Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.5 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.24 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.48830 | + | 1.66882i | −0.665587 | + | 0.746321i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.27974i | − | 0.861661i | −0.902433 | − | 0.430830i | \(-0.858221\pi\) | ||
0.902433 | − | 0.430830i | \(-0.141779\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.88669 | 1.17188 | 0.585940 | − | 0.810354i | \(-0.300725\pi\) | ||||
0.585940 | + | 0.810354i | \(0.300725\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.72160i | − | 0.754836i | −0.926043 | − | 0.377418i | \(-0.876812\pi\) | ||
0.926043 | − | 0.377418i | \(-0.123188\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.66882 | + | 1.48830i | 0.430888 | + | 0.384277i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.85402i | − | 0.934737i | −0.884063 | − | 0.467369i | \(-0.845202\pi\) | ||
0.884063 | − | 0.467369i | \(-0.154798\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.23474 | 0.283269 | 0.141635 | − | 0.989919i | \(-0.454764\pi\) | ||||
0.141635 | + | 0.989919i | \(0.454764\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.27974 | −0.497480 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 0.161725i | − | 0.0337221i | −0.999858 | − | 0.0168610i | \(-0.994633\pi\) | ||
0.999858 | − | 0.0168610i | \(-0.00536729\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.569943 | − | 4.96741i | −0.113989 | − | 0.993482i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.75486 | −1.81143 | −0.905716 | − | 0.423886i | \(-0.860666\pi\) | ||||
−0.905716 | + | 0.423886i | \(0.860666\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.8538 | 1.94940 | 0.974700 | − | 0.223518i | \(-0.0717542\pi\) | ||||
0.974700 | + | 0.223518i | \(0.0717542\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.88669i | − | 0.676585i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.80448 | + | 3.39293i | 0.643075 | + | 0.573510i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.23986i | 0.697028i | 0.937304 | + | 0.348514i | \(0.113314\pi\) | ||||
−0.937304 | + | 0.348514i | \(0.886686\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.72160 | −0.435805 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.12803 | −1.42556 | −0.712779 | − | 0.701388i | \(-0.752564\pi\) | ||||
−0.712779 | + | 0.701388i | \(0.752564\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.4359i | 1.89645i | 0.317595 | + | 0.948226i | \(0.397125\pi\) | ||||
−0.317595 | + | 0.948226i | \(0.602875\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.48830 | − | 1.66882i | 0.221862 | − | 0.248774i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.41740i | − | 1.08194i | −0.841042 | − | 0.540970i | \(-0.818057\pi\) | ||
0.841042 | − | 0.540970i | \(-0.181943\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.80279 | 0.257541 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.85402 | −0.539671 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.06751i | − | 0.696076i | −0.937480 | − | 0.348038i | \(-0.886848\pi\) | ||
0.937480 | − | 0.348038i | \(-0.113152\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.78454 | + | 6.48619i | −0.779988 | + | 0.874598i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.23474i | − | 0.163546i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.0652234 | −0.00849137 | −0.00424568 | − | 0.999991i | \(-0.501351\pi\) | ||||
−0.00424568 | + | 0.999991i | \(0.501351\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.45042 | 0.953928 | 0.476964 | − | 0.878923i | \(-0.341737\pi\) | ||||
0.476964 | + | 0.878923i | \(0.341737\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.27974i | 0.287220i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.54187 | + | 4.05055i | 0.563350 | + | 0.502409i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.161725 | −0.0194695 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.87486 | 0.459861 | 0.229931 | − | 0.973207i | \(-0.426150\pi\) | ||||
0.229931 | + | 0.973207i | \(0.426150\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.30792i | − | 0.270122i | −0.990837 | − | 0.135061i | \(-0.956877\pi\) | ||
0.990837 | − | 0.135061i | \(-0.0431231\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.96741 | + | 0.569943i | −0.573587 | + | 0.0658113i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 8.86063i | − | 1.00976i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.08570 | −0.909712 | −0.454856 | − | 0.890565i | \(-0.650309\pi\) | ||||
−0.454856 | + | 0.890565i | \(0.650309\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.86592i | − | 0.973161i | −0.873636 | − | 0.486580i | \(-0.838244\pi\) | ||
0.873636 | − | 0.486580i | \(-0.161756\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.43168 | + | 5.73593i | 0.697614 | + | 0.622149i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.75486i | 1.04583i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.68739 | −0.284863 | −0.142431 | − | 0.989805i | \(-0.545492\pi\) | ||||
−0.142431 | + | 0.989805i | \(0.545492\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.20454 | −0.650413 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 10.8538i | − | 1.12549i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.83766 | + | 2.06057i | −0.188540 | + | 0.211410i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.15108i | − | 0.116874i | −0.998291 | − | 0.0584371i | \(-0.981388\pi\) | ||
0.998291 | − | 0.0584371i | \(-0.0186117\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.88669 | −0.390627 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.13210 | 0.212151 | 0.106076 | − | 0.994358i | \(-0.466171\pi\) | ||||
0.106076 | + | 0.994358i | \(0.466171\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 15.5812i | − | 1.53526i | −0.640891 | − | 0.767632i | \(-0.721435\pi\) | ||
0.640891 | − | 0.767632i | \(-0.278565\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.39293 | − | 3.80448i | 0.331116 | − | 0.371280i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.09433i | − | 0.782508i | −0.920283 | − | 0.391254i | \(-0.872041\pi\) | ||
0.920283 | − | 0.391254i | \(-0.127959\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.78405 | −0.554012 | −0.277006 | − | 0.960868i | \(-0.589342\pi\) | ||||
−0.277006 | + | 0.960868i | \(0.589342\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.23986 | 0.402430 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.65478i | − | 0.343812i | −0.985113 | − | 0.171906i | \(-0.945007\pi\) | ||
