Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,6,Mod(1,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.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: | \(47.1528430250\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 294.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −26.0000 | −0.465102 | −0.232551 | − | 0.972584i | \(-0.574707\pi\) | ||||
−0.232551 | + | 0.972584i | \(0.574707\pi\) | |||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 104.000 | 0.328877 | ||||||||
\(11\) | 664.000 | 1.65457 | 0.827287 | − | 0.561779i | \(-0.189883\pi\) | ||||
0.827287 | + | 0.561779i | \(0.189883\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −318.000 | −0.521878 | −0.260939 | − | 0.965355i | \(-0.584032\pi\) | ||||
−0.260939 | + | 0.965355i | \(0.584032\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 234.000 | 0.268527 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1582.00 | −1.32765 | −0.663826 | − | 0.747887i | \(-0.731068\pi\) | ||||
−0.663826 | + | 0.747887i | \(0.731068\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −236.000 | −0.149978 | −0.0749891 | − | 0.997184i | \(-0.523892\pi\) | ||||
−0.0749891 | + | 0.997184i | \(0.523892\pi\) | |||||||
\(20\) | −416.000 | −0.232551 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2656.00 | −1.16996 | ||||||||
\(23\) | 2212.00 | 0.871898 | 0.435949 | − | 0.899971i | \(-0.356413\pi\) | ||||
0.435949 | + | 0.899971i | \(0.356413\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | −2449.00 | −0.783680 | ||||||||
\(26\) | 1272.00 | 0.369023 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4954.00 | −1.09386 | −0.546929 | − | 0.837179i | \(-0.684203\pi\) | ||||
−0.546929 | + | 0.837179i | \(0.684203\pi\) | |||||||
\(30\) | −936.000 | −0.189877 | ||||||||
\(31\) | 7128.00 | 1.33218 | 0.666091 | − | 0.745871i | \(-0.267966\pi\) | ||||
0.666091 | + | 0.745871i | \(0.267966\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −5976.00 | −0.955269 | ||||||||
\(34\) | 6328.00 | 0.938792 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 4358.00 | 0.523339 | 0.261669 | − | 0.965158i | \(-0.415727\pi\) | ||||
0.261669 | + | 0.965158i | \(0.415727\pi\) | |||||||
\(38\) | 944.000 | 0.106051 | ||||||||
\(39\) | 2862.00 | 0.301306 | ||||||||
\(40\) | 1664.00 | 0.164438 | ||||||||
\(41\) | −10542.0 | −0.979407 | −0.489704 | − | 0.871889i | \(-0.662895\pi\) | ||||
−0.489704 | + | 0.871889i | \(0.662895\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8452.00 | −0.697089 | −0.348545 | − | 0.937292i | \(-0.613324\pi\) | ||||
−0.348545 | + | 0.937292i | \(0.613324\pi\) | |||||||
\(44\) | 10624.0 | 0.827287 | ||||||||
\(45\) | −2106.00 | −0.155034 | ||||||||
\(46\) | −8848.00 | −0.616525 | ||||||||
\(47\) | −5352.00 | −0.353404 | −0.176702 | − | 0.984264i | \(-0.556543\pi\) | ||||
−0.176702 | + | 0.984264i | \(0.556543\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 9796.00 | 0.554145 | ||||||||
\(51\) | 14238.0 | 0.766520 | ||||||||
\(52\) | −5088.00 | −0.260939 | ||||||||
\(53\) | −33354.0 | −1.63102 | −0.815508 | − | 0.578746i | \(-0.803542\pi\) | ||||
−0.815508 | + | 0.578746i | \(0.803542\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | −17264.0 | −0.769546 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2124.00 | 0.0865899 | ||||||||
\(58\) | 19816.0 | 0.773475 | ||||||||
\(59\) | 15436.0 | 0.577304 | 0.288652 | − | 0.957434i | \(-0.406793\pi\) | ||||
0.288652 | + | 0.957434i | \(0.406793\pi\) | |||||||
\(60\) | 3744.00 | 0.134263 | ||||||||
\(61\) | 36762.0 | 1.26495 | 0.632477 | − | 0.774579i | \(-0.282038\pi\) | ||||
0.632477 | + | 0.774579i | \(0.282038\pi\) | |||||||
\(62\) | −28512.0 | −0.941995 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 8268.00 | 0.242726 | ||||||||
\(66\) | 23904.0 | 0.675477 | ||||||||
\(67\) | 40972.0 | 1.11506 | 0.557532 | − | 0.830155i | \(-0.311748\pi\) | ||||
0.557532 | + | 0.830155i | \(0.311748\pi\) | |||||||
\(68\) | −25312.0 | −0.663826 | ||||||||
\(69\) | −19908.0 | −0.503390 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9092.00 | −0.214049 | −0.107025 | − | 0.994256i | \(-0.534132\pi\) | ||||
−0.107025 | + | 0.994256i | \(0.534132\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 73454.0 | 1.61327 | 0.806637 | − | 0.591047i | \(-0.201285\pi\) | ||||
0.806637 | + | 0.591047i | \(0.201285\pi\) | |||||||
\(74\) | −17432.0 | −0.370056 | ||||||||
\(75\) | 22041.0 | 0.452458 | ||||||||
\(76\) | −3776.00 | −0.0749891 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −11448.0 | −0.213056 | ||||||||
\(79\) | 89400.0 | 1.61165 | 0.805823 | − | 0.592156i | \(-0.201723\pi\) | ||||
0.805823 | + | 0.592156i | \(0.201723\pi\) | |||||||
\(80\) | −6656.00 | −0.116276 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 42168.0 | 0.692546 | ||||||||
\(83\) | 6428.00 | 0.102419 | 0.0512095 | − | 0.998688i | \(-0.483692\pi\) | ||||
0.0512095 | + | 0.998688i | \(0.483692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41132.0 | 0.617494 | ||||||||
\(86\) | 33808.0 | 0.492916 | ||||||||
\(87\) | 44586.0 | 0.631539 | ||||||||
\(88\) | −42496.0 | −0.584980 | ||||||||
\(89\) | 122658. | 1.64142 | 0.820712 | − | 0.571342i | \(-0.193577\pi\) | ||||
0.820712 | + | 0.571342i | \(0.193577\pi\) | |||||||
\(90\) | 8424.00 | 0.109626 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 35392.0 | 0.435949 | ||||||||
\(93\) | −64152.0 | −0.769135 | ||||||||
\(94\) | 21408.0 | 0.249894 | ||||||||
\(95\) | 6136.00 | 0.0697552 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | −21370.0 | −0.230608 | −0.115304 | − | 0.993330i | \(-0.536784\pi\) | ||||
−0.115304 | + | 0.993330i | \(0.536784\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 53784.0 | 0.551525 | ||||||||
\(100\) | −39184.0 | −0.391840 | ||||||||
\(101\) | 36814.0 | 0.359095 | 0.179548 | − | 0.983749i | \(-0.442537\pi\) | ||||
0.179548 | + | 0.983749i | \(0.442537\pi\) | |||||||
\(102\) | −56952.0 | −0.542012 | ||||||||
\(103\) | −104528. | −0.970822 | −0.485411 | − | 0.874286i | \(-0.661330\pi\) | ||||
−0.485411 | + | 0.874286i | \(0.661330\pi\) | |||||||
\(104\) | 20352.0 | 0.184512 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 133416. | 1.15330 | ||||||||
\(107\) | 214440. | 1.81070 | 0.905350 | − | 0.424667i | \(-0.139609\pi\) | ||||
0.905350 | + | 0.424667i | \(0.139609\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | 28798.0 | 0.232165 | 0.116082 | − | 0.993240i | \(-0.462966\pi\) | ||||
0.116082 | + | 0.993240i | \(0.462966\pi\) | |||||||
\(110\) | 69056.0 | 0.544151 | ||||||||
\(111\) | −39222.0 | −0.302150 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −56014.0 | −0.412668 | −0.206334 | − | 0.978482i | \(-0.566153\pi\) | ||||
−0.206334 | + | 0.978482i | \(0.566153\pi\) | |||||||
\(114\) | −8496.00 | −0.0612283 | ||||||||
\(115\) | −57512.0 | −0.405521 | ||||||||
\(116\) | −79264.0 | −0.546929 | ||||||||
\(117\) | −25758.0 | −0.173959 | ||||||||
\(118\) | −61744.0 | −0.408216 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −14976.0 | −0.0949386 | ||||||||
\(121\) | 279845. | 1.73762 | ||||||||
\(122\) | −147048. | −0.894457 | ||||||||
