Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3648,2,Mod(1,3648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3648, 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("3648.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3648 = 2^{6} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3648.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: | \(29.1294266574\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1824) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3648.1 |
$q$-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 | ||||||||
\(5\) | 3.37228 | 1.50813 | 0.754065 | − | 0.656800i | \(-0.228090\pi\) | ||||
0.754065 | + | 0.656800i | \(0.228090\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.37228 | −1.27460 | −0.637301 | − | 0.770615i | \(-0.719949\pi\) | ||||
−0.637301 | + | 0.770615i | \(0.719949\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.627719 | −0.189264 | −0.0946322 | − | 0.995512i | \(-0.530167\pi\) | ||||
−0.0946322 | + | 0.995512i | \(0.530167\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.37228 | 0.870719 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.37228 | −1.30297 | −0.651485 | − | 0.758662i | \(-0.725854\pi\) | ||||
−0.651485 | + | 0.758662i | \(0.725854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.37228 | −0.735892 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.74456 | −0.989310 | −0.494655 | − | 0.869090i | \(-0.664706\pi\) | ||||
−0.494655 | + | 0.869090i | \(0.664706\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.37228 | 1.27446 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.74456 | 1.62382 | 0.811912 | − | 0.583779i | \(-0.198427\pi\) | ||||
0.811912 | + | 0.583779i | \(0.198427\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.627719 | −0.109272 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11.3723 | −1.92227 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.74456 | 1.36567 | 0.682836 | − | 0.730572i | \(-0.260747\pi\) | ||||
0.682836 | + | 0.730572i | \(0.260747\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.37228 | 1.12426 | 0.562131 | − | 0.827048i | \(-0.309982\pi\) | ||||
0.562131 | + | 0.827048i | \(0.309982\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.37228 | 0.502710 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.11684 | 1.18396 | 0.591982 | − | 0.805951i | \(-0.298346\pi\) | ||||
0.591982 | + | 0.805951i | \(0.298346\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.37228 | 0.624612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.37228 | −0.752270 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0000 | 1.37361 | 0.686803 | − | 0.726844i | \(-0.259014\pi\) | ||||
0.686803 | + | 0.726844i | \(0.259014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.11684 | −0.285435 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.74456 | −0.357312 | −0.178656 | − | 0.983912i | \(-0.557175\pi\) | ||||
−0.178656 | + | 0.983912i | \(0.557175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.37228 | −1.20000 | −0.599999 | − | 0.800001i | \(-0.704832\pi\) | ||||
−0.599999 | + | 0.800001i | \(0.704832\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.37228 | −0.424868 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.4891 | 1.67312 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.74456 | −0.823979 | −0.411990 | − | 0.911188i | \(-0.635166\pi\) | ||||
−0.411990 | + | 0.911188i | \(0.635166\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.74456 | −0.571178 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.7446 | 1.74986 | 0.874929 | − | 0.484252i | \(-0.160908\pi\) | ||||
0.874929 | + | 0.484252i | \(0.160908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.62772 | 0.307551 | 0.153776 | − | 0.988106i | \(-0.450857\pi\) | ||||
0.153776 | + | 0.988106i | \(0.450857\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.37228 | 0.735808 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.11684 | 0.241237 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.00000 | 0.225018 | 0.112509 | − | 0.993651i | \(-0.464111\pi\) | ||||
0.112509 | + | 0.993651i | \(0.464111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −18.1168 | −1.96505 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.74456 | 0.937516 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.48913 | −0.793846 | −0.396923 | − | 0.917852i | \(-0.629922\pi\) | ||||
−0.396923 | + | 0.917852i | \(0.629922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.4891 | −1.41404 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.37228 | −0.345989 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.25544 | 0.736678 | 0.368339 | − | 0.929692i | \(-0.379927\pi\) | ||||
0.368339 | + | 0.929692i | \(0.379927\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.627719 | −0.0630881 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.7446 | 1.46714 | 0.733569 | − | 0.679615i | \(-0.237853\pi\) | ||||
0.733569 | + | 0.679615i | \(0.237853\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0000 | 0.985329 | 0.492665 | − | 0.870219i | \(-0.336023\pi\) | ||||
0.492665 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.3723 | −1.10982 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.74456 | 0.265327 | 0.132663 | − | 0.991161i | \(-0.457647\pi\) | ||||
0.132663 | + | 0.991161i | \(0.457647\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.74456 | −0.646012 | −0.323006 | − | 0.946397i | \(-0.604693\pi\) | ||||
−0.323006 | + | 0.946397i | \(0.604693\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.74456 | −0.446331 | −0.223165 | − | 0.974781i | \(-0.571639\pi\) | ||||
−0.223165 | + | 0.974781i | \(0.571639\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.0000 | −1.49201 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.00000 | 0.369800 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.1168 | 1.66077 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6060 | −0.964179 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.74456 | 0.788471 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.62772 | 0.413916 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.2337 | 1.61798 | 0.808989 | − | 0.587824i | \(-0.200015\pi\) | ||||
