Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [608,4,Mod(1,608)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(608, 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("608.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 608 = 2^{5} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 608.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: | \(35.8731612835\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 608.1 |
$q$-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 | \(-0.469323\pi\) | ||||
0.0962250 | + | 0.995360i | \(0.469323\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.00000 | −0.715542 | −0.357771 | − | 0.933809i | \(-0.616463\pi\) | ||||
−0.357771 | + | 0.933809i | \(0.616463\pi\) | |||||||
\(6\) | 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 | \(-0.0910657\pi\) | ||||
0.959354 | + | 0.282204i | \(0.0910657\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −61.0000 | −1.30141 | −0.650706 | − | 0.759330i | \(-0.725527\pi\) | ||||
−0.650706 | + | 0.759330i | \(0.725527\pi\) | |||||||
\(14\) | 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 | \(-0.148413\pi\) | ||||
0.893259 | + | 0.449543i | \(0.148413\pi\) | |||||||
\(30\) | 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 | \(-0.524066\pi\) | ||||
−0.0755347 | + | 0.997143i | \(0.524066\pi\) | |||||||
\(38\) | 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 | \(-0.389417\pi\) | ||||
0.340462 | + | 0.940258i | \(0.389417\pi\) | |||||||
\(44\) | 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 | \(-0.445702\pi\) | ||||
0.169757 | + | 0.985486i | \(0.445702\pi\) | |||||||
\(54\) | 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 | \(-0.265475\pi\) | ||||
0.671907 | + | 0.740635i | \(0.265475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 338.000 | 0.709450 | 0.354725 | − | 0.934971i | \(-0.384574\pi\) | ||||
0.354725 | + | 0.934971i | \(0.384574\pi\) | |||||||
\(62\) | 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 | \(-0.361925\pi\) | ||||
0.420299 | + | 0.907386i | \(0.361925\pi\) | |||||||
\(68\) | 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 | \(-0.320087\pi\) | ||||
0.535597 | + | 0.844474i | \(0.320087\pi\) | |||||||
\(84\) | 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 | \(-0.707182\pi\) | ||||
−0.605889 | + | 0.795549i | \(0.707182\pi\) | |||||||
\(102\) | 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 | \(-0.199967\pi\) | ||||
0.809077 | + | 0.587702i | \(0.199967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −779.000 | −0.684538 | −0.342269 | − | 0.939602i | \(-0.611195\pi\) | ||||
−0.342269 | + | 0.939602i | \(0.611195\pi\) | |||||||
\(110\) | 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 | \(-0.768499\pi\) | ||||
−0.746984 | + | 0.664842i | \(0.768499\pi\) | |||||||
\(132\) | 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 | \(-0.247462\pi\) | ||||
0.712723 | + | 0.701446i | \(0.247462\pi\) | |||||||
\(140\) | 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 | \(-0.0825204\pi\) | ||||
0.966584 | + | 0.256351i | \(0.0825204\pi\) | |||||||
\(150\) | 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 | \(-0.300658\pi\) | ||||
0.586111 | + | 0.810231i | \(0.300658\pi\) | |||||||
\(158\) | 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 | \(-0.401138\pi\) | ||||
0.305616 | + | 0.952155i | \(0.401138\pi\) | |||||||
\(164\) | 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 | \(-0.805325\pi\) | ||||
−0.818736 | + | 0.574171i | \(0.805325\pi\) | |||||||
\(174\) | 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 | \(-0.429785\pi\) | ||||
0.218802 | + | 0.975769i | \(0.429785\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2678.00 | 1.09975 | 0.549873 | − | 0.835248i | \(-0.314676\pi\) | ||||
0.549873 | + | 0.835248i | \(0.314676\pi\) | |||||||
\(182\) | 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 | \(-0.517276\pi\) | ||||
−0.0542490 | + | 0.998527i | \(0.517276\pi\) | |||||||
\(198\) | 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 | \(-0.385986\pi\) | ||||
0.350576 | + | 0.936534i | \(0.385986\pi\) | |||||||
\(212\) | 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 | \(-0.484684\pi\) | ||||
0.0480980 | + | 0.998843i | \(0.484684\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 430.000 | 0.124084 | 0.0620419 | − | 0.998074i | \(-0.480239\pi\) | ||||
0.0620419 | + | 0.998074i | \(0.480239\pi\) | |||||||
\(230\) | 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 | \(-0.744070\pi\) | ||||