\(123\) | 94878.0 | 0.565461 | ||||||||
\(124\) | 114048. | 0.666091 | ||||||||
\(125\) | 144924. | 0.829593 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 185400. | 1.02000 | 0.510000 | − | 0.860174i | \(-0.329645\pi\) | ||||
0.510000 | + | 0.860174i | \(0.329645\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 76068.0 | 0.402465 | ||||||||
\(130\) | −33072.0 | −0.171634 | ||||||||
\(131\) | −64532.0 | −0.328547 | −0.164273 | − | 0.986415i | \(-0.552528\pi\) | ||||
−0.164273 | + | 0.986415i | \(0.552528\pi\) | |||||||
\(132\) | −95616.0 | −0.477635 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −163888. | −0.788470 | ||||||||
\(135\) | 18954.0 | 0.0895089 | ||||||||
\(136\) | 101248. | 0.469396 | ||||||||
\(137\) | 152930. | 0.696131 | 0.348066 | − | 0.937470i | \(-0.386839\pi\) | ||||
0.348066 | + | 0.937470i | \(0.386839\pi\) | |||||||
\(138\) | 79632.0 | 0.355951 | ||||||||
\(139\) | 343460. | 1.50778 | 0.753892 | − | 0.656998i | \(-0.228174\pi\) | ||||
0.753892 | + | 0.656998i | \(0.228174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 48168.0 | 0.204038 | ||||||||
\(142\) | 36368.0 | 0.151356 | ||||||||
\(143\) | −211152. | −0.863486 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 128804. | 0.508756 | ||||||||
\(146\) | −293816. | −1.14076 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 69728.0 | 0.261669 | ||||||||
\(149\) | −174858. | −0.645238 | −0.322619 | − | 0.946529i | \(-0.604563\pi\) | ||||
−0.322619 | + | 0.946529i | \(0.604563\pi\) | |||||||
\(150\) | −88164.0 | −0.319936 | ||||||||
\(151\) | −452552. | −1.61520 | −0.807600 | − | 0.589731i | \(-0.799234\pi\) | ||||
−0.807600 | + | 0.589731i | \(0.799234\pi\) | |||||||
\(152\) | 15104.0 | 0.0530253 | ||||||||
\(153\) | −128142. | −0.442551 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −185328. | −0.619601 | ||||||||
\(156\) | 45792.0 | 0.150653 | ||||||||
\(157\) | 499066. | 1.61588 | 0.807940 | − | 0.589265i | \(-0.200583\pi\) | ||||
0.807940 | + | 0.589265i | \(0.200583\pi\) | |||||||
\(158\) | −357600. | −1.13961 | ||||||||
\(159\) | 300186. | 0.941668 | ||||||||
\(160\) | 26624.0 | 0.0822192 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −475588. | −1.40204 | −0.701022 | − | 0.713139i | \(-0.747273\pi\) | ||||
−0.701022 | + | 0.713139i | \(0.747273\pi\) | |||||||
\(164\) | −168672. | −0.489704 | ||||||||
\(165\) | 155376. | 0.444298 | ||||||||
\(166\) | −25712.0 | −0.0724212 | ||||||||
\(167\) | −120224. | −0.333580 | −0.166790 | − | 0.985992i | \(-0.553340\pi\) | ||||
−0.166790 | + | 0.985992i | \(0.553340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −270169. | −0.727644 | ||||||||
\(170\) | −164528. | −0.436634 | ||||||||
\(171\) | −19116.0 | −0.0499927 | ||||||||
\(172\) | −135232. | −0.348545 | ||||||||
\(173\) | −508874. | −1.29269 | −0.646346 | − | 0.763045i | \(-0.723704\pi\) | ||||
−0.646346 | + | 0.763045i | \(0.723704\pi\) | |||||||
\(174\) | −178344. | −0.446566 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 169984. | 0.413644 | ||||||||
\(177\) | −138924. | −0.333307 | ||||||||
\(178\) | −490632. | −1.16066 | ||||||||
\(179\) | 487560. | 1.13735 | 0.568677 | − | 0.822561i | \(-0.307456\pi\) | ||||
0.568677 | + | 0.822561i | \(0.307456\pi\) | |||||||
\(180\) | −33696.0 | −0.0775170 | ||||||||
\(181\) | 544410. | 1.23518 | 0.617589 | − | 0.786501i | \(-0.288109\pi\) | ||||
0.617589 | + | 0.786501i | \(0.288109\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −330858. | −0.730321 | ||||||||
\(184\) | −141568. | −0.308262 | ||||||||
\(185\) | −113308. | −0.243406 | ||||||||
\(186\) | 256608. | 0.543861 | ||||||||
\(187\) | −1.05045e6 | −2.19670 | ||||||||
\(188\) | −85632.0 | −0.176702 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −24544.0 | −0.0493243 | ||||||||
\(191\) | 376404. | 0.746570 | 0.373285 | − | 0.927717i | \(-0.378231\pi\) | ||||
0.373285 | + | 0.927717i | \(0.378231\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | 844946. | 1.63281 | 0.816405 | − | 0.577480i | \(-0.195964\pi\) | ||||
0.816405 | + | 0.577480i | \(0.195964\pi\) | |||||||
\(194\) | 85480.0 | 0.163065 | ||||||||
\(195\) | −74412.0 | −0.140138 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −492794. | −0.904690 | −0.452345 | − | 0.891843i | \(-0.649412\pi\) | ||||
−0.452345 | + | 0.891843i | \(0.649412\pi\) | |||||||
\(198\) | −215136. | −0.389987 | ||||||||
\(199\) | 914776. | 1.63750 | 0.818751 | − | 0.574148i | \(-0.194667\pi\) | ||||
0.818751 | + | 0.574148i | \(0.194667\pi\) | |||||||
\(200\) | 156736. | 0.277073 | ||||||||
\(201\) | −368748. | −0.643783 | ||||||||
\(202\) | −147256. | −0.253919 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 227808. | 0.383260 | ||||||||
\(205\) | 274092. | 0.455524 | ||||||||
\(206\) | 418112. | 0.686475 | ||||||||
\(207\) | 179172. | 0.290633 | ||||||||
\(208\) | −81408.0 | −0.130469 | ||||||||
\(209\) | −156704. | −0.248150 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 311780. | 0.482106 | 0.241053 | − | 0.970512i | \(-0.422507\pi\) | ||||
0.241053 | + | 0.970512i | \(0.422507\pi\) | |||||||
\(212\) | −533664. | −0.815508 | ||||||||
\(213\) | 81828.0 | 0.123581 | ||||||||
\(214\) | −857760. | −1.28036 | ||||||||
\(215\) | 219752. | 0.324218 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −115192. | −0.164165 | ||||||||
\(219\) | −661086. | −0.931425 | ||||||||
\(220\) | −276224. | −0.384773 | ||||||||
\(221\) | 503076. | 0.692872 | ||||||||
\(222\) | 156888. | 0.213652 | ||||||||
\(223\) | 1.28776e6 | 1.73409 | 0.867047 | − | 0.498226i | \(-0.166015\pi\) | ||||
0.867047 | + | 0.498226i | \(0.166015\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −198369. | −0.261227 | ||||||||
\(226\) | 224056. | 0.291800 | ||||||||
\(227\) | −1.28905e6 | −1.66037 | −0.830187 | − | 0.557485i | \(-0.811766\pi\) | ||||
−0.830187 | + | 0.557485i | \(0.811766\pi\) | |||||||
\(228\) | 33984.0 | 0.0432950 | ||||||||
\(229\) | −678214. | −0.854630 | −0.427315 | − | 0.904103i | \(-0.640540\pi\) | ||||
−0.427315 | + | 0.904103i | \(0.640540\pi\) | |||||||
\(230\) | 230048. | 0.286747 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 317056. | 0.386737 | ||||||||
\(233\) | −1.11731e6 | −1.34829 | −0.674146 | − | 0.738598i | \(-0.735488\pi\) | ||||
−0.674146 | + | 0.738598i | \(0.735488\pi\) | |||||||
\(234\) | 103032. | 0.123008 | ||||||||
\(235\) | 139152. | 0.164369 | ||||||||
\(236\) | 246976. | 0.288652 | ||||||||
\(237\) | −804600. | −0.930485 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.26196e6 | −1.42906 | −0.714528 | − | 0.699606i | \(-0.753359\pi\) | ||||
−0.714528 | + | 0.699606i | \(0.753359\pi\) | |||||||
\(240\) | 59904.0 | 0.0671317 | ||||||||
\(241\) | −948218. | −1.05164 | −0.525818 | − | 0.850597i | \(-0.676241\pi\) | ||||
−0.525818 | + | 0.850597i | \(0.676241\pi\) | |||||||
\(242\) | −1.11938e6 | −1.22868 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 588192. | 0.632477 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −379512. | −0.399841 | ||||||||
\(247\) | 75048.0 | 0.0782703 | ||||||||
\(248\) | −456192. | −0.470997 | ||||||||
