Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 232) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | −2.92622 | −0.563151 | −0.281576 | − | 0.959539i | \(-0.590857\pi\) | ||||
−0.281576 | + | 0.959539i | \(0.590857\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −14.3315 | −1.28185 | −0.640925 | − | 0.767603i | \(-0.721449\pi\) | ||||
−0.640925 | + | 0.767603i | \(0.721449\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.8804 | 0.911454 | 0.455727 | − | 0.890120i | \(-0.349379\pi\) | ||||
0.455727 | + | 0.890120i | \(0.349379\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −18.4372 | −0.682860 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −16.5613 | −0.453948 | −0.226974 | − | 0.973901i | \(-0.572883\pi\) | ||||
−0.226974 | + | 0.973901i | \(0.572883\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −55.3675 | −1.18124 | −0.590622 | − | 0.806948i | \(-0.701118\pi\) | ||||
−0.590622 | + | 0.806948i | \(0.701118\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 41.9372 | 0.721876 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.28120 | 0.0896126 | 0.0448063 | − | 0.998996i | \(-0.485733\pi\) | ||||
0.0448063 | + | 0.998996i | \(0.485733\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 119.008 | 1.43696 | 0.718482 | − | 0.695545i | \(-0.244837\pi\) | ||||
0.718482 | + | 0.695545i | \(0.244837\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −49.3957 | −0.513287 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.5433 | 0.204374 | 0.102187 | − | 0.994765i | \(-0.467416\pi\) | ||||
0.102187 | + | 0.994765i | \(0.467416\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 80.3924 | 0.643139 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 132.959 | 0.947705 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 228.987 | 1.32669 | 0.663344 | − | 0.748314i | \(-0.269136\pi\) | ||||
0.663344 | + | 0.748314i | \(0.269136\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 48.4621 | 0.255642 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −241.921 | −1.16835 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −257.186 | −1.14273 | −0.571366 | − | 0.820696i | \(-0.693586\pi\) | ||||
−0.571366 | + | 0.820696i | \(0.693586\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 162.017 | 0.665219 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 382.208 | 1.45588 | 0.727938 | − | 0.685643i | \(-0.240479\pi\) | ||||
0.727938 | + | 0.685643i | \(0.240479\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 170.123 | 0.603337 | 0.301669 | − | 0.953413i | \(-0.402456\pi\) | ||||
0.301669 | + | 0.953413i | \(0.402456\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 264.234 | 0.875325 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −172.889 | −0.536564 | −0.268282 | − | 0.963340i | \(-0.586456\pi\) | ||||
−0.268282 | + | 0.963340i | \(0.586456\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −58.0532 | −0.169251 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.3802 | −0.0504654 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 69.2381 | 0.179445 | 0.0897224 | − | 0.995967i | \(-0.471402\pi\) | ||||
0.0897224 | + | 0.995967i | \(0.471402\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 237.349 | 0.581893 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −348.244 | −0.809229 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 43.6860 | 0.0963971 | 0.0481986 | − | 0.998838i | \(-0.484652\pi\) | ||||
0.0481986 | + | 0.998838i | \(0.484652\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −684.892 | −1.43756 | −0.718782 | − | 0.695235i | \(-0.755300\pi\) | ||||
−0.718782 | + | 0.695235i | \(0.755300\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −311.227 | −0.622396 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 793.500 | 1.51418 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 528.585 | 0.963835 | 0.481917 | − | 0.876217i | \(-0.339941\pi\) | ||||
0.481917 | + | 0.876217i | \(0.339941\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −65.9667 | −0.115094 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −488.054 | −0.815794 | −0.407897 | − | 0.913028i | \(-0.633738\pi\) | ||||
−0.407897 | + | 0.913028i | \(0.633738\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 80.3863 | 0.128884 | 0.0644418 | − | 0.997921i | \(-0.479473\pi\) | ||||
0.0644418 | + | 0.997921i | \(0.479473\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −235.246 | −0.362185 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −279.561 | −0.413753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −741.898 | −1.05658 | −0.528292 | − | 0.849063i | \(-0.677167\pi\) | ||||
−0.528292 | + | 0.849063i | \(0.677167\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 108.737 | 0.149159 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1360.29 | 1.79893 | 0.899466 | − | 0.436991i | \(-0.143956\pi\) | ||||
0.899466 | + | 0.436991i | \(0.143956\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −90.0191 | −0.114870 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −84.8604 | −0.104575 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 957.563 | 1.14047 | 0.570233 | − | 0.821483i | \(-0.306853\pi\) | ||||
0.570233 | + | 0.821483i | \(0.306853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −934.623 | −1.07665 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −670.068 | −0.747127 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1705.57 | −1.84197 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1111.59 | −1.16355 | −0.581776 | − | 0.813349i | \(-0.697642\pi\) | ||||
−0.581776 | + | 0.813349i | \(0.697642\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 305.345 | 0.309983 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1691.56 | 1.66650 | 0.833249 | − | 0.552898i | \(-0.186478\pi\) | ||||
0.833249 | + | 0.552898i | \(0.186478\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −439.312 | −0.420259 | −0.210130 | − | 0.977674i | \(-0.567389\pi\) | ||||
−0.210130 | + | 0.977674i | \(0.567389\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 707.915 | 0.657957 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 861.531 | 0.778387 | 0.389193 | − | 0.921156i | \(-0.372754\pi\) | ||||
0.389193 | + | 0.921156i | \(0.372754\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 459.780 | 0.404027 | 0.202013 | − | 0.979383i | \(-0.435252\pi\) | ||||
