Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1567,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4 x^{14} + 54 x^{12} - 112 x^{11} - 104 x^{10} + 1312 x^{9} - 3159 x^{8} + 2544 x^{7} + 4132 x^{6} - 16824 x^{5} + 27780 x^{4} - 26200 x^{3} + 14608 x^{2} + \cdots + 782 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.6 | ||
Root | \(0.812979 - 0.0402481i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1567 |
Dual form | 1764.2.b.n.1567.7 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.629640 | − | 1.26631i | −0.445223 | − | 0.895420i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.20711 | + | 1.59465i | −0.603553 | + | 0.797323i | ||||
\(5\) | 2.32685i | 1.04060i | 0.853984 | + | 0.520299i | \(0.174179\pi\) | ||||
−0.853984 | + | 0.520299i | \(0.825821\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.77937 | + | 0.524525i | 0.982654 | + | 0.185448i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.94652 | − | 1.46508i | 0.931771 | − | 0.463298i | ||||
\(11\) | − | 3.58168i | − | 1.07992i | −0.841692 | − | 0.539958i | \(-0.818440\pi\) | ||
0.841692 | − | 0.539958i | \(-0.181560\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.93015i | − | 0.812678i | −0.913722 | − | 0.406339i | \(-0.866805\pi\) | ||
0.913722 | − | 0.406339i | \(-0.133195\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.08579 | − | 3.84981i | −0.271447 | − | 0.962453i | ||||
\(17\) | 2.32685i | 0.564343i | 0.959364 | + | 0.282172i | \(0.0910547\pi\) | ||||
−0.959364 | + | 0.282172i | \(0.908945\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.33402 | −1.91195 | −0.955977 | − | 0.293440i | \(-0.905200\pi\) | ||||
−0.955977 | + | 0.293440i | \(0.905200\pi\) | |||||||
\(20\) | −3.71049 | − | 2.80875i | −0.829692 | − | 0.628056i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.53553 | + | 2.25517i | −0.966979 | + | 0.480804i | ||||
\(23\) | − | 1.48358i | − | 0.309348i | −0.987966 | − | 0.154674i | \(-0.950567\pi\) | ||
0.987966 | − | 0.154674i | \(-0.0494327\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.414214 | −0.0828427 | ||||||||
\(26\) | −3.71049 | + | 1.84494i | −0.727688 | + | 0.361823i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.86123 | 1.45979 | 0.729897 | − | 0.683557i | \(-0.239568\pi\) | ||||
0.729897 | + | 0.683557i | \(0.239568\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.45206 | 0.620009 | 0.310004 | − | 0.950735i | \(-0.399669\pi\) | ||||
0.310004 | + | 0.950735i | \(0.399669\pi\) | |||||||
\(32\) | −4.19142 | + | 3.79894i | −0.740946 | + | 0.671565i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.94652 | − | 1.46508i | 0.505324 | − | 0.251258i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.24264 | −1.35508 | −0.677541 | − | 0.735485i | \(-0.736954\pi\) | ||||
−0.677541 | + | 0.735485i | \(0.736954\pi\) | |||||||
\(38\) | 5.24743 | + | 10.5535i | 0.851246 | + | 1.71200i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.22049 | + | 6.46716i | −0.192976 | + | 1.02255i | ||||
\(41\) | − | 2.89143i | − | 0.451566i | −0.974178 | − | 0.225783i | \(-0.927506\pi\) | ||
0.974178 | − | 0.225783i | \(-0.0724940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.37858i | − | 0.972724i | −0.873757 | − | 0.486362i | \(-0.838324\pi\) | ||
0.873757 | − | 0.486362i | \(-0.161676\pi\) | |||||||
\(44\) | 5.71151 | + | 4.32347i | 0.861042 | + | 0.651788i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.87868 | + | 0.934122i | −0.276996 | + | 0.137729i | ||||
\(47\) | 10.4949 | 1.53083 | 0.765417 | − | 0.643535i | \(-0.222533\pi\) | ||||
0.765417 | + | 0.643535i | \(0.222533\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.260805 | + | 0.524525i | 0.0368835 | + | 0.0741790i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.67255 | + | 3.53701i | 0.647966 | + | 0.490494i | ||||
\(53\) | 8.59890 | 1.18115 | 0.590575 | − | 0.806983i | \(-0.298901\pi\) | ||||
0.590575 | + | 0.806983i | \(0.298901\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.33402 | 1.12376 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.94975 | − | 9.95480i | −0.649934 | − | 1.30713i | ||||
\(59\) | −10.4949 | −1.36631 | −0.683157 | − | 0.730271i | \(-0.739394\pi\) | ||||
−0.683157 | + | 0.730271i | \(0.739394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.93015i | 0.375167i | 0.982249 | + | 0.187584i | \(0.0600656\pi\) | ||||
−0.982249 | + | 0.187584i | \(0.939934\pi\) | |||||||
\(62\) | −2.17356 | − | 4.37140i | −0.276042 | − | 0.555168i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.44975 | + | 2.91569i | 0.931218 | + | 0.364462i | ||||
\(65\) | 6.81801 | 0.845670 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.02068i | − | 1.10205i | −0.834488 | − | 0.551025i | \(-0.814237\pi\) | ||
0.834488 | − | 0.551025i | \(-0.185763\pi\) | |||||||
\(68\) | −3.71049 | − | 2.80875i | −0.449964 | − | 0.340611i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.7450i | − | 1.27520i | −0.770367 | − | 0.637601i | \(-0.779927\pi\) | ||
0.770367 | − | 0.637601i | \(-0.220073\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.2179i | − | 1.31295i | −0.754347 | − | 0.656476i | \(-0.772046\pi\) | ||
0.754347 | − | 0.656476i | \(-0.227954\pi\) | |||||||
\(74\) | 5.18990 | + | 10.4378i | 0.603313 | + | 1.21337i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.0600 | − | 13.2898i | 1.15397 | − | 1.52444i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 15.3993i | − | 1.73255i | −0.499566 | − | 0.866276i | \(-0.666507\pi\) | ||
0.499566 | − | 0.866276i | \(-0.333493\pi\) | |||||||
\(80\) | 8.95793 | − | 2.52646i | 1.00153 | − | 0.282467i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.66147 | + | 1.82056i | −0.404341 | + | 0.201048i | ||||
\(83\) | 14.8420 | 1.62912 | 0.814559 | − | 0.580080i | \(-0.196979\pi\) | ||||
0.814559 | + | 0.580080i | \(0.196979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.41421 | −0.587254 | ||||||||
\(86\) | −8.07729 | + | 4.01621i | −0.870997 | + | 0.433079i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.87868 | − | 9.95480i | 0.200268 | − | 1.06118i | ||||
\(89\) | 13.5619i | 1.43755i | 0.695241 | + | 0.718777i | \(0.255298\pi\) | ||||
−0.695241 | + | 0.718777i | \(0.744702\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.36578 | + | 1.79084i | 0.246650 | + | 0.186708i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.60799 | − | 13.2898i | −0.681562 | − | 1.37074i | ||||
\(95\) | − | 19.3920i | − | 1.98957i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 5.35757i | − | 0.543979i | −0.962300 | − | 0.271989i | \(-0.912318\pi\) | ||
0.962300 | − | 0.271989i | \(-0.0876815\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.660524i | 0.0500000 | − | 0.0660524i | ||||
\(101\) | − | 9.47275i | − | 0.942574i | −0.881980 | − | 0.471287i | \(-0.843790\pi\) | ||
0.881980 | − | 0.471287i | \(-0.156210\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.45206 | 0.340142 | 0.170071 | − | 0.985432i | \(-0.445600\pi\) | ||||
0.170071 | + | 0.985432i | \(0.445600\pi\) | |||||||
\(104\) | 1.53694 | − | 8.14396i | 0.150709 | − | 0.798581i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.41421 | − | 10.8889i | −0.525875 | − | 1.05763i | ||||
\(107\) | − | 1.48358i | − | 0.143423i | −0.997425 | − | 0.0717116i | \(-0.977154\pi\) | ||