0.808989 | + | 0.587824i | \(0.200015\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.37228 | 0.649093 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.11684 | 0.184950 | 0.0924748 | − | 0.995715i | \(-0.470522\pi\) | ||||
0.0924748 | + | 0.995715i | \(0.470522\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.37228 | 0.292414 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.37228 | 0.290240 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −21.3723 | −1.82596 | −0.912979 | − | 0.408007i | \(-0.866224\pi\) | ||||
−0.912979 | + | 0.408007i | \(0.866224\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.62772 | −0.731794 | −0.365897 | − | 0.930655i | \(-0.619238\pi\) | ||||
−0.365897 | + | 0.930655i | \(0.619238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.11684 | 0.683562 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.51087 | −0.209970 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 29.4891 | 2.44894 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.37228 | 0.360620 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.8614 | −1.05365 | −0.526824 | − | 0.849975i | \(-0.676617\pi\) | ||||
−0.526824 | + | 0.849975i | \(0.676617\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4891 | −0.934972 | −0.467486 | − | 0.884001i | \(-0.654840\pi\) | ||||
−0.467486 | + | 0.884001i | \(0.654840\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.37228 | −0.434323 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.2337 | 1.62521 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.0000 | 0.793052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.0000 | 1.26098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.11684 | −0.164796 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −25.4891 | −1.97241 | −0.986204 | − | 0.165535i | \(-0.947065\pi\) | ||||
−0.986204 | + | 0.165535i | \(0.947065\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.00000 | 0.456172 | 0.228086 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228086 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.4891 | −1.62443 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.74456 | −0.206294 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.74456 | 0.501319 | 0.250660 | − | 0.968075i | \(-0.419352\pi\) | ||||
0.250660 | + | 0.968075i | \(0.419352\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.37228 | −0.692819 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.4891 | 0.991740 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.37228 | 0.246606 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.37228 | −0.245297 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.6060 | −1.56335 | −0.781677 | − | 0.623684i | \(-0.785635\pi\) | ||||
−0.781677 | + | 0.623684i | \(0.785635\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.9783 | 1.79797 | 0.898987 | − | 0.437975i | \(-0.144304\pi\) | ||||
0.898987 | + | 0.437975i | \(0.144304\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.4891 | 0.965976 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.23369 | −0.586626 | −0.293313 | − | 0.956016i | \(-0.594758\pi\) | ||||
−0.293313 | + | 0.956016i | \(0.594758\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.3723 | −1.37326 | −0.686632 | − | 0.727005i | \(-0.740912\pi\) | ||||
−0.686632 | + | 0.727005i | \(0.740912\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.74456 | −0.475725 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −29.4891 | −2.06973 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.4891 | 2.05961 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.74456 | −0.329770 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.627719 | 0.0434202 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.2337 | −1.11757 | −0.558787 | − | 0.829311i | \(-0.688733\pi\) | ||||
−0.558787 | + | 0.829311i | \(0.688733\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.7446 | 1.01028 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 24.8614 | 1.69553 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.2337 | −1.37355 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.62772 | 0.177565 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.4891 | −1.44551 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.7446 | 1.38916 | 0.694579 | − | 0.719416i | \(-0.255591\pi\) | ||||
0.694579 | + | 0.719416i | \(0.255591\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.37228 | 0.424819 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.48913 | 0.0988367 | 0.0494184 | − | 0.998778i | \(-0.484263\pi\) | ||||
0.0494184 | + | 0.998778i | \(0.484263\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.62772 | −0.173645 | −0.0868223 | − | 0.996224i | \(-0.527671\pi\) | ||||
−0.0868223 | + | 0.996224i | \(0.527671\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.11684 | 0.139278 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.3723 | 0.876047 | 0.438024 | − | 0.898963i | \(-0.355679\pi\) | ||||
0.438024 | + | 0.898963i | \(0.355679\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.3723 | 1.78557 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.00000 | 0.129914 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.1168 | −1.30125 | −0.650625 | − | 0.759399i | \(-0.725493\pi\) | ||||
−0.650625 | + | 0.759399i | \(0.725493\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.2337 | −1.43220 | −0.716099 | − | 0.697999i | \(-0.754074\pi\) | ||||
−0.716099 | + | 0.697999i | \(0.754074\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.7446 | 0.941996 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00000 | −0.254514 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.8614 | −1.06428 | −0.532141 | − | 0.846656i | \(-0.678612\pi\) | ||||
−0.532141 | + | 0.846656i | \(0.678612\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.97825 | 0.187241 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −18.1168 | −1.13452 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.2554 | 0.951608 | 0.475804 | − | 0.879551i | \(-0.342157\pi\) | ||||
