Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,4,Mod(1,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, 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("546.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.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: | \(32.2150428631\) |
Analytic rank: | \(1\) |
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 | \(\chi\) | \(=\) | 546.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −9.00000 | −0.804984 | −0.402492 | − | 0.915423i | \(-0.631856\pi\) | ||||
−0.402492 | + | 0.915423i | \(0.631856\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −18.0000 | −0.569210 | ||||||||
\(11\) | −18.0000 | −0.493382 | −0.246691 | − | 0.969094i | \(-0.579343\pi\) | ||||
−0.246691 | + | 0.969094i | \(0.579343\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 27.0000 | 0.464758 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 60.0000 | 0.856008 | 0.428004 | − | 0.903777i | \(-0.359217\pi\) | ||||
0.428004 | + | 0.903777i | \(0.359217\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | −43.0000 | −0.519204 | −0.259602 | − | 0.965716i | \(-0.583591\pi\) | ||||
−0.259602 | + | 0.965716i | \(0.583591\pi\) | |||||||
\(20\) | −36.0000 | −0.402492 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | −36.0000 | −0.348874 | ||||||||
\(23\) | 9.00000 | 0.0815926 | 0.0407963 | − | 0.999167i | \(-0.487011\pi\) | ||||
0.0407963 | + | 0.999167i | \(0.487011\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −44.0000 | −0.352000 | ||||||||
\(26\) | 26.0000 | 0.196116 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | −249.000 | −1.59442 | −0.797209 | − | 0.603703i | \(-0.793691\pi\) | ||||
−0.797209 | + | 0.603703i | \(0.793691\pi\) | |||||||
\(30\) | 54.0000 | 0.328634 | ||||||||
\(31\) | −79.0000 | −0.457704 | −0.228852 | − | 0.973461i | \(-0.573497\pi\) | ||||
−0.228852 | + | 0.973461i | \(0.573497\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 54.0000 | 0.284854 | ||||||||
\(34\) | 120.000 | 0.605289 | ||||||||
\(35\) | −63.0000 | −0.304256 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −412.000 | −1.83060 | −0.915302 | − | 0.402767i | \(-0.868048\pi\) | ||||
−0.915302 | + | 0.402767i | \(0.868048\pi\) | |||||||
\(38\) | −86.0000 | −0.367133 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | −72.0000 | −0.284605 | ||||||||
\(41\) | 222.000 | 0.845624 | 0.422812 | − | 0.906217i | \(-0.361043\pi\) | ||||
0.422812 | + | 0.906217i | \(0.361043\pi\) | |||||||
\(42\) | −42.0000 | −0.154303 | ||||||||
\(43\) | −295.000 | −1.04621 | −0.523106 | − | 0.852268i | \(-0.675227\pi\) | ||||
−0.523106 | + | 0.852268i | \(0.675227\pi\) | |||||||
\(44\) | −72.0000 | −0.246691 | ||||||||
\(45\) | −81.0000 | −0.268328 | ||||||||
\(46\) | 18.0000 | 0.0576947 | ||||||||
\(47\) | 411.000 | 1.27554 | 0.637771 | − | 0.770226i | \(-0.279856\pi\) | ||||
0.637771 | + | 0.770226i | \(0.279856\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −88.0000 | −0.248902 | ||||||||
\(51\) | −180.000 | −0.494217 | ||||||||
\(52\) | 52.0000 | 0.138675 | ||||||||
\(53\) | −237.000 | −0.614235 | −0.307117 | − | 0.951672i | \(-0.599364\pi\) | ||||
−0.307117 | + | 0.951672i | \(0.599364\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 162.000 | 0.397165 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 129.000 | 0.299763 | ||||||||
\(58\) | −498.000 | −1.12742 | ||||||||
\(59\) | −384.000 | −0.847331 | −0.423666 | − | 0.905819i | \(-0.639257\pi\) | ||||
−0.423666 | + | 0.905819i | \(0.639257\pi\) | |||||||
\(60\) | 108.000 | 0.232379 | ||||||||
\(61\) | −466.000 | −0.978118 | −0.489059 | − | 0.872251i | \(-0.662660\pi\) | ||||
−0.489059 | + | 0.872251i | \(0.662660\pi\) | |||||||
\(62\) | −158.000 | −0.323645 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −117.000 | −0.223263 | ||||||||
\(66\) | 108.000 | 0.201422 | ||||||||
\(67\) | −1042.00 | −1.90001 | −0.950004 | − | 0.312237i | \(-0.898922\pi\) | ||||
−0.950004 | + | 0.312237i | \(0.898922\pi\) | |||||||
\(68\) | 240.000 | 0.428004 | ||||||||
\(69\) | −27.0000 | −0.0471075 | ||||||||
\(70\) | −126.000 | −0.215141 | ||||||||
\(71\) | −288.000 | −0.481399 | −0.240699 | − | 0.970600i | \(-0.577377\pi\) | ||||
−0.240699 | + | 0.970600i | \(0.577377\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | −691.000 | −1.10788 | −0.553941 | − | 0.832556i | \(-0.686877\pi\) | ||||
−0.553941 | + | 0.832556i | \(0.686877\pi\) | |||||||
\(74\) | −824.000 | −1.29443 | ||||||||
\(75\) | 132.000 | 0.203227 | ||||||||
\(76\) | −172.000 | −0.259602 | ||||||||
\(77\) | −126.000 | −0.186481 | ||||||||
\(78\) | −78.0000 | −0.113228 | ||||||||
\(79\) | 1001.00 | 1.42559 | 0.712793 | − | 0.701374i | \(-0.247430\pi\) | ||||
0.712793 | + | 0.701374i | \(0.247430\pi\) | |||||||
\(80\) | −144.000 | −0.201246 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 444.000 | 0.597946 | ||||||||
\(83\) | 39.0000 | 0.0515760 | 0.0257880 | − | 0.999667i | \(-0.491791\pi\) | ||||
0.0257880 | + | 0.999667i | \(0.491791\pi\) | |||||||
\(84\) | −84.0000 | −0.109109 | ||||||||
\(85\) | −540.000 | −0.689073 | ||||||||
\(86\) | −590.000 | −0.739783 | ||||||||
\(87\) | 747.000 | 0.920538 | ||||||||
\(88\) | −144.000 | −0.174437 | ||||||||
\(89\) | −339.000 | −0.403752 | −0.201876 | − | 0.979411i | \(-0.564704\pi\) | ||||
−0.201876 | + | 0.979411i | \(0.564704\pi\) | |||||||
\(90\) | −162.000 | −0.189737 | ||||||||
\(91\) | 91.0000 | 0.104828 | ||||||||
\(92\) | 36.0000 | 0.0407963 | ||||||||
\(93\) | 237.000 | 0.264255 | ||||||||
\(94\) | 822.000 | 0.901945 | ||||||||
\(95\) | 387.000 | 0.417951 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 713.000 | 0.746332 | 0.373166 | − | 0.927765i | \(-0.378272\pi\) | ||||
0.373166 | + | 0.927765i | \(0.378272\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | −162.000 | −0.164461 | ||||||||
\(100\) | −176.000 | −0.176000 | ||||||||
\(101\) | 810.000 | 0.798000 | 0.399000 | − | 0.916951i | \(-0.369357\pi\) | ||||
0.399000 | + | 0.916951i | \(0.369357\pi\) | |||||||
\(102\) | −360.000 | −0.349464 | ||||||||
\(103\) | −1456.00 | −1.39285 | −0.696427 | − | 0.717628i | \(-0.745228\pi\) | ||||
−0.696427 | + | 0.717628i | \(0.745228\pi\) | |||||||
\(104\) | 104.000 | 0.0980581 | ||||||||
\(105\) | 189.000 | 0.175662 | ||||||||
\(106\) | −474.000 | −0.434330 | ||||||||
\(107\) | −924.000 | −0.834827 | −0.417413 | − | 0.908717i | \(-0.637063\pi\) | ||||
−0.417413 | + | 0.908717i | \(0.637063\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | 1154.00 | 1.01407 | 0.507033 | − | 0.861927i | \(-0.330742\pi\) | ||||
0.507033 | + | 0.861927i | \(0.330742\pi\) | |||||||
\(110\) | 324.000 | 0.280838 | ||||||||
\(111\) | 1236.00 | 1.05690 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | 1725.00 | 1.43606 | 0.718028 | − | 0.696014i | \(-0.245045\pi\) | ||||
0.718028 | + | 0.696014i | \(0.245045\pi\) | |||||||
\(114\) | 258.000 | 0.211964 | ||||||||
\(115\) | −81.0000 | −0.0656808 | ||||||||
\(116\) | −996.000 | −0.797209 | ||||||||
\(117\) | 117.000 | 0.0924500 | ||||||||
\(118\) | −768.000 | −0.599154 | ||||||||
