Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7098,2,Mod(1,7098)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7098, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7098.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7098.a (trivial) |
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: | yes |
Analytic conductor: | \(56.6778153547\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7098.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.56155 | −1.14556 | −0.572781 | − | 0.819709i | \(-0.694135\pi\) | ||||
−0.572781 | + | 0.819709i | \(0.694135\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.56155 | −0.810034 | ||||||||
\(11\) | 1.56155 | 0.470826 | 0.235413 | − | 0.971895i | \(-0.424356\pi\) | ||||
0.235413 | + | 0.971895i | \(0.424356\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.56155 | 0.661390 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −8.12311 | −1.97014 | −0.985071 | − | 0.172147i | \(-0.944930\pi\) | ||||
−0.985071 | + | 0.172147i | \(0.944930\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.56155 | 0.358245 | 0.179122 | − | 0.983827i | \(-0.442674\pi\) | ||||
0.179122 | + | 0.983827i | \(0.442674\pi\) | |||||||
\(20\) | −2.56155 | −0.572781 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 1.56155 | 0.332924 | ||||||||
\(23\) | 7.12311 | 1.48527 | 0.742635 | − | 0.669696i | \(-0.233576\pi\) | ||||
0.742635 | + | 0.669696i | \(0.233576\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.56155 | 0.312311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 2.12311 | 0.394251 | 0.197125 | − | 0.980378i | \(-0.436839\pi\) | ||||
0.197125 | + | 0.980378i | \(0.436839\pi\) | |||||||
\(30\) | 2.56155 | 0.467673 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.56155 | −0.271831 | ||||||||
\(34\) | −8.12311 | −1.39310 | ||||||||
\(35\) | −2.56155 | −0.432981 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.56155 | −1.07871 | −0.539356 | − | 0.842078i | \(-0.681332\pi\) | ||||
−0.539356 | + | 0.842078i | \(0.681332\pi\) | |||||||
\(38\) | 1.56155 | 0.253317 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.56155 | −0.405017 | ||||||||
\(41\) | 5.24621 | 0.819321 | 0.409660 | − | 0.912238i | \(-0.365647\pi\) | ||||
0.409660 | + | 0.912238i | \(0.365647\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 1.56155 | 0.235413 | ||||||||
\(45\) | −2.56155 | −0.381854 | ||||||||
\(46\) | 7.12311 | 1.05024 | ||||||||
\(47\) | −12.6847 | −1.85025 | −0.925124 | − | 0.379666i | \(-0.876039\pi\) | ||||
−0.925124 | + | 0.379666i | \(0.876039\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.56155 | 0.220837 | ||||||||
\(51\) | 8.12311 | 1.13746 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.00000 | 0.961524 | 0.480762 | − | 0.876851i | \(-0.340360\pi\) | ||||
0.480762 | + | 0.876851i | \(0.340360\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −1.56155 | −0.206833 | ||||||||
\(58\) | 2.12311 | 0.278777 | ||||||||
\(59\) | −3.12311 | −0.406594 | −0.203297 | − | 0.979117i | \(-0.565166\pi\) | ||||
−0.203297 | + | 0.979117i | \(0.565166\pi\) | |||||||
\(60\) | 2.56155 | 0.330695 | ||||||||
\(61\) | 5.24621 | 0.671709 | 0.335854 | − | 0.941914i | \(-0.390975\pi\) | ||||
0.335854 | + | 0.941914i | \(0.390975\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.56155 | −0.192214 | ||||||||
\(67\) | 0.876894 | 0.107130 | 0.0535648 | − | 0.998564i | \(-0.482942\pi\) | ||||
0.0535648 | + | 0.998564i | \(0.482942\pi\) | |||||||
\(68\) | −8.12311 | −0.985071 | ||||||||
\(69\) | −7.12311 | −0.857521 | ||||||||
\(70\) | −2.56155 | −0.306164 | ||||||||
\(71\) | 13.3693 | 1.58665 | 0.793323 | − | 0.608801i | \(-0.208349\pi\) | ||||
0.793323 | + | 0.608801i | \(0.208349\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −6.56155 | −0.767972 | −0.383986 | − | 0.923339i | \(-0.625449\pi\) | ||||
−0.383986 | + | 0.923339i | \(0.625449\pi\) | |||||||
\(74\) | −6.56155 | −0.762765 | ||||||||
\(75\) | −1.56155 | −0.180313 | ||||||||
\(76\) | 1.56155 | 0.179122 | ||||||||
\(77\) | 1.56155 | 0.177955 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.43845 | −0.274347 | −0.137173 | − | 0.990547i | \(-0.543802\pi\) | ||||
−0.137173 | + | 0.990547i | \(0.543802\pi\) | |||||||
\(80\) | −2.56155 | −0.286390 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.24621 | 0.579347 | ||||||||
\(83\) | 3.12311 | 0.342805 | 0.171403 | − | 0.985201i | \(-0.445170\pi\) | ||||
0.171403 | + | 0.985201i | \(0.445170\pi\) | |||||||
\(84\) | −1.00000 | −0.109109 | ||||||||
\(85\) | 20.8078 | 2.25692 | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | −2.12311 | −0.227621 | ||||||||
\(88\) | 1.56155 | 0.166462 | ||||||||
\(89\) | 7.56155 | 0.801523 | 0.400761 | − | 0.916182i | \(-0.368746\pi\) | ||||
0.400761 | + | 0.916182i | \(0.368746\pi\) | |||||||
\(90\) | −2.56155 | −0.270011 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.12311 | 0.742635 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.6847 | −1.30832 | ||||||||
\(95\) | −4.00000 | −0.410391 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −9.12311 | −0.926311 | −0.463156 | − | 0.886277i | \(-0.653283\pi\) | ||||
−0.463156 | + | 0.886277i | \(0.653283\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 1.56155 | 0.156942 | ||||||||
\(100\) | 1.56155 | 0.156155 | ||||||||
\(101\) | 14.8078 | 1.47343 | 0.736714 | − | 0.676205i | \(-0.236377\pi\) | ||||
0.736714 | + | 0.676205i | \(0.236377\pi\) | |||||||
\(102\) | 8.12311 | 0.804307 | ||||||||
\(103\) | −10.2462 | −1.00959 | −0.504795 | − | 0.863239i | \(-0.668432\pi\) | ||||
−0.504795 | + | 0.863239i | \(0.668432\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.56155 | 0.249982 | ||||||||
\(106\) | 7.00000 | 0.679900 | ||||||||
\(107\) | −14.9309 | −1.44342 | −0.721711 | − | 0.692195i | \(-0.756644\pi\) | ||||
−0.721711 | + | 0.692195i | \(0.756644\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 4.24621 | 0.406713 | 0.203357 | − | 0.979105i | \(-0.434815\pi\) | ||||
0.203357 | + | 0.979105i | \(0.434815\pi\) | |||||||
\(110\) | −4.00000 | −0.381385 | ||||||||
\(111\) | 6.56155 | 0.622795 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −2.56155 | −0.240971 | −0.120485 | − | 0.992715i | \(-0.538445\pi\) | ||||
−0.120485 | + | 0.992715i | \(0.538445\pi\) | |||||||
\(114\) | −1.56155 | −0.146253 | ||||||||
\(115\) | −18.2462 | −1.70147 | ||||||||
\(116\) | 2.12311 | 0.197125 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.12311 | −0.287505 | ||||||||
\(119\) | −8.12311 | −0.744644 | ||||||||
\(120\) | 2.56155 | 0.233837 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | 5.24621 | 0.474970 | ||||||||
