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: | \(\Q(\sqrt{65}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 930) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.53113\) 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 | ||||||||
\(7\) | −4.53113 | −1.71261 | −0.856303 | − | 0.516474i | \(-0.827244\pi\) | ||||
−0.856303 | + | 0.516474i | \(0.827244\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −6.53113 | −1.96921 | −0.984605 | − | 0.174796i | \(-0.944074\pi\) | ||||
−0.984605 | + | 0.174796i | \(0.944074\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | 4.53113 | 1.21100 | ||||||||
\(15\) | 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 | ||||||||
\(19\) | 4.53113 | 1.03951 | 0.519756 | − | 0.854315i | \(-0.326023\pi\) | ||||
0.519756 | + | 0.854315i | \(0.326023\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.53113 | 1.39244 | ||||||||
\(23\) | −6.53113 | −1.36183 | −0.680917 | − | 0.732360i | \(-0.738419\pi\) | ||||
−0.680917 | + | 0.732360i | \(0.738419\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.00000 | −1.17670 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.53113 | −0.856303 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | −4.53113 | −0.765901 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.06226 | −1.16103 | −0.580514 | − | 0.814250i | \(-0.697148\pi\) | ||||
−0.580514 | + | 0.814250i | \(0.697148\pi\) | |||||||
\(38\) | −4.53113 | −0.735046 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −7.06226 | −1.10294 | −0.551470 | − | 0.834195i | \(-0.685933\pi\) | ||||
−0.551470 | + | 0.834195i | \(0.685933\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.53113 | −1.30098 | −0.650492 | − | 0.759513i | \(-0.725437\pi\) | ||||
−0.650492 | + | 0.759513i | \(0.725437\pi\) | |||||||
\(44\) | −6.53113 | −0.984605 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.53113 | 0.962962 | ||||||||
\(47\) | 5.06226 | 0.738406 | 0.369203 | − | 0.929349i | \(-0.379631\pi\) | ||||
0.369203 | + | 0.929349i | \(0.379631\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.5311 | 1.93302 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.00000 | 0.832050 | ||||||||
\(53\) | 2.53113 | 0.347677 | 0.173839 | − | 0.984774i | \(-0.444383\pi\) | ||||
0.173839 | + | 0.984774i | \(0.444383\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.53113 | −0.880657 | ||||||||
\(56\) | 4.53113 | 0.605498 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.06226 | 1.17981 | 0.589903 | − | 0.807474i | \(-0.299166\pi\) | ||||
0.589903 | + | 0.807474i | \(0.299166\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.06226 | 0.648156 | 0.324078 | − | 0.946030i | \(-0.394946\pi\) | ||||
0.324078 | + | 0.946030i | \(0.394946\pi\) | |||||||
\(62\) | −1.00000 | −0.127000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.00000 | 0.744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.06226 | 0.618453 | 0.309227 | − | 0.950988i | \(-0.399930\pi\) | ||||
0.309227 | + | 0.950988i | \(0.399930\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.53113 | 0.541573 | ||||||||
\(71\) | 12.5311 | 1.48717 | 0.743586 | − | 0.668641i | \(-0.233124\pi\) | ||||
0.743586 | + | 0.668641i | \(0.233124\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.53113 | −0.998493 | −0.499247 | − | 0.866460i | \(-0.666390\pi\) | ||||
−0.499247 | + | 0.866460i | \(0.666390\pi\) | |||||||
\(74\) | 7.06226 | 0.820971 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.53113 | 0.519756 | ||||||||
\(77\) | 29.5934 | 3.37248 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.53113 | −0.959827 | −0.479913 | − | 0.877316i | \(-0.659332\pi\) | ||||
−0.479913 | + | 0.877316i | \(0.659332\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.06226 | 0.779896 | ||||||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 8.53113 | 0.919935 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.53113 | 0.696221 | ||||||||
\(89\) | 6.53113 | 0.692298 | 0.346149 | − | 0.938180i | \(-0.387489\pi\) | ||||
0.346149 | + | 0.938180i | \(0.387489\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −27.1868 | −2.84995 | ||||||||
\(92\) | −6.53113 | −0.680917 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.06226 | −0.522132 | ||||||||
\(95\) | 4.53113 | 0.464884 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.1245 | 1.63720 | 0.818598 | − | 0.574367i | \(-0.194752\pi\) | ||||
0.818598 | + | 0.574367i | \(0.194752\pi\) | |||||||
\(98\) | −13.5311 | −1.36685 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 9.46887 | 0.942188 | 0.471094 | − | 0.882083i | \(-0.343859\pi\) | ||||
0.471094 | + | 0.882083i | \(0.343859\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | −6.00000 | −0.588348 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.53113 | −0.245845 | ||||||||
\(107\) | −9.59339 | −0.927428 | −0.463714 | − | 0.885985i | \(-0.653483\pi\) | ||||
−0.463714 | + | 0.885985i | \(0.653483\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0623 | 1.44270 | 0.721351 | − | 0.692569i | \(-0.243521\pi\) | ||||
0.721351 | + | 0.692569i | \(0.243521\pi\) | |||||||
\(110\) | 6.53113 | 0.622719 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.53113 | −0.428151 | ||||||||
\(113\) | 7.59339 | 0.714326 | 0.357163 | − | 0.934042i | \(-0.383744\pi\) | ||||
0.357163 | + | 0.934042i | \(0.383744\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.53113 | −0.609031 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.06226 | −0.834248 | ||||||||
\(119\) | −18.1245 | −1.66147 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31.6556 | 2.87779 | ||||||||
\(122\) | −5.06226 | −0.458315 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.06226 | 0.626674 | 0.313337 | − | 0.949642i | \(-0.398553\pi\) | ||||
0.313337 | + | 0.949642i | \(0.398553\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.00000 | −0.526235 | ||||||||
\(131\) | 9.06226 | 0.791773 | 0.395887 | − | 0.918299i | \(-0.370437\pi\) | ||||
0.395887 | + | 0.918299i | \(0.370437\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.5311 | −1.78027 | ||||||||
