Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,4,Mod(1,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, 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("112.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.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: | \(6.60821392064\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 112.1 |
$q$-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 | ||||||||
\(3\) | 2.00000 | 0.384900 | 0.192450 | − | 0.981307i | \(-0.438357\pi\) | ||||
0.192450 | + | 0.981307i | \(0.438357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.0000 | −1.07331 | −0.536656 | − | 0.843801i | \(-0.680313\pi\) | ||||
−0.536656 | + | 0.843801i | \(0.680313\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −23.0000 | −0.851852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −48.0000 | −1.31569 | −0.657843 | − | 0.753155i | \(-0.728531\pi\) | ||||
−0.657843 | + | 0.753155i | \(0.728531\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 56.0000 | 1.19474 | 0.597369 | − | 0.801966i | \(-0.296213\pi\) | ||||
0.597369 | + | 0.801966i | \(0.296213\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −24.0000 | −0.413118 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −114.000 | −1.62642 | −0.813208 | − | 0.581974i | \(-0.802281\pi\) | ||||
−0.813208 | + | 0.581974i | \(0.802281\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.0241490 | −0.0120745 | − | 0.999927i | \(-0.503844\pi\) | ||||
−0.0120745 | + | 0.999927i | \(0.503844\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −14.0000 | −0.145479 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 120.000 | 1.08790 | 0.543951 | − | 0.839117i | \(-0.316928\pi\) | ||||
0.543951 | + | 0.839117i | \(0.316928\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0000 | 0.152000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −100.000 | −0.712778 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −54.0000 | −0.345778 | −0.172889 | − | 0.984941i | \(-0.555310\pi\) | ||||
−0.172889 | + | 0.984941i | \(0.555310\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −236.000 | −1.36732 | −0.683659 | − | 0.729802i | \(-0.739612\pi\) | ||||
−0.683659 | + | 0.729802i | \(0.739612\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −96.0000 | −0.506408 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 84.0000 | 0.405674 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 146.000 | 0.648710 | 0.324355 | − | 0.945936i | \(-0.394853\pi\) | ||||
0.324355 | + | 0.945936i | \(0.394853\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 112.000 | 0.459855 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 126.000 | 0.479949 | 0.239974 | − | 0.970779i | \(-0.422861\pi\) | ||||
0.239974 | + | 0.970779i | \(0.422861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 376.000 | 1.33348 | 0.666738 | − | 0.745292i | \(-0.267690\pi\) | ||||
0.666738 | + | 0.745292i | \(0.267690\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 276.000 | 0.914303 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.0000 | 0.0372421 | 0.0186211 | − | 0.999827i | \(-0.494072\pi\) | ||||
0.0186211 | + | 0.999827i | \(0.494072\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −228.000 | −0.626008 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 174.000 | 0.450957 | 0.225479 | − | 0.974248i | \(-0.427605\pi\) | ||||
0.225479 | + | 0.974248i | \(0.427605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 576.000 | 1.41214 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.00000 | −0.00929496 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −138.000 | −0.304510 | −0.152255 | − | 0.988341i | \(-0.548653\pi\) | ||||
−0.152255 | + | 0.988341i | \(0.548653\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 380.000 | 0.797607 | 0.398803 | − | 0.917036i | \(-0.369426\pi\) | ||||
0.398803 | + | 0.917036i | \(0.369426\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 161.000 | 0.321970 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −672.000 | −1.28233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 484.000 | 0.882537 | 0.441269 | − | 0.897375i | \(-0.354529\pi\) | ||||
0.441269 | + | 0.897375i | \(0.354529\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 240.000 | 0.418733 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −576.000 | −0.962798 | −0.481399 | − | 0.876502i | \(-0.659871\pi\) | ||||
−0.481399 | + | 0.876502i | \(0.659871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1150.00 | −1.84380 | −0.921899 | − | 0.387429i | \(-0.873363\pi\) | ||||
−0.921899 | + | 0.387429i | \(0.873363\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 38.0000 | 0.0585048 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 336.000 | 0.497283 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −776.000 | −1.10515 | −0.552575 | − | 0.833463i | \(-0.686355\pi\) | ||||
−0.552575 | + | 0.833463i | \(0.686355\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 421.000 | 0.577503 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −378.000 | −0.499890 | −0.249945 | − | 0.968260i | \(-0.580413\pi\) | ||||
−0.249945 | + | 0.968260i | \(0.580413\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1368.00 | 1.74565 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −108.000 | −0.133090 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −390.000 | −0.464493 | −0.232247 | − | 0.972657i | \(-0.574608\pi\) | ||||
−0.232247 | + | 0.972657i | \(0.574608\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −392.000 | −0.451569 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −472.000 | −0.526281 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 24.0000 | 0.0259195 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1330.00 | −1.39218 | −0.696088 | − | 0.717957i | \(-0.745078\pi\) | ||||
−0.696088 | + | 0.717957i | \(0.745078\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1104.00 | 1.12077 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1500.00 | −1.47778 | −0.738889 | − | 0.673827i | \(-0.764649\pi\) | ||||
−0.738889 | + | 0.673827i | \(0.764649\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −380.000 | −0.363520 | −0.181760 | − | 0.983343i | \(-0.558179\pi\) | ||||
−0.181760 | + | 0.983343i | \(0.558179\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 168.000 | 0.156144 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −636.000 | −0.574621 | −0.287310 | − | 0.957838i | \(-0.592761\pi\) | ||||
−0.287310 | + | 0.957838i | \(0.592761\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 146.000 | 0.128296 | 0.0641480 | − | 0.997940i | \(-0.479567\pi\) | ||||
