Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, 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("225.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(13.2754297513\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00000 | 1.06066 | 0.530330 | − | 0.847791i | \(-0.322068\pi\) | ||||
0.530330 | + | 0.847791i | \(0.322068\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.125000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −20.0000 | −1.07990 | −0.539949 | − | 0.841698i | \(-0.681557\pi\) | ||||
−0.539949 | + | 0.841698i | \(0.681557\pi\) | |||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24.0000 | 0.657843 | 0.328921 | − | 0.944357i | \(-0.393315\pi\) | ||||
0.328921 | + | 0.944357i | \(0.393315\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −74.0000 | −1.57876 | −0.789381 | − | 0.613904i | \(-0.789598\pi\) | ||||
−0.789381 | + | 0.613904i | \(0.789598\pi\) | |||||||
\(14\) | −60.0000 | −1.14541 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | 54.0000 | 0.770407 | 0.385204 | − | 0.922832i | \(-0.374131\pi\) | ||||
0.385204 | + | 0.922832i | \(0.374131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −124.000 | −1.49724 | −0.748620 | − | 0.663000i | \(-0.769283\pi\) | ||||
−0.748620 | + | 0.663000i | \(0.769283\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 72.0000 | 0.697748 | ||||||||
\(23\) | −120.000 | −1.08790 | −0.543951 | − | 0.839117i | \(-0.683072\pi\) | ||||
−0.543951 | + | 0.839117i | \(0.683072\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −222.000 | −1.67453 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −20.0000 | −0.134987 | ||||||||
\(29\) | 78.0000 | 0.499456 | 0.249728 | − | 0.968316i | \(-0.419659\pi\) | ||||
0.249728 | + | 0.968316i | \(0.419659\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 200.000 | 1.15874 | 0.579372 | − | 0.815063i | \(-0.303298\pi\) | ||||
0.579372 | + | 0.815063i | \(0.303298\pi\) | |||||||
\(32\) | −45.0000 | −0.248592 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 162.000 | 0.817140 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 70.0000 | 0.311025 | 0.155513 | − | 0.987834i | \(-0.450297\pi\) | ||||
0.155513 | + | 0.987834i | \(0.450297\pi\) | |||||||
\(38\) | −372.000 | −1.58806 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −330.000 | −1.25701 | −0.628504 | − | 0.777806i | \(-0.716332\pi\) | ||||
−0.628504 | + | 0.777806i | \(0.716332\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −92.0000 | −0.326276 | −0.163138 | − | 0.986603i | \(-0.552162\pi\) | ||||
−0.163138 | + | 0.986603i | \(0.552162\pi\) | |||||||
\(44\) | 24.0000 | 0.0822304 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −360.000 | −1.15389 | ||||||||
\(47\) | −24.0000 | −0.0744843 | −0.0372421 | − | 0.999306i | \(-0.511857\pi\) | ||||
−0.0372421 | + | 0.999306i | \(0.511857\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 57.0000 | 0.166181 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −74.0000 | −0.197345 | ||||||||
\(53\) | 450.000 | 1.16627 | 0.583134 | − | 0.812376i | \(-0.301826\pi\) | ||||
0.583134 | + | 0.812376i | \(0.301826\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 420.000 | 1.00223 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 234.000 | 0.529754 | ||||||||
\(59\) | −24.0000 | −0.0529582 | −0.0264791 | − | 0.999649i | \(-0.508430\pi\) | ||||
−0.0264791 | + | 0.999649i | \(0.508430\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −322.000 | −0.675867 | −0.337933 | − | 0.941170i | \(-0.609728\pi\) | ||||
−0.337933 | + | 0.941170i | \(0.609728\pi\) | |||||||
\(62\) | 600.000 | 1.22903 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 196.000 | 0.357391 | 0.178696 | − | 0.983904i | \(-0.442812\pi\) | ||||
0.178696 | + | 0.983904i | \(0.442812\pi\) | |||||||
\(68\) | 54.0000 | 0.0963009 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 288.000 | 0.481399 | 0.240699 | − | 0.970600i | \(-0.422623\pi\) | ||||
0.240699 | + | 0.970600i | \(0.422623\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 430.000 | 0.689420 | 0.344710 | − | 0.938709i | \(-0.387977\pi\) | ||||
0.344710 | + | 0.938709i | \(0.387977\pi\) | |||||||
\(74\) | 210.000 | 0.329892 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −124.000 | −0.187155 | ||||||||
\(77\) | −480.000 | −0.710404 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −520.000 | −0.740564 | −0.370282 | − | 0.928919i | \(-0.620739\pi\) | ||||
−0.370282 | + | 0.928919i | \(0.620739\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −990.000 | −1.33326 | ||||||||
\(83\) | 156.000 | 0.206304 | 0.103152 | − | 0.994666i | \(-0.467107\pi\) | ||||
0.103152 | + | 0.994666i | \(0.467107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −276.000 | −0.346068 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −504.000 | −0.610529 | ||||||||
\(89\) | −1026.00 | −1.22198 | −0.610988 | − | 0.791640i | \(-0.709227\pi\) | ||||
−0.610988 | + | 0.791640i | \(0.709227\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1480.00 | 1.70490 | ||||||||
\(92\) | −120.000 | −0.135988 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −72.0000 | −0.0790025 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 286.000 | 0.299370 | 0.149685 | − | 0.988734i | \(-0.452174\pi\) | ||||
0.149685 | + | 0.988734i | \(0.452174\pi\) | |||||||
\(98\) | 171.000 | 0.176261 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1734.00 | 1.70831 | 0.854156 | − | 0.520017i | \(-0.174075\pi\) | ||||
0.854156 | + | 0.520017i | \(0.174075\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −452.000 | −0.432397 | −0.216198 | − | 0.976349i | \(-0.569366\pi\) | ||||
−0.216198 | + | 0.976349i | \(0.569366\pi\) | |||||||
\(104\) | 1554.00 | 1.46521 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1350.00 | 1.23702 | ||||||||
\(107\) | −1404.00 | −1.26850 | −0.634251 | − | 0.773127i | \(-0.718692\pi\) | ||||
−0.634251 | + | 0.773127i | \(0.718692\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1474.00 | −1.29526 | −0.647631 | − | 0.761954i | \(-0.724240\pi\) | ||||
−0.647631 | + | 0.761954i | \(0.724240\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1420.00 | 1.19801 | ||||||||
\(113\) | 1086.00 | 0.904091 | 0.452046 | − | 0.891995i | \(-0.350694\pi\) | ||||
