Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(193,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.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: | \(8.04892052375\) |
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 | 961.4 | ||
Character | \(\chi\) | \(=\) | 1008.961 |
Dual form | 1008.2.t.k.193.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −0.577666 | − | 1.63288i | −0.333515 | − | 0.942745i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.85591 | 0.829990 | 0.414995 | − | 0.909824i | \(-0.363783\pi\) | ||||
0.414995 | + | 0.909824i | \(0.363783\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.60465 | − | 0.464545i | 0.984465 | − | 0.175582i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.33261 | + | 1.88652i | −0.777535 | + | 0.628840i | ||||
\(10\) | 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 | 0.930330 | + | 0.366724i | \(0.119521\pi\) |
−0.147573 | + | 0.989051i | \(0.547146\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.07210 | − | 3.03049i | −0.276814 | − | 0.782469i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.57951 | + | 6.19989i | 0.868158 | + | 1.50369i | 0.863876 | + | 0.503704i | \(0.168030\pi\) |
0.00428199 | + | 0.999991i | \(0.498637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.636599 | + | 1.10262i | −0.146046 | + | 0.252959i | −0.929763 | − | 0.368160i | \(-0.879988\pi\) |
0.783717 | + | 0.621118i | \(0.213321\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.26316 | − | 3.98473i | −0.493863 | − | 0.869540i | ||||
\(22\) | 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 | ||||||||
\(27\) | 4.42793 | + | 2.71909i | 0.852155 | + | 0.523289i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.923571 | − | 1.59967i | 0.171503 | − | 0.297051i | −0.767443 | − | 0.641118i | \(-0.778471\pi\) |
0.938945 | + | 0.344066i | \(0.111804\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.49552 | + | 2.59031i | −0.268602 | + | 0.465233i | −0.968501 | − | 0.249009i | \(-0.919895\pi\) |
0.699899 | + | 0.714242i | \(0.253228\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.48807 | − | 4.20632i | −0.259040 | − | 0.732226i | ||||
\(34\) | 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 | ||||||||
\(39\) | 6.35171 | − | 7.43225i | 1.01709 | − | 1.19011i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.733933 | − | 1.27121i | −0.114621 | − | 0.198529i | 0.803007 | − | 0.595969i | \(-0.203232\pi\) |
−0.917628 | + | 0.397440i | \(0.869899\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.14269 | + | 7.17535i | −0.631754 | + | 1.09423i | 0.355439 | + | 0.934700i | \(0.384331\pi\) |
−0.987193 | + | 0.159531i | \(0.949002\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.32912 | + | 3.50122i | −0.645346 | + | 0.521931i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.15723 | − | 10.6646i | −0.898124 | − | 1.55560i | −0.829890 | − | 0.557928i | \(-0.811597\pi\) |
−0.0682346 | − | 0.997669i | \(-0.521737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.56840 | − | 2.41995i | 0.938342 | − | 0.345708i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.05593 | − | 9.42638i | 1.12806 | − | 1.31996i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.35508 | + | 5.81117i | 0.460856 | + | 0.798226i | 0.999004 | − | 0.0446243i | \(-0.0142091\pi\) |
−0.538148 | + | 0.842851i | \(0.680876\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.78085 | 0.644650 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.16819 | + | 0.402544i | 0.287184 | + | 0.0533182i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.04139 | − | 1.80375i | 0.135578 | − | 0.234828i | −0.790240 | − | 0.612797i | \(-0.790044\pi\) |
0.925818 | + | 0.377969i | \(0.123378\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.47973 | − | 11.2232i | −0.829644 | − | 1.43699i | −0.898317 | − | 0.439347i | \(-0.855210\pi\) |
0.0686730 | − | 0.997639i | \(-0.478123\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.19925 | + | 5.99732i | −0.655043 | + | 0.755591i | ||||
\(64\) | 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 | \(-0.928687\pi\) |
0.679907 | + | 0.733298i | \(0.262020\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.139378 | + | 0.393977i | 0.0167791 | + | 0.0474293i | ||||
\(70\) | 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 | ||||||||
\(75\) | 0.898606 | + | 2.54008i | 0.103762 | + | 0.293303i | ||||
\(76\) | 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 | \(-0.233778\pi\) |
−0.951487 | + | 0.307689i | \(0.900444\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.88209 | − | 8.80101i | 0.209121 | − | 0.977890i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.00173 | − | 5.19915i | 0.329483 | − | 0.570681i | −0.652926 | − | 0.757421i | \(-0.726459\pi\) |
0.982409 | + | 0.186740i | \(0.0597922\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.64326 | + | 11.5065i | 0.720563 | + | 1.24805i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.14559 | − | 0.584007i | −0.337242 | − | 0.0626121i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.60349 | − | 11.4376i | 0.699968 | − | 1.21238i | −0.268509 | − | 0.963277i | \(-0.586531\pi\) |
0.968477 | − | 0.249103i | \(-0.0801359\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.62187 | + | 11.4213i | 1.00865 | + | 1.19728i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.09357 | + | 0.945667i | 0.528179 | + | 0.0980611i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.18147 | + | 2.04637i | −0.121217 | + | 0.209953i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.40860 | − | 11.1000i | 0.650695 | − | 1.12704i | −0.332260 | − | 0.943188i | \(-0.607811\pi\) |
0.982955 | − | 0.183848i | \(-0.0588556\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00881 | + | 4.85969i | −0.603908 | + | 0.488417i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.2013 | 1.21408 | 0.607039 | − | 0.794672i | \(-0.292357\pi\) | ||||
0.607039 | + | 0.794672i | \(0.292357\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.6433 | −1.34431 | −0.672155 | − | 0.740411i | \(-0.734631\pi\) | ||||
−0.672155 | + | 0.740411i | \(0.734631\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.20024 | − | 7.39532i | −0.409901 | − | 0.721710i | ||||
\(106\) | 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 | ||||||||