0.0641480 | + | 0.997940i | \(0.479567\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 292.000 | 0.249688 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 198.000 | 0.164834 | 0.0824171 | − | 0.996598i | \(-0.473736\pi\) | ||||
0.0824171 | + | 0.996598i | \(0.473736\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1440.00 | −1.16766 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1288.00 | −1.01774 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 798.000 | 0.614727 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 973.000 | 0.731029 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 252.000 | 0.184732 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1272.00 | 0.910169 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 376.000 | 0.262713 | 0.131357 | − | 0.991335i | \(-0.458067\pi\) | ||||
0.131357 | + | 0.991335i | \(0.458067\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 752.000 | 0.513255 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2130.00 | −1.42060 | −0.710301 | − | 0.703898i | \(-0.751441\pi\) | ||||
−0.710301 | + | 0.703898i | \(0.751441\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.0000 | 0.00912747 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1200.00 | 0.765034 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −78.0000 | −0.0486423 | −0.0243211 | − | 0.999704i | \(-0.507742\pi\) | ||||
−0.0243211 | + | 0.999704i | \(0.507742\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2338.00 | 1.42667 | 0.713333 | − | 0.700825i | \(-0.247185\pi\) | ||||
0.713333 | + | 0.700825i | \(0.247185\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.0000 | 0.0143345 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2688.00 | −1.57190 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 648.000 | 0.371127 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 98.0000 | 0.0549857 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1002.00 | −0.550920 | −0.275460 | − | 0.961313i | \(-0.588830\pi\) | ||||
−0.275460 | + | 0.961313i | \(0.588830\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2752.00 | 1.48314 | 0.741571 | − | 0.670874i | \(-0.234081\pi\) | ||||
0.741571 | + | 0.670874i | \(0.234081\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2622.00 | 1.38546 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2832.00 | 1.46756 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −520.000 | −0.264335 | −0.132167 | − | 0.991227i | \(-0.542194\pi\) | ||||
−0.132167 | + | 0.991227i | \(0.542194\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 348.000 | 0.173574 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −840.000 | −0.411188 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1280.00 | −0.615076 | −0.307538 | − | 0.951536i | \(-0.599505\pi\) | ||||
−0.307538 | + | 0.951536i | \(0.599505\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1152.00 | 0.543534 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1764.00 | −0.817380 | −0.408690 | − | 0.912673i | \(-0.634014\pi\) | ||||
−0.408690 | + | 0.912673i | \(0.634014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 939.000 | 0.427401 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 46.0000 | 0.0205714 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −768.000 | −0.337514 | −0.168757 | − | 0.985658i | \(-0.553975\pi\) | ||||
−0.168757 | + | 0.985658i | \(0.553975\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −133.000 | −0.0574506 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −276.000 | −0.117206 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1812.00 | −0.756621 | −0.378311 | − | 0.925679i | \(-0.623495\pi\) | ||||
−0.378311 | + | 0.925679i | \(0.623495\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −448.000 | −0.183976 | −0.0919878 | − | 0.995760i | \(-0.529322\pi\) | ||||
−0.0919878 | + | 0.995760i | \(0.529322\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 760.000 | 0.306999 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1752.00 | −0.696268 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5472.00 | 2.13985 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 700.000 | 0.269405 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2136.00 | 0.809191 | 0.404596 | − | 0.914496i | \(-0.367412\pi\) | ||||
0.404596 | + | 0.914496i | \(0.367412\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4430.00 | 1.65222 | 0.826110 | − | 0.563509i | \(-0.190549\pi\) | ||||
0.826110 | + | 0.563509i | \(0.190549\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1344.00 | −0.493568 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 198.000 | 0.0716087 | 0.0358044 | − | 0.999359i | \(-0.488601\pi\) | ||||
0.0358044 | + | 0.999359i | \(0.488601\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2284.00 | 0.813610 | 0.406805 | − | 0.913515i | \(-0.366643\pi\) | ||||
0.406805 | + | 0.913515i | \(0.366643\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 968.000 | 0.339689 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 378.000 | 0.130692 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1512.00 | −0.515135 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2760.00 | −0.926731 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 96.0000 | 0.0317725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4412.00 | −1.43950 | −0.719750 | − | 0.694233i | \(-0.755744\pi\) | ||||
−0.719750 | + | 0.694233i | \(0.755744\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1152.00 | −0.370581 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4512.00 | −1.43124 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1652.00 | 0.516798 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2300.00 | −0.709679 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6384.00 | −1.94314 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2072.00 | −0.622204 | −0.311102 | − | 0.950377i | \(-0.600698\pi\) | ||||
−0.311102 | + | 0.950377i | \(0.600698\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −437.000 | −0.129481 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 366.000 | 0.107014 | 0.0535072 | − | 0.998567i | \(-0.482960\pi\) | ||||
0.0535072 | + | 0.998567i | \(0.482960\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −376.000 | −0.108501 | −0.0542506 | − | 0.998527i | \(-0.517277\pi\) | ||||
−0.0542506 | + | 0.998527i | \(0.517277\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 672.000 | 0.191404 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2262.00 | −0.636002 | −0.318001 | − | 0.948090i | \(-0.603012\pi\) | ||||
−0.318001 | + | 0.948090i | \(0.603012\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −144.000 | −0.0399724 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1552.00 | −0.425372 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2592.00 | −0.701517 | −0.350758 | − | 0.936466i | \(-0.614076\pi\) | ||||