0.452046 | + | 0.891995i | \(0.350694\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 78.0000 | 0.0624321 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −72.0000 | −0.0561707 | ||||||||
\(119\) | −1080.00 | −0.831962 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −755.000 | −0.567243 | ||||||||
\(122\) | −966.000 | −0.716865 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 200.000 | 0.144843 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1244.00 | −0.869190 | −0.434595 | − | 0.900626i | \(-0.643109\pi\) | ||||
−0.434595 | + | 0.900626i | \(0.643109\pi\) | |||||||
\(128\) | 1659.00 | 1.14560 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2328.00 | −1.55266 | −0.776329 | − | 0.630327i | \(-0.782921\pi\) | ||||
−0.776329 | + | 0.630327i | \(0.782921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2480.00 | 1.61687 | ||||||||
\(134\) | 588.000 | 0.379071 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1134.00 | −0.714998 | ||||||||
\(137\) | 2118.00 | 1.32082 | 0.660412 | − | 0.750903i | \(-0.270382\pi\) | ||||
0.660412 | + | 0.750903i | \(0.270382\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2324.00 | 1.41812 | 0.709062 | − | 0.705147i | \(-0.249119\pi\) | ||||
0.709062 | + | 0.705147i | \(0.249119\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 864.000 | 0.510600 | ||||||||
\(143\) | −1776.00 | −1.03858 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1290.00 | 0.731241 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 70.0000 | 0.0388781 | ||||||||
\(149\) | −258.000 | −0.141854 | −0.0709268 | − | 0.997482i | \(-0.522596\pi\) | ||||
−0.0709268 | + | 0.997482i | \(0.522596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −808.000 | −0.435458 | −0.217729 | − | 0.976009i | \(-0.569865\pi\) | ||||
−0.217729 | + | 0.976009i | \(0.569865\pi\) | |||||||
\(152\) | 2604.00 | 1.38955 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1440.00 | −0.753497 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2378.00 | −1.20882 | −0.604411 | − | 0.796673i | \(-0.706592\pi\) | ||||
−0.604411 | + | 0.796673i | \(0.706592\pi\) | |||||||
\(158\) | −1560.00 | −0.785487 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2400.00 | 1.17482 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 52.0000 | 0.0249874 | 0.0124937 | − | 0.999922i | \(-0.496023\pi\) | ||||
0.0124937 | + | 0.999922i | \(0.496023\pi\) | |||||||
\(164\) | −330.000 | −0.157126 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 468.000 | 0.218818 | ||||||||
\(167\) | −3720.00 | −1.72373 | −0.861863 | − | 0.507141i | \(-0.830702\pi\) | ||||
−0.861863 | + | 0.507141i | \(0.830702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3279.00 | 1.49249 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −92.0000 | −0.0407845 | ||||||||
\(173\) | 426.000 | 0.187215 | 0.0936075 | − | 0.995609i | \(-0.470160\pi\) | ||||
0.0936075 | + | 0.995609i | \(0.470160\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1704.00 | −0.729795 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3078.00 | −1.29610 | ||||||||
\(179\) | 1440.00 | 0.601289 | 0.300644 | − | 0.953736i | \(-0.402798\pi\) | ||||
0.300644 | + | 0.953736i | \(0.402798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3130.00 | −1.28537 | −0.642683 | − | 0.766133i | \(-0.722179\pi\) | ||||
−0.642683 | + | 0.766133i | \(0.722179\pi\) | |||||||
\(182\) | 4440.00 | 1.80832 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2520.00 | 1.00966 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1296.00 | 0.506807 | ||||||||
\(188\) | −24.0000 | −0.00931053 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3576.00 | −1.35471 | −0.677357 | − | 0.735655i | \(-0.736875\pi\) | ||||
−0.677357 | + | 0.735655i | \(0.736875\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2666.00 | −0.994315 | −0.497158 | − | 0.867660i | \(-0.665623\pi\) | ||||
−0.497158 | + | 0.867660i | \(0.665623\pi\) | |||||||
\(194\) | 858.000 | 0.317530 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 57.0000 | 0.0207726 | ||||||||
\(197\) | −2718.00 | −0.982992 | −0.491496 | − | 0.870880i | \(-0.663550\pi\) | ||||
−0.491496 | + | 0.870880i | \(0.663550\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3832.00 | −1.36504 | −0.682521 | − | 0.730866i | \(-0.739116\pi\) | ||||
−0.682521 | + | 0.730866i | \(0.739116\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5202.00 | 1.81194 | ||||||||
\(203\) | −1560.00 | −0.539362 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1356.00 | −0.458626 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5254.00 | 1.75144 | ||||||||
\(209\) | −2976.00 | −0.984948 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1100.00 | 0.358896 | 0.179448 | − | 0.983767i | \(-0.442569\pi\) | ||||
0.179448 | + | 0.983767i | \(0.442569\pi\) | |||||||
\(212\) | 450.000 | 0.145784 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4212.00 | −1.34545 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4000.00 | −1.25133 | ||||||||
\(218\) | −4422.00 | −1.37383 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3996.00 | −1.21629 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1964.00 | −0.589772 | −0.294886 | − | 0.955532i | \(-0.595282\pi\) | ||||
−0.294886 | + | 0.955532i | \(0.595282\pi\) | |||||||
\(224\) | 900.000 | 0.268454 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3258.00 | 0.958933 | ||||||||
\(227\) | 660.000 | 0.192977 | 0.0964884 | − | 0.995334i | \(-0.469239\pi\) | ||||
0.0964884 | + | 0.995334i | \(0.469239\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1906.00 | −0.550009 | −0.275004 | − | 0.961443i | \(-0.588679\pi\) | ||||
−0.275004 | + | 0.961443i | \(0.588679\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1638.00 | −0.463534 | ||||||||
\(233\) | −1458.00 | −0.409943 | −0.204972 | − | 0.978768i | \(-0.565710\pi\) | ||||
−0.204972 | + | 0.978768i | \(0.565710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −24.0000 | −0.00661978 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3240.00 | −0.882429 | ||||||||
\(239\) | −1176.00 | −0.318281 | −0.159140 | − | 0.987256i | \(-0.550872\pi\) | ||||
