Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | 8.8.34309996544.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 8x^{6} + 28x^{5} + 31x^{4} - 36x^{3} - 22x^{2} + 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 2432) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.82681\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | 2.06644 | 1.19306 | 0.596529 | − | 0.802592i | \(-0.296546\pi\) | ||||
0.596529 | + | 0.802592i | \(0.296546\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.45635 | 0.651299 | 0.325649 | − | 0.945491i | \(-0.394417\pi\) | ||||
0.325649 | + | 0.945491i | \(0.394417\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.196723 | 0.0743544 | 0.0371772 | − | 0.999309i | \(-0.488163\pi\) | ||||
0.0371772 | + | 0.999309i | \(0.488163\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.27016 | 0.423387 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.27016 | −0.985990 | −0.492995 | − | 0.870032i | \(-0.664098\pi\) | ||||
−0.492995 | + | 0.870032i | \(0.664098\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.72211 | −1.86438 | −0.932189 | − | 0.361973i | \(-0.882103\pi\) | ||||
−0.932189 | + | 0.361973i | \(0.882103\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.00945 | 0.777037 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.82843 | −0.928530 | −0.464265 | − | 0.885696i | \(-0.653681\pi\) | ||||
−0.464265 | + | 0.885696i | \(0.653681\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.406516 | 0.0887090 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.72211 | 1.40166 | 0.700828 | − | 0.713330i | \(-0.252814\pi\) | ||||
0.700828 | + | 0.713330i | \(0.252814\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.87905 | −0.575810 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.57461 | −0.687933 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.26907 | 0.792747 | 0.396374 | − | 0.918089i | \(-0.370268\pi\) | ||||
0.396374 | + | 0.918089i | \(0.370268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.92215 | −1.06365 | −0.531824 | − | 0.846855i | \(-0.678493\pi\) | ||||
−0.531824 | + | 0.846855i | \(0.678493\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.75758 | −1.17634 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.286497 | 0.0484269 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.1782 | −1.67328 | −0.836639 | − | 0.547755i | \(-0.815483\pi\) | ||||
−0.836639 | + | 0.547755i | \(0.815483\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −13.8908 | −2.22431 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.16502 | 1.11899 | 0.559494 | − | 0.828834i | \(-0.310995\pi\) | ||||
0.559494 | + | 0.828834i | \(0.310995\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4194 | −1.58894 | −0.794470 | − | 0.607304i | \(-0.792251\pi\) | ||||
−0.794470 | + | 0.607304i | \(0.792251\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.84979 | 0.275751 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.61269 | 0.526965 | 0.263482 | − | 0.964664i | \(-0.415129\pi\) | ||||
0.263482 | + | 0.964664i | \(0.415129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96130 | −0.994471 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.91120 | −1.10779 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.52508 | 1.17101 | 0.585505 | − | 0.810669i | \(-0.300896\pi\) | ||||
0.585505 | + | 0.810669i | \(0.300896\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.76249 | −0.642174 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.06644 | 0.273706 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.137287 | −0.0178732 | −0.00893660 | − | 0.999960i | \(-0.502845\pi\) | ||||
−0.00893660 | + | 0.999960i | \(0.502845\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3879 | 1.33004 | 0.665020 | − | 0.746826i | \(-0.268423\pi\) | ||||
0.665020 | + | 0.746826i | \(0.268423\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.249870 | 0.0314806 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.78973 | −1.21427 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.22167 | −0.271420 | −0.135710 | − | 0.990749i | \(-0.543332\pi\) | ||||
−0.135710 | + | 0.990749i | \(0.543332\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.8908 | 1.67226 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.11856 | 0.963496 | 0.481748 | − | 0.876310i | \(-0.340002\pi\) | ||||
0.481748 | + | 0.876310i | \(0.340002\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.01634 | −0.235994 | −0.117997 | − | 0.993014i | \(-0.537647\pi\) | ||||
−0.117997 | + | 0.993014i | \(0.537647\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.94938 | −0.686975 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.643316 | −0.0733127 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.6473 | −1.53544 | −0.767719 | − | 0.640787i | \(-0.778608\pi\) | ||||
−0.767719 | + | 0.640787i | \(0.778608\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.1972 | −1.24413 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.14921 | 0.126142 | 0.0630711 | − | 0.998009i | \(-0.479911\pi\) | ||||
0.0630711 | + | 0.998009i | \(0.479911\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.57552 | −0.604750 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.82177 | 0.945793 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.11706 | −0.648407 | −0.324204 | − | 0.945987i | \(-0.605096\pi\) | ||||
−0.324204 | + | 0.945987i | \(0.605096\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.32239 | −0.138625 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.2377 | −1.26899 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.45635 | 0.149418 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.132873 | −0.0134912 | −0.00674560 | − | 0.999977i | \(-0.502147\pi\) | ||||
−0.00674560 | + | 0.999977i | \(0.502147\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.15362 | −0.417455 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.81876 | −0.777996 | −0.388998 | − | 0.921239i | \(-0.627179\pi\) | ||||
−0.388998 | + | 0.921239i | \(0.627179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.6631 | −1.93746 | −0.968729 | − | 0.248121i | \(-0.920187\pi\) | ||||
−0.968729 | + | 0.248121i | \(0.920187\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.592028 | 0.0577761 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.18952 | −0.308343 | −0.154171 | − | 0.988044i | \(-0.549271\pi\) | ||||
−0.154171 | + | 0.988044i | \(0.549271\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.44941 | 0.521959 | 0.260980 | − | 0.965344i | \(-0.415954\pi\) | ||||
