Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 31 x^{10} + 131 x^{9} + 309 x^{8} - 1453 x^{7} - 1072 x^{6} + 6350 x^{5} + \cdots + 3008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.716151\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(5\) | −0.716151 | −0.320272 | −0.160136 | − | 0.987095i | \(-0.551193\pi\) | ||||
−0.160136 | + | 0.987095i | \(0.551193\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.33002 | 1.25863 | 0.629314 | − | 0.777151i | \(-0.283336\pi\) | ||||
0.629314 | + | 0.777151i | \(0.283336\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.47099 | 0.443522 | 0.221761 | − | 0.975101i | \(-0.428820\pi\) | ||||
0.221761 | + | 0.975101i | \(0.428820\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.07152 | −0.297185 | −0.148593 | − | 0.988899i | \(-0.547474\pi\) | ||||
−0.148593 | + | 0.988899i | \(0.547474\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.716151 | 0.184909 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.68991 | 1.13747 | 0.568735 | − | 0.822520i | \(-0.307433\pi\) | ||||
0.568735 | + | 0.822520i | \(0.307433\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.60112 | 0.367321 | 0.183661 | − | 0.982990i | \(-0.441205\pi\) | ||||
0.183661 | + | 0.982990i | \(0.441205\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.33002 | −0.726669 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.96922 | −1.24467 | −0.622334 | − | 0.782752i | \(-0.713815\pi\) | ||||
−0.622334 | + | 0.782752i | \(0.713815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.48713 | −0.897426 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.73151 | 0.878620 | 0.439310 | − | 0.898336i | \(-0.355223\pi\) | ||||
0.439310 | + | 0.898336i | \(0.355223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.82346 | −1.58474 | −0.792370 | − | 0.610041i | \(-0.791153\pi\) | ||||
−0.792370 | + | 0.610041i | \(0.791153\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.47099 | −0.256067 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.38479 | −0.403104 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4028 | −1.71021 | −0.855106 | − | 0.518453i | \(-0.826508\pi\) | ||||
−0.855106 | + | 0.518453i | \(0.826508\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.07152 | 0.171580 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.92019 | −0.456058 | −0.228029 | − | 0.973654i | \(-0.573228\pi\) | ||||
−0.228029 | + | 0.973654i | \(0.573228\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.38527 | 1.27874 | 0.639371 | − | 0.768899i | \(-0.279195\pi\) | ||||
0.639371 | + | 0.768899i | \(0.279195\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.716151 | −0.106757 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.24255 | −0.910569 | −0.455285 | − | 0.890346i | \(-0.650462\pi\) | ||||
−0.455285 | + | 0.890346i | \(0.650462\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.08900 | 0.584143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.68991 | −0.656719 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.50501 | −1.30561 | −0.652807 | − | 0.757524i | \(-0.726409\pi\) | ||||
−0.652807 | + | 0.757524i | \(0.726409\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.05345 | −0.142048 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.60112 | −0.212073 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.74996 | 0.618393 | 0.309196 | − | 0.950998i | \(-0.399940\pi\) | ||||
0.309196 | + | 0.950998i | \(0.399940\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.09947 | 0.908993 | 0.454497 | − | 0.890748i | \(-0.349819\pi\) | ||||
0.454497 | + | 0.890748i | \(0.349819\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.33002 | 0.419543 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.767367 | 0.0951802 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6608 | −1.66893 | −0.834466 | − | 0.551059i | \(-0.814224\pi\) | ||||
−0.834466 | + | 0.551059i | \(0.814224\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.96922 | 0.718610 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.6859 | −1.62422 | −0.812109 | − | 0.583505i | \(-0.801681\pi\) | ||||
−0.812109 | + | 0.583505i | \(0.801681\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.30688 | 0.855205 | 0.427603 | − | 0.903967i | \(-0.359358\pi\) | ||||
0.427603 | + | 0.903967i | \(0.359358\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.48713 | 0.518129 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.89844 | 0.558229 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8036 | −1.44052 | −0.720259 | − | 0.693705i | \(-0.755977\pi\) | ||||
−0.720259 | + | 0.693705i | \(0.755977\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.24092 | −0.136209 | −0.0681045 | − | 0.997678i | \(-0.521695\pi\) | ||||
−0.0681045 | + | 0.997678i | \(0.521695\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.35869 | −0.364301 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.73151 | −0.507271 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.67545 | −0.813596 | −0.406798 | − | 0.913518i | \(-0.633355\pi\) | ||||
−0.406798 | + | 0.913518i | \(0.633355\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.56816 | −0.374045 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.82346 | 0.914950 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.14664 | −0.117643 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.4461 | 1.36525 | 0.682623 | − | 0.730771i | \(-0.260839\pi\) | ||||
0.682623 | + | 0.730771i | \(0.260839\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.47099 | 0.147841 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.372387 | −0.0370539 | −0.0185269 | − | 0.999828i | \(-0.505898\pi\) | ||||
−0.0185269 | + | 0.999828i | \(0.505898\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.26876 | −0.716213 | −0.358106 | − | 0.933681i | \(-0.616577\pi\) | ||||
−0.358106 | + | 0.933681i | \(0.616577\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.38479 | 0.232732 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.75739 | −0.749935 | −0.374968 | − | 0.927038i | \(-0.622346\pi\) | ||||
−0.374968 | + | 0.927038i | \(0.622346\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.49121 | 0.909094 | 0.454547 | − | 0.890723i | \(-0.349801\pi\) | ||||