−0.159140 | + | 0.987256i | \(0.550872\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 866.000 | 0.231469 | 0.115734 | − | 0.993280i | \(-0.463078\pi\) | ||||
0.115734 | + | 0.993280i | \(0.463078\pi\) | |||||||
\(242\) | −2265.00 | −0.601652 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −322.000 | −0.0844834 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9176.00 | 2.36379 | ||||||||
\(248\) | −4200.00 | −1.07540 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −432.000 | −0.108636 | −0.0543179 | − | 0.998524i | \(-0.517298\pi\) | ||||
−0.0543179 | + | 0.998524i | \(0.517298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2880.00 | −0.715668 | ||||||||
\(254\) | −3732.00 | −0.921915 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | 2526.00 | 0.613103 | 0.306552 | − | 0.951854i | \(-0.400825\pi\) | ||||
0.306552 | + | 0.951854i | \(0.400825\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1400.00 | −0.335876 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6984.00 | −1.64684 | ||||||||
\(263\) | 5448.00 | 1.27733 | 0.638666 | − | 0.769484i | \(-0.279487\pi\) | ||||
0.638666 | + | 0.769484i | \(0.279487\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7440.00 | 1.71495 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 196.000 | 0.0446739 | ||||||||
\(269\) | 2574.00 | 0.583418 | 0.291709 | − | 0.956507i | \(-0.405776\pi\) | ||||
0.291709 | + | 0.956507i | \(0.405776\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3184.00 | −0.713706 | −0.356853 | − | 0.934161i | \(-0.616150\pi\) | ||||
−0.356853 | + | 0.934161i | \(0.616150\pi\) | |||||||
\(272\) | −3834.00 | −0.854671 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6354.00 | 1.40095 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3962.00 | −0.859399 | −0.429699 | − | 0.902972i | \(-0.641380\pi\) | ||||
−0.429699 | + | 0.902972i | \(0.641380\pi\) | |||||||
\(278\) | 6972.00 | 1.50415 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8286.00 | 1.75908 | 0.879540 | − | 0.475825i | \(-0.157851\pi\) | ||||
0.879540 | + | 0.475825i | \(0.157851\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2716.00 | 0.570493 | 0.285246 | − | 0.958454i | \(-0.407925\pi\) | ||||
0.285246 | + | 0.958454i | \(0.407925\pi\) | |||||||
\(284\) | 288.000 | 0.0601748 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5328.00 | −1.10158 | ||||||||
\(287\) | 6600.00 | 1.35744 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 430.000 | 0.0861776 | ||||||||
\(293\) | 6018.00 | 1.19992 | 0.599958 | − | 0.800032i | \(-0.295184\pi\) | ||||
0.599958 | + | 0.800032i | \(0.295184\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1470.00 | −0.288655 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −774.000 | −0.150458 | ||||||||
\(299\) | 8880.00 | 1.71754 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1840.00 | 0.352345 | ||||||||
\(302\) | −2424.00 | −0.461873 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8804.00 | 1.66100 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9236.00 | −1.71702 | −0.858512 | − | 0.512793i | \(-0.828611\pi\) | ||||
−0.858512 | + | 0.512793i | \(0.828611\pi\) | |||||||
\(308\) | −480.000 | −0.0888004 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1536.00 | −0.280060 | −0.140030 | − | 0.990147i | \(-0.544720\pi\) | ||||
−0.140030 | + | 0.990147i | \(0.544720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7342.00 | 1.32586 | 0.662930 | − | 0.748681i | \(-0.269313\pi\) | ||||
0.662930 | + | 0.748681i | \(0.269313\pi\) | |||||||
\(314\) | −7134.00 | −1.28215 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −520.000 | −0.0925705 | ||||||||
\(317\) | −3894.00 | −0.689933 | −0.344967 | − | 0.938615i | \(-0.612110\pi\) | ||||
−0.344967 | + | 0.938615i | \(0.612110\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1872.00 | 0.328564 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7200.00 | 1.24609 | ||||||||
\(323\) | −6696.00 | −1.15348 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 156.000 | 0.0265032 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6930.00 | 1.16660 | ||||||||
\(329\) | 480.000 | 0.0804354 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3692.00 | 0.613084 | 0.306542 | − | 0.951857i | \(-0.400828\pi\) | ||||
0.306542 | + | 0.951857i | \(0.400828\pi\) | |||||||
\(332\) | 156.000 | 0.0257880 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11160.0 | −1.82829 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8998.00 | 1.45446 | 0.727229 | − | 0.686395i | \(-0.240808\pi\) | ||||
0.727229 | + | 0.686395i | \(0.240808\pi\) | |||||||
\(338\) | 9837.00 | 1.58302 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4800.00 | 0.762271 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5720.00 | 0.900440 | ||||||||
\(344\) | 1932.00 | 0.302809 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1278.00 | 0.198571 | ||||||||
\(347\) | 5244.00 | 0.811276 | 0.405638 | − | 0.914034i | \(-0.367049\pi\) | ||||
0.405638 | + | 0.914034i | \(0.367049\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6302.00 | 0.966585 | 0.483293 | − | 0.875459i | \(-0.339441\pi\) | ||||
0.483293 | + | 0.875459i | \(0.339441\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1080.00 | −0.163535 | ||||||||
\(353\) | 3414.00 | 0.514756 | 0.257378 | − | 0.966311i | \(-0.417141\pi\) | ||||
0.257378 | + | 0.966311i | \(0.417141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1026.00 | −0.152747 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4320.00 | 0.637763 | ||||||||
\(359\) | −4824.00 | −0.709195 | −0.354597 | − | 0.935019i | \(-0.615382\pi\) | ||||
−0.354597 | + | 0.935019i | \(0.615382\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8517.00 | 1.24173 | ||||||||
\(362\) | −9390.00 | −1.36334 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1480.00 | 0.213113 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3508.00 | 0.498954 | 0.249477 | − | 0.968381i | \(-0.419741\pi\) | ||||
0.249477 | + | 0.968381i | \(0.419741\pi\) | |||||||
\(368\) | 8520.00 | 1.20689 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9000.00 | −1.25945 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10802.0 | −1.49948 | −0.749740 | − | 0.661732i | \(-0.769822\pi\) | ||||