0.985113 | − | 0.171906i | \(-0.0549926\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.269891 | + | 0.240696i | 0.0251675 | + | 0.0224450i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.72160i | 0.251612i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.78616 | −0.805426 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.10633 | 0.373302 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.12803i | 0.823047i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.13797 | + | 6.44185i | 0.817325 | + | 0.576176i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.9034i | − | 1.14499i | −0.819909 | − | 0.572495i | \(-0.805976\pi\) | ||
0.819909 | − | 0.572495i | \(-0.194024\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4359 | 1.09492 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.9854 | −1.74613 | −0.873067 | − | 0.487600i | \(-0.837873\pi\) | ||||
−0.873067 | + | 0.487600i | \(0.837873\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2.81489i | − | 0.244082i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.66882 | − | 1.48830i | −0.143629 | − | 0.128092i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.53325i | 0.558173i | 0.960266 | + | 0.279086i | \(0.0900316\pi\) | ||||
−0.960266 | + | 0.279086i | \(0.909968\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.62443 | −0.477058 | −0.238529 | − | 0.971135i | \(-0.576665\pi\) | ||||
−0.238529 | + | 0.971135i | \(0.576665\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.41740 | −0.624658 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 10.5780i | − | 0.884578i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.5181 | − | 16.2791i | 1.20566 | − | 1.35191i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.80279i | − | 0.148691i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.5646 | −1.76664 | −0.883320 | − | 0.468770i | \(-0.844697\pi\) | ||||
−0.883320 | + | 0.468770i | \(0.844697\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.05311 | −0.411216 | −0.205608 | − | 0.978634i | \(-0.565917\pi\) | ||||
−0.205608 | + | 0.978634i | \(0.565917\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.85402i | 0.311579i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.1537 | + | 18.1131i | −1.29749 | + | 1.45488i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.8662i | − | 1.10664i | −0.832968 | − | 0.553321i | \(-0.813360\pi\) | ||
0.832968 | − | 0.553321i | \(-0.186640\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.06751 | −0.401880 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.368692 | −0.0290570 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.76448i | − | 0.451509i | −0.974184 | − | 0.225754i | \(-0.927515\pi\) | ||
0.974184 | − | 0.225754i | \(-0.0724847\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.48619 | + | 5.78454i | 0.504949 | + | 0.450326i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 18.8637i | − | 1.45972i | −0.683598 | − | 0.729858i | \(-0.739586\pi\) | ||
0.683598 | − | 0.729858i | \(-0.260414\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.59288 | 0.430222 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.23474 | −0.0944231 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 10.8368i | − | 0.823905i | −0.911205 | − | 0.411952i | \(-0.864847\pi\) | ||
0.911205 | − | 0.411952i | \(-0.135153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.3244 | + | 1.29932i | −0.856044 | + | 0.0982195i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0652234i | 0.00490249i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.6207 | −1.24229 | −0.621144 | − | 0.783697i | \(-0.713332\pi\) | ||||
−0.621144 | + | 0.783697i | \(0.713332\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.6918 | −0.943376 | −0.471688 | − | 0.881765i | \(-0.656355\pi\) | ||||
−0.471688 | + | 0.881765i | \(0.656355\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 7.45042i | − | 0.550751i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.07557 | − | 6.31017i | −0.520207 | − | 0.463933i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 14.9794i | − | 1.09540i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.27974 | 0.165827 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.01139 | −0.145539 | −0.0727695 | − | 0.997349i | \(-0.523184\pi\) | ||||
−0.0727695 | + | 0.997349i | \(0.523184\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.75904i | − | 0.342563i | −0.985222 | − | 0.171282i | \(-0.945209\pi\) | ||
0.985222 | − | 0.171282i | \(-0.0547908\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.05055 | − | 4.54187i | 0.290066 | − | 0.325250i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.07304i | 0.0764508i | 0.999269 | + | 0.0382254i | \(0.0121705\pi\) | ||||
−0.999269 | + | 0.0382254i | \(0.987830\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9745 | −0.777963 | −0.388981 | − | 0.921246i | \(-0.627173\pi\) | ||||
−0.388981 | + | 0.921246i | \(0.627173\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.2385i | 1.56084i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.5852 | − | 15.2331i | 0.948833 | − | 1.06392i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.161725i | 0.0112407i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.79906 | 0.331958 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.4378 | 1.68236 | 0.841182 | − | 0.540752i | \(-0.181860\pi\) | ||||
0.841182 | + | 0.540752i | \(0.181860\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 3.87486i | − | 0.265501i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.7533 | − | 18.5083i | −1.41536 | − | 1.26225i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 24.7438i | − | 1.67972i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.30792 | −0.155955 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4891 | −0.705574 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.32846i | 0.356820i | 0.983956 | + | 0.178410i | \(0.0570953\pi\) | ||||
−0.983956 | + | 0.178410i | \(0.942905\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.569943 | + | 4.96741i | 0.0379962 | + | 0.331161i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.7953i | 1.51298i | 0.654008 | + | 0.756488i | \(0.273086\pi\) | ||||
−0.654008 | + | 0.756488i | \(0.726914\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.67796 | 0.573456 | 0.286728 | − | 0.958012i | \(-0.407432\pi\) | ||||
0.286728 | + | 0.958012i | \(0.407432\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.86063 | −0.582987 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.66975i | − | 0.436950i | −0.975843 | − | 0.218475i | \(-0.929892\pi\) | ||
0.975843 | − | 0.218475i | \(-0.0701082\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.3783 | + | 11.0393i | 0.807474 | + | 0.720125i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.08570i | 0.525223i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.3814 | 0.994938 | 0.497469 | − | 0.867482i | \(-0.334263\pi\) | ||||
