Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1160,4,Mod(1,1160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1160.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1160 = 2^{3} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1160.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: | \(68.4422156067\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 121x^{5} + 38x^{4} + 4100x^{3} + 836x^{2} - 34400x - 6912 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-7.91868\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1160.1 |
$q$-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 | 0 | ||||||||
\(3\) | −7.91868 | −1.52395 | −0.761975 | − | 0.647606i | \(-0.775770\pi\) | ||||
−0.761975 | + | 0.647606i | \(0.775770\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 30.1700 | 1.62903 | 0.814514 | − | 0.580144i | \(-0.197004\pi\) | ||||
0.814514 | + | 0.580144i | \(0.197004\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 35.7055 | 1.32243 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −41.5009 | −1.13754 | −0.568772 | − | 0.822495i | \(-0.692581\pi\) | ||||
−0.568772 | + | 0.822495i | \(0.692581\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.4606 | 0.436519 | 0.218260 | − | 0.975891i | \(-0.429962\pi\) | ||||
0.218260 | + | 0.975891i | \(0.429962\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 39.5934 | 0.681531 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −44.4259 | −0.633815 | −0.316907 | − | 0.948456i | \(-0.602644\pi\) | ||||
−0.316907 | + | 0.948456i | \(0.602644\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −139.197 | −1.68073 | −0.840367 | − | 0.542018i | \(-0.817660\pi\) | ||||
−0.840367 | + | 0.542018i | \(0.817660\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −238.907 | −2.48256 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 164.416 | 1.49057 | 0.745286 | − | 0.666745i | \(-0.232313\pi\) | ||||
0.745286 | + | 0.666745i | \(0.232313\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −68.9361 | −0.491361 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 143.019 | 0.828614 | 0.414307 | − | 0.910137i | \(-0.364024\pi\) | ||||
0.414307 | + | 0.910137i | \(0.364024\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 328.632 | 1.73356 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −150.850 | −0.728524 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −178.297 | −0.792212 | −0.396106 | − | 0.918205i | \(-0.629639\pi\) | ||||
−0.396106 | + | 0.918205i | \(0.629639\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −162.021 | −0.665234 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 283.451 | 1.07970 | 0.539850 | − | 0.841761i | \(-0.318481\pi\) | ||||
0.539850 | + | 0.841761i | \(0.318481\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −400.334 | −1.41978 | −0.709888 | − | 0.704314i | \(-0.751255\pi\) | ||||
−0.709888 | + | 0.704314i | \(0.751255\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −178.527 | −0.591407 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 66.1270 | 0.205226 | 0.102613 | − | 0.994721i | \(-0.467280\pi\) | ||||
0.102613 | + | 0.994721i | \(0.467280\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 567.231 | 1.65373 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 351.794 | 0.965903 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 707.089 | 1.83257 | 0.916285 | − | 0.400527i | \(-0.131173\pi\) | ||||
0.916285 | + | 0.400527i | \(0.131173\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 207.504 | 0.508725 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1102.26 | 2.56136 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −385.448 | −0.850526 | −0.425263 | − | 0.905070i | \(-0.639818\pi\) | ||||
−0.425263 | + | 0.905070i | \(0.639818\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 207.613 | 0.435772 | 0.217886 | − | 0.975974i | \(-0.430084\pi\) | ||||
0.217886 | + | 0.975974i | \(0.430084\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1077.24 | 2.15427 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −102.303 | −0.195217 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1007.51 | 1.83712 | 0.918560 | − | 0.395282i | \(-0.129353\pi\) | ||||
0.918560 | + | 0.395282i | \(0.129353\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1301.96 | −2.27156 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.72980 | −0.00790597 | −0.00395299 | − | 0.999992i | \(-0.501258\pi\) | ||||
−0.00395299 | + | 0.999992i | \(0.501258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 259.868 | 0.416647 | 0.208324 | − | 0.978060i | \(-0.433199\pi\) | ||||
0.208324 | + | 0.978060i | \(0.433199\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −197.967 | −0.304790 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1252.08 | −1.85309 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −954.754 | −1.35972 | −0.679862 | − | 0.733340i | \(-0.737960\pi\) | ||||
−0.679862 | + | 0.733340i | \(0.737960\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −418.166 | −0.573616 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −883.835 | −1.16884 | −0.584419 | − | 0.811452i | \(-0.698678\pi\) | ||||
−0.584419 | + | 0.811452i | \(0.698678\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 222.129 | 0.283451 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 229.642 | 0.282991 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1256.60 | 1.49663 | 0.748313 | − | 0.663346i | \(-0.230864\pi\) | ||||
0.748313 | + | 0.663346i | \(0.230864\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 617.297 | 0.711103 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1132.53 | −1.26277 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 695.984 | 0.751647 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −396.847 | −0.415399 | −0.207699 | − | 0.978193i | \(-0.566598\pi\) | ||||
−0.207699 | + | 0.978193i | \(0.566598\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1481.81 | −1.50432 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1362.77 | 1.34258 | 0.671289 | − | 0.741195i | \(-0.265741\pi\) | ||||
0.671289 | + | 0.741195i | \(0.265741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1953.67 | −1.86894 | −0.934470 | − | 0.356042i | \(-0.884126\pi\) | ||||
−0.934470 | + | 0.356042i | \(0.884126\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1194.53 | 1.11023 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1773.39 | 1.60225 | 0.801123 | − | 0.598499i | \(-0.204236\pi\) | ||||
