Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [414,4,Mod(1,414)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(414, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("414.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 414.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: | \(24.4267907424\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 219x^{2} - 468x + 3240 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-11.4152\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 414.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 13.2306 | 1.18338 | 0.591690 | − | 0.806166i | \(-0.298461\pi\) | ||||
0.591690 | + | 0.806166i | \(0.298461\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.2926 | −0.555750 | −0.277875 | − | 0.960617i | \(-0.589630\pi\) | ||||
−0.277875 | + | 0.960617i | \(0.589630\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 26.4612 | 0.836776 | ||||||||
\(11\) | 14.6928 | 0.402730 | 0.201365 | − | 0.979516i | \(-0.435462\pi\) | ||||
0.201365 | + | 0.979516i | \(0.435462\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −23.2916 | −0.496918 | −0.248459 | − | 0.968642i | \(-0.579924\pi\) | ||||
−0.248459 | + | 0.968642i | \(0.579924\pi\) | |||||||
\(14\) | −20.5853 | −0.392974 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 119.245 | 1.70125 | 0.850623 | − | 0.525775i | \(-0.176225\pi\) | ||||
0.850623 | + | 0.525775i | \(0.176225\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 112.461 | 1.35791 | 0.678953 | − | 0.734182i | \(-0.262434\pi\) | ||||
0.678953 | + | 0.734182i | \(0.262434\pi\) | |||||||
\(20\) | 52.9223 | 0.591690 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 29.3855 | 0.284773 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 50.0484 | 0.400387 | ||||||||
\(26\) | −46.5833 | −0.351374 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −41.1705 | −0.277875 | ||||||||
\(29\) | −104.646 | −0.670078 | −0.335039 | − | 0.942204i | \(-0.608749\pi\) | ||||
−0.335039 | + | 0.942204i | \(0.608749\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −27.1038 | −0.157032 | −0.0785160 | − | 0.996913i | \(-0.525018\pi\) | ||||
−0.0785160 | + | 0.996913i | \(0.525018\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 238.490 | 1.20296 | ||||||||
\(35\) | −136.177 | −0.657663 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −24.7531 | −0.109983 | −0.0549917 | − | 0.998487i | \(-0.517513\pi\) | ||||
−0.0549917 | + | 0.998487i | \(0.517513\pi\) | |||||||
\(38\) | 224.921 | 0.960184 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 105.845 | 0.418388 | ||||||||
\(41\) | −174.061 | −0.663020 | −0.331510 | − | 0.943452i | \(-0.607558\pi\) | ||||
−0.331510 | + | 0.943452i | \(0.607558\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 506.208 | 1.79526 | 0.897628 | − | 0.440753i | \(-0.145289\pi\) | ||||
0.897628 | + | 0.440753i | \(0.145289\pi\) | |||||||
\(44\) | 58.7710 | 0.201365 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 256.367 | 0.795637 | 0.397819 | − | 0.917464i | \(-0.369767\pi\) | ||||
0.397819 | + | 0.917464i | \(0.369767\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −237.062 | −0.691142 | ||||||||
\(50\) | 100.097 | 0.283117 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −93.1665 | −0.248459 | ||||||||
\(53\) | 200.452 | 0.519514 | 0.259757 | − | 0.965674i | \(-0.416358\pi\) | ||||
0.259757 | + | 0.965674i | \(0.416358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 194.394 | 0.476583 | ||||||||
\(56\) | −82.3410 | −0.196487 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −209.292 | −0.473817 | ||||||||
\(59\) | −446.988 | −0.986319 | −0.493160 | − | 0.869939i | \(-0.664158\pi\) | ||||
−0.493160 | + | 0.869939i | \(0.664158\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 419.190 | 0.879866 | 0.439933 | − | 0.898031i | \(-0.355002\pi\) | ||||
0.439933 | + | 0.898031i | \(0.355002\pi\) | |||||||
\(62\) | −54.2077 | −0.111038 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −308.162 | −0.588043 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −70.3675 | −0.128310 | −0.0641549 | − | 0.997940i | \(-0.520435\pi\) | ||||
−0.0641549 | + | 0.997940i | \(0.520435\pi\) | |||||||
\(68\) | 476.981 | 0.850623 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −272.355 | −0.465038 | ||||||||
\(71\) | 190.743 | 0.318832 | 0.159416 | − | 0.987211i | \(-0.449039\pi\) | ||||
0.159416 | + | 0.987211i | \(0.449039\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 480.337 | 0.770125 | 0.385063 | − | 0.922890i | \(-0.374180\pi\) | ||||
0.385063 | + | 0.922890i | \(0.374180\pi\) | |||||||
\(74\) | −49.5063 | −0.0777701 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 449.842 | 0.678953 | ||||||||
\(77\) | −151.227 | −0.223817 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1321.34 | 1.88180 | 0.940901 | − | 0.338681i | \(-0.109981\pi\) | ||||
0.940901 | + | 0.338681i | \(0.109981\pi\) | |||||||
\(80\) | 211.689 | 0.295845 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −348.123 | −0.468826 | ||||||||
\(83\) | −407.398 | −0.538767 | −0.269384 | − | 0.963033i | \(-0.586820\pi\) | ||||
−0.269384 | + | 0.963033i | \(0.586820\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1577.68 | 2.01322 | ||||||||
\(86\) | 1012.42 | 1.26944 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 117.542 | 0.142387 | ||||||||
\(89\) | −1435.48 | −1.70967 | −0.854835 | − | 0.518899i | \(-0.826342\pi\) | ||||
−0.854835 | + | 0.518899i | \(0.826342\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 239.732 | 0.276162 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 512.734 | 0.562601 | ||||||||
\(95\) | 1487.92 | 1.60692 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −985.582 | −1.03166 | −0.515828 | − | 0.856692i | \(-0.672516\pi\) | ||||
−0.515828 | + | 0.856692i | \(0.672516\pi\) | |||||||
\(98\) | −474.124 | −0.488711 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 200.194 | 0.200194 | ||||||||
\(101\) | −1107.79 | −1.09138 | −0.545689 | − | 0.837988i | \(-0.683732\pi\) | ||||
−0.545689 | + | 0.837988i | \(0.683732\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 225.199 | 0.215432 | 0.107716 | − | 0.994182i | \(-0.465646\pi\) | ||||
0.107716 | + | 0.994182i | \(0.465646\pi\) | |||||||
\(104\) | −186.333 | −0.175687 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 400.904 | 0.367352 | ||||||||
\(107\) | −1020.49 | −0.922005 | −0.461002 | − | 0.887399i | \(-0.652510\pi\) | ||||
−0.461002 | + | 0.887399i | \(0.652510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −706.032 | −0.620418 | −0.310209 | − | 0.950668i | \(-0.600399\pi\) | ||||
−0.310209 | + | 0.950668i | \(0.600399\pi\) | |||||||
