Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2790,2,Mod(1,2790)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2790, 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("2790.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2790.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: | \(22.2782621639\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 310) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2790.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410 | 1.30931 | 0.654654 | − | 0.755929i | \(-0.272814\pi\) | ||||
0.654654 | + | 0.755929i | \(0.272814\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.732051 | −0.220722 | −0.110361 | − | 0.993892i | \(-0.535201\pi\) | ||||
−0.110361 | + | 0.993892i | \(0.535201\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.73205 | −1.31243 | −0.656217 | − | 0.754572i | \(-0.727845\pi\) | ||||
−0.656217 | + | 0.754572i | \(0.727845\pi\) | |||||||
\(14\) | 3.46410 | 0.925820 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.46410 | −0.335888 | −0.167944 | − | 0.985797i | \(-0.553713\pi\) | ||||
−0.167944 | + | 0.985797i | \(0.553713\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.732051 | −0.156074 | ||||||||
\(23\) | 7.46410 | 1.55637 | 0.778186 | − | 0.628033i | \(-0.216140\pi\) | ||||
0.778186 | + | 0.628033i | \(0.216140\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.73205 | −0.928032 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.46410 | 0.654654 | ||||||||
\(29\) | 2.73205 | 0.507329 | 0.253665 | − | 0.967292i | \(-0.418364\pi\) | ||||
0.253665 | + | 0.967292i | \(0.418364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 3.46410 | 0.585540 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.26795 | −0.537248 | −0.268624 | − | 0.963245i | \(-0.586569\pi\) | ||||
−0.268624 | + | 0.963245i | \(0.586569\pi\) | |||||||
\(38\) | −1.46410 | −0.237509 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 9.46410 | 1.47804 | 0.739022 | − | 0.673681i | \(-0.235288\pi\) | ||||
0.739022 | + | 0.673681i | \(0.235288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.73205 | 1.02663 | 0.513314 | − | 0.858201i | \(-0.328418\pi\) | ||||
0.513314 | + | 0.858201i | \(0.328418\pi\) | |||||||
\(44\) | −0.732051 | −0.110361 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.46410 | 1.10052 | ||||||||
\(47\) | −3.46410 | −0.505291 | −0.252646 | − | 0.967559i | \(-0.581301\pi\) | ||||
−0.252646 | + | 0.967559i | \(0.581301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.73205 | −0.656217 | ||||||||
\(53\) | 8.73205 | 1.19944 | 0.599720 | − | 0.800210i | \(-0.295279\pi\) | ||||
0.599720 | + | 0.800210i | \(0.295279\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.732051 | −0.0987097 | ||||||||
\(56\) | 3.46410 | 0.462910 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.73205 | 0.358736 | ||||||||
\(59\) | 1.46410 | 0.190610 | 0.0953049 | − | 0.995448i | \(-0.469617\pi\) | ||||
0.0953049 | + | 0.995448i | \(0.469617\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.1244 | −1.93648 | −0.968238 | − | 0.250032i | \(-0.919559\pi\) | ||||
−0.968238 | + | 0.250032i | \(0.919559\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.73205 | −0.586939 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.3923 | −1.51396 | −0.756980 | − | 0.653437i | \(-0.773326\pi\) | ||||
−0.756980 | + | 0.653437i | \(0.773326\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.46410 | 0.414039 | ||||||||
\(71\) | −13.8564 | −1.64445 | −0.822226 | − | 0.569160i | \(-0.807268\pi\) | ||||
−0.822226 | + | 0.569160i | \(0.807268\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.3923 | 1.91857 | 0.959287 | − | 0.282433i | \(-0.0911414\pi\) | ||||
0.959287 | + | 0.282433i | \(0.0911414\pi\) | |||||||
\(74\) | −3.26795 | −0.379891 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.46410 | −0.167944 | ||||||||
\(77\) | −2.53590 | −0.288992 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.5359 | 1.18538 | 0.592691 | − | 0.805430i | \(-0.298066\pi\) | ||||
0.592691 | + | 0.805430i | \(0.298066\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.46410 | 1.04514 | ||||||||
\(83\) | 1.26795 | 0.139176 | 0.0695878 | − | 0.997576i | \(-0.477832\pi\) | ||||
0.0695878 | + | 0.997576i | \(0.477832\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 6.73205 | 0.725936 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.732051 | −0.0780369 | ||||||||
\(89\) | 12.9282 | 1.37039 | 0.685193 | − | 0.728361i | \(-0.259718\pi\) | ||||
0.685193 | + | 0.728361i | \(0.259718\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.3923 | −1.71838 | ||||||||
\(92\) | 7.46410 | 0.778186 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.46410 | −0.357295 | ||||||||
\(95\) | −1.46410 | −0.150214 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.00000 | 0.406138 | 0.203069 | − | 0.979164i | \(-0.434908\pi\) | ||||
0.203069 | + | 0.979164i | \(0.434908\pi\) | |||||||
\(98\) | 5.00000 | 0.505076 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 3.07180 | 0.305655 | 0.152828 | − | 0.988253i | \(-0.451162\pi\) | ||||
0.152828 | + | 0.988253i | \(0.451162\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9282 | −1.07679 | −0.538394 | − | 0.842693i | \(-0.680969\pi\) | ||||
−0.538394 | + | 0.842693i | \(0.680969\pi\) | |||||||
\(104\) | −4.73205 | −0.464016 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.73205 | 0.848132 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.53590 | −0.817591 | −0.408795 | − | 0.912626i | \(-0.634051\pi\) | ||||
−0.408795 | + | 0.912626i | \(0.634051\pi\) | |||||||
\(110\) | −0.732051 | −0.0697983 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.46410 | 0.327327 | ||||||||
\(113\) | −8.00000 | −0.752577 | −0.376288 | − | 0.926503i | \(-0.622800\pi\) | ||||
−0.376288 | + | 0.926503i | \(0.622800\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.46410 | 0.696031 | ||||||||
\(116\) | 2.73205 | 0.253665 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.46410 | 0.134781 | ||||||||
\(119\) | 13.8564 | 1.27021 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4641 | −0.951282 | ||||||||
\(122\) | −15.1244 | −1.36929 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8564 | 1.05209 | 0.526043 | − | 0.850458i | \(-0.323675\pi\) | ||||
0.526043 | + | 0.850458i | \(0.323675\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.73205 | −0.415028 | ||||||||