0.801123 | + | 0.598499i | \(0.204236\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1705.45 | −1.49865 | −0.749323 | − | 0.662205i | \(-0.769621\pi\) | ||||
−0.749323 | + | 0.662205i | \(0.769621\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1411.88 | 1.20729 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1540.09 | −1.28212 | −0.641060 | − | 0.767490i | \(-0.721505\pi\) | ||||
−0.641060 | + | 0.767490i | \(0.721505\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −822.081 | −0.666604 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 730.556 | 0.577265 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1340.33 | −1.03250 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 391.325 | 0.294008 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2244.56 | −1.64541 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1521.76 | −1.06326 | −0.531630 | − | 0.846977i | \(-0.678420\pi\) | ||||
−0.531630 | + | 0.846977i | \(0.678420\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3170.12 | 2.16367 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −319.260 | −0.212931 | −0.106465 | − | 0.994316i | \(-0.533953\pi\) | ||||
−0.106465 | + | 0.994316i | \(0.533953\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4199.57 | −2.73796 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 344.680 | 0.219743 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1680.02 | −1.04769 | −0.523847 | − | 0.851812i | \(-0.675504\pi\) | ||||
−0.523847 | + | 0.851812i | \(0.675504\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −567.983 | −0.346587 | −0.173294 | − | 0.984870i | \(-0.555441\pi\) | ||||
−0.173294 | + | 0.984870i | \(0.555441\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −523.639 | −0.312754 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −849.134 | −0.496560 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 145.000 | 0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4491.72 | −2.52021 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2330.64 | 1.28143 | 0.640716 | − | 0.767778i | \(-0.278638\pi\) | ||||
0.640716 | + | 0.767778i | \(0.278638\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2335.72 | −1.25880 | −0.629398 | − | 0.777083i | \(-0.716698\pi\) | ||||
−0.629398 | + | 0.777083i | \(0.716698\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1586.25 | −0.838173 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −715.097 | −0.370568 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −598.686 | −0.304333 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5599.22 | −2.79275 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4960.44 | 2.42818 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2355.82 | −1.13204 | −0.566018 | − | 0.824393i | \(-0.691517\pi\) | ||||
−0.566018 | + | 0.824393i | \(0.691517\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1643.16 | −0.775273 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −975.190 | −0.451871 | −0.225936 | − | 0.974142i | \(-0.572544\pi\) | ||||
−0.225936 | + | 0.974142i | \(0.572544\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1778.36 | −0.809451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4970.09 | −2.22265 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1750.07 | 0.769106 | 0.384553 | − | 0.923103i | \(-0.374356\pi\) | ||||
0.384553 | + | 0.923103i | \(0.374356\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 754.251 | 0.325806 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3052.24 | 1.29616 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 215.951 | 0.0901728 | 0.0450864 | − | 0.998983i | \(-0.485644\pi\) | ||||
0.0450864 | + | 0.998983i | \(0.485644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 369.011 | 0.151538 | 0.0757690 | − | 0.997125i | \(-0.475859\pi\) | ||||
0.0757690 | + | 0.997125i | \(0.475859\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1644.02 | −0.664096 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 891.485 | 0.354288 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1843.71 | 0.720993 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2079.80 | −0.800441 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2981.01 | −1.12931 | −0.564655 | − | 0.825327i | \(-0.690991\pi\) | ||||
−0.564655 | + | 0.825327i | \(0.690991\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1421.80 | −0.530277 | −0.265138 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265138 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 810.105 | 0.297502 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 866.654 | 0.313434 | 0.156717 | − | 0.987644i | \(-0.449909\pi\) | ||||
0.156717 | + | 0.987644i | \(0.449909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2936.39 | −1.04601 | −0.523003 | − | 0.852331i | \(-0.675188\pi\) | ||||
−0.523003 | + | 0.852331i | \(0.675188\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7978.16 | −2.79968 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −874.931 | −0.302503 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1417.26 | −0.482856 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5870.56 | 1.97117 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5776.79 | 1.91191 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −242.085 | −0.0789851 | −0.0394925 | − | 0.999220i | \(-0.512574\pi\) | ||||
−0.0394925 | + | 0.999220i | \(0.512574\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 37.4538 | 0.0120483 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2001.67 | 0.634943 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4314.90 | 1.34984 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2057.81 | −0.634950 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −908.980 | −0.276673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −725.560 | −0.217879 | −0.108940 | − | 0.994048i | \(-0.534746\pi\) | ||||
−0.108940 | + | 0.994048i | \(0.534746\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 892.637 | 0.264485 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6224.96 | −1.82011 | −0.910055 | − | 0.414487i | \(-0.863961\pi\) | ||||
−0.910055 | + | 0.414487i | \(0.863961\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4182.45 | 1.20692 | 0.603459 | − | 0.797394i | \(-0.293789\pi\) | ||||
0.603459 | + | 0.797394i | \(0.293789\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9914.85 | 2.82402 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3487.32 | −0.980524 | −0.490262 | − | 0.871575i | \(-0.663099\pi\) | ||||