\(119\) | 420.000 | 0.323541 | ||||||||
\(120\) | 216.000 | 0.164317 | ||||||||
\(121\) | −1007.00 | −0.756574 | ||||||||
\(122\) | −932.000 | −0.691634 | ||||||||
\(123\) | −666.000 | −0.488221 | ||||||||
\(124\) | −316.000 | −0.228852 | ||||||||
\(125\) | 1521.00 | 1.08834 | ||||||||
\(126\) | 126.000 | 0.0890871 | ||||||||
\(127\) | −1204.00 | −0.841242 | −0.420621 | − | 0.907236i | \(-0.638188\pi\) | ||||
−0.420621 | + | 0.907236i | \(0.638188\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 885.000 | 0.604030 | ||||||||
\(130\) | −234.000 | −0.157870 | ||||||||
\(131\) | 828.000 | 0.552234 | 0.276117 | − | 0.961124i | \(-0.410952\pi\) | ||||
0.276117 | + | 0.961124i | \(0.410952\pi\) | |||||||
\(132\) | 216.000 | 0.142427 | ||||||||
\(133\) | −301.000 | −0.196241 | ||||||||
\(134\) | −2084.00 | −1.34351 | ||||||||
\(135\) | 243.000 | 0.154919 | ||||||||
\(136\) | 480.000 | 0.302645 | ||||||||
\(137\) | −2664.00 | −1.66132 | −0.830660 | − | 0.556780i | \(-0.812037\pi\) | ||||
−0.830660 | + | 0.556780i | \(0.812037\pi\) | |||||||
\(138\) | −54.0000 | −0.0333100 | ||||||||
\(139\) | −322.000 | −0.196487 | −0.0982435 | − | 0.995162i | \(-0.531322\pi\) | ||||
−0.0982435 | + | 0.995162i | \(0.531322\pi\) | |||||||
\(140\) | −252.000 | −0.152128 | ||||||||
\(141\) | −1233.00 | −0.736435 | ||||||||
\(142\) | −576.000 | −0.340400 | ||||||||
\(143\) | −234.000 | −0.136840 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 2241.00 | 1.28348 | ||||||||
\(146\) | −1382.00 | −0.783391 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | −1648.00 | −0.915302 | ||||||||
\(149\) | −1602.00 | −0.880812 | −0.440406 | − | 0.897799i | \(-0.645165\pi\) | ||||
−0.440406 | + | 0.897799i | \(0.645165\pi\) | |||||||
\(150\) | 264.000 | 0.143703 | ||||||||
\(151\) | 1928.00 | 1.03906 | 0.519531 | − | 0.854451i | \(-0.326107\pi\) | ||||
0.519531 | + | 0.854451i | \(0.326107\pi\) | |||||||
\(152\) | −344.000 | −0.183566 | ||||||||
\(153\) | 540.000 | 0.285336 | ||||||||
\(154\) | −252.000 | −0.131862 | ||||||||
\(155\) | 711.000 | 0.368444 | ||||||||
\(156\) | −156.000 | −0.0800641 | ||||||||
\(157\) | 1748.00 | 0.888571 | 0.444285 | − | 0.895885i | \(-0.353458\pi\) | ||||
0.444285 | + | 0.895885i | \(0.353458\pi\) | |||||||
\(158\) | 2002.00 | 1.00804 | ||||||||
\(159\) | 711.000 | 0.354629 | ||||||||
\(160\) | −288.000 | −0.142302 | ||||||||
\(161\) | 63.0000 | 0.0308391 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 3008.00 | 1.44543 | 0.722714 | − | 0.691147i | \(-0.242894\pi\) | ||||
0.722714 | + | 0.691147i | \(0.242894\pi\) | |||||||
\(164\) | 888.000 | 0.422812 | ||||||||
\(165\) | −486.000 | −0.229303 | ||||||||
\(166\) | 78.0000 | 0.0364697 | ||||||||
\(167\) | −1767.00 | −0.818770 | −0.409385 | − | 0.912362i | \(-0.634257\pi\) | ||||
−0.409385 | + | 0.912362i | \(0.634257\pi\) | |||||||
\(168\) | −168.000 | −0.0771517 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | −1080.00 | −0.487248 | ||||||||
\(171\) | −387.000 | −0.173068 | ||||||||
\(172\) | −1180.00 | −0.523106 | ||||||||
\(173\) | 96.0000 | 0.0421893 | 0.0210946 | − | 0.999777i | \(-0.493285\pi\) | ||||
0.0210946 | + | 0.999777i | \(0.493285\pi\) | |||||||
\(174\) | 1494.00 | 0.650919 | ||||||||
\(175\) | −308.000 | −0.133043 | ||||||||
\(176\) | −288.000 | −0.123346 | ||||||||
\(177\) | 1152.00 | 0.489207 | ||||||||
\(178\) | −678.000 | −0.285496 | ||||||||
\(179\) | 3345.00 | 1.39674 | 0.698372 | − | 0.715735i | \(-0.253908\pi\) | ||||
0.698372 | + | 0.715735i | \(0.253908\pi\) | |||||||
\(180\) | −324.000 | −0.134164 | ||||||||
\(181\) | 2378.00 | 0.976549 | 0.488274 | − | 0.872690i | \(-0.337627\pi\) | ||||
0.488274 | + | 0.872690i | \(0.337627\pi\) | |||||||
\(182\) | 182.000 | 0.0741249 | ||||||||
\(183\) | 1398.00 | 0.564717 | ||||||||
\(184\) | 72.0000 | 0.0288473 | ||||||||
\(185\) | 3708.00 | 1.47361 | ||||||||
\(186\) | 474.000 | 0.186857 | ||||||||
\(187\) | −1080.00 | −0.422339 | ||||||||
\(188\) | 1644.00 | 0.637771 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 774.000 | 0.295536 | ||||||||
\(191\) | −768.000 | −0.290945 | −0.145473 | − | 0.989362i | \(-0.546470\pi\) | ||||
−0.145473 | + | 0.989362i | \(0.546470\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | −3202.00 | −1.19422 | −0.597111 | − | 0.802158i | \(-0.703685\pi\) | ||||
−0.597111 | + | 0.802158i | \(0.703685\pi\) | |||||||
\(194\) | 1426.00 | 0.527736 | ||||||||
\(195\) | 351.000 | 0.128901 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −774.000 | −0.279925 | −0.139962 | − | 0.990157i | \(-0.544698\pi\) | ||||
−0.139962 | + | 0.990157i | \(0.544698\pi\) | |||||||
\(198\) | −324.000 | −0.116291 | ||||||||
\(199\) | −1060.00 | −0.377595 | −0.188798 | − | 0.982016i | \(-0.560459\pi\) | ||||
−0.188798 | + | 0.982016i | \(0.560459\pi\) | |||||||
\(200\) | −352.000 | −0.124451 | ||||||||
\(201\) | 3126.00 | 1.09697 | ||||||||
\(202\) | 1620.00 | 0.564271 | ||||||||
\(203\) | −1743.00 | −0.602634 | ||||||||
\(204\) | −720.000 | −0.247108 | ||||||||
\(205\) | −1998.00 | −0.680714 | ||||||||
\(206\) | −2912.00 | −0.984896 | ||||||||
\(207\) | 81.0000 | 0.0271975 | ||||||||
\(208\) | 208.000 | 0.0693375 | ||||||||
\(209\) | 774.000 | 0.256166 | ||||||||
\(210\) | 378.000 | 0.124212 | ||||||||
\(211\) | 2189.00 | 0.714204 | 0.357102 | − | 0.934065i | \(-0.383765\pi\) | ||||
0.357102 | + | 0.934065i | \(0.383765\pi\) | |||||||
\(212\) | −948.000 | −0.307117 | ||||||||
\(213\) | 864.000 | 0.277936 | ||||||||
\(214\) | −1848.00 | −0.590312 | ||||||||
\(215\) | 2655.00 | 0.842184 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −553.000 | −0.172996 | ||||||||
\(218\) | 2308.00 | 0.717053 | ||||||||
\(219\) | 2073.00 | 0.639636 | ||||||||
\(220\) | 648.000 | 0.198583 | ||||||||
\(221\) | 780.000 | 0.237414 | ||||||||
\(222\) | 2472.00 | 0.747341 | ||||||||
\(223\) | 2891.00 | 0.868142 | 0.434071 | − | 0.900879i | \(-0.357077\pi\) | ||||
0.434071 | + | 0.900879i | \(0.357077\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | −396.000 | −0.117333 | ||||||||
\(226\) | 3450.00 | 1.01545 | ||||||||
\(227\) | 3132.00 | 0.915763 | 0.457881 | − | 0.889013i | \(-0.348608\pi\) | ||||
0.457881 | + | 0.889013i | \(0.348608\pi\) | |||||||
\(228\) | 516.000 | 0.149881 | ||||||||
\(229\) | −1150.00 | −0.331852 | −0.165926 | − | 0.986138i | \(-0.553061\pi\) | ||||
−0.165926 | + | 0.986138i | \(0.553061\pi\) | |||||||
\(230\) | −162.000 | −0.0464433 | ||||||||
\(231\) | 378.000 | 0.107665 | ||||||||
\(232\) | −1992.00 | −0.563712 | ||||||||
\(233\) | 2847.00 | 0.800486 | 0.400243 | − | 0.916409i | \(-0.368926\pi\) | ||||
0.400243 | + | 0.916409i | \(0.368926\pi\) | |||||||
\(234\) | 234.000 | 0.0653720 | ||||||||
\(235\) | −3699.00 | −1.02679 | ||||||||
\(236\) | −1536.00 | −0.423666 | ||||||||
\(237\) | −3003.00 | −0.823062 | ||||||||
\(238\) | 840.000 | 0.228778 | ||||||||
\(239\) | 2220.00 | 0.600836 | 0.300418 | − | 0.953808i | \(-0.402874\pi\) | ||||
0.300418 | + | 0.953808i | \(0.402874\pi\) | |||||||
\(240\) | 432.000 | 0.116190 | ||||||||
