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 | \(-1.56155\) 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 | ||||||||
\(5\) | −0.561553 | −0.251134 | −0.125567 | − | 0.992085i | \(-0.540075\pi\) | ||||
−0.125567 | + | 0.992085i | \(0.540075\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.561553 | 0.177579 | ||||||||
\(11\) | 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 | ||||||||
\(15\) | −0.561553 | −0.144992 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.00000 | −1.21268 | −0.606339 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606339 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.68466 | 1.07473 | 0.537367 | − | 0.843348i | \(-0.319419\pi\) | ||||
0.537367 | + | 0.843348i | \(0.319419\pi\) | |||||||
\(20\) | −0.561553 | −0.125567 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.56155 | −0.332924 | ||||||||
\(23\) | −0.876894 | −0.182845 | −0.0914226 | − | 0.995812i | \(-0.529141\pi\) | ||||
−0.0914226 | + | 0.995812i | \(0.529141\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −4.68466 | −0.936932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 0.561553 | 0.102525 | ||||||||
\(31\) | 3.12311 | 0.560926 | 0.280463 | − | 0.959865i | \(-0.409512\pi\) | ||||
0.280463 | + | 0.959865i | \(0.409512\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.56155 | 0.271831 | ||||||||
\(34\) | 5.00000 | 0.857493 | ||||||||
\(35\) | −0.561553 | −0.0949197 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.8078 | −1.77679 | −0.888393 | − | 0.459084i | \(-0.848178\pi\) | ||||
−0.888393 | + | 0.459084i | \(0.848178\pi\) | |||||||
\(38\) | −4.68466 | −0.759952 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.561553 | 0.0887893 | ||||||||
\(41\) | 4.12311 | 0.643921 | 0.321960 | − | 0.946753i | \(-0.395658\pi\) | ||||
0.321960 | + | 0.946753i | \(0.395658\pi\) | |||||||
\(42\) | −1.00000 | −0.154303 | ||||||||
\(43\) | −11.1231 | −1.69626 | −0.848129 | − | 0.529790i | \(-0.822271\pi\) | ||||
−0.848129 | + | 0.529790i | \(0.822271\pi\) | |||||||
\(44\) | 1.56155 | 0.235413 | ||||||||
\(45\) | −0.561553 | −0.0837114 | ||||||||
\(46\) | 0.876894 | 0.129291 | ||||||||
\(47\) | −4.68466 | −0.683328 | −0.341664 | − | 0.939822i | \(-0.610990\pi\) | ||||
−0.341664 | + | 0.939822i | \(0.610990\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.68466 | 0.662511 | ||||||||
\(51\) | −5.00000 | −0.700140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.1231 | −1.66524 | −0.832618 | − | 0.553847i | \(-0.813159\pi\) | ||||
−0.832618 | + | 0.553847i | \(0.813159\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −0.876894 | −0.118240 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 4.68466 | 0.620498 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | −4.87689 | −0.634918 | −0.317459 | − | 0.948272i | \(-0.602830\pi\) | ||||
−0.317459 | + | 0.948272i | \(0.602830\pi\) | |||||||
\(60\) | −0.561553 | −0.0724962 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | −3.12311 | −0.396635 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.56155 | −0.192214 | ||||||||
\(67\) | 7.12311 | 0.870226 | 0.435113 | − | 0.900376i | \(-0.356708\pi\) | ||||
0.435113 | + | 0.900376i | \(0.356708\pi\) | |||||||
\(68\) | −5.00000 | −0.606339 | ||||||||
\(69\) | −0.876894 | −0.105566 | ||||||||
\(70\) | 0.561553 | 0.0671184 | ||||||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 6.56155 | 0.767972 | 0.383986 | − | 0.923339i | \(-0.374551\pi\) | ||||
0.383986 | + | 0.923339i | \(0.374551\pi\) | |||||||
\(74\) | 10.8078 | 1.25638 | ||||||||
\(75\) | −4.68466 | −0.540938 | ||||||||
\(76\) | 4.68466 | 0.537367 | ||||||||
\(77\) | 1.56155 | 0.177955 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.56155 | 0.625724 | 0.312862 | − | 0.949799i | \(-0.398712\pi\) | ||||
0.312862 | + | 0.949799i | \(0.398712\pi\) | |||||||
\(80\) | −0.561553 | −0.0627835 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.12311 | −0.455321 | ||||||||
\(83\) | −6.24621 | −0.685611 | −0.342805 | − | 0.939406i | \(-0.611377\pi\) | ||||
−0.342805 | + | 0.939406i | \(0.611377\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 2.80776 | 0.304545 | ||||||||
\(86\) | 11.1231 | 1.19944 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | −1.56155 | −0.166462 | ||||||||
\(89\) | −2.68466 | −0.284573 | −0.142287 | − | 0.989825i | \(-0.545445\pi\) | ||||
−0.142287 | + | 0.989825i | \(0.545445\pi\) | |||||||
\(90\) | 0.561553 | 0.0591929 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.876894 | −0.0914226 | ||||||||
\(93\) | 3.12311 | 0.323851 | ||||||||
\(94\) | 4.68466 | 0.483186 | ||||||||
\(95\) | −2.63068 | −0.269902 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.24621 | 0.431137 | 0.215569 | − | 0.976489i | \(-0.430839\pi\) | ||||
0.215569 | + | 0.976489i | \(0.430839\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 1.56155 | 0.156942 | ||||||||
\(100\) | −4.68466 | −0.468466 | ||||||||
\(101\) | −15.4384 | −1.53618 | −0.768091 | − | 0.640340i | \(-0.778793\pi\) | ||||
−0.768091 | + | 0.640340i | \(0.778793\pi\) | |||||||
\(102\) | 5.00000 | 0.495074 | ||||||||
\(103\) | 13.3693 | 1.31732 | 0.658659 | − | 0.752442i | \(-0.271124\pi\) | ||||
0.658659 | + | 0.752442i | \(0.271124\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.561553 | −0.0548019 | ||||||||
\(106\) | 12.1231 | 1.17750 | ||||||||
\(107\) | −13.5616 | −1.31104 | −0.655522 | − | 0.755176i | \(-0.727552\pi\) | ||||
−0.655522 | + | 0.755176i | \(0.727552\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −9.12311 | −0.873835 | −0.436918 | − | 0.899502i | \(-0.643930\pi\) | ||||
−0.436918 | + | 0.899502i | \(0.643930\pi\) | |||||||
\(110\) | 0.876894 | 0.0836086 | ||||||||
\(111\) | −10.8078 | −1.02583 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −11.9309 | −1.12236 | −0.561181 | − | 0.827693i | \(-0.689653\pi\) | ||||
−0.561181 | + | 0.827693i | \(0.689653\pi\) | |||||||
\(114\) | −4.68466 | −0.438758 | ||||||||
\(115\) | 0.492423 | 0.0459186 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.87689 | 0.448955 | ||||||||
\(119\) | −5.00000 | −0.458349 | ||||||||
\(120\) | 0.561553 | 0.0512625 | ||||||||
\(121\) | −8.56155 | −0.778323 | ||||||||
\(122\) | 1.00000 | 0.0905357 | ||||||||
\(123\) | 4.12311 | 0.371768 | ||||||||
\(124\) | 3.12311 | 0.280463 | ||||||||
\(125\) | 5.43845 | 0.486430 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −14.2462 | −1.26415 | −0.632073 | − | 0.774909i | \(-0.717796\pi\) | ||||
−0.632073 | + | 0.774909i | \(0.717796\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.1231 | −0.979335 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4924 | 1.44095 | 0.720475 | − | 0.693481i | \(-0.243924\pi\) | ||||
0.720475 | + | 0.693481i | \(0.243924\pi\) | |||||||
\(132\) | 1.56155 | 0.135916 | ||||||||
