Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(289,1512)]
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, 4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.t (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 | 361.3 | ||
Character | \(\chi\) | \(=\) | 1512.361 |
Dual form | 1512.2.t.d.289.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(5\) | −1.85591 | −0.829990 | −0.414995 | − | 0.909824i | \(-0.636217\pi\) | ||||
−0.414995 | + | 0.909824i | \(0.636217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.60465 | − | 0.464545i | −0.984465 | − | 0.175582i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.57601 | 0.776696 | 0.388348 | − | 0.921513i | \(-0.373046\pi\) | ||||
0.388348 | + | 0.921513i | \(0.373046\pi\) | |||||||
\(12\) | 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 | −0.00428199 | + | 0.999991i | \(0.501363\pi\) |
−0.863876 | + | 0.503704i | \(0.831970\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.636599 | + | 1.10262i | 0.146046 | + | 0.252959i | 0.929763 | − | 0.368160i | \(-0.120012\pi\) |
−0.783717 | + | 0.621118i | \(0.786679\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.241277 | −0.0503098 | −0.0251549 | − | 0.999684i | \(-0.508008\pi\) | ||||
−0.0251549 | + | 0.999684i | \(0.508008\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.55558 | −0.311116 | ||||||||
\(26\) | 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 | ||||||||
\(31\) | 1.49552 | + | 2.59031i | 0.268602 | + | 0.465233i | 0.968501 | − | 0.249009i | \(-0.0801049\pi\) |
−0.699899 | + | 0.714242i | \(0.746772\pi\) | |||||||
\(32\) | 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 | 0.892490 | − | 0.451067i | \(-0.148956\pi\) |
−0.836880 | + | 0.547386i | \(0.815623\pi\) | |||||||
\(38\) | 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 | ||||||||
\(47\) | −6.15723 | + | 10.6646i | −0.898124 | + | 1.55560i | −0.0682346 | + | 0.997669i | \(0.521737\pi\) |
−0.829890 | + | 0.557928i | \(0.811597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.56840 | + | 2.41995i | 0.938342 | + | 0.345708i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.35508 | + | 5.81117i | −0.460856 | + | 0.798226i | −0.999004 | − | 0.0446243i | \(-0.985791\pi\) |
0.538148 | + | 0.842851i | \(0.319124\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.78085 | −0.644650 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.04139 | + | 1.80375i | 0.135578 | + | 0.234828i | 0.925818 | − | 0.377969i | \(-0.123378\pi\) |
−0.790240 | + | 0.612797i | \(0.790044\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.47973 | + | 11.2232i | −0.829644 | + | 1.43699i | 0.0686730 | + | 0.997639i | \(0.478123\pi\) |
−0.898317 | + | 0.439347i | \(0.855210\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.23789 | + | 9.07230i | −0.649681 | + | 1.12528i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.41551 | + | 4.18379i | 0.295102 | + | 0.511131i | 0.975009 | − | 0.222167i | \(-0.0713132\pi\) |
−0.679907 | + | 0.733298i | \(0.737980\pi\) | |||||||
\(68\) | 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 | 0.171052 | + | 0.985262i | \(0.445283\pi\) |
−0.938788 | + | 0.344496i | \(0.888050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.70960 | − | 1.19667i | −0.764630 | − | 0.136373i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.86009 | − | 3.22177i | 0.209277 | − | 0.362478i | −0.742210 | − | 0.670167i | \(-0.766222\pi\) |
0.951487 | + | 0.307689i | \(0.0995558\pi\) | |||||||
\(80\) | 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 | −0.968477 | − | 0.249103i | \(-0.919864\pi\) |
0.268509 | − | 0.963277i | \(-0.413469\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.62187 | + | 11.4213i | −1.00865 | + | 1.19728i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.18147 | − | 2.04637i | −0.121217 | − | 0.209953i | ||||
\(96\) | 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 | ||||||||
\(101\) | −12.2013 | −1.21408 | −0.607039 | − | 0.794672i | \(-0.707643\pi\) | ||||
