Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(1,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.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: | \(79.6525785077\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 270) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1350.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −14.0000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −22.0000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 30.0000 | 0.640039 | 0.320019 | − | 0.947411i | \(-0.396311\pi\) | ||||
0.320019 | + | 0.947411i | \(0.396311\pi\) | |||||||
\(14\) | 28.0000 | 0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 7.00000 | 0.0998676 | 0.0499338 | − | 0.998753i | \(-0.484099\pi\) | ||||
0.0499338 | + | 0.998753i | \(0.484099\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −81.0000 | −0.978035 | −0.489018 | − | 0.872274i | \(-0.662645\pi\) | ||||
−0.489018 | + | 0.872274i | \(0.662645\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 44.0000 | 0.426401 | ||||||||
\(23\) | 151.000 | 1.36894 | 0.684471 | − | 0.729040i | \(-0.260033\pi\) | ||||
0.684471 | + | 0.729040i | \(0.260033\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −60.0000 | −0.452576 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −56.0000 | −0.377964 | ||||||||
\(29\) | 270.000 | 1.72889 | 0.864444 | − | 0.502729i | \(-0.167671\pi\) | ||||
0.864444 | + | 0.502729i | \(0.167671\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −113.000 | −0.654690 | −0.327345 | − | 0.944905i | \(-0.606154\pi\) | ||||
−0.327345 | + | 0.944905i | \(0.606154\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −14.0000 | −0.0706171 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 88.0000 | 0.391003 | 0.195501 | − | 0.980703i | \(-0.437367\pi\) | ||||
0.195501 | + | 0.980703i | \(0.437367\pi\) | |||||||
\(38\) | 162.000 | 0.691576 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −406.000 | −1.54650 | −0.773251 | − | 0.634101i | \(-0.781371\pi\) | ||||
−0.773251 | + | 0.634101i | \(0.781371\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 442.000 | 1.56754 | 0.783772 | − | 0.621049i | \(-0.213293\pi\) | ||||
0.783772 | + | 0.621049i | \(0.213293\pi\) | |||||||
\(44\) | −88.0000 | −0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −302.000 | −0.967988 | ||||||||
\(47\) | 56.0000 | 0.173797 | 0.0868983 | − | 0.996217i | \(-0.472304\pi\) | ||||
0.0868983 | + | 0.996217i | \(0.472304\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −147.000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 120.000 | 0.320019 | ||||||||
\(53\) | −141.000 | −0.365431 | −0.182715 | − | 0.983166i | \(-0.558489\pi\) | ||||
−0.182715 | + | 0.983166i | \(0.558489\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 112.000 | 0.267261 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −540.000 | −1.22251 | ||||||||
\(59\) | 274.000 | 0.604606 | 0.302303 | − | 0.953212i | \(-0.402245\pi\) | ||||
0.302303 | + | 0.953212i | \(0.402245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 41.0000 | 0.0860576 | 0.0430288 | − | 0.999074i | \(-0.486299\pi\) | ||||
0.0430288 | + | 0.999074i | \(0.486299\pi\) | |||||||
\(62\) | 226.000 | 0.462936 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −328.000 | −0.598083 | −0.299042 | − | 0.954240i | \(-0.596667\pi\) | ||||
−0.299042 | + | 0.954240i | \(0.596667\pi\) | |||||||
\(68\) | 28.0000 | 0.0499338 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 390.000 | 0.651894 | 0.325947 | − | 0.945388i | \(-0.394317\pi\) | ||||
0.325947 | + | 0.945388i | \(0.394317\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −626.000 | −1.00367 | −0.501834 | − | 0.864964i | \(-0.667341\pi\) | ||||
−0.501834 | + | 0.864964i | \(0.667341\pi\) | |||||||
\(74\) | −176.000 | −0.276481 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −324.000 | −0.489018 | ||||||||
\(77\) | 308.000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1215.00 | −1.73036 | −0.865178 | − | 0.501464i | \(-0.832795\pi\) | ||||
−0.865178 | + | 0.501464i | \(0.832795\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 812.000 | 1.09354 | ||||||||
\(83\) | 505.000 | 0.667843 | 0.333921 | − | 0.942601i | \(-0.391628\pi\) | ||||
0.333921 | + | 0.942601i | \(0.391628\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −884.000 | −1.10842 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 176.000 | 0.213201 | ||||||||
\(89\) | −514.000 | −0.612179 | −0.306089 | − | 0.952003i | \(-0.599021\pi\) | ||||
−0.306089 | + | 0.952003i | \(0.599021\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −420.000 | −0.483824 | ||||||||
\(92\) | 604.000 | 0.684471 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −112.000 | −0.122893 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1816.00 | −1.90090 | −0.950448 | − | 0.310884i | \(-0.899375\pi\) | ||||
−0.950448 | + | 0.310884i | \(0.899375\pi\) | |||||||
\(98\) | 294.000 | 0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 592.000 | 0.583230 | 0.291615 | − | 0.956536i | \(-0.405807\pi\) | ||||
0.291615 | + | 0.956536i | \(0.405807\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 848.000 | 0.811223 | 0.405611 | − | 0.914046i | \(-0.367059\pi\) | ||||
0.405611 | + | 0.914046i | \(0.367059\pi\) | |||||||
\(104\) | −240.000 | −0.226288 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 282.000 | 0.258399 | ||||||||
\(107\) | 1500.00 | 1.35524 | 0.677619 | − | 0.735413i | \(-0.263012\pi\) | ||||
0.677619 | + | 0.735413i | \(0.263012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −935.000 | −0.821622 | −0.410811 | − | 0.911721i | \(-0.634754\pi\) | ||||
−0.410811 | + | 0.911721i | \(0.634754\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −224.000 | −0.188982 | ||||||||
\(113\) | −1266.00 | −1.05394 | −0.526970 | − | 0.849884i | \(-0.676672\pi\) | ||||
−0.526970 | + | 0.849884i | \(0.676672\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1080.00 | 0.864444 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −548.000 | −0.427521 | ||||||||