\(133\) | 4.68466 | 0.406211 | ||||||||
\(134\) | −7.12311 | −0.615343 | ||||||||
\(135\) | −0.561553 | −0.0483308 | ||||||||
\(136\) | 5.00000 | 0.428746 | ||||||||
\(137\) | −14.8078 | −1.26511 | −0.632556 | − | 0.774514i | \(-0.717994\pi\) | ||||
−0.632556 | + | 0.774514i | \(0.717994\pi\) | |||||||
\(138\) | 0.876894 | 0.0746462 | ||||||||
\(139\) | 4.68466 | 0.397348 | 0.198674 | − | 0.980066i | \(-0.436337\pi\) | ||||
0.198674 | + | 0.980066i | \(0.436337\pi\) | |||||||
\(140\) | −0.561553 | −0.0474599 | ||||||||
\(141\) | −4.68466 | −0.394519 | ||||||||
\(142\) | −4.00000 | −0.335673 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0.561553 | 0.0466344 | ||||||||
\(146\) | −6.56155 | −0.543038 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | −10.8078 | −0.888393 | ||||||||
\(149\) | −2.80776 | −0.230021 | −0.115010 | − | 0.993364i | \(-0.536690\pi\) | ||||
−0.115010 | + | 0.993364i | \(0.536690\pi\) | |||||||
\(150\) | 4.68466 | 0.382501 | ||||||||
\(151\) | 21.5616 | 1.75465 | 0.877327 | − | 0.479893i | \(-0.159324\pi\) | ||||
0.877327 | + | 0.479893i | \(0.159324\pi\) | |||||||
\(152\) | −4.68466 | −0.379976 | ||||||||
\(153\) | −5.00000 | −0.404226 | ||||||||
\(154\) | −1.56155 | −0.125834 | ||||||||
\(155\) | −1.75379 | −0.140868 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8078 | 1.18179 | 0.590894 | − | 0.806749i | \(-0.298775\pi\) | ||||
0.590894 | + | 0.806749i | \(0.298775\pi\) | |||||||
\(158\) | −5.56155 | −0.442453 | ||||||||
\(159\) | −12.1231 | −0.961425 | ||||||||
\(160\) | 0.561553 | 0.0443946 | ||||||||
\(161\) | −0.876894 | −0.0691090 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −7.12311 | −0.557925 | −0.278962 | − | 0.960302i | \(-0.589990\pi\) | ||||
−0.278962 | + | 0.960302i | \(0.589990\pi\) | |||||||
\(164\) | 4.12311 | 0.321960 | ||||||||
\(165\) | −0.876894 | −0.0682661 | ||||||||
\(166\) | 6.24621 | 0.484800 | ||||||||
\(167\) | 12.4924 | 0.966693 | 0.483346 | − | 0.875429i | \(-0.339421\pi\) | ||||
0.483346 | + | 0.875429i | \(0.339421\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2.80776 | −0.215346 | ||||||||
\(171\) | 4.68466 | 0.358245 | ||||||||
\(172\) | −11.1231 | −0.848129 | ||||||||
\(173\) | −13.1231 | −0.997731 | −0.498866 | − | 0.866679i | \(-0.666250\pi\) | ||||
−0.498866 | + | 0.866679i | \(0.666250\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | −4.68466 | −0.354127 | ||||||||
\(176\) | 1.56155 | 0.117706 | ||||||||
\(177\) | −4.87689 | −0.366570 | ||||||||
\(178\) | 2.68466 | 0.201224 | ||||||||
\(179\) | 16.4924 | 1.23270 | 0.616351 | − | 0.787472i | \(-0.288610\pi\) | ||||
0.616351 | + | 0.787472i | \(0.288610\pi\) | |||||||
\(180\) | −0.561553 | −0.0418557 | ||||||||
\(181\) | −3.24621 | −0.241289 | −0.120644 | − | 0.992696i | \(-0.538496\pi\) | ||||
−0.120644 | + | 0.992696i | \(0.538496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 0.876894 | 0.0646455 | ||||||||
\(185\) | 6.06913 | 0.446211 | ||||||||
\(186\) | −3.12311 | −0.228997 | ||||||||
\(187\) | −7.80776 | −0.570960 | ||||||||
\(188\) | −4.68466 | −0.341664 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 2.63068 | 0.190850 | ||||||||
\(191\) | 22.2462 | 1.60968 | 0.804840 | − | 0.593492i | \(-0.202251\pi\) | ||||
0.804840 | + | 0.593492i | \(0.202251\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −4.36932 | −0.314510 | −0.157255 | − | 0.987558i | \(-0.550265\pi\) | ||||
−0.157255 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(194\) | −4.24621 | −0.304860 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −3.56155 | −0.253750 | −0.126875 | − | 0.991919i | \(-0.540495\pi\) | ||||
−0.126875 | + | 0.991919i | \(0.540495\pi\) | |||||||
\(198\) | −1.56155 | −0.110975 | ||||||||
\(199\) | 23.6155 | 1.67406 | 0.837030 | − | 0.547157i | \(-0.184290\pi\) | ||||
0.837030 | + | 0.547157i | \(0.184290\pi\) | |||||||
\(200\) | 4.68466 | 0.331255 | ||||||||
\(201\) | 7.12311 | 0.502425 | ||||||||
\(202\) | 15.4384 | 1.08625 | ||||||||
\(203\) | −1.00000 | −0.0701862 | ||||||||
\(204\) | −5.00000 | −0.350070 | ||||||||
\(205\) | −2.31534 | −0.161710 | ||||||||
\(206\) | −13.3693 | −0.931484 | ||||||||
\(207\) | −0.876894 | −0.0609484 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.31534 | 0.506013 | ||||||||
\(210\) | 0.561553 | 0.0387508 | ||||||||
\(211\) | −11.1231 | −0.765746 | −0.382873 | − | 0.923801i | \(-0.625065\pi\) | ||||
−0.382873 | + | 0.923801i | \(0.625065\pi\) | |||||||
\(212\) | −12.1231 | −0.832618 | ||||||||
\(213\) | 4.00000 | 0.274075 | ||||||||
\(214\) | 13.5616 | 0.927049 | ||||||||
\(215\) | 6.24621 | 0.425988 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 3.12311 | 0.212010 | ||||||||
\(218\) | 9.12311 | 0.617895 | ||||||||
\(219\) | 6.56155 | 0.443389 | ||||||||
\(220\) | −0.876894 | −0.0591202 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 10.8078 | 0.725370 | ||||||||
\(223\) | −16.4924 | −1.10441 | −0.552207 | − | 0.833707i | \(-0.686214\pi\) | ||||
−0.552207 | + | 0.833707i | \(0.686214\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −4.68466 | −0.312311 | ||||||||
\(226\) | 11.9309 | 0.793630 | ||||||||
\(227\) | −4.87689 | −0.323691 | −0.161845 | − | 0.986816i | \(-0.551745\pi\) | ||||
−0.161845 | + | 0.986816i | \(0.551745\pi\) | |||||||
\(228\) | 4.68466 | 0.310249 | ||||||||
\(229\) | −2.19224 | −0.144867 | −0.0724335 | − | 0.997373i | \(-0.523077\pi\) | ||||
−0.0724335 | + | 0.997373i | \(0.523077\pi\) | |||||||
\(230\) | −0.492423 | −0.0324694 | ||||||||
\(231\) | 1.56155 | 0.102743 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.63068 | 0.171607 | ||||||||
\(236\) | −4.87689 | −0.317459 | ||||||||
\(237\) | 5.56155 | 0.361262 | ||||||||
\(238\) | 5.00000 | 0.324102 | ||||||||
\(239\) | −4.00000 | −0.258738 | −0.129369 | − | 0.991596i | \(-0.541295\pi\) | ||||
−0.129369 | + | 0.991596i | \(0.541295\pi\) | |||||||
\(240\) | −0.561553 | −0.0362481 | ||||||||
\(241\) | −23.6847 | −1.52566 | −0.762831 | − | 0.646597i | \(-0.776191\pi\) | ||||
−0.762831 | + | 0.646597i | \(0.776191\pi\) | |||||||
\(242\) | 8.56155 | 0.550357 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | −0.561553 | −0.0358763 | ||||||||
\(246\) | −4.12311 | −0.262880 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.12311 | −0.198317 | ||||||||
\(249\) | −6.24621 | −0.395838 | ||||||||
\(250\) | −5.43845 | −0.343958 | ||||||||
\(251\) | −24.4924 | −1.54595 | −0.772974 | − | 0.634438i | \(-0.781232\pi\) | ||||
−0.772974 | + | 0.634438i | \(0.781232\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −1.36932 | −0.0860882 | ||||||||
\(254\) | 14.2462 | 0.893887 | ||||||||
\(255\) | 2.80776 | 0.175829 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −31.2462 | −1.94909 | −0.974543 | − | 0.224203i | \(-0.928022\pi\) | ||||