\(249\) | −57852.0 | −0.0591317 | ||||||||
\(250\) | −579696. | −0.586611 | ||||||||
\(251\) | 486396. | 0.487310 | 0.243655 | − | 0.969862i | \(-0.421653\pi\) | ||||
0.243655 | + | 0.969862i | \(0.421653\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.46877e6 | 1.44262 | ||||||||
\(254\) | −741600. | −0.721249 | ||||||||
\(255\) | −370188. | −0.356510 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.03910e6 | 0.981349 | 0.490675 | − | 0.871343i | \(-0.336750\pi\) | ||||
0.490675 | + | 0.871343i | \(0.336750\pi\) | |||||||
\(258\) | −304272. | −0.284585 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 132288. | 0.121363 | ||||||||
\(261\) | −401274. | −0.364619 | ||||||||
\(262\) | 258128. | 0.232317 | ||||||||
\(263\) | 1.35104e6 | 1.20443 | 0.602213 | − | 0.798335i | \(-0.294286\pi\) | ||||
0.602213 | + | 0.798335i | \(0.294286\pi\) | |||||||
\(264\) | 382464. | 0.337739 | ||||||||
\(265\) | 867204. | 0.758589 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.10392e6 | −0.947677 | ||||||||
\(268\) | 655552. | 0.557532 | ||||||||
\(269\) | 1.11811e6 | 0.942115 | 0.471057 | − | 0.882103i | \(-0.343872\pi\) | ||||
0.471057 | + | 0.882103i | \(0.343872\pi\) | |||||||
\(270\) | −75816.0 | −0.0632924 | ||||||||
\(271\) | 190104. | 0.157242 | 0.0786209 | − | 0.996905i | \(-0.474948\pi\) | ||||
0.0786209 | + | 0.996905i | \(0.474948\pi\) | |||||||
\(272\) | −404992. | −0.331913 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −611720. | −0.492239 | ||||||||
\(275\) | −1.62614e6 | −1.29666 | ||||||||
\(276\) | −318528. | −0.251695 | ||||||||
\(277\) | −200506. | −0.157010 | −0.0785051 | − | 0.996914i | \(-0.525015\pi\) | ||||
−0.0785051 | + | 0.996914i | \(0.525015\pi\) | |||||||
\(278\) | −1.37384e6 | −1.06616 | ||||||||
\(279\) | 577368. | 0.444061 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.09237e6 | 0.825285 | 0.412643 | − | 0.910893i | \(-0.364606\pi\) | ||||
0.412643 | + | 0.910893i | \(0.364606\pi\) | |||||||
\(282\) | −192672. | −0.144277 | ||||||||
\(283\) | −1.81258e6 | −1.34534 | −0.672669 | − | 0.739944i | \(-0.734852\pi\) | ||||
−0.672669 | + | 0.739944i | \(0.734852\pi\) | |||||||
\(284\) | −145472. | −0.107025 | ||||||||
\(285\) | −55224.0 | −0.0402732 | ||||||||
\(286\) | 844608. | 0.610577 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | 1.08287e6 | 0.762659 | ||||||||
\(290\) | −515216. | −0.359745 | ||||||||
\(291\) | 192330. | 0.133142 | ||||||||
\(292\) | 1.17526e6 | 0.806637 | ||||||||
\(293\) | −2.10031e6 | −1.42927 | −0.714634 | − | 0.699499i | \(-0.753407\pi\) | ||||
−0.714634 | + | 0.699499i | \(0.753407\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −401336. | −0.268505 | ||||||||
\(296\) | −278912. | −0.185028 | ||||||||
\(297\) | −484056. | −0.318423 | ||||||||
\(298\) | 699432. | 0.456252 | ||||||||
\(299\) | −703416. | −0.455024 | ||||||||
\(300\) | 352656. | 0.226229 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.81021e6 | 1.14212 | ||||||||
\(303\) | −331326. | −0.207324 | ||||||||
\(304\) | −60416.0 | −0.0374945 | ||||||||
\(305\) | −955812. | −0.588333 | ||||||||
\(306\) | 512568. | 0.312931 | ||||||||
\(307\) | 1.64104e6 | 0.993743 | 0.496872 | − | 0.867824i | \(-0.334482\pi\) | ||||
0.496872 | + | 0.867824i | \(0.334482\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 940752. | 0.560504 | ||||||||
\(310\) | 741312. | 0.438124 | ||||||||
\(311\) | 945232. | 0.554163 | 0.277081 | − | 0.960846i | \(-0.410633\pi\) | ||||
0.277081 | + | 0.960846i | \(0.410633\pi\) | |||||||
\(312\) | −183168. | −0.106528 | ||||||||
\(313\) | −415354. | −0.239639 | −0.119820 | − | 0.992796i | \(-0.538232\pi\) | ||||
−0.119820 | + | 0.992796i | \(0.538232\pi\) | |||||||
\(314\) | −1.99626e6 | −1.14260 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.43040e6 | 0.805823 | ||||||||
\(317\) | 1.18481e6 | 0.662220 | 0.331110 | − | 0.943592i | \(-0.392577\pi\) | ||||
0.331110 | + | 0.943592i | \(0.392577\pi\) | |||||||
\(318\) | −1.20074e6 | −0.665860 | ||||||||
\(319\) | −3.28946e6 | −1.80987 | ||||||||
\(320\) | −106496. | −0.0581378 | ||||||||
\(321\) | −1.92996e6 | −1.04541 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 373352. | 0.199119 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 778782. | 0.408985 | ||||||||
\(326\) | 1.90235e6 | 0.991395 | ||||||||
\(327\) | −259182. | −0.134040 | ||||||||
\(328\) | 674688. | 0.346273 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −621504. | −0.314166 | ||||||||
\(331\) | 1.37155e6 | 0.688083 | 0.344042 | − | 0.938954i | \(-0.388204\pi\) | ||||
0.344042 | + | 0.938954i | \(0.388204\pi\) | |||||||
\(332\) | 102848. | 0.0512095 | ||||||||
\(333\) | 352998. | 0.174446 | ||||||||
\(334\) | 480896. | 0.235877 | ||||||||
\(335\) | −1.06527e6 | −0.518619 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 963522. | 0.462154 | 0.231077 | − | 0.972935i | \(-0.425775\pi\) | ||||
0.231077 | + | 0.972935i | \(0.425775\pi\) | |||||||
\(338\) | 1.08068e6 | 0.514522 | ||||||||
\(339\) | 504126. | 0.238254 | ||||||||
\(340\) | 658112. | 0.308747 | ||||||||
\(341\) | 4.73299e6 | 2.20419 | ||||||||
\(342\) | 76464.0 | 0.0353502 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 540928. | 0.246458 | ||||||||
\(345\) | 517608. | 0.234128 | ||||||||
\(346\) | 2.03550e6 | 0.914071 | ||||||||
\(347\) | 2.57731e6 | 1.14906 | 0.574531 | − | 0.818483i | \(-0.305185\pi\) | ||||
0.574531 | + | 0.818483i | \(0.305185\pi\) | |||||||
\(348\) | 713376. | 0.315770 | ||||||||
\(349\) | 3.06751e6 | 1.34810 | 0.674051 | − | 0.738684i | \(-0.264553\pi\) | ||||
0.674051 | + | 0.738684i | \(0.264553\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 231822. | 0.100435 | ||||||||
\(352\) | −679936. | −0.292490 | ||||||||
\(353\) | 3.10144e6 | 1.32473 | 0.662364 | − | 0.749182i | \(-0.269553\pi\) | ||||
0.662364 | + | 0.749182i | \(0.269553\pi\) | |||||||
\(354\) | 555696. | 0.235683 | ||||||||
\(355\) | 236392. | 0.0995547 | ||||||||
\(356\) | 1.96253e6 | 0.820712 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.95024e6 | −0.804230 | ||||||||
\(359\) | −327508. | −0.134118 | −0.0670588 | − | 0.997749i | \(-0.521362\pi\) | ||||
−0.0670588 | + | 0.997749i | \(0.521362\pi\) | |||||||
\(360\) | 134784. | 0.0548128 | ||||||||
\(361\) | −2.42040e6 | −0.977507 | ||||||||
\(362\) | −2.17764e6 | −0.873403 | ||||||||
\(363\) | −2.51860e6 | −1.00321 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.90980e6 | −0.750337 | ||||||||
\(366\) | 1.32343e6 | 0.516415 | ||||||||
\(367\) | 2.86739e6 | 1.11128 | 0.555638 | − | 0.831424i | \(-0.312474\pi\) | ||||
0.555638 | + | 0.831424i | \(0.312474\pi\) | |||||||
\(368\) | 566272. | 0.217974 | ||||||||
\(369\) | −853902. | −0.326469 | ||||||||
\(370\) | 453232. | 0.172114 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.02643e6 | −0.384568 | ||||||||
\(373\) | 3.58029e6 | 1.33244 | 0.666218 | − | 0.745757i | \(-0.267912\pi\) | ||||
0.666218 | + | 0.745757i | \(0.267912\pi\) | |||||||
\(374\) | 4.20179e6 | 1.55330 | ||||||||
\(375\) | −1.30432e6 | −0.478966 | ||||||||
\(376\) | 342528. | 0.124947 | ||||||||