\(241\) | −6703.00 | −1.79161 | −0.895805 | − | 0.444447i | \(-0.853400\pi\) | ||||
−0.895805 | + | 0.444447i | \(0.853400\pi\) | |||||||
\(242\) | −2014.00 | −0.534979 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −1864.00 | −0.489059 | ||||||||
\(245\) | −441.000 | −0.114998 | ||||||||
\(246\) | −1332.00 | −0.345224 | ||||||||
\(247\) | −559.000 | −0.144001 | ||||||||
\(248\) | −632.000 | −0.161823 | ||||||||
\(249\) | −117.000 | −0.0297774 | ||||||||
\(250\) | 3042.00 | 0.769572 | ||||||||
\(251\) | 4770.00 | 1.19952 | 0.599760 | − | 0.800180i | \(-0.295263\pi\) | ||||
0.599760 | + | 0.800180i | \(0.295263\pi\) | |||||||
\(252\) | 252.000 | 0.0629941 | ||||||||
\(253\) | −162.000 | −0.0402563 | ||||||||
\(254\) | −2408.00 | −0.594848 | ||||||||
\(255\) | 1620.00 | 0.397837 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1062.00 | −0.257766 | −0.128883 | − | 0.991660i | \(-0.541139\pi\) | ||||
−0.128883 | + | 0.991660i | \(0.541139\pi\) | |||||||
\(258\) | 1770.00 | 0.427114 | ||||||||
\(259\) | −2884.00 | −0.691904 | ||||||||
\(260\) | −468.000 | −0.111631 | ||||||||
\(261\) | −2241.00 | −0.531473 | ||||||||
\(262\) | 1656.00 | 0.390489 | ||||||||
\(263\) | 5283.00 | 1.23865 | 0.619323 | − | 0.785137i | \(-0.287407\pi\) | ||||
0.619323 | + | 0.785137i | \(0.287407\pi\) | |||||||
\(264\) | 432.000 | 0.100711 | ||||||||
\(265\) | 2133.00 | 0.494450 | ||||||||
\(266\) | −602.000 | −0.138763 | ||||||||
\(267\) | 1017.00 | 0.233106 | ||||||||
\(268\) | −4168.00 | −0.950004 | ||||||||
\(269\) | −6672.00 | −1.51226 | −0.756132 | − | 0.654419i | \(-0.772913\pi\) | ||||
−0.756132 | + | 0.654419i | \(0.772913\pi\) | |||||||
\(270\) | 486.000 | 0.109545 | ||||||||
\(271\) | −5992.00 | −1.34313 | −0.671565 | − | 0.740946i | \(-0.734377\pi\) | ||||
−0.671565 | + | 0.740946i | \(0.734377\pi\) | |||||||
\(272\) | 960.000 | 0.214002 | ||||||||
\(273\) | −273.000 | −0.0605228 | ||||||||
\(274\) | −5328.00 | −1.17473 | ||||||||
\(275\) | 792.000 | 0.173671 | ||||||||
\(276\) | −108.000 | −0.0235538 | ||||||||
\(277\) | −5731.00 | −1.24311 | −0.621557 | − | 0.783369i | \(-0.713499\pi\) | ||||
−0.621557 | + | 0.783369i | \(0.713499\pi\) | |||||||
\(278\) | −644.000 | −0.138937 | ||||||||
\(279\) | −711.000 | −0.152568 | ||||||||
\(280\) | −504.000 | −0.107571 | ||||||||
\(281\) | 6402.00 | 1.35911 | 0.679557 | − | 0.733622i | \(-0.262172\pi\) | ||||
0.679557 | + | 0.733622i | \(0.262172\pi\) | |||||||
\(282\) | −2466.00 | −0.520738 | ||||||||
\(283\) | 7796.00 | 1.63754 | 0.818770 | − | 0.574121i | \(-0.194656\pi\) | ||||
0.818770 | + | 0.574121i | \(0.194656\pi\) | |||||||
\(284\) | −1152.00 | −0.240699 | ||||||||
\(285\) | −1161.00 | −0.241304 | ||||||||
\(286\) | −468.000 | −0.0967602 | ||||||||
\(287\) | 1554.00 | 0.319616 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −1313.00 | −0.267250 | ||||||||
\(290\) | 4482.00 | 0.907559 | ||||||||
\(291\) | −2139.00 | −0.430895 | ||||||||
\(292\) | −2764.00 | −0.553941 | ||||||||
\(293\) | 6279.00 | 1.25196 | 0.625978 | − | 0.779841i | \(-0.284700\pi\) | ||||
0.625978 | + | 0.779841i | \(0.284700\pi\) | |||||||
\(294\) | −294.000 | −0.0583212 | ||||||||
\(295\) | 3456.00 | 0.682088 | ||||||||
\(296\) | −3296.00 | −0.647217 | ||||||||
\(297\) | 486.000 | 0.0949514 | ||||||||
\(298\) | −3204.00 | −0.622828 | ||||||||
\(299\) | 117.000 | 0.0226297 | ||||||||
\(300\) | 528.000 | 0.101614 | ||||||||
\(301\) | −2065.00 | −0.395431 | ||||||||
\(302\) | 3856.00 | 0.734728 | ||||||||
\(303\) | −2430.00 | −0.460726 | ||||||||
\(304\) | −688.000 | −0.129801 | ||||||||
\(305\) | 4194.00 | 0.787370 | ||||||||
\(306\) | 1080.00 | 0.201763 | ||||||||
\(307\) | −1681.00 | −0.312507 | −0.156254 | − | 0.987717i | \(-0.549942\pi\) | ||||
−0.156254 | + | 0.987717i | \(0.549942\pi\) | |||||||
\(308\) | −504.000 | −0.0932405 | ||||||||
\(309\) | 4368.00 | 0.804165 | ||||||||
\(310\) | 1422.00 | 0.260530 | ||||||||
\(311\) | −1770.00 | −0.322725 | −0.161363 | − | 0.986895i | \(-0.551589\pi\) | ||||
−0.161363 | + | 0.986895i | \(0.551589\pi\) | |||||||
\(312\) | −312.000 | −0.0566139 | ||||||||
\(313\) | −4426.00 | −0.799273 | −0.399636 | − | 0.916674i | \(-0.630864\pi\) | ||||
−0.399636 | + | 0.916674i | \(0.630864\pi\) | |||||||
\(314\) | 3496.00 | 0.628314 | ||||||||
\(315\) | −567.000 | −0.101419 | ||||||||
\(316\) | 4004.00 | 0.712793 | ||||||||
\(317\) | −5592.00 | −0.990782 | −0.495391 | − | 0.868670i | \(-0.664975\pi\) | ||||
−0.495391 | + | 0.868670i | \(0.664975\pi\) | |||||||
\(318\) | 1422.00 | 0.250760 | ||||||||
\(319\) | 4482.00 | 0.786658 | ||||||||
\(320\) | −576.000 | −0.100623 | ||||||||
\(321\) | 2772.00 | 0.481987 | ||||||||
\(322\) | 126.000 | 0.0218065 | ||||||||
\(323\) | −2580.00 | −0.444443 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −572.000 | −0.0976272 | ||||||||
\(326\) | 6016.00 | 1.02207 | ||||||||
\(327\) | −3462.00 | −0.585471 | ||||||||
\(328\) | 1776.00 | 0.298973 | ||||||||
\(329\) | 2877.00 | 0.482110 | ||||||||
\(330\) | −972.000 | −0.162142 | ||||||||
\(331\) | −5938.00 | −0.986048 | −0.493024 | − | 0.870016i | \(-0.664109\pi\) | ||||
−0.493024 | + | 0.870016i | \(0.664109\pi\) | |||||||
\(332\) | 156.000 | 0.0257880 | ||||||||
\(333\) | −3708.00 | −0.610202 | ||||||||
\(334\) | −3534.00 | −0.578958 | ||||||||
\(335\) | 9378.00 | 1.52948 | ||||||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | 641.000 | 0.103613 | 0.0518064 | − | 0.998657i | \(-0.483502\pi\) | ||||
0.0518064 | + | 0.998657i | \(0.483502\pi\) | |||||||
\(338\) | 338.000 | 0.0543928 | ||||||||
\(339\) | −5175.00 | −0.829107 | ||||||||
\(340\) | −2160.00 | −0.344537 | ||||||||
\(341\) | 1422.00 | 0.225823 | ||||||||
\(342\) | −774.000 | −0.122378 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −2360.00 | −0.369891 | ||||||||
\(345\) | 243.000 | 0.0379208 | ||||||||
\(346\) | 192.000 | 0.0298323 | ||||||||
\(347\) | 5736.00 | 0.887391 | 0.443695 | − | 0.896178i | \(-0.353667\pi\) | ||||
0.443695 | + | 0.896178i | \(0.353667\pi\) | |||||||
\(348\) | 2988.00 | 0.460269 | ||||||||
\(349\) | −3535.00 | −0.542190 | −0.271095 | − | 0.962553i | \(-0.587386\pi\) | ||||
−0.271095 | + | 0.962553i | \(0.587386\pi\) | |||||||
\(350\) | −616.000 | −0.0940760 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | −576.000 | −0.0872185 | ||||||||
\(353\) | −3870.00 | −0.583511 | −0.291755 | − | 0.956493i | \(-0.594239\pi\) | ||||
−0.291755 | + | 0.956493i | \(0.594239\pi\) | |||||||
\(354\) | 2304.00 | 0.345922 | ||||||||
\(355\) | 2592.00 | 0.387519 | ||||||||
\(356\) | −1356.00 | −0.201876 | ||||||||
\(357\) | −1260.00 | −0.186796 | ||||||||
\(358\) | 6690.00 | 0.987647 | ||||||||
\(359\) | 7572.00 | 1.11319 | 0.556595 | − | 0.830784i | \(-0.312108\pi\) | ||||
0.556595 | + | 0.830784i | \(0.312108\pi\) | |||||||
\(360\) | −648.000 | −0.0948683 | ||||||||
\(361\) | −5010.00 | −0.730427 | ||||||||
\(362\) | 4756.00 | 0.690524 | ||||||||
\(363\) | 3021.00 | 0.436808 | ||||||||
\(364\) | 364.000 | 0.0524142 | ||||||||
\(365\) | 6219.00 | 0.891828 | ||||||||
\(366\) | 2796.00 | 0.399315 | ||||||||