−0.350758 | + | 0.936466i | \(0.614076\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 110.000 | 0.0294013 | 0.0147007 | − | 0.999892i | \(-0.495320\pi\) | ||||
0.0147007 | + | 0.999892i | \(0.495320\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3542.00 | 0.935059 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −588.000 | −0.153330 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −112.000 | −0.0288518 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −756.000 | −0.192408 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1890.00 | 0.475282 | 0.237641 | − | 0.971353i | \(-0.423626\pi\) | ||||
0.237641 | + | 0.971353i | \(0.423626\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5760.00 | −1.43134 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2736.00 | 0.671902 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2130.00 | 0.516987 | 0.258494 | − | 0.966013i | \(-0.416774\pi\) | ||||
0.258494 | + | 0.966013i | \(0.416774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1022.00 | −0.245189 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1242.00 | 0.294551 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4992.00 | 1.17042 | 0.585209 | − | 0.810883i | \(-0.301012\pi\) | ||||
0.585209 | + | 0.810883i | \(0.301012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2088.00 | −0.484018 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −780.000 | −0.178784 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6816.00 | 1.54490 | 0.772451 | − | 0.635074i | \(-0.219030\pi\) | ||||
0.772451 | + | 0.635074i | \(0.219030\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8192.00 | −1.83627 | −0.918134 | − | 0.396270i | \(-0.870304\pi\) | ||||
−0.918134 | + | 0.396270i | \(0.870304\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −784.000 | −0.173809 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −912.000 | −0.199984 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2414.00 | 0.523622 | 0.261811 | − | 0.965119i | \(-0.415680\pi\) | ||||
0.261811 | + | 0.965119i | \(0.415680\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5428.00 | 1.16475 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1962.00 | 0.416524 | 0.208262 | − | 0.978073i | \(-0.433219\pi\) | ||||
0.208262 | + | 0.978073i | \(0.433219\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5402.00 | −1.13468 | −0.567342 | − | 0.823482i | \(-0.692028\pi\) | ||||
−0.567342 | + | 0.823482i | \(0.692028\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 48.0000 | 0.00997640 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −882.000 | −0.181404 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8083.00 | 1.64523 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2660.00 | −0.535849 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4788.00 | −0.954669 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1656.00 | 0.326834 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4800.00 | 0.937792 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6720.00 | 1.29976 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2632.00 | −0.504007 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3000.00 | −0.568797 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4560.00 | −0.856081 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 574.000 | 0.106710 | 0.0533549 | − | 0.998576i | \(-0.483009\pi\) | ||||
0.0533549 | + | 0.998576i | \(0.483009\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −760.000 | −0.139919 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8808.00 | 1.60597 | 0.802984 | − | 0.596001i | \(-0.203245\pi\) | ||||
0.802984 | + | 0.596001i | \(0.203245\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2770.00 | −0.500223 | −0.250111 | − | 0.968217i | \(-0.580467\pi\) | ||||
−0.250111 | + | 0.968217i | \(0.580467\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1932.00 | −0.345574 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7566.00 | 1.34053 | 0.670266 | − | 0.742121i | \(-0.266180\pi\) | ||||
0.670266 | + | 0.742121i | \(0.266180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2592.00 | 0.454935 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1272.00 | −0.221172 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 228.000 | 0.0392763 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1064.00 | 0.181600 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 292.000 | 0.0493812 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −84.0000 | −0.0140762 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11320.0 | 1.87977 | 0.939884 | − | 0.341493i | \(-0.110932\pi\) | ||||
0.939884 | + | 0.341493i | \(0.110932\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3358.00 | −0.552604 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5808.00 | −0.947239 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4786.00 | −0.773620 | −0.386810 | − | 0.922159i | \(-0.626423\pi\) | ||||
−0.386810 | + | 0.922159i | \(0.626423\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 396.000 | 0.0634447 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11328.0 | 1.79896 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2880.00 | −0.449432 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12648.0 | −1.95672 | −0.978358 | − | 0.206921i | \(-0.933656\pi\) | ||||
−0.978358 | + | 0.206921i | \(0.933656\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9632.00 | 1.47733 | 0.738666 | − | 0.674071i | \(-0.235456\pi\) | ||||
0.738666 | + | 0.674071i | \(0.235456\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5600.00 | −0.851584 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3390.00 | −0.511137 | −0.255569 | − | 0.966791i | \(-0.582263\pi\) | ||||
−0.255569 | + | 0.966791i | \(0.582263\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6912.00 | 1.03338 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1596.00 | 0.236609 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10704.0 | 1.57364 | 0.786818 | − | 0.617185i | \(-0.211727\pi\) | ||||
0.786818 | + | 0.617185i | \(0.211727\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6855.00 | −0.999417 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1946.00 | 0.281373 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13800.0 | 1.97897 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8584.00 | 1.22093 | 0.610465 | − | 0.792043i | \(-0.290983\pi\) | ||||
0.610465 | + | 0.792043i | \(0.290983\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2898.00 | −0.408845 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1218.00 | −0.170446 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2122.00 | −0.294566 | −0.147283 | − | 0.989094i | \(-0.547053\pi\) | ||||
