Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5625,2,Mod(1,5625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("5625.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5625 = 3^{2} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5625.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: | \(44.9158511370\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5625.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.618034 | 0.437016 | 0.218508 | − | 0.975835i | \(-0.429881\pi\) | ||||
0.218508 | + | 0.975835i | \(0.429881\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.61803 | 0.611559 | 0.305780 | − | 0.952102i | \(-0.401083\pi\) | ||||
0.305780 | + | 0.952102i | \(0.401083\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.763932 | 0.230334 | 0.115167 | − | 0.993346i | \(-0.463260\pi\) | ||||
0.115167 | + | 0.993346i | \(0.463260\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.85410 | 1.34629 | 0.673143 | − | 0.739512i | \(-0.264944\pi\) | ||||
0.673143 | + | 0.739512i | \(0.264944\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | −0.763932 | −0.185281 | −0.0926404 | − | 0.995700i | \(-0.529531\pi\) | ||||
−0.0926404 | + | 0.995700i | \(0.529531\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.85410 | −1.34302 | −0.671512 | − | 0.740994i | \(-0.734355\pi\) | ||||
−0.671512 | + | 0.740994i | \(0.734355\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.472136 | 0.100660 | ||||||||
\(23\) | 8.23607 | 1.71734 | 0.858669 | − | 0.512530i | \(-0.171292\pi\) | ||||
0.858669 | + | 0.512530i | \(0.171292\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.00000 | 0.588348 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.61803 | −0.494762 | ||||||||
\(29\) | 1.38197 | 0.256625 | 0.128312 | − | 0.991734i | \(-0.459044\pi\) | ||||
0.128312 | + | 0.991734i | \(0.459044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 5.61803 | 0.993137 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.472136 | −0.0809706 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.23607 | −0.696405 | −0.348203 | − | 0.937419i | \(-0.613208\pi\) | ||||
−0.348203 | + | 0.937419i | \(0.613208\pi\) | |||||||
\(38\) | −3.61803 | −0.586923 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.23607 | 0.817736 | 0.408868 | − | 0.912593i | \(-0.365924\pi\) | ||||
0.408868 | + | 0.912593i | \(0.365924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.85410 | −0.282748 | −0.141374 | − | 0.989956i | \(-0.545152\pi\) | ||||
−0.141374 | + | 0.989956i | \(0.545152\pi\) | |||||||
\(44\) | −1.23607 | −0.186344 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.09017 | 0.750505 | ||||||||
\(47\) | −1.61803 | −0.236015 | −0.118007 | − | 0.993013i | \(-0.537651\pi\) | ||||
−0.118007 | + | 0.993013i | \(0.537651\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.38197 | −0.625995 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.85410 | −1.08917 | ||||||||
\(53\) | 5.47214 | 0.751656 | 0.375828 | − | 0.926690i | \(-0.377358\pi\) | ||||
0.375828 | + | 0.926690i | \(0.377358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.61803 | −0.483480 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.854102 | 0.112149 | ||||||||
\(59\) | 4.14590 | 0.539750 | 0.269875 | − | 0.962895i | \(-0.413018\pi\) | ||||
0.269875 | + | 0.962895i | \(0.413018\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.70820 | −0.602824 | −0.301412 | − | 0.953494i | \(-0.597458\pi\) | ||||
−0.301412 | + | 0.953494i | \(0.597458\pi\) | |||||||
\(62\) | −1.85410 | −0.235471 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.23607 | −1.12837 | −0.564183 | − | 0.825650i | \(-0.690809\pi\) | ||||
−0.564183 | + | 0.825650i | \(0.690809\pi\) | |||||||
\(68\) | 1.23607 | 0.149895 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.38197 | 0.520044 | 0.260022 | − | 0.965603i | \(-0.416270\pi\) | ||||
0.260022 | + | 0.965603i | \(0.416270\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.00000 | 1.05337 | 0.526685 | − | 0.850060i | \(-0.323435\pi\) | ||||
0.526685 | + | 0.850060i | \(0.323435\pi\) | |||||||
\(74\) | −2.61803 | −0.304340 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.47214 | 1.08653 | ||||||||
\(77\) | 1.23607 | 0.140863 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.09017 | 0.347671 | 0.173836 | − | 0.984775i | \(-0.444384\pi\) | ||||
0.173836 | + | 0.984775i | \(0.444384\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.23607 | 0.357364 | ||||||||
\(83\) | −1.76393 | −0.193617 | −0.0968083 | − | 0.995303i | \(-0.530863\pi\) | ||||
−0.0968083 | + | 0.995303i | \(0.530863\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.14590 | −0.123565 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.70820 | −0.182095 | ||||||||
\(89\) | −8.94427 | −0.948091 | −0.474045 | − | 0.880500i | \(-0.657207\pi\) | ||||
−0.474045 | + | 0.880500i | \(0.657207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.85410 | 0.823334 | ||||||||
\(92\) | −13.3262 | −1.38936 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.00000 | −0.103142 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.85410 | −0.289790 | −0.144895 | − | 0.989447i | \(-0.546284\pi\) | ||||
−0.144895 | + | 0.989447i | \(0.546284\pi\) | |||||||
\(98\) | −2.70820 | −0.273570 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.47214 | 0.743505 | 0.371753 | − | 0.928332i | \(-0.378757\pi\) | ||||
0.371753 | + | 0.928332i | \(0.378757\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.5623 | 1.13927 | 0.569634 | − | 0.821899i | \(-0.307085\pi\) | ||||
0.569634 | + | 0.821899i | \(0.307085\pi\) | |||||||
\(104\) | −10.8541 | −1.06433 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.38197 | 0.328486 | ||||||||
\(107\) | 10.4164 | 1.00699 | 0.503496 | − | 0.863998i | \(-0.332047\pi\) | ||||
0.503496 | + | 0.863998i | \(0.332047\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.00000 | 0.283473 | ||||||||
\(113\) | 10.1459 | 0.954446 | 0.477223 | − | 0.878782i | \(-0.341643\pi\) | ||||
0.477223 | + | 0.878782i | \(0.341643\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.23607 | −0.207614 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.56231 | 0.235879 | ||||||||
