Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,4,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(71.7463225670\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 608) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.192450 | −0.0962250 | − | 0.995360i | \(-0.530677\pi\) | ||||
−0.0962250 | + | 0.995360i | \(0.530677\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.00000 | 0.715542 | 0.357771 | − | 0.933809i | \(-0.383537\pi\) | ||||
0.357771 | + | 0.933809i | \(0.383537\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.0000 | 0.917914 | 0.458957 | − | 0.888459i | \(-0.348223\pi\) | ||||
0.458957 | + | 0.888459i | \(0.348223\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.0000 | −0.962963 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −70.0000 | −1.91871 | −0.959354 | − | 0.282204i | \(-0.908934\pi\) | ||||
−0.959354 | + | 0.282204i | \(0.908934\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 61.0000 | 1.30141 | 0.650706 | − | 0.759330i | \(-0.274473\pi\) | ||||
0.650706 | + | 0.759330i | \(0.274473\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.00000 | −0.137706 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 83.0000 | 1.18414 | 0.592072 | − | 0.805885i | \(-0.298310\pi\) | ||||
0.592072 | + | 0.805885i | \(0.298310\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −17.0000 | −0.176653 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −115.000 | −1.04257 | −0.521286 | − | 0.853382i | \(-0.674548\pi\) | ||||
−0.521286 | + | 0.853382i | \(0.674548\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −61.0000 | −0.488000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 53.0000 | 0.377772 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −279.000 | −1.78652 | −0.893259 | − | 0.449543i | \(-0.851587\pi\) | ||||
−0.893259 | + | 0.449543i | \(0.851587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 72.0000 | 0.417148 | 0.208574 | − | 0.978007i | \(-0.433118\pi\) | ||||
0.208574 | + | 0.978007i | \(0.433118\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 70.0000 | 0.369256 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 136.000 | 0.656806 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.0000 | 0.151069 | 0.0755347 | − | 0.997143i | \(-0.475934\pi\) | ||||
0.0755347 | + | 0.997143i | \(0.475934\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −61.0000 | −0.250457 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 108.000 | 0.411385 | 0.205692 | − | 0.978617i | \(-0.434055\pi\) | ||||
0.205692 | + | 0.978617i | \(0.434055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −192.000 | −0.680924 | −0.340462 | − | 0.940258i | \(-0.610583\pi\) | ||||
−0.340462 | + | 0.940258i | \(0.610583\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −208.000 | −0.689040 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 392.000 | 1.21658 | 0.608288 | − | 0.793716i | \(-0.291857\pi\) | ||||
0.608288 | + | 0.793716i | \(0.291857\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −54.0000 | −0.157434 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −83.0000 | −0.227889 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −131.000 | −0.339514 | −0.169757 | − | 0.985486i | \(-0.554298\pi\) | ||||
−0.169757 | + | 0.985486i | \(0.554298\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −560.000 | −1.37292 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −19.0000 | −0.0441511 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −609.000 | −1.34381 | −0.671907 | − | 0.740635i | \(-0.734525\pi\) | ||||
−0.671907 | + | 0.740635i | \(0.734525\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −338.000 | −0.709450 | −0.354725 | − | 0.934971i | \(-0.615426\pi\) | ||||
−0.354725 | + | 0.934971i | \(0.615426\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −442.000 | −0.883917 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 488.000 | 0.931215 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −461.000 | −0.840599 | −0.420299 | − | 0.907386i | \(-0.638075\pi\) | ||||
−0.420299 | + | 0.907386i | \(0.638075\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 115.000 | 0.200643 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −750.000 | −1.25364 | −0.626821 | − | 0.779163i | \(-0.715644\pi\) | ||||
−0.626821 | + | 0.779163i | \(0.715644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1177.00 | 1.88709 | 0.943544 | − | 0.331247i | \(-0.107469\pi\) | ||||
0.943544 | + | 0.331247i | \(0.107469\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 61.0000 | 0.0939156 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1190.00 | −1.76121 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 22.0000 | 0.0313316 | 0.0156658 | − | 0.999877i | \(-0.495013\pi\) | ||||
0.0156658 | + | 0.999877i | \(0.495013\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 649.000 | 0.890261 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −810.000 | −1.07119 | −0.535597 | − | 0.844474i | \(-0.679913\pi\) | ||||
−0.535597 | + | 0.844474i | \(0.679913\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 664.000 | 0.847305 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 279.000 | 0.343815 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −476.000 | −0.566920 | −0.283460 | − | 0.958984i | \(-0.591482\pi\) | ||||
−0.283460 | + | 0.958984i | \(0.591482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1037.00 | 1.19458 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −72.0000 | −0.0802801 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 152.000 | 0.164157 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1426.00 | 1.49266 | 0.746332 | − | 0.665574i | \(-0.231813\pi\) | ||||
0.746332 | + | 0.665574i | \(0.231813\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1820.00 | 1.84765 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1230.00 | 1.21178 | 0.605889 | − | 0.795549i | \(-0.292818\pi\) | ||||
0.605889 | + | 0.795549i | \(0.292818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −310.000 | −0.296555 | −0.148278 | − | 0.988946i | \(-0.547373\pi\) | ||||
−0.148278 | + | 0.988946i | \(0.547373\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −136.000 | −0.126402 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1791.00 | −1.61815 | −0.809077 | − | 0.587702i | \(-0.800033\pi\) | ||||
−0.809077 | + | 0.587702i | \(0.800033\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 779.000 | 0.684538 | 0.342269 | − | 0.939602i | \(-0.388805\pi\) | ||||
