Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,2,Mod(1088,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.1088");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.d (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: | \(8.69570878012\) |
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: | \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1088.7 | ||
Root | \(0.752864 - 0.902863i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.1088 |
Dual form | 1089.2.d.g.1088.8 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.253675 | −0.179376 | −0.0896878 | − | 0.995970i | \(-0.528587\pi\) | ||||
−0.0896878 | + | 0.995970i | \(0.528587\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.93565 | −0.967824 | ||||||||
\(5\) | − 2.92173i | − 1.30664i | −0.757084 | − | 0.653318i | \(-0.773376\pi\) | ||||
0.757084 | − | 0.653318i | \(-0.226624\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.71893i | − 1.02766i | −0.857892 | − | 0.513830i | \(-0.828226\pi\) | ||||
0.857892 | − | 0.513830i | \(-0.171774\pi\) | |||||||
\(8\) | 0.998377 | 0.352980 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.741170i | 0.234379i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.85596i | − 0.792102i | −0.918229 | − | 0.396051i | \(-0.870380\pi\) | ||||
0.918229 | − | 0.396051i | \(-0.129620\pi\) | |||||||
\(14\) | 0.689726i | 0.184337i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.61803 | 0.904508 | ||||||||
\(17\) | 4.46218 | 1.08224 | 0.541119 | − | 0.840946i | \(-0.318001\pi\) | ||||
0.541119 | + | 0.840946i | \(0.318001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.91115i | − 0.438449i | −0.975674 | − | 0.219224i | \(-0.929647\pi\) | ||||
0.975674 | − | 0.219224i | \(-0.0703527\pi\) | |||||||
\(20\) | 5.65544i | 1.26459i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.816370i | 0.170225i | 0.996371 | + | 0.0851124i | \(0.0271249\pi\) | ||||
−0.996371 | + | 0.0851124i | \(0.972875\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.53649 | −0.707297 | ||||||||
\(26\) | 0.724487i | 0.142084i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.26290i | 0.994594i | ||||||||
\(29\) | −9.54660 | −1.77276 | −0.886380 | − | 0.462959i | \(-0.846788\pi\) | ||||
−0.886380 | + | 0.462959i | \(0.846788\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.98605 | −1.07513 | −0.537563 | − | 0.843224i | \(-0.680655\pi\) | ||||
−0.537563 | + | 0.843224i | \(0.680655\pi\) | |||||||
\(32\) | −2.91456 | −0.515226 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.13195 | −0.194127 | ||||||||
\(35\) | −7.94398 | −1.34278 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.94628 | 0.977562 | 0.488781 | − | 0.872407i | \(-0.337442\pi\) | ||||
0.488781 | + | 0.872407i | \(0.337442\pi\) | |||||||
\(38\) | 0.484812i | 0.0786470i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 2.91698i | − 0.461216i | ||||||||
\(41\) | −8.43334 | −1.31707 | −0.658533 | − | 0.752552i | \(-0.728823\pi\) | ||||
−0.658533 | + | 0.752552i | \(0.728823\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 11.8763i | − 1.81112i | −0.424214 | − | 0.905562i | \(-0.639450\pi\) | ||||
0.424214 | − | 0.905562i | \(-0.360550\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 0.207093i | − 0.0305342i | ||||||||
\(47\) | 7.71816i | 1.12581i | 0.826522 | + | 0.562905i | \(0.190316\pi\) | ||||
−0.826522 | + | 0.562905i | \(0.809684\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.392594 | −0.0560848 | ||||||||
\(50\) | 0.897120 | 0.126872 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.52814i | 0.766615i | ||||||||
\(53\) | 10.4556i | 1.43618i | 0.695948 | + | 0.718092i | \(0.254984\pi\) | ||||
−0.695948 | + | 0.718092i | \(0.745016\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 2.71452i | − 0.362743i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.42174 | 0.317990 | ||||||||
\(59\) | 0.0932996i | 0.0121466i | 0.999982 | + | 0.00607329i | \(0.00193320\pi\) | ||||
−0.999982 | + | 0.00607329i | \(0.998067\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 2.14405i | − 0.274517i | −0.990535 | − | 0.137259i | \(-0.956171\pi\) | ||||
0.990535 | − | 0.137259i | \(-0.0438291\pi\) | |||||||
\(62\) | 1.51851 | 0.192851 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.49672 | −0.812089 | ||||||||
\(65\) | −8.34434 | −1.03499 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.40778 | −0.171988 | −0.0859941 | − | 0.996296i | \(-0.527407\pi\) | ||||
−0.0859941 | + | 0.996296i | \(0.527407\pi\) | |||||||
\(68\) | −8.63722 | −1.04742 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.01519 | 0.240861 | ||||||||
\(71\) | − 3.60916i | − 0.428328i | −0.976798 | − | 0.214164i | \(-0.931297\pi\) | ||||
0.976798 | − | 0.214164i | \(-0.0687028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.75950i | 0.205933i | 0.994685 | + | 0.102967i | \(0.0328335\pi\) | ||||
−0.994685 | + | 0.102967i | \(0.967167\pi\) | |||||||
\(74\) | −1.50842 | −0.175351 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.69932i | 0.424341i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 7.13289i | − 0.802512i | −0.915966 | − | 0.401256i | \(-0.868574\pi\) | ||||
0.915966 | − | 0.401256i | \(-0.131426\pi\) | |||||||
\(80\) | − 10.5709i | − 1.18186i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.13933 | 0.236249 | ||||||||
\(83\) | −7.83430 | −0.859926 | −0.429963 | − | 0.902847i | \(-0.641473\pi\) | ||||
−0.429963 | + | 0.902847i | \(0.641473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 13.0373i | − 1.41409i | ||||||||
\(86\) | 3.01273i | 0.324871i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 2.06830i | − 0.219240i | −0.993974 | − | 0.109620i | \(-0.965037\pi\) | ||||
0.993974 | − | 0.109620i | \(-0.0349633\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.76517 | −0.814011 | ||||||||
\(92\) | − 1.58021i | − 0.164748i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 1.95791i | − 0.201943i | ||||||||
\(95\) | −5.58387 | −0.572893 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.67044 | 0.169607 | 0.0848036 | − | 0.996398i | \(-0.472974\pi\) | ||||
0.0848036 | + | 0.996398i | \(0.472974\pi\) | |||||||
\(98\) | 0.0995913 | 0.0100602 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.84540 | 0.684540 | ||||||||
\(101\) | 9.04767 | 0.900277 | 0.450139 | − | 0.892959i | \(-0.351375\pi\) | ||||
0.450139 | + | 0.892959i | \(0.351375\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.5729 | −1.63298 | −0.816490 | − | 0.577360i | \(-0.804083\pi\) | ||||
−0.816490 | + | 0.577360i | \(0.804083\pi\) | |||||||
\(104\) | − 2.85133i | − 0.279596i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 2.65232i | − 0.257616i | ||||||||
\(107\) | 7.11298 | 0.687638 | 0.343819 | − | 0.939036i | \(-0.388279\pi\) | ||||