−0.974543 | + | 0.224203i | \(0.928022\pi\) | |||||||
\(258\) | 11.1231 | 0.692494 | ||||||||
\(259\) | −10.8078 | −0.671562 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −16.4924 | −1.01891 | ||||||||
\(263\) | 12.4924 | 0.770316 | 0.385158 | − | 0.922851i | \(-0.374147\pi\) | ||||
0.385158 | + | 0.922851i | \(0.374147\pi\) | |||||||
\(264\) | −1.56155 | −0.0961069 | ||||||||
\(265\) | 6.80776 | 0.418198 | ||||||||
\(266\) | −4.68466 | −0.287235 | ||||||||
\(267\) | −2.68466 | −0.164298 | ||||||||
\(268\) | 7.12311 | 0.435113 | ||||||||
\(269\) | −13.1231 | −0.800130 | −0.400065 | − | 0.916487i | \(-0.631012\pi\) | ||||
−0.400065 | + | 0.916487i | \(0.631012\pi\) | |||||||
\(270\) | 0.561553 | 0.0341750 | ||||||||
\(271\) | −4.87689 | −0.296250 | −0.148125 | − | 0.988969i | \(-0.547324\pi\) | ||||
−0.148125 | + | 0.988969i | \(0.547324\pi\) | |||||||
\(272\) | −5.00000 | −0.303170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.8078 | 0.894570 | ||||||||
\(275\) | −7.31534 | −0.441132 | ||||||||
\(276\) | −0.876894 | −0.0527828 | ||||||||
\(277\) | 0.561553 | 0.0337404 | 0.0168702 | − | 0.999858i | \(-0.494630\pi\) | ||||
0.0168702 | + | 0.999858i | \(0.494630\pi\) | |||||||
\(278\) | −4.68466 | −0.280967 | ||||||||
\(279\) | 3.12311 | 0.186975 | ||||||||
\(280\) | 0.561553 | 0.0335592 | ||||||||
\(281\) | 12.8078 | 0.764047 | 0.382024 | − | 0.924153i | \(-0.375227\pi\) | ||||
0.382024 | + | 0.924153i | \(0.375227\pi\) | |||||||
\(282\) | 4.68466 | 0.278967 | ||||||||
\(283\) | −24.4924 | −1.45592 | −0.727962 | − | 0.685618i | \(-0.759532\pi\) | ||||
−0.727962 | + | 0.685618i | \(0.759532\pi\) | |||||||
\(284\) | 4.00000 | 0.237356 | ||||||||
\(285\) | −2.63068 | −0.155828 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.12311 | 0.243379 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | −0.561553 | −0.0329755 | ||||||||
\(291\) | 4.24621 | 0.248917 | ||||||||
\(292\) | 6.56155 | 0.383986 | ||||||||
\(293\) | −7.68466 | −0.448943 | −0.224471 | − | 0.974481i | \(-0.572065\pi\) | ||||
−0.224471 | + | 0.974481i | \(0.572065\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 2.73863 | 0.159449 | ||||||||
\(296\) | 10.8078 | 0.628189 | ||||||||
\(297\) | 1.56155 | 0.0906105 | ||||||||
\(298\) | 2.80776 | 0.162649 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.68466 | −0.270469 | ||||||||
\(301\) | −11.1231 | −0.641125 | ||||||||
\(302\) | −21.5616 | −1.24073 | ||||||||
\(303\) | −15.4384 | −0.886916 | ||||||||
\(304\) | 4.68466 | 0.268684 | ||||||||
\(305\) | 0.561553 | 0.0321544 | ||||||||
\(306\) | 5.00000 | 0.285831 | ||||||||
\(307\) | 5.06913 | 0.289311 | 0.144655 | − | 0.989482i | \(-0.453793\pi\) | ||||
0.144655 | + | 0.989482i | \(0.453793\pi\) | |||||||
\(308\) | 1.56155 | 0.0889777 | ||||||||
\(309\) | 13.3693 | 0.760554 | ||||||||
\(310\) | 1.75379 | 0.0996085 | ||||||||
\(311\) | 18.4384 | 1.04555 | 0.522774 | − | 0.852471i | \(-0.324897\pi\) | ||||
0.522774 | + | 0.852471i | \(0.324897\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.6155 | −0.769595 | −0.384798 | − | 0.923001i | \(-0.625729\pi\) | ||||
−0.384798 | + | 0.923001i | \(0.625729\pi\) | |||||||
\(314\) | −14.8078 | −0.835650 | ||||||||
\(315\) | −0.561553 | −0.0316399 | ||||||||
\(316\) | 5.56155 | 0.312862 | ||||||||
\(317\) | 7.43845 | 0.417785 | 0.208892 | − | 0.977939i | \(-0.433014\pi\) | ||||
0.208892 | + | 0.977939i | \(0.433014\pi\) | |||||||
\(318\) | 12.1231 | 0.679830 | ||||||||
\(319\) | −1.56155 | −0.0874302 | ||||||||
\(320\) | −0.561553 | −0.0313918 | ||||||||
\(321\) | −13.5616 | −0.756932 | ||||||||
\(322\) | 0.876894 | 0.0488674 | ||||||||
\(323\) | −23.4233 | −1.30331 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.12311 | 0.394512 | ||||||||
\(327\) | −9.12311 | −0.504509 | ||||||||
\(328\) | −4.12311 | −0.227660 | ||||||||
\(329\) | −4.68466 | −0.258274 | ||||||||
\(330\) | 0.876894 | 0.0482714 | ||||||||
\(331\) | 10.6307 | 0.584315 | 0.292158 | − | 0.956370i | \(-0.405627\pi\) | ||||
0.292158 | + | 0.956370i | \(0.405627\pi\) | |||||||
\(332\) | −6.24621 | −0.342805 | ||||||||
\(333\) | −10.8078 | −0.592262 | ||||||||
\(334\) | −12.4924 | −0.683555 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 1.00000 | 0.0545545 | ||||||||
\(337\) | 3.49242 | 0.190244 | 0.0951222 | − | 0.995466i | \(-0.469676\pi\) | ||||
0.0951222 | + | 0.995466i | \(0.469676\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.9309 | −0.647996 | ||||||||
\(340\) | 2.80776 | 0.152272 | ||||||||
\(341\) | 4.87689 | 0.264099 | ||||||||
\(342\) | −4.68466 | −0.253317 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 11.1231 | 0.599718 | ||||||||
\(345\) | 0.492423 | 0.0265111 | ||||||||
\(346\) | 13.1231 | 0.705503 | ||||||||
\(347\) | −12.6847 | −0.680948 | −0.340474 | − | 0.940254i | \(-0.610588\pi\) | ||||
−0.340474 | + | 0.940254i | \(0.610588\pi\) | |||||||
\(348\) | −1.00000 | −0.0536056 | ||||||||
\(349\) | −26.4924 | −1.41811 | −0.709053 | − | 0.705155i | \(-0.750878\pi\) | ||||
−0.709053 | + | 0.705155i | \(0.750878\pi\) | |||||||
\(350\) | 4.68466 | 0.250406 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.56155 | −0.0832310 | ||||||||
\(353\) | −10.8078 | −0.575239 | −0.287620 | − | 0.957745i | \(-0.592864\pi\) | ||||
−0.287620 | + | 0.957745i | \(0.592864\pi\) | |||||||
\(354\) | 4.87689 | 0.259204 | ||||||||
\(355\) | −2.24621 | −0.119217 | ||||||||
\(356\) | −2.68466 | −0.142287 | ||||||||
\(357\) | −5.00000 | −0.264628 | ||||||||
\(358\) | −16.4924 | −0.871652 | ||||||||
\(359\) | 29.3693 | 1.55005 | 0.775027 | − | 0.631929i | \(-0.217736\pi\) | ||||
0.775027 | + | 0.631929i | \(0.217736\pi\) | |||||||
\(360\) | 0.561553 | 0.0295964 | ||||||||
\(361\) | 2.94602 | 0.155054 | ||||||||
\(362\) | 3.24621 | 0.170617 | ||||||||
\(363\) | −8.56155 | −0.449365 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.68466 | −0.192864 | ||||||||
\(366\) | 1.00000 | 0.0522708 | ||||||||
\(367\) | −13.3693 | −0.697873 | −0.348936 | − | 0.937146i | \(-0.613457\pi\) | ||||
−0.348936 | + | 0.937146i | \(0.613457\pi\) | |||||||
\(368\) | −0.876894 | −0.0457113 | ||||||||
\(369\) | 4.12311 | 0.214640 | ||||||||
\(370\) | −6.06913 | −0.315519 | ||||||||
\(371\) | −12.1231 | −0.629400 | ||||||||
\(372\) | 3.12311 | 0.161925 | ||||||||
\(373\) | 17.4384 | 0.902929 | 0.451464 | − | 0.892289i | \(-0.350902\pi\) | ||||
0.451464 | + | 0.892289i | \(0.350902\pi\) | |||||||
\(374\) | 7.80776 | 0.403730 | ||||||||
\(375\) | 5.43845 | 0.280840 | ||||||||
\(376\) | 4.68466 | 0.241593 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 32.4924 | 1.66902 | 0.834512 | − | 0.550990i | \(-0.185750\pi\) | ||||
0.834512 | + | 0.550990i | \(0.185750\pi\) | |||||||
\(380\) | −2.63068 | −0.134951 | ||||||||
\(381\) | −14.2462 | −0.729856 | ||||||||