0.342269 | + | 0.939602i | \(0.388805\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −34.0000 | −0.0290733 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1430.00 | −1.19047 | −0.595235 | − | 0.803552i | \(-0.702941\pi\) | ||||
−0.595235 | + | 0.803552i | \(0.702941\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −920.000 | −0.746004 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1586.00 | −1.25321 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1411.00 | 1.08694 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3569.00 | 2.68144 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −108.000 | −0.0791710 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1488.00 | −1.06473 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −466.000 | −0.325597 | −0.162798 | − | 0.986659i | \(-0.552052\pi\) | ||||
−0.162798 | + | 0.986659i | \(0.552052\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 192.000 | 0.131044 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2240.00 | 1.49397 | 0.746984 | − | 0.664842i | \(-0.231501\pi\) | ||||
0.746984 | + | 0.664842i | \(0.231501\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 323.000 | 0.210584 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 424.000 | 0.270312 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1145.00 | −0.714043 | −0.357022 | − | 0.934096i | \(-0.616208\pi\) | ||||
−0.357022 | + | 0.934096i | \(0.616208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2336.00 | −1.42545 | −0.712723 | − | 0.701446i | \(-0.752538\pi\) | ||||
−0.712723 | + | 0.701446i | \(0.752538\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −392.000 | −0.234130 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4270.00 | −2.49703 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2232.00 | −1.27833 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 54.0000 | 0.0302983 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3516.00 | −1.93317 | −0.966584 | − | 0.256351i | \(-0.917480\pi\) | ||||
−0.966584 | + | 0.256351i | \(0.917480\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 390.000 | 0.210184 | 0.105092 | − | 0.994463i | \(-0.466486\pi\) | ||||
0.105092 | + | 0.994463i | \(0.466486\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2158.00 | −1.14029 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 576.000 | 0.298487 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2306.00 | −1.17222 | −0.586111 | − | 0.810231i | \(-0.699342\pi\) | ||||
−0.586111 | + | 0.810231i | \(0.699342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 131.000 | 0.0653395 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1955.00 | −0.956991 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1272.00 | −0.611231 | −0.305616 | − | 0.952155i | \(-0.598862\pi\) | ||||
−0.305616 | + | 0.952155i | \(0.598862\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 560.000 | 0.264218 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1768.00 | −0.819233 | −0.409617 | − | 0.912258i | \(-0.634338\pi\) | ||||
−0.409617 | + | 0.912258i | \(0.634338\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1524.00 | 0.693673 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −494.000 | −0.220919 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3726.00 | 1.63747 | 0.818736 | − | 0.574171i | \(-0.194675\pi\) | ||||
0.818736 | + | 0.574171i | \(0.194675\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1037.00 | −0.447942 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 609.000 | 0.258617 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1048.00 | −0.437604 | −0.218802 | − | 0.975769i | \(-0.570215\pi\) | ||||
−0.218802 | + | 0.975769i | \(0.570215\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2678.00 | −1.09975 | −0.549873 | − | 0.835248i | \(-0.685324\pi\) | ||||
−0.549873 | + | 0.835248i | \(0.685324\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 338.000 | 0.136534 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 272.000 | 0.108096 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5810.00 | −2.27203 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 901.000 | 0.346762 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1443.00 | −0.546659 | −0.273329 | − | 0.961921i | \(-0.588125\pi\) | ||||
−0.273329 | + | 0.961921i | \(0.588125\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 890.000 | 0.331936 | 0.165968 | − | 0.986131i | \(-0.446925\pi\) | ||||
0.165968 | + | 0.986131i | \(0.446925\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −488.000 | −0.179212 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 300.000 | 0.108498 | 0.0542490 | − | 0.998527i | \(-0.482724\pi\) | ||||
0.0542490 | + | 0.998527i | \(0.482724\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3339.00 | −1.18942 | −0.594712 | − | 0.803939i | \(-0.702734\pi\) | ||||
−0.594712 | + | 0.803939i | \(0.702734\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 461.000 | 0.161773 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4743.00 | −1.63987 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 864.000 | 0.294363 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2990.00 | 1.00396 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1330.00 | −0.440182 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2149.00 | −0.701153 | −0.350576 | − | 0.936534i | \(-0.614014\pi\) | ||||
−0.350576 | + | 0.936534i | \(0.614014\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 750.000 | 0.241264 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1536.00 | −0.487229 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1224.00 | 0.382906 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1177.00 | −0.363170 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5063.00 | 1.54106 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3834.00 | −1.15132 | −0.575658 | − | 0.817690i | \(-0.695254\pi\) | ||||
−0.575658 | + | 0.817690i | \(0.695254\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1586.00 | 0.469926 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −329.000 | −0.0961960 | −0.0480980 | − | 0.998843i | \(-0.515316\pi\) | ||||
−0.0480980 | + | 0.998843i | \(0.515316\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −430.000 | −0.124084 | −0.0620419 | − | 0.998074i | \(-0.519761\pi\) | ||||
−0.0620419 | + | 0.998074i | \(0.519761\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1190.00 | 0.338945 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −438.000 | −0.123152 | −0.0615758 | − | 0.998102i | \(-0.519613\pi\) | ||||