0.343819 | + | 0.939036i | \(0.388279\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.62045i | 0.825690i | 0.910801 | + | 0.412845i | \(0.135465\pi\) | ||||
−0.910801 | + | 0.412845i | \(0.864535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 9.83719i | − 0.929527i | ||||||||
\(113\) | 11.4079i | 1.07316i | 0.843848 | + | 0.536582i | \(0.180285\pi\) | ||||
−0.843848 | + | 0.536582i | \(0.819715\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.38521 | 0.222422 | ||||||||
\(116\) | 18.4789 | 1.71572 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 0.0236678i | − 0.00217880i | ||||||||
\(119\) | − 12.1324i | − 1.11217i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0.543892i | 0.0492417i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.5869 | 1.04053 | ||||||||
\(125\) | − 4.27598i | − 0.382456i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.88308i | 0.255832i | 0.991785 | + | 0.127916i | \(0.0408288\pi\) | ||||
−0.991785 | + | 0.127916i | \(0.959171\pi\) | |||||||
\(128\) | 7.47718 | 0.660895 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.11675 | 0.185652 | ||||||||
\(131\) | 2.10155 | 0.183613 | 0.0918067 | − | 0.995777i | \(-0.470736\pi\) | ||||
0.0918067 | + | 0.995777i | \(0.470736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.19630 | −0.450576 | ||||||||
\(134\) | 0.357120 | 0.0308505 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.45494 | 0.382008 | ||||||||
\(137\) | − 5.07404i | − 0.433504i | −0.976227 | − | 0.216752i | \(-0.930454\pi\) | ||||
0.976227 | − | 0.216752i | \(-0.0695464\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 17.4839i | − 1.48297i | −0.670970 | − | 0.741484i | \(-0.734122\pi\) | ||||
0.670970 | − | 0.741484i | \(-0.265878\pi\) | |||||||
\(140\) | 15.3768 | 1.29957 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.915555i | 0.0768317i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 27.8926i | 2.31635i | ||||||||
\(146\) | − 0.446341i | − 0.0369394i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −11.5099 | −0.946108 | ||||||||
\(149\) | −5.65654 | −0.463402 | −0.231701 | − | 0.972787i | \(-0.574429\pi\) | ||||
−0.231701 | + | 0.972787i | \(0.574429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.17548i | 0.746690i | 0.927693 | + | 0.373345i | \(0.121789\pi\) | ||||
−0.927693 | + | 0.373345i | \(0.878211\pi\) | |||||||
\(152\) | − 1.90805i | − 0.154763i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.4896i | 1.40480i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.05372 | −0.243714 | −0.121857 | − | 0.992548i | \(-0.538885\pi\) | ||||
−0.121857 | + | 0.992548i | \(0.538885\pi\) | |||||||
\(158\) | 1.80944i | 0.143951i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.51555i | 0.673213i | ||||||||
\(161\) | 2.21965 | 0.174933 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.90450 | 0.619128 | 0.309564 | − | 0.950879i | \(-0.399817\pi\) | ||||
0.309564 | + | 0.950879i | \(0.399817\pi\) | |||||||
\(164\) | 16.3240 | 1.27469 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.98737 | 0.154250 | ||||||||
\(167\) | 16.4478 | 1.27277 | 0.636384 | − | 0.771372i | \(-0.280429\pi\) | ||||
0.636384 | + | 0.771372i | \(0.280429\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.84347 | 0.372575 | ||||||||
\(170\) | 3.30724i | 0.253653i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 22.9884i | 1.75285i | ||||||||
\(173\) | −15.5224 | −1.18015 | −0.590074 | − | 0.807349i | \(-0.700901\pi\) | ||||
−0.590074 | + | 0.807349i | \(0.700901\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.61547i | 0.726861i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.524677i | 0.0393262i | ||||||||
\(179\) | − 5.18936i | − 0.387871i | −0.981014 | − | 0.193936i | \(-0.937875\pi\) | ||||
0.981014 | − | 0.193936i | \(-0.0621253\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.31229 | 0.394859 | 0.197430 | − | 0.980317i | \(-0.436741\pi\) | ||||
0.197430 | + | 0.980317i | \(0.436741\pi\) | |||||||
\(182\) | 1.96983 | 0.146014 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.815045i | 0.0600859i | ||||||||
\(185\) | − 17.3734i | − 1.27732i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − 14.9396i | − 1.08959i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.41649 | 0.102763 | ||||||||
\(191\) | 10.8996i | 0.788669i | 0.918967 | + | 0.394335i | \(0.129025\pi\) | ||||
−0.918967 | + | 0.394335i | \(0.870975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 15.3664i | − 1.10610i | −0.833148 | − | 0.553050i | \(-0.813464\pi\) | ||||
0.833148 | − | 0.553050i | \(-0.186536\pi\) | |||||||
\(194\) | −0.423749 | −0.0304234 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.759923 | 0.0542802 | ||||||||
\(197\) | 7.24149 | 0.515935 | 0.257967 | − | 0.966154i | \(-0.416947\pi\) | ||||
0.257967 | + | 0.966154i | \(0.416947\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.3726 | −0.806181 | −0.403090 | − | 0.915160i | \(-0.632064\pi\) | ||||
−0.403090 | + | 0.915160i | \(0.632064\pi\) | |||||||
\(200\) | −3.53075 | −0.249662 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.29517 | −0.161488 | ||||||||
\(203\) | 25.9566i | 1.82179i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 24.6399i | 1.72093i | ||||||||
\(206\) | 4.20414 | 0.292917 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 10.3330i | − 0.716463i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3.69822i | − 0.254596i | −0.991864 | − | 0.127298i | \(-0.959369\pi\) | ||||
0.991864 | − | 0.127298i | \(-0.0406305\pi\) | |||||||
\(212\) | − 20.2383i | − 1.38997i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.80439 | −0.123345 | ||||||||
\(215\) | −34.6994 | −2.36648 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.2757i | 1.10486i | ||||||||
\(218\) | − 2.18680i | − 0.148109i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 12.7438i | − 0.857243i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.283223 | −0.0189660 | −0.00948302 | − | 0.999955i | \(-0.503019\pi\) | ||||
−0.00948302 | + | 0.999955i | \(0.503019\pi\) | |||||||
\(224\) | 7.92449i | 0.529477i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 2.89390i | − 0.192499i | ||||||||
\(227\) | 18.2560 | 1.21169 | 0.605846 | − | 0.795582i | \(-0.292835\pi\) | ||||
0.605846 | + | 0.795582i | \(0.292835\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.3758 | 1.74296 | 0.871482 | − | 0.490428i | \(-0.163160\pi\) | ||||
0.871482 | + | 0.490428i | \(0.163160\pi\) | |||||||
\(230\) | −0.605069 | −0.0398971 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.53111 | −0.625748 | ||||||||
\(233\) | 10.8022 | 0.707675 | 0.353838 | − | 0.935307i | \(-0.384877\pi\) | ||||
