Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(793,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.q (of order \(3\), degree \(2\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 793.9 | ||
Character | \(\chi\) | \(=\) | 1512.793 |
Dual form | 1512.2.q.c.1369.9 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.927957 | + | 1.60727i | 0.414995 | + | 0.718793i | 0.995428 | − | 0.0955156i | \(-0.0304500\pi\) |
−0.580433 | + | 0.814308i | \(0.697117\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.900017 | − | 2.48796i | 0.340174 | − | 0.940362i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.28800 | + | 2.23089i | −0.388348 | + | 0.672638i | −0.992227 | − | 0.124437i | \(-0.960287\pi\) |
0.603880 | + | 0.797076i | \(0.293621\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82227 | − | 4.88832i | 0.782757 | − | 1.35578i | −0.147573 | − | 0.989051i | \(-0.547146\pi\) |
0.930330 | − | 0.366724i | \(-0.119521\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.57951 | − | 6.19989i | −0.868158 | − | 1.50369i | −0.863876 | − | 0.503704i | \(-0.831970\pi\) |
−0.00428199 | − | 0.999991i | \(-0.501363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.636599 | − | 1.10262i | 0.146046 | − | 0.252959i | −0.783717 | − | 0.621118i | \(-0.786679\pi\) |
0.929763 | + | 0.368160i | \(0.120012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.120639 | + | 0.208952i | 0.0251549 | + | 0.0435696i | 0.878329 | − | 0.478057i | \(-0.158659\pi\) |
−0.853174 | + | 0.521627i | \(0.825325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.777791 | − | 1.34717i | 0.155558 | − | 0.269435i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.923571 | − | 1.59967i | −0.171503 | − | 0.297051i | 0.767443 | − | 0.641118i | \(-0.221529\pi\) |
−0.938945 | + | 0.344066i | \(0.888196\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.99103 | −0.537205 | −0.268602 | − | 0.963251i | \(-0.586562\pi\) | ||||
−0.268602 | + | 0.963251i | \(0.586562\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.83401 | − | 0.862156i | 0.817096 | − | 0.145731i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.338260 | − | 0.585884i | 0.0556097 | − | 0.0963188i | −0.836880 | − | 0.547386i | \(-0.815623\pi\) |
0.892490 | + | 0.451067i | \(0.148956\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.733933 | − | 1.27121i | 0.114621 | − | 0.198529i | −0.803007 | − | 0.595969i | \(-0.796768\pi\) |
0.917628 | + | 0.397440i | \(0.130101\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.14269 | + | 7.17535i | 0.631754 | + | 1.09423i | 0.987193 | + | 0.159531i | \(0.0509981\pi\) |
−0.355439 | + | 0.934700i | \(0.615669\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.3145 | 1.79625 | 0.898124 | − | 0.439742i | \(-0.144930\pi\) | ||||
0.898124 | + | 0.439742i | \(0.144930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.37994 | − | 4.47842i | −0.768563 | − | 0.639774i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.35508 | − | 5.81117i | −0.460856 | − | 0.798226i | 0.538148 | − | 0.842851i | \(-0.319124\pi\) |
−0.999004 | + | 0.0446243i | \(0.985791\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.78085 | −0.644650 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.08279 | −0.271156 | −0.135578 | − | 0.990767i | \(-0.543289\pi\) | ||||
−0.135578 | + | 0.990767i | \(0.543289\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9595 | 1.65929 | 0.829644 | − | 0.558292i | \(-0.188543\pi\) | ||||
0.829644 | + | 0.558292i | \(0.188543\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.4758 | 1.29936 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.83102 | −0.590203 | −0.295102 | − | 0.955466i | \(-0.595354\pi\) | ||||
−0.295102 | + | 0.955466i | \(0.595354\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.53621 | 0.182314 | 0.0911572 | − | 0.995837i | \(-0.470943\pi\) | ||||
0.0911572 | + | 0.995837i | \(0.470943\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.55954 | − | 11.3615i | −0.767736 | − | 1.32976i | −0.938788 | − | 0.344496i | \(-0.888050\pi\) |
0.171052 | − | 0.985262i | \(-0.445283\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.39115 | + | 5.21235i | 0.500418 | + | 0.594002i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.72018 | −0.418553 | −0.209277 | − | 0.977856i | \(-0.567111\pi\) | ||||
−0.209277 | + | 0.977856i | \(0.567111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.00173 | + | 5.19915i | 0.329483 | + | 0.570681i | 0.982409 | − | 0.186740i | \(-0.0597922\pi\) |
−0.652926 | + | 0.757421i | \(0.726459\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.64326 | − | 11.5065i | 0.720563 | − | 1.24805i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.60349 | + | 11.4376i | −0.699968 | + | 1.21238i | 0.268509 | + | 0.963277i | \(0.413469\pi\) |
−0.968477 | + | 0.249103i | \(0.919864\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.62187 | − | 11.4213i | −1.00865 | − | 1.19728i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.36294 | 0.242433 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.40860 | + | 11.1000i | 0.650695 | + | 1.12704i | 0.982955 | + | 0.183848i | \(0.0588556\pi\) |
−0.332260 | + | 0.943188i | \(0.607811\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.10066 | − | 10.5667i | 0.607039 | − | 1.05142i | −0.384687 | − | 0.923047i | \(-0.625691\pi\) |
0.991726 | − | 0.128375i | \(-0.0409760\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.82163 | − | 11.8154i | −0.672155 | − | 1.16421i | −0.977292 | − | 0.211898i | \(-0.932036\pi\) |
0.305137 | − | 0.952309i | \(-0.401298\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.48002 | − | 11.2237i | 0.626448 | − | 1.08504i | −0.361811 | − | 0.932251i | \(-0.617842\pi\) |
0.988259 | − | 0.152788i | \(-0.0488251\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.70089 | + | 13.3383i | 0.737612 | + | 1.27758i | 0.953568 | + | 0.301178i | \(0.0973799\pi\) |