\(123\) | −5.24621 | −0.473035 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.80776 | 0.787790 | ||||||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | −20.4924 | −1.81841 | −0.909204 | − | 0.416350i | \(-0.863309\pi\) | ||||
−0.909204 | + | 0.416350i | \(0.863309\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.24621 | −0.196252 | −0.0981262 | − | 0.995174i | \(-0.531285\pi\) | ||||
−0.0981262 | + | 0.995174i | \(0.531285\pi\) | |||||||
\(132\) | −1.56155 | −0.135916 | ||||||||
\(133\) | 1.56155 | 0.135404 | ||||||||
\(134\) | 0.876894 | 0.0757521 | ||||||||
\(135\) | 2.56155 | 0.220463 | ||||||||
\(136\) | −8.12311 | −0.696551 | ||||||||
\(137\) | 16.5616 | 1.41495 | 0.707474 | − | 0.706739i | \(-0.249834\pi\) | ||||
0.707474 | + | 0.706739i | \(0.249834\pi\) | |||||||
\(138\) | −7.12311 | −0.606359 | ||||||||
\(139\) | −9.56155 | −0.811000 | −0.405500 | − | 0.914095i | \(-0.632903\pi\) | ||||
−0.405500 | + | 0.914095i | \(0.632903\pi\) | |||||||
\(140\) | −2.56155 | −0.216491 | ||||||||
\(141\) | 12.6847 | 1.06824 | ||||||||
\(142\) | 13.3693 | 1.12193 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −5.43845 | −0.451638 | ||||||||
\(146\) | −6.56155 | −0.543038 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −6.56155 | −0.539356 | ||||||||
\(149\) | −11.4384 | −0.937074 | −0.468537 | − | 0.883444i | \(-0.655219\pi\) | ||||
−0.468537 | + | 0.883444i | \(0.655219\pi\) | |||||||
\(150\) | −1.56155 | −0.127500 | ||||||||
\(151\) | 6.93087 | 0.564026 | 0.282013 | − | 0.959411i | \(-0.408998\pi\) | ||||
0.282013 | + | 0.959411i | \(0.408998\pi\) | |||||||
\(152\) | 1.56155 | 0.126659 | ||||||||
\(153\) | −8.12311 | −0.656714 | ||||||||
\(154\) | 1.56155 | 0.125834 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.6847 | −1.09215 | −0.546077 | − | 0.837735i | \(-0.683880\pi\) | ||||
−0.546077 | + | 0.837735i | \(0.683880\pi\) | |||||||
\(158\) | −2.43845 | −0.193992 | ||||||||
\(159\) | −7.00000 | −0.555136 | ||||||||
\(160\) | −2.56155 | −0.202509 | ||||||||
\(161\) | 7.12311 | 0.561379 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −8.49242 | −0.665178 | −0.332589 | − | 0.943072i | \(-0.607922\pi\) | ||||
−0.332589 | + | 0.943072i | \(0.607922\pi\) | |||||||
\(164\) | 5.24621 | 0.409660 | ||||||||
\(165\) | 4.00000 | 0.311400 | ||||||||
\(166\) | 3.12311 | 0.242400 | ||||||||
\(167\) | −20.4924 | −1.58575 | −0.792876 | − | 0.609383i | \(-0.791417\pi\) | ||||
−0.792876 | + | 0.609383i | \(0.791417\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 20.8078 | 1.59588 | ||||||||
\(171\) | 1.56155 | 0.119415 | ||||||||
\(172\) | −8.00000 | −0.609994 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | −2.12311 | −0.160952 | ||||||||
\(175\) | 1.56155 | 0.118042 | ||||||||
\(176\) | 1.56155 | 0.117706 | ||||||||
\(177\) | 3.12311 | 0.234747 | ||||||||
\(178\) | 7.56155 | 0.566762 | ||||||||
\(179\) | −18.2462 | −1.36379 | −0.681893 | − | 0.731452i | \(-0.738843\pi\) | ||||
−0.681893 | + | 0.731452i | \(0.738843\pi\) | |||||||
\(180\) | −2.56155 | −0.190927 | ||||||||
\(181\) | −3.24621 | −0.241289 | −0.120644 | − | 0.992696i | \(-0.538496\pi\) | ||||
−0.120644 | + | 0.992696i | \(0.538496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.24621 | −0.387811 | ||||||||
\(184\) | 7.12311 | 0.525122 | ||||||||
\(185\) | 16.8078 | 1.23573 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.6847 | −0.927594 | ||||||||
\(188\) | −12.6847 | −0.925124 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 3.12311 | 0.225980 | 0.112990 | − | 0.993596i | \(-0.463957\pi\) | ||||
0.112990 | + | 0.993596i | \(0.463957\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −8.12311 | −0.584714 | −0.292357 | − | 0.956309i | \(-0.594440\pi\) | ||||
−0.292357 | + | 0.956309i | \(0.594440\pi\) | |||||||
\(194\) | −9.12311 | −0.655001 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 8.43845 | 0.601214 | 0.300607 | − | 0.953748i | \(-0.402811\pi\) | ||||
0.300607 | + | 0.953748i | \(0.402811\pi\) | |||||||
\(198\) | 1.56155 | 0.110975 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 1.56155 | 0.110418 | ||||||||
\(201\) | −0.876894 | −0.0618514 | ||||||||
\(202\) | 14.8078 | 1.04187 | ||||||||
\(203\) | 2.12311 | 0.149013 | ||||||||
\(204\) | 8.12311 | 0.568731 | ||||||||
\(205\) | −13.4384 | −0.938582 | ||||||||
\(206\) | −10.2462 | −0.713887 | ||||||||
\(207\) | 7.12311 | 0.495090 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.43845 | 0.168671 | ||||||||
\(210\) | 2.56155 | 0.176764 | ||||||||
\(211\) | −3.12311 | −0.215003 | −0.107502 | − | 0.994205i | \(-0.534285\pi\) | ||||
−0.107502 | + | 0.994205i | \(0.534285\pi\) | |||||||
\(212\) | 7.00000 | 0.480762 | ||||||||
\(213\) | −13.3693 | −0.916050 | ||||||||
\(214\) | −14.9309 | −1.02065 | ||||||||
\(215\) | 20.4924 | 1.39757 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.24621 | 0.287590 | ||||||||
\(219\) | 6.56155 | 0.443389 | ||||||||
\(220\) | −4.00000 | −0.269680 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 6.56155 | 0.440383 | ||||||||
\(223\) | 26.2462 | 1.75758 | 0.878788 | − | 0.477212i | \(-0.158353\pi\) | ||||
0.878788 | + | 0.477212i | \(0.158353\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 1.56155 | 0.104104 | ||||||||
\(226\) | −2.56155 | −0.170392 | ||||||||
\(227\) | −19.1231 | −1.26925 | −0.634623 | − | 0.772822i | \(-0.718844\pi\) | ||||
−0.634623 | + | 0.772822i | \(0.718844\pi\) | |||||||
\(228\) | −1.56155 | −0.103416 | ||||||||
\(229\) | −20.0540 | −1.32520 | −0.662602 | − | 0.748972i | \(-0.730548\pi\) | ||||
−0.662602 | + | 0.748972i | \(0.730548\pi\) | |||||||
\(230\) | −18.2462 | −1.20312 | ||||||||
\(231\) | −1.56155 | −0.102743 | ||||||||
\(232\) | 2.12311 | 0.139389 | ||||||||
\(233\) | −23.3693 | −1.53097 | −0.765487 | − | 0.643451i | \(-0.777502\pi\) | ||||
−0.765487 | + | 0.643451i | \(0.777502\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.4924 | 2.11957 | ||||||||
\(236\) | −3.12311 | −0.203297 | ||||||||
\(237\) | 2.43845 | 0.158394 | ||||||||
\(238\) | −8.12311 | −0.526543 | ||||||||
\(239\) | −5.36932 | −0.347312 | −0.173656 | − | 0.984806i | \(-0.555558\pi\) | ||||
−0.173656 | + | 0.984806i | \(0.555558\pi\) | |||||||
\(240\) | 2.56155 | 0.165348 | ||||||||
\(241\) | −20.8078 | −1.34035 | −0.670173 | − | 0.742205i | \(-0.733780\pi\) | ||||
−0.670173 | + | 0.742205i | \(0.733780\pi\) | |||||||
\(242\) | −8.56155 | −0.550357 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 5.24621 | 0.335854 | ||||||||
\(245\) | −2.56155 | −0.163652 | ||||||||
\(246\) | −5.24621 | −0.334486 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.12311 | −0.197919 | ||||||||
\(250\) | 8.80776 | 0.557052 | ||||||||
\(251\) | 27.6155 | 1.74308 | 0.871538 | − | 0.490327i | \(-0.163123\pi\) | ||||
0.871538 | + | 0.490327i | \(0.163123\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 11.1231 | 0.699304 | ||||||||