\(131\) | 8.39230 | 0.733239 | 0.366620 | − | 0.930371i | \(-0.380515\pi\) | ||||
0.366620 | + | 0.930371i | \(0.380515\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.07180 | −0.439781 | ||||||||
\(134\) | −12.3923 | −1.07053 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | −20.7846 | −1.77575 | −0.887875 | − | 0.460086i | \(-0.847819\pi\) | ||||
−0.887875 | + | 0.460086i | \(0.847819\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.66025 | −0.310459 | −0.155229 | − | 0.987878i | \(-0.549612\pi\) | ||||
−0.155229 | + | 0.987878i | \(0.549612\pi\) | |||||||
\(140\) | 3.46410 | 0.292770 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −13.8564 | −1.16280 | ||||||||
\(143\) | 3.46410 | 0.289683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.73205 | 0.226884 | ||||||||
\(146\) | 16.3923 | 1.35664 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.26795 | −0.268624 | ||||||||
\(149\) | −21.3205 | −1.74664 | −0.873322 | − | 0.487143i | \(-0.838039\pi\) | ||||
−0.873322 | + | 0.487143i | \(0.838039\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.46410 | −0.444662 | −0.222331 | − | 0.974971i | \(-0.571367\pi\) | ||||
−0.222331 | + | 0.974971i | \(0.571367\pi\) | |||||||
\(152\) | −1.46410 | −0.118754 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.53590 | −0.204349 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.85641 | 0.627009 | 0.313505 | − | 0.949587i | \(-0.398497\pi\) | ||||
0.313505 | + | 0.949587i | \(0.398497\pi\) | |||||||
\(158\) | 10.5359 | 0.838191 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 25.8564 | 2.03777 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.53590 | −0.198627 | −0.0993134 | − | 0.995056i | \(-0.531665\pi\) | ||||
−0.0993134 | + | 0.995056i | \(0.531665\pi\) | |||||||
\(164\) | 9.46410 | 0.739022 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.26795 | 0.0984119 | ||||||||
\(167\) | 17.3205 | 1.34030 | 0.670151 | − | 0.742225i | \(-0.266230\pi\) | ||||
0.670151 | + | 0.742225i | \(0.266230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.39230 | 0.722485 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.73205 | 0.513314 | ||||||||
\(173\) | 2.00000 | 0.152057 | 0.0760286 | − | 0.997106i | \(-0.475776\pi\) | ||||
0.0760286 | + | 0.997106i | \(0.475776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.46410 | 0.261861 | ||||||||
\(176\) | −0.732051 | −0.0551804 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.9282 | 0.969010 | ||||||||
\(179\) | 11.2679 | 0.842206 | 0.421103 | − | 0.907013i | \(-0.361643\pi\) | ||||
0.421103 | + | 0.907013i | \(0.361643\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.1244 | 1.12418 | 0.562092 | − | 0.827075i | \(-0.309997\pi\) | ||||
0.562092 | + | 0.827075i | \(0.309997\pi\) | |||||||
\(182\) | −16.3923 | −1.21508 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.46410 | 0.550261 | ||||||||
\(185\) | −3.26795 | −0.240264 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.92820 | −0.214131 | ||||||||
\(188\) | −3.46410 | −0.252646 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.46410 | −0.106217 | ||||||||
\(191\) | 2.00000 | 0.144715 | 0.0723575 | − | 0.997379i | \(-0.476948\pi\) | ||||
0.0723575 | + | 0.997379i | \(0.476948\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.8564 | −0.853443 | −0.426721 | − | 0.904383i | \(-0.640332\pi\) | ||||
−0.426721 | + | 0.904383i | \(0.640332\pi\) | |||||||
\(194\) | 4.00000 | 0.287183 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.00000 | 0.357143 | ||||||||
\(197\) | −24.7321 | −1.76209 | −0.881043 | − | 0.473037i | \(-0.843158\pi\) | ||||
−0.881043 | + | 0.473037i | \(0.843158\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.07180 | 0.216131 | ||||||||
\(203\) | 9.46410 | 0.664250 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.46410 | 0.661002 | ||||||||
\(206\) | −10.9282 | −0.761404 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.73205 | −0.328109 | ||||||||
\(209\) | 1.07180 | 0.0741377 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.0718 | 0.899900 | 0.449950 | − | 0.893054i | \(-0.351442\pi\) | ||||
0.449950 | + | 0.893054i | \(0.351442\pi\) | |||||||
\(212\) | 8.73205 | 0.599720 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.00000 | −0.273434 | ||||||||
\(215\) | 6.73205 | 0.459122 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.46410 | −0.235159 | ||||||||
\(218\) | −8.53590 | −0.578124 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.732051 | −0.0493549 | ||||||||
\(221\) | −18.9282 | −1.27325 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.0000 | 0.669650 | 0.334825 | − | 0.942280i | \(-0.391323\pi\) | ||||
0.334825 | + | 0.942280i | \(0.391323\pi\) | |||||||
\(224\) | 3.46410 | 0.231455 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.00000 | −0.532152 | ||||||||
\(227\) | 6.53590 | 0.433803 | 0.216901 | − | 0.976194i | \(-0.430405\pi\) | ||||
0.216901 | + | 0.976194i | \(0.430405\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0526 | 0.928619 | 0.464310 | − | 0.885673i | \(-0.346302\pi\) | ||||
0.464310 | + | 0.885673i | \(0.346302\pi\) | |||||||
\(230\) | 7.46410 | 0.492168 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.73205 | 0.179368 | ||||||||
\(233\) | 16.7846 | 1.09960 | 0.549798 | − | 0.835298i | \(-0.314705\pi\) | ||||
0.549798 | + | 0.835298i | \(0.314705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.46410 | −0.225973 | ||||||||
\(236\) | 1.46410 | 0.0953049 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.8564 | 0.898177 | ||||||||
\(239\) | 2.53590 | 0.164034 | 0.0820168 | − | 0.996631i | \(-0.473864\pi\) | ||||
0.0820168 | + | 0.996631i | \(0.473864\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.2487 | 1.81966 | 0.909830 | − | 0.414982i | \(-0.136212\pi\) | ||||
0.909830 | + | 0.414982i | \(0.136212\pi\) | |||||||
\(242\) | −10.4641 | −0.672658 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −15.1244 | −0.968238 | ||||||||
\(245\) | 5.00000 | 0.319438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.92820 | 0.440831 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −30.9808 | −1.95549 | −0.977744 | − | 0.209801i | \(-0.932718\pi\) | ||||
−0.977744 | + | 0.209801i | \(0.932718\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.46410 | −0.343525 | ||||||||