\(134\) | −5.06226 | −0.437312 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | −17.0623 | −1.45773 | −0.728864 | − | 0.684659i | \(-0.759951\pi\) | ||||
−0.728864 | + | 0.684659i | \(0.759951\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.00000 | 0.508913 | 0.254457 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254457 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(140\) | −4.53113 | −0.382950 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.5311 | −1.05159 | ||||||||
\(143\) | −39.1868 | −3.27696 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.53113 | 0.706041 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.06226 | −0.580514 | ||||||||
\(149\) | 18.5311 | 1.51813 | 0.759065 | − | 0.651015i | \(-0.225657\pi\) | ||||
0.759065 | + | 0.651015i | \(0.225657\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.1245 | 1.14944 | 0.574718 | − | 0.818351i | \(-0.305112\pi\) | ||||
0.574718 | + | 0.818351i | \(0.305112\pi\) | |||||||
\(152\) | −4.53113 | −0.367523 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −29.5934 | −2.38470 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.5311 | −1.79818 | −0.899090 | − | 0.437764i | \(-0.855771\pi\) | ||||
−0.899090 | + | 0.437764i | \(0.855771\pi\) | |||||||
\(158\) | 8.53113 | 0.678700 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 29.5934 | 2.33229 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.06226 | 0.396507 | 0.198253 | − | 0.980151i | \(-0.436473\pi\) | ||||
0.198253 | + | 0.980151i | \(0.436473\pi\) | |||||||
\(164\) | −7.06226 | −0.551470 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.00000 | −0.620920 | ||||||||
\(167\) | 23.5934 | 1.82571 | 0.912856 | − | 0.408283i | \(-0.133872\pi\) | ||||
0.912856 | + | 0.408283i | \(0.133872\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.53113 | −0.650492 | ||||||||
\(173\) | −14.0000 | −1.06440 | −0.532200 | − | 0.846619i | \(-0.678635\pi\) | ||||
−0.532200 | + | 0.846619i | \(0.678635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.53113 | −0.342521 | ||||||||
\(176\) | −6.53113 | −0.492302 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.53113 | −0.489529 | ||||||||
\(179\) | 3.06226 | 0.228884 | 0.114442 | − | 0.993430i | \(-0.463492\pi\) | ||||
0.114442 | + | 0.993430i | \(0.463492\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.40661 | 0.178882 | 0.0894411 | − | 0.995992i | \(-0.471492\pi\) | ||||
0.0894411 | + | 0.995992i | \(0.471492\pi\) | |||||||
\(182\) | 27.1868 | 2.01522 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.53113 | 0.481481 | ||||||||
\(185\) | −7.06226 | −0.519228 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.1245 | −1.91041 | ||||||||
\(188\) | 5.06226 | 0.369203 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.53113 | −0.328723 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | −16.1245 | −1.15767 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.5311 | 0.966509 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.53113 | −0.604756 | −0.302378 | − | 0.953188i | \(-0.597780\pi\) | ||||
−0.302378 | + | 0.953188i | \(0.597780\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.46887 | −0.666227 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.06226 | −0.493249 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.00000 | 0.416025 | ||||||||
\(209\) | −29.5934 | −2.04702 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.59339 | −0.109693 | −0.0548466 | − | 0.998495i | \(-0.517467\pi\) | ||||
−0.0548466 | + | 0.998495i | \(0.517467\pi\) | |||||||
\(212\) | 2.53113 | 0.173839 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.59339 | 0.655790 | ||||||||
\(215\) | −8.53113 | −0.581818 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.53113 | −0.307593 | ||||||||
\(218\) | −15.0623 | −1.02014 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.53113 | −0.440329 | ||||||||
\(221\) | 24.0000 | 1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00000 | 0.133930 | 0.0669650 | − | 0.997755i | \(-0.478668\pi\) | ||||
0.0669650 | + | 0.997755i | \(0.478668\pi\) | |||||||
\(224\) | 4.53113 | 0.302749 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.59339 | −0.505105 | ||||||||
\(227\) | 24.5311 | 1.62819 | 0.814094 | − | 0.580733i | \(-0.197234\pi\) | ||||
0.814094 | + | 0.580733i | \(0.197234\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.59339 | −0.369621 | −0.184811 | − | 0.982774i | \(-0.559167\pi\) | ||||
−0.184811 | + | 0.982774i | \(0.559167\pi\) | |||||||
\(230\) | 6.53113 | 0.430650 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.46887 | −0.0962289 | −0.0481145 | − | 0.998842i | \(-0.515321\pi\) | ||||
−0.0481145 | + | 0.998842i | \(0.515321\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.06226 | 0.330225 | ||||||||
\(236\) | 9.06226 | 0.589903 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 18.1245 | 1.17484 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | −31.6556 | −2.03490 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.06226 | 0.324078 | ||||||||
\(245\) | 13.5311 | 0.864472 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.1868 | 1.72985 | ||||||||
\(248\) | −1.00000 | −0.0635001 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −3.06226 | −0.193288 | −0.0966440 | − | 0.995319i | \(-0.530811\pi\) | ||||
−0.0966440 | + | 0.995319i | \(0.530811\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 42.6556 | 2.68174 | ||||||||
\(254\) | −7.06226 | −0.443125 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.6556 | −0.789437 | −0.394719 | − | 0.918802i | \(-0.629158\pi\) | ||||
−0.394719 | + | 0.918802i | \(0.629158\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.0000 | 1.98838 | ||||||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.06226 | −0.559868 | ||||||||
\(263\) | 23.0623 | 1.42208 | 0.711040 | − | 0.703152i | \(-0.248225\pi\) | ||||
0.711040 | + | 0.703152i | \(0.248225\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.53113 | 0.155486 | ||||||||