0.260980 | + | 0.965344i | \(0.415954\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.0325 | −1.99632 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.6890 | −1.19368 | −0.596841 | − | 0.802360i | \(-0.703578\pi\) | ||||
−0.596841 | + | 0.802360i | \(0.703578\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.78973 | 0.912897 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −8.53815 | −0.789352 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.753140 | −0.0690403 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.306056 | −0.0278233 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.8061 | 1.33502 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.4746 | −1.02632 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.83484 | 0.783965 | 0.391983 | − | 0.919973i | \(-0.371789\pi\) | ||||
0.391983 | + | 0.919973i | \(0.371789\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21.5310 | −1.89570 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.1285 | −1.84600 | −0.923001 | − | 0.384798i | \(-0.874271\pi\) | ||||
−0.923001 | + | 0.384798i | \(0.874271\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.196723 | 0.0170581 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.20587 | −0.448050 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.3464 | 1.05482 | 0.527411 | − | 0.849610i | \(-0.323163\pi\) | ||||
0.527411 | + | 0.849610i | \(0.323163\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.84638 | −0.835159 | −0.417579 | − | 0.908640i | \(-0.637121\pi\) | ||||
−0.417579 | + | 0.908640i | \(0.637121\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.46539 | 0.628699 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 21.9824 | 1.83826 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.21726 | 0.516315 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.3851 | −1.18646 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.06290 | −0.0870763 | −0.0435381 | − | 0.999052i | \(-0.513863\pi\) | ||||
−0.0435381 | + | 0.999052i | \(0.513863\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.91270 | 0.237032 | 0.118516 | − | 0.992952i | \(-0.462186\pi\) | ||||
0.118516 | + | 0.992952i | \(0.462186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.86271 | −0.393127 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.62470 | −0.692753 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.63179 | −0.688892 | −0.344446 | − | 0.938806i | \(-0.611933\pi\) | ||||
−0.344446 | + | 0.938806i | \(0.611933\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 17.6165 | 1.39708 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.32239 | 0.104219 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.45541 | 0.113996 | 0.0569982 | − | 0.998374i | \(-0.481847\pi\) | ||||
0.0569982 | + | 0.998374i | \(0.481847\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.84138 | −0.766151 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.5539 | 1.12622 | 0.563109 | − | 0.826383i | \(-0.309605\pi\) | ||||
0.563109 | + | 0.826383i | \(0.309605\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.1867 | 2.47590 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.27016 | 0.0971315 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.7002 | 1.34572 | 0.672861 | − | 0.739769i | \(-0.265065\pi\) | ||||
0.672861 | + | 0.739769i | \(0.265065\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.566376 | −0.0428140 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.283694 | −0.0213238 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.5725 | −0.864967 | −0.432483 | − | 0.901642i | \(-0.642363\pi\) | ||||
−0.432483 | + | 0.901642i | \(0.642363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.95620 | 0.294062 | 0.147031 | − | 0.989132i | \(-0.453028\pi\) | ||||
0.147031 | + | 0.989132i | \(0.453028\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 21.4660 | 1.58681 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.8229 | −1.08980 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.5196 | 0.915521 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.703208 | −0.0511508 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.02874 | 0.291510 | 0.145755 | − | 0.989321i | \(-0.453439\pi\) | ||||
0.145755 | + | 0.989321i | \(0.453439\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2979 | 0.957203 | 0.478602 | − | 0.878032i | \(-0.341144\pi\) | ||||
0.478602 | + | 0.878032i | \(0.341144\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −20.2298 | −1.44869 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.61228 | −0.471106 | −0.235553 | − | 0.971862i | \(-0.575690\pi\) | ||||
−0.235553 | + | 0.971862i | \(0.575690\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.3159 | 1.58193 | 0.790967 | − | 0.611859i | \(-0.209578\pi\) | ||||
0.790967 | + | 0.611859i | \(0.209578\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.59094 | −0.323820 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.839826 | 0.0589442 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.4348 | 0.728796 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.53815 | 0.593442 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.27016 | −0.226202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.2315 | −1.04858 | −0.524288 | − | 0.851541i | \(-0.675669\pi\) | ||||
−0.524288 | + | 0.851541i | \(0.675669\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.7765 | 1.14951 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.1742 | −1.03487 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.16502 | −0.0790869 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.16663 | −0.281555 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 25.7351 | 1.73113 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00343 | 0.0671947 | 0.0335973 | − | 0.999435i | \(-0.489304\pi\) | ||||
0.0335973 | + | 0.999435i | \(0.489304\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.65685 | −0.243790 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.20586 | −0.544642 | −0.272321 | − | 0.962206i | \(-0.587791\pi\) | ||||
−0.272321 | + | 0.962206i | \(0.587791\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.4321 | 1.68060 | 0.840300 | − | 0.542122i | \(-0.182379\pi\) | ||||
0.840300 | + | 0.542122i | \(0.182379\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.32937 | −0.0874662 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.8702 | 1.17072 | 0.585359 | − | 0.810774i | \(-0.300954\pi\) | ||||
