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 | 1567.11 | ||
Root | \(-2.22719 - 2.57288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1567 |
Dual form | 1764.2.b.n.1567.10 |
$q$-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 | \(-0.825821\pi\) | ||
0.853984 | − | 0.520299i | \(-0.174179\pi\) | |||||||
\(6\) | 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 | \(0.181560\pi\) | ||||
−0.841692 | + | 0.539958i | \(0.818440\pi\) | |||||||
\(12\) | 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 | \(-0.908945\pi\) | ||
0.959364 | − | 0.282172i | \(-0.0910547\pi\) | |||||||
\(18\) | 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 | \(0.0494327\pi\) | ||||
−0.987966 | + | 0.154674i | \(0.950567\pi\) | |||||||
\(24\) | 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 | \(-0.760432\pi\) | ||||
−0.729897 | + | 0.683557i | \(0.760432\pi\) | |||||||
\(30\) | 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 | \(0.0724940\pi\) | ||||
−0.974178 | + | 0.225783i | \(0.927506\pi\) | |||||||
\(42\) | 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 | \(-0.777467\pi\) | ||||
−0.765417 | + | 0.643535i | \(0.777467\pi\) | |||||||
\(48\) | 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 | \(-0.701099\pi\) | ||||
−0.590575 | + | 0.806983i | \(0.701099\pi\) | |||||||
\(54\) | 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 | \(-0.260606\pi\) | ||||
0.683157 | + | 0.730271i | \(0.260606\pi\) | |||||||
\(60\) | 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 | \(0.220073\pi\) | ||||
−0.770367 | + | 0.637601i | \(0.779927\pi\) | |||||||
\(72\) | 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 | \(-0.803021\pi\) | ||||
−0.814559 | + | 0.580080i | \(0.803021\pi\) | |||||||
\(84\) | 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 | \(-0.744702\pi\) | ||
0.695241 | − | 0.718777i | \(-0.255298\pi\) | |||||||
\(90\) | 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 | \(0.156210\pi\) | ||||
−0.881980 | + | 0.471287i | \(0.843790\pi\) | |||||||
\(102\) | 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 | \(0.0228461\pi\) | ||||
−0.997425 | + | 0.0717116i | \(0.977154\pi\) | |||||||
\(108\) | 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 | \(-0.384348\pi\) | ||||
0.355389 | + | 0.934718i | \(0.384348\pi\) | |||||||
\(114\) | 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 | \(-0.724551\pi\) | ||||
−0.648375 | + | 0.761321i | \(0.724551\pi\) | |||||||
\(132\) | 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 | \(-0.587947\pi\) | ||||
−0.272792 | + | 0.962073i | \(0.587947\pi\) | |||||||
\(138\) | 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 | \(-0.301649\pi\) | ||||
0.583585 | + | 0.812052i | \(0.301649\pi\) | |||||||
\(150\) | 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 | \(-0.553794\pi\) | ||||
−0.168195 | + | 0.985754i | \(0.553794\pi\) | |||||||
\(168\) | 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 | \(0.212532\pi\) | ||||
−0.785254 | + | 0.619174i | \(0.787468\pi\) | |||||||
\(174\) | 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 | \(0.350026\pi\) | ||||
−0.453917 | + | 0.891044i | \(0.649974\pi\) | |||||||
\(180\) | 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 | \(0.0761408\pi\) | ||||
−0.971527 | + | 0.236929i | \(0.923859\pi\) | |||||||
\(192\) | 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 | \(-0.511832\pi\) | ||||
−0.0371632 | + | 0.999309i | \(0.511832\pi\) | |||||||
\(198\) | 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 | \(-0.182066\pi\) | ||||
0.840833 | + | 0.541295i | \(0.182066\pi\) | |||||||
\(228\) | 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 | \(-0.638847\pi\) | ||||
−0.422500 | + | 0.906363i | \(0.638847\pi\) | |||||||
\(234\) | 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 | \(0.0902224\pi\) | ||||
−0.960099 | + | 0.279662i | \(0.909778\pi\) | |||||||
\(240\) | 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 | \(-0.543808\pi\) | ||||
−0.137194 | + | 0.990544i | \(0.543808\pi\) | |||||||
\(252\) | 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 | \(-0.709560\pi\) | ||
0.611814 | − | 0.791002i | \(-0.290440\pi\) | |||||||
\(258\) | 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 | \(0.0352221\pi\) | ||||
−0.993884 | + | 0.110428i | \(0.964778\pi\) | |||||||
\(264\) | 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 | \(0.0932502\pi\) | ||||