\(377\) | 1.57537e6 | 0.570860 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.64235e6 | 0.587310 | 0.293655 | − | 0.955912i | \(-0.405128\pi\) | ||||
0.293655 | + | 0.955912i | \(0.405128\pi\) | |||||||
\(380\) | 98176.0 | 0.0348776 | ||||||||
\(381\) | −1.66860e6 | −0.588898 | ||||||||
\(382\) | −1.50562e6 | −0.527905 | ||||||||
\(383\) | 2.05698e6 | 0.716527 | 0.358263 | − | 0.933621i | \(-0.383369\pi\) | ||||
0.358263 | + | 0.933621i | \(0.383369\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.37978e6 | −1.15457 | ||||||||
\(387\) | −684612. | −0.232363 | ||||||||
\(388\) | −341920. | −0.115304 | ||||||||
\(389\) | 616142. | 0.206446 | 0.103223 | − | 0.994658i | \(-0.467084\pi\) | ||||
0.103223 | + | 0.994658i | \(0.467084\pi\) | |||||||
\(390\) | 297648. | 0.0990927 | ||||||||
\(391\) | −3.49938e6 | −1.15758 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 580788. | 0.189686 | ||||||||
\(394\) | 1.97118e6 | 0.639713 | ||||||||
\(395\) | −2.32440e6 | −0.749580 | ||||||||
\(396\) | 860544. | 0.275762 | ||||||||
\(397\) | −2.19212e6 | −0.698052 | −0.349026 | − | 0.937113i | \(-0.613487\pi\) | ||||
−0.349026 | + | 0.937113i | \(0.613487\pi\) | |||||||
\(398\) | −3.65910e6 | −1.15789 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −626944. | −0.195920 | ||||||||
\(401\) | 3.28454e6 | 1.02003 | 0.510015 | − | 0.860165i | \(-0.329640\pi\) | ||||
0.510015 | + | 0.860165i | \(0.329640\pi\) | |||||||
\(402\) | 1.47499e6 | 0.455223 | ||||||||
\(403\) | −2.26670e6 | −0.695236 | ||||||||
\(404\) | 589024. | 0.179548 | ||||||||
\(405\) | −170586. | −0.0516780 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.89371e6 | 0.865903 | ||||||||
\(408\) | −911232. | −0.271006 | ||||||||
\(409\) | 3.61219e6 | 1.06773 | 0.533866 | − | 0.845569i | \(-0.320739\pi\) | ||||
0.533866 | + | 0.845569i | \(0.320739\pi\) | |||||||
\(410\) | −1.09637e6 | −0.322104 | ||||||||
\(411\) | −1.37637e6 | −0.401912 | ||||||||
\(412\) | −1.67245e6 | −0.485411 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −716688. | −0.205508 | ||||||||
\(415\) | −167128. | −0.0476353 | ||||||||
\(416\) | 325632. | 0.0922558 | ||||||||
\(417\) | −3.09114e6 | −0.870520 | ||||||||
\(418\) | 626816. | 0.175469 | ||||||||
\(419\) | −5.41489e6 | −1.50680 | −0.753398 | − | 0.657564i | \(-0.771587\pi\) | ||||
−0.753398 | + | 0.657564i | \(0.771587\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.60629e6 | 0.991644 | 0.495822 | − | 0.868424i | \(-0.334867\pi\) | ||||
0.495822 | + | 0.868424i | \(0.334867\pi\) | |||||||
\(422\) | −1.24712e6 | −0.340900 | ||||||||
\(423\) | −433512. | −0.117801 | ||||||||
\(424\) | 2.13466e6 | 0.576651 | ||||||||
\(425\) | 3.87432e6 | 1.04045 | ||||||||
\(426\) | −327312. | −0.0873852 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.43104e6 | 0.905350 | ||||||||
\(429\) | 1.90037e6 | 0.498534 | ||||||||
\(430\) | −879008. | −0.229257 | ||||||||
\(431\) | −2.78214e6 | −0.721416 | −0.360708 | − | 0.932679i | \(-0.617465\pi\) | ||||
−0.360708 | + | 0.932679i | \(0.617465\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | −6.27619e6 | −1.60871 | −0.804353 | − | 0.594152i | \(-0.797488\pi\) | ||||
−0.804353 | + | 0.594152i | \(0.797488\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.15924e6 | −0.293730 | ||||||||
\(436\) | 460768. | 0.116082 | ||||||||
\(437\) | −522032. | −0.130766 | ||||||||
\(438\) | 2.64434e6 | 0.658617 | ||||||||
\(439\) | −641592. | −0.158890 | −0.0794452 | − | 0.996839i | \(-0.525315\pi\) | ||||
−0.0794452 | + | 0.996839i | \(0.525315\pi\) | |||||||
\(440\) | 1.10490e6 | 0.272076 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.01230e6 | −0.489934 | ||||||||
\(443\) | 6.05546e6 | 1.46601 | 0.733006 | − | 0.680222i | \(-0.238117\pi\) | ||||
0.733006 | + | 0.680222i | \(0.238117\pi\) | |||||||
\(444\) | −627552. | −0.151075 | ||||||||
\(445\) | −3.18911e6 | −0.763430 | ||||||||
\(446\) | −5.15104e6 | −1.22619 | ||||||||
\(447\) | 1.57372e6 | 0.372528 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.16681e6 | −1.20950 | −0.604752 | − | 0.796414i | \(-0.706728\pi\) | ||||
−0.604752 | + | 0.796414i | \(0.706728\pi\) | |||||||
\(450\) | 793476. | 0.184715 | ||||||||
\(451\) | −6.99989e6 | −1.62050 | ||||||||
\(452\) | −896224. | −0.206334 | ||||||||
\(453\) | 4.07297e6 | 0.932536 | ||||||||
\(454\) | 5.15621e6 | 1.17406 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −135936. | −0.0306142 | ||||||||
\(457\) | −227798. | −0.0510222 | −0.0255111 | − | 0.999675i | \(-0.508121\pi\) | ||||
−0.0255111 | + | 0.999675i | \(0.508121\pi\) | |||||||
\(458\) | 2.71286e6 | 0.604315 | ||||||||
\(459\) | 1.15328e6 | 0.255507 | ||||||||
\(460\) | −920192. | −0.202761 | ||||||||
\(461\) | −585146. | −0.128237 | −0.0641183 | − | 0.997942i | \(-0.520423\pi\) | ||||
−0.0641183 | + | 0.997942i | \(0.520423\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.41454e6 | −0.740251 | −0.370126 | − | 0.928982i | \(-0.620685\pi\) | ||||
−0.370126 | + | 0.928982i | \(0.620685\pi\) | |||||||
\(464\) | −1.26822e6 | −0.273465 | ||||||||
\(465\) | 1.66795e6 | 0.357727 | ||||||||
\(466\) | 4.46924e6 | 0.953386 | ||||||||
\(467\) | −716300. | −0.151986 | −0.0759929 | − | 0.997108i | \(-0.524213\pi\) | ||||
−0.0759929 | + | 0.997108i | \(0.524213\pi\) | |||||||
\(468\) | −412128. | −0.0869796 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −556608. | −0.116226 | ||||||||
\(471\) | −4.49159e6 | −0.932928 | ||||||||
\(472\) | −987904. | −0.204108 | ||||||||
\(473\) | −5.61213e6 | −1.15339 | ||||||||
\(474\) | 3.21840e6 | 0.657952 | ||||||||
\(475\) | 577964. | 0.117535 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.70167e6 | −0.543672 | ||||||||
\(478\) | 5.04782e6 | 1.01050 | ||||||||
\(479\) | −5.24092e6 | −1.04368 | −0.521842 | − | 0.853042i | \(-0.674755\pi\) | ||||
−0.521842 | + | 0.853042i | \(0.674755\pi\) | |||||||
\(480\) | −239616. | −0.0474693 | ||||||||
\(481\) | −1.38584e6 | −0.273119 | ||||||||
\(482\) | 3.79287e6 | 0.743619 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.47752e6 | 0.868809 | ||||||||
\(485\) | 555620. | 0.107256 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | 1.11702e6 | 0.213421 | 0.106710 | − | 0.994290i | \(-0.465968\pi\) | ||||
0.106710 | + | 0.994290i | \(0.465968\pi\) | |||||||
\(488\) | −2.35277e6 | −0.447229 | ||||||||
\(489\) | 4.28029e6 | 0.809471 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.34458e6 | 0.251699 | 0.125850 | − | 0.992049i | \(-0.459834\pi\) | ||||
0.125850 | + | 0.992049i | \(0.459834\pi\) | |||||||
\(492\) | 1.51805e6 | 0.282731 | ||||||||
\(493\) | 7.83723e6 | 1.45226 | ||||||||
\(494\) | −300192. | −0.0553454 | ||||||||
\(495\) | −1.39838e6 | −0.256515 | ||||||||
\(496\) | 1.82477e6 | 0.333045 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 231408. | 0.0418124 | ||||||||
\(499\) | −6.54648e6 | −1.17695 | −0.588473 | − | 0.808517i | \(-0.700271\pi\) | ||||
−0.588473 | + | 0.808517i | \(0.700271\pi\) | |||||||
\(500\) | 2.31878e6 | 0.414797 | ||||||||
\(501\) | 1.08202e6 | 0.192592 | ||||||||
\(502\) | −1.94558e6 | −0.344580 | ||||||||
\(503\) | 8.22050e6 | 1.44870 | 0.724350 | − | 0.689432i | \(-0.242140\pi\) | ||||