0.585359 | + | 0.810774i | \(0.300954\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.26133 | 0.343211 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28.2012 | −1.83186 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.17212 | −0.334556 | −0.167278 | − | 0.985910i | \(-0.553498\pi\) | ||||
−0.167278 | + | 0.985910i | \(0.553498\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.9189 | 1.60516 | 0.802582 | − | 0.596542i | \(-0.203459\pi\) | ||||
0.802582 | + | 0.596542i | \(0.203459\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.4144 | −0.796386 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.1381 | −0.647698 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.72211 | −0.427717 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.37477 | 0.150495 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.4673 | −0.850051 | −0.425025 | − | 0.905181i | \(-0.639735\pi\) | ||||
−0.425025 | + | 0.905181i | \(0.639735\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.9824 | −1.38202 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.5215 | −0.721502 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.55666 | 0.471371 | 0.235686 | − | 0.971829i | \(-0.424266\pi\) | ||||
0.235686 | + | 0.971829i | \(0.424266\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.00228 | −0.124415 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.42241 | 0.335639 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3441 | 0.884498 | 0.442249 | − | 0.896892i | \(-0.354181\pi\) | ||||
0.442249 | + | 0.896892i | \(0.354181\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.4155 | 0.762677 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.6405 | −0.773587 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.1161 | −1.34844 | −0.674221 | − | 0.738530i | \(-0.735520\pi\) | ||||
−0.674221 | + | 0.738530i | \(0.735520\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.51563 | 0.335051 | 0.167525 | − | 0.985868i | \(-0.446422\pi\) | ||||
0.167525 | + | 0.985868i | \(0.446422\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.73264 | −0.165387 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.41496 | 0.567743 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.4135 | 0.866022 | 0.433011 | − | 0.901389i | \(-0.357451\pi\) | ||||
0.433011 | + | 0.901389i | \(0.357451\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.52207 | −0.450335 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.4956 | 1.10335 | 0.551677 | − | 0.834058i | \(-0.313988\pi\) | ||||
0.551677 | + | 0.834058i | \(0.313988\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.83004 | 0.287116 | 0.143558 | − | 0.989642i | \(-0.454146\pi\) | ||||
0.143558 | + | 0.989642i | \(0.454146\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.00945 | 0.178264 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.40953 | 0.0832017 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.34315 | −0.137832 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.274573 | −0.0160958 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.94022 | −0.113349 | −0.0566745 | − | 0.998393i | \(-0.518050\pi\) | ||||
−0.0566745 | + | 0.998393i | \(0.518050\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.199937 | −0.0116408 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.6895 | 0.678295 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −45.1867 | −2.61322 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.04973 | −0.118145 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.1570 | −0.928194 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.1285 | 0.866253 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.7053 | 0.782205 | 0.391103 | − | 0.920347i | \(-0.372094\pi\) | ||||
0.391103 | + | 0.920347i | \(0.372094\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −40.6325 | −2.31150 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.8349 | −1.69178 | −0.845890 | − | 0.533357i | \(-0.820930\pi\) | ||||
−0.845890 | + | 0.533357i | \(0.820930\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.2244 | −1.14315 | −0.571575 | − | 0.820550i | \(-0.693667\pi\) | ||||
−0.571575 | + | 0.820550i | \(0.693667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.363897 | 0.0205033 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.6037 | 0.764057 | 0.382029 | − | 0.924150i | \(-0.375226\pi\) | ||||
0.382029 | + | 0.924150i | \(0.375226\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.9606 | −0.781641 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.59094 | −0.367871 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.82843 | −0.213019 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.3533 | 1.07353 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.2609 | 0.622727 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.710700 | 0.0391821 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.66501 | −0.366342 | −0.183171 | − | 0.983081i | \(-0.558636\pi\) | ||||
−0.183171 | + | 0.983081i | \(0.558636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.9279 | −0.708443 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.23553 | −0.176776 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.8420 | 1.84349 | 0.921745 | − | 0.387796i | \(-0.126764\pi\) | ||||
0.921745 | + | 0.387796i | \(0.126764\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.2210 | −1.42413 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.3664 | 1.04875 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.74651 | −0.148298 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20.2298 | 1.08914 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.69716 | −0.252157 | −0.126079 | − | 0.992020i | \(-0.540239\pi\) | ||||
−0.126079 | + | 0.992020i | \(0.540239\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.27540 | −0.228857 | −0.114428 | − | 0.993431i | \(-0.536504\pi\) | ||||
−0.114428 | + | 0.993431i | \(0.536504\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.0289 | 1.28257 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.82401 | 0.256756 | 0.128378 | − | 0.991725i | \(-0.459023\pi\) | ||||
0.128378 | + | 0.991725i | \(0.459023\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.8235 | 0.627524 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.55632 | −0.0823690 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.52237 | −0.291460 | −0.145730 | − | 0.989324i | \(-0.546553\pi\) | ||||