0.497469 | + | 0.867482i | \(0.334263\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.01457 | −0.258601 | −0.129301 | − | 0.991605i | \(-0.541273\pi\) | ||||
−0.129301 | + | 0.991605i | \(0.541273\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.68308 | + | 3.00853i | −0.171416 | + | 0.192208i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.36048i | − | 0.213822i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.86592 | −0.561855 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.9509 | −0.691212 | −0.345606 | − | 0.938380i | \(-0.612327\pi\) | ||||
−0.345606 | + | 0.938380i | \(0.612327\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.628576i | − | 0.0395182i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.73593 | − | 6.43168i | 0.359198 | − | 0.402767i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.69302i | 0.105608i | 0.998605 | + | 0.0528038i | \(0.0168158\pi\) | ||||
−0.998605 | + | 0.0528038i | \(0.983184\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.66577 | 0.600602 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.75486 | 0.603811 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 0.998029i | − | 0.0615411i | −0.999526 | − | 0.0307706i | \(-0.990204\pi\) | ||
0.999526 | − | 0.0307706i | \(-0.00979612\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.45678 | + | 7.54196i | 0.519496 | + | 0.463299i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.68739i | 0.164466i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.88253 | −0.175751 | −0.0878755 | − | 0.996131i | \(-0.528008\pi\) | ||||
−0.0878755 | + | 0.996131i | \(0.528008\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.80680 | 0.109755 | 0.0548776 | − | 0.998493i | \(-0.482523\pi\) | ||||
0.0548776 | + | 0.998493i | \(0.482523\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.20454i | 0.375516i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.21519 | − | 19.3068i | −0.133581 | − | 1.16424i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 11.4411i | − | 0.687427i | −0.939075 | − | 0.343714i | \(-0.888315\pi\) | ||
0.939075 | − | 0.343714i | \(-0.111685\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.8538 | −0.649800 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.457325 | 0.0272817 | 0.0136409 | − | 0.999907i | \(-0.495658\pi\) | ||||
0.0136409 | + | 0.999907i | \(0.495658\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.02400i | 0.417533i | 0.977965 | + | 0.208767i | \(0.0669449\pi\) | ||||
−0.977965 | + | 0.208767i | \(0.933055\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.06057 | + | 1.83766i | 0.122057 | + | 0.108854i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.8095i | 1.22835i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.14653 | 0.126266 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.15108 | −0.0674773 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.84673i | 0.399990i | 0.979797 | + | 0.199995i | \(0.0640927\pi\) | ||||
−0.979797 | + | 0.199995i | \(0.935907\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0970719 | − | 0.108846i | 0.00565174 | − | 0.00633728i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.88669i | 0.225528i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.440152 | −0.0254547 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.3506 | 1.63410 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.13210i | − | 0.122486i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.0884 | + | 12.4334i | −0.634922 | + | 0.711936i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.8667i | 1.19093i | 0.803383 | + | 0.595463i | \(0.203031\pi\) | ||||
−0.803383 | + | 0.595463i | \(0.796969\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.5812 | −0.886385 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.8030 | 0.782697 | 0.391349 | − | 0.920243i | \(-0.372009\pi\) | ||||
0.391349 | + | 0.920243i | \(0.372009\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 22.4589i | − | 1.26945i | −0.772736 | − | 0.634727i | \(-0.781113\pi\) | ||
0.772736 | − | 0.634727i | \(-0.218887\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.80448 | − | 3.39293i | −0.214358 | − | 0.191170i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.73126i | 0.209569i | 0.994495 | + | 0.104784i | \(0.0334152\pi\) | ||||
−0.994495 | + | 0.104784i | \(0.966585\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −37.9141 | −2.12278 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.09433 | −0.451781 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 4.75872i | − | 0.264782i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.5193 | + | 1.55116i | −0.749916 | + | 0.0860427i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.78405i | 0.319859i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.9097 | −0.932265 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.1801 | −0.559549 | −0.279774 | − | 0.960066i | \(-0.590260\pi\) | ||||
−0.279774 | + | 0.960066i | \(0.590260\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 4.23986i | − | 0.232343i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.66882 | + | 1.48830i | 0.0911776 | + | 0.0813144i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.4260i | 0.894780i | 0.894339 | + | 0.447390i | \(0.147646\pi\) | ||||
−0.894339 | + | 0.447390i | \(0.852354\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.65478 | −0.198500 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 42.1853 | 2.28446 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.0681i | − | 1.08357i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.240696 | − | 0.269891i | 0.0129586 | − | 0.0145305i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 1.60438i | − | 0.0861276i | −0.999072 | − | 0.0430638i | \(-0.986288\pi\) | ||
0.999072 | − | 0.0430638i | \(-0.0137119\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.2484 | −0.923287 | −0.461643 | − | 0.887066i | \(-0.652740\pi\) | ||||
−0.461643 | + | 0.887066i | \(0.652740\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.72160 | 0.145268 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.5568i | 1.20058i | 0.799782 | + | 0.600290i | \(0.204948\pi\) | ||||
−0.799782 | + | 0.600290i | \(0.795052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.76695 | + | 6.46646i | −0.306078 | + | 0.343204i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.78616i | 0.465013i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.62266 | 0.402309 | 0.201154 | − | 0.979560i | \(-0.435531\pi\) | ||||
0.201154 | + | 0.979560i | \(0.435531\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4754 | −0.919758 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 4.10633i | − | 0.215526i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.85152 | + | 3.43488i | 0.201598 | + | 0.179790i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 19.3969i | − | 1.01251i | −0.862384 | − | 0.506255i | \(-0.831029\pi\) | ||