\(254\) | 11.8564 | 0.743937 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.07180 | −0.191613 | −0.0958067 | − | 0.995400i | \(-0.530543\pi\) | ||||
−0.0958067 | + | 0.995400i | \(0.530543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.3205 | −0.703422 | ||||||||
\(260\) | −4.73205 | −0.293469 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.39230 | 0.518478 | ||||||||
\(263\) | 14.7846 | 0.911658 | 0.455829 | − | 0.890067i | \(-0.349343\pi\) | ||||
0.455829 | + | 0.890067i | \(0.349343\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.73205 | 0.536406 | ||||||||
\(266\) | −5.07180 | −0.310972 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.3923 | −0.756980 | ||||||||
\(269\) | 17.6603 | 1.07676 | 0.538382 | − | 0.842701i | \(-0.319036\pi\) | ||||
0.538382 | + | 0.842701i | \(0.319036\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.46410 | 0.0889378 | 0.0444689 | − | 0.999011i | \(-0.485840\pi\) | ||||
0.0444689 | + | 0.999011i | \(0.485840\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.7846 | −1.25564 | ||||||||
\(275\) | −0.732051 | −0.0441443 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.87564 | −0.172781 | −0.0863904 | − | 0.996261i | \(-0.527533\pi\) | ||||
−0.0863904 | + | 0.996261i | \(0.527533\pi\) | |||||||
\(278\) | −3.66025 | −0.219527 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.46410 | 0.207020 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.53590 | 0.150744 | 0.0753718 | − | 0.997156i | \(-0.475986\pi\) | ||||
0.0753718 | + | 0.997156i | \(0.475986\pi\) | |||||||
\(284\) | −13.8564 | −0.822226 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.46410 | 0.204837 | ||||||||
\(287\) | 32.7846 | 1.93521 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 2.73205 | 0.160432 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.3923 | 0.959287 | ||||||||
\(293\) | −17.3205 | −1.01187 | −0.505937 | − | 0.862570i | \(-0.668853\pi\) | ||||
−0.505937 | + | 0.862570i | \(0.668853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.46410 | 0.0852433 | ||||||||
\(296\) | −3.26795 | −0.189946 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.3205 | −1.23506 | ||||||||
\(299\) | −35.3205 | −2.04264 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.3205 | 1.34417 | ||||||||
\(302\) | −5.46410 | −0.314424 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.46410 | −0.0839720 | ||||||||
\(305\) | −15.1244 | −0.866018 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.7846 | 0.957948 | 0.478974 | − | 0.877829i | \(-0.341009\pi\) | ||||
0.478974 | + | 0.877829i | \(0.341009\pi\) | |||||||
\(308\) | −2.53590 | −0.144496 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.00000 | −0.0567962 | ||||||||
\(311\) | −26.9282 | −1.52696 | −0.763479 | − | 0.645832i | \(-0.776510\pi\) | ||||
−0.763479 | + | 0.645832i | \(0.776510\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7846 | −0.722629 | −0.361314 | − | 0.932444i | \(-0.617672\pi\) | ||||
−0.361314 | + | 0.932444i | \(0.617672\pi\) | |||||||
\(314\) | 7.85641 | 0.443363 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.5359 | 0.592691 | ||||||||
\(317\) | −16.5359 | −0.928749 | −0.464374 | − | 0.885639i | \(-0.653721\pi\) | ||||
−0.464374 | + | 0.885639i | \(0.653721\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.00000 | −0.111979 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 25.8564 | 1.44092 | ||||||||
\(323\) | −5.85641 | −0.325859 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.73205 | −0.262487 | ||||||||
\(326\) | −2.53590 | −0.140450 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.46410 | 0.522568 | ||||||||
\(329\) | −12.0000 | −0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.7321 | −0.919677 | −0.459838 | − | 0.888003i | \(-0.652093\pi\) | ||||
−0.459838 | + | 0.888003i | \(0.652093\pi\) | |||||||
\(332\) | 1.26795 | 0.0695878 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.3205 | 0.947736 | ||||||||
\(335\) | −12.3923 | −0.677064 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.3923 | −1.76452 | −0.882261 | − | 0.470761i | \(-0.843979\pi\) | ||||
−0.882261 | + | 0.470761i | \(0.843979\pi\) | |||||||
\(338\) | 9.39230 | 0.510874 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | 0.732051 | 0.0396428 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.92820 | −0.374088 | ||||||||
\(344\) | 6.73205 | 0.362968 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | 0.107521 | ||||||||
\(347\) | −18.0526 | −0.969112 | −0.484556 | − | 0.874760i | \(-0.661019\pi\) | ||||
−0.484556 | + | 0.874760i | \(0.661019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.4641 | −1.89835 | −0.949175 | − | 0.314749i | \(-0.898080\pi\) | ||||
−0.949175 | + | 0.314749i | \(0.898080\pi\) | |||||||
\(350\) | 3.46410 | 0.185164 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.732051 | −0.0390184 | ||||||||
\(353\) | −4.39230 | −0.233779 | −0.116889 | − | 0.993145i | \(-0.537292\pi\) | ||||
−0.116889 | + | 0.993145i | \(0.537292\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.8564 | −0.735422 | ||||||||
\(356\) | 12.9282 | 0.685193 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.2679 | 0.595530 | ||||||||
\(359\) | 19.0718 | 1.00657 | 0.503285 | − | 0.864120i | \(-0.332124\pi\) | ||||
0.503285 | + | 0.864120i | \(0.332124\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.8564 | −0.887179 | ||||||||
\(362\) | 15.1244 | 0.794918 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.3923 | −0.859190 | ||||||||
\(365\) | 16.3923 | 0.858012 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.4641 | −1.85121 | −0.925606 | − | 0.378490i | \(-0.876444\pi\) | ||||
−0.925606 | + | 0.378490i | \(0.876444\pi\) | |||||||
\(368\) | 7.46410 | 0.389093 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.26795 | −0.169893 | ||||||||
\(371\) | 30.2487 | 1.57043 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.3205 | −1.31105 | −0.655523 | − | 0.755175i | \(-0.727552\pi\) | ||||
−0.655523 | + | 0.755175i | \(0.727552\pi\) | |||||||
\(374\) | −2.92820 | −0.151414 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.46410 | −0.178647 | ||||||||
\(377\) | −12.9282 | −0.665836 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.3205 | 1.40336 | 0.701680 | − | 0.712492i | \(-0.252434\pi\) | ||||
0.701680 | + | 0.712492i | \(0.252434\pi\) | |||||||
\(380\) | −1.46410 | −0.0751068 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.00000 | 0.102329 | ||||||||
