Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(1,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, 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("930.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.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: | \(7.42608738798\) |
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: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.53113\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −4.53113 | −1.71261 | −0.856303 | − | 0.516474i | \(-0.827244\pi\) | ||||
−0.856303 | + | 0.516474i | \(0.827244\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 6.53113 | 1.96921 | 0.984605 | − | 0.174796i | \(-0.0559265\pi\) | ||||
0.984605 | + | 0.174796i | \(0.0559265\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 6.00000 | 1.66410 | 0.832050 | − | 0.554700i | \(-0.187167\pi\) | ||||
0.832050 | + | 0.554700i | \(0.187167\pi\) | |||||||
\(14\) | −4.53113 | −1.21100 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.53113 | 1.03951 | 0.519756 | − | 0.854315i | \(-0.326023\pi\) | ||||
0.519756 | + | 0.854315i | \(0.326023\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −4.53113 | −0.988773 | ||||||||
\(22\) | 6.53113 | 1.39244 | ||||||||
\(23\) | 6.53113 | 1.36183 | 0.680917 | − | 0.732360i | \(-0.261581\pi\) | ||||
0.680917 | + | 0.732360i | \(0.261581\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.00000 | 1.17670 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.53113 | −0.856303 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.53113 | 1.13692 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 4.53113 | 0.765901 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.06226 | −1.16103 | −0.580514 | − | 0.814250i | \(-0.697148\pi\) | ||||
−0.580514 | + | 0.814250i | \(0.697148\pi\) | |||||||
\(38\) | 4.53113 | 0.735046 | ||||||||
\(39\) | 6.00000 | 0.960769 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 7.06226 | 1.10294 | 0.551470 | − | 0.834195i | \(-0.314067\pi\) | ||||
0.551470 | + | 0.834195i | \(0.314067\pi\) | |||||||
\(42\) | −4.53113 | −0.699168 | ||||||||
\(43\) | −8.53113 | −1.30098 | −0.650492 | − | 0.759513i | \(-0.725437\pi\) | ||||
−0.650492 | + | 0.759513i | \(0.725437\pi\) | |||||||
\(44\) | 6.53113 | 0.984605 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 6.53113 | 0.962962 | ||||||||
\(47\) | −5.06226 | −0.738406 | −0.369203 | − | 0.929349i | \(-0.620369\pi\) | ||||
−0.369203 | + | 0.929349i | \(0.620369\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 13.5311 | 1.93302 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 6.00000 | 0.832050 | ||||||||
\(53\) | −2.53113 | −0.347677 | −0.173839 | − | 0.984774i | \(-0.555617\pi\) | ||||
−0.173839 | + | 0.984774i | \(0.555617\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −6.53113 | −0.880657 | ||||||||
\(56\) | −4.53113 | −0.605498 | ||||||||
\(57\) | 4.53113 | 0.600163 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.06226 | −1.17981 | −0.589903 | − | 0.807474i | \(-0.700834\pi\) | ||||
−0.589903 | + | 0.807474i | \(0.700834\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | 5.06226 | 0.648156 | 0.324078 | − | 0.946030i | \(-0.394946\pi\) | ||||
0.324078 | + | 0.946030i | \(0.394946\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | −4.53113 | −0.570869 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.00000 | −0.744208 | ||||||||
\(66\) | 6.53113 | 0.803926 | ||||||||
\(67\) | 5.06226 | 0.618453 | 0.309227 | − | 0.950988i | \(-0.399930\pi\) | ||||
0.309227 | + | 0.950988i | \(0.399930\pi\) | |||||||
\(68\) | −4.00000 | −0.485071 | ||||||||
\(69\) | 6.53113 | 0.786256 | ||||||||
\(70\) | 4.53113 | 0.541573 | ||||||||
\(71\) | −12.5311 | −1.48717 | −0.743586 | − | 0.668641i | \(-0.766876\pi\) | ||||
−0.743586 | + | 0.668641i | \(0.766876\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −8.53113 | −0.998493 | −0.499247 | − | 0.866460i | \(-0.666390\pi\) | ||||
−0.499247 | + | 0.866460i | \(0.666390\pi\) | |||||||
\(74\) | −7.06226 | −0.820971 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 4.53113 | 0.519756 | ||||||||
\(77\) | −29.5934 | −3.37248 | ||||||||
\(78\) | 6.00000 | 0.679366 | ||||||||
\(79\) | −8.53113 | −0.959827 | −0.479913 | − | 0.877316i | \(-0.659332\pi\) | ||||
−0.479913 | + | 0.877316i | \(0.659332\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.06226 | 0.779896 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | −4.53113 | −0.494387 | ||||||||
\(85\) | 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 | \(-0.612511\pi\) | ||||
−0.346149 | + | 0.938180i | \(0.612511\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | −27.1868 | −2.84995 | ||||||||
\(92\) | 6.53113 | 0.680917 | ||||||||
\(93\) | 1.00000 | 0.103695 | ||||||||
\(94\) | −5.06226 | −0.522132 | ||||||||
\(95\) | −4.53113 | −0.464884 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 16.1245 | 1.63720 | 0.818598 | − | 0.574367i | \(-0.194752\pi\) | ||||
0.818598 | + | 0.574367i | \(0.194752\pi\) | |||||||
\(98\) | 13.5311 | 1.36685 | ||||||||
\(99\) | 6.53113 | 0.656403 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −9.46887 | −0.942188 | −0.471094 | − | 0.882083i | \(-0.656141\pi\) | ||||
−0.471094 | + | 0.882083i | \(0.656141\pi\) | |||||||
\(102\) | −4.00000 | −0.396059 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | 4.53113 | 0.442193 | ||||||||
\(106\) | −2.53113 | −0.245845 | ||||||||
\(107\) | 9.59339 | 0.927428 | 0.463714 | − | 0.885985i | \(-0.346517\pi\) | ||||
0.463714 | + | 0.885985i | \(0.346517\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 15.0623 | 1.44270 | 0.721351 | − | 0.692569i | \(-0.243521\pi\) | ||||
0.721351 | + | 0.692569i | \(0.243521\pi\) | |||||||
\(110\) | −6.53113 | −0.622719 | ||||||||
\(111\) | −7.06226 | −0.670320 | ||||||||
\(112\) | −4.53113 | −0.428151 | ||||||||
\(113\) | −7.59339 | −0.714326 | −0.357163 | − | 0.934042i | \(-0.616256\pi\) | ||||
−0.357163 | + | 0.934042i | \(0.616256\pi\) | |||||||
\(114\) | 4.53113 | 0.424379 | ||||||||
\(115\) | −6.53113 | −0.609031 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.00000 | 0.554700 | ||||||||
\(118\) | −9.06226 | −0.834248 | ||||||||
\(119\) | 18.1245 | 1.66147 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 31.6556 | 2.87779 | ||||||||
\(122\) | 5.06226 | 0.458315 | ||||||||
\(123\) | 7.06226 | 0.636782 | ||||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −4.53113 | −0.403665 | ||||||||
\(127\) | 7.06226 | 0.626674 | 0.313337 | − | 0.949642i | \(-0.398553\pi\) | ||||