−0.0615758 | + | 0.998102i | \(0.519613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3136.00 | 0.870511 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −22.0000 | −0.00602976 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2099.00 | −0.568088 | −0.284044 | − | 0.958811i | \(-0.591676\pi\) | ||||
−0.284044 | + | 0.958811i | \(0.591676\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2996.00 | −0.800786 | −0.400393 | − | 0.916344i | \(-0.631126\pi\) | ||||
−0.400393 | + | 0.916344i | \(0.631126\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2080.00 | −0.549103 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −432.000 | −0.112651 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1159.00 | 0.298564 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 810.000 | 0.206151 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5518.00 | 1.38762 | 0.693811 | − | 0.720157i | \(-0.255930\pi\) | ||||
0.693811 | + | 0.720157i | \(0.255930\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8050.00 | 2.00039 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −664.000 | −0.163064 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4068.00 | −0.987373 | −0.493687 | − | 0.869640i | \(-0.664351\pi\) | ||||
−0.493687 | + | 0.869640i | \(0.664351\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 578.000 | 0.138669 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7254.00 | 1.72035 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4992.00 | −1.17042 | −0.585209 | − | 0.810883i | \(-0.698988\pi\) | ||||
−0.585209 | + | 0.810883i | \(0.698988\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1048.00 | −0.242936 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 476.000 | 0.109104 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1970.00 | 0.446517 | 0.223258 | − | 0.974759i | \(-0.428331\pi\) | ||||
0.223258 | + | 0.974759i | \(0.428331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1861.00 | 0.417150 | 0.208575 | − | 0.978006i | \(-0.433117\pi\) | ||||
0.208575 | + | 0.978006i | \(0.433117\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1037.00 | −0.229898 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4270.00 | 0.936330 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1268.00 | 0.275042 | 0.137521 | − | 0.990499i | \(-0.456086\pi\) | ||||
0.137521 | + | 0.990499i | \(0.456086\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1872.00 | −0.401698 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8912.00 | −1.89198 | −0.945988 | − | 0.324201i | \(-0.894905\pi\) | ||||
−0.945988 | + | 0.324201i | \(0.894905\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3302.00 | 0.693581 | 0.346791 | − | 0.937943i | \(-0.387271\pi\) | ||||
0.346791 | + | 0.937943i | \(0.387271\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −152.000 | −0.0315919 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1836.00 | 0.377616 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1976.00 | 0.402198 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1426.00 | −0.287263 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5435.00 | 1.08367 | 0.541836 | − | 0.840484i | \(-0.317729\pi\) | ||||
0.541836 | + | 0.840484i | \(0.317729\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4872.00 | −0.961555 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3710.00 | −0.724835 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7015.00 | −1.35682 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3264.00 | −0.625029 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1230.00 | −0.233207 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2704.00 | −0.507641 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1740.00 | 0.323476 | 0.161738 | − | 0.986834i | \(-0.448290\pi\) | ||||
0.161738 | + | 0.986834i | \(0.448290\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 310.000 | 0.0570721 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2837.00 | 0.517272 | 0.258636 | − | 0.965975i | \(-0.416727\pi\) | ||||
0.258636 | + | 0.965975i | \(0.416727\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1579.00 | −0.285145 | −0.142572 | − | 0.989784i | \(-0.545537\pi\) | ||||
−0.142572 | + | 0.989784i | \(0.545537\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3536.00 | −0.632479 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10065.0 | −1.78330 | −0.891651 | − | 0.452723i | \(-0.850452\pi\) | ||||
−0.891651 | + | 0.452723i | \(0.850452\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19530.0 | 3.42781 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1791.00 | 0.311414 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1577.00 | 0.271661 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3721.00 | −0.635089 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −779.000 | −0.131739 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6664.00 | 1.11671 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2953.00 | 0.490367 | 0.245184 | − | 0.969477i | \(-0.421152\pi\) | ||||
0.245184 | + | 0.969477i | \(0.421152\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −884.000 | −0.145474 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3688.00 | −0.601483 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −988.000 | −0.159703 | −0.0798513 | − | 0.996807i | \(-0.525445\pi\) | ||||
−0.0798513 | + | 0.996807i | \(0.525445\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1430.00 | 0.229106 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5040.00 | −0.800385 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6749.00 | −1.06242 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 920.000 | 0.143569 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4458.00 | −0.689677 | −0.344839 | − | 0.938662i | \(-0.612066\pi\) | ||||
−0.344839 | + | 0.938662i | \(0.612066\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3522.00 | 0.540196 | 0.270098 | − | 0.962833i | \(-0.412944\pi\) | ||||
0.270098 | + | 0.962833i | \(0.412944\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3233.00 | 0.491638 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8809.00 | 1.32820 | 0.664102 | − | 0.747642i | \(-0.268814\pi\) | ||||
0.664102 | + | 0.747642i | \(0.268814\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6000.00 | −0.897034 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1411.00 | −0.209182 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12611.0 | 1.85399 | 0.926996 | − | 0.375071i | \(-0.122382\pi\) | ||||