\(383\) | 2.00000 | 0.102195 | 0.0510976 | − | 0.998694i | \(-0.483728\pi\) | ||||
0.0510976 | + | 0.998694i | \(0.483728\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.53590 | −0.129241 | ||||||||
\(386\) | −11.8564 | −0.603475 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.00000 | 0.203069 | ||||||||
\(389\) | −15.8038 | −0.801287 | −0.400643 | − | 0.916234i | \(-0.631213\pi\) | ||||
−0.400643 | + | 0.916234i | \(0.631213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.8564 | 1.50990 | ||||||||
\(392\) | 5.00000 | 0.252538 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −24.7321 | −1.24598 | ||||||||
\(395\) | 10.5359 | 0.530119 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.2487 | −1.61852 | −0.809258 | − | 0.587453i | \(-0.800131\pi\) | ||||
−0.809258 | + | 0.587453i | \(0.800131\pi\) | |||||||
\(398\) | −20.0000 | −1.00251 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 0.535898 | 0.0267615 | 0.0133807 | − | 0.999910i | \(-0.495741\pi\) | ||||
0.0133807 | + | 0.999910i | \(0.495741\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.73205 | 0.235720 | ||||||||
\(404\) | 3.07180 | 0.152828 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.46410 | 0.469695 | ||||||||
\(407\) | 2.39230 | 0.118582 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.4641 | −0.764651 | −0.382325 | − | 0.924028i | \(-0.624877\pi\) | ||||
−0.382325 | + | 0.924028i | \(0.624877\pi\) | |||||||
\(410\) | 9.46410 | 0.467399 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.9282 | −0.538394 | ||||||||
\(413\) | 5.07180 | 0.249567 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.26795 | 0.0622412 | ||||||||
\(416\) | −4.73205 | −0.232008 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.07180 | 0.0524233 | ||||||||
\(419\) | −16.3923 | −0.800816 | −0.400408 | − | 0.916337i | \(-0.631132\pi\) | ||||
−0.400408 | + | 0.916337i | \(0.631132\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.2487 | −0.791914 | −0.395957 | − | 0.918269i | \(-0.629587\pi\) | ||||
−0.395957 | + | 0.918269i | \(0.629587\pi\) | |||||||
\(422\) | 13.0718 | 0.636325 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.73205 | 0.424066 | ||||||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −52.3923 | −2.53544 | ||||||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.73205 | 0.324648 | ||||||||
\(431\) | 14.7846 | 0.712150 | 0.356075 | − | 0.934457i | \(-0.384115\pi\) | ||||
0.356075 | + | 0.934457i | \(0.384115\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.7846 | −1.19107 | −0.595536 | − | 0.803328i | \(-0.703060\pi\) | ||||
−0.595536 | + | 0.803328i | \(0.703060\pi\) | |||||||
\(434\) | −3.46410 | −0.166282 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.53590 | −0.408795 | ||||||||
\(437\) | −10.9282 | −0.522767 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.0000 | 1.05000 | 0.525001 | − | 0.851101i | \(-0.324065\pi\) | ||||
0.525001 | + | 0.851101i | \(0.324065\pi\) | |||||||
\(440\) | −0.732051 | −0.0348992 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18.9282 | −0.900323 | ||||||||
\(443\) | 21.0718 | 1.00115 | 0.500576 | − | 0.865693i | \(-0.333122\pi\) | ||||
0.500576 | + | 0.865693i | \(0.333122\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.9282 | 0.612856 | ||||||||
\(446\) | 10.0000 | 0.473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.46410 | 0.163663 | ||||||||
\(449\) | 5.32051 | 0.251090 | 0.125545 | − | 0.992088i | \(-0.459932\pi\) | ||||
0.125545 | + | 0.992088i | \(0.459932\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.92820 | −0.326236 | ||||||||
\(452\) | −8.00000 | −0.376288 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.53590 | 0.306745 | ||||||||
\(455\) | −16.3923 | −0.768483 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.07180 | 0.0501365 | 0.0250683 | − | 0.999686i | \(-0.492020\pi\) | ||||
0.0250683 | + | 0.999686i | \(0.492020\pi\) | |||||||
\(458\) | 14.0526 | 0.656633 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.46410 | 0.348016 | ||||||||
\(461\) | 30.7321 | 1.43133 | 0.715667 | − | 0.698441i | \(-0.246123\pi\) | ||||
0.715667 | + | 0.698441i | \(0.246123\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.3923 | 0.482971 | 0.241486 | − | 0.970404i | \(-0.422365\pi\) | ||||
0.241486 | + | 0.970404i | \(0.422365\pi\) | |||||||
\(464\) | 2.73205 | 0.126832 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.7846 | 0.777532 | ||||||||
\(467\) | −33.8564 | −1.56669 | −0.783344 | − | 0.621589i | \(-0.786488\pi\) | ||||
−0.783344 | + | 0.621589i | \(0.786488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −42.9282 | −1.98224 | ||||||||
\(470\) | −3.46410 | −0.159787 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.46410 | 0.0673907 | ||||||||
\(473\) | −4.92820 | −0.226599 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.46410 | −0.0671776 | ||||||||
\(476\) | 13.8564 | 0.635107 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.53590 | 0.115989 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.4641 | 0.705102 | ||||||||
\(482\) | 28.2487 | 1.28669 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.4641 | −0.475641 | ||||||||
\(485\) | 4.00000 | 0.181631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0000 | −0.453143 | −0.226572 | − | 0.973995i | \(-0.572752\pi\) | ||||
−0.226572 | + | 0.973995i | \(0.572752\pi\) | |||||||
\(488\) | −15.1244 | −0.684647 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.00000 | 0.225877 | ||||||||
\(491\) | −15.2679 | −0.689033 | −0.344516 | − | 0.938780i | \(-0.611957\pi\) | ||||
−0.344516 | + | 0.938780i | \(0.611957\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.9282 | 0.492182 | ||||||||
\(494\) | 6.92820 | 0.311715 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | −48.0000 | −2.15309 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.12436 | −0.229398 | −0.114699 | − | 0.993400i | \(-0.536590\pi\) | ||||
−0.114699 | + | 0.993400i | \(0.536590\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.9808 | −1.38274 | ||||||||
\(503\) | 38.6410 | 1.72292 | 0.861459 | − | 0.507827i | \(-0.169551\pi\) | ||||
0.861459 | + | 0.507827i | \(0.169551\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.07180 | 0.136693 | ||||||||
\(506\) | −5.46410 | −0.242909 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.8564 | 0.526043 | ||||||||