0.997425 | − | 0.0717116i | \(-0.0228461\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.58579 | −0.439239 | −0.219619 | − | 0.975586i | \(-0.570482\pi\) | ||||
−0.219619 | + | 0.975586i | \(0.570482\pi\) | |||||||
\(110\) | −5.24743 | − | 10.5535i | −0.500323 | − | 1.00624i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.55568 | −0.710779 | −0.355389 | − | 0.934718i | \(-0.615652\pi\) | ||||
−0.355389 | + | 0.934718i | \(0.615652\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.45206 | 0.321907 | ||||||||
\(116\) | −9.48935 | + | 12.5359i | −0.881064 | + | 1.16393i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.60799 | + | 13.2898i | 0.608314 | + | 1.22343i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.82843 | −0.166221 | ||||||||
\(122\) | 3.71049 | − | 1.84494i | 0.335932 | − | 0.167033i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.16701 | + | 5.50482i | −0.374208 | + | 0.494347i | ||||
\(125\) | 10.6704i | 0.954391i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.02068i | 0.800455i | 0.916416 | + | 0.400228i | \(0.131069\pi\) | ||||
−0.916416 | + | 0.400228i | \(0.868931\pi\) | |||||||
\(128\) | −0.998475 | − | 11.2696i | −0.0882535 | − | 0.996098i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.29289 | − | 8.63375i | −0.376512 | − | 0.757230i | ||||
\(131\) | 14.8420 | 1.29675 | 0.648375 | − | 0.761321i | \(-0.275449\pi\) | ||||
0.648375 | + | 0.761321i | \(0.275449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.4230 | + | 5.67978i | −0.986798 | + | 0.490658i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.22049 | + | 6.46716i | −0.104656 | + | 0.554554i | ||||
\(137\) | 6.38589 | 0.545584 | 0.272792 | − | 0.962073i | \(-0.412053\pi\) | ||||
0.272792 | + | 0.962073i | \(0.412053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.7861 | 0.999682 | 0.499841 | − | 0.866117i | \(-0.333392\pi\) | ||||
0.499841 | + | 0.866117i | \(0.333392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.6066 | + | 6.76551i | −1.14184 | + | 0.567749i | ||||
\(143\) | −10.4949 | −0.877624 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.2919i | 1.51906i | ||||||||
\(146\) | −14.2054 | + | 7.06322i | −1.17564 | + | 0.584556i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.94975 | − | 13.1441i | 0.817864 | − | 1.08044i | ||||
\(149\) | −14.2471 | −1.16717 | −0.583585 | − | 0.812052i | \(-0.698351\pi\) | ||||
−0.583585 | + | 0.812052i | \(0.698351\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.37858i | 0.519082i | 0.965732 | + | 0.259541i | \(0.0835712\pi\) | ||||
−0.965732 | + | 0.259541i | \(0.916429\pi\) | |||||||
\(152\) | −23.1633 | − | 4.37140i | −1.87879 | − | 0.354567i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.03242i | 0.645179i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3617i | 1.22600i | 0.790083 | + | 0.613000i | \(0.210037\pi\) | ||||
−0.790083 | + | 0.613000i | \(0.789963\pi\) | |||||||
\(158\) | −19.5003 | + | 9.69599i | −1.55136 | + | 0.771371i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.83956 | − | 9.75279i | −0.698829 | − | 0.771026i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 9.02068i | − | 0.706554i | −0.935519 | − | 0.353277i | \(-0.885067\pi\) | ||
0.935519 | − | 0.353277i | \(-0.114933\pi\) | |||||||
\(164\) | 4.61081 | + | 3.49027i | 0.360044 | + | 0.272544i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.34510 | − | 18.7946i | −0.725321 | − | 1.45875i | ||||
\(167\) | 4.34711 | 0.336390 | 0.168195 | − | 0.985754i | \(-0.446206\pi\) | ||||
0.168195 | + | 0.985754i | \(0.446206\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.41421 | 0.339555 | ||||||||
\(170\) | 3.40901 | + | 6.85610i | 0.261459 | + | 0.525839i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 10.1716 | + | 7.69963i | 0.775575 | + | 0.587091i | ||||
\(173\) | − | 16.2879i | − | 1.23835i | −0.785254 | − | 0.619174i | \(-0.787468\pi\) | ||
0.785254 | − | 0.619174i | \(-0.212532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.7888 | + | 3.88894i | −1.03937 | + | 0.293140i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.1736 | − | 8.53909i | 1.28721 | − | 0.640032i | ||||
\(179\) | − | 23.8427i | − | 1.78209i | −0.453917 | − | 0.891044i | \(-0.649974\pi\) | ||
0.453917 | − | 0.891044i | \(-0.350026\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.64659i | − | 0.345379i | −0.984976 | − | 0.172689i | \(-0.944754\pi\) | ||
0.984976 | − | 0.172689i | \(-0.0552457\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.778175 | − | 4.12341i | 0.0573678 | − | 0.303982i | ||||
\(185\) | − | 19.1794i | − | 1.41009i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.33402 | 0.609444 | ||||||||
\(188\) | −12.6684 | + | 16.7356i | −0.923939 | + | 1.22057i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −24.5563 | + | 12.2100i | −1.78150 | + | 0.885804i | ||||
\(191\) | − | 6.54884i | − | 0.473857i | −0.971527 | − | 0.236929i | \(-0.923859\pi\) | ||
0.971527 | − | 0.236929i | \(-0.0761408\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.65685 | 0.263226 | 0.131613 | − | 0.991301i | \(-0.457984\pi\) | ||||
0.131613 | + | 0.991301i | \(0.457984\pi\) | |||||||
\(194\) | −6.78437 | + | 3.37334i | −0.487089 | + | 0.242192i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.04322 | 0.0743265 | 0.0371632 | − | 0.999309i | \(-0.488168\pi\) | ||||
0.0371632 | + | 0.999309i | \(0.488168\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.88195 | 0.346073 | 0.173036 | − | 0.984915i | \(-0.444642\pi\) | ||||
0.173036 | + | 0.984915i | \(0.444642\pi\) | |||||||
\(200\) | −1.15125 | − | 0.217265i | −0.0814057 | − | 0.0153630i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.9955 | + | 5.96442i | −0.843999 | + | 0.419655i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.72792 | 0.469898 | ||||||||
\(206\) | −2.17356 | − | 4.37140i | −0.151439 | − | 0.304570i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.2805 | + | 3.18152i | −0.782165 | + | 0.220599i | ||||
\(209\) | 29.8498i | 2.06475i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7572i | 0.878239i | 0.898429 | + | 0.439120i | \(0.144710\pi\) | ||||
−0.898429 | + | 0.439120i | \(0.855290\pi\) | |||||||
\(212\) | −10.3798 | + | 13.7122i | −0.712887 | + | 0.941758i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.87868 | + | 0.934122i | −0.128424 | + | 0.0638552i | ||||
\(215\) | 14.8420 | 1.01221 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.88739 | + | 5.80705i | 0.195559 | + | 0.393303i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.0600 | + | 13.2898i | −0.678248 | + | 0.895998i | ||||
\(221\) | 6.81801 | 0.458629 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.6680 | −1.11617 | −0.558087 | − | 0.829782i | \(-0.688464\pi\) | ||||
−0.558087 | + | 0.829782i | \(0.688464\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.75736 | + | 9.56787i | 0.316455 | + | 0.636445i | ||||
\(227\) | −25.3368 | −1.68167 | −0.840833 | − | 0.541295i | \(-0.817934\pi\) | ||||
−0.840833 | + | 0.541295i | \(0.817934\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 21.2220i | − | 1.40239i | −0.712969 | − | 0.701196i | \(-0.752650\pi\) | ||
0.712969 | − | 0.701196i | \(-0.247350\pi\) | |||||||
\(230\) | −2.17356 | − | 4.37140i | −0.143320 | − | 0.288241i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 21.8492 | + | 4.12341i | 1.43447 | + | 0.270715i | ||||