0.313337 | + | 0.949642i | \(0.398553\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −8.53113 | −0.751124 | ||||||||
\(130\) | −6.00000 | −0.526235 | ||||||||
\(131\) | −9.06226 | −0.791773 | −0.395887 | − | 0.918299i | \(-0.629563\pi\) | ||||
−0.395887 | + | 0.918299i | \(0.629563\pi\) | |||||||
\(132\) | 6.53113 | 0.568462 | ||||||||
\(133\) | −20.5311 | −1.78027 | ||||||||
\(134\) | 5.06226 | 0.437312 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | 17.0623 | 1.45773 | 0.728864 | − | 0.684659i | \(-0.240049\pi\) | ||||
0.728864 | + | 0.684659i | \(0.240049\pi\) | |||||||
\(138\) | 6.53113 | 0.555967 | ||||||||
\(139\) | 6.00000 | 0.508913 | 0.254457 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254457 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(140\) | 4.53113 | 0.382950 | ||||||||
\(141\) | −5.06226 | −0.426319 | ||||||||
\(142\) | −12.5311 | −1.05159 | ||||||||
\(143\) | 39.1868 | 3.27696 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.53113 | −0.706041 | ||||||||
\(147\) | 13.5311 | 1.11603 | ||||||||
\(148\) | −7.06226 | −0.580514 | ||||||||
\(149\) | −18.5311 | −1.51813 | −0.759065 | − | 0.651015i | \(-0.774343\pi\) | ||||
−0.759065 | + | 0.651015i | \(0.774343\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 14.1245 | 1.14944 | 0.574718 | − | 0.818351i | \(-0.305112\pi\) | ||||
0.574718 | + | 0.818351i | \(0.305112\pi\) | |||||||
\(152\) | 4.53113 | 0.367523 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | −29.5934 | −2.38470 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | 6.00000 | 0.480384 | ||||||||
\(157\) | −22.5311 | −1.79818 | −0.899090 | − | 0.437764i | \(-0.855771\pi\) | ||||
−0.899090 | + | 0.437764i | \(0.855771\pi\) | |||||||
\(158\) | −8.53113 | −0.678700 | ||||||||
\(159\) | −2.53113 | −0.200732 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −29.5934 | −2.33229 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 5.06226 | 0.396507 | 0.198253 | − | 0.980151i | \(-0.436473\pi\) | ||||
0.198253 | + | 0.980151i | \(0.436473\pi\) | |||||||
\(164\) | 7.06226 | 0.551470 | ||||||||
\(165\) | −6.53113 | −0.508448 | ||||||||
\(166\) | −8.00000 | −0.620920 | ||||||||
\(167\) | −23.5934 | −1.82571 | −0.912856 | − | 0.408283i | \(-0.866128\pi\) | ||||
−0.912856 | + | 0.408283i | \(0.866128\pi\) | |||||||
\(168\) | −4.53113 | −0.349584 | ||||||||
\(169\) | 23.0000 | 1.76923 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | 4.53113 | 0.346504 | ||||||||
\(172\) | −8.53113 | −0.650492 | ||||||||
\(173\) | 14.0000 | 1.06440 | 0.532200 | − | 0.846619i | \(-0.321365\pi\) | ||||
0.532200 | + | 0.846619i | \(0.321365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.53113 | −0.342521 | ||||||||
\(176\) | 6.53113 | 0.492302 | ||||||||
\(177\) | −9.06226 | −0.681161 | ||||||||
\(178\) | −6.53113 | −0.489529 | ||||||||
\(179\) | −3.06226 | −0.228884 | −0.114442 | − | 0.993430i | \(-0.536508\pi\) | ||||
−0.114442 | + | 0.993430i | \(0.536508\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 2.40661 | 0.178882 | 0.0894411 | − | 0.995992i | \(-0.471492\pi\) | ||||
0.0894411 | + | 0.995992i | \(0.471492\pi\) | |||||||
\(182\) | −27.1868 | −2.01522 | ||||||||
\(183\) | 5.06226 | 0.374213 | ||||||||
\(184\) | 6.53113 | 0.481481 | ||||||||
\(185\) | 7.06226 | 0.519228 | ||||||||
\(186\) | 1.00000 | 0.0733236 | ||||||||
\(187\) | −26.1245 | −1.91041 | ||||||||
\(188\) | −5.06226 | −0.369203 | ||||||||
\(189\) | −4.53113 | −0.329591 | ||||||||
\(190\) | −4.53113 | −0.328723 | ||||||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 16.1245 | 1.15767 | ||||||||
\(195\) | −6.00000 | −0.429669 | ||||||||
\(196\) | 13.5311 | 0.966509 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 6.53113 | 0.464147 | ||||||||
\(199\) | −8.53113 | −0.604756 | −0.302378 | − | 0.953188i | \(-0.597780\pi\) | ||||
−0.302378 | + | 0.953188i | \(0.597780\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 5.06226 | 0.357064 | ||||||||
\(202\) | −9.46887 | −0.666227 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | −7.06226 | −0.493249 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.53113 | 0.453945 | ||||||||
\(208\) | 6.00000 | 0.416025 | ||||||||
\(209\) | 29.5934 | 2.04702 | ||||||||
\(210\) | 4.53113 | 0.312678 | ||||||||
\(211\) | −1.59339 | −0.109693 | −0.0548466 | − | 0.998495i | \(-0.517467\pi\) | ||||
−0.0548466 | + | 0.998495i | \(0.517467\pi\) | |||||||
\(212\) | −2.53113 | −0.173839 | ||||||||
\(213\) | −12.5311 | −0.858619 | ||||||||
\(214\) | 9.59339 | 0.655790 | ||||||||
\(215\) | 8.53113 | 0.581818 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −4.53113 | −0.307593 | ||||||||
\(218\) | 15.0623 | 1.02014 | ||||||||
\(219\) | −8.53113 | −0.576480 | ||||||||
\(220\) | −6.53113 | −0.440329 | ||||||||
\(221\) | −24.0000 | −1.61441 | ||||||||
\(222\) | −7.06226 | −0.473988 | ||||||||
\(223\) | 2.00000 | 0.133930 | 0.0669650 | − | 0.997755i | \(-0.478668\pi\) | ||||
0.0669650 | + | 0.997755i | \(0.478668\pi\) | |||||||
\(224\) | −4.53113 | −0.302749 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −7.59339 | −0.505105 | ||||||||
\(227\) | −24.5311 | −1.62819 | −0.814094 | − | 0.580733i | \(-0.802766\pi\) | ||||
−0.814094 | + | 0.580733i | \(0.802766\pi\) | |||||||
\(228\) | 4.53113 | 0.300081 | ||||||||
\(229\) | −5.59339 | −0.369621 | −0.184811 | − | 0.982774i | \(-0.559167\pi\) | ||||
−0.184811 | + | 0.982774i | \(0.559167\pi\) | |||||||
\(230\) | −6.53113 | −0.430650 | ||||||||
\(231\) | −29.5934 | −1.94710 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.46887 | 0.0962289 | 0.0481145 | − | 0.998842i | \(-0.484679\pi\) | ||||
0.0481145 | + | 0.998842i | \(0.484679\pi\) | |||||||
\(234\) | 6.00000 | 0.392232 | ||||||||
\(235\) | 5.06226 | 0.330225 | ||||||||
\(236\) | −9.06226 | −0.589903 | ||||||||
\(237\) | −8.53113 | −0.554156 | ||||||||
\(238\) | 18.1245 | 1.17484 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 31.6556 | 2.03490 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 5.06226 | 0.324078 | ||||||||
\(245\) | −13.5311 | −0.864472 | ||||||||
\(246\) | 7.06226 | 0.450273 | ||||||||
\(247\) | 27.1868 | 1.72985 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | −8.00000 | −0.506979 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 3.06226 | 0.193288 | 0.0966440 | − | 0.995319i | \(-0.469189\pi\) | ||||
0.0966440 | + | 0.995319i | \(0.469189\pi\) | |||||||
\(252\) | −4.53113 | −0.285434 | ||||||||
\(253\) | 42.6556 | 2.68174 | ||||||||
\(254\) | 7.06226 | 0.443125 | ||||||||