0.454547 | + | 0.890723i | \(0.349801\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.4028 | 0.987392 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.74341 | 0.258078 | 0.129039 | − | 0.991639i | \(-0.458811\pi\) | ||||
0.129039 | + | 0.991639i | \(0.458811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.27486 | 0.398633 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.07152 | −0.0990617 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.6175 | 1.43165 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.83617 | −0.803289 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.92019 | 0.263305 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.79422 | 0.607693 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.0695 | −1.33720 | −0.668600 | − | 0.743622i | \(-0.733106\pi\) | ||||
−0.668600 | + | 0.743622i | \(0.733106\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.38527 | −0.738282 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.64719 | 0.755508 | 0.377754 | − | 0.925906i | \(-0.376696\pi\) | ||||
0.377754 | + | 0.925906i | \(0.376696\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.33174 | 0.462321 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.716151 | 0.0616365 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.9735 | 1.19383 | 0.596917 | − | 0.802303i | \(-0.296392\pi\) | ||||
0.596917 | + | 0.802303i | \(0.296392\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.76531 | −0.828283 | −0.414141 | − | 0.910213i | \(-0.635918\pi\) | ||||
−0.414141 | + | 0.910213i | \(0.635918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.24255 | 0.525717 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.57619 | −0.131808 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.38848 | −0.281398 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.08900 | −0.337255 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.6591 | 1.03708 | 0.518538 | − | 0.855054i | \(-0.326476\pi\) | ||||
0.518538 | + | 0.855054i | \(0.326476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2773 | 0.836352 | 0.418176 | − | 0.908366i | \(-0.362669\pi\) | ||||
0.418176 | + | 0.908366i | \(0.362669\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.68991 | 0.379157 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.31893 | 0.507549 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.3312 | 1.38318 | 0.691590 | − | 0.722291i | \(-0.256911\pi\) | ||||
0.691590 | + | 0.722291i | \(0.256911\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.50501 | 0.753797 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.8776 | −1.56657 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.39092 | −0.500576 | −0.250288 | − | 0.968171i | \(-0.580525\pi\) | ||||
−0.250288 | + | 0.968171i | \(0.580525\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.05345 | 0.0820113 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.8519 | −0.911681 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.60112 | 0.122440 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.0601 | 1.75323 | 0.876614 | − | 0.481195i | \(-0.159797\pi\) | ||||
0.876614 | + | 0.481195i | \(0.159797\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.9422 | −1.12952 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.74996 | −0.357029 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.56721 | 0.117139 | 0.0585693 | − | 0.998283i | \(-0.481346\pi\) | ||||
0.0585693 | + | 0.998283i | \(0.481346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.66369 | −0.718297 | −0.359148 | − | 0.933281i | \(-0.616933\pi\) | ||||
−0.359148 | + | 0.933281i | \(0.616933\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.09947 | −0.524808 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.44999 | 0.547734 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.89884 | 0.504493 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.33002 | −0.242223 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.1174 | −1.09386 | −0.546930 | − | 0.837179i | \(-0.684204\pi\) | ||||
−0.546930 | + | 0.837179i | \(0.684204\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.9243 | 1.07427 | 0.537137 | − | 0.843495i | \(-0.319506\pi\) | ||||
0.537137 | + | 0.843495i | \(0.319506\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.767367 | −0.0549523 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.7458 | −0.979350 | −0.489675 | − | 0.871905i | \(-0.662885\pi\) | ||||
−0.489675 | + | 0.871905i | \(0.662885\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.45882 | −0.670518 | −0.335259 | − | 0.942126i | \(-0.608824\pi\) | ||||
−0.335259 | + | 0.942126i | \(0.608824\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.6608 | 0.963558 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.7560 | 1.10586 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.09130 | 0.146063 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.96922 | −0.414889 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.35523 | 0.162915 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.5293 | −1.34445 | −0.672227 | − | 0.740345i | \(-0.734662\pi\) | ||||
−0.672227 | + | 0.740345i | \(0.734662\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.6859 | 0.937743 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.00512 | −0.409546 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.3822 | −1.99460 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.30688 | −0.493753 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.02532 | −0.338039 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.37221 | −0.359750 | −0.179875 | − | 0.983690i | \(-0.557569\pi\) | ||||
−0.179875 | + | 0.983690i | \(0.557569\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.48713 | −0.299142 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.0420 | 1.79484 | 0.897421 | − | 0.441174i | \(-0.145438\pi\) | ||||
0.897421 | + | 0.441174i | \(0.145438\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.6136 | −0.833527 | −0.416764 | − | 0.909015i | \(-0.636836\pi\) | ||||
−0.416764 | + | 0.909015i | \(0.636836\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.89844 | −0.322293 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.6565 | 1.68082 | 0.840408 | − | 0.541954i | \(-0.182315\pi\) | ||||
0.840408 | + | 0.541954i | \(0.182315\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.47061 | 0.291630 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.8036 | 0.831684 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.74058 | −0.177273 | −0.0886367 | − | 0.996064i | \(-0.528251\pi\) | ||||