\(119\) | −98.0000 | −0.0754928 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −847.000 | −0.636364 | ||||||||
\(122\) | −82.0000 | −0.0608519 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −452.000 | −0.327345 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.0000 | 0.0111793 | 0.00558965 | − | 0.999984i | \(-0.498221\pi\) | ||||
0.00558965 | + | 0.999984i | \(0.498221\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2304.00 | 1.53665 | 0.768326 | − | 0.640059i | \(-0.221090\pi\) | ||||
0.768326 | + | 0.640059i | \(0.221090\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1134.00 | 0.739325 | ||||||||
\(134\) | 656.000 | 0.422909 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −56.0000 | −0.0353085 | ||||||||
\(137\) | 1341.00 | 0.836273 | 0.418136 | − | 0.908384i | \(-0.362683\pi\) | ||||
0.418136 | + | 0.908384i | \(0.362683\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2564.00 | −1.56457 | −0.782286 | − | 0.622919i | \(-0.785947\pi\) | ||||
−0.782286 | + | 0.622919i | \(0.785947\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −780.000 | −0.460959 | ||||||||
\(143\) | −660.000 | −0.385958 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1252.00 | 0.709700 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 352.000 | 0.195501 | ||||||||
\(149\) | −3122.00 | −1.71654 | −0.858269 | − | 0.513200i | \(-0.828460\pi\) | ||||
−0.858269 | + | 0.513200i | \(0.828460\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3004.00 | 1.61895 | 0.809477 | − | 0.587152i | \(-0.199751\pi\) | ||||
0.809477 | + | 0.587152i | \(0.199751\pi\) | |||||||
\(152\) | 648.000 | 0.345788 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −616.000 | −0.322329 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3566.00 | 1.81272 | 0.906362 | − | 0.422501i | \(-0.138848\pi\) | ||||
0.906362 | + | 0.422501i | \(0.138848\pi\) | |||||||
\(158\) | 2430.00 | 1.22355 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2114.00 | −1.03482 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −556.000 | −0.267174 | −0.133587 | − | 0.991037i | \(-0.542649\pi\) | ||||
−0.133587 | + | 0.991037i | \(0.542649\pi\) | |||||||
\(164\) | −1624.00 | −0.773251 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1010.00 | −0.472236 | ||||||||
\(167\) | −129.000 | −0.0597744 | −0.0298872 | − | 0.999553i | \(-0.509515\pi\) | ||||
−0.0298872 | + | 0.999553i | \(0.509515\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1297.00 | −0.590350 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1768.00 | 0.783772 | ||||||||
\(173\) | 1277.00 | 0.561205 | 0.280603 | − | 0.959824i | \(-0.409466\pi\) | ||||
0.280603 | + | 0.959824i | \(0.409466\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −352.000 | −0.150756 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1028.00 | 0.432876 | ||||||||
\(179\) | 1180.00 | 0.492723 | 0.246361 | − | 0.969178i | \(-0.420765\pi\) | ||||
0.246361 | + | 0.969178i | \(0.420765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2527.00 | −1.03774 | −0.518869 | − | 0.854854i | \(-0.673647\pi\) | ||||
−0.518869 | + | 0.854854i | \(0.673647\pi\) | |||||||
\(182\) | 840.000 | 0.342115 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1208.00 | −0.483994 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −154.000 | −0.0602224 | ||||||||
\(188\) | 224.000 | 0.0868983 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3480.00 | −1.31835 | −0.659173 | − | 0.751992i | \(-0.729093\pi\) | ||||
−0.659173 | + | 0.751992i | \(0.729093\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3170.00 | −1.18229 | −0.591144 | − | 0.806566i | \(-0.701324\pi\) | ||||
−0.591144 | + | 0.806566i | \(0.701324\pi\) | |||||||
\(194\) | 3632.00 | 1.34414 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −588.000 | −0.214286 | ||||||||
\(197\) | −2335.00 | −0.844476 | −0.422238 | − | 0.906485i | \(-0.638755\pi\) | ||||
−0.422238 | + | 0.906485i | \(0.638755\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1512.00 | −0.538607 | −0.269304 | − | 0.963055i | \(-0.586794\pi\) | ||||
−0.269304 | + | 0.963055i | \(0.586794\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1184.00 | −0.412406 | ||||||||
\(203\) | −3780.00 | −1.30692 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1696.00 | −0.573621 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 480.000 | 0.160010 | ||||||||
\(209\) | 1782.00 | 0.589778 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5919.00 | −1.93119 | −0.965594 | − | 0.260053i | \(-0.916260\pi\) | ||||
−0.965594 | + | 0.260053i | \(0.916260\pi\) | |||||||
\(212\) | −564.000 | −0.182715 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3000.00 | −0.958298 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1582.00 | 0.494899 | ||||||||
\(218\) | 1870.00 | 0.580974 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 210.000 | 0.0639191 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 412.000 | 0.123720 | 0.0618600 | − | 0.998085i | \(-0.480297\pi\) | ||||
0.0618600 | + | 0.998085i | \(0.480297\pi\) | |||||||
\(224\) | 448.000 | 0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2532.00 | 0.745248 | ||||||||
\(227\) | −5843.00 | −1.70843 | −0.854215 | − | 0.519920i | \(-0.825962\pi\) | ||||
−0.854215 | + | 0.519920i | \(0.825962\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4153.00 | −1.19842 | −0.599210 | − | 0.800592i | \(-0.704518\pi\) | ||||
−0.599210 | + | 0.800592i | \(0.704518\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2160.00 | −0.611254 | ||||||||
\(233\) | −562.000 | −0.158016 | −0.0790082 | − | 0.996874i | \(-0.525175\pi\) | ||||
−0.0790082 | + | 0.996874i | \(0.525175\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1096.00 | 0.302303 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 196.000 | 0.0533815 | ||||||||
\(239\) | 836.000 | 0.226261 | 0.113130 | − | 0.993580i | \(-0.463912\pi\) | ||||
0.113130 | + | 0.993580i | \(0.463912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1529.00 | −0.408679 | −0.204339 | − | 0.978900i | \(-0.565505\pi\) | ||||