−0.215956 | + | 0.976403i | \(0.569287\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.73446 | − | 13.3965i | 0.727597 | − | 1.26023i | −0.230299 | − | 0.973120i | \(-0.573971\pi\) |
0.957896 | − | 0.287115i | \(-0.0926961\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.223895 | + | 0.387797i | −0.0208783 | + | 0.0361623i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.6467 | + | 3.32569i | −1.70934 | + | 0.304865i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.18209 | + | 3.77949i | 0.198372 | + | 0.343590i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1666 | 1.08821 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.19404 | −0.283425 | −0.141713 | − | 0.989908i | \(-0.545261\pi\) | ||||
−0.141713 | + | 0.989908i | \(0.545261\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.04338 | + | 12.1995i | 0.615383 | + | 1.06587i | 0.990317 | + | 0.138823i | \(0.0443318\pi\) |
−0.374935 | + | 0.927051i | \(0.622335\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.17033 | − | 2.57621i | −0.188192 | − | 0.223386i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.84818 | − | 11.8614i | 0.585079 | − | 1.01339i | −0.409786 | − | 0.912182i | \(-0.634397\pi\) |
0.994866 | − | 0.101206i | \(-0.0322700\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.94131 | + | 8.55859i | −0.419116 | + | 0.725931i | −0.995851 | − | 0.0910010i | \(-0.970993\pi\) |
0.576735 | + | 0.816932i | \(0.304327\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.27019 | + | 12.5923i | 0.607964 | + | 1.05302i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.71407 | − | 2.96885i | 0.142346 | − | 0.246550i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.96015 | − | 3.39507i | −0.160581 | − | 0.278135i | 0.774496 | − | 0.632579i | \(-0.218004\pi\) |
−0.935077 | + | 0.354444i | \(0.884670\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.78920 | + | 16.9554i | −0.796634 | + | 1.37981i | 0.125162 | + | 0.992136i | \(0.460055\pi\) |
−0.921796 | + | 0.387674i | \(0.873278\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.77555 | − | 4.80739i | −0.222937 | − | 0.386139i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.7927 | 1.18059 | 0.590295 | − | 0.807188i | \(-0.299012\pi\) | ||||
0.590295 | + | 0.807188i | \(0.299012\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.628443 | − | 0.112084i | 0.0495282 | − | 0.00883347i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.54686 | − | 13.0715i | 0.591116 | − | 1.02384i | −0.402967 | − | 0.915215i | \(-0.632021\pi\) |
0.994082 | − | 0.108628i | \(-0.0346456\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.92946 | + | 3.34192i | −0.149306 | + | 0.258605i | −0.930971 | − | 0.365093i | \(-0.881037\pi\) |
0.781665 | + | 0.623698i | \(0.214371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.43043 | − | 16.3340i | −0.725418 | − | 1.25646i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.651571 | −0.0495380 | −0.0247690 | − | 0.999693i | \(-0.507885\pi\) | ||||
−0.0247690 | + | 0.999693i | \(0.507885\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.65170 | − | 3.14760i | −0.200449 | − | 0.237936i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.9059 | − | 18.8896i | −0.815145 | − | 1.41187i | −0.909223 | − | 0.416308i | \(-0.863324\pi\) |
0.0940781 | − | 0.995565i | \(-0.470010\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.0338 | −1.86075 | −0.930374 | − | 0.366613i | \(-0.880517\pi\) | ||||
−0.930374 | + | 0.366613i | \(0.880517\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.25556 | 0.0923109 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.4417 | 1.34859 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.66073 | −0.626668 | −0.313334 | − | 0.949643i | \(-0.601446\pi\) | ||||
−0.313334 | + | 0.949643i | \(0.601446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.61664 | 0.116369 | 0.0581843 | − | 0.998306i | \(-0.481469\pi\) | ||||
0.0581843 | + | 0.998306i | \(0.481469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.7746 | −0.767659 | −0.383829 | − | 0.923404i | \(-0.625395\pi\) | ||||
−0.383829 | + | 0.923404i | \(0.625395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.38768 | + | 4.13558i | 0.169258 | + | 0.293163i | 0.938159 | − | 0.346204i | \(-0.112530\pi\) |
−0.768901 | + | 0.639368i | \(0.779196\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.81115 | + | 0.858080i | −0.337677 | + | 0.0602254i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.72423 | 0.190269 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.63988 | + | 2.84036i | 0.113433 | + | 0.196472i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.42787 | − | 4.20520i | 0.167142 | − | 0.289498i | −0.770272 | − | 0.637715i | \(-0.779880\pi\) |
0.937414 | + | 0.348218i | \(0.113213\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.68848 | + | 13.3168i | −0.524350 | + | 0.908200i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.69198 | + | 7.44158i | −0.182743 | + | 0.505167i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −40.4094 | −2.71823 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.86187 | + | 6.68896i | 0.258610 | + | 0.447926i | 0.965870 | − | 0.259028i | \(-0.0834021\pi\) |
−0.707260 | + | 0.706954i | \(0.750069\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.97457 | + | 12.0803i | −0.462919 | + | 0.801799i | −0.999105 | − | 0.0423011i | \(-0.986531\pi\) |
0.536186 | + | 0.844100i | \(0.319864\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.800136 | − | 1.38588i | −0.0528745 | − | 0.0915812i | 0.838377 | − | 0.545091i | \(-0.183505\pi\) |
−0.891251 | + | 0.453510i | \(0.850172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.69939 | + | 6.40753i | −0.242355 | + | 0.419771i | −0.961385 | − | 0.275208i | \(-0.911253\pi\) |
0.719030 | + | 0.694979i | \(0.244587\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.4273 | + | 19.7926i | 0.745434 | + | 1.29113i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.25117 | − | 2.16709i | 0.0809316 | − | 0.140178i | −0.822719 | − | 0.568449i | \(-0.807544\pi\) |