\(233\) | 12.8984 | 0.844999 | 0.422500 | − | 0.906363i | \(-0.361153\pi\) | ||||
0.422500 | + | 0.906363i | \(0.361153\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.4199i | 1.59298i | ||||||||
\(236\) | 12.6684 | − | 16.7356i | 0.824644 | − | 1.08939i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 8.64694i | − | 0.559324i | −0.960099 | − | 0.279662i | \(-0.909778\pi\) | ||
0.960099 | − | 0.279662i | \(-0.0902224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 7.07401i | − | 0.455677i | −0.973699 | − | 0.227839i | \(-0.926834\pi\) | ||
0.973699 | − | 0.227839i | \(-0.0731658\pi\) | |||||||
\(242\) | 1.15125 | + | 2.31536i | 0.0740052 | + | 0.148837i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.67255 | − | 3.53701i | −0.299129 | − | 0.226434i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.4199i | 1.55380i | ||||||||
\(248\) | 9.59455 | + | 1.81069i | 0.609254 | + | 0.114979i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.5121 | − | 6.71852i | 0.854581 | − | 0.424917i | ||||
\(251\) | 4.34711 | 0.274387 | 0.137194 | − | 0.990544i | \(-0.456192\pi\) | ||||
0.137194 | + | 0.990544i | \(0.456192\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.31371 | −0.334070 | ||||||||
\(254\) | 11.4230 | − | 5.67978i | 0.716744 | − | 0.356381i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.6421 | + | 8.36015i | −0.852633 | + | 0.522509i | ||||
\(257\) | 25.3614i | 1.58200i | 0.611814 | + | 0.791002i | \(0.290440\pi\) | ||||
−0.611814 | + | 0.791002i | \(0.709560\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −8.23007 | + | 10.8723i | −0.510407 | + | 0.674272i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.34510 | − | 18.7946i | −0.577342 | − | 1.16114i | ||||
\(263\) | − | 3.58168i | − | 0.220856i | −0.993884 | − | 0.110428i | \(-0.964778\pi\) | ||
0.993884 | − | 0.110428i | \(-0.0352221\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.0083i | 1.22910i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.3848 | + | 10.8889i | 0.878690 | + | 0.665147i | ||||
\(269\) | − | 9.47275i | − | 0.577564i | −0.957395 | − | 0.288782i | \(-0.906750\pi\) | ||
0.957395 | − | 0.288782i | \(-0.0932502\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.2381 | −0.925651 | −0.462826 | − | 0.886449i | \(-0.653164\pi\) | ||||
−0.462826 | + | 0.886449i | \(0.653164\pi\) | |||||||
\(272\) | 8.95793 | − | 2.52646i | 0.543154 | − | 0.153189i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.02082 | − | 8.08655i | −0.242906 | − | 0.488527i | ||||
\(275\) | 1.48358i | 0.0894633i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.7990 | −0.949269 | −0.474635 | − | 0.880183i | \(-0.657420\pi\) | ||||
−0.474635 | + | 0.880183i | \(0.657420\pi\) | |||||||
\(278\) | −7.42099 | − | 14.9249i | −0.445081 | − | 0.895135i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0219 | −1.19441 | −0.597204 | − | 0.802090i | \(-0.703722\pi\) | ||||
−0.597204 | + | 0.802090i | \(0.703722\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.45206 | −0.205204 | −0.102602 | − | 0.994722i | \(-0.532717\pi\) | ||||
−0.102602 | + | 0.994722i | \(0.532717\pi\) | |||||||
\(284\) | 17.1345 | + | 12.9704i | 1.01675 | + | 0.769652i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.60799 | + | 13.2898i | 0.390738 | + | 0.785842i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.5858 | 0.681517 | ||||||||
\(290\) | 23.1633 | − | 11.5173i | 1.36019 | − | 0.676319i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.8885 | + | 13.5412i | 1.04685 | + | 0.792437i | ||||
\(293\) | − | 21.5062i | − | 1.25641i | −0.778050 | − | 0.628203i | \(-0.783791\pi\) | ||
0.778050 | − | 0.628203i | \(-0.216209\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 24.4199i | − | 1.42178i | ||||||
\(296\) | −22.9093 | − | 4.32347i | −1.33158 | − | 0.251297i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.97056 | + | 18.0414i | 0.519651 | + | 1.04511i | ||||
\(299\) | −4.34711 | −0.251400 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.07729 | − | 4.01621i | 0.464796 | − | 0.231107i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.04896 | + | 32.0844i | 0.518994 | + | 1.84017i | ||||
\(305\) | −6.81801 | −0.390398 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.0242 | −1.54235 | −0.771177 | − | 0.636621i | \(-0.780332\pi\) | ||||
−0.771177 | + | 0.636621i | \(0.780332\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.1716 | − | 5.05753i | 0.577707 | − | 0.287249i | ||||
\(311\) | 4.34711 | 0.246502 | 0.123251 | − | 0.992376i | \(-0.460668\pi\) | ||||
0.123251 | + | 0.992376i | \(0.460668\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 11.2179i | − | 0.634072i | −0.948414 | − | 0.317036i | \(-0.897312\pi\) | ||
0.948414 | − | 0.317036i | \(-0.102688\pi\) | |||||||
\(314\) | 19.4528 | − | 9.67236i | 1.09778 | − | 0.545843i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.5563 | + | 18.5885i | 1.38140 | + | 1.04569i | ||||
\(317\) | −1.04322 | −0.0585932 | −0.0292966 | − | 0.999571i | \(-0.509327\pi\) | ||||
−0.0292966 | + | 0.999571i | \(0.509327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 28.1564i | − | 1.57646i | ||||||
\(320\) | −6.78437 | + | 17.3344i | −0.379258 | + | 0.969023i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 19.3920i | − | 1.07900i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.21371i | 0.0673244i | ||||||||
\(326\) | −11.4230 | + | 5.67978i | −0.632662 | + | 0.314574i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.51663 | − | 8.03635i | 0.0837418 | − | 0.443733i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0414i | 0.991642i | 0.868425 | + | 0.495821i | \(0.165133\pi\) | ||||
−0.868425 | + | 0.495821i | \(0.834867\pi\) | |||||||
\(332\) | −17.9159 | + | 23.6677i | −0.983260 | + | 1.29893i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.73712 | − | 5.50482i | −0.149768 | − | 0.301210i | ||||
\(335\) | 20.9897 | 1.14679 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.38478 | 0.129907 | 0.0649535 | − | 0.997888i | \(-0.479310\pi\) | ||||
0.0649535 | + | 0.997888i | \(0.479310\pi\) | |||||||
\(338\) | −2.77937 | − | 5.58978i | −0.151178 | − | 0.304044i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.53553 | − | 8.63375i | 0.354439 | − | 0.468231i | ||||
\(341\) | − | 12.3642i | − | 0.669558i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.34572 | − | 17.7284i | 0.180389 | − | 0.955852i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.6256 | + | 10.2555i | −1.10884 | + | 0.551341i | ||||
\(347\) | 11.6141i | 0.623478i | 0.950168 | + | 0.311739i | \(0.100911\pi\) | ||||
−0.950168 | + | 0.311739i | \(0.899089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.21371i | 0.0649683i | 0.999472 | + | 0.0324842i | \(0.0103418\pi\) | ||||
−0.999472 | + | 0.0324842i | \(0.989658\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.6066 | + | 15.0123i | 0.725234 | + | 0.800160i | ||||
\(353\) | 21.5062i | 1.14466i | 0.820023 | + | 0.572330i | \(0.193960\pi\) | ||||
−0.820023 | + | 0.572330i | \(0.806040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.0021 | 1.32697 | ||||||||
\(356\) | −21.6263 | − | 16.3706i | −1.14619 | − | 0.867640i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −30.1924 | + | 15.0123i | −1.59572 | + | 0.793426i | ||||