\(110\) | 388.788 | 0.336995 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −164.682 | −0.138937 | ||||||||
\(113\) | −1639.57 | −1.36494 | −0.682468 | − | 0.730915i | \(-0.739094\pi\) | ||||
−0.682468 | + | 0.730915i | \(0.739094\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 304.303 | 0.246752 | ||||||||
\(116\) | −418.584 | −0.335039 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −893.975 | −0.697433 | ||||||||
\(119\) | −1227.35 | −0.945467 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1115.12 | −0.837808 | ||||||||
\(122\) | 838.381 | 0.622159 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −108.415 | −0.0785160 | ||||||||
\(125\) | −991.653 | −0.709569 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1639.53 | −1.14555 | −0.572774 | − | 0.819714i | \(-0.694133\pi\) | ||||
−0.572774 | + | 0.819714i | \(0.694133\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −616.324 | −0.415809 | ||||||||
\(131\) | 629.817 | 0.420056 | 0.210028 | − | 0.977695i | \(-0.432644\pi\) | ||||
0.210028 | + | 0.977695i | \(0.432644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1157.51 | −0.754656 | ||||||||
\(134\) | −140.735 | −0.0907287 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 953.961 | 0.601482 | ||||||||
\(137\) | 1140.97 | 0.711528 | 0.355764 | − | 0.934576i | \(-0.384221\pi\) | ||||
0.355764 | + | 0.934576i | \(0.384221\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −136.295 | −0.0831682 | −0.0415841 | − | 0.999135i | \(-0.513240\pi\) | ||||
−0.0415841 | + | 0.999135i | \(0.513240\pi\) | |||||||
\(140\) | −544.710 | −0.328831 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 381.487 | 0.225448 | ||||||||
\(143\) | −342.218 | −0.200124 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1384.53 | −0.792957 | ||||||||
\(146\) | 960.673 | 0.544561 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −99.0125 | −0.0549917 | ||||||||
\(149\) | 2087.11 | 1.14754 | 0.573768 | − | 0.819018i | \(-0.305481\pi\) | ||||
0.573768 | + | 0.819018i | \(0.305481\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1944.71 | 1.04807 | 0.524034 | − | 0.851697i | \(-0.324427\pi\) | ||||
0.524034 | + | 0.851697i | \(0.324427\pi\) | |||||||
\(152\) | 899.684 | 0.480092 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −302.454 | −0.158263 | ||||||||
\(155\) | −358.600 | −0.185828 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −734.564 | −0.373405 | −0.186702 | − | 0.982417i | \(-0.559780\pi\) | ||||
−0.186702 | + | 0.982417i | \(0.559780\pi\) | |||||||
\(158\) | 2642.68 | 1.33064 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 423.379 | 0.209194 | ||||||||
\(161\) | −236.730 | −0.115882 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2737.81 | −1.31559 | −0.657796 | − | 0.753196i | \(-0.728511\pi\) | ||||
−0.657796 | + | 0.753196i | \(0.728511\pi\) | |||||||
\(164\) | −696.245 | −0.331510 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −814.795 | −0.380966 | ||||||||
\(167\) | −1702.98 | −0.789103 | −0.394551 | − | 0.918874i | \(-0.629100\pi\) | ||||
−0.394551 | + | 0.918874i | \(0.629100\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1654.50 | −0.753072 | ||||||||
\(170\) | 3155.37 | 1.42356 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2024.83 | 0.897628 | ||||||||
\(173\) | −139.362 | −0.0612456 | −0.0306228 | − | 0.999531i | \(-0.509749\pi\) | ||||
−0.0306228 | + | 0.999531i | \(0.509749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −515.130 | −0.222515 | ||||||||
\(176\) | 235.084 | 0.100683 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2870.96 | −1.20892 | ||||||||
\(179\) | 982.417 | 0.410219 | 0.205110 | − | 0.978739i | \(-0.434245\pi\) | ||||
0.205110 | + | 0.978739i | \(0.434245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3593.96 | −1.47590 | −0.737948 | − | 0.674858i | \(-0.764205\pi\) | ||||
−0.737948 | + | 0.674858i | \(0.764205\pi\) | |||||||
\(182\) | 479.464 | 0.195276 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | −327.498 | −0.130152 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1752.04 | 0.685144 | ||||||||
\(188\) | 1025.47 | 0.397819 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2975.84 | 1.13626 | ||||||||
\(191\) | 51.6405 | 0.0195632 | 0.00978161 | − | 0.999952i | \(-0.496886\pi\) | ||||
0.00978161 | + | 0.999952i | \(0.496886\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1176.44 | 0.438768 | 0.219384 | − | 0.975639i | \(-0.429595\pi\) | ||||
0.219384 | + | 0.975639i | \(0.429595\pi\) | |||||||
\(194\) | −1971.16 | −0.729492 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −948.247 | −0.345571 | ||||||||
\(197\) | 1092.50 | 0.395113 | 0.197557 | − | 0.980291i | \(-0.436699\pi\) | ||||
0.197557 | + | 0.980291i | \(0.436699\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 155.379 | 0.0553495 | 0.0276747 | − | 0.999617i | \(-0.491190\pi\) | ||||
0.0276747 | + | 0.999617i | \(0.491190\pi\) | |||||||
\(200\) | 400.387 | 0.141558 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2215.58 | −0.771721 | ||||||||
\(203\) | 1077.08 | 0.372396 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2302.93 | −0.784604 | ||||||||
\(206\) | 450.398 | 0.152334 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −372.666 | −0.124230 | ||||||||
\(209\) | 1652.36 | 0.546870 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5365.96 | −1.75075 | −0.875374 | − | 0.483447i | \(-0.839385\pi\) | ||||
−0.875374 | + | 0.483447i | \(0.839385\pi\) | |||||||
\(212\) | 801.809 | 0.259757 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2040.98 | −0.651956 | ||||||||
\(215\) | 6697.43 | 2.12447 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 278.970 | 0.0872705 | ||||||||
\(218\) | −1412.06 | −0.438702 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 777.575 | 0.238291 | ||||||||
\(221\) | −2777.41 | −0.845380 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 446.221 | 0.133996 | 0.0669982 | − | 0.997753i | \(-0.478658\pi\) | ||||
0.0669982 | + | 0.997753i | \(0.478658\pi\) | |||||||
\(224\) | −329.364 | −0.0982436 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3279.14 | −0.965156 | ||||||||
\(227\) | −2263.94 | −0.661950 | −0.330975 | − | 0.943639i | \(-0.607378\pi\) | ||||
−0.330975 | + | 0.943639i | \(0.607378\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1722.70 | 0.497116 | 0.248558 | − | 0.968617i | \(-0.420043\pi\) | ||||
0.248558 | + | 0.968617i | \(0.420043\pi\) | |||||||
\(230\) | 608.607 | 0.174480 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −837.167 | −0.236908 | ||||||||
\(233\) | −4122.28 | −1.15905 | −0.579527 | − | 0.814953i | \(-0.696763\pi\) | ||||