0.353838 | + | 0.935307i | \(0.384877\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 22.5504 | 1.47102 | ||||||||
\(236\) | − 0.180595i | − 0.0117558i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.07768i | 0.199497i | ||||||||
\(239\) | −7.42332 | −0.480175 | −0.240087 | − | 0.970751i | \(-0.577176\pi\) | ||||
−0.240087 | + | 0.970751i | \(0.577176\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.66873i | 0.171908i | 0.996299 | + | 0.0859539i | \(0.0273938\pi\) | ||||
−0.996299 | + | 0.0859539i | \(0.972606\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.15012i | 0.265684i | ||||||||
\(245\) | 1.14705i | 0.0732824i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.45818 | −0.347296 | ||||||||
\(248\) | −5.97633 | −0.379498 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.08471i | 0.0686032i | ||||||||
\(251\) | − 24.2656i | − 1.53163i | −0.643060 | − | 0.765816i | \(-0.722335\pi\) | ||||
0.643060 | − | 0.765816i | \(-0.277665\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − 0.731367i | − 0.0458901i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.0967 | 0.693541 | ||||||||
\(257\) | − 16.7561i | − 1.04522i | −0.852573 | − | 0.522608i | \(-0.824959\pi\) | ||||
0.852573 | − | 0.522608i | \(-0.175041\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 16.1675i | − 1.00460i | ||||||||
\(260\) | 16.1517 | 1.00169 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.533112 | −0.0329357 | ||||||||
\(263\) | −10.9146 | −0.673021 | −0.336511 | − | 0.941680i | \(-0.609247\pi\) | ||||
−0.336511 | + | 0.941680i | \(0.609247\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 30.5484 | 1.87657 | ||||||||
\(266\) | 1.31817 | 0.0808223 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.72498 | 0.166454 | ||||||||
\(269\) | 15.6867i | 0.956435i | 0.878241 | + | 0.478218i | \(0.158717\pi\) | ||||
−0.878241 | + | 0.478218i | \(0.841283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.90507i | 0.176471i | 0.996100 | + | 0.0882353i | \(0.0281227\pi\) | ||||
−0.996100 | + | 0.0882353i | \(0.971877\pi\) | |||||||
\(272\) | 16.1443 | 0.978894 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.28716i | 0.0777601i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.1150i | 1.26868i | 0.773056 | + | 0.634338i | \(0.218727\pi\) | ||||
−0.773056 | + | 0.634338i | \(0.781273\pi\) | |||||||
\(278\) | 4.43524i | 0.266008i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.93109 | −0.473973 | ||||||||
\(281\) | −3.09036 | −0.184355 | −0.0921777 | − | 0.995743i | \(-0.529383\pi\) | ||||
−0.0921777 | + | 0.995743i | \(0.529383\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 22.4247i | − 1.33301i | −0.745500 | − | 0.666505i | \(-0.767789\pi\) | ||||
0.745500 | − | 0.666505i | \(-0.232211\pi\) | |||||||
\(284\) | 6.98607i | 0.414547i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.9297i | 1.35350i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.91107 | 0.171239 | ||||||||
\(290\) | − 7.07565i | − 0.415497i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 3.40576i | − 0.199307i | ||||||||
\(293\) | 20.7409 | 1.21170 | 0.605849 | − | 0.795579i | \(-0.292833\pi\) | ||||
0.605849 | + | 0.795579i | \(0.292833\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.272596 | 0.0158712 | ||||||||
\(296\) | 5.93663 | 0.345059 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.43492 | 0.0831229 | ||||||||
\(299\) | 2.33152 | 0.134835 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.2909 | −1.86122 | ||||||||
\(302\) | − 2.32759i | − 0.133938i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 6.91462i | − 0.396581i | ||||||||
\(305\) | −6.26432 | −0.358694 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 15.0077i | − 0.856533i | −0.903652 | − | 0.428267i | \(-0.859124\pi\) | ||||
0.903652 | − | 0.428267i | \(-0.140876\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 4.43668i | − 0.251986i | ||||||||
\(311\) | − 2.05901i | − 0.116756i | −0.998295 | − | 0.0583780i | \(-0.981407\pi\) | ||||
0.998295 | − | 0.0583780i | \(-0.0185929\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.8725 | −1.40588 | −0.702939 | − | 0.711250i | \(-0.748130\pi\) | ||||
−0.702939 | + | 0.711250i | \(0.748130\pi\) | |||||||
\(314\) | 0.774654 | 0.0437163 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.8068i | 0.776691i | ||||||||
\(317\) | 0.432728i | 0.0243044i | 0.999926 | + | 0.0121522i | \(0.00386827\pi\) | ||||
−0.999926 | + | 0.0121522i | \(0.996132\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 18.9816i | 1.06111i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.563072 | −0.0313787 | ||||||||
\(323\) | − 8.52791i | − 0.474506i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.1001i | 0.560251i | ||||||||
\(326\) | −2.00518 | −0.111056 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.41965 | −0.464897 | ||||||||
\(329\) | 20.9852 | 1.15695 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.3090 | −0.951391 | −0.475696 | − | 0.879610i | \(-0.657804\pi\) | ||||
−0.475696 | + | 0.879610i | \(0.657804\pi\) | |||||||
\(332\) | 15.1644 | 0.832257 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.17240 | −0.228304 | ||||||||
\(335\) | 4.11316i | 0.224726i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 25.0649i | − 1.36537i | −0.730712 | − | 0.682686i | \(-0.760812\pi\) | ||||
0.730712 | − | 0.682686i | \(-0.239188\pi\) | |||||||
\(338\) | −1.22867 | −0.0668308 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 25.2356i | 1.36859i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 17.9651i | − 0.970024i | ||||||||
\(344\) | − 11.8571i | − 0.639290i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.93765 | 0.211690 | ||||||||
\(347\) | 20.8730 | 1.12052 | 0.560260 | − | 0.828317i | \(-0.310701\pi\) | ||||
0.560260 | + | 0.828317i | \(0.310701\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 18.0205i | − 0.964617i | −0.876002 | − | 0.482308i | \(-0.839798\pi\) | ||||
0.876002 | − | 0.482308i | \(-0.160202\pi\) | |||||||
\(350\) | − 2.43921i | − 0.130381i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 16.2953i | − 0.867313i | −0.901078 | − | 0.433656i | \(-0.857223\pi\) | ||||
0.901078 | − | 0.433656i | \(-0.142777\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.5450 | −0.559669 | ||||||||
\(356\) | 4.00351i | 0.212185i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.31641i | 0.0695746i | ||||||||
\(359\) | −24.7842 | −1.30806 | −0.654031 | − | 0.756468i | \(-0.726923\pi\) | ||||
−0.654031 | + | 0.756468i | \(0.726923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.3475 | 0.807763 | ||||||||
\(362\) | −1.34760 | −0.0708281 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15.0306 | 0.787820 | ||||||||