−0.693811 | + | 0.720157i | \(0.744070\pi\) | |||||||
\(252\) | 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 | \(-0.571669\pi\) | ||||
−0.223258 | + | 0.974759i | \(0.571669\pi\) | |||||||
\(270\) | 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 | \(-0.543914\pi\) | ||||
−0.137521 | + | 0.990499i | \(0.543914\pi\) | |||||||
\(278\) | 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 | \(-0.612729\pi\) | ||||
−0.346791 | + | 0.937943i | \(0.612729\pi\) | |||||||
\(284\) | 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 | \(-0.682271\pi\) | ||||
−0.541836 | + | 0.840484i | \(0.682271\pi\) | |||||||
\(294\) | 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 | \(-0.551710\pi\) | ||||
−0.161738 | + | 0.986834i | \(0.551710\pi\) | |||||||
\(308\) | 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 | \(-0.149548\pi\) | ||||
0.891651 | + | 0.452723i | \(0.149548\pi\) | |||||||
\(318\) | 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 | \(-0.578848\pi\) | ||||
−0.245184 | + | 0.969477i | \(0.578848\pi\) | |||||||
\(332\) | 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 | \(-0.387934\pi\) | ||||
0.344839 | + | 0.938662i | \(0.387934\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3522.00 | −0.540196 | −0.270098 | − | 0.962833i | \(-0.587056\pi\) | ||||
−0.270098 | + | 0.962833i | \(0.587056\pi\) | |||||||
\(350\) | 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 | \(-0.349701\pi\) | ||||
0.454828 | + | 0.890579i | \(0.349701\pi\) | |||||||
\(374\) | 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 | \(-0.905490\pi\) | ||||
−0.956245 | + | 0.292568i | \(0.905490\pi\) | |||||||
\(380\) | 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 | \(-0.494648\pi\) | ||||
0.0168138 | + | 0.999859i | \(0.494648\pi\) | |||||||
\(390\) | 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 | \(-0.475348\pi\) | ||||
0.0773688 | + | 0.997003i | \(0.475348\pi\) | |||||||
\(398\) | 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 | \(-0.657554\pi\) | ||||
−0.475007 | + | 0.879982i | \(0.657554\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13849.0 | −1.60323 | −0.801614 | − | 0.597842i | \(-0.796025\pi\) | ||||
−0.801614 | + | 0.597842i | \(0.796025\pi\) | |||||||
\(422\) | 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 | \(-0.419641\pi\) | ||||
0.249784 | + | 0.968302i | \(0.419641\pi\) | |||||||
\(444\) | 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 | \(-0.698098\pi\) | ||||
−0.582941 | + | 0.812515i | \(0.698098\pi\) | |||||||
\(462\) | 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 | \(-0.790762\pi\) | ||||
−0.791621 | + | 0.611013i | \(0.790762\pi\) | |||||||
\(468\) | 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 | \(-0.392094\pi\) | ||||
0.332542 | + | 0.943088i | \(0.392094\pi\) | |||||||
\(492\) | 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 | \(-0.483602\pi\) | ||||
0.0514945 | + | 0.998673i | \(0.483602\pi\) | |||||||
\(500\) | 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 | \(-0.380190\pi\) | ||||
0.367569 | + | 0.929996i | \(0.380190\pi\) | |||||||
\(510\) | 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 | \(-0.637473\pi\) | ||||
−0.418583 | + | 0.908179i | \(0.637473\pi\) | |||||||
\(524\) | 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 | \(-0.303280\pi\) | ||||
0.579417 | + | 0.815031i | \(0.303280\pi\) | |||||||
\(542\) | 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 | \(-0.747051\pi\) | ||||
−0.700526 | + | 0.713627i | \(0.747051\pi\) | |||||||
\(548\) | 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 | \(-0.349674\pi\) | ||||
0.454903 | + | 0.890541i | \(0.349674\pi\) | |||||||
\(558\) | 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 | \(-0.516067\pi\) | ||||
−0.0504542 | + | 0.998726i | \(0.516067\pi\) | |||||||
\(564\) | 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 | \(-0.222230\pi\) | ||||
0.766029 | + | 0.642806i | \(0.222230\pi\) | |||||||
\(572\) | 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 | \(-0.299707\pi\) | ||||
0.588530 | + | 0.808476i | \(0.299707\pi\) | |||||||
\(588\) | 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 | \(-0.294099\pi\) | ||||
0.602682 | + | 0.797982i | \(0.294099\pi\) | |||||||
\(614\) | 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 | \(-0.306926\pi\) | ||||
0.570045 | + | 0.821614i | \(0.306926\pi\) | |||||||
\(620\) | 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 | \(-0.503143\pi\) | ||||