\(367\) | 3206.00 | 0.456000 | 0.228000 | − | 0.973661i | \(-0.426781\pi\) | ||||
0.228000 | + | 0.973661i | \(0.426781\pi\) | |||||||
\(368\) | 144.000 | 0.0203981 | ||||||||
\(369\) | 1998.00 | 0.281875 | ||||||||
\(370\) | 7416.00 | 1.04200 | ||||||||
\(371\) | −1659.00 | −0.232159 | ||||||||
\(372\) | 948.000 | 0.132128 | ||||||||
\(373\) | −9034.00 | −1.25406 | −0.627028 | − | 0.778997i | \(-0.715729\pi\) | ||||
−0.627028 | + | 0.778997i | \(0.715729\pi\) | |||||||
\(374\) | −2160.00 | −0.298639 | ||||||||
\(375\) | −4563.00 | −0.628353 | ||||||||
\(376\) | 3288.00 | 0.450972 | ||||||||
\(377\) | −3237.00 | −0.442212 | ||||||||
\(378\) | −378.000 | −0.0514344 | ||||||||
\(379\) | 8570.00 | 1.16151 | 0.580754 | − | 0.814079i | \(-0.302758\pi\) | ||||
0.580754 | + | 0.814079i | \(0.302758\pi\) | |||||||
\(380\) | 1548.00 | 0.208976 | ||||||||
\(381\) | 3612.00 | 0.485691 | ||||||||
\(382\) | −1536.00 | −0.205729 | ||||||||
\(383\) | 10836.0 | 1.44568 | 0.722838 | − | 0.691018i | \(-0.242837\pi\) | ||||
0.722838 | + | 0.691018i | \(0.242837\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 1134.00 | 0.150114 | ||||||||
\(386\) | −6404.00 | −0.844443 | ||||||||
\(387\) | −2655.00 | −0.348737 | ||||||||
\(388\) | 2852.00 | 0.373166 | ||||||||
\(389\) | −6282.00 | −0.818792 | −0.409396 | − | 0.912357i | \(-0.634261\pi\) | ||||
−0.409396 | + | 0.912357i | \(0.634261\pi\) | |||||||
\(390\) | 702.000 | 0.0911465 | ||||||||
\(391\) | 540.000 | 0.0698439 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | −2484.00 | −0.318833 | ||||||||
\(394\) | −1548.00 | −0.197937 | ||||||||
\(395\) | −9009.00 | −1.14757 | ||||||||
\(396\) | −648.000 | −0.0822304 | ||||||||
\(397\) | 4745.00 | 0.599861 | 0.299930 | − | 0.953961i | \(-0.403037\pi\) | ||||
0.299930 | + | 0.953961i | \(0.403037\pi\) | |||||||
\(398\) | −2120.00 | −0.267000 | ||||||||
\(399\) | 903.000 | 0.113300 | ||||||||
\(400\) | −704.000 | −0.0880000 | ||||||||
\(401\) | −5328.00 | −0.663510 | −0.331755 | − | 0.943366i | \(-0.607641\pi\) | ||||
−0.331755 | + | 0.943366i | \(0.607641\pi\) | |||||||
\(402\) | 6252.00 | 0.775675 | ||||||||
\(403\) | −1027.00 | −0.126944 | ||||||||
\(404\) | 3240.00 | 0.399000 | ||||||||
\(405\) | −729.000 | −0.0894427 | ||||||||
\(406\) | −3486.00 | −0.426126 | ||||||||
\(407\) | 7416.00 | 0.903188 | ||||||||
\(408\) | −1440.00 | −0.174732 | ||||||||
\(409\) | −13795.0 | −1.66777 | −0.833886 | − | 0.551937i | \(-0.813889\pi\) | ||||
−0.833886 | + | 0.551937i | \(0.813889\pi\) | |||||||
\(410\) | −3996.00 | −0.481337 | ||||||||
\(411\) | 7992.00 | 0.959164 | ||||||||
\(412\) | −5824.00 | −0.696427 | ||||||||
\(413\) | −2688.00 | −0.320261 | ||||||||
\(414\) | 162.000 | 0.0192316 | ||||||||
\(415\) | −351.000 | −0.0415179 | ||||||||
\(416\) | 416.000 | 0.0490290 | ||||||||
\(417\) | 966.000 | 0.113442 | ||||||||
\(418\) | 1548.00 | 0.181137 | ||||||||
\(419\) | 4398.00 | 0.512784 | 0.256392 | − | 0.966573i | \(-0.417466\pi\) | ||||
0.256392 | + | 0.966573i | \(0.417466\pi\) | |||||||
\(420\) | 756.000 | 0.0878310 | ||||||||
\(421\) | −484.000 | −0.0560302 | −0.0280151 | − | 0.999607i | \(-0.508919\pi\) | ||||
−0.0280151 | + | 0.999607i | \(0.508919\pi\) | |||||||
\(422\) | 4378.00 | 0.505018 | ||||||||
\(423\) | 3699.00 | 0.425181 | ||||||||
\(424\) | −1896.00 | −0.217165 | ||||||||
\(425\) | −2640.00 | −0.301315 | ||||||||
\(426\) | 1728.00 | 0.196530 | ||||||||
\(427\) | −3262.00 | −0.369694 | ||||||||
\(428\) | −3696.00 | −0.417413 | ||||||||
\(429\) | 702.000 | 0.0790044 | ||||||||
\(430\) | 5310.00 | 0.595514 | ||||||||
\(431\) | −3414.00 | −0.381547 | −0.190773 | − | 0.981634i | \(-0.561100\pi\) | ||||
−0.190773 | + | 0.981634i | \(0.561100\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | 812.000 | 0.0901206 | 0.0450603 | − | 0.998984i | \(-0.485652\pi\) | ||||
0.0450603 | + | 0.998984i | \(0.485652\pi\) | |||||||
\(434\) | −1106.00 | −0.122326 | ||||||||
\(435\) | −6723.00 | −0.741019 | ||||||||
\(436\) | 4616.00 | 0.507033 | ||||||||
\(437\) | −387.000 | −0.0423632 | ||||||||
\(438\) | 4146.00 | 0.452291 | ||||||||
\(439\) | 7778.00 | 0.845612 | 0.422806 | − | 0.906220i | \(-0.361045\pi\) | ||||
0.422806 | + | 0.906220i | \(0.361045\pi\) | |||||||
\(440\) | 1296.00 | 0.140419 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 1560.00 | 0.167877 | ||||||||
\(443\) | −6987.00 | −0.749351 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(444\) | 4944.00 | 0.528450 | ||||||||
\(445\) | 3051.00 | 0.325014 | ||||||||
\(446\) | 5782.00 | 0.613869 | ||||||||
\(447\) | 4806.00 | 0.508537 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | 16344.0 | 1.71786 | 0.858932 | − | 0.512089i | \(-0.171128\pi\) | ||||
0.858932 | + | 0.512089i | \(0.171128\pi\) | |||||||
\(450\) | −792.000 | −0.0829672 | ||||||||
\(451\) | −3996.00 | −0.417216 | ||||||||
\(452\) | 6900.00 | 0.718028 | ||||||||
\(453\) | −5784.00 | −0.599903 | ||||||||
\(454\) | 6264.00 | 0.647542 | ||||||||
\(455\) | −819.000 | −0.0843853 | ||||||||
\(456\) | 1032.00 | 0.105982 | ||||||||
\(457\) | −17116.0 | −1.75198 | −0.875988 | − | 0.482334i | \(-0.839789\pi\) | ||||
−0.875988 | + | 0.482334i | \(0.839789\pi\) | |||||||
\(458\) | −2300.00 | −0.234655 | ||||||||
\(459\) | −1620.00 | −0.164739 | ||||||||
\(460\) | −324.000 | −0.0328404 | ||||||||
\(461\) | −6882.00 | −0.695286 | −0.347643 | − | 0.937627i | \(-0.613018\pi\) | ||||
−0.347643 | + | 0.937627i | \(0.613018\pi\) | |||||||
\(462\) | 756.000 | 0.0761305 | ||||||||
\(463\) | 3854.00 | 0.386848 | 0.193424 | − | 0.981115i | \(-0.438041\pi\) | ||||
0.193424 | + | 0.981115i | \(0.438041\pi\) | |||||||
\(464\) | −3984.00 | −0.398605 | ||||||||
\(465\) | −2133.00 | −0.212722 | ||||||||
\(466\) | 5694.00 | 0.566029 | ||||||||
\(467\) | 1830.00 | 0.181333 | 0.0906663 | − | 0.995881i | \(-0.471100\pi\) | ||||
0.0906663 | + | 0.995881i | \(0.471100\pi\) | |||||||
\(468\) | 468.000 | 0.0462250 | ||||||||
\(469\) | −7294.00 | −0.718136 | ||||||||
\(470\) | −7398.00 | −0.726052 | ||||||||
\(471\) | −5244.00 | −0.513016 | ||||||||
\(472\) | −3072.00 | −0.299577 | ||||||||
\(473\) | 5310.00 | 0.516182 | ||||||||
\(474\) | −6006.00 | −0.581993 | ||||||||
\(475\) | 1892.00 | 0.182760 | ||||||||
\(476\) | 1680.00 | 0.161770 | ||||||||
\(477\) | −2133.00 | −0.204745 | ||||||||
\(478\) | 4440.00 | 0.424855 | ||||||||
\(479\) | −12663.0 | −1.20791 | −0.603953 | − | 0.797020i | \(-0.706409\pi\) | ||||
−0.603953 | + | 0.797020i | \(0.706409\pi\) | |||||||
\(480\) | 864.000 | 0.0821584 | ||||||||
\(481\) | −5356.00 | −0.507718 | ||||||||
\(482\) | −13406.0 | −1.26686 | ||||||||
\(483\) | −189.000 | −0.0178050 | ||||||||
\(484\) | −4028.00 | −0.378287 | ||||||||
\(485\) | −6417.00 | −0.600785 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | −5578.00 | −0.519021 | −0.259511 | − | 0.965740i | \(-0.583561\pi\) | ||||
−0.259511 | + | 0.965740i | \(0.583561\pi\) | |||||||
\(488\) | −3728.00 | −0.345817 | ||||||||
\(489\) | −9024.00 | −0.834518 | ||||||||
\(490\) | −882.000 | −0.0813157 | ||||||||
\(491\) | −17724.0 | −1.62907 | −0.814535 | − | 0.580115i | \(-0.803008\pi\) | ||||