\(382\) | −22.2462 | −1.13822 | ||||||||
\(383\) | −20.6847 | −1.05694 | −0.528468 | − | 0.848953i | \(-0.677233\pi\) | ||||
−0.528468 | + | 0.848953i | \(0.677233\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −0.876894 | −0.0446907 | ||||||||
\(386\) | 4.36932 | 0.222392 | ||||||||
\(387\) | −11.1231 | −0.565419 | ||||||||
\(388\) | 4.24621 | 0.215569 | ||||||||
\(389\) | 6.31534 | 0.320201 | 0.160100 | − | 0.987101i | \(-0.448818\pi\) | ||||
0.160100 | + | 0.987101i | \(0.448818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.38447 | 0.221732 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 16.4924 | 0.831933 | ||||||||
\(394\) | 3.56155 | 0.179428 | ||||||||
\(395\) | −3.12311 | −0.157140 | ||||||||
\(396\) | 1.56155 | 0.0784710 | ||||||||
\(397\) | 10.6847 | 0.536248 | 0.268124 | − | 0.963384i | \(-0.413596\pi\) | ||||
0.268124 | + | 0.963384i | \(0.413596\pi\) | |||||||
\(398\) | −23.6155 | −1.18374 | ||||||||
\(399\) | 4.68466 | 0.234526 | ||||||||
\(400\) | −4.68466 | −0.234233 | ||||||||
\(401\) | 30.1771 | 1.50697 | 0.753486 | − | 0.657464i | \(-0.228371\pi\) | ||||
0.753486 | + | 0.657464i | \(0.228371\pi\) | |||||||
\(402\) | −7.12311 | −0.355268 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −15.4384 | −0.768091 | ||||||||
\(405\) | −0.561553 | −0.0279038 | ||||||||
\(406\) | 1.00000 | 0.0496292 | ||||||||
\(407\) | −16.8769 | −0.836557 | ||||||||
\(408\) | 5.00000 | 0.247537 | ||||||||
\(409\) | 34.5616 | 1.70896 | 0.854479 | − | 0.519485i | \(-0.173876\pi\) | ||||
0.854479 | + | 0.519485i | \(0.173876\pi\) | |||||||
\(410\) | 2.31534 | 0.114347 | ||||||||
\(411\) | −14.8078 | −0.730413 | ||||||||
\(412\) | 13.3693 | 0.658659 | ||||||||
\(413\) | −4.87689 | −0.239976 | ||||||||
\(414\) | 0.876894 | 0.0430970 | ||||||||
\(415\) | 3.50758 | 0.172180 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.68466 | 0.229409 | ||||||||
\(418\) | −7.31534 | −0.357805 | ||||||||
\(419\) | −26.7386 | −1.30627 | −0.653134 | − | 0.757242i | \(-0.726546\pi\) | ||||
−0.653134 | + | 0.757242i | \(0.726546\pi\) | |||||||
\(420\) | −0.561553 | −0.0274010 | ||||||||
\(421\) | −12.5616 | −0.612213 | −0.306106 | − | 0.951997i | \(-0.599026\pi\) | ||||
−0.306106 | + | 0.951997i | \(0.599026\pi\) | |||||||
\(422\) | 11.1231 | 0.541464 | ||||||||
\(423\) | −4.68466 | −0.227776 | ||||||||
\(424\) | 12.1231 | 0.588750 | ||||||||
\(425\) | 23.4233 | 1.13620 | ||||||||
\(426\) | −4.00000 | −0.193801 | ||||||||
\(427\) | −1.00000 | −0.0483934 | ||||||||
\(428\) | −13.5616 | −0.655522 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.24621 | −0.301219 | ||||||||
\(431\) | −30.7386 | −1.48063 | −0.740314 | − | 0.672261i | \(-0.765323\pi\) | ||||
−0.740314 | + | 0.672261i | \(0.765323\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −17.6847 | −0.849870 | −0.424935 | − | 0.905224i | \(-0.639703\pi\) | ||||
−0.424935 | + | 0.905224i | \(0.639703\pi\) | |||||||
\(434\) | −3.12311 | −0.149914 | ||||||||
\(435\) | 0.561553 | 0.0269244 | ||||||||
\(436\) | −9.12311 | −0.436918 | ||||||||
\(437\) | −4.10795 | −0.196510 | ||||||||
\(438\) | −6.56155 | −0.313523 | ||||||||
\(439\) | 4.49242 | 0.214412 | 0.107206 | − | 0.994237i | \(-0.465810\pi\) | ||||
0.107206 | + | 0.994237i | \(0.465810\pi\) | |||||||
\(440\) | 0.876894 | 0.0418043 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 27.4233 | 1.30292 | 0.651460 | − | 0.758683i | \(-0.274157\pi\) | ||||
0.651460 | + | 0.758683i | \(0.274157\pi\) | |||||||
\(444\) | −10.8078 | −0.512914 | ||||||||
\(445\) | 1.50758 | 0.0714660 | ||||||||
\(446\) | 16.4924 | 0.780939 | ||||||||
\(447\) | −2.80776 | −0.132803 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 4.68466 | 0.220837 | ||||||||
\(451\) | 6.43845 | 0.303175 | ||||||||
\(452\) | −11.9309 | −0.561181 | ||||||||
\(453\) | 21.5616 | 1.01305 | ||||||||
\(454\) | 4.87689 | 0.228884 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.68466 | −0.219379 | ||||||||
\(457\) | 25.6847 | 1.20148 | 0.600739 | − | 0.799445i | \(-0.294873\pi\) | ||||
0.600739 | + | 0.799445i | \(0.294873\pi\) | |||||||
\(458\) | 2.19224 | 0.102436 | ||||||||
\(459\) | −5.00000 | −0.233380 | ||||||||
\(460\) | 0.492423 | 0.0229593 | ||||||||
\(461\) | 7.05398 | 0.328536 | 0.164268 | − | 0.986416i | \(-0.447474\pi\) | ||||
0.164268 | + | 0.986416i | \(0.447474\pi\) | |||||||
\(462\) | −1.56155 | −0.0726500 | ||||||||
\(463\) | −0.684658 | −0.0318188 | −0.0159094 | − | 0.999873i | \(-0.505064\pi\) | ||||
−0.0159094 | + | 0.999873i | \(0.505064\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | −1.75379 | −0.0813300 | ||||||||
\(466\) | 6.00000 | 0.277945 | ||||||||
\(467\) | 28.0000 | 1.29569 | 0.647843 | − | 0.761774i | \(-0.275671\pi\) | ||||
0.647843 | + | 0.761774i | \(0.275671\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.12311 | 0.328914 | ||||||||
\(470\) | −2.63068 | −0.121344 | ||||||||
\(471\) | 14.8078 | 0.682306 | ||||||||
\(472\) | 4.87689 | 0.224477 | ||||||||
\(473\) | −17.3693 | −0.798642 | ||||||||
\(474\) | −5.56155 | −0.255451 | ||||||||
\(475\) | −21.9460 | −1.00695 | ||||||||
\(476\) | −5.00000 | −0.229175 | ||||||||
\(477\) | −12.1231 | −0.555079 | ||||||||
\(478\) | 4.00000 | 0.182956 | ||||||||
\(479\) | −1.56155 | −0.0713492 | −0.0356746 | − | 0.999363i | \(-0.511358\pi\) | ||||
−0.0356746 | + | 0.999363i | \(0.511358\pi\) | |||||||
\(480\) | 0.561553 | 0.0256313 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 23.6847 | 1.07881 | ||||||||
\(483\) | −0.876894 | −0.0399001 | ||||||||
\(484\) | −8.56155 | −0.389161 | ||||||||
\(485\) | −2.38447 | −0.108273 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −11.3153 | −0.512747 | −0.256374 | − | 0.966578i | \(-0.582528\pi\) | ||||
−0.256374 | + | 0.966578i | \(0.582528\pi\) | |||||||
\(488\) | 1.00000 | 0.0452679 | ||||||||
\(489\) | −7.12311 | −0.322118 | ||||||||
\(490\) | 0.561553 | 0.0253684 | ||||||||
\(491\) | −18.2462 | −0.823440 | −0.411720 | − | 0.911310i | \(-0.635072\pi\) | ||||
−0.411720 | + | 0.911310i | \(0.635072\pi\) | |||||||
\(492\) | 4.12311 | 0.185884 | ||||||||
\(493\) | 5.00000 | 0.225189 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.876894 | −0.0394135 | ||||||||
\(496\) | 3.12311 | 0.140232 | ||||||||
\(497\) | 4.00000 | 0.179425 | ||||||||
\(498\) | 6.24621 | 0.279899 | ||||||||
\(499\) | 2.63068 | 0.117766 | 0.0588828 | − | 0.998265i | \(-0.481246\pi\) | ||||
0.0588828 | + | 0.998265i | \(0.481246\pi\) | |||||||
\(500\) | 5.43845 | 0.243215 | ||||||||
\(501\) | 12.4924 | 0.558120 | ||||||||
\(502\) | 24.4924 | 1.09315 | ||||||||
\(503\) | −12.4924 | −0.557010 | −0.278505 | − | 0.960435i | \(-0.589839\pi\) | ||||
−0.278505 | + | 0.960435i | \(0.589839\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 8.66950 | 0.385788 | ||||||||