0.202013 | + | 0.979383i | \(0.435252\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 752.582 | 0.643531 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.56230 | −0.00796058 | −0.00398029 | − | 0.999992i | \(-0.501267\pi\) | ||||
−0.00398029 | + | 0.999992i | \(0.501267\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −323.080 | −0.261977 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1020.82 | 0.806625 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 106.029 | 0.0816777 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1056.72 | −0.793931 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1118.43 | −0.819879 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 639.294 | 0.457442 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 905.522 | 0.632694 | 0.316347 | − | 0.948644i | \(-0.397544\pi\) | ||||
0.316347 | + | 0.948644i | \(0.397544\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −497.817 | −0.339770 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1039.43 | −0.693250 | −0.346625 | − | 0.938004i | \(-0.612672\pi\) | ||||
−0.346625 | + | 0.938004i | \(0.612672\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2008.90 | 1.30973 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1905.51 | −1.21482 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1146.58 | 0.715028 | 0.357514 | − | 0.933908i | \(-0.383624\pi\) | ||||
0.357514 | + | 0.933908i | \(0.383624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 573.043 | 0.349675 | 0.174838 | − | 0.984597i | \(-0.444060\pi\) | ||||
0.174838 | + | 0.984597i | \(0.444060\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 505.912 | 0.302167 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 916.959 | 0.536224 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −415.614 | −0.238034 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 169.877 | 0.0953142 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2324.32 | −1.27796 | −0.638979 | − | 0.769224i | \(-0.720643\pi\) | ||||
−0.638979 | + | 0.769224i | \(0.720643\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3188.68 | −1.71848 | −0.859242 | − | 0.511570i | \(-0.829064\pi\) | ||||
−0.859242 | + | 0.511570i | \(0.829064\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −115.808 | −0.0611929 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3281.74 | −1.70062 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2960.71 | 1.50503 | 0.752516 | − | 0.658574i | \(-0.228840\pi\) | ||||
0.752516 | + | 0.658574i | \(0.228840\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −202.606 | −0.101055 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 380.540 | 0.186278 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3417.14 | −1.64203 | −0.821015 | − | 0.570907i | \(-0.806592\pi\) | ||||
−0.821015 | + | 0.570907i | \(0.806592\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −694.536 | −0.327694 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −677.988 | −0.314158 | −0.157079 | − | 0.987586i | \(-0.550208\pi\) | ||||
−0.157079 | + | 0.987586i | \(0.550208\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 868.556 | 0.395337 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2194.18 | −0.981246 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 773.271 | 0.339831 | 0.169915 | − | 0.985459i | \(-0.445651\pi\) | ||||
0.169915 | + | 0.985459i | \(0.445651\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1357.05 | 0.586192 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −127.835 | −0.0542862 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1413.92 | −0.590399 | −0.295199 | − | 0.955436i | \(-0.595386\pi\) | ||||
−0.295199 | + | 0.955436i | \(0.595386\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2160.51 | −0.887234 | −0.443617 | − | 0.896216i | \(-0.646305\pi\) | ||||
−0.443617 | + | 0.896216i | \(0.646305\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2004.15 | 0.809567 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3685.86 | 1.46481 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −104.025 | −0.0406795 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2244.40 | 0.863790 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1586.39 | 0.600981 | 0.300490 | − | 0.953785i | \(-0.402850\pi\) | ||||
0.300490 | + | 0.953785i | \(0.402850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1970.84 | −0.735047 | −0.367523 | − | 0.930014i | \(-0.619794\pi\) | ||||
−0.367523 | + | 0.930014i | \(0.619794\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2321.96 | −0.852711 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4803.57 | −1.73726 | −0.868629 | − | 0.495463i | \(-0.834998\pi\) | ||||
−0.868629 | + | 0.495463i | \(0.834998\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2692.85 | −0.959252 | −0.479626 | − | 0.877473i | \(-0.659228\pi\) | ||||
−0.479626 | + | 0.877473i | \(0.659228\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1546.76 | −0.542785 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 489.531 | 0.169253 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5477.63 | −1.86621 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −415.636 | −0.139559 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1970.93 | −0.652308 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 703.260 | 0.229452 | 0.114726 | − | 0.993397i | \(-0.463401\pi\) | ||||
0.114726 | + | 0.993397i | \(0.463401\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1428.15 | 0.459415 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2438.12 | −0.773388 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3865.39 | 1.20922 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −235.228 | −0.0725810 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −347.774 | −0.105854 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3965.95 | −1.19094 | −0.595469 | − | 0.803378i | \(-0.703034\pi\) | ||||
−0.595469 | + | 0.803378i | \(0.703034\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1482.21 | −0.439174 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3976.09 | −1.16256 | −0.581282 | − | 0.813702i | \(-0.697449\pi\) | ||||
−0.581282 | + | 0.813702i | \(0.697449\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 611.004 | 0.176316 | 0.0881578 | − | 0.996107i | \(-0.471902\pi\) | ||||
0.0881578 | + | 0.996107i | \(0.471902\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 818.058 | 0.233006 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1051.90 | −0.295761 | −0.147880 | − | 0.989005i | \(-0.547245\pi\) | ||||