−0.579527 | + | 0.814953i | \(0.696763\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3391.88 | 0.941541 | ||||||||
\(236\) | −1787.95 | −0.493160 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2454.69 | −0.668546 | ||||||||
\(239\) | 1199.74 | 0.324707 | 0.162353 | − | 0.986733i | \(-0.448092\pi\) | ||||
0.162353 | + | 0.986733i | \(0.448092\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7262.37 | 1.94112 | 0.970561 | − | 0.240855i | \(-0.0774278\pi\) | ||||
0.970561 | + | 0.240855i | \(0.0774278\pi\) | |||||||
\(242\) | −2230.25 | −0.592420 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1676.76 | 0.439933 | ||||||||
\(245\) | −3136.47 | −0.817884 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2619.39 | −0.674768 | ||||||||
\(248\) | −216.831 | −0.0555192 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1983.31 | −0.501741 | ||||||||
\(251\) | −1662.11 | −0.417974 | −0.208987 | − | 0.977918i | \(-0.567017\pi\) | ||||
−0.208987 | + | 0.977918i | \(0.567017\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 337.933 | 0.0839751 | ||||||||
\(254\) | −3279.05 | −0.810024 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −3216.11 | −0.780605 | −0.390302 | − | 0.920687i | \(-0.627630\pi\) | ||||
−0.390302 | + | 0.920687i | \(0.627630\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 254.775 | 0.0611233 | ||||||||
\(260\) | −1232.65 | −0.294021 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1259.63 | 0.297025 | ||||||||
\(263\) | −1552.10 | −0.363903 | −0.181951 | − | 0.983308i | \(-0.558241\pi\) | ||||
−0.181951 | + | 0.983308i | \(0.558241\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2652.10 | 0.614782 | ||||||||
\(266\) | −2315.03 | −0.533622 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −281.470 | −0.0641549 | ||||||||
\(269\) | 4575.50 | 1.03707 | 0.518537 | − | 0.855055i | \(-0.326477\pi\) | ||||
0.518537 | + | 0.855055i | \(0.326477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2277.78 | −0.510574 | −0.255287 | − | 0.966865i | \(-0.582170\pi\) | ||||
−0.255287 | + | 0.966865i | \(0.582170\pi\) | |||||||
\(272\) | 1907.92 | 0.425312 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2281.93 | 0.503127 | ||||||||
\(275\) | 735.350 | 0.161248 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 780.955 | 0.169397 | 0.0846986 | − | 0.996407i | \(-0.473007\pi\) | ||||
0.0846986 | + | 0.996407i | \(0.473007\pi\) | |||||||
\(278\) | −272.590 | −0.0588088 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1089.42 | −0.232519 | ||||||||
\(281\) | 52.7391 | 0.0111963 | 0.00559813 | − | 0.999984i | \(-0.498218\pi\) | ||||
0.00559813 | + | 0.999984i | \(0.498218\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6200.42 | −1.30239 | −0.651196 | − | 0.758910i | \(-0.725732\pi\) | ||||
−0.651196 | + | 0.758910i | \(0.725732\pi\) | |||||||
\(284\) | 762.973 | 0.159416 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −684.437 | −0.141509 | ||||||||
\(287\) | 1791.55 | 0.368473 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9306.41 | 1.89424 | ||||||||
\(290\) | −2769.05 | −0.560705 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1921.35 | 0.385063 | ||||||||
\(293\) | −6131.11 | −1.22247 | −0.611234 | − | 0.791450i | \(-0.709327\pi\) | ||||
−0.611234 | + | 0.791450i | \(0.709327\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5913.91 | −1.16719 | ||||||||
\(296\) | −198.025 | −0.0388850 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4174.23 | 0.811431 | ||||||||
\(299\) | −535.707 | −0.103615 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5210.21 | −0.997713 | ||||||||
\(302\) | 3889.42 | 0.741096 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1799.37 | 0.339476 | ||||||||
\(305\) | 5546.13 | 1.04122 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7056.18 | −1.31178 | −0.655892 | − | 0.754855i | \(-0.727707\pi\) | ||||
−0.655892 | + | 0.754855i | \(0.727707\pi\) | |||||||
\(308\) | −604.908 | −0.111909 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −717.199 | −0.131401 | ||||||||
\(311\) | 7368.26 | 1.34346 | 0.671730 | − | 0.740796i | \(-0.265552\pi\) | ||||
0.671730 | + | 0.740796i | \(0.265552\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9068.44 | 1.63763 | 0.818816 | − | 0.574056i | \(-0.194631\pi\) | ||||
0.818816 | + | 0.574056i | \(0.194631\pi\) | |||||||
\(314\) | −1469.13 | −0.264037 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5285.36 | 0.940901 | ||||||||
\(317\) | −1952.28 | −0.345902 | −0.172951 | − | 0.984930i | \(-0.555330\pi\) | ||||
−0.172951 | + | 0.984930i | \(0.555330\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1537.54 | −0.269861 | ||||||||
\(320\) | 846.758 | 0.147922 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −473.461 | −0.0819408 | ||||||||
\(323\) | 13410.4 | 2.31013 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1165.71 | −0.198960 | ||||||||
\(326\) | −5475.61 | −0.930264 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1392.49 | −0.234413 | ||||||||
\(329\) | −2638.69 | −0.442175 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11508.2 | 1.91102 | 0.955511 | − | 0.294956i | \(-0.0953051\pi\) | ||||
0.955511 | + | 0.294956i | \(0.0953051\pi\) | |||||||
\(332\) | −1629.59 | −0.269384 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3405.95 | −0.557980 | ||||||||
\(335\) | −931.003 | −0.151839 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −425.493 | −0.0687776 | −0.0343888 | − | 0.999409i | \(-0.510948\pi\) | ||||
−0.0343888 | + | 0.999409i | \(0.510948\pi\) | |||||||
\(338\) | −3309.00 | −0.532503 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6310.73 | 1.00661 | ||||||||
\(341\) | −398.230 | −0.0632416 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5970.36 | 0.939852 | ||||||||
\(344\) | 4049.67 | 0.634719 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −278.724 | −0.0433072 | ||||||||
\(347\) | 1438.94 | 0.222612 | 0.111306 | − | 0.993786i | \(-0.464497\pi\) | ||||
0.111306 | + | 0.993786i | \(0.464497\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −681.032 | −0.104455 | −0.0522275 | − | 0.998635i | \(-0.516632\pi\) | ||||
−0.0522275 | + | 0.998635i | \(0.516632\pi\) | |||||||
\(350\) | −1030.26 | −0.157342 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 470.168 | 0.0711933 | ||||||||
\(353\) | −6608.06 | −0.996350 | −0.498175 | − | 0.867076i | \(-0.665996\pi\) | ||||
−0.498175 | + | 0.867076i | \(0.665996\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2523.65 | 0.377299 | ||||||||
\(356\) | −5741.92 | −0.854835 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1964.83 | 0.290069 | ||||||||
\(359\) | −2801.68 | −0.411886 | −0.205943 | − | 0.978564i | \(-0.566026\pi\) | ||||