\(266\) | 20.5311 | 1.25884 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.06226 | 0.309227 | ||||||||
\(269\) | 19.1868 | 1.16984 | 0.584919 | − | 0.811092i | \(-0.301126\pi\) | ||||
0.584919 | + | 0.811092i | \(0.301126\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.4689 | −0.696684 | −0.348342 | − | 0.937367i | \(-0.613255\pi\) | ||||
−0.348342 | + | 0.937367i | \(0.613255\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.0623 | 1.03077 | ||||||||
\(275\) | −6.53113 | −0.393842 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.0623 | −0.905003 | −0.452502 | − | 0.891764i | \(-0.649468\pi\) | ||||
−0.452502 | + | 0.891764i | \(0.649468\pi\) | |||||||
\(278\) | −6.00000 | −0.359856 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.53113 | 0.270787 | ||||||||
\(281\) | −15.0623 | −0.898539 | −0.449269 | − | 0.893396i | \(-0.648316\pi\) | ||||
−0.449269 | + | 0.893396i | \(0.648316\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.0000 | −0.713326 | −0.356663 | − | 0.934233i | \(-0.616086\pi\) | ||||
−0.356663 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(284\) | 12.5311 | 0.743586 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 39.1868 | 2.31716 | ||||||||
\(287\) | 32.0000 | 1.88890 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.53113 | −0.499247 | ||||||||
\(293\) | 14.0000 | 0.817889 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.06226 | 0.527625 | ||||||||
\(296\) | 7.06226 | 0.410485 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.5311 | −1.07348 | ||||||||
\(299\) | −39.1868 | −2.26623 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.6556 | 2.22807 | ||||||||
\(302\) | −14.1245 | −0.812775 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.53113 | 0.259878 | ||||||||
\(305\) | 5.06226 | 0.289864 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −30.1245 | −1.71930 | −0.859648 | − | 0.510886i | \(-0.829317\pi\) | ||||
−0.859648 | + | 0.510886i | \(0.829317\pi\) | |||||||
\(308\) | 29.5934 | 1.68624 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.00000 | −0.0567962 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.9377 | 0.618238 | 0.309119 | − | 0.951023i | \(-0.399966\pi\) | ||||
0.309119 | + | 0.951023i | \(0.399966\pi\) | |||||||
\(314\) | 22.5311 | 1.27151 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.53113 | −0.479913 | ||||||||
\(317\) | −12.9377 | −0.726656 | −0.363328 | − | 0.931661i | \(-0.618360\pi\) | ||||
−0.363328 | + | 0.931661i | \(0.618360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −29.5934 | −1.64917 | ||||||||
\(323\) | 18.1245 | 1.00848 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00000 | 0.332820 | ||||||||
\(326\) | −5.06226 | −0.280373 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.06226 | 0.389948 | ||||||||
\(329\) | −22.9377 | −1.26460 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.9377 | 0.711123 | 0.355561 | − | 0.934653i | \(-0.384290\pi\) | ||||
0.355561 | + | 0.934653i | \(0.384290\pi\) | |||||||
\(332\) | 8.00000 | 0.439057 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −23.5934 | −1.29097 | ||||||||
\(335\) | 5.06226 | 0.276581 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19.1868 | −1.04517 | −0.522585 | − | 0.852587i | \(-0.675032\pi\) | ||||
−0.522585 | + | 0.852587i | \(0.675032\pi\) | |||||||
\(338\) | −23.0000 | −1.25104 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | −6.53113 | −0.353680 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −29.5934 | −1.59789 | ||||||||
\(344\) | 8.53113 | 0.459968 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.0000 | 0.752645 | ||||||||
\(347\) | −10.1245 | −0.543512 | −0.271756 | − | 0.962366i | \(-0.587604\pi\) | ||||
−0.271756 | + | 0.962366i | \(0.587604\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.93774 | 0.478426 | 0.239213 | − | 0.970967i | \(-0.423111\pi\) | ||||
0.239213 | + | 0.970967i | \(0.423111\pi\) | |||||||
\(350\) | 4.53113 | 0.242199 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.53113 | 0.348110 | ||||||||
\(353\) | 6.93774 | 0.369259 | 0.184629 | − | 0.982808i | \(-0.440892\pi\) | ||||
0.184629 | + | 0.982808i | \(0.440892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.5311 | 0.665083 | ||||||||
\(356\) | 6.53113 | 0.346149 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.06226 | −0.161845 | ||||||||
\(359\) | −3.46887 | −0.183080 | −0.0915400 | − | 0.995801i | \(-0.529179\pi\) | ||||
−0.0915400 | + | 0.995801i | \(0.529179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.53113 | 0.0805857 | ||||||||
\(362\) | −2.40661 | −0.126489 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −27.1868 | −1.42497 | ||||||||
\(365\) | −8.53113 | −0.446540 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.0000 | −0.521996 | −0.260998 | − | 0.965339i | \(-0.584052\pi\) | ||||
−0.260998 | + | 0.965339i | \(0.584052\pi\) | |||||||
\(368\) | −6.53113 | −0.340459 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.06226 | 0.367149 | ||||||||
\(371\) | −11.4689 | −0.595434 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.5311 | −0.959505 | −0.479753 | − | 0.877404i | \(-0.659274\pi\) | ||||
−0.479753 | + | 0.877404i | \(0.659274\pi\) | |||||||
\(374\) | 26.1245 | 1.35087 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.06226 | −0.261066 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.5934 | 1.10918 | 0.554589 | − | 0.832124i | \(-0.312876\pi\) | ||||
0.554589 | + | 0.832124i | \(0.312876\pi\) | |||||||
\(380\) | 4.53113 | 0.232442 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.00000 | −0.409316 | ||||||||
\(383\) | 3.06226 | 0.156474 | 0.0782370 | − | 0.996935i | \(-0.475071\pi\) | ||||
0.0782370 | + | 0.996935i | \(0.475071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29.5934 | 1.50822 | ||||||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.1245 | 0.818598 | ||||||||
\(389\) | −10.9377 | −0.554566 | −0.277283 | − | 0.960788i | \(-0.589434\pi\) | ||||