−0.607039 | + | 0.794672i | \(0.707643\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.6433 | 1.34431 | 0.672155 | − | 0.740411i | \(-0.265369\pi\) | ||||
0.672155 | + | 0.740411i | \(0.265369\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.48002 | + | 11.2237i | 0.626448 | + | 1.08504i | 0.988259 | + | 0.152788i | \(0.0488251\pi\) |
−0.361811 | + | 0.932251i | \(0.617842\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.70089 | − | 13.3383i | 0.737612 | − | 1.27758i | −0.215956 | − | 0.976403i | \(-0.569287\pi\) |
0.953568 | − | 0.301178i | \(-0.0973799\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 0.447790 | 0.0417566 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.2035 | − | 14.4857i | 1.11869 | − | 1.32790i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.36418 | −0.396744 | ||||||||
\(122\) | 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 | ||||||||
\(131\) | −14.0868 | −1.23077 | −0.615383 | − | 0.788229i | \(-0.710998\pi\) | ||||
−0.615383 | + | 0.788229i | \(0.710998\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.14590 | − | 3.16767i | −0.0993620 | − | 0.274672i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.6964 | −1.17016 | −0.585079 | − | 0.810976i | \(-0.698937\pi\) | ||||
−0.585079 | + | 0.810976i | \(0.698937\pi\) | |||||||
\(138\) | 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 | ||||||||
\(149\) | 3.92029 | 0.321163 | 0.160581 | − | 0.987023i | \(-0.448663\pi\) | ||||
0.160581 | + | 0.987023i | \(0.448663\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.5784 | 1.59327 | 0.796634 | − | 0.604462i | \(-0.206612\pi\) | ||||
0.796634 | + | 0.604462i | \(0.206612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.77555 | − | 4.80739i | −0.222937 | − | 0.386139i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.39637 | − | 12.8109i | −0.590295 | − | 1.02242i | −0.994193 | − | 0.107616i | \(-0.965678\pi\) |
0.403898 | − | 0.914804i | \(-0.367655\pi\) | |||||||
\(158\) | 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 | 0.994082 | + | 0.108628i | \(0.0346456\pi\) |
−0.402967 | + | 0.915215i | \(0.632021\pi\) | |||||||
\(164\) | 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 | ||||||||
\(173\) | 0.325786 | − | 0.564277i | 0.0247690 | − | 0.0429012i | −0.853375 | − | 0.521297i | \(-0.825448\pi\) |
0.878144 | + | 0.478396i | \(0.158782\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.05174 | + | 0.722638i | 0.306283 | + | 0.0546263i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.9059 | + | 18.8896i | −0.815145 | + | 1.41187i | 0.0940781 | + | 0.995565i | \(0.470010\pi\) |
−0.909223 | + | 0.416308i | \(0.863324\pi\) | |||||||
\(180\) | 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 | ||||||||
\(185\) | −0.627782 | − | 1.08735i | −0.0461555 | − | 0.0799436i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.22085 | + | 15.9710i | −0.674295 | + | 1.16791i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.33036 | − | 7.50041i | 0.313334 | − | 0.542711i | −0.665748 | − | 0.746177i | \(-0.731887\pi\) |
0.979082 | + | 0.203466i | \(0.0652207\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.808322 | − | 1.40006i | −0.0581843 | − | 0.100778i | 0.835466 | − | 0.549542i | \(-0.185198\pi\) |
−0.893650 | + | 0.448764i | \(0.851864\pi\) | |||||||
\(194\) | 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 | −0.768901 | − | 0.639368i | \(-0.779196\pi\) |
0.938159 | + | 0.346204i | \(0.112530\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.66246 | + | 4.59562i | 0.116682 | + | 0.322549i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.36212 | + | 2.35925i | −0.0951343 | + | 0.164777i | ||||
\(206\) | 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 | ||||||||
\(221\) | 20.2047 | + | 34.9955i | 1.35911 | + | 2.35406i | ||||
\(222\) | 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 | ||||||||
\(227\) | 13.9491 | 0.925837 | 0.462919 | − | 0.886401i | \(-0.346802\pi\) | ||||
0.462919 | + | 0.886401i | \(0.346802\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.60027 | 0.105749 | 0.0528745 | − | 0.998601i | \(-0.483162\pi\) | ||||
