Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8664,2,Mod(1,8664)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8664, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8664.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8664 = 2^{3} \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8664.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: | \(69.1823883112\) |
Analytic rank: | \(0\) |
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 456) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8664.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.56155 | 1.14556 | 0.572781 | − | 0.819709i | \(-0.305865\pi\) | ||||
0.572781 | + | 0.819709i | \(0.305865\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.56155 | 0.968176 | 0.484088 | − | 0.875019i | \(-0.339151\pi\) | ||||
0.484088 | + | 0.875019i | \(0.339151\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.43845 | 0.433708 | 0.216854 | − | 0.976204i | \(-0.430420\pi\) | ||||
0.216854 | + | 0.976204i | \(0.430420\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.12311 | 1.42089 | 0.710447 | − | 0.703751i | \(-0.248493\pi\) | ||||
0.710447 | + | 0.703751i | \(0.248493\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.56155 | −0.661390 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.68466 | −1.37873 | −0.689366 | − | 0.724413i | \(-0.742111\pi\) | ||||
−0.689366 | + | 0.724413i | \(0.742111\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.56155 | −0.558977 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.876894 | 0.182845 | 0.0914226 | − | 0.995812i | \(-0.470859\pi\) | ||||
0.0914226 | + | 0.995812i | \(0.470859\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.56155 | 0.312311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.24621 | −1.53128 | −0.765641 | − | 0.643268i | \(-0.777578\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.43845 | −0.250402 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.56155 | 1.10910 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.12311 | −0.820353 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.12311 | −0.487747 | −0.243874 | − | 0.969807i | \(-0.578418\pi\) | ||||
−0.243874 | + | 0.969807i | \(0.578418\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.56155 | 0.390633 | 0.195317 | − | 0.980740i | \(-0.437427\pi\) | ||||
0.195317 | + | 0.980740i | \(0.437427\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.56155 | 0.381854 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.68466 | 0.829193 | 0.414596 | − | 0.910005i | \(-0.363923\pi\) | ||||
0.414596 | + | 0.910005i | \(0.363923\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.438447 | −0.0626353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.68466 | 0.796011 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.2462 | 1.68215 | 0.841073 | − | 0.540921i | \(-0.181924\pi\) | ||||
0.841073 | + | 0.540921i | \(0.181924\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.68466 | 0.496839 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.0000 | −1.56227 | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||||
−0.781133 | + | 0.624364i | \(0.785358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.68466 | −0.727846 | −0.363923 | − | 0.931429i | \(-0.618563\pi\) | ||||
−0.363923 | + | 0.931429i | \(0.618563\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.56155 | 0.322725 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.1231 | 1.62772 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.2462 | 1.25177 | 0.625887 | − | 0.779914i | \(-0.284737\pi\) | ||||
0.625887 | + | 0.779914i | \(0.284737\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.876894 | −0.105566 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.9309 | 1.39640 | 0.698201 | − | 0.715901i | \(-0.253984\pi\) | ||||
0.698201 | + | 0.715901i | \(0.253984\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.56155 | −0.180313 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.68466 | 0.419906 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.3693 | 1.50417 | 0.752083 | − | 0.659069i | \(-0.229049\pi\) | ||||
0.752083 | + | 0.659069i | \(0.229049\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.00000 | 0.439057 | 0.219529 | − | 0.975606i | \(-0.429548\pi\) | ||||
0.219529 | + | 0.975606i | \(0.429548\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.5616 | −1.57942 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.24621 | 0.884087 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.1231 | 1.37568 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2462 | 1.24341 | 0.621707 | − | 0.783250i | \(-0.286439\pi\) | ||||
0.621707 | + | 0.783250i | \(0.286439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.43845 | 0.144569 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.12311 | −0.111753 | −0.0558766 | − | 0.998438i | \(-0.517795\pi\) | ||||
−0.0558766 | + | 0.998438i | \(0.517795\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000 | 0.591198 | 0.295599 | − | 0.955312i | \(-0.404481\pi\) | ||||
0.295599 | + | 0.955312i | \(0.404481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.56155 | −0.640342 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.3693 | −1.09911 | −0.549557 | − | 0.835456i | \(-0.685203\pi\) | ||||
−0.549557 | + | 0.835456i | \(0.685203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.2462 | −1.36454 | −0.682270 | − | 0.731101i | \(-0.739007\pi\) | ||||
−0.682270 | + | 0.731101i | \(0.739007\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.24621 | 0.209460 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.12311 | 0.473631 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.5616 | −1.33486 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.93087 | −0.811897 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.12311 | 0.281601 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.80776 | −0.787790 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0000 | 1.59724 | 0.798621 | − | 0.601834i | \(-0.205563\pi\) | ||||