−0.204339 | + | 0.978900i | \(0.565505\pi\) | |||||||
\(242\) | 1694.00 | 0.449977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 164.000 | 0.0430288 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2430.00 | −0.625981 | ||||||||
\(248\) | 904.000 | 0.231468 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 252.000 | 0.0633709 | 0.0316855 | − | 0.999498i | \(-0.489913\pi\) | ||||
0.0316855 | + | 0.999498i | \(0.489913\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3322.00 | −0.825503 | ||||||||
\(254\) | −32.0000 | −0.00790496 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −6111.00 | −1.48324 | −0.741622 | − | 0.670818i | \(-0.765943\pi\) | ||||
−0.741622 | + | 0.670818i | \(0.765943\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1232.00 | −0.295570 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4608.00 | −1.08658 | ||||||||
\(263\) | −3104.00 | −0.727760 | −0.363880 | − | 0.931446i | \(-0.618548\pi\) | ||||
−0.363880 | + | 0.931446i | \(0.618548\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2268.00 | −0.522782 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1312.00 | −0.299042 | ||||||||
\(269\) | 3240.00 | 0.734373 | 0.367186 | − | 0.930147i | \(-0.380321\pi\) | ||||
0.367186 | + | 0.930147i | \(0.380321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2395.00 | 0.536848 | 0.268424 | − | 0.963301i | \(-0.413497\pi\) | ||||
0.268424 | + | 0.963301i | \(0.413497\pi\) | |||||||
\(272\) | 112.000 | 0.0249669 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2682.00 | −0.591334 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6574.00 | 1.42597 | 0.712984 | − | 0.701180i | \(-0.247343\pi\) | ||||
0.712984 | + | 0.701180i | \(0.247343\pi\) | |||||||
\(278\) | 5128.00 | 1.10632 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4230.00 | −0.898009 | −0.449005 | − | 0.893529i | \(-0.648221\pi\) | ||||
−0.449005 | + | 0.893529i | \(0.648221\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5678.00 | 1.19266 | 0.596329 | − | 0.802740i | \(-0.296625\pi\) | ||||
0.596329 | + | 0.802740i | \(0.296625\pi\) | |||||||
\(284\) | 1560.00 | 0.325947 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1320.00 | 0.272913 | ||||||||
\(287\) | 5684.00 | 1.16904 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4864.00 | −0.990026 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2504.00 | −0.501834 | ||||||||
\(293\) | −4587.00 | −0.914592 | −0.457296 | − | 0.889315i | \(-0.651182\pi\) | ||||
−0.457296 | + | 0.889315i | \(0.651182\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −704.000 | −0.138240 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6244.00 | 1.21378 | ||||||||
\(299\) | 4530.00 | 0.876176 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6188.00 | −1.18495 | ||||||||
\(302\) | −6008.00 | −1.14477 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1296.00 | −0.244509 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7140.00 | −1.32737 | −0.663683 | − | 0.748014i | \(-0.731008\pi\) | ||||
−0.663683 | + | 0.748014i | \(0.731008\pi\) | |||||||
\(308\) | 1232.00 | 0.227921 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7122.00 | 1.29856 | 0.649279 | − | 0.760550i | \(-0.275071\pi\) | ||||
0.649279 | + | 0.760550i | \(0.275071\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6740.00 | −1.21715 | −0.608574 | − | 0.793497i | \(-0.708258\pi\) | ||||
−0.608574 | + | 0.793497i | \(0.708258\pi\) | |||||||
\(314\) | −7132.00 | −1.28179 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4860.00 | −0.865178 | ||||||||
\(317\) | −5441.00 | −0.964028 | −0.482014 | − | 0.876163i | \(-0.660095\pi\) | ||||
−0.482014 | + | 0.876163i | \(0.660095\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5940.00 | −1.04256 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4228.00 | 0.731731 | ||||||||
\(323\) | −567.000 | −0.0976741 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1112.00 | 0.188920 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3248.00 | 0.546771 | ||||||||
\(329\) | −784.000 | −0.131378 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −380.000 | −0.0631018 | −0.0315509 | − | 0.999502i | \(-0.510045\pi\) | ||||
−0.0315509 | + | 0.999502i | \(0.510045\pi\) | |||||||
\(332\) | 2020.00 | 0.333921 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 258.000 | 0.0422669 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3146.00 | −0.508527 | −0.254263 | − | 0.967135i | \(-0.581833\pi\) | ||||
−0.254263 | + | 0.967135i | \(0.581833\pi\) | |||||||
\(338\) | 2594.00 | 0.417441 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2486.00 | 0.394793 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6860.00 | 1.07990 | ||||||||
\(344\) | −3536.00 | −0.554210 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2554.00 | −0.396832 | ||||||||
\(347\) | −8904.00 | −1.37750 | −0.688749 | − | 0.725000i | \(-0.741840\pi\) | ||||
−0.688749 | + | 0.725000i | \(0.741840\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10429.0 | 1.59957 | 0.799787 | − | 0.600283i | \(-0.204946\pi\) | ||||
0.799787 | + | 0.600283i | \(0.204946\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 704.000 | 0.106600 | ||||||||
\(353\) | −10018.0 | −1.51049 | −0.755247 | − | 0.655440i | \(-0.772483\pi\) | ||||
−0.755247 | + | 0.655440i | \(0.772483\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2056.00 | −0.306089 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2360.00 | −0.348407 | ||||||||
\(359\) | −8532.00 | −1.25432 | −0.627161 | − | 0.778889i | \(-0.715783\pi\) | ||||
−0.627161 | + | 0.778889i | \(0.715783\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −298.000 | −0.0434466 | ||||||||
\(362\) | 5054.00 | 0.733791 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1680.00 | −0.241912 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3586.00 | 0.510048 | 0.255024 | − | 0.966935i | \(-0.417917\pi\) | ||||
0.255024 | + | 0.966935i | \(0.417917\pi\) | |||||||