\(359\) | 1.48358i | 0.0783004i | 0.999233 | + | 0.0391502i | \(0.0124651\pi\) | ||||
−0.999233 | + | 0.0391502i | \(0.987535\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 50.4558 | 2.65557 | ||||||||
\(362\) | −5.88405 | + | 2.92568i | −0.309259 | + | 0.153770i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.1023 | 1.36625 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.3582 | −1.84569 | −0.922843 | − | 0.385177i | \(-0.874140\pi\) | ||||
−0.922843 | + | 0.385177i | \(0.874140\pi\) | |||||||
\(368\) | −5.71151 | + | 1.61085i | −0.297733 | + | 0.0839714i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −24.2871 | + | 12.0761i | −1.26263 | + | 0.627806i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.82843 | −0.146450 | −0.0732252 | − | 0.997315i | \(-0.523329\pi\) | ||||
−0.0732252 | + | 0.997315i | \(0.523329\pi\) | |||||||
\(374\) | −5.24743 | − | 10.5535i | −0.271338 | − | 0.545708i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 29.1691 | + | 5.50482i | 1.50428 | + | 0.283889i | ||||
\(377\) | − | 23.0346i | − | 1.18634i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 30.9233 | + | 23.4082i | 1.58633 | + | 1.20081i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.29289 | + | 4.12341i | −0.424301 | + | 0.210972i | ||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.30250 | − | 4.63073i | −0.117194 | − | 0.235698i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.54342 | + | 6.46716i | 0.433726 | + | 0.328320i | ||||
\(389\) | 25.0590 | 1.27054 | 0.635272 | − | 0.772289i | \(-0.280888\pi\) | ||||
0.635272 | + | 0.772289i | \(0.280888\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.45206 | 0.174578 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.656854 | − | 1.32105i | −0.0330918 | − | 0.0665534i | ||||
\(395\) | 35.8317 | 1.80289 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.9385i | − | 1.15125i | −0.817714 | − | 0.575625i | \(-0.804759\pi\) | ||
0.817714 | − | 0.575625i | \(-0.195241\pi\) | |||||||
\(398\) | −3.07387 | − | 6.18209i | −0.154079 | − | 0.309880i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.449747 | + | 1.59465i | 0.0224874 | + | 0.0797323i | ||||
\(401\) | −7.25013 | −0.362054 | −0.181027 | − | 0.983478i | \(-0.557942\pi\) | ||||
−0.181027 | + | 0.983478i | \(0.557942\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 10.1151i | − | 0.503867i | ||||||
\(404\) | 15.1057 | + | 11.4346i | 0.751535 | + | 0.568894i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.5225i | 1.46338i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.2233i | 0.604405i | 0.953244 | + | 0.302203i | \(0.0977219\pi\) | ||||
−0.953244 | + | 0.302203i | \(0.902278\pi\) | |||||||
\(410\) | −4.23617 | − | 8.51967i | −0.209209 | − | 0.420756i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.16701 | + | 5.50482i | −0.205294 | + | 0.271203i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.5350i | 1.69526i | ||||||||
\(416\) | 11.1315 | + | 12.2815i | 0.545766 | + | 0.602150i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 37.7992 | − | 18.7946i | 1.84882 | − | 0.919275i | ||||
\(419\) | −19.1891 | −0.937448 | −0.468724 | − | 0.883345i | \(-0.655286\pi\) | ||||
−0.468724 | + | 0.883345i | \(0.655286\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0000 | 0.779792 | 0.389896 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389896 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(422\) | 16.1546 | − | 8.03242i | 0.786393 | − | 0.391012i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 23.8995 | + | 4.51034i | 1.16066 | + | 0.219041i | ||||
\(425\) | − | 0.963811i | − | 0.0467517i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.36578 | + | 1.79084i | 0.114354 | + | 0.0865635i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.34510 | − | 18.7946i | −0.450661 | − | 0.906357i | ||||
\(431\) | 3.58168i | 0.172523i | 0.996273 | + | 0.0862617i | \(0.0274921\pi\) | ||||
−0.996273 | + | 0.0862617i | \(0.972508\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.5152i | 1.46647i | 0.679976 | + | 0.733234i | \(0.261990\pi\) | ||||
−0.679976 | + | 0.733234i | \(0.738010\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.53553 | − | 7.31270i | 0.265104 | − | 0.350215i | ||||
\(437\) | 12.3642i | 0.591459i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.88195 | 0.233003 | 0.116501 | − | 0.993191i | \(-0.462832\pi\) | ||||
0.116501 | + | 0.993191i | \(0.462832\pi\) | |||||||
\(440\) | 23.1633 | + | 4.37140i | 1.10427 | + | 0.208398i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.29289 | − | 8.63375i | −0.204192 | − | 0.410666i | ||||
\(443\) | 4.81072i | 0.228564i | 0.993448 | + | 0.114282i | \(0.0364568\pi\) | ||||
−0.993448 | + | 0.114282i | \(0.963543\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.5563 | −1.49591 | ||||||||
\(446\) | 10.4949 | + | 21.1070i | 0.496946 | + | 0.999444i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.4017 | 1.43475 | 0.717373 | − | 0.696690i | \(-0.245344\pi\) | ||||
0.717373 | + | 0.696690i | \(0.245344\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.3562 | −0.487654 | ||||||||
\(452\) | 9.12051 | − | 12.0486i | 0.428993 | − | 0.566720i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.9531 | + | 32.0844i | 0.748716 | + | 1.50580i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.5147 | 0.725748 | 0.362874 | − | 0.931838i | \(-0.381796\pi\) | ||||
0.362874 | + | 0.931838i | \(0.381796\pi\) | |||||||
\(458\) | −26.8738 | + | 13.3622i | −1.25573 | + | 0.624377i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.16701 | + | 5.50482i | −0.194288 | + | 0.256663i | ||||
\(461\) | 10.0373i | 0.467485i | 0.972298 | + | 0.233743i | \(0.0750973\pi\) | ||||
−0.972298 | + | 0.233743i | \(0.924903\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.28419i | − | 0.245577i | −0.992433 | − | 0.122789i | \(-0.960816\pi\) | ||
0.992433 | − | 0.122789i | \(-0.0391837\pi\) | |||||||
\(464\) | −8.53562 | − | 30.2643i | −0.396256 | − | 1.40498i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.12132 | − | 16.3334i | −0.376213 | − | 0.756629i | ||||
\(467\) | 10.4949 | 0.485644 | 0.242822 | − | 0.970071i | \(-0.421927\pi\) | ||||
0.242822 | + | 0.970071i | \(0.421927\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 30.9233 | − | 15.3758i | 1.42639 | − | 0.709231i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −29.1691 | − | 5.50482i | −1.34261 | − | 0.253380i | ||||
\(473\) | −22.8460 | −1.05046 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.45206 | 0.158392 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.9497 | + | 5.44446i | −0.500830 | + | 0.249024i | ||||
\(479\) | −19.1891 | −0.876772 | −0.438386 | − | 0.898787i | \(-0.644450\pi\) | ||||
−0.438386 | + | 0.898787i | \(0.644450\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.1522i | 1.10124i | ||||||||
\(482\) | −8.95793 | + | 4.45408i | −0.408022 | + | 0.202878i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.20711 | − | 2.91569i | 0.100323 | − | 0.132531i | ||||
\(485\) | 12.4662 | 0.566063 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.4199i | 1.10657i | 0.832991 | + | 0.553286i | \(0.186626\pi\) | ||||
−0.832991 | + | 0.553286i | \(0.813374\pi\) | |||||||
\(488\) | −1.53694 | + | 8.14396i | −0.0695739 | + | 0.368660i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.41790i | − | 0.334765i | −0.985892 | − | 0.167383i | \(-0.946468\pi\) | ||