−0.0886367 | + | 0.996064i | \(0.528251\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.6085 | −1.26310 | −0.631548 | − | 0.775337i | \(-0.717580\pi\) | ||||
−0.631548 | + | 0.775337i | \(0.717580\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.92834 | −0.187085 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.71562 | −0.109162 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.24092 | 0.0786403 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4602 | 0.975842 | 0.487921 | − | 0.872888i | \(-0.337755\pi\) | ||||
0.487921 | + | 0.872888i | \(0.337755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.78069 | −0.552037 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.35869 | 0.210329 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.2550 | −1.76250 | −0.881250 | − | 0.472650i | \(-0.843298\pi\) | ||||
−0.881250 | + | 0.472650i | \(0.843298\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −34.6415 | −2.15252 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.73151 | 0.292873 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.0685960 | 0.00422981 | 0.00211490 | − | 0.999998i | \(-0.499327\pi\) | ||||
0.00211490 | + | 0.999998i | \(0.499327\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.80702 | 0.418152 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.67545 | 0.469730 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.3857 | −0.999053 | −0.499526 | − | 0.866299i | \(-0.666493\pi\) | ||||
−0.499526 | + | 0.866299i | \(0.666493\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.90565 | 0.540980 | 0.270490 | − | 0.962723i | \(-0.412814\pi\) | ||||
0.270490 | + | 0.962723i | \(0.412814\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.56816 | 0.215955 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.60054 | −0.398028 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.7421 | −0.645430 | −0.322715 | − | 0.946496i | \(-0.604596\pi\) | ||||
−0.322715 | + | 0.946496i | \(0.604596\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.82346 | −0.528247 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.4669 | −1.22095 | −0.610475 | − | 0.792035i | \(-0.709022\pi\) | ||||
−0.610475 | + | 0.792035i | \(0.709022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.746921 | −0.0443998 | −0.0221999 | − | 0.999754i | \(-0.507067\pi\) | ||||
−0.0221999 | + | 0.999754i | \(0.507067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.14664 | 0.0679212 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.72429 | −0.574007 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.99528 | 0.293840 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.4461 | −0.788225 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.0541 | 1.34683 | 0.673417 | − | 0.739263i | \(-0.264826\pi\) | ||||
0.673417 | + | 0.739263i | \(0.264826\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.40169 | −0.198054 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.47099 | −0.0853558 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.39611 | 0.369897 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 27.9231 | 1.60946 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.372387 | 0.0213931 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.08429 | −0.291126 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.1854 | 1.15204 | 0.576021 | − | 0.817435i | \(-0.304605\pi\) | ||||
0.576021 | + | 0.817435i | \(0.304605\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.26876 | 0.413506 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.6993 | 1.06034 | 0.530171 | − | 0.847891i | \(-0.322128\pi\) | ||||
0.530171 | + | 0.847891i | \(0.322128\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −33.3300 | −1.88392 | −0.941962 | − | 0.335719i | \(-0.891021\pi\) | ||||
−0.941962 | + | 0.335719i | \(0.891021\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.38479 | −0.134368 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.7905 | −0.774553 | −0.387277 | − | 0.921964i | \(-0.626584\pi\) | ||||
−0.387277 | + | 0.921964i | \(0.626584\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.96003 | 0.389687 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.75739 | 0.432975 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.50910 | 0.417817 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.80803 | 0.266701 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.49121 | −0.524865 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.7878 | −1.14607 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.26826 | −0.399500 | −0.199750 | − | 0.979847i | \(-0.564013\pi\) | ||||
−0.199750 | + | 0.979847i | \(0.564013\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.4028 | −0.570071 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.78319 | 0.534513 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.75359 | −0.367891 | −0.183946 | − | 0.982936i | \(-0.558887\pi\) | ||||
−0.183946 | + | 0.982936i | \(0.558887\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.74341 | −0.149002 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.9793 | −0.702866 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.69367 | −0.523409 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.27486 | −0.230151 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.61353 | −0.0866191 | −0.0433095 | − | 0.999062i | \(-0.513790\pi\) | ||||
−0.0433095 | + | 0.999062i | \(0.513790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.36893 | 0.287392 | 0.143696 | − | 0.989622i | \(-0.454101\pi\) | ||||
0.143696 | + | 0.989622i | \(0.454101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.07152 | 0.0571933 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.70610 | −0.250480 | −0.125240 | − | 0.992126i | \(-0.539970\pi\) | ||||
−0.125240 | + | 0.992126i | \(0.539970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.80118 | 0.520192 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.6175 | −0.826565 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.9268 | 1.15725 | 0.578625 | − | 0.815594i | \(-0.303590\pi\) | ||||