−0.749740 | + | 0.661732i | \(0.769822\pi\) | |||||||
\(374\) | 3888.00 | 0.537550 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 504.000 | 0.0691272 | ||||||||
\(377\) | −5772.00 | −0.788523 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1460.00 | 0.197876 | 0.0989382 | − | 0.995094i | \(-0.468455\pi\) | ||||
0.0989382 | + | 0.995094i | \(0.468455\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10728.0 | −1.43689 | ||||||||
\(383\) | −4872.00 | −0.649994 | −0.324997 | − | 0.945715i | \(-0.605363\pi\) | ||||
−0.324997 | + | 0.945715i | \(0.605363\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7998.00 | −1.05463 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 286.000 | 0.0374213 | ||||||||
\(389\) | 14046.0 | 1.83075 | 0.915373 | − | 0.402606i | \(-0.131896\pi\) | ||||
0.915373 | + | 0.402606i | \(0.131896\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6480.00 | −0.838127 | ||||||||
\(392\) | −1197.00 | −0.154229 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8154.00 | −1.04262 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2734.00 | 0.345631 | 0.172816 | − | 0.984954i | \(-0.444714\pi\) | ||||
0.172816 | + | 0.984954i | \(0.444714\pi\) | |||||||
\(398\) | −11496.0 | −1.44785 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15942.0 | 1.98530 | 0.992650 | − | 0.121019i | \(-0.0386161\pi\) | ||||
0.992650 | + | 0.121019i | \(0.0386161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14800.0 | −1.82938 | ||||||||
\(404\) | 1734.00 | 0.213539 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4680.00 | −0.572080 | ||||||||
\(407\) | 1680.00 | 0.204606 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8714.00 | 1.05350 | 0.526748 | − | 0.850022i | \(-0.323411\pi\) | ||||
0.526748 | + | 0.850022i | \(0.323411\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −452.000 | −0.0540496 | ||||||||
\(413\) | 480.000 | 0.0571895 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3330.00 | 0.392468 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8928.00 | −1.04470 | ||||||||
\(419\) | −11976.0 | −1.39634 | −0.698169 | − | 0.715933i | \(-0.746002\pi\) | ||||
−0.698169 | + | 0.715933i | \(0.746002\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11054.0 | 1.27967 | 0.639833 | − | 0.768514i | \(-0.279004\pi\) | ||||
0.639833 | + | 0.768514i | \(0.279004\pi\) | |||||||
\(422\) | 3300.00 | 0.380667 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9450.00 | −1.08239 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6440.00 | 0.729868 | ||||||||
\(428\) | −1404.00 | −0.158563 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −720.000 | −0.0804668 | −0.0402334 | − | 0.999190i | \(-0.512810\pi\) | ||||
−0.0402334 | + | 0.999190i | \(0.512810\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15622.0 | 1.73382 | 0.866912 | − | 0.498462i | \(-0.166102\pi\) | ||||
0.866912 | + | 0.498462i | \(0.166102\pi\) | |||||||
\(434\) | −12000.0 | −1.32723 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1474.00 | −0.161908 | ||||||||
\(437\) | 14880.0 | 1.62885 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9880.00 | −1.07414 | −0.537069 | − | 0.843538i | \(-0.680469\pi\) | ||||
−0.537069 | + | 0.843538i | \(0.680469\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11988.0 | −1.29007 | ||||||||
\(443\) | −16116.0 | −1.72843 | −0.864215 | − | 0.503123i | \(-0.832184\pi\) | ||||
−0.864215 | + | 0.503123i | \(0.832184\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5892.00 | −0.625548 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8660.00 | −0.913274 | ||||||||
\(449\) | −9018.00 | −0.947852 | −0.473926 | − | 0.880565i | \(-0.657164\pi\) | ||||
−0.473926 | + | 0.880565i | \(0.657164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7920.00 | −0.826914 | ||||||||
\(452\) | 1086.00 | 0.113011 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1980.00 | 0.204683 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3670.00 | 0.375657 | 0.187829 | − | 0.982202i | \(-0.439855\pi\) | ||||
0.187829 | + | 0.982202i | \(0.439855\pi\) | |||||||
\(458\) | −5718.00 | −0.583372 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17562.0 | −1.77428 | −0.887141 | − | 0.461499i | \(-0.847312\pi\) | ||||
−0.887141 | + | 0.461499i | \(0.847312\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1172.00 | −0.117640 | −0.0588202 | − | 0.998269i | \(-0.518734\pi\) | ||||
−0.0588202 | + | 0.998269i | \(0.518734\pi\) | |||||||
\(464\) | −5538.00 | −0.554084 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4374.00 | −0.434810 | ||||||||
\(467\) | 6876.00 | 0.681335 | 0.340667 | − | 0.940184i | \(-0.389347\pi\) | ||||
0.340667 | + | 0.940184i | \(0.389347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3920.00 | −0.385946 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 504.000 | 0.0491493 | ||||||||
\(473\) | −2208.00 | −0.214638 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1080.00 | −0.103995 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3528.00 | −0.337588 | ||||||||
\(479\) | −2280.00 | −0.217486 | −0.108743 | − | 0.994070i | \(-0.534683\pi\) | ||||
−0.108743 | + | 0.994070i | \(0.534683\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5180.00 | −0.491035 | ||||||||
\(482\) | 2598.00 | 0.245510 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −755.000 | −0.0709053 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3076.00 | 0.286215 | 0.143108 | − | 0.989707i | \(-0.454290\pi\) | ||||
0.143108 | + | 0.989707i | \(0.454290\pi\) | |||||||
\(488\) | 6762.00 | 0.627257 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18912.0 | 1.73826 | 0.869131 | − | 0.494582i | \(-0.164679\pi\) | ||||
0.869131 | + | 0.494582i | \(0.164679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4212.00 | 0.384785 | ||||||||
\(494\) | 27528.0 | 2.50717 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14200.0 | −1.28548 | ||||||||
\(497\) | −5760.00 | −0.519862 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9956.00 | 0.893170 | 0.446585 | − | 0.894741i | \(-0.352640\pi\) | ||||
0.446585 | + | 0.894741i | \(0.352640\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1296.00 | −0.115226 | ||||||||
\(503\) | −10656.0 | −0.944588 | −0.472294 | − | 0.881441i | \(-0.656574\pi\) | ||||