0.985892 | − | 0.167383i | \(-0.0535315\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.2919i | 0.823825i | ||||||||
\(494\) | 30.9233 | − | 15.3758i | 1.39131 | − | 0.691788i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.74820 | − | 13.2898i | −0.168299 | − | 0.596730i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.64209i | 0.118276i | 0.998250 | + | 0.0591382i | \(0.0188353\pi\) | ||||
−0.998250 | + | 0.0591382i | \(0.981165\pi\) | |||||||
\(500\) | −17.0155 | − | 12.8803i | −0.760958 | − | 0.576026i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.73712 | − | 5.50482i | −0.122164 | − | 0.245692i | ||||
\(503\) | −35.8317 | −1.59766 | −0.798828 | − | 0.601559i | \(-0.794546\pi\) | ||||
−0.798828 | + | 0.601559i | \(0.794546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.0416 | 0.980840 | ||||||||
\(506\) | 3.34572 | + | 6.72883i | 0.148736 | + | 0.299133i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.3848 | − | 10.8889i | −0.638221 | − | 0.483118i | ||||
\(509\) | 21.5062i | 0.953246i | 0.879108 | + | 0.476623i | \(0.158139\pi\) | ||||
−0.879108 | + | 0.476623i | \(0.841861\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 19.1762 | + | 12.0114i | 0.847477 | + | 0.530832i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 32.1156 | − | 15.9686i | 1.41656 | − | 0.704344i | ||||
\(515\) | 8.03242i | 0.353951i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 37.5892i | − | 1.65317i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 18.9497 | + | 3.57622i | 0.831001 | + | 0.156827i | ||||
\(521\) | 36.5965i | 1.60332i | 0.597780 | + | 0.801660i | \(0.296049\pi\) | ||||
−0.597780 | + | 0.801660i | \(0.703951\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.88195 | −0.213473 | −0.106736 | − | 0.994287i | \(-0.534040\pi\) | ||||
−0.106736 | + | 0.994287i | \(0.534040\pi\) | |||||||
\(524\) | −17.9159 | + | 23.6677i | −0.782658 | + | 1.03393i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.53553 | + | 2.25517i | −0.197759 | + | 0.0983300i | ||||
\(527\) | 8.03242i | 0.349898i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.7990 | 0.904304 | ||||||||
\(530\) | 25.3368 | − | 12.5980i | 1.10056 | − | 0.547224i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.47234 | −0.366978 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.45206 | 0.149246 | ||||||||
\(536\) | 4.73157 | − | 25.0718i | 0.204373 | − | 1.08293i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.9955 | + | 5.96442i | −0.517162 | + | 0.257145i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.1127 | 1.25165 | 0.625826 | − | 0.779962i | \(-0.284762\pi\) | ||||
0.625826 | + | 0.779962i | \(0.284762\pi\) | |||||||
\(542\) | 9.59455 | + | 19.2963i | 0.412121 | + | 0.828847i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.83956 | − | 9.75279i | −0.378993 | − | 0.418148i | ||||
\(545\) | − | 10.6704i | − | 0.457071i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.3993i | 0.658425i | 0.944256 | + | 0.329212i | \(0.106783\pi\) | ||||
−0.944256 | + | 0.329212i | \(0.893217\pi\) | |||||||
\(548\) | −7.70846 | + | 10.1832i | −0.329289 | + | 0.435006i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.87868 | − | 0.934122i | 0.0801072 | − | 0.0398311i | ||||
\(551\) | −65.5157 | −2.79106 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.94768 | + | 20.0065i | 0.422636 | + | 0.849995i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.2271 | + | 18.7946i | −0.603362 | + | 0.797069i | ||||
\(557\) | −23.8893 | −1.01222 | −0.506110 | − | 0.862469i | \(-0.668917\pi\) | ||||
−0.506110 | + | 0.862469i | \(0.668917\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.6902 | −0.790511 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.6066 | + | 25.3541i | 0.531777 | + | 1.06950i | ||||
\(563\) | 25.3368 | 1.06782 | 0.533910 | − | 0.845541i | \(-0.320722\pi\) | ||||
0.533910 | + | 0.845541i | \(0.320722\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 17.5809i | − | 0.739634i | ||||||
\(566\) | 2.17356 | + | 4.37140i | 0.0913614 | + | 0.183744i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.63604 | − | 29.8644i | 0.236483 | − | 1.25308i | ||||
\(569\) | 17.9355 | 0.751894 | 0.375947 | − | 0.926641i | \(-0.377317\pi\) | ||||
0.375947 | + | 0.926641i | \(0.377317\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 11.6628i | − | 0.488072i | −0.969766 | − | 0.244036i | \(-0.921529\pi\) | ||
0.969766 | − | 0.244036i | \(-0.0784715\pi\) | |||||||
\(572\) | 12.6684 | − | 16.7356i | 0.529693 | − | 0.699750i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.614519i | 0.0256272i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 24.6549i | − | 1.02640i | −0.858270 | − | 0.513199i | \(-0.828460\pi\) | ||
0.858270 | − | 0.513199i | \(-0.171540\pi\) | |||||||
\(578\) | −7.29488 | − | 14.6713i | −0.303427 | − | 0.610244i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −29.1691 | − | 22.0803i | −1.21118 | − | 0.916833i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 30.7985i | − | 1.27554i | ||||||
\(584\) | 5.88405 | − | 31.1786i | 0.243484 | − | 1.29018i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.2336 | + | 13.5412i | −1.12501 | + | 0.559380i | ||||
\(587\) | −19.1891 | −0.792019 | −0.396009 | − | 0.918247i | \(-0.629605\pi\) | ||||
−0.396009 | + | 0.918247i | \(0.629605\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.7696 | −1.18543 | ||||||||
\(590\) | −30.9233 | + | 15.3758i | −1.27309 | + | 0.633010i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.94975 | + | 31.7326i | 0.367832 | + | 1.30420i | ||||
\(593\) | − | 12.7634i | − | 0.524130i | −0.965050 | − | 0.262065i | \(-0.915596\pi\) | ||
0.965050 | − | 0.262065i | \(-0.0844035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.1978 | − | 22.7191i | 0.704450 | − | 0.930611i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.73712 | + | 5.50482i | 0.111929 | + | 0.225109i | ||||
\(599\) | 42.3656i | 1.73101i | 0.500898 | + | 0.865506i | \(0.333003\pi\) | ||||
−0.500898 | + | 0.865506i | \(0.666997\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.6508i | 0.597617i | 0.954313 | + | 0.298808i | \(0.0965892\pi\) | ||||
−0.954313 | + | 0.298808i | \(0.903411\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.1716 | − | 7.69963i | −0.413875 | − | 0.313293i | ||||
\(605\) | − | 4.25447i | − | 0.172969i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.4541 | 1.15492 | 0.577458 | − | 0.816420i | \(-0.304045\pi\) | ||||
0.577458 | + | 0.816420i | \(0.304045\pi\) | |||||||
\(608\) | 34.9314 | − | 31.6605i | 1.41665 | − | 1.28400i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.29289 | + | 8.63375i | 0.173814 | + | 0.349570i | ||||
\(611\) | − | 30.7515i | − | 1.24407i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.0416 | −1.05181 | −0.525906 | − | 0.850543i | \(-0.676274\pi\) | ||||
−0.525906 | + | 0.850543i | \(0.676274\pi\) | |||||||
\(614\) | 17.0155 | + | 34.2212i | 0.686691 | + | 1.38105i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.9848 | −0.603265 | −0.301633 | − | 0.953424i | \(-0.597532\pi\) | ||||
−0.301633 | + | 0.953424i | \(0.597532\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.7861 | 0.473723 | 0.236861 | − | 0.971543i | \(-0.423881\pi\) | ||||