\(255\) | 4.00000 | 0.250490 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.6556 | 0.789437 | 0.394719 | − | 0.918802i | \(-0.370842\pi\) | ||||
0.394719 | + | 0.918802i | \(0.370842\pi\) | |||||||
\(258\) | −8.53113 | −0.531125 | ||||||||
\(259\) | 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 | \(-0.751775\pi\) | ||||
−0.711040 | + | 0.703152i | \(0.751775\pi\) | |||||||
\(264\) | 6.53113 | 0.401963 | ||||||||
\(265\) | 2.53113 | 0.155486 | ||||||||
\(266\) | −20.5311 | −1.25884 | ||||||||
\(267\) | −6.53113 | −0.399699 | ||||||||
\(268\) | 5.06226 | 0.309227 | ||||||||
\(269\) | −19.1868 | −1.16984 | −0.584919 | − | 0.811092i | \(-0.698874\pi\) | ||||
−0.584919 | + | 0.811092i | \(0.698874\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −11.4689 | −0.696684 | −0.348342 | − | 0.937367i | \(-0.613255\pi\) | ||||
−0.348342 | + | 0.937367i | \(0.613255\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | −27.1868 | −1.64542 | ||||||||
\(274\) | 17.0623 | 1.03077 | ||||||||
\(275\) | 6.53113 | 0.393842 | ||||||||
\(276\) | 6.53113 | 0.393128 | ||||||||
\(277\) | −15.0623 | −0.905003 | −0.452502 | − | 0.891764i | \(-0.649468\pi\) | ||||
−0.452502 | + | 0.891764i | \(0.649468\pi\) | |||||||
\(278\) | 6.00000 | 0.359856 | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | 4.53113 | 0.270787 | ||||||||
\(281\) | 15.0623 | 0.898539 | 0.449269 | − | 0.893396i | \(-0.351684\pi\) | ||||
0.449269 | + | 0.893396i | \(0.351684\pi\) | |||||||
\(282\) | −5.06226 | −0.301453 | ||||||||
\(283\) | −12.0000 | −0.713326 | −0.356663 | − | 0.934233i | \(-0.616086\pi\) | ||||
−0.356663 | + | 0.934233i | \(0.616086\pi\) | |||||||
\(284\) | −12.5311 | −0.743586 | ||||||||
\(285\) | −4.53113 | −0.268401 | ||||||||
\(286\) | 39.1868 | 2.31716 | ||||||||
\(287\) | −32.0000 | −1.88890 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.1245 | 0.945236 | ||||||||
\(292\) | −8.53113 | −0.499247 | ||||||||
\(293\) | −14.0000 | −0.817889 | −0.408944 | − | 0.912559i | \(-0.634103\pi\) | ||||
−0.408944 | + | 0.912559i | \(0.634103\pi\) | |||||||
\(294\) | 13.5311 | 0.789151 | ||||||||
\(295\) | 9.06226 | 0.527625 | ||||||||
\(296\) | −7.06226 | −0.410485 | ||||||||
\(297\) | 6.53113 | 0.378975 | ||||||||
\(298\) | −18.5311 | −1.07348 | ||||||||
\(299\) | 39.1868 | 2.26623 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 38.6556 | 2.22807 | ||||||||
\(302\) | 14.1245 | 0.812775 | ||||||||
\(303\) | −9.46887 | −0.543972 | ||||||||
\(304\) | 4.53113 | 0.259878 | ||||||||
\(305\) | −5.06226 | −0.289864 | ||||||||
\(306\) | −4.00000 | −0.228665 | ||||||||
\(307\) | −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 | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 6.00000 | 0.339683 | ||||||||
\(313\) | 10.9377 | 0.618238 | 0.309119 | − | 0.951023i | \(-0.399966\pi\) | ||||
0.309119 | + | 0.951023i | \(0.399966\pi\) | |||||||
\(314\) | −22.5311 | −1.27151 | ||||||||
\(315\) | 4.53113 | 0.255300 | ||||||||
\(316\) | −8.53113 | −0.479913 | ||||||||
\(317\) | 12.9377 | 0.726656 | 0.363328 | − | 0.931661i | \(-0.381640\pi\) | ||||
0.363328 | + | 0.931661i | \(0.381640\pi\) | |||||||
\(318\) | −2.53113 | −0.141939 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 9.59339 | 0.535451 | ||||||||
\(322\) | −29.5934 | −1.64917 | ||||||||
\(323\) | −18.1245 | −1.00848 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 6.00000 | 0.332820 | ||||||||
\(326\) | 5.06226 | 0.280373 | ||||||||
\(327\) | 15.0623 | 0.832945 | ||||||||
\(328\) | 7.06226 | 0.389948 | ||||||||
\(329\) | 22.9377 | 1.26460 | ||||||||
\(330\) | −6.53113 | −0.359527 | ||||||||
\(331\) | 12.9377 | 0.711123 | 0.355561 | − | 0.934653i | \(-0.384290\pi\) | ||||
0.355561 | + | 0.934653i | \(0.384290\pi\) | |||||||
\(332\) | −8.00000 | −0.439057 | ||||||||
\(333\) | −7.06226 | −0.387009 | ||||||||
\(334\) | −23.5934 | −1.29097 | ||||||||
\(335\) | −5.06226 | −0.276581 | ||||||||
\(336\) | −4.53113 | −0.247193 | ||||||||
\(337\) | −19.1868 | −1.04517 | −0.522585 | − | 0.852587i | \(-0.675032\pi\) | ||||
−0.522585 | + | 0.852587i | \(0.675032\pi\) | |||||||
\(338\) | 23.0000 | 1.25104 | ||||||||
\(339\) | −7.59339 | −0.412416 | ||||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | 6.53113 | 0.353680 | ||||||||
\(342\) | 4.53113 | 0.245015 | ||||||||
\(343\) | −29.5934 | −1.59789 | ||||||||
\(344\) | −8.53113 | −0.459968 | ||||||||
\(345\) | −6.53113 | −0.351624 | ||||||||
\(346\) | 14.0000 | 0.752645 | ||||||||
\(347\) | 10.1245 | 0.543512 | 0.271756 | − | 0.962366i | \(-0.412396\pi\) | ||||
0.271756 | + | 0.962366i | \(0.412396\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | 6.00000 | 0.320256 | ||||||||
\(352\) | 6.53113 | 0.348110 | ||||||||
\(353\) | −6.93774 | −0.369259 | −0.184629 | − | 0.982808i | \(-0.559108\pi\) | ||||
−0.184629 | + | 0.982808i | \(0.559108\pi\) | |||||||
\(354\) | −9.06226 | −0.481654 | ||||||||
\(355\) | 12.5311 | 0.665083 | ||||||||
\(356\) | −6.53113 | −0.346149 | ||||||||
\(357\) | 18.1245 | 0.959251 | ||||||||
\(358\) | −3.06226 | −0.161845 | ||||||||
\(359\) | 3.46887 | 0.183080 | 0.0915400 | − | 0.995801i | \(-0.470821\pi\) | ||||
0.0915400 | + | 0.995801i | \(0.470821\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 1.53113 | 0.0805857 | ||||||||
\(362\) | 2.40661 | 0.126489 | ||||||||
\(363\) | 31.6556 | 1.66149 | ||||||||
\(364\) | −27.1868 | −1.42497 | ||||||||
\(365\) | 8.53113 | 0.446540 | ||||||||
\(366\) | 5.06226 | 0.264608 | ||||||||
\(367\) | −10.0000 | −0.521996 | −0.260998 | − | 0.965339i | \(-0.584052\pi\) | ||||
−0.260998 | + | 0.965339i | \(0.584052\pi\) | |||||||
\(368\) | 6.53113 | 0.340459 | ||||||||
\(369\) | 7.06226 | 0.367646 | ||||||||
\(370\) | 7.06226 | 0.367149 | ||||||||
\(371\) | 11.4689 | 0.595434 | ||||||||
\(372\) | 1.00000 | 0.0518476 | ||||||||
\(373\) | −18.5311 | −0.959505 | −0.479753 | − | 0.877404i | \(-0.659274\pi\) | ||||
−0.479753 | + | 0.877404i | \(0.659274\pi\) | |||||||
\(374\) | −26.1245 | −1.35087 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −5.06226 | −0.261066 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.53113 | −0.233056 | ||||||||
\(379\) | 21.5934 | 1.10918 | 0.554589 | − | 0.832124i | \(-0.312876\pi\) | ||||
0.554589 | + | 0.832124i | \(0.312876\pi\) | |||||||
\(380\) | −4.53113 | −0.232442 | ||||||||
\(381\) | 7.06226 | 0.361810 | ||||||||
\(382\) | −8.00000 | −0.409316 | ||||||||
\(383\) | −3.06226 | −0.156474 | −0.0782370 | − | 0.996935i | \(-0.524929\pi\) | ||||
−0.0782370 | + | 0.996935i | \(0.524929\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 29.5934 | 1.50822 | ||||||||