−0.490262 | + | 0.871575i | \(0.663099\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −330.635 | −0.0917798 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7560.39 | 2.07215 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1596.56 | −0.432104 | −0.216052 | − | 0.976382i | \(-0.569318\pi\) | ||||
−0.216052 | + | 0.976382i | \(0.569318\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6924.23 | 1.85074 | 0.925371 | − | 0.379062i | \(-0.123753\pi\) | ||||
0.925371 | + | 0.379062i | \(0.123753\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5172.60 | 1.36552 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2836.15 | −0.739572 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2848.05 | −0.733673 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6998.81 | 1.78125 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5781.91 | 1.45399 | 0.726994 | − | 0.686644i | \(-0.240917\pi\) | ||||
0.726994 | + | 0.686644i | \(0.240917\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6823.42 | −1.69559 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1758.97 | −0.431965 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −145.551 | −0.0353277 | −0.0176639 | − | 0.999844i | \(-0.505623\pi\) | ||||
−0.0176639 | + | 0.999844i | \(0.505623\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5379.22 | −1.29054 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1035.46 | −0.245568 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3122.63 | 0.732128 | 0.366064 | − | 0.930590i | \(-0.380705\pi\) | ||||
0.366064 | + | 0.930590i | \(0.380705\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3535.45 | −0.819550 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9950.64 | −2.28078 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 750.382 | 0.170080 | 0.0850402 | − | 0.996378i | \(-0.472898\pi\) | ||||
0.0850402 | + | 0.996378i | \(0.472898\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4817.42 | −1.07984 | −0.539921 | − | 0.841715i | \(-0.681546\pi\) | ||||
−0.539921 | + | 0.841715i | \(0.681546\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4888.18 | −1.08369 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1037.52 | −0.227509 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2441.36 | −0.529556 | −0.264778 | − | 0.964309i | \(-0.585299\pi\) | ||||
−0.264778 | + | 0.964309i | \(0.585299\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5106.58 | 1.09578 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5596.93 | 1.18820 | 0.594101 | − | 0.804391i | \(-0.297508\pi\) | ||||
0.594101 | + | 0.804391i | \(0.297508\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2573.05 | −0.540467 | −0.270234 | − | 0.962795i | \(-0.587101\pi\) | ||||
−0.270234 | + | 0.962795i | \(0.587101\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5511.28 | −1.14547 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8551.74 | 1.75886 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2939.34 | −0.598279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3142.50 | 0.633047 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4699.84 | −0.937090 | −0.468545 | − | 0.883440i | \(-0.655222\pi\) | ||||
−0.468545 | + | 0.883440i | \(0.655222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1927.24 | 0.380367 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2860.91 | 0.558945 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3364.06 | 0.650664 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12078.1 | −2.31286 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10791.3 | −2.04602 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1038.06 | −0.194883 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2818.58 | −0.523989 | −0.261995 | − | 0.965069i | \(-0.584380\pi\) | ||||
−0.261995 | + | 0.965069i | \(0.584380\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15470.5 | 2.84817 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 340.672 | 0.0621148 | 0.0310574 | − | 0.999518i | \(-0.490113\pi\) | ||||
0.0310574 | + | 0.999518i | \(0.490113\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6854.04 | −1.23774 | −0.618871 | − | 0.785492i | \(-0.712410\pi\) | ||||
−0.618871 | + | 0.785492i | \(0.712410\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5386.18 | −0.963419 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6510.76 | −1.15357 | −0.576783 | − | 0.816897i | \(-0.695692\pi\) | ||||
−0.576783 | + | 0.816897i | \(0.695692\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1203.53 | 0.211237 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14042.9 | −2.44174 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6183.94 | 1.06527 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 511.515 | 0.0873039 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13504.9 | 2.28386 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1995.05 | 0.334319 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3135.36 | −0.520649 | −0.260324 | − | 0.965521i | \(-0.583829\pi\) | ||||
−0.260324 | + | 0.965521i | \(0.583829\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6366.18 | −1.04764 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5037.55 | −0.821585 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5459.28 | 0.882451 | 0.441225 | − | 0.897396i | \(-0.354544\pi\) | ||||
0.441225 | + | 0.897396i | \(0.354544\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12195.5 | 1.95389 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5935.43 | −0.942586 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6765.04 | 1.06495 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6509.80 | 1.01587 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4476.98 | −0.692613 | −0.346306 | − | 0.938121i | \(-0.612564\pi\) | ||||
−0.346306 | + | 0.938121i | \(0.612564\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3769.50 | −0.578157 | −0.289078 | − | 0.957305i | \(-0.593349\pi\) | ||||
−0.289078 | + | 0.957305i | \(0.593349\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1410.47 | −0.214489 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10801.6 | 1.62865 | 0.814323 | − | 0.580412i | \(-0.197109\pi\) | ||||
0.814323 | + | 0.580412i | \(0.197109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.6490 | 0.00353566 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10613.6 | 1.57348 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −83.1926 | −0.0122305 | −0.00611523 | − | 0.999981i | \(-0.501947\pi\) | ||||