−0.00987437 | + | 0.999951i | \(0.503143\pi\) | |||||||
\(644\) | 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 | \(-0.355321\pi\) | ||||
0.439033 | + | 0.898471i | \(0.355321\pi\) | |||||||
\(654\) | 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 | \(-0.708522\pi\) | ||||
−0.609233 | + | 0.792992i | \(0.708522\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7875.00 | −0.463392 | −0.231696 | − | 0.972788i | \(-0.574427\pi\) | ||||
−0.231696 | + | 0.972788i | \(0.574427\pi\) | |||||||
\(662\) | 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 | \(-0.370301\pi\) | ||||
0.396281 | + | 0.918129i | \(0.370301\pi\) | |||||||
\(678\) | 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 | \(-0.429996\pi\) | ||||
0.218155 | + | 0.975914i | \(0.429996\pi\) | |||||||
\(684\) | 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 | \(-0.394865\pi\) | ||||
0.324319 | + | 0.945948i | \(0.394865\pi\) | |||||||
\(692\) | 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 | \(-0.709446\pi\) | ||||
−0.611532 | + | 0.791220i | \(0.709446\pi\) | |||||||
\(702\) | 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 | \(-0.395608\pi\) | ||||
0.322111 | + | 0.946702i | \(0.395608\pi\) | |||||||
\(710\) | 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 | \(-0.544672\pi\) | ||||
−0.139883 | + | 0.990168i | \(0.544672\pi\) | |||||||
\(734\) | 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 | \(-0.606017\pi\) | ||||
−0.326939 | + | 0.945046i | \(0.606017\pi\) | |||||||
\(740\) | 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 | \(-0.418052\pi\) | ||||
0.254611 | + | 0.967043i | \(0.418052\pi\) | |||||||
\(758\) | 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 | \(-0.826619\pi\) | ||||
−0.855287 | + | 0.518155i | \(0.826619\pi\) | |||||||
\(774\) | 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 | \(-0.754433\pi\) | ||||
−0.716886 | + | 0.697190i | \(0.754433\pi\) | |||||||
\(788\) | 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 | \(-0.592878\pi\) | ||||
−0.287663 | + | 0.957732i | \(0.592878\pi\) | |||||||
\(798\) | 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 | \(-0.720300\pi\) | ||||
−0.638149 | + | 0.769913i | \(0.720300\pi\) | |||||||
\(812\) | 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 | \(-0.511883\pi\) | ||||
−0.0373233 | + | 0.999303i | \(0.511883\pi\) | |||||||
\(822\) | 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 | \(-0.520512\pi\) | ||||
−0.0643960 | + | 0.997924i | \(0.520512\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25467.0 | −1.06695 | −0.533477 | − | 0.845814i | \(-0.679115\pi\) | ||||
−0.533477 | + | 0.845814i | \(0.679115\pi\) | |||||||
\(830\) | 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 | \(-0.486414\pi\) | ||||
0.0426687 | + | 0.999089i | \(0.486414\pi\) | |||||||
\(854\) | 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 | \(-0.508662\pi\) | ||||
−0.0272083 | + | 0.999630i | \(0.508662\pi\) | |||||||
\(860\) | 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 | \(-0.376728\pi\) | ||||
0.377662 | + | 0.925944i | \(0.376728\pi\) | |||||||
\(878\) | 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 | \(-0.734510\pi\) | ||||
−0.671872 | + | 0.740667i | \(0.734510\pi\) | |||||||
\(884\) | 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 | \(-0.312027\pi\) | ||||
0.556806 | + | 0.830642i | \(0.312027\pi\) | |||||||
\(908\) | 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 | \(-0.906235\pi\) | ||||
−0.956926 | + | 0.290331i | \(0.906235\pi\) | |||||||
\(942\) | 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 | \(-0.881556\pi\) | ||||
−0.931564 | + | 0.363576i | \(0.881556\pi\) | |||||||
\(948\) | 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 | \(-0.692947\pi\) | ||||
−0.569715 | + | 0.821842i | \(0.692947\pi\) | |||||||
\(972\) | 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 | \(-0.629510\pi\) | ||||
−0.395736 | + | 0.918364i | \(0.629510\pi\) | |||||||
\(998\) | 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 | 608.4.a.b.1.1 | yes | 1 | |
4.3 | odd | 2 | 608.4.a.a.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 1216.4.a.d.1.1 | 1 | |||
8.5 | even | 2 | 1216.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.4.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
608.4.a.b.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
1216.4.a.c.1.1 | 1 | 8.5 | even | 2 | |||
1216.4.a.d.1.1 | 1 | 8.3 | odd | 2 |