0.862384 | − | 0.506255i | \(-0.168971\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.12803 | 0.475186 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.5526 | −0.599782 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 12.8379i | − | 0.664719i | −0.943153 | − | 0.332360i | \(-0.892155\pi\) | ||
0.943153 | − | 0.332360i | \(-0.107845\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.44185 | − | 9.13797i | 0.332656 | − | 0.471883i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 26.5488i | 1.36733i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.10468 | −0.416309 | −0.208155 | − | 0.978096i | \(-0.566746\pi\) | ||||
−0.208155 | + | 0.978096i | \(0.566746\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.9034 | −0.661060 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 8.55938i | − | 0.437364i | −0.975796 | − | 0.218682i | \(-0.929824\pi\) | ||
0.975796 | − | 0.218682i | \(-0.0701757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.7868 | + | 13.1873i | 0.753607 | + | 0.672085i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 12.4359i | − | 0.632151i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.87946 | 0.500908 | 0.250454 | − | 0.968128i | \(-0.419420\pi\) | ||||
0.250454 | + | 0.968128i | \(0.419420\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.623293 | −0.0315213 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.9854i | 1.00813i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.0339 | − | 13.4936i | 0.605492 | − | 0.678937i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 20.7352i | − | 1.04067i | −0.853963 | − | 0.520334i | \(-0.825807\pi\) | ||
0.853963 | − | 0.520334i | \(-0.174193\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.81489 | −0.140921 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.4242 | 1.66913 | 0.834563 | − | 0.550912i | \(-0.185720\pi\) | ||||
0.834563 | + | 0.550912i | \(0.185720\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 29.5397i | − | 1.47148i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.48830 | + | 1.66882i | −0.0739541 | + | 0.0829245i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.4790i | 0.816834i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.6294 | 1.51453 | 0.757264 | − | 0.653109i | \(-0.226536\pi\) | ||||
0.757264 | + | 0.653109i | \(0.226536\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.53325 | 0.322261 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.148692i | 0.00731668i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.7957 | + | 13.1951i | 0.726290 | + | 0.647723i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.62443i | 0.275430i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.0095 | 1.02638 | 0.513190 | − | 0.858275i | \(-0.328463\pi\) | ||||
0.513190 | + | 0.858275i | \(0.328463\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.1206 | 0.834409 | 0.417204 | − | 0.908813i | \(-0.363010\pi\) | ||||
0.417204 | + | 0.908813i | \(0.363010\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.41740i | 0.360646i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.1445 | + | 2.19657i | −0.928645 | + | 0.106549i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 16.9850i | − | 0.821962i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.5780 | −0.510711 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.5836 | −0.750634 | −0.375317 | − | 0.926896i | \(-0.622466\pi\) | ||||
−0.375317 | + | 0.926896i | \(0.622466\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.486658i | 0.0233873i | 0.999932 | + | 0.0116937i | \(0.00372229\pi\) | ||||
−0.999932 | + | 0.0116937i | \(0.996278\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −16.2791 | − | 14.5181i | −0.780525 | − | 0.696091i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.199689i | − | 0.00955243i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.0056 | −1.90936 | −0.954682 | − | 0.297627i | \(-0.903805\pi\) | ||||
−0.954682 | + | 0.297627i | \(0.903805\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.80279 | −0.0858470 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.02574i | 0.191269i | 0.995417 | + | 0.0956343i | \(0.0304879\pi\) | ||||
−0.995417 | + | 0.0956343i | \(0.969512\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.99964 | − | 4.48478i | 0.189601 | − | 0.212599i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.5646i | 1.01997i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −40.3821 | −1.90575 | −0.952874 | − | 0.303365i | \(-0.901890\pi\) | ||||
−0.952874 | + | 0.303365i | \(0.901890\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −35.4778 | −1.67058 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.05311i | 0.237416i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.23420 | − | 10.3543i | 0.432906 | − | 0.485416i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.4734i | 0.910928i | 0.890254 | + | 0.455464i | \(0.150527\pi\) | ||||
−0.890254 | + | 0.455464i | \(0.849473\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.85402 | 0.179890 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.6889 | 0.917004 | 0.458502 | − | 0.888693i | \(-0.348386\pi\) | ||||
0.458502 | + | 0.888693i | \(0.348386\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12.4105i | − | 0.576764i | −0.957515 | − | 0.288382i | \(-0.906883\pi\) | ||
0.957515 | − | 0.288382i | \(-0.0931173\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 18.1131 | + | 16.1537i | 0.839974 | + | 0.749109i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 20.1256i | 0.931301i | 0.884969 | + | 0.465651i | \(0.154180\pi\) | ||||
−0.884969 | + | 0.465651i | \(0.845820\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.27974 | −0.105269 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.8662 | −0.638920 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 48.3343i | 2.22242i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.703733 | − | 6.13347i | −0.0322895 | − | 0.281423i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.06751i | 0.232025i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.59480 | 0.255633 | 0.127817 | − | 0.991798i | \(-0.459203\pi\) | ||||
0.127817 | + | 0.991798i | \(0.459203\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.5392 | 0.526142 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.368692i | 0.0167761i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.92094 | + | 1.71314i | 0.0872256 | + | 0.0777899i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.0557i | 1.54321i | 0.636102 | + | 0.771605i | \(0.280546\pi\) | ||||
−0.636102 | + | 0.771605i | \(0.719454\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.76448 | −0.260679 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.9025 | 1.25922 | 0.629610 | − | 0.776911i | \(-0.283215\pi\) | ||||