−0.147880 | + | 0.989005i | \(0.547245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2477.77 | 0.687794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2170.96 | 0.595017 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2085.97 | 0.564561 | 0.282280 | − | 0.959332i | \(-0.408909\pi\) | ||||
0.282280 | + | 0.959332i | \(0.408909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6064.55 | −1.62096 | −0.810481 | − | 0.585765i | \(-0.800794\pi\) | ||||
−0.810481 | + | 0.585765i | \(0.800794\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3908.09 | −1.03170 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 831.991 | 0.216955 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6589.18 | −1.69741 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3980.51 | −1.01307 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5169.26 | −1.29992 | −0.649962 | − | 0.759967i | \(-0.725215\pi\) | ||||
−0.649962 | + | 0.759967i | \(0.725215\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −373.347 | −0.0927753 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 263.416 | 0.0646891 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7238.84 | −1.75699 | −0.878495 | − | 0.477751i | \(-0.841452\pi\) | ||||
−0.878495 | + | 0.477751i | \(0.841452\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4341.39 | −1.04155 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −534.680 | −0.126804 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4855.39 | 1.13839 | 0.569195 | − | 0.822203i | \(-0.307255\pi\) | ||||
0.569195 | + | 0.822203i | \(0.307255\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −992.286 | −0.230021 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2802.04 | −0.642255 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5559.70 | −1.26015 | −0.630076 | − | 0.776533i | \(-0.716976\pi\) | ||||
−0.630076 | + | 0.776533i | \(0.716976\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2534.36 | 0.568087 | 0.284044 | − | 0.958811i | \(-0.408324\pi\) | ||||
0.284044 | + | 0.958811i | \(0.408324\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2734.91 | 0.606317 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1331.41 | −0.291952 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7540.72 | −1.63566 | −0.817831 | − | 0.575459i | \(-0.804823\pi\) | ||||
−0.817831 | + | 0.575459i | \(0.804823\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4221.89 | −0.905943 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5426.97 | 1.15212 | 0.576060 | − | 0.817407i | \(-0.304589\pi\) | ||||
0.576060 | + | 0.817407i | \(0.304589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1297.75 | −0.272590 | −0.136295 | − | 0.990668i | \(-0.543520\pi\) | ||||
−0.136295 | + | 0.990668i | \(0.543520\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4990.87 | 1.03731 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6451.82 | 1.32696 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4873.55 | −0.991970 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3252.75 | 0.655256 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6201.84 | 1.23657 | 0.618285 | − | 0.785954i | \(-0.287828\pi\) | ||||
0.618285 | + | 0.785954i | \(0.287828\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −626.086 | −0.123567 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2201.98 | −0.430209 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1248.17 | −0.241416 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2871.74 | 0.549914 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4949.87 | −0.938491 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9815.55 | 1.84274 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9181.06 | 1.70681 | 0.853406 | − | 0.521247i | \(-0.174533\pi\) | ||||
0.853406 | + | 0.521247i | \(0.174533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1285.52 | 0.236670 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3753.29 | 0.684339 | 0.342170 | − | 0.939638i | \(-0.388838\pi\) | ||||
0.342170 | + | 0.939638i | \(0.388838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2115.29 | 0.381991 | 0.190996 | − | 0.981591i | \(-0.438828\pi\) | ||||
0.190996 | + | 0.981591i | \(0.438828\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4460.36 | 0.797818 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4739.89 | 0.839807 | 0.419903 | − | 0.907569i | \(-0.362064\pi\) | ||||
0.419903 | + | 0.907569i | \(0.362064\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −480.279 | −0.0842961 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2521.03 | −0.438350 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 747.513 | 0.128770 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4451.12 | −0.759705 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1345.42 | −0.227528 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2918.43 | −0.489053 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6958.68 | 1.15554 | 0.577770 | − | 0.816200i | \(-0.303923\pi\) | ||||
0.577770 | + | 0.816200i | \(0.303923\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4741.79 | 0.780326 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7575.42 | −1.23549 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2997.55 | 0.484530 | 0.242265 | − | 0.970210i | \(-0.422110\pi\) | ||||
0.242265 | + | 0.970210i | \(0.422110\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 27.9814 | 0.00448301 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3792.34 | −0.602248 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6769.93 | −1.06572 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 945.404 | 0.147533 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7788.46 | −1.20492 | −0.602459 | − | 0.798150i | \(-0.705812\pi\) | ||||
−0.602459 | + | 0.798150i | \(0.705812\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6404.16 | 0.982254 | 0.491127 | − | 0.871088i | \(-0.336585\pi\) | ||||
0.491127 | + | 0.871088i | \(0.336585\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7361.62 | −1.11947 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5869.46 | −0.884986 | −0.442493 | − | 0.896772i | \(-0.645906\pi\) | ||||
−0.442493 | + | 0.896772i | \(0.645906\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6994.55 | 1.04572 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −310.264 | −0.0459969 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2761.48 | −0.405975 | −0.202988 | − | 0.979181i | \(-0.565065\pi\) | ||||
