Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,2,Mod(2255,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.2255");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.h (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: | \(18.7808145554\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2255.4 | ||
Root | \(-1.65831 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.2255 |
Dual form | 2352.2.h.j.2255.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.65831 | + | 0.500000i | 0.957427 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.31662i | − | 1.48324i | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||
0.670820 | − | 0.741620i | \(-0.265942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.50000 | + | 1.65831i | 0.833333 | + | 0.552771i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.31662 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.65831 | − | 5.50000i | 0.428174 | − | 1.42009i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.31662i | 0.804400i | 0.915552 | + | 0.402200i | \(0.131754\pi\) | ||||
−0.915552 | + | 0.402200i | \(0.868246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.00000i | 1.60591i | 0.596040 | + | 0.802955i | \(0.296740\pi\) | ||||
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.31662 | 0.691564 | 0.345782 | − | 0.938315i | \(-0.387614\pi\) | ||||
0.345782 | + | 0.938315i | \(0.387614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.00000 | −1.20000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.31662 | + | 4.00000i | 0.638285 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.63325i | − | 1.23176i | −0.787839 | − | 0.615882i | \(-0.788800\pi\) | ||
0.787839 | − | 0.615882i | \(-0.211200\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000i | 0.538816i | 0.963026 | + | 0.269408i | \(0.0868280\pi\) | ||||
−0.963026 | + | 0.269408i | \(0.913172\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.50000 | + | 1.65831i | 0.957427 | + | 0.288675i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.63325 | + | 2.00000i | 1.06217 | + | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.63325i | − | 1.03594i | −0.855399 | − | 0.517970i | \(-0.826688\pi\) | ||
0.855399 | − | 0.517970i | \(-0.173312\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000i | 0.304997i | 0.988304 | + | 0.152499i | \(0.0487319\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.50000 | − | 8.29156i | 0.819892 | − | 1.23603i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.94987 | −1.45134 | −0.725669 | − | 0.688044i | \(-0.758470\pi\) | ||||
−0.725669 | + | 0.688044i | \(0.758470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.65831 | + | 5.50000i | −0.232210 | + | 0.770154i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.31662i | 0.455573i | 0.973711 | + | 0.227787i | \(0.0731489\pi\) | ||||
−0.973711 | + | 0.227787i | \(0.926851\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 11.0000i | − | 1.48324i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.50000 | + | 11.6082i | −0.463586 | + | 1.53754i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.31662 | 0.431788 | 0.215894 | − | 0.976417i | \(-0.430733\pi\) | ||||
0.215894 | + | 0.976417i | \(0.430733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | −0.384111 | −0.192055 | − | 0.981384i | \(-0.561515\pi\) | ||||
−0.192055 | + | 0.981384i | \(0.561515\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 13.2665i | − | 1.64551i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.00000i | − | 1.09952i | −0.835321 | − | 0.549762i | \(-0.814718\pi\) | ||
0.835321 | − | 0.549762i | \(-0.185282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.50000 | + | 1.65831i | 0.662122 | + | 0.199637i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.2665 | 1.57444 | 0.787222 | − | 0.616670i | \(-0.211519\pi\) | ||||
0.787222 | + | 0.616670i | \(0.211519\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.94987 | − | 3.00000i | −1.14891 | − | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 9.00000i | − | 1.01258i | −0.862364 | − | 0.506290i | \(-0.831017\pi\) | ||
0.862364 | − | 0.506290i | \(-0.168983\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.50000 | + | 8.29156i | 0.388889 | + | 0.921285i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.2665 | 1.45619 | 0.728094 | − | 0.685478i | \(-0.240407\pi\) | ||||
0.728094 | + | 0.685478i | \(0.240407\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.0000 | 1.19312 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.31662 | − | 11.0000i | 0.355580 | − | 1.17932i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.31662i | 0.351562i | 0.984429 | + | 0.175781i | \(0.0562450\pi\) | ||||
−0.984429 | + | 0.175781i | \(0.943755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | + | 4.97494i | −0.155543 | + | 0.515877i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.2164 | 2.38195 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.29156 | + | 5.50000i | 0.833333 | + | 0.552771i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.31662i | 0.330017i | 0.986292 | + | 0.165008i | \(0.0527651\pi\) | ||||
−0.986292 | + | 0.165008i | \(0.947235\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.0000i | − | 1.08386i | −0.840423 | − | 0.541931i | \(-0.817693\pi\) | ||
0.840423 | − | 0.541931i | \(-0.182307\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.31662 | −0.320630 | −0.160315 | − | 0.987066i | \(-0.551251\pi\) | ||||
−0.160315 | + | 0.987066i | \(0.551251\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.65831 | − | 0.500000i | −0.157400 | − | 0.0474579i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.63325i | − | 0.624004i | −0.950082 | − | 0.312002i | \(-0.899000\pi\) | ||
0.950082 | − | 0.312002i | \(-0.101000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 11.0000i | − | 1.02576i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.0000 | + | 6.63325i | 0.924500 | + | 0.613244i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.31662 | − | 11.0000i | 0.299050 | − | 0.991837i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.31662i | 0.296648i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.00000 | + | 3.31662i | −0.0880451 | + | 0.292013i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.5831 | −1.44887 | −0.724437 | − | 0.689341i | \(-0.757900\pi\) | ||||