−0.00611523 | + | 0.999981i | \(0.501947\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12516.8 | 1.82487 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3098.77 | −0.448054 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1299.34 | −0.186330 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5161.95 | −0.734201 | −0.367101 | − | 0.930181i | \(-0.619649\pi\) | ||||
−0.367101 | + | 0.930181i | \(0.619649\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10120.8 | 1.42782 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21332.9 | 2.98531 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3535.69 | −0.490807 | −0.245403 | − | 0.969421i | \(-0.578920\pi\) | ||||
−0.245403 | + | 0.969421i | \(0.578920\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 989.835 | 0.136306 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −593.358 | −0.0810596 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10014.9 | 1.35734 | 0.678668 | − | 0.734445i | \(-0.262558\pi\) | ||||
0.678668 | + | 0.734445i | \(0.262558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12050.3 | 1.62035 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2999.55 | −0.400183 | −0.200091 | − | 0.979777i | \(-0.564124\pi\) | ||||
−0.200091 | + | 0.979777i | \(0.564124\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6260.42 | 0.828728 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14294.1 | −1.87755 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3981.88 | −0.518996 | −0.259498 | − | 0.965744i | \(-0.583557\pi\) | ||||
−0.259498 | + | 0.965744i | \(0.583557\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7304.33 | −0.944747 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2528.12 | 0.324496 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4773.77 | 0.608087 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4023.09 | −0.508597 | −0.254298 | − | 0.967126i | \(-0.581845\pi\) | ||||
−0.254298 | + | 0.967126i | \(0.581845\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 33255.1 | 4.17252 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15809.5 | −1.96881 | −0.984403 | − | 0.175930i | \(-0.943707\pi\) | ||||
−0.984403 | + | 0.175930i | \(0.943707\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2926.27 | 0.361706 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2090.83 | 0.256529 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7399.49 | 0.901177 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8040.42 | −0.972061 | −0.486031 | − | 0.873942i | \(-0.661556\pi\) | ||||
−0.486031 | + | 0.873942i | \(0.661556\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13303.6 | 1.59663 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11629.0 | −1.38553 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4419.18 | 0.522720 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4497.67 | 0.528182 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16378.7 | −1.90967 | −0.954833 | − | 0.297142i | \(-0.903967\pi\) | ||||
−0.954833 | + | 0.297142i | \(0.903967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11576.6 | 1.34016 | 0.670082 | − | 0.742287i | \(-0.266259\pi\) | ||||
0.670082 | + | 0.742287i | \(0.266259\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2361.10 | 0.271396 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1110.65 | −0.126763 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6263.69 | 0.709886 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6724.02 | 0.756734 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 747.175 | 0.0835039 | 0.0417519 | − | 0.999128i | \(-0.486706\pi\) | ||||
0.0417519 | + | 0.999128i | \(0.486706\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8711.47 | 0.966851 | 0.483425 | − | 0.875386i | \(-0.339392\pi\) | ||||
0.483425 | + | 0.875386i | \(0.339392\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1148.21 | −0.126557 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22886.2 | −2.50525 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2056.40 | −0.223568 | −0.111784 | − | 0.993733i | \(-0.535657\pi\) | ||||
−0.111784 | + | 0.993733i | \(0.535657\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20253.2 | 2.18694 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16175.5 | −1.73481 | −0.867404 | − | 0.497605i | \(-0.834213\pi\) | ||||
−0.867404 | + | 0.497605i | \(0.834213\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6283.02 | −0.669312 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18455.6 | −1.95284 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11865.6 | −1.24715 | −0.623575 | − | 0.781764i | \(-0.714320\pi\) | ||||
−0.623575 | + | 0.781764i | \(0.714320\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11763.5 | −1.22821 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18495.8 | 1.91834 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3086.49 | −0.318015 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7236.71 | −0.740742 | −0.370371 | − | 0.928884i | \(-0.620769\pi\) | ||||
−0.370371 | + | 0.928884i | \(0.620769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3062.54 | 0.311432 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8760.00 | −0.885019 | −0.442509 | − | 0.896764i | \(-0.645912\pi\) | ||||
−0.442509 | + | 0.896764i | \(0.645912\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14811.5 | −1.48672 | −0.743358 | − | 0.668894i | \(-0.766768\pi\) | ||||
−0.743358 | + | 0.668894i | \(0.766768\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5662.63 | 0.564727 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 568.520 | 0.0563340 | 0.0281670 | − | 0.999603i | \(-0.491033\pi\) | ||||
0.0281670 | + | 0.999603i | \(0.491033\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30396.6 | 2.99272 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4740.80 | 0.463789 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16614.2 | 1.61506 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3479.92 | −0.336147 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 25247.0 | 2.42344 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14218.8 | −1.35631 | −0.678157 | − | 0.734917i | \(-0.737221\pi\) | ||||