−0.145730 | + | 0.989324i | \(0.546553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.632446 | −0.0331948 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.93649 | −0.153703 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.1750 | −0.531133 | −0.265566 | − | 0.964093i | \(-0.585559\pi\) | ||||
−0.265566 | + | 0.964093i | \(0.585559\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.10072 | 0.473765 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.67708 | 0.0870697 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.640102 | −0.0331432 | −0.0165716 | − | 0.999863i | \(-0.505275\pi\) | ||||
−0.0165716 | + | 0.999863i | \(0.505275\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −23.7116 | −1.22446 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.6972 | −1.47798 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.9406 | −1.69204 | −0.846022 | − | 0.533149i | \(-0.821009\pi\) | ||||
−0.846022 | + | 0.533149i | \(0.821009\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.2566 | 0.935316 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.11545 | 0.414680 | 0.207340 | − | 0.978269i | \(-0.433519\pi\) | ||||
0.207340 | + | 0.978269i | \(0.433519\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.936892 | −0.0477484 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.2343 | −0.672735 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.5702 | −1.65138 | −0.825689 | − | 0.564126i | \(-0.809213\pi\) | ||||
−0.825689 | + | 0.564126i | \(0.809213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.7351 | −1.30148 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −43.6606 | −2.20239 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −19.8752 | −1.00003 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.6380 | 1.38711 | 0.693557 | − | 0.720402i | \(-0.256043\pi\) | ||||
0.693557 | + | 0.720402i | \(0.256043\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.406516 | 0.0203512 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.4219 | 1.86876 | 0.934381 | − | 0.356275i | \(-0.115953\pi\) | ||||
0.934381 | + | 0.356275i | \(0.115953\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 39.8093 | 1.98304 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.3070 | −0.810300 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 33.2842 | 1.64984 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.5114 | −1.31090 | −0.655452 | − | 0.755237i | \(-0.727522\pi\) | ||||
−0.655452 | + | 0.755237i | \(0.727522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.5130 | 1.25846 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.0270075 | −0.00132895 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.67365 | 0.0821563 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20.3469 | −0.996392 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 29.3006 | 1.43143 | 0.715714 | − | 0.698393i | \(-0.246101\pi\) | ||||
0.715714 | + | 0.698393i | \(0.246101\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.10610 | −0.200119 | −0.100060 | − | 0.994981i | \(-0.531903\pi\) | ||||
−0.100060 | + | 0.994981i | \(0.531903\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.58869 | 0.223110 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.0222 | 0.534657 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.04355 | 0.0988943 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 45.4252 | 2.19315 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.0502 | −0.821277 | −0.410639 | − | 0.911798i | \(-0.634694\pi\) | ||||
−0.410639 | + | 0.911798i | \(0.634694\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.1356 | 0.775427 | 0.387713 | − | 0.921780i | \(-0.373265\pi\) | ||||
0.387713 | + | 0.921780i | \(0.373265\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.8476 | 0.615994 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.72211 | 0.321562 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.3232 | 1.78134 | 0.890670 | − | 0.454651i | \(-0.150236\pi\) | ||||
0.890670 | + | 0.454651i | \(0.150236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.84196 | −0.421046 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.2254 | −0.533337 | −0.266668 | − | 0.963788i | \(-0.585923\pi\) | ||||
−0.266668 | + | 0.963788i | \(0.585923\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.90857 | −0.422307 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.19642 | −0.103887 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.3791 | −0.725783 | −0.362891 | − | 0.931831i | \(-0.618210\pi\) | ||||
−0.362891 | + | 0.931831i | \(0.618210\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.4308 | −1.10331 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.01890 | 0.282793 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.92587 | −0.0902860 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.8093 | −1.16053 | −0.580265 | − | 0.814428i | \(-0.697051\pi\) | ||||
−0.580265 | + | 0.814428i | \(0.697051\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13.6851 | 0.638767 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.74289 | −0.267473 | −0.133737 | − | 0.991017i | \(-0.542698\pi\) | ||||
−0.133737 | + | 0.991017i | \(0.542698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.5494 | −1.09443 | −0.547217 | − | 0.836991i | \(-0.684313\pi\) | ||||
−0.547217 | + | 0.836991i | \(0.684313\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.8224 | −0.826494 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.2375 | 1.21413 | 0.607063 | − | 0.794653i | \(-0.292347\pi\) | ||||
0.607063 | + | 0.794653i | \(0.292347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.437054 | −0.0201813 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.8371 | −0.821888 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 34.0730 | 1.56668 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.87905 | −0.132100 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8282 | 0.495790 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.5262 | −0.892176 | −0.446088 | − | 0.894989i | \(-0.647183\pi\) | ||||
−0.446088 | + | 0.894989i | \(0.647183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 68.4186 | 3.11962 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.73264 | 0.124340 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.193509 | −0.00878680 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.5206 | −1.24708 | −0.623539 | − | 0.781792i | \(-0.714306\pi\) | ||||