0.903650 | + | 0.428271i | \(0.140877\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.12148 | + | 3.67452i | −0.136657 | + | 0.236697i | −0.926229 | − | 0.376961i | \(-0.876969\pi\) |
0.789572 | + | 0.613658i | \(0.210302\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.20567 | − | 12.8028i | 0.140915 | − | 0.817940i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.59331 | − | 6.22379i | −0.228637 | − | 0.396010i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5381 | 0.854516 | 0.427258 | − | 0.904130i | \(-0.359480\pi\) | ||||
0.427258 | + | 0.904130i | \(0.359480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.621532 | −0.0390754 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.07747 | − | 5.33034i | −0.191968 | − | 0.332497i | 0.753935 | − | 0.656949i | \(-0.228153\pi\) |
−0.945902 | + | 0.324452i | \(0.894820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.15322 | − | 1.36889i | −0.0716576 | − | 0.0850584i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.6706 | + | 21.9460i | −0.781300 | + | 1.35325i | 0.149885 | + | 0.988703i | \(0.452110\pi\) |
−0.931185 | + | 0.364547i | \(0.881224\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.22675 | − | 10.7850i | 0.382506 | − | 0.662520i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.42092 | + | 9.38931i | 0.330519 | + | 0.572476i | 0.982614 | − | 0.185662i | \(-0.0594428\pi\) |
−0.652095 | + | 0.758138i | \(0.726109\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0184 | + | 26.0127i | −0.912306 | + | 1.58016i | −0.101507 | + | 0.994835i | \(0.532366\pi\) |
−0.810799 | + | 0.585325i | \(0.800967\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00360 | + | 3.47033i | 0.120821 | + | 0.209269i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.88147 | + | 17.1152i | −0.593720 | + | 1.02835i | 0.400006 | + | 0.916513i | \(0.369008\pi\) |
−0.993726 | + | 0.111841i | \(0.964325\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.98596 | + | 6.90388i | 0.237782 | + | 0.411851i | 0.960078 | − | 0.279734i | \(-0.0902462\pi\) |
−0.722295 | + | 0.691585i | \(0.756913\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.2127 | 1.37985 | 0.689926 | − | 0.723880i | \(-0.257643\pi\) | ||||
0.689926 | + | 0.723880i | \(0.257643\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.50217 | − | 2.97011i | −0.147698 | − | 0.175320i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.1258 | + | 29.6627i | −1.00740 | + | 1.74486i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.8556 | + | 20.5345i | −0.692612 | + | 1.19964i | 0.278367 | + | 0.960475i | \(0.410207\pi\) |
−0.970979 | + | 0.239164i | \(0.923126\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.93274 | − | 3.34760i | −0.112528 | − | 0.194905i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.36190 | 0.0787607 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.5805 | − | 3.84893i | 1.24388 | − | 0.221849i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0258 | + | 20.8293i | 0.688597 | + | 1.19268i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.87810 | 0.221335 | 0.110668 | − | 0.993857i | \(-0.464701\pi\) | ||||
0.110668 | + | 0.993857i | \(0.464701\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.92439 | 0.392646 | 0.196323 | − | 0.980539i | \(-0.437100\pi\) | ||||
0.196323 | + | 0.980539i | \(0.437100\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.2313 | 1.70878 | 0.854388 | − | 0.519636i | \(-0.173932\pi\) | ||||
0.854388 | + | 0.519636i | \(0.173932\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.37399 | −0.526496 | −0.263248 | − | 0.964728i | \(-0.584794\pi\) | ||||
−0.263248 | + | 0.964728i | \(0.584794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.75825 | 0.266411 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.11484 | −0.507163 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.39027 | − | 7.60418i | −0.243529 | − | 0.421804i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.0832 | − | 30.6379i | 0.611038 | − | 1.68912i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.5441 | 1.51396 | 0.756979 | − | 0.653439i | \(-0.226674\pi\) | ||||
0.756979 | + | 0.653439i | \(0.226674\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.48298 | − | 7.76475i | −0.244931 | − | 0.424234i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.41673 | + | 5.91796i | −0.186121 | + | 0.322372i | −0.943954 | − | 0.330078i | \(-0.892925\pi\) |
0.757832 | + | 0.652449i | \(0.226258\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.85246 | − | 6.67266i | 0.208622 | − | 0.361345i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.9842 | + | 9.35445i | −0.863065 | + | 0.505093i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.1919 | −1.08396 | −0.541979 | − | 0.840392i | \(-0.682325\pi\) | ||||
−0.541979 | + | 0.840392i | \(0.682325\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.25154 | − | 7.36388i | −0.227580 | − | 0.394180i | 0.729511 | − | 0.683970i | \(-0.239748\pi\) |
−0.957090 | + | 0.289790i | \(0.906415\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.35452 | − | 4.07815i | 0.125318 | − | 0.217058i | −0.796539 | − | 0.604587i | \(-0.793338\pi\) |
0.921857 | + | 0.387529i | \(0.126671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.42554 | + | 2.46910i | 0.0756596 | + | 0.131046i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.03357 | + | 10.4504i | −0.318440 | + | 0.551554i | −0.980163 | − | 0.198195i | \(-0.936492\pi\) |
0.661723 | + | 0.749748i | \(0.269825\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.68948 | + | 15.0506i | 0.457341 | + | 0.792138i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.1739 | − | 21.0859i | 0.637213 | − | 1.10369i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.480356 | + | 0.832001i | −0.0250744 | + | 0.0434301i | −0.878290 | − | 0.478128i | \(-0.841316\pi\) |