0.475804 | + | 0.879551i | \(0.342157\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.4891 | −0.838173 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.74456 | 0.541275 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.3723 | −0.824570 | −0.412285 | − | 0.911055i | \(-0.635269\pi\) | ||||
−0.412285 | + | 0.911055i | \(0.635269\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.7228 | 2.07158 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.48913 | −0.458327 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.9783 | −1.27907 | −0.639533 | − | 0.768763i | \(-0.720872\pi\) | ||||
−0.639533 | + | 0.768763i | \(0.720872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.4891 | −0.816399 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.00000 | −0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.1168 | −1.92971 | −0.964857 | − | 0.262775i | \(-0.915362\pi\) | ||||
−0.964857 | + | 0.262775i | \(0.915362\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.51087 | −0.507716 | −0.253858 | − | 0.967241i | \(-0.581700\pi\) | ||||
−0.253858 | + | 0.967241i | \(0.581700\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.86141 | 0.288981 | 0.144490 | − | 0.989506i | \(-0.453846\pi\) | ||||
0.144490 | + | 0.989506i | \(0.453846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.37228 | −0.199757 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −29.4891 | −1.74069 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.8614 | 0.697730 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.25544 | 0.425321 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.7446 | 1.67928 | 0.839638 | − | 0.543147i | \(-0.182767\pi\) | ||||
0.839638 | + | 0.543147i | \(0.182767\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.25544 | −0.538872 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.627719 | −0.0364239 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.9783 | −1.09754 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −24.8614 | −1.43299 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.7446 | 0.847053 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31.6060 | −1.80975 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.2337 | −1.15480 | −0.577399 | − | 0.816462i | \(-0.695932\pi\) | ||||
−0.577399 | + | 0.816462i | \(0.695932\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0000 | 0.568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.86141 | −0.162255 | −0.0811277 | − | 0.996704i | \(-0.525852\pi\) | ||||
−0.0811277 | + | 0.996704i | \(0.525852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.9783 | −1.18576 | −0.592880 | − | 0.805291i | \(-0.702009\pi\) | ||||
−0.592880 | + | 0.805291i | \(0.702009\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.3723 | −0.640755 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.510875 | 0.0286936 | 0.0143468 | − | 0.999897i | \(-0.495433\pi\) | ||||
0.0143468 | + | 0.999897i | \(0.495433\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.48913 | −0.307332 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.74456 | 0.153187 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.37228 | 0.298922 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.4891 | 1.41388 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.74456 | −0.372975 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.3723 | −1.50908 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 28.2337 | 1.55186 | 0.775932 | − | 0.630817i | \(-0.217280\pi\) | ||||
0.775932 | + | 0.630817i | \(0.217280\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.00000 | 0.219199 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −22.7446 | −1.24267 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2337 | 1.21115 | 0.605573 | − | 0.795790i | \(-0.292944\pi\) | ||||
0.605573 | + | 0.795790i | \(0.292944\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.74456 | −0.257689 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.76631 | −0.203957 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.86141 | 0.478471 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.0000 | −0.861411 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.88316 | −0.101093 | −0.0505466 | − | 0.998722i | \(-0.516096\pi\) | ||||
−0.0505466 | + | 0.998722i | \(0.516096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.37228 | 0.0734565 | 0.0367283 | − | 0.999325i | \(-0.488306\pi\) | ||||
0.0367283 | + | 0.999325i | \(0.488306\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.9783 | 1.11656 | 0.558280 | − | 0.829653i | \(-0.311462\pi\) | ||||
0.558280 | + | 0.829653i | \(0.311462\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 49.7228 | 2.63901 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.1168 | 0.958845 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.3505 | 0.862948 | 0.431474 | − | 0.902125i | \(-0.357994\pi\) | ||||
0.431474 | + | 0.902125i | \(0.357994\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.6060 | −0.556669 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.86141 | 0.463827 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.4674 | 1.69478 | 0.847392 | − | 0.530968i | \(-0.178172\pi\) | ||||
0.847392 | + | 0.530968i | \(0.178172\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.74456 | 0.455224 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −33.7228 | −1.75080 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.48913 | −0.491328 | −0.245664 | − | 0.969355i | \(-0.579006\pi\) | ||||
−0.245664 | + | 0.969355i | \(0.579006\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.62772 | 0.238974 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.9783 | 1.80147 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.7446 | 1.57924 | 0.789621 | − | 0.613595i | \(-0.210277\pi\) | ||||