−0.623539 | + | 0.781792i | \(0.714306\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.00751 | 0.136004 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.870365 | 0.0392790 | 0.0196395 | − | 0.999807i | \(-0.493748\pi\) | ||||
0.0196395 | + | 0.999807i | \(0.493748\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.3438 | −0.736090 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.04912 | −0.271888 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.59711 | 0.0716402 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.37036 | −0.0613456 | −0.0306728 | − | 0.999529i | \(-0.509765\pi\) | ||||
−0.0306728 | + | 0.999529i | \(0.509765\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.0748 | 1.34364 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.2354 | −0.991430 | −0.495715 | − | 0.868485i | \(-0.665094\pi\) | ||||
−0.495715 | + | 0.868485i | \(0.665094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.3868 | −0.506708 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 66.5118 | 2.95389 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.0391 | −0.843895 | −0.421947 | − | 0.906620i | \(-0.638653\pi\) | ||||
−0.421947 | + | 0.906620i | \(0.638653\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.396660 | −0.0175472 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.57461 | −0.157823 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28.6362 | −1.26186 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.8141 | −0.519582 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36.5764 | 1.60552 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.8425 | 0.781694 | 0.390847 | − | 0.920456i | \(-0.372182\pi\) | ||||
0.390847 | + | 0.920456i | \(0.372182\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.9928 | −1.74876 | −0.874382 | − | 0.485239i | \(-0.838733\pi\) | ||||
−0.874382 | + | 0.485239i | \(0.838733\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.17038 | −0.0510796 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.6725 | 0.987630 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.1867 | 0.964641 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.174376 | −0.00756727 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −48.1641 | −2.08622 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.64505 | −0.200823 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.9138 | −1.03196 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.7646 | 0.980539 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.3449 | −1.08966 | −0.544830 | − | 0.838546i | \(-0.683406\pi\) | ||||
−0.544830 | + | 0.838546i | \(0.683406\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.17524 | 0.350833 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.93624 | 0.339951 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.4541 | −0.960068 | −0.480034 | − | 0.877250i | \(-0.659376\pi\) | ||||
−0.480034 | + | 0.877250i | \(0.659376\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.1943 | 0.563121 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.26907 | 0.181869 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.68473 | −0.114166 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −30.6306 | −1.30020 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.8511 | −1.13772 | −0.568860 | − | 0.822434i | \(-0.692615\pi\) | ||||
−0.568860 | + | 0.822434i | \(0.692615\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 70.0401 | 2.96238 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 25.8709 | 1.09227 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 37.0560 | 1.56172 | 0.780862 | − | 0.624703i | \(-0.214780\pi\) | ||||
0.780862 | + | 0.624703i | \(0.214780\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.4796 | −0.777443 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.20274 | −0.0925065 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.20600 | 0.0924804 | 0.0462402 | − | 0.998930i | \(-0.485276\pi\) | ||||
0.0462402 | + | 0.998930i | \(0.485276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.4444 | 0.855571 | 0.427786 | − | 0.903880i | \(-0.359294\pi\) | ||||
0.427786 | + | 0.903880i | \(0.359294\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.32514 | 0.347788 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −19.3533 | −0.807088 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −41.8850 | −1.74369 | −0.871847 | − | 0.489779i | \(-0.837077\pi\) | ||||
−0.871847 | + | 0.489779i | \(0.837077\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.4793 | 1.14200 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.226076 | 0.00937923 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −27.8784 | −1.15460 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.4345 | −0.514104 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −33.4301 | −1.37981 | −0.689904 | − | 0.723901i | \(-0.742347\pi\) | ||||
−0.689904 | + | 0.723901i | \(0.742347\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.92215 | −0.244018 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.6639 | −0.562056 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.83769 | 0.198660 | 0.0993301 | − | 0.995055i | \(-0.468330\pi\) | ||||
0.0993301 | + | 0.995055i | \(0.468330\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.09683 | −0.0449658 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 46.1144 | 1.88734 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.64816 | 0.189919 | 0.0949594 | − | 0.995481i | \(-0.469728\pi\) | ||||
0.0949594 | + | 0.995481i | \(0.469728\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.8661 | −0.524819 | −0.262409 | − | 0.964957i | \(-0.584517\pi\) | ||||
−0.262409 | + | 0.964957i | \(0.584517\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.82188 | −0.114916 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.445725 | −0.0181213 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.4246 | 0.585477 | 0.292739 | − | 0.956193i | \(-0.405433\pi\) | ||||
0.292739 | + | 0.956193i | \(0.405433\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.73545 | 0.0703238 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.2849 | −0.982461 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.2502 | 1.50452 | 0.752261 | − | 0.658865i | \(-0.228963\pi\) | ||||
0.752261 | + | 0.658865i | \(0.228963\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21.5628 | 0.869495 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.6841 | 1.15478 | 0.577388 | − | 0.816470i | \(-0.304072\pi\) | ||||
0.577388 | + | 0.816470i | \(0.304072\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.26470 | −0.171413 | −0.0857063 | − | 0.996320i | \(-0.527315\pi\) | ||||