0.926996 | + | 0.375071i | \(0.122382\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3569.00 | −0.516044 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9416.00 | 1.35029 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9412.00 | −1.33870 | −0.669349 | − | 0.742948i | \(-0.733427\pi\) | ||||
−0.669349 | + | 0.742948i | \(0.733427\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2808.00 | −0.396148 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2227.00 | −0.311644 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6553.00 | −0.909655 | −0.454828 | − | 0.890579i | \(-0.650299\pi\) | ||||
−0.454828 | + | 0.890579i | \(0.650299\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1488.00 | 0.204907 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17019.0 | −2.32499 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14111.0 | 1.91249 | 0.956245 | − | 0.292568i | \(-0.0945099\pi\) | ||||
0.956245 | + | 0.292568i | \(0.0945099\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 466.000 | 0.0626612 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9902.00 | 1.32107 | 0.660533 | − | 0.750797i | \(-0.270330\pi\) | ||||
0.660533 | + | 0.750797i | \(0.270330\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9520.00 | −1.26022 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4992.00 | 0.655704 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −258.000 | −0.0336276 | −0.0168138 | − | 0.999859i | \(-0.505352\pi\) | ||||
−0.0168138 | + | 0.999859i | \(0.505352\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9545.00 | −1.23456 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2240.00 | −0.287514 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 176.000 | 0.0224190 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1224.00 | −0.154738 | −0.0773688 | − | 0.997003i | \(-0.524652\pi\) | ||||
−0.0773688 | + | 0.997003i | \(0.524652\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −323.000 | −0.0405269 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12104.0 | 1.50734 | 0.753672 | − | 0.657251i | \(-0.228281\pi\) | ||||
0.753672 | + | 0.657251i | \(0.228281\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4392.00 | 0.542881 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5192.00 | 0.637019 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2380.00 | −0.289858 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6076.00 | 0.734569 | 0.367285 | − | 0.930109i | \(-0.380287\pi\) | ||||
0.367285 | + | 0.930109i | \(0.380287\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1145.00 | 0.137418 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10353.0 | −1.23351 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6480.00 | −0.766484 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2336.00 | 0.274327 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8148.00 | 0.950014 | 0.475007 | − | 0.879982i | \(-0.342446\pi\) | ||||
0.475007 | + | 0.879982i | \(0.342446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13849.0 | 1.60323 | 0.801614 | − | 0.597842i | \(-0.203975\pi\) | ||||
0.801614 | + | 0.597842i | \(0.203975\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10192.0 | −1.17152 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5063.00 | −0.577863 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5746.00 | −0.651214 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4270.00 | 0.480554 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9322.00 | 1.04182 | 0.520911 | − | 0.853611i | \(-0.325592\pi\) | ||||
0.520911 | + | 0.853611i | \(0.325592\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7090.00 | 0.786891 | 0.393445 | − | 0.919348i | \(-0.371283\pi\) | ||||
0.393445 | + | 0.919348i | \(0.371283\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2232.00 | 0.246014 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2185.00 | −0.239182 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9740.00 | −1.05892 | −0.529459 | − | 0.848336i | \(-0.677605\pi\) | ||||
−0.529459 | + | 0.848336i | \(0.677605\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1404.00 | 0.151603 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4658.00 | −0.499567 | −0.249784 | − | 0.968302i | \(-0.580359\pi\) | ||||
−0.249784 | + | 0.968302i | \(0.580359\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3808.00 | −0.405655 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3516.00 | 0.372038 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14314.0 | 1.50450 | 0.752249 | − | 0.658879i | \(-0.228969\pi\) | ||||
0.752249 | + | 0.658879i | \(0.228969\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7560.00 | −0.789327 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −390.000 | −0.0404499 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8296.00 | 0.854775 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3641.00 | 0.372689 | 0.186344 | − | 0.982484i | \(-0.440336\pi\) | ||||
0.186344 | + | 0.982484i | \(0.440336\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4399.00 | 0.447337 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11540.0 | 1.16588 | 0.582941 | − | 0.812515i | \(-0.301902\pi\) | ||||
0.582941 | + | 0.812515i | \(0.301902\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13732.0 | 1.37836 | 0.689179 | − | 0.724591i | \(-0.257971\pi\) | ||||
0.689179 | + | 0.724591i | \(0.257971\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −576.000 | −0.0574438 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15978.0 | 1.58324 | 0.791621 | − | 0.611013i | \(-0.209238\pi\) | ||||
0.791621 | + | 0.611013i | \(0.209238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7837.00 | −0.771597 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2306.00 | 0.225594 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13440.0 | 1.30649 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1159.00 | −0.111955 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3406.00 | 0.326939 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4300.00 | 0.410171 | 0.205086 | − | 0.978744i | \(-0.434253\pi\) | ||||
0.205086 | + | 0.978744i | \(0.434253\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2074.00 | 0.196603 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1955.00 | 0.184173 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11408.0 | 1.06806 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12326.0 | 1.14691 | 0.573454 | − | 0.819238i | \(-0.305603\pi\) | ||||