0.578625 | + | 0.815594i | \(0.303590\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4364 | −0.865075 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.83617 | 0.463779 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.23283 | −0.273899 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.5650 | −1.23008 | −0.615040 | − | 0.788496i | \(-0.710860\pi\) | ||||
−0.615040 | + | 0.788496i | \(0.710860\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.92019 | −0.152019 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.6518 | −1.64328 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.522216 | 0.0270393 | 0.0135197 | − | 0.999909i | \(-0.495696\pi\) | ||||
0.0135197 | + | 0.999909i | \(0.495696\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.79422 | −0.350852 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.06989 | −0.261113 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.0093 | −1.54147 | −0.770737 | − | 0.637153i | \(-0.780112\pi\) | ||||
−0.770737 | + | 0.637153i | \(0.780112\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.0695 | 0.772033 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.1272 | −0.568572 | −0.284286 | − | 0.958740i | \(-0.591756\pi\) | ||||
−0.284286 | + | 0.958740i | \(0.591756\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.50802 | −0.178785 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.38527 | 0.426247 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.8762 | 1.31198 | 0.655989 | − | 0.754771i | \(-0.272252\pi\) | ||||
0.655989 | + | 0.754771i | \(0.272252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.9951 | −1.41577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.64719 | −0.436193 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.16932 | 0.461358 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.1106 | −0.808569 | −0.404284 | − | 0.914633i | \(-0.632479\pi\) | ||||
−0.404284 | + | 0.914633i | \(0.632479\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.33174 | −0.266921 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.7106 | 1.53361 | 0.766807 | − | 0.641878i | \(-0.221844\pi\) | ||||
0.766807 | + | 0.641878i | \(0.221844\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.45448 | 0.470961 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.716151 | −0.0355858 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.3025 | −0.758516 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.7712 | 1.07652 | 0.538259 | − | 0.842779i | \(-0.319082\pi\) | ||||
0.538259 | + | 0.842779i | \(0.319082\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.9735 | −0.689260 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.8175 | 0.778326 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.888688 | 0.0436240 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.76531 | 0.478209 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.38933 | 0.0678734 | 0.0339367 | − | 0.999424i | \(-0.489196\pi\) | ||||
0.0339367 | + | 0.999424i | \(0.489196\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.4498 | 1.43530 | 0.717648 | − | 0.696406i | \(-0.245219\pi\) | ||||
0.717648 | + | 0.696406i | \(0.245219\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.24255 | −0.303523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.0442 | −1.02080 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.6413 | 1.14408 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.57619 | 0.0760994 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.1214 | 0.680202 | 0.340101 | − | 0.940389i | \(-0.389539\pi\) | ||||
0.340101 | + | 0.940389i | \(0.389539\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.8372 | −1.57806 | −0.789028 | − | 0.614357i | \(-0.789415\pi\) | ||||
−0.789028 | + | 0.614357i | \(0.789415\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.38848 | 0.162465 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.55742 | −0.457193 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.4769 | −1.78868 | −0.894338 | − | 0.447392i | \(-0.852353\pi\) | ||||
−0.894338 | + | 0.447392i | \(0.852353\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.08900 | 0.194714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.76333 | −0.416358 | −0.208179 | − | 0.978091i | \(-0.566754\pi\) | ||||
−0.208179 | + | 0.978091i | \(0.566754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.49678 | 0.260572 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.6591 | −0.598757 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.19198 | −0.386603 | −0.193302 | − | 0.981139i | \(-0.561920\pi\) | ||||
−0.193302 | + | 0.981139i | \(0.561920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.29559 | −0.202271 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.2773 | −0.482868 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.55534 | 0.119796 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.6671 | 1.24743 | 0.623717 | − | 0.781651i | \(-0.285622\pi\) | ||||
0.623717 | + | 0.781651i | \(0.285622\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.68991 | −0.218906 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.6394 | −1.28730 | −0.643648 | − | 0.765322i | \(-0.722580\pi\) | ||||
−0.643648 | + | 0.765322i | \(0.722580\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.7468 | 1.84719 | 0.923595 | − | 0.383371i | \(-0.125237\pi\) | ||||
0.923595 | + | 0.383371i | \(0.125237\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.31893 | −0.293033 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.99234 | 0.184743 | 0.0923717 | − | 0.995725i | \(-0.470555\pi\) | ||||
0.0923717 | + | 0.995725i | \(0.470555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −45.4907 | −2.10056 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.3312 | −0.798579 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.3347 | 0.567149 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.18442 | −0.329644 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.50501 | −0.435205 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.4282 | 0.933390 | 0.466695 | − | 0.884418i | \(-0.345445\pi\) | ||||
0.466695 | + | 0.884418i | \(0.345445\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.1468 | 0.508250 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.8776 | 0.904462 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.62944 | −0.437251 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.7212 | 1.34680 | 0.673399 | − | 0.739280i | \(-0.264834\pi\) | ||||