−0.0857063 | + | 0.996320i | \(0.527315\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.0289 | −0.964246 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.20337 | −0.0482119 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.31581 | −0.0926324 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.75758 | −0.269872 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 38.9663 | 1.55369 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.34444 | −0.371996 | −0.185998 | − | 0.982550i | \(-0.559552\pi\) | ||||
−0.185998 | + | 0.982550i | \(0.559552\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −31.4748 | −1.25101 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.8666 | 0.510596 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46.7946 | 1.85407 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.3119 | 0.407931 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.0359 | 1.30484 | 0.652420 | − | 0.757858i | \(-0.273754\pi\) | ||||
0.652420 | + | 0.757858i | \(0.273754\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.53485 | −0.139401 | −0.0697005 | − | 0.997568i | \(-0.522204\pi\) | ||||
−0.0697005 | + | 0.997568i | \(0.522204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31.3566 | −1.23466 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.0925 | 1.41894 | 0.709471 | − | 0.704734i | \(-0.248934\pi\) | ||||
0.709471 | + | 0.704734i | \(0.248934\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.448949 | 0.0176228 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.40745 | −0.0943553 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.8193 | 0.775588 | 0.387794 | − | 0.921746i | \(-0.373237\pi\) | ||||
0.387794 | + | 0.921746i | \(0.373237\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.7704 | −1.20230 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.56107 | −0.0999169 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.8393 | −1.59087 | −0.795437 | − | 0.606036i | \(-0.792759\pi\) | ||||
−0.795437 | + | 0.606036i | \(0.792759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.8218 | −1.04325 | −0.521623 | − | 0.853176i | \(-0.674673\pi\) | ||||
−0.521623 | + | 0.853176i | \(0.674673\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 53.1799 | 2.06534 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.286497 | 0.0111099 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.6972 | 1.11116 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.07352 | 0.0801671 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −33.9702 | −1.31141 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.6633 | 1.10489 | 0.552445 | − | 0.833549i | \(-0.313695\pi\) | ||||
0.552445 | + | 0.833549i | \(0.313695\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.2915 | 0.396119 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.30155 | 0.280621 | 0.140311 | − | 0.990108i | \(-0.455190\pi\) | ||||
0.140311 | + | 0.990108i | \(0.455190\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0261392 | −0.00100313 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.9569 | −0.649789 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.3780 | −0.971063 | −0.485531 | − | 0.874219i | \(-0.661374\pi\) | ||||
−0.485531 | + | 0.874219i | \(0.661374\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.9806 | 0.687005 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 52.5538 | 2.00505 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −57.3065 | −2.18320 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32.3136 | 1.22927 | 0.614633 | − | 0.788813i | \(-0.289304\pi\) | ||||
0.614633 | + | 0.788813i | \(0.289304\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.817114 | −0.0310396 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.3397 | −0.543938 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.4308 | −1.03901 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 36.9277 | 1.39673 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.8573 | −0.485612 | −0.242806 | − | 0.970075i | \(-0.578068\pi\) | ||||
−0.242806 | + | 0.970075i | \(0.578068\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.1782 | −0.383876 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.8722 | 0.409471 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.53813 | −0.0578474 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −41.1583 | −1.54573 | −0.772867 | − | 0.634568i | \(-0.781178\pi\) | ||||
−0.772867 | + | 0.634568i | \(0.781178\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.3342 | −0.650083 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.8093 | −1.49087 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.0140 | 1.19725 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.6878 | −0.399145 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.3230 | 1.35462 | 0.677309 | − | 0.735698i | \(-0.263146\pi\) | ||||
0.677309 | + | 0.735698i | \(0.263146\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.86818 | −0.144058 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 51.4932 | 1.91505 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.2909 | −0.456472 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.34652 | 0.0499398 | 0.0249699 | − | 0.999688i | \(-0.492051\pi\) | ||||
0.0249699 | + | 0.999688i | \(0.492051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.93789 | 0.293996 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.8898 | 1.47538 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.03789 | 0.333822 | 0.166911 | − | 0.985972i | \(-0.446621\pi\) | ||||
0.166911 | + | 0.985972i | \(0.446621\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20.9497 | −0.772741 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.26522 | 0.267618 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.7004 | −1.35005 | −0.675023 | − | 0.737796i | \(-0.735866\pi\) | ||||
−0.675023 | + | 0.737796i | \(0.735866\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.8908 | −0.510292 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.7973 | −1.34996 | −0.674981 | − | 0.737835i | \(-0.735848\pi\) | ||||
−0.674981 | + | 0.737835i | \(0.735848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.54795 | −0.0567127 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.45968 | 0.0534069 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.627453 | −0.0229266 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.2062 | −1.54013 | −0.770064 | − | 0.637967i | \(-0.779776\pi\) | ||||