−0.202988 | + | 0.979181i | \(0.565065\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7303.93 | 1.06487 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3092.20 | 0.447103 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1152.06 | −0.165209 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3039.36 | 0.432298 | 0.216149 | − | 0.976360i | \(-0.430650\pi\) | ||||
0.216149 | + | 0.976360i | \(0.430650\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7046.86 | −0.994160 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1168.76 | 0.163556 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2051.57 | −0.284789 | −0.142394 | − | 0.989810i | \(-0.545480\pi\) | ||||
−0.142394 | + | 0.989810i | \(0.545480\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1870.72 | −0.257609 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1605.66 | −0.219351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1852.42 | 0.251062 | 0.125531 | − | 0.992090i | \(-0.459937\pi\) | ||||
0.125531 | + | 0.992090i | \(0.459937\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2649.76 | −0.356302 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5723.43 | 0.763587 | 0.381793 | − | 0.924248i | \(-0.375307\pi\) | ||||
0.381793 | + | 0.924248i | \(0.375307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4006.54 | 0.530369 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3136.59 | −0.411995 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4946.70 | 0.644750 | 0.322375 | − | 0.946612i | \(-0.395519\pi\) | ||||
0.322375 | + | 0.946612i | \(0.395519\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 141.599 | 0.0183145 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3041.61 | 0.390405 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10632.5 | 1.35438 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9275.78 | −1.17264 | −0.586320 | − | 0.810080i | \(-0.699424\pi\) | ||||
−0.586320 | + | 0.810080i | \(0.699424\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5878.49 | −0.737575 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5051.01 | 0.629016 | 0.314508 | − | 0.949255i | \(-0.398161\pi\) | ||||
0.314508 | + | 0.949255i | \(0.398161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12678.4 | −1.56714 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1558.36 | −0.191199 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4259.34 | 0.518741 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5049.42 | 0.610459 | 0.305229 | − | 0.952279i | \(-0.401267\pi\) | ||||
0.305229 | + | 0.952279i | \(0.401267\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3355.14 | −0.402669 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 737.435 | 0.0878616 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19495.0 | −2.30596 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1676.85 | −0.196920 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5332.54 | −0.621746 | −0.310873 | − | 0.950451i | \(-0.600621\pi\) | ||||
−0.310873 | + | 0.950451i | \(0.600621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6195.89 | −0.717266 | −0.358633 | − | 0.933479i | \(-0.616757\pi\) | ||||
−0.358633 | + | 0.933479i | \(0.616757\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3187.60 | 0.366398 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 504.961 | 0.0576334 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11561.2 | −1.31027 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2683.22 | −0.301975 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1399.50 | 0.156408 | 0.0782038 | − | 0.996937i | \(-0.475082\pi\) | ||||
0.0782038 | + | 0.996937i | \(0.475082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1689.45 | 0.187505 | 0.0937526 | − | 0.995596i | \(-0.470114\pi\) | ||||
0.0937526 | + | 0.995596i | \(0.470114\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1216.18 | 0.134049 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2682.84 | 0.293679 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12352.8 | −1.34298 | −0.671491 | − | 0.741013i | \(-0.734346\pi\) | ||||
−0.671491 | + | 0.741013i | \(0.734346\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1070.34 | 0.115575 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13427.1 | 1.44005 | 0.720023 | − | 0.693950i | \(-0.244131\pi\) | ||||
0.720023 | + | 0.693950i | \(0.244131\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13723.3 | −1.46191 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6801.47 | 0.719684 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2912.34 | 0.306107 | 0.153053 | − | 0.988218i | \(-0.451089\pi\) | ||||
0.153053 | + | 0.988218i | \(0.451089\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6329.88 | −0.660892 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9330.78 | 0.967767 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13394.6 | 1.38010 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5906.26 | 0.604558 | 0.302279 | − | 0.953219i | \(-0.402253\pi\) | ||||
0.302279 | + | 0.953219i | \(0.402253\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 835.144 | 0.0849263 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2847.28 | −0.287659 | −0.143830 | − | 0.989602i | \(-0.545942\pi\) | ||||
−0.143830 | + | 0.989602i | \(0.545942\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8561.02 | 0.859319 | 0.429659 | − | 0.902991i | \(-0.358634\pi\) | ||||
0.429659 | + | 0.902991i | \(0.358634\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9603.09 | 0.957704 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14998.9 | −1.48622 | −0.743112 | − | 0.669167i | \(-0.766651\pi\) | ||||
−0.743112 | + | 0.669167i | \(0.766651\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8922.71 | 0.878491 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8663.68 | −0.847561 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2817.46 | −0.273884 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9567.35 | 0.924169 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1276.56 | −0.122536 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8422.27 | −0.803389 | −0.401695 | − | 0.915774i | \(-0.631579\pi\) | ||||
−0.401695 | + | 0.915774i | \(0.631579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14239.7 | 1.34984 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1113.54 | −0.104903 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15930.7 | 1.49150 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1773.91 | −0.165058 | −0.0825291 | − | 0.996589i | \(-0.526300\pi\) | ||||