\(119\) | −1.23607 | −0.113310 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4164 | −0.946946 | ||||||||
\(122\) | −2.90983 | −0.263444 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.85410 | 0.435911 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.8885 | 1.40988 | 0.704940 | − | 0.709267i | \(-0.250974\pi\) | ||||
0.704940 | + | 0.709267i | \(0.250974\pi\) | |||||||
\(128\) | −11.3820 | −1.00603 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.7984 | 1.55505 | 0.777526 | − | 0.628851i | \(-0.216475\pi\) | ||||
0.777526 | + | 0.628851i | \(0.216475\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.47214 | −0.821338 | ||||||||
\(134\) | −5.70820 | −0.493114 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.70820 | 0.146477 | ||||||||
\(137\) | 5.94427 | 0.507853 | 0.253927 | − | 0.967223i | \(-0.418278\pi\) | ||||
0.253927 | + | 0.967223i | \(0.418278\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000 | 0.424094 | 0.212047 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.70820 | 0.227267 | ||||||||
\(143\) | 3.70820 | 0.310096 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.56231 | 0.460340 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.85410 | 0.563404 | ||||||||
\(149\) | −13.9443 | −1.14236 | −0.571180 | − | 0.820825i | \(-0.693514\pi\) | ||||
−0.571180 | + | 0.820825i | \(0.693514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.56231 | −0.452654 | −0.226327 | − | 0.974051i | \(-0.572672\pi\) | ||||
−0.226327 | + | 0.974051i | \(0.572672\pi\) | |||||||
\(152\) | 13.0902 | 1.06175 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.763932 | 0.0615594 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.18034 | 0.732671 | 0.366335 | − | 0.930483i | \(-0.380612\pi\) | ||||
0.366335 | + | 0.930483i | \(0.380612\pi\) | |||||||
\(158\) | 1.90983 | 0.151938 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.3262 | 1.05025 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.0000 | −0.861586 | −0.430793 | − | 0.902451i | \(-0.641766\pi\) | ||||
−0.430793 | + | 0.902451i | \(0.641766\pi\) | |||||||
\(164\) | −8.47214 | −0.661563 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.09017 | −0.0846136 | ||||||||
\(167\) | −5.56231 | −0.430424 | −0.215212 | − | 0.976567i | \(-0.569044\pi\) | ||||
−0.215212 | + | 0.976567i | \(0.569044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5623 | 0.812485 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.00000 | 0.228748 | ||||||||
\(173\) | −16.8885 | −1.28401 | −0.642006 | − | 0.766700i | \(-0.721898\pi\) | ||||
−0.642006 | + | 0.766700i | \(0.721898\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.41641 | 0.106766 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.52786 | −0.414331 | ||||||||
\(179\) | 9.47214 | 0.707981 | 0.353990 | − | 0.935249i | \(-0.384825\pi\) | ||||
0.353990 | + | 0.935249i | \(0.384825\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7082 | 1.01892 | 0.509461 | − | 0.860494i | \(-0.329845\pi\) | ||||
0.509461 | + | 0.860494i | \(0.329845\pi\) | |||||||
\(182\) | 4.85410 | 0.359810 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.4164 | −1.35768 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.583592 | −0.0426765 | ||||||||
\(188\) | 2.61803 | 0.190940 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.1803 | 1.74963 | 0.874814 | − | 0.484459i | \(-0.160984\pi\) | ||||
0.874814 | + | 0.484459i | \(0.160984\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.70820 | 0.410886 | 0.205443 | − | 0.978669i | \(-0.434137\pi\) | ||||
0.205443 | + | 0.978669i | \(0.434137\pi\) | |||||||
\(194\) | −1.76393 | −0.126643 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.09017 | 0.506441 | ||||||||
\(197\) | −9.70820 | −0.691681 | −0.345840 | − | 0.938293i | \(-0.612406\pi\) | ||||
−0.345840 | + | 0.938293i | \(0.612406\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.56231 | 0.181637 | 0.0908185 | − | 0.995867i | \(-0.471052\pi\) | ||||
0.0908185 | + | 0.995867i | \(0.471052\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.61803 | 0.324924 | ||||||||
\(203\) | 2.23607 | 0.156941 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.14590 | 0.497878 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.00000 | 0.624038 | ||||||||
\(209\) | −4.47214 | −0.309344 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.1803 | 0.907372 | 0.453686 | − | 0.891162i | \(-0.350109\pi\) | ||||
0.453686 | + | 0.891162i | \(0.350109\pi\) | |||||||
\(212\) | −8.85410 | −0.608102 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.43769 | 0.440072 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.85410 | −0.329518 | ||||||||
\(218\) | 6.18034 | 0.418585 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.70820 | −0.249441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.1803 | −1.48531 | −0.742653 | − | 0.669677i | \(-0.766433\pi\) | ||||
−0.742653 | + | 0.669677i | \(0.766433\pi\) | |||||||
\(224\) | 9.09017 | 0.607363 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.27051 | 0.417108 | ||||||||
\(227\) | 19.2361 | 1.27674 | 0.638371 | − | 0.769729i | \(-0.279608\pi\) | ||||
0.638371 | + | 0.769729i | \(0.279608\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.29180 | 0.547937 | 0.273969 | − | 0.961739i | \(-0.411664\pi\) | ||||
0.273969 | + | 0.961739i | \(0.411664\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.09017 | −0.202880 | ||||||||
\(233\) | 14.9443 | 0.979032 | 0.489516 | − | 0.871994i | \(-0.337174\pi\) | ||||
0.489516 | + | 0.871994i | \(0.337174\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.70820 | −0.436667 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.763932 | −0.0495184 | ||||||||
\(239\) | 29.4721 | 1.90639 | 0.953197 | − | 0.302350i | \(-0.0977711\pi\) | ||||
0.953197 | + | 0.302350i | \(0.0977711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4721 | 0.738985 | 0.369493 | − | 0.929234i | \(-0.379532\pi\) | ||||
0.369493 | + | 0.929234i | \(0.379532\pi\) | |||||||
\(242\) | −6.43769 | −0.413831 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.61803 | 0.487695 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.4164 | −1.80809 | ||||||||