−0.205943 | + | 0.978564i | \(0.566026\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5788.36 | 0.843908 | ||||||||
\(362\) | −7187.93 | −1.04362 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 958.928 | 0.138081 | ||||||||
\(365\) | 6355.14 | 0.911351 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8642.79 | 1.22929 | 0.614645 | − | 0.788803i | \(-0.289299\pi\) | ||||
0.614645 | + | 0.788803i | \(0.289299\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −654.997 | −0.0920315 | ||||||||
\(371\) | −2063.18 | −0.288720 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9923.81 | −1.37757 | −0.688787 | − | 0.724963i | \(-0.741857\pi\) | ||||
−0.688787 | + | 0.724963i | \(0.741857\pi\) | |||||||
\(374\) | 3504.08 | 0.484470 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2050.94 | 0.281300 | ||||||||
\(377\) | 2437.37 | 0.332974 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5030.01 | 0.681727 | 0.340863 | − | 0.940113i | \(-0.389281\pi\) | ||||
0.340863 | + | 0.940113i | \(0.389281\pi\) | |||||||
\(380\) | 5951.67 | 0.803459 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 103.281 | 0.0138333 | ||||||||
\(383\) | 2494.31 | 0.332776 | 0.166388 | − | 0.986060i | \(-0.446790\pi\) | ||||
0.166388 | + | 0.986060i | \(0.446790\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2000.82 | −0.264861 | ||||||||
\(386\) | 2352.89 | 0.310256 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3942.33 | −0.515828 | ||||||||
\(389\) | −6948.47 | −0.905659 | −0.452830 | − | 0.891597i | \(-0.649585\pi\) | ||||
−0.452830 | + | 0.891597i | \(0.649585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2742.64 | 0.354735 | ||||||||
\(392\) | −1896.49 | −0.244356 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2185.00 | 0.279387 | ||||||||
\(395\) | 17482.1 | 2.22689 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7921.85 | 1.00148 | 0.500738 | − | 0.865599i | \(-0.333062\pi\) | ||||
0.500738 | + | 0.865599i | \(0.333062\pi\) | |||||||
\(398\) | 310.759 | 0.0391380 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 800.775 | 0.100097 | ||||||||
\(401\) | −10902.0 | −1.35765 | −0.678826 | − | 0.734299i | \(-0.737511\pi\) | ||||
−0.678826 | + | 0.734299i | \(0.737511\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 631.292 | 0.0780320 | ||||||||
\(404\) | −4431.16 | −0.545689 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2154.16 | 0.263323 | ||||||||
\(407\) | −363.692 | −0.0442937 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3070.16 | −0.371172 | −0.185586 | − | 0.982628i | \(-0.559418\pi\) | ||||
−0.185586 | + | 0.982628i | \(0.559418\pi\) | |||||||
\(410\) | −4605.87 | −0.554799 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 900.796 | 0.107716 | ||||||||
\(413\) | 4600.68 | 0.548146 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5390.11 | −0.637566 | ||||||||
\(416\) | −745.332 | −0.0878435 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3304.71 | 0.386695 | ||||||||
\(419\) | −9682.14 | −1.12889 | −0.564443 | − | 0.825472i | \(-0.690909\pi\) | ||||
−0.564443 | + | 0.825472i | \(0.690909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7481.37 | 0.866080 | 0.433040 | − | 0.901375i | \(-0.357441\pi\) | ||||
0.433040 | + | 0.901375i | \(0.357441\pi\) | |||||||
\(422\) | −10731.9 | −1.23797 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1603.62 | 0.183676 | ||||||||
\(425\) | 5968.03 | 0.681158 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4314.57 | −0.488985 | ||||||||
\(428\) | −4081.96 | −0.461002 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13394.9 | 1.50223 | ||||||||
\(431\) | 16513.5 | 1.84554 | 0.922768 | − | 0.385356i | \(-0.125921\pi\) | ||||
0.922768 | + | 0.385356i | \(0.125921\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11765.8 | 1.30583 | 0.652917 | − | 0.757429i | \(-0.273545\pi\) | ||||
0.652917 | + | 0.757429i | \(0.273545\pi\) | |||||||
\(434\) | 557.939 | 0.0617095 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2824.13 | −0.310209 | ||||||||
\(437\) | 2586.59 | 0.283143 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16715.0 | 1.81722 | 0.908612 | − | 0.417640i | \(-0.137143\pi\) | ||||
0.908612 | + | 0.417640i | \(0.137143\pi\) | |||||||
\(440\) | 1555.15 | 0.168498 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5554.83 | −0.597774 | ||||||||
\(443\) | 12687.1 | 1.36068 | 0.680341 | − | 0.732895i | \(-0.261832\pi\) | ||||
0.680341 | + | 0.732895i | \(0.261832\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18992.3 | −2.02319 | ||||||||
\(446\) | 892.442 | 0.0947497 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −658.728 | −0.0694687 | ||||||||
\(449\) | −16077.7 | −1.68987 | −0.844937 | − | 0.534866i | \(-0.820362\pi\) | ||||
−0.844937 | + | 0.534866i | \(0.820362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2557.44 | −0.267018 | ||||||||
\(452\) | −6558.28 | −0.682468 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4527.87 | −0.468070 | ||||||||
\(455\) | 3171.80 | 0.326805 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7930.19 | 0.811726 | 0.405863 | − | 0.913934i | \(-0.366971\pi\) | ||||
0.405863 | + | 0.913934i | \(0.366971\pi\) | |||||||
\(458\) | 3445.41 | 0.351514 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1217.21 | 0.123376 | ||||||||
\(461\) | 11530.0 | 1.16487 | 0.582436 | − | 0.812877i | \(-0.302100\pi\) | ||||
0.582436 | + | 0.812877i | \(0.302100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7590.41 | −0.761893 | −0.380947 | − | 0.924597i | \(-0.624402\pi\) | ||||
−0.380947 | + | 0.924597i | \(0.624402\pi\) | |||||||
\(464\) | −1674.33 | −0.167519 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8244.56 | −0.819575 | ||||||||
\(467\) | 6686.26 | 0.662534 | 0.331267 | − | 0.943537i | \(-0.392524\pi\) | ||||
0.331267 | + | 0.943537i | \(0.392524\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 724.266 | 0.0713081 | ||||||||
\(470\) | 6783.77 | 0.665770 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3575.90 | −0.348716 | ||||||||
\(473\) | 7437.60 | 0.723004 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5628.47 | 0.543688 | ||||||||
\(476\) | −4909.38 | −0.472734 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2399.49 | 0.229602 | ||||||||
\(479\) | 12072.0 | 1.15153 | 0.575766 | − | 0.817614i | \(-0.304704\pi\) | ||||
0.575766 | + | 0.817614i | \(0.304704\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 576.541 | 0.0546528 | ||||||||
\(482\) | 14524.7 | 1.37258 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4460.49 | −0.418904 | ||||||||