0.853216 | + | 0.521558i | \(0.174649\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.4776 | + | 3.11717i | −0.907393 | + | 0.161836i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.52499 | + | 6.10547i | 0.182517 | + | 0.316129i | 0.942737 | − | 0.333537i | \(-0.108242\pi\) |
−0.760220 | + | 0.649666i | \(0.774909\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.4263 | −0.536980 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.1330 | −1.90739 | −0.953697 | − | 0.300769i | \(-0.902757\pi\) | ||||
−0.953697 | + | 0.300769i | \(0.902757\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.0988 | + | 27.8839i | 0.822608 | + | 1.42480i | 0.903734 | + | 0.428095i | \(0.140815\pi\) |
−0.0811254 | + | 0.996704i | \(0.525851\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.30285 | + | 11.8946i | −0.219293 | + | 0.606204i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.8713 | + | 22.2937i | −0.652600 | + | 1.13034i | 0.329889 | + | 0.944020i | \(0.392989\pi\) |
−0.982490 | + | 0.186317i | \(0.940345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.863654 | − | 1.49589i | 0.0436769 | − | 0.0756506i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.45217 | − | 5.97933i | −0.173697 | − | 0.300853i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.44903 | − | 16.3662i | 0.474233 | − | 0.821396i | −0.525332 | − | 0.850898i | \(-0.676059\pi\) |
0.999565 | + | 0.0295016i | \(0.00939202\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.60193 | + | 13.1669i | 0.379622 | + | 0.657525i | 0.991007 | − | 0.133808i | \(-0.0427206\pi\) |
−0.611385 | + | 0.791333i | \(0.709387\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.44150 | + | 14.6211i | −0.420501 | + | 0.728329i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.871362 | + | 1.50924i | 0.0431918 | + | 0.0748104i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.9458 | −1.48073 | −0.740363 | − | 0.672207i | \(-0.765346\pi\) | ||||
−0.740363 | + | 0.672207i | \(0.765346\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.87454 | + | 5.18191i | −0.0922403 | + | 0.254985i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.57096 | + | 9.64918i | −0.273468 | + | 0.473660i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.2660 | − | 21.2453i | 0.599231 | − | 1.03790i | −0.393704 | − | 0.919237i | \(-0.628806\pi\) |
0.992935 | − | 0.118661i | \(-0.0378603\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.37791 | − | 4.11866i | −0.115892 | − | 0.200731i | 0.802244 | − | 0.596996i | \(-0.203639\pi\) |
−0.918136 | + | 0.396265i | \(0.870306\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.1364 | −0.540197 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.6637 | − | 32.2427i | 0.564448 | − | 1.56033i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.36446 | − | 2.36331i | −0.0657237 | − | 0.113837i | 0.831291 | − | 0.555837i | \(-0.187602\pi\) |
−0.897015 | + | 0.442000i | \(0.854269\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.5592 | 0.699672 | 0.349836 | − | 0.936811i | \(-0.386237\pi\) | ||||
0.349836 | + | 0.936811i | \(0.386237\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.307194 | 0.0146951 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.88131 | −0.137517 | −0.0687587 | − | 0.997633i | \(-0.521904\pi\) | ||||
−0.0687587 | + | 0.997633i | \(0.521904\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.9731 | −1.18651 | −0.593254 | − | 0.805016i | \(-0.702157\pi\) | ||||
−0.593254 | + | 0.805016i | \(0.702157\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.5110 | −1.16193 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.99154 | 0.141180 | 0.0705898 | − | 0.997505i | \(-0.477512\pi\) | ||||
0.0705898 | + | 0.997505i | \(0.477512\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.89062 | + | 3.27464i | 0.0890257 | + | 0.154197i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.42838 | − | 26.0634i | 0.442009 | − | 1.22187i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.6171 | −1.19832 | −0.599158 | − | 0.800631i | \(-0.704498\pi\) | ||||
−0.599158 | + | 0.800631i | \(0.704498\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.45759 | + | 11.1849i | 0.300760 | + | 0.520931i | 0.976308 | − | 0.216384i | \(-0.0694264\pi\) |
−0.675548 | + | 0.737316i | \(0.736093\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.2457 | + | 21.2102i | −0.569108 | + | 0.985724i | 0.427547 | + | 0.903993i | \(0.359378\pi\) |
−0.996654 | + | 0.0817305i | \(0.973955\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.4087 | − | 18.0283i | 0.481655 | − | 0.834251i | −0.518123 | − | 0.855306i | \(-0.673369\pi\) |
0.999778 | + | 0.0210550i | \(0.00670252\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.34800 | + | 12.0194i | −0.200772 | + | 0.555005i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.3432 | −0.981362 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.990281 | − | 1.71522i | −0.0454372 | − | 0.0786996i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.7436 | − | 23.8047i | 0.627962 | − | 1.08766i | −0.359998 | − | 0.932953i | \(-0.617223\pi\) |
0.987960 | − | 0.154709i | \(-0.0494441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.90932 | − | 3.30705i | −0.0870577 | − | 0.150788i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.8938 | + | 20.6007i | −0.540070 | + | 0.935429i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.32927 | − | 10.9626i | −0.286807 | − | 0.496763i | 0.686239 | − | 0.727376i | \(-0.259260\pi\) |
−0.973046 | + | 0.230613i | \(0.925927\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.40618 | − | 2.43557i | 0.0634598 | − | 0.109916i | −0.832550 | − | 0.553950i | \(-0.813120\pi\) |