0.236861 | + | 0.971543i | \(0.423881\pi\) | |||||||
\(620\) | −12.8089 | − | 9.69599i | −0.514416 | − | 0.389400i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.73712 | − | 5.50482i | −0.109748 | − | 0.220723i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.8995 | −1.07598 | ||||||||
\(626\) | −14.2054 | + | 7.06322i | −0.567760 | + | 0.282303i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −24.4965 | − | 18.5432i | −0.977517 | − | 0.739956i | ||||
\(629\) | − | 19.1794i | − | 0.764731i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.0827i | 1.43643i | 0.695821 | + | 0.718215i | \(0.255040\pi\) | ||||
−0.695821 | + | 0.718215i | \(0.744960\pi\) | |||||||
\(632\) | 8.07729 | − | 42.8002i | 0.321297 | − | 1.70250i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.656854 | + | 1.32105i | 0.0260870 | + | 0.0524655i | ||||
\(635\) | −20.9897 | −0.832952 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −35.6549 | + | 17.7284i | −1.41159 | + | 0.701874i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 26.2225 | − | 2.32330i | 1.03654 | − | 0.0918364i | ||||
\(641\) | −28.0097 | −1.10632 | −0.553159 | − | 0.833076i | \(-0.686578\pi\) | ||||
−0.553159 | + | 0.833076i | \(0.686578\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.47423 | 0.215883 | 0.107941 | − | 0.994157i | \(-0.465574\pi\) | ||||
0.107941 | + | 0.994157i | \(0.465574\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.5563 | + | 12.2100i | −0.966157 | + | 0.480395i | ||||
\(647\) | 31.4846 | 1.23779 | 0.618893 | − | 0.785475i | \(-0.287581\pi\) | ||||
0.618893 | + | 0.785475i | \(0.287581\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.5892i | 1.47551i | ||||||||
\(650\) | 1.53694 | − | 0.764199i | 0.0602836 | − | 0.0299744i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.3848 | + | 10.8889i | 0.563351 | + | 0.426443i | ||||
\(653\) | −33.0468 | −1.29322 | −0.646611 | − | 0.762820i | \(-0.723814\pi\) | ||||
−0.646611 | + | 0.762820i | \(0.723814\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.5350i | 1.34939i | ||||||||
\(656\) | −11.1315 | + | 3.13948i | −0.434611 | + | 0.122576i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.1046i | 0.861073i | 0.902573 | + | 0.430536i | \(0.141676\pi\) | ||||
−0.902573 | + | 0.430536i | \(0.858324\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.2166i | 0.786333i | 0.919467 | + | 0.393167i | \(0.128620\pi\) | ||||
−0.919467 | + | 0.393167i | \(0.871380\pi\) | |||||||
\(662\) | 22.8460 | − | 11.3596i | 0.887936 | − | 0.441502i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 41.2513 | + | 7.78498i | 1.60086 | + | 0.302116i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.6628i | − | 0.451584i | ||||||
\(668\) | −5.24743 | + | 6.93210i | −0.203029 | + | 0.268211i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.2160 | − | 26.5796i | −0.510578 | − | 1.02686i | ||||
\(671\) | 10.4949 | 0.405150 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.8995 | −1.38382 | −0.691912 | − | 0.721982i | \(-0.743231\pi\) | ||||
−0.691912 | + | 0.721982i | \(0.743231\pi\) | |||||||
\(674\) | −1.50155 | − | 3.01988i | −0.0578376 | − | 0.116321i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.32843 | + | 7.03910i | −0.204940 | + | 0.270735i | ||||
\(677\) | − | 32.9751i | − | 1.26733i | −0.773606 | − | 0.633667i | \(-0.781549\pi\) | ||
0.773606 | − | 0.633667i | \(-0.218451\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −15.0481 | − | 2.83989i | −0.577068 | − | 0.108905i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.6569 | + | 7.78498i | −0.599536 | + | 0.298102i | ||||
\(683\) | 42.3656i | 1.62108i | 0.585686 | + | 0.810538i | \(0.300825\pi\) | ||||
−0.585686 | + | 0.810538i | \(0.699175\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.8590i | 0.567733i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24.5563 | + | 6.92578i | −0.936202 | + | 0.264043i | ||||
\(689\) | − | 25.1961i | − | 0.959894i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.5722 | −0.896727 | −0.448364 | − | 0.893851i | \(-0.647993\pi\) | ||||
−0.448364 | + | 0.893851i | \(0.647993\pi\) | |||||||
\(692\) | 25.9735 | + | 19.6613i | 0.987363 | + | 0.747409i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.7071 | − | 7.31270i | 0.558274 | − | 0.277586i | ||||
\(695\) | 27.4244i | 1.04027i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.72792 | 0.254838 | ||||||||
\(698\) | 1.53694 | − | 0.764199i | 0.0581739 | − | 0.0289254i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.38589 | −0.241192 | −0.120596 | − | 0.992702i | \(-0.538481\pi\) | ||||
−0.120596 | + | 0.992702i | \(0.538481\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 68.6943 | 2.59085 | ||||||||
\(704\) | 10.4431 | − | 26.6826i | 0.393588 | − | 1.00564i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.2336 | − | 13.5412i | 1.02495 | − | 0.509629i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.5858 | −1.07356 | −0.536781 | − | 0.843722i | \(-0.680360\pi\) | ||||
−0.536781 | + | 0.843722i | \(0.680360\pi\) | |||||||
\(710\) | −15.7423 | − | 31.6605i | −0.590798 | − | 1.18820i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.11353 | + | 37.6934i | −0.266591 | + | 1.41262i | ||||
\(713\) | − | 5.12141i | − | 0.191798i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 24.4199i | − | 0.913254i | ||||||
\(716\) | 38.0207 | + | 28.7807i | 1.42090 | + | 1.07559i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.87868 | − | 0.934122i | 0.0701117 | − | 0.0348611i | ||||
\(719\) | 8.69423 | 0.324240 | 0.162120 | − | 0.986771i | \(-0.448167\pi\) | ||||
0.162120 | + | 0.986771i | \(0.448167\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −31.7690 | − | 63.8930i | −1.18232 | − | 2.37785i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.40967 | + | 5.60894i | 0.275378 | + | 0.208454i | ||||
\(725\) | −3.25623 | −0.120933 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.1201 | 0.746213 | 0.373107 | − | 0.927788i | \(-0.378293\pi\) | ||||
0.373107 | + | 0.927788i | \(0.378293\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −16.4350 | − | 33.0537i | −0.608288 | − | 1.22337i | ||||
\(731\) | 14.8420 | 0.548950 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 37.7975i | − | 1.39608i | −0.716058 | − | 0.698041i | \(-0.754055\pi\) | ||
0.716058 | − | 0.698041i | \(-0.245945\pi\) | |||||||
\(734\) | 22.2630 | + | 44.7747i | 0.821741 | + | 1.65266i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.63604 | + | 6.21831i | 0.207747 | + | 0.229210i | ||||
\(737\) | −32.3092 | −1.19012 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.5143i | 0.938560i | 0.883050 | + | 0.469280i | \(0.155486\pi\) | ||||
−0.883050 | + | 0.469280i | \(0.844514\pi\) | |||||||
\(740\) | 30.5843 | + | 23.1515i | 1.12430 | + | 0.851067i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.6794i | 0.611906i | 0.952047 | + | 0.305953i | \(0.0989751\pi\) | ||||
−0.952047 | + | 0.305953i | \(0.901025\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 33.1509i | − | 1.21455i | ||||||
\(746\) | 1.78089 | + | 3.58168i | 0.0652031 | + | 0.131135i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.0600 | + | 13.2898i | −0.367832 | + | 0.485923i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 47.2922i | − | 1.72572i | −0.505447 | − | 0.862858i | \(-0.668672\pi\) | ||