−0.724437 | + | 0.689341i | \(0.757900\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.2665 | − | 11.0000i | 1.14180 | − | 0.946729i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 16.5831i | − | 1.41679i | −0.705815 | − | 0.708396i | \(-0.749419\pi\) | ||
0.705815 | − | 0.708396i | \(-0.250581\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000i | 0.848189i | 0.905618 | + | 0.424094i | \(0.139408\pi\) | ||||
−0.905618 | + | 0.424094i | \(0.860592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.5000 | − | 4.97494i | −1.38955 | − | 0.418965i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.2665 | 1.10940 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.0000 | −1.82700 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.5831i | 1.35854i | 0.733887 | + | 0.679271i | \(0.237704\pi\) | ||||
−0.733887 | + | 0.679271i | \(0.762296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 7.00000i | − | 0.569652i | −0.958579 | − | 0.284826i | \(-0.908064\pi\) | ||
0.958579 | − | 0.284826i | \(-0.0919358\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.50000 | + | 8.29156i | −0.444649 | + | 0.670333i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.94987 | 0.799193 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.00000 | −0.239426 | −0.119713 | − | 0.992809i | \(-0.538197\pi\) | ||||
−0.119713 | + | 0.992809i | \(0.538197\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.65831 | + | 5.50000i | −0.131513 | + | 0.436178i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.00000i | 0.548282i | 0.961689 | + | 0.274141i | \(0.0883936\pi\) | ||||
−0.961689 | + | 0.274141i | \(0.911606\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.50000 | − | 18.2414i | 0.428174 | − | 1.42009i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.63325 | −0.513296 | −0.256648 | − | 0.966505i | \(-0.582618\pi\) | ||||
−0.256648 | + | 0.966505i | \(0.582618\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.6082 | + | 17.5000i | −0.887700 | + | 1.33826i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 9.94987i | − | 0.756475i | −0.925709 | − | 0.378237i | \(-0.876530\pi\) | ||
0.925709 | − | 0.378237i | \(-0.123470\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.50000 | + | 1.65831i | 0.413405 | + | 0.124646i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.31662 | 0.247896 | 0.123948 | − | 0.992289i | \(-0.460444\pi\) | ||||
0.123948 | + | 0.992289i | \(0.460444\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.0000 | −1.33793 | −0.668965 | − | 0.743294i | \(-0.733262\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.97494 | − | 1.50000i | −0.367758 | − | 0.110883i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.31662i | 0.243843i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.0000i | 0.804400i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.94987 | 0.719948 | 0.359974 | − | 0.932962i | \(-0.382786\pi\) | ||||
0.359974 | + | 0.932962i | \(0.382786\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.00000 | −0.215945 | −0.107972 | − | 0.994154i | \(-0.534436\pi\) | ||||
−0.107972 | + | 0.994154i | \(0.534436\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.63325 | − | 22.0000i | 0.475017 | − | 1.57545i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.8997i | 1.41780i | 0.705310 | + | 0.708899i | \(0.250808\pi\) | ||||
−0.705310 | + | 0.708899i | \(0.749192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.00000i | − | 0.0708881i | −0.999372 | − | 0.0354441i | \(-0.988715\pi\) | ||
0.999372 | − | 0.0354441i | \(-0.0112846\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.50000 | − | 14.9248i | 0.317406 | − | 1.05272i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.0000 | −1.53655 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.29156 | + | 5.50000i | 0.576303 | + | 0.382276i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.2164i | 1.60591i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 26.0000i | − | 1.78991i | −0.446153 | − | 0.894957i | \(-0.647206\pi\) | ||
0.446153 | − | 0.894957i | \(-0.352794\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.0000 | + | 6.63325i | 1.50742 | + | 0.454503i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.63325 | 0.452384 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.6082 | − | 3.50000i | −0.784409 | − | 0.236508i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.2665i | 0.892401i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.0000i | 0.937509i | 0.883328 | + | 0.468755i | \(0.155297\pi\) | ||||
−0.883328 | + | 0.468755i | \(0.844703\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.0000 | − | 9.94987i | −1.00000 | − | 0.663325i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.31662 | −0.220132 | −0.110066 | − | 0.993924i | \(-0.535106\pi\) | ||||
−0.110066 | + | 0.993924i | \(0.535106\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.0000 | −1.91637 | −0.958187 | − | 0.286143i | \(-0.907627\pi\) | ||||
−0.958187 | + | 0.286143i | \(0.907627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.5831i | 1.08640i | 0.839604 | + | 0.543198i | \(0.182787\pi\) | ||||
−0.839604 | + | 0.543198i | \(0.817213\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.0000i | 2.15268i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.50000 | − | 14.9248i | 0.292306 | − | 0.969471i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.63325 | −0.429069 | −0.214535 | − | 0.976716i | \(-0.568823\pi\) | ||||
−0.214535 | + | 0.976716i | \(0.568823\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.0000 | −1.22390 | −0.611949 | − | 0.790897i | \(-0.709614\pi\) | ||||
−0.611949 | + | 0.790897i | \(0.709614\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.65831 | + | 15.5000i | 0.106381 | + | 0.994325i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28.0000i | 1.78160i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.0000 | + | 6.63325i | 1.39419 | + | 0.420365i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.8997 | 1.25606 | 0.628031 | − | 0.778189i | \(-0.283861\pi\) | ||||