0.0528745 | + | 0.998601i | \(0.483162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.69939 | − | 6.40753i | −0.242355 | − | 0.419771i | 0.719030 | − | 0.694979i | \(-0.244587\pi\) |
−0.961385 | + | 0.275208i | \(0.911253\pi\) | |||||||
\(234\) | 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 | ||||||||
\(241\) | 4.24297 | 0.273314 | 0.136657 | − | 0.990618i | \(-0.456364\pi\) | ||||
0.136657 | + | 0.990618i | \(0.456364\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.1904 | − | 4.49123i | −0.778815 | − | 0.286934i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.18661 | 0.457273 | ||||||||
\(248\) | 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 | ||||||||
\(257\) | 6.15495 | 0.383935 | 0.191968 | − | 0.981401i | \(-0.438513\pi\) | ||||
0.191968 | + | 0.981401i | \(0.438513\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.608880 | − | 1.68316i | −0.0378340 | − | 0.104586i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.3411 | 1.56260 | 0.781300 | − | 0.624156i | \(-0.214557\pi\) | ||||
0.781300 | + | 0.624156i | \(0.214557\pi\) | |||||||
\(264\) | 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 | −0.652095 | − | 0.758138i | \(-0.726109\pi\) |
0.982614 | + | 0.185662i | \(0.0594428\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0184 | − | 26.0127i | −0.912306 | − | 1.58016i | −0.810799 | − | 0.585325i | \(-0.800967\pi\) |
−0.101507 | − | 0.994835i | \(-0.532366\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.00719 | −0.241643 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.7629 | 1.18744 | 0.593720 | − | 0.804672i | \(-0.297659\pi\) | ||||
0.593720 | + | 0.804672i | \(0.297659\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −11.6063 | − | 20.1028i | −0.689926 | − | 1.19499i | −0.971861 | − | 0.235553i | \(-0.924310\pi\) |
0.281936 | − | 0.959433i | \(-0.409023\pi\) | |||||||
\(284\) | 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 | ||||||||
\(299\) | −0.680950 | + | 1.17944i | −0.0393803 | + | 0.0682088i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.45698 | − | 20.6137i | −0.429813 | − | 1.18816i | ||||
\(302\) | 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 | ||||||||
\(311\) | −3.46220 | − | 5.99670i | −0.196323 | − | 0.340042i | 0.751010 | − | 0.660290i | \(-0.229567\pi\) |
−0.947333 | + | 0.320249i | \(0.896233\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.1157 | + | 26.1811i | −0.854388 | + | 1.47984i | 0.0228236 | + | 0.999740i | \(0.492734\pi\) |
−0.877212 | + | 0.480104i | \(0.840599\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.68699 | − | 8.11811i | 0.263248 | − | 0.455959i | −0.703855 | − | 0.710343i | \(-0.748540\pi\) |
0.967103 | + | 0.254385i | \(0.0818730\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.37913 | − | 4.12077i | −0.133205 | − | 0.230719i | ||||
\(320\) | 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 | ||||||||
\(329\) | 20.9916 | − | 24.9173i | 1.15731 | − | 1.37374i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.7720 | + | 23.8539i | −0.756979 | + | 1.31113i | 0.187405 | + | 0.982283i | \(0.439992\pi\) |
−0.944384 | + | 0.328844i | \(0.893341\pi\) | |||||||
\(332\) | 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 | ||||||||
\(347\) | 10.0959 | + | 17.4867i | 0.541979 | + | 0.938735i | 0.998790 | + | 0.0491714i | \(0.0156581\pi\) |
−0.456812 | + | 0.889564i | \(0.651009\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | −4.70904 | −0.250637 | −0.125318 | − | 0.992117i | \(-0.539995\pi\) | ||||
−0.125318 | + | 0.992117i | \(0.539995\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.85107 | −0.151319 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.03357 | − | 10.4504i | −0.318440 | − | 0.551554i | 0.661723 | − | 0.749748i | \(-0.269825\pi\) |
−0.980163 | + | 0.198195i | \(0.936492\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | 0.960711 | 0.0501487 | 0.0250744 | − | 0.999686i | \(-0.492018\pi\) | ||||
