 | ||||||||
\(987\) | − 2.53590i | − 0.0807185i | ||||||||
\(988\) | 1.26795i | 0.0403388i | ||||||||
\(989\) | −8.09103 | −0.257280 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.7846 | −0.882607 | −0.441304 | − | 0.897358i | \(-0.645484\pi\) | ||||
−0.441304 | + | 0.897358i | \(0.645484\pi\) | |||||||
\(992\) | − 7.92820i | − 0.251721i | ||||||||
\(993\) | − 8.80385i | − 0.279382i | ||||||||
\(994\) | 0.143594 | 0.00455451 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.660254 | 0.0209209 | ||||||||
\(997\) | − 40.6603i | − 1.28772i | −0.765142 | − | 0.643862i | \(-0.777331\pi\) | ||||
0.765142 | − | 0.643862i | \(-0.222669\pi\) | |||||||
\(998\) | − 11.1244i | − 0.352135i | ||||||||
\(999\) | 4.92820 | 0.155921 |
(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 | 2850.2.d.u.799.2 | 4 | ||
5.2 | odd | 4 | 2850.2.a.bh.1.1 | yes | 2 | ||
5.3 | odd | 4 | 2850.2.a.be.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 2850.2.d.u.799.3 | 4 | ||
15.2 | even | 4 | 8550.2.a.bt.1.1 | 2 | |||
15.8 | even | 4 | 8550.2.a.bz.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2850.2.a.be.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
2850.2.a.bh.1.1 | yes | 2 | 5.2 | odd | 4 | ||
2850.2.d.u.799.2 | 4 | 1.1 | even | 1 | trivial | ||
2850.2.d.u.799.3 | 4 | 5.4 | even | 2 | inner | ||
8550.2.a.bt.1.1 | 2 | 15.2 | even | 4 | |||
8550.2.a.bz.1.2 | 2 | 15.8 | even | 4 |