0.628031 | + | 0.778189i | \(0.283861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.0000 | 0.691564 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 18.2414 | + | 5.50000i | 1.14232 | + | 0.344423i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.2164i | 1.44820i | 0.689696 | + | 0.724099i | \(0.257744\pi\) | ||||
−0.689696 | + | 0.724099i | \(0.742256\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.0000 | − | 16.5831i | 0.680883 | − | 1.02647i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.31662 | −0.204512 | −0.102256 | − | 0.994758i | \(-0.532606\pi\) | ||||
−0.102256 | + | 0.994758i | \(0.532606\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.0000 | 0.675725 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.65831 | + | 5.50000i | −0.101487 | + | 0.336595i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 16.5831i | − | 1.01109i | −0.862800 | − | 0.505545i | \(-0.831291\pi\) | ||
0.862800 | − | 0.505545i | \(-0.168709\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.0000i | 1.03268i | 0.856385 | + | 0.516338i | \(0.172705\pi\) | ||||
−0.856385 | + | 0.516338i | \(0.827295\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19.8997 | −1.20000 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.0000 | −0.781094 | −0.390547 | − | 0.920583i | \(-0.627714\pi\) | ||||
−0.390547 | + | 0.920583i | \(0.627714\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.97494 | + | 7.50000i | −0.297842 | + | 0.449013i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.63325i | 0.395706i | 0.980232 | + | 0.197853i | \(0.0633969\pi\) | ||||
−0.980232 | + | 0.197853i | \(0.936603\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.0000i | 0.891657i | 0.895118 | + | 0.445829i | \(0.147091\pi\) | ||||
−0.895118 | + | 0.445829i | \(0.852909\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 38.5000 | + | 11.6082i | 2.28054 | + | 0.687610i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.00000 | 0.352941 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.2665 | − | 4.00000i | −0.777696 | − | 0.234484i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 13.2665i | − | 0.775037i | −0.921862 | − | 0.387519i | \(-0.873332\pi\) | ||
0.921862 | − | 0.387519i | \(-0.126668\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 11.0000i | − | 0.640445i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.0000 | + | 13.2665i | 0.638285 | + | 0.769800i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.2665 | 0.767221 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.65831 | + | 5.50000i | −0.0952676 | + | 0.315967i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.94987i | 0.569728i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.00000i | − | 0.342438i | −0.985233 | − | 0.171219i | \(-0.945229\pi\) | ||
0.985233 | − | 0.171219i | \(-0.0547706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.50000 | − | 18.2414i | 0.312884 | − | 1.03772i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.94987 | −0.564206 | −0.282103 | − | 0.959384i | \(-0.591032\pi\) | ||||
−0.282103 | + | 0.959384i | \(0.591032\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.00000 | 0.508710 | 0.254355 | − | 0.967111i | \(-0.418137\pi\) | ||||
0.254355 | + | 0.967111i | \(0.418137\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 29.8496i | − | 1.67652i | −0.545269 | − | 0.838261i | \(-0.683573\pi\) | ||
0.545269 | − | 0.838261i | \(-0.316427\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 22.0000i | − | 1.23176i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.50000 | − | 1.65831i | −0.306980 | − | 0.0925580i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.2164 | −1.29179 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.0000 | −1.33128 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.29156 | + | 2.50000i | 0.458524 | + | 0.138250i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.0000i | − | 0.934405i | −0.884150 | − | 0.467202i | \(-0.845262\pi\) | ||
0.884150 | − | 0.467202i | \(-0.154738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.50000 | − | 1.65831i | −0.136999 | − | 0.0908750i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −29.8496 | −1.63086 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.0000 | 1.52526 | 0.762629 | − | 0.646837i | \(-0.223908\pi\) | ||||
0.762629 | + | 0.646837i | \(0.223908\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.31662 | − | 11.0000i | 0.180134 | − | 0.597438i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.94987i | 0.538816i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.50000 | − | 18.2414i | 0.296110 | − | 0.982086i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.8496 | −1.60241 | −0.801206 | − | 0.598389i | \(-0.795808\pi\) | ||||
−0.801206 | + | 0.598389i | \(0.795808\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.00000 | 0.428230 | 0.214115 | − | 0.976808i | \(-0.431313\pi\) | ||||
0.214115 | + | 0.976808i | \(0.431313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.2665 | + | 16.0000i | 0.708113 | + | 0.854017i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 36.4829i | − | 1.94179i | −0.239511 | − | 0.970894i | \(-0.576987\pi\) | ||
0.239511 | − | 0.970894i | \(-0.423013\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 44.0000i | − | 2.33528i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 36.4829 | 1.92549 | 0.962746 | − | 0.270407i | \(-0.0871582\pi\) | ||||
0.962746 | + | 0.270407i | \(0.0871582\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −30.0000 | −1.57895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.2164i | 1.21520i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.00000i | 0.0521996i | 0.999659 | + | 0.0260998i | \(0.00830876\pi\) | ||||
−0.999659 | + | 0.0260998i | \(0.991691\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.0000 | − | 16.5831i | 0.572637 | − | 0.863283i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.0000 | −0.673114 | −0.336557 | − | 0.941663i | \(-0.609263\pi\) | ||||
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.65831 | + | 5.50000i | −0.0856349 | + | 0.284019i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 26.5330i | − | 1.36652i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0000i | 1.23280i | 0.787434 | + | 0.616399i | \(0.211409\pi\) | ||||