\(254\) | −20.4924 | −1.28581 | ||||||||
\(255\) | −20.8078 | −1.30303 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.369317 | 0.0230374 | 0.0115187 | − | 0.999934i | \(-0.496333\pi\) | ||||
0.0115187 | + | 0.999934i | \(0.496333\pi\) | |||||||
\(258\) | 8.00000 | 0.498058 | ||||||||
\(259\) | −6.56155 | −0.407715 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.12311 | 0.131417 | ||||||||
\(262\) | −2.24621 | −0.138771 | ||||||||
\(263\) | −3.12311 | −0.192579 | −0.0962895 | − | 0.995353i | \(-0.530697\pi\) | ||||
−0.0962895 | + | 0.995353i | \(0.530697\pi\) | |||||||
\(264\) | −1.56155 | −0.0961069 | ||||||||
\(265\) | −17.9309 | −1.10148 | ||||||||
\(266\) | 1.56155 | 0.0957449 | ||||||||
\(267\) | −7.56155 | −0.462760 | ||||||||
\(268\) | 0.876894 | 0.0535648 | ||||||||
\(269\) | 18.8769 | 1.15094 | 0.575472 | − | 0.817821i | \(-0.304818\pi\) | ||||
0.575472 | + | 0.817821i | \(0.304818\pi\) | |||||||
\(270\) | 2.56155 | 0.155891 | ||||||||
\(271\) | 26.7386 | 1.62426 | 0.812128 | − | 0.583479i | \(-0.198309\pi\) | ||||
0.812128 | + | 0.583479i | \(0.198309\pi\) | |||||||
\(272\) | −8.12311 | −0.492536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.5616 | 1.00052 | ||||||||
\(275\) | 2.43845 | 0.147044 | ||||||||
\(276\) | −7.12311 | −0.428761 | ||||||||
\(277\) | −15.4384 | −0.927606 | −0.463803 | − | 0.885938i | \(-0.653516\pi\) | ||||
−0.463803 | + | 0.885938i | \(0.653516\pi\) | |||||||
\(278\) | −9.56155 | −0.573464 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.56155 | −0.153082 | ||||||||
\(281\) | −15.9309 | −0.950356 | −0.475178 | − | 0.879890i | \(-0.657616\pi\) | ||||
−0.475178 | + | 0.879890i | \(0.657616\pi\) | |||||||
\(282\) | 12.6847 | 0.755360 | ||||||||
\(283\) | −20.0000 | −1.18888 | −0.594438 | − | 0.804141i | \(-0.702626\pi\) | ||||
−0.594438 | + | 0.804141i | \(0.702626\pi\) | |||||||
\(284\) | 13.3693 | 0.793323 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.24621 | 0.309674 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 48.9848 | 2.88146 | ||||||||
\(290\) | −5.43845 | −0.319357 | ||||||||
\(291\) | 9.12311 | 0.534806 | ||||||||
\(292\) | −6.56155 | −0.383986 | ||||||||
\(293\) | 21.9309 | 1.28122 | 0.640608 | − | 0.767868i | \(-0.278683\pi\) | ||||
0.640608 | + | 0.767868i | \(0.278683\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | −6.56155 | −0.381383 | ||||||||
\(297\) | −1.56155 | −0.0906105 | ||||||||
\(298\) | −11.4384 | −0.662611 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.56155 | −0.0901563 | ||||||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 6.93087 | 0.398827 | ||||||||
\(303\) | −14.8078 | −0.850684 | ||||||||
\(304\) | 1.56155 | 0.0895612 | ||||||||
\(305\) | −13.4384 | −0.769483 | ||||||||
\(306\) | −8.12311 | −0.464367 | ||||||||
\(307\) | 18.9309 | 1.08044 | 0.540221 | − | 0.841523i | \(-0.318341\pi\) | ||||
0.540221 | + | 0.841523i | \(0.318341\pi\) | |||||||
\(308\) | 1.56155 | 0.0889777 | ||||||||
\(309\) | 10.2462 | 0.582887 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.93087 | −0.393014 | −0.196507 | − | 0.980502i | \(-0.562960\pi\) | ||||
−0.196507 | + | 0.980502i | \(0.562960\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | −13.6847 | −0.772270 | ||||||||
\(315\) | −2.56155 | −0.144327 | ||||||||
\(316\) | −2.43845 | −0.137173 | ||||||||
\(317\) | 16.5616 | 0.930189 | 0.465095 | − | 0.885261i | \(-0.346020\pi\) | ||||
0.465095 | + | 0.885261i | \(0.346020\pi\) | |||||||
\(318\) | −7.00000 | −0.392541 | ||||||||
\(319\) | 3.31534 | 0.185623 | ||||||||
\(320\) | −2.56155 | −0.143195 | ||||||||
\(321\) | 14.9309 | 0.833360 | ||||||||
\(322\) | 7.12311 | 0.396955 | ||||||||
\(323\) | −12.6847 | −0.705793 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.49242 | −0.470352 | ||||||||
\(327\) | −4.24621 | −0.234816 | ||||||||
\(328\) | 5.24621 | 0.289674 | ||||||||
\(329\) | −12.6847 | −0.699328 | ||||||||
\(330\) | 4.00000 | 0.220193 | ||||||||
\(331\) | −5.36932 | −0.295124 | −0.147562 | − | 0.989053i | \(-0.547143\pi\) | ||||
−0.147562 | + | 0.989053i | \(0.547143\pi\) | |||||||
\(332\) | 3.12311 | 0.171403 | ||||||||
\(333\) | −6.56155 | −0.359571 | ||||||||
\(334\) | −20.4924 | −1.12130 | ||||||||
\(335\) | −2.24621 | −0.122724 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 19.4924 | 1.06182 | 0.530910 | − | 0.847428i | \(-0.321850\pi\) | ||||
0.530910 | + | 0.847428i | \(0.321850\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.56155 | 0.139124 | ||||||||
\(340\) | 20.8078 | 1.12846 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.56155 | 0.0844391 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 18.2462 | 0.982343 | ||||||||
\(346\) | −18.0000 | −0.967686 | ||||||||
\(347\) | −22.0540 | −1.18392 | −0.591960 | − | 0.805968i | \(-0.701646\pi\) | ||||
−0.591960 | + | 0.805968i | \(0.701646\pi\) | |||||||
\(348\) | −2.12311 | −0.113810 | ||||||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | 1.56155 | 0.0834685 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.56155 | 0.0832310 | ||||||||
\(353\) | −13.1922 | −0.702152 | −0.351076 | − | 0.936347i | \(-0.614184\pi\) | ||||
−0.351076 | + | 0.936347i | \(0.614184\pi\) | |||||||
\(354\) | 3.12311 | 0.165991 | ||||||||
\(355\) | −34.2462 | −1.81760 | ||||||||
\(356\) | 7.56155 | 0.400761 | ||||||||
\(357\) | 8.12311 | 0.429920 | ||||||||
\(358\) | −18.2462 | −0.964342 | ||||||||
\(359\) | −18.2462 | −0.962998 | −0.481499 | − | 0.876447i | \(-0.659908\pi\) | ||||
−0.481499 | + | 0.876447i | \(0.659908\pi\) | |||||||
\(360\) | −2.56155 | −0.135006 | ||||||||
\(361\) | −16.5616 | −0.871661 | ||||||||
\(362\) | −3.24621 | −0.170617 | ||||||||
\(363\) | 8.56155 | 0.449365 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.8078 | 0.879759 | ||||||||
\(366\) | −5.24621 | −0.274224 | ||||||||
\(367\) | −27.6155 | −1.44152 | −0.720759 | − | 0.693185i | \(-0.756207\pi\) | ||||
−0.720759 | + | 0.693185i | \(0.756207\pi\) | |||||||
\(368\) | 7.12311 | 0.371318 | ||||||||
\(369\) | 5.24621 | 0.273107 | ||||||||
\(370\) | 16.8078 | 0.873794 | ||||||||
\(371\) | 7.00000 | 0.363422 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.9309 | −1.65332 | −0.826659 | − | 0.562703i | \(-0.809761\pi\) | ||||
−0.826659 | + | 0.562703i | \(0.809761\pi\) | |||||||
\(374\) | −12.6847 | −0.655908 | ||||||||
\(375\) | −8.80776 | −0.454831 | ||||||||
\(376\) | −12.6847 | −0.654161 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | −3.61553 | −0.185717 | −0.0928586 | − | 0.995679i | \(-0.529600\pi\) | ||||
−0.0928586 | + | 0.995679i | \(0.529600\pi\) | |||||||
\(380\) | −4.00000 | −0.205196 | ||||||||
\(381\) | 20.4924 | 1.04986 | ||||||||
\(382\) | 3.12311 | 0.159792 | ||||||||