0.798621 | + | 0.601834i | \(0.205563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.56155 | −0.225532 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.31534 | 0.726515 | 0.363257 | − | 0.931689i | \(-0.381665\pi\) | ||||
0.363257 | + | 0.931689i | \(0.381665\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.56155 | −0.220463 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.80776 | 0.581627 | 0.290813 | − | 0.956780i | \(-0.406074\pi\) | ||||
0.290813 | + | 0.956780i | \(0.406074\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.8078 | 1.08634 | 0.543170 | − | 0.839623i | \(-0.317224\pi\) | ||||
0.543170 | + | 0.839623i | \(0.317224\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.68466 | −0.478735 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.36932 | 0.616253 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.1231 | −1.75418 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.438447 | 0.0361625 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.8078 | −1.37695 | −0.688473 | − | 0.725262i | \(-0.741719\pi\) | ||||
−0.688473 | + | 0.725262i | \(0.741719\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.87689 | 0.722391 | 0.361196 | − | 0.932490i | \(-0.382369\pi\) | ||||
0.361196 | + | 0.932490i | \(0.382369\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.68466 | −0.459577 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.12311 | 0.411498 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.24621 | 0.338885 | 0.169442 | − | 0.985540i | \(-0.445803\pi\) | ||||
0.169442 | + | 0.985540i | \(0.445803\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.2462 | −0.971188 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.24621 | 0.177026 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.2462 | 1.11585 | 0.557925 | − | 0.829892i | \(-0.311598\pi\) | ||||
0.557925 | + | 0.829892i | \(0.311598\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.68466 | −0.286850 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.1231 | 1.32503 | 0.662513 | − | 0.749051i | \(-0.269490\pi\) | ||||
0.662513 | + | 0.749051i | \(0.269490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.2462 | 1.01894 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.2462 | −0.931062 | −0.465531 | − | 0.885032i | \(-0.654137\pi\) | ||||
−0.465531 | + | 0.885032i | \(0.654137\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | 0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.87689 | 0.514003 | 0.257002 | − | 0.966411i | \(-0.417265\pi\) | ||||
0.257002 | + | 0.966411i | \(0.417265\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.87689 | −0.511156 | −0.255578 | − | 0.966789i | \(-0.582266\pi\) | ||||
−0.255578 | + | 0.966789i | \(0.582266\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.68466 | 0.420222 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.4924 | 1.50663 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.17708 | −0.597967 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.56155 | −0.186326 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6847 | −0.990187 | −0.495094 | − | 0.868840i | \(-0.664866\pi\) | ||||
−0.495094 | + | 0.868840i | \(0.664866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −27.1231 | −1.95236 | −0.976182 | − | 0.216954i | \(-0.930388\pi\) | ||||
−0.976182 | + | 0.216954i | \(0.930388\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.1231 | −0.939765 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.3693 | 1.66499 | 0.832497 | − | 0.554029i | \(-0.186910\pi\) | ||||
0.832497 | + | 0.554029i | \(0.186910\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.9309 | −1.83819 | −0.919095 | − | 0.394035i | \(-0.871079\pi\) | ||||
−0.919095 | + | 0.394035i | \(0.871079\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.2462 | −0.722712 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21.1231 | −1.48255 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.00000 | −0.558744 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.876894 | 0.0609484 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.2462 | −1.53149 | −0.765746 | − | 0.643143i | \(-0.777630\pi\) | ||||
−0.765746 | + | 0.643143i | \(0.777630\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.56155 | 0.447494 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.12311 | 0.347779 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.9309 | −0.806213 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.1231 | −1.95903 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3693 | −0.895276 | −0.447638 | − | 0.894215i | \(-0.647735\pi\) | ||||
−0.447638 | + | 0.894215i | \(0.647735\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.56155 | 0.104104 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.1231 | 1.13650 | 0.568250 | − | 0.822856i | \(-0.307621\pi\) | ||||
0.568250 | + | 0.822856i | \(0.307621\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.561553 | −0.0371085 | −0.0185542 | − | 0.999828i | \(-0.505906\pi\) | ||||
−0.0185542 | + | 0.999828i | \(0.505906\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.68466 | −0.242433 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.31534 | −0.151683 | −0.0758415 | − | 0.997120i | \(-0.524164\pi\) | ||||
−0.0758415 | + | 0.997120i | \(0.524164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.5616 | 0.949891 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.3693 | −0.868430 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.8078 | 1.73405 | 0.867025 | − | 0.498265i | \(-0.166029\pi\) | ||||
0.867025 | + | 0.498265i | \(0.166029\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3693 | −0.861193 | −0.430597 | − | 0.902544i | \(-0.641697\pi\) | ||||