\(509\) | 29.6603 | 1.31467 | 0.657334 | − | 0.753600i | \(-0.271684\pi\) | ||||
0.657334 | + | 0.753600i | \(0.271684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 56.7846 | 2.51200 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.07180 | −0.135491 | ||||||||
\(515\) | −10.9282 | −0.481554 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.53590 | 0.111529 | ||||||||
\(518\) | −11.3205 | −0.497395 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.73205 | −0.207514 | ||||||||
\(521\) | 8.92820 | 0.391152 | 0.195576 | − | 0.980689i | \(-0.437342\pi\) | ||||
0.195576 | + | 0.980689i | \(0.437342\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.8038 | −0.865962 | −0.432981 | − | 0.901403i | \(-0.642538\pi\) | ||||
−0.432981 | + | 0.901403i | \(0.642538\pi\) | |||||||
\(524\) | 8.39230 | 0.366620 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.7846 | 0.644640 | ||||||||
\(527\) | −4.00000 | −0.174243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.7128 | 1.42230 | ||||||||
\(530\) | 8.73205 | 0.379296 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.07180 | −0.219890 | ||||||||
\(533\) | −44.7846 | −1.93984 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | −0.172935 | ||||||||
\(536\) | −12.3923 | −0.535266 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.6603 | 0.761388 | ||||||||
\(539\) | −3.66025 | −0.157658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.3205 | 0.572693 | 0.286347 | − | 0.958126i | \(-0.407559\pi\) | ||||
0.286347 | + | 0.958126i | \(0.407559\pi\) | |||||||
\(542\) | 1.46410 | 0.0628885 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | −8.53590 | −0.365638 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.32051 | 0.141975 | 0.0709873 | − | 0.997477i | \(-0.477385\pi\) | ||||
0.0709873 | + | 0.997477i | \(0.477385\pi\) | |||||||
\(548\) | −20.7846 | −0.887875 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.732051 | −0.0312148 | ||||||||
\(551\) | −4.00000 | −0.170406 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 36.4974 | 1.55203 | ||||||||
\(554\) | −2.87564 | −0.122174 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.66025 | −0.155229 | ||||||||
\(557\) | −2.87564 | −0.121845 | −0.0609225 | − | 0.998143i | \(-0.519404\pi\) | ||||
−0.0609225 | + | 0.998143i | \(0.519404\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.8564 | −1.34738 | ||||||||
\(560\) | 3.46410 | 0.146385 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.0000 | −0.421825 | ||||||||
\(563\) | −28.3923 | −1.19659 | −0.598296 | − | 0.801275i | \(-0.704156\pi\) | ||||
−0.598296 | + | 0.801275i | \(0.704156\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.00000 | −0.336563 | ||||||||
\(566\) | 2.53590 | 0.106592 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −13.8564 | −0.581402 | ||||||||
\(569\) | 5.32051 | 0.223047 | 0.111524 | − | 0.993762i | \(-0.464427\pi\) | ||||
0.111524 | + | 0.993762i | \(0.464427\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.58846 | −0.108324 | −0.0541618 | − | 0.998532i | \(-0.517249\pi\) | ||||
−0.0541618 | + | 0.998532i | \(0.517249\pi\) | |||||||
\(572\) | 3.46410 | 0.144841 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 32.7846 | 1.36840 | ||||||||
\(575\) | 7.46410 | 0.311275 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.07180 | −0.211142 | −0.105571 | − | 0.994412i | \(-0.533667\pi\) | ||||
−0.105571 | + | 0.994412i | \(0.533667\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.73205 | 0.113442 | ||||||||
\(581\) | 4.39230 | 0.182224 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.39230 | −0.264742 | ||||||||
\(584\) | 16.3923 | 0.678318 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.3205 | −0.715504 | ||||||||
\(587\) | −14.0526 | −0.580011 | −0.290006 | − | 0.957025i | \(-0.593657\pi\) | ||||
−0.290006 | + | 0.957025i | \(0.593657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.46410 | 0.0603273 | ||||||||
\(590\) | 1.46410 | 0.0602761 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.26795 | −0.134312 | ||||||||
\(593\) | −8.00000 | −0.328521 | −0.164260 | − | 0.986417i | \(-0.552524\pi\) | ||||
−0.164260 | + | 0.986417i | \(0.552524\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.8564 | 0.568057 | ||||||||
\(596\) | −21.3205 | −0.873322 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −35.3205 | −1.44436 | ||||||||
\(599\) | −0.143594 | −0.00586707 | −0.00293354 | − | 0.999996i | \(-0.500934\pi\) | ||||
−0.00293354 | + | 0.999996i | \(0.500934\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0718 | 0.614791 | 0.307396 | − | 0.951582i | \(-0.400542\pi\) | ||||
0.307396 | + | 0.951582i | \(0.400542\pi\) | |||||||
\(602\) | 23.3205 | 0.950473 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.46410 | −0.222331 | ||||||||
\(605\) | −10.4641 | −0.425426 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0000 | 0.487065 | 0.243532 | − | 0.969893i | \(-0.421694\pi\) | ||||
0.243532 | + | 0.969893i | \(0.421694\pi\) | |||||||
\(608\) | −1.46410 | −0.0593772 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.1244 | −0.612367 | ||||||||
\(611\) | 16.3923 | 0.663162 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.5885 | −0.589222 | −0.294611 | − | 0.955617i | \(-0.595190\pi\) | ||||
−0.294611 | + | 0.955617i | \(0.595190\pi\) | |||||||
\(614\) | 16.7846 | 0.677372 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.53590 | −0.102174 | ||||||||
\(617\) | −8.14359 | −0.327849 | −0.163924 | − | 0.986473i | \(-0.552415\pi\) | ||||
−0.163924 | + | 0.986473i | \(0.552415\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.1962 | 0.409818 | 0.204909 | − | 0.978781i | \(-0.434310\pi\) | ||||
0.204909 | + | 0.978781i | \(0.434310\pi\) | |||||||
\(620\) | −1.00000 | −0.0401610 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.9282 | −1.07972 | ||||||||
\(623\) | 44.7846 | 1.79426 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −12.7846 | −0.510976 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.85641 | 0.313505 | ||||||||
\(629\) | −13.0718 | −0.521207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.3923 | −0.811805 | −0.405902 | − | 0.913916i | \(-0.633043\pi\) | ||||
−0.405902 | + | 0.913916i | \(0.633043\pi\) | |||||||
\(632\) | 10.5359 | 0.419096 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.5359 | −0.656724 | ||||||||
\(635\) | 11.8564 | 0.470507 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −23.6603 | −0.937453 | ||||||||