\(248\) | 6.70820 | 0.425971 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.81966 | 0.430453 | 0.215227 | − | 0.976564i | \(-0.430951\pi\) | ||||
0.215227 | + | 0.976564i | \(0.430951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.29180 | 0.395562 | ||||||||
\(254\) | 9.81966 | 0.616140 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 16.1459 | 1.00715 | 0.503577 | − | 0.863951i | \(-0.332017\pi\) | ||||
0.503577 | + | 0.863951i | \(0.332017\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.85410 | −0.425893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.0000 | 0.679582 | ||||||||
\(263\) | −22.0902 | −1.36214 | −0.681069 | − | 0.732219i | \(-0.738485\pi\) | ||||
−0.681069 | + | 0.732219i | \(0.738485\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.85410 | −0.358938 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.9443 | 0.912867 | ||||||||
\(269\) | 17.2361 | 1.05090 | 0.525451 | − | 0.850824i | \(-0.323897\pi\) | ||||
0.525451 | + | 0.850824i | \(0.323897\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | −1.41641 | −0.0858823 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.67376 | 0.221940 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.2918 | 0.678458 | 0.339229 | − | 0.940704i | \(-0.389834\pi\) | ||||
0.339229 | + | 0.940704i | \(0.389834\pi\) | |||||||
\(278\) | 3.09017 | 0.185336 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.09017 | 0.0650341 | 0.0325170 | − | 0.999471i | \(-0.489648\pi\) | ||||
0.0325170 | + | 0.999471i | \(0.489648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.1459 | 1.37588 | 0.687940 | − | 0.725767i | \(-0.258515\pi\) | ||||
0.687940 | + | 0.725767i | \(0.258515\pi\) | |||||||
\(284\) | −7.09017 | −0.420724 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.29180 | 0.135517 | ||||||||
\(287\) | 8.47214 | 0.500094 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.5623 | −0.852194 | ||||||||
\(293\) | −28.4721 | −1.66336 | −0.831680 | − | 0.555255i | \(-0.812621\pi\) | ||||
−0.831680 | + | 0.555255i | \(0.812621\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.47214 | 0.550557 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.61803 | −0.499229 | ||||||||
\(299\) | 39.9787 | 2.31203 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | −0.172917 | ||||||||
\(302\) | −3.43769 | −0.197817 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.8541 | −0.622525 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.76393 | −0.271892 | −0.135946 | − | 0.990716i | \(-0.543407\pi\) | ||||
−0.135946 | + | 0.990716i | \(0.543407\pi\) | |||||||
\(308\) | −2.00000 | −0.113961 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.5066 | 1.67316 | 0.836582 | − | 0.547841i | \(-0.184550\pi\) | ||||
0.836582 | + | 0.547841i | \(0.184550\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.2361 | 1.20033 | 0.600167 | − | 0.799875i | \(-0.295101\pi\) | ||||
0.600167 | + | 0.799875i | \(0.295101\pi\) | |||||||
\(314\) | 5.67376 | 0.320189 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.00000 | −0.281272 | ||||||||
\(317\) | −23.6525 | −1.32846 | −0.664228 | − | 0.747530i | \(-0.731239\pi\) | ||||
−0.664228 | + | 0.747530i | \(0.731239\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.05573 | 0.0591094 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.23607 | 0.458978 | ||||||||
\(323\) | 4.47214 | 0.248836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.79837 | −0.376527 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.7082 | −0.646477 | ||||||||
\(329\) | −2.61803 | −0.144337 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1246 | 0.941254 | 0.470627 | − | 0.882332i | \(-0.344028\pi\) | ||||
0.470627 | + | 0.882332i | \(0.344028\pi\) | |||||||
\(332\) | 2.85410 | 0.156639 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.43769 | −0.188102 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.14590 | −0.0624210 | −0.0312105 | − | 0.999513i | \(-0.509936\pi\) | ||||
−0.0312105 | + | 0.999513i | \(0.509936\pi\) | |||||||
\(338\) | 6.52786 | 0.355069 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.29180 | −0.124108 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4164 | −0.994393 | ||||||||
\(344\) | 4.14590 | 0.223532 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.4377 | −0.561134 | ||||||||
\(347\) | −31.0902 | −1.66901 | −0.834504 | − | 0.551002i | \(-0.814246\pi\) | ||||
−0.834504 | + | 0.551002i | \(0.814246\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.29180 | 0.443850 | 0.221925 | − | 0.975064i | \(-0.428766\pi\) | ||||
0.221925 | + | 0.975064i | \(0.428766\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.29180 | 0.228753 | ||||||||
\(353\) | 24.0902 | 1.28219 | 0.641095 | − | 0.767461i | \(-0.278480\pi\) | ||||
0.641095 | + | 0.767461i | \(0.278480\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.4721 | 0.767022 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.85410 | 0.309399 | ||||||||
\(359\) | 28.7426 | 1.51698 | 0.758489 | − | 0.651685i | \(-0.225938\pi\) | ||||
0.758489 | + | 0.651685i | \(0.225938\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2705 | 0.803711 | ||||||||
\(362\) | 8.47214 | 0.445286 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.7082 | −0.666091 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.43769 | 0.283845 | 0.141923 | − | 0.989878i | \(-0.454672\pi\) | ||||
0.141923 | + | 0.989878i | \(0.454672\pi\) | |||||||
\(368\) | 15.2705 | 0.796030 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.85410 | 0.459682 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.27051 | −0.272897 | −0.136448 | − | 0.990647i | \(-0.543569\pi\) | ||||
−0.136448 | + | 0.990647i | \(0.543569\pi\) | |||||||
\(374\) | −0.360680 | −0.0186503 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.61803 | 0.186586 | ||||||||
\(377\) | 6.70820 | 0.345490 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −34.5967 | −1.77712 | −0.888558 | − | 0.458765i | \(-0.848292\pi\) | ||||
−0.888558 | + | 0.458765i | \(0.848292\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.9443 | 0.764615 | ||||||||
\(383\) | −11.3607 | −0.580504 | −0.290252 | − | 0.956950i | \(-0.593739\pi\) | ||||