\(111\) | −1.15208 | − | 0.213894i | −0.109351 | − | 0.0203019i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.73446 | − | 13.3965i | −0.727597 | − | 1.26023i | −0.957896 | − | 0.287115i | \(-0.907304\pi\) |
0.230299 | − | 0.973120i | \(-0.426029\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.447790 | −0.0417566 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.8051 | − | 6.07824i | −1.46119 | − | 0.561934i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 12.2035 | + | 14.4857i | 1.11869 | + | 1.32790i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.36418 | −0.396744 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.65177 | + | 1.93276i | −0.148935 | + | 0.174271i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1666 | −1.08821 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.19404 | 0.283425 | 0.141713 | − | 0.989908i | \(-0.454739\pi\) | ||||
0.141713 | + | 0.989908i | \(0.454739\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.1096 | + | 2.61957i | 1.24228 | + | 0.230640i | ||||
\(130\) | 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 | ||||||||
\(135\) | 8.21785 | + | 5.04640i | 0.707280 | + | 0.434325i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.6964 | 1.17016 | 0.585079 | − | 0.810976i | \(-0.301063\pi\) | ||||
0.585079 | + | 0.810976i | \(0.301063\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.94131 | + | 8.55859i | 0.419116 | + | 0.725931i | 0.995851 | − | 0.0910010i | \(-0.0290067\pi\) |
−0.576735 | + | 0.816932i | \(0.695673\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.8573 | + | 16.2146i | −1.16699 | + | 1.36552i | ||||
\(142\) | 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 | ||||||||
\(147\) | −7.74583 | − | 9.32749i | −0.638866 | − | 0.769318i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.92029 | −0.321163 | −0.160581 | − | 0.987023i | \(-0.551337\pi\) | ||||
−0.160581 | + | 0.987023i | \(0.551337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5784 | −1.59327 | −0.796634 | − | 0.604462i | \(-0.793388\pi\) | ||||
−0.796634 | + | 0.604462i | \(0.793388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −20.0458 | − | 7.70909i | −1.62061 | − | 0.623243i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.77555 | + | 4.80739i | −0.222937 | + | 0.386139i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.39637 | + | 12.8109i | −0.590295 | + | 1.02242i | 0.403898 | + | 0.914804i | \(0.367655\pi\) |
−0.994193 | + | 0.107616i | \(0.965678\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.55084 | − | 8.83537i | 0.598821 | − | 0.700690i | ||||
\(160\) | 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 | \(0.367979\pi\) |
−0.994082 | + | 0.108628i | \(0.965354\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.76173 | − | 7.80656i | −0.215001 | − | 0.607740i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.92946 | − | 3.34192i | −0.149306 | − | 0.258605i | 0.781665 | − | 0.623698i | \(-0.214371\pi\) |
−0.930971 | + | 0.365093i | \(0.881037\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.43043 | + | 16.3340i | −0.725418 | + | 1.25646i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.595183 | − | 3.77293i | −0.0455147 | − | 0.288524i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.325786 | − | 0.564277i | −0.0247690 | − | 0.0429012i | 0.853375 | − | 0.521297i | \(-0.174552\pi\) |
−0.878144 | + | 0.478396i | \(0.841218\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.05174 | + | 0.722638i | −0.306283 | + | 0.0546263i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.54688 | − | 0.658511i | −0.266600 | − | 0.0494967i | ||||
\(178\) | 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 | ||||||||
\(183\) | −14.5831 | + | 17.0639i | −1.07801 | + | 1.26140i | ||||
\(184\) | 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 | ||||||||
\(189\) | 12.7963 | + | 5.02531i | 0.930797 | + | 0.365537i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.33036 | + | 7.50041i | 0.313334 | + | 0.542711i | 0.979082 | − | 0.203466i | \(-0.0652207\pi\) |
−0.665748 | + | 0.746177i | \(0.731887\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.808322 | + | 1.40006i | −0.0581843 | + | 0.100778i | −0.893650 | − | 0.448764i | \(-0.851864\pi\) |
0.835466 | + | 0.549542i | \(0.185198\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.7882 | − | 13.7936i | 0.844173 | − | 0.987781i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.7746 | 0.767659 | 0.383829 | − | 0.923404i | \(-0.374605\pi\) | ||||
0.383829 | + | 0.923404i | \(0.374605\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.38768 | − | 4.13558i | −0.169258 | − | 0.293163i | 0.768901 | − | 0.639368i | \(-0.220804\pi\) |
−0.938159 | + | 0.346204i | \(0.887470\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.22699 | + | 1.52741i | 0.580287 | + | 0.107735i | ||||
\(202\) | 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 | ||||||||
\(207\) | 0.562805 | − | 0.455174i | 0.0391176 | − | 0.0316368i | ||||
\(208\) | 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 | \(-0.220120\pi\) |
−0.937414 | + | 0.348218i | \(0.886787\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.887415 | − | 2.50845i | −0.0608046 | − | 0.171876i | ||||
\(214\) | 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 | ||||||||
\(219\) | −14.7627 | + | 17.2741i | −0.997570 | + | 1.16727i | ||||
\(220\) | 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 | \(-0.916598\pi\) |
0.707260 | + | 0.706954i | \(0.249931\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.62856 | − | 2.93463i | 0.241904 | − | 0.195642i | ||||
\(226\) | 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 | ||||||||
\(231\) | −5.82993 | − | 10.2647i | −0.383581 | − | 0.675368i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.69939 | − | 6.40753i | 0.242355 | − | 0.419771i | −0.719030 | − | 0.694979i | \(-0.755413\pi\) |
0.961385 | + | 0.275208i | \(0.0887468\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.4273 | − | 19.7926i | −0.745434 | − | 1.29113i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.18626 | + | 4.89841i | −0.271927 | + | 0.318186i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.25117 | + | 2.16709i | 0.0809316 | + | 0.140178i | 0.903650 | − | 0.428271i | \(-0.140877\pi\) |