−0.787434 | + | 0.616399i | \(0.788591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.00000 | + | 3.31662i | −0.0512316 | + | 0.169916i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.5831 | 0.847358 | 0.423679 | − | 0.905812i | \(-0.360738\pi\) | ||||
0.423679 | + | 0.905812i | \(0.360738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.31662 | + | 5.00000i | −0.168594 | + | 0.254164i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.31662i | − | 0.168160i | −0.996459 | − | 0.0840798i | \(-0.973205\pi\) | ||
0.996459 | − | 0.0840798i | \(-0.0267951\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.0000i | 0.556294i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −27.5000 | − | 8.29156i | −1.38719 | − | 0.418254i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.8496 | −1.50190 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0000 | −0.652451 | −0.326226 | − | 0.945292i | \(-0.605777\pi\) | ||||
−0.326226 | + | 0.945292i | \(0.605777\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5831i | 0.828122i | 0.910249 | + | 0.414061i | \(0.135890\pi\) | ||||
−0.910249 | + | 0.414061i | \(0.864110\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0000i | 0.597763i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27.5000 | − | 11.6082i | 1.36649 | − | 0.576815i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.31662 | −0.164399 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.0000 | 0.741702 | 0.370851 | − | 0.928692i | \(-0.379066\pi\) | ||||
0.370851 | + | 0.928692i | \(0.379066\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.29156 | − | 27.5000i | 0.408993 | − | 1.35647i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 44.0000i | − | 2.15988i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.00000 | + | 16.5831i | −0.244851 | + | 0.812079i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.5330 | −1.29622 | −0.648111 | − | 0.761546i | \(-0.724441\pi\) | ||||
−0.648111 | + | 0.761546i | \(0.724441\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24.8747 | − | 16.5000i | −1.20945 | − | 0.802257i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 19.8997i | − | 0.965280i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.0000 | + | 6.63325i | 1.06217 | + | 0.320256i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.2164 | −1.11829 | −0.559147 | − | 0.829069i | \(-0.688871\pi\) | ||||
−0.559147 | + | 0.829069i | \(0.688871\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.0000 | 0.961139 | 0.480569 | − | 0.876957i | \(-0.340430\pi\) | ||||
0.480569 | + | 0.876957i | \(0.340430\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −36.4829 | − | 11.0000i | −1.74922 | − | 0.527410i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.2164i | 1.11059i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 9.00000i | − | 0.429547i | −0.976664 | − | 0.214773i | \(-0.931099\pi\) | ||
0.976664 | − | 0.214773i | \(-0.0689013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.8496 | −1.41820 | −0.709099 | − | 0.705109i | \(-0.750898\pi\) | ||||
−0.709099 | + | 0.705109i | \(0.750898\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.0000 | 0.521450 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.29156 | + | 27.5000i | −0.392177 | + | 1.30071i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.8997i | − | 0.939127i | −0.882899 | − | 0.469564i | \(-0.844411\pi\) | ||
0.882899 | − | 0.469564i | \(-0.155589\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 22.0000i | − | 1.03594i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.50000 | − | 11.6082i | 0.164444 | − | 0.545400i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.00000 | 0.140334 | 0.0701670 | − | 0.997535i | \(-0.477647\pi\) | ||||
0.0701670 | + | 0.997535i | \(0.477647\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.2665 | + | 11.0000i | −0.619227 | + | 0.513436i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.1662i | 1.54471i | 0.635193 | + | 0.772353i | \(0.280920\pi\) | ||||
−0.635193 | + | 0.772353i | \(0.719080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.0000i | 1.76601i | 0.469364 | + | 0.883005i | \(0.344483\pi\) | ||||
−0.469364 | + | 0.883005i | \(0.655517\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.5000 | + | 4.97494i | 0.765169 | + | 0.230707i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.31662 | −0.153475 | −0.0767375 | − | 0.997051i | \(-0.524450\pi\) | ||||
−0.0767375 | + | 0.997051i | \(0.524450\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.97494 | − | 1.50000i | −0.229233 | − | 0.0691164i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.63325i | 0.304997i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 42.0000i | − | 1.92709i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.50000 | + | 8.29156i | −0.251828 | + | 0.379645i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.5831 | 0.757702 | 0.378851 | − | 0.925458i | \(-0.376319\pi\) | ||||
0.378851 | + | 0.925458i | \(0.376319\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.5330i | 1.20480i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.0000i | − | 0.770344i | −0.922845 | − | 0.385172i | \(-0.874142\pi\) | ||
0.922845 | − | 0.385172i | \(-0.125858\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.50000 | + | 11.6082i | −0.158275 | + | 0.524940i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.63325 | −0.299354 | −0.149677 | − | 0.988735i | \(-0.547823\pi\) | ||||
−0.149677 | + | 0.988735i | \(0.547823\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.0000 | 0.990830 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18.2414 | − | 27.5000i | 0.819892 | − | 1.23603i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.0000i | 1.56682i | 0.621508 | + | 0.783408i | \(0.286520\pi\) | ||||
−0.621508 | + | 0.783408i | \(0.713480\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.0000 | − | 3.31662i | −0.491444 | − | 0.148176i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.0000 | 0.489494 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.97494 | + | 1.50000i | 0.220945 | + | 0.0666173i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 16.5831i | − | 0.735034i | −0.930017 | − | 0.367517i | \(-0.880208\pi\) | ||