\(485\) | −13039.8 | −1.22084 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1155.32 | −0.107500 | −0.0537499 | − | 0.998554i | \(-0.517117\pi\) | ||||
−0.0537499 | + | 0.998554i | \(0.517117\pi\) | |||||||
\(488\) | 3353.52 | 0.311080 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6272.93 | −0.578331 | ||||||||
\(491\) | 7251.93 | 0.666548 | 0.333274 | − | 0.942830i | \(-0.391847\pi\) | ||||
0.333274 | + | 0.942830i | \(0.391847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12478.5 | −1.13997 | ||||||||
\(494\) | −5238.78 | −0.477133 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −433.661 | −0.0392580 | ||||||||
\(497\) | −1963.25 | −0.177191 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11437.9 | 1.02612 | 0.513059 | − | 0.858354i | \(-0.328512\pi\) | ||||
0.513059 | + | 0.858354i | \(0.328512\pi\) | |||||||
\(500\) | −3966.61 | −0.354785 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3324.22 | −0.295552 | ||||||||
\(503\) | 5624.43 | 0.498570 | 0.249285 | − | 0.968430i | \(-0.419804\pi\) | ||||
0.249285 | + | 0.968430i | \(0.419804\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14656.7 | −1.29152 | ||||||||
\(506\) | 675.867 | 0.0593794 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6558.11 | −0.572774 | ||||||||
\(509\) | −14983.3 | −1.30476 | −0.652381 | − | 0.757891i | \(-0.726230\pi\) | ||||
−0.652381 | + | 0.757891i | \(0.726230\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4943.93 | −0.427997 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6432.22 | −0.551971 | ||||||||
\(515\) | 2979.51 | 0.254938 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3766.74 | 0.320427 | ||||||||
\(518\) | 509.549 | 0.0432207 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2465.30 | −0.207904 | ||||||||
\(521\) | 11536.9 | 0.970139 | 0.485069 | − | 0.874476i | \(-0.338794\pi\) | ||||
0.485069 | + | 0.874476i | \(0.338794\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12093.5 | 1.01111 | 0.505555 | − | 0.862794i | \(-0.331288\pi\) | ||||
0.505555 | + | 0.862794i | \(0.331288\pi\) | |||||||
\(524\) | 2519.27 | 0.210028 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3104.20 | −0.257318 | ||||||||
\(527\) | −3232.00 | −0.267150 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 5304.20 | 0.434716 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4630.06 | −0.377328 | ||||||||
\(533\) | 4054.17 | 0.329467 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13501.7 | −1.09108 | ||||||||
\(536\) | −562.940 | −0.0453644 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9150.99 | 0.733322 | ||||||||
\(539\) | −3483.09 | −0.278344 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5566.83 | 0.442397 | 0.221198 | − | 0.975229i | \(-0.429003\pi\) | ||||
0.221198 | + | 0.975229i | \(0.429003\pi\) | |||||||
\(542\) | −4555.57 | −0.361030 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3815.85 | 0.300741 | ||||||||
\(545\) | −9341.21 | −0.734190 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19574.6 | −1.53007 | −0.765034 | − | 0.643989i | \(-0.777278\pi\) | ||||
−0.765034 | + | 0.643989i | \(0.777278\pi\) | |||||||
\(548\) | 4563.87 | 0.355764 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1470.70 | 0.114020 | ||||||||
\(551\) | −11768.5 | −0.909903 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13600.1 | −1.04581 | ||||||||
\(554\) | 1561.91 | 0.119782 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −545.180 | −0.0415841 | ||||||||
\(557\) | −18416.6 | −1.40096 | −0.700481 | − | 0.713671i | \(-0.747031\pi\) | ||||
−0.700481 | + | 0.713671i | \(0.747031\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11790.4 | −0.892095 | ||||||||
\(560\) | −2178.84 | −0.164416 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 105.478 | 0.00791695 | ||||||||
\(563\) | −3944.28 | −0.295260 | −0.147630 | − | 0.989043i | \(-0.547165\pi\) | ||||
−0.147630 | + | 0.989043i | \(0.547165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21692.5 | −1.61524 | ||||||||
\(566\) | −12400.8 | −0.920930 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1525.95 | 0.112724 | ||||||||
\(569\) | −22904.6 | −1.68754 | −0.843769 | − | 0.536707i | \(-0.819668\pi\) | ||||
−0.843769 | + | 0.536707i | \(0.819668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9613.06 | 0.704543 | 0.352272 | − | 0.935898i | \(-0.385409\pi\) | ||||
0.352272 | + | 0.935898i | \(0.385409\pi\) | |||||||
\(572\) | −1368.87 | −0.100062 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3583.10 | 0.260550 | ||||||||
\(575\) | 1151.11 | 0.0834865 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7910.77 | 0.570762 | 0.285381 | − | 0.958414i | \(-0.407880\pi\) | ||||
0.285381 | + | 0.958414i | \(0.407880\pi\) | |||||||
\(578\) | 18612.8 | 1.33943 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5538.11 | −0.396478 | ||||||||
\(581\) | 4193.19 | 0.299420 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2945.20 | 0.209224 | ||||||||
\(584\) | 3842.69 | 0.272280 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12262.2 | −0.864416 | ||||||||
\(587\) | −3351.56 | −0.235662 | −0.117831 | − | 0.993034i | \(-0.537594\pi\) | ||||
−0.117831 | + | 0.993034i | \(0.537594\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3048.11 | −0.213235 | ||||||||
\(590\) | −11827.8 | −0.825328 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −396.050 | −0.0274959 | ||||||||
\(593\) | −12072.3 | −0.836002 | −0.418001 | − | 0.908447i | \(-0.637269\pi\) | ||||
−0.418001 | + | 0.908447i | \(0.637269\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16238.5 | −1.11885 | ||||||||
\(596\) | 8348.45 | 0.573768 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1071.41 | −0.0732666 | ||||||||
\(599\) | 13998.0 | 0.954826 | 0.477413 | − | 0.878679i | \(-0.341575\pi\) | ||||
0.477413 | + | 0.878679i | \(0.341575\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7796.28 | 0.529146 | 0.264573 | − | 0.964366i | \(-0.414769\pi\) | ||||
0.264573 | + | 0.964366i | \(0.414769\pi\) | |||||||
\(602\) | −10420.4 | −0.705490 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7778.84 | 0.524034 | ||||||||
\(605\) | −14753.7 | −0.991445 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5202.79 | −0.347899 | −0.173950 | − | 0.984755i | \(-0.555653\pi\) | ||||
−0.173950 | + | 0.984755i | \(0.555653\pi\) | |||||||
\(608\) | 3598.74 | 0.240046 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11092.3 | 0.736251 | ||||||||
\(611\) | −5971.20 | −0.395367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15697.6 | −1.03429 | −0.517144 | − | 0.855898i | \(-0.673005\pi\) | ||||
−0.517144 | + | 0.855898i | \(0.673005\pi\) | |||||||