−0.822719 | + | 0.568449i | \(0.807544\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.24297 | 0.273314 | 0.136657 | − | 0.990618i | \(-0.456364\pi\) | ||||
0.136657 | + | 0.990618i | \(0.456364\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4582 | + | 2.01080i | −0.991645 | + | 0.128993i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.1904 | − | 4.49123i | 0.778815 | − | 0.286934i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.18661 | −0.457273 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.2236 | − | 1.89810i | −0.647894 | − | 0.120287i | ||||
\(250\) | 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 | ||||||||
\(255\) | 14.9511 | − | 17.4946i | 0.936275 | − | 1.09555i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.15495 | −0.383935 | −0.191968 | − | 0.981401i | \(-0.561487\pi\) | ||||
−0.191968 | + | 0.981401i | \(0.561487\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.608880 | − | 1.68316i | 0.0378340 | − | 0.104586i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.863485 | + | 5.47373i | 0.0534484 | + | 0.338816i | ||||
\(262\) | 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 | ||||||||
\(267\) | −22.4908 | − | 4.17562i | −1.37642 | − | 0.255544i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.42092 | − | 9.38931i | −0.330519 | − | 0.572476i | 0.652095 | − | 0.758138i | \(-0.273891\pi\) |
−0.982614 | + | 0.185662i | \(0.940557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.0184 | − | 26.0127i | 0.912306 | − | 1.58016i | 0.101507 | − | 0.994835i | \(-0.467634\pi\) |
0.810799 | − | 0.585325i | \(-0.199033\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.0914 | − | 22.3091i | 0.792326 | − | 1.35021i | ||||
\(274\) | 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 | ||||||||
\(279\) | −1.39822 | − | 8.86348i | −0.0837092 | − | 0.530643i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.98596 | + | 6.90388i | −0.237782 | + | 0.411851i | −0.960078 | − | 0.279734i | \(-0.909754\pi\) |
0.722295 | + | 0.691585i | \(0.243087\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.6063 | − | 20.1028i | 0.689926 | − | 1.19499i | −0.281936 | − | 0.959433i | \(-0.590977\pi\) |
0.971861 | − | 0.235553i | \(-0.0756901\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.02398 | + | 0.747087i | 0.238360 | + | 0.0442536i | ||||
\(286\) | 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 | ||||||||
\(291\) | −21.8270 | − | 4.05239i | −1.27952 | − | 0.237555i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.8556 | + | 20.5345i | 0.692612 | + | 1.19964i | 0.970979 | + | 0.239164i | \(0.0768735\pi\) |
−0.278367 | + | 0.960475i | \(0.589793\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.93274 | − | 3.34760i | 0.112528 | − | 0.194905i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.4064 | + | 7.00440i | 0.661865 | + | 0.406437i | ||||
\(298\) | 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 | ||||||||
\(303\) | −7.04829 | − | 19.9233i | −0.404913 | − | 1.14456i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.0258 | − | 20.8293i | −0.688597 | − | 1.19268i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.87810 | −0.221335 | −0.110668 | − | 0.993857i | \(-0.535299\pi\) | ||||
−0.110668 | + | 0.993857i | \(0.535299\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.88124 | + | 22.2778i | 0.448348 | + | 1.26734i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.46220 | + | 5.99670i | −0.196323 | + | 0.340042i | −0.947333 | − | 0.320249i | \(-0.896233\pi\) |
0.751010 | + | 0.660290i | \(0.229567\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.1157 | − | 26.1811i | −0.854388 | − | 1.47984i | −0.877212 | − | 0.480104i | \(-0.840599\pi\) |
0.0228236 | − | 0.999740i | \(-0.492734\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.64935 | + | 11.1305i | −0.543679 | + | 0.627133i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.68699 | − | 8.11811i | −0.263248 | − | 0.455959i | 0.703855 | − | 0.710343i | \(-0.251460\pi\) |
−0.967103 | + | 0.254385i | \(0.918127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.37913 | − | 4.12077i | 0.133205 | − | 0.230719i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.0703 | − | 4.09755i | −1.23184 | − | 0.228703i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.11484 | −0.507163 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.39027 | − | 7.60418i | −0.243529 | − | 0.421804i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.3314 | − | 20.2797i | 0.958428 | − | 1.12147i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.9916 | − | 24.9173i | −1.15731 | − | 1.37374i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.7720 | + | 23.8539i | 0.756979 | + | 1.31113i | 0.944384 | + | 0.328844i | \(0.106659\pi\) |
−0.187405 | + | 0.982283i | \(0.560008\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.316254 | + | 2.00477i | 0.0173306 | + | 0.109861i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.48298 | + | 7.76475i | −0.244931 | + | 0.424234i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.41673 | − | 5.91796i | −0.186121 | − | 0.322372i | 0.757832 | − | 0.652449i | \(-0.226258\pi\) |
−0.943954 | + | 0.330078i | \(0.892925\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.4069 | + | 20.3681i | −0.945415 | + | 1.10625i | ||||
\(340\) | 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 | ||||||||
\(345\) | 0.258673 | + | 0.731188i | 0.0139265 | + | 0.0393658i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.0959 | − | 17.4867i | 0.541979 | − | 0.938735i | −0.456812 | − | 0.889564i | \(-0.651009\pi\) |
0.998790 | − | 0.0491714i | \(-0.0156581\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.25154 | + | 7.36388i | −0.227580 | + | 0.394180i | −0.957090 | − | 0.289790i | \(-0.906415\pi\) |
0.729511 | + | 0.683970i | \(0.239748\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.794966 | + | 29.3191i | −0.0424321 | + | 1.56494i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.70904 | 0.250637 | 0.125318 | − | 0.992117i | \(-0.460005\pi\) | ||||
0.125318 | + | 0.992117i | \(0.460005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.85107 | 0.151319 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 16.6039 | − | 28.2948i | 0.878771 | − | 1.49752i | ||||