\(383\) | 7.80776 | 0.398958 | 0.199479 | − | 0.979902i | \(-0.436075\pi\) | ||||
0.199479 | + | 0.979902i | \(0.436075\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | −8.12311 | −0.413455 | ||||||||
\(387\) | −8.00000 | −0.406663 | ||||||||
\(388\) | −9.12311 | −0.463156 | ||||||||
\(389\) | −17.6847 | −0.896648 | −0.448324 | − | 0.893871i | \(-0.647979\pi\) | ||||
−0.448324 | + | 0.893871i | \(0.647979\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −57.8617 | −2.92619 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 2.24621 | 0.113306 | ||||||||
\(394\) | 8.43845 | 0.425123 | ||||||||
\(395\) | 6.24621 | 0.314281 | ||||||||
\(396\) | 1.56155 | 0.0784710 | ||||||||
\(397\) | −0.930870 | −0.0467190 | −0.0233595 | − | 0.999727i | \(-0.507436\pi\) | ||||
−0.0233595 | + | 0.999727i | \(0.507436\pi\) | |||||||
\(398\) | −16.0000 | −0.802008 | ||||||||
\(399\) | −1.56155 | −0.0781754 | ||||||||
\(400\) | 1.56155 | 0.0780776 | ||||||||
\(401\) | 18.8078 | 0.939215 | 0.469607 | − | 0.882875i | \(-0.344395\pi\) | ||||
0.469607 | + | 0.882875i | \(0.344395\pi\) | |||||||
\(402\) | −0.876894 | −0.0437355 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 14.8078 | 0.736714 | ||||||||
\(405\) | −2.56155 | −0.127285 | ||||||||
\(406\) | 2.12311 | 0.105368 | ||||||||
\(407\) | −10.2462 | −0.507886 | ||||||||
\(408\) | 8.12311 | 0.402154 | ||||||||
\(409\) | −7.43845 | −0.367808 | −0.183904 | − | 0.982944i | \(-0.558873\pi\) | ||||
−0.183904 | + | 0.982944i | \(0.558873\pi\) | |||||||
\(410\) | −13.4384 | −0.663678 | ||||||||
\(411\) | −16.5616 | −0.816921 | ||||||||
\(412\) | −10.2462 | −0.504795 | ||||||||
\(413\) | −3.12311 | −0.153678 | ||||||||
\(414\) | 7.12311 | 0.350082 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.56155 | 0.468231 | ||||||||
\(418\) | 2.43845 | 0.119268 | ||||||||
\(419\) | −1.36932 | −0.0668955 | −0.0334478 | − | 0.999440i | \(-0.510649\pi\) | ||||
−0.0334478 | + | 0.999440i | \(0.510649\pi\) | |||||||
\(420\) | 2.56155 | 0.124991 | ||||||||
\(421\) | 31.3002 | 1.52548 | 0.762739 | − | 0.646707i | \(-0.223854\pi\) | ||||
0.762739 | + | 0.646707i | \(0.223854\pi\) | |||||||
\(422\) | −3.12311 | −0.152030 | ||||||||
\(423\) | −12.6847 | −0.616749 | ||||||||
\(424\) | 7.00000 | 0.339950 | ||||||||
\(425\) | −12.6847 | −0.615296 | ||||||||
\(426\) | −13.3693 | −0.647746 | ||||||||
\(427\) | 5.24621 | 0.253882 | ||||||||
\(428\) | −14.9309 | −0.721711 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20.4924 | 0.988232 | ||||||||
\(431\) | −5.36932 | −0.258631 | −0.129315 | − | 0.991604i | \(-0.541278\pi\) | ||||
−0.129315 | + | 0.991604i | \(0.541278\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −33.6847 | −1.61878 | −0.809391 | − | 0.587271i | \(-0.800202\pi\) | ||||
−0.809391 | + | 0.587271i | \(0.800202\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.43845 | 0.260754 | ||||||||
\(436\) | 4.24621 | 0.203357 | ||||||||
\(437\) | 11.1231 | 0.532090 | ||||||||
\(438\) | 6.56155 | 0.313523 | ||||||||
\(439\) | −9.75379 | −0.465523 | −0.232761 | − | 0.972534i | \(-0.574776\pi\) | ||||
−0.232761 | + | 0.972534i | \(0.574776\pi\) | |||||||
\(440\) | −4.00000 | −0.190693 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0540 | 0.477679 | 0.238839 | − | 0.971059i | \(-0.423233\pi\) | ||||
0.238839 | + | 0.971059i | \(0.423233\pi\) | |||||||
\(444\) | 6.56155 | 0.311398 | ||||||||
\(445\) | −19.3693 | −0.918194 | ||||||||
\(446\) | 26.2462 | 1.24279 | ||||||||
\(447\) | 11.4384 | 0.541020 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −31.3693 | −1.48041 | −0.740205 | − | 0.672381i | \(-0.765271\pi\) | ||||
−0.740205 | + | 0.672381i | \(0.765271\pi\) | |||||||
\(450\) | 1.56155 | 0.0736123 | ||||||||
\(451\) | 8.19224 | 0.385757 | ||||||||
\(452\) | −2.56155 | −0.120485 | ||||||||
\(453\) | −6.93087 | −0.325641 | ||||||||
\(454\) | −19.1231 | −0.897492 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.56155 | −0.0731264 | ||||||||
\(457\) | 0.0691303 | 0.00323378 | 0.00161689 | − | 0.999999i | \(-0.499485\pi\) | ||||
0.00161689 | + | 0.999999i | \(0.499485\pi\) | |||||||
\(458\) | −20.0540 | −0.937061 | ||||||||
\(459\) | 8.12311 | 0.379154 | ||||||||
\(460\) | −18.2462 | −0.850734 | ||||||||
\(461\) | −31.0540 | −1.44633 | −0.723164 | − | 0.690676i | \(-0.757313\pi\) | ||||
−0.723164 | + | 0.690676i | \(0.757313\pi\) | |||||||
\(462\) | −1.56155 | −0.0726500 | ||||||||
\(463\) | 24.6847 | 1.14719 | 0.573597 | − | 0.819138i | \(-0.305548\pi\) | ||||
0.573597 | + | 0.819138i | \(0.305548\pi\) | |||||||
\(464\) | 2.12311 | 0.0985627 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.3693 | −1.08256 | ||||||||
\(467\) | 28.9848 | 1.34126 | 0.670629 | − | 0.741793i | \(-0.266024\pi\) | ||||
0.670629 | + | 0.741793i | \(0.266024\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.876894 | 0.0404912 | ||||||||
\(470\) | 32.4924 | 1.49876 | ||||||||
\(471\) | 13.6847 | 0.630556 | ||||||||
\(472\) | −3.12311 | −0.143753 | ||||||||
\(473\) | −12.4924 | −0.574402 | ||||||||
\(474\) | 2.43845 | 0.112002 | ||||||||
\(475\) | 2.43845 | 0.111884 | ||||||||
\(476\) | −8.12311 | −0.372322 | ||||||||
\(477\) | 7.00000 | 0.320508 | ||||||||
\(478\) | −5.36932 | −0.245587 | ||||||||
\(479\) | 26.9309 | 1.23050 | 0.615251 | − | 0.788331i | \(-0.289054\pi\) | ||||
0.615251 | + | 0.788331i | \(0.289054\pi\) | |||||||
\(480\) | 2.56155 | 0.116918 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −20.8078 | −0.947768 | ||||||||
\(483\) | −7.12311 | −0.324113 | ||||||||
\(484\) | −8.56155 | −0.389161 | ||||||||
\(485\) | 23.3693 | 1.06115 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 11.3153 | 0.512747 | 0.256374 | − | 0.966578i | \(-0.417472\pi\) | ||||
0.256374 | + | 0.966578i | \(0.417472\pi\) | |||||||
\(488\) | 5.24621 | 0.237485 | ||||||||
\(489\) | 8.49242 | 0.384041 | ||||||||
\(490\) | −2.56155 | −0.115719 | ||||||||
\(491\) | 16.4924 | 0.744293 | 0.372146 | − | 0.928174i | \(-0.378622\pi\) | ||||
0.372146 | + | 0.928174i | \(0.378622\pi\) | |||||||
\(492\) | −5.24621 | −0.236517 | ||||||||
\(493\) | −17.2462 | −0.776730 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.00000 | −0.179787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.3693 | 0.599696 | ||||||||
\(498\) | −3.12311 | −0.139950 | ||||||||
\(499\) | 13.7538 | 0.615704 | 0.307852 | − | 0.951434i | \(-0.400390\pi\) | ||||
0.307852 | + | 0.951434i | \(0.400390\pi\) | |||||||
\(500\) | 8.80776 | 0.393895 | ||||||||
\(501\) | 20.4924 | 0.915534 | ||||||||
\(502\) | 27.6155 | 1.23254 | ||||||||
\(503\) | 4.49242 | 0.200307 | 0.100154 | − | 0.994972i | \(-0.468067\pi\) | ||||
0.100154 | + | 0.994972i | \(0.468067\pi\) | |||||||
\(504\) | 1.00000 | 0.0445435 | ||||||||