−0.472294 | + | 0.881441i | \(0.656574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8640.00 | −0.759081 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1244.00 | −0.108649 | ||||||||
\(509\) | 2766.00 | 0.240866 | 0.120433 | − | 0.992721i | \(-0.461572\pi\) | ||||
0.120433 | + | 0.992721i | \(0.461572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8600.00 | −0.744504 | ||||||||
\(512\) | −8733.00 | −0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7578.00 | 0.650294 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −576.000 | −0.0489989 | ||||||||
\(518\) | −4200.00 | −0.356250 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10530.0 | −0.885466 | −0.442733 | − | 0.896654i | \(-0.645991\pi\) | ||||
−0.442733 | + | 0.896654i | \(0.645991\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12692.0 | −1.06115 | −0.530576 | − | 0.847637i | \(-0.678024\pi\) | ||||
−0.530576 | + | 0.847637i | \(0.678024\pi\) | |||||||
\(524\) | −2328.00 | −0.194082 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16344.0 | 1.35481 | ||||||||
\(527\) | 10800.0 | 0.892705 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2233.00 | 0.183529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2480.00 | 0.202108 | ||||||||
\(533\) | 24420.0 | 1.98452 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4116.00 | −0.331687 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7722.00 | 0.618809 | ||||||||
\(539\) | 1368.00 | 0.109321 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18110.0 | 1.43920 | 0.719602 | − | 0.694386i | \(-0.244324\pi\) | ||||
0.719602 | + | 0.694386i | \(0.244324\pi\) | |||||||
\(542\) | −9552.00 | −0.756999 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2430.00 | −0.191517 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3620.00 | −0.282962 | −0.141481 | − | 0.989941i | \(-0.545186\pi\) | ||||
−0.141481 | + | 0.989941i | \(0.545186\pi\) | |||||||
\(548\) | 2118.00 | 0.165103 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9672.00 | −0.747806 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10400.0 | 0.799734 | ||||||||
\(554\) | −11886.0 | −0.911530 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2324.00 | 0.177265 | ||||||||
\(557\) | −14166.0 | −1.07762 | −0.538809 | − | 0.842428i | \(-0.681125\pi\) | ||||
−0.538809 | + | 0.842428i | \(0.681125\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6808.00 | 0.515112 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24858.0 | 1.86579 | ||||||||
\(563\) | −13404.0 | −1.00339 | −0.501697 | − | 0.865043i | \(-0.667291\pi\) | ||||
−0.501697 | + | 0.865043i | \(0.667291\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8148.00 | 0.605099 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6048.00 | −0.446775 | ||||||||
\(569\) | 18654.0 | 1.37437 | 0.687185 | − | 0.726483i | \(-0.258846\pi\) | ||||
0.687185 | + | 0.726483i | \(0.258846\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7684.00 | −0.563162 | −0.281581 | − | 0.959537i | \(-0.590859\pi\) | ||||
−0.281581 | + | 0.959537i | \(0.590859\pi\) | |||||||
\(572\) | −1776.00 | −0.129822 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 19800.0 | 1.43978 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1726.00 | 0.124531 | 0.0622654 | − | 0.998060i | \(-0.480167\pi\) | ||||
0.0622654 | + | 0.998060i | \(0.480167\pi\) | |||||||
\(578\) | −5991.00 | −0.431129 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3120.00 | −0.222787 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10800.0 | 0.767222 | ||||||||
\(584\) | −9030.00 | −0.639836 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18054.0 | 1.27270 | ||||||||
\(587\) | 10596.0 | 0.745049 | 0.372524 | − | 0.928022i | \(-0.378492\pi\) | ||||
0.372524 | + | 0.928022i | \(0.378492\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24800.0 | −1.73492 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4970.00 | −0.345043 | ||||||||
\(593\) | 2862.00 | 0.198193 | 0.0990963 | − | 0.995078i | \(-0.468405\pi\) | ||||
0.0990963 | + | 0.995078i | \(0.468405\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −258.000 | −0.0177317 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26640.0 | 1.82172 | ||||||||
\(599\) | 23592.0 | 1.60925 | 0.804627 | − | 0.593781i | \(-0.202365\pi\) | ||||
0.804627 | + | 0.593781i | \(0.202365\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9574.00 | −0.649803 | −0.324902 | − | 0.945748i | \(-0.605331\pi\) | ||||
−0.324902 | + | 0.945748i | \(0.605331\pi\) | |||||||
\(602\) | 5520.00 | 0.373718 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −808.000 | −0.0544322 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17444.0 | −1.16644 | −0.583221 | − | 0.812314i | \(-0.698208\pi\) | ||||
−0.583221 | + | 0.812314i | \(0.698208\pi\) | |||||||
\(608\) | 5580.00 | 0.372202 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1776.00 | 0.117593 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2374.00 | 0.156419 | 0.0782096 | − | 0.996937i | \(-0.475080\pi\) | ||||
0.0782096 | + | 0.996937i | \(0.475080\pi\) | |||||||
\(614\) | −27708.0 | −1.82118 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10080.0 | 0.659310 | ||||||||
\(617\) | −12162.0 | −0.793555 | −0.396778 | − | 0.917915i | \(-0.629872\pi\) | ||||
−0.396778 | + | 0.917915i | \(0.629872\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8804.00 | 0.571668 | 0.285834 | − | 0.958279i | \(-0.407729\pi\) | ||||
0.285834 | + | 0.958279i | \(0.407729\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4608.00 | −0.297048 | ||||||||
\(623\) | 20520.0 | 1.31961 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 22026.0 | 1.40629 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2378.00 | −0.151103 | ||||||||
\(629\) | 3780.00 | 0.239616 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12688.0 | −0.800478 | −0.400239 | − | 0.916411i | \(-0.631073\pi\) | ||||
−0.400239 | + | 0.916411i | \(0.631073\pi\) | |||||||
\(632\) | 10920.0 | 0.687301 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11682.0 | −0.731785 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4218.00 | −0.262360 | ||||||||