\(358\) | 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 | ||||||||
\(363\) | 2.52104 | + | 7.12619i | 0.132320 | + | 0.374028i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.1739 | − | 21.0859i | −0.637213 | − | 1.10369i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.960711 | −0.0501487 | −0.0250744 | − | 0.999686i | \(-0.507982\pi\) | ||||
−0.0250744 | + | 0.999686i | \(0.507982\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.11013 | + | 1.58065i | 0.213965 | + | 0.0822854i | ||||
\(370\) | 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 | ||||||||
\(375\) | 7.02822 | + | 19.8666i | 0.362936 | + | 1.02591i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.4263 | 0.536980 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.1330 | 1.90739 | 0.953697 | − | 0.300769i | \(-0.0972434\pi\) | ||||
0.953697 | + | 0.300769i | \(0.0972434\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.84509 | − | 5.21549i | −0.0945267 | − | 0.267198i | ||||
\(382\) | 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 | ||||||||
\(387\) | −3.87317 | − | 24.5525i | −0.196884 | − | 1.24807i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.7426 | −1.30520 | −0.652600 | − | 0.757702i | \(-0.726322\pi\) | ||||
−0.652600 | + | 0.757702i | \(0.726322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.863654 | − | 1.49589i | −0.0436769 | − | 0.0756506i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.13743 | + | 23.0020i | 0.410479 | + | 1.16030i | ||||
\(394\) | 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 | ||||||||
\(399\) | 5.83438 | + | 0.0412635i | 0.292084 | + | 0.00206576i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.2039 | 0.759245 | 0.379622 | − | 0.925142i | \(-0.376054\pi\) | ||||
0.379622 | + | 0.925142i | \(0.376054\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.8830 | −0.841002 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.49300 | − | 16.3339i | 0.173569 | − | 0.811639i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.871362 | − | 1.50924i | 0.0431918 | − | 0.0748104i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9729 | − | 25.9339i | 0.740363 | − | 1.28235i | −0.211967 | − | 0.977277i | \(-0.567987\pi\) |
0.952330 | − | 0.305070i | \(-0.0986798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.91191 | − | 22.3645i | −0.390266 | − | 1.10316i | ||||
\(412\) | 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 | ||||||||
\(417\) | 11.1207 | − | 13.0126i | 0.544585 | − | 0.637229i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.2660 | + | 21.2453i | 0.599231 | + | 1.03790i | 0.992935 | + | 0.118661i | \(0.0378603\pi\) |
−0.393704 | + | 0.919237i | \(0.628806\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.37791 | + | 4.11866i | −0.115892 | + | 0.200731i | −0.918136 | − | 0.396265i | \(-0.870306\pi\) |
0.802244 | + | 0.596996i | \(0.203639\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 34.4814 | + | 13.2606i | 1.67654 | + | 0.644755i | ||||
\(424\) | 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 | ||||||||
\(429\) | 16.3621 | − | 19.1455i | 0.789968 | − | 0.924355i | ||||
\(430\) | 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 | ||||||||
\(435\) | −5.83794 | − | 1.08387i | −0.279908 | − | 0.0519674i | ||||
\(436\) | 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 | \(-0.188571\pi\) |
−0.898355 | + | 0.439270i | \(0.855237\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.7562 | + | 18.0362i | −0.512199 | + | 0.858867i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.4865 | + | 21.6273i | 0.593254 | + | 1.02755i | 0.993791 | + | 0.111265i | \(0.0354902\pi\) |
−0.400537 | + | 0.916281i | \(0.631176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.2555 | − | 21.2272i | 0.580967 | − | 1.00626i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.26462 | + | 6.40138i | 0.107113 | + | 0.302775i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.99154 | −0.141180 | −0.0705898 | − | 0.997505i | \(-0.522488\pi\) | ||||
−0.0705898 | + | 0.997505i | \(0.522488\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.89062 | − | 3.27464i | −0.0890257 | − | 0.154197i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.3098 | + | 31.9692i | 0.531379 | + | 1.50205i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.8574 | + | 21.1969i | 0.837166 | + | 0.993727i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.8085 | + | 22.1850i | 0.599158 | + | 1.03777i | 0.992946 | + | 0.118571i | \(0.0378312\pi\) |
−0.393788 | + | 0.919201i | \(0.628835\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00826 | + | 37.1857i | −0.0470616 | + | 1.73568i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.45759 | + | 11.1849i | −0.300760 | + | 0.520931i | −0.976308 | − | 0.216384i | \(-0.930574\pi\) |
0.675548 | + | 0.737316i | \(0.263907\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.2457 | + | 21.2102i | 0.569108 | + | 0.985724i | 0.996654 | + | 0.0817305i | \(0.0260447\pi\) |
−0.427547 | + | 0.903993i | \(0.640622\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.45324 | + | 1.75508i | 0.438383 | + | 0.0813898i | ||||
\(466\) | 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 | ||||||||
\(471\) | 25.1913 | + | 4.67699i | 1.16075 | + | 0.215504i | ||||
\(472\) | 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 | ||||||||
\(477\) | −18.7890 | − | 7.22575i | −0.860288 | − | 0.330844i | ||||
\(478\) | 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 | ||||||||
\(483\) | 0.546050 | + | 0.961425i | 0.0248461 | + | 0.0437464i | ||||
\(484\) | 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 | \(-0.0740730\pi\) |
−0.686239 | + | 0.727376i | \(0.740740\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.7038 | + | 4.77215i | 1.16237 | + | 0.215804i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.40618 | + | 2.43557i | 0.0634598 | + | 0.109916i | 0.896010 | − | 0.444034i | \(-0.146453\pi\) |
−0.832550 | + | 0.553950i | \(0.813120\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.2237 | 0.595566 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.1518 | + | 9.01917i | −0.501238 | + | 0.405381i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.00128 | − | 0.713638i | 0.179482 | − | 0.0320110i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.24205 | 0.189900 | 0.0949502 | − | 0.995482i | \(-0.469731\pi\) | ||||