−0.814535 | + | 0.580115i | \(0.803008\pi\) | |||||||
\(492\) | −2664.00 | −0.244111 | ||||||||
\(493\) | −14940.0 | −1.36484 | ||||||||
\(494\) | −1118.00 | −0.101824 | ||||||||
\(495\) | 1458.00 | 0.132388 | ||||||||
\(496\) | −1264.00 | −0.114426 | ||||||||
\(497\) | −2016.00 | −0.181952 | ||||||||
\(498\) | −234.000 | −0.0210558 | ||||||||
\(499\) | −15820.0 | −1.41924 | −0.709620 | − | 0.704585i | \(-0.751133\pi\) | ||||
−0.709620 | + | 0.704585i | \(0.751133\pi\) | |||||||
\(500\) | 6084.00 | 0.544170 | ||||||||
\(501\) | 5301.00 | 0.472717 | ||||||||
\(502\) | 9540.00 | 0.848189 | ||||||||
\(503\) | 414.000 | 0.0366985 | 0.0183493 | − | 0.999832i | \(-0.494159\pi\) | ||||
0.0183493 | + | 0.999832i | \(0.494159\pi\) | |||||||
\(504\) | 504.000 | 0.0445435 | ||||||||
\(505\) | −7290.00 | −0.642378 | ||||||||
\(506\) | −324.000 | −0.0284655 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | −4816.00 | −0.420621 | ||||||||
\(509\) | −1521.00 | −0.132450 | −0.0662251 | − | 0.997805i | \(-0.521096\pi\) | ||||
−0.0662251 | + | 0.997805i | \(0.521096\pi\) | |||||||
\(510\) | 3240.00 | 0.281313 | ||||||||
\(511\) | −4837.00 | −0.418740 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 1161.00 | 0.0999209 | ||||||||
\(514\) | −2124.00 | −0.182268 | ||||||||
\(515\) | 13104.0 | 1.12123 | ||||||||
\(516\) | 3540.00 | 0.302015 | ||||||||
\(517\) | −7398.00 | −0.629330 | ||||||||
\(518\) | −5768.00 | −0.489250 | ||||||||
\(519\) | −288.000 | −0.0243580 | ||||||||
\(520\) | −936.000 | −0.0789352 | ||||||||
\(521\) | 2436.00 | 0.204843 | 0.102421 | − | 0.994741i | \(-0.467341\pi\) | ||||
0.102421 | + | 0.994741i | \(0.467341\pi\) | |||||||
\(522\) | −4482.00 | −0.375808 | ||||||||
\(523\) | 13178.0 | 1.10179 | 0.550893 | − | 0.834576i | \(-0.314287\pi\) | ||||
0.550893 | + | 0.834576i | \(0.314287\pi\) | |||||||
\(524\) | 3312.00 | 0.276117 | ||||||||
\(525\) | 924.000 | 0.0768127 | ||||||||
\(526\) | 10566.0 | 0.875855 | ||||||||
\(527\) | −4740.00 | −0.391798 | ||||||||
\(528\) | 864.000 | 0.0712136 | ||||||||
\(529\) | −12086.0 | −0.993343 | ||||||||
\(530\) | 4266.00 | 0.349629 | ||||||||
\(531\) | −3456.00 | −0.282444 | ||||||||
\(532\) | −1204.00 | −0.0981203 | ||||||||
\(533\) | 2886.00 | 0.234534 | ||||||||
\(534\) | 2034.00 | 0.164831 | ||||||||
\(535\) | 8316.00 | 0.672022 | ||||||||
\(536\) | −8336.00 | −0.671754 | ||||||||
\(537\) | −10035.0 | −0.806410 | ||||||||
\(538\) | −13344.0 | −1.06933 | ||||||||
\(539\) | −882.000 | −0.0704832 | ||||||||
\(540\) | 972.000 | 0.0774597 | ||||||||
\(541\) | 13700.0 | 1.08874 | 0.544371 | − | 0.838845i | \(-0.316769\pi\) | ||||
0.544371 | + | 0.838845i | \(0.316769\pi\) | |||||||
\(542\) | −11984.0 | −0.949736 | ||||||||
\(543\) | −7134.00 | −0.563811 | ||||||||
\(544\) | 1920.00 | 0.151322 | ||||||||
\(545\) | −10386.0 | −0.816307 | ||||||||
\(546\) | −546.000 | −0.0427960 | ||||||||
\(547\) | −6649.00 | −0.519727 | −0.259864 | − | 0.965645i | \(-0.583678\pi\) | ||||
−0.259864 | + | 0.965645i | \(0.583678\pi\) | |||||||
\(548\) | −10656.0 | −0.830660 | ||||||||
\(549\) | −4194.00 | −0.326039 | ||||||||
\(550\) | 1584.00 | 0.122804 | ||||||||
\(551\) | 10707.0 | 0.827829 | ||||||||
\(552\) | −216.000 | −0.0166550 | ||||||||
\(553\) | 7007.00 | 0.538821 | ||||||||
\(554\) | −11462.0 | −0.879014 | ||||||||
\(555\) | −11124.0 | −0.850788 | ||||||||
\(556\) | −1288.00 | −0.0982435 | ||||||||
\(557\) | −1272.00 | −0.0967619 | −0.0483809 | − | 0.998829i | \(-0.515406\pi\) | ||||
−0.0483809 | + | 0.998829i | \(0.515406\pi\) | |||||||
\(558\) | −1422.00 | −0.107882 | ||||||||
\(559\) | −3835.00 | −0.290167 | ||||||||
\(560\) | −1008.00 | −0.0760639 | ||||||||
\(561\) | 3240.00 | 0.243838 | ||||||||
\(562\) | 12804.0 | 0.961039 | ||||||||
\(563\) | −17052.0 | −1.27648 | −0.638238 | − | 0.769839i | \(-0.720336\pi\) | ||||
−0.638238 | + | 0.769839i | \(0.720336\pi\) | |||||||
\(564\) | −4932.00 | −0.368217 | ||||||||
\(565\) | −15525.0 | −1.15600 | ||||||||
\(566\) | 15592.0 | 1.15792 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | −2304.00 | −0.170200 | ||||||||
\(569\) | −19713.0 | −1.45239 | −0.726197 | − | 0.687487i | \(-0.758714\pi\) | ||||
−0.726197 | + | 0.687487i | \(0.758714\pi\) | |||||||
\(570\) | −2322.00 | −0.170628 | ||||||||
\(571\) | 16625.0 | 1.21845 | 0.609225 | − | 0.792998i | \(-0.291481\pi\) | ||||
0.609225 | + | 0.792998i | \(0.291481\pi\) | |||||||
\(572\) | −936.000 | −0.0684198 | ||||||||
\(573\) | 2304.00 | 0.167977 | ||||||||
\(574\) | 3108.00 | 0.226002 | ||||||||
\(575\) | −396.000 | −0.0287206 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −7234.00 | −0.521933 | −0.260967 | − | 0.965348i | \(-0.584041\pi\) | ||||
−0.260967 | + | 0.965348i | \(0.584041\pi\) | |||||||
\(578\) | −2626.00 | −0.188974 | ||||||||
\(579\) | 9606.00 | 0.689485 | ||||||||
\(580\) | 8964.00 | 0.641741 | ||||||||
\(581\) | 273.000 | 0.0194939 | ||||||||
\(582\) | −4278.00 | −0.304689 | ||||||||
\(583\) | 4266.00 | 0.303053 | ||||||||
\(584\) | −5528.00 | −0.391696 | ||||||||
\(585\) | −1053.00 | −0.0744208 | ||||||||
\(586\) | 12558.0 | 0.885267 | ||||||||
\(587\) | −7737.00 | −0.544021 | −0.272010 | − | 0.962294i | \(-0.587689\pi\) | ||||
−0.272010 | + | 0.962294i | \(0.587689\pi\) | |||||||
\(588\) | −588.000 | −0.0412393 | ||||||||
\(589\) | 3397.00 | 0.237642 | ||||||||
\(590\) | 6912.00 | 0.482309 | ||||||||
\(591\) | 2322.00 | 0.161615 | ||||||||
\(592\) | −6592.00 | −0.457651 | ||||||||
\(593\) | 18723.0 | 1.29656 | 0.648281 | − | 0.761401i | \(-0.275488\pi\) | ||||
0.648281 | + | 0.761401i | \(0.275488\pi\) | |||||||
\(594\) | 972.000 | 0.0671408 | ||||||||
\(595\) | −3780.00 | −0.260445 | ||||||||
\(596\) | −6408.00 | −0.440406 | ||||||||
\(597\) | 3180.00 | 0.218005 | ||||||||
\(598\) | 234.000 | 0.0160016 | ||||||||
\(599\) | −24855.0 | −1.69541 | −0.847703 | − | 0.530472i | \(-0.822015\pi\) | ||||
−0.847703 | + | 0.530472i | \(0.822015\pi\) | |||||||
\(600\) | 1056.00 | 0.0718517 | ||||||||
\(601\) | 5114.00 | 0.347096 | 0.173548 | − | 0.984825i | \(-0.444477\pi\) | ||||
0.173548 | + | 0.984825i | \(0.444477\pi\) | |||||||
\(602\) | −4130.00 | −0.279612 | ||||||||
\(603\) | −9378.00 | −0.633336 | ||||||||
\(604\) | 7712.00 | 0.519531 | ||||||||
\(605\) | 9063.00 | 0.609030 | ||||||||
\(606\) | −4860.00 | −0.325782 | ||||||||
\(607\) | 16886.0 | 1.12913 | 0.564565 | − | 0.825389i | \(-0.309044\pi\) | ||||
0.564565 | + | 0.825389i | \(0.309044\pi\) | |||||||
\(608\) | −1376.00 | −0.0917832 | ||||||||
\(609\) | 5229.00 | 0.347931 | ||||||||
\(610\) | 8388.00 | 0.556754 | ||||||||
\(611\) | 5343.00 | 0.353772 | ||||||||
\(612\) | 2160.00 | 0.142668 | ||||||||
\(613\) | 812.000 | 0.0535014 | 0.0267507 | − | 0.999642i | \(-0.491484\pi\) | ||||
0.0267507 | + | 0.999642i | \(0.491484\pi\) | |||||||
\(614\) | −3362.00 | −0.220976 | ||||||||
\(615\) | 5994.00 | 0.393010 | ||||||||
\(616\) | −1008.00 | −0.0659310 | ||||||||
\(617\) | 11094.0 | 0.723870 | 0.361935 | − | 0.932203i | \(-0.382116\pi\) | ||||
0.361935 | + | 0.932203i | \(0.382116\pi\) | |||||||