0.505447 | − | 0.862858i | \(-0.331328\pi\) | |||||||
\(752\) | −11.3952 | − | 40.4033i | −0.415539 | − | 1.47336i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −29.1691 | + | 14.5035i | −1.06227 | + | 0.528187i | ||||
\(755\) | −14.8420 | −0.540155 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.89949 | −0.287112 | −0.143556 | − | 0.989642i | \(-0.545854\pi\) | ||||
−0.143556 | + | 0.989642i | \(0.545854\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 10.1716 | − | 53.8974i | 0.368962 | − | 1.95506i | ||||
\(761\) | − | 53.8482i | − | 1.95200i | −0.217781 | − | 0.975998i | \(-0.569882\pi\) | ||
0.217781 | − | 0.975998i | \(-0.430118\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 10.4431 | + | 7.90515i | 0.377817 | + | 0.285998i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 30.7515i | 1.11037i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 20.2166i | − | 0.729028i | −0.931198 | − | 0.364514i | \(-0.881235\pi\) | ||
0.931198 | − | 0.364514i | \(-0.118765\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.41421 | + | 5.83138i | −0.158871 | + | 0.209876i | ||||
\(773\) | 18.5463i | 0.667063i | 0.942739 | + | 0.333532i | \(0.108240\pi\) | ||||
−0.942739 | + | 0.333532i | \(0.891760\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.42989 | −0.0513632 | ||||||||
\(776\) | 2.81018 | − | 14.8906i | 0.100879 | − | 0.534543i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.7782 | − | 31.7326i | −0.565675 | − | 1.13767i | ||||
\(779\) | 24.0973i | 0.863374i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.4853 | −1.37711 | ||||||||
\(782\) | −2.17356 | − | 4.37140i | −0.0777262 | − | 0.156321i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −35.7444 | −1.27577 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.6459 | −0.522069 | −0.261034 | − | 0.965330i | \(-0.584064\pi\) | ||||
−0.261034 | + | 0.965330i | \(0.584064\pi\) | |||||||
\(788\) | −1.25928 | + | 1.66357i | −0.0448600 | + | 0.0592622i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22.5611 | − | 45.3742i | −0.802687 | − | 1.61434i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.58579 | 0.304890 | ||||||||
\(794\) | −29.0473 | + | 14.4430i | −1.03085 | + | 0.512562i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.89304 | + | 7.78498i | −0.208873 | + | 0.275931i | ||||
\(797\) | 17.9817i | 0.636944i | 0.947932 | + | 0.318472i | \(0.103170\pi\) | ||||
−0.947932 | + | 0.318472i | \(0.896830\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.4199i | 0.863915i | ||||||||
\(800\) | 1.73614 | − | 1.57357i | 0.0613820 | − | 0.0556343i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.56497 | + | 9.18095i | 0.161195 | + | 0.324190i | ||||
\(803\) | −40.1788 | −1.41788 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.8089 | + | 6.36885i | −0.451173 | + | 0.224333i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.96869 | − | 26.3282i | 0.174798 | − | 0.926224i | ||||
\(809\) | 53.0688 | 1.86580 | 0.932899 | − | 0.360138i | \(-0.117270\pi\) | ||||
0.932899 | + | 0.360138i | \(0.117270\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.85978 | 0.100421 | 0.0502103 | − | 0.998739i | \(-0.484011\pi\) | ||||
0.0502103 | + | 0.998739i | \(0.484011\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 37.3848 | − | 18.5885i | 1.31034 | − | 0.651528i | ||||
\(815\) | 20.9897 | 0.735238 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 53.1592i | 1.85981i | ||||||||
\(818\) | 15.4786 | − | 7.69630i | 0.541196 | − | 0.269095i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.12132 | + | 10.7286i | −0.283609 | + | 0.374661i | ||||
\(821\) | 33.3524 | 1.16401 | 0.582003 | − | 0.813187i | \(-0.302269\pi\) | ||||
0.582003 | + | 0.813187i | \(0.302269\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 37.1771i | − | 1.29591i | −0.761678 | − | 0.647956i | \(-0.775624\pi\) | ||
0.761678 | − | 0.647956i | \(-0.224376\pi\) | |||||||
\(824\) | 9.59455 | + | 1.81069i | 0.334242 | + | 0.0630785i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20.0065i | − | 0.695694i | −0.937551 | − | 0.347847i | \(-0.886913\pi\) | ||
0.937551 | − | 0.347847i | \(-0.113087\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.0782i | 0.593149i | 0.955010 | + | 0.296575i | \(0.0958444\pi\) | ||||
−0.955010 | + | 0.296575i | \(0.904156\pi\) | |||||||
\(830\) | 43.7322 | − | 21.7446i | 1.51797 | − | 0.754767i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.54342 | − | 21.8289i | 0.296190 | − | 0.756780i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.1151i | 0.350046i | ||||||||
\(836\) | −47.5998 | − | 36.0319i | −1.64627 | − | 1.24619i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.0822 | + | 24.2994i | 0.417373 | + | 0.839410i | ||||
\(839\) | 16.6426 | 0.574567 | 0.287283 | − | 0.957846i | \(-0.407248\pi\) | ||||
0.287283 | + | 0.957846i | \(0.407248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.7990 | 1.13100 | ||||||||
\(842\) | −10.0742 | − | 20.2610i | −0.347181 | − | 0.698241i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.3431 | − | 15.3993i | −0.700240 | − | 0.530064i | ||||
\(845\) | 10.2712i | 0.353340i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.33657 | − | 33.1042i | −0.320619 | − | 1.13680i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.22049 | + | 0.606854i | −0.0418624 | + | 0.0208149i | ||||
\(851\) | 12.2286i | 0.419192i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 42.2358i | − | 1.44613i | −0.690781 | − | 0.723064i | \(-0.742733\pi\) | ||
0.690781 | − | 0.723064i | \(-0.257267\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.778175 | − | 4.12341i | 0.0265975 | − | 0.140935i | ||||
\(857\) | − | 32.9751i | − | 1.12641i | −0.826318 | − | 0.563203i | \(-0.809569\pi\) | ||
0.826318 | − | 0.563203i | \(-0.190431\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.0021 | −0.853059 | −0.426530 | − | 0.904474i | \(-0.640264\pi\) | ||||
−0.426530 | + | 0.904474i | \(0.640264\pi\) | |||||||
\(860\) | −17.9159 | + | 23.6677i | −0.610925 | + | 0.807061i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.53553 | − | 2.25517i | 0.154481 | − | 0.0768114i | ||||
\(863\) | 3.22170i | 0.109668i | 0.998495 | + | 0.0548340i | \(0.0174630\pi\) | ||||
−0.998495 | + | 0.0548340i | \(0.982537\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.8995 | 1.28862 | ||||||||
\(866\) | 38.6419 | − | 19.2136i | 1.31310 | − | 0.652905i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −55.1552 | −1.87101 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.4319 | −0.895612 | ||||||||
\(872\) | −12.7456 | − | 2.40536i | −0.431620 | − | 0.0814557i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 15.6569 | − | 7.78498i | 0.529604 | − | 0.263331i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.2426 | −0.345869 | −0.172935 | − | 0.984933i | \(-0.555325\pi\) | ||||
−0.172935 | + | 0.984933i | \(0.555325\pi\) | |||||||
\(878\) | −3.07387 | − | 6.18209i | −0.103738 | − | 0.208635i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.04896 | − | 32.0844i | −0.305040 | − | 1.08157i | ||||
\(881\) | 16.6187i | 0.559897i | 0.960015 | + | 0.279948i | \(0.0903173\pi\) | ||||
−0.960015 | + | 0.279948i | \(0.909683\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 53.6707i | − | 1.80616i | −0.429468 | − | 0.903082i | \(-0.641299\pi\) | ||