0.0949502 | + | 0.995482i | \(0.469731\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.34237 | + | 5.08108i | −0.194003 | + | 0.227006i | ||||
\(502\) | 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 | ||||||||
\(507\) | 32.1191 | + | 5.96319i | 1.42646 | + | 0.264835i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.85469 | −0.215180 | −0.107590 | − | 0.994195i | \(-0.534313\pi\) | ||||
−0.107590 | + | 0.994195i | \(0.534313\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22.3632 | − | 26.5454i | −0.989290 | − | 1.17430i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.81694 | + | 3.15136i | −0.256824 | + | 0.139136i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.3207 | −1.11576 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.8611 | − | 27.4722i | −0.697569 | − | 1.20823i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.733203 | + | 0.857933i | −0.0321840 | + | 0.0376591i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.92316 | + | 13.7233i | 0.347120 | + | 0.601229i | 0.985737 | − | 0.168296i | \(-0.0538263\pi\) |
−0.638617 | + | 0.769525i | \(0.720493\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.7605 | + | 18.6377i | −0.470524 | + | 0.814972i | −0.999432 | − | 0.0337078i | \(-0.989268\pi\) |
0.528908 | + | 0.848679i | \(0.322602\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.52054 | + | 6.19858i | 0.153649 | + | 0.270528i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.4128 | −0.932758 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9418 | −0.997469 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.973643 | + | 6.17204i | 0.0422525 | + | 0.267844i | ||||
\(532\) | 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 | ||||||||
\(537\) | −24.5445 | + | 28.7199i | −1.05917 | + | 1.23936i | ||||
\(538\) | 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 | ||||||||
\(543\) | 14.4612 | + | 40.8772i | 0.620588 | + | 1.75421i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.2922 | + | 24.7548i | 0.612211 | + | 1.06038i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4532 | − | 33.6939i | 0.831757 | − | 1.44065i | −0.0648863 | − | 0.997893i | \(-0.520668\pi\) |
0.896644 | − | 0.442753i | \(-0.145998\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.2875 | + | 13.9552i | 1.54871 | + | 0.595594i | ||||
\(550\) | 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 | ||||||||
\(555\) | −2.13816 | − | 0.396969i | −0.0907600 | − | 0.0168504i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.37036 | − | 9.30173i | −0.227549 | − | 0.394127i | 0.729532 | − | 0.683947i | \(-0.239738\pi\) |
−0.957081 | + | 0.289820i | \(0.906405\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.7672 | −1.97804 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.7521 | − | 24.2824i | 0.876156 | − | 1.02520i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.7380 | + | 20.3308i | −0.494697 | + | 0.856840i | −0.999981 | − | 0.00611281i | \(-0.998054\pi\) |
0.505285 | + | 0.862953i | \(0.331388\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.3545 | − | 24.8627i | −0.603898 | − | 1.04598i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.813726 | − | 23.7979i | 0.0341733 | − | 0.999416i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.9681 | + | 32.8537i | 0.795183 | + | 1.37730i | 0.922723 | + | 0.385463i | \(0.125958\pi\) |
−0.127540 | + | 0.991833i | \(0.540708\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.15815 | + | 3.73803i | −0.0903158 | + | 0.156432i | −0.907644 | − | 0.419741i | \(-0.862121\pi\) |
0.817328 | + | 0.576172i | \(0.195454\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.74578 | − | 11.4037i | 0.407136 | − | 0.476396i | ||||
\(574\) | 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 | ||||||||
\(579\) | 2.75306 | + | 0.511131i | 0.114413 | + | 0.0212419i | ||||
\(580\) | 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 | ||||||||
\(585\) | −29.3330 | − | 11.2807i | −1.21277 | − | 0.466400i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.10992 | − | 7.11859i | 0.169635 | − | 0.293816i | −0.768657 | − | 0.639661i | \(-0.779075\pi\) |
0.938291 | + | 0.345846i | \(0.112408\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.90409 | − | 3.29797i | −0.0784565 | − | 0.135891i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.22412 | − | 17.5937i | −0.256026 | − | 0.723706i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.8434 | − | 37.8339i | 0.897002 | − | 1.55365i | 0.0656957 | − | 0.997840i | \(-0.479073\pi\) |
0.831307 | − | 0.555814i | \(-0.187593\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.6486 | + | 26.8842i | 0.928504 | + | 1.10215i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.37363 | + | 6.28778i | −0.219928 | + | 0.257342i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.63946 | + | 13.2319i | −0.312140 | + | 0.540642i | −0.978825 | − | 0.204697i | \(-0.934379\pi\) |
0.666686 | + | 0.745339i | \(0.267712\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.65696 | − | 13.2622i | 0.312334 | − | 0.540978i | −0.666533 | − | 0.745475i | \(-0.732223\pi\) |
0.978867 | + | 0.204497i | \(0.0655559\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.25836 | − | 14.3160i | −0.0919676 | − | 0.582994i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.09955 | −0.329293 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.66981 | 0.108364 | 0.0541821 | − | 0.998531i | \(-0.482745\pi\) | ||||
0.0541821 | + | 0.998531i | \(0.482745\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.46445 | − | 0.0598647i | −0.342997 | − | 0.00242584i | ||||
\(610\) | 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 | ||||||||
\(615\) | −3.06554 | + | 3.58703i | −0.123614 | + | 0.144643i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.6058 | − | 30.4942i | −0.708785 | − | 1.22765i | −0.965308 | − | 0.261113i | \(-0.915910\pi\) |
0.256524 | − | 0.966538i | \(-0.417423\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.2681 | 1.25677 | 0.628385 | − | 0.777902i | \(-0.283716\pi\) | ||||