\(506\) | 1.36932 | 0.0608736 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.2462 | −0.632073 | ||||||||
\(509\) | −39.6847 | −1.75899 | −0.879496 | − | 0.475907i | \(-0.842120\pi\) | ||||
−0.879496 | + | 0.475907i | \(0.842120\pi\) | |||||||
\(510\) | −2.80776 | −0.124330 | ||||||||
\(511\) | 6.56155 | 0.290266 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.68466 | 0.206833 | ||||||||
\(514\) | 31.2462 | 1.37821 | ||||||||
\(515\) | −7.50758 | −0.330823 | ||||||||
\(516\) | −11.1231 | −0.489667 | ||||||||
\(517\) | −7.31534 | −0.321728 | ||||||||
\(518\) | 10.8078 | 0.474866 | ||||||||
\(519\) | −13.1231 | −0.576040 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0000 | −0.744784 | −0.372392 | − | 0.928076i | \(-0.621462\pi\) | ||||
−0.372392 | + | 0.928076i | \(0.621462\pi\) | |||||||
\(522\) | 1.00000 | 0.0437688 | ||||||||
\(523\) | 35.8078 | 1.56576 | 0.782882 | − | 0.622170i | \(-0.213749\pi\) | ||||
0.782882 | + | 0.622170i | \(0.213749\pi\) | |||||||
\(524\) | 16.4924 | 0.720475 | ||||||||
\(525\) | −4.68466 | −0.204455 | ||||||||
\(526\) | −12.4924 | −0.544696 | ||||||||
\(527\) | −15.6155 | −0.680223 | ||||||||
\(528\) | 1.56155 | 0.0679579 | ||||||||
\(529\) | −22.2311 | −0.966568 | ||||||||
\(530\) | −6.80776 | −0.295710 | ||||||||
\(531\) | −4.87689 | −0.211639 | ||||||||
\(532\) | 4.68466 | 0.203106 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 2.68466 | 0.116177 | ||||||||
\(535\) | 7.61553 | 0.329248 | ||||||||
\(536\) | −7.12311 | −0.307671 | ||||||||
\(537\) | 16.4924 | 0.711701 | ||||||||
\(538\) | 13.1231 | 0.565777 | ||||||||
\(539\) | 1.56155 | 0.0672608 | ||||||||
\(540\) | −0.561553 | −0.0241654 | ||||||||
\(541\) | 2.56155 | 0.110130 | 0.0550649 | − | 0.998483i | \(-0.482463\pi\) | ||||
0.0550649 | + | 0.998483i | \(0.482463\pi\) | |||||||
\(542\) | 4.87689 | 0.209481 | ||||||||
\(543\) | −3.24621 | −0.139308 | ||||||||
\(544\) | 5.00000 | 0.214373 | ||||||||
\(545\) | 5.12311 | 0.219450 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.7386 | 1.14326 | 0.571631 | − | 0.820511i | \(-0.306311\pi\) | ||||
0.571631 | + | 0.820511i | \(0.306311\pi\) | |||||||
\(548\) | −14.8078 | −0.632556 | ||||||||
\(549\) | −1.00000 | −0.0426790 | ||||||||
\(550\) | 7.31534 | 0.311927 | ||||||||
\(551\) | −4.68466 | −0.199573 | ||||||||
\(552\) | 0.876894 | 0.0373231 | ||||||||
\(553\) | 5.56155 | 0.236501 | ||||||||
\(554\) | −0.561553 | −0.0238581 | ||||||||
\(555\) | 6.06913 | 0.257620 | ||||||||
\(556\) | 4.68466 | 0.198674 | ||||||||
\(557\) | 27.7386 | 1.17532 | 0.587662 | − | 0.809107i | \(-0.300049\pi\) | ||||
0.587662 | + | 0.809107i | \(0.300049\pi\) | |||||||
\(558\) | −3.12311 | −0.132212 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.561553 | −0.0237299 | ||||||||
\(561\) | −7.80776 | −0.329644 | ||||||||
\(562\) | −12.8078 | −0.540263 | ||||||||
\(563\) | −25.3693 | −1.06919 | −0.534595 | − | 0.845109i | \(-0.679536\pi\) | ||||
−0.534595 | + | 0.845109i | \(0.679536\pi\) | |||||||
\(564\) | −4.68466 | −0.197260 | ||||||||
\(565\) | 6.69981 | 0.281863 | ||||||||
\(566\) | 24.4924 | 1.02949 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −29.6155 | −1.24155 | −0.620774 | − | 0.783990i | \(-0.713181\pi\) | ||||
−0.620774 | + | 0.783990i | \(0.713181\pi\) | |||||||
\(570\) | 2.63068 | 0.110187 | ||||||||
\(571\) | 30.2462 | 1.26576 | 0.632882 | − | 0.774248i | \(-0.281872\pi\) | ||||
0.632882 | + | 0.774248i | \(0.281872\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 22.2462 | 0.929349 | ||||||||
\(574\) | −4.12311 | −0.172095 | ||||||||
\(575\) | 4.10795 | 0.171313 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −43.6847 | −1.81862 | −0.909308 | − | 0.416124i | \(-0.863388\pi\) | ||||
−0.909308 | + | 0.416124i | \(0.863388\pi\) | |||||||
\(578\) | −8.00000 | −0.332756 | ||||||||
\(579\) | −4.36932 | −0.181583 | ||||||||
\(580\) | 0.561553 | 0.0233172 | ||||||||
\(581\) | −6.24621 | −0.259137 | ||||||||
\(582\) | −4.24621 | −0.176011 | ||||||||
\(583\) | −18.9309 | −0.784037 | ||||||||
\(584\) | −6.56155 | −0.271519 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.68466 | 0.317450 | ||||||||
\(587\) | −6.63068 | −0.273678 | −0.136839 | − | 0.990593i | \(-0.543694\pi\) | ||||
−0.136839 | + | 0.990593i | \(0.543694\pi\) | |||||||
\(588\) | 1.00000 | 0.0412393 | ||||||||
\(589\) | 14.6307 | 0.602847 | ||||||||
\(590\) | −2.73863 | −0.112748 | ||||||||
\(591\) | −3.56155 | −0.146503 | ||||||||
\(592\) | −10.8078 | −0.444196 | ||||||||
\(593\) | 8.61553 | 0.353797 | 0.176899 | − | 0.984229i | \(-0.443394\pi\) | ||||
0.176899 | + | 0.984229i | \(0.443394\pi\) | |||||||
\(594\) | −1.56155 | −0.0640713 | ||||||||
\(595\) | 2.80776 | 0.115107 | ||||||||
\(596\) | −2.80776 | −0.115010 | ||||||||
\(597\) | 23.6155 | 0.966519 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.1231 | −1.27166 | −0.635828 | − | 0.771831i | \(-0.719341\pi\) | ||||
−0.635828 | + | 0.771831i | \(0.719341\pi\) | |||||||
\(600\) | 4.68466 | 0.191250 | ||||||||
\(601\) | 8.06913 | 0.329147 | 0.164573 | − | 0.986365i | \(-0.447375\pi\) | ||||
0.164573 | + | 0.986365i | \(0.447375\pi\) | |||||||
\(602\) | 11.1231 | 0.453344 | ||||||||
\(603\) | 7.12311 | 0.290075 | ||||||||
\(604\) | 21.5616 | 0.877327 | ||||||||
\(605\) | 4.80776 | 0.195463 | ||||||||
\(606\) | 15.4384 | 0.627144 | ||||||||
\(607\) | 12.8769 | 0.522657 | 0.261329 | − | 0.965250i | \(-0.415839\pi\) | ||||
0.261329 | + | 0.965250i | \(0.415839\pi\) | |||||||
\(608\) | −4.68466 | −0.189988 | ||||||||
\(609\) | −1.00000 | −0.0405220 | ||||||||
\(610\) | −0.561553 | −0.0227366 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −5.00000 | −0.202113 | ||||||||
\(613\) | 17.3002 | 0.698748 | 0.349374 | − | 0.936983i | \(-0.386394\pi\) | ||||
0.349374 | + | 0.936983i | \(0.386394\pi\) | |||||||
\(614\) | −5.06913 | −0.204573 | ||||||||
\(615\) | −2.31534 | −0.0933636 | ||||||||
\(616\) | −1.56155 | −0.0629168 | ||||||||
\(617\) | −34.4233 | −1.38583 | −0.692915 | − | 0.721019i | \(-0.743674\pi\) | ||||
−0.692915 | + | 0.721019i | \(0.743674\pi\) | |||||||
\(618\) | −13.3693 | −0.537793 | ||||||||
\(619\) | −16.6847 | −0.670613 | −0.335307 | − | 0.942109i | \(-0.608840\pi\) | ||||
−0.335307 | + | 0.942109i | \(0.608840\pi\) | |||||||
\(620\) | −1.75379 | −0.0704339 | ||||||||
\(621\) | −0.876894 | −0.0351886 | ||||||||
\(622\) | −18.4384 | −0.739314 | ||||||||
\(623\) | −2.68466 | −0.107559 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | 13.6155 | 0.544186 | ||||||||
\(627\) | 7.31534 | 0.292147 | ||||||||
\(628\) | 14.8078 | 0.590894 | ||||||||
\(629\) | 54.0388 | 2.15467 | ||||||||
\(630\) | 0.561553 | 0.0223728 | ||||||||
\(631\) | −43.8078 | −1.74396 | −0.871980 | − | 0.489542i | \(-0.837164\pi\) | ||||
−0.871980 | + | 0.489542i | \(0.837164\pi\) | |||||||