−0.147283 | + | 0.989094i | \(0.547053\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2544.00 | 0.350324 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3024.00 | −0.413114 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4912.00 | 0.665732 | 0.332866 | − | 0.942974i | \(-0.391984\pi\) | ||||
0.332866 | + | 0.942974i | \(0.391984\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 752.000 | 0.101118 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9060.00 | −1.20873 | −0.604366 | − | 0.796707i | \(-0.706574\pi\) | ||||
−0.604366 | + | 0.796707i | \(0.706574\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4032.00 | −0.533740 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8648.00 | −1.13592 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8994.00 | 1.17227 | 0.586136 | − | 0.810213i | \(-0.300648\pi\) | ||||
0.586136 | + | 0.810213i | \(0.300648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13680.0 | −1.76938 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4260.00 | −0.546790 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9312.00 | 1.18617 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12976.0 | −1.64042 | −0.820210 | − | 0.572062i | \(-0.806143\pi\) | ||||
−0.820210 | + | 0.572062i | \(0.806143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 28.0000 | 0.00351317 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3522.00 | −0.438604 | −0.219302 | − | 0.975657i | \(-0.570378\pi\) | ||||
−0.219302 | + | 0.975657i | \(0.570378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13216.0 | −1.63359 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5052.00 | −0.619842 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7008.00 | −0.853498 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12710.0 | 1.53660 | 0.768300 | − | 0.640090i | \(-0.221103\pi\) | ||||
0.768300 | + | 0.640090i | \(0.221103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −156.000 | −0.0187224 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 966.000 | 0.115094 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4536.00 | 0.536539 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4676.00 | 0.549124 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1638.00 | −0.190982 | −0.0954911 | − | 0.995430i | \(-0.530442\pi\) | ||||
−0.0954911 | + | 0.995430i | \(0.530442\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12850.0 | −1.48758 | −0.743789 | − | 0.668414i | \(-0.766973\pi\) | ||||
−0.743789 | + | 0.668414i | \(0.766973\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −276.000 | −0.0317248 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2166.00 | −0.247215 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2660.00 | −0.301467 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5376.00 | −0.605025 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8016.00 | 0.895863 | 0.447932 | − | 0.894068i | \(-0.352161\pi\) | ||||
0.447932 | + | 0.894068i | \(0.352161\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2198.00 | 0.243947 | 0.121974 | − | 0.992533i | \(-0.461078\pi\) | ||||
0.121974 | + | 0.992533i | \(0.461078\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1296.00 | 0.142847 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −240.000 | −0.0262718 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 376.000 | 0.0408781 | 0.0204391 | − | 0.999791i | \(-0.493494\pi\) | ||||
0.0204391 | + | 0.999791i | \(0.493494\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1127.00 | −0.121693 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7188.00 | −0.770908 | −0.385454 | − | 0.922727i | \(-0.625955\pi\) | ||||
−0.385454 | + | 0.922727i | \(0.625955\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4680.00 | 0.498547 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2004.00 | −0.212049 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14670.0 | −1.54192 | −0.770958 | − | 0.636886i | \(-0.780222\pi\) | ||||
−0.770958 | + | 0.636886i | \(0.780222\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6048.00 | −0.631462 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5504.00 | 0.570862 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4704.00 | 0.484675 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5146.00 | −0.526739 | −0.263370 | − | 0.964695i | \(-0.584834\pi\) | ||||
−0.263370 | + | 0.964695i | \(0.584834\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11400.0 | 1.15927 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1512.00 | −0.152757 | −0.0763784 | − | 0.997079i | \(-0.524336\pi\) | ||||
−0.0763784 | + | 0.997079i | \(0.524336\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7184.00 | −0.721099 | −0.360549 | − | 0.932740i | \(-0.617411\pi\) | ||||
−0.360549 | + | 0.932740i | \(0.617411\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5664.00 | 0.564864 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16518.0 | 1.63675 | 0.818375 | − | 0.574685i | \(-0.194875\pi\) | ||||
0.818375 | + | 0.574685i | \(0.194875\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3388.00 | −0.333568 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1040.00 | −0.101742 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18048.0 | −1.75444 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.0000 | −0.00367065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4002.00 | −0.384149 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10092.0 | −0.962662 | −0.481331 | − | 0.876539i | \(-0.659847\pi\) | ||||
−0.481331 | + | 0.876539i | \(0.659847\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8176.00 | 0.775038 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1680.00 | −0.158266 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15960.0 | 1.49424 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7832.00 | −0.728751 | −0.364376 | − | 0.931252i | \(-0.618718\pi\) | ||||
−0.364376 | + | 0.931252i | \(0.618718\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2560.00 | −0.236743 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6732.00 | 0.618759 | 0.309380 | − | 0.950939i | \(-0.399879\pi\) | ||||
0.309380 | + | 0.950939i | \(0.399879\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6156.00 | 0.562378 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13248.0 | −1.20294 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4032.00 | 0.363903 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18668.0 | −1.67474 | −0.837369 | − | 0.546638i | \(-0.815907\pi\) | ||||
−0.837369 | + | 0.546638i | \(0.815907\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3528.00 | −0.314610 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6048.00 | 0.536117 | 0.268059 | − | 0.963403i | \(-0.413618\pi\) | ||||