\(365\) | 5.14076 | 0.269080 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.95366 | 0.467377 | 0.233689 | − | 0.972311i | \(-0.424920\pi\) | ||||
0.233689 | + | 0.972311i | \(0.424920\pi\) | |||||||
\(368\) | 2.95365i | 0.153970i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.40720i | 0.229120i | ||||||||
\(371\) | 28.4280 | 1.47591 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.9007i | 0.875088i | 0.899197 | + | 0.437544i | \(0.144152\pi\) | ||||
−0.899197 | + | 0.437544i | \(0.855848\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.70564i | 0.397388i | ||||||||
\(377\) | 27.2647i | 1.40421i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.7308 | 1.01350 | 0.506751 | − | 0.862092i | \(-0.330846\pi\) | ||||
0.506751 | + | 0.862092i | \(0.330846\pi\) | |||||||
\(380\) | 10.8084 | 0.554460 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 2.76497i | − 0.141468i | ||||||||
\(383\) | 4.99993i | 0.255485i | 0.991807 | + | 0.127742i | \(0.0407730\pi\) | ||||
−0.991807 | + | 0.127742i | \(0.959227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.89808i | 0.198407i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.23338 | −0.164150 | ||||||||
\(389\) | 9.85341i | 0.499588i | 0.968299 | + | 0.249794i | \(0.0803629\pi\) | ||||
−0.968299 | + | 0.249794i | \(0.919637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.64279i | 0.184224i | ||||||||
\(392\) | −0.391956 | −0.0197968 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.83699 | −0.0925461 | ||||||||
\(395\) | −20.8403 | −1.04859 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.0245 | −0.954812 | −0.477406 | − | 0.878683i | \(-0.658423\pi\) | ||||
−0.477406 | + | 0.878683i | \(0.658423\pi\) | |||||||
\(398\) | 2.88494 | 0.144609 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −12.7951 | −0.639757 | ||||||||
\(401\) | − 30.7055i | − 1.53336i | −0.642030 | − | 0.766680i | \(-0.721907\pi\) | ||||
0.642030 | − | 0.766680i | \(-0.278093\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.0959i | 0.851609i | ||||||||
\(404\) | −17.5131 | −0.871310 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − 6.58454i | − 0.326785i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 11.8735i | − 0.587105i | −0.955943 | − | 0.293552i | \(-0.905162\pi\) | ||||
0.955943 | − | 0.293552i | \(-0.0948375\pi\) | |||||||
\(410\) | − 6.25054i | − 0.308692i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 32.0794 | 1.58044 | ||||||||
\(413\) | 0.253675 | 0.0124825 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.8897i | 1.12361i | ||||||||
\(416\) | 8.32388i | 0.408112i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 10.0629i | − 0.491606i | −0.969320 | − | 0.245803i | \(-0.920948\pi\) | ||||
0.969320 | − | 0.245803i | \(-0.0790516\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.25651 | −0.304923 | −0.152462 | − | 0.988309i | \(-0.548720\pi\) | ||||
−0.152462 | + | 0.988309i | \(0.548720\pi\) | |||||||
\(422\) | 0.938148i | 0.0456684i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.4386i | 0.506944i | ||||||||
\(425\) | −15.7804 | −0.765464 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.82952 | −0.282110 | ||||||||
\(428\) | −13.7682 | −0.665512 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.80238 | 0.424489 | ||||||||
\(431\) | −19.6392 | −0.945988 | −0.472994 | − | 0.881066i | \(-0.656827\pi\) | ||||
−0.472994 | + | 0.881066i | \(0.656827\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.2889 | 1.50365 | 0.751825 | − | 0.659362i | \(-0.229174\pi\) | ||||
0.751825 | + | 0.659362i | \(0.229174\pi\) | |||||||
\(434\) | − 4.12873i | − 0.198186i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − 16.6862i | − 0.799123i | ||||||||
\(437\) | 1.56021 | 0.0746349 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 20.1935i | − 0.963782i | −0.876231 | − | 0.481891i | \(-0.839950\pi\) | ||||
0.876231 | − | 0.481891i | \(-0.160050\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.23279i | 0.153768i | ||||||||
\(443\) | − 24.3679i | − 1.15775i | −0.815415 | − | 0.578876i | \(-0.803491\pi\) | ||||
0.815415 | − | 0.578876i | \(-0.196509\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.04301 | −0.286466 | ||||||||
\(446\) | 0.0718468 | 0.00340205 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.6641i | 0.834552i | ||||||||
\(449\) | − 3.30192i | − 0.155827i | −0.996960 | − | 0.0779136i | \(-0.975174\pi\) | ||||
0.996960 | − | 0.0779136i | \(-0.0248258\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 22.0817i | − 1.03863i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.63109 | −0.217348 | ||||||||
\(455\) | 22.6877i | 1.06362i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.6174i | 0.730551i | 0.930899 | + | 0.365276i | \(0.119025\pi\) | ||||
−0.930899 | + | 0.365276i | \(0.880975\pi\) | |||||||
\(458\) | −6.69090 | −0.312645 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.61693 | −0.215265 | ||||||||
\(461\) | 36.5685 | 1.70316 | 0.851582 | − | 0.524221i | \(-0.175644\pi\) | ||||
0.851582 | + | 0.524221i | \(0.175644\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.45531 | 0.207056 | 0.103528 | − | 0.994627i | \(-0.466987\pi\) | ||||
0.103528 | + | 0.994627i | \(0.466987\pi\) | |||||||
\(464\) | −34.5399 | −1.60348 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.74025 | −0.126940 | ||||||||
\(467\) | − 41.6268i | − 1.92626i | −0.269037 | − | 0.963130i | \(-0.586706\pi\) | ||||
0.269037 | − | 0.963130i | \(-0.413294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.82767i | 0.176745i | ||||||||
\(470\) | −5.72047 | −0.263866 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.0931482i | 0.00428749i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.75877i | 0.310114i | ||||||||
\(476\) | 23.4840i | 1.07639i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.88311 | 0.0861316 | ||||||||
\(479\) | 3.52150 | 0.160902 | 0.0804508 | − | 0.996759i | \(-0.474364\pi\) | ||||
0.0804508 | + | 0.996759i | \(0.474364\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 16.9823i | − 0.774328i | ||||||||
\(482\) | − 0.676990i | − 0.0308360i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4.88056i | − 0.221615i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.9004 | 1.44554 | 0.722772 | − | 0.691087i | \(-0.242868\pi\) | ||||
0.722772 | + | 0.691087i | \(0.242868\pi\) | |||||||
\(488\) | − 2.14057i | − 0.0968990i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − 0.290979i | − 0.0131451i | ||||||||
\(491\) | −24.4192 | −1.10202 | −0.551012 | − | 0.834497i | \(-0.685758\pi\) | ||||
−0.551012 | + | 0.834497i | \(0.685758\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.5987 | −1.91855 | ||||||||
\(494\) | 1.38461 | 0.0622964 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.6577 | −0.972460 | ||||||||