\(618\) | 8736.00 | 0.568630 | ||||||||
\(619\) | −21508.0 | −1.39657 | −0.698287 | − | 0.715818i | \(-0.746054\pi\) | ||||
−0.698287 | + | 0.715818i | \(0.746054\pi\) | |||||||
\(620\) | 2844.00 | 0.184222 | ||||||||
\(621\) | −243.000 | −0.0157025 | ||||||||
\(622\) | −3540.00 | −0.228201 | ||||||||
\(623\) | −2373.00 | −0.152604 | ||||||||
\(624\) | −624.000 | −0.0400320 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | −8852.00 | −0.565171 | ||||||||
\(627\) | −2322.00 | −0.147898 | ||||||||
\(628\) | 6992.00 | 0.444285 | ||||||||
\(629\) | −24720.0 | −1.56701 | ||||||||
\(630\) | −1134.00 | −0.0717137 | ||||||||
\(631\) | 15014.0 | 0.947223 | 0.473612 | − | 0.880734i | \(-0.342950\pi\) | ||||
0.473612 | + | 0.880734i | \(0.342950\pi\) | |||||||
\(632\) | 8008.00 | 0.504021 | ||||||||
\(633\) | −6567.00 | −0.412346 | ||||||||
\(634\) | −11184.0 | −0.700589 | ||||||||
\(635\) | 10836.0 | 0.677187 | ||||||||
\(636\) | 2844.00 | 0.177314 | ||||||||
\(637\) | 637.000 | 0.0396214 | ||||||||
\(638\) | 8964.00 | 0.556251 | ||||||||
\(639\) | −2592.00 | −0.160466 | ||||||||
\(640\) | −1152.00 | −0.0711512 | ||||||||
\(641\) | 12321.0 | 0.759205 | 0.379602 | − | 0.925150i | \(-0.376061\pi\) | ||||
0.379602 | + | 0.925150i | \(0.376061\pi\) | |||||||
\(642\) | 5544.00 | 0.340817 | ||||||||
\(643\) | 13376.0 | 0.820370 | 0.410185 | − | 0.912002i | \(-0.365464\pi\) | ||||
0.410185 | + | 0.912002i | \(0.365464\pi\) | |||||||
\(644\) | 252.000 | 0.0154196 | ||||||||
\(645\) | −7965.00 | −0.486235 | ||||||||
\(646\) | −5160.00 | −0.314269 | ||||||||
\(647\) | −15150.0 | −0.920569 | −0.460284 | − | 0.887772i | \(-0.652253\pi\) | ||||
−0.460284 | + | 0.887772i | \(0.652253\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 6912.00 | 0.418058 | ||||||||
\(650\) | −1144.00 | −0.0690329 | ||||||||
\(651\) | 1659.00 | 0.0998792 | ||||||||
\(652\) | 12032.0 | 0.722714 | ||||||||
\(653\) | −414.000 | −0.0248102 | −0.0124051 | − | 0.999923i | \(-0.503949\pi\) | ||||
−0.0124051 | + | 0.999923i | \(0.503949\pi\) | |||||||
\(654\) | −6924.00 | −0.413991 | ||||||||
\(655\) | −7452.00 | −0.444540 | ||||||||
\(656\) | 3552.00 | 0.211406 | ||||||||
\(657\) | −6219.00 | −0.369294 | ||||||||
\(658\) | 5754.00 | 0.340903 | ||||||||
\(659\) | 20631.0 | 1.21953 | 0.609765 | − | 0.792583i | \(-0.291264\pi\) | ||||
0.609765 | + | 0.792583i | \(0.291264\pi\) | |||||||
\(660\) | −1944.00 | −0.114652 | ||||||||
\(661\) | 25589.0 | 1.50574 | 0.752872 | − | 0.658167i | \(-0.228668\pi\) | ||||
0.752872 | + | 0.658167i | \(0.228668\pi\) | |||||||
\(662\) | −11876.0 | −0.697241 | ||||||||
\(663\) | −2340.00 | −0.137071 | ||||||||
\(664\) | 312.000 | 0.0182349 | ||||||||
\(665\) | 2709.00 | 0.157971 | ||||||||
\(666\) | −7416.00 | −0.431478 | ||||||||
\(667\) | −2241.00 | −0.130093 | ||||||||
\(668\) | −7068.00 | −0.409385 | ||||||||
\(669\) | −8673.00 | −0.501222 | ||||||||
\(670\) | 18756.0 | 1.08150 | ||||||||
\(671\) | 8388.00 | 0.482586 | ||||||||
\(672\) | −672.000 | −0.0385758 | ||||||||
\(673\) | 32105.0 | 1.83887 | 0.919433 | − | 0.393247i | \(-0.128648\pi\) | ||||
0.919433 | + | 0.393247i | \(0.128648\pi\) | |||||||
\(674\) | 1282.00 | 0.0732653 | ||||||||
\(675\) | 1188.00 | 0.0677424 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | 29022.0 | 1.64757 | 0.823786 | − | 0.566901i | \(-0.191858\pi\) | ||||
0.823786 | + | 0.566901i | \(0.191858\pi\) | |||||||
\(678\) | −10350.0 | −0.586267 | ||||||||
\(679\) | 4991.00 | 0.282087 | ||||||||
\(680\) | −4320.00 | −0.243624 | ||||||||
\(681\) | −9396.00 | −0.528716 | ||||||||
\(682\) | 2844.00 | 0.159681 | ||||||||
\(683\) | 18960.0 | 1.06220 | 0.531101 | − | 0.847308i | \(-0.321778\pi\) | ||||
0.531101 | + | 0.847308i | \(0.321778\pi\) | |||||||
\(684\) | −1548.00 | −0.0865340 | ||||||||
\(685\) | 23976.0 | 1.33734 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 3450.00 | 0.191595 | ||||||||
\(688\) | −4720.00 | −0.261553 | ||||||||
\(689\) | −3081.00 | −0.170358 | ||||||||
\(690\) | 486.000 | 0.0268141 | ||||||||
\(691\) | −20653.0 | −1.13701 | −0.568507 | − | 0.822678i | \(-0.692479\pi\) | ||||
−0.568507 | + | 0.822678i | \(0.692479\pi\) | |||||||
\(692\) | 384.000 | 0.0210946 | ||||||||
\(693\) | −1134.00 | −0.0621603 | ||||||||
\(694\) | 11472.0 | 0.627480 | ||||||||
\(695\) | 2898.00 | 0.158169 | ||||||||
\(696\) | 5976.00 | 0.325459 | ||||||||
\(697\) | 13320.0 | 0.723861 | ||||||||
\(698\) | −7070.00 | −0.383386 | ||||||||
\(699\) | −8541.00 | −0.462161 | ||||||||
\(700\) | −1232.00 | −0.0665217 | ||||||||
\(701\) | −33543.0 | −1.80728 | −0.903639 | − | 0.428295i | \(-0.859114\pi\) | ||||
−0.903639 | + | 0.428295i | \(0.859114\pi\) | |||||||
\(702\) | −702.000 | −0.0377426 | ||||||||
\(703\) | 17716.0 | 0.950457 | ||||||||
\(704\) | −1152.00 | −0.0616728 | ||||||||
\(705\) | 11097.0 | 0.592819 | ||||||||
\(706\) | −7740.00 | −0.412604 | ||||||||
\(707\) | 5670.00 | 0.301616 | ||||||||
\(708\) | 4608.00 | 0.244603 | ||||||||
\(709\) | 2630.00 | 0.139311 | 0.0696557 | − | 0.997571i | \(-0.477810\pi\) | ||||
0.0696557 | + | 0.997571i | \(0.477810\pi\) | |||||||
\(710\) | 5184.00 | 0.274017 | ||||||||
\(711\) | 9009.00 | 0.475195 | ||||||||
\(712\) | −2712.00 | −0.142748 | ||||||||
\(713\) | −711.000 | −0.0373452 | ||||||||
\(714\) | −2520.00 | −0.132085 | ||||||||
\(715\) | 2106.00 | 0.110154 | ||||||||
\(716\) | 13380.0 | 0.698372 | ||||||||
\(717\) | −6660.00 | −0.346893 | ||||||||
\(718\) | 15144.0 | 0.787144 | ||||||||
\(719\) | 21414.0 | 1.11072 | 0.555360 | − | 0.831610i | \(-0.312581\pi\) | ||||
0.555360 | + | 0.831610i | \(0.312581\pi\) | |||||||
\(720\) | −1296.00 | −0.0670820 | ||||||||
\(721\) | −10192.0 | −0.526449 | ||||||||
\(722\) | −10020.0 | −0.516490 | ||||||||
\(723\) | 20109.0 | 1.03439 | ||||||||
\(724\) | 9512.00 | 0.488274 | ||||||||
\(725\) | 10956.0 | 0.561235 | ||||||||
\(726\) | 6042.00 | 0.308870 | ||||||||
\(727\) | 13466.0 | 0.686969 | 0.343484 | − | 0.939158i | \(-0.388393\pi\) | ||||
0.343484 | + | 0.939158i | \(0.388393\pi\) | |||||||
\(728\) | 728.000 | 0.0370625 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 12438.0 | 0.630618 | ||||||||
\(731\) | −17700.0 | −0.895565 | ||||||||
\(732\) | 5592.00 | 0.282358 | ||||||||
\(733\) | −3895.00 | −0.196269 | −0.0981345 | − | 0.995173i | \(-0.531288\pi\) | ||||
−0.0981345 | + | 0.995173i | \(0.531288\pi\) | |||||||
\(734\) | 6412.00 | 0.322440 | ||||||||
\(735\) | 1323.00 | 0.0663940 | ||||||||
\(736\) | 288.000 | 0.0144237 | ||||||||
\(737\) | 18756.0 | 0.937430 | ||||||||
\(738\) | 3996.00 | 0.199315 | ||||||||
\(739\) | −27250.0 | −1.35644 | −0.678219 | − | 0.734860i | \(-0.737248\pi\) | ||||
−0.678219 | + | 0.734860i | \(0.737248\pi\) | |||||||
\(740\) | 14832.0 | 0.736804 | ||||||||
\(741\) | 1677.00 | 0.0831392 | ||||||||
\(742\) | −3318.00 | −0.164161 | ||||||||
\(743\) | −19632.0 | −0.969352 | −0.484676 | − | 0.874694i | \(-0.661062\pi\) | ||||
−0.484676 | + | 0.874694i | \(0.661062\pi\) | |||||||
\(744\) | 1896.00 | 0.0934284 | ||||||||
\(745\) | 14418.0 | 0.709040 | ||||||||