0.930017 | − | 0.367517i | \(-0.119792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −28.0000 | + | 23.2164i | −1.23623 | + | 1.02503i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.4829 | −1.60763 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.0000 | −1.45134 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.97494 | − | 16.5000i | 0.218376 | − | 0.724270i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.2164i | 1.01713i | 0.861024 | + | 0.508564i | \(0.169823\pi\) | ||||
−0.861024 | + | 0.508564i | \(0.830177\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.0000i | 0.830812i | 0.909636 | + | 0.415406i | \(0.136360\pi\) | ||||
−0.909636 | + | 0.415406i | \(0.863640\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.94987 | −0.433423 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.0000 | −0.521739 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.29156 | + | 5.50000i | 0.359823 | + | 0.238680i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 26.5330i | − | 1.14927i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.0000i | 0.475571i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.50000 | + | 1.65831i | 0.237343 | + | 0.0715615i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.0000 | 1.59075 | 0.795377 | − | 0.606115i | \(-0.207273\pi\) | ||||
0.795377 | + | 0.606115i | \(0.207273\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −29.8496 | − | 9.00000i | −1.28097 | − | 0.386227i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 16.5831i | − | 0.710343i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.0000i | 1.71028i | 0.518400 | + | 0.855138i | \(0.326528\pi\) | ||||
−0.518400 | + | 0.855138i | \(0.673472\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.50000 | − | 4.97494i | −0.320092 | − | 0.212325i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 46.4327 | 1.97810 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.65831 | + | 5.50000i | −0.0703914 | + | 0.233462i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 3.31662i | − | 0.140530i | −0.997528 | − | 0.0702650i | \(-0.977616\pi\) | ||
0.997528 | − | 0.0702650i | \(-0.0223845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000i | 0.338364i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.50000 | + | 18.2414i | −0.232210 | + | 0.770154i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.94987 | −0.419337 | −0.209669 | − | 0.977773i | \(-0.567239\pi\) | ||||
−0.209669 | + | 0.977773i | \(0.567239\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.0000 | −0.925547 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 29.8496i | − | 1.25136i | −0.780079 | − | 0.625681i | \(-0.784821\pi\) | ||
0.780079 | − | 0.625681i | \(-0.215179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.00000i | 0.209243i | 0.994512 | + | 0.104622i | \(0.0333632\pi\) | ||||
−0.994512 | + | 0.104622i | \(0.966637\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.5000 | + | 4.97494i | 0.689297 | + | 0.207831i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.8997 | −0.829877 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.0000 | −1.45707 | −0.728535 | − | 0.685009i | \(-0.759798\pi\) | ||||
−0.728535 | + | 0.685009i | \(0.759798\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.97494 | − | 1.50000i | −0.206751 | − | 0.0623379i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.0000i | 0.455573i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22.0000 | − | 33.1662i | 0.909588 | − | 1.37126i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.5330 | 1.09513 | 0.547567 | − | 0.836762i | \(-0.315554\pi\) | ||||
0.547567 | + | 0.836762i | \(0.315554\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.0000 | −0.865290 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.94987 | + | 33.0000i | −0.409283 | + | 1.35744i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 3.31662i | − | 0.136197i | −0.997679 | − | 0.0680987i | \(-0.978307\pi\) | ||
0.997679 | − | 0.0680987i | \(-0.0216933\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.500000 | − | 1.65831i | 0.0204636 | − | 0.0678702i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.94987 | 0.406541 | 0.203270 | − | 0.979123i | \(-0.434843\pi\) | ||||
0.203270 | + | 0.979123i | \(0.434843\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0000 | 0.652654 | 0.326327 | − | 0.945257i | \(-0.394189\pi\) | ||||
0.326327 | + | 0.945257i | \(0.394189\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.9248 | − | 22.5000i | 0.607785 | − | 0.916271i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.00000i | 0.284121i | 0.989858 | + | 0.142061i | \(0.0453728\pi\) | ||||
−0.989858 | + | 0.142061i | \(0.954627\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.7995 | −1.61012 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.00000 | 0.0403896 | 0.0201948 | − | 0.999796i | \(-0.493571\pi\) | ||||
0.0201948 | + | 0.999796i | \(0.493571\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −36.4829 | − | 11.0000i | −1.47113 | − | 0.443563i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.63325i | 0.267045i | 0.991046 | + | 0.133522i | \(0.0426288\pi\) | ||||
−0.991046 | + | 0.133522i | \(0.957371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.0000i | 1.00483i | 0.864625 | + | 0.502417i | \(0.167556\pi\) | ||||
−0.864625 | + | 0.502417i | \(0.832444\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.0000 | + | 13.2665i | 0.441415 | + | 0.532366i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.6082 | + | 38.5000i | −0.463586 | + | 1.53754i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 3.31662i | − | 0.132242i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 18.0000i | − | 0.716569i | −0.933613 | − | 0.358284i | \(-0.883362\pi\) | ||
0.933613 | − | 0.358284i | \(-0.116638\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.0000 | − | 43.1161i | 0.516704 | − | 1.71371i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.63325 | 0.263232 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33.1662 | + | 22.0000i | 1.31204 | + | 0.870307i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 36.4829i | − | 1.44099i | −0.693462 | − | 0.720493i | \(-0.743915\pi\) | ||