0.673399 | + | 0.739280i | \(0.264834\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.39092 | 0.289007 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.6530 | 1.29309 | 0.646546 | − | 0.762875i | \(-0.276213\pi\) | ||||
0.646546 | + | 0.762875i | \(0.276213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.1904 | 0.999404 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.05345 | −0.0473493 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −45.5743 | −2.04429 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.6063 | 0.698636 | 0.349318 | − | 0.937004i | \(-0.386413\pi\) | ||||
0.349318 | + | 0.937004i | \(0.386413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.5905 | −0.962671 | −0.481335 | − | 0.876536i | \(-0.659848\pi\) | ||||
−0.481335 | + | 0.876536i | \(0.659848\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.266685 | 0.0118673 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.8519 | 0.526359 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.2493 | −1.42942 | −0.714712 | − | 0.699419i | \(-0.753442\pi\) | ||||
−0.714712 | + | 0.699419i | \(0.753442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.3320 | 1.07638 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.60112 | −0.0706910 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.20553 | 0.229383 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.18276 | −0.403857 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23.0601 | −1.01223 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.29471 | −0.231965 | −0.115983 | − | 0.993251i | \(-0.537002\pi\) | ||||
−0.115983 | + | 0.993251i | \(0.537002\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.7766 | −1.34577 | −0.672884 | − | 0.739748i | \(-0.734945\pi\) | ||||
−0.672884 | + | 0.739748i | \(0.734945\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.9422 | 0.652131 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −41.3812 | −1.80260 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.6316 | 0.549199 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.74996 | 0.206131 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.12903 | 0.135534 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.55546 | 0.240184 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.56721 | −0.0676300 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.01490 | 0.259080 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.15500 | −0.178637 | −0.0893187 | − | 0.996003i | \(-0.528469\pi\) | ||||
−0.0893187 | + | 0.996003i | \(0.528469\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.66369 | 0.414709 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.79714 | −0.291158 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.6839 | −1.44022 | −0.720110 | − | 0.693860i | \(-0.755909\pi\) | ||||
−0.720110 | + | 0.693860i | \(0.755909\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.09947 | 0.302998 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.57570 | 0.322736 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −42.6362 | −1.81308 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.44999 | −0.316234 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −42.2475 | −1.79008 | −0.895042 | − | 0.445983i | \(-0.852854\pi\) | ||||
−0.895042 | + | 0.445983i | \(0.852854\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.98495 | −0.380023 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.89884 | −0.291269 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.759500 | 0.0320091 | 0.0160046 | − | 0.999872i | \(-0.494905\pi\) | ||||
0.0160046 | + | 0.999872i | \(0.494905\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.96470 | −0.0826554 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.33002 | 0.139848 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.2088 | 1.55987 | 0.779937 | − | 0.625858i | \(-0.215251\pi\) | ||||
0.779937 | + | 0.625858i | \(0.215251\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.3536 | −0.893621 | −0.446811 | − | 0.894629i | \(-0.647440\pi\) | ||||
−0.446811 | + | 0.894629i | \(0.647440\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.1174 | 0.631540 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.7846 | 1.11700 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.837781 | 0.0348773 | 0.0174386 | − | 0.999848i | \(-0.494449\pi\) | ||||
0.0174386 | + | 0.999848i | \(0.494449\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.9243 | −0.620233 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.13229 | −0.171436 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.9818 | −0.579068 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.767367 | 0.0317267 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.10109 | −0.375642 | −0.187821 | − | 0.982203i | \(-0.560143\pi\) | ||||
−0.187821 | + | 0.982203i | \(0.560143\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.1274 | −0.582109 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.7458 | 0.565428 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −32.8995 | −1.35102 | −0.675510 | − | 0.737351i | \(-0.736076\pi\) | ||||
−0.675510 | + | 0.737351i | \(0.736076\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.1845 | −0.458519 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.45882 | 0.387124 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.9054 | −0.609018 | −0.304509 | − | 0.952509i | \(-0.598492\pi\) | ||||
−0.304509 | + | 0.952509i | \(0.598492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.6503 | 1.86212 | 0.931058 | − | 0.364871i | \(-0.118887\pi\) | ||||
0.931058 | + | 0.364871i | \(0.118887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.6608 | −0.556311 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.32803 | 0.257271 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.14482 | 0.289999 | 0.145000 | − | 0.989432i | \(-0.453682\pi\) | ||||
0.145000 | + | 0.989432i | \(0.453682\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.7560 | −0.638466 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.68899 | 0.270608 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.0707 | 0.487530 | 0.243765 | − | 0.969834i | \(-0.421617\pi\) | ||||