\(505\) | −37.9309 | −1.68790 | ||||||||
\(506\) | 11.1231 | 0.494482 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20.4924 | −0.909204 | ||||||||
\(509\) | −21.1922 | −0.939329 | −0.469665 | − | 0.882845i | \(-0.655625\pi\) | ||||
−0.469665 | + | 0.882845i | \(0.655625\pi\) | |||||||
\(510\) | −20.8078 | −0.921383 | ||||||||
\(511\) | −6.56155 | −0.290266 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.56155 | −0.0689442 | ||||||||
\(514\) | 0.369317 | 0.0162899 | ||||||||
\(515\) | 26.2462 | 1.15655 | ||||||||
\(516\) | 8.00000 | 0.352180 | ||||||||
\(517\) | −19.8078 | −0.871144 | ||||||||
\(518\) | −6.56155 | −0.288298 | ||||||||
\(519\) | 18.0000 | 0.790112 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.1231 | 1.49496 | 0.747480 | − | 0.664284i | \(-0.231263\pi\) | ||||
0.747480 | + | 0.664284i | \(0.231263\pi\) | |||||||
\(522\) | 2.12311 | 0.0929258 | ||||||||
\(523\) | 3.80776 | 0.166502 | 0.0832509 | − | 0.996529i | \(-0.473470\pi\) | ||||
0.0832509 | + | 0.996529i | \(0.473470\pi\) | |||||||
\(524\) | −2.24621 | −0.0981262 | ||||||||
\(525\) | −1.56155 | −0.0681518 | ||||||||
\(526\) | −3.12311 | −0.136174 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.56155 | −0.0679579 | ||||||||
\(529\) | 27.7386 | 1.20603 | ||||||||
\(530\) | −17.9309 | −0.778867 | ||||||||
\(531\) | −3.12311 | −0.135531 | ||||||||
\(532\) | 1.56155 | 0.0677019 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −7.56155 | −0.327220 | ||||||||
\(535\) | 38.2462 | 1.65353 | ||||||||
\(536\) | 0.876894 | 0.0378761 | ||||||||
\(537\) | 18.2462 | 0.787382 | ||||||||
\(538\) | 18.8769 | 0.813841 | ||||||||
\(539\) | 1.56155 | 0.0672608 | ||||||||
\(540\) | 2.56155 | 0.110232 | ||||||||
\(541\) | −26.1771 | −1.12544 | −0.562720 | − | 0.826647i | \(-0.690245\pi\) | ||||
−0.562720 | + | 0.826647i | \(0.690245\pi\) | |||||||
\(542\) | 26.7386 | 1.14852 | ||||||||
\(543\) | 3.24621 | 0.139308 | ||||||||
\(544\) | −8.12311 | −0.348275 | ||||||||
\(545\) | −10.8769 | −0.465915 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.61553 | 0.325616 | 0.162808 | − | 0.986658i | \(-0.447945\pi\) | ||||
0.162808 | + | 0.986658i | \(0.447945\pi\) | |||||||
\(548\) | 16.5616 | 0.707474 | ||||||||
\(549\) | 5.24621 | 0.223903 | ||||||||
\(550\) | 2.43845 | 0.103976 | ||||||||
\(551\) | 3.31534 | 0.141238 | ||||||||
\(552\) | −7.12311 | −0.303180 | ||||||||
\(553\) | −2.43845 | −0.103693 | ||||||||
\(554\) | −15.4384 | −0.655917 | ||||||||
\(555\) | −16.8078 | −0.713450 | ||||||||
\(556\) | −9.56155 | −0.405500 | ||||||||
\(557\) | 3.87689 | 0.164269 | 0.0821346 | − | 0.996621i | \(-0.473826\pi\) | ||||
0.0821346 | + | 0.996621i | \(0.473826\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.56155 | −0.108245 | ||||||||
\(561\) | 12.6847 | 0.535547 | ||||||||
\(562\) | −15.9309 | −0.672003 | ||||||||
\(563\) | −22.2462 | −0.937566 | −0.468783 | − | 0.883313i | \(-0.655307\pi\) | ||||
−0.468783 | + | 0.883313i | \(0.655307\pi\) | |||||||
\(564\) | 12.6847 | 0.534120 | ||||||||
\(565\) | 6.56155 | 0.276047 | ||||||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 13.3693 | 0.560964 | ||||||||
\(569\) | −22.0000 | −0.922288 | −0.461144 | − | 0.887325i | \(-0.652561\pi\) | ||||
−0.461144 | + | 0.887325i | \(0.652561\pi\) | |||||||
\(570\) | 4.00000 | 0.167542 | ||||||||
\(571\) | −12.8769 | −0.538881 | −0.269441 | − | 0.963017i | \(-0.586839\pi\) | ||||
−0.269441 | + | 0.963017i | \(0.586839\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.12311 | −0.130470 | ||||||||
\(574\) | 5.24621 | 0.218973 | ||||||||
\(575\) | 11.1231 | 0.463866 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −31.4384 | −1.30880 | −0.654400 | − | 0.756149i | \(-0.727079\pi\) | ||||
−0.654400 | + | 0.756149i | \(0.727079\pi\) | |||||||
\(578\) | 48.9848 | 2.03750 | ||||||||
\(579\) | 8.12311 | 0.337585 | ||||||||
\(580\) | −5.43845 | −0.225819 | ||||||||
\(581\) | 3.12311 | 0.129568 | ||||||||
\(582\) | 9.12311 | 0.378165 | ||||||||
\(583\) | 10.9309 | 0.452710 | ||||||||
\(584\) | −6.56155 | −0.271519 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.9309 | 0.905956 | ||||||||
\(587\) | −14.2462 | −0.588004 | −0.294002 | − | 0.955805i | \(-0.594987\pi\) | ||||
−0.294002 | + | 0.955805i | \(0.594987\pi\) | |||||||
\(588\) | −1.00000 | −0.0412393 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 8.00000 | 0.329355 | ||||||||
\(591\) | −8.43845 | −0.347111 | ||||||||
\(592\) | −6.56155 | −0.269678 | ||||||||
\(593\) | 31.9848 | 1.31346 | 0.656730 | − | 0.754126i | \(-0.271939\pi\) | ||||
0.656730 | + | 0.754126i | \(0.271939\pi\) | |||||||
\(594\) | −1.56155 | −0.0640713 | ||||||||
\(595\) | 20.8078 | 0.853035 | ||||||||
\(596\) | −11.4384 | −0.468537 | ||||||||
\(597\) | 16.0000 | 0.654836 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.8617 | −1.38355 | −0.691777 | − | 0.722112i | \(-0.743172\pi\) | ||||
−0.691777 | + | 0.722112i | \(0.743172\pi\) | |||||||
\(600\) | −1.56155 | −0.0637501 | ||||||||
\(601\) | −25.3002 | −1.03202 | −0.516008 | − | 0.856584i | \(-0.672583\pi\) | ||||
−0.516008 | + | 0.856584i | \(0.672583\pi\) | |||||||
\(602\) | −8.00000 | −0.326056 | ||||||||
\(603\) | 0.876894 | 0.0357099 | ||||||||
\(604\) | 6.93087 | 0.282013 | ||||||||
\(605\) | 21.9309 | 0.891617 | ||||||||
\(606\) | −14.8078 | −0.601524 | ||||||||
\(607\) | 16.9848 | 0.689394 | 0.344697 | − | 0.938714i | \(-0.387982\pi\) | ||||
0.344697 | + | 0.938714i | \(0.387982\pi\) | |||||||
\(608\) | 1.56155 | 0.0633293 | ||||||||
\(609\) | −2.12311 | −0.0860326 | ||||||||
\(610\) | −13.4384 | −0.544107 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −8.12311 | −0.328357 | ||||||||
\(613\) | 17.4384 | 0.704332 | 0.352166 | − | 0.935938i | \(-0.385445\pi\) | ||||
0.352166 | + | 0.935938i | \(0.385445\pi\) | |||||||
\(614\) | 18.9309 | 0.763988 | ||||||||
\(615\) | 13.4384 | 0.541890 | ||||||||
\(616\) | 1.56155 | 0.0629168 | ||||||||
\(617\) | −22.1771 | −0.892816 | −0.446408 | − | 0.894830i | \(-0.647297\pi\) | ||||
−0.446408 | + | 0.894830i | \(0.647297\pi\) | |||||||
\(618\) | 10.2462 | 0.412163 | ||||||||
\(619\) | 30.9309 | 1.24322 | 0.621608 | − | 0.783328i | \(-0.286480\pi\) | ||||
0.621608 | + | 0.783328i | \(0.286480\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.12311 | −0.285840 | ||||||||
\(622\) | −6.93087 | −0.277903 | ||||||||
\(623\) | 7.56155 | 0.302947 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3693 | −1.21477 | ||||||||
\(626\) | −6.00000 | −0.239808 | ||||||||
\(627\) | −2.43845 | −0.0973822 | ||||||||
\(628\) | −13.6847 | −0.546077 | ||||||||
\(629\) | 53.3002 | 2.12522 | ||||||||
\(630\) | −2.56155 | −0.102055 | ||||||||
\(631\) | −38.9309 | −1.54981 | −0.774907 | − | 0.632076i | \(-0.782203\pi\) | ||||