0.724350 | + | 0.689432i | \(0.242140\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −957164. | −0.167016 | ||||||||
\(506\) | −5.87507e6 | −1.02009 | ||||||||
\(507\) | 2.43152e6 | 0.420105 | ||||||||
\(508\) | 2.96640e6 | 0.510000 | ||||||||
\(509\) | 5.11045e6 | 0.874308 | 0.437154 | − | 0.899387i | \(-0.355987\pi\) | ||||
0.437154 | + | 0.899387i | \(0.355987\pi\) | |||||||
\(510\) | 1.48075e6 | 0.252091 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 172044. | 0.0288633 | ||||||||
\(514\) | −4.15639e6 | −0.693919 | ||||||||
\(515\) | 2.71773e6 | 0.451531 | ||||||||
\(516\) | 1.21709e6 | 0.201232 | ||||||||
\(517\) | −3.55373e6 | −0.584733 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.57987e6 | 0.746336 | ||||||||
\(520\) | −529152. | −0.0858168 | ||||||||
\(521\) | −9.69999e6 | −1.56559 | −0.782793 | − | 0.622282i | \(-0.786206\pi\) | ||||
−0.782793 | + | 0.622282i | \(0.786206\pi\) | |||||||
\(522\) | 1.60510e6 | 0.257825 | ||||||||
\(523\) | 3.17295e6 | 0.507234 | 0.253617 | − | 0.967305i | \(-0.418380\pi\) | ||||
0.253617 | + | 0.967305i | \(0.418380\pi\) | |||||||
\(524\) | −1.03251e6 | −0.164273 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.40418e6 | −0.851658 | ||||||||
\(527\) | −1.12765e7 | −1.76867 | ||||||||
\(528\) | −1.52986e6 | −0.238817 | ||||||||
\(529\) | −1.54340e6 | −0.239794 | ||||||||
\(530\) | −3.46882e6 | −0.536403 | ||||||||
\(531\) | 1.25032e6 | 0.192435 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.35236e6 | 0.511131 | ||||||||
\(534\) | 4.41569e6 | 0.670109 | ||||||||
\(535\) | −5.57544e6 | −0.842160 | ||||||||
\(536\) | −2.62221e6 | −0.394235 | ||||||||
\(537\) | −4.38804e6 | −0.656651 | ||||||||
\(538\) | −4.47244e6 | −0.666176 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 303264. | 0.0447545 | ||||||||
\(541\) | −6.62575e6 | −0.973289 | −0.486644 | − | 0.873600i | \(-0.661779\pi\) | ||||
−0.486644 | + | 0.873600i | \(0.661779\pi\) | |||||||
\(542\) | −760416. | −0.111187 | ||||||||
\(543\) | −4.89969e6 | −0.713131 | ||||||||
\(544\) | 1.61997e6 | 0.234698 | ||||||||
\(545\) | −748748. | −0.107980 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.84707e6 | 0.549745 | 0.274873 | − | 0.961481i | \(-0.411364\pi\) | ||||
0.274873 | + | 0.961481i | \(0.411364\pi\) | |||||||
\(548\) | 2.44688e6 | 0.348066 | ||||||||
\(549\) | 2.97772e6 | 0.421651 | ||||||||
\(550\) | 6.50454e6 | 0.916875 | ||||||||
\(551\) | 1.16914e6 | 0.164055 | ||||||||
\(552\) | 1.27411e6 | 0.177975 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 802024. | 0.111023 | ||||||||
\(555\) | 1.01977e6 | 0.140531 | ||||||||
\(556\) | 5.49536e6 | 0.753892 | ||||||||
\(557\) | 5.00176e6 | 0.683101 | 0.341550 | − | 0.939863i | \(-0.389048\pi\) | ||||
0.341550 | + | 0.939863i | \(0.389048\pi\) | |||||||
\(558\) | −2.30947e6 | −0.313998 | ||||||||
\(559\) | 2.68774e6 | 0.363795 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.45403e6 | 1.26826 | ||||||||
\(562\) | −4.36948e6 | −0.583565 | ||||||||
\(563\) | −2.27772e6 | −0.302852 | −0.151426 | − | 0.988469i | \(-0.548386\pi\) | ||||
−0.151426 | + | 0.988469i | \(0.548386\pi\) | |||||||
\(564\) | 770688. | 0.102019 | ||||||||
\(565\) | 1.45636e6 | 0.191933 | ||||||||
\(566\) | 7.25032e6 | 0.951297 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 581888. | 0.0756778 | ||||||||
\(569\) | 8.86979e6 | 1.14850 | 0.574252 | − | 0.818678i | \(-0.305293\pi\) | ||||
0.574252 | + | 0.818678i | \(0.305293\pi\) | |||||||
\(570\) | 220896. | 0.0284774 | ||||||||
\(571\) | 1.40102e7 | 1.79826 | 0.899132 | − | 0.437678i | \(-0.144199\pi\) | ||||
0.899132 | + | 0.437678i | \(0.144199\pi\) | |||||||
\(572\) | −3.37843e6 | −0.431743 | ||||||||
\(573\) | −3.38764e6 | −0.431033 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.41719e6 | −0.683289 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −8.75327e6 | −1.09454 | −0.547269 | − | 0.836957i | \(-0.684332\pi\) | ||||
−0.547269 | + | 0.836957i | \(0.684332\pi\) | |||||||
\(578\) | −4.33147e6 | −0.539281 | ||||||||
\(579\) | −7.60451e6 | −0.942703 | ||||||||
\(580\) | 2.06086e6 | 0.254378 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −769320. | −0.0941455 | ||||||||
\(583\) | −2.21471e7 | −2.69864 | ||||||||
\(584\) | −4.70106e6 | −0.570379 | ||||||||
\(585\) | 669708. | 0.0809088 | ||||||||
\(586\) | 8.40122e6 | 1.01064 | ||||||||
\(587\) | 1.06117e7 | 1.27113 | 0.635564 | − | 0.772048i | \(-0.280768\pi\) | ||||
0.635564 | + | 0.772048i | \(0.280768\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.68221e6 | −0.199798 | ||||||||
\(590\) | 1.60534e6 | 0.189862 | ||||||||
\(591\) | 4.43515e6 | 0.522323 | ||||||||
\(592\) | 1.11565e6 | 0.130835 | ||||||||
\(593\) | −1.88552e6 | −0.220188 | −0.110094 | − | 0.993921i | \(-0.535115\pi\) | ||||
−0.110094 | + | 0.993921i | \(0.535115\pi\) | |||||||
\(594\) | 1.93622e6 | 0.225159 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.79773e6 | −0.322619 | ||||||||
\(597\) | −8.23298e6 | −0.945413 | ||||||||
\(598\) | 2.81366e6 | 0.321751 | ||||||||
\(599\) | 1.27256e7 | 1.44915 | 0.724573 | − | 0.689198i | \(-0.242037\pi\) | ||||
0.724573 | + | 0.689198i | \(0.242037\pi\) | |||||||
\(600\) | −1.41062e6 | −0.159968 | ||||||||
\(601\) | −7.18846e6 | −0.811801 | −0.405900 | − | 0.913917i | \(-0.633042\pi\) | ||||
−0.405900 | + | 0.913917i | \(0.633042\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.31873e6 | 0.371688 | ||||||||
\(604\) | −7.24083e6 | −0.807600 | ||||||||
\(605\) | −7.27597e6 | −0.808170 | ||||||||
\(606\) | 1.32530e6 | 0.146600 | ||||||||
\(607\) | −1.08494e7 | −1.19519 | −0.597593 | − | 0.801800i | \(-0.703876\pi\) | ||||
−0.597593 | + | 0.801800i | \(0.703876\pi\) | |||||||
\(608\) | 241664. | 0.0265126 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.82325e6 | 0.416014 | ||||||||
\(611\) | 1.70194e6 | 0.184434 | ||||||||
\(612\) | −2.05027e6 | −0.221275 | ||||||||
\(613\) | −4.90511e6 | −0.527227 | −0.263614 | − | 0.964628i | \(-0.584914\pi\) | ||||
−0.263614 | + | 0.964628i | \(0.584914\pi\) | |||||||
\(614\) | −6.56418e6 | −0.702683 | ||||||||
\(615\) | −2.46683e6 | −0.262997 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.58445e6 | 0.273310 | 0.136655 | − | 0.990619i | \(-0.456365\pi\) | ||||
0.136655 | + | 0.990619i | \(0.456365\pi\) | |||||||
\(618\) | −3.76301e6 | −0.396336 | ||||||||
\(619\) | 4.99336e6 | 0.523801 | 0.261901 | − | 0.965095i | \(-0.415651\pi\) | ||||
0.261901 | + | 0.965095i | \(0.415651\pi\) | |||||||
\(620\) | −2.96525e6 | −0.309800 | ||||||||
\(621\) | −1.61255e6 | −0.167797 | ||||||||
\(622\) | −3.78093e6 | −0.391852 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 732672. | 0.0753266 | ||||||||
\(625\) | 3.88510e6 | 0.397834 | ||||||||
\(626\) | 1.66142e6 | 0.169450 | ||||||||
\(627\) | 1.41034e6 | 0.143269 | ||||||||
\(628\) | 7.98506e6 | 0.807940 | ||||||||
\(629\) | −6.89436e6 | −0.694812 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.18219e7 | −1.18199 | −0.590997 | − | 0.806674i | \(-0.701265\pi\) | ||||
−0.590997 | + | 0.806674i | \(0.701265\pi\) | |||||||
\(632\) | −5.72160e6 | −0.569803 | ||||||||