0.243765 | + | 0.969834i | \(0.421617\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.09130 | −0.0843294 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.6455 | −0.750640 | −0.375320 | − | 0.926895i | \(-0.622467\pi\) | ||||
−0.375320 | + | 0.926895i | \(0.622467\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −46.6989 | −1.87699 | −0.938495 | − | 0.345294i | \(-0.887779\pi\) | ||||
−0.938495 | + | 0.345294i | \(0.887779\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.96922 | 0.239537 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.5594 | −1.02401 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.5700 | 0.702798 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.35523 | −0.0940590 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −48.7883 | −1.94532 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.4683 | −1.49159 | −0.745794 | − | 0.666177i | \(-0.767930\pi\) | ||||
−0.745794 | + | 0.666177i | \(0.767930\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.5293 | 0.776221 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.7920 | 0.428269 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.38143 | −0.173599 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.6859 | −0.541406 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19.3368 | 0.763757 | 0.381878 | − | 0.924213i | \(-0.375277\pi\) | ||||
0.381878 | + | 0.924213i | \(0.375277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.6061 | −1.40417 | −0.702083 | − | 0.712095i | \(-0.747747\pi\) | ||||
−0.702083 | + | 0.712095i | \(0.747747\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00512 | 0.236451 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.6666 | 0.969743 | 0.484872 | − | 0.874585i | \(-0.338866\pi\) | ||||
0.484872 | + | 0.874585i | \(0.338866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.98717 | 0.274271 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.3822 | 1.15158 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.6448 | 1.47315 | 0.736577 | − | 0.676353i | \(-0.236441\pi\) | ||||
0.736577 | + | 0.676353i | \(0.236441\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.19269 | −0.241968 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.30688 | 0.285068 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.0705 | 0.587063 | 0.293532 | − | 0.955949i | \(-0.405169\pi\) | ||||
0.293532 | + | 0.955949i | \(0.405169\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.4489 | −0.600892 | −0.300446 | − | 0.953799i | \(-0.597136\pi\) | ||||
−0.300446 | + | 0.953799i | \(0.597136\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.02532 | 0.195167 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.81833 | −0.148069 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.2434 | −1.09359 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.37221 | 0.207702 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.4433 | 0.403158 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.7469 | −0.761187 | −0.380593 | − | 0.924743i | \(-0.624280\pi\) | ||||
−0.380593 | + | 0.924743i | \(0.624280\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.48713 | 0.172710 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.4498 | 1.74678 | 0.873388 | − | 0.487025i | \(-0.161918\pi\) | ||||
0.873388 | + | 0.487025i | \(0.161918\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 44.7757 | 1.71834 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −27.0420 | −1.03625 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.5432 | 0.518217 | 0.259108 | − | 0.965848i | \(-0.416571\pi\) | ||||
0.259108 | + | 0.965848i | \(0.416571\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.0071 | −0.382352 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.6136 | 0.481237 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.1848 | 0.388009 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.4424 | 0.397250 | 0.198625 | − | 0.980076i | \(-0.436352\pi\) | ||||
0.198625 | + | 0.980076i | \(0.436352\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.89844 | 0.186076 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.99344 | 0.265276 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.6955 | −0.518752 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −25.6565 | −0.970420 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.26217 | −0.236519 | −0.118259 | − | 0.992983i | \(-0.537731\pi\) | ||||
−0.118259 | + | 0.992983i | \(0.537731\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.6561 | −0.628198 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.47061 | −0.168373 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.24005 | −0.0466371 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.7936 | −1.45692 | −0.728462 | − | 0.685086i | \(-0.759765\pi\) | ||||
−0.728462 | + | 0.685086i | \(0.759765\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.8036 | −0.480173 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.6692 | 1.97248 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.12879 | 0.0422145 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.74058 | 0.102349 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.4655 | −0.986997 | −0.493498 | − | 0.869747i | \(-0.664282\pi\) | ||||
−0.493498 | + | 0.869747i | \(0.664282\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.2051 | −0.901445 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.6085 | 0.729249 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.2309 | −0.788496 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.0571 | −1.59690 | −0.798450 | − | 0.602062i | \(-0.794346\pi\) | ||||
−0.798450 | + | 0.602062i | \(0.794346\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.3262 | 1.45453 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.9645 | −0.811276 | −0.405638 | − | 0.914034i | \(-0.632951\pi\) | ||||
−0.405638 | + | 0.914034i | \(0.632951\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.92834 | 0.108014 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20.0950 | −0.740208 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.2983 | −0.599542 | −0.299771 | − | 0.954011i | \(-0.596910\pi\) | ||||
−0.299771 | + | 0.954011i | \(0.596910\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.71562 | 0.0630250 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.0904 | −1.17728 | −0.588642 | − | 0.808394i | \(-0.700337\pi\) | ||||