−0.277283 | + | 0.960788i | \(0.589434\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −26.1245 | −1.32117 | ||||||||
\(392\) | −13.5311 | −0.683425 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | −8.53113 | −0.429248 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.7179 | 1.89301 | 0.946504 | − | 0.322693i | \(-0.104588\pi\) | ||||
0.946504 | + | 0.322693i | \(0.104588\pi\) | |||||||
\(398\) | 8.53113 | 0.427627 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −21.7179 | −1.08454 | −0.542270 | − | 0.840204i | \(-0.682435\pi\) | ||||
−0.542270 | + | 0.840204i | \(0.682435\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.00000 | 0.298881 | ||||||||
\(404\) | 9.46887 | 0.471094 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 46.1245 | 2.28631 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.06226 | 0.349206 | 0.174603 | − | 0.984639i | \(-0.444136\pi\) | ||||
0.174603 | + | 0.984639i | \(0.444136\pi\) | |||||||
\(410\) | 7.06226 | 0.348780 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −41.0623 | −2.02054 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | −6.00000 | −0.294174 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 29.5934 | 1.44746 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.2490 | −1.27930 | −0.639650 | − | 0.768667i | \(-0.720921\pi\) | ||||
−0.639650 | + | 0.768667i | \(0.720921\pi\) | |||||||
\(422\) | 1.59339 | 0.0775648 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.53113 | −0.122922 | ||||||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.9377 | −1.11004 | ||||||||
\(428\) | −9.59339 | −0.463714 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.53113 | 0.411408 | ||||||||
\(431\) | 24.0000 | 1.15604 | 0.578020 | − | 0.816023i | \(-0.303826\pi\) | ||||
0.578020 | + | 0.816023i | \(0.303826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.5934 | −1.22994 | −0.614970 | − | 0.788551i | \(-0.710832\pi\) | ||||
−0.614970 | + | 0.788551i | \(0.710832\pi\) | |||||||
\(434\) | 4.53113 | 0.217501 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.0623 | 0.721351 | ||||||||
\(437\) | −29.5934 | −1.41564 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.0623 | −1.19616 | −0.598078 | − | 0.801438i | \(-0.704069\pi\) | ||||
−0.598078 | + | 0.801438i | \(0.704069\pi\) | |||||||
\(440\) | 6.53113 | 0.311359 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.0000 | −1.14156 | ||||||||
\(443\) | −14.4066 | −0.684479 | −0.342239 | − | 0.939613i | \(-0.611185\pi\) | ||||
−0.342239 | + | 0.939613i | \(0.611185\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.53113 | 0.309605 | ||||||||
\(446\) | −2.00000 | −0.0947027 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.53113 | −0.214076 | ||||||||
\(449\) | 4.12452 | 0.194648 | 0.0973240 | − | 0.995253i | \(-0.468972\pi\) | ||||
0.0973240 | + | 0.995253i | \(0.468972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 46.1245 | 2.17192 | ||||||||
\(452\) | 7.59339 | 0.357163 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −24.5311 | −1.15130 | ||||||||
\(455\) | −27.1868 | −1.27454 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.9377 | 0.698758 | 0.349379 | − | 0.936981i | \(-0.386393\pi\) | ||||
0.349379 | + | 0.936981i | \(0.386393\pi\) | |||||||
\(458\) | 5.59339 | 0.261362 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.53113 | −0.304515 | ||||||||
\(461\) | −24.0000 | −1.11779 | −0.558896 | − | 0.829238i | \(-0.688775\pi\) | ||||
−0.558896 | + | 0.829238i | \(0.688775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.1868 | 0.612841 | 0.306421 | − | 0.951896i | \(-0.400869\pi\) | ||||
0.306421 | + | 0.951896i | \(0.400869\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.46887 | 0.0680441 | ||||||||
\(467\) | 22.1245 | 1.02380 | 0.511900 | − | 0.859045i | \(-0.328942\pi\) | ||||
0.511900 | + | 0.859045i | \(0.328942\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.9377 | −1.05917 | ||||||||
\(470\) | −5.06226 | −0.233505 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.06226 | −0.417124 | ||||||||
\(473\) | 55.7179 | 2.56191 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.53113 | 0.207902 | ||||||||
\(476\) | −18.1245 | −0.830736 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.00000 | −0.365911 | ||||||||
\(479\) | −1.34436 | −0.0614252 | −0.0307126 | − | 0.999528i | \(-0.509778\pi\) | ||||
−0.0307126 | + | 0.999528i | \(0.509778\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.3735 | −1.93207 | ||||||||
\(482\) | −2.00000 | −0.0910975 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 31.6556 | 1.43889 | ||||||||
\(485\) | 16.1245 | 0.732177 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.0623 | 1.04505 | 0.522525 | − | 0.852624i | \(-0.324990\pi\) | ||||
0.522525 | + | 0.852624i | \(0.324990\pi\) | |||||||
\(488\) | −5.06226 | −0.229158 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.5311 | −0.611274 | ||||||||
\(491\) | 7.59339 | 0.342685 | 0.171342 | − | 0.985212i | \(-0.445190\pi\) | ||||
0.171342 | + | 0.985212i | \(0.445190\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −27.1868 | −1.22319 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | −56.7802 | −2.54694 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.06226 | −0.316150 | −0.158075 | − | 0.987427i | \(-0.550529\pi\) | ||||
−0.158075 | + | 0.987427i | \(0.550529\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.06226 | 0.136675 | ||||||||
\(503\) | −16.0000 | −0.713405 | −0.356702 | − | 0.934218i | \(-0.616099\pi\) | ||||
−0.356702 | + | 0.934218i | \(0.616099\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.46887 | 0.421359 | ||||||||
\(506\) | −42.6556 | −1.89627 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.06226 | 0.313337 | ||||||||
\(509\) | −38.1245 | −1.68984 | −0.844920 | − | 0.534893i | \(-0.820352\pi\) | ||||
−0.844920 | + | 0.534893i | \(0.820352\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.6556 | 1.71003 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.6556 | 0.558217 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.0623 | −1.45408 | ||||||||