\(497\) | −9.81306 | −0.440176 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.2692 | −1.04167 | −0.520836 | − | 0.853657i | \(-0.674380\pi\) | ||||
−0.520836 | + | 0.853657i | \(0.674380\pi\) | |||||||
\(500\) | 8.27680i | 0.370150i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.15559i | 0.274737i | ||||||||
\(503\) | −36.5209 | −1.62839 | −0.814193 | − | 0.580595i | \(-0.802820\pi\) | ||||
−0.814193 | + | 0.580595i | \(0.802820\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 26.4348i | − 1.17633i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 5.58064i | − 0.247601i | ||||||||
\(509\) | 24.8510i | 1.10150i | 0.834670 | + | 0.550751i | \(0.185659\pi\) | ||||
−0.834670 | + | 0.550751i | \(0.814341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.78395 | 0.211629 | ||||||||
\(512\) | −17.7693 | −0.785300 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.25060i | 0.187486i | ||||||||
\(515\) | 48.4216i | 2.13371i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.10130i | 0.180201i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.33080 | −0.365330 | ||||||||
\(521\) | 9.74005i | 0.426719i | 0.976974 | + | 0.213360i | \(0.0684406\pi\) | ||||
−0.976974 | + | 0.213360i | \(0.931559\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 33.2649i | − 1.45457i | −0.686335 | − | 0.727285i | \(-0.740782\pi\) | ||||
0.686335 | − | 0.727285i | \(-0.259218\pi\) | |||||||
\(524\) | −4.06786 | −0.177705 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.76876 | 0.120724 | ||||||||
\(527\) | −26.7108 | −1.16354 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.3335 | 0.971023 | ||||||||
\(530\) | −7.74936 | −0.336611 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 10.0582 | 0.436079 | ||||||||
\(533\) | 24.0853i | 1.04325i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 20.7822i | − 0.898492i | ||||||||
\(536\) | −1.40550 | −0.0607084 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 3.97933i | − 0.171561i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 11.6552i | − 0.501096i | −0.968104 | − | 0.250548i | \(-0.919389\pi\) | ||||
0.968104 | − | 0.250548i | \(-0.0806108\pi\) | |||||||
\(542\) | − 0.736945i | − 0.0316545i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.0053 | −0.557598 | ||||||||
\(545\) | 25.1866 | 1.07888 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.812785i | 0.0347522i | 0.999849 | + | 0.0173761i | \(0.00553126\pi\) | ||||
−0.999849 | + | 0.0173761i | \(0.994469\pi\) | |||||||
\(548\) | 9.82156i | 0.419556i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 18.2450i | 0.777264i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.3938 | −0.824710 | ||||||||
\(554\) | − 5.35635i | − 0.227569i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 33.8428i | 1.43525i | ||||||||
\(557\) | −6.95247 | −0.294586 | −0.147293 | − | 0.989093i | \(-0.547056\pi\) | ||||
−0.147293 | + | 0.989093i | \(0.547056\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.9184 | −1.43459 | ||||||||
\(560\) | −28.7416 | −1.21455 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.783948 | 0.0330689 | ||||||||
\(563\) | −28.7576 | −1.21199 | −0.605994 | − | 0.795469i | \(-0.707224\pi\) | ||||
−0.605994 | + | 0.795469i | \(0.707224\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.3307 | 1.40223 | ||||||||
\(566\) | 5.68859i | 0.239109i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 3.60330i | − 0.151191i | ||||||||
\(569\) | 10.4489 | 0.438042 | 0.219021 | − | 0.975720i | \(-0.429714\pi\) | ||||
0.219021 | + | 0.975720i | \(0.429714\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.2530i | 0.889409i | 0.895677 | + | 0.444704i | \(0.146691\pi\) | ||||
−0.895677 | + | 0.444704i | \(0.853309\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − 5.81669i | − 0.242784i | ||||||||
\(575\) | − 2.88708i | − 0.120400i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.6803 | 0.652779 | 0.326390 | − | 0.945235i | \(-0.394168\pi\) | ||||
0.326390 | + | 0.945235i | \(0.394168\pi\) | |||||||
\(578\) | −0.738466 | −0.0307162 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 53.9902i | − 2.24182i | ||||||||
\(581\) | 21.3009i | 0.883711i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.75664i | 0.0726903i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.26146 | −0.217349 | ||||||||
\(587\) | − 20.1556i | − 0.831912i | −0.909385 | − | 0.415956i | \(-0.863447\pi\) | ||||
0.909385 | − | 0.415956i | \(-0.136553\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.4403i | 0.471387i | ||||||||
\(590\) | −0.0691509 | −0.00284690 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 21.5138 | 0.884213 | ||||||||
\(593\) | −40.5694 | −1.66599 | −0.832993 | − | 0.553284i | \(-0.813374\pi\) | ||||
−0.832993 | + | 0.553284i | \(0.813374\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −35.4475 | −1.45320 | ||||||||
\(596\) | 10.9491 | 0.448491 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.591450 | −0.0241862 | ||||||||
\(599\) | − 10.9375i | − 0.446894i | −0.974716 | − | 0.223447i | \(-0.928269\pi\) | ||||
0.974716 | − | 0.223447i | \(-0.0717309\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 16.3562i | − 0.667182i | −0.942718 | − | 0.333591i | \(-0.891740\pi\) | ||||
0.942718 | − | 0.333591i | \(-0.108260\pi\) | |||||||
\(602\) | 8.19142 | 0.333857 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 17.7605i | − 0.722665i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 23.8646i | − 0.968633i | −0.874893 | − | 0.484317i | \(-0.839068\pi\) | ||||
0.874893 | − | 0.484317i | \(-0.160932\pi\) | |||||||
\(608\) | 5.57017i | 0.225900i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.58910 | 0.0643410 | ||||||||
\(611\) | 22.0428 | 0.891756 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.0485285i | 0.00196005i | 1.00000 | 0.000980023i | \(0.000311951\pi\) | |||||
−1.00000 | 0.000980023i | \(0.999688\pi\) | ||||||||
\(614\) | 3.80708i | 0.153641i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 8.24561i | − 0.331956i | −0.986129 | − | 0.165978i | \(-0.946922\pi\) | ||||
0.986129 | − | 0.165978i | \(-0.0530780\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.73927 | −0.0699072 | −0.0349536 | − | 0.999389i | \(-0.511128\pi\) | ||||
−0.0349536 | + | 0.999389i | \(0.511128\pi\) | |||||||
\(620\) | − 33.8537i | − 1.35960i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.522321i | 0.0209432i | ||||||||
\(623\) | −5.62357 | −0.225304 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.1757 | −1.20703 | ||||||||
\(626\) | 6.30955 | 0.252180 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.91094 | 0.235872 | ||||||||
\(629\) | 26.5334 | 1.05795 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.3475 | −1.04888 | −0.524439 | − | 0.851448i | \(-0.675725\pi\) | ||||