0.268059 | + | 0.963403i | \(0.413618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18000.0 | 1.58612 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1878.00 | 0.164507 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11328.0 | 0.986453 | 0.493227 | − | 0.869901i | \(-0.335817\pi\) | ||||
0.493227 | + | 0.869901i | \(0.335817\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8050.00 | 0.696890 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 200.000 | 0.0172129 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4560.00 | 0.390170 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −576.000 | −0.0489989 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1536.00 | −0.129909 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4146.00 | −0.348636 | −0.174318 | − | 0.984689i | \(-0.555772\pi\) | ||||
−0.174318 | + | 0.984689i | \(0.555772\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1006.00 | 0.0841096 | 0.0420548 | − | 0.999115i | \(-0.486610\pi\) | ||||
0.0420548 | + | 0.999115i | \(0.486610\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −266.000 | −0.0221127 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26904.0 | 2.22383 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2233.00 | 0.183529 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3174.00 | 0.259397 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7056.00 | 0.573413 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7632.00 | 0.616748 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3624.00 | −0.291224 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2352.00 | −0.187955 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14722.0 | −1.16996 | −0.584980 | − | 0.811048i | \(-0.698898\pi\) | ||||
−0.584980 | + | 0.811048i | \(0.698898\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −896.000 | −0.0708122 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1752.00 | −0.137702 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13480.0 | 1.05368 | 0.526840 | − | 0.849964i | \(-0.323377\pi\) | ||||
0.526840 | + | 0.849964i | \(0.323377\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8740.00 | −0.679443 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 108.000 | 0.00835019 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5432.00 | 0.417707 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3504.00 | −0.267994 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6222.00 | 0.473312 | 0.236656 | − | 0.971594i | \(-0.423949\pi\) | ||||
0.236656 | + | 0.971594i | \(0.423949\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21056.0 | 1.59316 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10944.0 | 0.823629 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4926.00 | −0.368750 | −0.184375 | − | 0.982856i | \(-0.559026\pi\) | ||||
−0.184375 | + | 0.982856i | \(0.559026\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2376.00 | −0.176919 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2947.00 | −0.218276 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22182.0 | 1.63430 | 0.817151 | − | 0.576424i | \(-0.195552\pi\) | ||||
0.817151 | + | 0.576424i | \(0.195552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3296.00 | −0.241564 | −0.120782 | − | 0.992679i | \(-0.538540\pi\) | ||||
−0.120782 | + | 0.992679i | \(0.538540\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4272.00 | 0.311458 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2280.00 | 0.165361 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24334.0 | −1.75570 | −0.877849 | − | 0.478938i | \(-0.841022\pi\) | ||||
−0.877849 | + | 0.478938i | \(0.841022\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8860.00 | 0.635940 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2646.00 | 0.188941 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8352.00 | −0.593318 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15456.0 | 1.09235 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1638.00 | −0.115175 | −0.0575873 | − | 0.998340i | \(-0.518341\pi\) | ||||
−0.0575873 | + | 0.998340i | \(0.518341\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 472.000 | 0.0330194 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 396.000 | 0.0275622 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7446.00 | −0.515633 | −0.257817 | − | 0.966194i | \(-0.583003\pi\) | ||||
−0.257817 | + | 0.966194i | \(0.583003\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9576.00 | −0.659794 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4568.00 | 0.313159 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6504.00 | 0.443650 | 0.221825 | − | 0.975087i | \(-0.428799\pi\) | ||||
0.221825 | + | 0.975087i | \(0.428799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16058.0 | 1.08988 | 0.544941 | − | 0.838474i | \(-0.316552\pi\) | ||||
0.544941 | + | 0.838474i | \(0.316552\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11132.0 | −0.751791 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11676.0 | −0.784623 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10208.0 | −0.682586 | −0.341293 | − | 0.939957i | \(-0.610865\pi\) | ||||
−0.341293 | + | 0.939957i | \(0.610865\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 756.000 | 0.0503032 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 672.000 | 0.0444946 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14974.0 | −0.986614 | −0.493307 | − | 0.869855i | \(-0.664212\pi\) | ||||
−0.493307 | + | 0.869855i | \(0.664212\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3024.00 | −0.198276 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7254.00 | 0.473314 | 0.236657 | − | 0.971593i | \(-0.423948\pi\) | ||||
0.236657 | + | 0.971593i | \(0.423948\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12458.0 | −0.808933 | −0.404466 | − | 0.914553i | \(-0.632543\pi\) | ||||
−0.404466 | + | 0.914553i | \(0.632543\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12000.0 | −0.775432 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2730.00 | 0.175562 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17639.0 | −1.12890 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 192.000 | 0.0122293 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −16644.0 | −1.05507 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28352.0 | −1.78871 | −0.894354 | − | 0.447359i | \(-0.852365\pi\) | ||||