0.0250744 | + | 0.999686i | \(0.492018\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.4384 | − | 13.5775i | 0.593850 | − | 0.704908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.04998 | −0.365034 | −0.182517 | − | 0.983203i | \(-0.558425\pi\) | ||||
−0.182517 | + | 0.983203i | \(0.558425\pi\) | |||||||
\(374\) | 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 | ||||||||
\(383\) | −32.1975 | −1.64522 | −0.822608 | − | 0.568609i | \(-0.807482\pi\) | ||||
−0.822608 | + | 0.568609i | \(0.807482\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.4524 | + | 2.22092i | 0.634635 | + | 0.113189i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.7426 | 1.30520 | 0.652600 | − | 0.757702i | \(-0.273678\pi\) | ||||
0.652600 | + | 0.757702i | \(0.273678\pi\) | |||||||
\(390\) | 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 | 0.999565 | − | 0.0295016i | \(-0.00939202\pi\) |
−0.525332 | + | 0.850898i | \(0.676059\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.2039 | −0.759245 | −0.379622 | − | 0.925142i | \(-0.623946\pi\) | ||||
−0.379622 | + | 0.925142i | \(0.623946\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.8830 | 0.841002 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.871362 | + | 1.50924i | 0.0431918 | + | 0.0748104i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9729 | + | 25.9339i | 0.740363 | + | 1.28235i | 0.952330 | + | 0.305070i | \(0.0986798\pi\) |
−0.211967 | + | 0.977277i | \(0.567987\pi\) | |||||||
\(410\) | 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 | ||||||||
\(425\) | 5.56822 | − | 9.64444i | 0.270098 | − | 0.467824i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.0911 | − | 26.2224i | 1.06906 | − | 1.26899i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.36446 | + | 2.36331i | −0.0657237 | + | 0.113837i | −0.897015 | − | 0.442000i | \(-0.854269\pi\) |
0.831291 | + | 0.555837i | \(0.187602\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | −0.153597 | − | 0.266037i | −0.00734753 | − | 0.0127263i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.44066 | − | 2.49529i | 0.0687587 | − | 0.119094i | −0.829596 | − | 0.558363i | \(-0.811429\pi\) |
0.898355 | + | 0.439270i | \(0.144763\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.4865 | − | 21.6273i | 0.593254 | − | 1.02755i | −0.400537 | − | 0.916281i | \(-0.631176\pi\) |
0.993791 | − | 0.111265i | \(-0.0354902\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.2555 | + | 21.2272i | 0.580967 | + | 1.00626i | ||||
\(446\) | 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 | ||||||||
\(455\) | 17.8574 | − | 21.1969i | 0.837166 | − | 0.993727i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.8085 | − | 22.1850i | 0.599158 | − | 1.03777i | −0.393788 | − | 0.919201i | \(-0.628835\pi\) |
0.992946 | − | 0.118571i | \(-0.0378312\pi\) | |||||||
\(458\) | 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 | 0.999778 | − | 0.0210550i | \(-0.00670252\pi\) |
−0.518123 | + | 0.855306i | \(0.673369\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.34800 | − | 12.0194i | −0.200772 | − | 0.555005i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.6716 | + | 18.4838i | 0.490681 | + | 0.849884i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.990281 | − | 1.71522i | −0.0454372 | − | 0.0786996i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −27.4873 | −1.25592 | −0.627962 | − | 0.778244i | \(-0.716111\pi\) | ||||
−0.627962 | + | 0.778244i | \(0.716111\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.81865 | 0.174115 | ||||||||
\(482\) | 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 | −0.973046 | − | 0.230613i | \(-0.925927\pi\) |
0.686239 | + | 0.727376i | \(0.259260\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 13.2237 | 0.595566 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.00128 | − | 0.713638i | −0.179482 | − | 0.0320110i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.24205 | −0.189900 | −0.0949502 | − | 0.995482i | \(-0.530269\pi\) | ||||
−0.0949502 | + | 0.995482i | \(0.530269\pi\) | |||||||
\(500\) | 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 | ||||||||