\(638\) | −2.00000 | −0.0791808 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −3.46410 | −0.136824 | −0.0684119 | − | 0.997657i | \(-0.521793\pi\) | ||||
−0.0684119 | + | 0.997657i | \(0.521793\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 45.6603 | 1.80066 | 0.900332 | − | 0.435203i | \(-0.143323\pi\) | ||||
0.900332 | + | 0.435203i | \(0.143323\pi\) | |||||||
\(644\) | 25.8564 | 1.01889 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.85641 | −0.230417 | ||||||||
\(647\) | −18.0000 | −0.707653 | −0.353827 | − | 0.935311i | \(-0.615120\pi\) | ||||
−0.353827 | + | 0.935311i | \(0.615120\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.07180 | −0.0420717 | ||||||||
\(650\) | −4.73205 | −0.185606 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.53590 | −0.0993134 | ||||||||
\(653\) | −0.928203 | −0.0363234 | −0.0181617 | − | 0.999835i | \(-0.505781\pi\) | ||||
−0.0181617 | + | 0.999835i | \(0.505781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.39230 | 0.327914 | ||||||||
\(656\) | 9.46410 | 0.369511 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.0000 | −0.467809 | ||||||||
\(659\) | −14.5359 | −0.566238 | −0.283119 | − | 0.959085i | \(-0.591369\pi\) | ||||
−0.283119 | + | 0.959085i | \(0.591369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.2487 | −0.632002 | −0.316001 | − | 0.948759i | \(-0.602340\pi\) | ||||
−0.316001 | + | 0.948759i | \(0.602340\pi\) | |||||||
\(662\) | −16.7321 | −0.650310 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.26795 | 0.0492060 | ||||||||
\(665\) | −5.07180 | −0.196676 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.3923 | 0.789593 | ||||||||
\(668\) | 17.3205 | 0.670151 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.3923 | −0.478757 | ||||||||
\(671\) | 11.0718 | 0.427422 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.78461 | −0.184433 | −0.0922166 | − | 0.995739i | \(-0.529395\pi\) | ||||
−0.0922166 | + | 0.995739i | \(0.529395\pi\) | |||||||
\(674\) | −32.3923 | −1.24770 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.39230 | 0.361242 | ||||||||
\(677\) | −28.0526 | −1.07815 | −0.539074 | − | 0.842259i | \(-0.681226\pi\) | ||||
−0.539074 | + | 0.842259i | \(0.681226\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.8564 | 0.531760 | ||||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.732051 | 0.0280317 | ||||||||
\(683\) | 39.7128 | 1.51957 | 0.759784 | − | 0.650175i | \(-0.225305\pi\) | ||||
0.759784 | + | 0.650175i | \(0.225305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.7846 | −0.794139 | ||||||||
\(686\) | −6.92820 | −0.264520 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.73205 | 0.256657 | ||||||||
\(689\) | −41.3205 | −1.57419 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.7846 | 1.39935 | 0.699676 | − | 0.714460i | \(-0.253328\pi\) | ||||
0.699676 | + | 0.714460i | \(0.253328\pi\) | |||||||
\(692\) | 2.00000 | 0.0760286 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.0526 | −0.685266 | ||||||||
\(695\) | −3.66025 | −0.138841 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.8564 | 1.43391 | ||||||||
\(698\) | −35.4641 | −1.34234 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.46410 | 0.130931 | ||||||||
\(701\) | −27.0718 | −1.02249 | −0.511244 | − | 0.859436i | \(-0.670815\pi\) | ||||
−0.511244 | + | 0.859436i | \(0.670815\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.78461 | 0.180455 | ||||||||
\(704\) | −0.732051 | −0.0275902 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.39230 | −0.165307 | ||||||||
\(707\) | 10.6410 | 0.400197 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.0526 | 1.12865 | 0.564324 | − | 0.825554i | \(-0.309137\pi\) | ||||
0.564324 | + | 0.825554i | \(0.309137\pi\) | |||||||
\(710\) | −13.8564 | −0.520022 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.9282 | 0.484505 | ||||||||
\(713\) | −7.46410 | −0.279533 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.46410 | 0.129550 | ||||||||
\(716\) | 11.2679 | 0.421103 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.0718 | 0.711753 | ||||||||
\(719\) | −1.85641 | −0.0692323 | −0.0346161 | − | 0.999401i | \(-0.511021\pi\) | ||||
−0.0346161 | + | 0.999401i | \(0.511021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −37.8564 | −1.40985 | ||||||||
\(722\) | −16.8564 | −0.627330 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.1244 | 0.562092 | ||||||||
\(725\) | 2.73205 | 0.101466 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.78461 | −0.177451 | −0.0887257 | − | 0.996056i | \(-0.528279\pi\) | ||||
−0.0887257 | + | 0.996056i | \(0.528279\pi\) | |||||||
\(728\) | −16.3923 | −0.607539 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.3923 | 0.606706 | ||||||||
\(731\) | 26.9282 | 0.995976 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.3923 | −1.41805 | −0.709026 | − | 0.705182i | \(-0.750865\pi\) | ||||
−0.709026 | + | 0.705182i | \(0.750865\pi\) | |||||||
\(734\) | −35.4641 | −1.30900 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.46410 | 0.275130 | ||||||||
\(737\) | 9.07180 | 0.334164 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.1962 | 1.25793 | 0.628963 | − | 0.777435i | \(-0.283480\pi\) | ||||
0.628963 | + | 0.777435i | \(0.283480\pi\) | |||||||
\(740\) | −3.26795 | −0.120132 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30.2487 | 1.11047 | ||||||||
\(743\) | −33.7128 | −1.23680 | −0.618402 | − | 0.785862i | \(-0.712219\pi\) | ||||
−0.618402 | + | 0.785862i | \(0.712219\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.3205 | −0.781123 | ||||||||
\(746\) | −25.3205 | −0.927050 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.92820 | −0.107066 | ||||||||
\(749\) | −13.8564 | −0.506302 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.8564 | 0.724571 | 0.362285 | − | 0.932067i | \(-0.381997\pi\) | ||||
0.362285 | + | 0.932067i | \(0.381997\pi\) | |||||||
\(752\) | −3.46410 | −0.126323 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.9282 | −0.470817 | ||||||||
\(755\) | −5.46410 | −0.198859 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.4449 | −1.61538 | −0.807688 | − | 0.589610i | \(-0.799281\pi\) | ||||
−0.807688 | + | 0.589610i | \(0.799281\pi\) | |||||||
\(758\) | 27.3205 | 0.992326 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.46410 | −0.0531085 | ||||||||