−0.894354 | + | 0.447359i | \(0.852365\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8824.00 | −0.554064 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4512.00 | −0.281974 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2744.00 | 0.170677 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13248.0 | 0.820161 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27390.0 | 1.68774 | 0.843869 | − | 0.536549i | \(-0.180272\pi\) | ||||
0.843869 | + | 0.536549i | \(0.180272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21490.0 | 1.31801 | 0.659007 | − | 0.752137i | \(-0.270977\pi\) | ||||
0.659007 | + | 0.752137i | \(0.270977\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9024.00 | −0.550883 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17652.0 | −1.07260 | −0.536300 | − | 0.844028i | \(-0.680178\pi\) | ||||
−0.536300 | + | 0.844028i | \(0.680178\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6624.00 | 0.400639 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3304.00 | 0.198915 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4782.00 | −0.286576 | −0.143288 | − | 0.989681i | \(-0.545768\pi\) | ||||
−0.143288 | + | 0.989681i | \(0.545768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25560.0 | 1.52475 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26450.0 | 1.57064 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27144.0 | 1.60452 | 0.802261 | − | 0.596973i | \(-0.203630\pi\) | ||||
0.802261 | + | 0.596973i | \(0.203630\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11860.0 | −0.697883 | −0.348941 | − | 0.937145i | \(-0.613459\pi\) | ||||
−0.348941 | + | 0.937145i | \(0.613459\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12768.0 | −0.747916 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −168.000 | −0.00979663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6480.00 | −0.376172 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4144.00 | −0.239486 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18240.0 | −1.04940 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5546.00 | 0.317656 | 0.158828 | − | 0.987306i | \(-0.449228\pi\) | ||||
0.158828 | + | 0.987306i | \(0.449228\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1900.00 | −0.108342 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14880.0 | −0.844734 | −0.422367 | − | 0.906425i | \(-0.638801\pi\) | ||||
−0.422367 | + | 0.906425i | \(0.638801\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9310.00 | 0.526193 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 732.000 | 0.0411899 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20964.0 | −1.17447 | −0.587237 | − | 0.809415i | \(-0.699784\pi\) | ||||
−0.587237 | + | 0.809415i | \(0.699784\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 936.000 | 0.0522084 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −752.000 | −0.0417621 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9744.00 | 0.538776 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13106.0 | −0.721528 | −0.360764 | − | 0.932657i | \(-0.617484\pi\) | ||||
−0.360764 | + | 0.932657i | \(0.617484\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7728.00 | −0.423611 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28056.0 | −1.53126 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14364.0 | −0.780596 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4524.00 | −0.244797 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4590.00 | −0.247307 | −0.123653 | − | 0.992325i | \(-0.539461\pi\) | ||||
−0.123653 | + | 0.992325i | \(0.539461\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −292.000 | −0.0156657 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −288.000 | −0.0153854 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10500.0 | 0.558548 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −862.000 | −0.0456602 | −0.0228301 | − | 0.999739i | \(-0.507268\pi\) | ||||
−0.0228301 | + | 0.999739i | \(0.507268\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17848.0 | 0.941424 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28320.0 | −1.48751 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32256.0 | 1.68714 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5184.00 | −0.270014 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3540.00 | 0.183616 | 0.0918079 | − | 0.995777i | \(-0.470735\pi\) | ||||
0.0918079 | + | 0.995777i | \(0.470735\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2660.00 | 0.137397 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 220.000 | 0.0113166 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1026.00 | −0.0525582 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4228.00 | 0.215692 | 0.107846 | − | 0.994168i | \(-0.465605\pi\) | ||||
0.107846 | + | 0.994168i | \(0.465605\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4283.00 | −0.217599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −42864.0 | −2.16879 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5420.00 | 0.273114 | 0.136557 | − | 0.990632i | \(-0.456396\pi\) | ||||
0.136557 | + | 0.990632i | \(0.456396\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1176.00 | −0.0590169 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23232.0 | −1.16114 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1280.00 | −0.0637152 | −0.0318576 | − | 0.999492i | \(-0.510142\pi\) | ||||
−0.0318576 | + | 0.999492i | \(0.510142\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −224.000 | −0.0111051 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35712.0 | 1.76332 | 0.881660 | − | 0.471886i | \(-0.156427\pi\) | ||||
0.881660 | + | 0.471886i | \(0.156427\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12024.0 | 0.591309 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8694.00 | 0.425832 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4452.00 | 0.217186 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24464.0 | −1.18869 | −0.594344 | − | 0.804211i | \(-0.702588\pi\) | ||||
−0.594344 | + | 0.804211i | \(0.702588\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3780.00 | 0.182936 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −33024.0 | −1.59188 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30242.0 | 1.45200 | 0.726000 | − | 0.687695i | \(-0.241377\pi\) | ||||
0.726000 | + | 0.687695i | \(0.241377\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11520.0 | −0.550922 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2154.00 | −0.102605 | −0.0513025 | − | 0.998683i | \(-0.516337\pi\) | ||||
−0.0513025 | + | 0.998683i | \(0.516337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1022.00 | −0.0484913 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −31464.0 | −1.48704 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7728.00 | −0.363810 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10262.0 | 0.481219 | 0.240609 | − | 0.970622i | \(-0.422653\pi\) | ||||