−0.957395 | + | 0.288782i | \(0.906750\pi\) | |||||||
\(270\) | 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 | \(-0.296278\pi\) | ||||
0.597204 | + | 0.802090i | \(0.296278\pi\) | |||||||
\(282\) | 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 | \(0.216209\pi\) | ||||
−0.778050 | + | 0.628203i | \(0.783791\pi\) | |||||||
\(294\) | 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 | \(-0.539332\pi\) | ||||
−0.123251 | + | 0.992376i | \(0.539332\pi\) | |||||||
\(312\) | 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 | \(-0.490673\pi\) | ||||
0.0292966 | + | 0.999571i | \(0.490673\pi\) | |||||||
\(318\) | 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 | \(-0.899089\pi\) | ||
0.950168 | − | 0.311739i | \(-0.100911\pi\) | |||||||
\(348\) | 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 | \(-0.806040\pi\) | ||
0.820023 | − | 0.572330i | \(-0.193960\pi\) | |||||||
\(354\) | 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 | \(-0.987535\pi\) | ||
0.999233 | − | 0.0391502i | \(-0.0124651\pi\) | |||||||
\(360\) | 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 | \(-0.719112\pi\) | ||||
−0.635272 | + | 0.772289i | \(0.719112\pi\) | |||||||
\(390\) | 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 | \(-0.442058\pi\) | ||||
0.181027 | + | 0.983478i | \(0.442058\pi\) | |||||||
\(402\) | 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 | \(-0.344714\pi\) | ||||
0.468724 | + | 0.883345i | \(0.344714\pi\) | |||||||
\(420\) | 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 | \(-0.972508\pi\) | ||
0.996273 | − | 0.0862617i | \(-0.0274921\pi\) | |||||||
\(432\) | 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 | \(-0.963543\pi\) | ||
0.993448 | − | 0.114282i | \(-0.0364568\pi\) | |||||||
\(444\) | 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 | \(-0.754656\pi\) | ||||
−0.717373 | + | 0.696690i | \(0.754656\pi\) | |||||||
\(450\) | 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 | \(-0.924903\pi\) | ||
0.972298 | − | 0.233743i | \(-0.0750973\pi\) | |||||||
\(462\) | 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 | \(-0.578073\pi\) | ||||
−0.242822 | + | 0.970071i | \(0.578073\pi\) | |||||||
\(468\) | 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 | \(-0.355550\pi\) | ||||
0.438386 | + | 0.898787i | \(0.355550\pi\) | |||||||
\(480\) | 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 | \(0.0535315\pi\) | ||||
−0.985892 | + | 0.167383i | \(0.946468\pi\) | |||||||
\(492\) | 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 | \(-0.205454\pi\) | ||||
0.798828 | + | 0.601559i | \(0.205454\pi\) | |||||||
\(504\) | 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 | \(-0.841861\pi\) | ||
0.879108 | − | 0.476623i | \(-0.158139\pi\) | |||||||
\(510\) | 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 | \(-0.703951\pi\) | ||
0.597780 | − | 0.801660i | \(-0.296049\pi\) | |||||||
\(522\) | 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 | \(-0.331083\pi\) | ||||
0.506110 | + | 0.862469i | \(0.331083\pi\) | |||||||
\(558\) | 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 | \(-0.679278\pi\) | ||||
−0.533910 | + | 0.845541i | \(0.679278\pi\) | |||||||
\(564\) | 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 | \(-0.622683\pi\) | ||||
−0.375947 | + | 0.926641i | \(0.622683\pi\) | |||||||
\(570\) | 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 | \(-0.370395\pi\) | ||||
0.396009 | + | 0.918247i | \(0.370395\pi\) | |||||||
\(588\) | 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 | \(0.0844035\pi\) | ||||
−0.965050 | + | 0.262065i | \(0.915596\pi\) | |||||||
\(594\) | 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 | \(-0.666997\pi\) | ||
0.500898 | − | 0.865506i | \(-0.333003\pi\) | |||||||
\(600\) | 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 | \(-0.402468\pi\) | ||||
0.301633 | + | 0.953424i | \(0.402468\pi\) | |||||||
\(618\) | 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 | \(-0.313422\pi\) | ||||
0.553159 | + | 0.833076i | \(0.313422\pi\) | |||||||
\(642\) | 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 | \(-0.712419\pi\) | ||||
−0.618893 | + | 0.785475i | \(0.712419\pi\) | |||||||
\(648\) | 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 | \(-0.276186\pi\) | ||||
0.646611 | + | 0.762820i | \(0.276186\pi\) | |||||||
\(654\) | 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 | \(-0.858324\pi\) | ||
0.902573 | − | 0.430536i | \(-0.141676\pi\) | |||||||