0.789621 | + | 0.613595i | \(0.210277\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.2337 | 0.934140 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.2554 | −0.881712 | −0.440856 | − | 0.897578i | \(-0.645325\pi\) | ||||
−0.440856 | + | 0.897578i | \(0.645325\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.13859 | 0.363816 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.37228 | 0.374754 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.8832 | 0.703904 | 0.351952 | − | 0.936018i | \(-0.385518\pi\) | ||||
0.351952 | + | 0.936018i | \(0.385518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.4891 | 1.28904 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.11684 | 0.106781 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.74456 | 0.339356 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 36.3505 | 1.82438 | 0.912190 | − | 0.409766i | \(-0.134390\pi\) | ||||
0.912190 | + | 0.409766i | \(0.134390\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.37228 | 0.168825 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.48913 | −0.174239 | −0.0871193 | − | 0.996198i | \(-0.527766\pi\) | ||||
−0.0871193 | + | 0.996198i | \(0.527766\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.0000 | 1.19553 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.37228 | 0.167570 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.51087 | −0.124459 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.9783 | 1.63067 | 0.815335 | − | 0.578990i | \(-0.196553\pi\) | ||||
0.815335 | + | 0.578990i | \(0.196553\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −21.3723 | −1.05422 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.25544 | 0.455430 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.62772 | −0.422501 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.7446 | 0.913554 | 0.456777 | − | 0.889581i | \(-0.349004\pi\) | ||||
0.456777 | + | 0.889581i | \(0.349004\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.11684 | 0.394654 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.2337 | −1.66058 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.6060 | 1.52952 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.51087 | −0.121226 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.00000 | −0.192673 | −0.0963366 | − | 0.995349i | \(-0.530713\pi\) | ||||
−0.0963366 | + | 0.995349i | \(0.530713\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.76631 | 0.0848835 | 0.0424418 | − | 0.999099i | \(-0.486486\pi\) | ||||
0.0424418 | + | 0.999099i | \(0.486486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 29.4891 | 1.41390 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.74456 | 0.226963 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.23369 | −0.297518 | −0.148759 | − | 0.988874i | \(-0.547528\pi\) | ||||
−0.148759 | + | 0.988874i | \(0.547528\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.37228 | 0.208204 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.1168 | 1.43089 | 0.715447 | − | 0.698667i | \(-0.246223\pi\) | ||||
0.715447 | + | 0.698667i | \(0.246223\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.2554 | −1.19722 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.8614 | −0.608324 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.25544 | 0.342405 | 0.171203 | − | 0.985236i | \(-0.445235\pi\) | ||||
0.171203 | + | 0.985236i | \(0.445235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.48913 | −0.258473 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.4891 | −0.539806 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −45.4891 | −2.13256 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.1168 | −1.50236 | −0.751181 | − | 0.660096i | \(-0.770516\pi\) | ||||
−0.751181 | + | 0.660096i | \(0.770516\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.37228 | −0.250757 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.8832 | −0.832902 | −0.416451 | − | 0.909158i | \(-0.636726\pi\) | ||||
−0.416451 | + | 0.909158i | \(0.636726\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.6277 | −0.958651 | −0.479326 | − | 0.877637i | \(-0.659119\pi\) | ||||
−0.479326 | + | 0.877637i | \(0.659119\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.2337 | 0.938315 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.3723 | −0.896442 | −0.448221 | − | 0.893923i | \(-0.647942\pi\) | ||||
−0.448221 | + | 0.893923i | \(0.647942\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.7446 | 1.05025 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.00000 | −0.0921551 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.62772 | −0.212783 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.37228 | −0.292380 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.0000 | 0.457869 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.76631 | −0.0807049 | −0.0403524 | − | 0.999186i | \(-0.512848\pi\) | ||||
−0.0403524 | + | 0.999186i | \(0.512848\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | 0.729537 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.0000 | 0.728025 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 24.4674 | 1.11101 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.4674 | −1.38061 | −0.690304 | − | 0.723519i | \(-0.742523\pi\) | ||||
−0.690304 | + | 0.723519i | \(0.742523\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.0000 | 0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.48913 | −0.247721 | −0.123860 | − | 0.992300i | \(-0.539527\pi\) | ||||
−0.123860 | + | 0.992300i | \(0.539527\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −46.9783 | −2.11579 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.11684 | −0.0951451 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −49.7228 | −2.23037 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.6060 | 0.519555 | 0.259777 | − | 0.965669i | \(-0.416351\pi\) | ||||
0.259777 | + | 0.965669i | \(0.416351\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.4891 | −1.13877 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 31.7228 | 1.41445 | 0.707225 | − | 0.706988i | \(-0.249947\pi\) | ||||