−0.588642 | + | 0.808394i | \(0.700337\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.06585 | −0.332147 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.24092 | −0.0454030 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.8322 | −0.943889 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.8716 | 0.761616 | 0.380808 | − | 0.924654i | \(-0.375646\pi\) | ||||
0.380808 | + | 0.924654i | \(0.375646\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15.4602 | −0.563403 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.36008 | −0.267861 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.00358 | 0.145512 | 0.0727562 | − | 0.997350i | \(-0.476820\pi\) | ||||
0.0727562 | + | 0.997350i | \(0.476820\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.78069 | 0.318719 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.4521 | −1.53889 | −0.769443 | − | 0.638716i | \(-0.779466\pi\) | ||||
−0.769443 | + | 0.638716i | \(0.779466\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.6059 | 1.14421 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.35869 | −0.121434 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.08966 | −0.183777 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.42722 | 0.303893 | 0.151947 | − | 0.988389i | \(-0.451446\pi\) | ||||
0.151947 | + | 0.988389i | \(0.451446\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.2550 | 1.01758 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.4061 | 1.34540 | 0.672702 | − | 0.739914i | \(-0.265134\pi\) | ||||
0.672702 | + | 0.739914i | \(0.265134\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.5920 | 1.42219 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 34.6415 | 1.24276 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.67557 | −0.167520 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.1319 | −0.720376 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.73151 | −0.169090 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.4117 | −0.442994 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.8673 | −0.494316 | −0.247158 | − | 0.968975i | \(-0.579497\pi\) | ||||
−0.247158 | + | 0.968975i | \(0.579497\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.0685960 | −0.00244208 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.13560 | 0.324825 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.60719 | −0.270139 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.80702 | −0.241420 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.2739 | −1.00151 | −0.500756 | − | 0.865588i | \(-0.666945\pi\) | ||||
−0.500756 | + | 0.865588i | \(0.666945\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.2770 | −1.03575 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.67545 | −0.271199 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.7484 | 0.379302 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.2354 | 0.501730 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.3857 | 0.576803 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.5606 | 1.60183 | 0.800913 | − | 0.598781i | \(-0.204348\pi\) | ||||
0.800913 | + | 0.598781i | \(0.204348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.1207 | 1.37371 | 0.686856 | − | 0.726794i | \(-0.258990\pi\) | ||||
0.686856 | + | 0.726794i | \(0.258990\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.90565 | −0.312335 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.57686 | 0.160321 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.4258 | 0.469709 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.56816 | −0.124682 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.50395 | 0.331690 | 0.165845 | − | 0.986152i | \(-0.446965\pi\) | ||||
0.165845 | + | 0.986152i | \(0.446965\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.2413 | 1.26329 | 0.631646 | − | 0.775257i | \(-0.282380\pi\) | ||||
0.631646 | + | 0.775257i | \(0.282380\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.60054 | 0.229801 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.0245 | −0.974508 | −0.487254 | − | 0.873260i | \(-0.662001\pi\) | ||||
−0.487254 | + | 0.873260i | \(0.662001\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37.6916 | −1.30908 | −0.654542 | − | 0.756026i | \(-0.727138\pi\) | ||||
−0.654542 | + | 0.756026i | \(0.727138\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.7421 | 0.372639 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19.1771 | 0.664446 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.716151 | 0.0247834 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.82346 | 0.304983 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.3962 | 0.462490 | 0.231245 | − | 0.972896i | \(-0.425720\pi\) | ||||
0.231245 | + | 0.972896i | \(0.425720\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.61279 | −0.228027 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.4669 | 0.704916 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.48772 | 0.291986 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.4246 | −1.01104 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.746921 | 0.0256343 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 62.0967 | 2.12865 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.22324 | 0.0761223 | 0.0380611 | − | 0.999275i | \(-0.487882\pi\) | ||||
0.0380611 | + | 0.999275i | \(0.487882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.14664 | −0.0392143 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.5709 | −1.52251 | −0.761257 | − | 0.648451i | \(-0.775417\pi\) | ||||
−0.761257 | + | 0.648451i | \(0.775417\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.70998 | −0.331300 | −0.165650 | − | 0.986185i | \(-0.552972\pi\) | ||||
−0.165650 | + | 0.986185i | \(0.552972\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.72429 | 0.331403 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.7865 | −0.775662 | −0.387831 | − | 0.921731i | \(-0.626776\pi\) | ||||
−0.387831 | + | 0.921731i | \(0.626776\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.5145 | −0.561511 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.99528 | −0.169649 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.8340 | −0.638901 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.6378 | 0.495982 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13.4461 | 0.455082 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.6248 | 0.764859 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.2439 | 0.616051 | 0.308026 | − | 0.951378i | \(-0.400332\pi\) | ||||