−0.290252 | + | 0.956950i | \(0.593739\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.52786 | 0.179564 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.61803 | 0.234445 | ||||||||
\(389\) | −15.0000 | −0.760530 | −0.380265 | − | 0.924878i | \(-0.624167\pi\) | ||||
−0.380265 | + | 0.924878i | \(0.624167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.29180 | −0.318190 | ||||||||
\(392\) | 9.79837 | 0.494893 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.0344419 | 0.00172859 | 0.000864294 | − | 1.00000i | \(-0.499725\pi\) | ||||
0.000864294 | 1.00000i | \(0.499725\pi\) | ||||||||
\(398\) | 1.58359 | 0.0793783 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.5967 | 1.12843 | 0.564214 | − | 0.825629i | \(-0.309179\pi\) | ||||
0.564214 | + | 0.825629i | \(0.309179\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.5623 | −0.725400 | ||||||||
\(404\) | −12.0902 | −0.601508 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.38197 | 0.0685858 | ||||||||
\(407\) | −3.23607 | −0.160406 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.4164 | 1.40510 | 0.702550 | − | 0.711634i | \(-0.252045\pi\) | ||||
0.702550 | + | 0.711634i | \(0.252045\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −18.7082 | −0.921687 | ||||||||
\(413\) | 6.70820 | 0.330089 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 27.2705 | 1.33705 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.76393 | −0.135188 | ||||||||
\(419\) | 0.527864 | 0.0257878 | 0.0128939 | − | 0.999917i | \(-0.495896\pi\) | ||||
0.0128939 | + | 0.999917i | \(0.495896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.0000 | 1.55958 | 0.779792 | − | 0.626038i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626038i | \(0.215325\pi\) | |||||||
\(422\) | 8.14590 | 0.396536 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.2361 | −0.594236 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.61803 | −0.368663 | ||||||||
\(428\) | −16.8541 | −0.814674 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.8328 | −1.14799 | −0.573993 | − | 0.818860i | \(-0.694606\pi\) | ||||
−0.573993 | + | 0.818860i | \(0.694606\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.1459 | −0.968150 | −0.484075 | − | 0.875026i | \(-0.660844\pi\) | ||||
−0.484075 | + | 0.875026i | \(0.660844\pi\) | |||||||
\(434\) | −3.00000 | −0.144005 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.1803 | −0.774898 | ||||||||
\(437\) | −48.2148 | −2.30643 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.97871 | 0.285348 | 0.142674 | − | 0.989770i | \(-0.454430\pi\) | ||||
0.142674 | + | 0.989770i | \(0.454430\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.29180 | −0.109010 | ||||||||
\(443\) | 12.0557 | 0.572785 | 0.286392 | − | 0.958112i | \(-0.407544\pi\) | ||||
0.286392 | + | 0.958112i | \(0.407544\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.7082 | −0.649102 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.381966 | −0.0180462 | ||||||||
\(449\) | −20.3262 | −0.959254 | −0.479627 | − | 0.877472i | \(-0.659228\pi\) | ||||
−0.479627 | + | 0.877472i | \(0.659228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | −16.4164 | −0.772163 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.8885 | 0.557957 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.41641 | −0.253369 | −0.126684 | − | 0.991943i | \(-0.540434\pi\) | ||||
−0.126684 | + | 0.991943i | \(0.540434\pi\) | |||||||
\(458\) | 5.12461 | 0.239457 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.1803 | −1.07962 | −0.539808 | − | 0.841788i | \(-0.681503\pi\) | ||||
−0.539808 | + | 0.841788i | \(0.681503\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.1246 | −0.749374 | −0.374687 | − | 0.927151i | \(-0.622250\pi\) | ||||
−0.374687 | + | 0.927151i | \(0.622250\pi\) | |||||||
\(464\) | 2.56231 | 0.118952 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.23607 | 0.427853 | ||||||||
\(467\) | −28.4508 | −1.31655 | −0.658274 | − | 0.752778i | \(-0.728713\pi\) | ||||
−0.658274 | + | 0.752778i | \(0.728713\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.9443 | −0.690062 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.27051 | −0.426710 | ||||||||
\(473\) | −1.41641 | −0.0651265 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.00000 | 0.0916698 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.2148 | 0.833125 | ||||||||
\(479\) | 4.14590 | 0.189431 | 0.0947155 | − | 0.995504i | \(-0.469806\pi\) | ||||
0.0947155 | + | 0.995504i | \(0.469806\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.5623 | −0.937560 | ||||||||
\(482\) | 7.09017 | 0.322948 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.8541 | 0.766096 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.58359 | 0.434274 | 0.217137 | − | 0.976141i | \(-0.430328\pi\) | ||||
0.217137 | + | 0.976141i | \(0.430328\pi\) | |||||||
\(488\) | 10.5279 | 0.476574 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.2492 | −1.68103 | −0.840517 | − | 0.541785i | \(-0.817749\pi\) | ||||
−0.840517 | + | 0.541785i | \(0.817749\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.05573 | −0.0475476 | ||||||||
\(494\) | −17.5623 | −0.790165 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.56231 | −0.249755 | ||||||||
\(497\) | 7.09017 | 0.318038 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.5623 | −0.562366 | −0.281183 | − | 0.959654i | \(-0.590727\pi\) | ||||
−0.281183 | + | 0.959654i | \(0.590727\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.21478 | 0.188115 | ||||||||
\(503\) | −10.5836 | −0.471899 | −0.235950 | − | 0.971765i | \(-0.575820\pi\) | ||||
−0.235950 | + | 0.971765i | \(0.575820\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.88854 | 0.172867 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −25.7082 | −1.14062 | ||||||||
\(509\) | 4.67376 | 0.207161 | 0.103580 | − | 0.994621i | \(-0.466970\pi\) | ||||
0.103580 | + | 0.994621i | \(0.466970\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.5623 | 0.644198 | ||||||||
\(512\) | 18.7082 | 0.826794 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.97871 | 0.440142 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.23607 | −0.0543622 | ||||||||