0.629610 | + | 0.776911i | \(0.283215\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 37.5954i | 1.69321i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.78454 | − | 6.48619i | 0.259996 | − | 0.291533i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.83368i | − | 0.396244i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.38592 | −0.196341 | −0.0981704 | − | 0.995170i | \(-0.531299\pi\) | ||||
−0.0981704 | + | 0.995170i | \(0.531299\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.8637 | −0.842768 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 31.2404i | − | 1.39294i | −0.717587 | − | 0.696469i | \(-0.754753\pi\) | ||
0.717587 | − | 0.696469i | \(-0.245247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.17319 | + | 3.55809i | −0.141205 | + | 0.158333i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 5.59288i | − | 0.248389i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.63552 | −0.116817 | −0.0584086 | − | 0.998293i | \(-0.518603\pi\) | ||||
−0.0584086 | + | 0.998293i | \(0.518603\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.26147 | −0.232754 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.23474i | 0.0545152i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.0023 | + | 23.1895i | 1.14580 | + | 1.02185i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 28.8291i | − | 1.26790i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.8368 | −0.475681 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.6715 | −0.949447 | −0.474724 | − | 0.880135i | \(-0.657452\pi\) | ||||
−0.474724 | + | 0.880135i | \(0.657452\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 21.1240i | − | 0.923689i | −0.886961 | − | 0.461844i | \(-0.847188\pi\) | ||
0.886961 | − | 0.461844i | \(-0.152812\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.29932 | + | 11.3244i | 0.0567070 | + | 0.494237i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 41.8308i | − | 1.82218i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9738 | 0.998863 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.0652234 | 0.00283046 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.8429i | 1.07606i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.5080 | + | 12.0468i | 0.584002 | + | 0.520827i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.6207i | 0.717235i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.00687 | 0.301807 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.66496 | −0.157569 | −0.0787845 | − | 0.996892i | \(-0.525104\pi\) | ||||
−0.0787845 | + | 0.996892i | \(0.525104\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.6918i | 0.544659i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.60839 | − | 9.65256i | 0.368743 | − | 0.413470i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 39.5115i | − | 1.68939i | −0.535247 | − | 0.844695i | \(-0.679782\pi\) | ||
0.535247 | − | 0.844695i | \(-0.320218\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.45042 | −0.317976 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0447 | −0.513123 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.4333i | 0.783863i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.31017 | + | 7.07557i | −0.267852 | + | 0.300341i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.3346i | 0.649746i | 0.945758 | + | 0.324873i | \(0.105322\pi\) | ||||
−0.945758 | + | 0.324873i | \(0.894678\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.8455 | 1.43151 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.9794 | −0.632429 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 18.3118i | − | 0.771752i | −0.922551 | − | 0.385876i | \(-0.873899\pi\) | ||
0.922551 | − | 0.385876i | \(-0.126101\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.09917 | + | 5.43939i | 0.256594 | + | 0.228837i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.27974i | − | 0.0957401i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.12196 | −0.382412 | −0.191206 | − | 0.981550i | \(-0.561240\pi\) | ||||
−0.191206 | + | 0.981550i | \(0.561240\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.7529 | 0.491845 | 0.245923 | − | 0.969289i | \(-0.420909\pi\) | ||||
0.245923 | + | 0.969289i | \(0.420909\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.01139i | 0.0840270i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.803357 | + | 0.0921743i | −0.0335023 | + | 0.00384393i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 34.5379i | 1.43783i | 0.695097 | + | 0.718916i | \(0.255361\pi\) | ||||
−0.695097 | + | 0.718916i | \(0.744639\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.75904 | −0.197779 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.2120 | −0.838535 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 19.6958i | − | 0.815718i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.54187 | − | 4.05055i | −0.187783 | − | 0.167470i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 12.3284i | − | 0.508846i | −0.967093 | − | 0.254423i | \(-0.918114\pi\) | ||
0.967093 | − | 0.254423i | \(-0.0818856\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.4016 | 0.552205 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.07304 | 0.0441389 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 23.4776i | − | 0.964109i | −0.876141 | − | 0.482055i | \(-0.839891\pi\) | ||
0.876141 | − | 0.482055i | \(-0.160109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.0764 | − | 14.6626i | 0.536081 | − | 0.601106i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.9745i | 0.449157i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −34.7559 | −1.42009 | −0.710044 | − | 0.704157i | \(-0.751325\pi\) | ||||
−0.710044 | + | 0.704157i | \(0.751325\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.6597 | 1.69933 | 0.849666 | − | 0.527321i | \(-0.176803\pi\) | ||||
0.849666 | + | 0.527321i | \(0.176803\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.11143 | + | 6.85273i | −0.248465 | + | 0.278603i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.5458i | 1.19923i | 0.800289 | + | 0.599614i | \(0.204679\pi\) | ||||
−0.800289 | + | 0.599614i | \(0.795321\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.2385 | 0.901151 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.1872 | −0.816687 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 10.0608i | − | 0.406350i | −0.979142 | − | 0.203175i | \(-0.934874\pi\) | ||
0.979142 | − | 0.203175i | \(-0.0651261\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.2331 | − | 13.5852i | −0.614257 | − | 0.547809i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 26.6890i | − | 1.07446i | −0.843436 | − | 0.537230i | \(-0.819471\pi\) | ||