\(614\) | −14112.4 | −0.927571 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1209.82 | −0.0791313 | ||||||||
\(617\) | 26268.4 | 1.71398 | 0.856991 | − | 0.515331i | \(-0.172331\pi\) | ||||
0.856991 | + | 0.515331i | \(0.172331\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1486.34 | 0.0965124 | 0.0482562 | − | 0.998835i | \(-0.484634\pi\) | ||||
0.0482562 | + | 0.998835i | \(0.484634\pi\) | |||||||
\(620\) | −1434.40 | −0.0929142 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14736.5 | 0.949969 | ||||||||
\(623\) | 14774.9 | 0.950149 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19376.2 | −1.24008 | ||||||||
\(626\) | 18136.9 | 1.15798 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2938.25 | −0.186702 | ||||||||
\(629\) | −2951.69 | −0.187109 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9554.18 | 0.602767 | 0.301384 | − | 0.953503i | \(-0.402552\pi\) | ||||
0.301384 | + | 0.953503i | \(0.402552\pi\) | |||||||
\(632\) | 10570.7 | 0.665318 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3904.55 | −0.244589 | ||||||||
\(635\) | −21691.9 | −1.35562 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5521.56 | 0.343441 | ||||||||
\(638\) | −3075.07 | −0.190820 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1693.52 | 0.104597 | ||||||||
\(641\) | −28526.3 | −1.75776 | −0.878879 | − | 0.477045i | \(-0.841708\pi\) | ||||
−0.878879 | + | 0.477045i | \(0.841708\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21360.4 | −1.31006 | −0.655032 | − | 0.755601i | \(-0.727345\pi\) | ||||
−0.655032 | + | 0.755601i | \(0.727345\pi\) | |||||||
\(644\) | −946.922 | −0.0579409 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26820.7 | 1.63351 | ||||||||
\(647\) | −17343.0 | −1.05382 | −0.526910 | − | 0.849921i | \(-0.676650\pi\) | ||||
−0.526910 | + | 0.849921i | \(0.676650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6567.48 | −0.397221 | ||||||||
\(650\) | −2331.42 | −0.140686 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10951.2 | −0.657796 | ||||||||
\(653\) | 6044.46 | 0.362233 | 0.181116 | − | 0.983462i | \(-0.442029\pi\) | ||||
0.181116 | + | 0.983462i | \(0.442029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8332.85 | 0.497086 | ||||||||
\(656\) | −2784.98 | −0.165755 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5277.38 | −0.312665 | ||||||||
\(659\) | −29374.0 | −1.73634 | −0.868172 | − | 0.496264i | \(-0.834705\pi\) | ||||
−0.868172 | + | 0.496264i | \(0.834705\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16562.1 | 0.974572 | 0.487286 | − | 0.873242i | \(-0.337987\pi\) | ||||
0.487286 | + | 0.873242i | \(0.337987\pi\) | |||||||
\(662\) | 23016.4 | 1.35130 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3259.18 | −0.190483 | ||||||||
\(665\) | −15314.6 | −0.893044 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2406.86 | −0.139721 | ||||||||
\(668\) | −6811.90 | −0.394551 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1862.01 | −0.107367 | ||||||||
\(671\) | 6159.06 | 0.354349 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1304.30 | −0.0747059 | −0.0373529 | − | 0.999302i | \(-0.511893\pi\) | ||||
−0.0373529 | + | 0.999302i | \(0.511893\pi\) | |||||||
\(674\) | −850.985 | −0.0486331 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6618.00 | −0.376536 | ||||||||
\(677\) | 8890.43 | 0.504708 | 0.252354 | − | 0.967635i | \(-0.418795\pi\) | ||||
0.252354 | + | 0.967635i | \(0.418795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10144.2 | 0.573343 | ||||||||
\(680\) | 12621.5 | 0.711781 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −796.460 | −0.0447185 | ||||||||
\(683\) | −16635.8 | −0.931991 | −0.465995 | − | 0.884787i | \(-0.654304\pi\) | ||||
−0.465995 | + | 0.884787i | \(0.654304\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15095.7 | 0.842008 | ||||||||
\(686\) | 11940.7 | 0.664576 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8099.33 | 0.448814 | ||||||||
\(689\) | −4668.86 | −0.258156 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22690.2 | 1.24917 | 0.624585 | − | 0.780957i | \(-0.285268\pi\) | ||||
0.624585 | + | 0.780957i | \(0.285268\pi\) | |||||||
\(692\) | −557.448 | −0.0306228 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2877.88 | 0.157411 | ||||||||
\(695\) | −1803.26 | −0.0984196 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20756.0 | −1.12796 | ||||||||
\(698\) | −1362.06 | −0.0738608 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2060.52 | −0.111258 | ||||||||
\(701\) | 32623.6 | 1.75774 | 0.878872 | − | 0.477059i | \(-0.158297\pi\) | ||||
0.878872 | + | 0.477059i | \(0.158297\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2783.75 | −0.149347 | ||||||||
\(704\) | 940.337 | 0.0503413 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13216.1 | −0.704526 | ||||||||
\(707\) | 11402.1 | 0.606533 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26739.1 | −1.41637 | −0.708187 | − | 0.706025i | \(-0.750486\pi\) | ||||
−0.708187 | + | 0.706025i | \(0.750486\pi\) | |||||||
\(710\) | 5047.29 | 0.266791 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11483.8 | −0.604460 | ||||||||
\(713\) | −623.388 | −0.0327434 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4527.75 | −0.236823 | ||||||||
\(716\) | 3929.67 | 0.205110 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5603.36 | −0.291248 | ||||||||
\(719\) | −20628.0 | −1.06995 | −0.534976 | − | 0.844867i | \(-0.679679\pi\) | ||||
−0.534976 | + | 0.844867i | \(0.679679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2317.89 | −0.119726 | ||||||||
\(722\) | 11576.7 | 0.596733 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14375.9 | −0.737948 | ||||||||
\(725\) | −5237.36 | −0.268291 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35027.0 | −1.78691 | −0.893453 | − | 0.449158i | \(-0.851724\pi\) | ||||
−0.893453 | + | 0.449158i | \(0.851724\pi\) | |||||||
\(728\) | 1917.86 | 0.0976380 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12710.3 | 0.644422 | ||||||||
\(731\) | 60362.9 | 3.05417 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17949.2 | −0.904460 | −0.452230 | − | 0.891901i | \(-0.649371\pi\) | ||||
−0.452230 | + | 0.891901i | \(0.649371\pi\) | |||||||
\(734\) | 17285.6 | 0.869240 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | −1033.89 | −0.0516742 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9531.78 | −0.474469 | −0.237234 | − | 0.971452i | \(-0.576241\pi\) | ||||
−0.237234 | + | 0.971452i | \(0.576241\pi\) | |||||||
\(740\) | −1309.99 | −0.0650761 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4126.36 | −0.204156 | ||||||||
\(743\) | 12341.6 | 0.609378 | 0.304689 | − | 0.952452i | \(-0.401448\pi\) | ||||