\(386\) | 14.0000 | 0.712581 | ||||||||
\(387\) | −8.53113 | −0.433662 | ||||||||
\(388\) | 16.1245 | 0.818598 | ||||||||
\(389\) | 10.9377 | 0.554566 | 0.277283 | − | 0.960788i | \(-0.410566\pi\) | ||||
0.277283 | + | 0.960788i | \(0.410566\pi\) | |||||||
\(390\) | −6.00000 | −0.303822 | ||||||||
\(391\) | −26.1245 | −1.32117 | ||||||||
\(392\) | 13.5311 | 0.683425 | ||||||||
\(393\) | −9.06226 | −0.457130 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | 8.53113 | 0.429248 | ||||||||
\(396\) | 6.53113 | 0.328202 | ||||||||
\(397\) | 37.7179 | 1.89301 | 0.946504 | − | 0.322693i | \(-0.104588\pi\) | ||||
0.946504 | + | 0.322693i | \(0.104588\pi\) | |||||||
\(398\) | −8.53113 | −0.427627 | ||||||||
\(399\) | −20.5311 | −1.02784 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 21.7179 | 1.08454 | 0.542270 | − | 0.840204i | \(-0.317565\pi\) | ||||
0.542270 | + | 0.840204i | \(0.317565\pi\) | |||||||
\(402\) | 5.06226 | 0.252482 | ||||||||
\(403\) | 6.00000 | 0.298881 | ||||||||
\(404\) | −9.46887 | −0.471094 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −46.1245 | −2.28631 | ||||||||
\(408\) | −4.00000 | −0.198030 | ||||||||
\(409\) | 7.06226 | 0.349206 | 0.174603 | − | 0.984639i | \(-0.444136\pi\) | ||||
0.174603 | + | 0.984639i | \(0.444136\pi\) | |||||||
\(410\) | −7.06226 | −0.348780 | ||||||||
\(411\) | 17.0623 | 0.841619 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 41.0623 | 2.02054 | ||||||||
\(414\) | 6.53113 | 0.320987 | ||||||||
\(415\) | 8.00000 | 0.392705 | ||||||||
\(416\) | 6.00000 | 0.294174 | ||||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | 29.5934 | 1.44746 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 4.53113 | 0.221096 | ||||||||
\(421\) | −26.2490 | −1.27930 | −0.639650 | − | 0.768667i | \(-0.720921\pi\) | ||||
−0.639650 | + | 0.768667i | \(0.720921\pi\) | |||||||
\(422\) | −1.59339 | −0.0775648 | ||||||||
\(423\) | −5.06226 | −0.246135 | ||||||||
\(424\) | −2.53113 | −0.122922 | ||||||||
\(425\) | −4.00000 | −0.194029 | ||||||||
\(426\) | −12.5311 | −0.607135 | ||||||||
\(427\) | −22.9377 | −1.11004 | ||||||||
\(428\) | 9.59339 | 0.463714 | ||||||||
\(429\) | 39.1868 | 1.89196 | ||||||||
\(430\) | 8.53113 | 0.411408 | ||||||||
\(431\) | −24.0000 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −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 | ||||||||
\(438\) | −8.53113 | −0.407633 | ||||||||
\(439\) | −25.0623 | −1.19616 | −0.598078 | − | 0.801438i | \(-0.704069\pi\) | ||||
−0.598078 | + | 0.801438i | \(0.704069\pi\) | |||||||
\(440\) | −6.53113 | −0.311359 | ||||||||
\(441\) | 13.5311 | 0.644339 | ||||||||
\(442\) | −24.0000 | −1.14156 | ||||||||
\(443\) | 14.4066 | 0.684479 | 0.342239 | − | 0.939613i | \(-0.388815\pi\) | ||||
0.342239 | + | 0.939613i | \(0.388815\pi\) | |||||||
\(444\) | −7.06226 | −0.335160 | ||||||||
\(445\) | 6.53113 | 0.309605 | ||||||||
\(446\) | 2.00000 | 0.0947027 | ||||||||
\(447\) | −18.5311 | −0.876492 | ||||||||
\(448\) | −4.53113 | −0.214076 | ||||||||
\(449\) | −4.12452 | −0.194648 | −0.0973240 | − | 0.995253i | \(-0.531028\pi\) | ||||
−0.0973240 | + | 0.995253i | \(0.531028\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 46.1245 | 2.17192 | ||||||||
\(452\) | −7.59339 | −0.357163 | ||||||||
\(453\) | 14.1245 | 0.663628 | ||||||||
\(454\) | −24.5311 | −1.15130 | ||||||||
\(455\) | 27.1868 | 1.27454 | ||||||||
\(456\) | 4.53113 | 0.212190 | ||||||||
\(457\) | 14.9377 | 0.698758 | 0.349379 | − | 0.936981i | \(-0.386393\pi\) | ||||
0.349379 | + | 0.936981i | \(0.386393\pi\) | |||||||
\(458\) | −5.59339 | −0.261362 | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | −6.53113 | −0.304515 | ||||||||
\(461\) | 24.0000 | 1.11779 | 0.558896 | − | 0.829238i | \(-0.311225\pi\) | ||||
0.558896 | + | 0.829238i | \(0.311225\pi\) | |||||||
\(462\) | −29.5934 | −1.37681 | ||||||||
\(463\) | 13.1868 | 0.612841 | 0.306421 | − | 0.951896i | \(-0.400869\pi\) | ||||
0.306421 | + | 0.951896i | \(0.400869\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.00000 | −0.0463739 | ||||||||
\(466\) | 1.46887 | 0.0680441 | ||||||||
\(467\) | −22.1245 | −1.02380 | −0.511900 | − | 0.859045i | \(-0.671058\pi\) | ||||
−0.511900 | + | 0.859045i | \(0.671058\pi\) | |||||||
\(468\) | 6.00000 | 0.277350 | ||||||||
\(469\) | −22.9377 | −1.05917 | ||||||||
\(470\) | 5.06226 | 0.233505 | ||||||||
\(471\) | −22.5311 | −1.03818 | ||||||||
\(472\) | −9.06226 | −0.417124 | ||||||||
\(473\) | −55.7179 | −2.56191 | ||||||||
\(474\) | −8.53113 | −0.391848 | ||||||||
\(475\) | 4.53113 | 0.207902 | ||||||||
\(476\) | 18.1245 | 0.830736 | ||||||||
\(477\) | −2.53113 | −0.115892 | ||||||||
\(478\) | −8.00000 | −0.365911 | ||||||||
\(479\) | 1.34436 | 0.0614252 | 0.0307126 | − | 0.999528i | \(-0.490222\pi\) | ||||
0.0307126 | + | 0.999528i | \(0.490222\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −42.3735 | −1.93207 | ||||||||
\(482\) | 2.00000 | 0.0910975 | ||||||||
\(483\) | −29.5934 | −1.34655 | ||||||||
\(484\) | 31.6556 | 1.43889 | ||||||||
\(485\) | −16.1245 | −0.732177 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 23.0623 | 1.04505 | 0.522525 | − | 0.852624i | \(-0.324990\pi\) | ||||
0.522525 | + | 0.852624i | \(0.324990\pi\) | |||||||
\(488\) | 5.06226 | 0.229158 | ||||||||
\(489\) | 5.06226 | 0.228923 | ||||||||
\(490\) | −13.5311 | −0.611274 | ||||||||
\(491\) | −7.59339 | −0.342685 | −0.171342 | − | 0.985212i | \(-0.554810\pi\) | ||||
−0.171342 | + | 0.985212i | \(0.554810\pi\) | |||||||
\(492\) | 7.06226 | 0.318391 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 27.1868 | 1.22319 | ||||||||
\(495\) | −6.53113 | −0.293552 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 56.7802 | 2.54694 | ||||||||
\(498\) | −8.00000 | −0.358489 | ||||||||
\(499\) | −7.06226 | −0.316150 | −0.158075 | − | 0.987427i | \(-0.550529\pi\) | ||||
−0.158075 | + | 0.987427i | \(0.550529\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −23.5934 | −1.05407 | ||||||||
\(502\) | 3.06226 | 0.136675 | ||||||||
\(503\) | 16.0000 | 0.713405 | 0.356702 | − | 0.934218i | \(-0.383901\pi\) | ||||
0.356702 | + | 0.934218i | \(0.383901\pi\) | |||||||
\(504\) | −4.53113 | −0.201833 | ||||||||
\(505\) | 9.46887 | 0.421359 | ||||||||
\(506\) | 42.6556 | 1.89627 | ||||||||
\(507\) | 23.0000 | 1.02147 | ||||||||
\(508\) | 7.06226 | 0.313337 | ||||||||
\(509\) | 38.1245 | 1.68984 | 0.844920 | − | 0.534893i | \(-0.179648\pi\) | ||||
0.844920 | + | 0.534893i | \(0.179648\pi\) | |||||||