−0.678157 | + | 0.734917i | \(0.737221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3648.07 | −0.345816 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −39280.2 | −3.70043 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1984.23 | 0.185772 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2724.74 | −0.253532 | −0.126766 | − | 0.991933i | \(-0.540460\pi\) | ||||
−0.126766 | + | 0.991933i | \(0.540460\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18655.0 | 1.72517 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21133.2 | 1.94242 | 0.971209 | − | 0.238231i | \(-0.0765674\pi\) | ||||
0.971209 | + | 0.238231i | \(0.0765674\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1288.35 | 0.117696 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7409.05 | 0.672752 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −142.698 | −0.0128791 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11748.1 | 1.05394 | 0.526970 | − | 0.849884i | \(-0.323328\pi\) | ||||
0.526970 | + | 0.849884i | \(0.323328\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7722.22 | 0.688629 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20052.9 | 1.77757 | 0.888783 | − | 0.458328i | \(-0.151552\pi\) | ||||
0.888783 | + | 0.458328i | \(0.151552\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6813.84 | −0.600419 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14082.3 | 1.23356 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17437.0 | −1.51843 | −0.759214 | − | 0.650841i | \(-0.774417\pi\) | ||||
−0.759214 | + | 0.650841i | \(0.774417\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7840.23 | 0.678731 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9595.68 | 0.825847 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9768.35 | 0.835815 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2744.33 | −0.233454 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13858.2 | −1.17208 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13465.5 | 1.13231 | 0.566154 | − | 0.824299i | \(-0.308431\pi\) | ||||
0.566154 | + | 0.824299i | \(0.308431\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −226.324 | −0.0189224 | −0.00946122 | − | 0.999955i | \(-0.503012\pi\) | ||||
−0.00946122 | + | 0.999955i | \(0.503012\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5972.67 | −0.496512 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6353.76 | −0.525188 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14865.7 | 1.22180 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13762.6 | −1.12476 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5799.59 | 0.471310 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8866.96 | −0.716546 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1710.05 | −0.137419 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23540.6 | −1.88120 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1099.62 | 0.0873866 | 0.0436933 | − | 0.999045i | \(-0.486088\pi\) | ||||
0.0436933 | + | 0.999045i | \(0.486088\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2922.08 | −0.230936 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8527.24 | 0.670215 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −325.266 | −0.0254248 | −0.0127124 | − | 0.999919i | \(-0.504047\pi\) | ||||
−0.0127124 | + | 0.999919i | \(0.504047\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7412.92 | 0.576277 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4036.71 | 0.312104 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28805.0 | −2.21503 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7059.38 | −0.539917 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11078.0 | −0.842715 | −0.421357 | − | 0.906895i | \(-0.638446\pi\) | ||||
−0.421357 | + | 0.906895i | \(0.638446\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8191.08 | −0.619760 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14599.8 | −1.09876 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4301.09 | −0.321971 | −0.160985 | − | 0.986957i | \(-0.551467\pi\) | ||||
−0.160985 | + | 0.986957i | \(0.551467\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7700.46 | 0.573382 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12616.1 | −0.934436 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13912.2 | −1.02501 | −0.512503 | − | 0.858686i | \(-0.671282\pi\) | ||||
−0.512503 | + | 0.858686i | \(0.671282\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5249.89 | 0.384765 | 0.192383 | − | 0.981320i | \(-0.438379\pi\) | ||||
0.192383 | + | 0.981320i | \(0.438379\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23605.7 | 1.72101 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4110.41 | 0.298114 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23793.2 | 1.71668 | 0.858338 | − | 0.513085i | \(-0.171497\pi\) | ||||
0.858338 | + | 0.513085i | \(0.171497\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11258.8 | 0.808116 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26665.3 | −1.90407 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29344.8 | −2.08463 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3652.78 | −0.258161 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1345.64 | 0.0946174 | 0.0473087 | − | 0.998880i | \(-0.484936\pi\) | ||||
0.0473087 | + | 0.998880i | \(0.484936\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19907.9 | −1.39268 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6862.76 | −0.477659 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12716.6 | −0.880618 | −0.440309 | − | 0.897846i | \(-0.645131\pi\) | ||||
−0.440309 | + | 0.897846i | \(0.645131\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6701.65 | 0.461749 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23252.3 | 1.59406 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20205.6 | −1.37826 | −0.689131 | − | 0.724637i | \(-0.742008\pi\) | ||||
−0.689131 | + | 0.724637i | \(0.742008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5770.48 | −0.391652 | −0.195826 | − | 0.980639i | \(-0.562739\pi\) | ||||
−0.195826 | + | 0.980639i | \(0.562739\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 35973.7 | 2.42945 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1956.62 | −0.131484 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3069.56 | 0.205255 | 0.102627 | − | 0.994720i | \(-0.467275\pi\) | ||||
0.102627 | + | 0.994720i | \(0.467275\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6928.30 | 0.461000 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1353.00 | 0.0895851 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15942.9 | −1.05045 | −0.525227 | − | 0.850962i | \(-0.676020\pi\) | ||||