−0.524439 | + | 0.851448i | \(0.675725\pi\) | |||||||
\(632\) | − 7.12131i | − 0.283270i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − 0.109772i | − 0.00435962i | ||||||||
\(635\) | 8.42358 | 0.334280 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.12123i | 0.0444249i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 21.8463i | − 0.863550i | ||||||||
\(641\) | 8.69577i | 0.343462i | 0.985144 | + | 0.171731i | \(0.0549361\pi\) | ||||
−0.985144 | + | 0.171731i | \(0.945064\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.6159 | −0.852450 | −0.426225 | − | 0.904617i | \(-0.640157\pi\) | ||||
−0.426225 | + | 0.904617i | \(0.640157\pi\) | |||||||
\(644\) | −4.29647 | −0.169305 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.16332i | 0.0851147i | ||||||||
\(647\) | 29.3673i | 1.15455i | 0.816551 | + | 0.577273i | \(0.195883\pi\) | ||||
−0.816551 | + | 0.577273i | \(0.804117\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − 2.56214i | − 0.100495i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.3003 | −0.599207 | ||||||||
\(653\) | − 23.6935i | − 0.927199i | −0.886045 | − | 0.463599i | \(-0.846558\pi\) | ||||
0.886045 | − | 0.463599i | \(-0.153442\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 6.14016i | − 0.239916i | ||||||||
\(656\) | −30.5121 | −1.19130 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.32342 | −0.207528 | ||||||||
\(659\) | −34.5941 | −1.34759 | −0.673797 | − | 0.738916i | \(-0.735338\pi\) | ||||
−0.673797 | + | 0.738916i | \(0.735338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.4913 | 1.38045 | 0.690225 | − | 0.723595i | \(-0.257512\pi\) | ||||
0.690225 | + | 0.723595i | \(0.257512\pi\) | |||||||
\(662\) | 4.39088 | 0.170656 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.82158 | −0.303536 | ||||||||
\(665\) | 15.1822i | 0.588739i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 7.79356i | − 0.301768i | ||||||||
\(668\) | −31.8372 | −1.23182 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 1.04341i | − 0.0403104i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 20.9013i | − 0.805684i | −0.915270 | − | 0.402842i | \(-0.868022\pi\) | ||||
0.915270 | − | 0.402842i | \(-0.131978\pi\) | |||||||
\(674\) | 6.35835i | 0.244914i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.37527 | −0.360587 | ||||||||
\(677\) | 24.2380 | 0.931543 | 0.465772 | − | 0.884905i | \(-0.345777\pi\) | ||||
0.465772 | + | 0.884905i | \(0.345777\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 4.54181i | − 0.174299i | ||||||||
\(680\) | − 13.0161i | − 0.499145i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.6311i | 0.674636i | 0.941391 | + | 0.337318i | \(0.109520\pi\) | ||||
−0.941391 | + | 0.337318i | \(0.890480\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.8250 | −0.566433 | ||||||||
\(686\) | 4.55730i | 0.173999i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 42.9690i | − 1.63818i | ||||||||
\(689\) | 29.8608 | 1.13760 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.1363 | 1.10840 | 0.554199 | − | 0.832384i | \(-0.313024\pi\) | ||||
0.554199 | + | 0.832384i | \(0.313024\pi\) | |||||||
\(692\) | 30.0459 | 1.14218 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.29496 | −0.200994 | ||||||||
\(695\) | −51.0833 | −1.93770 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.6311 | −1.42538 | ||||||||
\(698\) | 4.57136i | 0.173029i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − 18.6122i | − 0.703474i | ||||||||
\(701\) | 14.7015 | 0.555268 | 0.277634 | − | 0.960687i | \(-0.410450\pi\) | ||||
0.277634 | + | 0.960687i | \(0.410450\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 11.3642i | − 0.428611i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.13372i | 0.155575i | ||||||||
\(707\) | − 24.6000i | − 0.925179i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.7824 | 0.404940 | 0.202470 | − | 0.979288i | \(-0.435103\pi\) | ||||
0.202470 | + | 0.979288i | \(0.435103\pi\) | |||||||
\(710\) | 2.67500 | 0.100391 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 2.06495i | − 0.0773871i | ||||||||
\(713\) | − 4.88683i | − 0.183013i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.0448i | 0.375391i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.28715 | 0.234634 | ||||||||
\(719\) | 31.7500i | 1.18407i | 0.805911 | + | 0.592037i | \(0.201676\pi\) | ||||
−0.805911 | + | 0.592037i | \(0.798324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.0607i | 1.67815i | ||||||||
\(722\) | −3.89328 | −0.144893 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.2827 | −0.382154 | ||||||||
\(725\) | 33.7614 | 1.25387 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.6418 | 0.876828 | 0.438414 | − | 0.898773i | \(-0.355540\pi\) | ||||
0.438414 | + | 0.898773i | \(0.355540\pi\) | |||||||
\(728\) | −7.75257 | −0.287329 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.30409 | −0.0482664 | ||||||||
\(731\) | − 52.9944i | − 1.96007i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 16.4244i | − 0.606651i | −0.952887 | − | 0.303325i | \(-0.901903\pi\) | ||||
0.952887 | − | 0.303325i | \(-0.0980969\pi\) | |||||||
\(734\) | −2.27132 | −0.0838361 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − 2.37936i | − 0.0877043i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.8449i | 1.28179i | 0.767629 | + | 0.640895i | \(0.221437\pi\) | ||||
−0.767629 | + | 0.640895i | \(0.778563\pi\) | |||||||
\(740\) | 33.6288i | 1.23622i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.21149 | −0.264742 | ||||||||
\(743\) | −52.7926 | −1.93677 | −0.968386 | − | 0.249458i | \(-0.919748\pi\) | ||||
−0.968386 | + | 0.249458i | \(0.919748\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.5269i | 0.605497i | ||||||||
\(746\) | − 4.28730i | − 0.156969i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 19.3397i | − 0.706657i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.3777 | 1.87480 | 0.937400 | − | 0.348255i | \(-0.113226\pi\) | ||||
0.937400 | + | 0.348255i | \(0.113226\pi\) | |||||||
\(752\) | 27.9246i | 1.01830i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 6.91639i | − 0.251880i | ||||||||
\(755\) | 26.8083 | 0.975652 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.06878 | −0.256919 | −0.128460 | − | 0.991715i | \(-0.541003\pi\) | ||||
−0.128460 | + | 0.991715i | \(0.541003\pi\) | |||||||
\(758\) | −5.00521 | −0.181797 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.57481 | −0.202219 | ||||||||
\(761\) | 29.1327 | 1.05606 | 0.528030 | − | 0.849226i | \(-0.322931\pi\) | ||||
0.528030 | + | 0.849226i | \(0.322931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.4384 | 0.848528 | ||||||||