0.304689 | + | 0.952452i | \(0.401448\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27613.7 | 1.35797 | ||||||||
\(746\) | −19847.6 | −0.974092 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7008.16 | 0.342572 | ||||||||
\(749\) | 10503.5 | 0.512404 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20118.7 | 0.977553 | 0.488777 | − | 0.872409i | \(-0.337443\pi\) | ||||
0.488777 | + | 0.872409i | \(0.337443\pi\) | |||||||
\(752\) | 4101.87 | 0.198909 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4874.75 | 0.235448 | ||||||||
\(755\) | 25729.6 | 1.24026 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40167.2 | 1.92854 | 0.964269 | − | 0.264926i | \(-0.0853476\pi\) | ||||
0.964269 | + | 0.264926i | \(0.0853476\pi\) | |||||||
\(758\) | 10060.0 | 0.482054 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11903.3 | 0.568131 | ||||||||
\(761\) | −21242.6 | −1.01188 | −0.505941 | − | 0.862568i | \(-0.668855\pi\) | ||||
−0.505941 | + | 0.862568i | \(0.668855\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7266.92 | 0.344797 | ||||||||
\(764\) | 206.562 | 0.00978161 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4988.62 | 0.235308 | ||||||||
\(767\) | 10411.1 | 0.490120 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40261.8 | −1.88801 | −0.944003 | − | 0.329937i | \(-0.892973\pi\) | ||||
−0.944003 | + | 0.329937i | \(0.892973\pi\) | |||||||
\(770\) | −4001.65 | −0.187285 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4705.77 | 0.219384 | ||||||||
\(773\) | −3861.68 | −0.179683 | −0.0898415 | − | 0.995956i | \(-0.528636\pi\) | ||||
−0.0898415 | + | 0.995956i | \(0.528636\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1356.50 | −0.0628736 | ||||||||
\(776\) | −7884.66 | −0.364746 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13896.9 | −0.640398 | ||||||||
\(779\) | −19575.0 | −0.900318 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2802.55 | 0.128403 | ||||||||
\(782\) | 5485.28 | 0.250835 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3792.99 | −0.172786 | ||||||||
\(785\) | −9718.71 | −0.441880 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40478.2 | 1.83341 | 0.916704 | − | 0.399568i | \(-0.130840\pi\) | ||||
0.916704 | + | 0.399568i | \(0.130840\pi\) | |||||||
\(788\) | 4370.00 | 0.197557 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 34964.2 | 1.57465 | ||||||||
\(791\) | 16875.5 | 0.758563 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9763.62 | −0.437221 | ||||||||
\(794\) | 15843.7 | 0.708151 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 621.517 | 0.0276747 | ||||||||
\(797\) | −7456.91 | −0.331415 | −0.165707 | − | 0.986175i | \(-0.552991\pi\) | ||||
−0.165707 | + | 0.986175i | \(0.552991\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30570.5 | 1.35358 | ||||||||
\(800\) | 1601.55 | 0.0707792 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21804.0 | −0.960005 | ||||||||
\(803\) | 7057.47 | 0.310153 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3132.08 | −0.137132 | ||||||||
\(806\) | 1262.58 | 0.0551770 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8862.32 | −0.385861 | ||||||||
\(809\) | 4767.72 | 0.207199 | 0.103600 | − | 0.994619i | \(-0.466964\pi\) | ||||
0.103600 | + | 0.994619i | \(0.466964\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19199.4 | 0.831298 | 0.415649 | − | 0.909525i | \(-0.363554\pi\) | ||||
0.415649 | + | 0.909525i | \(0.363554\pi\) | |||||||
\(812\) | 4308.33 | 0.186198 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −727.384 | −0.0313204 | ||||||||
\(815\) | −36222.8 | −1.55685 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56928.4 | 2.43779 | ||||||||
\(818\) | −6140.31 | −0.262458 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9211.73 | −0.392302 | ||||||||
\(821\) | −1595.59 | −0.0678277 | −0.0339138 | − | 0.999425i | \(-0.510797\pi\) | ||||
−0.0339138 | + | 0.999425i | \(0.510797\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2041.80 | 0.0864795 | 0.0432398 | − | 0.999065i | \(-0.486232\pi\) | ||||
0.0432398 | + | 0.999065i | \(0.486232\pi\) | |||||||
\(824\) | 1801.59 | 0.0761668 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9201.35 | 0.387598 | ||||||||
\(827\) | −13117.5 | −0.551559 | −0.275780 | − | 0.961221i | \(-0.588936\pi\) | ||||
−0.275780 | + | 0.961221i | \(0.588936\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20788.1 | 0.870930 | 0.435465 | − | 0.900206i | \(-0.356584\pi\) | ||||
0.435465 | + | 0.900206i | \(0.356584\pi\) | |||||||
\(830\) | −10780.2 | −0.450828 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1490.66 | −0.0621148 | ||||||||
\(833\) | −28268.5 | −1.17580 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22531.4 | −0.933808 | ||||||||
\(836\) | 6609.42 | 0.273435 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −19364.3 | −0.798243 | ||||||||
\(839\) | 27202.7 | 1.11936 | 0.559680 | − | 0.828709i | \(-0.310924\pi\) | ||||
0.559680 | + | 0.828709i | \(0.310924\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13438.2 | −0.550996 | ||||||||
\(842\) | 14962.7 | 0.612411 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21463.8 | −0.875374 | ||||||||
\(845\) | −21890.0 | −0.891171 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11477.5 | 0.465612 | ||||||||
\(848\) | 3207.24 | 0.129878 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 11936.1 | 0.481651 | ||||||||
\(851\) | −569.322 | −0.0229331 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21562.1 | 0.865501 | 0.432750 | − | 0.901514i | \(-0.357543\pi\) | ||||
0.432750 | + | 0.901514i | \(0.357543\pi\) | |||||||
\(854\) | −8629.14 | −0.345765 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8163.92 | −0.325978 | ||||||||
\(857\) | −15694.8 | −0.625581 | −0.312790 | − | 0.949822i | \(-0.601264\pi\) | ||||
−0.312790 | + | 0.949822i | \(0.601264\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12667.3 | 0.503144 | 0.251572 | − | 0.967839i | \(-0.419052\pi\) | ||||
0.251572 | + | 0.967839i | \(0.419052\pi\) | |||||||
\(860\) | 26789.7 | 1.06224 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33026.9 | 1.30499 | ||||||||
\(863\) | 5118.43 | 0.201893 | 0.100946 | − | 0.994892i | \(-0.467813\pi\) | ||||
0.100946 | + | 0.994892i | \(0.467813\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1843.84 | −0.0724768 | ||||||||
\(866\) | 23531.5 | 0.923364 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1115.88 | 0.0436352 | ||||||||
\(869\) | 19414.1 | 0.757859 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1638.97 | 0.0637595 | ||||||||
\(872\) | −5648.25 | −0.219351 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5173.18 | 0.200212 | ||||||||