−0.525227 | + | 0.850962i | \(0.676020\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11222.8 | 0.735849 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7071.49 | 0.461406 | 0.230703 | − | 0.973024i | \(-0.425897\pi\) | ||||
0.230703 | + | 0.973024i | \(0.425897\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14764.2 | 0.958679 | 0.479339 | − | 0.877630i | \(-0.340876\pi\) | ||||
0.479339 | + | 0.877630i | \(0.340876\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11334.2 | −0.732409 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 37911.8 | 2.43805 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −45744.6 | −2.91366 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7921.00 | 0.502116 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28574.8 | 1.80277 | 0.901383 | − | 0.433023i | \(-0.142553\pi\) | ||||
0.901383 | + | 0.433023i | \(0.142553\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1917.00 | 0.120369 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7608.78 | 0.475504 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11605.9 | 0.721887 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −168.880 | −0.0104551 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24087.2 | −1.48422 | −0.742112 | − | 0.670276i | \(-0.766176\pi\) | ||||
−0.742112 | + | 0.670276i | \(0.766176\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1460.69 | 0.0895865 | 0.0447932 | − | 0.998996i | \(-0.485737\pi\) | ||||
0.0447932 | + | 0.998996i | \(0.485737\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15850.6 | −0.967623 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6718.59 | 0.408246 | 0.204123 | − | 0.978945i | \(-0.434566\pi\) | ||||
0.204123 | + | 0.978945i | \(0.434566\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15996.4 | 0.967512 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −34168.3 | −2.05708 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −98.3814 | −0.00589580 | −0.00294790 | − | 0.999996i | \(-0.500938\pi\) | ||||
−0.00294790 | + | 0.999996i | \(0.500938\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1596.30 | 0.0952254 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9278.72 | 0.550985 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14606.4 | 0.863408 | 0.431704 | − | 0.902015i | \(-0.357913\pi\) | ||||
0.431704 | + | 0.902015i | \(0.357913\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 89.9790 | 0.00529467 | 0.00264734 | − | 0.999996i | \(-0.499157\pi\) | ||||
0.00264734 | + | 0.999996i | \(0.499157\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7197.92 | 0.421635 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20997.9 | 1.22445 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4768.07 | −0.276792 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5745.48 | 0.332038 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8616.12 | −0.495711 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13820.9 | −0.791613 | −0.395806 | − | 0.918334i | \(-0.629535\pi\) | ||||
−0.395806 | + | 0.918334i | \(0.629535\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1723.40 | −0.0982722 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32389.0 | 1.83871 | 0.919357 | − | 0.393423i | \(-0.128709\pi\) | ||||
0.919357 | + | 0.393423i | \(0.128709\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11972.9 | −0.676697 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 49293.5 | 2.77376 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12912.1 | 0.723379 | 0.361689 | − | 0.932299i | \(-0.382200\pi\) | ||||
0.361689 | + | 0.932299i | \(0.382200\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8400.12 | 0.468543 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33119.5 | −1.83928 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14467.5 | 0.799952 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2598.12 | 0.143035 | 0.0715176 | − | 0.997439i | \(-0.477216\pi\) | ||||
0.0715176 | + | 0.997439i | \(0.477216\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −44706.3 | −2.45058 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2839.91 | 0.154999 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12592.6 | −0.684329 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27615.0 | 1.49427 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14722.0 | −0.793212 | −0.396606 | − | 0.917989i | \(-0.629812\pi\) | ||||
−0.396606 | + | 0.917989i | \(0.629812\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24818.4 | 1.33150 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2618.19 | 0.139868 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 41114.7 | 2.18710 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20819.7 | −1.10282 | −0.551410 | − | 0.834234i | \(-0.685910\pi\) | ||||
−0.551410 | + | 0.834234i | \(0.685910\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34090.0 | −1.79813 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23514.7 | 1.23511 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4245.67 | 0.222069 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12642.7 | 0.658506 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9197.06 | 0.477041 | 0.238520 | − | 0.971137i | \(-0.423338\pi\) | ||||
0.238520 | + | 0.971137i | \(0.423338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −58942.3 | −3.04456 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −54830.8 | −2.82044 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −725.000 | −0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7105.85 | −0.362505 | −0.181253 | − | 0.983437i | \(-0.558015\pi\) | ||||
−0.181253 | + | 0.983437i | \(0.558015\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29669.7 | −1.50737 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17785.2 | 0.899876 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −999.375 | −0.0503585 | −0.0251792 | − | 0.999683i | \(-0.508016\pi\) | ||||
−0.0251792 | + | 0.999683i | \(0.508016\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22458.6 | 1.12707 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −41812.6 | −2.08981 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31121.4 | 1.54914 | 0.774572 | − | 0.632486i | \(-0.217965\pi\) | ||||
0.774572 | + | 0.632486i | \(0.217965\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 22552.8 | 1.11808 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3438.14 | −0.169762 | −0.0848811 | − | 0.996391i | \(-0.527051\pi\) | ||||