−0.770064 | + | 0.637967i | \(0.779776\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.8294 | −1.01416 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.24190 | 0.154378 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.89431 | −0.323269 | −0.161635 | − | 0.986851i | \(-0.551677\pi\) | ||||
−0.161635 | + | 0.986851i | \(0.551677\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −45.4252 | −1.64883 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.3702 | 1.31842 | 0.659210 | − | 0.751959i | \(-0.270891\pi\) | ||||
0.659210 | + | 0.751959i | \(0.270891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.07203 | 0.0388099 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.08180 | −0.256043 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.922856 | 0.0333224 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.11654 | 0.292690 | 0.146345 | − | 0.989234i | \(-0.453249\pi\) | ||||
0.146345 | + | 0.989234i | \(0.453249\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.6154 | 0.562373 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.0053 | 1.47486 | 0.737429 | − | 0.675424i | \(-0.236039\pi\) | ||||
0.737429 | + | 0.675424i | \(0.236039\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.0502 | 0.612460 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.13758 | −0.148435 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.16502 | 0.256714 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.5490 | −0.949998 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −15.2603 | −0.545357 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.5709 | −0.448674 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.1644 | −0.968305 | −0.484153 | − | 0.874984i | \(-0.660872\pi\) | ||||
−0.484153 | + | 0.874984i | \(0.660872\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.6413 | 1.05526 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.49622 | −0.0887554 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −69.8289 | −2.47970 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.6558 | 0.909918 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.55623 | 0.161390 | 0.0806949 | − | 0.996739i | \(-0.474286\pi\) | ||||
0.0806949 | + | 0.996739i | \(0.474286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.8309 | −0.489303 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.76964 | −0.274527 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.59375 | 0.232688 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.92587 | 0.0678779 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −45.7015 | −1.60877 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.5386 | −0.792414 | −0.396207 | − | 0.918161i | \(-0.629674\pi\) | ||||
−0.396207 | + | 0.918161i | \(0.629674\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.0887 | 1.26725 | 0.633623 | − | 0.773642i | \(-0.281567\pi\) | ||||
0.633623 | + | 0.773642i | \(0.281567\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.3977 | 0.399735 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.11958 | 0.0742457 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.4194 | −0.364528 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.67965 | −0.0586918 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.0875 | 0.491658 | 0.245829 | − | 0.969313i | \(-0.420940\pi\) | ||||
0.245829 | + | 0.969313i | \(0.420940\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.0424 | 1.29122 | 0.645608 | − | 0.763669i | \(-0.276604\pi\) | ||||
0.645608 | + | 0.763669i | \(0.276604\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19.4554 | 0.677350 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.03700 | −0.175154 | −0.0875768 | − | 0.996158i | \(-0.527912\pi\) | ||||
−0.0875768 | + | 0.996158i | \(0.527912\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.9611 | −1.00586 | −0.502930 | − | 0.864327i | \(-0.667745\pi\) | ||||
−0.502930 | + | 0.864327i | \(0.667745\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.7845 | 1.03321 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.6508 | 0.923397 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.1956 | 0.733504 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.1693 | 0.731719 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.5197 | −1.26080 | −0.630400 | − | 0.776270i | \(-0.717109\pi\) | ||||
−0.630400 | + | 0.776270i | \(0.717109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.7750 | −0.371552 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.2200 | 1.31637 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 46.8751 | 1.61255 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0602084 | −0.00206878 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.98097 | 0.342546 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −68.4186 | −2.34536 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.19322 | −0.177812 | −0.0889062 | − | 0.996040i | \(-0.528337\pi\) | ||||
−0.0889062 | + | 0.996040i | \(0.528337\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.84979 | 0.0632616 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.1808 | 0.723524 | 0.361762 | − | 0.932271i | \(-0.382175\pi\) | ||||
0.361762 | + | 0.932271i | \(0.382175\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.3430 | 0.455257 | 0.227629 | − | 0.973748i | \(-0.426903\pi\) | ||||
0.227629 | + | 0.973748i | \(0.426903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.91270 | 0.0992644 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.8361 | −1.25392 | −0.626958 | − | 0.779053i | \(-0.715700\pi\) | ||||
−0.626958 | + | 0.779053i | \(0.715700\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.7777 | 0.876467 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.84196 | −0.164442 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.6287 | 1.51393 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.9343 | 0.506030 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.168770 | −0.00571199 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.25733 | −0.0763116 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.1343 | 0.511047 | 0.255524 | − | 0.966803i | \(-0.417752\pi\) | ||||
0.255524 | + | 0.966803i | \(0.417752\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.00935 | −0.135232 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.9345 | −1.74972 | −0.874859 | − | 0.484377i | \(-0.839046\pi\) | ||||