\(509\) | 4.85469 | 0.215180 | 0.107590 | − | 0.994195i | \(-0.465687\pi\) | ||||
0.107590 | + | 0.994195i | \(0.465687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.3632 | − | 26.5454i | 0.989290 | − | 1.17430i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.3207 | −1.11576 | ||||||||
\(516\) | 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 | −0.985737 | − | 0.168296i | \(-0.946174\pi\) |
0.638617 | + | 0.769525i | \(0.279507\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.7605 | + | 18.6377i | 0.470524 | + | 0.814972i | 0.999432 | − | 0.0337078i | \(-0.0107316\pi\) |
−0.528908 | + | 0.848679i | \(0.677398\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.4128 | −0.932758 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9418 | −0.997469 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.14271 | − | 7.17539i | −0.179441 | − | 0.310801i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0264 | − | 20.8303i | −0.519945 | − | 0.900572i | ||||
\(536\) | 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 | 0.981516 | − | 0.191378i | \(-0.0612957\pi\) |
−0.656497 | + | 0.754329i | \(0.727962\pi\) | |||||||
\(542\) | 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 | ||||||||
\(551\) | 1.17589 | − | 2.03670i | 0.0500945 | − | 0.0867662i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.34154 | + | 7.52749i | −0.269670 | + | 0.320101i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.37036 | − | 9.30173i | 0.227549 | − | 0.394127i | −0.729532 | − | 0.683947i | \(-0.760262\pi\) |
0.957081 | + | 0.289820i | \(0.0935954\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.7672 | 1.97804 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.7380 | − | 20.3308i | −0.494697 | − | 0.856840i | 0.505285 | − | 0.862953i | \(-0.331388\pi\) |
−0.999981 | + | 0.00611281i | \(0.998054\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.3545 | + | 24.8627i | −0.603898 | + | 1.04598i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.9681 | + | 32.8537i | −0.795183 | + | 1.37730i | 0.127540 | + | 0.991833i | \(0.459292\pi\) |
−0.922723 | + | 0.385463i | \(0.874042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.15815 | + | 3.73803i | 0.0903158 | + | 0.156432i | 0.907644 | − | 0.419741i | \(-0.137879\pi\) |
−0.817328 | + | 0.576172i | \(0.804546\pi\) | |||||||
\(572\) | 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 | −0.951908 | − | 0.306383i | \(-0.900881\pi\) |
0.741290 | + | 0.671185i | \(0.234214\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.40322 | − | 14.9364i | −0.224163 | − | 0.619667i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.64272 | + | 14.9696i | −0.357945 | + | 0.619979i | ||||
\(584\) | 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 | −0.831307 | − | 0.555814i | \(-0.812407\pi\) |
−0.0656957 | − | 0.997840i | \(-0.520927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.6486 | + | 26.8842i | −0.928504 | + | 1.10215i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.63946 | − | 13.2319i | −0.312140 | − | 0.540642i | 0.666686 | − | 0.745339i | \(-0.267712\pi\) |
−0.978825 | + | 0.204697i | \(0.934379\pi\) | |||||||
\(600\) | 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 | ||||||||
\(605\) | 8.09955 | 0.329293 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.66981 | −0.108364 | −0.0541821 | − | 0.998531i | \(-0.517255\pi\) | ||||
−0.0541821 | + | 0.998531i | \(0.517255\pi\) | |||||||
\(608\) | 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 | 0.449562 | + | 0.893249i | \(0.351580\pi\) |
−0.998357 | + | 0.0572929i | \(0.981753\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | −31.2681 | −1.25677 | −0.628385 | − | 0.777902i | \(-0.716284\pi\) | ||||
−0.628385 | + | 0.777902i | \(0.716284\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.8865 | + | 32.8585i | 0.476223 | + | 1.31645i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.8023 | −0.592090 | ||||||||
\(626\) | 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 | ||||||||