−0.0825291 | + | 0.996589i | \(0.526300\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9999.30 | 0.924711 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2157.20 | 0.198275 | 0.0991375 | − | 0.995074i | \(-0.468392\pi\) | ||||
0.0991375 | + | 0.995074i | \(0.468392\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 182.155 | 0.0166406 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4376.06 | −0.397352 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8238.53 | −0.743558 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4303.31 | −0.386058 | −0.193029 | − | 0.981193i | \(-0.561831\pi\) | ||||
−0.193029 | + | 0.981193i | \(0.561831\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1983.94 | 0.176918 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16020.5 | 1.42011 | 0.710057 | − | 0.704144i | \(-0.248669\pi\) | ||||
0.710057 | + | 0.704144i | \(0.248669\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24242.6 | −2.13620 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2541.59 | −0.222635 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18269.6 | −1.59094 | −0.795469 | − | 0.605994i | \(-0.792776\pi\) | ||||
−0.795469 | + | 0.605994i | \(0.792776\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1356.95 | 0.117472 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15823.2 | 1.36182 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6296.01 | 0.538709 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2863.28 | 0.243572 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2262.76 | −0.191376 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13128.7 | 1.10399 | 0.551996 | − | 0.833847i | \(-0.313866\pi\) | ||||
0.551996 | + | 0.833847i | \(0.313866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8295.67 | −0.693583 | −0.346792 | − | 0.937942i | \(-0.612729\pi\) | ||||
−0.346792 | + | 0.937942i | \(0.612729\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3971.04 | −0.330115 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1438.31 | 0.118888 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11658.8 | −0.958231 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −805.449 | −0.0658258 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21161.9 | −1.71974 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12347.1 | −0.997775 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4137.44 | 0.332484 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 961.439 | 0.0768314 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23563.6 | −1.87261 | −0.936303 | − | 0.351194i | \(-0.885776\pi\) | ||||
−0.936303 | + | 0.351194i | \(0.885776\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6322.13 | 0.499647 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6589.34 | −0.517902 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17151.4 | −1.34066 | −0.670330 | − | 0.742063i | \(-0.733848\pi\) | ||||
−0.670330 | + | 0.742063i | \(0.733848\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12627.5 | 0.981656 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3451.23 | 0.266838 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12523.5 | −0.963027 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10785.6 | −0.824910 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18572.6 | −1.41283 | −0.706415 | − | 0.707798i | \(-0.749689\pi\) | ||||
−0.706415 | + | 0.707798i | \(0.749689\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9419.27 | −0.712688 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 304.400 | 0.0229087 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7835.40 | −0.586541 | −0.293270 | − | 0.956030i | \(-0.594744\pi\) | ||||
−0.293270 | + | 0.956030i | \(0.594744\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 137.042 | 0.0102043 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1835.52 | 0.135951 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5891.09 | 0.434038 | 0.217019 | − | 0.976167i | \(-0.430367\pi\) | ||||
0.217019 | + | 0.976167i | \(0.430367\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20083.8 | 1.47195 | 0.735973 | − | 0.677010i | \(-0.236725\pi\) | ||||
0.735973 | + | 0.677010i | \(0.236725\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4642.13 | −0.338443 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1812.31 | 0.131441 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21008.9 | −1.51579 | −0.757896 | − | 0.652375i | \(-0.773773\pi\) | ||||
−0.757896 | + | 0.652375i | \(0.773773\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5767.11 | 0.413943 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22962.2 | 1.63964 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1146.67 | −0.0814587 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14629.9 | −1.03397 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20222.3 | 1.42192 | 0.710958 | − | 0.703235i | \(-0.248262\pi\) | ||||
0.710958 | + | 0.703235i | \(0.248262\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27251.4 | 1.90640 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14056.3 | 0.978339 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18803.0 | 1.30210 | 0.651051 | − | 0.759034i | \(-0.274328\pi\) | ||||
0.651051 | + | 0.759034i | \(0.274328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1519.55 | −0.104699 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7879.87 | 0.540204 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10612.1 | 0.723872 | 0.361936 | − | 0.932203i | \(-0.382116\pi\) | ||||
0.361936 | + | 0.932203i | \(0.382116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27709.6 | 1.88070 | 0.940350 | − | 0.340210i | \(-0.110498\pi\) | ||||
0.940350 | + | 0.340210i | \(0.110498\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9745.64 | −0.658164 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15144.4 | 1.01770 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21945.0 | −1.46741 | −0.733707 | − | 0.679466i | \(-0.762212\pi\) | ||||
−0.733707 | + | 0.679466i | \(0.762212\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1432.47 | −0.0953150 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9572.44 | 0.633813 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11777.0 | 0.775971 | 0.387985 | − | 0.921665i | \(-0.373171\pi\) | ||||
0.387985 | + | 0.921665i | \(0.373171\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16028.7 | 1.05096 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27161.1 | −1.77223 | −0.886115 | − | 0.463465i | \(-0.846606\pi\) | ||||