0.573454 | + | 0.819238i | \(0.305603\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1272.00 | 0.117632 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7236.00 | −0.665084 | −0.332542 | − | 0.943088i | \(-0.607906\pi\) | ||||
−0.332542 | + | 0.943088i | \(0.607906\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23157.0 | −2.11549 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14560.0 | 1.32207 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12750.0 | −1.15074 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1148.00 | −0.102989 | −0.0514945 | − | 0.998673i | \(-0.516398\pi\) | ||||
−0.0514945 | + | 0.998673i | \(0.516398\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1768.00 | 0.157662 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5739.00 | −0.508726 | −0.254363 | − | 0.967109i | \(-0.581866\pi\) | ||||
−0.254363 | + | 0.967109i | \(0.581866\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9840.00 | 0.867078 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1524.00 | −0.133497 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8442.00 | −0.735138 | −0.367569 | − | 0.929996i | \(-0.619810\pi\) | ||||
−0.367569 | + | 0.929996i | \(0.619810\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20009.0 | 1.73218 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1007.00 | 0.0866669 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2480.00 | −0.212198 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −27440.0 | −2.33425 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3726.00 | −0.315131 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 744.000 | 0.0625628 | 0.0312814 | − | 0.999511i | \(-0.490041\pi\) | ||||
0.0312814 | + | 0.999511i | \(0.490041\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10013.0 | 0.837166 | 0.418583 | − | 0.908179i | \(-0.362527\pi\) | ||||
0.418583 | + | 0.908179i | \(0.362527\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1037.00 | 0.0862065 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5976.00 | 0.493963 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1058.00 | 0.0869565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15834.0 | 1.29404 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6588.00 | 0.535381 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −14328.0 | −1.15786 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1048.00 | 0.0842170 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3780.00 | 0.302071 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14582.0 | −1.15883 | −0.579417 | − | 0.815031i | \(-0.696720\pi\) | ||||
−0.579417 | + | 0.815031i | \(0.696720\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2678.00 | 0.211646 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6232.00 | 0.489816 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17924.0 | 1.40105 | 0.700526 | − | 0.713627i | \(-0.252949\pi\) | ||||
0.700526 | + | 0.713627i | \(0.252949\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8788.00 | 0.683174 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5301.00 | −0.409855 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 374.000 | 0.0287597 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −272.000 | −0.0208032 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11960.0 | −0.909805 | −0.454903 | − | 0.890541i | \(-0.650326\pi\) | ||||
−0.454903 | + | 0.890541i | \(0.650326\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11712.0 | −0.886162 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5810.00 | 0.437252 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1348.00 | 0.100908 | 0.0504542 | − | 0.998726i | \(-0.483933\pi\) | ||||
0.0504542 | + | 0.998726i | \(0.483933\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11440.0 | −0.851831 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11033.0 | 0.817182 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9820.00 | −0.723508 | −0.361754 | − | 0.932274i | \(-0.617822\pi\) | ||||
−0.361754 | + | 0.932274i | \(0.617822\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20904.0 | −1.53206 | −0.766029 | − | 0.642806i | \(-0.777770\pi\) | ||||
−0.766029 | + | 0.642806i | \(0.777770\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1443.00 | 0.105205 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7015.00 | 0.508775 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15093.0 | −1.08896 | −0.544480 | − | 0.838774i | \(-0.683273\pi\) | ||||
−0.544480 | + | 0.838774i | \(0.683273\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −890.000 | −0.0638811 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13770.0 | −0.983263 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9170.00 | 0.651428 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12688.0 | −0.896725 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16740.0 | −1.17706 | −0.588530 | − | 0.808476i | \(-0.700293\pi\) | ||||
−0.588530 | + | 0.808476i | \(0.700293\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1368.00 | 0.0957003 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −300.000 | −0.0208805 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3042.00 | 0.210658 | 0.105329 | − | 0.994437i | \(-0.466410\pi\) | ||||
0.105329 | + | 0.994437i | \(0.466410\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11288.0 | 0.777753 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3339.00 | 0.228905 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27816.0 | −1.89738 | −0.948690 | − | 0.316207i | \(-0.897591\pi\) | ||||
−0.948690 | + | 0.316207i | \(0.897591\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19320.0 | 1.31128 | 0.655640 | − | 0.755074i | \(-0.272399\pi\) | ||||
0.655640 | + | 0.755074i | \(0.272399\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11986.0 | 0.809465 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 28552.0 | 1.91868 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17926.0 | −1.19867 | −0.599336 | − | 0.800498i | \(-0.704569\pi\) | ||||
−0.599336 | + | 0.800498i | \(0.704569\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4743.00 | 0.315593 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23912.0 | 1.58327 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18294.0 | −1.20536 | −0.602682 | − | 0.797982i | \(-0.705901\pi\) | ||||
−0.602682 | + | 0.797982i | \(0.705901\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −864.000 | −0.0566502 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22538.0 | 1.47058 | 0.735288 | − | 0.677755i | \(-0.237047\pi\) | ||||