\(632\) | −5.56155 | −0.221227 | ||||||||
\(633\) | −11.1231 | −0.442104 | ||||||||
\(634\) | −7.43845 | −0.295418 | ||||||||
\(635\) | 8.00000 | 0.317470 | ||||||||
\(636\) | −12.1231 | −0.480712 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.56155 | 0.0618225 | ||||||||
\(639\) | 4.00000 | 0.158238 | ||||||||
\(640\) | 0.561553 | 0.0221973 | ||||||||
\(641\) | 8.06913 | 0.318711 | 0.159356 | − | 0.987221i | \(-0.449058\pi\) | ||||
0.159356 | + | 0.987221i | \(0.449058\pi\) | |||||||
\(642\) | 13.5616 | 0.535232 | ||||||||
\(643\) | 22.4384 | 0.884886 | 0.442443 | − | 0.896797i | \(-0.354112\pi\) | ||||
0.442443 | + | 0.896797i | \(0.354112\pi\) | |||||||
\(644\) | −0.876894 | −0.0345545 | ||||||||
\(645\) | 6.24621 | 0.245944 | ||||||||
\(646\) | 23.4233 | 0.921577 | ||||||||
\(647\) | −0.192236 | −0.00755757 | −0.00377879 | − | 0.999993i | \(-0.501203\pi\) | ||||
−0.00377879 | + | 0.999993i | \(0.501203\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −7.61553 | −0.298936 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.12311 | 0.122404 | ||||||||
\(652\) | −7.12311 | −0.278962 | ||||||||
\(653\) | 1.80776 | 0.0707433 | 0.0353716 | − | 0.999374i | \(-0.488739\pi\) | ||||
0.0353716 | + | 0.999374i | \(0.488739\pi\) | |||||||
\(654\) | 9.12311 | 0.356742 | ||||||||
\(655\) | −9.26137 | −0.361872 | ||||||||
\(656\) | 4.12311 | 0.160980 | ||||||||
\(657\) | 6.56155 | 0.255991 | ||||||||
\(658\) | 4.68466 | 0.182627 | ||||||||
\(659\) | −40.6847 | −1.58485 | −0.792425 | − | 0.609970i | \(-0.791182\pi\) | ||||
−0.792425 | + | 0.609970i | \(0.791182\pi\) | |||||||
\(660\) | −0.876894 | −0.0341331 | ||||||||
\(661\) | −10.8078 | −0.420373 | −0.210187 | − | 0.977661i | \(-0.567407\pi\) | ||||
−0.210187 | + | 0.977661i | \(0.567407\pi\) | |||||||
\(662\) | −10.6307 | −0.413173 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.24621 | 0.242400 | ||||||||
\(665\) | −2.63068 | −0.102014 | ||||||||
\(666\) | 10.8078 | 0.418792 | ||||||||
\(667\) | 0.876894 | 0.0339535 | ||||||||
\(668\) | 12.4924 | 0.483346 | ||||||||
\(669\) | −16.4924 | −0.637634 | ||||||||
\(670\) | 4.00000 | 0.154533 | ||||||||
\(671\) | −1.56155 | −0.0602831 | ||||||||
\(672\) | −1.00000 | −0.0385758 | ||||||||
\(673\) | 25.2462 | 0.973170 | 0.486585 | − | 0.873633i | \(-0.338242\pi\) | ||||
0.486585 | + | 0.873633i | \(0.338242\pi\) | |||||||
\(674\) | −3.49242 | −0.134523 | ||||||||
\(675\) | −4.68466 | −0.180313 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −49.6155 | −1.90688 | −0.953440 | − | 0.301583i | \(-0.902485\pi\) | ||||
−0.953440 | + | 0.301583i | \(0.902485\pi\) | |||||||
\(678\) | 11.9309 | 0.458202 | ||||||||
\(679\) | 4.24621 | 0.162955 | ||||||||
\(680\) | −2.80776 | −0.107673 | ||||||||
\(681\) | −4.87689 | −0.186883 | ||||||||
\(682\) | −4.87689 | −0.186746 | ||||||||
\(683\) | −4.00000 | −0.153056 | −0.0765279 | − | 0.997067i | \(-0.524383\pi\) | ||||
−0.0765279 | + | 0.997067i | \(0.524383\pi\) | |||||||
\(684\) | 4.68466 | 0.179122 | ||||||||
\(685\) | 8.31534 | 0.317713 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −2.19224 | −0.0836390 | ||||||||
\(688\) | −11.1231 | −0.424064 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.492423 | −0.0187462 | ||||||||
\(691\) | −4.49242 | −0.170900 | −0.0854499 | − | 0.996342i | \(-0.527233\pi\) | ||||
−0.0854499 | + | 0.996342i | \(0.527233\pi\) | |||||||
\(692\) | −13.1231 | −0.498866 | ||||||||
\(693\) | 1.56155 | 0.0593185 | ||||||||
\(694\) | 12.6847 | 0.481503 | ||||||||
\(695\) | −2.63068 | −0.0997875 | ||||||||
\(696\) | 1.00000 | 0.0379049 | ||||||||
\(697\) | −20.6155 | −0.780869 | ||||||||
\(698\) | 26.4924 | 1.00275 | ||||||||
\(699\) | −6.00000 | −0.226941 | ||||||||
\(700\) | −4.68466 | −0.177063 | ||||||||
\(701\) | −28.0540 | −1.05958 | −0.529792 | − | 0.848128i | \(-0.677730\pi\) | ||||
−0.529792 | + | 0.848128i | \(0.677730\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −50.6307 | −1.90957 | ||||||||
\(704\) | 1.56155 | 0.0588532 | ||||||||
\(705\) | 2.63068 | 0.0990773 | ||||||||
\(706\) | 10.8078 | 0.406756 | ||||||||
\(707\) | −15.4384 | −0.580623 | ||||||||
\(708\) | −4.87689 | −0.183285 | ||||||||
\(709\) | 33.3002 | 1.25061 | 0.625307 | − | 0.780379i | \(-0.284974\pi\) | ||||
0.625307 | + | 0.780379i | \(0.284974\pi\) | |||||||
\(710\) | 2.24621 | 0.0842988 | ||||||||
\(711\) | 5.56155 | 0.208575 | ||||||||
\(712\) | 2.68466 | 0.100612 | ||||||||
\(713\) | −2.73863 | −0.102563 | ||||||||
\(714\) | 5.00000 | 0.187120 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.4924 | 0.616351 | ||||||||
\(717\) | −4.00000 | −0.149383 | ||||||||
\(718\) | −29.3693 | −1.09605 | ||||||||
\(719\) | −6.93087 | −0.258478 | −0.129239 | − | 0.991613i | \(-0.541253\pi\) | ||||
−0.129239 | + | 0.991613i | \(0.541253\pi\) | |||||||
\(720\) | −0.561553 | −0.0209278 | ||||||||
\(721\) | 13.3693 | 0.497899 | ||||||||
\(722\) | −2.94602 | −0.109640 | ||||||||
\(723\) | −23.6847 | −0.880842 | ||||||||
\(724\) | −3.24621 | −0.120644 | ||||||||
\(725\) | 4.68466 | 0.173984 | ||||||||
\(726\) | 8.56155 | 0.317749 | ||||||||
\(727\) | 33.7538 | 1.25186 | 0.625929 | − | 0.779880i | \(-0.284720\pi\) | ||||
0.625929 | + | 0.779880i | \(0.284720\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.68466 | 0.136375 | ||||||||
\(731\) | 55.6155 | 2.05701 | ||||||||
\(732\) | −1.00000 | −0.0369611 | ||||||||
\(733\) | 8.61553 | 0.318222 | 0.159111 | − | 0.987261i | \(-0.449137\pi\) | ||||
0.159111 | + | 0.987261i | \(0.449137\pi\) | |||||||
\(734\) | 13.3693 | 0.493470 | ||||||||
\(735\) | −0.561553 | −0.0207132 | ||||||||
\(736\) | 0.876894 | 0.0323228 | ||||||||
\(737\) | 11.1231 | 0.409725 | ||||||||
\(738\) | −4.12311 | −0.151774 | ||||||||
\(739\) | −22.6307 | −0.832483 | −0.416242 | − | 0.909254i | \(-0.636653\pi\) | ||||
−0.416242 | + | 0.909254i | \(0.636653\pi\) | |||||||
\(740\) | 6.06913 | 0.223106 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.1231 | 0.445053 | ||||||||
\(743\) | −33.3693 | −1.22420 | −0.612101 | − | 0.790780i | \(-0.709675\pi\) | ||||
−0.612101 | + | 0.790780i | \(0.709675\pi\) | |||||||
\(744\) | −3.12311 | −0.114499 | ||||||||
\(745\) | 1.57671 | 0.0577661 | ||||||||
\(746\) | −17.4384 | −0.638467 | ||||||||
\(747\) | −6.24621 | −0.228537 | ||||||||
\(748\) | −7.80776 | −0.285480 | ||||||||
\(749\) | −13.5616 | −0.495528 | ||||||||
\(750\) | −5.43845 | −0.198584 | ||||||||
\(751\) | 19.8078 | 0.722796 | 0.361398 | − | 0.932412i | \(-0.382300\pi\) | ||||
0.361398 | + | 0.932412i | \(0.382300\pi\) | |||||||
\(752\) | −4.68466 | −0.170832 | ||||||||
\(753\) | −24.4924 | −0.892553 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.1080 | −0.440653 | ||||||||
\(756\) | 1.00000 | 0.0363696 | ||||||||