−0.886115 | + | 0.463465i | \(0.846606\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10366.3 | 0.673116 | 0.336558 | − | 0.941663i | \(-0.390737\pi\) | ||||
0.336558 | + | 0.941663i | \(0.390737\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2997.35 | 0.193687 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16164.0 | 1.03948 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19211.1 | −1.22951 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5767.38 | 0.367348 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1615.43 | −0.102403 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11208.4 | −0.707132 | −0.353566 | − | 0.935410i | \(-0.615031\pi\) | ||||
−0.353566 | + | 0.935410i | \(0.615031\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2057.89 | −0.129216 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12977.5 | −0.811018 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3214.26 | 0.199927 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8998.36 | 0.557073 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 351.957 | 0.0216872 | 0.0108436 | − | 0.999941i | \(-0.496548\pi\) | ||||
0.0108436 | + | 0.999941i | \(0.496548\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27628.0 | −1.69447 | −0.847234 | − | 0.531220i | \(-0.821734\pi\) | ||||
−0.847234 | + | 0.531220i | \(0.821734\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7134.48 | 0.435534 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10858.0 | −0.659771 | −0.329886 | − | 0.944021i | \(-0.607010\pi\) | ||||
−0.329886 | + | 0.944021i | \(0.607010\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −723.498 | −0.0437593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11311.0 | −0.680972 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9714.54 | 0.582174 | 0.291087 | − | 0.956697i | \(-0.405983\pi\) | ||||
0.291087 | + | 0.956697i | \(0.405983\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14896.7 | 0.888643 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1482.10 | −0.0880095 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1918.79 | −0.113422 | −0.0567111 | − | 0.998391i | \(-0.518061\pi\) | ||||
−0.0567111 | + | 0.998391i | \(0.518061\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12106.3 | 0.712375 | 0.356188 | − | 0.934414i | \(-0.384076\pi\) | ||||
0.356188 | + | 0.934414i | \(0.384076\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1017.66 | 0.0596120 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −28790.6 | −1.67887 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 653.756 | 0.0379513 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11605.2 | 0.670679 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11342.7 | 0.652580 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16348.0 | 0.936355 | 0.468178 | − | 0.883634i | \(-0.344911\pi\) | ||||
0.468178 | + | 0.883634i | \(0.344911\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10688.9 | 0.609507 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19298.2 | 1.09555 | 0.547776 | − | 0.836625i | \(-0.315475\pi\) | ||||
0.547776 | + | 0.836625i | \(0.315475\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18764.0 | −1.06052 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11634.9 | 0.654700 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9938.38 | −0.556781 | −0.278390 | − | 0.960468i | \(-0.589801\pi\) | ||||
−0.278390 | + | 0.960468i | \(0.589801\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16432.2 | −0.916558 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1787.93 | −0.0992924 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3833.54 | −0.211968 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18610.4 | 1.02456 | 0.512282 | − | 0.858817i | \(-0.328800\pi\) | ||||
0.512282 | + | 0.858817i | \(0.328800\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5154.34 | 0.282536 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8212.58 | −0.448231 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2400.73 | 0.130465 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3078.09 | 0.166558 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26877.8 | −1.44816 | −0.724080 | − | 0.689716i | \(-0.757735\pi\) | ||||
−0.724080 | + | 0.689716i | \(0.757735\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30607.2 | −1.64206 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7250.49 | −0.387332 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28554.1 | 1.51894 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3141.28 | 0.166394 | 0.0831970 | − | 0.996533i | \(-0.473487\pi\) | ||||
0.0831970 | + | 0.996533i | \(0.473487\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13678.6 | 0.721499 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5162.14 | 0.271141 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13141.4 | −0.687358 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6104.00 | −0.317933 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27198.6 | 1.41076 | 0.705379 | − | 0.708830i | \(-0.250777\pi\) | ||||
0.705379 | + | 0.708830i | \(0.250777\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7415.75 | −0.383047 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17746.2 | 0.912847 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2331.38 | 0.119428 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15713.1 | 0.801603 | 0.400802 | − | 0.916165i | \(-0.368732\pi\) | ||||
0.400802 | + | 0.916165i | \(0.368732\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8500.05 | 0.431847 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1068.58 | 0.0540666 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10977.4 | −0.553153 | −0.276576 | − | 0.960992i | \(-0.589200\pi\) | ||||
−0.276576 | + | 0.960992i | \(0.589200\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2434.59 | −0.122178 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8754.07 | −0.437531 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12586.3 | −0.626515 | −0.313258 | − | 0.949668i | \(-0.601420\pi\) | ||||
−0.313258 | + | 0.949668i | \(0.601420\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19281.4 | 0.955897 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21237.6 | 1.04863 | 0.524315 | − | 0.851524i | \(-0.324321\pi\) | ||||