0.240609 | + | 0.970622i | \(0.422653\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4260.00 | 0.198989 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9084.00 | 0.422676 | 0.211338 | − | 0.977413i | \(-0.432218\pi\) | ||||
0.211338 | + | 0.977413i | \(0.432218\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4484.00 | −0.207832 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2044.00 | −0.0943733 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −252.000 | −0.0115903 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27648.0 | 1.26674 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5400.00 | 0.246463 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6240.00 | 0.283714 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19798.0 | 0.896725 | 0.448362 | − | 0.893852i | \(-0.352007\pi\) | ||||
0.448362 | + | 0.893852i | \(0.352007\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9984.00 | 0.450494 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1386.00 | −0.0623015 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21280.0 | 0.952932 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4176.00 | −0.186299 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30240.0 | 1.34398 | 0.671992 | − | 0.740558i | \(-0.265439\pi\) | ||||
0.671992 | + | 0.740558i | \(0.265439\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1368.00 | −0.0605712 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8970.00 | 0.395680 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 55200.0 | 2.42586 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10080.0 | 0.441333 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13632.0 | 0.594633 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2346.00 | −0.101954 | −0.0509771 | − | 0.998700i | \(-0.516234\pi\) | ||||
−0.0509771 | + | 0.998700i | \(0.516234\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29806.0 | 1.29054 | 0.645271 | − | 0.763953i | \(-0.276744\pi\) | ||||
0.645271 | + | 0.763953i | \(0.276744\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16384.0 | −0.706780 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15360.0 | 0.660169 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −752.000 | −0.0322021 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9016.00 | 0.384670 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1506.00 | −0.0640192 | −0.0320096 | − | 0.999488i | \(-0.510191\pi\) | ||||
−0.0320096 | + | 0.999488i | \(0.510191\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20392.0 | 0.863694 | 0.431847 | − | 0.901947i | \(-0.357862\pi\) | ||||
0.431847 | + | 0.901947i | \(0.357862\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1824.00 | −0.0769740 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36108.0 | −1.51826 | −0.759128 | − | 0.650941i | \(-0.774374\pi\) | ||||
−0.759128 | + | 0.650941i | \(0.774374\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13876.0 | −0.581343 | −0.290672 | − | 0.956823i | \(-0.593879\pi\) | ||||
−0.290672 | + | 0.956823i | \(0.593879\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4828.00 | 0.201542 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5586.00 | −0.232345 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21168.0 | 0.877304 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23600.0 | 0.974594 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23436.0 | −0.964363 | −0.482182 | − | 0.876071i | \(-0.660155\pi\) | ||||
−0.482182 | + | 0.876071i | \(0.660155\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21473.0 | −0.880438 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3924.00 | 0.160320 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11268.0 | −0.458735 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6811.00 | −0.276303 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10804.0 | −0.436740 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17520.0 | 0.705732 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8120.00 | 0.325936 | 0.162968 | − | 0.986631i | \(-0.447893\pi\) | ||||
0.162968 | + | 0.986631i | \(0.447893\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −552.000 | −0.0220795 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −50010.0 | −1.99336 | −0.996680 | − | 0.0814218i | \(-0.974054\pi\) | ||||
−0.996680 | + | 0.0814218i | \(0.974054\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34526.0 | −1.37138 | −0.685688 | − | 0.727896i | \(-0.740499\pi\) | ||||
−0.685688 | + | 0.727896i | \(0.740499\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1764.00 | −0.0698223 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17256.0 | 0.680650 | 0.340325 | − | 0.940308i | \(-0.389463\pi\) | ||||
0.340325 | + | 0.940308i | \(0.389463\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9216.00 | 0.362258 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16166.0 | 0.633248 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37248.0 | 1.45403 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27104.0 | 1.05440 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30590.0 | 1.18593 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8904.00 | −0.344012 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8714.00 | 0.335520 | 0.167760 | − | 0.985828i | \(-0.446347\pi\) | ||||
0.167760 | + | 0.985828i | \(0.446347\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9576.00 | −0.367452 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22806.0 | −0.872138 | −0.436069 | − | 0.899913i | \(-0.643630\pi\) | ||||
−0.436069 | + | 0.899913i | \(0.643630\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40196.0 | −1.53194 | −0.765970 | − | 0.642876i | \(-0.777741\pi\) | ||||
−0.765970 | + | 0.642876i | \(0.777741\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3312.00 | 0.125798 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −40812.0 | −1.54491 | −0.772454 | − | 0.635071i | \(-0.780971\pi\) | ||||
−0.772454 | + | 0.635071i | \(0.780971\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2632.00 | −0.0992963 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20208.0 | −0.759813 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.0000 | −0.000899361 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21744.0 | 0.812091 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13440.0 | 0.500277 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12744.0 | 0.472788 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19836.0 | −0.733444 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5264.00 | −0.193992 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5376.00 | 0.197463 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13588.0 | 0.497444 | 0.248722 | − | 0.968575i | \(-0.419989\pi\) | ||||