0.735288 | + | 0.677755i | \(0.237047\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17558.0 | −1.14009 | −0.570045 | − | 0.821614i | \(-0.693074\pi\) | ||||
−0.570045 | + | 0.821614i | \(0.693074\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6095.00 | −0.393855 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8092.00 | −0.520384 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4279.00 | −0.273856 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1330.00 | 0.0847131 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2822.00 | 0.178888 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12440.0 | 0.784831 | 0.392416 | − | 0.919788i | \(-0.371639\pi\) | ||||
0.392416 | + | 0.919788i | \(0.371639\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2149.00 | 0.134937 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3728.00 | −0.232978 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3294.00 | −0.204887 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19500.0 | 1.20721 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10842.0 | −0.668071 | −0.334035 | − | 0.942561i | \(-0.608410\pi\) | ||||
−0.334035 | + | 0.942561i | \(0.608410\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 322.000 | 0.0197487 | 0.00987437 | − | 0.999951i | \(-0.496857\pi\) | ||||
0.00987437 | + | 0.999951i | \(0.496857\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1536.00 | 0.0937674 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2995.00 | −0.181987 | −0.0909935 | − | 0.995851i | \(-0.529004\pi\) | ||||
−0.0909935 | + | 0.995851i | \(0.529004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 42630.0 | 2.57839 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1224.00 | −0.0736902 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14652.0 | −0.878066 | −0.439033 | − | 0.898471i | \(-0.644679\pi\) | ||||
−0.439033 | + | 0.898471i | \(0.644679\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17920.0 | 1.06900 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30602.0 | −1.81720 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20613.0 | 1.21847 | 0.609233 | − | 0.792992i | \(-0.291478\pi\) | ||||
0.609233 | + | 0.792992i | \(0.291478\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7875.00 | 0.463392 | 0.231696 | − | 0.972788i | \(-0.425573\pi\) | ||||
0.231696 | + | 0.972788i | \(0.425573\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5063.00 | −0.296577 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2584.00 | 0.150682 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32085.0 | 1.86257 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3834.00 | 0.221571 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23660.0 | 1.36123 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6216.00 | 0.356031 | 0.178016 | − | 0.984028i | \(-0.443032\pi\) | ||||
0.178016 | + | 0.984028i | \(0.443032\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3233.00 | −0.184353 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13961.0 | −0.792563 | −0.396281 | − | 0.918129i | \(-0.629699\pi\) | ||||
−0.396281 | + | 0.918129i | \(0.629699\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24242.0 | 1.37014 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 329.000 | 0.0185129 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7788.00 | −0.436310 | −0.218155 | − | 0.975914i | \(-0.570004\pi\) | ||||
−0.218155 | + | 0.975914i | \(0.570004\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9160.00 | −0.510928 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 430.000 | 0.0238799 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7991.00 | −0.441847 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11782.0 | −0.648637 | −0.324319 | − | 0.945948i | \(-0.605135\pi\) | ||||
−0.324319 | + | 0.945948i | \(0.605135\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 30940.0 | 1.69598 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18688.0 | −1.01997 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8964.00 | 0.487139 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 438.000 | 0.0237005 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22700.0 | 1.22306 | 0.611532 | − | 0.791220i | \(-0.290554\pi\) | ||||
0.611532 | + | 0.791220i | \(0.290554\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 646.000 | 0.0346577 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3136.00 | −0.167530 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20910.0 | 1.11231 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12162.0 | −0.644222 | −0.322111 | − | 0.946702i | \(-0.604392\pi\) | ||||
−0.322111 | + | 0.946702i | \(0.604392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −572.000 | −0.0301711 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8280.00 | −0.434907 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −34160.0 | −1.78673 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2099.00 | 0.109329 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2199.00 | −0.114060 | −0.0570298 | − | 0.998372i | \(-0.518163\pi\) | ||||
−0.0570298 | + | 0.998372i | \(0.518163\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5270.00 | −0.272212 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2996.00 | 0.154111 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17019.0 | 0.871820 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18965.0 | 0.967501 | 0.483750 | − | 0.875206i | \(-0.339274\pi\) | ||||
0.483750 | + | 0.875206i | \(0.339274\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15443.0 | −0.784586 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15936.0 | −0.806312 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5552.00 | 0.279765 | 0.139883 | − | 0.990168i | \(-0.455328\pi\) | ||||
0.139883 | + | 0.990168i | \(0.455328\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 432.000 | 0.0216797 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32270.0 | 1.61286 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13136.0 | 0.653878 | 0.326939 | − | 0.945046i | \(-0.393983\pi\) | ||||
0.326939 | + | 0.945046i | \(0.393983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1159.00 | −0.0574587 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13416.0 | 0.662430 | 0.331215 | − | 0.943555i | \(-0.392541\pi\) | ||||