\(638\) | 5616.00 | 0.348495 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9150.00 | 0.563812 | 0.281906 | − | 0.959442i | \(-0.409033\pi\) | ||||
0.281906 | + | 0.959442i | \(0.409033\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25292.0 | −1.55120 | −0.775598 | − | 0.631227i | \(-0.782552\pi\) | ||||
−0.775598 | + | 0.631227i | \(0.782552\pi\) | |||||||
\(644\) | 2400.00 | 0.146853 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20088.0 | −1.22345 | ||||||||
\(647\) | −2736.00 | −0.166249 | −0.0831246 | − | 0.996539i | \(-0.526490\pi\) | ||||
−0.0831246 | + | 0.996539i | \(0.526490\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −576.000 | −0.0348382 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 52.0000 | 0.00312343 | ||||||||
\(653\) | 22218.0 | 1.33148 | 0.665741 | − | 0.746183i | \(-0.268116\pi\) | ||||
0.665741 | + | 0.746183i | \(0.268116\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 23430.0 | 1.39449 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1440.00 | 0.0853147 | ||||||||
\(659\) | −14520.0 | −0.858299 | −0.429149 | − | 0.903234i | \(-0.641187\pi\) | ||||
−0.429149 | + | 0.903234i | \(0.641187\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10618.0 | −0.624799 | −0.312400 | − | 0.949951i | \(-0.601133\pi\) | ||||
−0.312400 | + | 0.949951i | \(0.601133\pi\) | |||||||
\(662\) | 11076.0 | 0.650273 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3276.00 | −0.191466 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9360.00 | −0.543359 | ||||||||
\(668\) | −3720.00 | −0.215466 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7728.00 | −0.444614 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1370.00 | −0.0784690 | −0.0392345 | − | 0.999230i | \(-0.512492\pi\) | ||||
−0.0392345 | + | 0.999230i | \(0.512492\pi\) | |||||||
\(674\) | 26994.0 | 1.54269 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3279.00 | 0.186561 | ||||||||
\(677\) | −13758.0 | −0.781038 | −0.390519 | − | 0.920595i | \(-0.627704\pi\) | ||||
−0.390519 | + | 0.920595i | \(0.627704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5720.00 | −0.323289 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14400.0 | 0.808511 | ||||||||
\(683\) | 11988.0 | 0.671608 | 0.335804 | − | 0.941932i | \(-0.390992\pi\) | ||||
0.335804 | + | 0.941932i | \(0.390992\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17160.0 | 0.955061 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6532.00 | 0.361962 | ||||||||
\(689\) | −33300.0 | −1.84126 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32996.0 | 1.81654 | 0.908268 | − | 0.418388i | \(-0.137405\pi\) | ||||
0.908268 | + | 0.418388i | \(0.137405\pi\) | |||||||
\(692\) | 426.000 | 0.0234019 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15732.0 | 0.860488 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17820.0 | −0.968408 | ||||||||
\(698\) | 18906.0 | 1.02522 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25902.0 | 1.39558 | 0.697792 | − | 0.716300i | \(-0.254166\pi\) | ||||
0.697792 | + | 0.716300i | \(0.254166\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8680.00 | −0.465679 | ||||||||
\(704\) | 10392.0 | 0.556340 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10242.0 | 0.545981 | ||||||||
\(707\) | −34680.0 | −1.84480 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27394.0 | −1.45106 | −0.725531 | − | 0.688189i | \(-0.758406\pi\) | ||||
−0.725531 | + | 0.688189i | \(0.758406\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 21546.0 | 1.13409 | ||||||||
\(713\) | −24000.0 | −1.26060 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1440.00 | 0.0751611 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14472.0 | −0.752215 | ||||||||
\(719\) | −34848.0 | −1.80753 | −0.903763 | − | 0.428033i | \(-0.859207\pi\) | ||||
−0.903763 | + | 0.428033i | \(0.859207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9040.00 | 0.466945 | ||||||||
\(722\) | 25551.0 | 1.31705 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3130.00 | −0.160671 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28028.0 | −1.42985 | −0.714925 | − | 0.699201i | \(-0.753539\pi\) | ||||
−0.714925 | + | 0.699201i | \(0.753539\pi\) | |||||||
\(728\) | −31080.0 | −1.58228 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4968.00 | −0.251365 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18002.0 | −0.907120 | −0.453560 | − | 0.891226i | \(-0.649846\pi\) | ||||
−0.453560 | + | 0.891226i | \(0.649846\pi\) | |||||||
\(734\) | 10524.0 | 0.529221 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5400.00 | 0.270444 | ||||||||
\(737\) | 4704.00 | 0.235107 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15284.0 | 0.760800 | 0.380400 | − | 0.924822i | \(-0.375786\pi\) | ||||
0.380400 | + | 0.924822i | \(0.375786\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −27000.0 | −1.33585 | ||||||||
\(743\) | −18768.0 | −0.926691 | −0.463345 | − | 0.886178i | \(-0.653351\pi\) | ||||
−0.463345 | + | 0.886178i | \(0.653351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −32406.0 | −1.59044 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1296.00 | 0.0633509 | ||||||||
\(749\) | 28080.0 | 1.36985 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8696.00 | 0.422532 | 0.211266 | − | 0.977429i | \(-0.432241\pi\) | ||||
0.211266 | + | 0.977429i | \(0.432241\pi\) | |||||||
\(752\) | 1704.00 | 0.0826310 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17316.0 | −0.836355 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38662.0 | 1.85627 | 0.928134 | − | 0.372247i | \(-0.121413\pi\) | ||||
0.928134 | + | 0.372247i | \(0.121413\pi\) | |||||||
\(758\) | 4380.00 | 0.209880 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −23874.0 | −1.13723 | −0.568615 | − | 0.822604i | \(-0.692521\pi\) | ||||
−0.568615 | + | 0.822604i | \(0.692521\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29480.0 | 1.39875 | ||||||||
\(764\) | −3576.00 | −0.169339 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14616.0 | −0.689422 | ||||||||
\(767\) | 1776.00 | 0.0836084 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23618.0 | 1.10753 | 0.553763 | − | 0.832675i | \(-0.313192\pi\) | ||||