−0.0848811 | + | 0.996391i | \(0.527051\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11653.2 | −0.573073 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −31557.8 | −1.54570 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 53503.3 | 2.61010 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12142.4 | −0.589992 | −0.294996 | − | 0.955499i | \(-0.595318\pi\) | ||||
−0.294996 | + | 0.955499i | \(0.595318\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −45785.1 | −2.21581 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11678.6 | 0.562951 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18697.6 | 0.897722 | 0.448861 | − | 0.893602i | \(-0.351830\pi\) | ||||
0.448861 | + | 0.893602i | \(0.351830\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 54032.5 | 2.58400 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1401.86 | −0.0667772 | −0.0333886 | − | 0.999442i | \(-0.510630\pi\) | ||||
−0.0333886 | + | 0.999442i | \(0.510630\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −51453.4 | −2.44134 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7931.24 | 0.374842 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7886.50 | −0.371271 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12563.3 | 0.589134 | 0.294567 | − | 0.955631i | \(-0.404825\pi\) | ||||
0.294567 | + | 0.955631i | \(0.404825\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1152.57 | 0.0538377 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22987.3 | 1.06960 | 0.534798 | − | 0.844980i | \(-0.320388\pi\) | ||||
0.534798 | + | 0.844980i | \(0.320388\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3575.49 | 0.165723 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 42596.4 | 1.96671 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −39455.5 | −1.81469 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 196.291 | 0.00899340 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1999.15 | 0.0912435 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2993.43 | 0.136102 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13115.7 | −0.594058 | −0.297029 | − | 0.954868i | \(-0.595996\pi\) | ||||
−0.297029 | + | 0.954868i | \(0.595996\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −24727.1 | −1.11573 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46464.6 | −2.08861 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4247.89 | 0.190223 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27996.1 | 1.24895 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6717.43 | 0.298549 | 0.149274 | − | 0.988796i | \(-0.452306\pi\) | ||||
0.149274 | + | 0.988796i | \(0.452306\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2937.75 | −0.130075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 44867.7 | 1.97918 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10784.8 | −0.473955 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24802.2 | −1.08592 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5942.04 | −0.259194 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19473.0 | 0.846270 | 0.423135 | − | 0.906067i | \(-0.360930\pi\) | ||||
0.423135 | + | 0.906067i | \(0.360930\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 217.936 | 0.00943623 | 0.00471811 | − | 0.999989i | \(-0.498498\pi\) | ||||
0.00471811 | + | 0.999989i | \(0.498498\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 38147.6 | 1.64563 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11779.1 | 0.506262 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 55725.3 | 2.38627 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 22040.9 | 0.940380 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6337.86 | −0.269419 | −0.134709 | − | 0.990885i | \(-0.543010\pi\) | ||||
−0.134709 | + | 0.990885i | \(0.543010\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33154.8 | 1.40426 | 0.702128 | − | 0.712051i | \(-0.252233\pi\) | ||||
0.702128 | + | 0.712051i | \(0.252233\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8215.81 | 0.346712 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20191.4 | −0.849003 | −0.424501 | − | 0.905427i | \(-0.639551\pi\) | ||||
−0.424501 | + | 0.905427i | \(0.639551\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28296.8 | −1.18551 | −0.592756 | − | 0.805382i | \(-0.701960\pi\) | ||||
−0.592756 | + | 0.805382i | \(0.701960\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19332.3 | 0.807017 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25199.7 | −1.04816 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4875.95 | 0.202083 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9859.20 | −0.407149 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38620.6 | 1.58919 | 0.794596 | − | 0.607138i | \(-0.207683\pi\) | ||||
0.794596 | + | 0.607138i | \(0.207683\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −44320.3 | −1.81076 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8891.82 | 0.361997 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11806.3 | 0.478947 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20375.2 | 0.823645 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29314.9 | −1.18085 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25417.1 | −1.02024 | −0.510119 | − | 0.860104i | \(-0.670399\pi\) | ||||
−0.510119 | + | 0.860104i | \(0.670399\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 24850.5 | 0.993997 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25926.0 | 1.03339 | 0.516695 | − | 0.856170i | \(-0.327162\pi\) | ||||
0.516695 | + | 0.856170i | \(0.327162\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7972.29 | −0.316660 | −0.158330 | − | 0.987386i | \(-0.550611\pi\) | ||||
−0.158330 | + | 0.987386i | \(0.550611\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −67718.5 | −2.68042 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10304.2 | −0.406440 | −0.203220 | − | 0.979133i | \(-0.565141\pi\) | ||||
−0.203220 | + | 0.979133i | \(0.565141\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8750.34 | −0.343954 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23275.7 | 0.911747 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39623.2 | 1.54675 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20614.3 | 0.801939 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −14169.6 | −0.549334 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3771.25 | −0.145705 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6900.23 | −0.265683 | −0.132842 | − | 0.991137i | \(-0.542410\pi\) | ||||