\(368\) | 2416.00 | 0.342236 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1974.00 | 0.276240 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10500.0 | −1.45756 | −0.728779 | − | 0.684749i | \(-0.759912\pi\) | ||||
−0.728779 | + | 0.684749i | \(0.759912\pi\) | |||||||
\(374\) | 308.000 | 0.0425837 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −448.000 | −0.0614464 | ||||||||
\(377\) | 8100.00 | 1.10655 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6811.00 | −0.923107 | −0.461554 | − | 0.887112i | \(-0.652708\pi\) | ||||
−0.461554 | + | 0.887112i | \(0.652708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6960.00 | 0.932211 | ||||||||
\(383\) | −6913.00 | −0.922292 | −0.461146 | − | 0.887324i | \(-0.652562\pi\) | ||||
−0.461146 | + | 0.887324i | \(0.652562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6340.00 | 0.836004 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7264.00 | −0.950448 | ||||||||
\(389\) | −5998.00 | −0.781776 | −0.390888 | − | 0.920438i | \(-0.627832\pi\) | ||||
−0.390888 | + | 0.920438i | \(0.627832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1057.00 | 0.136713 | ||||||||
\(392\) | 1176.00 | 0.151523 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4670.00 | 0.597135 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5902.00 | 0.746128 | 0.373064 | − | 0.927806i | \(-0.378307\pi\) | ||||
0.373064 | + | 0.927806i | \(0.378307\pi\) | |||||||
\(398\) | 3024.00 | 0.380853 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2396.00 | −0.298380 | −0.149190 | − | 0.988809i | \(-0.547667\pi\) | ||||
−0.149190 | + | 0.988809i | \(0.547667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3390.00 | −0.419027 | ||||||||
\(404\) | 2368.00 | 0.291615 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7560.00 | 0.924129 | ||||||||
\(407\) | −1936.00 | −0.235784 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8141.00 | 0.984221 | 0.492111 | − | 0.870533i | \(-0.336226\pi\) | ||||
0.492111 | + | 0.870533i | \(0.336226\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3392.00 | 0.405611 | ||||||||
\(413\) | −3836.00 | −0.457039 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −960.000 | −0.113144 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3564.00 | −0.417036 | ||||||||
\(419\) | −9094.00 | −1.06031 | −0.530156 | − | 0.847900i | \(-0.677867\pi\) | ||||
−0.530156 | + | 0.847900i | \(0.677867\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6751.00 | 0.781529 | 0.390764 | − | 0.920491i | \(-0.372211\pi\) | ||||
0.390764 | + | 0.920491i | \(0.372211\pi\) | |||||||
\(422\) | 11838.0 | 1.36556 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1128.00 | 0.129199 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −574.000 | −0.0650534 | ||||||||
\(428\) | 6000.00 | 0.677619 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5594.00 | 0.625182 | 0.312591 | − | 0.949888i | \(-0.398803\pi\) | ||||
0.312591 | + | 0.949888i | \(0.398803\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15610.0 | 1.73249 | 0.866246 | − | 0.499618i | \(-0.166526\pi\) | ||||
0.866246 | + | 0.499618i | \(0.166526\pi\) | |||||||
\(434\) | −3164.00 | −0.349947 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3740.00 | −0.410811 | ||||||||
\(437\) | −12231.0 | −1.33887 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5751.00 | 0.625240 | 0.312620 | − | 0.949878i | \(-0.398793\pi\) | ||||
0.312620 | + | 0.949878i | \(0.398793\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −420.000 | −0.0451977 | ||||||||
\(443\) | −2331.00 | −0.249998 | −0.124999 | − | 0.992157i | \(-0.539893\pi\) | ||||
−0.124999 | + | 0.992157i | \(0.539893\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −824.000 | −0.0874833 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −896.000 | −0.0944911 | ||||||||
\(449\) | 7158.00 | 0.752354 | 0.376177 | − | 0.926548i | \(-0.377238\pi\) | ||||
0.376177 | + | 0.926548i | \(0.377238\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8932.00 | 0.932575 | ||||||||
\(452\) | −5064.00 | −0.526970 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11686.0 | 1.20804 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3196.00 | 0.327139 | 0.163570 | − | 0.986532i | \(-0.447699\pi\) | ||||
0.163570 | + | 0.986532i | \(0.447699\pi\) | |||||||
\(458\) | 8306.00 | 0.847410 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13368.0 | 1.35056 | 0.675282 | − | 0.737560i | \(-0.264022\pi\) | ||||
0.675282 | + | 0.737560i | \(0.264022\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9912.00 | 0.994924 | 0.497462 | − | 0.867486i | \(-0.334265\pi\) | ||||
0.497462 | + | 0.867486i | \(0.334265\pi\) | |||||||
\(464\) | 4320.00 | 0.432222 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1124.00 | 0.111735 | ||||||||
\(467\) | 13137.0 | 1.30173 | 0.650865 | − | 0.759194i | \(-0.274406\pi\) | ||||
0.650865 | + | 0.759194i | \(0.274406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4592.00 | 0.452108 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2192.00 | −0.213761 | ||||||||
\(473\) | −9724.00 | −0.945264 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −392.000 | −0.0377464 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1672.00 | −0.159991 | ||||||||
\(479\) | 4946.00 | 0.471792 | 0.235896 | − | 0.971778i | \(-0.424197\pi\) | ||||
0.235896 | + | 0.971778i | \(0.424197\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2640.00 | 0.250257 | ||||||||
\(482\) | 3058.00 | 0.288979 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3388.00 | −0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15966.0 | −1.48560 | −0.742801 | − | 0.669512i | \(-0.766503\pi\) | ||||
−0.742801 | + | 0.669512i | \(0.766503\pi\) | |||||||
\(488\) | −328.000 | −0.0304259 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11196.0 | −1.02906 | −0.514530 | − | 0.857472i | \(-0.672034\pi\) | ||||
−0.514530 | + | 0.857472i | \(0.672034\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1890.00 | 0.172660 | ||||||||