\(764\) | − 21.0979i | − 0.763294i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 1.26836i | − 0.0458277i | ||||||||
\(767\) | 0.266460 | 0.00962132 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.2408i | 1.59536i | 0.603079 | + | 0.797682i | \(0.293940\pi\) | ||||
−0.603079 | + | 0.797682i | \(0.706060\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 29.7440i | 1.07051i | ||||||||
\(773\) | − 40.0382i | − 1.44007i | −0.693936 | − | 0.720037i | \(-0.744125\pi\) | ||||
0.693936 | − | 0.720037i | \(-0.255875\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.1696 | 0.760434 | ||||||||
\(776\) | 1.66773 | 0.0598679 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 2.49957i | − 0.0896139i | ||||||||
\(779\) | 16.1174i | 0.577466i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 0.924086i | − 0.0330453i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.42042 | −0.0507292 | ||||||||
\(785\) | 8.92215i | 0.318445i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.3641i | 1.01107i | 0.862806 | + | 0.505535i | \(0.168705\pi\) | ||||
−0.862806 | + | 0.505535i | \(0.831295\pi\) | |||||||
\(788\) | −14.0170 | −0.499334 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.28668 | 0.188092 | ||||||||
\(791\) | 31.0173 | 1.10285 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.12332 | −0.217446 | ||||||||
\(794\) | 4.82605 | 0.171270 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.0133 | 0.780241 | ||||||||
\(797\) | 14.9437i | 0.529334i | 0.964340 | + | 0.264667i | \(0.0852621\pi\) | ||||
−0.964340 | + | 0.264667i | \(0.914738\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.4398i | 1.21839i | ||||||||
\(800\) | 10.3073 | 0.364418 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.78923i | 0.275047i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 6.48522i | − 0.228574i | ||||||||
\(806\) | − 4.33682i | − 0.152758i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.03299 | 0.317779 | ||||||||
\(809\) | 29.7759 | 1.04687 | 0.523433 | − | 0.852067i | \(-0.324651\pi\) | ||||
0.523433 | + | 0.852067i | \(0.324651\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.1463i | 1.55019i | 0.631846 | + | 0.775094i | \(0.282297\pi\) | ||||
−0.631846 | + | 0.775094i | \(0.717703\pi\) | |||||||
\(812\) | − 50.2428i | − 1.76318i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 23.0948i | − 0.808975i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.6975 | −0.794085 | ||||||||
\(818\) | 3.01200i | 0.105312i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − 47.6942i | − 1.66555i | ||||||||
\(821\) | 4.00495 | 0.139774 | 0.0698868 | − | 0.997555i | \(-0.477736\pi\) | ||||
0.0698868 | + | 0.997555i | \(0.477736\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.1823 | 1.47038 | 0.735191 | − | 0.677860i | \(-0.237093\pi\) | ||||
0.735191 | + | 0.677860i | \(0.237093\pi\) | |||||||
\(824\) | −16.5460 | −0.576409 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.0643512 | −0.00223906 | ||||||||
\(827\) | −26.5981 | −0.924907 | −0.462454 | − | 0.886643i | \(-0.653031\pi\) | ||||
−0.462454 | + | 0.886643i | \(0.653031\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.2316 | 0.424819 | 0.212410 | − | 0.977181i | \(-0.431869\pi\) | ||||
0.212410 | + | 0.977181i | \(0.431869\pi\) | |||||||
\(830\) | − 5.80655i | − 0.201548i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 18.5544i | 0.643257i | ||||||||
\(833\) | −1.75182 | −0.0606971 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 48.0560i | − 1.66305i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.55271i | 0.0881820i | ||||||||
\(839\) | 9.64647i | 0.333033i | 0.986039 | + | 0.166517i | \(0.0532519\pi\) | ||||
−0.986039 | + | 0.166517i | \(0.946748\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62.1376 | 2.14268 | ||||||||
\(842\) | 1.58712 | 0.0546958 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.15846i | 0.246405i | ||||||||
\(845\) | − 14.1513i | − 0.486820i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 37.8287i | 1.29904i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.00311 | 0.137306 | ||||||||
\(851\) | 4.85436i | 0.166405i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.7386i | 0.401921i | 0.979599 | + | 0.200960i | \(0.0644063\pi\) | ||||
−0.979599 | + | 0.200960i | \(0.935594\pi\) | |||||||
\(854\) | 1.47881 | 0.0506037 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.10143 | 0.242722 | ||||||||
\(857\) | 48.7738 | 1.66608 | 0.833041 | − | 0.553212i | \(-0.186598\pi\) | ||||
0.833041 | + | 0.553212i | \(0.186598\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.0880 | −1.06071 | −0.530355 | − | 0.847776i | \(-0.677941\pi\) | ||||
−0.530355 | + | 0.847776i | \(0.677941\pi\) | |||||||
\(860\) | 67.1659 | 2.29034 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.98199 | 0.169687 | ||||||||
\(863\) | 52.1380i | 1.77480i | 0.461002 | + | 0.887399i | \(0.347490\pi\) | ||||
−0.461002 | + | 0.887399i | \(0.652510\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 45.3522i | 1.54202i | ||||||||
\(866\) | −7.93723 | −0.269718 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 31.5040i | − 1.06931i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.02058i | 0.136232i | ||||||||
\(872\) | 8.60646i | 0.291452i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.395786 | −0.0133877 | ||||||||
\(875\) | −11.6261 | −0.393034 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.9878i | 0.573637i | 0.957985 | + | 0.286819i | \(0.0925977\pi\) | ||||
−0.957985 | + | 0.286819i | \(0.907402\pi\) | |||||||
\(878\) | 5.12259i | 0.172879i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 50.3115i | − 1.69504i | −0.530765 | − | 0.847519i | \(-0.678095\pi\) | ||||
0.530765 | − | 0.847519i | \(-0.321905\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.3693 | 0.483567 | 0.241783 | − | 0.970330i | \(-0.422268\pi\) | ||||
0.241783 | + | 0.970330i | \(0.422268\pi\) | |||||||
\(884\) | 24.6676i | 0.829660i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.18153i | 0.207673i | ||||||||
\(887\) | −41.3003 | −1.38673 | −0.693365 | − | 0.720587i | \(-0.743873\pi\) | ||||
−0.693365 | + | 0.720587i | \(0.743873\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.83891 | 0.262909 | ||||||||
\(890\) | 1.53296 | 0.0513851 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.548221 | 0.0183558 | ||||||||
\(893\) | 14.7506 | 0.493610 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.1619 | −0.506807 | ||||||||
\(896\) | − 20.3299i | − 0.679176i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.837616i | 0.0279516i | ||||||||
\(899\) | 57.1464 | 1.90594 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.6547i | 1.55429i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.3894i | 0.378805i | ||||||||