−0.132842 | + | 0.991137i | \(0.542410\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 37216.5 | 1.42808 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28477.9 | −1.08904 | −0.544521 | − | 0.838747i | \(-0.683288\pi\) | ||||
−0.544521 | + | 0.838747i | \(0.683288\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16775.0 | −0.639326 | −0.319663 | − | 0.947531i | \(-0.603570\pi\) | ||||
−0.319663 | + | 0.947531i | \(0.603570\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15261.2 | −0.579661 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20332.1 | 0.769657 | 0.384829 | − | 0.922988i | \(-0.374261\pi\) | ||||
0.384829 | + | 0.922988i | \(0.374261\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45911.4 | −1.73208 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17354.3 | 0.652513 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9204.67 | −0.344930 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1079.75 | −0.0403265 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26638.9 | −0.991579 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4147.56 | −0.153870 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31413.1 | −1.16151 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 95642.6 | 3.52468 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1845.05 | −0.0677698 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33419.1 | 1.22344 | 0.611722 | − | 0.791073i | \(-0.290477\pi\) | ||||
0.611722 | + | 0.791073i | \(0.290477\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 48658.3 | 1.77546 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9108.80 | 0.331271 | 0.165636 | − | 0.986187i | \(-0.447032\pi\) | ||||
0.165636 | + | 0.986187i | \(0.447032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36680.0 | 1.32961 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8220.10 | 0.296993 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9632.09 | −0.346870 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26246.3 | 0.942095 | 0.471047 | − | 0.882108i | \(-0.343876\pi\) | ||||
0.471047 | + | 0.882108i | \(0.343876\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22319.4 | 0.798534 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −96.7746 | −0.00345111 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4457.42 | −0.158442 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −69756.8 | −2.47153 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20844.2 | 0.736143 | 0.368072 | − | 0.929797i | \(-0.380018\pi\) | ||||
0.368072 | + | 0.929797i | \(0.380018\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −78956.7 | −2.77949 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2697.67 | −0.0946600 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9218.57 | −0.322438 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19289.8 | −0.672540 | −0.336270 | − | 0.941766i | \(-0.609166\pi\) | ||||
−0.336270 | + | 0.941766i | \(0.609166\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 54275.0 | 1.88626 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10216.4 | 0.353926 | 0.176963 | − | 0.984217i | \(-0.443373\pi\) | ||||
0.176963 | + | 0.984217i | \(0.443373\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46604.0 | 1.60937 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10399.0 | 0.357968 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28349.2 | −0.972783 | −0.486391 | − | 0.873741i | \(-0.661687\pi\) | ||||
−0.486391 | + | 0.873741i | \(0.661687\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5317.06 | 0.181875 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 51556.6 | 1.75798 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7660.89 | −0.260399 | −0.130200 | − | 0.991488i | \(-0.541562\pi\) | ||||
−0.130200 | + | 0.991488i | \(0.541562\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14905.0 | 0.505043 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9530.34 | −0.321914 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −50686.4 | −1.70672 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9336.44 | −0.313398 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 63319.9 | 2.11885 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7109.00 | 0.237147 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46016.5 | 1.53029 | 0.765145 | − | 0.643858i | \(-0.222667\pi\) | ||||
0.765145 | + | 0.643858i | \(0.222667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −48968.6 | −1.62343 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41993.2 | −1.38787 | −0.693937 | − | 0.720036i | \(-0.744125\pi\) | ||||
−0.693937 | + | 0.720036i | \(0.744125\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17136.1 | −0.564601 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4050.53 | −0.133047 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8008.89 | 0.262259 | 0.131130 | − | 0.991365i | \(-0.458140\pi\) | ||||
0.131130 | + | 0.991365i | \(0.458140\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −52150.2 | −1.70248 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −60893.9 | −1.98185 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36234.8 | −1.17570 | −0.587849 | − | 0.808971i | \(-0.700025\pi\) | ||||
−0.587849 | + | 0.808971i | \(0.700025\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4333.27 | −0.140172 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −15798.2 | −0.509485 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −65821.4 | −2.11628 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28132.9 | −0.901786 | −0.450893 | − | 0.892578i | \(-0.648894\pi\) | ||||
−0.450893 | + | 0.892578i | \(0.648894\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24827.9 | 0.793443 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14682.0 | 0.467788 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −33.2275 | −0.00105549 | −0.000527746 | − | 1.00000i | \(-0.500168\pi\) | ||||
−0.000527746 | 1.00000i | \(0.500168\pi\) | ||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12291.1 | 0.389262 |
(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 | 1160.4.a.c.1.1 | ✓ | 7 | |
4.3 | odd | 2 | 2320.4.a.r.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1160.4.a.c.1.1 | ✓ | 7 | 1.1 | even | 1 | trivial | |
2320.4.a.r.1.7 | 7 | 4.3 | odd | 2 |