\(757\) | 1.12311 | 0.0408200 | 0.0204100 | − | 0.999792i | \(-0.493503\pi\) | ||||
0.0204100 | + | 0.999792i | \(0.493503\pi\) | |||||||
\(758\) | −32.4924 | −1.18018 | ||||||||
\(759\) | −1.36932 | −0.0497031 | ||||||||
\(760\) | 2.63068 | 0.0954249 | ||||||||
\(761\) | 9.50758 | 0.344649 | 0.172325 | − | 0.985040i | \(-0.444872\pi\) | ||||
0.172325 | + | 0.985040i | \(0.444872\pi\) | |||||||
\(762\) | 14.2462 | 0.516086 | ||||||||
\(763\) | −9.12311 | −0.330279 | ||||||||
\(764\) | 22.2462 | 0.804840 | ||||||||
\(765\) | 2.80776 | 0.101515 | ||||||||
\(766\) | 20.6847 | 0.747367 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −42.9848 | −1.55007 | −0.775037 | − | 0.631916i | \(-0.782269\pi\) | ||||
−0.775037 | + | 0.631916i | \(0.782269\pi\) | |||||||
\(770\) | 0.876894 | 0.0316011 | ||||||||
\(771\) | −31.2462 | −1.12530 | ||||||||
\(772\) | −4.36932 | −0.157255 | ||||||||
\(773\) | 6.49242 | 0.233516 | 0.116758 | − | 0.993160i | \(-0.462750\pi\) | ||||
0.116758 | + | 0.993160i | \(0.462750\pi\) | |||||||
\(774\) | 11.1231 | 0.399812 | ||||||||
\(775\) | −14.6307 | −0.525550 | ||||||||
\(776\) | −4.24621 | −0.152430 | ||||||||
\(777\) | −10.8078 | −0.387726 | ||||||||
\(778\) | −6.31534 | −0.226416 | ||||||||
\(779\) | 19.3153 | 0.692044 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.24621 | 0.223507 | ||||||||
\(782\) | −4.38447 | −0.156788 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −8.31534 | −0.296787 | ||||||||
\(786\) | −16.4924 | −0.588265 | ||||||||
\(787\) | 19.8078 | 0.706071 | 0.353035 | − | 0.935610i | \(-0.385150\pi\) | ||||
0.353035 | + | 0.935610i | \(0.385150\pi\) | |||||||
\(788\) | −3.56155 | −0.126875 | ||||||||
\(789\) | 12.4924 | 0.444742 | ||||||||
\(790\) | 3.12311 | 0.111115 | ||||||||
\(791\) | −11.9309 | −0.424213 | ||||||||
\(792\) | −1.56155 | −0.0554874 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −10.6847 | −0.379184 | ||||||||
\(795\) | 6.80776 | 0.241447 | ||||||||
\(796\) | 23.6155 | 0.837030 | ||||||||
\(797\) | 50.1080 | 1.77491 | 0.887457 | − | 0.460890i | \(-0.152470\pi\) | ||||
0.887457 | + | 0.460890i | \(0.152470\pi\) | |||||||
\(798\) | −4.68466 | −0.165835 | ||||||||
\(799\) | 23.4233 | 0.828657 | ||||||||
\(800\) | 4.68466 | 0.165628 | ||||||||
\(801\) | −2.68466 | −0.0948577 | ||||||||
\(802\) | −30.1771 | −1.06559 | ||||||||
\(803\) | 10.2462 | 0.361581 | ||||||||
\(804\) | 7.12311 | 0.251213 | ||||||||
\(805\) | 0.492423 | 0.0173556 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.1231 | −0.461955 | ||||||||
\(808\) | 15.4384 | 0.543123 | ||||||||
\(809\) | 17.9309 | 0.630416 | 0.315208 | − | 0.949023i | \(-0.397926\pi\) | ||||
0.315208 | + | 0.949023i | \(0.397926\pi\) | |||||||
\(810\) | 0.561553 | 0.0197310 | ||||||||
\(811\) | −22.2462 | −0.781170 | −0.390585 | − | 0.920567i | \(-0.627727\pi\) | ||||
−0.390585 | + | 0.920567i | \(0.627727\pi\) | |||||||
\(812\) | −1.00000 | −0.0350931 | ||||||||
\(813\) | −4.87689 | −0.171040 | ||||||||
\(814\) | 16.8769 | 0.591535 | ||||||||
\(815\) | 4.00000 | 0.140114 | ||||||||
\(816\) | −5.00000 | −0.175035 | ||||||||
\(817\) | −52.1080 | −1.82303 | ||||||||
\(818\) | −34.5616 | −1.20842 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.31534 | −0.0808552 | ||||||||
\(821\) | 40.9309 | 1.42850 | 0.714249 | − | 0.699892i | \(-0.246769\pi\) | ||||
0.714249 | + | 0.699892i | \(0.246769\pi\) | |||||||
\(822\) | 14.8078 | 0.516480 | ||||||||
\(823\) | −2.24621 | −0.0782980 | −0.0391490 | − | 0.999233i | \(-0.512465\pi\) | ||||
−0.0391490 | + | 0.999233i | \(0.512465\pi\) | |||||||
\(824\) | −13.3693 | −0.465742 | ||||||||
\(825\) | −7.31534 | −0.254688 | ||||||||
\(826\) | 4.87689 | 0.169689 | ||||||||
\(827\) | 44.4924 | 1.54715 | 0.773577 | − | 0.633703i | \(-0.218466\pi\) | ||||
0.773577 | + | 0.633703i | \(0.218466\pi\) | |||||||
\(828\) | −0.876894 | −0.0304742 | ||||||||
\(829\) | −45.1080 | −1.56666 | −0.783332 | − | 0.621604i | \(-0.786481\pi\) | ||||
−0.783332 | + | 0.621604i | \(0.786481\pi\) | |||||||
\(830\) | −3.50758 | −0.121750 | ||||||||
\(831\) | 0.561553 | 0.0194801 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.00000 | −0.173240 | ||||||||
\(834\) | −4.68466 | −0.162216 | ||||||||
\(835\) | −7.01515 | −0.242769 | ||||||||
\(836\) | 7.31534 | 0.253006 | ||||||||
\(837\) | 3.12311 | 0.107950 | ||||||||
\(838\) | 26.7386 | 0.923671 | ||||||||
\(839\) | −8.00000 | −0.276191 | −0.138095 | − | 0.990419i | \(-0.544098\pi\) | ||||
−0.138095 | + | 0.990419i | \(0.544098\pi\) | |||||||
\(840\) | 0.561553 | 0.0193754 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 12.5616 | 0.432900 | ||||||||
\(843\) | 12.8078 | 0.441123 | ||||||||
\(844\) | −11.1231 | −0.382873 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.68466 | 0.161062 | ||||||||
\(847\) | −8.56155 | −0.294178 | ||||||||
\(848\) | −12.1231 | −0.416309 | ||||||||
\(849\) | −24.4924 | −0.840578 | ||||||||
\(850\) | −23.4233 | −0.803412 | ||||||||
\(851\) | 9.47727 | 0.324877 | ||||||||
\(852\) | 4.00000 | 0.137038 | ||||||||
\(853\) | −24.3693 | −0.834390 | −0.417195 | − | 0.908817i | \(-0.636987\pi\) | ||||
−0.417195 | + | 0.908817i | \(0.636987\pi\) | |||||||
\(854\) | 1.00000 | 0.0342193 | ||||||||
\(855\) | −2.63068 | −0.0899675 | ||||||||
\(856\) | 13.5616 | 0.463524 | ||||||||
\(857\) | 31.3002 | 1.06919 | 0.534597 | − | 0.845107i | \(-0.320463\pi\) | ||||
0.534597 | + | 0.845107i | \(0.320463\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.1922 | −0.552472 | −0.276236 | − | 0.961090i | \(-0.589087\pi\) | ||||
−0.276236 | + | 0.961090i | \(0.589087\pi\) | |||||||
\(860\) | 6.24621 | 0.212994 | ||||||||
\(861\) | 4.12311 | 0.140515 | ||||||||
\(862\) | 30.7386 | 1.04696 | ||||||||
\(863\) | 48.1080 | 1.63761 | 0.818807 | − | 0.574069i | \(-0.194636\pi\) | ||||
0.818807 | + | 0.574069i | \(0.194636\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 7.36932 | 0.250564 | ||||||||
\(866\) | 17.6847 | 0.600949 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 3.12311 | 0.106005 | ||||||||
\(869\) | 8.68466 | 0.294607 | ||||||||
\(870\) | −0.561553 | −0.0190384 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 9.12311 | 0.308947 | ||||||||
\(873\) | 4.24621 | 0.143712 | ||||||||
\(874\) | 4.10795 | 0.138954 | ||||||||
\(875\) | 5.43845 | 0.183853 | ||||||||
\(876\) | 6.56155 | 0.221694 | ||||||||
\(877\) | 45.3002 | 1.52968 | 0.764839 | − | 0.644221i | \(-0.222818\pi\) | ||||
0.764839 | + | 0.644221i | \(0.222818\pi\) | |||||||
\(878\) | −4.49242 | −0.151612 | ||||||||
\(879\) | −7.68466 | −0.259197 | ||||||||
\(880\) | −0.876894 | −0.0295601 | ||||||||
\(881\) | 1.82292 | 0.0614157 | 0.0307079 | − | 0.999528i | \(-0.490224\pi\) | ||||
0.0307079 | + | 0.999528i | \(0.490224\pi\) | |||||||
\(882\) | −1.00000 | −0.0336718 | ||||||||