0.553763 | + | 0.832675i | \(0.313192\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2666.00 | −0.124289 | ||||||||
\(773\) | 11538.0 | 0.536860 | 0.268430 | − | 0.963299i | \(-0.413495\pi\) | ||||
0.268430 | + | 0.963299i | \(0.413495\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6006.00 | −0.277839 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 42138.0 | 1.94180 | ||||||||
\(779\) | 40920.0 | 1.88204 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6912.00 | 0.316685 | ||||||||
\(782\) | −19440.0 | −0.888968 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4047.00 | −0.184357 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14884.0 | 0.674152 | 0.337076 | − | 0.941478i | \(-0.390562\pi\) | ||||
0.337076 | + | 0.941478i | \(0.390562\pi\) | |||||||
\(788\) | −2718.00 | −0.122874 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21720.0 | −0.976327 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23828.0 | 1.06703 | ||||||||
\(794\) | 8202.00 | 0.366597 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3832.00 | −0.170630 | ||||||||
\(797\) | −11334.0 | −0.503728 | −0.251864 | − | 0.967763i | \(-0.581043\pi\) | ||||
−0.251864 | + | 0.967763i | \(0.581043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1296.00 | −0.0573832 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 47826.0 | 2.10573 | ||||||||
\(803\) | 10320.0 | 0.453530 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −44400.0 | −1.94035 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −36414.0 | −1.58545 | ||||||||
\(809\) | −44730.0 | −1.94391 | −0.971955 | − | 0.235167i | \(-0.924436\pi\) | ||||
−0.971955 | + | 0.235167i | \(0.924436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42748.0 | −1.85091 | −0.925453 | − | 0.378862i | \(-0.876316\pi\) | ||||
−0.925453 | + | 0.378862i | \(0.876316\pi\) | |||||||
\(812\) | −1560.00 | −0.0674203 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5040.00 | 0.217017 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11408.0 | 0.488513 | ||||||||
\(818\) | 26142.0 | 1.11740 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31686.0 | 1.34695 | 0.673477 | − | 0.739208i | \(-0.264800\pi\) | ||||
0.673477 | + | 0.739208i | \(0.264800\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11036.0 | −0.467425 | −0.233713 | − | 0.972306i | \(-0.575087\pi\) | ||||
−0.233713 | + | 0.972306i | \(0.575087\pi\) | |||||||
\(824\) | 9492.00 | 0.401298 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1440.00 | 0.0606586 | ||||||||
\(827\) | 25884.0 | 1.08836 | 0.544181 | − | 0.838968i | \(-0.316841\pi\) | ||||
0.544181 | + | 0.838968i | \(0.316841\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15950.0 | 0.668234 | 0.334117 | − | 0.942532i | \(-0.391562\pi\) | ||||
0.334117 | + | 0.942532i | \(0.391562\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −32042.0 | −1.33516 | ||||||||
\(833\) | 3078.00 | 0.128027 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2976.00 | −0.123119 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −35928.0 | −1.48104 | ||||||||
\(839\) | −13800.0 | −0.567853 | −0.283927 | − | 0.958846i | \(-0.591637\pi\) | ||||
−0.283927 | + | 0.958846i | \(0.591637\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18305.0 | −0.750543 | ||||||||
\(842\) | 33162.0 | 1.35729 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1100.00 | 0.0448620 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15100.0 | 0.612565 | ||||||||
\(848\) | −31950.0 | −1.29383 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8400.00 | −0.338365 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27862.0 | 1.11838 | 0.559189 | − | 0.829040i | \(-0.311113\pi\) | ||||
0.559189 | + | 0.829040i | \(0.311113\pi\) | |||||||
\(854\) | 19320.0 | 0.774141 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29484.0 | 1.17727 | ||||||||
\(857\) | −7314.00 | −0.291530 | −0.145765 | − | 0.989319i | \(-0.546564\pi\) | ||||
−0.145765 | + | 0.989319i | \(0.546564\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28780.0 | −1.14314 | −0.571572 | − | 0.820552i | \(-0.693666\pi\) | ||||
−0.571572 | + | 0.820552i | \(0.693666\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2160.00 | −0.0853479 | ||||||||
\(863\) | −32688.0 | −1.28935 | −0.644677 | − | 0.764455i | \(-0.723008\pi\) | ||||
−0.644677 | + | 0.764455i | \(0.723008\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 46866.0 | 1.83900 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4000.00 | −0.156416 | ||||||||
\(869\) | −12480.0 | −0.487175 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14504.0 | −0.564236 | ||||||||
\(872\) | 30954.0 | 1.20210 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 44640.0 | 1.72766 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36650.0 | −1.41115 | −0.705577 | − | 0.708633i | \(-0.749312\pi\) | ||||
−0.705577 | + | 0.708633i | \(0.749312\pi\) | |||||||
\(878\) | −29640.0 | −1.13930 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2646.00 | 0.101187 | 0.0505936 | − | 0.998719i | \(-0.483889\pi\) | ||||
0.0505936 | + | 0.998719i | \(0.483889\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10892.0 | −0.415113 | −0.207557 | − | 0.978223i | \(-0.566551\pi\) | ||||
−0.207557 | + | 0.978223i | \(0.566551\pi\) | |||||||
\(884\) | −3996.00 | −0.152036 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −48348.0 | −1.83328 | ||||||||
\(887\) | −43464.0 | −1.64530 | −0.822648 | − | 0.568550i | \(-0.807504\pi\) | ||||
−0.822648 | + | 0.568550i | \(0.807504\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 24880.0 | 0.938637 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1964.00 | −0.0737215 | ||||||||
\(893\) | 2976.00 | 0.111521 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −33180.0 | −1.23713 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −27054.0 | −1.00535 | ||||||||
\(899\) | 15600.0 | 0.578742 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24300.0 | 0.898502 | ||||||||
\(902\) | −23760.0 | −0.877075 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22806.0 | −0.839067 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14884.0 | 0.544890 | 0.272445 | − | 0.962171i | \(-0.412168\pi\) | ||||
0.272445 | + | 0.962171i | \(0.412168\pi\) | |||||||