0.707225 | + | 0.706988i | \(0.249947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 49.7228 | 2.21264 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.00000 | 0.133235 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.74456 | −0.387596 | −0.193798 | − | 0.981041i | \(-0.562081\pi\) | ||||
−0.193798 | + | 0.981041i | \(0.562081\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.86141 | −0.392006 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33.7228 | 1.48600 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.09509 | −0.224082 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.7228 | 0.774965 | 0.387482 | − | 0.921877i | \(-0.373345\pi\) | ||||
0.387482 | + | 0.921877i | \(0.373345\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.4891 | −0.937862 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.2337 | −1.40412 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.489125 | −0.0212663 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.74456 | −0.119104 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.9783 | 1.51508 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.25544 | 0.400147 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.00000 | 0.172613 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.74456 | −0.118217 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.3505 | −1.39086 | −0.695429 | − | 0.718595i | \(-0.744786\pi\) | ||||
−0.695429 | + | 0.718595i | \(0.744786\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.74456 | 0.289437 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22.7446 | −0.974270 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.51087 | −0.107357 | −0.0536786 | − | 0.998558i | \(-0.517095\pi\) | ||||
−0.0536786 | + | 0.998558i | \(0.517095\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.37228 | −0.399999 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.74456 | −0.372531 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.74456 | −0.286808 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.4891 | 0.572581 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −44.8614 | −1.90084 | −0.950419 | − | 0.310971i | \(-0.899346\pi\) | ||||
−0.950419 | + | 0.310971i | \(0.899346\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.4891 | 1.24726 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.37228 | 0.142378 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −33.4891 | −1.41140 | −0.705699 | − | 0.708512i | \(-0.749367\pi\) | ||||
−0.705699 | + | 0.708512i | \(0.749367\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.0000 | −0.673125 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.37228 | −0.141623 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.2554 | −0.807230 | −0.403615 | − | 0.914929i | \(-0.632246\pi\) | ||||
−0.403615 | + | 0.914929i | \(0.632246\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.4891 | −0.731897 | −0.365949 | − | 0.930635i | \(-0.619255\pi\) | ||||
−0.365949 | + | 0.930635i | \(0.619255\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.6060 | −0.902602 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −30.2337 | −1.26083 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.13859 | −0.213922 | −0.106961 | − | 0.994263i | \(-0.534112\pi\) | ||||
−0.106961 | + | 0.994263i | \(0.534112\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.9783 | 1.03806 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.27719 | −0.259975 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.4891 | 0.557707 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −42.3505 | −1.74799 | −0.873997 | − | 0.485932i | \(-0.838480\pi\) | ||||
−0.873997 | + | 0.485932i | \(0.838480\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.23369 | −0.338689 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.4891 | −0.471802 | −0.235901 | − | 0.971777i | \(-0.575804\pi\) | ||||
−0.235901 | + | 0.971777i | \(0.575804\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 61.0951 | 2.50465 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.3723 | −0.792855 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.23369 | −0.336419 | −0.168210 | − | 0.985751i | \(-0.553799\pi\) | ||||
−0.168210 | + | 0.985751i | \(0.553799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.9783 | −1.67154 | −0.835769 | − | 0.549081i | \(-0.814978\pi\) | ||||
−0.835769 | + | 0.549081i | \(0.814978\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.74456 | −0.274660 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35.7663 | −1.45411 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.2119 | 1.67274 | 0.836370 | − | 0.548165i | \(-0.184673\pi\) | ||||
0.836370 | + | 0.548165i | \(0.184673\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −29.4891 | −1.19496 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.4674 | 1.31349 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.6277 | −0.913925 | −0.456962 | − | 0.889486i | \(-0.651063\pi\) | ||||
−0.456962 | + | 0.889486i | \(0.651063\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 29.4891 | 1.18912 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.1168 | 0.487806 | 0.243903 | − | 0.969800i | \(-0.421572\pi\) | ||||
0.243903 | + | 0.969800i | \(0.421572\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.9783 | −0.602027 | −0.301013 | − | 0.953620i | \(-0.597325\pi\) | ||||
−0.301013 | + | 0.953620i | \(0.597325\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.74456 | −0.190393 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25.2554 | 1.01184 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.2554 | −0.650217 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.627719 | 0.0250687 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.4891 | −0.856828 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.1168 | 0.561983 | 0.280991 | − | 0.959710i | \(-0.409337\pi\) | ||||
0.280991 | + | 0.959710i | \(0.409337\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.2337 | −0.645231 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 61.4891 | 2.44012 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.4891 | 0.692944 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.7446 | 0.583286 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.23369 | 0.0882254 | 0.0441127 | − | 0.999027i | \(-0.485954\pi\) | ||||