\(635\) | 5.92787 | 0.235240 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.3673 | − | 25.2786i | 1.20320 | − | 1.00158i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.5310 | 1.32440 | 0.662198 | − | 0.749329i | \(-0.269624\pi\) | ||||
0.662198 | + | 0.749329i | \(0.269624\pi\) | |||||||
\(642\) | 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 | −0.315763 | − | 0.948838i | \(-0.602261\pi\) |
0.979599 | − | 0.200960i | \(-0.0644061\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.68264 | + | 4.64647i | 0.105303 | + | 0.182390i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0115 | −0.704845 | −0.352423 | − | 0.935841i | \(-0.614642\pi\) | ||||
−0.352423 | + | 0.935841i | \(0.614642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.1438 | 1.02152 | ||||||||
\(656\) | 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 | ||||||||
\(661\) | −7.02746 | − | 12.1719i | −0.273337 | − | 0.473433i | 0.696378 | − | 0.717676i | \(-0.254794\pi\) |
−0.969714 | + | 0.244243i | \(0.921461\pi\) | |||||||
\(662\) | 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 | ||||||||
\(677\) | −18.1093 | + | 31.3663i | −0.695998 | + | 1.20550i | 0.273845 | + | 0.961774i | \(0.411705\pi\) |
−0.969843 | + | 0.243731i | \(0.921629\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.5357 | − | 31.8887i | −0.442699 | − | 1.22378i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.84350 | + | 15.3174i | −0.338387 | + | 0.586104i | −0.984130 | − | 0.177452i | \(-0.943215\pi\) |
0.645742 | + | 0.763555i | \(0.276548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.4193 | 0.971220 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.9379 | + | 32.8014i | 0.721477 | + | 1.24963i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.2049 | + | 19.4074i | −0.426253 | + | 0.738292i | −0.996537 | − | 0.0831559i | \(-0.973500\pi\) |
0.570283 | + | 0.821448i | \(0.306833\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.17064 | − | 15.8840i | 0.347862 | − | 0.602515i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.25424 | + | 9.10061i | 0.199018 | + | 0.344710i | ||||
\(698\) | 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 | ||||||||
\(707\) | 31.7802 | + | 5.66806i | 1.19522 | + | 0.213170i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.02492 | − | 6.97137i | 0.151159 | − | 0.261815i | −0.780495 | − | 0.625162i | \(-0.785033\pi\) |
0.931654 | + | 0.363347i | \(0.118366\pi\) | |||||||
\(710\) | 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 | 0.930132 | + | 0.367226i | \(0.119692\pi\) |
−0.147039 | + | 0.989131i | \(0.546974\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −35.5359 | − | 6.33791i | −1.32343 | − | 0.236036i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.43669 | + | 2.48842i | 0.0533573 | + | 0.0924176i | ||||
\(726\) | 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 | ||||||||
\(731\) | −59.3152 | −2.19385 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.4749 | 1.08868 | 0.544340 | − | 0.838865i | \(-0.316780\pi\) | ||||
0.544340 | + | 0.838865i | \(0.316780\pi\) | |||||||
\(734\) | 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 | −0.636041 | − | 0.771655i | \(-0.719429\pi\) |
0.986294 | + | 0.165000i | \(0.0527625\pi\) | |||||||
\(740\) | 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 | ||||||||
\(745\) | −7.27573 | −0.266562 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.6643 | − | 32.2441i | −0.426203 | − | 1.17818i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.8763 | 1.27265 | 0.636327 | − | 0.771420i | \(-0.280453\pi\) | ||||
0.636327 | + | 0.771420i | \(0.280453\pi\) | |||||||
\(752\) | 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 | ||||||||
\(761\) | 5.48977 | 0.199004 | 0.0995021 | − | 0.995037i | \(-0.468275\pi\) | ||||
0.0995021 | + | 0.995037i | \(0.468275\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.2544 | + | 31.1643i | −0.950473 | + | 1.12822i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.7564 | 0.424499 | ||||||||