−0.430597 | + | 0.902544i | \(0.641697\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.12311 | −0.0717526 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.00000 | −0.253490 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.8078 | 0.808419 | 0.404209 | − | 0.914666i | \(-0.367547\pi\) | ||||
0.404209 | + | 0.914666i | \(0.367547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.26137 | 0.0793014 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.5616 | 0.911880 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.87689 | −0.304212 | −0.152106 | − | 0.988364i | \(-0.548606\pi\) | ||||
−0.152106 | + | 0.988364i | \(0.548606\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.4924 | 1.27334 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.24621 | −0.510428 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.31534 | −0.142770 | −0.0713850 | − | 0.997449i | \(-0.522742\pi\) | ||||
−0.0713850 | + | 0.997449i | \(0.522742\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 31.3693 | 1.92700 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0000 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.1231 | −0.794246 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.24621 | 0.135452 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.31534 | −0.379452 | −0.189726 | − | 0.981837i | \(-0.560760\pi\) | ||||
−0.189726 | + | 0.981837i | \(0.560760\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.00000 | 0.119737 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.75379 | 0.462552 | 0.231276 | − | 0.972888i | \(-0.425710\pi\) | ||||
0.231276 | + | 0.972888i | \(0.425710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.3153 | 0.969846 | 0.484923 | − | 0.874557i | \(-0.338848\pi\) | ||||
0.484923 | + | 0.874557i | \(0.338848\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.3153 | 0.900902 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2462 | −0.717886 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.12311 | −0.416136 | −0.208068 | − | 0.978114i | \(-0.566718\pi\) | ||||
−0.208068 | + | 0.978114i | \(0.566718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.7386 | −1.78967 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.43845 | −0.0834672 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.49242 | 0.259804 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.56155 | 0.378202 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.12311 | 0.0645207 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.5616 | −0.833792 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.4924 | −1.62615 | −0.813074 | − | 0.582160i | \(-0.802208\pi\) | ||||
−0.813074 | + | 0.582160i | \(0.802208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.00000 | −0.341328 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.93087 | 0.449718 | 0.224859 | − | 0.974391i | \(-0.427808\pi\) | ||||
0.224859 | + | 0.974391i | \(0.427808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.56155 | 0.369702 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 27.1231 | 1.52339 | 0.761693 | − | 0.647938i | \(-0.224369\pi\) | ||||
0.761693 | + | 0.647938i | \(0.224369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.8617 | −0.664130 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.3693 | 0.634573 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.00000 | 0.443760 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.2462 | 0.787817 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.5616 | 0.802804 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.00000 | 0.438397 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 26.2462 | 1.43398 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.7386 | 1.56549 | 0.782747 | − | 0.622341i | \(-0.213818\pi\) | ||||
0.782747 | + | 0.622341i | \(0.213818\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.00000 | −0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.87689 | 0.155793 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.0540 | −1.02882 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.24621 | −0.120932 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.4233 | −1.84794 | −0.923970 | − | 0.382466i | \(-0.875075\pi\) | ||||
−0.923970 | + | 0.382466i | \(0.875075\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.6847 | 1.58898 | 0.794492 | − | 0.607275i | \(-0.207737\pi\) | ||||
0.794492 | + | 0.607275i | \(0.207737\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.12311 | −0.273451 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.7538 | −0.625591 | −0.312796 | − | 0.949820i | \(-0.601265\pi\) | ||||
−0.312796 | + | 0.949820i | \(0.601265\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.5616 | 0.770679 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.56155 | 0.240750 | 0.120375 | − | 0.992729i | \(-0.461590\pi\) | ||||
0.120375 | + | 0.992729i | \(0.461590\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.93087 | 0.468749 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.5616 | 1.59966 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.2462 | −0.743646 | −0.371823 | − | 0.928304i | \(-0.621267\pi\) | ||||
−0.371823 | + | 0.928304i | \(0.621267\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.12311 | −0.162582 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 31.3693 | 1.62861 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.50758 | 0.181615 | 0.0908077 | − | 0.995868i | \(-0.471055\pi\) | ||||
0.0908077 | + | 0.995868i | \(0.471055\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.80776 | 0.454831 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −42.2462 | −2.17579 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.1231 | 1.49595 | 0.747977 | − | 0.663725i | \(-0.231025\pi\) | ||||