\(510\) | 4.00000 | 0.177123 | ||||||||
\(511\) | 38.6556 | 1.71003 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.53113 | 0.200054 | ||||||||
\(514\) | 12.6556 | 0.558217 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.53113 | −0.375562 | ||||||||
\(517\) | −33.0623 | −1.45408 | ||||||||
\(518\) | 32.0000 | 1.40600 | ||||||||
\(519\) | 14.0000 | 0.614532 | ||||||||
\(520\) | −6.00000 | −0.263117 | ||||||||
\(521\) | −12.1245 | −0.531185 | −0.265592 | − | 0.964085i | \(-0.585568\pi\) | ||||
−0.265592 | + | 0.964085i | \(0.585568\pi\) | |||||||
\(522\) | 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 | ||||||||
\(525\) | −4.53113 | −0.197755 | ||||||||
\(526\) | −23.0623 | −1.00556 | ||||||||
\(527\) | −4.00000 | −0.174243 | ||||||||
\(528\) | 6.53113 | 0.284231 | ||||||||
\(529\) | 19.6556 | 0.854593 | ||||||||
\(530\) | 2.53113 | 0.109945 | ||||||||
\(531\) | −9.06226 | −0.393268 | ||||||||
\(532\) | −20.5311 | −0.890137 | ||||||||
\(533\) | 42.3735 | 1.83540 | ||||||||
\(534\) | −6.53113 | −0.282630 | ||||||||
\(535\) | −9.59339 | −0.414758 | ||||||||
\(536\) | 5.06226 | 0.218656 | ||||||||
\(537\) | −3.06226 | −0.132146 | ||||||||
\(538\) | −19.1868 | −0.827201 | ||||||||
\(539\) | 88.3735 | 3.80652 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −4.12452 | −0.177327 | −0.0886634 | − | 0.996062i | \(-0.528260\pi\) | ||||
−0.0886634 | + | 0.996062i | \(0.528260\pi\) | |||||||
\(542\) | −11.4689 | −0.492630 | ||||||||
\(543\) | 2.40661 | 0.103278 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | −15.0623 | −0.645196 | ||||||||
\(546\) | −27.1868 | −1.16349 | ||||||||
\(547\) | −7.18677 | −0.307284 | −0.153642 | − | 0.988127i | \(-0.549100\pi\) | ||||
−0.153642 | + | 0.988127i | \(0.549100\pi\) | |||||||
\(548\) | 17.0623 | 0.728864 | ||||||||
\(549\) | 5.06226 | 0.216052 | ||||||||
\(550\) | 6.53113 | 0.278488 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 6.53113 | 0.277983 | ||||||||
\(553\) | 38.6556 | 1.64381 | ||||||||
\(554\) | −15.0623 | −0.639934 | ||||||||
\(555\) | 7.06226 | 0.299776 | ||||||||
\(556\) | 6.00000 | 0.254457 | ||||||||
\(557\) | −26.7802 | −1.13471 | −0.567356 | − | 0.823473i | \(-0.692034\pi\) | ||||
−0.567356 | + | 0.823473i | \(0.692034\pi\) | |||||||
\(558\) | 1.00000 | 0.0423334 | ||||||||
\(559\) | −51.1868 | −2.16497 | ||||||||
\(560\) | 4.53113 | 0.191475 | ||||||||
\(561\) | −26.1245 | −1.10298 | ||||||||
\(562\) | 15.0623 | 0.635363 | ||||||||
\(563\) | −4.00000 | −0.168580 | −0.0842900 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842900 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(564\) | −5.06226 | −0.213160 | ||||||||
\(565\) | 7.59339 | 0.319456 | ||||||||
\(566\) | −12.0000 | −0.504398 | ||||||||
\(567\) | −4.53113 | −0.190290 | ||||||||
\(568\) | −12.5311 | −0.525794 | ||||||||
\(569\) | 9.46887 | 0.396956 | 0.198478 | − | 0.980105i | \(-0.436400\pi\) | ||||
0.198478 | + | 0.980105i | \(0.436400\pi\) | |||||||
\(570\) | −4.53113 | −0.189788 | ||||||||
\(571\) | 36.1245 | 1.51176 | 0.755882 | − | 0.654708i | \(-0.227208\pi\) | ||||
0.755882 | + | 0.654708i | \(0.227208\pi\) | |||||||
\(572\) | 39.1868 | 1.63848 | ||||||||
\(573\) | −8.00000 | −0.334205 | ||||||||
\(574\) | −32.0000 | −1.33565 | ||||||||
\(575\) | 6.53113 | 0.272367 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 37.1868 | 1.54811 | 0.774053 | − | 0.633121i | \(-0.218226\pi\) | ||||
0.774053 | + | 0.633121i | \(0.218226\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 14.0000 | 0.581820 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.2490 | 1.50386 | ||||||||
\(582\) | 16.1245 | 0.668383 | ||||||||
\(583\) | −16.5311 | −0.684649 | ||||||||
\(584\) | −8.53113 | −0.353021 | ||||||||
\(585\) | −6.00000 | −0.248069 | ||||||||
\(586\) | −14.0000 | −0.578335 | ||||||||
\(587\) | −44.2490 | −1.82635 | −0.913176 | − | 0.407564i | \(-0.866378\pi\) | ||||
−0.913176 | + | 0.407564i | \(0.866378\pi\) | |||||||
\(588\) | 13.5311 | 0.558014 | ||||||||
\(589\) | 4.53113 | 0.186702 | ||||||||
\(590\) | 9.06226 | 0.373087 | ||||||||
\(591\) | 6.00000 | 0.246807 | ||||||||
\(592\) | −7.06226 | −0.290257 | ||||||||
\(593\) | −14.0000 | −0.574911 | −0.287456 | − | 0.957794i | \(-0.592809\pi\) | ||||
−0.287456 | + | 0.957794i | \(0.592809\pi\) | |||||||
\(594\) | 6.53113 | 0.267975 | ||||||||
\(595\) | −18.1245 | −0.743033 | ||||||||
\(596\) | −18.5311 | −0.759065 | ||||||||
\(597\) | −8.53113 | −0.349156 | ||||||||
\(598\) | 39.1868 | 1.60247 | ||||||||
\(599\) | −13.5934 | −0.555411 | −0.277705 | − | 0.960666i | \(-0.589574\pi\) | ||||
−0.277705 | + | 0.960666i | \(0.589574\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | 30.0000 | 1.22373 | 0.611863 | − | 0.790964i | \(-0.290420\pi\) | ||||
0.611863 | + | 0.790964i | \(0.290420\pi\) | |||||||
\(602\) | 38.6556 | 1.57549 | ||||||||
\(603\) | 5.06226 | 0.206151 | ||||||||
\(604\) | 14.1245 | 0.574718 | ||||||||
\(605\) | −31.6556 | −1.28698 | ||||||||
\(606\) | −9.46887 | −0.384647 | ||||||||
\(607\) | −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 | ||||||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | −30.0000 | −1.21169 | −0.605844 | − | 0.795583i | \(-0.707165\pi\) | ||||
−0.605844 | + | 0.795583i | \(0.707165\pi\) | |||||||
\(614\) | −30.1245 | −1.21573 | ||||||||
\(615\) | −7.06226 | −0.284778 | ||||||||
\(616\) | −29.5934 | −1.19235 | ||||||||
\(617\) | −3.59339 | −0.144664 | −0.0723321 | − | 0.997381i | \(-0.523044\pi\) | ||||
−0.0723321 | + | 0.997381i | \(0.523044\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | 6.53113 | 0.262085 | ||||||||
\(622\) | −8.00000 | −0.320771 | ||||||||
\(623\) | 29.5934 | 1.18563 | ||||||||
\(624\) | 6.00000 | 0.240192 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.9377 | 0.437160 | ||||||||
\(627\) | 29.5934 | 1.18185 | ||||||||
\(628\) | −22.5311 | −0.899090 | ||||||||
\(629\) | 28.2490 | 1.12636 | ||||||||
\(630\) | 4.53113 | 0.180524 | ||||||||
\(631\) | 30.6556 | 1.22038 | 0.610191 | − | 0.792254i | \(-0.291093\pi\) | ||||
0.610191 | + | 0.792254i | \(0.291093\pi\) | |||||||
\(632\) | −8.53113 | −0.339350 | ||||||||
\(633\) | −1.59339 | −0.0633314 | ||||||||
\(634\) | 12.9377 | 0.513823 | ||||||||
\(635\) | −7.06226 | −0.280257 | ||||||||
\(636\) | −2.53113 | −0.100366 | ||||||||
\(637\) | 81.1868 | 3.21674 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.5311 | −0.495724 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −22.0000 | −0.868948 | −0.434474 | − | 0.900684i | \(-0.643066\pi\) | ||||