\(761\) | −7.46410 | −0.270573 | −0.135287 | − | 0.990806i | \(-0.543196\pi\) | ||||
−0.135287 | + | 0.990806i | \(0.543196\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.5692 | −1.07048 | ||||||||
\(764\) | 2.00000 | 0.0723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.00000 | 0.0722629 | ||||||||
\(767\) | −6.92820 | −0.250163 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.67949 | 0.168747 | 0.0843734 | − | 0.996434i | \(-0.473111\pi\) | ||||
0.0843734 | + | 0.996434i | \(0.473111\pi\) | |||||||
\(770\) | −2.53590 | −0.0913874 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.8564 | −0.426721 | ||||||||
\(773\) | 2.48334 | 0.0893195 | 0.0446598 | − | 0.999002i | \(-0.485780\pi\) | ||||
0.0446598 | + | 0.999002i | \(0.485780\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 4.00000 | 0.143592 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.8038 | −0.566595 | ||||||||
\(779\) | −13.8564 | −0.496457 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.1436 | 0.362966 | ||||||||
\(782\) | 29.8564 | 1.06766 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.00000 | 0.178571 | ||||||||
\(785\) | 7.85641 | 0.280407 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.66025 | 0.344351 | 0.172175 | − | 0.985066i | \(-0.444920\pi\) | ||||
0.172175 | + | 0.985066i | \(0.444920\pi\) | |||||||
\(788\) | −24.7321 | −0.881043 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.5359 | 0.374850 | ||||||||
\(791\) | −27.7128 | −0.985354 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 71.5692 | 2.54150 | ||||||||
\(794\) | −32.2487 | −1.14446 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.0000 | −0.708881 | ||||||||
\(797\) | 36.8372 | 1.30484 | 0.652420 | − | 0.757858i | \(-0.273754\pi\) | ||||
0.652420 | + | 0.757858i | \(0.273754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.8564 | −0.490204 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.535898 | 0.0189232 | ||||||||
\(803\) | −12.0000 | −0.423471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.8564 | 0.911319 | ||||||||
\(806\) | 4.73205 | 0.166679 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.07180 | 0.108065 | ||||||||
\(809\) | −32.2487 | −1.13380 | −0.566902 | − | 0.823785i | \(-0.691858\pi\) | ||||
−0.566902 | + | 0.823785i | \(0.691858\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.39230 | 0.154235 | 0.0771173 | − | 0.997022i | \(-0.475428\pi\) | ||||
0.0771173 | + | 0.997022i | \(0.475428\pi\) | |||||||
\(812\) | 9.46410 | 0.332125 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.39230 | 0.0838502 | ||||||||
\(815\) | −2.53590 | −0.0888286 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.85641 | −0.344832 | ||||||||
\(818\) | −15.4641 | −0.540690 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.46410 | 0.330501 | ||||||||
\(821\) | 35.5167 | 1.23954 | 0.619770 | − | 0.784784i | \(-0.287226\pi\) | ||||
0.619770 | + | 0.784784i | \(0.287226\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.1436 | −0.841593 | −0.420796 | − | 0.907155i | \(-0.638249\pi\) | ||||
−0.420796 | + | 0.907155i | \(0.638249\pi\) | |||||||
\(824\) | −10.9282 | −0.380702 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.07180 | 0.176470 | ||||||||
\(827\) | −11.5167 | −0.400474 | −0.200237 | − | 0.979748i | \(-0.564171\pi\) | ||||
−0.200237 | + | 0.979748i | \(0.564171\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.875644 | −0.0304124 | −0.0152062 | − | 0.999884i | \(-0.504840\pi\) | ||||
−0.0152062 | + | 0.999884i | \(0.504840\pi\) | |||||||
\(830\) | 1.26795 | 0.0440112 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.73205 | −0.164054 | ||||||||
\(833\) | 20.0000 | 0.692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.3205 | 0.599401 | ||||||||
\(836\) | 1.07180 | 0.0370689 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.3923 | −0.566263 | ||||||||
\(839\) | 46.7846 | 1.61518 | 0.807592 | − | 0.589742i | \(-0.200770\pi\) | ||||
0.807592 | + | 0.589742i | \(0.200770\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.5359 | −0.742617 | ||||||||
\(842\) | −16.2487 | −0.559968 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.0718 | 0.449950 | ||||||||
\(845\) | 9.39230 | 0.323105 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.2487 | −1.24552 | ||||||||
\(848\) | 8.73205 | 0.299860 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.00000 | 0.137199 | ||||||||
\(851\) | −24.3923 | −0.836157 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.1436 | −0.826661 | −0.413330 | − | 0.910581i | \(-0.635635\pi\) | ||||
−0.413330 | + | 0.910581i | \(0.635635\pi\) | |||||||
\(854\) | −52.3923 | −1.79283 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | 11.0718 | 0.378205 | 0.189103 | − | 0.981957i | \(-0.439442\pi\) | ||||
0.189103 | + | 0.981957i | \(0.439442\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.4449 | 0.697570 | 0.348785 | − | 0.937203i | \(-0.386594\pi\) | ||||
0.348785 | + | 0.937203i | \(0.386594\pi\) | |||||||
\(860\) | 6.73205 | 0.229561 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.7846 | 0.503566 | ||||||||
\(863\) | 31.8564 | 1.08440 | 0.542202 | − | 0.840248i | \(-0.317591\pi\) | ||||
0.542202 | + | 0.840248i | \(0.317591\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | 0.0680020 | ||||||||
\(866\) | −24.7846 | −0.842215 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.46410 | −0.117579 | ||||||||
\(869\) | −7.71281 | −0.261639 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 58.6410 | 1.98698 | ||||||||
\(872\) | −8.53590 | −0.289062 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.9282 | −0.369652 | ||||||||
\(875\) | 3.46410 | 0.117108 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.3205 | 1.53036 | 0.765182 | − | 0.643814i | \(-0.222649\pi\) | ||||
0.765182 | + | 0.643814i | \(0.222649\pi\) | |||||||
\(878\) | 22.0000 | 0.742464 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.732051 | −0.0246774 | ||||||||
\(881\) | −35.5692 | −1.19836 | −0.599179 | − | 0.800615i | \(-0.704506\pi\) | ||||
−0.599179 | + | 0.800615i | \(0.704506\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.33975 | −0.0787387 | −0.0393694 | − | 0.999225i | \(-0.512535\pi\) | ||||
−0.0393694 | + | 0.999225i | \(0.512535\pi\) | |||||||
\(884\) | −18.9282 | −0.636624 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21.0718 | 0.707921 | ||||||||