\(875\) | 10206.7 | 0.394343 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46908.3 | 1.80614 | 0.903068 | − | 0.429498i | \(-0.141309\pi\) | ||||
0.903068 | + | 0.429498i | \(0.141309\pi\) | |||||||
\(878\) | 33429.9 | 1.28497 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3110.30 | 0.119146 | ||||||||
\(881\) | 8248.69 | 0.315443 | 0.157722 | − | 0.987484i | \(-0.449585\pi\) | ||||
0.157722 | + | 0.987484i | \(0.449585\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12437.1 | 0.473999 | 0.237000 | − | 0.971510i | \(-0.423836\pi\) | ||||
0.237000 | + | 0.971510i | \(0.423836\pi\) | |||||||
\(884\) | −11109.7 | −0.422690 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25374.2 | 0.962148 | ||||||||
\(887\) | −43105.2 | −1.63172 | −0.815858 | − | 0.578253i | \(-0.803735\pi\) | ||||
−0.815858 | + | 0.578253i | \(0.803735\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16875.0 | 0.636637 | ||||||||
\(890\) | −37984.5 | −1.43061 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1784.88 | 0.0669982 | ||||||||
\(893\) | 28831.1 | 1.08040 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12997.9 | 0.485445 | ||||||||
\(896\) | −1317.46 | −0.0491218 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −32155.4 | −1.19492 | ||||||||
\(899\) | 2836.31 | 0.105224 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23903.0 | 0.883821 | ||||||||
\(902\) | −5114.88 | −0.188810 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13116.6 | −0.482578 | ||||||||
\(905\) | −47550.2 | −1.74655 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9236.78 | −0.338150 | −0.169075 | − | 0.985603i | \(-0.554078\pi\) | ||||
−0.169075 | + | 0.985603i | \(0.554078\pi\) | |||||||
\(908\) | −9055.74 | −0.330975 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6343.59 | 0.231086 | ||||||||
\(911\) | −34284.3 | −1.24686 | −0.623431 | − | 0.781879i | \(-0.714262\pi\) | ||||
−0.623431 | + | 0.781879i | \(0.714262\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5985.80 | −0.216978 | ||||||||
\(914\) | 15860.4 | 0.573977 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6890.82 | 0.248558 | ||||||||
\(917\) | −6482.47 | −0.233446 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47474.8 | −1.70408 | −0.852039 | − | 0.523478i | \(-0.824634\pi\) | ||||
−0.852039 | + | 0.523478i | \(0.824634\pi\) | |||||||
\(920\) | 2434.43 | 0.0872399 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23060.0 | 0.823689 | ||||||||
\(923\) | −4442.72 | −0.158433 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1238.86 | −0.0440360 | ||||||||
\(926\) | −15180.8 | −0.538740 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3348.67 | −0.118454 | ||||||||
\(929\) | 10436.4 | 0.368577 | 0.184288 | − | 0.982872i | \(-0.441002\pi\) | ||||
0.184288 | + | 0.982872i | \(0.441002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26660.1 | −0.938506 | ||||||||
\(932\) | −16489.1 | −0.579527 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13372.5 | 0.468482 | ||||||||
\(935\) | 23180.5 | 0.810785 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24205.7 | 0.843935 | 0.421967 | − | 0.906611i | \(-0.361340\pi\) | ||||
0.421967 | + | 0.906611i | \(0.361340\pi\) | |||||||
\(938\) | 1448.53 | 0.0504224 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13567.5 | 0.470771 | ||||||||
\(941\) | −50113.7 | −1.73609 | −0.868045 | − | 0.496485i | \(-0.834624\pi\) | ||||
−0.868045 | + | 0.496485i | \(0.834624\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4003.41 | −0.138249 | ||||||||
\(944\) | −7151.80 | −0.246580 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14875.2 | 0.511241 | ||||||||
\(947\) | 30633.5 | 1.05117 | 0.525583 | − | 0.850742i | \(-0.323847\pi\) | ||||
0.525583 | + | 0.850742i | \(0.323847\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11187.8 | −0.382689 | ||||||||
\(950\) | 11256.9 | 0.384446 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9818.77 | −0.334273 | ||||||||
\(953\) | 15558.4 | 0.528842 | 0.264421 | − | 0.964407i | \(-0.414819\pi\) | ||||
0.264421 | + | 0.964407i | \(0.414819\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 683.234 | 0.0231507 | ||||||||
\(956\) | 4798.97 | 0.162353 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24144.0 | 0.814256 | ||||||||
\(959\) | −11743.5 | −0.395432 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29056.4 | −0.975341 | ||||||||
\(962\) | 1153.08 | 0.0386454 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 29049.5 | 0.970561 | ||||||||
\(965\) | 15565.0 | 0.519229 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6567.58 | 0.218406 | 0.109203 | − | 0.994019i | \(-0.465170\pi\) | ||||
0.109203 | + | 0.994019i | \(0.465170\pi\) | |||||||
\(968\) | −8920.98 | −0.296210 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −26079.7 | −0.863266 | ||||||||
\(971\) | 41067.3 | 1.35727 | 0.678636 | − | 0.734474i | \(-0.262571\pi\) | ||||
0.678636 | + | 0.734474i | \(0.262571\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1402.83 | 0.0462207 | ||||||||
\(974\) | −2310.63 | −0.0760139 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6707.05 | 0.219966 | ||||||||
\(977\) | 55639.7 | 1.82198 | 0.910989 | − | 0.412430i | \(-0.135320\pi\) | ||||
0.910989 | + | 0.412430i | \(0.135320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21091.2 | −0.688536 | ||||||||
\(980\) | −12545.9 | −0.408942 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14503.9 | 0.471320 | ||||||||
\(983\) | −60200.2 | −1.95329 | −0.976646 | − | 0.214854i | \(-0.931073\pi\) | ||||
−0.976646 | + | 0.214854i | \(0.931073\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14454.4 | 0.467569 | ||||||||
\(986\) | −24957.0 | −0.806079 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10477.6 | −0.337384 | ||||||||
\(989\) | 11642.8 | 0.374337 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12965.4 | −0.415599 | −0.207800 | − | 0.978171i | \(-0.566630\pi\) | ||||
−0.207800 | + | 0.978171i | \(0.566630\pi\) | |||||||
\(992\) | −867.323 | −0.0277596 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3926.50 | −0.125293 | ||||||||
\(995\) | 2055.76 | 0.0654995 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5425.12 | −0.172332 | −0.0861661 | − | 0.996281i | \(-0.527462\pi\) | ||||
−0.0861661 | + | 0.996281i | \(0.527462\pi\) | |||||||
\(998\) | 22875.9 | 0.725574 | ||||||||
\(999\) | 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 | 414.4.a.n.1.4 | yes | 4 | |
3.2 | odd | 2 | 414.4.a.m.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
414.4.a.m.1.1 | ✓ | 4 | 3.2 | odd | 2 | ||
414.4.a.n.1.4 | yes | 4 | 1.1 | even | 1 | trivial |