0.0441127 | + | 0.999027i | \(0.485954\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.39403 | 0.173284 | 0.0866418 | − | 0.996240i | \(-0.472386\pi\) | ||||
0.0866418 | + | 0.996240i | \(0.472386\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.8614 | 0.978917 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 40.3505 | 1.58634 | 0.793172 | − | 0.608998i | \(-0.208428\pi\) | ||||
0.793172 | + | 0.608998i | \(0.208428\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.72281 | 0.0676263 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.2337 | −0.793021 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.1386 | 0.435887 | 0.217943 | − | 0.975961i | \(-0.430065\pi\) | ||||
0.217943 | + | 0.975961i | \(0.430065\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.13859 | 0.278928 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.62772 | 0.102517 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.23369 | 0.320739 | 0.160369 | − | 0.987057i | \(-0.448731\pi\) | ||||
0.160369 | + | 0.987057i | \(0.448731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.51087 | 0.253244 | 0.126622 | − | 0.991951i | \(-0.459587\pi\) | ||||
0.126622 | + | 0.991951i | \(0.459587\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.4891 | −0.834568 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11.3723 | 0.440998 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −41.4891 | −1.60647 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.7446 | 0.802031 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.88316 | 0.227117 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.00000 | 0.231283 | 0.115642 | − | 0.993291i | \(-0.463108\pi\) | ||||
0.115642 | + | 0.993291i | \(0.463108\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.37228 | 0.245269 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.7228 | −1.52667 | −0.763336 | − | 0.646002i | \(-0.776440\pi\) | ||||
−0.763336 | + | 0.646002i | \(0.776440\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.4674 | −0.938972 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.48913 | 0.0570634 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.4891 | 0.669203 | 0.334601 | − | 0.942360i | \(-0.391398\pi\) | ||||
0.334601 | + | 0.942360i | \(0.391398\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −72.0733 | −2.75378 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.62772 | −0.100254 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.0000 | 1.52388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.62772 | 0.328214 | 0.164107 | − | 0.986443i | \(-0.447526\pi\) | ||||
0.164107 | + | 0.986443i | \(0.447526\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.11684 | 0.0804123 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.0951 | −1.10364 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −46.9783 | −1.77943 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13.3723 | 0.505786 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.25544 | −0.0474172 | −0.0237086 | − | 0.999719i | \(-0.507547\pi\) | ||||
−0.0237086 | + | 0.999719i | \(0.507547\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.00000 | −0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 27.3723 | 1.03090 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −49.7228 | −1.87002 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.0000 | 1.57734 | 0.788672 | − | 0.614815i | \(-0.210769\pi\) | ||||
0.788672 | + | 0.614815i | \(0.210769\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.00000 | 0.0750059 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.4674 | −1.06611 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.46738 | −0.316662 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.1168 | −0.751277 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.6277 | −0.843872 | −0.421936 | − | 0.906626i | \(-0.638649\pi\) | ||||
−0.421936 | + | 0.906626i | \(0.638649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.7228 | −1.25590 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22.2337 | −0.826880 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 55.7228 | 2.06949 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.8397 | 1.47757 | 0.738786 | − | 0.673941i | \(-0.235400\pi\) | ||||
0.738786 | + | 0.673941i | \(0.235400\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −39.6060 | −1.46488 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.0000 | −1.25582 | −0.627909 | − | 0.778287i | \(-0.716089\pi\) | ||||
−0.627909 | + | 0.778287i | \(0.716089\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14.7446 | 0.543861 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.23369 | 0.155950 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.1168 | −1.10787 | −0.553933 | − | 0.832561i | \(-0.686874\pi\) | ||||
−0.553933 | + | 0.832561i | \(0.686874\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.00000 | −0.146944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.7228 | −0.503441 | −0.251721 | − | 0.967800i | \(-0.580996\pi\) | ||||
−0.251721 | + | 0.967800i | \(0.580996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.3723 | −1.58904 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.25544 | −0.338186 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.74456 | 0.319094 | 0.159547 | − | 0.987190i | \(-0.448997\pi\) | ||||
0.159547 | + | 0.987190i | \(0.448997\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.8614 | −0.614464 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.7446 | −1.41006 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.0951 | 1.27555 | 0.637776 | − | 0.770222i | \(-0.279854\pi\) | ||||
0.637776 | + | 0.770222i | \(0.279854\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.97825 | 0.108104 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.3723 | −0.484745 | −0.242372 | − | 0.970183i | \(-0.577926\pi\) | ||||