0.747977 | + | 0.663725i | \(0.231025\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.0000 | −0.922168 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.1231 | −1.07934 | −0.539670 | − | 0.841877i | \(-0.681451\pi\) | ||||
−0.539670 | + | 0.841877i | \(0.681451\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.43845 | 0.481028 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.56155 | 0.130211 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.93087 | −0.503515 | −0.251758 | − | 0.967790i | \(-0.581009\pi\) | ||||
−0.251758 | + | 0.967790i | \(0.581009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.98485 | −0.252094 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.31534 | −0.419453 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 34.2462 | 1.72311 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.3153 | −0.517712 | −0.258856 | − | 0.965916i | \(-0.583346\pi\) | ||||
−0.258856 | + | 0.965916i | \(0.583346\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.3693 | 1.26688 | 0.633442 | − | 0.773790i | \(-0.281642\pi\) | ||||
0.633442 | + | 0.773790i | \(0.281642\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.2462 | 0.510400 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.56155 | 0.127285 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.5076 | 0.570409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.2462 | −0.803323 | −0.401662 | − | 0.915788i | \(-0.631567\pi\) | ||||
−0.401662 | + | 0.915788i | \(0.631567\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.80776 | −0.335802 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −30.7386 | −1.51255 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.2462 | 0.502967 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.8078 | −0.627199 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.7386 | 1.11085 | 0.555427 | − | 0.831565i | \(-0.312555\pi\) | ||||
0.555427 | + | 0.831565i | \(0.312555\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.1231 | −0.639581 | −0.319791 | − | 0.947488i | \(-0.603613\pi\) | ||||
−0.319791 | + | 0.947488i | \(0.603613\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.68466 | 0.276398 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.87689 | −0.430593 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.5616 | −0.704683 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.36932 | −0.355794 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.6155 | −1.42653 | −0.713265 | − | 0.700895i | \(-0.752784\pi\) | ||||
−0.713265 | + | 0.700895i | \(0.752784\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.24621 | −0.396288 | −0.198144 | − | 0.980173i | \(-0.563491\pi\) | ||||
−0.198144 | + | 0.980173i | \(0.563491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 21.1231 | 1.01278 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.7538 | −0.560978 | −0.280489 | − | 0.959857i | \(-0.590497\pi\) | ||||
−0.280489 | + | 0.959857i | \(0.590497\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.438447 | −0.0208784 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.8078 | 1.55874 | 0.779372 | − | 0.626562i | \(-0.215538\pi\) | ||||
0.779372 | + | 0.626562i | \(0.215538\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.3693 | 0.728575 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.8078 | 0.794980 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.6307 | −0.501693 | −0.250846 | − | 0.968027i | \(-0.580709\pi\) | ||||
−0.250846 | + | 0.968027i | \(0.580709\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.49242 | −0.211540 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.87689 | −0.417073 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 33.6155 | 1.57592 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.94602 | −0.137809 | −0.0689046 | − | 0.997623i | \(-0.521950\pi\) | ||||
−0.0689046 | + | 0.997623i | \(0.521950\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.68466 | 0.265337 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.3002 | −0.992049 | −0.496024 | − | 0.868309i | \(-0.665207\pi\) | ||||
−0.496024 | + | 0.868309i | \(0.665207\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.1922 | 0.520147 | 0.260074 | − | 0.965589i | \(-0.416253\pi\) | ||||
0.260074 | + | 0.965589i | \(0.416253\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.12311 | −0.237578 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.9309 | −0.829742 | −0.414871 | − | 0.909880i | \(-0.636173\pi\) | ||||
−0.414871 | + | 0.909880i | \(0.636173\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.2462 | 1.21194 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.24621 | −0.195655 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.68466 | 0.169421 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.2462 | 0.560715 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.36932 | −0.428095 | −0.214048 | − | 0.976823i | \(-0.568665\pi\) | ||||
−0.214048 | + | 0.976823i | \(0.568665\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 40.9848 | 1.86875 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.24621 | −0.102206 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.3693 | 1.42441 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.8769 | 1.12728 | 0.563640 | − | 0.826021i | \(-0.309401\pi\) | ||||
0.563640 | + | 0.826021i | \(0.309401\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.2462 | −0.644236 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.7386 | 1.56773 | 0.783866 | − | 0.620930i | \(-0.213245\pi\) | ||||
0.783866 | + | 0.620930i | \(0.213245\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.8769 | 2.11123 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.68466 | 0.165613 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.1771 | 1.61951 | 0.809754 | − | 0.586769i | \(-0.199600\pi\) | ||||