0.628385 | + | 0.777902i | \(0.283716\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.06836 | − | 0.656055i | −0.0428717 | − | 0.0263266i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.8865 | − | 32.8585i | 0.476223 | − | 1.31645i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.8023 | −0.592090 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.58528 | + | 1.03696i | 0.223055 | + | 0.0414121i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.84322 | 0.193112 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.5090 | −0.617403 | −0.308702 | − | 0.951159i | \(-0.599894\pi\) | ||||
−0.308702 | + | 0.951159i | \(0.599894\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.46409 | + | 6.39363i | −0.217178 | + | 0.254124i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.92787 | 0.235240 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.3673 | + | 25.2786i | 1.20320 | + | 1.00158i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.58337 | + | 2.89809i | −0.141756 | + | 0.114647i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.5310 | −1.32440 | −0.662198 | − | 0.749329i | \(-0.730376\pi\) | ||||
−0.662198 | + | 0.749329i | \(0.730376\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.2721 | + | 17.7918i | 0.405093 | + | 0.701641i | 0.994332 | − | 0.106317i | \(-0.0339059\pi\) |
−0.589239 | + | 0.807958i | \(0.700573\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 26.1862 | + | 4.86170i | 1.03108 | + | 0.191429i | ||||
\(646\) | 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 | ||||||||
\(651\) | 13.7063 | + | 0.0969374i | 0.537191 | + | 0.00379928i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.0115 | 0.704845 | 0.352423 | − | 0.935841i | \(-0.385358\pi\) | ||||
0.352423 | + | 0.935841i | \(0.385358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.1438 | −1.02152 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.7344 | + | 14.1271i | 1.43315 | + | 0.551150i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.42710 | + | 2.47180i | −0.0555918 | + | 0.0962878i | −0.892482 | − | 0.451083i | \(-0.851038\pi\) |
0.836890 | + | 0.547371i | \(0.184371\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.02746 | + | 12.1719i | −0.273337 | + | 0.473433i | −0.969714 | − | 0.244243i | \(-0.921461\pi\) |
0.696378 | + | 0.717676i | \(0.254794\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 68.8151 | + | 12.7761i | 2.67256 | + | 0.496184i | ||||
\(664\) | 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 | ||||||||
\(669\) | 13.1532 | + | 2.44200i | 0.508530 | + | 0.0944132i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.6918 | − | 28.9111i | −0.644381 | − | 1.11610i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.54157 | + | 13.0624i | −0.290706 | + | 0.503518i | −0.973977 | − | 0.226647i | \(-0.927223\pi\) |
0.683271 | + | 0.730165i | \(0.260557\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.88800 | − | 4.22977i | −0.265119 | − | 0.162804i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.1093 | + | 31.3663i | 0.695998 | + | 1.20550i | 0.969843 | + | 0.243731i | \(0.0783713\pi\) |
−0.273845 | + | 0.961774i | \(0.588295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.5357 | − | 31.8887i | 0.442699 | − | 1.22378i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.05794 | − | 22.7773i | −0.308781 | − | 0.872828i | ||||
\(682\) | 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 | ||||||||
\(687\) | −0.924422 | − | 2.61305i | −0.0352689 | − | 0.0996942i | ||||
\(688\) | 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 | \(-0.0265000\pi\) |
−0.570283 | + | 0.821448i | \(0.693167\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.3933 | + | 15.4491i | −0.508769 | + | 0.586865i | ||||
\(694\) | 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 | ||||||||
\(699\) | −12.5997 | − | 2.33925i | −0.476566 | − | 0.0884787i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.1776 | −1.17756 | −0.588781 | − | 0.808293i | \(-0.700392\pi\) | ||||
−0.588781 | + | 0.808293i | \(0.700392\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.430672 | + | 0.745946i | 0.0162431 | + | 0.0281339i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −25.7179 | + | 30.0929i | −0.968592 | + | 1.13337i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.7802 | − | 5.66806i | 1.19522 | − | 0.213170i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.02492 | + | 6.97137i | 0.151159 | + | 0.261815i | 0.931654 | − | 0.363347i | \(-0.118366\pi\) |
−0.780495 | + | 0.625162i | \(0.785033\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.4168 | + | 4.00602i | 0.390660 | + | 0.150238i | ||||
\(712\) | 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 | ||||||||
\(717\) | 2.81585 | − | 3.29487i | 0.105160 | − | 0.123049i | ||||
\(718\) | 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 | ||||||||
\(723\) | −2.45102 | − | 6.92827i | −0.0911543 | − | 0.257665i | ||||
\(724\) | 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 | \(-0.841229\pi\) |
0.853357 | + | 0.521327i | \(0.174563\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.2131 | + | 24.0799i | 0.452337 | + | 0.891847i | ||||
\(730\) | 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 | ||||||||
\(735\) | −14.3756 | − | 17.3110i | −0.530252 | − | 0.638527i | ||||
\(736\) | 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 | \(-0.280571\pi\) |
−0.986294 | + | 0.165000i | \(0.947238\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.15146 | + | 11.7349i | 0.152508 | + | 0.431092i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.6613 | − | 37.5185i | −0.794676 | − | 1.37642i | −0.923045 | − | 0.384693i | \(-0.874307\pi\) |
0.128369 | − | 0.991726i | \(-0.459026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.27573 | −0.266562 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.80645 | + | 17.7904i | 0.102682 | + | 0.650917i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.6643 | − | 32.2441i | 0.426203 | − | 1.17818i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −34.8763 | −1.27265 | −0.636327 | − | 0.771420i | \(-0.719547\pi\) | ||||
−0.636327 | + | 0.771420i | \(0.719547\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −7.82049 | − | 22.1061i | −0.284994 | − | 0.805591i | ||||
\(754\) | 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 | ||||||||