0.896010 | + | 0.444034i | \(0.146453\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.61186 | + | 11.4521i | −0.297783 | + | 0.515776i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.38261 | − | 3.82203i | 0.0620187 | − | 0.171442i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.12103 | + | 3.67373i | 0.0949502 | + | 0.164459i | 0.909588 | − | 0.415512i | \(-0.136397\pi\) |
−0.814638 | + | 0.579970i | \(0.803064\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.2162 | −0.990570 | −0.495285 | − | 0.868730i | \(-0.664936\pi\) | ||||
−0.495285 | + | 0.868730i | \(0.664936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.6446 | 1.00767 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.42735 | − | 4.20429i | −0.107590 | − | 0.186352i | 0.807203 | − | 0.590273i | \(-0.200980\pi\) |
−0.914794 | + | 0.403922i | \(0.867647\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −34.1706 | + | 6.09440i | −1.51162 | + | 0.269601i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.6604 | − | 21.9284i | 0.557882 | − | 0.966280i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.8611 | + | 27.4722i | −0.697569 | + | 1.20823i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.92316 | − | 13.7233i | −0.347120 | − | 0.601229i | 0.638617 | − | 0.769525i | \(-0.279507\pi\) |
−0.985737 | + | 0.168296i | \(0.946174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.7605 | − | 18.6377i | 0.470524 | − | 0.814972i | −0.528908 | − | 0.848679i | \(-0.677398\pi\) |
0.999432 | + | 0.0337078i | \(0.0107316\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.7064 | + | 18.5441i | 0.466379 | + | 0.807792i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4709 | − | 19.8682i | 0.498734 | − | 0.863833i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.14271 | − | 7.17539i | −0.179441 | − | 0.310801i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.0527 | 1.03989 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.9202 | − | 6.23382i | 0.728806 | − | 0.268510i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.55977 | − | 13.0939i | 0.325020 | − | 0.562951i | −0.656497 | − | 0.754329i | \(-0.727962\pi\) |
0.981516 | + | 0.191378i | \(0.0612957\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.2922 | + | 24.7548i | −0.612211 | + | 1.06038i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.4532 | − | 33.6939i | −0.831757 | − | 1.44065i | −0.896644 | − | 0.442753i | \(-0.854002\pi\) |
0.0648863 | − | 0.997893i | \(-0.479332\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.35177 | −0.100189 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.34823 | + | 9.25568i | −0.142381 | + | 0.393592i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.37036 | + | 9.30173i | 0.227549 | + | 0.394127i | 0.957081 | − | 0.289820i | \(-0.0935954\pi\) |
−0.729532 | + | 0.683947i | \(0.760262\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.7672 | 1.97804 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.4760 | 0.989394 | 0.494697 | − | 0.869066i | \(-0.335279\pi\) | ||||
0.494697 | + | 0.869066i | \(0.335279\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.7090 | 1.20780 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.9361 | 1.59037 | 0.795183 | − | 0.606370i | \(-0.207375\pi\) | ||||
0.795183 | + | 0.606370i | \(0.207375\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.31630 | −0.180632 | −0.0903158 | − | 0.995913i | \(-0.528788\pi\) | ||||
−0.0903158 | + | 0.995913i | \(0.528788\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.375326 | 0.0156522 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.05923 | − | 8.76284i | −0.210618 | − | 0.364802i | 0.741290 | − | 0.671185i | \(-0.234214\pi\) |
−0.951908 | + | 0.306383i | \(0.900881\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.6369 | − | 2.78888i | 0.648729 | − | 0.115702i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.2854 | 0.715890 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.10992 | + | 7.11859i | 0.169635 | + | 0.293816i | 0.938291 | − | 0.345846i | \(-0.112408\pi\) |
−0.768657 | + | 0.639661i | \(0.779075\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.90409 | + | 3.29797i | −0.0784565 | + | 0.135891i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.8434 | + | 37.8339i | −0.897002 | + | 1.55365i | −0.0656957 | + | 0.997840i | \(0.520927\pi\) |
−0.831307 | + | 0.555814i | \(0.812407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.6486 | − | 26.8842i | −0.928504 | − | 1.10215i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.2789 | 0.624280 | 0.312140 | − | 0.950036i | \(-0.398954\pi\) | ||||
0.312140 | + | 0.950036i | \(0.398954\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.65696 | + | 13.2622i | 0.312334 | + | 0.540978i | 0.978867 | − | 0.204497i | \(-0.0655559\pi\) |
−0.666533 | + | 0.745475i | \(0.732223\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.04977 | + | 7.01441i | −0.164647 | + | 0.285176i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.33490 | + | 2.31212i | 0.0541821 | + | 0.0938461i | 0.891844 | − | 0.452342i | \(-0.149412\pi\) |
−0.837662 | + | 0.546189i | \(0.816078\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.7547 | − | 60.1970i | 1.40603 | − | 2.43531i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.5875 | − | 23.5343i | −0.548796 | − | 0.950542i | −0.998357 | − | 0.0572929i | \(-0.981753\pi\) |
0.449562 | − | 0.893249i | \(-0.351580\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.6058 | − | 30.4942i | 0.708785 | − | 1.22765i | −0.256524 | − | 0.966538i | \(-0.582577\pi\) |
0.965308 | − | 0.261113i | \(-0.0840895\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.6340 | − | 27.0790i | 0.628385 | − | 1.08840i | −0.359490 | − | 0.933149i | \(-0.617049\pi\) |
0.987876 | − | 0.155247i | \(-0.0496172\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.5130 | + | 26.7233i | 0.901966 | + | 1.07064i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.40113 | + | 12.8191i | 0.296045 | + | 0.512765i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.84322 | −0.193112 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.5090 | 0.617403 | 0.308702 | − | 0.951159i | \(-0.400106\pi\) | ||||