0.809754 | + | 0.586769i | \(0.199600\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.1231 | −0.765004 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.6155 | −0.696262 | −0.348131 | − | 0.937446i | \(-0.613184\pi\) | ||||
−0.348131 | + | 0.937446i | \(0.613184\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.87689 | −0.128020 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.2462 | −0.588285 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.0000 | −1.15243 | −0.576215 | − | 0.817298i | \(-0.695471\pi\) | ||||
−0.576215 | + | 0.817298i | \(0.695471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.5616 | 1.35196 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.3693 | 0.677253 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.17708 | 0.359628 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.2462 | 0.537549 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.6155 | 1.38510 | 0.692551 | − | 0.721369i | \(-0.256487\pi\) | ||||
0.692551 | + | 0.721369i | \(0.256487\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.36932 | 0.322238 | 0.161119 | − | 0.986935i | \(-0.448490\pi\) | ||||
0.161119 | + | 0.986935i | \(0.448490\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.00000 | −0.174574 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −11.3693 | −0.495255 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.2311 | −0.966568 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.0000 | −0.693037 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.1231 | −1.25910 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.87689 | −0.296760 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.630683 | −0.0271654 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.80776 | 0.120715 | 0.0603576 | − | 0.998177i | \(-0.480776\pi\) | ||||
0.0603576 | + | 0.998177i | \(0.480776\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.87689 | 0.295116 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −36.4924 | −1.56316 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 41.6155 | 1.77935 | 0.889676 | − | 0.456593i | \(-0.150930\pi\) | ||||
0.889676 | + | 0.456593i | \(0.150930\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.68466 | −0.242615 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.2462 | 1.45630 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −20.4924 | −0.869855 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.4384 | 1.75580 | 0.877902 | − | 0.478841i | \(-0.158943\pi\) | ||||
0.877902 | + | 0.478841i | \(0.158943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.1231 | 0.555048 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.17708 | 0.345237 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.00000 | −0.168580 | −0.0842900 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842900 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.12311 | 0.215531 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.56155 | 0.107575 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.4924 | −0.607554 | −0.303777 | − | 0.952743i | \(-0.598248\pi\) | ||||
−0.303777 | + | 0.952743i | \(0.598248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.7386 | −1.78856 | −0.894278 | − | 0.447512i | \(-0.852310\pi\) | ||||
−0.894278 | + | 0.447512i | \(0.852310\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.6847 | 0.571685 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.36932 | 0.0571045 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.43845 | −0.309667 | −0.154833 | − | 0.987941i | \(-0.549484\pi\) | ||||
−0.154833 | + | 0.987941i | \(0.549484\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.1231 | 1.12720 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.2462 | 0.425084 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.6155 | 0.729561 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.1231 | 0.542574 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.0540 | 0.786442 | 0.393221 | − | 0.919444i | \(-0.371361\pi\) | ||||
0.393221 | + | 0.919444i | \(0.371361\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.3693 | −0.961285 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.50758 | 0.226169 | 0.113085 | − | 0.993585i | \(-0.463927\pi\) | ||||
0.113085 | + | 0.993585i | \(0.463927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −37.3002 | −1.52916 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.9309 | 1.06128 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −48.4924 | −1.98135 | −0.990673 | − | 0.136258i | \(-0.956492\pi\) | ||||
−0.990673 | + | 0.136258i | \(0.956492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.8617 | 0.728596 | 0.364298 | − | 0.931283i | \(-0.381309\pi\) | ||||
0.364298 | + | 0.931283i | \(0.381309\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.2462 | 0.417258 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.8769 | −0.930078 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −42.9848 | −1.74470 | −0.872351 | − | 0.488881i | \(-0.837405\pi\) | ||||
−0.872351 | + | 0.488881i | \(0.837405\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.1231 | 0.855951 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.1231 | 1.17819 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.7926 | −1.93033 | −0.965163 | − | 0.261651i | \(-0.915733\pi\) | ||||
−0.965163 | + | 0.261651i | \(0.915733\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.00000 | 0.322591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 39.3002 | 1.58217 | 0.791083 | − | 0.611709i | \(-0.209518\pi\) | ||||
0.791083 | + | 0.611709i | \(0.209518\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.876894 | −0.0351886 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.3693 | 0.615759 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3693 | −1.21477 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −45.4773 | −1.81330 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.93087 | −0.236104 | −0.118052 | − | 0.993007i | \(-0.537665\pi\) | ||||