\(518\) | −4.23607 | −0.186122 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.3607 | 0.672964 | 0.336482 | − | 0.941690i | \(-0.390763\pi\) | ||||
0.336482 | + | 0.941690i | \(0.390763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.8541 | 0.868159 | 0.434080 | − | 0.900875i | \(-0.357074\pi\) | ||||
0.434080 | + | 0.900875i | \(0.357074\pi\) | |||||||
\(524\) | −28.7984 | −1.25806 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.6525 | −0.595276 | ||||||||
\(527\) | 2.29180 | 0.0998322 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.8328 | 1.94925 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.3262 | 0.664477 | ||||||||
\(533\) | 25.4164 | 1.10091 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 20.6525 | 0.892051 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.6525 | 0.459261 | ||||||||
\(539\) | −3.34752 | −0.144188 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1246 | −0.564271 | −0.282136 | − | 0.959375i | \(-0.591043\pi\) | ||||
−0.282136 | + | 0.959375i | \(0.591043\pi\) | |||||||
\(542\) | −4.94427 | −0.212375 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.29180 | −0.184009 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.7082 | 1.48402 | 0.742008 | − | 0.670391i | \(-0.233874\pi\) | ||||
0.742008 | + | 0.670391i | \(0.233874\pi\) | |||||||
\(548\) | −9.61803 | −0.410862 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.09017 | −0.344653 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.00000 | 0.212622 | ||||||||
\(554\) | 6.97871 | 0.296497 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.09017 | −0.343100 | ||||||||
\(557\) | 9.23607 | 0.391345 | 0.195672 | − | 0.980669i | \(-0.437311\pi\) | ||||
0.195672 | + | 0.980669i | \(0.437311\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.00000 | −0.380659 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.673762 | 0.0284209 | ||||||||
\(563\) | 9.61803 | 0.405352 | 0.202676 | − | 0.979246i | \(-0.435036\pi\) | ||||
0.202676 | + | 0.979246i | \(0.435036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.3050 | 0.601282 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.79837 | −0.411131 | ||||||||
\(569\) | −29.4721 | −1.23554 | −0.617768 | − | 0.786360i | \(-0.711963\pi\) | ||||
−0.617768 | + | 0.786360i | \(0.711963\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.1246 | 1.34437 | 0.672187 | − | 0.740382i | \(-0.265355\pi\) | ||||
0.672187 | + | 0.740382i | \(0.265355\pi\) | |||||||
\(572\) | −6.00000 | −0.250873 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.23607 | 0.218549 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −37.7771 | −1.57268 | −0.786340 | − | 0.617794i | \(-0.788027\pi\) | ||||
−0.786340 | + | 0.617794i | \(0.788027\pi\) | |||||||
\(578\) | −10.1459 | −0.422014 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.85410 | −0.118408 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.18034 | 0.173132 | ||||||||
\(584\) | −20.1246 | −0.832762 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.5967 | −0.726915 | ||||||||
\(587\) | 18.7082 | 0.772170 | 0.386085 | − | 0.922463i | \(-0.373827\pi\) | ||||
0.386085 | + | 0.922463i | \(0.373827\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.5623 | 0.723642 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.85410 | −0.322802 | ||||||||
\(593\) | −22.0902 | −0.907135 | −0.453567 | − | 0.891222i | \(-0.649849\pi\) | ||||
−0.453567 | + | 0.891222i | \(0.649849\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.5623 | 0.924188 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 24.7082 | 1.01039 | ||||||||
\(599\) | 0.527864 | 0.0215679 | 0.0107840 | − | 0.999942i | \(-0.496567\pi\) | ||||
0.0107840 | + | 0.999942i | \(0.496567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2705 | 1.47950 | 0.739752 | − | 0.672879i | \(-0.234943\pi\) | ||||
0.739752 | + | 0.672879i | \(0.234943\pi\) | |||||||
\(602\) | −1.85410 | −0.0755676 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 9.00000 | 0.366205 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.4377 | 0.626597 | 0.313298 | − | 0.949655i | \(-0.398566\pi\) | ||||
0.313298 | + | 0.949655i | \(0.398566\pi\) | |||||||
\(608\) | −32.8885 | −1.33381 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.85410 | −0.317743 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.9787 | −1.29161 | −0.645804 | − | 0.763503i | \(-0.723478\pi\) | ||||
−0.645804 | + | 0.763503i | \(0.723478\pi\) | |||||||
\(614\) | −2.94427 | −0.118821 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.76393 | −0.111362 | ||||||||
\(617\) | 9.76393 | 0.393081 | 0.196541 | − | 0.980496i | \(-0.437029\pi\) | ||||
0.196541 | + | 0.980496i | \(0.437029\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.4721 | 1.58652 | 0.793260 | − | 0.608884i | \(-0.208382\pi\) | ||||
0.793260 | + | 0.608884i | \(0.208382\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.2361 | 0.731200 | ||||||||
\(623\) | −14.4721 | −0.579814 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.1246 | 0.524565 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.8541 | −0.592743 | ||||||||
\(629\) | 3.23607 | 0.129030 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.76393 | −0.229459 | −0.114729 | − | 0.993397i | \(-0.536600\pi\) | ||||
−0.114729 | + | 0.993397i | \(0.536600\pi\) | |||||||
\(632\) | −6.90983 | −0.274858 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.6180 | −0.580556 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.2705 | −0.842768 | ||||||||
\(638\) | 0.652476 | 0.0258318 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.0902 | −0.398538 | −0.199269 | − | 0.979945i | \(-0.563857\pi\) | ||||
−0.199269 | + | 0.979945i | \(0.563857\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.8328 | −0.900438 | −0.450219 | − | 0.892918i | \(-0.648654\pi\) | ||||
−0.450219 | + | 0.892918i | \(0.648654\pi\) | |||||||
\(644\) | −21.5623 | −0.849674 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.76393 | 0.108745 | ||||||||
\(647\) | 30.5410 | 1.20069 | 0.600346 | − | 0.799741i | \(-0.295030\pi\) | ||||