0.331215 | + | 0.943555i | \(0.392541\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28128.0 | −1.38326 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21060.0 | 1.03152 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −30447.0 | −1.48533 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33348.0 | 1.62035 | 0.810177 | − | 0.586185i | \(-0.199371\pi\) | ||||
0.810177 | + | 0.586185i | \(0.199371\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5518.00 | −0.267048 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3120.00 | 0.150395 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10606.0 | −0.509223 | −0.254611 | − | 0.967043i | \(-0.581948\pi\) | ||||
−0.254611 | + | 0.967043i | \(0.581948\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8050.00 | −0.384976 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29061.0 | −1.38431 | −0.692155 | − | 0.721749i | \(-0.743339\pi\) | ||||
−0.692155 | + | 0.721749i | \(0.743339\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13243.0 | 0.628347 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −17264.0 | −0.815923 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37149.0 | −1.74886 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15955.0 | −0.748182 | −0.374091 | − | 0.927392i | \(-0.622045\pi\) | ||||
−0.374091 | + | 0.927392i | \(0.622045\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4068.00 | 0.190020 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36763.0 | 1.71057 | 0.855287 | − | 0.518155i | \(-0.173381\pi\) | ||||
0.855287 | + | 0.518155i | \(0.173381\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4392.00 | −0.203568 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −578.000 | −0.0266868 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2052.00 | 0.0943781 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52500.0 | 2.40537 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −14787.0 | −0.674897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18448.0 | −0.838774 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31655.0 | 1.43377 | 0.716886 | − | 0.697190i | \(-0.245567\pi\) | ||||
0.716886 | + | 0.697190i | \(0.245567\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4992.00 | 0.225247 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −24310.0 | −1.09275 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20618.0 | −0.923287 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1048.00 | 0.0467531 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12945.0 | 0.575327 | 0.287663 | − | 0.957732i | \(-0.407122\pi\) | ||||
0.287663 | + | 0.957732i | \(0.407122\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32536.0 | 1.44060 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12376.0 | 0.545923 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −82390.0 | −3.62077 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15640.0 | −0.684767 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1970.00 | −0.0859322 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20263.0 | −0.880605 | −0.440302 | − | 0.897850i | \(-0.645129\pi\) | ||||
−0.440302 | + | 0.897850i | \(0.645129\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29477.0 | 1.27630 | 0.638149 | − | 0.769913i | \(-0.279700\pi\) | ||||
0.638149 | + | 0.769913i | \(0.279700\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1861.00 | −0.0802806 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10176.0 | −0.437362 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3648.00 | −0.156215 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26962.0 | −1.15034 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1756.00 | 0.0746466 | 0.0373233 | − | 0.999303i | \(-0.488117\pi\) | ||||
0.0373233 | + | 0.999303i | \(0.488117\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1721.00 | −0.0728922 | −0.0364461 | − | 0.999336i | \(-0.511604\pi\) | ||||
−0.0364461 | + | 0.999336i | \(0.511604\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4270.00 | −0.180197 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3063.00 | 0.128792 | 0.0643960 | − | 0.997924i | \(-0.479488\pi\) | ||||
0.0643960 | + | 0.997924i | \(0.479488\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25467.0 | 1.06695 | 0.533477 | − | 0.845814i | \(-0.320885\pi\) | ||||
0.533477 | + | 0.845814i | \(0.320885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1268.00 | −0.0529319 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4482.00 | −0.186425 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14144.0 | −0.586196 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3816.00 | 0.157587 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2976.00 | −0.122459 | −0.0612294 | − | 0.998124i | \(-0.519502\pi\) | ||||
−0.0612294 | + | 0.998124i | \(0.519502\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53452.0 | 2.19164 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8912.00 | 0.364111 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12192.0 | 0.496352 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 60673.0 | 2.46133 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3302.00 | −0.133480 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3910.00 | −0.157501 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2126.00 | −0.0853375 | −0.0426687 | − | 0.999089i | \(-0.513586\pi\) | ||||
−0.0426687 | + | 0.999089i | \(0.513586\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3952.00 | −0.158077 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4684.00 | −0.186701 | −0.0933503 | − | 0.995633i | \(-0.529758\pi\) | ||||
−0.0933503 | + | 0.995633i | \(0.529758\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1370.00 | 0.0544165 | 0.0272083 | − | 0.999630i | \(-0.491338\pi\) | ||||
0.0272083 | + | 0.999630i | \(0.491338\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1836.00 | −0.0726721 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −30630.0 | −1.20818 | −0.604089 | − | 0.796917i | \(-0.706463\pi\) | ||||
−0.604089 | + | 0.796917i | \(0.706463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29808.0 | 1.17168 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1976.00 | −0.0774031 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1540.00 | −0.0601161 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28121.0 | −1.09397 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −37076.0 | −1.43738 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25296.0 | −0.977327 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19617.0 | −0.755324 | −0.377662 | − | 0.925944i | \(-0.623272\pi\) | ||||