−0.774907 | + | 0.632076i | \(0.782203\pi\) | |||||||
\(632\) | −2.43845 | −0.0969962 | ||||||||
\(633\) | 3.12311 | 0.124132 | ||||||||
\(634\) | 16.5616 | 0.657743 | ||||||||
\(635\) | 52.4924 | 2.08310 | ||||||||
\(636\) | −7.00000 | −0.277568 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.31534 | 0.131256 | ||||||||
\(639\) | 13.3693 | 0.528882 | ||||||||
\(640\) | −2.56155 | −0.101254 | ||||||||
\(641\) | 12.5616 | 0.496152 | 0.248076 | − | 0.968741i | \(-0.420202\pi\) | ||||
0.248076 | + | 0.968741i | \(0.420202\pi\) | |||||||
\(642\) | 14.9309 | 0.589274 | ||||||||
\(643\) | 35.3153 | 1.39270 | 0.696351 | − | 0.717702i | \(-0.254806\pi\) | ||||
0.696351 | + | 0.717702i | \(0.254806\pi\) | |||||||
\(644\) | 7.12311 | 0.280690 | ||||||||
\(645\) | −20.4924 | −0.806888 | ||||||||
\(646\) | −12.6847 | −0.499071 | ||||||||
\(647\) | −46.0540 | −1.81057 | −0.905284 | − | 0.424806i | \(-0.860342\pi\) | ||||
−0.905284 | + | 0.424806i | \(0.860342\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −4.87689 | −0.191435 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.49242 | −0.332589 | ||||||||
\(653\) | 16.4384 | 0.643286 | 0.321643 | − | 0.946861i | \(-0.395765\pi\) | ||||
0.321643 | + | 0.946861i | \(0.395765\pi\) | |||||||
\(654\) | −4.24621 | −0.166040 | ||||||||
\(655\) | 5.75379 | 0.224819 | ||||||||
\(656\) | 5.24621 | 0.204830 | ||||||||
\(657\) | −6.56155 | −0.255991 | ||||||||
\(658\) | −12.6847 | −0.494499 | ||||||||
\(659\) | 30.9309 | 1.20490 | 0.602448 | − | 0.798158i | \(-0.294192\pi\) | ||||
0.602448 | + | 0.798158i | \(0.294192\pi\) | |||||||
\(660\) | 4.00000 | 0.155700 | ||||||||
\(661\) | 17.0540 | 0.663323 | 0.331661 | − | 0.943398i | \(-0.392391\pi\) | ||||
0.331661 | + | 0.943398i | \(0.392391\pi\) | |||||||
\(662\) | −5.36932 | −0.208684 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.12311 | 0.121200 | ||||||||
\(665\) | −4.00000 | −0.155113 | ||||||||
\(666\) | −6.56155 | −0.254255 | ||||||||
\(667\) | 15.1231 | 0.585569 | ||||||||
\(668\) | −20.4924 | −0.792876 | ||||||||
\(669\) | −26.2462 | −1.01474 | ||||||||
\(670\) | −2.24621 | −0.0867787 | ||||||||
\(671\) | 8.19224 | 0.316258 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | −19.2462 | −0.741887 | −0.370943 | − | 0.928655i | \(-0.620966\pi\) | ||||
−0.370943 | + | 0.928655i | \(0.620966\pi\) | |||||||
\(674\) | 19.4924 | 0.750820 | ||||||||
\(675\) | −1.56155 | −0.0601042 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.7386 | 0.950783 | 0.475391 | − | 0.879774i | \(-0.342306\pi\) | ||||
0.475391 | + | 0.879774i | \(0.342306\pi\) | |||||||
\(678\) | 2.56155 | 0.0983758 | ||||||||
\(679\) | −9.12311 | −0.350113 | ||||||||
\(680\) | 20.8078 | 0.797941 | ||||||||
\(681\) | 19.1231 | 0.732799 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.50758 | 0.287269 | 0.143635 | − | 0.989631i | \(-0.454121\pi\) | ||||
0.143635 | + | 0.989631i | \(0.454121\pi\) | |||||||
\(684\) | 1.56155 | 0.0597075 | ||||||||
\(685\) | −42.4233 | −1.62091 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 20.0540 | 0.765107 | ||||||||
\(688\) | −8.00000 | −0.304997 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.2462 | 0.694621 | ||||||||
\(691\) | 32.9848 | 1.25480 | 0.627401 | − | 0.778696i | \(-0.284119\pi\) | ||||
0.627401 | + | 0.778696i | \(0.284119\pi\) | |||||||
\(692\) | −18.0000 | −0.684257 | ||||||||
\(693\) | 1.56155 | 0.0593185 | ||||||||
\(694\) | −22.0540 | −0.837157 | ||||||||
\(695\) | 24.4924 | 0.929051 | ||||||||
\(696\) | −2.12311 | −0.0804761 | ||||||||
\(697\) | −42.6155 | −1.61418 | ||||||||
\(698\) | −18.0000 | −0.681310 | ||||||||
\(699\) | 23.3693 | 0.883909 | ||||||||
\(700\) | 1.56155 | 0.0590211 | ||||||||
\(701\) | 14.3002 | 0.540111 | 0.270055 | − | 0.962845i | \(-0.412958\pi\) | ||||
0.270055 | + | 0.962845i | \(0.412958\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.2462 | −0.386443 | ||||||||
\(704\) | 1.56155 | 0.0588532 | ||||||||
\(705\) | −32.4924 | −1.22374 | ||||||||
\(706\) | −13.1922 | −0.496496 | ||||||||
\(707\) | 14.8078 | 0.556903 | ||||||||
\(708\) | 3.12311 | 0.117373 | ||||||||
\(709\) | 15.3002 | 0.574611 | 0.287305 | − | 0.957839i | \(-0.407241\pi\) | ||||
0.287305 | + | 0.957839i | \(0.407241\pi\) | |||||||
\(710\) | −34.2462 | −1.28524 | ||||||||
\(711\) | −2.43845 | −0.0914489 | ||||||||
\(712\) | 7.56155 | 0.283381 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 8.12311 | 0.304000 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.2462 | −0.681893 | ||||||||
\(717\) | 5.36932 | 0.200521 | ||||||||
\(718\) | −18.2462 | −0.680943 | ||||||||
\(719\) | −19.8078 | −0.738705 | −0.369352 | − | 0.929289i | \(-0.620420\pi\) | ||||
−0.369352 | + | 0.929289i | \(0.620420\pi\) | |||||||
\(720\) | −2.56155 | −0.0954634 | ||||||||
\(721\) | −10.2462 | −0.381589 | ||||||||
\(722\) | −16.5616 | −0.616357 | ||||||||
\(723\) | 20.8078 | 0.773849 | ||||||||
\(724\) | −3.24621 | −0.120644 | ||||||||
\(725\) | 3.31534 | 0.123129 | ||||||||
\(726\) | 8.56155 | 0.317749 | ||||||||
\(727\) | 40.0000 | 1.48352 | 0.741759 | − | 0.670667i | \(-0.233992\pi\) | ||||
0.741759 | + | 0.670667i | \(0.233992\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 16.8078 | 0.622083 | ||||||||
\(731\) | 64.9848 | 2.40355 | ||||||||
\(732\) | −5.24621 | −0.193906 | ||||||||
\(733\) | 28.8617 | 1.06603 | 0.533016 | − | 0.846105i | \(-0.321058\pi\) | ||||
0.533016 | + | 0.846105i | \(0.321058\pi\) | |||||||
\(734\) | −27.6155 | −1.01931 | ||||||||
\(735\) | 2.56155 | 0.0944843 | ||||||||
\(736\) | 7.12311 | 0.262561 | ||||||||
\(737\) | 1.36932 | 0.0504394 | ||||||||
\(738\) | 5.24621 | 0.193116 | ||||||||
\(739\) | −9.36932 | −0.344656 | −0.172328 | − | 0.985040i | \(-0.555129\pi\) | ||||
−0.172328 | + | 0.985040i | \(0.555129\pi\) | |||||||
\(740\) | 16.8078 | 0.617866 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.00000 | 0.256978 | ||||||||
\(743\) | 28.4924 | 1.04529 | 0.522643 | − | 0.852552i | \(-0.324946\pi\) | ||||
0.522643 | + | 0.852552i | \(0.324946\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.3002 | 1.07348 | ||||||||
\(746\) | −31.9309 | −1.16907 | ||||||||
\(747\) | 3.12311 | 0.114268 | ||||||||
\(748\) | −12.6847 | −0.463797 | ||||||||
\(749\) | −14.9309 | −0.545562 | ||||||||
\(750\) | −8.80776 | −0.321614 | ||||||||
\(751\) | −20.1922 | −0.736825 | −0.368413 | − | 0.929662i | \(-0.620099\pi\) | ||||
−0.368413 | + | 0.929662i | \(0.620099\pi\) | |||||||
\(752\) | −12.6847 | −0.462562 | ||||||||
\(753\) | −27.6155 | −1.00637 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.7538 | −0.646127 | ||||||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 3.26137 | 0.118536 | 0.0592682 | − | 0.998242i | \(-0.481123\pi\) | ||||