0.600346 | + | 0.799741i | \(0.295030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.16718 | 0.124323 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.7984 | 0.697038 | ||||||||
\(653\) | 7.90983 | 0.309536 | 0.154768 | − | 0.987951i | \(-0.450537\pi\) | ||||
0.154768 | + | 0.987951i | \(0.450537\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.70820 | 0.379042 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.61803 | −0.0630775 | ||||||||
\(659\) | −24.4721 | −0.953299 | −0.476650 | − | 0.879093i | \(-0.658149\pi\) | ||||
−0.476650 | + | 0.879093i | \(0.658149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.6869 | −1.58254 | −0.791269 | − | 0.611468i | \(-0.790579\pi\) | ||||
−0.791269 | + | 0.611468i | \(0.790579\pi\) | |||||||
\(662\) | 10.5836 | 0.411343 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.94427 | 0.153067 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.3820 | 0.440711 | ||||||||
\(668\) | 9.00000 | 0.348220 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.59675 | −0.138851 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.1803 | 0.392423 | 0.196212 | − | 0.980562i | \(-0.437136\pi\) | ||||
0.196212 | + | 0.980562i | \(0.437136\pi\) | |||||||
\(674\) | −0.708204 | −0.0272790 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.0902 | −0.657314 | ||||||||
\(677\) | 8.38197 | 0.322145 | 0.161073 | − | 0.986943i | \(-0.448505\pi\) | ||||
0.161073 | + | 0.986943i | \(0.448505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.61803 | −0.177224 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.41641 | −0.0542371 | ||||||||
\(683\) | −4.52786 | −0.173254 | −0.0866270 | − | 0.996241i | \(-0.527609\pi\) | ||||
−0.0866270 | + | 0.996241i | \(0.527609\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.3820 | −0.434565 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.43769 | −0.131061 | ||||||||
\(689\) | 26.5623 | 1.01194 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.72949 | 0.103835 | 0.0519173 | − | 0.998651i | \(-0.483467\pi\) | ||||
0.0519173 | + | 0.998651i | \(0.483467\pi\) | |||||||
\(692\) | 27.3262 | 1.03879 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.2148 | −0.729383 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | −0.151511 | ||||||||
\(698\) | 5.12461 | 0.193969 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.0132 | −1.32243 | −0.661214 | − | 0.750197i | \(-0.729959\pi\) | ||||
−0.661214 | + | 0.750197i | \(0.729959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.7984 | 0.935288 | ||||||||
\(704\) | −0.180340 | −0.00679682 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.8885 | 0.560338 | ||||||||
\(707\) | 12.0902 | 0.454698 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.5410 | 1.25966 | 0.629830 | − | 0.776733i | \(-0.283125\pi\) | ||||
0.629830 | + | 0.776733i | \(0.283125\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20.0000 | 0.749532 | ||||||||
\(713\) | −24.7082 | −0.925330 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.3262 | −0.572768 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.7639 | 0.662944 | ||||||||
\(719\) | 36.7082 | 1.36899 | 0.684493 | − | 0.729020i | \(-0.260024\pi\) | ||||
0.684493 | + | 0.729020i | \(0.260024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.7082 | 0.696730 | ||||||||
\(722\) | 9.43769 | 0.351235 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.1803 | −0.824326 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.43769 | −0.164585 | −0.0822925 | − | 0.996608i | \(-0.526224\pi\) | ||||
−0.0822925 | + | 0.996608i | \(0.526224\pi\) | |||||||
\(728\) | −17.5623 | −0.650902 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.41641 | 0.0523877 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.9787 | −0.996482 | −0.498241 | − | 0.867039i | \(-0.666020\pi\) | ||||
−0.498241 | + | 0.867039i | \(0.666020\pi\) | |||||||
\(734\) | 3.36068 | 0.124045 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 46.2705 | 1.70555 | ||||||||
\(737\) | −7.05573 | −0.259901 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.9787 | −1.13957 | −0.569785 | − | 0.821794i | \(-0.692974\pi\) | ||||
−0.569785 | + | 0.821794i | \(0.692974\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.47214 | 0.200888 | ||||||||
\(743\) | −16.3607 | −0.600215 | −0.300108 | − | 0.953905i | \(-0.597023\pi\) | ||||
−0.300108 | + | 0.953905i | \(0.597023\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.25735 | −0.119260 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.944272 | 0.0345260 | ||||||||
\(749\) | 16.8541 | 0.615835 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.8885 | −1.49204 | −0.746022 | − | 0.665921i | \(-0.768039\pi\) | ||||
−0.746022 | + | 0.665921i | \(0.768039\pi\) | |||||||
\(752\) | −3.00000 | −0.109399 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.14590 | 0.150985 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.58359 | −0.130248 | −0.0651239 | − | 0.997877i | \(-0.520744\pi\) | ||||
−0.0651239 | + | 0.997877i | \(0.520744\pi\) | |||||||
\(758\) | −21.3820 | −0.776628 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −37.4508 | −1.35759 | −0.678796 | − | 0.734327i | \(-0.737498\pi\) | ||||
−0.678796 | + | 0.734327i | \(0.737498\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.1803 | 0.585768 | ||||||||
\(764\) | −39.1246 | −1.41548 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.02129 | −0.253689 | ||||||||
\(767\) | 20.1246 | 0.726658 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4164 | −0.483808 | −0.241904 | − | 0.970300i | \(-0.577772\pi\) | ||||
−0.241904 | + | 0.970300i | \(0.577772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.23607 | −0.332413 | ||||||||
\(773\) | 33.1591 | 1.19265 | 0.596324 | − | 0.802744i | \(-0.296627\pi\) | ||||
0.596324 | + | 0.802744i | \(0.296627\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.38197 | 0.229099 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.27051 | −0.332364 | ||||||||
\(779\) | −30.6525 | −1.09824 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.34752 | 0.119784 | ||||||||