−0.434474 | + | 0.900684i | \(0.643066\pi\) | |||||||
\(642\) | 9.59339 | 0.378621 | ||||||||
\(643\) | −17.5934 | −0.693815 | −0.346908 | − | 0.937899i | \(-0.612768\pi\) | ||||
−0.346908 | + | 0.937899i | \(0.612768\pi\) | |||||||
\(644\) | −29.5934 | −1.16614 | ||||||||
\(645\) | 8.53113 | 0.335913 | ||||||||
\(646\) | −18.1245 | −0.713100 | ||||||||
\(647\) | −6.53113 | −0.256765 | −0.128383 | − | 0.991725i | \(-0.540979\pi\) | ||||
−0.128383 | + | 0.991725i | \(0.540979\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −59.1868 | −2.32328 | ||||||||
\(650\) | 6.00000 | 0.235339 | ||||||||
\(651\) | −4.53113 | −0.177589 | ||||||||
\(652\) | 5.06226 | 0.198253 | ||||||||
\(653\) | 38.2490 | 1.49680 | 0.748400 | − | 0.663248i | \(-0.230822\pi\) | ||||
0.748400 | + | 0.663248i | \(0.230822\pi\) | |||||||
\(654\) | 15.0623 | 0.588981 | ||||||||
\(655\) | 9.06226 | 0.354092 | ||||||||
\(656\) | 7.06226 | 0.275735 | ||||||||
\(657\) | −8.53113 | −0.332831 | ||||||||
\(658\) | 22.9377 | 0.894206 | ||||||||
\(659\) | 16.0000 | 0.623272 | 0.311636 | − | 0.950202i | \(-0.399123\pi\) | ||||
0.311636 | + | 0.950202i | \(0.399123\pi\) | |||||||
\(660\) | −6.53113 | −0.254224 | ||||||||
\(661\) | −10.0000 | −0.388955 | −0.194477 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194477 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(662\) | 12.9377 | 0.502840 | ||||||||
\(663\) | −24.0000 | −0.932083 | ||||||||
\(664\) | −8.00000 | −0.310460 | ||||||||
\(665\) | 20.5311 | 0.796163 | ||||||||
\(666\) | −7.06226 | −0.273657 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −23.5934 | −0.912856 | ||||||||
\(669\) | 2.00000 | 0.0773245 | ||||||||
\(670\) | −5.06226 | −0.195572 | ||||||||
\(671\) | 33.0623 | 1.27635 | ||||||||
\(672\) | −4.53113 | −0.174792 | ||||||||
\(673\) | −9.06226 | −0.349324 | −0.174662 | − | 0.984628i | \(-0.555883\pi\) | ||||
−0.174662 | + | 0.984628i | \(0.555883\pi\) | |||||||
\(674\) | −19.1868 | −0.739047 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | 27.5934 | 1.06050 | 0.530250 | − | 0.847841i | \(-0.322098\pi\) | ||||
0.530250 | + | 0.847841i | \(0.322098\pi\) | |||||||
\(678\) | −7.59339 | −0.291622 | ||||||||
\(679\) | −73.0623 | −2.80387 | ||||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | −24.5311 | −0.940035 | ||||||||
\(682\) | 6.53113 | 0.250090 | ||||||||
\(683\) | 7.46887 | 0.285788 | 0.142894 | − | 0.989738i | \(-0.454359\pi\) | ||||
0.142894 | + | 0.989738i | \(0.454359\pi\) | |||||||
\(684\) | 4.53113 | 0.173252 | ||||||||
\(685\) | −17.0623 | −0.651915 | ||||||||
\(686\) | −29.5934 | −1.12988 | ||||||||
\(687\) | −5.59339 | −0.213401 | ||||||||
\(688\) | −8.53113 | −0.325246 | ||||||||
\(689\) | −15.1868 | −0.578570 | ||||||||
\(690\) | −6.53113 | −0.248636 | ||||||||
\(691\) | 0.531129 | 0.0202051 | 0.0101025 | − | 0.999949i | \(-0.496784\pi\) | ||||
0.0101025 | + | 0.999949i | \(0.496784\pi\) | |||||||
\(692\) | 14.0000 | 0.532200 | ||||||||
\(693\) | −29.5934 | −1.12416 | ||||||||
\(694\) | 10.1245 | 0.384321 | ||||||||
\(695\) | −6.00000 | −0.227593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.2490 | −1.07001 | ||||||||
\(698\) | 8.93774 | 0.338299 | ||||||||
\(699\) | 1.46887 | 0.0555578 | ||||||||
\(700\) | −4.53113 | −0.171261 | ||||||||
\(701\) | −13.4689 | −0.508712 | −0.254356 | − | 0.967111i | \(-0.581864\pi\) | ||||
−0.254356 | + | 0.967111i | \(0.581864\pi\) | |||||||
\(702\) | 6.00000 | 0.226455 | ||||||||
\(703\) | −32.0000 | −1.20690 | ||||||||
\(704\) | 6.53113 | 0.246151 | ||||||||
\(705\) | 5.06226 | 0.190656 | ||||||||
\(706\) | −6.93774 | −0.261105 | ||||||||
\(707\) | 42.9047 | 1.61360 | ||||||||
\(708\) | −9.06226 | −0.340581 | ||||||||
\(709\) | 49.5934 | 1.86252 | 0.931259 | − | 0.364357i | \(-0.118711\pi\) | ||||
0.931259 | + | 0.364357i | \(0.118711\pi\) | |||||||
\(710\) | 12.5311 | 0.470285 | ||||||||
\(711\) | −8.53113 | −0.319942 | ||||||||
\(712\) | −6.53113 | −0.244764 | ||||||||
\(713\) | 6.53113 | 0.244593 | ||||||||
\(714\) | 18.1245 | 0.678293 | ||||||||
\(715\) | −39.1868 | −1.46550 | ||||||||
\(716\) | −3.06226 | −0.114442 | ||||||||
\(717\) | −8.00000 | −0.298765 | ||||||||
\(718\) | 3.46887 | 0.129457 | ||||||||
\(719\) | 15.1868 | 0.566371 | 0.283186 | − | 0.959065i | \(-0.408609\pi\) | ||||
0.283186 | + | 0.959065i | \(0.408609\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.53113 | 0.0569827 | ||||||||
\(723\) | 2.00000 | 0.0743808 | ||||||||
\(724\) | 2.40661 | 0.0894411 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 31.6556 | 1.17485 | ||||||||
\(727\) | 37.8424 | 1.40350 | 0.701749 | − | 0.712424i | \(-0.252403\pi\) | ||||
0.701749 | + | 0.712424i | \(0.252403\pi\) | |||||||
\(728\) | −27.1868 | −1.00761 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.53113 | 0.315751 | ||||||||
\(731\) | 34.1245 | 1.26214 | ||||||||
\(732\) | 5.06226 | 0.187106 | ||||||||
\(733\) | −28.1245 | −1.03880 | −0.519401 | − | 0.854530i | \(-0.673845\pi\) | ||||
−0.519401 | + | 0.854530i | \(0.673845\pi\) | |||||||
\(734\) | −10.0000 | −0.369107 | ||||||||
\(735\) | −13.5311 | −0.499103 | ||||||||
\(736\) | 6.53113 | 0.240741 | ||||||||
\(737\) | 33.0623 | 1.21786 | ||||||||
\(738\) | 7.06226 | 0.259965 | ||||||||
\(739\) | −21.1868 | −0.779368 | −0.389684 | − | 0.920949i | \(-0.627416\pi\) | ||||
−0.389684 | + | 0.920949i | \(0.627416\pi\) | |||||||
\(740\) | 7.06226 | 0.259614 | ||||||||
\(741\) | 27.1868 | 0.998731 | ||||||||
\(742\) | 11.4689 | 0.421036 | ||||||||
\(743\) | −28.6556 | −1.05127 | −0.525637 | − | 0.850709i | \(-0.676173\pi\) | ||||
−0.525637 | + | 0.850709i | \(0.676173\pi\) | |||||||
\(744\) | 1.00000 | 0.0366618 | ||||||||
\(745\) | 18.5311 | 0.678928 | ||||||||
\(746\) | −18.5311 | −0.678473 | ||||||||
\(747\) | −8.00000 | −0.292705 | ||||||||
\(748\) | −26.1245 | −0.955207 | ||||||||
\(749\) | −43.4689 | −1.58832 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 30.9377 | 1.12893 | 0.564467 | − | 0.825456i | \(-0.309082\pi\) | ||||
0.564467 | + | 0.825456i | \(0.309082\pi\) | |||||||
\(752\) | −5.06226 | −0.184602 | ||||||||
\(753\) | 3.06226 | 0.111595 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14.1245 | −0.514044 | ||||||||
\(756\) | −4.53113 | −0.164796 | ||||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 21.5934 | 0.784307 | ||||||||
\(759\) | 42.6556 | 1.54830 | ||||||||
\(760\) | −4.53113 | −0.164361 | ||||||||
\(761\) | 11.5934 | 0.420260 | 0.210130 | − | 0.977673i | \(-0.432611\pi\) | ||||
0.210130 | + | 0.977673i | \(0.432611\pi\) | |||||||