−0.377662 | + | 0.925944i | \(0.623272\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5435.00 | −0.208553 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1614.00 | 0.0617220 | 0.0308610 | − | 0.999524i | \(-0.490175\pi\) | ||||
0.0308610 | + | 0.999524i | \(0.490175\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35258.0 | 1.34374 | 0.671872 | − | 0.740667i | \(-0.265490\pi\) | ||||
0.671872 | + | 0.740667i | \(0.265490\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4872.00 | 0.185051 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2166.00 | −0.0819923 | −0.0409961 | − | 0.999159i | \(-0.513053\pi\) | ||||
−0.0409961 | + | 0.999159i | \(0.513053\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7922.00 | −0.298870 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −45430.0 | −1.70815 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7448.00 | 0.279102 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8384.00 | −0.313124 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7015.00 | 0.261119 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20088.0 | −0.745242 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10873.0 | −0.402033 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3264.00 | 0.120287 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21424.0 | −0.786915 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −30419.0 | −1.11361 | −0.556806 | − | 0.830642i | \(-0.687973\pi\) | ||||
−0.556806 | + | 0.830642i | \(0.687973\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31980.0 | −1.16690 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32864.0 | −1.19521 | −0.597603 | − | 0.801792i | \(-0.703880\pi\) | ||||
−0.597603 | + | 0.801792i | \(0.703880\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56700.0 | 2.05531 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2704.00 | 0.0976956 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 38080.0 | 1.37133 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20225.0 | −0.725964 | −0.362982 | − | 0.931796i | \(-0.618241\pi\) | ||||
−0.362982 | + | 0.931796i | \(0.618241\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1740.00 | −0.0622529 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −45750.0 | −1.63151 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2074.00 | −0.0737218 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8060.00 | 0.285572 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29415.0 | −1.03883 | −0.519416 | − | 0.854522i | \(-0.673850\pi\) | ||||
−0.519416 | + | 0.854522i | \(0.673850\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1026.00 | −0.0361179 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2837.00 | −0.0995490 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −46480.0 | −1.62573 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3697.00 | 0.128896 | 0.0644481 | − | 0.997921i | \(-0.479471\pi\) | ||||
0.0644481 | + | 0.997921i | \(0.479471\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1579.00 | 0.0548762 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55245.0 | 1.91385 | 0.956926 | − | 0.290331i | \(-0.0937653\pi\) | ||||
0.956926 | + | 0.290331i | \(0.0937653\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12420.0 | −0.428898 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7208.00 | 0.248123 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54296.0 | 1.86313 | 0.931564 | − | 0.363576i | \(-0.118444\pi\) | ||||
0.931564 | + | 0.363576i | \(0.118444\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 71797.0 | 2.45588 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10065.0 | 0.343197 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25770.0 | −0.875941 | −0.437971 | − | 0.898989i | \(-0.644303\pi\) | ||||
−0.437971 | + | 0.898989i | \(0.644303\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11544.0 | −0.391157 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19530.0 | −0.659682 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −19465.0 | −0.655430 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24607.0 | −0.825988 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 46566.0 | 1.55822 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7120.00 | 0.237514 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20296.0 | −0.674949 | −0.337474 | − | 0.941335i | \(-0.609573\pi\) | ||||
−0.337474 | + | 0.941335i | \(0.609573\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1577.00 | −0.0522813 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34476.0 | 1.13943 | 0.569715 | − | 0.821842i | \(-0.307053\pi\) | ||||
0.569715 | + | 0.821842i | \(0.307053\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −39712.0 | −1.30844 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3721.00 | 0.122223 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39952.0 | 1.30827 | 0.654134 | − | 0.756379i | \(-0.273033\pi\) | ||||
0.654134 | + | 0.756379i | \(0.273033\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33320.0 | 1.08775 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20254.0 | −0.659185 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56942.0 | 1.84758 | 0.923788 | − | 0.382904i | \(-0.125076\pi\) | ||||
0.923788 | + | 0.382904i | \(0.125076\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2400.00 | 0.0776349 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6664.00 | −0.214911 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22080.0 | 0.709912 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45772.0 | −1.46720 | −0.733600 | − | 0.679581i | \(-0.762161\pi\) | ||||
−0.733600 | + | 0.679581i | \(0.762161\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2953.00 | −0.0943712 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26712.0 | −0.851083 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24916.0 | 0.791472 | 0.395736 | − | 0.918364i | \(-0.370490\pi\) | ||||
0.395736 | + | 0.918364i | \(0.370490\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1802.00 | 0.0570698 |
(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 | 1216.4.a.c.1.1 | 1 | ||
4.3 | odd | 2 | 1216.4.a.d.1.1 | 1 | |||
8.3 | odd | 2 | 608.4.a.a.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 608.4.a.b.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.4.a.a.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
608.4.a.b.1.1 | yes | 1 | 8.5 | even | 2 | ||
1216.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1216.4.a.d.1.1 | 1 | 4.3 | odd | 2 |