−0.242372 | + | 0.970183i | \(0.577926\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.7446 | 0.823408 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.1168 | −0.655016 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.9783 | −0.396402 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.0951 | −1.12132 | −0.560659 | − | 0.828047i | \(-0.689452\pi\) | ||||
−0.560659 | + | 0.828047i | \(0.689452\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.2554 | 0.549411 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.00000 | −0.0719350 | −0.0359675 | − | 0.999353i | \(-0.511451\pi\) | ||||
−0.0359675 | + | 0.999353i | \(0.511451\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.2337 | 1.37339 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.4891 | −0.483920 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.74456 | −0.313306 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.25544 | −0.331186 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.74456 | 0.312505 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.74456 | −0.240724 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.9565 | −1.49559 | −0.747794 | − | 0.663931i | \(-0.768887\pi\) | ||||
−0.747794 | + | 0.663931i | \(0.768887\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.3723 | −0.476066 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.0000 | 0.568895 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.4891 | −1.33128 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.7228 | 1.19602 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.4891 | 0.406966 | 0.203483 | − | 0.979079i | \(-0.434774\pi\) | ||||
0.203483 | + | 0.979079i | \(0.434774\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −43.6060 | −1.54267 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.48913 | −0.264615 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.64947 | −0.0582085 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 53.9565 | 1.90172 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.9783 | −0.738469 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.8832 | 0.980320 | 0.490160 | − | 0.871633i | \(-0.336938\pi\) | ||||
0.490160 | + | 0.871633i | \(0.336938\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.0000 | −1.12367 | −0.561836 | − | 0.827249i | \(-0.689905\pi\) | ||||
−0.561836 | + | 0.827249i | \(0.689905\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.00000 | 0.280572 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 40.4674 | 1.41751 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.37228 | −0.257923 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.4891 | −0.471348 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.3505 | −1.33844 | −0.669221 | − | 0.743063i | \(-0.733372\pi\) | ||||
−0.669221 | + | 0.743063i | \(0.733372\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.1168 | 1.04981 | 0.524904 | − | 0.851162i | \(-0.324101\pi\) | ||||
0.524904 | + | 0.851162i | \(0.324101\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.00000 | −0.139262 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.7446 | −0.930000 | −0.465000 | − | 0.885311i | \(-0.653946\pi\) | ||||
−0.465000 | + | 0.885311i | \(0.653946\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.5109 | −0.642909 | −0.321455 | − | 0.946925i | \(-0.604172\pi\) | ||||
−0.321455 | + | 0.946925i | \(0.604172\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32.1168 | −1.11412 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.4891 | −0.813850 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −85.9565 | −2.97465 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.00000 | 0.207390 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.74456 | 0.0947528 | 0.0473764 | − | 0.998877i | \(-0.484914\pi\) | ||||
0.0473764 | + | 0.998877i | \(0.484914\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.4674 | 1.63681 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.51087 | −0.293130 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.1168 | 0.348030 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35.7663 | 1.22895 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.86141 | 0.166843 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.9783 | −0.650566 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.4891 | 0.530338 | 0.265169 | − | 0.964202i | \(-0.414572\pi\) | ||||
0.265169 | + | 0.964202i | \(0.414572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.37228 | −0.115330 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.978251 | 0.0334164 | 0.0167082 | − | 0.999860i | \(-0.494681\pi\) | ||||
0.0167082 | + | 0.999860i | \(0.494681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.3505 | 1.17203 | 0.586013 | − | 0.810302i | \(-0.300697\pi\) | ||||
0.586013 | + | 0.810302i | \(0.300697\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.4891 | −1.00499 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.4674 | 1.78601 | 0.893005 | − | 0.450046i | \(-0.148593\pi\) | ||||
0.893005 | + | 0.450046i | \(0.148593\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.2337 | 0.687966 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.8614 | 0.402834 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.25544 | −0.0425878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.9783 | −0.914123 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.25544 | 0.245559 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.6060 | −0.527578 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.7663 | 0.532391 | 0.266195 | − | 0.963919i | \(-0.414233\pi\) | ||||
0.266195 | + | 0.963919i | \(0.414233\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 28.7446 | 0.969530 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.3723 | −0.854814 | −0.427407 | − | 0.904059i | \(-0.640573\pi\) | ||||
−0.427407 | + | 0.904059i | \(0.640573\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.8614 | 1.77893 | 0.889464 | − | 0.457005i | \(-0.151078\pi\) | ||||