\(762\) | 7.06226 | 0.255839 | ||||||||
\(763\) | −68.2490 | −2.47078 | ||||||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 4.00000 | 0.144620 | ||||||||
\(766\) | −3.06226 | −0.110644 | ||||||||
\(767\) | −54.3735 | −1.96331 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −4.40661 | −0.158907 | −0.0794533 | − | 0.996839i | \(-0.525317\pi\) | ||||
−0.0794533 | + | 0.996839i | \(0.525317\pi\) | |||||||
\(770\) | 29.5934 | 1.06647 | ||||||||
\(771\) | 12.6556 | 0.455782 | ||||||||
\(772\) | 14.0000 | 0.503871 | ||||||||
\(773\) | 22.5311 | 0.810388 | 0.405194 | − | 0.914231i | \(-0.367204\pi\) | ||||
0.405194 | + | 0.914231i | \(0.367204\pi\) | |||||||
\(774\) | −8.53113 | −0.306645 | ||||||||
\(775\) | 1.00000 | 0.0359211 | ||||||||
\(776\) | 16.1245 | 0.578836 | ||||||||
\(777\) | 32.0000 | 1.14799 | ||||||||
\(778\) | 10.9377 | 0.392137 | ||||||||
\(779\) | 32.0000 | 1.14652 | ||||||||
\(780\) | −6.00000 | −0.214834 | ||||||||
\(781\) | −81.8424 | −2.92855 | ||||||||
\(782\) | −26.1245 | −0.934211 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.5311 | 0.483255 | ||||||||
\(785\) | 22.5311 | 0.804170 | ||||||||
\(786\) | −9.06226 | −0.323240 | ||||||||
\(787\) | −36.5311 | −1.30219 | −0.651097 | − | 0.758994i | \(-0.725691\pi\) | ||||
−0.651097 | + | 0.758994i | \(0.725691\pi\) | |||||||
\(788\) | 6.00000 | 0.213741 | ||||||||
\(789\) | −23.0623 | −0.821038 | ||||||||
\(790\) | 8.53113 | 0.303524 | ||||||||
\(791\) | 34.4066 | 1.22336 | ||||||||
\(792\) | 6.53113 | 0.232074 | ||||||||
\(793\) | 30.3735 | 1.07860 | ||||||||
\(794\) | 37.7179 | 1.33856 | ||||||||
\(795\) | 2.53113 | 0.0897699 | ||||||||
\(796\) | −8.53113 | −0.302378 | ||||||||
\(797\) | 12.1245 | 0.429472 | 0.214736 | − | 0.976672i | \(-0.431111\pi\) | ||||
0.214736 | + | 0.976672i | \(0.431111\pi\) | |||||||
\(798\) | −20.5311 | −0.726794 | ||||||||
\(799\) | 20.2490 | 0.716359 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −6.53113 | −0.230766 | ||||||||
\(802\) | 21.7179 | 0.766886 | ||||||||
\(803\) | −55.7179 | −1.96624 | ||||||||
\(804\) | 5.06226 | 0.178532 | ||||||||
\(805\) | 29.5934 | 1.04303 | ||||||||
\(806\) | 6.00000 | 0.211341 | ||||||||
\(807\) | −19.1868 | −0.675406 | ||||||||
\(808\) | −9.46887 | −0.333114 | ||||||||
\(809\) | 15.5934 | 0.548234 | 0.274117 | − | 0.961696i | \(-0.411614\pi\) | ||||
0.274117 | + | 0.961696i | \(0.411614\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 32.7802 | 1.15107 | 0.575534 | − | 0.817778i | \(-0.304794\pi\) | ||||
0.575534 | + | 0.817778i | \(0.304794\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −11.4689 | −0.402231 | ||||||||
\(814\) | −46.1245 | −1.61666 | ||||||||
\(815\) | −5.06226 | −0.177323 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | −38.6556 | −1.35239 | ||||||||
\(818\) | 7.06226 | 0.246926 | ||||||||
\(819\) | −27.1868 | −0.949983 | ||||||||
\(820\) | −7.06226 | −0.246625 | ||||||||
\(821\) | 42.1245 | 1.47016 | 0.735078 | − | 0.677983i | \(-0.237146\pi\) | ||||
0.735078 | + | 0.677983i | \(0.237146\pi\) | |||||||
\(822\) | 17.0623 | 0.595115 | ||||||||
\(823\) | 40.1245 | 1.39865 | 0.699326 | − | 0.714803i | \(-0.253483\pi\) | ||||
0.699326 | + | 0.714803i | \(0.253483\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.53113 | 0.227385 | ||||||||
\(826\) | 41.0623 | 1.42874 | ||||||||
\(827\) | 8.00000 | 0.278187 | 0.139094 | − | 0.990279i | \(-0.455581\pi\) | ||||
0.139094 | + | 0.990279i | \(0.455581\pi\) | |||||||
\(828\) | 6.53113 | 0.226972 | ||||||||
\(829\) | 30.6556 | 1.06471 | 0.532357 | − | 0.846520i | \(-0.321306\pi\) | ||||
0.532357 | + | 0.846520i | \(0.321306\pi\) | |||||||
\(830\) | 8.00000 | 0.277684 | ||||||||
\(831\) | −15.0623 | −0.522504 | ||||||||
\(832\) | 6.00000 | 0.208013 | ||||||||
\(833\) | −54.1245 | −1.87530 | ||||||||
\(834\) | 6.00000 | 0.207763 | ||||||||
\(835\) | 23.5934 | 0.816483 | ||||||||
\(836\) | 29.5934 | 1.02351 | ||||||||
\(837\) | 1.00000 | 0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 33.8424 | 1.16837 | 0.584185 | − | 0.811621i | \(-0.301414\pi\) | ||||
0.584185 | + | 0.811621i | \(0.301414\pi\) | |||||||
\(840\) | 4.53113 | 0.156339 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | −26.2490 | −0.904601 | ||||||||
\(843\) | 15.0623 | 0.518772 | ||||||||
\(844\) | −1.59339 | −0.0548466 | ||||||||
\(845\) | −23.0000 | −0.791224 | ||||||||
\(846\) | −5.06226 | −0.174044 | ||||||||
\(847\) | −143.436 | −4.92851 | ||||||||
\(848\) | −2.53113 | −0.0869193 | ||||||||
\(849\) | −12.0000 | −0.411839 | ||||||||
\(850\) | −4.00000 | −0.137199 | ||||||||
\(851\) | −46.1245 | −1.58113 | ||||||||
\(852\) | −12.5311 | −0.429309 | ||||||||
\(853\) | 57.7179 | 1.97622 | 0.988112 | − | 0.153738i | \(-0.0491311\pi\) | ||||
0.988112 | + | 0.153738i | \(0.0491311\pi\) | |||||||
\(854\) | −22.9377 | −0.784913 | ||||||||
\(855\) | −4.53113 | −0.154961 | ||||||||
\(856\) | 9.59339 | 0.327895 | ||||||||
\(857\) | 14.0000 | 0.478231 | 0.239115 | − | 0.970991i | \(-0.423143\pi\) | ||||
0.239115 | + | 0.970991i | \(0.423143\pi\) | |||||||
\(858\) | 39.1868 | 1.33781 | ||||||||
\(859\) | −23.0623 | −0.786874 | −0.393437 | − | 0.919352i | \(-0.628714\pi\) | ||||
−0.393437 | + | 0.919352i | \(0.628714\pi\) | |||||||
\(860\) | 8.53113 | 0.290909 | ||||||||
\(861\) | −32.0000 | −1.09056 | ||||||||
\(862\) | −24.0000 | −0.817443 | ||||||||
\(863\) | 33.4689 | 1.13929 | 0.569647 | − | 0.821890i | \(-0.307080\pi\) | ||||
0.569647 | + | 0.821890i | \(0.307080\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −14.0000 | −0.476014 | ||||||||
\(866\) | −25.5934 | −0.869699 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −4.53113 | −0.153797 | ||||||||
\(869\) | −55.7179 | −1.89010 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.3735 | 1.02917 | ||||||||
\(872\) | 15.0623 | 0.510072 | ||||||||
\(873\) | 16.1245 | 0.545732 | ||||||||
\(874\) | 29.5934 | 1.00101 | ||||||||
\(875\) | 4.53113 | 0.153180 | ||||||||
\(876\) | −8.53113 | −0.288240 | ||||||||
\(877\) | 11.8755 | 0.401007 | 0.200503 | − | 0.979693i | \(-0.435742\pi\) | ||||
0.200503 | + | 0.979693i | \(0.435742\pi\) | |||||||
\(878\) | −25.0623 | −0.845810 | ||||||||
\(879\) | −14.0000 | −0.472208 | ||||||||
\(880\) | −6.53113 | −0.220164 | ||||||||
\(881\) | 3.87548 | 0.130568 | 0.0652842 | − | 0.997867i | \(-0.479205\pi\) | ||||
0.0652842 | + | 0.997867i | \(0.479205\pi\) | |||||||
\(882\) | 13.5311 | 0.455617 | ||||||||
\(883\) | −13.3444 | −0.449073 | −0.224537 | − | 0.974466i | \(-0.572087\pi\) | ||||