\(768\) | 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 | −0.713097 | − | 0.701065i | \(-0.752708\pi\) |
0.963689 | + | 0.267028i | \(0.0860415\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.32640 | − | 4.02944i | −0.0835666 | − | 0.144742i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.86888 | 0.0669597 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.95729 | 0.141603 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.7270 | + | 23.7759i | 0.489939 | + | 0.848599i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.78923 | − | 15.2234i | −0.313302 | − | 0.542655i | 0.665773 | − | 0.746154i | \(-0.268102\pi\) |
−0.979075 | + | 0.203499i | \(0.934769\pi\) | |||||||
\(788\) | 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 | ||||||||
\(803\) | −16.8974 | + | 29.2672i | −0.596297 | + | 1.03282i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.16634 | − | 0.208019i | −0.0411079 | − | 0.00733169i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.3481 | + | 24.8517i | −0.504453 | + | 0.873738i | 0.495534 | + | 0.868589i | \(0.334972\pi\) |
−0.999987 | + | 0.00514935i | \(0.998361\pi\) | |||||||
\(810\) | 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 | ||||||||
\(815\) | −14.0063 | − | 24.2597i | −0.490620 | − | 0.849779i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.27446 | + | 9.13563i | −0.184530 | + | 0.319615i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.3854 | + | 33.5765i | −0.676554 | + | 1.17183i | 0.299458 | + | 0.954110i | \(0.403194\pi\) |
−0.976012 | + | 0.217717i | \(0.930139\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.3920 | + | 19.7316i | 0.397101 | + | 0.687799i | 0.993367 | − | 0.114988i | \(-0.0366830\pi\) |
−0.596266 | + | 0.802787i | \(0.703350\pi\) | |||||||
\(824\) | 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 | 0.0680673 | + | 0.997681i | \(0.478317\pi\) |
−0.898051 | + | 0.439892i | \(0.855017\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.5151 | + | 32.0611i | −1.33447 | + | 1.11085i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.58090 | − | 6.20231i | 0.123922 | − | 0.214640i | ||||
\(836\) | 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 | ||||||||
\(851\) | −0.0816145 | − | 0.141361i | −0.00279771 | − | 0.00484578i | ||||
\(852\) | 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 | ||||||||
\(857\) | 48.2584 | 1.64848 | 0.824239 | − | 0.566243i | \(-0.191603\pi\) | ||||
0.824239 | + | 0.566243i | \(0.191603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.1506 | −0.346332 | −0.173166 | − | 0.984893i | \(-0.555400\pi\) | ||||
−0.173166 | + | 0.984893i | \(0.555400\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −25.7981 | − | 44.6837i | −0.878179 | − | 1.52105i | −0.853338 | − | 0.521359i | \(-0.825425\pi\) |
−0.0248411 | − | 0.999691i | \(-0.507908\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | 27.2689 | 0.923972 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −31.6897 | − | 5.65193i | −1.07131 | − | 0.191070i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.3978 | −0.351109 | −0.175555 | − | 0.984470i | \(-0.556172\pi\) | ||||
−0.175555 | + | 0.984470i | \(0.556172\pi\) | |||||||
\(878\) | 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 | ||||||||
\(887\) | −42.2505 | −1.41863 | −0.709316 | − | 0.704891i | \(-0.750996\pi\) | ||||
−0.709316 | + | 0.704891i | \(0.750996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.31936 | + | 1.48378i | 0.279022 | + | 0.0497643i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.6787 | −0.524669 | ||||||||
\(894\) | 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 | ||||||||
\(905\) | 46.4606 | 1.54440 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40.8807 | −1.35742 | −0.678711 | − | 0.734405i | \(-0.737461\pi\) | ||||
−0.678711 | + | 0.734405i | \(0.737461\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | 7.73249 | + | 13.3931i | 0.255908 | + | 0.443246i | ||||
\(914\) | 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 | 0.961095 | + | 0.276219i | \(0.0890815\pi\) |