0.843436 | − | 0.537230i | \(-0.180529\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.5096 | 1.34687 | 0.673433 | − | 0.739249i | \(-0.264819\pi\) | ||||
0.673433 | + | 0.739249i | \(0.264819\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.161725 | 0.00648982 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.12655i | 0.245455i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.3503 | + | 5.66228i | −0.974013 | + | 0.226491i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 4.79906i | − | 0.191656i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.3405 | 0.651538 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.9025 | −0.792304 | −0.396152 | − | 0.918185i | \(-0.629655\pi\) | ||||
−0.396152 | + | 0.918185i | \(0.629655\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 24.4378i | − | 0.971313i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.5334 | + | 19.2041i | 0.854529 | + | 0.762090i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.90647i | − | 0.194401i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.87486 | −0.153287 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.56821 | 0.377922 | 0.188961 | − | 0.981985i | \(-0.439488\pi\) | ||||
0.188961 | + | 0.981985i | \(0.439488\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.7300i | 0.502021i | 0.967984 | + | 0.251010i | \(0.0807628\pi\) | ||||
−0.967984 | + | 0.251010i | \(0.919237\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.5083 | + | 20.7533i | −0.728763 | + | 0.817159i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 18.0478i | − | 0.709531i | −0.934955 | − | 0.354765i | \(-0.884561\pi\) | ||
0.934955 | − | 0.354765i | \(-0.115439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.253503 | −0.00995086 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.7438 | −0.969787 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 20.1281i | − | 0.787672i | −0.919181 | − | 0.393836i | \(-0.871148\pi\) | ||
0.919181 | − | 0.393836i | \(-0.128852\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.7443 | − | 33.3521i | 1.16220 | − | 1.30318i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.30792i | 0.0900407i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.1040 | −1.01687 | −0.508434 | − | 0.861101i | \(-0.669775\pi\) | ||||
−0.508434 | + | 0.861101i | \(0.669775\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.2574 | −0.515651 | −0.257826 | − | 0.966191i | \(-0.583006\pi\) | ||||
−0.257826 | + | 0.966191i | \(0.583006\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.4891i | 0.407363i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.69756 | + | 4.18939i | 0.182163 | + | 0.162458i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.57761i | 0.0610853i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.32846 | 0.206010 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.9574 | 1.11789 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 28.2301i | − | 1.08819i | −0.839023 | − | 0.544096i | \(-0.816873\pi\) | ||
0.839023 | − | 0.544096i | \(-0.183127\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.96741 | − | 0.569943i | 0.191196 | − | 0.0219371i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.3356i | 0.666260i | 0.942881 | + | 0.333130i | \(0.108105\pi\) | ||||
−0.942881 | + | 0.333130i | \(0.891895\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.62416 | −0.100706 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 22.7953 | 0.873517 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.7676i | 1.25382i | 0.779093 | + | 0.626908i | \(0.215680\pi\) | ||||
−0.779093 | + | 0.626908i | \(0.784320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.9028 | − | 9.72341i | −0.416576 | − | 0.371512i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 8.67796i | − | 0.331085i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.7917 | −0.525424 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.08102 | 0.155249 | 0.0776246 | − | 0.996983i | \(-0.475266\pi\) | ||||
0.0776246 | + | 0.996983i | \(0.475266\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.86063i | 0.336588i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.37083 | − | 9.38619i | 0.317524 | − | 0.356038i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.1796i | 1.33252i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.66975 | −0.252273 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.90316 | 0.374037 | 0.187019 | − | 0.982356i | \(-0.440118\pi\) | ||||
0.187019 | + | 0.982356i | \(0.440118\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.23513i | 0.197447i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.0393 | − | 12.3783i | 0.415764 | − | 0.466195i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.86062i | − | 0.182803i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.9691 | 1.46351 | 0.731757 | − | 0.681565i | \(-0.238700\pi\) | ||||
0.731757 | + | 0.681565i | \(0.238700\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.08570 | 0.303237 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.75534i | − | 0.0657378i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.6528 | + | 15.7432i | 0.660178 | + | 0.588763i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 15.3814i | − | 0.574428i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.2921 | 1.76370 | 0.881849 | − | 0.471532i | \(-0.156299\pi\) | ||||
0.881849 | + | 0.471532i | \(0.156299\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.5212 | −1.32288 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.01457i | 0.149303i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.55971 | + | 48.4564i | 0.206483 | + | 1.79962i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5783i | 0.726119i | 0.931766 | + | 0.363059i | \(0.118268\pi\) | ||||
−0.931766 | + | 0.363059i | \(0.881732\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 47.9281 | 1.77269 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0434i | 0.444834i | 0.974952 | + | 0.222417i | \(0.0713946\pi\) | ||||
−0.974952 | + | 0.222417i | \(0.928605\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.00853 | + | 2.68308i | 0.110971 | + | 0.0989670i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.88669i | − | 0.143168i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.0068 | 1.47167 | 0.735837 | − | 0.677159i | \(-0.236789\pi\) | ||||
0.735837 | + | 0.677159i | \(0.236789\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.36048 | −0.123450 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.5666i | 1.15807i | 0.815304 | + | 0.579034i | \(0.196570\pi\) | ||||