−0.224537 | + | 0.974466i | \(0.572087\pi\) | |||||||
\(884\) | −24.0000 | −0.807207 | ||||||||
\(885\) | 9.06226 | 0.304624 | ||||||||
\(886\) | 14.4066 | 0.484000 | ||||||||
\(887\) | 23.1868 | 0.778536 | 0.389268 | − | 0.921125i | \(-0.372728\pi\) | ||||
0.389268 | + | 0.921125i | \(0.372728\pi\) | |||||||
\(888\) | −7.06226 | −0.236994 | ||||||||
\(889\) | −32.0000 | −1.07325 | ||||||||
\(890\) | 6.53113 | 0.218924 | ||||||||
\(891\) | 6.53113 | 0.218801 | ||||||||
\(892\) | 2.00000 | 0.0669650 | ||||||||
\(893\) | −22.9377 | −0.767582 | ||||||||
\(894\) | −18.5311 | −0.619774 | ||||||||
\(895\) | 3.06226 | 0.102360 | ||||||||
\(896\) | −4.53113 | −0.151374 | ||||||||
\(897\) | 39.1868 | 1.30841 | ||||||||
\(898\) | −4.12452 | −0.137637 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 10.1245 | 0.337297 | ||||||||
\(902\) | 46.1245 | 1.53578 | ||||||||
\(903\) | 38.6556 | 1.28638 | ||||||||
\(904\) | −7.59339 | −0.252552 | ||||||||
\(905\) | −2.40661 | −0.0799985 | ||||||||
\(906\) | 14.1245 | 0.469256 | ||||||||
\(907\) | 32.2490 | 1.07081 | 0.535406 | − | 0.844595i | \(-0.320159\pi\) | ||||
0.535406 | + | 0.844595i | \(0.320159\pi\) | |||||||
\(908\) | −24.5311 | −0.814094 | ||||||||
\(909\) | −9.46887 | −0.314063 | ||||||||
\(910\) | 27.1868 | 0.901233 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | 4.53113 | 0.150041 | ||||||||
\(913\) | −52.2490 | −1.72919 | ||||||||
\(914\) | 14.9377 | 0.494097 | ||||||||
\(915\) | −5.06226 | −0.167353 | ||||||||
\(916\) | −5.59339 | −0.184811 | ||||||||
\(917\) | 41.0623 | 1.35600 | ||||||||
\(918\) | −4.00000 | −0.132020 | ||||||||
\(919\) | −25.0623 | −0.826728 | −0.413364 | − | 0.910566i | \(-0.635646\pi\) | ||||
−0.413364 | + | 0.910566i | \(0.635646\pi\) | |||||||
\(920\) | −6.53113 | −0.215325 | ||||||||
\(921\) | −30.1245 | −0.992637 | ||||||||
\(922\) | 24.0000 | 0.790398 | ||||||||
\(923\) | −75.1868 | −2.47480 | ||||||||
\(924\) | −29.5934 | −0.973551 | ||||||||
\(925\) | −7.06226 | −0.232206 | ||||||||
\(926\) | 13.1868 | 0.433344 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.8424 | −1.70089 | −0.850447 | − | 0.526060i | \(-0.823669\pi\) | ||||
−0.850447 | + | 0.526060i | \(0.823669\pi\) | |||||||
\(930\) | −1.00000 | −0.0327913 | ||||||||
\(931\) | 61.3113 | 2.00940 | ||||||||
\(932\) | 1.46887 | 0.0481145 | ||||||||
\(933\) | −8.00000 | −0.261908 | ||||||||
\(934\) | −22.1245 | −0.723936 | ||||||||
\(935\) | 26.1245 | 0.854363 | ||||||||
\(936\) | 6.00000 | 0.196116 | ||||||||
\(937\) | −8.93774 | −0.291983 | −0.145992 | − | 0.989286i | \(-0.546637\pi\) | ||||
−0.145992 | + | 0.989286i | \(0.546637\pi\) | |||||||
\(938\) | −22.9377 | −0.748944 | ||||||||
\(939\) | 10.9377 | 0.356940 | ||||||||
\(940\) | 5.06226 | 0.165113 | ||||||||
\(941\) | −54.1245 | −1.76441 | −0.882204 | − | 0.470867i | \(-0.843941\pi\) | ||||
−0.882204 | + | 0.470867i | \(0.843941\pi\) | |||||||
\(942\) | −22.5311 | −0.734104 | ||||||||
\(943\) | 46.1245 | 1.50202 | ||||||||
\(944\) | −9.06226 | −0.294951 | ||||||||
\(945\) | 4.53113 | 0.147398 | ||||||||
\(946\) | −55.7179 | −1.81155 | ||||||||
\(947\) | 18.9377 | 0.615394 | 0.307697 | − | 0.951484i | \(-0.400442\pi\) | ||||
0.307697 | + | 0.951484i | \(0.400442\pi\) | |||||||
\(948\) | −8.53113 | −0.277078 | ||||||||
\(949\) | −51.1868 | −1.66159 | ||||||||
\(950\) | 4.53113 | 0.147009 | ||||||||
\(951\) | 12.9377 | 0.419535 | ||||||||
\(952\) | 18.1245 | 0.587419 | ||||||||
\(953\) | 21.8755 | 0.708616 | 0.354308 | − | 0.935129i | \(-0.384716\pi\) | ||||
0.354308 | + | 0.935129i | \(0.384716\pi\) | |||||||
\(954\) | −2.53113 | −0.0819483 | ||||||||
\(955\) | 8.00000 | 0.258874 | ||||||||
\(956\) | −8.00000 | −0.258738 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.34436 | 0.0434342 | ||||||||
\(959\) | −77.3113 | −2.49651 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −42.3735 | −1.36618 | ||||||||
\(963\) | 9.59339 | 0.309143 | ||||||||
\(964\) | 2.00000 | 0.0644157 | ||||||||
\(965\) | −14.0000 | −0.450676 | ||||||||
\(966\) | −29.5934 | −0.952152 | ||||||||
\(967\) | −0.937742 | −0.0301558 | −0.0150779 | − | 0.999886i | \(-0.504800\pi\) | ||||
−0.0150779 | + | 0.999886i | \(0.504800\pi\) | |||||||
\(968\) | 31.6556 | 1.01745 | ||||||||
\(969\) | −18.1245 | −0.582243 | ||||||||
\(970\) | −16.1245 | −0.517727 | ||||||||
\(971\) | 15.1868 | 0.487367 | 0.243683 | − | 0.969855i | \(-0.421644\pi\) | ||||
0.243683 | + | 0.969855i | \(0.421644\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −27.1868 | −0.871568 | ||||||||
\(974\) | 23.0623 | 0.738962 | ||||||||
\(975\) | 6.00000 | 0.192154 | ||||||||
\(976\) | 5.06226 | 0.162039 | ||||||||
\(977\) | −38.0000 | −1.21573 | −0.607864 | − | 0.794041i | \(-0.707973\pi\) | ||||
−0.607864 | + | 0.794041i | \(0.707973\pi\) | |||||||
\(978\) | 5.06226 | 0.161873 | ||||||||
\(979\) | −42.6556 | −1.36328 | ||||||||
\(980\) | −13.5311 | −0.432236 | ||||||||
\(981\) | 15.0623 | 0.480901 | ||||||||
\(982\) | −7.59339 | −0.242315 | ||||||||
\(983\) | 0.937742 | 0.0299093 | 0.0149547 | − | 0.999888i | \(-0.495240\pi\) | ||||
0.0149547 | + | 0.999888i | \(0.495240\pi\) | |||||||
\(984\) | 7.06226 | 0.225137 | ||||||||
\(985\) | −6.00000 | −0.191176 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.9377 | 0.730116 | ||||||||
\(988\) | 27.1868 | 0.864926 | ||||||||
\(989\) | −55.7179 | −1.77173 | ||||||||
\(990\) | −6.53113 | −0.207573 | ||||||||
\(991\) | −32.5311 | −1.03339 | −0.516693 | − | 0.856171i | \(-0.672837\pi\) | ||||
−0.516693 | + | 0.856171i | \(0.672837\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | 12.9377 | 0.410567 | ||||||||
\(994\) | 56.7802 | 1.80096 | ||||||||
\(995\) | 8.53113 | 0.270455 | ||||||||
\(996\) | −8.00000 | −0.253490 | ||||||||
\(997\) | −2.24903 | −0.0712275 | −0.0356138 | − | 0.999366i | \(-0.511339\pi\) | ||||
−0.0356138 | + | 0.999366i | \(0.511339\pi\) | |||||||
\(998\) | −7.06226 | −0.223552 | ||||||||
\(999\) | −7.06226 | −0.223440 |
(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 | 930.2.a.q.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 2790.2.a.bf.1.1 | 2 | |||
4.3 | odd | 2 | 7440.2.a.bd.1.2 | 2 | |||
5.2 | odd | 4 | 4650.2.d.bg.3349.3 | 4 | |||
5.3 | odd | 4 | 4650.2.d.bg.3349.2 | 4 | |||
5.4 | even | 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 | 1.1 | even | 1 | trivial | |
2790.2.a.bf.1.1 | 2 | 3.2 | odd | 2 | |||
4650.2.a.bz.1.2 | 2 | 5.4 | even | 2 | |||
4650.2.d.bg.3349.2 | 4 | 5.3 | odd | 4 | |||
4650.2.d.bg.3349.3 | 4 | 5.2 | odd | 4 | |||
7440.2.a.bd.1.2 | 2 | 4.3 | odd | 2 |