\(887\) | 50.1051 | 1.68237 | 0.841183 | − | 0.540751i | \(-0.181860\pi\) | ||||
0.841183 | + | 0.540751i | \(0.181860\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41.0718 | 1.37750 | ||||||||
\(890\) | 12.9282 | 0.433354 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.0000 | 0.334825 | ||||||||
\(893\) | 5.07180 | 0.169721 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.2679 | 0.376646 | ||||||||
\(896\) | 3.46410 | 0.115728 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.32051 | 0.177548 | ||||||||
\(899\) | −2.73205 | −0.0911190 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.9282 | 1.16363 | ||||||||
\(902\) | −6.92820 | −0.230684 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.00000 | −0.266076 | ||||||||
\(905\) | 15.1244 | 0.502751 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.85641 | −0.327277 | −0.163638 | − | 0.986520i | \(-0.552323\pi\) | ||||
−0.163638 | + | 0.986520i | \(0.552323\pi\) | |||||||
\(908\) | 6.53590 | 0.216901 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −16.3923 | −0.543400 | ||||||||
\(911\) | 30.9282 | 1.02470 | 0.512349 | − | 0.858778i | \(-0.328776\pi\) | ||||
0.512349 | + | 0.858778i | \(0.328776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.928203 | −0.0307190 | ||||||||
\(914\) | 1.07180 | 0.0354519 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.0526 | 0.464310 | ||||||||
\(917\) | 29.0718 | 0.960035 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.7846 | −1.34536 | −0.672680 | − | 0.739933i | \(-0.734857\pi\) | ||||
−0.672680 | + | 0.739933i | \(0.734857\pi\) | |||||||
\(920\) | 7.46410 | 0.246084 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.7321 | 1.01211 | ||||||||
\(923\) | 65.5692 | 2.15824 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.26795 | −0.107450 | ||||||||
\(926\) | 10.3923 | 0.341512 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.73205 | 0.0896840 | ||||||||
\(929\) | 22.3923 | 0.734668 | 0.367334 | − | 0.930089i | \(-0.380271\pi\) | ||||
0.367334 | + | 0.930089i | \(0.380271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.32051 | −0.239920 | ||||||||
\(932\) | 16.7846 | 0.549798 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33.8564 | −1.10782 | ||||||||
\(935\) | −2.92820 | −0.0957625 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32.9282 | −1.07572 | −0.537859 | − | 0.843035i | \(-0.680767\pi\) | ||||
−0.537859 | + | 0.843035i | \(0.680767\pi\) | |||||||
\(938\) | −42.9282 | −1.40166 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.46410 | −0.112987 | ||||||||
\(941\) | 23.4115 | 0.763194 | 0.381597 | − | 0.924329i | \(-0.375374\pi\) | ||||
0.381597 | + | 0.924329i | \(0.375374\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 70.6410 | 2.30039 | ||||||||
\(944\) | 1.46410 | 0.0476524 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.92820 | −0.160230 | ||||||||
\(947\) | −0.196152 | −0.00637410 | −0.00318705 | − | 0.999995i | \(-0.501014\pi\) | ||||
−0.00318705 | + | 0.999995i | \(0.501014\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −77.5692 | −2.51800 | ||||||||
\(950\) | −1.46410 | −0.0475017 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.8564 | 0.449089 | ||||||||
\(953\) | −17.0718 | −0.553010 | −0.276505 | − | 0.961013i | \(-0.589176\pi\) | ||||
−0.276505 | + | 0.961013i | \(0.589176\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.00000 | 0.0647185 | ||||||||
\(956\) | 2.53590 | 0.0820168 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −72.0000 | −2.32500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 15.4641 | 0.498583 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 28.2487 | 0.909830 | ||||||||
\(965\) | −11.8564 | −0.381671 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.8564 | −1.28170 | −0.640848 | − | 0.767668i | \(-0.721417\pi\) | ||||
−0.640848 | + | 0.767668i | \(0.721417\pi\) | |||||||
\(968\) | −10.4641 | −0.336329 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.00000 | 0.128432 | ||||||||
\(971\) | 48.0000 | 1.54039 | 0.770197 | − | 0.637806i | \(-0.220158\pi\) | ||||
0.770197 | + | 0.637806i | \(0.220158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.6795 | −0.406486 | ||||||||
\(974\) | −10.0000 | −0.320421 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −15.1244 | −0.484119 | ||||||||
\(977\) | −1.21539 | −0.0388838 | −0.0194419 | − | 0.999811i | \(-0.506189\pi\) | ||||
−0.0194419 | + | 0.999811i | \(0.506189\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.46410 | −0.302474 | ||||||||
\(980\) | 5.00000 | 0.159719 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15.2679 | −0.487220 | ||||||||
\(983\) | −17.7128 | −0.564951 | −0.282475 | − | 0.959275i | \(-0.591156\pi\) | ||||
−0.282475 | + | 0.959275i | \(0.591156\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.7321 | −0.788029 | ||||||||
\(986\) | 10.9282 | 0.348025 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.92820 | 0.220416 | ||||||||
\(989\) | 50.2487 | 1.59782 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.9282 | 0.855403 | 0.427701 | − | 0.903920i | \(-0.359324\pi\) | ||||
0.427701 | + | 0.903920i | \(0.359324\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −48.0000 | −1.52247 | ||||||||
\(995\) | −20.0000 | −0.634043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.1769 | 1.24075 | 0.620373 | − | 0.784307i | \(-0.286981\pi\) | ||||
0.620373 | + | 0.784307i | \(0.286981\pi\) | |||||||
\(998\) | −5.12436 | −0.162209 | ||||||||
\(999\) | 0 | 0 |
(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 | 2790.2.a.bh.1.2 | 2 | ||
3.2 | odd | 2 | 310.2.a.c.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 2480.2.a.s.1.2 | 2 | |||
15.2 | even | 4 | 1550.2.b.h.249.2 | 4 | |||
15.8 | even | 4 | 1550.2.b.h.249.3 | 4 | |||
15.14 | odd | 2 | 1550.2.a.j.1.2 | 2 | |||
24.5 | odd | 2 | 9920.2.a.bt.1.2 | 2 | |||
24.11 | even | 2 | 9920.2.a.bl.1.1 | 2 | |||
93.92 | even | 2 | 9610.2.a.j.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
310.2.a.c.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
1550.2.a.j.1.2 | 2 | 15.14 | odd | 2 | |||
1550.2.b.h.249.2 | 4 | 15.2 | even | 4 | |||
1550.2.b.h.249.3 | 4 | 15.8 | even | 4 | |||
2480.2.a.s.1.2 | 2 | 12.11 | even | 2 | |||
2790.2.a.bh.1.2 | 2 | 1.1 | even | 1 | trivial | ||
9610.2.a.j.1.2 | 2 | 93.92 | even | 2 | |||
9920.2.a.bl.1.1 | 2 | 24.11 | even | 2 | |||
9920.2.a.bt.1.2 | 2 | 24.5 | odd | 2 |