\(494\) | 4860.00 | 0.442635 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1808.00 | −0.163673 | ||||||||
\(497\) | −5460.00 | −0.492786 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1485.00 | −0.133222 | −0.0666110 | − | 0.997779i | \(-0.521219\pi\) | ||||
−0.0666110 | + | 0.997779i | \(0.521219\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −504.000 | −0.0448100 | ||||||||
\(503\) | 10635.0 | 0.942726 | 0.471363 | − | 0.881939i | \(-0.343762\pi\) | ||||
0.471363 | + | 0.881939i | \(0.343762\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6644.00 | 0.583719 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 64.0000 | 0.00558965 | ||||||||
\(509\) | 13176.0 | 1.14738 | 0.573690 | − | 0.819073i | \(-0.305512\pi\) | ||||
0.573690 | + | 0.819073i | \(0.305512\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8764.00 | 0.758702 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12222.0 | 1.04881 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1232.00 | −0.104803 | ||||||||
\(518\) | 2464.00 | 0.209000 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12542.0 | −1.05465 | −0.527327 | − | 0.849662i | \(-0.676806\pi\) | ||||
−0.527327 | + | 0.849662i | \(0.676806\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3778.00 | −0.315871 | −0.157935 | − | 0.987449i | \(-0.550484\pi\) | ||||
−0.157935 | + | 0.987449i | \(0.550484\pi\) | |||||||
\(524\) | 9216.00 | 0.768326 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6208.00 | 0.514604 | ||||||||
\(527\) | −791.000 | −0.0653824 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10634.0 | 0.874003 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4536.00 | 0.369663 | ||||||||
\(533\) | −12180.0 | −0.989821 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2624.00 | 0.211454 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6480.00 | −0.519280 | ||||||||
\(539\) | 3234.00 | 0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1150.00 | 0.0913907 | 0.0456953 | − | 0.998955i | \(-0.485450\pi\) | ||||
0.0456953 | + | 0.998955i | \(0.485450\pi\) | |||||||
\(542\) | −4790.00 | −0.379609 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −224.000 | −0.0176543 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23726.0 | −1.85457 | −0.927286 | − | 0.374355i | \(-0.877864\pi\) | ||||
−0.927286 | + | 0.374355i | \(0.877864\pi\) | |||||||
\(548\) | 5364.00 | 0.418136 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21870.0 | −1.69091 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17010.0 | 1.30803 | ||||||||
\(554\) | −13148.0 | −1.00831 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10256.0 | −0.782286 | ||||||||
\(557\) | 15786.0 | 1.20085 | 0.600426 | − | 0.799681i | \(-0.294998\pi\) | ||||
0.600426 | + | 0.799681i | \(0.294998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13260.0 | 1.00329 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8460.00 | 0.634989 | ||||||||
\(563\) | −4468.00 | −0.334465 | −0.167232 | − | 0.985917i | \(-0.553483\pi\) | ||||
−0.167232 | + | 0.985917i | \(0.553483\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11356.0 | −0.843336 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3120.00 | −0.230479 | ||||||||
\(569\) | −13102.0 | −0.965315 | −0.482658 | − | 0.875809i | \(-0.660328\pi\) | ||||
−0.482658 | + | 0.875809i | \(0.660328\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13711.0 | 1.00488 | 0.502441 | − | 0.864612i | \(-0.332435\pi\) | ||||
0.502441 | + | 0.864612i | \(0.332435\pi\) | |||||||
\(572\) | −2640.00 | −0.192979 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11368.0 | −0.826640 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8374.00 | 0.604184 | 0.302092 | − | 0.953279i | \(-0.402315\pi\) | ||||
0.302092 | + | 0.953279i | \(0.402315\pi\) | |||||||
\(578\) | 9728.00 | 0.700054 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7070.00 | −0.504842 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3102.00 | 0.220363 | ||||||||
\(584\) | 5008.00 | 0.354850 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9174.00 | 0.646714 | ||||||||
\(587\) | 11499.0 | 0.808543 | 0.404271 | − | 0.914639i | \(-0.367525\pi\) | ||||
0.404271 | + | 0.914639i | \(0.367525\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9153.00 | 0.640310 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1408.00 | 0.0977507 | ||||||||
\(593\) | 24753.0 | 1.71414 | 0.857069 | − | 0.515202i | \(-0.172283\pi\) | ||||
0.857069 | + | 0.515202i | \(0.172283\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12488.0 | −0.858269 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9060.00 | −0.619550 | ||||||||
\(599\) | −378.000 | −0.0257841 | −0.0128920 | − | 0.999917i | \(-0.504104\pi\) | ||||
−0.0128920 | + | 0.999917i | \(0.504104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15917.0 | 1.08031 | 0.540156 | − | 0.841565i | \(-0.318365\pi\) | ||||
0.540156 | + | 0.841565i | \(0.318365\pi\) | |||||||
\(602\) | 12376.0 | 0.837887 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12016.0 | 0.809477 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −718.000 | −0.0480111 | −0.0240055 | − | 0.999712i | \(-0.507642\pi\) | ||||
−0.0240055 | + | 0.999712i | \(0.507642\pi\) | |||||||
\(608\) | 2592.00 | 0.172894 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1680.00 | 0.111237 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24848.0 | −1.63720 | −0.818598 | − | 0.574367i | \(-0.805248\pi\) | ||||
−0.818598 | + | 0.574367i | \(0.805248\pi\) | |||||||
\(614\) | 14280.0 | 0.938589 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2464.00 | −0.161165 | ||||||||
\(617\) | −29681.0 | −1.93665 | −0.968324 | − | 0.249696i | \(-0.919669\pi\) | ||||
−0.968324 | + | 0.249696i | \(0.919669\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30308.0 | 1.96798 | 0.983991 | − | 0.178216i | \(-0.0570325\pi\) | ||||
0.983991 | + | 0.178216i | \(0.0570325\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14244.0 | −0.918219 | ||||||||