\(759\) | 0.359038 | + | 1.01489i | 0.0130322 | + | 0.0368381i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.48977 | −0.199004 | −0.0995021 | − | 0.995037i | \(-0.531725\pi\) | ||||
−0.0995021 | + | 0.995037i | \(0.531725\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 26.2544 | + | 31.1643i | 0.950473 | + | 1.12822i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −37.2033 | − | 14.3074i | −1.34509 | − | 0.517285i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.7564 | 0.424499 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.81365 | + | 3.14134i | 0.0654021 | + | 0.113280i | 0.896872 | − | 0.442290i | \(-0.145834\pi\) |
−0.831470 | + | 0.555569i | \(0.812500\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.55550 | + | 10.0503i | 0.128048 | + | 0.361953i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.96717 | − | 12.0675i | −0.250592 | − | 0.434037i | 0.713097 | − | 0.701065i | \(-0.247292\pi\) |
−0.963689 | + | 0.267028i | \(0.913958\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.32640 | − | 4.02944i | 0.0835666 | − | 0.144742i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.10013 | − | 0.0219256i | −0.111217 | − | 0.000786577i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.86888 | 0.0669597 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.95729 | 0.141603 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.43916 | − | 4.57196i | 0.301591 | − | 0.163388i | ||||
\(784\) | 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 | \(-0.731898\pi\) |
0.979075 | + | 0.203499i | \(0.0652314\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.6387 | − | 41.3790i | −0.521151 | − | 1.47313i | ||||
\(790\) | 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 | ||||||||
\(795\) | 14.0137 | − | 16.3977i | 0.497015 | − | 0.581566i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.57971 | + | 9.66434i | 0.197644 | + | 0.342329i | 0.947764 | − | 0.318973i | \(-0.103338\pi\) |
−0.750120 | + | 0.661301i | \(0.770004\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.0797 | − | 76.3483i | 1.55943 | − | 2.70101i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.17388 | + | 39.1370i | 0.218143 | + | 1.38284i | ||||
\(802\) | 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 | ||||||||
\(807\) | −12.2001 | + | 14.2756i | −0.429466 | + | 0.502525i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.3481 | + | 24.8517i | 0.504453 | + | 0.873738i | 0.999987 | + | 0.00514935i | \(0.00163910\pi\) |
−0.495534 | + | 0.868589i | \(0.665028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.1695 | −1.65635 | −0.828173 | − | 0.560473i | \(-0.810620\pi\) | ||||
−0.828173 | + | 0.560473i | \(0.810620\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −51.1513 | − | 9.49670i | −1.79396 | − | 0.333064i | ||||
\(814\) | 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 | ||||||||
\(819\) | −43.9905 | − | 8.48949i | −1.53715 | − | 0.296647i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.3854 | + | 33.5765i | 0.676554 | + | 1.17183i | 0.976012 | + | 0.217717i | \(0.0698609\pi\) |
−0.299458 | + | 0.954110i | \(0.596806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.3920 | + | 19.7316i | −0.397101 | + | 0.687799i | −0.993367 | − | 0.114988i | \(-0.963317\pi\) |
0.596266 | + | 0.802787i | \(0.296650\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.31482 | + | 6.54327i | 0.0805916 | + | 0.227807i | ||||
\(826\) | 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 | ||||||||
\(831\) | −11.4164 | − | 32.2706i | −0.396030 | − | 1.11945i | ||||
\(832\) | 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 | ||||||||
\(837\) | −13.6653 | + | 7.40326i | −0.472342 | + | 0.255894i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.5804 | + | 33.9142i | −0.675990 | + | 1.17085i | 0.300188 | + | 0.953880i | \(0.402951\pi\) |
−0.976178 | + | 0.216970i | \(0.930383\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7940 | + | 22.1599i | 0.441174 | + | 0.764135i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.5758 | + | 2.52046i | 0.467574 | + | 0.0868093i | ||||
\(844\) | 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 | ||||||||
\(849\) | −39.5301 | − | 7.33911i | −1.35667 | − | 0.251877i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0816145 | + | 0.141361i | −0.00279771 | + | 0.00484578i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.5234 | − | 25.1552i | 0.497270 | − | 0.861298i | −0.502725 | − | 0.864447i | \(-0.667669\pi\) |
0.999995 | + | 0.00314895i | \(0.00100234\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.10461 | − | 7.00224i | −0.0377768 | − | 0.239472i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −48.2584 | −1.64848 | −0.824239 | − | 0.566243i | \(-0.808397\pi\) | ||||
−0.824239 | + | 0.566243i | \(0.808397\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.1506 | 0.346332 | 0.173166 | − | 0.984893i | \(-0.444600\pi\) | ||||
0.173166 | + | 0.984893i | \(0.444600\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.40442 | + | 5.80148i | −0.116022 | + | 0.197714i | ||||
\(862\) | 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 | ||||||||
\(867\) | 58.3287 | + | 10.8292i | 1.98094 | + | 0.367780i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.79161 | − | 8.29931i | −0.162544 | − | 0.281535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.2689 | −0.923972 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.99167 | + | 37.9819i | 0.202787 | + | 1.28549i | ||||
\(874\) | 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 | ||||||||
\(879\) | 26.6819 | − | 31.2209i | 0.899957 | − | 1.05305i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.6562 | 0.796996 | 0.398498 | − | 0.917169i | \(-0.369532\pi\) | ||||
0.398498 | + | 0.917169i | \(0.369532\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.8601 | −1.40871 | −0.704353 | − | 0.709850i | \(-0.748763\pi\) | ||||
−0.704353 | + | 0.709850i | \(0.748763\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.58271 | − | 1.22214i | −0.221276 | − | 0.0410818i | ||||
\(886\) | 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 | ||||||||
\(891\) | 4.84829 | − | 22.6715i | 0.162424 | − | 0.759523i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.6787 | 0.524669 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.2404 | − | 35.0574i | −0.676563 | − | 1.17184i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.53252 | + | 1.79323i | −0.0511695 | + | 0.0598743i | ||||