0.693462 | − | 0.720493i | \(-0.256085\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.00000i | 0.0788723i | 0.999222 | + | 0.0394362i | \(0.0125562\pi\) | ||||
−0.999222 | + | 0.0394362i | \(0.987444\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 11.0000 | + | 3.31662i | 0.433125 | + | 0.130592i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.31662 | 0.130390 | 0.0651950 | − | 0.997873i | \(-0.479233\pi\) | ||||
0.0651950 | + | 0.997873i | \(0.479233\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.0000 | 0.431788 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 3.31662i | − | 0.129790i | −0.997892 | − | 0.0648948i | \(-0.979329\pi\) | ||
0.997892 | − | 0.0648948i | \(-0.0206712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 55.0000i | 2.14903i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −17.5000 | − | 11.6082i | −0.682740 | − | 0.452878i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −26.5330 | −1.03358 | −0.516789 | − | 0.856113i | \(-0.672873\pi\) | ||||
−0.516789 | + | 0.856113i | \(0.672873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.0000 | −1.51692 | −0.758462 | − | 0.651717i | \(-0.774049\pi\) | ||||
−0.758462 | + | 0.651717i | \(0.774049\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.63325 | + | 22.0000i | −0.257614 | + | 0.854409i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 22.0000i | − | 0.851843i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.00000 | + | 23.2164i | −0.270636 | + | 0.897597i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.94987 | −0.384111 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.0000 | 1.54189 | 0.770943 | − | 0.636904i | \(-0.219785\pi\) | ||||
0.770943 | + | 0.636904i | \(0.219785\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.8997 | − | 24.0000i | −0.765942 | − | 0.923760i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.94987i | 0.382405i | 0.981551 | + | 0.191202i | \(0.0612387\pi\) | ||||
−0.981551 | + | 0.191202i | \(0.938761\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.50000 | − | 1.65831i | −0.210760 | − | 0.0635467i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.2164 | −0.888350 | −0.444175 | − | 0.895940i | \(-0.646503\pi\) | ||||
−0.444175 | + | 0.895940i | \(0.646503\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −55.0000 | −2.10144 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −48.0911 | − | 14.5000i | −1.83479 | − | 0.553210i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.2665i | 0.505413i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.0000i | 1.25538i | 0.778464 | + | 0.627690i | \(0.215999\pi\) | ||||
−0.778464 | + | 0.627690i | \(0.784001\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.1662 | 1.25807 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.0000 | 0.833309 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.29156 | + | 27.5000i | −0.313616 | + | 1.04015i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.2665i | − | 0.501069i | −0.968108 | − | 0.250534i | \(-0.919394\pi\) | ||
0.968108 | − | 0.250534i | \(-0.0806063\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7.00000i | − | 0.264010i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.5000 | + | 54.7243i | −0.621426 | + | 2.06104i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.0000 | −1.23934 | −0.619671 | − | 0.784862i | \(-0.712734\pi\) | ||||
−0.619671 | + | 0.784862i | \(0.712734\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.9248 | − | 22.5000i | 0.559724 | − | 0.843816i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.94987i | 0.372626i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 44.0000i | − | 1.64551i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.0000 | − | 3.31662i | −0.410803 | − | 0.123862i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23.2164 | 0.865825 | 0.432912 | − | 0.901436i | \(-0.357486\pi\) | ||||
0.432912 | + | 0.901436i | \(0.357486\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −31.5079 | − | 9.50000i | −1.17179 | − | 0.353309i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39.7995i | 1.47812i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.0000i | 0.370879i | 0.982656 | + | 0.185440i | \(0.0593710\pi\) | ||||
−0.982656 | + | 0.185440i | \(0.940629\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.00000 | + | 26.5330i | −0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.63325 | −0.245340 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.00000 | −0.258551 | −0.129275 | − | 0.991609i | \(-0.541265\pi\) | ||||
−0.129275 | + | 0.991609i | \(0.541265\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 29.8496i | − | 1.09952i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 31.0000i | − | 1.14035i | −0.821522 | − | 0.570177i | \(-0.806875\pi\) | ||
0.821522 | − | 0.570177i | \(-0.193125\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.0000 | + | 46.4327i | −0.514303 | + | 1.70575i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.2665 | 0.486701 | 0.243350 | − | 0.969938i | \(-0.421754\pi\) | ||||
0.243350 | + | 0.969938i | \(0.421754\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55.0000 | 2.01504 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 33.1662 | + | 22.0000i | 1.21349 | + | 0.804938i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.00000i | 0.182453i | 0.995830 | + | 0.0912263i | \(0.0290787\pi\) | ||||
−0.995830 | + | 0.0912263i | \(0.970921\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.0000 | + | 9.94987i | 1.20259 | + | 0.362594i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.2164 | −0.844930 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.0000 | −1.74459 | −0.872295 | − | 0.488980i | \(-0.837369\pi\) | ||||
−0.872295 | + | 0.488980i | \(0.837369\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18.2414 | + | 5.50000i | 0.662122 | + | 0.199637i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.2164i | 0.841593i | 0.907155 | + | 0.420796i | \(0.138249\pi\) | ||||
−0.907155 | + | 0.420796i | \(0.861751\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 27.5000 | + | 18.2414i | 0.994265 | + | 0.659521i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 13.2665 | 0.479026 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0000 | 0.576975 | 0.288487 | − | 0.957484i | \(-0.406848\pi\) | ||||