\(660\) | 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 | \(0.218451\pi\) | ||||
−0.773606 | + | 0.633667i | \(0.781549\pi\) | |||||||
\(678\) | 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 | \(-0.699175\pi\) | ||
0.585686 | − | 0.810538i | \(-0.300825\pi\) | |||||||
\(684\) | 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 | \(-0.461519\pi\) | ||||
0.120596 | + | 0.992702i | \(0.461519\pi\) | |||||||
\(702\) | 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 | \(-0.551833\pi\) | ||||
−0.162120 | + | 0.986771i | \(0.551833\pi\) | |||||||
\(720\) | 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 | \(-0.901025\pi\) | ||
0.952047 | − | 0.305953i | \(-0.0989751\pi\) | |||||||
\(744\) | 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 | \(0.430118\pi\) | ||||
−0.217781 | + | 0.975998i | \(0.569882\pi\) | |||||||
\(762\) | 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 | \(-0.891760\pi\) | ||
0.942739 | − | 0.333532i | \(-0.108240\pi\) | |||||||
\(774\) | 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 | \(-0.896830\pi\) | ||
0.947932 | − | 0.318472i | \(-0.103170\pi\) | |||||||
\(798\) | 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 | \(-0.882730\pi\) | ||||
−0.932899 | + | 0.360138i | \(0.882730\pi\) | |||||||
\(810\) | 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 | \(-0.697731\pi\) | ||||
−0.582003 | + | 0.813187i | \(0.697731\pi\) | |||||||
\(822\) | 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 | \(0.113087\pi\) | ||||
−0.937551 | + | 0.347847i | \(0.886913\pi\) | |||||||
\(828\) | 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 | \(-0.592752\pi\) | ||||
−0.287283 | + | 0.957846i | \(0.592752\pi\) | |||||||
\(840\) | 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 | \(0.190431\pi\) | ||||
−0.826318 | + | 0.563203i | \(0.809569\pi\) | |||||||
\(858\) | 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 | \(-0.982537\pi\) | ||
0.998495 | − | 0.0548340i | \(-0.0174630\pi\) | |||||||
\(864\) | 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 | \(-0.909683\pi\) | ||
0.960015 | − | 0.279948i | \(-0.0903173\pi\) | |||||||
\(882\) | 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 | \(-0.443622\pi\) | ||||
0.176191 | + | 0.984356i | \(0.443622\pi\) | |||||||
\(888\) | 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 | \(-0.773651\pi\) | ||
0.757647 | − | 0.652665i | \(-0.226349\pi\) | |||||||
\(912\) | 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 | \(0.0347926\pi\) | ||||
−0.994032 | + | 0.109087i | \(0.965207\pi\) | |||||||
\(930\) | 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 | \(-0.773109\pi\) | ||
0.756535 | − | 0.653953i | \(-0.226891\pi\) | |||||||
\(942\) | 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 | \(-0.792753\pi\) | ||
0.795427 | − | 0.606050i | \(-0.207247\pi\) | |||||||
\(948\) | 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 | \(-0.559897\pi\) | ||||
−0.187064 | + | 0.982348i | \(0.559897\pi\) | |||||||
\(954\) | 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 | \(-0.356592\pi\) | ||||
0.435441 | + | 0.900217i | \(0.356592\pi\) | |||||||
\(972\) | 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 | \(-0.392933\pi\) | ||||
0.330054 | + | 0.943962i | \(0.392933\pi\) | |||||||
\(978\) | 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 | \(-0.391353\pi\) | ||||
0.334734 | + | 0.942313i | \(0.391353\pi\) | |||||||
\(984\) | 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.1567.11 | yes | 16 | |
3.2 | odd | 2 | inner | 1764.2.b.n.1567.6 | yes | 16 | |
4.3 | odd | 2 | inner | 1764.2.b.n.1567.9 | yes | 16 | |
7.6 | odd | 2 | inner | 1764.2.b.n.1567.12 | yes | 16 | |
12.11 | even | 2 | inner | 1764.2.b.n.1567.8 | yes | 16 | |
21.20 | even | 2 | inner | 1764.2.b.n.1567.5 | ✓ | 16 | |
28.27 | even | 2 | inner | 1764.2.b.n.1567.10 | yes | 16 | |
84.83 | odd | 2 | inner | 1764.2.b.n.1567.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.b.n.1567.5 | ✓ | 16 | 21.20 | even | 2 | inner | |
1764.2.b.n.1567.6 | yes | 16 | 3.2 | odd | 2 | inner | |
1764.2.b.n.1567.7 | yes | 16 | 84.83 | odd | 2 | inner | |
1764.2.b.n.1567.8 | yes | 16 | 12.11 | even | 2 | inner | |
1764.2.b.n.1567.9 | yes | 16 | 4.3 | odd | 2 | inner | |
1764.2.b.n.1567.10 | yes | 16 | 28.27 | even | 2 | inner | |
1764.2.b.n.1567.11 | yes | 16 | 1.1 | even | 1 | trivial | |
1764.2.b.n.1567.12 | yes | 16 | 7.6 | odd | 2 | inner |