0.248722 | + | 0.968575i | \(0.419989\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 34500.0 | 1.25885 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47304.0 | 1.72036 | 0.860182 | − | 0.509987i | \(-0.170350\pi\) | ||||
0.860182 | + | 0.509987i | \(0.170350\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18144.0 | 0.657699 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9120.00 | −0.329506 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14910.0 | 0.536937 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1784.00 | −0.0640356 | −0.0320178 | − | 0.999487i | \(-0.510193\pi\) | ||||
−0.0320178 | + | 0.999487i | \(0.510193\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1148.00 | 0.0410726 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32256.0 | −1.15029 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2774.00 | 0.0986038 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8740.00 | 0.309665 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35922.0 | −1.26864 | −0.634318 | − | 0.773072i | \(-0.718719\pi\) | ||||
−0.634318 | + | 0.773072i | \(0.718719\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −98.0000 | −0.00344986 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17616.0 | 0.618137 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −65664.0 | −2.29673 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26782.0 | −0.933756 | −0.466878 | − | 0.884322i | \(-0.654621\pi\) | ||||
−0.466878 | + | 0.884322i | \(0.654621\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5540.00 | −0.192536 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4044.00 | 0.140096 | 0.0700482 | − | 0.997544i | \(-0.477685\pi\) | ||||
0.0700482 | + | 0.997544i | \(0.477685\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15120.0 | 0.522137 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8400.00 | −0.289156 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2136.00 | 0.0732953 | 0.0366477 | − | 0.999328i | \(-0.488332\pi\) | ||||
0.0366477 | + | 0.999328i | \(0.488332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −64400.0 | −2.20286 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15132.0 | 0.515971 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15174.0 | −0.515776 | −0.257888 | − | 0.966175i | \(-0.583026\pi\) | ||||
−0.257888 | + | 0.966175i | \(0.583026\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25632.0 | −0.868515 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5184.00 | 0.175104 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 546.000 | 0.0183850 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25905.0 | 0.869558 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14628.0 | 0.489492 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −53160.0 | −1.77335 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25832.0 | −0.859050 | −0.429525 | − | 0.903055i | \(-0.641319\pi\) | ||||
−0.429525 | + | 0.903055i | \(0.641319\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 456.000 | 0.0151175 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37686.0 | 1.24552 | 0.622761 | − | 0.782412i | \(-0.286011\pi\) | ||||
0.622761 | + | 0.782412i | \(0.286011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16366.0 | −0.539229 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2128.00 | 0.0698980 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −54006.0 | −1.76848 | −0.884240 | − | 0.467033i | \(-0.845323\pi\) | ||||
−0.884240 | + | 0.467033i | \(0.845323\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18720.0 | 0.611127 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3358.00 | −0.109289 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33276.0 | −1.07969 | −0.539847 | − | 0.841763i | \(-0.681518\pi\) | ||||
−0.539847 | + | 0.841763i | \(0.681518\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2376.00 | −0.0768585 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −168.000 | −0.00541793 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 45120.0 | 1.45069 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3760.00 | 0.120525 | 0.0602625 | − | 0.998183i | \(-0.480806\pi\) | ||||
0.0602625 | + | 0.998183i | \(0.480806\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22640.0 | 0.723523 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27408.0 | −0.873258 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36524.0 | 1.16021 | 0.580104 | − | 0.814543i | \(-0.303012\pi\) | ||||
0.580104 | + | 0.814543i | \(0.303012\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14600.0 | −0.462386 |
(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 | 112.4.a.e.1.1 | 1 | ||
3.2 | odd | 2 | 1008.4.a.r.1.1 | 1 | |||
4.3 | odd | 2 | 14.4.a.b.1.1 | ✓ | 1 | ||
7.6 | odd | 2 | 784.4.a.h.1.1 | 1 | |||
8.3 | odd | 2 | 448.4.a.k.1.1 | 1 | |||
8.5 | even | 2 | 448.4.a.g.1.1 | 1 | |||
12.11 | even | 2 | 126.4.a.d.1.1 | 1 | |||
20.3 | even | 4 | 350.4.c.g.99.1 | 2 | |||
20.7 | even | 4 | 350.4.c.g.99.2 | 2 | |||
20.19 | odd | 2 | 350.4.a.f.1.1 | 1 | |||
28.3 | even | 6 | 98.4.c.b.79.1 | 2 | |||
28.11 | odd | 6 | 98.4.c.c.79.1 | 2 | |||
28.19 | even | 6 | 98.4.c.b.67.1 | 2 | |||
28.23 | odd | 6 | 98.4.c.c.67.1 | 2 | |||
28.27 | even | 2 | 98.4.a.e.1.1 | 1 | |||
44.43 | even | 2 | 1694.4.a.b.1.1 | 1 | |||
52.51 | odd | 2 | 2366.4.a.c.1.1 | 1 | |||
84.11 | even | 6 | 882.4.g.p.667.1 | 2 | |||
84.23 | even | 6 | 882.4.g.p.361.1 | 2 | |||
84.47 | odd | 6 | 882.4.g.v.361.1 | 2 | |||
84.59 | odd | 6 | 882.4.g.v.667.1 | 2 | |||
84.83 | odd | 2 | 882.4.a.b.1.1 | 1 | |||
140.139 | even | 2 | 2450.4.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.4.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
98.4.a.e.1.1 | 1 | 28.27 | even | 2 | |||
98.4.c.b.67.1 | 2 | 28.19 | even | 6 | |||
98.4.c.b.79.1 | 2 | 28.3 | even | 6 | |||
98.4.c.c.67.1 | 2 | 28.23 | odd | 6 | |||
98.4.c.c.79.1 | 2 | 28.11 | odd | 6 | |||
112.4.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
126.4.a.d.1.1 | 1 | 12.11 | even | 2 | |||
350.4.a.f.1.1 | 1 | 20.19 | odd | 2 | |||
350.4.c.g.99.1 | 2 | 20.3 | even | 4 | |||
350.4.c.g.99.2 | 2 | 20.7 | even | 4 | |||
448.4.a.g.1.1 | 1 | 8.5 | even | 2 | |||
448.4.a.k.1.1 | 1 | 8.3 | odd | 2 | |||
784.4.a.h.1.1 | 1 | 7.6 | odd | 2 | |||
882.4.a.b.1.1 | 1 | 84.83 | odd | 2 | |||
882.4.g.p.361.1 | 2 | 84.23 | even | 6 | |||
882.4.g.p.667.1 | 2 | 84.11 | even | 6 | |||
882.4.g.v.361.1 | 2 | 84.47 | odd | 6 | |||
882.4.g.v.667.1 | 2 | 84.59 | odd | 6 | |||
1008.4.a.r.1.1 | 1 | 3.2 | odd | 2 | |||
1694.4.a.b.1.1 | 1 | 44.43 | even | 2 | |||
2366.4.a.c.1.1 | 1 | 52.51 | odd | 2 | |||
2450.4.a.i.1.1 | 1 | 140.139 | even | 2 |