\(883\) | 8.87689 | 0.298731 | 0.149366 | − | 0.988782i | \(-0.452277\pi\) | ||||
0.149366 | + | 0.988782i | \(0.452277\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.73863 | 0.0920582 | ||||||||
\(886\) | −27.4233 | −0.921304 | ||||||||
\(887\) | 9.56155 | 0.321046 | 0.160523 | − | 0.987032i | \(-0.448682\pi\) | ||||
0.160523 | + | 0.987032i | \(0.448682\pi\) | |||||||
\(888\) | 10.8078 | 0.362685 | ||||||||
\(889\) | −14.2462 | −0.477803 | ||||||||
\(890\) | −1.50758 | −0.0505341 | ||||||||
\(891\) | 1.56155 | 0.0523140 | ||||||||
\(892\) | −16.4924 | −0.552207 | ||||||||
\(893\) | −21.9460 | −0.734396 | ||||||||
\(894\) | 2.80776 | 0.0939057 | ||||||||
\(895\) | −9.26137 | −0.309573 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0000 | 0.600668 | ||||||||
\(899\) | −3.12311 | −0.104161 | ||||||||
\(900\) | −4.68466 | −0.156155 | ||||||||
\(901\) | 60.6155 | 2.01940 | ||||||||
\(902\) | −6.43845 | −0.214377 | ||||||||
\(903\) | −11.1231 | −0.370154 | ||||||||
\(904\) | 11.9309 | 0.396815 | ||||||||
\(905\) | 1.82292 | 0.0605959 | ||||||||
\(906\) | −21.5616 | −0.716335 | ||||||||
\(907\) | 31.1231 | 1.03343 | 0.516713 | − | 0.856159i | \(-0.327155\pi\) | ||||
0.516713 | + | 0.856159i | \(0.327155\pi\) | |||||||
\(908\) | −4.87689 | −0.161845 | ||||||||
\(909\) | −15.4384 | −0.512061 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.7386 | −1.81357 | −0.906786 | − | 0.421591i | \(-0.861472\pi\) | ||||
−0.906786 | + | 0.421591i | \(0.861472\pi\) | |||||||
\(912\) | 4.68466 | 0.155125 | ||||||||
\(913\) | −9.75379 | −0.322803 | ||||||||
\(914\) | −25.6847 | −0.849573 | ||||||||
\(915\) | 0.561553 | 0.0185644 | ||||||||
\(916\) | −2.19224 | −0.0724335 | ||||||||
\(917\) | 16.4924 | 0.544628 | ||||||||
\(918\) | 5.00000 | 0.165025 | ||||||||
\(919\) | 2.43845 | 0.0804370 | 0.0402185 | − | 0.999191i | \(-0.487195\pi\) | ||||
0.0402185 | + | 0.999191i | \(0.487195\pi\) | |||||||
\(920\) | −0.492423 | −0.0162347 | ||||||||
\(921\) | 5.06913 | 0.167034 | ||||||||
\(922\) | −7.05398 | −0.232310 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.56155 | 0.0513713 | ||||||||
\(925\) | 50.6307 | 1.66473 | ||||||||
\(926\) | 0.684658 | 0.0224993 | ||||||||
\(927\) | 13.3693 | 0.439106 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | −34.6155 | −1.13570 | −0.567849 | − | 0.823133i | \(-0.692224\pi\) | ||||
−0.567849 | + | 0.823133i | \(0.692224\pi\) | |||||||
\(930\) | 1.75379 | 0.0575090 | ||||||||
\(931\) | 4.68466 | 0.153533 | ||||||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 18.4384 | 0.603648 | ||||||||
\(934\) | −28.0000 | −0.916188 | ||||||||
\(935\) | 4.38447 | 0.143388 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.43845 | 0.308341 | 0.154170 | − | 0.988044i | \(-0.450730\pi\) | ||||
0.154170 | + | 0.988044i | \(0.450730\pi\) | |||||||
\(938\) | −7.12311 | −0.232578 | ||||||||
\(939\) | −13.6155 | −0.444326 | ||||||||
\(940\) | 2.63068 | 0.0858034 | ||||||||
\(941\) | −28.6307 | −0.933334 | −0.466667 | − | 0.884433i | \(-0.654545\pi\) | ||||
−0.466667 | + | 0.884433i | \(0.654545\pi\) | |||||||
\(942\) | −14.8078 | −0.482463 | ||||||||
\(943\) | −3.61553 | −0.117738 | ||||||||
\(944\) | −4.87689 | −0.158729 | ||||||||
\(945\) | −0.561553 | −0.0182673 | ||||||||
\(946\) | 17.3693 | 0.564725 | ||||||||
\(947\) | 12.6847 | 0.412196 | 0.206098 | − | 0.978531i | \(-0.433923\pi\) | ||||
0.206098 | + | 0.978531i | \(0.433923\pi\) | |||||||
\(948\) | 5.56155 | 0.180631 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 21.9460 | 0.712023 | ||||||||
\(951\) | 7.43845 | 0.241208 | ||||||||
\(952\) | 5.00000 | 0.162051 | ||||||||
\(953\) | −3.26137 | −0.105646 | −0.0528230 | − | 0.998604i | \(-0.516822\pi\) | ||||
−0.0528230 | + | 0.998604i | \(0.516822\pi\) | |||||||
\(954\) | 12.1231 | 0.392500 | ||||||||
\(955\) | −12.4924 | −0.404245 | ||||||||
\(956\) | −4.00000 | −0.129369 | ||||||||
\(957\) | −1.56155 | −0.0504778 | ||||||||
\(958\) | 1.56155 | 0.0504515 | ||||||||
\(959\) | −14.8078 | −0.478168 | ||||||||
\(960\) | −0.561553 | −0.0181240 | ||||||||
\(961\) | −21.2462 | −0.685362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.5616 | −0.437015 | ||||||||
\(964\) | −23.6847 | −0.762831 | ||||||||
\(965\) | 2.45360 | 0.0789842 | ||||||||
\(966\) | 0.876894 | 0.0282136 | ||||||||
\(967\) | −28.4924 | −0.916255 | −0.458127 | − | 0.888887i | \(-0.651480\pi\) | ||||
−0.458127 | + | 0.888887i | \(0.651480\pi\) | |||||||
\(968\) | 8.56155 | 0.275179 | ||||||||
\(969\) | −23.4233 | −0.752465 | ||||||||
\(970\) | 2.38447 | 0.0765608 | ||||||||
\(971\) | −19.1231 | −0.613690 | −0.306845 | − | 0.951760i | \(-0.599273\pi\) | ||||
−0.306845 | + | 0.951760i | \(0.599273\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 4.68466 | 0.150183 | ||||||||
\(974\) | 11.3153 | 0.362567 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 35.0540 | 1.12148 | 0.560738 | − | 0.827993i | \(-0.310517\pi\) | ||||
0.560738 | + | 0.827993i | \(0.310517\pi\) | |||||||
\(978\) | 7.12311 | 0.227772 | ||||||||
\(979\) | −4.19224 | −0.133984 | ||||||||
\(980\) | −0.561553 | −0.0179381 | ||||||||
\(981\) | −9.12311 | −0.291278 | ||||||||
\(982\) | 18.2462 | 0.582260 | ||||||||
\(983\) | 27.2311 | 0.868536 | 0.434268 | − | 0.900784i | \(-0.357007\pi\) | ||||
0.434268 | + | 0.900784i | \(0.357007\pi\) | |||||||
\(984\) | −4.12311 | −0.131440 | ||||||||
\(985\) | 2.00000 | 0.0637253 | ||||||||
\(986\) | −5.00000 | −0.159232 | ||||||||
\(987\) | −4.68466 | −0.149114 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.75379 | 0.310152 | ||||||||
\(990\) | 0.876894 | 0.0278695 | ||||||||
\(991\) | −5.56155 | −0.176669 | −0.0883343 | − | 0.996091i | \(-0.528154\pi\) | ||||
−0.0883343 | + | 0.996091i | \(0.528154\pi\) | |||||||
\(992\) | −3.12311 | −0.0991587 | ||||||||
\(993\) | 10.6307 | 0.337355 | ||||||||
\(994\) | −4.00000 | −0.126872 | ||||||||
\(995\) | −13.2614 | −0.420414 | ||||||||
\(996\) | −6.24621 | −0.197919 | ||||||||
\(997\) | −17.0000 | −0.538395 | −0.269198 | − | 0.963085i | \(-0.586759\pi\) | ||||
−0.269198 | + | 0.963085i | \(0.586759\pi\) | |||||||
\(998\) | −2.63068 | −0.0832728 | ||||||||
\(999\) | −10.8078 | −0.341943 |
(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.bq.1.1 | 2 | ||
13.4 | even | 6 | 546.2.l.i.211.2 | ✓ | 4 | ||
13.10 | even | 6 | 546.2.l.i.295.2 | yes | 4 | ||
13.12 | even | 2 | 7098.2.a.bw.1.2 | 2 | |||
39.17 | odd | 6 | 1638.2.r.z.757.1 | 4 | |||
39.23 | odd | 6 | 1638.2.r.z.1387.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.i.211.2 | ✓ | 4 | 13.4 | even | 6 | ||
546.2.l.i.295.2 | yes | 4 | 13.10 | even | 6 | ||
1638.2.r.z.757.1 | 4 | 39.17 | odd | 6 | |||
1638.2.r.z.1387.1 | 4 | 39.23 | odd | 6 | |||
7098.2.a.bq.1.1 | 2 | 1.1 | even | 1 | trivial | ||
7098.2.a.bw.1.2 | 2 | 13.12 | even | 2 |