\(633\) | −2.80602e6 | −0.278344 | ||||||||
\(634\) | −4.73926e6 | −0.468260 | ||||||||
\(635\) | −4.82040e6 | −0.474404 | ||||||||
\(636\) | 4.80298e6 | 0.470834 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.31578e7 | 1.27977 | ||||||||
\(639\) | −736452. | −0.0713497 | ||||||||
\(640\) | 425984. | 0.0411096 | ||||||||
\(641\) | −5.47007e6 | −0.525833 | −0.262916 | − | 0.964819i | \(-0.584684\pi\) | ||||
−0.262916 | + | 0.964819i | \(0.584684\pi\) | |||||||
\(642\) | 7.71984e6 | 0.739215 | ||||||||
\(643\) | −9.64934e6 | −0.920386 | −0.460193 | − | 0.887819i | \(-0.652220\pi\) | ||||
−0.460193 | + | 0.887819i | \(0.652220\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.97777e6 | −0.187187 | ||||||||
\(646\) | −1.49341e6 | −0.140798 | ||||||||
\(647\) | −292368. | −0.0274580 | −0.0137290 | − | 0.999906i | \(-0.504370\pi\) | ||||
−0.0137290 | + | 0.999906i | \(0.504370\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 1.02495e7 | 0.955193 | ||||||||
\(650\) | −3.11513e6 | −0.289196 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.60941e6 | −0.701022 | ||||||||
\(653\) | 6.94081e6 | 0.636982 | 0.318491 | − | 0.947926i | \(-0.396824\pi\) | ||||
0.318491 | + | 0.947926i | \(0.396824\pi\) | |||||||
\(654\) | 1.03673e6 | 0.0947808 | ||||||||
\(655\) | 1.67783e6 | 0.152808 | ||||||||
\(656\) | −2.69875e6 | −0.244852 | ||||||||
\(657\) | 5.94977e6 | 0.537758 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.32912e7 | −1.19221 | −0.596104 | − | 0.802908i | \(-0.703285\pi\) | ||||
−0.596104 | + | 0.802908i | \(0.703285\pi\) | |||||||
\(660\) | 2.48602e6 | 0.222149 | ||||||||
\(661\) | −2.05219e6 | −0.182690 | −0.0913448 | − | 0.995819i | \(-0.529117\pi\) | ||||
−0.0913448 | + | 0.995819i | \(0.529117\pi\) | |||||||
\(662\) | −5.48619e6 | −0.486548 | ||||||||
\(663\) | −4.52768e6 | −0.400030 | ||||||||
\(664\) | −411392. | −0.0362106 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.41199e6 | −0.123352 | ||||||||
\(667\) | −1.09582e7 | −0.953732 | ||||||||
\(668\) | −1.92358e6 | −0.166790 | ||||||||
\(669\) | −1.15898e7 | −1.00118 | ||||||||
\(670\) | 4.26109e6 | 0.366719 | ||||||||
\(671\) | 2.44100e7 | 2.09296 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.57039e7 | −1.33650 | −0.668252 | − | 0.743935i | \(-0.732957\pi\) | ||||
−0.668252 | + | 0.743935i | \(0.732957\pi\) | |||||||
\(674\) | −3.85409e6 | −0.326792 | ||||||||
\(675\) | 1.78532e6 | 0.150819 | ||||||||
\(676\) | −4.32270e6 | −0.363822 | ||||||||
\(677\) | 969534. | 0.0813002 | 0.0406501 | − | 0.999173i | \(-0.487057\pi\) | ||||
0.0406501 | + | 0.999173i | \(0.487057\pi\) | |||||||
\(678\) | −2.01650e6 | −0.168471 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.63245e6 | −0.218317 | ||||||||
\(681\) | 1.16015e7 | 0.958617 | ||||||||
\(682\) | −1.89320e7 | −1.55860 | ||||||||
\(683\) | −1.49908e7 | −1.22962 | −0.614812 | − | 0.788673i | \(-0.710768\pi\) | ||||
−0.614812 | + | 0.788673i | \(0.710768\pi\) | |||||||
\(684\) | −305856. | −0.0249964 | ||||||||
\(685\) | −3.97618e6 | −0.323772 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.10393e6 | 0.493421 | ||||||||
\(688\) | −2.16371e6 | −0.174272 | ||||||||
\(689\) | 1.06066e7 | 0.851191 | ||||||||
\(690\) | −2.07043e6 | −0.165553 | ||||||||
\(691\) | 7.16038e6 | 0.570481 | 0.285240 | − | 0.958456i | \(-0.407927\pi\) | ||||
0.285240 | + | 0.958456i | \(0.407927\pi\) | |||||||
\(692\) | −8.14198e6 | −0.646346 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.03092e7 | −0.812509 | ||||||||
\(695\) | −8.92996e6 | −0.701274 | ||||||||
\(696\) | −2.85350e6 | −0.223283 | ||||||||
\(697\) | 1.66774e7 | 1.30031 | ||||||||
\(698\) | −1.22701e7 | −0.953253 | ||||||||
\(699\) | 1.00558e7 | 0.778437 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −91834.0 | −0.00705844 | −0.00352922 | − | 0.999994i | \(-0.501123\pi\) | ||||
−0.00352922 | + | 0.999994i | \(0.501123\pi\) | |||||||
\(702\) | −927288. | −0.0710186 | ||||||||
\(703\) | −1.02849e6 | −0.0784894 | ||||||||
\(704\) | 2.71974e6 | 0.206822 | ||||||||
\(705\) | −1.25237e6 | −0.0948985 | ||||||||
\(706\) | −1.24058e7 | −0.936725 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.22278e6 | −0.166653 | ||||||||
\(709\) | 2.20981e7 | 1.65097 | 0.825487 | − | 0.564422i | \(-0.190901\pi\) | ||||
0.825487 | + | 0.564422i | \(0.190901\pi\) | |||||||
\(710\) | −945568. | −0.0703958 | ||||||||
\(711\) | 7.24140e6 | 0.537216 | ||||||||
\(712\) | −7.85011e6 | −0.580331 | ||||||||
\(713\) | 1.57671e7 | 1.16153 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.48995e6 | 0.401609 | ||||||||
\(716\) | 7.80096e6 | 0.568677 | ||||||||
\(717\) | 1.13576e7 | 0.825066 | ||||||||
\(718\) | 1.31003e6 | 0.0948355 | ||||||||
\(719\) | −1.58388e7 | −1.14262 | −0.571308 | − | 0.820736i | \(-0.693564\pi\) | ||||
−0.571308 | + | 0.820736i | \(0.693564\pi\) | |||||||
\(720\) | −539136. | −0.0387585 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.68161e6 | 0.691202 | ||||||||
\(723\) | 8.53396e6 | 0.607163 | ||||||||
\(724\) | 8.71056e6 | 0.617589 | ||||||||
\(725\) | 1.21323e7 | 0.857235 | ||||||||
\(726\) | 1.00744e7 | 0.709379 | ||||||||
\(727\) | −6.31418e6 | −0.443078 | −0.221539 | − | 0.975151i | \(-0.571108\pi\) | ||||
−0.221539 | + | 0.975151i | \(0.571108\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 7.63922e6 | 0.530569 | ||||||||
\(731\) | 1.33711e7 | 0.925492 | ||||||||
\(732\) | −5.29373e6 | −0.365161 | ||||||||
\(733\) | −6.93003e6 | −0.476404 | −0.238202 | − | 0.971216i | \(-0.576558\pi\) | ||||
−0.238202 | + | 0.971216i | \(0.576558\pi\) | |||||||
\(734\) | −1.14696e7 | −0.785791 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.26509e6 | −0.154131 | ||||||||
\(737\) | 2.72054e7 | 1.84496 | ||||||||
\(738\) | 3.41561e6 | 0.230849 | ||||||||
\(739\) | 1.42331e7 | 0.958714 | 0.479357 | − | 0.877620i | \(-0.340870\pi\) | ||||
0.479357 | + | 0.877620i | \(0.340870\pi\) | |||||||
\(740\) | −1.81293e6 | −0.121703 | ||||||||
\(741\) | −675432. | −0.0451894 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.94460e6 | −0.395048 | −0.197524 | − | 0.980298i | \(-0.563290\pi\) | ||||
−0.197524 | + | 0.980298i | \(0.563290\pi\) | |||||||
\(744\) | 4.10573e6 | 0.271930 | ||||||||
\(745\) | 4.54631e6 | 0.300102 | ||||||||
\(746\) | −1.43212e7 | −0.942175 | ||||||||
\(747\) | 520668. | 0.0341397 | ||||||||
\(748\) | −1.68072e7 | −1.09835 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.21726e6 | 0.338680 | ||||||||
\(751\) | −682752. | −0.0441736 | −0.0220868 | − | 0.999756i | \(-0.507031\pi\) | ||||
−0.0220868 | + | 0.999756i | \(0.507031\pi\) | |||||||
\(752\) | −1.37011e6 | −0.0883510 | ||||||||
\(753\) | −4.37756e6 | −0.281349 | ||||||||
\(754\) | −6.30149e6 | −0.403659 | ||||||||
\(755\) | 1.17664e7 | 0.751233 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.46333e7 | 0.928116 | 0.464058 | − | 0.885805i | \(-0.346393\pi\) | ||||
0.464058 | + | 0.885805i | \(0.346393\pi\) | |||||||
\(758\) | −6.56939e6 | −0.415291 | ||||||||
\(759\) | −1.32189e7 | −0.832897 | ||||||||
\(760\) | −392704. | −0.0246622 | ||||||||
\(761\) | 1.16367e7 | 0.728399 | 0.364200 | − | 0.931321i | \(-0.381343\pi\) | ||||