−0.241335 | + | 0.970442i | \(0.577585\pi\) | |||||||
\(920\) | 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 | ||||||||
\(929\) | −13.7377 | + | 23.7944i | −0.450719 | + | 0.780668i | −0.998431 | − | 0.0559990i | \(-0.982166\pi\) |
0.547712 | + | 0.836667i | \(0.315499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.51314 | + | 8.78299i | 0.0495911 | + | 0.287851i | ||||
\(932\) | 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 | ||||||||
\(941\) | −13.0608 | − | 22.6219i | −0.425769 | − | 0.737454i | 0.570723 | − | 0.821143i | \(-0.306663\pi\) |
−0.996492 | + | 0.0836892i | \(0.973330\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.177081 | + | 0.306714i | −0.00576656 | + | 0.00998797i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.59015 | + | 6.21833i | −0.116664 | + | 0.202068i | −0.918444 | − | 0.395551i | \(-0.870553\pi\) |
0.801780 | + | 0.597620i | \(0.203887\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.0256 | + | 64.1302i | 1.20190 | + | 2.08176i | ||||
\(950\) | 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 | ||||||||
\(959\) | 35.6742 | + | 6.36257i | 1.15198 | + | 0.205458i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0269 | − | 19.0991i | 0.355705 | − | 0.616100i | ||||
\(962\) | 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 | −0.978138 | − | 0.207957i | \(-0.933319\pi\) |
0.308973 | − | 0.951071i | \(-0.400015\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.8462 | − | 19.9967i | 0.540065 | − | 0.641064i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.61437 | + | 4.52823i | 0.0836412 | + | 0.144871i | 0.904811 | − | 0.425813i | \(-0.140012\pi\) |
−0.821170 | + | 0.570683i | \(0.806678\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.0106 | − | 29.4633i | −0.543662 | − | 0.941651i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.90697 | −0.220298 | −0.110149 | − | 0.993915i | \(-0.535133\pi\) | ||||
−0.110149 | + | 0.993915i | \(0.535133\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.9967 | 0.637149 | ||||||||
\(986\) | 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 | −0.828990 | − | 0.559263i | \(-0.811084\pi\) |
0.898831 | + | 0.438295i | \(0.144417\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.43133 | + | 7.67528i | −0.140482 | + | 0.243323i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.0359 | −0.887907 | −0.443954 | − | 0.896050i | \(-0.646425\pi\) | ||||
−0.443954 | + | 0.896050i | \(0.646425\pi\) | |||||||
\(998\) | 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.t.d.361.3 | 22 | ||
3.2 | odd | 2 | 504.2.t.d.193.8 | yes | 22 | ||
4.3 | odd | 2 | 3024.2.t.l.1873.3 | 22 | |||
7.2 | even | 3 | 1512.2.q.c.793.9 | 22 | |||
9.2 | odd | 6 | 504.2.q.d.25.7 | ✓ | 22 | ||
9.7 | even | 3 | 1512.2.q.c.1369.9 | 22 | |||
12.11 | even | 2 | 1008.2.t.k.193.4 | 22 | |||
21.2 | odd | 6 | 504.2.q.d.121.7 | yes | 22 | ||
28.23 | odd | 6 | 3024.2.q.k.2305.9 | 22 | |||
36.7 | odd | 6 | 3024.2.q.k.2881.9 | 22 | |||
36.11 | even | 6 | 1008.2.q.k.529.5 | 22 | |||
63.2 | odd | 6 | 504.2.t.d.457.8 | yes | 22 | ||
63.16 | even | 3 | inner | 1512.2.t.d.289.3 | 22 | ||
84.23 | even | 6 | 1008.2.q.k.625.5 | 22 | |||
252.79 | odd | 6 | 3024.2.t.l.289.3 | 22 | |||
252.191 | even | 6 | 1008.2.t.k.961.4 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.7 | ✓ | 22 | 9.2 | odd | 6 | ||
504.2.q.d.121.7 | yes | 22 | 21.2 | odd | 6 | ||
504.2.t.d.193.8 | yes | 22 | 3.2 | odd | 2 | ||
504.2.t.d.457.8 | yes | 22 | 63.2 | odd | 6 | ||
1008.2.q.k.529.5 | 22 | 36.11 | even | 6 | |||
1008.2.q.k.625.5 | 22 | 84.23 | even | 6 | |||
1008.2.t.k.193.4 | 22 | 12.11 | even | 2 | |||
1008.2.t.k.961.4 | 22 | 252.191 | even | 6 | |||
1512.2.q.c.793.9 | 22 | 7.2 | even | 3 | |||
1512.2.q.c.1369.9 | 22 | 9.7 | even | 3 | |||
1512.2.t.d.289.3 | 22 | 63.16 | even | 3 | inner | ||
1512.2.t.d.361.3 | 22 | 1.1 | even | 1 | trivial | ||
3024.2.q.k.2305.9 | 22 | 28.23 | odd | 6 | |||
3024.2.q.k.2881.9 | 22 | 36.7 | odd | 6 | |||
3024.2.t.l.289.3 | 22 | 252.79 | odd | 6 | |||
3024.2.t.l.1873.3 | 22 | 4.3 | odd | 2 |