0.0592682 | + | 0.998242i | \(0.481123\pi\) | |||||||
\(758\) | −3.61553 | −0.131322 | ||||||||
\(759\) | −11.1231 | −0.403743 | ||||||||
\(760\) | −4.00000 | −0.145095 | ||||||||
\(761\) | −14.9848 | −0.543200 | −0.271600 | − | 0.962410i | \(-0.587553\pi\) | ||||
−0.271600 | + | 0.962410i | \(0.587553\pi\) | |||||||
\(762\) | 20.4924 | 0.742362 | ||||||||
\(763\) | 4.24621 | 0.153723 | ||||||||
\(764\) | 3.12311 | 0.112990 | ||||||||
\(765\) | 20.8078 | 0.752306 | ||||||||
\(766\) | 7.80776 | 0.282106 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 13.1231 | 0.473231 | 0.236616 | − | 0.971603i | \(-0.423962\pi\) | ||||
0.236616 | + | 0.971603i | \(0.423962\pi\) | |||||||
\(770\) | −4.00000 | −0.144150 | ||||||||
\(771\) | −0.369317 | −0.0133006 | ||||||||
\(772\) | −8.12311 | −0.292357 | ||||||||
\(773\) | −28.7386 | −1.03366 | −0.516828 | − | 0.856089i | \(-0.672887\pi\) | ||||
−0.516828 | + | 0.856089i | \(0.672887\pi\) | |||||||
\(774\) | −8.00000 | −0.287554 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.12311 | −0.327500 | ||||||||
\(777\) | 6.56155 | 0.235394 | ||||||||
\(778\) | −17.6847 | −0.634026 | ||||||||
\(779\) | 8.19224 | 0.293517 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.8769 | 0.747034 | ||||||||
\(782\) | −57.8617 | −2.06913 | ||||||||
\(783\) | −2.12311 | −0.0758736 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 35.0540 | 1.25113 | ||||||||
\(786\) | 2.24621 | 0.0801197 | ||||||||
\(787\) | 45.1771 | 1.61039 | 0.805195 | − | 0.593011i | \(-0.202061\pi\) | ||||
0.805195 | + | 0.593011i | \(0.202061\pi\) | |||||||
\(788\) | 8.43845 | 0.300607 | ||||||||
\(789\) | 3.12311 | 0.111186 | ||||||||
\(790\) | 6.24621 | 0.222230 | ||||||||
\(791\) | −2.56155 | −0.0910783 | ||||||||
\(792\) | 1.56155 | 0.0554874 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.930870 | −0.0330353 | ||||||||
\(795\) | 17.9309 | 0.635942 | ||||||||
\(796\) | −16.0000 | −0.567105 | ||||||||
\(797\) | 17.5076 | 0.620150 | 0.310075 | − | 0.950712i | \(-0.399646\pi\) | ||||
0.310075 | + | 0.950712i | \(0.399646\pi\) | |||||||
\(798\) | −1.56155 | −0.0552784 | ||||||||
\(799\) | 103.039 | 3.64525 | ||||||||
\(800\) | 1.56155 | 0.0552092 | ||||||||
\(801\) | 7.56155 | 0.267174 | ||||||||
\(802\) | 18.8078 | 0.664125 | ||||||||
\(803\) | −10.2462 | −0.361581 | ||||||||
\(804\) | −0.876894 | −0.0309257 | ||||||||
\(805\) | −18.2462 | −0.643094 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.8769 | −0.664498 | ||||||||
\(808\) | 14.8078 | 0.520935 | ||||||||
\(809\) | −19.9309 | −0.700732 | −0.350366 | − | 0.936613i | \(-0.613943\pi\) | ||||
−0.350366 | + | 0.936613i | \(0.613943\pi\) | |||||||
\(810\) | −2.56155 | −0.0900038 | ||||||||
\(811\) | 24.0000 | 0.842754 | 0.421377 | − | 0.906886i | \(-0.361547\pi\) | ||||
0.421377 | + | 0.906886i | \(0.361547\pi\) | |||||||
\(812\) | 2.12311 | 0.0745064 | ||||||||
\(813\) | −26.7386 | −0.937765 | ||||||||
\(814\) | −10.2462 | −0.359130 | ||||||||
\(815\) | 21.7538 | 0.762002 | ||||||||
\(816\) | 8.12311 | 0.284366 | ||||||||
\(817\) | −12.4924 | −0.437055 | ||||||||
\(818\) | −7.43845 | −0.260079 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.4384 | −0.469291 | ||||||||
\(821\) | −26.3002 | −0.917883 | −0.458941 | − | 0.888467i | \(-0.651771\pi\) | ||||
−0.458941 | + | 0.888467i | \(0.651771\pi\) | |||||||
\(822\) | −16.5616 | −0.577650 | ||||||||
\(823\) | −21.7538 | −0.758289 | −0.379145 | − | 0.925337i | \(-0.623782\pi\) | ||||
−0.379145 | + | 0.925337i | \(0.623782\pi\) | |||||||
\(824\) | −10.2462 | −0.356944 | ||||||||
\(825\) | −2.43845 | −0.0848958 | ||||||||
\(826\) | −3.12311 | −0.108667 | ||||||||
\(827\) | 17.7538 | 0.617360 | 0.308680 | − | 0.951166i | \(-0.400113\pi\) | ||||
0.308680 | + | 0.951166i | \(0.400113\pi\) | |||||||
\(828\) | 7.12311 | 0.247545 | ||||||||
\(829\) | 24.3693 | 0.846381 | 0.423191 | − | 0.906041i | \(-0.360910\pi\) | ||||
0.423191 | + | 0.906041i | \(0.360910\pi\) | |||||||
\(830\) | −8.00000 | −0.277684 | ||||||||
\(831\) | 15.4384 | 0.535554 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.12311 | −0.281449 | ||||||||
\(834\) | 9.56155 | 0.331089 | ||||||||
\(835\) | 52.4924 | 1.81658 | ||||||||
\(836\) | 2.43845 | 0.0843355 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.36932 | −0.0473023 | ||||||||
\(839\) | 1.75379 | 0.0605475 | 0.0302738 | − | 0.999542i | \(-0.490362\pi\) | ||||
0.0302738 | + | 0.999542i | \(0.490362\pi\) | |||||||
\(840\) | 2.56155 | 0.0883820 | ||||||||
\(841\) | −24.4924 | −0.844566 | ||||||||
\(842\) | 31.3002 | 1.07868 | ||||||||
\(843\) | 15.9309 | 0.548688 | ||||||||
\(844\) | −3.12311 | −0.107502 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.6847 | −0.436108 | ||||||||
\(847\) | −8.56155 | −0.294178 | ||||||||
\(848\) | 7.00000 | 0.240381 | ||||||||
\(849\) | 20.0000 | 0.686398 | ||||||||
\(850\) | −12.6847 | −0.435080 | ||||||||
\(851\) | −46.7386 | −1.60218 | ||||||||
\(852\) | −13.3693 | −0.458025 | ||||||||
\(853\) | 5.63068 | 0.192791 | 0.0963955 | − | 0.995343i | \(-0.469269\pi\) | ||||
0.0963955 | + | 0.995343i | \(0.469269\pi\) | |||||||
\(854\) | 5.24621 | 0.179522 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | −14.9309 | −0.510327 | ||||||||
\(857\) | 20.5616 | 0.702369 | 0.351185 | − | 0.936306i | \(-0.385779\pi\) | ||||
0.351185 | + | 0.936306i | \(0.385779\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.9309 | −0.372956 | −0.186478 | − | 0.982459i | \(-0.559707\pi\) | ||||
−0.186478 | + | 0.982459i | \(0.559707\pi\) | |||||||
\(860\) | 20.4924 | 0.698786 | ||||||||
\(861\) | −5.24621 | −0.178790 | ||||||||
\(862\) | −5.36932 | −0.182880 | ||||||||
\(863\) | 32.8769 | 1.11914 | 0.559571 | − | 0.828782i | \(-0.310966\pi\) | ||||
0.559571 | + | 0.828782i | \(0.310966\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 46.1080 | 1.56772 | ||||||||
\(866\) | −33.6847 | −1.14465 | ||||||||
\(867\) | −48.9848 | −1.66361 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.80776 | −0.129170 | ||||||||
\(870\) | 5.43845 | 0.184381 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.24621 | 0.143795 | ||||||||
\(873\) | −9.12311 | −0.308770 | ||||||||
\(874\) | 11.1231 | 0.376245 | ||||||||
\(875\) | 8.80776 | 0.297757 | ||||||||
\(876\) | 6.56155 | 0.221694 | ||||||||
\(877\) | 41.5464 | 1.40292 | 0.701461 | − | 0.712708i | \(-0.252531\pi\) | ||||
0.701461 | + | 0.712708i | \(0.252531\pi\) | |||||||
\(878\) | −9.75379 | −0.329174 | ||||||||
\(879\) | −21.9309 | −0.739710 | ||||||||
\(880\) | −4.00000 | −0.134840 | ||||||||
\(881\) | 57.0540 | 1.92220 | 0.961099 | − | 0.276205i | \(-0.0890770\pi\) | ||||
0.961099 | + | 0.276205i | \(0.0890770\pi\) | |||||||
\(882\) | 1.00000 | 0.0336718 | ||||||||