0.288487 | + | 0.957484i | \(0.406848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.6082 | + | 38.5000i | −0.418059 | + | 1.38654i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.5831i | 0.596454i | 0.954495 | + | 0.298227i | \(0.0963952\pi\) | ||||
−0.954495 | + | 0.298227i | \(0.903605\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 18.0000i | − | 0.646579i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 46.4327 | 1.66363 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44.0000 | 1.57444 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.5330 | − | 22.0000i | 0.948212 | − | 0.786216i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.94987i | 0.355126i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.0000i | 1.60408i | 0.597272 | + | 0.802038i | \(0.296251\pi\) | ||||
−0.597272 | + | 0.802038i | \(0.703749\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.50000 | − | 1.65831i | −0.195805 | − | 0.0590375i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0000 | −0.426132 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.2414 | + | 5.50000i | 0.646957 | + | 0.195065i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 6.63325i | − | 0.234962i | −0.993075 | − | 0.117481i | \(-0.962518\pi\) | ||
0.993075 | − | 0.117481i | \(-0.0374819\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 33.0000i | − | 1.16746i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.50000 | + | 8.29156i | −0.194333 | + | 0.292968i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.2164 | −0.819288 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.29156 | − | 27.5000i | 0.291877 | − | 0.968046i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.31662i | 0.116606i | 0.998299 | + | 0.0583032i | \(0.0185690\pi\) | ||||
−0.998299 | + | 0.0583032i | \(0.981431\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0000i | 1.05344i | 0.850038 | + | 0.526721i | \(0.176579\pi\) | ||||
−0.850038 | + | 0.526721i | \(0.823421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.50000 | + | 28.1913i | −0.298108 | + | 0.988712i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.2164 | 0.813234 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.0000 | −0.489798 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 36.4829i | − | 1.27326i | −0.771169 | − | 0.636631i | \(-0.780328\pi\) | ||
0.771169 | − | 0.636631i | \(-0.219672\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.0000i | 0.522867i | 0.965221 | + | 0.261434i | \(0.0841952\pi\) | ||||
−0.965221 | + | 0.261434i | \(0.915805\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −33.0000 | − | 9.94987i | −1.14891 | − | 0.346410i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.7995 | 1.38396 | 0.691982 | − | 0.721915i | \(-0.256738\pi\) | ||||
0.691982 | + | 0.721915i | \(0.256738\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.0000 | −1.00721 | −0.503606 | − | 0.863934i | \(-0.667994\pi\) | ||||
−0.503606 | + | 0.863934i | \(0.667994\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.5581 | − | 6.50000i | −0.747841 | − | 0.225483i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.0000i | 0.761341i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12.0000 | + | 9.94987i | −0.414781 | + | 0.343918i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.2665 | −0.458010 | −0.229005 | − | 0.973425i | \(-0.573547\pi\) | ||||
−0.229005 | + | 0.973425i | \(0.573547\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.0000 | −0.517241 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.31662 | + | 11.0000i | −0.114231 | + | 0.378860i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 9.94987i | − | 0.342286i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.50000 | + | 24.8747i | −0.257399 | + | 0.853697i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.31662 | −0.113692 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.0000 | 0.684787 | 0.342393 | − | 0.939557i | \(-0.388762\pi\) | ||||
0.342393 | + | 0.939557i | \(0.388762\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 58.0409 | + | 38.5000i | 1.98496 | + | 1.31667i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 16.5831i | − | 0.566469i | −0.959051 | − | 0.283234i | \(-0.908593\pi\) | ||
0.959051 | − | 0.283234i | \(-0.0914074\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 17.0000i | − | 0.580033i | −0.957022 | − | 0.290016i | \(-0.906339\pi\) | ||
0.957022 | − | 0.290016i | \(-0.0936607\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.4829 | −1.24189 | −0.620946 | − | 0.783854i | \(-0.713251\pi\) | ||||
−0.620946 | + | 0.783854i | \(0.713251\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.0000 | −1.12203 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.94987 | + | 3.00000i | 0.337915 | + | 0.101885i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 29.8496i | − | 1.01258i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 36.0000i | − | 1.21981i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.0000 | − | 13.2665i | −0.676897 | − | 0.449003i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.0000 | −0.776655 | −0.388327 | − | 0.921521i | \(-0.626947\pi\) | ||||
−0.388327 | + | 0.921521i | \(0.626947\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.63325 | − | 22.0000i | 0.223734 | − | 0.742042i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 6.00000i | − | 0.201916i | −0.994891 | − | 0.100958i | \(-0.967809\pi\) | ||
0.994891 | − | 0.100958i | \(-0.0321908\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.50000 | − | 18.2414i | 0.184880 | − | 0.613179i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.2164 | −0.779530 | −0.389765 | − | 0.920914i | \(-0.627444\pi\) | ||||
−0.389765 | + | 0.920914i | \(0.627444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11.6082 | + | 27.5000i | 0.388889 | + | 0.921285i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 69.6491i | − | 2.33072i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 11.0000i | − | 0.367689i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.0000 | + | 6.63325i | 0.734559 | + | 0.221478i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.8997 | 0.663694 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.0000 | −0.366463 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 59.6992i | 1.98447i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 53.0000i | − | 1.75984i | −0.475125 | − | 0.879918i | \(-0.657597\pi\) | ||