−0.118052 | + | 0.993007i | \(0.537665\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.2462 | 0.884208 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 46.1080 | 1.82974 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.24621 | −0.0889981 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.73863 | −0.345155 | −0.172578 | − | 0.984996i | \(-0.555210\pi\) | ||||
−0.172578 | + | 0.984996i | \(0.555210\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 47.0540 | 1.85563 | 0.927814 | − | 0.373044i | \(-0.121686\pi\) | ||||
0.927814 | + | 0.373044i | \(0.121686\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.56155 | −0.258361 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.19224 | −0.0468716 | −0.0234358 | − | 0.999725i | \(-0.507461\pi\) | ||||
−0.0234358 | + | 0.999725i | \(0.507461\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.2614 | −0.677568 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.12311 | −0.200790 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.3002 | −0.520477 | −0.260238 | − | 0.965544i | \(-0.583801\pi\) | ||||
−0.260238 | + | 0.965544i | \(0.583801\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.3002 | 0.832267 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.9309 | 0.465468 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.36932 | 0.131250 | 0.0656250 | − | 0.997844i | \(-0.479096\pi\) | ||||
0.0656250 | + | 0.997844i | \(0.479096\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.73863 | −0.262102 | −0.131051 | − | 0.991376i | \(-0.541835\pi\) | ||||
−0.131051 | + | 0.991376i | \(0.541835\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 29.1231 | 1.13105 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.23106 | −0.279988 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.3693 | 0.516888 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.17708 | −0.315673 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.8617 | −0.996897 | −0.498448 | − | 0.866919i | \(-0.666097\pi\) | ||||
−0.498448 | + | 0.866919i | \(0.666097\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.56155 | −0.0601042 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.0000 | −1.46046 | −0.730229 | − | 0.683202i | \(-0.760587\pi\) | ||||
−0.730229 | + | 0.683202i | \(0.760587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.3693 | 1.20384 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.1231 | −0.656159 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −47.8617 | −1.83138 | −0.915689 | − | 0.401887i | \(-0.868354\pi\) | ||||
−0.915689 | + | 0.401887i | \(0.868354\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.4384 | 0.666289 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.561553 | 0.0214246 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 62.7386 | 2.39015 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.9309 | 1.89946 | 0.949730 | − | 0.313070i | \(-0.101358\pi\) | ||||
0.949730 | + | 0.313070i | \(0.101358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.68466 | 0.139969 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.8078 | 1.24447 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.7538 | 0.672473 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.31534 | 0.0875743 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8769 | 0.561893 | 0.280946 | − | 0.959723i | \(-0.409352\pi\) | ||||
0.280946 | + | 0.959723i | \(0.409352\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.5616 | −0.548420 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.87689 | −0.108197 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.4924 | 1.59584 | 0.797918 | − | 0.602766i | \(-0.205935\pi\) | ||||
0.797918 | + | 0.602766i | \(0.205935\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.3693 | 0.501389 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.75379 | 0.0656799 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.8769 | 0.705956 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.8078 | −1.00115 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.4233 | −0.910835 | −0.455418 | − | 0.890278i | \(-0.650510\pi\) | ||||
−0.455418 | + | 0.890278i | \(0.650510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3693 | 0.572383 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.3693 | 0.497210 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.8769 | −0.478236 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.43845 | 0.350053 | 0.175026 | − | 0.984564i | \(-0.443999\pi\) | ||||
0.175026 | + | 0.984564i | \(0.443999\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.5616 | −0.538578 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.4924 | 0.535290 | 0.267645 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267645 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.12311 | 0.0414264 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.7386 | 0.542905 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.1771 | −0.742226 | −0.371113 | − | 0.928588i | \(-0.621024\pi\) | ||||
−0.371113 | + | 0.928588i | \(0.621024\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.50758 | −0.275426 | −0.137713 | − | 0.990472i | \(-0.543975\pi\) | ||||
−0.137713 | + | 0.990472i | \(0.543975\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.0540 | −1.57738 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.00000 | 0.146352 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.1231 | −1.06414 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.61553 | 0.277895 | 0.138947 | − | 0.990300i | \(-0.455628\pi\) | ||||
0.138947 | + | 0.990300i | \(0.455628\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.8078 | −0.466741 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.7386 | 0.827544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.05398 | 0.183690 | 0.0918449 | − | 0.995773i | \(-0.470724\pi\) | ||||