0.308702 | + | 0.951159i | \(0.400106\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.96393 | − | 5.13369i | −0.117620 | − | 0.203724i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −37.0756 | + | 13.6595i | −1.46899 | + | 0.541210i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.7655 | + | 29.0387i | −0.662198 | + | 1.14696i | 0.317839 | + | 0.948145i | \(0.397043\pi\) |
−0.980037 | + | 0.198816i | \(0.936290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.2721 | + | 17.7918i | −0.405093 | + | 0.701641i | −0.994332 | − | 0.106317i | \(-0.966094\pi\) |
0.589239 | + | 0.807958i | \(0.299427\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.8855 | + | 29.2465i | 0.663836 | + | 1.14980i | 0.979599 | + | 0.200960i | \(0.0644061\pi\) |
−0.315763 | + | 0.948838i | \(0.602261\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.68264 | − | 4.64647i | 0.105303 | − | 0.182390i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.00576 | + | 15.5984i | 0.352423 | + | 0.610414i | 0.986673 | − | 0.162714i | \(-0.0520247\pi\) |
−0.634251 | + | 0.773127i | \(0.718691\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.0719 | + | 22.6412i | −0.510762 | + | 0.884665i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.42710 | − | 2.47180i | −0.0555918 | − | 0.0962878i | 0.836890 | − | 0.547371i | \(-0.184371\pi\) |
−0.892482 | + | 0.451083i | \(0.851038\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0549 | 0.546673 | 0.273337 | − | 0.961918i | \(-0.411873\pi\) | ||||
0.273337 | + | 0.961918i | \(0.411873\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.12669 | − | 5.87892i | 0.0824695 | − | 0.227975i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.222837 | − | 0.385964i | 0.00862827 | − | 0.0149446i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.6918 | + | 28.9111i | −0.644381 | + | 1.11610i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.54157 | − | 13.0624i | −0.290706 | − | 0.503518i | 0.683271 | − | 0.730165i | \(-0.260557\pi\) |
−0.973977 | + | 0.226647i | \(0.927223\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.2187 | 1.39200 | 0.695998 | − | 0.718043i | \(-0.254962\pi\) | ||||
0.695998 | + | 0.718043i | \(0.254962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.3843 | − | 5.95417i | 1.28117 | − | 0.228500i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.84350 | − | 15.3174i | −0.338387 | − | 0.586104i | 0.645742 | − | 0.763555i | \(-0.276548\pi\) |
−0.984130 | + | 0.177452i | \(0.943215\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.4193 | 0.971220 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −37.8758 | −1.44295 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.4097 | 0.852506 | 0.426253 | − | 0.904604i | \(-0.359833\pi\) | ||||
0.426253 | + | 0.904604i | \(0.359833\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.3413 | −0.695725 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.5085 | −0.398037 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.1776 | 1.17756 | 0.588781 | − | 0.808293i | \(-0.299608\pi\) | ||||
0.588781 | + | 0.808293i | \(0.299608\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.430672 | − | 0.745946i | −0.0162431 | − | 0.0281339i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.7988 | − | 24.6884i | −0.782218 | − | 0.928503i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.04985 | −0.302318 | −0.151159 | − | 0.988509i | \(-0.548301\pi\) | ||||
−0.151159 | + | 0.988509i | \(0.548301\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.360834 | − | 0.624982i | −0.0135133 | − | 0.0234058i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.4929 | + | 23.3703i | −0.504604 | + | 0.874000i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.9980 | − | 36.3696i | 0.783093 | − | 1.35636i | −0.147039 | − | 0.989131i | \(-0.546974\pi\) |
0.930132 | − | 0.367226i | \(-0.119692\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.5359 | + | 6.33791i | −1.32343 | + | 0.236036i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.87338 | −0.106715 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.668774 | + | 1.15835i | 0.0248035 | + | 0.0429609i | 0.878161 | − | 0.478366i | \(-0.158771\pi\) |
−0.853357 | + | 0.521327i | \(0.825437\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.6576 | − | 51.3684i | 1.09693 | − | 1.89993i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.7374 | − | 25.5260i | −0.544340 | − | 0.942824i | −0.998648 | − | 0.0519798i | \(-0.983447\pi\) |
0.454308 | − | 0.890845i | \(-0.349886\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.22238 | − | 10.7775i | 0.229204 | − | 0.396993i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.52146 | + | 16.4916i | 0.350252 | + | 0.606655i | 0.986294 | − | 0.165000i | \(-0.0527625\pi\) |
−0.636041 | + | 0.771655i | \(0.719429\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.6613 | + | 37.5185i | −0.794676 | + | 1.37642i | 0.128369 | + | 0.991726i | \(0.459026\pi\) |
−0.923045 | + | 0.384693i | \(0.874307\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.63786 | − | 6.30097i | 0.133281 | − | 0.230850i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.0921 | − | 26.2236i | −0.807228 | − | 0.958190i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.4381 | − | 30.2037i | −0.636327 | − | 1.10215i | −0.986232 | − | 0.165365i | \(-0.947120\pi\) |
0.349906 | − | 0.936785i | \(-0.386214\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −36.3358 | −1.32240 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.67255 | 0.315209 | 0.157605 | − | 0.987502i | \(-0.449623\pi\) | ||||
0.157605 | + | 0.987502i | \(0.449623\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.74489 | − | 4.75428i | −0.0995021 | − | 0.172343i | 0.811977 | − | 0.583690i | \(-0.198392\pi\) |