0.475125 | − | 0.879918i | \(-0.342403\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.50000 | + | 8.29156i | −0.182423 | + | 0.275014i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.5330 | −0.879077 | −0.439539 | − | 0.898224i | \(-0.644858\pi\) | ||||
−0.439539 | + | 0.898224i | \(0.644858\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.0000 | 1.45619 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.97494 | + | 16.5000i | −0.164466 | + | 0.545473i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 23.0000i | − | 0.758700i | −0.925253 | − | 0.379350i | \(-0.876148\pi\) | ||
0.925253 | − | 0.379350i | \(-0.123852\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.00000 | − | 9.94987i | 0.0988534 | − | 0.327860i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 53.0660 | 1.74669 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.2414 | − | 27.5000i | 0.599127 | − | 0.903219i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 23.2164i | − | 0.761705i | −0.924636 | − | 0.380852i | \(-0.875631\pi\) | ||
0.924636 | − | 0.380852i | \(-0.124369\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.5000 | − | 4.97494i | −0.540186 | − | 0.162872i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 36.4829 | 1.19312 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.9248 | + | 4.50000i | 0.487053 | + | 0.146852i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.94987i | 0.324357i | 0.986761 | + | 0.162178i | \(0.0518520\pi\) | ||||
−0.986761 | + | 0.162178i | \(0.948148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 22.0000i | − | 0.716419i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.94987 | −0.323327 | −0.161664 | − | 0.986846i | \(-0.551686\pi\) | ||||
−0.161664 | + | 0.986846i | \(0.551686\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.0000 | −0.908918 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.9248 | − | 49.5000i | 0.483970 | − | 1.60515i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 19.8997i | − | 0.644616i | −0.946635 | − | 0.322308i | \(-0.895541\pi\) | ||
0.946635 | − | 0.322308i | \(-0.104459\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 33.0000i | − | 1.06785i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.0000 | − | 36.4829i | 0.355580 | − | 1.17932i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.0000 | 0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.29156 | − | 5.50000i | −0.267192 | − | 0.177235i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.94987i | 0.320298i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.00000i | 0.0643157i | 0.999483 | + | 0.0321578i | \(0.0102379\pi\) | ||||
−0.999483 | + | 0.0321578i | \(0.989762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −38.5000 | − | 11.6082i | −1.23680 | − | 0.372909i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.5831 | −0.532178 | −0.266089 | − | 0.963948i | \(-0.585731\pi\) | ||||
−0.266089 | + | 0.963948i | \(0.585731\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −39.7995 | − | 12.0000i | −1.27460 | − | 0.384308i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 3.31662i | − | 0.106108i | −0.998592 | − | 0.0530541i | \(-0.983104\pi\) | ||
0.998592 | − | 0.0530541i | \(-0.0168956\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.0000i | 0.351562i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.5000 | + | 8.29156i | 0.399094 | + | 0.264729i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −56.3826 | −1.79833 | −0.899163 | − | 0.437614i | \(-0.855824\pi\) | ||||
−0.899163 | + | 0.437614i | \(0.855824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 66.0000 | 2.10293 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.63325i | 0.210925i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.0000i | 1.36594i | 0.730446 | + | 0.682970i | \(0.239312\pi\) | ||||
−0.730446 | + | 0.682970i | \(0.760688\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8.50000 | − | 28.1913i | 0.269739 | − | 0.894624i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.31662 | −0.105144 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.00000 | 0.158352 | 0.0791758 | − | 0.996861i | \(-0.474771\pi\) | ||||
0.0791758 | + | 0.996861i | \(0.474771\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.31662 | − | 4.00000i | −0.104933 | − | 0.126554i |
(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 | 2352.2.h.j.2255.4 | 4 | ||
3.2 | odd | 2 | inner | 2352.2.h.j.2255.2 | 4 | ||
4.3 | odd | 2 | inner | 2352.2.h.j.2255.1 | 4 | ||
7.3 | odd | 6 | 336.2.bj.f.191.3 | yes | 8 | ||
7.5 | odd | 6 | 336.2.bj.f.95.4 | yes | 8 | ||
7.6 | odd | 2 | 2352.2.h.i.2255.1 | 4 | |||
12.11 | even | 2 | inner | 2352.2.h.j.2255.3 | 4 | ||
21.5 | even | 6 | 336.2.bj.f.95.2 | yes | 8 | ||
21.17 | even | 6 | 336.2.bj.f.191.1 | yes | 8 | ||
21.20 | even | 2 | 2352.2.h.i.2255.3 | 4 | |||
28.3 | even | 6 | 336.2.bj.f.191.2 | yes | 8 | ||
28.19 | even | 6 | 336.2.bj.f.95.1 | ✓ | 8 | ||
28.27 | even | 2 | 2352.2.h.i.2255.4 | 4 | |||
84.47 | odd | 6 | 336.2.bj.f.95.3 | yes | 8 | ||
84.59 | odd | 6 | 336.2.bj.f.191.4 | yes | 8 | ||
84.83 | odd | 2 | 2352.2.h.i.2255.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.bj.f.95.1 | ✓ | 8 | 28.19 | even | 6 | ||
336.2.bj.f.95.2 | yes | 8 | 21.5 | even | 6 | ||
336.2.bj.f.95.3 | yes | 8 | 84.47 | odd | 6 | ||
336.2.bj.f.95.4 | yes | 8 | 7.5 | odd | 6 | ||
336.2.bj.f.191.1 | yes | 8 | 21.17 | even | 6 | ||
336.2.bj.f.191.2 | yes | 8 | 28.3 | even | 6 | ||
336.2.bj.f.191.3 | yes | 8 | 7.3 | odd | 6 | ||
336.2.bj.f.191.4 | yes | 8 | 84.59 | odd | 6 | ||
2352.2.h.i.2255.1 | 4 | 7.6 | odd | 2 | |||
2352.2.h.i.2255.2 | 4 | 84.83 | odd | 2 | |||
2352.2.h.i.2255.3 | 4 | 21.20 | even | 2 | |||
2352.2.h.i.2255.4 | 4 | 28.27 | even | 2 | |||
2352.2.h.j.2255.1 | 4 | 4.3 | odd | 2 | inner | ||
2352.2.h.j.2255.2 | 4 | 3.2 | odd | 2 | inner | ||
2352.2.h.j.2255.3 | 4 | 12.11 | even | 2 | inner | ||
2352.2.h.j.2255.4 | 4 | 1.1 | even | 1 | trivial |