0.0918449 | + | 0.995773i | \(0.470724\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.26137 | −0.0457847 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.6695 | −1.11177 | −0.555884 | − | 0.831260i | \(-0.687620\pi\) | ||||
−0.555884 | + | 0.831260i | \(0.687620\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.4924 | −1.32111 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.5616 | −0.526474 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −61.4773 | −2.21982 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.3002 | 0.695983 | 0.347991 | − | 0.937498i | \(-0.386864\pi\) | ||||
0.347991 | + | 0.937498i | \(0.386864\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.87689 | 0.175637 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.6155 | 0.849392 | 0.424696 | − | 0.905336i | \(-0.360381\pi\) | ||||
0.424696 | + | 0.905336i | \(0.360381\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.12311 | 0.112185 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.4924 | −0.735162 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.24621 | 0.294696 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.8769 | 0.388213 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.24621 | 0.222653 | 0.111327 | − | 0.993784i | \(-0.464490\pi\) | ||||
0.111327 | + | 0.993784i | \(0.464490\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.31534 | 0.0824283 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.12311 | 0.182157 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −29.1231 | −1.03419 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −31.3693 | −1.11256 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.384472 | −0.0136187 | −0.00680935 | − | 0.999977i | \(-0.502167\pi\) | ||||
−0.00680935 | + | 0.999977i | \(0.502167\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.3153 | −1.14323 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.1619 | 0.605631 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.75379 | 0.202794 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0000 | 0.352017 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.0540 | −1.58401 | −0.792007 | − | 0.610512i | \(-0.790964\pi\) | ||||
−0.792007 | + | 0.610512i | \(0.790964\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.8769 | 0.943775 | 0.471888 | − | 0.881659i | \(-0.343573\pi\) | ||||
0.471888 | + | 0.881659i | \(0.343573\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.0000 | −0.701431 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 36.4924 | 1.27827 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13.1231 | 0.458558 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.0540 | −1.36299 | −0.681497 | − | 0.731821i | \(-0.738671\pi\) | ||||
−0.681497 | + | 0.731821i | \(0.738671\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.3002 | 0.463615 | 0.231808 | − | 0.972762i | \(-0.425536\pi\) | ||||
0.231808 | + | 0.972762i | \(0.425536\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.24621 | −0.0782030 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.7386 | −1.20798 | −0.603990 | − | 0.796992i | \(-0.706423\pi\) | ||||
−0.603990 | + | 0.796992i | \(0.706423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.00000 | −0.138926 | −0.0694629 | − | 0.997585i | \(-0.522129\pi\) | ||||
−0.0694629 | + | 0.997585i | \(0.522129\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.31534 | 0.219077 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.49242 | 0.0863573 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.8617 | 1.51790 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.86174 | −0.271417 | −0.135709 | − | 0.990749i | \(-0.543331\pi\) | ||||
−0.135709 | + | 0.990749i | \(0.543331\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 39.0000 | 1.34483 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.75379 | −0.267055 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33.9309 | 1.16726 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.8769 | −0.786059 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.3153 | −0.559941 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.01515 | 0.240476 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −56.7386 | −1.94269 | −0.971347 | − | 0.237666i | \(-0.923618\pi\) | ||||
−0.971347 | + | 0.237666i | \(0.923618\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.8617 | 1.42997 | 0.714985 | − | 0.699140i | \(-0.246434\pi\) | ||||
0.714985 | + | 0.699140i | \(0.246434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.3002 | 0.863231 | 0.431616 | − | 0.902058i | \(-0.357944\pi\) | ||||
0.431616 | + | 0.902058i | \(0.357944\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.00000 | 0.272639 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.0000 | 0.408485 | 0.204242 | − | 0.978920i | \(-0.434527\pi\) | ||||
0.204242 | + | 0.978920i | \(0.434527\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −31.3693 | −1.06659 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.3153 | −0.520136 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.2311 | 0.652369 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.4924 | 1.77864 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.2462 | 0.414471 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −22.5616 | −0.762720 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47.3693 | 1.59955 | 0.799774 | − | 0.600301i | \(-0.204953\pi\) | ||||
0.799774 | + | 0.600301i | \(0.204953\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.12311 | 0.240256 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.3002 | 0.785003 | 0.392502 | − | 0.919751i | \(-0.371610\pi\) | ||||
0.392502 | + | 0.919751i | \(0.371610\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.6847 | −1.60472 | −0.802358 | − | 0.596843i | \(-0.796422\pi\) | ||||