−0.911479 | + | 0.411347i | \(0.865058\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.1163 | − | 7.15482i | 1.45231 | − | 0.259022i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.87819 | + | 10.1813i | −0.212249 | + | 0.367627i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.81365 | − | 3.14134i | 0.0654021 | − | 0.113280i | −0.831470 | − | 0.555569i | \(-0.812500\pi\) |
0.896872 | + | 0.442290i | \(0.145834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.96717 | + | 12.0675i | 0.250592 | + | 0.434037i | 0.963689 | − | 0.267028i | \(-0.0860415\pi\) |
−0.713097 | + | 0.701065i | \(0.752708\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.32640 | + | 4.02944i | −0.0835666 | + | 0.144742i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.934441 | − | 1.61850i | −0.0334798 | − | 0.0579888i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.97864 | + | 3.42711i | −0.0708014 | + | 0.122632i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.7270 | + | 23.7759i | 0.489939 | + | 0.848599i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.5785 | 0.626604 | 0.313302 | − | 0.949654i | \(-0.398565\pi\) | ||||
0.313302 | + | 0.949654i | \(0.398565\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.3688 | − | 31.3001i | −0.937567 | − | 1.11290i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.5751 | − | 63.3499i | 1.29882 | − | 2.24962i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.57971 | + | 9.66434i | −0.197644 | + | 0.342329i | −0.947764 | − | 0.318973i | \(-0.896662\pi\) |
0.750120 | + | 0.661301i | \(0.229996\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44.0797 | − | 76.3483i | −1.55943 | − | 2.70101i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 33.7949 | 1.19259 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.763317 | + | 0.906067i | 0.0269034 | + | 0.0319347i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.3481 | − | 24.8517i | −0.504453 | − | 0.873738i | −0.999987 | − | 0.00514935i | \(-0.998361\pi\) |
0.495534 | − | 0.868589i | \(-0.334972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.1695 | 1.65635 | 0.828173 | − | 0.560473i | \(-0.189380\pi\) | ||||
0.828173 | + | 0.560473i | \(0.189380\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.0126 | 0.981240 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.5489 | 0.369060 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.7707 | 1.35311 | 0.676554 | − | 0.736393i | \(-0.263472\pi\) | ||||
0.676554 | + | 0.736393i | \(0.263472\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.7840 | −0.794202 | −0.397101 | − | 0.917775i | \(-0.629984\pi\) | ||||
−0.397101 | + | 0.917775i | \(0.629984\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.55152 | 0.0539515 | 0.0269758 | − | 0.999636i | \(-0.491412\pi\) | ||||
0.0269758 | + | 0.999636i | \(0.491412\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.8972 | − | 41.3911i | −0.829983 | − | 1.43757i | −0.898051 | − | 0.439892i | \(-0.855017\pi\) |
0.0680673 | − | 0.997681i | \(-0.478317\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.50818 | + | 49.3856i | −0.294791 | + | 1.71111i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.16181 | −0.247845 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.5804 | − | 33.9142i | −0.675990 | − | 1.17085i | −0.976178 | − | 0.216970i | \(-0.930383\pi\) |
0.300188 | − | 0.953880i | \(-0.402951\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7940 | − | 22.1599i | 0.441174 | − | 0.764135i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.5021 | − | 30.3145i | 0.602089 | − | 1.04285i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.3672 | − | 2.02736i | 0.390580 | − | 0.0696609i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.163229 | 0.00559542 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.5234 | + | 25.1552i | 0.497270 | + | 0.861298i | 0.999995 | − | 0.00314895i | \(-0.00100234\pi\) |
−0.502725 | + | 0.864447i | \(0.667669\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.1292 | + | 41.7930i | −0.824239 | + | 1.42762i | 0.0782612 | + | 0.996933i | \(0.475063\pi\) |
−0.902500 | + | 0.430690i | \(0.858270\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.07528 | + | 8.79063i | 0.173166 | + | 0.299933i | 0.939525 | − | 0.342480i | \(-0.111267\pi\) |
−0.766359 | + | 0.642413i | \(0.777934\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.7981 | + | 44.6837i | −0.878179 | + | 1.52105i | −0.0248411 | + | 0.999691i | \(0.507908\pi\) |
−0.853338 | + | 0.521359i | \(0.825425\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.604630 | − | 1.04725i | −0.0205580 | − | 0.0356076i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.79161 | − | 8.29931i | 0.162544 | − | 0.281535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.6345 | + | 23.6156i | −0.461986 | + | 0.800183i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.9501 | − | 30.2701i | 0.370182 | − | 1.02332i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.19891 | + | 9.00477i | 0.175555 | + | 0.304069i | 0.940353 | − | 0.340200i | \(-0.110495\pi\) |
−0.764798 | + | 0.644270i | \(0.777161\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.6562 | −0.796996 | −0.398498 | − | 0.917169i | \(-0.630468\pi\) | ||||
−0.398498 | + | 0.917169i | \(0.630468\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.8601 | 1.40871 | 0.704353 | − | 0.709850i | \(-0.251237\pi\) | ||||
0.704353 | + | 0.709850i | \(0.251237\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.1252 | + | 36.5900i | 0.709316 | + | 1.22857i | 0.965111 | + | 0.261840i | \(0.0843294\pi\) |
−0.255795 | + | 0.966731i | \(0.582337\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.87469 | + | 7.94667i | −0.0964141 | + | 0.266523i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.83937 | − | 13.5782i | 0.262334 | − | 0.454377i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.2404 | − | 35.0574i | 0.676563 | − | 1.17184i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.76243 | + | 4.78467i | 0.0921321 | + | 0.159578i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.0191 | + | 41.6023i | −0.800192 | + | 1.38597i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.2303 | − | 40.2360i | −0.772201 | − | 1.33749i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.4404 | − | 35.4037i | 0.678711 | − | 1.17556i | −0.296658 | − | 0.954984i | \(-0.595872\pi\) |