\(905\) | − 15.5210i | − 0.515937i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.1167 | −0.867190 | −0.433595 | − | 0.901108i | \(-0.642755\pi\) | ||||
−0.433595 | + | 0.901108i | \(0.642755\pi\) | |||||||
\(908\) | −35.3371 | −1.17270 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | − 5.75531i | − 0.190787i | ||||||||
\(911\) | − 45.4127i | − 1.50459i | −0.658826 | − | 0.752296i | \(-0.728946\pi\) | ||||
0.658826 | − | 0.752296i | \(-0.271054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − 3.96175i | − 0.131043i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51.0543 | −1.68688 | ||||||||
\(917\) | − 5.71398i | − 0.188692i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.8566i | 0.918905i | 0.888202 | + | 0.459453i | \(0.151954\pi\) | ||||
−0.888202 | + | 0.459453i | \(0.848046\pi\) | |||||||
\(920\) | 2.38134 | 0.0785104 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.27652 | −0.305506 | ||||||||
\(923\) | −10.3076 | −0.339280 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.0289 | −0.691427 | ||||||||
\(926\) | −1.13020 | −0.0371408 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 27.8241 | 0.913372 | ||||||||
\(929\) | 49.7545i | 1.63239i | 0.577774 | + | 0.816197i | \(0.303921\pi\) | ||||
−0.577774 | + | 0.816197i | \(0.696079\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.750306i | 0.0245903i | ||||||||
\(932\) | −20.9093 | −0.684905 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.5597i | 0.345524i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.4059i | 0.666633i | 0.942815 | + | 0.333316i | \(0.108168\pi\) | ||||
−0.942815 | + | 0.333316i | \(0.891832\pi\) | |||||||
\(938\) | − 0.970986i | − 0.0317038i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −43.6496 | −1.42369 | ||||||||
\(941\) | 17.5434 | 0.571898 | 0.285949 | − | 0.958245i | \(-0.407691\pi\) | ||||
0.285949 | + | 0.958245i | \(0.407691\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 6.88472i | − 0.224197i | ||||||||
\(944\) | 0.337561i | 0.0109867i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.0672i | 1.52948i | 0.644340 | + | 0.764739i | \(0.277132\pi\) | ||||
−0.644340 | + | 0.764739i | \(0.722868\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.02505 | 0.163120 | ||||||||
\(950\) | − 1.71453i | − 0.0556268i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 12.1127i | − 0.392574i | ||||||||
\(953\) | 51.6298 | 1.67245 | 0.836227 | − | 0.548384i | \(-0.184757\pi\) | ||||
0.836227 | + | 0.548384i | \(0.184757\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.8457 | 1.03050 | ||||||||
\(956\) | 14.3689 | 0.464725 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.893318 | −0.0288618 | ||||||||
\(959\) | −13.7960 | −0.445495 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.83277 | 0.155896 | ||||||||
\(962\) | 4.30800i | 0.138896i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 5.16572i | − 0.166376i | ||||||||
\(965\) | −44.8965 | −1.44527 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.6964i | 1.08360i | 0.840506 | + | 0.541802i | \(0.182258\pi\) | ||||
−0.840506 | + | 0.541802i | \(0.817742\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.23808i | 0.0397523i | ||||||||
\(971\) | − 55.8818i | − 1.79333i | −0.442708 | − | 0.896666i | \(-0.645982\pi\) | ||||
0.442708 | − | 0.896666i | \(-0.354018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −47.5376 | −1.52399 | ||||||||
\(974\) | −8.09233 | −0.259295 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 7.75724i | − 0.248303i | ||||||||
\(977\) | − 20.6593i | − 0.660949i | −0.943815 | − | 0.330475i | \(-0.892791\pi\) | ||||
0.943815 | − | 0.330475i | \(-0.107209\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − 2.22029i | − 0.0709245i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.19455 | 0.197676 | ||||||||
\(983\) | − 50.1274i | − 1.59882i | −0.600789 | − | 0.799408i | \(-0.705147\pi\) | ||||
0.600789 | − | 0.799408i | \(-0.294853\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 21.1577i | − 0.674139i | ||||||||
\(986\) | 10.8062 | 0.344141 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 10.5651 | 0.336121 | ||||||||
\(989\) | 9.69548 | 0.308298 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.3068 | 1.43922 | 0.719609 | − | 0.694379i | \(-0.244321\pi\) | ||||
0.719609 | + | 0.694379i | \(0.244321\pi\) | |||||||
\(992\) | 17.4467 | 0.553933 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.48933 | 0.0789568 | ||||||||
\(995\) | 33.2276i | 1.05338i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 10.2799i | − 0.325567i | −0.986662 | − | 0.162784i | \(-0.947953\pi\) | ||||
0.986662 | − | 0.162784i | \(-0.0520473\pi\) | |||||||
\(998\) | 5.90282 | 0.186850 | ||||||||
\(999\) | 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 | 1089.2.d.g.1088.7 | 16 | ||
3.2 | odd | 2 | inner | 1089.2.d.g.1088.10 | 16 | ||
11.6 | odd | 10 | 99.2.j.a.8.2 | ✓ | 16 | ||
11.9 | even | 5 | 99.2.j.a.62.3 | yes | 16 | ||
11.10 | odd | 2 | inner | 1089.2.d.g.1088.9 | 16 | ||
33.17 | even | 10 | 99.2.j.a.8.3 | yes | 16 | ||
33.20 | odd | 10 | 99.2.j.a.62.2 | yes | 16 | ||
33.32 | even | 2 | inner | 1089.2.d.g.1088.8 | 16 | ||
44.31 | odd | 10 | 1584.2.cd.c.161.3 | 16 | |||
44.39 | even | 10 | 1584.2.cd.c.305.2 | 16 | |||
99.20 | odd | 30 | 891.2.u.c.458.2 | 32 | |||
99.31 | even | 15 | 891.2.u.c.755.2 | 32 | |||
99.50 | even | 30 | 891.2.u.c.107.3 | 32 | |||
99.61 | odd | 30 | 891.2.u.c.701.3 | 32 | |||
99.83 | even | 30 | 891.2.u.c.701.2 | 32 | |||
99.86 | odd | 30 | 891.2.u.c.755.3 | 32 | |||
99.94 | odd | 30 | 891.2.u.c.107.2 | 32 | |||
99.97 | even | 15 | 891.2.u.c.458.3 | 32 | |||
132.83 | odd | 10 | 1584.2.cd.c.305.3 | 16 | |||
132.119 | even | 10 | 1584.2.cd.c.161.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.j.a.8.2 | ✓ | 16 | 11.6 | odd | 10 | ||
99.2.j.a.8.3 | yes | 16 | 33.17 | even | 10 | ||
99.2.j.a.62.2 | yes | 16 | 33.20 | odd | 10 | ||
99.2.j.a.62.3 | yes | 16 | 11.9 | even | 5 | ||
891.2.u.c.107.2 | 32 | 99.94 | odd | 30 | |||
891.2.u.c.107.3 | 32 | 99.50 | even | 30 | |||
891.2.u.c.458.2 | 32 | 99.20 | odd | 30 | |||
891.2.u.c.458.3 | 32 | 99.97 | even | 15 | |||
891.2.u.c.701.2 | 32 | 99.83 | even | 30 | |||
891.2.u.c.701.3 | 32 | 99.61 | odd | 30 | |||
891.2.u.c.755.2 | 32 | 99.31 | even | 15 | |||
891.2.u.c.755.3 | 32 | 99.86 | odd | 30 | |||
1089.2.d.g.1088.7 | 16 | 1.1 | even | 1 | trivial | ||
1089.2.d.g.1088.8 | 16 | 33.32 | even | 2 | inner | ||
1089.2.d.g.1088.9 | 16 | 11.10 | odd | 2 | inner | ||
1089.2.d.g.1088.10 | 16 | 3.2 | odd | 2 | inner | ||
1584.2.cd.c.161.2 | 16 | 132.119 | even | 10 | |||
1584.2.cd.c.161.3 | 16 | 44.31 | odd | 10 | |||
1584.2.cd.c.305.2 | 16 | 44.39 | even | 10 | |||
1584.2.cd.c.305.3 | 16 | 132.83 | odd | 10 |