−0.802358 | + | 0.596843i | \(0.796422\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 30.7386 | 1.03327 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31.2311 | 1.04864 | 0.524318 | − | 0.851522i | \(-0.324320\pi\) | ||||
0.524318 | + | 0.851522i | \(0.324320\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 46.1080 | 1.54641 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.43845 | 0.0481898 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.6155 | 0.588822 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.49242 | −0.149998 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.4924 | −0.550053 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −69.6155 | −2.31923 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.56155 | −0.218355 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −17.6155 | −0.585560 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.8769 | 1.15807 | 0.579034 | − | 0.815303i | \(-0.303430\pi\) | ||||
0.579034 | + | 0.815303i | \(0.303430\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.12311 | −0.0372511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.12311 | −0.0372101 | −0.0186051 | − | 0.999827i | \(-0.505923\pi\) | ||||
−0.0186051 | + | 0.999827i | \(0.505923\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.75379 | 0.190423 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 14.5616 | 0.481390 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.3002 | 0.703394 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44.4924 | 1.46767 | 0.733835 | − | 0.679328i | \(-0.237729\pi\) | ||||
0.733835 | + | 0.679328i | \(0.237729\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.4924 | 0.938857 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.4924 | 0.410748 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.00000 | 0.197066 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.0000 | 0.459325 | 0.229663 | − | 0.973270i | \(-0.426238\pi\) | ||||
0.229663 | + | 0.973270i | \(0.426238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.93087 | −0.259645 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.9460 | −0.685008 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.5616 | −0.541042 | −0.270521 | − | 0.962714i | \(-0.587196\pi\) | ||||
−0.270521 | + | 0.962714i | \(0.587196\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0000 | 0.326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.0000 | 0.977972 | 0.488986 | − | 0.872292i | \(-0.337367\pi\) | ||||
0.488986 | + | 0.872292i | \(0.337367\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.73863 | −0.0891822 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.56155 | −0.213447 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.00000 | 0.129983 | 0.0649913 | − | 0.997886i | \(-0.479298\pi\) | ||||
0.0649913 | + | 0.997886i | \(0.479298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 61.1231 | 1.98414 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.1231 | −0.879527 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.6155 | 0.376264 | 0.188132 | − | 0.982144i | \(-0.439757\pi\) | ||||
0.188132 | + | 0.982144i | \(0.439757\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35.0540 | −1.13432 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.8617 | 0.383436 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.4384 | 0.563117 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.3693 | −0.366371 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −69.4773 | −2.23655 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.7386 | −0.859856 | −0.429928 | − | 0.902863i | \(-0.641461\pi\) | ||||
−0.429928 | + | 0.902863i | \(0.641461\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.0000 | −0.641831 | −0.320915 | − | 0.947108i | \(-0.603990\pi\) | ||||
−0.320915 | + | 0.947108i | \(0.603990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.8078 | 1.05177 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.00000 | −0.256205 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.98485 | −0.223465 | −0.111732 | − | 0.993738i | \(-0.535640\pi\) | ||||
−0.111732 | + | 0.993738i | \(0.535640\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.63068 | 0.275838 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.2462 | −0.454847 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.7386 | −0.980410 | −0.490205 | − | 0.871607i | \(-0.663078\pi\) | ||||
−0.490205 | + | 0.871607i | \(0.663078\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59.8617 | 1.90735 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.5616 | −0.463499 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.24621 | 0.0714254 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.8617 | 0.694461 | 0.347231 | − | 0.937780i | \(-0.387122\pi\) | ||||
0.347231 | + | 0.937780i | \(0.387122\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −66.4233 | −2.10576 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −55.7926 | −1.76697 | −0.883485 | − | 0.468460i | \(-0.844809\pi\) | ||||
−0.883485 | + | 0.468460i | \(0.844809\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.00000 | −0.253109 |
(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 | 8664.2.a.r.1.2 | 2 | ||
19.18 | odd | 2 | 456.2.a.f.1.2 | ✓ | 2 | ||
57.56 | even | 2 | 1368.2.a.k.1.1 | 2 | |||
76.75 | even | 2 | 912.2.a.m.1.2 | 2 | |||
152.37 | odd | 2 | 3648.2.a.bl.1.1 | 2 | |||
152.75 | even | 2 | 3648.2.a.br.1.1 | 2 | |||
228.227 | odd | 2 | 2736.2.a.z.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.a.f.1.2 | ✓ | 2 | 19.18 | odd | 2 | ||
912.2.a.m.1.2 | 2 | 76.75 | even | 2 | |||
1368.2.a.k.1.1 | 2 | 57.56 | even | 2 | |||
2736.2.a.z.1.1 | 2 | 228.227 | odd | 2 | |||
3648.2.a.bl.1.1 | 2 | 152.37 | odd | 2 | |||
3648.2.a.br.1.1 | 2 | 152.75 | even | 2 | |||
8664.2.a.r.1.2 | 2 | 1.1 | even | 1 | trivial |