−0.874859 | + | 0.484377i | \(0.839046\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.5238 | 0.825293 | 0.412646 | − | 0.910891i | \(-0.364605\pi\) | ||||
0.412646 | + | 0.910891i | \(0.364605\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.413157 | −0.0138881 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45.2252 | 1.51851 | 0.759257 | − | 0.650791i | \(-0.225562\pi\) | ||||
0.759257 | + | 0.650791i | \(0.225562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.73802 | 0.0582912 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.6165 | 1.22670 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.61269 | 0.120894 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.8535 | −0.563352 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −93.3755 | −3.11772 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.2821 | −0.843205 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.6376 | −1.08732 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.23564 | −0.140953 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.76161 | 0.191522 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.25715 | 0.174561 | 0.0872804 | − | 0.996184i | \(-0.472182\pi\) | ||||
0.0872804 | + | 0.996184i | \(0.472182\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.93108 | −0.329393 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.95774 | 0.296783 | 0.148392 | − | 0.988929i | \(-0.452590\pi\) | ||||
0.148392 | + | 0.988929i | \(0.452590\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.75810 | −0.124375 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.2620 | 1.03349 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.15646 | −0.137258 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.1737 | 0.962351 | 0.481175 | − | 0.876624i | \(-0.340210\pi\) | ||||
0.481175 | + | 0.876624i | \(0.340210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.3212 | 0.933216 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −54.5739 | −1.79632 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.3034 | 0.963490 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.9752 | −0.820294 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.2930 | −1.28916 | −0.644580 | − | 0.764537i | \(-0.722968\pi\) | ||||
−0.644580 | + | 0.764537i | \(0.722968\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.96130 | −0.228147 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −61.6519 | −2.01839 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.2328 | 0.596278 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.4973 | −0.408271 | −0.204135 | − | 0.978943i | \(-0.565438\pi\) | ||||
−0.204135 | + | 0.978943i | \(0.565438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −41.7924 | −1.36384 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.1052 | −0.753207 | −0.376603 | − | 0.926375i | \(-0.622908\pi\) | ||||
−0.376603 | + | 0.926375i | \(0.622908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 48.1641 | 1.56844 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.02411 | −0.0333145 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.97265 | 0.129094 | 0.0645468 | − | 0.997915i | \(-0.479440\pi\) | ||||
0.0645468 | + | 0.997915i | \(0.479440\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.5540 | 0.439983 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.1111 | 0.911565 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.4951 | 0.339968 | 0.169984 | − | 0.985447i | \(-0.445628\pi\) | ||||
0.169984 | + | 0.985447i | \(0.445628\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.86725 | 0.189860 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −28.8486 | −0.932543 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.42882 | 0.0784307 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.07181 | 0.131349 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.05120 | −0.130548 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.3664 | 0.623425 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36.6501 | −1.17859 | −0.589294 | − | 0.807919i | \(-0.700594\pi\) | ||||
−0.589294 | + | 0.807919i | \(0.700594\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.91120 | −0.254144 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.3202 | 1.45439 | 0.727197 | − | 0.686429i | \(-0.240823\pi\) | ||||
0.727197 | + | 0.686429i | \(0.240823\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.93701 | −0.0620977 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 39.9923 | 1.28078 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.1618 | 0.709018 | 0.354509 | − | 0.935053i | \(-0.384648\pi\) | ||||
0.354509 | + | 0.935053i | \(0.384648\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0038 | 0.639323 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.92162 | 0.220990 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.6385 | −1.35996 | −0.679978 | − | 0.733233i | \(-0.738011\pi\) | ||||
−0.679978 | + | 0.733233i | \(0.738011\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.62978 | −0.306830 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.46862 | 0.0467465 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −70.0401 | −2.22715 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.20296 | 0.101745 | 0.0508727 | − | 0.998705i | \(-0.483800\pi\) | ||||
0.0508727 | + | 0.998705i | \(0.483800\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.7728 | −0.437068 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 32.4997 | 1.03031 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.5267 | −0.428395 | −0.214198 | − | 0.976790i | \(-0.568714\pi\) | ||||
−0.214198 | + | 0.976790i | \(0.568714\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.3829 | 1.15110 |
(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 | 4864.2.a.bm.1.8 | 8 | ||
4.3 | odd | 2 | 4864.2.a.br.1.2 | 8 | |||
8.3 | odd | 2 | inner | 4864.2.a.bm.1.7 | 8 | ||
8.5 | even | 2 | 4864.2.a.br.1.1 | 8 | |||
16.3 | odd | 4 | 2432.2.c.i.1217.3 | ✓ | 16 | ||
16.5 | even | 4 | 2432.2.c.i.1217.4 | yes | 16 | ||
16.11 | odd | 4 | 2432.2.c.i.1217.14 | yes | 16 | ||
16.13 | even | 4 | 2432.2.c.i.1217.13 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.i.1217.3 | ✓ | 16 | 16.3 | odd | 4 | ||
2432.2.c.i.1217.4 | yes | 16 | 16.5 | even | 4 | ||
2432.2.c.i.1217.13 | yes | 16 | 16.13 | even | 4 | ||
2432.2.c.i.1217.14 | yes | 16 | 16.11 | odd | 4 | ||
4864.2.a.bm.1.7 | 8 | 8.3 | odd | 2 | inner | ||
4864.2.a.bm.1.8 | 8 | 1.1 | even | 1 | trivial | ||
4864.2.a.br.1.1 | 8 | 8.5 | even | 2 | |||
4864.2.a.br.1.2 | 8 | 4.3 | odd | 2 |