0.975369 | − | 0.220578i | \(-0.0707945\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.4235 | − | 24.9823i | −0.477873 | − | 0.827701i | 0.521805 | − | 0.853065i | \(-0.325259\pi\) |
−0.999678 | + | 0.0253641i | \(0.991925\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.4650 | −0.511816 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.6910 | − | 6.54393i | 1.21165 | − | 0.216100i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.8195 | − | 37.7925i | 0.719760 | − | 1.24666i | −0.241335 | − | 0.970442i | \(-0.577585\pi\) |
0.961095 | − | 0.276219i | \(-0.0890815\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.33560 | − | 7.50947i | 0.142708 | − | 0.247177i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.526192 | − | 0.911391i | −0.0173011 | − | 0.0299663i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.4754 | 0.901438 | 0.450719 | − | 0.892666i | \(-0.351168\pi\) | ||||
0.450719 | + | 0.892666i | \(0.351168\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.36286 | + | 3.08108i | −0.274082 | + | 0.100978i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17.1131 | + | 29.6408i | 0.559658 | + | 0.969356i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.11920 | −0.101900 | −0.0509500 | − | 0.998701i | \(-0.516225\pi\) | ||||
−0.0509500 | + | 0.998701i | \(0.516225\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.1215 | 0.851538 | 0.425769 | − | 0.904832i | \(-0.360004\pi\) | ||||
0.425769 | + | 0.904832i | \(0.360004\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.354163 | 0.0115331 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.18031 | 0.233329 | 0.116664 | − | 0.993171i | \(-0.462780\pi\) | ||||
0.116664 | + | 0.993171i | \(0.462780\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −74.0512 | −2.40380 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.1187 | 1.04043 | 0.520214 | − | 0.854036i | \(-0.325852\pi\) | ||||
0.520214 | + | 0.854036i | \(0.325852\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.03678 | − | 13.9201i | −0.260064 | − | 0.450444i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.3473 | − | 27.7135i | −0.753922 | − | 0.894915i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0537 | −0.711411 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.50018 | + | 2.59838i | 0.0482924 | + | 0.0836449i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.4860 | + | 47.6071i | −0.883890 | + | 1.53094i | −0.0369085 | + | 0.999319i | \(0.511751\pi\) |
−0.846981 | + | 0.531623i | \(0.821582\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.8518 | + | 36.1163i | −0.669165 | + | 1.15903i | 0.308973 | + | 0.951071i | \(0.400015\pi\) |
−0.978138 | + | 0.207957i | \(0.933319\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.8462 | + | 19.9967i | 0.540065 | + | 0.641064i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.22874 | −0.167282 | −0.0836412 | − | 0.996496i | \(-0.526655\pi\) | ||||
−0.0836412 | + | 0.996496i | \(0.526655\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.0106 | − | 29.4633i | −0.543662 | − | 0.941651i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.45349 | − | 5.98162i | 0.110149 | − | 0.190784i | −0.805681 | − | 0.592349i | \(-0.798200\pi\) |
0.915830 | + | 0.401566i | \(0.131534\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.99837 | − | 17.3177i | −0.318575 | − | 0.551788i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.999537 | + | 1.73125i | −0.0317834 | + | 0.0550505i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.19861 | + | 3.80811i | 0.0698412 | + | 0.120968i | 0.898831 | − | 0.438295i | \(-0.144417\pi\) |
−0.828990 | + | 0.559263i | \(0.811084\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.43133 | + | 7.67528i | −0.140482 | + | 0.243323i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.0180 | − | 24.2798i | 0.443954 | − | 0.768950i | −0.554025 | − | 0.832500i | \(-0.686909\pi\) |
0.997979 | + | 0.0635498i | \(0.0202422\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.q.c.793.9 | 22 | ||
3.2 | odd | 2 | 504.2.q.d.121.7 | yes | 22 | ||
4.3 | odd | 2 | 3024.2.q.k.2305.9 | 22 | |||
7.4 | even | 3 | 1512.2.t.d.361.3 | 22 | |||
9.2 | odd | 6 | 504.2.t.d.457.8 | yes | 22 | ||
9.7 | even | 3 | 1512.2.t.d.289.3 | 22 | |||
12.11 | even | 2 | 1008.2.q.k.625.5 | 22 | |||
21.11 | odd | 6 | 504.2.t.d.193.8 | yes | 22 | ||
28.11 | odd | 6 | 3024.2.t.l.1873.3 | 22 | |||
36.7 | odd | 6 | 3024.2.t.l.289.3 | 22 | |||
36.11 | even | 6 | 1008.2.t.k.961.4 | 22 | |||
63.11 | odd | 6 | 504.2.q.d.25.7 | ✓ | 22 | ||
63.25 | even | 3 | inner | 1512.2.q.c.1369.9 | 22 | ||
84.11 | even | 6 | 1008.2.t.k.193.4 | 22 | |||
252.11 | even | 6 | 1008.2.q.k.529.5 | 22 | |||
252.151 | odd | 6 | 3024.2.q.k.2881.9 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.7 | ✓ | 22 | 63.11 | odd | 6 | ||
504.2.q.d.121.7 | yes | 22 | 3.2 | odd | 2 | ||
504.2.t.d.193.8 | yes | 22 | 21.11 | odd | 6 | ||
504.2.t.d.457.8 | yes | 22 | 9.2 | odd | 6 | ||
1008.2.q.k.529.5 | 22 | 252.11 | even | 6 | |||
1008.2.q.k.625.5 | 22 | 12.11 | even | 2 | |||
1008.2.t.k.193.4 | 22 | 84.11 | even | 6 | |||
1008.2.t.k.961.4 | 22 | 36.11 | even | 6 | |||
1512.2.q.c.793.9 | 22 | 1.1 | even | 1 | trivial | ||
1512.2.q.c.1369.9 | 22 | 63.25 | even | 3 | inner | ||
1512.2.t.d.289.3 | 22 | 9.7 | even | 3 | |||
1512.2.t.d.361.3 | 22 | 7.4 | even | 3 | |||
3024.2.q.k.2305.9 | 22 | 4.3 | odd | 2 | |||
3024.2.q.k.2881.9 | 22 | 252.151 | odd | 6 | |||
3024.2.t.l.289.3 | 22 | 36.7 | odd | 6 | |||
3024.2.t.l.1873.3 | 22 | 28.11 | odd | 6 |