\(518\) | −32.0000 | −1.40600 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.00000 | −0.263117 | ||||||||
\(521\) | 12.1245 | 0.531185 | 0.265592 | − | 0.964085i | \(-0.414432\pi\) | ||||
0.265592 | + | 0.964085i | \(0.414432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.59339 | 0.419490 | 0.209745 | − | 0.977756i | \(-0.432737\pi\) | ||||
0.209745 | + | 0.977756i | \(0.432737\pi\) | |||||||
\(524\) | 9.06226 | 0.395887 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.0623 | −1.00556 | ||||||||
\(527\) | 4.00000 | 0.174243 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.6556 | 0.854593 | ||||||||
\(530\) | −2.53113 | −0.109945 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −20.5311 | −0.890137 | ||||||||
\(533\) | −42.3735 | −1.83540 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.59339 | −0.414758 | ||||||||
\(536\) | −5.06226 | −0.218656 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19.1868 | −0.827201 | ||||||||
\(539\) | −88.3735 | −3.80652 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.12452 | −0.177327 | −0.0886634 | − | 0.996062i | \(-0.528260\pi\) | ||||
−0.0886634 | + | 0.996062i | \(0.528260\pi\) | |||||||
\(542\) | 11.4689 | 0.492630 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | 15.0623 | 0.645196 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.18677 | −0.307284 | −0.153642 | − | 0.988127i | \(-0.549100\pi\) | ||||
−0.153642 | + | 0.988127i | \(0.549100\pi\) | |||||||
\(548\) | −17.0623 | −0.728864 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.53113 | 0.278488 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 38.6556 | 1.64381 | ||||||||
\(554\) | 15.0623 | 0.639934 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.00000 | 0.254457 | ||||||||
\(557\) | 26.7802 | 1.13471 | 0.567356 | − | 0.823473i | \(-0.307966\pi\) | ||||
0.567356 | + | 0.823473i | \(0.307966\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −51.1868 | −2.16497 | ||||||||
\(560\) | −4.53113 | −0.191475 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.0623 | 0.635363 | ||||||||
\(563\) | 4.00000 | 0.168580 | 0.0842900 | − | 0.996441i | \(-0.473138\pi\) | ||||
0.0842900 | + | 0.996441i | \(0.473138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.59339 | 0.319456 | ||||||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.5311 | −0.525794 | ||||||||
\(569\) | −9.46887 | −0.396956 | −0.198478 | − | 0.980105i | \(-0.563600\pi\) | ||||
−0.198478 | + | 0.980105i | \(0.563600\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.1245 | 1.51176 | 0.755882 | − | 0.654708i | \(-0.227208\pi\) | ||||
0.755882 | + | 0.654708i | \(0.227208\pi\) | |||||||
\(572\) | −39.1868 | −1.63848 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −32.0000 | −1.33565 | ||||||||
\(575\) | −6.53113 | −0.272367 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.1868 | 1.54811 | 0.774053 | − | 0.633121i | \(-0.218226\pi\) | ||||
0.774053 | + | 0.633121i | \(0.218226\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −36.2490 | −1.50386 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −16.5311 | −0.684649 | ||||||||
\(584\) | 8.53113 | 0.353021 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | 44.2490 | 1.82635 | 0.913176 | − | 0.407564i | \(-0.133622\pi\) | ||||
0.913176 | + | 0.407564i | \(0.133622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.53113 | 0.186702 | ||||||||
\(590\) | −9.06226 | −0.373087 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.06226 | −0.290257 | ||||||||
\(593\) | 14.0000 | 0.574911 | 0.287456 | − | 0.957794i | \(-0.407191\pi\) | ||||
0.287456 | + | 0.957794i | \(0.407191\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −18.1245 | −0.743033 | ||||||||
\(596\) | 18.5311 | 0.759065 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 39.1868 | 1.60247 | ||||||||
\(599\) | 13.5934 | 0.555411 | 0.277705 | − | 0.960666i | \(-0.410426\pi\) | ||||
0.277705 | + | 0.960666i | \(0.410426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.0000 | 1.22373 | 0.611863 | − | 0.790964i | \(-0.290420\pi\) | ||||
0.611863 | + | 0.790964i | \(0.290420\pi\) | |||||||
\(602\) | −38.6556 | −1.57549 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.1245 | 0.574718 | ||||||||
\(605\) | 31.6556 | 1.28698 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.4066 | −0.584746 | −0.292373 | − | 0.956304i | \(-0.594445\pi\) | ||||
−0.292373 | + | 0.956304i | \(0.594445\pi\) | |||||||
\(608\) | −4.53113 | −0.183762 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.06226 | −0.204965 | ||||||||
\(611\) | 30.3735 | 1.22878 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.0000 | −1.21169 | −0.605844 | − | 0.795583i | \(-0.707165\pi\) | ||||
−0.605844 | + | 0.795583i | \(0.707165\pi\) | |||||||
\(614\) | 30.1245 | 1.21573 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −29.5934 | −1.19235 | ||||||||
\(617\) | 3.59339 | 0.144664 | 0.0723321 | − | 0.997381i | \(-0.476956\pi\) | ||||
0.0723321 | + | 0.997381i | \(0.476956\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.0000 | −1.36658 | −0.683288 | − | 0.730149i | \(-0.739451\pi\) | ||||
−0.683288 | + | 0.730149i | \(0.739451\pi\) | |||||||
\(620\) | 1.00000 | 0.0401610 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.00000 | −0.320771 | ||||||||
\(623\) | −29.5934 | −1.18563 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.9377 | −0.437160 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.5311 | −0.899090 | ||||||||
\(629\) | −28.2490 | −1.12636 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.6556 | 1.22038 | 0.610191 | − | 0.792254i | \(-0.291093\pi\) | ||||
0.610191 | + | 0.792254i | \(0.291093\pi\) | |||||||
\(632\) | 8.53113 | 0.339350 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.9377 | 0.513823 | ||||||||
\(635\) | 7.06226 | 0.280257 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 81.1868 | 3.21674 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 22.0000 | 0.868948 | 0.434474 | − | 0.900684i | \(-0.356934\pi\) | ||||