\(623\) | 7196.00 | 0.462763 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13480.0 | 0.860654 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14264.0 | 0.906362 | ||||||||
\(629\) | 616.000 | 0.0390485 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15475.0 | −0.976307 | −0.488154 | − | 0.872758i | \(-0.662329\pi\) | ||||
−0.488154 | + | 0.872758i | \(0.662329\pi\) | |||||||
\(632\) | 9720.00 | 0.611773 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10882.0 | 0.681671 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4410.00 | −0.274302 | ||||||||
\(638\) | 11880.0 | 0.737200 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29984.0 | 1.84758 | 0.923788 | − | 0.382903i | \(-0.125076\pi\) | ||||
0.923788 | + | 0.382903i | \(0.125076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22530.0 | −1.38180 | −0.690899 | − | 0.722951i | \(-0.742785\pi\) | ||||
−0.690899 | + | 0.722951i | \(0.742785\pi\) | |||||||
\(644\) | −8456.00 | −0.517412 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1134.00 | 0.0690660 | ||||||||
\(647\) | 31179.0 | 1.89455 | 0.947274 | − | 0.320424i | \(-0.103825\pi\) | ||||
0.947274 | + | 0.320424i | \(0.103825\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6028.00 | −0.364591 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2224.00 | −0.133587 | ||||||||
\(653\) | −5.00000 | −0.000299640 0 | −0.000149820 | − | 1.00000i | \(-0.500048\pi\) | ||||
−0.000149820 | 1.00000i | \(0.500048\pi\) | ||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6496.00 | −0.386625 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1568.00 | 0.0928982 | ||||||||
\(659\) | 17938.0 | 1.06034 | 0.530171 | − | 0.847891i | \(-0.322128\pi\) | ||||
0.530171 | + | 0.847891i | \(0.322128\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8722.00 | −0.513232 | −0.256616 | − | 0.966513i | \(-0.582608\pi\) | ||||
−0.256616 | + | 0.966513i | \(0.582608\pi\) | |||||||
\(662\) | 760.000 | 0.0446197 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4040.00 | −0.236118 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40770.0 | 2.36675 | ||||||||
\(668\) | −516.000 | −0.0298872 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −902.000 | −0.0518947 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14598.0 | 0.836124 | 0.418062 | − | 0.908418i | \(-0.362709\pi\) | ||||
0.418062 | + | 0.908418i | \(0.362709\pi\) | |||||||
\(674\) | 6292.00 | 0.359583 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5188.00 | −0.295175 | ||||||||
\(677\) | −8258.00 | −0.468805 | −0.234402 | − | 0.972140i | \(-0.575313\pi\) | ||||
−0.234402 | + | 0.972140i | \(0.575313\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25424.0 | 1.43694 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4972.00 | −0.279161 | ||||||||
\(683\) | −11075.0 | −0.620458 | −0.310229 | − | 0.950662i | \(-0.600406\pi\) | ||||
−0.310229 | + | 0.950662i | \(0.600406\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13720.0 | −0.763604 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7072.00 | 0.391886 | ||||||||
\(689\) | −4230.00 | −0.233890 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2315.00 | −0.127448 | −0.0637241 | − | 0.997968i | \(-0.520298\pi\) | ||||
−0.0637241 | + | 0.997968i | \(0.520298\pi\) | |||||||
\(692\) | 5108.00 | 0.280603 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17808.0 | 0.974038 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2842.00 | −0.154445 | ||||||||
\(698\) | −20858.0 | −1.13107 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4180.00 | −0.225216 | −0.112608 | − | 0.993639i | \(-0.535920\pi\) | ||||
−0.112608 | + | 0.993639i | \(0.535920\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7128.00 | −0.382415 | ||||||||
\(704\) | −1408.00 | −0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20036.0 | 1.06808 | ||||||||
\(707\) | −8288.00 | −0.440880 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −222.000 | −0.0117594 | −0.00587968 | − | 0.999983i | \(-0.501872\pi\) | ||||
−0.00587968 | + | 0.999983i | \(0.501872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4112.00 | 0.216438 | ||||||||
\(713\) | −17063.0 | −0.896233 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4720.00 | 0.246361 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17064.0 | 0.886940 | ||||||||
\(719\) | −16816.0 | −0.872227 | −0.436113 | − | 0.899892i | \(-0.643645\pi\) | ||||
−0.436113 | + | 0.899892i | \(0.643645\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11872.0 | −0.613227 | ||||||||
\(722\) | 596.000 | 0.0307214 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10108.0 | −0.518869 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21996.0 | 1.12213 | 0.561064 | − | 0.827773i | \(-0.310392\pi\) | ||||
0.561064 | + | 0.827773i | \(0.310392\pi\) | |||||||
\(728\) | 3360.00 | 0.171058 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3094.00 | 0.156547 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21112.0 | −1.06383 | −0.531916 | − | 0.846797i | \(-0.678528\pi\) | ||||
−0.531916 | + | 0.846797i | \(0.678528\pi\) | |||||||
\(734\) | −7172.00 | −0.360659 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4832.00 | −0.241997 | ||||||||
\(737\) | 7216.00 | 0.360658 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 49.0000 | 0.00243910 | 0.00121955 | − | 0.999999i | \(-0.499612\pi\) | ||||
0.00121955 | + | 0.999999i | \(0.499612\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3948.00 | −0.195331 | ||||||||
\(743\) | 3876.00 | 0.191382 | 0.0956909 | − | 0.995411i | \(-0.469494\pi\) | ||||
0.0956909 | + | 0.995411i | \(0.469494\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 21000.0 | 1.03065 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −616.000 | −0.0301112 | ||||||||
\(749\) | −21000.0 | −1.02446 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8395.00 | −0.407907 | −0.203953 | − | 0.978981i | \(-0.565379\pi\) | ||||
−0.203953 | + | 0.978981i | \(0.565379\pi\) | |||||||