0.364200 | + | 0.931321i | \(0.381343\pi\) | |||||||
\(762\) | 6.67440e6 | 0.416414 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6.02246e6 | 0.373285 | ||||||||
\(765\) | 3.33169e6 | 0.205831 | ||||||||
\(766\) | −8.22790e6 | −0.506661 | ||||||||
\(767\) | −4.90865e6 | −0.301282 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | −1.91472e7 | −1.16759 | −0.583793 | − | 0.811902i | \(-0.698432\pi\) | ||||
−0.583793 | + | 0.811902i | \(0.698432\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.35188e6 | −0.566582 | ||||||||
\(772\) | 1.35191e7 | 0.816405 | ||||||||
\(773\) | 5.39261e6 | 0.324601 | 0.162301 | − | 0.986741i | \(-0.448109\pi\) | ||||
0.162301 | + | 0.986741i | \(0.448109\pi\) | |||||||
\(774\) | 2.73845e6 | 0.164305 | ||||||||
\(775\) | −1.74565e7 | −1.04400 | ||||||||
\(776\) | 1.36768e6 | 0.0815324 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.46457e6 | −0.145979 | ||||||||
\(779\) | 2.48791e6 | 0.146890 | ||||||||
\(780\) | −1.19059e6 | −0.0700691 | ||||||||
\(781\) | −6.03709e6 | −0.354160 | ||||||||
\(782\) | 1.39975e7 | 0.818530 | ||||||||
\(783\) | 3.61147e6 | 0.210513 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.29757e7 | −0.751549 | ||||||||
\(786\) | −2.32315e6 | −0.134129 | ||||||||
\(787\) | −3.04348e6 | −0.175159 | −0.0875796 | − | 0.996158i | \(-0.527913\pi\) | ||||
−0.0875796 | + | 0.996158i | \(0.527913\pi\) | |||||||
\(788\) | −7.88470e6 | −0.452345 | ||||||||
\(789\) | −1.21594e7 | −0.695376 | ||||||||
\(790\) | 9.29760e6 | 0.530033 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.44218e6 | −0.194993 | ||||||||
\(793\) | −1.16903e7 | −0.660151 | ||||||||
\(794\) | 8.76847e6 | 0.493597 | ||||||||
\(795\) | −7.80484e6 | −0.437972 | ||||||||
\(796\) | 1.46364e7 | 0.818751 | ||||||||
\(797\) | −2.29652e7 | −1.28063 | −0.640316 | − | 0.768111i | \(-0.721197\pi\) | ||||
−0.640316 | + | 0.768111i | \(0.721197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.46686e6 | 0.469197 | ||||||||
\(800\) | 2.50778e6 | 0.138536 | ||||||||
\(801\) | 9.93530e6 | 0.547141 | ||||||||
\(802\) | −1.31382e7 | −0.721271 | ||||||||
\(803\) | 4.87735e7 | 2.66928 | ||||||||
\(804\) | −5.89997e6 | −0.321892 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.06682e6 | 0.491606 | ||||||||
\(807\) | −1.00630e7 | −0.543930 | ||||||||
\(808\) | −2.35610e6 | −0.126959 | ||||||||
\(809\) | 1.90787e7 | 1.02489 | 0.512445 | − | 0.858720i | \(-0.328740\pi\) | ||||
0.512445 | + | 0.858720i | \(0.328740\pi\) | |||||||
\(810\) | 682344. | 0.0365419 | ||||||||
\(811\) | −1.09414e7 | −0.584147 | −0.292074 | − | 0.956396i | \(-0.594345\pi\) | ||||
−0.292074 | + | 0.956396i | \(0.594345\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.71094e6 | −0.0907836 | ||||||||
\(814\) | −1.15748e7 | −0.612286 | ||||||||
\(815\) | 1.23653e7 | 0.652094 | ||||||||
\(816\) | 3.64493e6 | 0.191630 | ||||||||
\(817\) | 1.99467e6 | 0.104548 | ||||||||
\(818\) | −1.44488e7 | −0.755001 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.38547e6 | 0.227762 | ||||||||
\(821\) | 2.12594e7 | 1.10076 | 0.550380 | − | 0.834914i | \(-0.314483\pi\) | ||||
0.550380 | + | 0.834914i | \(0.314483\pi\) | |||||||
\(822\) | 5.50548e6 | 0.284194 | ||||||||
\(823\) | −1.42256e7 | −0.732103 | −0.366052 | − | 0.930595i | \(-0.619291\pi\) | ||||
−0.366052 | + | 0.930595i | \(0.619291\pi\) | |||||||
\(824\) | 6.68979e6 | 0.343237 | ||||||||
\(825\) | 1.46352e7 | 0.748625 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.76103e6 | 0.140381 | 0.0701904 | − | 0.997534i | \(-0.477639\pi\) | ||||
0.0701904 | + | 0.997534i | \(0.477639\pi\) | |||||||
\(828\) | 2.86675e6 | 0.145316 | ||||||||
\(829\) | 3.82147e7 | 1.93127 | 0.965637 | − | 0.259895i | \(-0.0836880\pi\) | ||||
0.965637 | + | 0.259895i | \(0.0836880\pi\) | |||||||
\(830\) | 668512. | 0.0336832 | ||||||||
\(831\) | 1.80455e6 | 0.0906499 | ||||||||
\(832\) | −1.30253e6 | −0.0652347 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.23646e7 | 0.615550 | ||||||||
\(835\) | 3.12582e6 | 0.155149 | ||||||||
\(836\) | −2.50726e6 | −0.124075 | ||||||||
\(837\) | −5.19631e6 | −0.256378 | ||||||||
\(838\) | 2.16596e7 | 1.06547 | ||||||||
\(839\) | −1.06044e7 | −0.520094 | −0.260047 | − | 0.965596i | \(-0.583738\pi\) | ||||
−0.260047 | + | 0.965596i | \(0.583738\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.03097e6 | 0.196526 | ||||||||
\(842\) | −1.44252e7 | −0.701198 | ||||||||
\(843\) | −9.83133e6 | −0.476479 | ||||||||
\(844\) | 4.98848e6 | 0.241053 | ||||||||
\(845\) | 7.02439e6 | 0.338429 | ||||||||
\(846\) | 1.73405e6 | 0.0832981 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.53862e6 | −0.407754 | ||||||||
\(849\) | 1.63132e7 | 0.776731 | ||||||||
\(850\) | −1.54973e7 | −0.735712 | ||||||||
\(851\) | 9.63990e6 | 0.456298 | ||||||||
\(852\) | 1.30925e6 | 0.0617907 | ||||||||
\(853\) | 4.07009e7 | 1.91527 | 0.957637 | − | 0.287977i | \(-0.0929826\pi\) | ||||
0.957637 | + | 0.287977i | \(0.0929826\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 497016. | 0.0232517 | ||||||||
\(856\) | −1.37242e7 | −0.640179 | ||||||||
\(857\) | 3.10120e7 | 1.44237 | 0.721187 | − | 0.692741i | \(-0.243597\pi\) | ||||
0.721187 | + | 0.692741i | \(0.243597\pi\) | |||||||
\(858\) | −7.60147e6 | −0.352517 | ||||||||
\(859\) | −1.09104e7 | −0.504495 | −0.252247 | − | 0.967663i | \(-0.581170\pi\) | ||||
−0.252247 | + | 0.967663i | \(0.581170\pi\) | |||||||
\(860\) | 3.51603e6 | 0.162109 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.11286e7 | 0.510118 | ||||||||
\(863\) | 1.04089e7 | 0.475751 | 0.237875 | − | 0.971296i | \(-0.423549\pi\) | ||||
0.237875 | + | 0.971296i | \(0.423549\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 1.32307e7 | 0.601234 | ||||||||
\(866\) | 2.51048e7 | 1.13753 | ||||||||
\(867\) | −9.74580e6 | −0.440321 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.93616e7 | 2.66659 | ||||||||
\(870\) | 4.63694e6 | 0.207699 | ||||||||
\(871\) | −1.30291e7 | −0.581928 | ||||||||
\(872\) | −1.84307e6 | −0.0820826 | ||||||||
\(873\) | −1.73097e6 | −0.0768695 | ||||||||
\(874\) | 2.08813e6 | 0.0924652 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.05774e7 | −0.465712 | ||||||||
\(877\) | 1.64064e7 | 0.720299 | 0.360150 | − | 0.932895i | \(-0.382726\pi\) | ||||
0.360150 | + | 0.932895i | \(0.382726\pi\) | |||||||
\(878\) | 2.56637e6 | 0.112352 | ||||||||
\(879\) | 1.89028e7 | 0.825188 | ||||||||
\(880\) | −4.41958e6 | −0.192387 | ||||||||
\(881\) | −1.48577e7 | −0.644927 | −0.322464 | − | 0.946582i | \(-0.604511\pi\) | ||||
−0.322464 | + | 0.946582i | \(0.604511\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.72018e7 | −1.17407 | −0.587037 | − | 0.809560i | \(-0.699706\pi\) | ||||
−0.587037 | + | 0.809560i | \(0.699706\pi\) | |||||||
\(884\) | 8.04922e6 | 0.346436 | ||||||||
\(885\) | 3.61202e6 | 0.155022 | ||||||||
\(886\) | −2.42218e7 | −1.03663 | ||||||||
\(887\) | −2.71242e7 | −1.15757 | −0.578785 | − | 0.815480i | \(-0.696473\pi\) | ||||
−0.578785 | + | 0.815480i | \(0.696473\pi\) | |||||||