0.434474 | + | 0.900684i | \(0.356934\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.5934 | −0.693815 | −0.346908 | − | 0.937899i | \(-0.612768\pi\) | ||||
−0.346908 | + | 0.937899i | \(0.612768\pi\) | |||||||
\(644\) | 29.5934 | 1.16614 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.1245 | −0.713100 | ||||||||
\(647\) | 6.53113 | 0.256765 | 0.128383 | − | 0.991725i | \(-0.459021\pi\) | ||||
0.128383 | + | 0.991725i | \(0.459021\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −59.1868 | −2.32328 | ||||||||
\(650\) | −6.00000 | −0.235339 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.06226 | 0.198253 | ||||||||
\(653\) | −38.2490 | −1.49680 | −0.748400 | − | 0.663248i | \(-0.769178\pi\) | ||||
−0.748400 | + | 0.663248i | \(0.769178\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.06226 | 0.354092 | ||||||||
\(656\) | −7.06226 | −0.275735 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 22.9377 | 0.894206 | ||||||||
\(659\) | −16.0000 | −0.623272 | −0.311636 | − | 0.950202i | \(-0.600877\pi\) | ||||
−0.311636 | + | 0.950202i | \(0.600877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0000 | −0.388955 | −0.194477 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194477 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(662\) | −12.9377 | −0.502840 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | −20.5311 | −0.796163 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 23.5934 | 0.912856 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.06226 | −0.195572 | ||||||||
\(671\) | −33.0623 | −1.27635 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.06226 | −0.349324 | −0.174662 | − | 0.984628i | \(-0.555883\pi\) | ||||
−0.174662 | + | 0.984628i | \(0.555883\pi\) | |||||||
\(674\) | 19.1868 | 0.739047 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | −27.5934 | −1.06050 | −0.530250 | − | 0.847841i | \(-0.677902\pi\) | ||||
−0.530250 | + | 0.847841i | \(0.677902\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −73.0623 | −2.80387 | ||||||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.53113 | 0.250090 | ||||||||
\(683\) | −7.46887 | −0.285788 | −0.142894 | − | 0.989738i | \(-0.545641\pi\) | ||||
−0.142894 | + | 0.989738i | \(0.545641\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.0623 | −0.651915 | ||||||||
\(686\) | 29.5934 | 1.12988 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.53113 | −0.325246 | ||||||||
\(689\) | 15.1868 | 0.578570 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.531129 | 0.0202051 | 0.0101025 | − | 0.999949i | \(-0.496784\pi\) | ||||
0.0101025 | + | 0.999949i | \(0.496784\pi\) | |||||||
\(692\) | −14.0000 | −0.532200 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.1245 | 0.384321 | ||||||||
\(695\) | 6.00000 | 0.227593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.2490 | −1.07001 | ||||||||
\(698\) | −8.93774 | −0.338299 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.53113 | −0.171261 | ||||||||
\(701\) | 13.4689 | 0.508712 | 0.254356 | − | 0.967111i | \(-0.418136\pi\) | ||||
0.254356 | + | 0.967111i | \(0.418136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.0000 | −1.20690 | ||||||||
\(704\) | −6.53113 | −0.246151 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.93774 | −0.261105 | ||||||||
\(707\) | −42.9047 | −1.61360 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.5934 | 1.86252 | 0.931259 | − | 0.364357i | \(-0.118711\pi\) | ||||
0.931259 | + | 0.364357i | \(0.118711\pi\) | |||||||
\(710\) | −12.5311 | −0.470285 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.53113 | −0.244764 | ||||||||
\(713\) | −6.53113 | −0.244593 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −39.1868 | −1.46550 | ||||||||
\(716\) | 3.06226 | 0.114442 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.46887 | 0.129457 | ||||||||
\(719\) | −15.1868 | −0.566371 | −0.283186 | − | 0.959065i | \(-0.591391\pi\) | ||||
−0.283186 | + | 0.959065i | \(0.591391\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.53113 | −0.0569827 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.40661 | 0.0894411 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.8424 | 1.40350 | 0.701749 | − | 0.712424i | \(-0.252403\pi\) | ||||
0.701749 | + | 0.712424i | \(0.252403\pi\) | |||||||
\(728\) | 27.1868 | 1.00761 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.53113 | 0.315751 | ||||||||
\(731\) | −34.1245 | −1.26214 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.1245 | −1.03880 | −0.519401 | − | 0.854530i | \(-0.673845\pi\) | ||||
−0.519401 | + | 0.854530i | \(0.673845\pi\) | |||||||
\(734\) | 10.0000 | 0.369107 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.53113 | 0.240741 | ||||||||
\(737\) | −33.0623 | −1.21786 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.1868 | −0.779368 | −0.389684 | − | 0.920949i | \(-0.627416\pi\) | ||||
−0.389684 | + | 0.920949i | \(0.627416\pi\) | |||||||
\(740\) | −7.06226 | −0.259614 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.4689 | 0.421036 | ||||||||
\(743\) | 28.6556 | 1.05127 | 0.525637 | − | 0.850709i | \(-0.323827\pi\) | ||||
0.525637 | + | 0.850709i | \(0.323827\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.5311 | 0.678928 | ||||||||
\(746\) | 18.5311 | 0.678473 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −26.1245 | −0.955207 | ||||||||
\(749\) | 43.4689 | 1.58832 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.9377 | 1.12893 | 0.564467 | − | 0.825456i | \(-0.309082\pi\) | ||||
0.564467 | + | 0.825456i | \(0.309082\pi\) | |||||||
\(752\) | 5.06226 | 0.184602 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.1245 | 0.514044 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | −21.5934 | −0.784307 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.53113 | −0.164361 | ||||||||
\(761\) | −11.5934 | −0.420260 | −0.210130 | − | 0.977673i | \(-0.567389\pi\) | ||||
−0.210130 | + | 0.977673i | \(0.567389\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −68.2490 | −2.47078 | ||||||||