\(752\) | 896.000 | 0.0434491 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16200.0 | −0.782453 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1892.00 | −0.0908400 | −0.0454200 | − | 0.998968i | \(-0.514463\pi\) | ||||
−0.0454200 | + | 0.998968i | \(0.514463\pi\) | |||||||
\(758\) | 13622.0 | 0.652735 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2034.00 | 0.0968889 | 0.0484444 | − | 0.998826i | \(-0.484574\pi\) | ||||
0.0484444 | + | 0.998826i | \(0.484574\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13090.0 | 0.621088 | ||||||||
\(764\) | −13920.0 | −0.659173 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13826.0 | 0.652159 | ||||||||
\(767\) | 8220.00 | 0.386971 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5439.00 | −0.255052 | −0.127526 | − | 0.991835i | \(-0.540704\pi\) | ||||
−0.127526 | + | 0.991835i | \(0.540704\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12680.0 | −0.591144 | ||||||||
\(773\) | −8829.00 | −0.410811 | −0.205406 | − | 0.978677i | \(-0.565851\pi\) | ||||
−0.205406 | + | 0.978677i | \(0.565851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 14528.0 | 0.672068 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11996.0 | 0.552799 | ||||||||
\(779\) | 32886.0 | 1.51253 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8580.00 | −0.393107 | ||||||||
\(782\) | −2114.00 | −0.0966707 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2352.00 | −0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15694.0 | 0.710839 | 0.355420 | − | 0.934707i | \(-0.384338\pi\) | ||||
0.355420 | + | 0.934707i | \(0.384338\pi\) | |||||||
\(788\) | −9340.00 | −0.422238 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17724.0 | 0.796704 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1230.00 | 0.0550802 | ||||||||
\(794\) | −11804.0 | −0.527592 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6048.00 | −0.269304 | ||||||||
\(797\) | −4859.00 | −0.215953 | −0.107977 | − | 0.994153i | \(-0.534437\pi\) | ||||
−0.107977 | + | 0.994153i | \(0.534437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 392.000 | 0.0173566 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4792.00 | 0.210987 | ||||||||
\(803\) | 13772.0 | 0.605235 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6780.00 | 0.296297 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4736.00 | −0.206203 | ||||||||
\(809\) | −5862.00 | −0.254755 | −0.127378 | − | 0.991854i | \(-0.540656\pi\) | ||||
−0.127378 | + | 0.991854i | \(0.540656\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 376.000 | 0.0162801 | 0.00814004 | − | 0.999967i | \(-0.497409\pi\) | ||||
0.00814004 | + | 0.999967i | \(0.497409\pi\) | |||||||
\(812\) | −15120.0 | −0.653458 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3872.00 | 0.166724 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −35802.0 | −1.53311 | ||||||||
\(818\) | −16282.0 | −0.695950 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13804.0 | 0.586800 | 0.293400 | − | 0.955990i | \(-0.405213\pi\) | ||||
0.293400 | + | 0.955990i | \(0.405213\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18714.0 | 0.792623 | 0.396312 | − | 0.918116i | \(-0.370290\pi\) | ||||
0.396312 | + | 0.918116i | \(0.370290\pi\) | |||||||
\(824\) | −6784.00 | −0.286810 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7672.00 | 0.323176 | ||||||||
\(827\) | 36163.0 | 1.52057 | 0.760285 | − | 0.649590i | \(-0.225059\pi\) | ||||
0.760285 | + | 0.649590i | \(0.225059\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26862.0 | 1.12540 | 0.562700 | − | 0.826662i | \(-0.309763\pi\) | ||||
0.562700 | + | 0.826662i | \(0.309763\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1920.00 | 0.0800048 | ||||||||
\(833\) | −1029.00 | −0.0428004 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7128.00 | 0.294889 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18188.0 | 0.749754 | ||||||||
\(839\) | −29564.0 | −1.21652 | −0.608261 | − | 0.793737i | \(-0.708133\pi\) | ||||
−0.608261 | + | 0.793737i | \(0.708133\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48511.0 | 1.98905 | ||||||||
\(842\) | −13502.0 | −0.552624 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23676.0 | −0.965594 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11858.0 | 0.481046 | ||||||||
\(848\) | −2256.00 | −0.0913577 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13288.0 | 0.535261 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8108.00 | 0.325454 | 0.162727 | − | 0.986671i | \(-0.447971\pi\) | ||||
0.162727 | + | 0.986671i | \(0.447971\pi\) | |||||||
\(854\) | 1148.00 | 0.0459997 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12000.0 | −0.479149 | ||||||||
\(857\) | −861.000 | −0.0343188 | −0.0171594 | − | 0.999853i | \(-0.505462\pi\) | ||||
−0.0171594 | + | 0.999853i | \(0.505462\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12725.0 | 0.505438 | 0.252719 | − | 0.967540i | \(-0.418675\pi\) | ||||
0.252719 | + | 0.967540i | \(0.418675\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11188.0 | −0.442071 | ||||||||
\(863\) | −18801.0 | −0.741592 | −0.370796 | − | 0.928714i | \(-0.620915\pi\) | ||||
−0.370796 | + | 0.928714i | \(0.620915\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −31220.0 | −1.22506 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6328.00 | 0.247450 | ||||||||
\(869\) | 26730.0 | 1.04344 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9840.00 | −0.382796 | ||||||||
\(872\) | 7480.00 | 0.290487 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 24462.0 | 0.946727 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10438.0 | −0.401900 | −0.200950 | − | 0.979602i | \(-0.564403\pi\) | ||||
−0.200950 | + | 0.979602i | \(0.564403\pi\) | |||||||
\(878\) | −11502.0 | −0.442111 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1170.00 | 0.0447427 | 0.0223713 | − | 0.999750i | \(-0.492878\pi\) | ||||
0.0223713 | + | 0.999750i | \(0.492878\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20334.0 | −0.774964 | −0.387482 | − | 0.921877i | \(-0.626655\pi\) | ||||