0.429468 | − | 0.903082i | \(-0.358701\pi\) | |||||||
\(884\) | −8.23007 | + | 10.8723i | −0.276807 | + | 0.365675i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.09188 | − | 3.02902i | 0.204661 | − | 0.101762i | ||||
\(887\) | −10.4949 | −0.352383 | −0.176191 | − | 0.984356i | \(-0.556378\pi\) | ||||
−0.176191 | + | 0.984356i | \(0.556378\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 19.8691 | + | 39.9603i | 0.666015 | + | 1.33947i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.1201 | − | 26.5796i | 0.673671 | − | 0.889951i | ||||
\(893\) | −87.4644 | −2.92688 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 55.4783 | 1.85444 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.1421 | − | 38.4981i | −0.638781 | − | 1.28470i | ||||
\(899\) | 27.1375 | 0.905085 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.0083i | 0.666574i | ||||||||
\(902\) | 6.52067 | + | 13.1142i | 0.217115 | + | 0.436655i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21.0000 | − | 3.96314i | −0.698450 | − | 0.131812i | ||||
\(905\) | 10.8119 | 0.359400 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 55.2184i | − | 1.83350i | −0.399463 | − | 0.916749i | \(-0.630804\pi\) | ||
0.399463 | − | 0.916749i | \(-0.369196\pi\) | |||||||
\(908\) | 30.5843 | − | 40.4033i | 1.01497 | − | 1.34083i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.3985i | 1.30533i | 0.757647 | + | 0.652665i | \(0.226349\pi\) | ||||
−0.757647 | + | 0.652665i | \(0.773651\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 53.1592i | − | 1.75931i | ||||||
\(914\) | −9.76869 | − | 19.6465i | −0.323119 | − | 0.649849i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33.8416 | + | 25.6173i | 1.11816 | + | 0.846418i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 24.4199i | − | 0.805539i | −0.915301 | − | 0.402770i | \(-0.868048\pi\) | ||
0.915301 | − | 0.402770i | \(-0.131952\pi\) | |||||||
\(920\) | 9.59455 | + | 1.81069i | 0.316323 | + | 0.0596968i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.7104 | − | 6.31991i | 0.418596 | − | 0.208135i | ||||
\(923\) | −31.4846 | −1.03633 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.41421 | 0.112259 | ||||||||
\(926\) | −6.69145 | + | 3.32714i | −0.219895 | + | 0.109337i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −32.9497 | + | 29.8644i | −1.08163 | + | 0.980347i | ||||
\(929\) | − | 6.64981i | − | 0.218173i | −0.994032 | − | 0.109087i | \(-0.965207\pi\) | ||
0.994032 | − | 0.109087i | \(-0.0347926\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.5697 | + | 20.5683i | −0.510002 | + | 0.673737i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.60799 | − | 13.2898i | −0.216220 | − | 0.434856i | ||||
\(935\) | 19.3920i | 0.634185i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.79592i | 0.320019i | 0.987115 | + | 0.160009i | \(0.0511525\pi\) | ||||
−0.987115 | + | 0.160009i | \(0.948848\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −38.9411 | − | 29.4775i | −1.27012 | − | 0.961449i | ||||
\(941\) | 40.1210i | 1.30791i | 0.756535 | + | 0.653953i | \(0.226891\pi\) | ||||
−0.756535 | + | 0.653953i | \(0.773109\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.28967 | −0.139691 | ||||||||
\(944\) | 11.3952 | + | 40.4033i | 0.370881 | + | 1.31501i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.3848 | + | 28.9303i | 0.467689 | + | 0.940604i | ||||
\(947\) | 37.3004i | 1.21210i | 0.795427 | + | 0.606050i | \(0.207247\pi\) | ||||
−0.795427 | + | 0.606050i | \(0.792753\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.8701 | −1.06701 | ||||||||
\(950\) | −2.17356 | − | 4.37140i | −0.0705195 | − | 0.141827i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.5496 | 0.374128 | 0.187064 | − | 0.982348i | \(-0.440103\pi\) | ||||
0.187064 | + | 0.982348i | \(0.440103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.2381 | 0.493095 | ||||||||
\(956\) | 13.7888 | + | 10.4378i | 0.445962 | + | 0.337582i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.0822 | + | 24.2994i | 0.390359 | + | 0.785079i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0833 | −0.615589 | ||||||||
\(962\) | 30.5843 | − | 15.2072i | 0.986076 | − | 0.490299i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.2805 | + | 8.53909i | 0.363322 | + | 0.275025i | ||||
\(965\) | 8.50894i | 0.273912i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 12.7572i | − | 0.410243i | −0.978737 | − | 0.205121i | \(-0.934241\pi\) | ||
0.978737 | − | 0.205121i | \(-0.0657589\pi\) | |||||||
\(968\) | −5.08187 | − | 0.959055i | −0.163337 | − | 0.0308252i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.84924 | − | 15.7862i | −0.252024 | − | 0.506864i | ||||
\(971\) | −27.1375 | −0.870883 | −0.435441 | − | 0.900217i | \(-0.643408\pi\) | ||||
−0.435441 | + | 0.900217i | \(0.643408\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 30.9233 | − | 15.3758i | 0.990847 | − | 0.492671i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.2805 | − | 3.18152i | 0.361081 | − | 0.101838i | ||||
\(977\) | −20.6330 | −0.660109 | −0.330054 | − | 0.943962i | \(-0.607067\pi\) | ||||
−0.330054 | + | 0.943962i | \(0.607067\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.5742 | 1.55244 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.39340 | + | 4.67061i | −0.299755 | + | 0.149045i | ||||
\(983\) | −20.9897 | −0.669468 | −0.334734 | − | 0.942313i | \(-0.608647\pi\) | ||||
−0.334734 | + | 0.942313i | \(0.608647\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.42742i | 0.0773439i | ||||||||
\(986\) | 23.1633 | − | 11.5173i | 0.737669 | − | 0.366786i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −38.9411 | − | 29.4775i | −1.23888 | − | 0.937803i | ||||
\(989\) | −9.46314 | −0.300910 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15.3993i | − | 0.489173i | −0.969627 | − | 0.244587i | \(-0.921348\pi\) | ||
0.969627 | − | 0.244587i | \(-0.0786523\pi\) | |||||||
\(992\) | −14.4691 | + | 13.1142i | −0.459393 | + | 0.416376i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3596i | 0.360122i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31.9372i | 1.01146i | 0.862692 | + | 0.505730i | \(0.168777\pi\) | ||||
−0.862692 | + | 0.505730i | \(0.831223\pi\) | |||||||
\(998\) | 3.34572 | − | 1.66357i | 0.105907 | − | 0.0526593i | ||||
\(999\) | 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 | 1764.2.b.n.1567.6 | yes | 16 | |
3.2 | odd | 2 | inner | 1764.2.b.n.1567.11 | yes | 16 | |
4.3 | odd | 2 | inner | 1764.2.b.n.1567.8 | yes | 16 | |
7.6 | odd | 2 | inner | 1764.2.b.n.1567.5 | ✓ | 16 | |
12.11 | even | 2 | inner | 1764.2.b.n.1567.9 | yes | 16 | |
21.20 | even | 2 | inner | 1764.2.b.n.1567.12 | yes | 16 | |
28.27 | even | 2 | inner | 1764.2.b.n.1567.7 | yes | 16 | |
84.83 | odd | 2 | inner | 1764.2.b.n.1567.10 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.b.n.1567.5 | ✓ | 16 | 7.6 | odd | 2 | inner | |
1764.2.b.n.1567.6 | yes | 16 | 1.1 | even | 1 | trivial | |
1764.2.b.n.1567.7 | yes | 16 | 28.27 | even | 2 | inner | |
1764.2.b.n.1567.8 | yes | 16 | 4.3 | odd | 2 | inner | |
1764.2.b.n.1567.9 | yes | 16 | 12.11 | even | 2 | inner | |
1764.2.b.n.1567.10 | yes | 16 | 84.83 | odd | 2 | inner | |
1764.2.b.n.1567.11 | yes | 16 | 3.2 | odd | 2 | inner | |
1764.2.b.n.1567.12 | yes | 16 | 21.20 | even | 2 | inner |