\(883\) | −20.0000 | −0.673054 | −0.336527 | − | 0.941674i | \(-0.609252\pi\) | ||||
−0.336527 | + | 0.941674i | \(0.609252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.00000 | −0.268917 | ||||||||
\(886\) | 10.0540 | 0.337770 | ||||||||
\(887\) | −46.0540 | −1.54634 | −0.773171 | − | 0.634198i | \(-0.781330\pi\) | ||||
−0.773171 | + | 0.634198i | \(0.781330\pi\) | |||||||
\(888\) | 6.56155 | 0.220191 | ||||||||
\(889\) | −20.4924 | −0.687294 | ||||||||
\(890\) | −19.3693 | −0.649261 | ||||||||
\(891\) | 1.56155 | 0.0523140 | ||||||||
\(892\) | 26.2462 | 0.878788 | ||||||||
\(893\) | −19.8078 | −0.662842 | ||||||||
\(894\) | 11.4384 | 0.382559 | ||||||||
\(895\) | 46.7386 | 1.56230 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −31.3693 | −1.04681 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.56155 | 0.0520518 | ||||||||
\(901\) | −56.8617 | −1.89434 | ||||||||
\(902\) | 8.19224 | 0.272772 | ||||||||
\(903\) | 8.00000 | 0.266223 | ||||||||
\(904\) | −2.56155 | −0.0851960 | ||||||||
\(905\) | 8.31534 | 0.276411 | ||||||||
\(906\) | −6.93087 | −0.230263 | ||||||||
\(907\) | 7.12311 | 0.236519 | 0.118259 | − | 0.992983i | \(-0.462269\pi\) | ||||
0.118259 | + | 0.992983i | \(0.462269\pi\) | |||||||
\(908\) | −19.1231 | −0.634623 | ||||||||
\(909\) | 14.8078 | 0.491143 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.6155 | −0.914943 | −0.457472 | − | 0.889224i | \(-0.651245\pi\) | ||||
−0.457472 | + | 0.889224i | \(0.651245\pi\) | |||||||
\(912\) | −1.56155 | −0.0517082 | ||||||||
\(913\) | 4.87689 | 0.161402 | ||||||||
\(914\) | 0.0691303 | 0.00228663 | ||||||||
\(915\) | 13.4384 | 0.444261 | ||||||||
\(916\) | −20.0540 | −0.662602 | ||||||||
\(917\) | −2.24621 | −0.0741764 | ||||||||
\(918\) | 8.12311 | 0.268102 | ||||||||
\(919\) | −17.0691 | −0.563059 | −0.281529 | − | 0.959553i | \(-0.590842\pi\) | ||||
−0.281529 | + | 0.959553i | \(0.590842\pi\) | |||||||
\(920\) | −18.2462 | −0.601560 | ||||||||
\(921\) | −18.9309 | −0.623793 | ||||||||
\(922\) | −31.0540 | −1.02271 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.56155 | −0.0513713 | ||||||||
\(925\) | −10.2462 | −0.336893 | ||||||||
\(926\) | 24.6847 | 0.811188 | ||||||||
\(927\) | −10.2462 | −0.336530 | ||||||||
\(928\) | 2.12311 | 0.0696944 | ||||||||
\(929\) | −19.2462 | −0.631448 | −0.315724 | − | 0.948851i | \(-0.602247\pi\) | ||||
−0.315724 | + | 0.948851i | \(0.602247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.56155 | 0.0511778 | ||||||||
\(932\) | −23.3693 | −0.765487 | ||||||||
\(933\) | 6.93087 | 0.226906 | ||||||||
\(934\) | 28.9848 | 0.948413 | ||||||||
\(935\) | 32.4924 | 1.06262 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.5616 | −1.25975 | −0.629876 | − | 0.776696i | \(-0.716894\pi\) | ||||
−0.629876 | + | 0.776696i | \(0.716894\pi\) | |||||||
\(938\) | 0.876894 | 0.0286316 | ||||||||
\(939\) | 6.00000 | 0.195803 | ||||||||
\(940\) | 32.4924 | 1.05979 | ||||||||
\(941\) | −35.3693 | −1.15301 | −0.576503 | − | 0.817095i | \(-0.695583\pi\) | ||||
−0.576503 | + | 0.817095i | \(0.695583\pi\) | |||||||
\(942\) | 13.6847 | 0.445870 | ||||||||
\(943\) | 37.3693 | 1.21691 | ||||||||
\(944\) | −3.12311 | −0.101648 | ||||||||
\(945\) | 2.56155 | 0.0833273 | ||||||||
\(946\) | −12.4924 | −0.406164 | ||||||||
\(947\) | 54.4384 | 1.76901 | 0.884506 | − | 0.466529i | \(-0.154496\pi\) | ||||
0.884506 | + | 0.466529i | \(0.154496\pi\) | |||||||
\(948\) | 2.43845 | 0.0791971 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.43845 | 0.0791137 | ||||||||
\(951\) | −16.5616 | −0.537045 | ||||||||
\(952\) | −8.12311 | −0.263271 | ||||||||
\(953\) | 21.1231 | 0.684245 | 0.342122 | − | 0.939655i | \(-0.388854\pi\) | ||||
0.342122 | + | 0.939655i | \(0.388854\pi\) | |||||||
\(954\) | 7.00000 | 0.226633 | ||||||||
\(955\) | −8.00000 | −0.258874 | ||||||||
\(956\) | −5.36932 | −0.173656 | ||||||||
\(957\) | −3.31534 | −0.107170 | ||||||||
\(958\) | 26.9309 | 0.870097 | ||||||||
\(959\) | 16.5616 | 0.534800 | ||||||||
\(960\) | 2.56155 | 0.0826738 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.9309 | −0.481141 | ||||||||
\(964\) | −20.8078 | −0.670173 | ||||||||
\(965\) | 20.8078 | 0.669826 | ||||||||
\(966\) | −7.12311 | −0.229182 | ||||||||
\(967\) | 4.49242 | 0.144467 | 0.0722333 | − | 0.997388i | \(-0.476987\pi\) | ||||
0.0722333 | + | 0.997388i | \(0.476987\pi\) | |||||||
\(968\) | −8.56155 | −0.275179 | ||||||||
\(969\) | 12.6847 | 0.407490 | ||||||||
\(970\) | 23.3693 | 0.750344 | ||||||||
\(971\) | 0.384472 | 0.0123383 | 0.00616914 | − | 0.999981i | \(-0.498036\pi\) | ||||
0.00616914 | + | 0.999981i | \(0.498036\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −9.56155 | −0.306529 | ||||||||
\(974\) | 11.3153 | 0.362567 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.24621 | 0.167927 | ||||||||
\(977\) | 4.17708 | 0.133637 | 0.0668183 | − | 0.997765i | \(-0.478715\pi\) | ||||
0.0668183 | + | 0.997765i | \(0.478715\pi\) | |||||||
\(978\) | 8.49242 | 0.271558 | ||||||||
\(979\) | 11.8078 | 0.377378 | ||||||||
\(980\) | −2.56155 | −0.0818258 | ||||||||
\(981\) | 4.24621 | 0.135571 | ||||||||
\(982\) | 16.4924 | 0.526294 | ||||||||
\(983\) | −30.7386 | −0.980410 | −0.490205 | − | 0.871607i | \(-0.663078\pi\) | ||||
−0.490205 | + | 0.871607i | \(0.663078\pi\) | |||||||
\(984\) | −5.24621 | −0.167243 | ||||||||
\(985\) | −21.6155 | −0.688728 | ||||||||
\(986\) | −17.2462 | −0.549231 | ||||||||
\(987\) | 12.6847 | 0.403757 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −56.9848 | −1.81201 | ||||||||
\(990\) | −4.00000 | −0.127128 | ||||||||
\(991\) | 49.6695 | 1.57780 | 0.788902 | − | 0.614519i | \(-0.210650\pi\) | ||||
0.788902 | + | 0.614519i | \(0.210650\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.36932 | 0.170390 | ||||||||
\(994\) | 13.3693 | 0.424049 | ||||||||
\(995\) | 40.9848 | 1.29931 | ||||||||
\(996\) | −3.12311 | −0.0989594 | ||||||||
\(997\) | 23.9848 | 0.759608 | 0.379804 | − | 0.925067i | \(-0.375991\pi\) | ||||
0.379804 | + | 0.925067i | \(0.375991\pi\) | |||||||
\(998\) | 13.7538 | 0.435369 | ||||||||
\(999\) | 6.56155 | 0.207598 |
(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 | 7098.2.a.bt.1.1 | 2 | ||
13.3 | even | 3 | 546.2.l.l.295.1 | yes | 4 | ||
13.9 | even | 3 | 546.2.l.l.211.1 | ✓ | 4 | ||
13.12 | even | 2 | 7098.2.a.bi.1.2 | 2 | |||
39.29 | odd | 6 | 1638.2.r.y.1387.2 | 4 | |||
39.35 | odd | 6 | 1638.2.r.y.757.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.l.211.1 | ✓ | 4 | 13.9 | even | 3 | ||
546.2.l.l.295.1 | yes | 4 | 13.3 | even | 3 | ||
1638.2.r.y.757.2 | 4 | 39.35 | odd | 6 | |||
1638.2.r.y.1387.2 | 4 | 39.29 | odd | 6 | |||
7098.2.a.bi.1.2 | 2 | 13.12 | even | 2 | |||
7098.2.a.bt.1.1 | 2 | 1.1 | even | 1 | trivial |