−0.815304 | + | 0.579034i | \(0.803430\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.0945 | − | 35.9875i | 1.17585 | − | 1.31848i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.86592i | 0.324387i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.4530 | −0.674257 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.72646 | 0.318433 | 0.159216 | − | 0.987244i | \(-0.449103\pi\) | ||||
0.159216 | + | 0.987244i | \(0.449103\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.9509i | 0.399072i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.52053 | − | 8.43275i | 0.273700 | − | 0.306899i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.1970i | 0.515997i | 0.966145 | + | 0.257999i | \(0.0830630\pi\) | ||||
−0.966145 | + | 0.257999i | \(0.916937\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.628576 | −0.0228159 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.3610 | 1.28183 | 0.640917 | − | 0.767610i | \(-0.278554\pi\) | ||||
0.640917 | + | 0.767610i | \(0.278554\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.1861i | 0.477370i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.43168 | − | 5.73593i | −0.232538 | − | 0.207383i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.177512i | 0.00640959i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.779635 | −0.0281143 | −0.0140572 | − | 0.999901i | \(-0.504475\pi\) | ||||
−0.0140572 | + | 0.999901i | \(0.504475\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.69302 | 0.0609726 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 52.1308i | 1.87502i | 0.347964 | + | 0.937508i | \(0.386873\pi\) | ||||
−0.347964 | + | 0.937508i | \(0.613127\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.18605 | − | 53.9153i | −0.222209 | − | 1.93669i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 9.66577i | − | 0.346758i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.2708 | −0.403817 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.0604 | 0.538902 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 9.75486i | − | 0.348610i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.1402 | + | 20.6370i | 0.825910 | + | 0.736566i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 51.9579i | 1.85210i | 0.377401 | + | 0.926050i | \(0.376818\pi\) | ||||
−0.377401 | + | 0.926050i | \(0.623182\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.998029 | −0.0355308 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.33194 | −0.296250 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 20.2771i | − | 0.720060i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.54196 | − | 8.45678i | 0.267486 | − | 0.299931i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 28.5644i | − | 1.01180i | −0.862591 | − | 0.505902i | \(-0.831160\pi\) | ||
0.862591 | − | 0.505902i | \(-0.168840\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.5868 | −1.01133 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.68739 | 0.0949543 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 8.97018i | − | 0.316551i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.548723 | − | 0.615282i | 0.0193400 | − | 0.0216858i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.88253i | 0.101470i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.5004 | −1.17781 | −0.588906 | − | 0.808201i | \(-0.700441\pi\) | ||||
−0.588906 | + | 0.808201i | \(0.700441\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.9318 | 1.08616 | 0.543080 | − | 0.839681i | \(-0.317258\pi\) | ||||
0.543080 | + | 0.839681i | \(0.317258\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.80680i | − | 0.0633671i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.61989 | + | 8.57926i | 0.336970 | + | 0.300518i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.3551i | 0.537207i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.20454 | 0.216804 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5969 | 0.579237 | 0.289618 | − | 0.957142i | \(-0.406472\pi\) | ||||
0.289618 | + | 0.957142i | \(0.406472\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 25.7367i | − | 0.897126i | −0.893751 | − | 0.448563i | \(-0.851936\pi\) | ||
0.893751 | − | 0.448563i | \(-0.148064\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.3068 | + | 2.21519i | −0.672175 | + | 0.0771230i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 38.4310i | − | 1.33638i | −0.743993 | − | 0.668188i | \(-0.767070\pi\) | ||
0.743993 | − | 0.668188i | \(-0.232930\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.4655 | −0.710796 | −0.355398 | − | 0.934715i | \(-0.615655\pi\) | ||||
−0.355398 | + | 0.934715i | \(0.615655\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.4411 | −0.396886 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 6.94798i | − | 0.240733i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.4802 | + | 28.0748i | 1.08942 | + | 0.971568i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.8538i | 0.375162i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.9168 | 1.61975 | 0.809874 | − | 0.586604i | \(-0.199535\pi\) | ||||
0.809874 | + | 0.586604i | \(0.199535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 66.1572 | 2.28128 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 0.457325i | − | 0.0157511i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.32387 | + | 9.33354i | −0.286350 | + | 0.321083i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.36135i | − | 0.321660i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.02400 | 0.241063 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.685693 | 0.0235053 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 38.3929i | − | 1.31455i | −0.753651 | − | 0.657275i | \(-0.771709\pi\) | ||
0.753651 | − | 0.657275i | \(-0.228291\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.83766 | − | 2.06057i | 0.0628468 | − | 0.0704699i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 10.9002i | − | 0.372345i | −0.982517 | − | 0.186173i | \(-0.940392\pi\) | ||
0.982517 | − | 0.186173i | \(-0.0596084\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.0685 | −1.19652 | −0.598260 | − | 0.801302i | \(-0.704141\pi\) | ||||
−0.598260 | + | 0.801302i | \(0.704141\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.8095 | 0.709187 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 23.5963i | − | 0.803228i | −0.915809 | − | 0.401614i | \(-0.868449\pi\) | ||
0.915809 | − | 0.401614i | \(-0.131551\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.0847 | + | 16.1283i | 0.614897 | + | 0.548380i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2.14653i | − | 0.0729000i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.4266 | −1.06607 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.72160 | −0.0922180 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.15108i | 0.0389581i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.6857 | − | 20.8322i | 0.496469 | − | 0.704257i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 7.93938i | − | 0.268094i | −0.990975 | − | 0.134047i | \(-0.957203\pi\) | ||