−0.387482 | + | 0.921877i | \(0.626655\pi\) | |||||||
\(884\) | 840.000 | 0.0319596 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4662.00 | 0.176775 | ||||||||
\(887\) | −30693.0 | −1.16186 | −0.580930 | − | 0.813953i | \(-0.697311\pi\) | ||||
−0.580930 | + | 0.813953i | \(0.697311\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −224.000 | −0.00845075 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1648.00 | 0.0618600 | ||||||||
\(893\) | −4536.00 | −0.169979 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1792.00 | 0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14316.0 | −0.531995 | ||||||||
\(899\) | −30510.0 | −1.13189 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −987.000 | −0.0364947 | ||||||||
\(902\) | −17864.0 | −0.659430 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10128.0 | 0.372624 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2616.00 | 0.0957694 | 0.0478847 | − | 0.998853i | \(-0.484752\pi\) | ||||
0.0478847 | + | 0.998853i | \(0.484752\pi\) | |||||||
\(908\) | −23372.0 | −0.854215 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47802.0 | −1.73848 | −0.869238 | − | 0.494395i | \(-0.835390\pi\) | ||||
−0.869238 | + | 0.494395i | \(0.835390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11110.0 | −0.402724 | ||||||||
\(914\) | −6392.00 | −0.231322 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16612.0 | −0.599210 | ||||||||
\(917\) | −32256.0 | −1.16160 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44064.0 | −1.58165 | −0.790825 | − | 0.612042i | \(-0.790348\pi\) | ||||
−0.790825 | + | 0.612042i | \(0.790348\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −26736.0 | −0.954993 | ||||||||
\(923\) | 11700.0 | 0.417237 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −19824.0 | −0.703517 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8640.00 | −0.305627 | ||||||||
\(929\) | 1290.00 | 0.0455582 | 0.0227791 | − | 0.999741i | \(-0.492749\pi\) | ||||
0.0227791 | + | 0.999741i | \(0.492749\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11907.0 | 0.419158 | ||||||||
\(932\) | −2248.00 | −0.0790082 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26274.0 | −0.920462 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43804.0 | −1.52723 | −0.763615 | − | 0.645672i | \(-0.776577\pi\) | ||||
−0.763615 | + | 0.645672i | \(0.776577\pi\) | |||||||
\(938\) | −9184.00 | −0.319689 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18148.0 | −0.628701 | −0.314351 | − | 0.949307i | \(-0.601787\pi\) | ||||
−0.314351 | + | 0.949307i | \(0.601787\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61306.0 | −2.11707 | ||||||||
\(944\) | 4384.00 | 0.151152 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19448.0 | 0.668403 | ||||||||
\(947\) | −5079.00 | −0.174282 | −0.0871411 | − | 0.996196i | \(-0.527773\pi\) | ||||
−0.0871411 | + | 0.996196i | \(0.527773\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18780.0 | −0.642386 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 784.000 | 0.0266907 | ||||||||
\(953\) | 28394.0 | 0.965133 | 0.482567 | − | 0.875859i | \(-0.339705\pi\) | ||||
0.482567 | + | 0.875859i | \(0.339705\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3344.00 | 0.113130 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9892.00 | −0.333608 | ||||||||
\(959\) | −18774.0 | −0.632163 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17022.0 | −0.571381 | ||||||||
\(962\) | −5280.00 | −0.176958 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6116.00 | −0.204339 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41228.0 | 1.37105 | 0.685524 | − | 0.728050i | \(-0.259573\pi\) | ||||
0.685524 | + | 0.728050i | \(0.259573\pi\) | |||||||
\(968\) | 6776.00 | 0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21528.0 | 0.711500 | 0.355750 | − | 0.934581i | \(-0.384225\pi\) | ||||
0.355750 | + | 0.934581i | \(0.384225\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35896.0 | 1.18271 | ||||||||
\(974\) | 31932.0 | 1.05048 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 656.000 | 0.0215144 | ||||||||
\(977\) | −49146.0 | −1.60933 | −0.804667 | − | 0.593726i | \(-0.797656\pi\) | ||||
−0.804667 | + | 0.593726i | \(0.797656\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11308.0 | 0.369158 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22392.0 | 0.727655 | ||||||||
\(983\) | 33467.0 | 1.08589 | 0.542946 | − | 0.839768i | \(-0.317309\pi\) | ||||
0.542946 | + | 0.839768i | \(0.317309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3780.00 | −0.122089 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9720.00 | −0.312990 | ||||||||
\(989\) | 66742.0 | 2.14588 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23183.0 | −0.743120 | −0.371560 | − | 0.928409i | \(-0.621177\pi\) | ||||
−0.371560 | + | 0.928409i | \(0.621177\pi\) | |||||||
\(992\) | 3616.00 | 0.115734 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10920.0 | 0.348452 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 60282.0 | 1.91489 | 0.957447 | − | 0.288608i | \(-0.0931924\pi\) | ||||
0.957447 | + | 0.288608i | \(0.0931924\pi\) | |||||||
\(998\) | 2970.00 | 0.0942021 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1350.4.a.d.1.1 | 1 | ||
3.2 | odd | 2 | 1350.4.a.s.1.1 | 1 | |||
5.2 | odd | 4 | 270.4.c.b.109.1 | yes | 2 | ||
5.3 | odd | 4 | 270.4.c.b.109.2 | yes | 2 | ||
5.4 | even | 2 | 1350.4.a.x.1.1 | 1 | |||
15.2 | even | 4 | 270.4.c.a.109.2 | yes | 2 | ||
15.8 | even | 4 | 270.4.c.a.109.1 | ✓ | 2 | ||
15.14 | odd | 2 | 1350.4.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.4.c.a.109.1 | ✓ | 2 | 15.8 | even | 4 | ||
270.4.c.a.109.2 | yes | 2 | 15.2 | even | 4 | ||
270.4.c.b.109.1 | yes | 2 | 5.2 | odd | 4 | ||
270.4.c.b.109.2 | yes | 2 | 5.3 | odd | 4 | ||
1350.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1350.4.a.j.1.1 | 1 | 15.14 | odd | 2 | |||
1350.4.a.s.1.1 | 1 | 3.2 | odd | 2 | |||
1350.4.a.x.1.1 | 1 | 5.4 | even | 2 |