\(746\) | −18068.0 | −0.886751 | ||||||||
\(747\) | 351.000 | 0.0171920 | ||||||||
\(748\) | −4320.00 | −0.211170 | ||||||||
\(749\) | −6468.00 | −0.315535 | ||||||||
\(750\) | −9126.00 | −0.444313 | ||||||||
\(751\) | −3499.00 | −0.170014 | −0.0850069 | − | 0.996380i | \(-0.527091\pi\) | ||||
−0.0850069 | + | 0.996380i | \(0.527091\pi\) | |||||||
\(752\) | 6576.00 | 0.318886 | ||||||||
\(753\) | −14310.0 | −0.692544 | ||||||||
\(754\) | −6474.00 | −0.312691 | ||||||||
\(755\) | −17352.0 | −0.836429 | ||||||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | 10469.0 | 0.502645 | 0.251323 | − | 0.967903i | \(-0.419135\pi\) | ||||
0.251323 | + | 0.967903i | \(0.419135\pi\) | |||||||
\(758\) | 17140.0 | 0.821310 | ||||||||
\(759\) | 486.000 | 0.0232420 | ||||||||
\(760\) | 3096.00 | 0.147768 | ||||||||
\(761\) | 5607.00 | 0.267088 | 0.133544 | − | 0.991043i | \(-0.457364\pi\) | ||||
0.133544 | + | 0.991043i | \(0.457364\pi\) | |||||||
\(762\) | 7224.00 | 0.343436 | ||||||||
\(763\) | 8078.00 | 0.383281 | ||||||||
\(764\) | −3072.00 | −0.145473 | ||||||||
\(765\) | −4860.00 | −0.229691 | ||||||||
\(766\) | 21672.0 | 1.02225 | ||||||||
\(767\) | −4992.00 | −0.235007 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 14843.0 | 0.696037 | 0.348018 | − | 0.937488i | \(-0.386855\pi\) | ||||
0.348018 | + | 0.937488i | \(0.386855\pi\) | |||||||
\(770\) | 2268.00 | 0.106147 | ||||||||
\(771\) | 3186.00 | 0.148821 | ||||||||
\(772\) | −12808.0 | −0.597111 | ||||||||
\(773\) | −7518.00 | −0.349811 | −0.174905 | − | 0.984585i | \(-0.555962\pi\) | ||||
−0.174905 | + | 0.984585i | \(0.555962\pi\) | |||||||
\(774\) | −5310.00 | −0.246594 | ||||||||
\(775\) | 3476.00 | 0.161112 | ||||||||
\(776\) | 5704.00 | 0.263868 | ||||||||
\(777\) | 8652.00 | 0.399471 | ||||||||
\(778\) | −12564.0 | −0.578973 | ||||||||
\(779\) | −9546.00 | −0.439051 | ||||||||
\(780\) | 1404.00 | 0.0644503 | ||||||||
\(781\) | 5184.00 | 0.237514 | ||||||||
\(782\) | 1080.00 | 0.0493871 | ||||||||
\(783\) | 6723.00 | 0.306846 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −15732.0 | −0.715286 | ||||||||
\(786\) | −4968.00 | −0.225449 | ||||||||
\(787\) | 35813.0 | 1.62210 | 0.811052 | − | 0.584974i | \(-0.198895\pi\) | ||||
0.811052 | + | 0.584974i | \(0.198895\pi\) | |||||||
\(788\) | −3096.00 | −0.139962 | ||||||||
\(789\) | −15849.0 | −0.715132 | ||||||||
\(790\) | −18018.0 | −0.811458 | ||||||||
\(791\) | 12075.0 | 0.542778 | ||||||||
\(792\) | −1296.00 | −0.0581456 | ||||||||
\(793\) | −6058.00 | −0.271281 | ||||||||
\(794\) | 9490.00 | 0.424166 | ||||||||
\(795\) | −6399.00 | −0.285471 | ||||||||
\(796\) | −4240.00 | −0.188798 | ||||||||
\(797\) | 35718.0 | 1.58745 | 0.793724 | − | 0.608278i | \(-0.208139\pi\) | ||||
0.793724 | + | 0.608278i | \(0.208139\pi\) | |||||||
\(798\) | 1806.00 | 0.0801149 | ||||||||
\(799\) | 24660.0 | 1.09187 | ||||||||
\(800\) | −1408.00 | −0.0622254 | ||||||||
\(801\) | −3051.00 | −0.134584 | ||||||||
\(802\) | −10656.0 | −0.469173 | ||||||||
\(803\) | 12438.0 | 0.546610 | ||||||||
\(804\) | 12504.0 | 0.548485 | ||||||||
\(805\) | −567.000 | −0.0248250 | ||||||||
\(806\) | −2054.00 | −0.0897631 | ||||||||
\(807\) | 20016.0 | 0.873106 | ||||||||
\(808\) | 6480.00 | 0.282136 | ||||||||
\(809\) | 10401.0 | 0.452014 | 0.226007 | − | 0.974126i | \(-0.427433\pi\) | ||||
0.226007 | + | 0.974126i | \(0.427433\pi\) | |||||||
\(810\) | −1458.00 | −0.0632456 | ||||||||
\(811\) | 21548.0 | 0.932987 | 0.466494 | − | 0.884525i | \(-0.345517\pi\) | ||||
0.466494 | + | 0.884525i | \(0.345517\pi\) | |||||||
\(812\) | −6972.00 | −0.301317 | ||||||||
\(813\) | 17976.0 | 0.775456 | ||||||||
\(814\) | 14832.0 | 0.638650 | ||||||||
\(815\) | −27072.0 | −1.16355 | ||||||||
\(816\) | −2880.00 | −0.123554 | ||||||||
\(817\) | 12685.0 | 0.543197 | ||||||||
\(818\) | −27590.0 | −1.17929 | ||||||||
\(819\) | 819.000 | 0.0349428 | ||||||||
\(820\) | −7992.00 | −0.340357 | ||||||||
\(821\) | −7554.00 | −0.321116 | −0.160558 | − | 0.987026i | \(-0.551329\pi\) | ||||
−0.160558 | + | 0.987026i | \(0.551329\pi\) | |||||||
\(822\) | 15984.0 | 0.678231 | ||||||||
\(823\) | 13448.0 | 0.569584 | 0.284792 | − | 0.958589i | \(-0.408075\pi\) | ||||
0.284792 | + | 0.958589i | \(0.408075\pi\) | |||||||
\(824\) | −11648.0 | −0.492448 | ||||||||
\(825\) | −2376.00 | −0.100269 | ||||||||
\(826\) | −5376.00 | −0.226459 | ||||||||
\(827\) | −10728.0 | −0.451087 | −0.225544 | − | 0.974233i | \(-0.572416\pi\) | ||||
−0.225544 | + | 0.974233i | \(0.572416\pi\) | |||||||
\(828\) | 324.000 | 0.0135988 | ||||||||
\(829\) | −42190.0 | −1.76757 | −0.883787 | − | 0.467889i | \(-0.845015\pi\) | ||||
−0.883787 | + | 0.467889i | \(0.845015\pi\) | |||||||
\(830\) | −702.000 | −0.0293576 | ||||||||
\(831\) | 17193.0 | 0.717712 | ||||||||
\(832\) | 832.000 | 0.0346688 | ||||||||
\(833\) | 2940.00 | 0.122287 | ||||||||
\(834\) | 1932.00 | 0.0802155 | ||||||||
\(835\) | 15903.0 | 0.659097 | ||||||||
\(836\) | 3096.00 | 0.128083 | ||||||||
\(837\) | 2133.00 | 0.0880851 | ||||||||
\(838\) | 8796.00 | 0.362593 | ||||||||
\(839\) | −14856.0 | −0.611306 | −0.305653 | − | 0.952143i | \(-0.598875\pi\) | ||||
−0.305653 | + | 0.952143i | \(0.598875\pi\) | |||||||
\(840\) | 1512.00 | 0.0621059 | ||||||||
\(841\) | 37612.0 | 1.54217 | ||||||||
\(842\) | −968.000 | −0.0396193 | ||||||||
\(843\) | −19206.0 | −0.784685 | ||||||||
\(844\) | 8756.00 | 0.357102 | ||||||||
\(845\) | −1521.00 | −0.0619219 | ||||||||
\(846\) | 7398.00 | 0.300648 | ||||||||
\(847\) | −7049.00 | −0.285958 | ||||||||
\(848\) | −3792.00 | −0.153559 | ||||||||
\(849\) | −23388.0 | −0.945435 | ||||||||
\(850\) | −5280.00 | −0.213062 | ||||||||
\(851\) | −3708.00 | −0.149364 | ||||||||
\(852\) | 3456.00 | 0.138968 | ||||||||
\(853\) | −29185.0 | −1.17148 | −0.585742 | − | 0.810498i | \(-0.699197\pi\) | ||||
−0.585742 | + | 0.810498i | \(0.699197\pi\) | |||||||
\(854\) | −6524.00 | −0.261413 | ||||||||
\(855\) | 3483.00 | 0.139317 | ||||||||
\(856\) | −7392.00 | −0.295156 | ||||||||
\(857\) | −2178.00 | −0.0868134 | −0.0434067 | − | 0.999057i | \(-0.513821\pi\) | ||||
−0.0434067 | + | 0.999057i | \(0.513821\pi\) | |||||||
\(858\) | 1404.00 | 0.0558645 | ||||||||
\(859\) | 11702.0 | 0.464805 | 0.232402 | − | 0.972620i | \(-0.425341\pi\) | ||||
0.232402 | + | 0.972620i | \(0.425341\pi\) | |||||||
\(860\) | 10620.0 | 0.421092 | ||||||||
\(861\) | −4662.00 | −0.184530 | ||||||||
\(862\) | −6828.00 | −0.269794 | ||||||||
\(863\) | 31044.0 | 1.22451 | 0.612254 | − | 0.790661i | \(-0.290263\pi\) | ||||
0.612254 | + | 0.790661i | \(0.290263\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | −864.000 | −0.0339617 | ||||||||
\(866\) | 1624.00 | 0.0637249 | ||||||||
\(867\) | 3939.00 | 0.154297 | ||||||||
\(868\) | −2212.00 | −0.0864979 | ||||||||
\(869\) | −18018.0 | −0.703359 | ||||||||
\(870\) | −13446.0 | −0.523979 | ||||||||
\(871\) | −13546.0 | −0.526968 | ||||||||
\(872\) | 9232.00 | 0.358526 | ||||||||
\(873\) | 6417.00 | 0.248777 | ||||||||
\(874\) | −774.000 | −0.0299553 | ||||||||
\(875\) | 10647.0 | 0.411353 | ||||||||