\(898\) | 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 | ||||||||
\(903\) | 37.9674 | + | 0.268524i | 1.26348 | + | 0.00893592i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −46.4606 | −1.54440 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.8807 | 1.35742 | 0.678711 | − | 0.734405i | \(-0.262539\pi\) | ||||
0.678711 | + | 0.734405i | \(0.262539\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.4609 | + | 23.0180i | −0.943988 | + | 0.763460i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.4235 | + | 24.9823i | −0.477873 | + | 0.827701i | −0.999678 | − | 0.0253641i | \(-0.991925\pi\) |
0.521805 | + | 0.853065i | \(0.325259\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.73249 | − | 13.3931i | 0.255908 | − | 0.443246i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27.0649 | + | 31.6691i | −0.894739 | + | 1.04695i | ||||
\(916\) | 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 | \(0.422415\pi\) |
−0.961095 | + | 0.276219i | \(0.910919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.24025 | + | 6.33248i | 0.0738186 | + | 0.208662i | ||||
\(922\) | 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 | ||||||||
\(927\) | 31.8243 | − | 25.7383i | 1.04525 | − | 0.845355i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.7377 | + | 23.7944i | 0.450719 | + | 0.780668i | 0.998431 | − | 0.0559990i | \(-0.0178344\pi\) |
−0.547712 | + | 0.836667i | \(0.684501\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.51314 | + | 8.78299i | −0.0495911 | + | 0.287851i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11.7919 | + | 2.18927i | 0.386049 | + | 0.0716735i | ||||
\(934\) | 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 | ||||||||
\(939\) | −34.0188 | + | 39.8060i | −1.11016 | + | 1.29902i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.0608 | − | 22.6219i | 0.425769 | − | 0.737454i | −0.570723 | − | 0.821143i | \(-0.693337\pi\) |
0.996492 | + | 0.0836892i | \(0.0266703\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.177081 | + | 0.306714i | 0.00576656 | + | 0.00998797i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 23.7489 | + | 9.32654i | 0.772552 | + | 0.303392i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.59015 | − | 6.21833i | −0.116664 | − | 0.202068i | 0.801780 | − | 0.597620i | \(-0.203887\pi\) |
−0.918444 | + | 0.395551i | \(0.870553\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.0256 | − | 64.1302i | 1.20190 | − | 2.08176i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.5484 | + | 12.3429i | −0.342055 | + | 0.400245i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.1187 | −1.04043 | −0.520214 | − | 0.854036i | \(-0.674148\pi\) | ||||
−0.520214 | + | 0.854036i | \(0.674148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.03678 | + | 13.9201i | 0.260064 | + | 0.450444i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.10306 | − | 1.50441i | −0.261935 | − | 0.0486305i | ||||
\(958\) | 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 | ||||||||
\(963\) | 6.05844 | + | 38.4052i | 0.195231 | + | 1.23759i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.50018 | + | 2.59838i | −0.0482924 | + | 0.0836449i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.4860 | + | 47.6071i | 0.883890 | + | 1.53094i | 0.846981 | + | 0.531623i | \(0.178418\pi\) |
0.0369085 | + | 0.999319i | \(0.488249\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.26533 | + | 14.8835i | 0.169147 | + | 0.478126i | ||||
\(970\) | 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 | ||||||||
\(975\) | −9.88061 | + | 11.5615i | −0.316433 | + | 0.370263i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.61437 | + | 4.52823i | −0.0836412 | + | 0.144871i | −0.904811 | − | 0.425813i | \(-0.859988\pi\) |
0.821170 | + | 0.570683i | \(0.193322\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.0106 | − | 29.4633i | 0.543662 | − | 0.941651i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −43.1262 | − | 16.5852i | −1.37691 | − | 0.529525i | ||||
\(982\) | 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 | ||||||||
\(987\) | −28.5609 | + | 48.6707i | −0.909103 | + | 1.54921i | ||||
\(988\) | 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 | \(-0.188916\pi\) |
−0.898831 | + | 0.438295i | \(0.855583\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.9949 | − | 36.2676i | 0.983593 | − | 1.15092i | ||||
\(994\) | 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 | ||||||||
\(999\) | 3.09086 | − | 1.67449i | 0.0977906 | − | 0.0529786i |
(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 | 1008.2.t.k.961.4 | 22 | ||
3.2 | odd | 2 | 3024.2.t.l.289.3 | 22 | |||
4.3 | odd | 2 | 504.2.t.d.457.8 | yes | 22 | ||
7.4 | even | 3 | 1008.2.q.k.529.5 | 22 | |||
9.4 | even | 3 | 1008.2.q.k.625.5 | 22 | |||
9.5 | odd | 6 | 3024.2.q.k.2305.9 | 22 | |||
12.11 | even | 2 | 1512.2.t.d.289.3 | 22 | |||
21.11 | odd | 6 | 3024.2.q.k.2881.9 | 22 | |||
28.11 | odd | 6 | 504.2.q.d.25.7 | ✓ | 22 | ||
36.23 | even | 6 | 1512.2.q.c.793.9 | 22 | |||
36.31 | odd | 6 | 504.2.q.d.121.7 | yes | 22 | ||
63.4 | even | 3 | inner | 1008.2.t.k.193.4 | 22 | ||
63.32 | odd | 6 | 3024.2.t.l.1873.3 | 22 | |||
84.11 | even | 6 | 1512.2.q.c.1369.9 | 22 | |||
252.67 | odd | 6 | 504.2.t.d.193.8 | yes | 22 | ||
252.95 | even | 6 | 1512.2.t.d.361.3 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.d.25.7 | ✓ | 22 | 28.11 | odd | 6 | ||
504.2.q.d.121.7 | yes | 22 | 36.31 | odd | 6 | ||
504.2.t.d.193.8 | yes | 22 | 252.67 | odd | 6 | ||
504.2.t.d.457.8 | yes | 22 | 4.3 | odd | 2 | ||
1008.2.q.k.529.5 | 22 | 7.4 | even | 3 | |||
1008.2.q.k.625.5 | 22 | 9.4 | even | 3 | |||
1008.2.t.k.193.4 | 22 | 63.4 | even | 3 | inner | ||
1008.2.t.k.961.4 | 22 | 1.1 | even | 1 | trivial | ||
1512.2.q.c.793.9 | 22 | 36.23 | even | 6 | |||
1512.2.q.c.1369.9 | 22 | 84.11 | even | 6 | |||
1512.2.t.d.289.3 | 22 | 12.11 | even | 2 | |||
1512.2.t.d.361.3 | 22 | 252.95 | even | 6 | |||
3024.2.q.k.2305.9 | 22 | 9.5 | odd | 6 | |||
3024.2.q.k.2881.9 | 22 | 21.11 | odd | 6 | |||
3024.2.t.l.289.3 | 22 | 3.2 | odd | 2 | |||
3024.2.t.l.1873.3 | 22 | 63.32 | odd | 6 |