0.990975 | − | 0.134047i | \(-0.0427973\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.84673 | 0.230935 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.2818 | 0.413784 | 0.206892 | − | 0.978364i | \(-0.433665\pi\) | ||||
0.206892 | + | 0.978364i | \(0.433665\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.0387i | 1.85220i | 0.377279 | + | 0.926100i | \(0.376860\pi\) | ||||
−0.377279 | + | 0.926100i | \(0.623140\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.108846 | − | 0.0970719i | −0.00365883 | − | 0.00326303i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 29.0853i | − | 0.976590i | −0.872679 | − | 0.488295i | \(-0.837619\pi\) | ||
0.872679 | − | 0.488295i | \(-0.162381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.4163 | −0.986592 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.88669 | 0.130209 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 9.15858i | − | 0.306480i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.7365 | − | 27.7370i | 0.826850 | − | 0.927144i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.440152i | 0.0146963i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −105.877 | −3.53120 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.5303 | −0.650648 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 28.3506i | − | 0.943447i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.8892 | − | 21.1804i | 0.627899 | − | 0.704061i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 40.5491i | − | 1.34641i | −0.739455 | − | 0.673206i | \(-0.764917\pi\) | ||
0.739455 | − | 0.673206i | \(-0.235083\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.13210 | −0.0707171 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.4870 | −0.446843 | −0.223422 | − | 0.974722i | \(-0.571723\pi\) | ||||
−0.223422 | + | 0.974722i | \(0.571723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 34.4590i | − | 1.14043i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.4334 | + | 11.0884i | 0.411036 | + | 0.366572i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.5616i | 1.50458i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.9824 | −0.956040 | −0.478020 | − | 0.878349i | \(-0.658645\pi\) | ||||
−0.478020 | + | 0.878349i | \(0.658645\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.8667 | 0.687581 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 10.5458i | − | 0.347120i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.0611 | − | 2.41648i | 0.692485 | − | 0.0794533i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.5812i | 0.511755i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.6344 | −0.709801 | −0.354900 | − | 0.934904i | \(-0.615485\pi\) | ||||
−0.354900 | + | 0.934904i | \(0.615485\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.22598 | 0.0729535 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 13.8030i | − | 0.451890i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.9979 | + | 22.2937i | 0.817519 | + | 0.729083i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.0595i | 1.37403i | 0.726645 | + | 0.687013i | \(0.241078\pi\) | ||||
−0.726645 | + | 0.687013i | \(0.758922\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.4589 | −0.732920 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.5898 | 1.25799 | 0.628995 | − | 0.777409i | \(-0.283467\pi\) | ||||
0.628995 | + | 0.777409i | \(0.283467\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.47623i | 0.0480728i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.39293 | + | 3.80448i | −0.110372 | + | 0.123760i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.6306i | 0.605412i | 0.953084 | + | 0.302706i | \(0.0978901\pi\) | ||||
−0.953084 | + | 0.302706i | \(0.902110\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.28125 | −0.203898 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.73126 | 0.120994 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31.6650i | − | 1.02573i | −0.858469 | − | 0.512865i | \(-0.828584\pi\) | ||
0.858469 | − | 0.512865i | \(-0.171416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.99355 | − | 3.35666i | 0.0968689 | − | 0.108619i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 37.9141i | 1.22559i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.8941 | 0.480956 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 86.8049 | 2.80016 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.09433i | 0.260836i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.94199 | + | 7.08286i | 0.255662 | + | 0.228005i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 17.2507i | − | 0.554745i | −0.960762 | − | 0.277372i | \(-0.910536\pi\) | ||
0.960762 | − | 0.277372i | \(-0.0894636\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.75872 | −0.152872 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.75845 | −0.281072 | −0.140536 | − | 0.990076i | \(-0.544883\pi\) | ||||
−0.140536 | + | 0.990076i | \(0.544883\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.8222i | 0.411062i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.55116 | + | 13.5193i | 0.0496768 | + | 0.432964i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 0.555060i | − | 0.0177579i | −0.999961 | − | 0.00887897i | \(-0.997174\pi\) | ||
0.999961 | − | 0.00887897i | \(-0.00282630\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.4450 | −0.333825 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.78405 | 0.184671 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.8498i | 1.52617i | 0.646297 | + | 0.763086i | \(0.276317\pi\) | ||||
−0.646297 | + | 0.763086i | \(0.723683\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.79071 | − | 1.59700i | −0.0570568 | − | 0.0508846i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 16.9097i | 0.538243i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.01120 | 0.0639524 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.3471 | 0.868709 | 0.434355 | − | 0.900742i | \(-0.356976\pi\) | ||||
0.434355 | + | 0.900742i | \(0.356976\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.1801i | 0.323056i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.3333 | − | 18.3145i | 0.517802 | − | 0.580610i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.6216i | 1.12815i | 0.825724 | + | 0.564074i | \(0.190767\pi\) | ||||
−0.825724 | + | 0.564074i | \(0.809233\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.23986 | −0.134143 |
(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 | 4020.2.g.c.1609.5 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.24 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.5 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.24 | yes | 38 | 5.4 | even | 2 | inner |