\(888\) | 2.51021e6 | 0.106826 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.27564e7 | 0.539827 | ||||||||
\(891\) | 4.35650e6 | 0.183842 | ||||||||
\(892\) | 2.06042e7 | 0.867047 | ||||||||
\(893\) | 1.26307e6 | 0.0530029 | ||||||||
\(894\) | −6.29489e6 | −0.263417 | ||||||||
\(895\) | −1.26766e7 | −0.528986 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.33074e6 | 0.262708 | ||||||||
\(898\) | 2.06673e7 | 0.855248 | ||||||||
\(899\) | −3.53121e7 | −1.45722 | ||||||||
\(900\) | −3.17390e6 | −0.130613 | ||||||||
\(901\) | 5.27660e7 | 2.16542 | ||||||||
\(902\) | 2.79996e7 | 1.14587 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.58490e6 | 0.145900 | ||||||||
\(905\) | −1.41547e7 | −0.574484 | ||||||||
\(906\) | −1.62919e7 | −0.659402 | ||||||||
\(907\) | −8.42269e6 | −0.339964 | −0.169982 | − | 0.985447i | \(-0.554371\pi\) | ||||
−0.169982 | + | 0.985447i | \(0.554371\pi\) | |||||||
\(908\) | −2.06248e7 | −0.830187 | ||||||||
\(909\) | 2.98193e6 | 0.119698 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.08637e7 | 1.23212 | 0.616060 | − | 0.787700i | \(-0.288728\pi\) | ||||
0.616060 | + | 0.787700i | \(0.288728\pi\) | |||||||
\(912\) | 543744. | 0.0216475 | ||||||||
\(913\) | 4.26819e6 | 0.169460 | ||||||||
\(914\) | 911192. | 0.0360782 | ||||||||
\(915\) | 8.60231e6 | 0.339674 | ||||||||
\(916\) | −1.08514e7 | −0.427315 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.61311e6 | −0.180671 | ||||||||
\(919\) | 4.93895e6 | 0.192906 | 0.0964531 | − | 0.995338i | \(-0.469250\pi\) | ||||
0.0964531 | + | 0.995338i | \(0.469250\pi\) | |||||||
\(920\) | 3.68077e6 | 0.143373 | ||||||||
\(921\) | −1.47694e7 | −0.573738 | ||||||||
\(922\) | 2.34058e6 | 0.0906770 | ||||||||
\(923\) | 2.89126e6 | 0.111707 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.06727e7 | −0.410130 | ||||||||
\(926\) | 1.36581e7 | 0.523437 | ||||||||
\(927\) | −8.46677e6 | −0.323607 | ||||||||
\(928\) | 5.07290e6 | 0.193369 | ||||||||
\(929\) | −5.62575e6 | −0.213866 | −0.106933 | − | 0.994266i | \(-0.534103\pi\) | ||||
−0.106933 | + | 0.994266i | \(0.534103\pi\) | |||||||
\(930\) | −6.67181e6 | −0.252951 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.78770e7 | −0.674146 | ||||||||
\(933\) | −8.50709e6 | −0.319946 | ||||||||
\(934\) | 2.86520e6 | 0.107470 | ||||||||
\(935\) | 2.73116e7 | 1.02169 | ||||||||
\(936\) | 1.64851e6 | 0.0615039 | ||||||||
\(937\) | −2.60073e7 | −0.967714 | −0.483857 | − | 0.875147i | \(-0.660764\pi\) | ||||
−0.483857 | + | 0.875147i | \(0.660764\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.73819e6 | 0.138356 | ||||||||
\(940\) | 2.22643e6 | 0.0821845 | ||||||||
\(941\) | −3.02160e6 | −0.111241 | −0.0556203 | − | 0.998452i | \(-0.517714\pi\) | ||||
−0.0556203 | + | 0.998452i | \(0.517714\pi\) | |||||||
\(942\) | 1.79664e7 | 0.659680 | ||||||||
\(943\) | −2.33189e7 | −0.853943 | ||||||||
\(944\) | 3.95162e6 | 0.144326 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.24485e7 | 0.815567 | ||||||||
\(947\) | −3.48282e7 | −1.26199 | −0.630995 | − | 0.775787i | \(-0.717353\pi\) | ||||
−0.630995 | + | 0.775787i | \(0.717353\pi\) | |||||||
\(948\) | −1.28736e7 | −0.465242 | ||||||||
\(949\) | −2.33584e7 | −0.841932 | ||||||||
\(950\) | −2.31186e6 | −0.0831097 | ||||||||
\(951\) | −1.06633e7 | −0.382333 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.39009e6 | −0.334917 | −0.167459 | − | 0.985879i | \(-0.553556\pi\) | ||||
−0.167459 | + | 0.985879i | \(0.553556\pi\) | |||||||
\(954\) | 1.08067e7 | 0.384434 | ||||||||
\(955\) | −9.78650e6 | −0.347232 | ||||||||
\(956\) | −2.01913e7 | −0.714528 | ||||||||
\(957\) | 2.96051e7 | 1.04493 | ||||||||
\(958\) | 2.09637e7 | 0.737996 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 958464. | 0.0335659 | ||||||||
\(961\) | 2.21792e7 | 0.774708 | ||||||||
\(962\) | 5.54338e6 | 0.193124 | ||||||||
\(963\) | 1.73696e7 | 0.603566 | ||||||||
\(964\) | −1.51715e7 | −0.525818 | ||||||||
\(965\) | −2.19686e7 | −0.759423 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.44768e7 | 0.497860 | 0.248930 | − | 0.968521i | \(-0.419921\pi\) | ||||
0.248930 | + | 0.968521i | \(0.419921\pi\) | |||||||
\(968\) | −1.79101e7 | −0.614340 | ||||||||
\(969\) | −3.36017e6 | −0.114961 | ||||||||
\(970\) | −2.22248e6 | −0.0758418 | ||||||||
\(971\) | −9.24976e6 | −0.314834 | −0.157417 | − | 0.987532i | \(-0.550317\pi\) | ||||
−0.157417 | + | 0.987532i | \(0.550317\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.46806e6 | −0.150911 | ||||||||
\(975\) | −7.00904e6 | −0.236128 | ||||||||
\(976\) | 9.41107e6 | 0.316238 | ||||||||
\(977\) | −4.97780e7 | −1.66840 | −0.834202 | − | 0.551459i | \(-0.814071\pi\) | ||||
−0.834202 | + | 0.551459i | \(0.814071\pi\) | |||||||
\(978\) | −1.71212e7 | −0.572382 | ||||||||
\(979\) | 8.14449e7 | 2.71586 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.33264e6 | 0.0773882 | ||||||||
\(982\) | −5.37830e6 | −0.177978 | ||||||||
\(983\) | 8.95601e6 | 0.295618 | 0.147809 | − | 0.989016i | \(-0.452778\pi\) | ||||
0.147809 | + | 0.989016i | \(0.452778\pi\) | |||||||
\(984\) | −6.07219e6 | −0.199921 | ||||||||
\(985\) | 1.28126e7 | 0.420773 | ||||||||
\(986\) | −3.13489e7 | −1.02690 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.20077e6 | 0.0391351 | ||||||||
\(989\) | −1.86958e7 | −0.607790 | ||||||||
\(990\) | 5.59354e6 | 0.181384 | ||||||||
\(991\) | 2.62400e7 | 0.848751 | 0.424376 | − | 0.905486i | \(-0.360494\pi\) | ||||
0.424376 | + | 0.905486i | \(0.360494\pi\) | |||||||
\(992\) | −7.29907e6 | −0.235499 | ||||||||
\(993\) | −1.23439e7 | −0.397265 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.37842e7 | −0.761606 | ||||||||
\(996\) | −925632. | −0.0295658 | ||||||||
\(997\) | −2.80506e7 | −0.893727 | −0.446863 | − | 0.894602i | \(-0.647459\pi\) | ||||
−0.446863 | + | 0.894602i | \(0.647459\pi\) | |||||||
\(998\) | 2.61859e7 | 0.832226 | ||||||||
\(999\) | −3.17698e6 | −0.100717 |
(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 | 294.6.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 882.6.a.s.1.1 | 1 | |||
7.2 | even | 3 | 294.6.e.p.67.1 | 2 | |||
7.3 | odd | 6 | 294.6.e.i.79.1 | 2 | |||
7.4 | even | 3 | 294.6.e.p.79.1 | 2 | |||
7.5 | odd | 6 | 294.6.e.i.67.1 | 2 | |||
7.6 | odd | 2 | 42.6.a.d.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 126.6.a.i.1.1 | 1 | |||
28.27 | even | 2 | 336.6.a.h.1.1 | 1 | |||
35.13 | even | 4 | 1050.6.g.i.799.2 | 2 | |||
35.27 | even | 4 | 1050.6.g.i.799.1 | 2 | |||
35.34 | odd | 2 | 1050.6.a.k.1.1 | 1 | |||
84.83 | odd | 2 | 1008.6.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.6.a.d.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
126.6.a.i.1.1 | 1 | 21.20 | even | 2 | |||
294.6.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
294.6.e.i.67.1 | 2 | 7.5 | odd | 6 | |||
294.6.e.i.79.1 | 2 | 7.3 | odd | 6 | |||
294.6.e.p.67.1 | 2 | 7.2 | even | 3 | |||
294.6.e.p.79.1 | 2 | 7.4 | even | 3 | |||
336.6.a.h.1.1 | 1 | 28.27 | even | 2 | |||
882.6.a.s.1.1 | 1 | 3.2 | odd | 2 | |||
1008.6.a.j.1.1 | 1 | 84.83 | odd | 2 | |||
1050.6.a.k.1.1 | 1 | 35.34 | odd | 2 | |||
1050.6.g.i.799.1 | 2 | 35.27 | even | 4 | |||
1050.6.g.i.799.2 | 2 | 35.13 | even | 4 |