\(782\) | −3.88854 | −0.139054 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.12461 | −0.290165 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.1803 | 1.21840 | 0.609199 | − | 0.793018i | \(-0.291491\pi\) | ||||
0.609199 | + | 0.793018i | \(0.291491\pi\) | |||||||
\(788\) | 15.7082 | 0.559582 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.4164 | 0.583700 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.8541 | −0.811573 | ||||||||
\(794\) | 0.0212862 | 0.000755420 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.14590 | −0.146947 | ||||||||
\(797\) | 14.2361 | 0.504267 | 0.252134 | − | 0.967692i | \(-0.418868\pi\) | ||||
0.252134 | + | 0.967692i | \(0.418868\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.23607 | 0.0437289 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.9656 | 0.493141 | ||||||||
\(803\) | 6.87539 | 0.242627 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.00000 | −0.317011 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.7082 | −0.587793 | ||||||||
\(809\) | 15.9787 | 0.561782 | 0.280891 | − | 0.959740i | \(-0.409370\pi\) | ||||
0.280891 | + | 0.959740i | \(0.409370\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.29180 | −0.0453611 | −0.0226805 | − | 0.999743i | \(-0.507220\pi\) | ||||
−0.0226805 | + | 0.999743i | \(0.507220\pi\) | |||||||
\(812\) | −3.61803 | −0.126968 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.00000 | −0.0701000 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.8541 | 0.379737 | ||||||||
\(818\) | 17.5623 | 0.614052 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.6869 | −0.687078 | −0.343539 | − | 0.939138i | \(-0.611626\pi\) | ||||
−0.343539 | + | 0.939138i | \(0.611626\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.2918 | −1.19534 | −0.597668 | − | 0.801743i | \(-0.703906\pi\) | ||||
−0.597668 | + | 0.801743i | \(0.703906\pi\) | |||||||
\(824\) | −25.8541 | −0.900670 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.14590 | 0.144254 | ||||||||
\(827\) | −30.0344 | −1.04440 | −0.522200 | − | 0.852823i | \(-0.674889\pi\) | ||||
−0.522200 | + | 0.852823i | \(0.674889\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.1459 | −1.01228 | −0.506139 | − | 0.862452i | \(-0.668928\pi\) | ||||
−0.506139 | + | 0.862452i | \(0.668928\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.14590 | −0.0397269 | ||||||||
\(833\) | 3.34752 | 0.115985 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.23607 | 0.250265 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.326238 | 0.0112697 | ||||||||
\(839\) | −4.14590 | −0.143132 | −0.0715661 | − | 0.997436i | \(-0.522800\pi\) | ||||
−0.0715661 | + | 0.997436i | \(0.522800\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0902 | −0.934144 | ||||||||
\(842\) | 19.7771 | 0.681563 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.3262 | −0.734079 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.8541 | −0.579114 | ||||||||
\(848\) | 10.1459 | 0.348412 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.8885 | −1.19596 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.3050 | −1.61969 | −0.809845 | − | 0.586643i | \(-0.800449\pi\) | ||||
−0.809845 | + | 0.586643i | \(0.800449\pi\) | |||||||
\(854\) | −4.70820 | −0.161111 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23.2918 | −0.796097 | ||||||||
\(857\) | −40.6869 | −1.38984 | −0.694919 | − | 0.719088i | \(-0.744560\pi\) | ||||
−0.694919 | + | 0.719088i | \(0.744560\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.4164 | −0.969555 | −0.484778 | − | 0.874637i | \(-0.661099\pi\) | ||||
−0.484778 | + | 0.874637i | \(0.661099\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.7295 | −0.501688 | ||||||||
\(863\) | −41.5623 | −1.41480 | −0.707399 | − | 0.706815i | \(-0.750131\pi\) | ||||
−0.707399 | + | 0.706815i | \(0.750131\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12.4508 | −0.423097 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.85410 | 0.266586 | ||||||||
\(869\) | 2.36068 | 0.0800806 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.8328 | −1.51910 | ||||||||
\(872\) | −22.3607 | −0.757228 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −29.7984 | −1.00795 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.5410 | −1.03130 | −0.515648 | − | 0.856800i | \(-0.672449\pi\) | ||||
−0.515648 | + | 0.856800i | \(0.672449\pi\) | |||||||
\(878\) | 3.69505 | 0.124702 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.36068 | −0.146915 | −0.0734575 | − | 0.997298i | \(-0.523403\pi\) | ||||
−0.0734575 | + | 0.997298i | \(0.523403\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.4164 | 1.59569 | 0.797845 | − | 0.602863i | \(-0.205974\pi\) | ||||
0.797845 | + | 0.602863i | \(0.205974\pi\) | |||||||
\(884\) | 6.00000 | 0.201802 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.45085 | 0.250316 | ||||||||
\(887\) | −5.88854 | −0.197718 | −0.0988590 | − | 0.995101i | \(-0.531519\pi\) | ||||
−0.0988590 | + | 0.995101i | \(0.531519\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.7082 | 0.862225 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 35.8885 | 1.20164 | ||||||||
\(893\) | 9.47214 | 0.316973 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −18.4164 | −0.615249 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.5623 | −0.419210 | ||||||||
\(899\) | −4.14590 | −0.138273 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.18034 | −0.139267 | ||||||||
\(902\) | 2.47214 | 0.0823131 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.6869 | −0.754556 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −47.2492 | −1.56888 | −0.784442 | − | 0.620202i | \(-0.787051\pi\) | ||||
−0.784442 | + | 0.620202i | \(0.787051\pi\) | |||||||
\(908\) | −31.1246 | −1.03291 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.7639 | 1.18491 | 0.592456 | − | 0.805603i | \(-0.298158\pi\) | ||||
0.592456 | + | 0.805603i | \(0.298158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.34752 | −0.0445965 | ||||||||
\(914\) | −3.34752 | −0.110726 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.4164 | −0.443291 | ||||||||
\(917\) | 28.7984 | 0.951006 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.78522 | −0.0588889 | −0.0294445 | − | 0.999566i | \(-0.509374\pi\) | ||||