\(764\) | 8.00000 | 0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.06226 | −0.110644 | ||||||||
\(767\) | 54.3735 | 1.96331 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.40661 | −0.158907 | −0.0794533 | − | 0.996839i | \(-0.525317\pi\) | ||||
−0.0794533 | + | 0.996839i | \(0.525317\pi\) | |||||||
\(770\) | −29.5934 | −1.06647 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | −22.5311 | −0.810388 | −0.405194 | − | 0.914231i | \(-0.632796\pi\) | ||||
−0.405194 | + | 0.914231i | \(0.632796\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | −16.1245 | −0.578836 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.9377 | 0.392137 | ||||||||
\(779\) | −32.0000 | −1.14652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −81.8424 | −2.92855 | ||||||||
\(782\) | 26.1245 | 0.934211 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.5311 | 0.483255 | ||||||||
\(785\) | −22.5311 | −0.804170 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36.5311 | −1.30219 | −0.651097 | − | 0.758994i | \(-0.725691\pi\) | ||||
−0.651097 | + | 0.758994i | \(0.725691\pi\) | |||||||
\(788\) | −6.00000 | −0.213741 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.53113 | 0.303524 | ||||||||
\(791\) | −34.4066 | −1.22336 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.3735 | 1.07860 | ||||||||
\(794\) | −37.7179 | −1.33856 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.53113 | −0.302378 | ||||||||
\(797\) | −12.1245 | −0.429472 | −0.214736 | − | 0.976672i | \(-0.568889\pi\) | ||||
−0.214736 | + | 0.976672i | \(0.568889\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.2490 | 0.716359 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.7179 | 0.766886 | ||||||||
\(803\) | 55.7179 | 1.96624 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29.5934 | 1.04303 | ||||||||
\(806\) | −6.00000 | −0.211341 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.46887 | −0.333114 | ||||||||
\(809\) | −15.5934 | −0.548234 | −0.274117 | − | 0.961696i | \(-0.588386\pi\) | ||||
−0.274117 | + | 0.961696i | \(0.588386\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.7802 | 1.15107 | 0.575534 | − | 0.817778i | \(-0.304794\pi\) | ||||
0.575534 | + | 0.817778i | \(0.304794\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −46.1245 | −1.61666 | ||||||||
\(815\) | 5.06226 | 0.177323 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38.6556 | −1.35239 | ||||||||
\(818\) | −7.06226 | −0.246926 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.06226 | −0.246625 | ||||||||
\(821\) | −42.1245 | −1.47016 | −0.735078 | − | 0.677983i | \(-0.762854\pi\) | ||||
−0.735078 | + | 0.677983i | \(0.762854\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.1245 | 1.39865 | 0.699326 | − | 0.714803i | \(-0.253483\pi\) | ||||
0.699326 | + | 0.714803i | \(0.253483\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 41.0623 | 1.42874 | ||||||||
\(827\) | −8.00000 | −0.278187 | −0.139094 | − | 0.990279i | \(-0.544419\pi\) | ||||
−0.139094 | + | 0.990279i | \(0.544419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.6556 | 1.06471 | 0.532357 | − | 0.846520i | \(-0.321306\pi\) | ||||
0.532357 | + | 0.846520i | \(0.321306\pi\) | |||||||
\(830\) | −8.00000 | −0.277684 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.00000 | 0.208013 | ||||||||
\(833\) | 54.1245 | 1.87530 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.5934 | 0.816483 | ||||||||
\(836\) | −29.5934 | −1.02351 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.8424 | −1.16837 | −0.584185 | − | 0.811621i | \(-0.698586\pi\) | ||||
−0.584185 | + | 0.811621i | \(0.698586\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 26.2490 | 0.904601 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.59339 | −0.0548466 | ||||||||
\(845\) | 23.0000 | 0.791224 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −143.436 | −4.92851 | ||||||||
\(848\) | 2.53113 | 0.0869193 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.00000 | −0.137199 | ||||||||
\(851\) | 46.1245 | 1.58113 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 57.7179 | 1.97622 | 0.988112 | − | 0.153738i | \(-0.0491311\pi\) | ||||
0.988112 | + | 0.153738i | \(0.0491311\pi\) | |||||||
\(854\) | 22.9377 | 0.784913 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.59339 | 0.327895 | ||||||||
\(857\) | −14.0000 | −0.478231 | −0.239115 | − | 0.970991i | \(-0.576857\pi\) | ||||
−0.239115 | + | 0.970991i | \(0.576857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.0623 | −0.786874 | −0.393437 | − | 0.919352i | \(-0.628714\pi\) | ||||
−0.393437 | + | 0.919352i | \(0.628714\pi\) | |||||||
\(860\) | −8.53113 | −0.290909 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.0000 | −0.817443 | ||||||||
\(863\) | −33.4689 | −1.13929 | −0.569647 | − | 0.821890i | \(-0.692920\pi\) | ||||
−0.569647 | + | 0.821890i | \(0.692920\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.0000 | −0.476014 | ||||||||
\(866\) | 25.5934 | 0.869699 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.53113 | −0.153797 | ||||||||
\(869\) | 55.7179 | 1.89010 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.3735 | 1.02917 | ||||||||
\(872\) | −15.0623 | −0.510072 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.5934 | 1.00101 | ||||||||
\(875\) | −4.53113 | −0.153180 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.8755 | 0.401007 | 0.200503 | − | 0.979693i | \(-0.435742\pi\) | ||||
0.200503 | + | 0.979693i | \(0.435742\pi\) | |||||||
\(878\) | 25.0623 | 0.845810 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.53113 | −0.220164 | ||||||||
\(881\) | −3.87548 | −0.130568 | −0.0652842 | − | 0.997867i | \(-0.520795\pi\) | ||||
−0.0652842 | + | 0.997867i | \(0.520795\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.3444 | −0.449073 | −0.224537 | − | 0.974466i | \(-0.572087\pi\) | ||||
−0.224537 | + | 0.974466i | \(0.572087\pi\) | |||||||
\(884\) | 24.0000 | 0.807207 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.4066 | 0.484000 | ||||||||