0.524315 | + | 0.851524i | \(0.324321\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33311.0 | 1.63815 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −25080.0 | −1.22842 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14543.0 | 0.709464 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31114.2 | 1.51181 | 0.755907 | − | 0.654679i | \(-0.227196\pi\) | ||||
0.755907 | + | 0.654679i | \(0.227196\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15126.4 | 0.732054 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 45698.6 | 2.20284 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12838.7 | −0.616423 | −0.308211 | − | 0.951318i | \(-0.599730\pi\) | ||||
−0.308211 | + | 0.951318i | \(0.599730\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1092.50 | 0.0522466 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11665.6 | −0.555689 | −0.277844 | − | 0.960626i | \(-0.589620\pi\) | ||||
−0.277844 | + | 0.960626i | \(0.589620\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7761.25 | 0.368252 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1659.70 | 0.0784401 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2418.78 | −0.113869 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33339.3 | −1.56339 | −0.781693 | − | 0.623663i | \(-0.785644\pi\) | ||||
−0.781693 | + | 0.623663i | \(0.785644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21182.4 | 0.989452 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17895.2 | 0.832660 | 0.416330 | − | 0.909214i | \(-0.363316\pi\) | ||||
0.416330 | + | 0.909214i | \(0.363316\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18408.9 | 0.853246 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12703.9 | 0.586549 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 45485.9 | 2.09204 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8082.82 | 0.370328 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3855.82 | 0.175984 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42431.4 | −1.92923 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15816.4 | 0.716384 | 0.358192 | − | 0.933648i | \(-0.383393\pi\) | ||||
0.358192 | + | 0.933648i | \(0.383393\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14208.0 | −0.641086 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −161.415 | −0.00725570 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37920.7 | 1.69811 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2903.65 | 0.129537 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21146.2 | −0.939822 | −0.469911 | − | 0.882714i | \(-0.655714\pi\) | ||||
−0.469911 | + | 0.882714i | \(0.655714\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1085.95 | −0.0480828 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17654.8 | −0.778779 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1331.30 | −0.0585065 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5453.71 | −0.238780 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16268.9 | 0.709657 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19190.2 | −0.833982 | −0.416991 | − | 0.908911i | \(-0.636915\pi\) | ||||
−0.416991 | + | 0.908911i | \(0.636915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37890.9 | 1.64060 | 0.820302 | − | 0.571931i | \(-0.193806\pi\) | ||||
0.820302 | + | 0.571931i | \(0.193806\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7416.11 | −0.319919 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48972.8 | 2.10484 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20246.0 | 0.866974 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 17231.9 | 0.735201 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11006.2 | 0.467868 | 0.233934 | − | 0.972252i | \(-0.424840\pi\) | ||||
0.233934 | + | 0.972252i | \(0.424840\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42361.2 | 1.79419 | 0.897094 | − | 0.441839i | \(-0.145674\pi\) | ||||
0.897094 | + | 0.441839i | \(0.145674\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3895.99 | 0.164413 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1786.13 | 0.0751028 | 0.0375514 | − | 0.999295i | \(-0.488044\pi\) | ||||
0.0375514 | + | 0.999295i | \(0.488044\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12070.8 | −0.505712 | −0.252856 | − | 0.967504i | \(-0.581370\pi\) | ||||
−0.252856 | + | 0.967504i | \(0.581370\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22065.8 | 0.921125 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −364.644 | −0.0151671 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9716.60 | 0.402703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30446.0 | 1.25731 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39687.9 | −1.63311 | −0.816555 | − | 0.577267i | \(-0.804119\pi\) | ||||
−0.816555 | + | 0.577267i | \(0.804119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15880.5 | −0.648818 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12447.7 | −0.506763 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17837.9 | −0.723632 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3797.50 | 0.153510 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5797.82 | −0.233545 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36146.8 | −1.45093 | −0.725466 | − | 0.688258i | \(-0.758376\pi\) | ||||
−0.725466 | + | 0.688258i | \(0.758376\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31445.9 | 1.25781 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1778.90 | 0.0709054 | 0.0354527 | − | 0.999371i | \(-0.488713\pi\) | ||||
0.0354527 | + | 0.999371i | \(0.488713\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37890.5 | −1.50501 | −0.752507 | − | 0.658584i | \(-0.771156\pi\) | ||||
−0.752507 | + | 0.658584i | \(0.771156\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18879.4 | −0.747282 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22754.4 | −0.897529 | −0.448764 | − | 0.893650i | \(-0.648136\pi\) | ||||
−0.448764 | + | 0.893650i | \(0.648136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11082.1 | −0.435612 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14261.1 | 0.558629 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12286.8 | 0.479634 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29266.4 | −1.13852 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20494.6 | 0.794543 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10791.5 | 0.416937 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28543.9 | −1.09904 | −0.549521 | − | 0.835480i | \(-0.685190\pi\) | ||||