0.889464 | + | 0.457005i | \(0.151078\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.25544 | −0.311118 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37.7228 | −1.26661 | −0.633304 | − | 0.773903i | \(-0.718302\pi\) | ||||
−0.633304 | + | 0.773903i | \(0.718302\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −61.4891 | −2.06228 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.627719 | −0.0210294 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.11684 | −0.271620 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.4891 | 0.450892 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.9783 | −0.633665 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 52.4674 | 1.74988 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.7228 | −1.78977 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −24.8614 | −0.827336 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22.7446 | 0.756055 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.2554 | −0.838593 | −0.419297 | − | 0.907849i | \(-0.637723\pi\) | ||||
−0.419297 | + | 0.907849i | \(0.637723\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.7446 | 0.489046 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.25544 | 0.174120 | 0.0870602 | − | 0.996203i | \(-0.472253\pi\) | ||||
0.0870602 | + | 0.996203i | \(0.472253\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −31.6060 | −1.04486 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.13859 | −0.235737 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.4891 | 0.840809 | 0.420404 | − | 0.907337i | \(-0.361888\pi\) | ||||
0.420404 | + | 0.907337i | \(0.361888\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.2337 | −0.666723 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 58.9783 | 1.94129 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.4891 | 0.838077 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.0000 | 0.328443 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.9783 | 0.557038 | 0.278519 | − | 0.960431i | \(-0.410156\pi\) | ||||
0.278519 | + | 0.960431i | \(0.410156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.37228 | −0.143296 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.86141 | −0.0936782 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.3723 | 0.371913 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.5842 | 1.58718 | 0.793589 | − | 0.608455i | \(-0.208210\pi\) | ||||
0.793589 | + | 0.608455i | \(0.208210\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.9783 | −0.684599 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.9783 | −0.944664 | −0.472332 | − | 0.881421i | \(-0.656588\pi\) | ||||
−0.472332 | + | 0.881421i | \(0.656588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.4891 | −1.35107 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.3723 | −0.369940 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.4891 | −1.21823 | −0.609116 | − | 0.793081i | \(-0.708476\pi\) | ||||
−0.609116 | + | 0.793081i | \(0.708476\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.5109 | 0.341197 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.510875 | 0.0165662 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23.4891 | 0.760887 | 0.380444 | − | 0.924804i | \(-0.375771\pi\) | ||||
0.380444 | + | 0.924804i | \(0.375771\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −72.8614 | −2.35774 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.48913 | −0.177438 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 72.0733 | 2.32737 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.74456 | 0.0884423 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 84.2337 | 2.71158 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.9783 | 1.63935 | 0.819675 | − | 0.572829i | \(-0.194154\pi\) | ||||
0.819675 | + | 0.572829i | \(0.194154\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.37228 | 0.172583 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.9783 | 0.737407 | 0.368704 | − | 0.929547i | \(-0.379802\pi\) | ||||
0.368704 | + | 0.929547i | \(0.379802\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.0951 | 0.932746 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25.4891 | 0.816305 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.9783 | 0.671154 | 0.335577 | − | 0.942013i | \(-0.391069\pi\) | ||||
0.335577 | + | 0.942013i | \(0.391069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.70106 | 0.150247 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.74456 | −0.215337 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.51087 | −0.0800845 | −0.0400422 | − | 0.999198i | \(-0.512749\pi\) | ||||
−0.0400422 | + | 0.999198i | \(0.512749\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.7663 | −0.884708 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.3723 | −0.871269 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −34.9783 | −1.11224 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.2337 | 0.579212 | 0.289606 | − | 0.957146i | \(-0.406476\pi\) | ||||
0.289606 | + | 0.957146i | \(0.406476\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.2337 | 0.895969 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −65.3288 | −2.07106 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.1168 | −0.383744 | −0.191872 | − | 0.981420i | \(-0.561456\pi\) | ||||
−0.191872 | + | 0.981420i | \(0.561456\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.00000 | 0.126554 |
(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 | 3648.2.a.bt.1.2 | 2 | ||
4.3 | odd | 2 | 3648.2.a.bm.1.2 | 2 | |||
8.3 | odd | 2 | 1824.2.a.r.1.1 | yes | 2 | ||
8.5 | even | 2 | 1824.2.a.o.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 5472.2.a.bd.1.2 | 2 | |||
24.11 | even | 2 | 5472.2.a.be.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1824.2.a.o.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
1824.2.a.r.1.1 | yes | 2 | 8.3 | odd | 2 | ||
3648.2.a.bm.1.2 | 2 | 4.3 | odd | 2 | |||
3648.2.a.bt.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5472.2.a.bd.1.2 | 2 | 24.5 | odd | 2 | |||
5472.2.a.be.1.2 | 2 | 24.11 | even | 2 |