\(908\) | 660.000 | 0.0241221 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1248.00 | 0.0453876 | 0.0226938 | − | 0.999742i | \(-0.492776\pi\) | ||||
0.0226938 | + | 0.999742i | \(0.492776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3744.00 | 0.135716 | ||||||||
\(914\) | 11010.0 | 0.398445 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1906.00 | −0.0687511 | ||||||||
\(917\) | 46560.0 | 1.67671 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6640.00 | −0.238339 | −0.119169 | − | 0.992874i | \(-0.538023\pi\) | ||||
−0.119169 | + | 0.992874i | \(0.538023\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −52686.0 | −1.88191 | ||||||||
\(923\) | −21312.0 | −0.760014 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3516.00 | −0.124776 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3510.00 | −0.124161 | ||||||||
\(929\) | −29946.0 | −1.05758 | −0.528792 | − | 0.848751i | \(-0.677355\pi\) | ||||
−0.528792 | + | 0.848751i | \(0.677355\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7068.00 | −0.248812 | ||||||||
\(932\) | −1458.00 | −0.0512429 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20628.0 | 0.722665 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45002.0 | −1.56900 | −0.784499 | − | 0.620130i | \(-0.787080\pi\) | ||||
−0.784499 | + | 0.620130i | \(0.787080\pi\) | |||||||
\(938\) | −11760.0 | −0.409358 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6090.00 | −0.210976 | −0.105488 | − | 0.994421i | \(-0.533640\pi\) | ||||
−0.105488 | + | 0.994421i | \(0.533640\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39600.0 | 1.36750 | ||||||||
\(944\) | 1704.00 | 0.0587505 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6624.00 | −0.227658 | ||||||||
\(947\) | 56388.0 | 1.93491 | 0.967457 | − | 0.253035i | \(-0.0814288\pi\) | ||||
0.967457 | + | 0.253035i | \(0.0814288\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31820.0 | −1.08843 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22680.0 | 0.772125 | ||||||||
\(953\) | 10854.0 | 0.368936 | 0.184468 | − | 0.982839i | \(-0.440944\pi\) | ||||
0.184468 | + | 0.982839i | \(0.440944\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1176.00 | −0.0397851 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6840.00 | −0.230679 | ||||||||
\(959\) | −42360.0 | −1.42636 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10209.0 | 0.342687 | ||||||||
\(962\) | −15540.0 | −0.520821 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 866.000 | 0.0289336 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42316.0 | 1.40723 | 0.703615 | − | 0.710582i | \(-0.251568\pi\) | ||||
0.703615 | + | 0.710582i | \(0.251568\pi\) | |||||||
\(968\) | 15855.0 | 0.526445 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24480.0 | −0.809063 | −0.404532 | − | 0.914524i | \(-0.632565\pi\) | ||||
−0.404532 | + | 0.914524i | \(0.632565\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −46480.0 | −1.53143 | ||||||||
\(974\) | 9228.00 | 0.303577 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22862.0 | 0.749790 | ||||||||
\(977\) | −6906.00 | −0.226144 | −0.113072 | − | 0.993587i | \(-0.536069\pi\) | ||||
−0.113072 | + | 0.993587i | \(0.536069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24624.0 | −0.803868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 56736.0 | 1.84371 | ||||||||
\(983\) | 6960.00 | 0.225829 | 0.112914 | − | 0.993605i | \(-0.463981\pi\) | ||||
0.112914 | + | 0.993605i | \(0.463981\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12636.0 | 0.408126 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9176.00 | 0.295473 | ||||||||
\(989\) | 11040.0 | 0.354956 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47792.0 | 1.53195 | 0.765975 | − | 0.642870i | \(-0.222256\pi\) | ||||
0.765975 | + | 0.642870i | \(0.222256\pi\) | |||||||
\(992\) | −9000.00 | −0.288055 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17280.0 | −0.551397 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9938.00 | −0.315687 | −0.157843 | − | 0.987464i | \(-0.550454\pi\) | ||||
−0.157843 | + | 0.987464i | \(0.550454\pi\) | |||||||
\(998\) | 29868.0 | 0.947350 | ||||||||
\(999\) | 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 | 225.4.a.g.1.1 | 1 | ||
3.2 | odd | 2 | 75.4.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 225.4.b.d.199.2 | 2 | |||
5.3 | odd | 4 | 225.4.b.d.199.1 | 2 | |||
5.4 | even | 2 | 45.4.a.b.1.1 | 1 | |||
12.11 | even | 2 | 1200.4.a.o.1.1 | 1 | |||
15.2 | even | 4 | 75.4.b.a.49.1 | 2 | |||
15.8 | even | 4 | 75.4.b.a.49.2 | 2 | |||
15.14 | odd | 2 | 15.4.a.b.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 720.4.a.r.1.1 | 1 | |||
35.34 | odd | 2 | 2205.4.a.c.1.1 | 1 | |||
45.4 | even | 6 | 405.4.e.k.136.1 | 2 | |||
45.14 | odd | 6 | 405.4.e.d.136.1 | 2 | |||
45.29 | odd | 6 | 405.4.e.d.271.1 | 2 | |||
45.34 | even | 6 | 405.4.e.k.271.1 | 2 | |||
60.23 | odd | 4 | 1200.4.f.m.49.1 | 2 | |||
60.47 | odd | 4 | 1200.4.f.m.49.2 | 2 | |||
60.59 | even | 2 | 240.4.a.f.1.1 | 1 | |||
105.104 | even | 2 | 735.4.a.i.1.1 | 1 | |||
120.29 | odd | 2 | 960.4.a.bi.1.1 | 1 | |||
120.59 | even | 2 | 960.4.a.l.1.1 | 1 | |||
165.164 | even | 2 | 1815.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.4.a.b.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
45.4.a.b.1.1 | 1 | 5.4 | even | 2 | |||
75.4.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
75.4.b.a.49.1 | 2 | 15.2 | even | 4 | |||
75.4.b.a.49.2 | 2 | 15.8 | even | 4 | |||
225.4.a.g.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.4.b.d.199.1 | 2 | 5.3 | odd | 4 | |||
225.4.b.d.199.2 | 2 | 5.2 | odd | 4 | |||
240.4.a.f.1.1 | 1 | 60.59 | even | 2 | |||
405.4.e.d.136.1 | 2 | 45.14 | odd | 6 | |||
405.4.e.d.271.1 | 2 | 45.29 | odd | 6 | |||
405.4.e.k.136.1 | 2 | 45.4 | even | 6 | |||
405.4.e.k.271.1 | 2 | 45.34 | even | 6 | |||
720.4.a.r.1.1 | 1 | 20.19 | odd | 2 | |||
735.4.a.i.1.1 | 1 | 105.104 | even | 2 | |||
960.4.a.l.1.1 | 1 | 120.59 | even | 2 | |||
960.4.a.bi.1.1 | 1 | 120.29 | odd | 2 | |||
1200.4.a.o.1.1 | 1 | 12.11 | even | 2 | |||
1200.4.f.m.49.1 | 2 | 60.23 | odd | 4 | |||
1200.4.f.m.49.2 | 2 | 60.47 | odd | 4 | |||
1815.4.a.a.1.1 | 1 | 165.164 | even | 2 | |||
2205.4.a.c.1.1 | 1 | 35.34 | odd | 2 |