−0.549521 | + | 0.835480i | \(0.685190\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18147.9 | −0.696376 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46848.4 | 1.79156 | 0.895779 | − | 0.444499i | \(-0.146618\pi\) | ||||
0.895779 | + | 0.444499i | \(0.146618\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7020.06 | −0.267547 | −0.133773 | − | 0.991012i | \(-0.542709\pi\) | ||||
−0.133773 | + | 0.991012i | \(0.542709\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1832.07 | 0.0695867 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19200.5 | 0.726820 | 0.363410 | − | 0.931629i | \(-0.381612\pi\) | ||||
0.363410 | + | 0.931629i | \(0.381612\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15285.5 | 0.576671 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1800.83 | −0.0677104 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20575.2 | −0.771023 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20263.6 | 0.756803 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3652.41 | 0.135954 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6640.63 | 0.246360 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 434.898 | 0.0160805 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8403.34 | −0.309685 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30963.4 | 1.13730 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36098.6 | 1.32154 | 0.660768 | − | 0.750590i | \(-0.270231\pi\) | ||||
0.660768 | + | 0.750590i | \(0.270231\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31187.6 | −1.13799 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19193.8 | −0.698047 | −0.349023 | − | 0.937114i | \(-0.613487\pi\) | ||||
−0.349023 | + | 0.937114i | \(0.613487\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22528.2 | −0.816622 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28722.5 | −1.03774 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17546.0 | −0.631866 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49242.2 | 1.76752 | 0.883760 | − | 0.467941i | \(-0.155004\pi\) | ||||
0.883760 | + | 0.467941i | \(0.155004\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26865.8 | −0.961193 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27022.3 | 0.963651 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20675.8 | −0.734936 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8099.70 | 0.286978 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43350.9 | −1.53100 | −0.765498 | − | 0.643438i | \(-0.777507\pi\) | ||||
−0.765498 | + | 0.643438i | \(0.777507\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6908.80 | −0.243208 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10983.0 | −0.385387 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1490.84 | 0.0521450 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39167.8 | 1.36559 | 0.682794 | − | 0.730611i | \(-0.260765\pi\) | ||||
0.682794 | + | 0.730611i | \(0.260765\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6189.81 | −0.215119 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13329.9 | 0.461789 | 0.230895 | − | 0.972979i | \(-0.425835\pi\) | ||||
0.230895 | + | 0.972979i | \(0.425835\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8616.25 | 0.297544 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −32165.7 | −1.10725 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19115.3 | 0.655926 | 0.327963 | − | 0.944690i | \(-0.393638\pi\) | ||||
0.327963 | + | 0.944690i | \(0.393638\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4450.78 | −0.152243 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13870.0 | −0.472938 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29008.4 | −0.986018 | −0.493009 | − | 0.870024i | \(-0.664103\pi\) | ||||
−0.493009 | + | 0.870024i | \(0.664103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22735.4 | −0.770367 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1405.40 | 0.0474715 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19354.7 | 0.651715 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22644.2 | 0.760103 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15884.3 | −0.531529 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28245.1 | 0.942220 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55491.5 | 1.84538 | 0.922691 | − | 0.385539i | \(-0.125985\pi\) | ||||
0.922691 | + | 0.385539i | \(0.125985\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2187.39 | −0.0725171 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39721.0 | −1.31278 | −0.656389 | − | 0.754422i | \(-0.727917\pi\) | ||||
−0.656389 | + | 0.754422i | \(0.727917\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9673.18 | 0.318713 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13025.0 | 0.427829 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4352.89 | 0.142540 | 0.0712699 | − | 0.997457i | \(-0.477295\pi\) | ||||
0.0712699 | + | 0.997457i | \(0.477295\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15858.5 | −0.517712 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8477.07 | −0.275894 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10317.1 | −0.334754 | −0.167377 | − | 0.985893i | \(-0.553530\pi\) | ||||
−0.167377 | + | 0.985893i | \(0.553530\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 68842.4 | 2.22690 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8539.98 | 0.275411 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3835.13 | 0.123307 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45439.0 | −1.45653 | −0.728264 | − | 0.685297i | \(-0.759672\pi\) | ||||
−0.728264 | + | 0.685297i | \(0.759672\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20362.6 | −0.650744 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38592.6 | 1.22962 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31888.0 | −1.01294 | −0.506471 | − | 0.862257i | \(-0.669050\pi\) | ||||
−0.506471 | + | 0.862257i | \(0.669050\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −34195.2 | −1.08297 |
(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 | 1856.4.a.p.1.2 | 3 | ||
4.3 | odd | 2 | 1856.4.a.u.1.2 | 3 | |||
8.3 | odd | 2 | 464.4.a.g.1.2 | 3 | |||
8.5 | even | 2 | 232.4.a.b.1.2 | ✓ | 3 | ||
24.5 | odd | 2 | 2088.4.a.b.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.b.1.2 | ✓ | 3 | 8.5 | even | 2 | ||
464.4.a.g.1.2 | 3 | 8.3 | odd | 2 | |||
1856.4.a.p.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1856.4.a.u.1.2 | 3 | 4.3 | odd | 2 | |||
2088.4.a.b.1.1 | 3 | 24.5 | odd | 2 |