0.308026 | + | 0.951378i | \(0.400332\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.0541 | −0.777595 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.2386 | 1.28829 | 0.644145 | − | 0.764904i | \(-0.277213\pi\) | ||||
0.644145 | + | 0.764904i | \(0.277213\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0956 | 0.777228 | 0.388614 | − | 0.921401i | \(-0.372954\pi\) | ||||
0.388614 | + | 0.921401i | \(0.372954\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.40169 | 0.114347 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.8961 | −0.466584 | −0.233292 | − | 0.972407i | \(-0.574950\pi\) | ||||
−0.233292 | + | 0.972407i | \(0.574950\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.1816 | −1.68304 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.47099 | 0.0492802 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.99505 | −0.334471 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.12236 | −0.0375163 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.39611 | −0.213560 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.7483 | −1.39238 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44.5777 | −1.48510 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −27.9231 | −0.929222 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.92066 | 0.230051 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.7844 | 1.75268 | 0.876339 | − | 0.481694i | \(-0.159978\pi\) | ||||
0.876339 | + | 0.481694i | \(0.159978\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.372387 | −0.0123513 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.2105 | −1.89547 | −0.947735 | − | 0.319059i | \(-0.896633\pi\) | ||||
−0.947735 | + | 0.319059i | \(0.896633\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.82539 | −0.0604116 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.08429 | 0.168081 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.7953 | 0.950903 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.2303 | 0.931230 | 0.465615 | − | 0.884987i | \(-0.345833\pi\) | ||||
0.465615 | + | 0.884987i | \(0.345833\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.1854 | −0.665131 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.6647 | 0.482693 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 46.6788 | 1.53479 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.26876 | −0.238738 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −44.0655 | −1.44574 | −0.722871 | − | 0.690983i | \(-0.757178\pi\) | ||||
−0.722871 | + | 0.690983i | \(0.757178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.54697 | 0.214568 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.6993 | −0.612189 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.94061 | −0.161575 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.3892 | 0.666087 | 0.333043 | − | 0.942912i | \(-0.391924\pi\) | ||||
0.333043 | + | 0.942912i | \(0.391924\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.3300 | 1.08768 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.8213 | 1.00475 | 0.502373 | − | 0.864651i | \(-0.332460\pi\) | ||||
0.502373 | + | 0.864651i | \(0.332460\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.4313 | 0.567641 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.38479 | 0.0775773 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.8708 | 1.26313 | 0.631566 | − | 0.775322i | \(-0.282413\pi\) | ||||
0.631566 | + | 0.775322i | \(0.282413\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.82943 | −0.254154 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.7905 | 0.447188 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.3760 | −0.627649 | −0.313824 | − | 0.949481i | \(-0.601610\pi\) | ||||
−0.313824 | + | 0.949481i | \(0.601610\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.8264 | 0.350333 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.96003 | −0.224986 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46.5318 | 1.50259 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.8534 | 1.51140 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.75739 | −0.249978 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.6880 | −0.344060 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.4967 | 0.787761 | 0.393880 | − | 0.919162i | \(-0.371132\pi\) | ||||
0.393880 | + | 0.919162i | \(0.371132\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.50910 | −0.241227 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.0223 | 0.449996 | 0.224998 | − | 0.974359i | \(-0.427762\pi\) | ||||
0.224998 | + | 0.974359i | \(0.427762\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.5186 | −1.04250 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.80803 | −0.153980 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.1355 | −0.644191 | −0.322096 | − | 0.946707i | \(-0.604387\pi\) | ||||
−0.322096 | + | 0.946707i | \(0.604387\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.2905 | −0.360847 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.49121 | 0.303031 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.0705 | −1.15047 | −0.575235 | − | 0.817988i | \(-0.695089\pi\) | ||||
−0.575235 | + | 0.817988i | \(0.695089\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.84409 | 0.313659 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 20.7878 | 0.661682 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −50.0535 | −1.59161 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.6331 | 0.909561 | 0.454780 | − | 0.890604i | \(-0.349718\pi\) | ||||
0.454780 | + | 0.890604i | \(0.349718\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.26826 | 0.230651 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.77395 | 0.214749 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.1826 | 0.607518 | 0.303759 | − | 0.952749i | \(-0.401758\pi\) | ||||
0.303759 | + | 0.952749i | \(0.401758\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.4028 | 0.329131 |
(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 | 8016.2.a.bf.1.5 | 12 | ||
4.3 | odd | 2 | 4008.2.a.l.1.5 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.l.1.5 | ✓ | 12 | 4.3 | odd | 2 | ||
8016.2.a.bf.1.5 | 12 | 1.1 | even | 1 | trivial |