\(876\) | 8292.00 | 0.319818 | ||||||||
\(877\) | 13700.0 | 0.527498 | 0.263749 | − | 0.964591i | \(-0.415041\pi\) | ||||
0.263749 | + | 0.964591i | \(0.415041\pi\) | |||||||
\(878\) | 15556.0 | 0.597938 | ||||||||
\(879\) | −18837.0 | −0.722817 | ||||||||
\(880\) | 2592.00 | 0.0992913 | ||||||||
\(881\) | −19710.0 | −0.753742 | −0.376871 | − | 0.926266i | \(-0.623000\pi\) | ||||
−0.376871 | + | 0.926266i | \(0.623000\pi\) | |||||||
\(882\) | 882.000 | 0.0336718 | ||||||||
\(883\) | 12476.0 | 0.475482 | 0.237741 | − | 0.971329i | \(-0.423593\pi\) | ||||
0.237741 | + | 0.971329i | \(0.423593\pi\) | |||||||
\(884\) | 3120.00 | 0.118707 | ||||||||
\(885\) | −10368.0 | −0.393804 | ||||||||
\(886\) | −13974.0 | −0.529871 | ||||||||
\(887\) | 14940.0 | 0.565542 | 0.282771 | − | 0.959187i | \(-0.408746\pi\) | ||||
0.282771 | + | 0.959187i | \(0.408746\pi\) | |||||||
\(888\) | 9888.00 | 0.373671 | ||||||||
\(889\) | −8428.00 | −0.317960 | ||||||||
\(890\) | 6102.00 | 0.229820 | ||||||||
\(891\) | −1458.00 | −0.0548202 | ||||||||
\(892\) | 11564.0 | 0.434071 | ||||||||
\(893\) | −17673.0 | −0.662267 | ||||||||
\(894\) | 9612.00 | 0.359590 | ||||||||
\(895\) | −30105.0 | −1.12436 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | −351.000 | −0.0130653 | ||||||||
\(898\) | 32688.0 | 1.21471 | ||||||||
\(899\) | 19671.0 | 0.729772 | ||||||||
\(900\) | −1584.00 | −0.0586667 | ||||||||
\(901\) | −14220.0 | −0.525790 | ||||||||
\(902\) | −7992.00 | −0.295016 | ||||||||
\(903\) | 6195.00 | 0.228302 | ||||||||
\(904\) | 13800.0 | 0.507723 | ||||||||
\(905\) | −21402.0 | −0.786107 | ||||||||
\(906\) | −11568.0 | −0.424195 | ||||||||
\(907\) | 12953.0 | 0.474198 | 0.237099 | − | 0.971486i | \(-0.423803\pi\) | ||||
0.237099 | + | 0.971486i | \(0.423803\pi\) | |||||||
\(908\) | 12528.0 | 0.457881 | ||||||||
\(909\) | 7290.00 | 0.266000 | ||||||||
\(910\) | −1638.00 | −0.0596694 | ||||||||
\(911\) | 15411.0 | 0.560471 | 0.280236 | − | 0.959931i | \(-0.409587\pi\) | ||||
0.280236 | + | 0.959931i | \(0.409587\pi\) | |||||||
\(912\) | 2064.00 | 0.0749406 | ||||||||
\(913\) | −702.000 | −0.0254467 | ||||||||
\(914\) | −34232.0 | −1.23883 | ||||||||
\(915\) | −12582.0 | −0.454588 | ||||||||
\(916\) | −4600.00 | −0.165926 | ||||||||
\(917\) | 5796.00 | 0.208725 | ||||||||
\(918\) | −3240.00 | −0.116488 | ||||||||
\(919\) | 22520.0 | 0.808342 | 0.404171 | − | 0.914683i | \(-0.367560\pi\) | ||||
0.404171 | + | 0.914683i | \(0.367560\pi\) | |||||||
\(920\) | −648.000 | −0.0232217 | ||||||||
\(921\) | 5043.00 | 0.180426 | ||||||||
\(922\) | −13764.0 | −0.491641 | ||||||||
\(923\) | −3744.00 | −0.133516 | ||||||||
\(924\) | 1512.00 | 0.0538324 | ||||||||
\(925\) | 18128.0 | 0.644373 | ||||||||
\(926\) | 7708.00 | 0.273543 | ||||||||
\(927\) | −13104.0 | −0.464285 | ||||||||
\(928\) | −7968.00 | −0.281856 | ||||||||
\(929\) | 31803.0 | 1.12317 | 0.561584 | − | 0.827420i | \(-0.310192\pi\) | ||||
0.561584 | + | 0.827420i | \(0.310192\pi\) | |||||||
\(930\) | −4266.00 | −0.150417 | ||||||||
\(931\) | −2107.00 | −0.0741720 | ||||||||
\(932\) | 11388.0 | 0.400243 | ||||||||
\(933\) | 5310.00 | 0.186325 | ||||||||
\(934\) | 3660.00 | 0.128221 | ||||||||
\(935\) | 9720.00 | 0.339976 | ||||||||
\(936\) | 936.000 | 0.0326860 | ||||||||
\(937\) | −30148.0 | −1.05111 | −0.525556 | − | 0.850759i | \(-0.676143\pi\) | ||||
−0.525556 | + | 0.850759i | \(0.676143\pi\) | |||||||
\(938\) | −14588.0 | −0.507799 | ||||||||
\(939\) | 13278.0 | 0.461460 | ||||||||
\(940\) | −14796.0 | −0.513396 | ||||||||
\(941\) | 5709.00 | 0.197777 | 0.0988885 | − | 0.995099i | \(-0.468471\pi\) | ||||
0.0988885 | + | 0.995099i | \(0.468471\pi\) | |||||||
\(942\) | −10488.0 | −0.362757 | ||||||||
\(943\) | 1998.00 | 0.0689966 | ||||||||
\(944\) | −6144.00 | −0.211833 | ||||||||
\(945\) | 1701.00 | 0.0585540 | ||||||||
\(946\) | 10620.0 | 0.364996 | ||||||||
\(947\) | −42474.0 | −1.45747 | −0.728733 | − | 0.684798i | \(-0.759890\pi\) | ||||
−0.728733 | + | 0.684798i | \(0.759890\pi\) | |||||||
\(948\) | −12012.0 | −0.411531 | ||||||||
\(949\) | −8983.00 | −0.307271 | ||||||||
\(950\) | 3784.00 | 0.129231 | ||||||||
\(951\) | 16776.0 | 0.572028 | ||||||||
\(952\) | 3360.00 | 0.114389 | ||||||||
\(953\) | 10953.0 | 0.372301 | 0.186150 | − | 0.982521i | \(-0.440399\pi\) | ||||
0.186150 | + | 0.982521i | \(0.440399\pi\) | |||||||
\(954\) | −4266.00 | −0.144777 | ||||||||
\(955\) | 6912.00 | 0.234206 | ||||||||
\(956\) | 8880.00 | 0.300418 | ||||||||
\(957\) | −13446.0 | −0.454177 | ||||||||
\(958\) | −25326.0 | −0.854119 | ||||||||
\(959\) | −18648.0 | −0.627920 | ||||||||
\(960\) | 1728.00 | 0.0580948 | ||||||||
\(961\) | −23550.0 | −0.790507 | ||||||||
\(962\) | −10712.0 | −0.359011 | ||||||||
\(963\) | −8316.00 | −0.278276 | ||||||||
\(964\) | −26812.0 | −0.895805 | ||||||||
\(965\) | 28818.0 | 0.961331 | ||||||||
\(966\) | −378.000 | −0.0125900 | ||||||||
\(967\) | −4498.00 | −0.149582 | −0.0747911 | − | 0.997199i | \(-0.523829\pi\) | ||||
−0.0747911 | + | 0.997199i | \(0.523829\pi\) | |||||||
\(968\) | −8056.00 | −0.267489 | ||||||||
\(969\) | 7740.00 | 0.256599 | ||||||||
\(970\) | −12834.0 | −0.424819 | ||||||||
\(971\) | 42978.0 | 1.42042 | 0.710211 | − | 0.703989i | \(-0.248600\pi\) | ||||
0.710211 | + | 0.703989i | \(0.248600\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | −2254.00 | −0.0742651 | ||||||||
\(974\) | −11156.0 | −0.367003 | ||||||||
\(975\) | 1716.00 | 0.0563651 | ||||||||
\(976\) | −7456.00 | −0.244529 | ||||||||
\(977\) | −1554.00 | −0.0508873 | −0.0254436 | − | 0.999676i | \(-0.508100\pi\) | ||||
−0.0254436 | + | 0.999676i | \(0.508100\pi\) | |||||||
\(978\) | −18048.0 | −0.590093 | ||||||||
\(979\) | 6102.00 | 0.199204 | ||||||||
\(980\) | −1764.00 | −0.0574989 | ||||||||
\(981\) | 10386.0 | 0.338022 | ||||||||
\(982\) | −35448.0 | −1.15193 | ||||||||
\(983\) | 15597.0 | 0.506070 | 0.253035 | − | 0.967457i | \(-0.418571\pi\) | ||||
0.253035 | + | 0.967457i | \(0.418571\pi\) | |||||||
\(984\) | −5328.00 | −0.172612 | ||||||||
\(985\) | 6966.00 | 0.225335 | ||||||||
\(986\) | −29880.0 | −0.965084 | ||||||||
\(987\) | −8631.00 | −0.278346 | ||||||||
\(988\) | −2236.00 | −0.0720006 | ||||||||
\(989\) | −2655.00 | −0.0853631 | ||||||||
\(990\) | 2916.00 | 0.0936127 | ||||||||
\(991\) | 52004.0 | 1.66696 | 0.833482 | − | 0.552546i | \(-0.186344\pi\) | ||||
0.833482 | + | 0.552546i | \(0.186344\pi\) | |||||||
\(992\) | −2528.00 | −0.0809114 | ||||||||
\(993\) | 17814.0 | 0.569295 | ||||||||
\(994\) | −4032.00 | −0.128659 | ||||||||
\(995\) | 9540.00 | 0.303958 | ||||||||
\(996\) | −468.000 | −0.0148887 | ||||||||
\(997\) | 16184.0 | 0.514095 | 0.257047 | − | 0.966399i | \(-0.417250\pi\) | ||||
0.257047 | + | 0.966399i | \(0.417250\pi\) | |||||||
\(998\) | −31640.0 | −1.00355 | ||||||||
\(999\) | 11124.0 | 0.352300 |
(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 | 546.4.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 1638.4.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.4.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
1638.4.a.f.1.1 | 1 | 3.2 | odd | 2 |