\(887\) | −23.1868 | −0.778536 | −0.389268 | − | 0.921125i | \(-0.627272\pi\) | ||||
−0.389268 | + | 0.921125i | \(0.627272\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −32.0000 | −1.07325 | ||||||||
\(890\) | −6.53113 | −0.218924 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.00000 | 0.0669650 | ||||||||
\(893\) | 22.9377 | 0.767582 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.06226 | 0.102360 | ||||||||
\(896\) | 4.53113 | 0.151374 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.12452 | −0.137637 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.1245 | 0.337297 | ||||||||
\(902\) | −46.1245 | −1.53578 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.59339 | −0.252552 | ||||||||
\(905\) | 2.40661 | 0.0799985 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.2490 | 1.07081 | 0.535406 | − | 0.844595i | \(-0.320159\pi\) | ||||
0.535406 | + | 0.844595i | \(0.320159\pi\) | |||||||
\(908\) | 24.5311 | 0.814094 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 27.1868 | 0.901233 | ||||||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.2490 | −1.72919 | ||||||||
\(914\) | −14.9377 | −0.494097 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.59339 | −0.184811 | ||||||||
\(917\) | −41.0623 | −1.35600 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0623 | −0.826728 | −0.413364 | − | 0.910566i | \(-0.635646\pi\) | ||||
−0.413364 | + | 0.910566i | \(0.635646\pi\) | |||||||
\(920\) | 6.53113 | 0.215325 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 24.0000 | 0.790398 | ||||||||
\(923\) | 75.1868 | 2.47480 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.06226 | −0.232206 | ||||||||
\(926\) | −13.1868 | −0.433344 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51.8424 | 1.70089 | 0.850447 | − | 0.526060i | \(-0.176331\pi\) | ||||
0.850447 | + | 0.526060i | \(0.176331\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 61.3113 | 2.00940 | ||||||||
\(932\) | −1.46887 | −0.0481145 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.1245 | −0.723936 | ||||||||
\(935\) | −26.1245 | −0.854363 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.93774 | −0.291983 | −0.145992 | − | 0.989286i | \(-0.546637\pi\) | ||||
−0.145992 | + | 0.989286i | \(0.546637\pi\) | |||||||
\(938\) | 22.9377 | 0.748944 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.06226 | 0.165113 | ||||||||
\(941\) | 54.1245 | 1.76441 | 0.882204 | − | 0.470867i | \(-0.156059\pi\) | ||||
0.882204 | + | 0.470867i | \(0.156059\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.1245 | 1.50202 | ||||||||
\(944\) | 9.06226 | 0.294951 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −55.7179 | −1.81155 | ||||||||
\(947\) | −18.9377 | −0.615394 | −0.307697 | − | 0.951484i | \(-0.599558\pi\) | ||||
−0.307697 | + | 0.951484i | \(0.599558\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −51.1868 | −1.66159 | ||||||||
\(950\) | −4.53113 | −0.147009 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.1245 | 0.587419 | ||||||||
\(953\) | −21.8755 | −0.708616 | −0.354308 | − | 0.935129i | \(-0.615284\pi\) | ||||
−0.354308 | + | 0.935129i | \(0.615284\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | 0.258874 | ||||||||
\(956\) | 8.00000 | 0.258738 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.34436 | 0.0434342 | ||||||||
\(959\) | 77.3113 | 2.49651 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 42.3735 | 1.36618 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.00000 | 0.0644157 | ||||||||
\(965\) | 14.0000 | 0.450676 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.937742 | −0.0301558 | −0.0150779 | − | 0.999886i | \(-0.504800\pi\) | ||||
−0.0150779 | + | 0.999886i | \(0.504800\pi\) | |||||||
\(968\) | −31.6556 | −1.01745 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −16.1245 | −0.517727 | ||||||||
\(971\) | −15.1868 | −0.487367 | −0.243683 | − | 0.969855i | \(-0.578356\pi\) | ||||
−0.243683 | + | 0.969855i | \(0.578356\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.1868 | −0.871568 | ||||||||
\(974\) | −23.0623 | −0.738962 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.06226 | 0.162039 | ||||||||
\(977\) | 38.0000 | 1.21573 | 0.607864 | − | 0.794041i | \(-0.292027\pi\) | ||||
0.607864 | + | 0.794041i | \(0.292027\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.6556 | −1.36328 | ||||||||
\(980\) | 13.5311 | 0.432236 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.59339 | −0.242315 | ||||||||
\(983\) | −0.937742 | −0.0299093 | −0.0149547 | − | 0.999888i | \(-0.504760\pi\) | ||||
−0.0149547 | + | 0.999888i | \(0.504760\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00000 | −0.191176 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 27.1868 | 0.864926 | ||||||||
\(989\) | 55.7179 | 1.77173 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.5311 | −1.03339 | −0.516693 | − | 0.856171i | \(-0.672837\pi\) | ||||
−0.516693 | + | 0.856171i | \(0.672837\pi\) | |||||||
\(992\) | −1.00000 | −0.0317500 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 56.7802 | 1.80096 | ||||||||
\(995\) | −8.53113 | −0.270455 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.24903 | −0.0712275 | −0.0356138 | − | 0.999366i | \(-0.511339\pi\) | ||||
−0.0356138 | + | 0.999366i | \(0.511339\pi\) | |||||||
\(998\) | 7.06226 | 0.223552 | ||||||||
\(999\) | 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.bf.1.1 | 2 | ||
3.2 | odd | 2 | 930.2.a.q.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 7440.2.a.bd.1.2 | 2 | |||
15.2 | even | 4 | 4650.2.d.bg.3349.3 | 4 | |||
15.8 | even | 4 | 4650.2.d.bg.3349.2 | 4 | |||
15.14 | odd | 2 | 4650.2.a.bz.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.a.q.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
2790.2.a.bf.1.1 | 2 | 1.1 | even | 1 | trivial | ||
4650.2.a.bz.1.2 | 2 | 15.14 | odd | 2 | |||
4650.2.d.bg.3349.2 | 4 | 15.8 | even | 4 | |||
4650.2.d.bg.3349.3 | 4 | 15.2 | even | 4 | |||
7440.2.a.bd.1.2 | 2 | 12.11 | even | 2 |