−0.0294445 | + | 0.999566i | \(0.509374\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.3262 | −0.471810 | ||||||||
\(923\) | 21.2705 | 0.700127 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.96556 | −0.327489 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.76393 | 0.254864 | ||||||||
\(929\) | 36.6312 | 1.20183 | 0.600915 | − | 0.799313i | \(-0.294803\pi\) | ||||
0.600915 | + | 0.799313i | \(0.294803\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.6525 | 0.840726 | ||||||||
\(932\) | −24.1803 | −0.792053 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.5836 | −0.575353 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.2705 | −1.67493 | −0.837467 | − | 0.546487i | \(-0.815965\pi\) | ||||
−0.837467 | + | 0.546487i | \(0.815965\pi\) | |||||||
\(938\) | −9.23607 | −0.301568 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.5836 | 0.638407 | 0.319203 | − | 0.947686i | \(-0.396585\pi\) | ||||
0.319203 | + | 0.947686i | \(0.396585\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.1246 | 1.40433 | ||||||||
\(944\) | 7.68692 | 0.250188 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.875388 | −0.0284613 | ||||||||
\(947\) | −28.6525 | −0.931080 | −0.465540 | − | 0.885027i | \(-0.654140\pi\) | ||||
−0.465540 | + | 0.885027i | \(0.654140\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 43.6869 | 1.41814 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.76393 | 0.0895796 | ||||||||
\(953\) | 34.7426 | 1.12542 | 0.562712 | − | 0.826653i | \(-0.309758\pi\) | ||||
0.562712 | + | 0.826653i | \(0.309758\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −47.6869 | −1.54231 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.56231 | 0.0827843 | ||||||||
\(959\) | 9.61803 | 0.310583 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | −12.7082 | −0.409729 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.5623 | −0.597852 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.8885 | −1.28273 | −0.641365 | − | 0.767236i | \(-0.721631\pi\) | ||||
−0.641365 | + | 0.767236i | \(0.721631\pi\) | |||||||
\(968\) | 23.2918 | 0.748627 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.38197 | −0.108532 | −0.0542662 | − | 0.998527i | \(-0.517282\pi\) | ||||
−0.0542662 | + | 0.998527i | \(0.517282\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.09017 | 0.259359 | ||||||||
\(974\) | 5.92299 | 0.189785 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.72949 | −0.279424 | ||||||||
\(977\) | −33.6525 | −1.07664 | −0.538319 | − | 0.842741i | \(-0.680940\pi\) | ||||
−0.538319 | + | 0.842741i | \(0.680940\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.83282 | −0.218378 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23.0213 | −0.734639 | ||||||||
\(983\) | 7.38197 | 0.235448 | 0.117724 | − | 0.993046i | \(-0.462440\pi\) | ||||
0.117724 | + | 0.993046i | \(0.462440\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.652476 | −0.0207791 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 45.9787 | 1.46278 | ||||||||
\(989\) | −15.2705 | −0.485574 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.3607 | 0.932673 | 0.466336 | − | 0.884607i | \(-0.345574\pi\) | ||||
0.466336 | + | 0.884607i | \(0.345574\pi\) | |||||||
\(992\) | −16.8541 | −0.535118 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.38197 | 0.138988 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.8885 | 0.344844 | 0.172422 | − | 0.985023i | \(-0.444841\pi\) | ||||
0.172422 | + | 0.985023i | \(0.444841\pi\) | |||||||
\(998\) | −7.76393 | −0.245763 | ||||||||
\(999\) | 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 | 5625.2.a.d.1.2 | 2 | ||
3.2 | odd | 2 | 625.2.a.c.1.1 | 2 | |||
5.4 | even | 2 | 5625.2.a.f.1.1 | 2 | |||
12.11 | even | 2 | 10000.2.a.l.1.1 | 2 | |||
15.2 | even | 4 | 625.2.b.a.624.2 | 4 | |||
15.8 | even | 4 | 625.2.b.a.624.3 | 4 | |||
15.14 | odd | 2 | 625.2.a.b.1.2 | 2 | |||
25.4 | even | 10 | 225.2.h.b.91.1 | 4 | |||
25.19 | even | 10 | 225.2.h.b.136.1 | 4 | |||
60.59 | even | 2 | 10000.2.a.c.1.2 | 2 | |||
75.2 | even | 20 | 625.2.e.c.124.1 | 8 | |||
75.8 | even | 20 | 125.2.e.a.74.1 | 8 | |||
75.11 | odd | 10 | 625.2.d.b.501.1 | 4 | |||
75.14 | odd | 10 | 625.2.d.h.501.1 | 4 | |||
75.17 | even | 20 | 125.2.e.a.74.2 | 8 | |||
75.23 | even | 20 | 625.2.e.c.124.2 | 8 | |||
75.29 | odd | 10 | 25.2.d.a.16.1 | yes | 4 | ||
75.38 | even | 20 | 625.2.e.c.499.1 | 8 | |||
75.41 | odd | 10 | 625.2.d.b.126.1 | 4 | |||
75.44 | odd | 10 | 25.2.d.a.11.1 | ✓ | 4 | ||
75.47 | even | 20 | 125.2.e.a.49.1 | 8 | |||
75.53 | even | 20 | 125.2.e.a.49.2 | 8 | |||
75.56 | odd | 10 | 125.2.d.a.51.1 | 4 | |||
75.59 | odd | 10 | 625.2.d.h.126.1 | 4 | |||
75.62 | even | 20 | 625.2.e.c.499.2 | 8 | |||
75.71 | odd | 10 | 125.2.d.a.76.1 | 4 | |||
300.119 | even | 10 | 400.2.u.b.161.1 | 4 | |||
300.179 | even | 10 | 400.2.u.b.241.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.d.a.11.1 | ✓ | 4 | 75.44 | odd | 10 | ||
25.2.d.a.16.1 | yes | 4 | 75.29 | odd | 10 | ||
125.2.d.a.51.1 | 4 | 75.56 | odd | 10 | |||
125.2.d.a.76.1 | 4 | 75.71 | odd | 10 | |||
125.2.e.a.49.1 | 8 | 75.47 | even | 20 | |||
125.2.e.a.49.2 | 8 | 75.53 | even | 20 | |||
125.2.e.a.74.1 | 8 | 75.8 | even | 20 | |||
125.2.e.a.74.2 | 8 | 75.17 | even | 20 | |||
225.2.h.b.91.1 | 4 | 25.4 | even | 10 | |||
225.2.h.b.136.1 | 4 | 25.19 | even | 10 | |||
400.2.u.b.161.1 | 4 | 300.119 | even | 10 | |||
400.2.u.b.241.1 | 4 | 300.179 | even | 10 | |||
625.2.a.b.1.2 | 2 | 15.14 | odd | 2 | |||
625.2.a.c.1.1 | 2 | 3.2 | odd | 2 | |||
625.2.b.a.624.2 | 4 | 15.2 | even | 4 | |||
625.2.b.a.624.3 | 4 | 15.8 | even | 4 | |||
625.2.d.b.126.1 | 4 | 75.41 | odd | 10 | |||
625.2.d.b.501.1 | 4 | 75.11 | odd | 10 | |||
625.2.d.h.126.1 | 4 | 75.59 | odd | 10 | |||
625.2.d.h.501.1 | 4 | 75.14 | odd | 10 | |||
625.2.e.c.124.1 | 8 | 75.2 | even | 20 | |||
625.2.e.c.124.2 | 8 | 75.23 | even | 20 | |||
625.2.e.c.499.1 | 8 | 75.38 | even | 20 | |||
625.2.e.c.499.2 | 8 | 75.62 | even | 20 | |||
5625.2.a.d.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5625.2.a.f.1.1 | 2 | 5.4 | even | 2 | |||
10000.2.a.c.1.2 | 2 | 60.59 | even | 2 | |||
10000.2.a.l.1.1 | 2 | 12.11 | even | 2 |